Final Tier 2 Rule:
Air Quality
Estimation,
Selected Health
and Welfare
Benefits Methods,
and Benefit
analysis Results
EPA420-R-99-032
December 1999
Prepared/or
Office of Air Quality Planning
and Standards
U.S. Environmental Protection
Agency
Research Triangle Park, NC
Prepared by
Lisa Akeson
Kenneth Davidson
Leland Deck
Brad Firlie
Emily King
Stephen Lange
Don McCubbin
Ellen Post
Work funded through
Contract No. 68-D-98-001
Work Assignment 2-37
Lisa Conner, Work Assignment
Manager
Nancy Riley, Project Officer
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DISCLAIMER
This document was developed by Abt Associates Inc. under technical direction from U.S. EPA's
Office of Air Quality Planning and Standards. The analysis and conclusions presented in this report are
those of the authors and should not be interpreted as necessarily reflecting the official views or policies of
the U.S. EPA. The analysis is useful to derive estimates of air quality, costs, benefits, and/or economic
impacts. However, the analysis inputs and outputs associated with any emissions source, county, or local
area are subject to significant uncertainties and should not be used to predict attainment status, costs,
benefits, and/or economic impacts at this level of detail.
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ACKNOWLEDGEMENTS
The Work Assignment Manager, Lisa Conner, as well as Bryan Hubbell, Tyler Fox, Scott
Mathias, and Norm Possiel of the U.S. Environmental Protection Agency, provided a variety of
constructive suggestions, comments, and technical direction at all stages of work on this report.
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FINAL TIER 2 RULE: AIR QUALITY ESTIMATION, SELECTED HEALTH
AND WELFARE BENEFITS METHODS, AND BENEFIT ANALYSIS RESULTS
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TABLE OF CONTENTS
1 INTRODUCTION 1-1
2 DEVELOPMENT OF OZONE AND PM AIR QUALITY INPUTS FOR USE IN BENEFITS
ANALYSIS 2-1
2.1 OZONE AIR QUALITY 2-1
2.2 PM AIR QUALITY 2-3
2.2.1 Forecasting PM Based on CRDM 2-3
3 GENERAL ISSUES IN ESTIMATING HEALTH AND WELFARE BENEFITS 3-1
3.1 ESTIMATING ADVERSE HEALTH EFFECTS 3-1
3. .1 Basic Concentration-Response Model 3-1
3. .2 Calculation of Adverse Health Effects with CAPMS 3-3
3. .3 Population Projections 3-4
3. .4 Overlapping Health Effects 3-6
3. .5 Baseline Incidences 3-6
3. .6 Thresholds 3-6
3. .7 Application of a Single C-R Function Everywhere 3-8
3. .8 Estimating Pollutant-Specific Benefits Using Single Pollutant vs. Multi-Pollutant
Models 3-8
3.1.9 Pooling Study Results 3-9
3.2 VALUING CHANGES IN HEALTH AND WELFARE EFFECTS 3-10
3.2.1 WTP Estimation 3-10
3.2.2 Change Over Time in WTP in Real Dollars 3-13
3.2.3 Adjusting Benefits Estimates from 1990 Dollars to 1997 Dollars 3-13
3.2.4 Aggregation of Monetized Benefits 3-16
3.3 CHARACTERIZATION OF UNCERTAINTY 3-19
3.3.1 Alternative and Supplementary Calculations 3-21
3.3.2 Sensitivity Analyses 3-25
3.3.3 Statistical Uncertainty Bounds 3-25
3.3.4 Unquantified Benefits 3-26
4 HEALTH BENEFITS 4-1
4.1 PREMATURE MORTALITY 4-5
4.1.1 Short-Term Versus Long-Term Studies 4-5
4.1.2 Degree of Prematurity of Mortality 4-5
4.1.3 Estimating PM-Related Premature Mortality 4-6
4.1.4 Valuing Premature Mortality 4-8
4.2 CHRONIC ILLNESS 4-13
4.2.1 Chronic Bronchitis 4-13
4.2.2 Chronic Asthma 4-17
4.3 HOSPITAL ADMISSIONS 4-18
4.3.1 Respiratory and Cardiovascular Hospital Admissions 4-18
4.3.2 Asthma-Related Emergency Room (ER) Visits 4-25
4.4 ACUTE ILLNESSES AND SYMPTOMS NOT REQUIRING HOSPITALIZATION
4-26
4.4.1 Acute Bronchitis 4-26
4.4.2 Upper Respiratory Symptoms (URS) 4-27
4.4.3 Lower Respiratory Symptoms (LRS) 4-29
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4.4.4 "Any of 19 Respiratory Symptoms" and Minor Restricted Activity Days
(MRADs) 4-32
4.4.5 Shortness of Breath 4-34
4.4.6 Work Loss Days (WLD) 4-35
4.4.7 Worker Productivity 4-36
4.4.8 Supplemental Endpoints: Acute Illnesses And Symptoms Not Requiring
Hospitalization 4-36
5 WELFARE BENEFITS 5-1
5.1 VISIBILITY BENEFITS 5-1
5.1.1 Basic Utility Model 5-2
5.1.2 Measure of Visibility: Environmental "Goods" Versus "Bads" 5-3
5.1.3 Estimating the Parameters for Visibility at Class I Areas: the y's and 8's . . . . 5-5
5.1.4 Estimating the Parameter for Visibility in Residential Areas: 6 5-13
5.1.5 Putting it All Together: the Household Utility and WTP Functions 5-13
5.2 AGRICULTURAL BENEFITS 5-14
5.2.1 Exposure-Response Functions 5-14
5.2.2 Estimation of Yield Changes 5-17
5.2.3 AGSIM© MODEL 5-17
5.3 CONSUMER CLEANING COST SAVINGS 5-27
5.4 NITROGEN DEPOSITION 5-28
6 RESULTS 6-1
7 REFERENCES 7-1
APPENDIX A: RESULTS FOR SUPPLEMENTARY CALCULATIONS AND SENSITIVITY
ANALYSES A-l
APPENDIX B: OZONE CONCENTRATION-RESPONSE FUNCTIONS B-l
B.I SHORT-TERM OZONE-RELATED MORTALITY (FOURU.S. STUDIES) B-l
B.I.I Short-Term Mortality (U.S.) (Ito et al., 1996) B-l
B.I.2 Short-Term Mortality (U.S.) (Kinney et al., 1995) B-2
B.I.3 Short-Term Mortality (U.S.) (Moolgavkar et al., 1995) B-3
B.I.4 Short-Term Mortality (U.S.) (Samet et al., 1997) B-4
B.2 CHRONIC ILLNESS B-5
B.2.1 Asthma Adult Onset (McDonnell et al., 1999) B-5
B.3 HOSPITAL ADMISSIONS B-6
B.3.1 Hospital Admissions for Asthma (Burnett etal., 1999, Toronto) B-6
B.3.2 Hospital Admissions for Obstructive Lung Disease (Burnett et al., 1999, ToronB>y
B.3.3 Hospital Admissions for Respiratory Infection (Burnett et al., 1999, Toronto)
B-8
B.3.4 Hospital Admissions for All Respiratory (Burnett etal., 1997, Toronto) .... B-9
B.3.5 Hospital Admissions for All Respiratory (Thurston et al., 1994, Toronto) .. B-10
B.3.6 Hospital Admissions for Pneumonia (Moolgavkar et al., 1997, Minneapolis)
B-ll
B.3.7 Hospital Admissions for COPD (Moolgavkar etal., 1997, Minneapolis) ... B-12
B.3.8 Hospital Admissions for Pneumonia (Schwartz, 1994c, Minneapolis) B-13
B.3.9 Hospital Admissions for Pneumonia (Schwartz, 1994b, Detroit) B-14
B.3.10 Hospital Admissions for COPD (Schwartz, 1994b, Detroit) B-15
B.3.11 Hospital Admissions for All Respiratory (Schwartz, 1995, New Haven) ... B-16
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B.3.12 Hospital Admissions for All Respiratory (Schwartz, 1995, Tacoma) B-18
B.3.13 Hospital Admissions for Cardiac (Burnett et al., 1997, Toronto) B-20
B.3.14 Hospital Admissions for Dysrhythmias (Burnett etal., 1999, Toronto) .... B-21
B.4 EMERGENCY ROOM VISITS B-22
B.4.1 Emergency Room Visits for Asthma (Cody et al., 1992, Northern NJ) B-22
B.4.2 Emergency Room Visits for Asthma (Weisel et al., 1995, Northern NJ) . . . . B-23
B.4.3 Emergency Room Visits for Asthma (Stieb et al., 1996, New Brunswick) . . B-25
B.5 ACUTE MORBIDITY B-26
B.5.1 Any of 19 Respiratory Symptoms: Krupnick (1990) B-26
B.5.2 Minor Restricted Activity Days: Ostro and Rothschild (1989b) B-29
B.5.3 Asthma Attacks: Whittemore and Korn (1980) B-31
B.5.4 Worker Productivity: Crocker and Horst (1981) B-33
APPENDIX C: PARTICULATE MATTER C-R FUNCTIONS C-l
3.1 MORTALITY C-l
3.1.1 Mortality (Pope etal., 1995) C-l
3.1.2 Mortality (Dockery et al., 1993) C-3
3.1.3 Neonatal Mortality (Woodruff et al., 1997) C-5
3.1.4 Short-Term Mortality (Schwartz et al., 1996) C-7
3.2 CHRONIC MORBIDITY C-8
3.2.1 Chronic Bronchitis (Schwartz, 1993) C-8
3.2.2 Chronic Bronchitis (Abbey et al., 1993, California) C-ll
3.2.3 Chronic Bronchitis (Abbey et al., 1995b, California) C-12
3.3 HOSPITAL ADMISSIONS C-14
3.3.1 Hospital Admissions for Asthma (Burnett etal., 1999, Toronto) C-14
3.3.2 Hospital Admissions for Obstructive Lung Disease (Burnett et al., 1999, ToroEtd)5
3.3.3 Hospital Admissions for Respiratory Infection (Burnett et al., 1999, Toronto)
C-17
3.3.4 Hospital Admissions for All Respiratory (Burnett etal., 1997, Toronto) ... C-18
3.3.5 Hospital Admissions for All Respiratory (Thurston et al., 1994, Toronto) .. C-19
3.3.6 Hospital Admissions for Pneumonia (Moolgavkar et al., 1997, Minneapolis)
C-20
3.3.7 Hospital Admissions for COPD (Moolgavkar etal., 1997, Minneapolis) ... C-22
3.3.8 Hospital Admissions for Pneumonia (Schwartz, 1994c, Minneapolis) C-24
3.3.9 Hospital Admissions for COPD (Schwartz, 1994c, Minneapolis) C-25
3.3.10 Hospital Admissions for Pneumonia (Schwartz, 1994a, Birmingham) C-26
3.3.11 Hospital Admissions for COPD (Schwartz, 1994a, Birmingham) C-27
3.3.12 Hospital Admissions for Pneumonia (Schwartz, 1994b, Detroit) C-28
3.3.13 Hospital Admissions for COPD (Schwartz, 1994b, Detroit) C-29
3.3.14 Hospital Admissions for All Respiratory (Schwartz, 1996, Spokane) C-30
3.3.15 Hospital Admissions for All Respiratory (Schwartz, 1995, New Haven) ... C-32
3.3.16 Hospital Admissions for All Respiratory (Schwartz, 1995, Tacoma) C-34
3.3.17 Hospital Admissions for Asthma (Sheppard etal., 1999, Seattle) C-36
3.3.18 Hospital Admissions for Cardiovascular (Schwartz, 1999, Eight Counties)
C-38
3.3.19 Hospital Admissions for Cardiovascular (Schwartz, 1997, Tucson) C-40
3.3.20 Hospital Admissions for Cardiac (Burnett et al., 1997, Toronto) C-42
3.3.21 Hospital Admissions for Ischemic Heart Disease (Schwartz et al., 1995) ... C-43
3.3.22 Hospital Admissions for Congestive Heart Failure (Schwartz et al., 1995)
C-45
3.3.23 Hospital Admissions for Dysrhythmias (Burnett etal., 1999, Toronto) .... C-47
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3.4 EMERGENCY ROOM VISITS C-48
3.4.1 Emergency Room Visits for Asthma (Schwartz etal., 1993, Seattle) C-48
3.5 ACUTE MORBIDITY C-49
3.5.1 Acute Bronchitis C-R Function (Dockery et al, 1996) C-49
3.5.2 Lower Respiratory Symptoms (Schwartz et al., 1994) C-52
3.5.3 Upper Respiratory Symptoms (Pope et al., 1991) C-55
3.5.4 Any of 19 Respiratory Symptoms (Krupnick et al., 1990) C-56
3.5.5 Shortness of Breath (Ostro et al., 1995) C-59
3.5.6 Moderate (or Worse) Asthma (Ostro et al., 1991) C-61
3.5.7 Minor Restricted Activity Days (Ostro et al., 1989b) C-62
3.5.8 Work Loss Days (Ostro, 1987) C-64
3.5.9 Restricted Activity Days (Ostro, 1987) C-66
3.5.10 Asthma Attacks: Whittemore and Korn (1980) C-68
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List of Exhibits
Exhibit 3-1 Bases of Benefits Estimation 3-14
Exhibit 3-2 Consumer Price Indexes Used to Adjust WTP-Based and Cost-of-Illness-Based Benefits
Estimates from 1990 Dollars to 1997 Dollars 3-14
Exhibit 3-3 Key Sources of Uncertainty in the Benefit Analysis 3-20
Exhibit 3-4 Alternative and Supplemental Benefits Calculations for the Tier II 2030 Control Scenario
3-23
Exhibit 3-5 Sensitivity Analyses for the Tier II 2030 Control Scenario 3-25
Exhibit 4-1 PM-Related Health Endpoints 4-2
Exhibit 4-2 Ozone-Related Health Endpoints 4-3
Exhibit 4-3 Unit Values for Economic Valuation of Health Endpoints (1997 $) 4-4
Exhibit 4-4 Mortality Lag Structure 4-8
Exhibit 4-5 Summary of Mortality Valuation Estimates 4-10
Exhibit 4-6 Potential Sources of Bias in Estimates of Mean WTP to Reduce the Risk of PM Related
Mortality Based on Wage-Risk Studies 4-12
Exhibit 4-7 Chronic Bronchitis Studies 4-13
Exhibit 4-8 Respiratory Hospital Admission Studies 4-19
Exhibit 4-9 Cardiovascular Hospital Admission Studies 4-19
Exhibit 4-10 Unit Values for Respiratory Hospital Admissions 4-23
Exhibit 4-11 Unit Values for Cardiovascular Hospital Admissions 4-24
Exhibit 4-12 Asthma-Related Emergency Room Visit Studies 4-25
Exhibit 4-13 Median WTP Estimates and Derived Midrange Estimates (in 1997 $) 4-28
Exhibit 4-14 Estimates of MWTP to Avoid Upper Respiratory Symptoms (1997 $) 4-28
Exhibit 4-15 Estimates of MWTP to Avoid Lower Respiratory Symptoms (1997 $) 4-30
Exhibit 4-16 Comparison of the Means of Discrete and Continuous Uniform Distributions of MWTP
Associated with URS and LRS (1990 $) 4-32
Exhibit 5-1 Available Information on WTP for Visibility Improvements in National Parks 5-6
Exhibit 5-2 Summary of Region-Specific Recreational Visibility Parameters to be Estimated in Household
Utility Functions 5-7
Exhibit 5-3 Ozone Exposure-Response Functions for Selected Crops (SUM06) 5-15
Exhibit 6-1 Baseline Percentages 6-2
Exhibit 6-2 Estimated PM-Related Health and Welfare Benefits Associated with Air Quality Changes
Resulting from the Final Tier II Rule 2030 Control Scenario 6-3
Exhibit 6-3 Estimated Ozone-Related Health and Welfare Benefits Associated with Air Quality Changes
Resulting from the Final Tier II Rule 2030 Control Scenario 6-4
Exhibit 6-4 Alternative Benefit Calculations for the Tier II 2030 Control Scenario 6-5
Exhibit 6-5 Measures of Aggregate Uncertainty in the Benefits Analysis 6-6
Exhibit A-l Supplemental Benefit Estimates for the Final Tier II Rule 2030 Control Scenario A-l
Exhibit A-2 Sensitivity Analysis Results for the Tier II 2030 Control Scenario A-2
Exhibit A-3 Sensitivity Analysis: Effect of Thresholds on Estimated PM-Related Mortality Based on Pope
et al. (1995) A-3
Exhibit A-4 Underlying Estimates and Weights for Pooled Estimate of PM-Related Respiratory Hospital
Admissions A-4
Exhibit A-5 Underlying Estimates and Weights for Pooled Estimate of Ozone-Related Respiratory
Hospital Admissions A-5
Exhibit A-6 Underlying Estimates and Weights for Pooled Estimate of PM-Related Cardiovascular
Hospital Admissions A-5
Exhibit A-7 Underlying Estimates and Weights for Pooled Estimate of Ozone-Related Asthma ER Visits
A-6
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Exhibit A-8 Underlying Estimates and Weights for Pooled Estimate of PM-Related Chronic Bronchitis
Studies A-6
Exhibit A-9 Underlying Estimates and Weights for Pooled Estimate of PM-related MRAD and Any-of-19
Studies A-6
Exhibit A-10 Underlying Estimates and Weights for Pooled Estimate of Ozone-related MRAD and Any-of-
19 Studies A-7
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INTRODUCTION
In July 1998, the U.S. Environmental Protection Agency (EPA) submitted a report to Congress on
the potential need for, and technical feasibility of, more stringent (Tier II) motor vehicle tailpipe standards.
The Clean Air Act Amendments of 1990 (CAAA) set specific exhaust emission standards, beginning with
the 1994 model year for light-duty vehicles and light-duty trucks. These are Tier I standards. The CAAA
also requires EPA to study whether further reductions in emissions from these vehicles should be required.
These are the Tier II standards, which would not take effect before the 2004 model year. A phase-in would
occur between 2004 and 2009, and gradually lead to nearly a full fleet of Tier II compliant vehicles in
2030. This analysis presents estimates of the potential benefits from the Tier II/Gasoline Sulfur rule
occurring in 2030.
Chapter 2 describes the methods used to estimate changes in ozone and particulate matter (PM)
concentrations and changes in visibility and nitrogen deposition. Chapter 3 describes general issues arising
in estimating and valuing changes in adverse health and welfare effects associated with changes in ozone,
PM, visibility, and nitrogen deposition. Chapter 4 describes in some detail the methods used for estimating
and valuing adverse health effects, while Chapter 5 describes the methods used for welfare effects: crop
damage, visibility, nitrogen deposition, and household soiling. The results of these analyses follow in
Chapter 6.
This document has three appendices. Appendix A presents the physical and monetary benefits
associated with sensitivity calculations for the Tier II 2030 control scenario not considered in the primary
analysis. Appendix B presents the ozone C-R functions used in this analysis, and Appendix C presents the
PMC-R functions.
Abt Associates Inc. 1-1 December 1999
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DEVELOPMENT OF OZONE AND PM AIR QUALITY INPUTS FOR USE IN
BENEFITS ANALYSIS
This chapter describes the methods used to forecast changes in ozone, PM, visibility, and nitrogen
deposition. Several types of air quality models are used to make these forecasts. In some cases, such as
with nitrogen deposition, the model results are ready to be used in the valuation step.1 In other cases, such
as in the case of ozone and PM, we need to carry out a number of steps prior to be able to use these model
results. The following sub-sections summarize how air quality model results are used in conjunction with
the Criteria Air Pollutant Modeling System (CAPMS) to estimate ozone and PM exposure.
CAPMS is a population-based system for modeling exposures to criteria air pollutants, and is used
to estimate health and visibility benefits. CAPMS divides the United States into eight kilometer by eight
kilometer grid cells, and estimates the changes in incidence of adverse health and welfare effects associated
with given changes in air quality in each grid cell. The national incidence change (or the changes within
individual states or counties) is then calculated as the sum of grid-cell-specific changes.
2.1 OZONE AIR QUALITY
To develop baseline and control forecasts for ozone, we use the results of the variable-grid Urban
Airshed Model (UAM-V) and observed ozone season data for 1995 and 1996. The modeling data are used
to generate "adjustment factors" that quantify the relationship between modeled levels of ozone in the base-
year (1995 for the Eastern U.S. and 1996 for the Western U.S.) and the future-year (2030). The
adjustment factors are combined with actual monitoring data to generate estimates of the future-year levels
of ozone. Note that the modeling data are not used directly (i.e., in an absolute sense) to estimate future-
year ozone levels. Instead, we use them in a relative sense to simply adjust actual monitor levels.
For this study, the U.S. was split into an eastern and a western UAM-V modeling region. The
eastern region is bounded by longitude -98.5° to -66.5° (roughly east of central South Dakota through
central Texas) and latitude 26.33° to 46.67°. Note that small portions of the Eastern U.S. are not covered
by the UAM-V modeling (e.g., northern Maine). Thus, in these areas, we assume that ozone levels in the
control scenario are identical with those in the baseline scenario. The two simulation periods for the
eastern U.S. are based on meteorology for June 12-24 and July 7-15, 1995, and are based on an emission
inventory for 1996. The western region is bounded by longitude -126.5° to -98.5° and latitude 26.33° to
51.56°. The two simulation periods for the western U.S. are based on meteorology for July 8-15 and July
21-31, 1996, and are based on an emission inventory for 1996.
We collected ozone monitoring data for the ozone season, defined for this analysis as May through
September.2 An ozone monitor record was considered complete if data were available for 50 percent of
days in a given season. Each of these days in turn had to have at least nine hourly observations between
8:00am and 7:59pm.
'Pechan-Avanti (1999) discuss the estimation of changes in visibility and nitrogen deposition.
2 EPA has a direct link to the AIRS database: http://www.epa.gov/airs/; however, the data used in this analysis were
downloaded from the (password-protected) mainframe version of AIRS, available at: epaibm.rtpnc.epa.gov. Both sets of data are
identical; the mainframe allows larger data queries.
Abt Associates Inc. 2-1 December 1999
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In calculating adjustment factors, the UAM-V modeled hourly values from 8:00 am to 7:59 pm are
sorted by concentration level for the base-year and the future-year.3 For each set of modeled data, the
ordered hourly values are split evenly into the ten rank-ordered deciles.4 The average of hourly values in
each decile is selected as the representative value for that decile. This means that the first decile's
representative ozone level is set equal to the average of values within that decile, and so on for the other
deciles. The decile adjustment factors are then calculated as the ratio of the UAM-V future-year scenario's
decile to the corresponding UAM-V base-year's decile. Separate decile adjustment factors are calculated
for the future baseline and the control scenarios.
We use enhanced Voronoi Neighbor Averaging (eVNA) to interpolate air quality at every
population grid cell by first identifying the set of monitors (or pseudo-monitors) that best "surround" the
center of the grid cell. Once this set of neighboring monitors is identified for each grid cell, an inverse-
distance weight is estimated for each monitor. Using the inverse-distance weights, decile adjustment factors
and ozone monitoring data, we calculate hourly ozone values at each CAPMS grid cell in the Eastern U.S.
as follows:
CAPMS cell,^^ = (UAMVIJ:2030\
m°nh,j,k,1995
di
^ UAMVhj,1995 j
where:
CAPMS celly)Uo3o = predicted concentration at CAPMS cell /', decile group j, hourly observation k
UAMVj j 2030 = average UAMV modeled 2030 concentration in decile group j of model gridcell closest
to CAPMS cell i
N = number of neighboring monitors for CAPMS gridcell i
monhj k 1995 = observed 1995 ozone level at monitor h, decile group j, hourly observation k
UAMVjy jl995 = average UAMV modeled 1995 concentration in decile group j of model gridcell closest
to monitor h
dh j = inverse-distance weight for cell /' to monitor h .
Similarly, we calculate ozone forecasts for CAPMS gridcells in the Western U.S. The difference is
that we use values for 1996 for the Western U.S., rather than the 1995 values used in the Eastern U.S.
After calculating both baseline and control hourly ozone levels at each CAPMS gridcell, we then
calculate the ozone measures that are needed to estimate adverse health effects. For example, a number of
studies use the 24-hour daily average ozone level, so for each CAPMS gridcell we get 2030 baseline and
control estimates for the 24-hour daily average.
To reduce computational time when estimating the change in health effects associated with daily
ozone levels, CAPMS approximates a season's worth of daily ozone measures at each CAPMS gridcell by
20 "bins." Each bin represents five percent of the daily ozone concentrations, and the value for each bin is
set at the midpoint of the percentile range it represents. The first bin represents the first (lowest) five
percent of the distribution of daily ozone values, and is set at the 2.5th percentile value; the second bin
3 The data format of Eastern UAM-V modeled hourly output presents all grid cell data starting at 12:00 am., and the
Western UAM-V output presents all gridcells starting at 12:00am PST. In processing of data, a correction was encoded to ensure that
calculations were based on 8:00 am to 7:59 pm of the appropriate local time zone of the grid cell.
4The use of more adjustment factors is generally considered desirable because it provides flexibility; however, it can lead to
unreasonably large adjustment factors for lower ozone values, unless a threshold is used (e.g., one ppb as used in this analysis).
Abt Associates Inc. 2-2 December 1999
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represents the next five percent of the distribution of daily values, and is set at the 7.5th percentile value,
and so on. Each of the twenty bins therefore represents 7.65 (=153/20) days, since there are 153 days
between May and September.
After generating 20 bins for both the baseline and control scenarios, we take the difference between
these two values at each bin. We subtract the baseline value in the first bin from the control value in the
first bin, and so on for each of the 20 bins. For each CAPMS gridcell, we then get 20 values representing
the difference between the baseline and control, and we use these to estimate the change in adverse effects
associated with the implementation of the policy. Note that since each value represents 7.65 days, we then
multiply each of the 20 incidence change estimates by 7.65 to reconstruct an entire season's worth of
incidence changes in the CAPMS grid cell.
2.2 PM AIR QUALITY
We used the results from the Source Receptor (S-R) matrix based on the Climatological Regional
Dispersion Model (CRDM) to forecast changes in the ambient concentration of both PM10 and PM2 5 at the
center of each county. Ambient concentrations of PM are composed of directly emitted particles and of
secondary aerosols of sulfate, nitrate, and organics. Relative to more sophisticated and resource-intensive
three-dimensional modeling approaches, the S-R Matrix does not fully account for all the complex chemical
interactions that take place in the atmosphere in the secondary formation of PM.
The S-R Matrix consists of fixed coefficients that reflect the relationship between annual average
PM concentration values at a single receptor in each county (i.e., a hypothetical monitor sited at the county
population centroid) and the contribution by PM species to this concentration from each emission source in
all counties in the 48 contiguous states. The methodology used in this RIA for estimating PM air quality
concentrations is detailed in Pechan-Avanti (1999). The following sections describe the steps taken to
input these modeled PM levels into CAPMS.
2.2.1 Forecasting PM Based on CRDM
Pechan-Avanti (1999) use the S-R matrix to estimate the 2030 baseline and control scenario mean
PM levels, and use regional peak/mean ratios to estimate the peak PM levels for each county in the United
States. We then take these mean and peak values to estimate the daily average, annual mean, and annual
median PM concentrations that are used in a number of C-R functions.5 These results are then
extrapolated from monitored to unmonitored locations to estimate PM levels at each CAPMS grid-cell
based on Voronoi Neighbor Averaging (VNA).
VNA is somewhat different from the eVNA method used to interpolate ozone levels. First, the
estimates generated by the S-R matrix are used directly, rather than as a scaling factor that is multiplied
with actual ambient PM measures. Second, the model estimates are for each county center, whereas the
ozone estimates are generated for UAM-V cells. Third, the interpolation of PM levels to each CAPMS
' C-R functions are described in detail in later sections.
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gridcell is based on binned data, rather than daily or hourly values.6 The value for a given bin at a CAPMS
gridcell is calculated as follows:
N
CAPMS celll:m:2030 = X onh:m:2030 dh,
h=l
where:
CAPMS cellj m 2030 = predicted concentration at CAPMS cell /' for bin m (out of 20 bins)
N = number of neighboring monitors for CAPMS gridcell i
monhm 1995 = observed 1995 ozone level at monitor h for bin m
dh; = inverse-distance weight for cell / to monitor h .
Once we have estimates for 20 bins for both the baseline and control scenarios, we follow the same
procedure that we used with the binned ozone estimates. We take the difference between the baseline and
control to estimate the impact of the policy. We subtract the baseline value in the first bin from the control
value in the first bin, and so on for each of the 20 bins. For each CAPMS gridcell, we then get 20 values
representing the difference between the baseline and control, and we use these to estimate the change in
adverse effects associated with the implementation of the policy. Note that since we are interested in PM
values for the whole year, each binned value represents 18.25 days (365/20). We then multiply each of the
20 incidence change estimates by 18.25 to reconstruct an entire year's worth of incidence changes in the
CAPMS grid cell.
As described below, we develop daily average and the median exposure estimates by first assuming
that a gamma distribution is reasonably representative of the PM distribution, and then by using a
maximum likelihood estimation procedure to estimate the gamma distribution parameters for each county
most consistent with the mean and peak values.7 A distribution of daily PM values is then estimated for
both the baseline and the control scenario in each county, and then the estimated change in PM. This
analysis assumes that the order of PM concentrations across days does not change from the baseline to any
control scenario, so the change in PM on the nth percentile day equals baseline PM on the nth percentile day
minus control scenario PM on the nth percentile day.
Note that for PM10, the peak value is defined as the value corresponding to the 99.7th percentile
value of the distribution of actual daily 24-hour average PM10 values. For PM25, the peak value is defined
as the value corresponding to the 98th percentile value of the distribution of estimated daily 24-hour average
PM2 5 values. Also note that daily PM10 and PM2 5 values derived from the gamma distribution generation
procedure are adjusted to reflect the natural occurrence of background concentrations of PM10 and PM25
(the level at which a given PM constituent exists naturally in the environment). Prior to the distribution
estimation, an assumed background concentration is subtracted from the mean and peak PM concentrations
used to predict the gamma distribution. Once the distribution of daily PM values is predicted, the
background concentration is added back to the representative air quality value that has been estimated. In
instances where the initial mean value is below a given background concentration assumption, estimates of
daily air quality are generated directly from the mean and peak PM values without any background
6 Recall that in the eVNA method, hourly values were interpolated to each CAPMS gridcell, and the ozone measures of
interest were calculated (e.g., 24-hour daily average), then the resulting measures were placed into 20 bins.
7We compared a number of different distributions with the distribution of actual PM observations and found the gamma
distribution to be most representative.
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adjustment. Eastern states are assigned a background threshold of 8ug/m3 for PM10 and 3.5ug/m3 for
PM25. Western states are assigned a background threshold of 6ug/m3 for PM10 and 2.5ug/m3 for PM25.
Estimating the Parameters of a Gamma Distribution, Given the Mean and a Peak Value
The gamma distribution has two parameters, which will be denoted as A and r, that must be
estimated for each county in order for the distribution of daily average PM concentrations to be completely
specified. The parameters of a distribution are usually estimated from a random sample drawn from the
distribution. Given a sample from the distribution, one of several possible standard methods (for example,
maximum likelihood estimation or the method of moments) could be used to estimate the parameters, A and
r. Even given only the sample mean and the sample variance, A and r could be estimated by the method of
moments.
However, neither the whole sample nor the sample variance are available. Instead, the only
available information about the distribution is the sample mean and a peak statistic (e.g.,the eighth largest
daily average is the 98th percentile point of 365 daily values). The following method, which combines
aspects of both the method of moments and maximum likelihood estimation, was therefore used to estimate
the two parameters of the gamma distribution from the available statistics.
As in the method of moments, equate the sample mean with the population mean, E(x). The
population mean of a gamma distribution is:
E(X}-r-.
Therefore, denoting the sample mean as x,., set:
r
I
Xs = E(X) = - .
Solving for A as a function of xs and r yields:
The first piece of information, the sample mean, has been used to reduce the problem from one of
estimating two parameters to one of estimating only one parameter. An estimate of r will yield an estimate
of A, given the sample mean.
In the second step, the peak statistic (e.g., the eighth largest daily average PM concentration) is
used to estimate r. The distribution of the peak can be derived from the distribution of the daily average
PM concentrations.
The peak PM concentration has a probability density function (pdf) that is itself a function of the
pdf of the daily PM concentration and the corresponding cumulative distribution function (cdf) of the daily
PM concentration. (The cumulative distribution function describes the probability of being less than any
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given value.) In particular, if the daily average PM concentration is distributed according to a pdf denoted
as f(x; A, r), and the corresponding cumulative distribution function (cdf) is denoted as F(x; A, r), then the
probability density function of the peak, denoted as fn,+1(x;A, r), can be shown to be:
where n=365 (because there are 365 days in a year) and a represents the peak (e.g., «=358 for the eighth
highest PM25 value out of 365 days)8. (Note that the pdf of any order statistic can be derived analogously.)
Because A is a function of r, there is only one unknown parameter that requires estimation.
Maximum likelihood estimation is used to estimate r in the pdf of the peak PM concentration, using
the one observation from that pdf-- the peak PM concentration.
The method described above for estimating A and r has two features that guarantee reasonable
estimates. First, the method constrains the estimation of the two parameters so that the estimated
population mean, which is a function of both parameters, equals the sample mean. This is reasonable,
since the sample mean is the best guess at what the population mean is. Second, this method produces the
"most likely" estimate of r, given this constraint. That is, it produces the value of r that maximizes the
chance of having gotten the particular second daily maximum PM concentration.
To generate 365 daily PM concentrations from the distribution whose parameters are estimated, we
could use Monte Carlo techniques. If the number of iterations in a Monte Carlo exercise is large enough,
the frequency distribution of generated observations will approximate the distribution from which the
observations were generated. The smaller the number of iterations, however, the rougher the
approximation. Instead of generating observations by Monte Carlo techniques, values corresponding to
evenly-spaced percentile points of the estimated distribution are used. This guarantees that the sample
distribution will correspond to the assumed distribution. First, the percentile of the eighth highest
concentration (given) is calculated from the estimated distribution. The percentiles of the 364 other
concentrations are evenly spaced around this percentile. The percentile of the highest observation was set
midway between the percentile of the second highest observation and the 100th percentile.
Forecasting PM10_2 5
The forecast for daily average coarse PM10_25 (i.e., PM10 minus PM25) is necessary for some C-R
functions. To calculate these forecasts, we simply take the difference between the daily PM10 and daily
PM2 5 values for both the baseline and control scenarios. To ensure that coarse PM values remain
consistent with both the predicted PM2 5 and PM10 values, a background concentration adjustment is also
applied to coarse PM2 5_10 levels. Since coarse PM is equal to the difference between PM10 and PM2 5, the
background threshold for coarse PM is calculated by subtracting PM2 5 background concentrations from
PM10 background concentrations. Eastern coarse PM background is 4.5ug/m3 and Western coarse PM is
3.5ug/m3. Differences between PM10 and PM25 that fall below the background concentration are set to the
background level.
8The probability density function of the peak is from Mood et al.(1974, p. 254).
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GENERAL ISSUES IN ESTIMATING HEALTH AND WELFARE BENEFITS
Changes in ozone, PM, nitrogen oxides, and visibility levels result in changes in a number of health
and welfare effects, or "endpoints," that society values. This chapter discusses key issues in the estimation
of adverse health effects and in the valuation of health and welfare benefits. Section 1 describes general
issues that particularly affect the estimation of changes in health effects. Section 2 describes general issues
in valuing health and welfare changes. Finally, Section 3 discusses how uncertainty is characterized in this
analysis.
3.1 ESTIMATING ADVERSE HEALTH EFFECTS
This section reviews issues that arise in the estimation of adverse health effects. It reviews the
derivation of C-R functions, and it reviews how CAPMS combines air quality data and C-R functions. In
addition, we discuss how we handle overlapping health effects, thresholds, estimating the baseline incidence
rates for the C-R functions, and other issues.
3.1.1 Basic Concentration-Response Model
The methods discussed in this sub-section apply to the estimation of both ozone-related and PM-
related changes in adverse health effects. For expository simplicity, the discussion focuses primarily on
PM-related changes. The methods, however, are equally applicable to ozone-related changes in effects.
Similarly, while several health endpoints have been associated with ozone and PM, the discussion below
refers only to a generic "health endpoint," denoted as y. Finally, the discussion refers to estimation of
changes in the incidence of the health endpoint at a single location (the population cell, which is equivalent
to the CAPMS gridcell). Region-wide changes are estimated by summing the estimated changes over all
population cells in the region.
Different epidemiological studies may have estimated the relationship between PM and a particular
health endpoint in different locations. The C-R functions estimated by these different studies may differ
from each other in several ways. They may have different functional forms; they may have measured PM
concentrations in different ways; they may have characterized the health endpoint, y, in slightly different
ways; or they may have considered different types of populations. For example, some studies of the
relationship between ambient PM concentrations and mortality have excluded accidental deaths from their
mortality counts; others have included all deaths. One study may have measured daily (24-hour) average
PM concentrations while another study may have used two-day averages. Some studies have assumed that
the relationship between y and PM is best described by a linear form (i.e., the relationship between y and
PM is estimated by a linear regression in which y is the dependent variable and PM is one of several
independent variables). Other studies have assumed that the relationship is best described by a log-linear
form (i.e., the relationship between the natural logarithm of y and PM is estimated by a linear regression).9
Finally, one study may have considered changes in the health endpoint only among members of a particular
9The log-linear form used in the epidemiological literature on PM-related health effects is often referred to as "Poisson
regression" because the underlying dependent variable is a count (e.g., number of deaths), believed to be Poisson distributed. The
model may be estimated by regression techniques but is often estimated by maximum likelihood techniques. The form of the model,
however, is still log-linear.
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subgroup of the population (e.g., individuals 65 and older), while other studies may have considered the
entire population in the study location.
The estimated relationship between PM and a health endpoint in a study location is specific to the
type of population studied, the measure of PM used, and the characterization of the health endpoint
considered. For example, a study may have estimated the relationship between daily average PM
concentrations and daily hospital admissions for "respiratory illness," among individuals age 65 and older,
where "respiratory illness" includes International Classification of Disease (ICD) codes A, B, and C.10 If
any of the inputs had been different (for example, if the entire population had been considered, or if
"respiratory illness" had consisted of a different set of ICD codes), the estimated C-R function would have
been different. When using a C-R function estimated in an epidemiological study to estimate changes in the
incidence of a health endpoint corresponding to a particular change in PM in a population cell, then, it is
important that the inputs be appropriate for the C-R function being used ~ i.e., that the measure of PM, the
type of population, and the characterization of the health endpoint be the same as (or as close as possible
to) those used in the study that estimated the C-R function.
Estimating the relationship between PM and a health endpoint, y, consists of (1) choosing a
functional form of the relationship and (2) estimating the values of the parameters in the function assumed.
The two most common functional forms in the epidemiological literature on PM (and ozone) and health
effects are the log -linear and the linear relationship. The log -linear relationship is of the form:
or, equivalently,
ln(y) = a
where the parameter B is the incidence of y when the concentration of PM is zero, the parameter p is the
coefficient of PM, ln(y) is the natural logarithm of y, and a = In(B).11 If the functional form of the C-R
relationship is log-linear, the relationship between APM and Ay is:
= y-
where y is the baseline incidence of the health effect (i.e., the incidence before the change in PM). For a
log-linear C-R function, the relative risk (RR) associated with the change APM is:
10 The International Classification Codes are described at the website of the Medical Center Information Systems: Duke
University Health Systems (1999).
11 Other covariates besides pollution clearly affect mortality. The parameter B might be thought of as containing these other
covariates, for example, evaluated at their means. That is, B = Boexpjp^ + ... + pnxn}, where B0 is the incidence of y when all
covariates in the model are zero, and x1;... , xn are the other covariates evaluated at their mean values. The parameter B drops out of
the model, however, when changes in incidences are calculated, and is therefore not important.
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Epidemiological studies often report a relative risk for a given APM, rather than the coefficient, p, in the C-
R function. The coefficient can be derived from the reported relative risk and APM, however, by solving
forp:
InQRK)
^ " APM '
The linear relationship is of the form:
y = a + j8 PM ,
where a incorporates all the other independent variables in the regression (evaluated at their mean values,
for example) times their respective coefficients. When the C-R function is linear, the relationship between
a relative risk and the coefficient, p, is not quite as straightforward as it is when the function is log-linear.
Studies using linear functions usually report the coefficient directly.
If the functional form of the C-R relationship is linear, the relationship between APM and Ay is
simply:
A few epidemiological studies, estimating the relationship between certain morbidity endpoints and
PM, have used functional forms other than linear or log-linear forms. Of these, logistic regressions are the
most common. Abt Associates (1999, Appendix A) provides further details on the derivation of dose-
response functions.
3.1.2 Calculation of Adverse Health Effects with CAPMS
CAPMS is a population-based system for modeling exposure to ambient levels of criteria air
pollutants and estimating the adverse health effects associated with this exposure. CAPMS divides the
United States into multiple grid cells, and estimates the changes in incidence of adverse health and welfare
effects associated with given changes in air quality in each grid cell. The national incidence change (or the
changes within individual states or counties) is then calculated as the sum of grid-cell-specific changes.
To calculate point estimates of the changes in incidence of a given selection of adverse health and
welfare effects associated with a given set of air quality changes, CAPMS goes through the following steps
at each CAPMS grid cell:
Interpolate the air quality in the baseline scenario and in the control scenario at the CAPMS grid
cell center, as described in Chapter 2. If the daily values have been binned at the monitors from
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which the interpolation is carried out, the resulting baseline and control scenario air quality data at
the CAPMS grid cell center is also binned.
Calculate the changes in air quality from baseline to control scenario in the CAPMS grid cell. The
changes in air quality are calculated as the differences between the baseline bins and the
corresponding control scenario bins. The change in the nth bin concentration is the difference
between the baseline nth bin concentration and the control scenario nth bin concentration.
Access the selected C-R functions being used, and the required baseline incidence rates and grid
cell population.
Using the above inputs, calculate the change in incidence of each adverse health effect for which a
C-R function has been accessed.
For functions based on changes in daily average pollutant concentrations, estimated incidence
changes corresponding to air quality changes in each of the 20 bins are summed. This summed incidence,
however, is the result of 20 representative air quality changes (one for each bin). Recall that each bin
represents 18.25 days for PM (to represent a year's worth of exposure) and 7.65 days for ozone (to
represent an ozone season's worth of exposure). To adjust the summed incidence estimate, it is multiplied
by either 18.25 to produce an annual change, or by 7.65 to produce a seasonal change. This procedure is
applied to each grid cell in CAPMS. The resulting incidence change is stored, and CAPMS proceeds to the
next grid cell, where the above process is repeated. The national change (or the change in any designated
geographical area) is calculated at the end of the process by summing the grid cell-specific changes.
To reflect the uncertainty surrounding predicted incidence changes resulting from the uncertainty
surrounding the pollutant coefficients in the C-R functions used, CAPMS produces a distribution of
possible incidence changes for each adverse health, rather than a single point estimate. To do this, it uses
both the point estimate of the pollutant coefficient (p in the above equation) and the standard error of the
estimate to produce a normal distribution with mean equal to the estimate of p and standard deviation equal
to the standard error of the estimate. Using a Latin Hypercube method,12 we take the nth percentile value of
p from this normal distribution, for n = 0.5, 1.5, ..., 99.5, and follow the procedure outlined in the section
above to produce an estimate of the incidence change, given the p selected. Repeating the procedure for
each value of p selected results in a distribution of incidence changes in the CAPMS grid cell. This
distribution is stored, and CAPMS proceeds to the next grid cell, where the process is repeated. A
distribution of the national change (or change in a designated geographical area) is calculated by summing
the nth percentile grid cell-specific changes, for n = 0.5, 1.5, ..., 99.5.
3.1.3 Population Projections
Benefits for the Tier II analysis are based on health and welfare effect incidence changes due to
predicted air quality improvements in the year 2030. Integral to the estimation of such benefits is an
accurate estimate of future population projections. Though similar benefits analyses have preceded this
12The Latin Hypercube method is used to enhance computer processing efficiency. It is a sampling method that divides a
probability distribution into intervals of equal probability, with an assumption value for each interval assigned according to the
interval's probability distribution. Compared with conventional Monte Carlo sampling, the Latin Hypercube approach is more precise
over a fewer number of trials because the distribution is sampled in a more even, consistent manner (Decisioneering, 1996, pp. 104-
105).
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one, using population projections out to various future years, no analysis has been conducted out to the
year 2030. This section describes the method used to estimate county-level 2030 populations.
The underlying data used to create county-level 2030 population projections is based on: (1) 1990
county-level population statistics for all U.S. counties collected by the U.S. Census (Wessex, 1994), and
(2) future-year state and metropolitan area population estimates provided by the Bureau of Economic
Analysis (1995). Growth factors are calculated using the BEA data and are applied to the 1990 county-
level populations.
A growth factor is calculated by taking the ratio of an estimated region's 2030 population divided
by the!990 population for that same area. Population estimates for the years 1990-93, 2000, 2005, 2010,
2015, 2025 and 2045 were collected by the BEA. A 2030 population estimate was not provided. Instead,
2030 state and metropolitan area populations were interpolated linearly using estimates from the years
2025 and 2045.
Growth factors are calculated for both urban areas and rural areas. An urban area is defined as a
county that falls within one of the metropolitan areas for which the beapop file contains population data.
This includes metropolitan statistical areas (MSAs), primary metropolitan statistical areas (PMSAs),
consolidated metropolitan statistical areas (CMSAs), and New England county metropolitan areas
(NECMAs) (as defined by U.S. Census Bureau, 1999).13 In this section, however, all metropolitan areas
are referred to as MAs. A rural area is defined as a county that falls outside the defined metropolitan
areas.
Urban areas grow according to the growth rate calculated for the particular metropolitan area
within which they are located. This adjustment is very straightforward, simply taking the ratio of future
year to base year metropolitan area population and multiplying that factor by the base year county
population. The equation is:
2030CountyPopi = 1990CountyPom-
y P y P 1990MAPopi
where:
2030CountyPop1 = projected 2030 population in urban county i
1990CountyPop1 = actual 1990 population for county i
2030MAPop! = projected 2030 population in metropolitan area for county i
1990MAPop! = actual 1990 population for metropolitan area for county i.
Rural areas grow according to the growth rate calculated for the particular state within which they
are located, adjusted to subtract out metropolitan area populations. Before the ratio of future year to base
year state population is calculated, the population attributed to all metropolitan areas located within that
state is subtracted from the future year and base year population totals. Once this metropolitan area
adjustment has been made, the rural growth factor is multiplied by the base-year population in all non-MA
counties to get future-year population projections. The equation is:
' The Census Bureau definitions are available at: http://www.census.gov/population/www/estimates/aboutmetro.html .
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(2030StatePop, -1 2030MAPop,)
2030CountyPoPi = 1990CountyPopt-- ^^
y P y P (1990StatePopi-IJ1990MAPopi)
where:
2030CountyPop1 = projected 2030 population in rural county i
1990CountyPop1 = actual 1990 population for county i
2030StatePop1 = projected 2030 population in state where county i is located
1990State Popj = actual 1990 population for state where county i is located
E2030MAPop! = projected 2030 population in metropolitan areas located in state with county i
El990MAPop! = actual 1990 population for metropolitan areas located in state with county i .
One problem that exists with this method is that many metropolitan areas cross state boundaries.
To accurately subtract urban populations from state populations, we need to know the urban county
populations for both 1990 and 2030. Using the county populations for 1990, we can estimate the portion
of a particular metropolitan area's population that belongs to a given state. However, we do not have 2030
county population projections with which to apportion 2030 metropolitan area populations. To remedy
this, we apply the same percent of the population a given county contributes to a metropolitan area in 1990
to 2030 metropolitan areas when apportioning populations between states.
3.1.4 Overlapping Health Effects
Several endpoints reported in the health effects literature overlap with each other. Hospital
admissions for single respiratory ailments (e.g. pneumonia) overlap with estimates of hospital admissions
for "all respiratory" ailments.14 Similarly, several studies quantify the occurrence of respiratory symptoms
where the definitions of symptoms are not unique (e.g., shortness of breath or upper respiratory symptoms).
In choosing studies to include in the aggregated benefits estimate (discussed below), this analysis carefully
considers the issue of double-counting benefits that might arise from overlapping health effects.
3.1.5 Baseline Incidences
As noted above, most of the relevant C-R functions are log-linear, and the estimation of incidence
changes based on a log-linear C-R function requires a baseline incidence. The baseline incidence for a
given CAPMS population cell is the baseline incidence rate in that location multiplied by the relevant
population. County mortality rates are used in the estimation of air pollution-related mortality, and all
CAPMS population cells in the county are assumed to have the same mortality rate. Hospital admissions
are only available at the national level, so all areas are assumed to have the same incidence rate for a given
population age group. For some endpoints, such as respiratory symptoms and illnesses and restricted
activity days, baseline incidence rates are not available even at the national level. The only sources of
estimates of baseline incidence rates in such cases are the studies reporting the C-R functions for those
health endpoints. The baseline incidence rate and its source are given for each C-R function in Appendices
B and C.
"Pneumonia is often classified with the International Classification of Diseases (ICD) codes of 480-486, while all
respiratory admissions are classified with ICD codes 460-519.
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3.1.6 Thresholds
A very important issue in applied modeling of changes in PM is whether to apply the C-R
functions to all predicted changes in ambient concentrations, even small changes occurring at levels
approaching the concentration in which they exist in the natural environment (without interference from
humans), referred to as "anthropogenic background." Different assumptions about whether to model
thresholds, and if so, at what levels, can have a major effect on the resulting benefits estimates.15
None of the epidemiological functions relating PM to various health and welfare endpoints
incorporate thresholds. Instead, all of these functions are continuous and differentiable down to zero
pollutant levels. A threshold may be imposed on these models, however, in several ways, and there are
various points at which the threshold could be set. (A threshold can be set at any point. There are some
points, however, that may be considered more obvious candidates than others.) One possible threshold
might be the background level of the pollutant. Another might be a relevant standard for the pollutant.
Whatever the threshold, the implication is that there are no effects below the threshold.
A threshold model can be constructed in more than one way. One method is to simply truncate the
C-R function at the threshold (i.e., to not include any physical effect changes associated with PM
concentrations below the designated threshold). This method uses the original C-R function, but calculates
the change in PM as [max(T,baseline PM) - max(T, regulatory alternative PM)], where T denotes the
designated threshold. This threshold model will predict a smaller incidence of the health effect than the
original model without a threshold. Clearly, as T increases, the predicted incidence of the health effect will
decrease.
An alternative method is to replace the original C-R function with a "hockey stick" model that best
approximates the original function that was estimated using actual data. The hockey stick model is
horizontal up to a designated threshold PM level, T, and is linear with a positive slope for PM
concentrations greater than T. Recall the log-linear C-R function:
y = a + ft PM .
Assuming that the value of the coefficient, p, depends on the level of PM, we get:
ln(» = a' , for PM< T ,and
,forPM>T.
Ideally, the coefficients would be estimated based on the data in the original study - that is, a
hockey stick model would be fit to the original data, so that the threshold model that is most consistent with
the available information would be chosen. If a threshold model could be estimated from the original data,
it is unlikely that «' would equal a or that p' would equal p, because such a hockey stick model would be
consistently below the original model, except at PM=0 (where the two models would coincide). If that were
the hockey stick model that best fit the data, then it is unlikely that the best fitting linear model would be
consistently above it. Instead, the hockey stick model that best fits the same data would most likely have
«'>« and p'>p. A graph of this model would therefore cross the graph of the linear model at two points.
15Thresholds may also apply to ozone, however, recent RIAs have not explicitly modeled ozone thresholds.
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Whether such a hockey stick threshold model predicted a greater or smaller incidence of the health effect
than the linear model would depend on the distribution of PM levels. It is worth noting that the graph of
the first type of threshold model, in which the C-R function is simply truncated at the threshold, would be
discontinuous at the threshold. This is highly unlikely to be a good model of the actual relationship
between PM and any health endpoint.
There is some evidence that, at least for particulate matter, not only is there no threshold, but the
PM coefficient may actually be larger at lower levels of PM and smaller at higher levels. Examining the
relationship between particulate matter (measured as TSP) and mortality in Milan, Italy during the ten year
period 1980-1989, Rossi et al. (1999) fitted a model with one slope across the entire range of TSP and an
additional slope for TSP greater than 200 (jg/m3 . The second slope was statistically significant
(p<0.0001) and negative, indicating a lower slope at higher TSP levels.
3.1.7 Application of a Single C-R Function Everywhere
Whether the C-R relationship between a pollutant and a given health endpoint is estimated by a
single function from a single study or by a pooled function of C-R functions from several studies, that same
C-R relationship is applied everywhere in the benefits analysis. Although the C-R relationship may in fact
vary somewhat from one location to another (for example, due to differences in population susceptibilities
or differences in the composition of PM), location-specific C-R functions are available only for those
locations in which studies were conducted. While a single function applied everywhere may result in
overestimates of incidence changes in some locations and underestimates of incidence changes in other
locations, these location-specific biases will to some extent cancel each other out when the total incidence
change is calculated. It is not possible to know the extent or direction of the bias in the total incidence
change based on application of a single C-R function everywhere.
3.1.8 Estimating Pollutant-Specific Benefits Using Single Pollutant vs. Multi-Pollutant Models
Many studies include both ozone and particulate matter in their final models. It is often difficult to
separate out the effect of a single pollutant from the effects of other pollutants in the mix. Multi-pollutant
models have the advantage that the coefficient for a single pollutant in such a model will be unbiased (so
that the effects of other pollutants will not be attributed falsely to the single pollutant). However, the
variance of the estimator of the coefficient of the pollutant of interest will increase as the correlations
between the other pollutants in the model and that pollutant increase. If the other pollutants in the model
are highly correlated with the pollutant of interest, we would have an unbiased but unstable (high variance)
estimator. However, while single pollutant models have the advantage of more stable estimators, the
coefficient estimate in a single pollutant model could be biased in such a model. We could consider the
single pollutant as an "indicator pollutant" - i.e., an indicator of a pollution mix - if we use single pollutant
models. However, there is no guarantee that the composition of the pollution mix will remain the same
under a control scenario that targets only a single pollutant.
This analysis uses both single pollutant and multi-pollutant models to derive pollutant-specific
benefits estimates. When more than one study has estimated the relationship between a given endpoint and
a given pollutant, information from both single-pollutant and multi-pollutant models may be pooled to
derive pollutant-specific benefits estimates. For example, the benefits predicted by a model with only PM
may be pooled with the benefits predicted by a model with both PM and ozone to derive an estimate of the
PM-related benefits associated with a given endpoint. If the benefits of PM-related and ozone-related
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incidence changes are both being calculated and added together, there is the possibility of overestimating
benefits if some of the studies used are single pollutant models. Suppose, for example, that only ozone is
actually associated with a given endpoint, but PM appears to be associated only because it is correlated
with ozone. The benefits predicted by a single pollutant PM model would, in that case, actually reflect the
benefits of reducing ozone, to the extent that PM and ozone are correlated. If those "PM-related" benefits
were then added to the ozone-related benefits calculated from other models, a likely result would be the
overstatement of benefits of reducing ozone. If only one pollutant is being associated with the endpoint in
this analysis (e.g., chronic bronchitis is associated only with PM in this analysis, while chronic asthma is
associated only with ozone), this is not a problem.
3.1.9 Pooling Study Results
When only a single study has estimated the C-R relationship between a pollutant and a given health
endpoint, the estimation of a population cell-specific incidence change, Ay, is straightforward, as noted
above. When several studies have estimated C-R relationships between a pollutant and a given health
endpoint, the results of the studies can be pooled to derive a single estimate of the function. If the
functional forms, pollutant averaging times, and study populations are all the same (or very similar), a
pooled, "central tendency" C-R function can be derived from multiple study-specific C-R functions. Even
if there are differences among the studies, however, that make a pooled C-R function infeasible, a pooled
estimate of the incidence change, Ay, and/or the monetary benefit of the incidence change can be obtained
by incorporating the appropriate air quality data into the study-specific C-R functions and pooling the
resulting study-specific predictions of incidence change. Similarly, study-specific predictions of incidence
change can be combined with unit dollar values to produce study-specific predictions of benefits.
Whether the pooling is done in "coefficient space," "incidence change space," or "dollar space,"
the question of the relative weights assigned to the estimates (of coefficients, incidence changes, or dollar
benefits) from each input study must be addressed. One possibility is simply averaging the estimates from
all the studies. This has the advantage of simplicity, but the disadvantage of not taking into account the
measured uncertainty of each of the estimates. Estimates with great uncertainty surrounding them are
given the same weight as estimates with very little uncertainty.
An alternative approach to pooling incidence estimates from different studies is to give more
weight to studies with little estimated variance than to studies with a great deal of estimated variance. The
exact way in which weights are assigned to estimates from different studies in a pooled analysis depends on
the underlying assumption about how the different estimates are related to each other. Under the
assumption that there is actually a distribution of true effect coefficients, or p's, that differ by location
and/or study (referred to as the random effects model), the different coefficients reported by different
studies may be estimates of different underlying coefficients, rather than just different estimates of the same
coefficient. In contrast to the "fixed-effects" model (which assumes that there is only one p everywhere),
the random-effects model allows the possibility that different studies are estimating different parameters.16
16 In studies of the effects of PM10 on mortality, for example, if the composition of PM10 varies among study locations the
underlying relationship between mortality and PM10 may be different from one study location to another. For example, fine particles
make up a greater fraction of PM10 in Philadelphia County than in Southeast Los Angeles County. If fine particles are
disproportionately responsible for mortality relative to coarse particles, then one would expect the true value of p for PM10 in
Philadelphia County to be greater than the true value of p for PM10 in Southeast Los Angeles County. This would violate the
assumption of the "fixed effects" model. However, applying a random effects model assumes that the observed set of coefficients in
the policy region.
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A third approach to pooling studies is to apply subjective weights to the studies, rather than
conducting a random effects pooling analysis. If the analyst is aware of specific strengths and weaknesses
of the studies involved, this prior information may be used as input to the calculation of weights which
reflect the relative reliability of the estimates from the studies.
In those cases in which pooling of information from multiple studies was an option in this analysis,
pooling was done in both "incidence change space" and "dollar benefit space." The hypothesis of fixed
effects was tested. If this hypothesis was rejected, an underlying random effects model was used as the
basis for weighting of studies. A more detailed description of the pooling procedure used is given below in
the section on hospital admissions.
3.2 VALUING CHANGES IN HEALTH AND WELFARE EFFECTS
This section discusses a number of issues that arise in valuing changes in health and welfare
effects. The first section provides some background on willingness to pay (WTP). The second section
discusses the possibility that as income changes then WTP would also change. The third section describes
how WTP estimates, that were originally calculated in 1990 dollars, are corrected for inflation to get
estimates in 1997 dollars. In the last section, we briefly review how we aggregate benefits estimates.
3.2.1 WTP Estimation
WTP is a measure of value an individual places on gaining an outcome viewed as desirable, be it
something that can be purchased in a market or not. The WTP measure, therefore, is the amount of money
such that the individual would be indifferent between having the good (or service) and having the money.
An alternative measure of economic value is willingness to accept (WTA) a monetary compensation to
offset a deterioration in welfare, such that the individual would be indifferent between having the money
and not having the deterioration. Whether WTP or WTA is the appropriate measure depends on how
property rights are assigned. Consider an increase in air pollution. If society has assigned property rights
so that people have a right to clean air, then they must be compensated for an increase in the level of air
pollution. The appropriate measure of the value of avoiding an increase in air pollution, in this case, would
be the amount people would be willing to accept in compensation for the more polluted air. If, on the other
hand, society has not assigned people the right to clean air, then the appropriate measure of the value of
avoiding an increase in air pollution would be what people are willing to pay to avoid it. The assignment of
property rights in our society is unclear. WTP is by far the more common measure used in benefits
analyses, however, reflecting the fact that this is a much more common measure in the empirical valuation
literature. In this analysis, wherever possible, the valuation measures are in terms of WTP. Where such
estimates are not available, alternative measures are used, such as cost-of-illness and wage-risk studies.
These are discussed for each endpoint where applicable.
For both market and non-market goods, WTP reflects individuals' preferences. Because
preferences are likely to vary from one individual to another, WTP for both market (e.g., the purchase of a
new automobile) and non-market goods (e.g., health-related improvements in environmental quality) is
likely to vary from one individual to another. In contrast to market goods, however, non-market goods,
such as environmental quality improvements, are public goods whose benefits are shared by many
individuals. The individuals who benefit from the environmental quality improvement may have different
WTPs for this non-market good. The total social value of the good is the sum of the WTPs of all
individuals who "consume" (i.e., benefit from) the good.
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In the case of health improvements related to pollution reduction, it is not certain specifically who
will receive particular benefits of reduced pollution. For example, the analysis may predict 100 hospital
admissions for respiratory illnesses avoided, but the analysis does not estimate which individuals will be
spared those cases of respiratory illness that would have required hospitalization. The health benefits
conferred on individuals by a reduction in pollution concentrations are, then, actually reductions in the risk
of having to endure certain health problems. These benefits (reductions in risk) may not be the same for all
individuals (and could be zero for some individuals). Likewise, the WTP for a given benefit is likely to
vary from one individual to another. In theory, the total social value associated with the decrease in risk of
a given health problem resulting from a given reduction in pollution concentrations is:
N
i=\
where Bj is the benefit (i.e., the reduction in risk of having to endure the health problem) conferred on the ith
individual (out of a total of N) by the reduction in pollution concentrations, and WTPj(Bj) is the ith
individual's WTP for that benefit.
If a reduction in pollution concentrations affects the risks of several health endpoints, the total
health-related social value of the reduction in pollution concentrations is:
where B^ is the benefit related to the jth health endpoint (i.e., the reduction in risk of having to endure the j
^
health problem) conferred on the ith individual by the reduction in pollution concentrations, and WTP^B^) is
the ith individual's WTP for that benefit.
The reduction in risk of each health problem for each individual is not known, nor is each
individual's WTP for each possible benefit he or she might receive known. Therefore, in practice, benefits
analysis estimates the value of a statistical health problem avoided. For example, although a reduction in
pollutant concentrations may save actual lives (i.e., avoid premature mortality), whose lives will be saved
cannot be known ex ante. What is known is that the reduction in air pollutant concentrations results in a
reduction in mortality risk. It is this reduction in mortality risk that is valued in a monetized benefit
analysis. Individual WTPs for small reductions in mortality risk are summed over enough individuals to
infer the value of a statistical life saved. This is different from the value of a particular, identified life
saved. Rather than "WTP to avoid a death," then, it is more accurate to use the term "the value of a
statistical life."
Suppose, for example, that a given reduction in PM concentrations results in a decrease in
mortality risk of 1/10,000. Then for every 10,000 individuals, one individual would be expected to die in
the absence of the reduction in PM concentrations (who would not die in the presence of the reduction in
PM concentrations). If WTP for this 1/10,000 decrease in mortality risk is $500 (assuming, for now, that
all individuals' WTPs are the same), then the value of a statistical life is 10,000 x $500, or $5 million.
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A given reduction in PM concentrations is unlikely, however, to confer the same risk reduction
(e.g., mortality risk reduction) on all exposed individuals in the population. (In terms of the expressions
above, B; is not necessarily equal to Bj , for i #j). In addition, different individuals may not be willing to
pay the same amount for the same risk reduction. The above expression for the total social value
associated with the decrease in risk of a given health problem resulting from a given reduction in pollution
concentrations may be rewritten to more accurately convey this. Using mortality risk as an example, for a
given unit risk reduction (e.g., 1/1,000,000), the total mortality-related benefit of a given pollution
reduction can be written as:
H "i
^marginal WTP^xjdx,
where marginal WTPj(x) is the ith individual's marginal willingness to pay curve, nj is the number of units
of risk reduction conferred on the 1th exposed individual as a result of the pollution reduction, and N is the
total number of exposed individuals.
The values of a statistical life implied by the value-of-life studies were derived from specific risk
reductions. Implicit in applying these values to a situation involving possibly different risk reductions is
the assumption that the marginal willingness to pay curve is horizontal - that is, that WTP for n units of
risk reduction is n times WTP for one unit of risk reduction. If the marginal willingness to pay curve is
horizontal, the integral in the above expression becomes a simple product of the number of units of risk
reduction times the WTP per unit. The total mortality-related benefit (the expression above) then becomes:
N ( WTP ^
Y (number of units of risk reduction) ' .
~[^ '' \unitojriskreduction)
If different subgroups of the population have substantially different WTPs for a unit risk reduction
and substantially different numbers of units of risk reduction conferred on them, then estimating the total
social benefit by multiplying the population mean WTP (MWTP) to save a statistical life times the
predicted number of statistical lives saved could yield a biased result. Suppose, for example, that older
individuals' WTP per unit risk reduction is less than that of younger individuals (e.g., because they have
fewer years of expected life to lose). Then the total benefit will be less than it would be if everyone's WTP
were the same. In addition, if each older individual has a larger number of units of risk reduction conferred
on him (because a given pollution reduction results in a greater absolute reduction in risk for older
individuals than for younger individuals), this, in combination with smaller WTPs of older individuals,
would further reduce the total benefit.
While the estimation of WTP for a market good (i.e., the estimation of a demand schedule) is not a
simple matter, the estimation of WTP for a non-market good, such as a decrease in the risk of having a
particular health problem, is substantially more difficult. Estimation of WTP for decreases in very specific
health risks (e.g., WTP to decrease the risk of a day of coughing or WTP to decrease the risk of admission
to the hospital for respiratory illness) is further limited by a paucity of information.17 Derivation of the
dollar value estimates discussed below was often limited by available information.
17 Some health effects, such as technical measures of pulmonary functioning (e.g., forced expiratory volume in one second)
are frequently studied by epidemiologists, but there has been very little work by economists on valuing these changes (e.g., Ostro et
al., 1989a).
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3.2.2 Change Over Time in WTP in Real Dollars
The WTP for health-related environmental improvements (in real dollars) could change between
now and the year 2030. If real income increases between now and the year 2030, for example, it is
reasonable to expect that WTP, in real dollars, would also increase. Below we summarize the evidence
regarding this effect, however we do not adjust our results in this analysis, because of the uncertainty
regarding the size of the effect.
Based on historical trends, the U.S. Bureau of Economic Analysis projects that, for the United
States as a whole as well as for regions and states within the U.S., mean per capita real income will
increase. For the U.S. as a whole, for example, mean per capita personal income is projected to increase
by about 16 percent from 1993 to 2005 (U.S. Bureau of Economic Analysis, 1995).
The mean WTP in the population is the correct measure of the value of a health problem avoided,
and that WTP is a function of income. If the mean per capita real income rises by the year 2030, the mean
WTP would probably rise as well. While this is most likely true, the degree to which mean WTP rises with
a rise in mean per capita income is unclear unless the elasticity of WTP with respect to changes over time
in real income is 1.0.
There is some evidence (Alberini et al., 1997; Loehman and De, 1982; Mitchell and Carson, 1986)
that the elasticity of WTP for health-related environmental improvements with respect to real income is less
than 1.0, possibly substantially so. If this is the case, then changes in mean income cannot be readily
translated into corresponding changes in mean WTP. Although an increase in mean income is likely to
imply an increase in mean WTP, the degree of the increase cannot be ascertained from information only
about the means.
Several factors, in addition to real income, that could affect the estimated benefit associated with
reductions in air pollution concentrations could also change by the year 2030. Demographic characteristics
of exposed populations could change. Technological advances could change both the nature of precursor
emissions to the ambient air and the susceptibility of individuals to air pollution. Any such changes would
be reflected in C-R functions that differ from those that describe current relationships between ambient
concentrations and the various health endpoints. While adjustments of WTP to reflect changes in real
income are of interest, such adjustments would by no means necessarily reflect all possible changes that
could affect the benefits of reduced air pollution in 2030.
3.2.3 Adjusting Benefits Estimates from 1990 Dollars to 1997 Dollars
This section describes the methods used to convert benefits estimates into constant dollars. In past
RIA analyses, cost and benefit estimates have been presented in constant 1990 dollars. Benefits estimates
in this analysis, however, are presented in constant 1997 dollars. To adjust benefits estimates from 1990
dollars to 1997 dollars, the method of adjustment depends on the basis of the benefits estimates. These
methods are presented below. Four different bases of estimates are delineated in Exhibit 3-1, including that
for agricultural benefits.18
^Agricultural benefits are discussed in Chapter 3.
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Exhibit 3-1 Bases of Benefits Estimation
Basis of Benefit Estimation
Cost of illness
Direct estimates of WTP
Earnings
Changes in yields and prices of market commodities
Benefit Endpoints
Hospital admissions avoided
Statistical lives saved; statistical life-years saved
Chronic bronchitis; chronic asthma
Morbidity endpoints using WTP
Visibility residential
Visibility recreational
Consumer cleaning cost savings
Work loss days (WLDs) avoided
Increased worker productivity
Agricultural benefits
Benefits estimates based on cost-of-illness have been adjusted by using the consumer price indexes
(CPI-Us) for medical care. Because increases in medical costs have been significantly greater than the
general rate of inflation, using a general inflator (the CPI-U for "all items" or some other general inflator)
to adjust from 1990 to 1997 dollars would downward bias cost-of-illness estimates in 1997 dollars.
Benefits estimates based directly on estimates of WTP have been adjusted using the CPI-U for "all
items." (The CPI-Us, published by the U.S. Dept. of Labor, Bureau of Labor Statistics, can also be found
in Council of Economic Advisers (e.g.1997)) An overview of the adjustments from 1990 to 1997 dollars
for WTP-based and cost-of-illness based valuations is given in Exhibit 3-2.
Exhibit 3-2 Consumer Price Indexes Used to Adjust WTP-Based and Cost-of-Illness-Based Benefits
Estimates from 1990 Dollars to 1997 Dollars
CPI-U for "All Items" b
CPI-U for Medical Care b
1990
(1)
130.7
162.8
1997
(2)
160.5
234.6
Adjustment Factor "
(2)/(l)
1.228
1.441
Relevant Endpoints
WTP-based valuation:
1. Statistical lives saved c
2. Chronic bronchitis; chronic asthma
3. Morbidity endpoints using WTP d
3. Visibility residential
4. Visibility recreational
5. Consumer cleaning cost savings
Cost-of-illness based valuation:
Hospital admissions avoided e
* Benefits estimates in 1990 dollars are multiplied by the adjustment factor to derive benefits estimates in 1997 dollars.
b Source: Dept. of Labor, Bureau of Labor Statistics; reported in Council of Economic Advisers (1998, Table B-60)
c Adjustments to 1990 $ were originally made by Industrial Economics Inc. using the CPI-U for "all items" (IEcl992).
d Adjustments of WTP-based benefits for morbidity endpoints to 1990 $ were originally made by Industrial Economics Inc. (1993)
using the CPI-U for "all items."
e Adjustments of cost-of-illness based estimates of all hospital admissions avoided to 1990 $ were made by Abt Associates Inc. in
previous analyses, such as the NAAQS RIA (U.S. EPA, 1997c).
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3-14
December 1999
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Benefits estimates for two endpoints, work loss days (WLDs) avoided and increased worker
productivity, have in past analyses been based on the mean or median daily wage. Consistent with
economic welfare theory, the valuation of benefits associated with increased worker productivity resulting
from improved ozone air quality used the average daily income for outdoor workers engaged in strenuous
activity, reported by the 1990 U.S. Census ($73 per day, in 1990). The valuation of the benefit of avoiding
a work loss day used the median daily income rather than the mean. The income distribution in the United
States is highly skewed, so that the mean income is substantially larger than the median income. However,
the incomes of those individuals who lose work days due to pollution are not likely to be a random sample
from this income distribution. In particular, the probability of being drawn from the upper tail of the
distribution is likely to be substantially less than the probability mass in that tail. To reflect this likelihood,
we used the median income rather than the mean income as the value of a work loss day. This is explained
more fully below in the section on valuing work loss days.
The benefits estimates for WLDs avoided and for increases in worker productivity can be put into
1997 dollars in several ways. The most straightforward approach for WLDs is to obtain the 1997 median
weekly earnings (and divide by five to derive the median daily earnings) rather than relying on adjustments
from 1990 to 1997 dollars. The median weekly earnings of full-time wage and salary workers in 1997 was
$503 (U.S. Bureau of the Census 1998, Table 696). This implies a median daily earnings of $100.6, or
rounded to the nearest dollar, $101. Alternatively, we can adjust the median daily wage for 1990 to 1997
dollars, using the CPI-U for "all items." The result turns out to be the same. The adjustment factor (the
ratio of the 1997 CPI-U to the 1990 CPI-U) is 1.228. Applied to the median daily earnings of $82.4 in
1990, the median daily earnings in 1997 would be $101.2, or rounded to the nearest dollar, $101.
The simplest method to adjust the benefits estimate for increased worker productivity would be to
use the CPI-U for "all items" to adjust the current estimate of $73 per day, in 1990 dollars, to 1997 dollars.
This would result in an estimate of $73*1.228 = $89.6 per day, or rounded to the nearest dollar, $90 per
day, in 1997 dollars. Alternatively, we could try to obtain an estimate of the average daily income for
outdoor workers engaged in strenuous activity in 1997, as we previously did for 1990. It is not entirely
clear, however, which categories of workers were included among "outdoor workers engaged in strenuous
activity" to obtain the 1990 estimate of $73 per day. It is therefore not clear which categories to include to
derive an equivalent figure for 1997.
Finally, agricultural benefits (changes in farm income and consumer welfare) predicted to result in
a future year have been adjusted to 1997 dollars from 2010 using a GDP price deflator. In this analysis,
2010 benefits were adjusted to 1997 dollars by multiplying by 0.6735, the ratio of the 1997 GDP price
deflator (of 112.3 from:Council of Economic Advisers, 1997, Table B-3) to a projected 2010 GDP price
index (of 167.16) forecasted from the trend between 1997 and 2007, obtained from the USDA baseline
projections (U.S. Department of Agriculture, 1988b, electronic file TabOl.wkl).
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3.2.4 Aggregation of Monetized Benefits
The total monetized benefit associated with attaining a given set of pollution changes in a given
location is just the sum of the non-overlapping benefits associated with these changes. In theory, the total
health-related social value of the reduction in pollution concentrations is:
where B^ is the benefit related to the jth health endpoint (i.e., the reduction in probability of having to endure
the jth health problem) conferred on the ith individual by the reduction in pollution concentrations, and
i) is the ith individual's WTP for that benefit.
However, the reduction in probability of each health problem for each individual is not known, nor
do we know each individual's WTP for each possible benefit he or she might receive. Therefore, in
practice, benefits analysis estimates the value of a statistical health problem avoided. The benefit in the kth
location associated with the jth health endpoint is just the change in incidence of the jth health endpoint in the
kth location, Ayjk, times the value of an avoided occurrence of the jth health endpoint.
Assuming that WTP to avoid the risk of a health effect varies from one individual to another, there
is a distribution of WTPs to avoid the risk of that health effect. This population distribution has a mean.
It is this population mean of WTPs to avoid or reduce the risk of the jth health effect, MWTPj, that is the
appropriate value in the benefit analysis.19 The monetized benefit associated with the jth health endpoint
resulting from attainment of standard(s) in the kth location, then, is:
benefit ]k = ^y]k-MWTP]
and total monetized benefit in the kth location (TMBk) may be written as the sum of the monetized benefits
associated with all non-overlapping endpoints:
The location- and health endpoint-specific incidence change, Ayjk, is modeled as the population
response to the change in pollutant concentrations in the kth location. The discussion below uses particulate
matter as an example but is equally applicable to any other pollutant, such as ozone. Assuming a log-linear
C-R function, the change in incidence of the jth health endpoint in the kth location corresponding to a change
in PM, APMk, in the kth location is:
19The population of interest has not been defined. In a location-specific analysis, the population of interest is the population
in that location. The MWTP is ideally the mean of the WTPs of all individuals in the location. There is insufficient information,
however, to estimate the MWTP for any risk reduction in any particular location. Instead, estimates of MWTP for each type of risk
reduction will be taken to be estimates of the MWTP in the United States as a whole, and it will be assumed that MWTP;, i=l,..., N in
each location is approximately the same as in the United States as a whole.
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where yjk is the baseline incidence of the j* health endpoint in the k* location and pjk is the value of Pj, the
coefficient of PM in the C-R relationship between PM and the jth health endpoint, in the kth location.
This approach assumes that there is a distribution of Pj's across the United States, that is, that the
value of Pj in one location may not be the same as the value of Pj in another location. The value of Pj in the
kth location is denoted as pjk .
The total PM-related monetized benefit for the kth location can now be rewritten as:
TMBk = f y]k (e**-* - l) MWTP] ,
The total monetized PM-related benefit to be estimated for a location is thus a function of 2N parameters:
the coefficient of PM, pjk , in the C-R function for the jth health (or welfare) endpoint, for j=l, ..., N,
specific to the kth location, and the population mean WTP to reduce the risk of the j* health endpoint,
MWTPj,j=l, ...,N.
The above model assumes that total monetized benefit is the sum of the monetized benefits from all
non-overlapping endpoints. If two or more endpoints were overlapping, or if one was contained within the
other (as, for example, hospital admissions for Chronic Obstructive Pulmonary Disease - COPD - is
contained within hospital admissions for "all respiratory illnesses"), then adding the monetized benefits
associated with those endpoints would result in double (or multiple) counting of monetized benefits. If
some endpoints that are not contained within endpoints included in the analysis are omitted, then the
aggregated monetized benefits will be less than the total monetized benefits.
The total monetized benefit (TMB) is the sum of the total monetized benefits achieved in each
location:
k=\
where TMBk denotes the total monetized benefit achieved in the kth location, and K is the number of
locations.
Theoretically, the nation-wide analysis could use location-specific C-R functions to estimate
location-specific benefits. Total monetized benefits (TMB), then, would just be the sum of these location-
specific benefits:
k=l
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There are many locations in the United States, however, and the individual location-specific values of Pj
(the Pjk's) are not known.20 Since the national incidence of the jth health endpoint attributed to PM, IJ5 is a
continuous function of the set of pjk's, that is, since:
k=\ k=l
is a continuous function of the set of pjk's, there is some value of Pj, which can be denoted Pj*, that, if
applied in all locations, would yield the same result as the proper set of location-specific pjk's. This
follows from the Intermediate Value Theorem. While Pj* will result in overestimates of incidence in some
locations, it will result in underestimates in others. If Pj* is applied in all locations, however, the total
regional change in incidence will be correct. That is,
k=\ k=\
K
Z
yjk
k=\
The total regional monetized PM-related benefit can now be rewritten as:
.
^PMt - \\
N K
MWTP]
The total regional monetized (PM-related) benefit is thus a function of 2N population means: the p* for the
jth health (or welfare) endpoint (Pj* , for j=l, ..., N) and the population mean WTP to reduce the risk of the
jth health endpoint (MWTPj, j=l, ..., N).
The above formulation of the total monetized benefits associated with a given set of changes in PM
across K locations is applied to ozone as well. The set of health and welfare endpoints may be different for
ozone, but the calculation of benefits is the same, with Aozonek substituted for APMk everywhere.
Both the endpoint-specific coefficients (the yj's) and the endpoint-specific mean WTPs (the
MWTP;'s) are uncertain. One approach to estimating the total monetized benefit is to simply use the mean
values of the endpoint-specific coefficients and mean WTPs in the above formula. We term this approach
the "simple mean." Alternatively, we can characterize not only the mean total monetized benefit but the
20This may also be true of the y^'s. It may be desirable to apply the uncertainty analysis used for the p's to these population
parameters as well. In the current discussion, however, it is assumed that the location-specific incidences are known and therefore
have no uncertainty associated with them. It is also assumed that MWTP; is the same in all locations.
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distribution of possible values of total monetized benefit, using a Monte Carlo approach. The Monte Carlo
approach has three steps. First, in each of 5000 iterations, we randomly select a value from the distribution
of (national) incidence change of the health or welfare effect. Second, we randomly select a value from the
distribution of unit dollar values for that health or welfare effect. And third, we multiply the two values.
The result is a distribution of (5000) monetized benefits associated with the given health or welfare effect.
From this distribution, we present the mean as well as the 5th and 95th percentiles. We discuss the
background of the Monte Carlo in the following sub-section.
3.3 CHARACTERIZATION OF UNCERTAINTY
In any complex analysis using estimated parameters and inputs from numerous different models,
there are likely to be many sources of uncertainty. This analysis is no exception. There are many inputs
that are used to derive the final estimate of benefits, including emission inventories, air quality models (with
their associated parameters and inputs), epidemiological estimates of C-R functions, estimates of values
(both from WTP and cost-of-illness studies), population estimates, income estimates, and estimates of the
future state of the world, i.e. regulations, technology, and human behavior. Each of these inputs may be
uncertain, and depending on their location in the benefits analysis, may have a disproportionately large
impact on final estimates of total benefits. For example, emissions estimates are used in the first stage of
the analysis. As such, any uncertainty in emissions estimates will be propagated through the entire
analysis. When compounded with uncertainty in later stages, small uncertainties in emissions can lead to
much larger impacts on total benefits.
Exhibit 3-3 summarizes the wide variety of sources for uncertainty in this analysis. Some key
sources of uncertainty in each stage of the benefits analysis are:
gaps in scientific data and inquiry
variability in estimated relationships, such as C-R functions, introduced through differences in
study design and statistical modeling
errors in measurement and projection for variables such as population growth rates
errors due to misspecification of model structures, including the use of surrogate variables, such
as using PM10 when PM25 is not available, excluded variables, and simplification of complex
functions
biases due to omissions or other research limitations.
Our approach to characterizing model uncertainty in the estimate of total benefits is to present a
primary estimate, based on the best available scientific literature and methods, and to provide estimates of
the effects of uncertainty about key analytical assumptions. However, in some cases, it was not possible to
quantify uncertainty. For example, many benefits categories, while known to exist, do not have enough
information available to provide a quantified or monetized estimate. The uncertainty regarding these
endpoints is such that we could determine neither a primary estimate nor a plausible range of values. To
the extent possible, we address uncertainty by presenting alternative calculations, supplemental calculations
sensitivity analyses, and probabilistic assessments. We discuss each approach in turn.
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Exhibit 3-3 Key Sources of Uncertainty in the Benefit Analysis
1. Uncertainties Associated With Concentration-Response Functions
-The value of the ozone- or PM-coefficient in each C-R function.
-Application of a single C-R function to pollutant changes and populations in all locations.
-Similarity of future year C-R relationships to current C-R relationships.
-Correct functional form of each C-R relationship.
-Extrapolation of C-R relationships beyond the range of ozone or PM concentrations observed in the study.
2. Uncertainties Associated With Ozone and PM Concentrations
-Estimating future-year baseline and hourly ozone and daily PM concentrations.
-Estimating the change in ozone and PM resulting from the control policy.
3. Uncertainties Associated with PM Mortality Risk
-No scientific literature supporting a direct biological mechanism for observed epidemiological evidence.
-Direct causal agents within the complex mixture of PM responsible for reported health effects have not been identified.
-The extent to which adverse health effects are associated with low level exposures that occur many times in the year
versus peak exposures.
-Possible confounding in the epidemiological studies of PM25, effects with other factors (e.g., other air pollutants,
weather, indoor/outdoor air, etc.).
-The extent to which effects reported in the long-term studies are associated with historically higher levels of PM rather
than the levels occurring during the period of study.
-Reliability of the limited ambient PM25 monitoring data in reflecting actual PM25 exposures.
4. Uncertainties Associated With Possible Lagged Effects
-What portion of the PM-related long-term exposure mortality effects associated with changes in annual PM levels would
occur in a single year, and what portion might occur in subsequent years.
5. Uncertainties Associated With Baseline Incidence Rates
-Some baseline incidence rates are not location-specific (e.g., those taken from studies) and may therefore not accurately
represent the actual location-specific rates.
-Current baseline incidence rates may not well approximate what baseline incidence rates will be in the year 2030.
-Projected population and demographics used to derive incidences - may not well approximate future-year population
and demographics.
6. Uncertainties Associated With Economic Valuation
-Unit dollar values associated with health and welfare endpoints are only estimates of mean WTP and therefore have
uncertainty surrounding them.
-Mean WTP (in constant dollars) for each type of risk reduction may differ from current estimates due to differences in
income or other factors.
7. Uncertainties Associated With Aggregation of Monetized Benefits
-Health and welfare benefits estimates are limited to the available C-R functions. Thus, unquantified benefit categories
will cause total benefits to be underestimated.
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3.3.1 Alternative and Supplementary Calculations
The alternative calculations included in this analysis are based on relatively plausible alternatives
to the assumptions used in deriving the primary benefit estimates. We do not attempt to assign
probabilities to these alternative calculations, as we believe this would only add to the uncertainty of the
analysis or present a false picture about the precision of the results21. Instead, the reader is invited to
examine the impact of applying the different assumptions on the estimate of total benefits. While it is
possible to combine all of the alternative calculations with a positive impact on benefits to form a "high"
estimate or all of the alternative calculations with a negative impact on benefits to form a "low" estimate,
we do not recommend this because the probability of all of these alternative assumptions occurring
simultaneously is likely to be very low. Instead, the alternative calculations are intended to demonstrate the
sensitivity of our benefits results to key parameters which may be uncertain. Exhibit 3-4 summarizes the
alternative calculations included in this analysis.
Exhibit 3-4 also summarizes supplemental calculations prepared for this analysis. Supplemental
calculations are intended to provide additional information about specific health effects, but are not suitable
for inclusion in the primary or alternative estimates due to concerns about double-counting of benefits or
the high degree of uncertainty about the estimates. Results from the supplemental calculations can be
found in Appendix A.
Alternative Calculations
The Dockery et al. (1993) estimate of the relationship between PM exposure and premature
mortality is a plausible alternative to that based on the Pope et al. (1995) However, the Dockery et al.
study had a more limited geographic scope (and a smaller study population) than the Pope et al. study. The
Dockery et al. study also covered a broader age category (25 and older compared to 30 and older in the
Pope et al. study) and followed the cohort for a longer period (15 years compared to 8 years in the Pope et
al. study). For these reasons, the Dockery et al. study is considered to be a plausible alternative estimate of
the avoided premature mortality incidences.
The value of statistical life years alternative calculation recognizes that individuals who die from
air pollution related causes tend to be older than the average age of individuals in the VSL studies used to
develop the $5.9 million value. To employ the value of statistical life-year (VSLY) approach, we first
estimated the age distribution of those lives projected to be saved by reducing air pollution. Based on life
expectancy tables, we calculate the life-years saved from each statistical life saved within each age and
gender cohort. To value these statistical life-years, we hypothesized a conceptual model which depicted the
relationship between the value of life and the value of life-years. The average number of life-years saved
across all age groups for which data were available is 14 for PM-related mortality. The average for PM, in
particular, differs from the 35-year expected remaining lifespan derived from existing wage-risk studies.
Using the same distribution of value of life estimates used above, we estimated a distribution for the value
of a life-year and combined it with the total number of estimated life-years lost.
21 Some recent benefit-cost analyses in Canada and Europe (Holland et al., 1999; Lang et al., 1995) have estimated ranges
of benefits by assigning ad hoc probabilities to ranges of parameter values for different endpoints. Although this does generate a
quantitative estimate of an uncertainty range, the estimated points on these distributions are themselves highly uncertain and very
sensitive to the subjective judgements of the analyst. To avoid these subjective judgements, we choose to allow the reader to
determine the weights they would assign to alternative estimates.
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Reversals in chronic bronchitis incidences are defined as those cases where an individual reported
having chronic bronchitis at the beginning of the study period but reported not having chronic bronchitis in
follow-up interviews at a later point in the study period. Since, by definition, chronic diseases are long-
lasting or permanent, if the disease goes away it is not chronic. In the primary analysis, these reversals are
given a value of zero. As an alternative calculation, we estimate reversals and value each as a case of the
mildest form of chronic bronchitis.
The alternative calculation for residential visibility is based on the McClelland et al. (1991) study
of WTP for visibility changes in Chicago and Atlanta. The residential visibility estimates from the
available literature have been determined by the SAB to be inadequate for use in a primary estimate in a
benefit-cost analysis, because they have not undergone rigorous peer review (EPA-SAB-COUNCIL-ADV-
00-002, 1999). However, residential visibility is likely to have some value and the McClelland et al. study
is probably the best in estimating the likely magnitude of the benefits of residential visibility improvements.
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Exhibit 3-4 Alternative and Supplemental Benefits Calculations for the Tier II 2030 Control
Scenario
Alternative/Supplemental
Calculations
Description
Alternative Calculations
PM-related premature mortality
based on Dockery et al. (1993)
Value of avoided premature mortality
incidences based on statistical life
years.
Reversals in chronic bronchitis
treated as lowest severity cases
Value of visibility changes in Eastern
U.S. residential areas
Household soiling damage
Avoided costs of reducing nitrogen
loadings in East coast estuaries
Uncertainty bounds of aggregate
benefit totals
The Dockery ,et al. study provides an alternative estimate of the relationship between
chronic PM exposure and mortality.
Calculate the incremental number of life-years lost from exposure to changes in ambient
PM and use the value of a statistical life year based on a $5.9 million value of a statistical
life.
Instead of omitting those cases of chronic bronchitis that reverse after a period of time, they
are treated as being cases with the lowest severity rating.
Value of visibility changes outside of Class I areas are estimated for the Eastern U.S. based
on the reported values for Chicago and Atlanta derived from McClelland et al. (1991).
Value of decreases in expenditures on cleaning are estimated using values derived from
Manuel et al. (1982).
Estuarine benefits in 12 East coast estuaries from reduced atmospheric nitrogen deposition
are approximated using the avoided costs of removing or preventing loadings from
terrestrial sources.
5th and 95th percentile values of the distribution of total estimated benefits for ozone, PM,
and ozone + PM.
Supplemental Calculations
Short-term mortality
Post-neonatal mortality
Ozone mortality
Asthma Attacks
Restricted activity days
Ozone-related cardiovascular disease
The Schwartz et al. (1996) study provides an estimate of the relationship between acute
PM exposure and mortality.
The Woodruff et al. (1997) study provides an estimate of the relationship between chronic
exposure and infant mortality.
Ozone-related mortality benefits estimated using a pooled analysis based on four U.S.
studies.
Due to the potential for overlap with health effects covered in the pooled estimate of
MRADs and Any-of-19 Respiratory Symptoms, cases of PM-related moderate or worse
asthma (Ostro et al. (1991)) and cases of both PM- and Ozone-related asthma attacks
(Whittemore and Korn (1980)) are presented separately.
Restricted activity days are presented separately because they overlap with work loss days
and minor restricted activity days.
Burnett et al. (1997) provides an estimate of cardiovascular-related hospital admissions.
The alternative calculation for household soiling is based on the Manuel et al. (1982) study of
consumer expenditures on cleaning and household maintenance. However, the data used to estimate
household soiling damages in the Manuel et al. study is from a 1972 consumer expenditure survey and as
such may not accurately represent consumer preferences in the future.
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The alternative calculation for the avoided costs of reductions in nitrogen loadings is constructed
by examining the avoided costs to surrounding communities of reduced nitrogen loadings for three case
study estuaries (Albemarle-Pamlico Sounds, Chesapeake Bay, and Tampa Bay). The three case study
estuaries are chosen because they have agreed upon nitrogen reduction goals and the necessary nitrogen
control cost data. The estimated costs for these three case-study estuaries are then averaged and applied to
nine other estuaries, chosen for their prominence in the eastern U.S.
Uncertainty bounds are provided as an alternative calculation for aggregate totals of benefits. The
5th and 95th percentile alternative calculations are estimated by holding air quality changes, population
estimates, and other factors constant and determining the distribution of total benefits that would be
generated by a large number of random draws from the distributions of C-R functions and economic
valuation functions. These alternative calculations thus show how the primary estimate of benefits changes
in response to uncertainty in the measurement of C-R and valuation functions.
Supplemental Calculations
Studies examining the relationship between short-term exposures and premature mortality can
reveal what proportion of premature mortality is due to immediate response to daily variations in PM.
There is only one short-term study (presenting results from 6 separate U.S. cities) that uses PM2 5 as the
metric of PM (Schwartz et al. (1996)). As such, the supplemental estimate for premature mortality related
to short-term PM exposures is based on the pooled city-specific, short-term PM2 5 results from Schwartz et
al.
The estimated effect of PM exposure on premature mortality in infants (post-neonatal) is based on
a single U.S. study (Woodruff et al. (1997)) that, on recommendation of the SAB, was deemed too
uncertain to include in the primary analysis. Adding this endpoint to the primary benefits estimate would
result in an increase in total benefits.
In previous regulatory analyses, estimated incidences of ozone-related premature mortality have
been estimated as a primary endpoint. Based on recent advice from the Science Advisory Board (SAB)
(EPA-SAB-Council-ADV-99-012, 1999), however, we have converted this endpoint to a supplemental
estimate to avoid potential double-counting of benefits captured by the Pope et al. PM premature mortality
endpoint. There are many studies of the relationship between ambient ozone levels and daily mortality
levels. The supplemental estimate is calculated using results from only four U.S. studies (Ito and Thurston
(1996), Kinney et al. (1995), Moolgavkar et al. (1995), and Samet et al. (1997)), based on the assumption
that demographic and environmental conditions on average would be more similar between these studies
and the conditions prevailing when this regulation is implemented.
Due to the potential for overlap with health effects covered in the pooled estimate of MRADs and
Any-of-19 Respiratory Symptoms, cases of PM-related moderate or worse asthma (Ostro et al. (1991)) and
cases of both PM- and ozone-related asthma attacks (Whittemore and Korn (1980)) are presented
separately as supplemental calculations. To include them would lead to a potential double-counting of
benefits related to the avoidance of asthma-related health effects.
Restricted activity days (Ostro, 1987) is another health effect that overlaps with endpoints included
in the primary analysis. Restricted activity days are defined as work loss days, missed school days, days
spent in bed, and other restricted activity days (Adams and Benson, 1992, p. 4). Health effects included in
this definition overlap with health effects included in both measures of work loss days and minor restricted
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activity days. To include both of these endpoints along with restricted activity days would lead to a double-
counting of benefits, therefore restricted activity days are presented as a supplemental calculation.
The last supplemental calculation is an alternative measure of ozone-related cardiovascular
disease. There are only two studies that are relevant for this endpoint, Burnett et al. (1997) and Burnett et
al. (1999). Burnett et al. (1997) gives implausibly large estimates of cardiovascular disease. The link
between ozone and cardiovascular problems is not as well established as that between ozone and
respiratory problems. Other studies have not found a link between ozone and cardiovascular problems, and
instead have found associations with other pollutants, like PM. Acknowledging the uncertainty in our
estimate, we use only the results of the Burnett et al. (1999) study that focused on a narrow subset of
cardiovascular problems, the relationship between ozone and abnormal heart rhythms or "dysrhythmias."
3.3.2 Sensitivity Analyses
In addition to alternative calculations and supplementary calculations, we will perform sensitivity
analyses, briefly described in Exhibit 3-5. Sensitivity analyses, as opposed to alternative calculations,
examine the sensitivity of estimated benefits results to less plausible alternatives to the assumptions used in
the primary analysis. Sensitivity calculations also demonstrate the sensitivity of our benefits results to key
analytical parameters. The sensitivity analyses calculated for this analysis will include the impact of a
threshold assumption on Pope et al. (1995) mortality, alternative lag structures when valuing mortality, and
the extrapolation of benefits from reduced nitrogen loadings to all East coast nutrient-sensitive estuaries.
Results from the sensitivity analyses are presented in Appendix A.
Exhibit 3-5 Sensitivity Analyses for the Tier II 2030 Control Scenario
Sensitivity Analysis
Threshold assumptions
Alternative mortality lag structures
Avoided costs of reducing nitrogen
loadings in East coast estuaries
Description
Calculate the impact varying threshold assumptions have on the estimation of mortality
incidence based on the Pope et al. (1995) study.
Calculate the impact different lag structures have on the estimation of benefits associated
with avoided mortality incidence.
Estuarine benefits attributed to 12 nutrient-sensitive East coast estuaries extrapolated to
represent benefits associated with reductions in nitrogen at all nutrient-sensitive East coast
estuaries.
3.3.3 Statistical Uncertainty Bounds
Although there are several sources of uncertainty affecting estimates of endpoint-specific benefits,
the sources of uncertainty that are most readily quantifiable in this analysis are the C-R relationships and
uncertainty about unit dollar values. The total dollar benefit associated with a given endpoint depends on
how much the endpoint will change due to the final standard (e.g., how many premature deaths will be
avoided) and how much each unit of change is worth (e.g., how much a premature death avoided is
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worth).22 Based on these distributions, we provide estimates of the 5th and 95th percentile values of the
distribution of estimated benefits. However, we hasten to add that this omits important sources of
uncertainty, such as the contribution of air quality changes, baseline population incidences, projected
populations exposed, transferability of the C-R function to diverse locations, and uncertainty about
premature mortality. Thus, a confidence interval based on the standard error would provide a misleading
picture about the overall uncertainty in the estimates. The empirical evidence about uncertainty is
presented where it is available.
Both the uncertainty about the incidence changes and uncertainty about unit dollar values can be
characterized by distributions. Each "uncertainty distribution" characterizes our beliefs about what the
true value of an unknown (e.g., the true change in incidence of a given health effect) is likely to be, based
on the available information from relevant studies.23 Unlike a sampling distribution (which describes the
possible values that an estimator of an unknown value might take on), this uncertainty distribution
describes our beliefs about what values the unknown value itself might be. Such uncertainty distributions
can be constructed for each underlying unknown (such as a particular pollutant coefficient for a particular
location) or for a function of several underlying unknowns (such as the total dollar benefit of a regulation).
In either case, an uncertainty distribution is a characterization of our beliefs about what the unknown (or
the function of unknowns) is likely to be, based on all the available relevant information. Uncertainty
statements based on such distributions are typically expressed as 90 percent credible intervals. This is the
interval from the fifth percentile point of the uncertainty distribution to the ninety-fifth percentile point.
The 90 percent credible interval is a "credible range" within which, according to the available information
(embodied in the uncertainty distribution of possible values), we believe the true value to lie with 90
percent probability.
The uncertainty about the total dollar benefit associated with any single endpoint combines the
uncertainties from these two sources, and is estimated with a Monte Carlo method. In each iteration of the
Monte Carlo procedure, a value is randomly drawn from the incidence distribution and a value is randomly
drawn from the unit dollar value distribution, and the total dollar benefit for that iteration is the product of
the two.24 If this is repeated for many (e.g., thousands of) iterations, the distribution of total dollar benefits
associated with the endpoint is generated.
Using this Monte Carlo procedure, a distribution of dollar benefits may be generated for each
endpoint. The mean and median of this Monte Carlo-generated distribution are good candidates for a point
estimate of total monetary benefits for the endpoint. As the number of Monte Carlo draws gets larger and
larger, the Monte Carlo-generated distribution becomes a better and better approximation to the underlying
uncertainty distribution of total monetary benefits for the endpoint. In the limit, it is identical to the
underlying distribution.
22 Because this is a regional analysis in which, for each endpoint, a single C-R function is applied everywhere, there are two
sources of uncertainty about incidence: (1) statistical uncertainty (due to sampling error) about the true value of the pollutant
coefficient in the location where the C-R function was estimated, and (2) uncertainty about how well any given pollutant coefficient
approximates p*.
23 Although such an "uncertainty distribution" is not formally a Bayesian posterior distribution, it is very similar in concept
and function (see, for example, the discussion of the Bayesian approach in Kennedyl990, pp. 168-172).
24 This method assumes that the incidence change and the unit dollar value for an endpoint are stochastically independent.
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3.3.4 Unquantified Benefits
In considering the monetized benefits estimates, the reader should remain aware of the limitations.
One significant limitation of both the health and welfare benefits analyses is the inability to quantify many
of the PM and ozone-induced adverse effects. For many health and welfare effects, such as PM-related
materials damage, reliable C-R functions and/or valuation functions are not currently available. In general,
if it were possible to monetize these benefits categories, the benefits estimates presented in this RIA would
increase. In addition to unqualified benefits, there may also be environmental costs that we are unable to
quantify. Several of these environmental cost categories are related to nitrogen deposition, while one
category is related to the issue of ultraviolet light. The net effect of excluding benefit and disbenefit
categories from the estimate of total benefits depends on the relative magnitude of the effects.
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HEALTH BENEFITS
The most significant monetized benefits of reducing ambient concentrations of PM and ozone are
attributable to reductions in health risks associated with air pollution. This Chapter describes individual
effects and the methods used to quantify and monetize changes in the expected number of incidences of
various health effects.
We estimate the incidence of adverse health effects using C-R functions based on PM and ozone.
The changes in incidence of PM-related and ozone-related adverse health effects and corresponding
monetized benefits associated with these changes are estimated separately. The PM- and ozone-related
health endpoints for which C-R functions are estimated are shown in Exhibits 4-1 and 4-2, respectively.
The unit monetary values for each of these endpoints, and associated uncertainty distributions, are
presented in Exhibit 4-3. In some cases there are alternative and/or supplemental endpoints, studies, or unit
dollar values that could be used in calculating the benefits of a change in pollution. These alternatives are
presented where appropriate in Exhibits 4-1, 4-2, and 4-3 in italics to indicate that they are not used in the
primary analysis but may be used in alternative analyses or used to supplement the existing analyses.
Appendices B and C present the functional forms for each C-R function and how they were derived.
Issues relating to the calculation of changes in incidence and the monetization of these changes are
discussed below for each endpoint. For some of the endpoint-pollutant combinations, there are several
epidemiological studies that have estimated C-R functions. In these cases, the information in the multiple
studies is pooled, so that the estimation of the change in incidence and the corresponding monetized value
of that change is based on a synthesis of the information in all the available studies. A general discussion
of pooling issues is provided above. A detailed description of the method used to pool multiple studies in
this analysis is given below for those endpoints for which pooling was used.
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Exhibit 4-1 PM-Related Health Endpoints
Endpoint
Population to Which
Applied
PM
Indicator
Study
Mortality
Associated with long-term exposure
Associated with long-term exposure a
Ages 30+
All ages
PM2.5
PMis
Pope etal. (1995)
Dockeryetal. (1993)
Chronic Illness
Chronic Bronchitis
varies by study
varies by
study
Multiple studies b
Hospital Admissions
Respiratory
Cardiovascular
Asthma-related ER visits
varies by study
varies by study
<65
varies by
study
varies by
study
PM10
Multiple studies b
Multiple studies b
Schwartz etal. (1993)
Respiratory Symptoms/Illnesses Not Requiring Hospitalization
Acute bronchitis
Lower respiratory symptoms (LRS)
Upper respiratory symptoms (URS)
Shortness of breath (days with)
Minor restricted activity day (MRAD)/ Any
of 19 respiratory symptoms c
Work loss days (WLDs)
Asthma
Restricted Activity Days (RADs)
Ages 8-12
Ages 7- 14
Asthmatics, ages 9-11
African- American
asthmatics, ages 7- 12
Ages 18-65
Ages 18-65
Asthmatics, all ages
Ages 18-65
PM2.5
PM25
PM10
PM10
varies by
study
PM2.5
PM2i,
PM10
PM2.5
Dockery et al. (1989)
Schwartz etal. (1994)
Pope etal. (1991)
Ostro etal. (1995)
Ostro and Rothschild (1989b), Krupnick
etal. (1990)
Ostro (1987)
Ostro et al. (1991), Whittemore and
Korn (1980)
Ostro (1987)
* Italicized entries are either alternative or supplemental calculations to the endpoints and/or studies used in the primary analysis.
b The incidence changes, and the associated monetized benefits, predicted by several studies are pooled. The separate studies and
the method of pooling are described below.
c The incidence changes, and the associated monetized benefits, from these two related endpoints are pooled.
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Exhibit 4-2 Ozone-Related Health Endpoints
Endpoint
Chronic Illness
Chronic asthma
Population to Which
Applied
non-asthmatic males, age 27+
Study
McDonnell et al. (1999)
Hospital Admissions
Respiratory
Cardiovascular
Asthma-related ER visits
varies by study
varies by study
varies by study
Multiple studies "
Multiple studies a
Multiple studies "
Symptoms/Illnesses Not Requiring Hospitalization
Minor restricted activity day (MRAD) / Any of 19
respiratory symptoms b
Worker productivity
Asthma attacks c
Ages 18-65
Working population
Asthmatics, ullages
Ostro and Rothschild (1989b), Krupnick et
al. (1990)
Crocker and Horst (1981) and EPA (1994)
Whittemore and Korn (1980)
1 The incidence changes, and the associated monetized benefits, predicted by several studies are pooled. The separate studies and
the method of pooling are described below.
b The incidence changes, and the associated monetized benefits, from these two related endpoints are pooled.
c Italicized entries are alternative or supplemental calculations to the endpoints and/or studies used in the primary analysis.
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Exhibit 4-3 Unit Values for Economic Valuation of Health Endpoints (1997 $)
Health Endpoint
Mean Estimate "
Uncertainty Distribution "
Mortality
Value of a statistical life
Value of a statistical life
vearb
$5.9 million per statistical life
$2. 8 million per statistical life
(mean of 24 years of life saved)
Weibull distribution, mean = $5.9 million;
std. dev. = $3.98 million.
Based on the Weibull distribution for the value of a statistical
life, from which the value of a statistical life year is derived.
Chronic Bronchitis
WTP approach
$3 19,000 per case
A Monte Carlo-generated distribution, based on three underlying
distributions.
Chronic Asthma
$3 1,000 per case
Triangular distribution centered at $31,000 over the interval
[$23,000, $37,000].
Hospital Admissions
Respiratory
Cardiovascular
Asthma-related ER visits
C
c
$279. 55 per visit
C
c
Triangular distribution centered at $280 over the interval
[$207.50, $387.63].
Respiratory Ailments Not Requiring Hospitalization
Acute bronchitis
Lower resp. Symptoms
Upper resp. Symptoms
Any of 19 acute
respiratory symptoms/
minor restricted activity
day (MRAD) d
Shortness of breath
Work loss days
Worker productivity
Asthma - acute
Asthma moderate or
worse
Restricted activity day
(RAD)
$55.26 per case
$14.74 per symptom-day
$23.33 per symptom-day
Any of 19 symptoms: $22.10 per
symptom-day
MRAD: $46.66 per day
$6.51 per symptom-day
$101. 92 per day
Change in daily wages adjusted by
regional variations in income
$39.30 per symptom-day
$39.30
Based on MRAD valuation
Continuous uniform distribution over [$15.96, $94.56].
Continuous uniform distribution over [$6.14, $23.33].
Continuous uniform distribution over [$8.60,$40.52].
Any of 19 symptoms: Continuous uniform distribution over the
interval [$0,$45.44].
MRAD: Triangular distribution centered at $46.66 over [$19.65,
$74.91].
Continuous uniform distribution over [$0, $13.02]
None available
None available
Continuous uniform distribution over [$14. 74, $66.31]
Continuous uniform distribution over [$14. 74, $66.31]
Values based on MRAD valuation
* The derivation of each of the estimates is discussed in the text. All WTP-based dollar values were obtained by multiplying rounded
1990 $ values used in the §812 Prospective Analysis by 1.228 to adjust to 1997 $. Entries in italics are not used in the primary
benefits analysis.
b Based on a 5 percent discount rate, a value of $360,000 (rounded from $359,981) per life year (in 1997 $), a five-year lag
structure, 1997 life expectancies, and 22,837 implied deaths (derived from the number of estimated life years lost). This is explained
in greater detail in the text below.
c Definitions of endpoints vary by study. For example, "all respiratory illnesses" includes ICD-9 codes 460-519 in some studies, but
only subsets of that group in other studies. Cost of illness unit dollar values were derived for each separate set of ICD codes for
which a C-R model was estimated. These are given below.
d These two endpoints are pooled.
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4.1 PREMATURE MORTALITY
Changes in PM concentrations on mortality may be estimated by a count of the expected number of
deaths avoided due to a given reduction in PM concentrations. An alternative measure is to infer the
number of years of life that are saved by a given reduction in PM concentrations: years of life that each
individual was expected to live and that would have been lost had the reduction in PM concentrations not
occurred. If life-years saved is used as a measure of the PM impact, then the value of a premature death
avoided will likely depend on the age of the individual. Both measures of mortality are estimated in this
analysis to provide a range of the possible cost of premature mortality.
Both ozone and particulate matter have been associated with increased risk of premature mortality,
which is a very important health endpoint in this economic analysis due to the high monetary value
associated with risks to life. There are two types of exposure to elevated levels of air pollution that may
result in premature mortality. Acute (short-term) exposure (e.g., exposure on a given day) to peak
pollutant concentrations may result in excess mortality on the same day or within a few days of the elevated
exposure. Chronic (long-term) exposure (e.g., exposure over a period of a year or more) to levels of
pollution that are generally higher may result in mortality in excess of what it would be if pollution levels
were generally lower. The excess mortality that occurs will not necessarily be associated with any
particular episode of elevated air pollution levels.
4.1.1 Short-Term Versus Long-Term Studies
There are two types of epidemiological studies that examine the relationship between mortality and
exposure. Long-term studies (e.g., Pope et al., 1995) estimate the association between long-term (chronic)
exposure to air pollution and the survival of members of a large study population over an extended period
of time. Such studies examine the health endpoint of concern in relation to the general long-term level of
the pollutant of concern, for example, relating annual mortality to some measure of annual pollutant level.
Daily peak concentrations would impact the results only insofar as they affect the measure of long-term
(e.g., annual) pollutant concentration. In contrast, short-term studies relate daily levels of the pollutant to
daily mortality. By their basic design, daily studies can detect acute effects but cannot detect the effects of
long-term exposures. A chronic exposure study design (a prospective cohort study, such as the Pope study)
is best able to identify the long-term exposure effects, and may detect some of the short-term exposure
effects as well. Because a long-term exposure study may detect some of the same short-term exposure
effects detected by short-term studies, including both types of study in a benefit analysis would likely result
in some degree of double counting of benefits. While the long-term study design is preferred, these types of
studies are expensive to conduct and consequently there are relatively few well designed long-term studies.
4.1.2 Degree of Prematurity of Mortality
It is possible that the short-term studies are detecting an association between PM and mortality that
is primarily occurring among terminally ill people. Critics of the use of short-term studies for policy
analysis purposes correctly point out that an added risk factor that results in terminally ill people dying a
few days or weeks earlier than they otherwise would have (referred to as "short-term harvesting") is
potentially included in the measured PM mortality "signal" detected in such a study. While some of the
detected excess deaths may have resulted in a substantial loss of life (measuring loss of life in terms of lost
years of remaining life), others may have lost a relatively short amount of lifespan. However, there is little
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evidence to bear on this question. Studies by Spix et al (1993) and Pope et al. (1992) yield conflicting
evidence, suggesting that harvesting may represent anywhere from zero to 50 percent of the deaths
estimated in short-term studies. A recent study by Zeger et al. (1999), that focused exclusively on this
issue, reported that short-term harvesting may be a quite small fraction of mortality.25
It is not likely, however, that the excess mortality reported in a long-term prospective cohort study
like Pope et al. (1995) contains any significant amount of this short-term harvesting. The Cox proportional
hazard statistical model used in the Pope study examines the question of survivability throughout the study
period (ten years). Deaths that are premature by only a few days or weeks within the ten-year study period
(for example, the deaths of terminally ill patients, triggered by a short duration PM episode) are likely to
have little impact on the calculation of the average probability of surviving the entire ten-year interval.
4.1.3 Estimating PM-Related Premature Mortality
The benefits analysis estimates PM-related mortality using the PM2 5 relationship from Pope et al.
(1995). This decision reflects the Science Advisory Board's explicit recommendation for modeling the
mortality effects of PM in both the completed §812 Retrospective Report to Congress and the ongoing
§812 Prospective study (U.S. EPA, 1999b, p. 12). The Pope et al. study estimated the association between
long-term (chronic) exposure to PM25 and the survival of members of a large study population. This
relationship is selected for use in the benefits analysis instead of short-term (daily pollution) studies for a
number of reasons.
We selected the Pope et al. (1995) long-term study as providing the best available estimate of the
relationship between PM and mortality. It is used alone- rather than considering the total effect to be the
sum of estimated short-term and long-term effects- because summing creates the possibility of double-
counting a portion of PM-related mortality. We selected the Pope et al. study in preference to other
available long-term studies because it uses better statistical methods, has a much larger sample size, the
longest exposure interval, and more locations (51 cities) in the United States, than other studies. It is
unlikely that the Pope et al. study contains any significant amount of short-term harvesting. First, the
health status of each individual tracked in the study is known at the beginning of the study period. Persons
with known pre-existing serious illnesses were excluded from the study population. Second, the statistical
model used in the Pope study examines the question of survivability throughout the study period (ten
years). Deaths that are premature by only a few days or weeks within the ten-year study period (for
example, the deaths of terminally ill patients, triggered by a short duration PM episode) are likely to have
little impact on the calculation of the average probability of surviving the entire ten year interval. In
relation to the "Six-cities" study by Dockery et al. (1993), the Pope et al. study found a smaller increase in
excess mortality for a given PM air quality change.
It is currently unknown whether there is a time lag (a delay between changes in PM exposures and
changes in mortality rates) in the chronic PM/premature mortality relationship. The existence of such a lag
is important for the valuation of premature mortality incidences because economic theory suggests that
benefits occurring in the future should be discounted. Although there is no specific scientific evidence of
the existence or structure of a PM effects lag, current scientific literature on adverse health effects, such as
25Zeger et al. (1999, p. 171) reported that: "The TSP-mortality association in Philadelphia is inconsistent with the
harvesting-only hypothesis, and the harvesting-resistant estimates of the TSP relative risk are actually larger - not smaller - than the
ordinary estimates."
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those associated with PM (e.g., smoking related disease) and the difference in the effect size between
chronic exposure studies and daily mortality studies suggest that all incidences of premature mortality
reduction associated with a given incremental change in PM exposure probably would not occur in the
same year as the exposure reduction. This same smoking-related literature implies that lags of up to a few
years are plausible. Following explicit advice from the SAB, we assume a five-year lag structure, with 25
percent of premature deaths occurring in the first year, another 25 percent in the second year, and 16.7
percent in each of the remaining three years (EPA-SAB-COUNCIL-ADV-00-001, 1999). Readers should
note that the selection of a five-year lag structure is not directly supported by any PM-specific literature.
Rather, it is intended to be a best guess at the appropriate distribution of avoided incidences of PM-related
mortality.
Alternative Calculation: PM-Related Mortality Based on Dockery et al. (1993)
As an alternative to Pope et al. (1995), this analysis calculates the impact of PM on mortality using
Dockery et al. (1993), another long-term PM-mortality study. Dockery et al. (1993) examined the
relationship between PM exposure and mortality in a cohort of 8,111 individuals aged 25 and older, living
in six U.S. cities. They surveyed these individuals in 1974-1977 and followed their health status until
1991. While they used a smaller sample of individuals from fewer cities than the study by Pope et al., they
used improved exposure estimates, a slightly broader study population (adults aged 25 and older), and a
follow-up period nearly twice as long as that of Pope et al. (1995). Perhaps because of these differences,
Dockery et al. study found a larger effect of PM on premature mortality than that found by Pope et al.
Sensitivity Calculation: Mortality Lag Structure
To account for the uncertainty about when PM-related mortality will not occur in relation to the
year that air pollution is reduced, we examine the sensitivity of mortality-related benefits to alternative lag
structures. Exhibit 4-4 presents the lags that are used in these sensitivity calculations. As stated earlier,
the primary analysis uses a five-year lag structure in the valuation of mortality and chronic bronchitis, with
incidence apportioned as follows: 25 percent in the first year, 25 percent in the second year, and 16.67
percent in the last three years. To examine the effect alternate lag-structures have on the estimation of both
mortality and chronic bronchitis valuation, the mortality benefits will be calculated using five alternative
lag structures. Lag 1 will apportion the occurrence of all incidence to the first year. Valuation of these
cases will not be discounted. In lag 2, based on the length of the study period for the Dockery et al. (1993)
study, 100 percent of mortality incidence occurs in fifteen years from the modeled future-year. Lag 3,
based on the length of the study period for the Pope et al. (1995) study, assigns 100 percent of the
occurrence of mortality incidence to the eighth year out from the modeled future-year. Lag 4 front loads
the occurrence of mortality incidence. Incidence is apportioned in decreasing amounts out to fifteen years.
Lag 5 apportions incidence over fifteen years, assigning a lesser percentage of incidence in the beginning
years, with the percentage of incidence increasing over time out to fifteen years. The latter two lag
structures are intended to show how the distribution of incidences within a lag period affects benefit
estimates.
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Exhibit 4-4 Mortality Lag Structure
Year
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Primary
25
25
16.67
16.67
16.67
0
0
0
0
0
0
0
0
0
0
Sensitivity 1
100
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Sensitivity 2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
100
Sensitivity 3
0
0
0
0
0
0
0
100
0
0
0
0
0
0
0
Sensitivity 4
30
25
15
6
4
3
3
3
2
2
2
2
1
1
1
Sensitivity 5
1
1
1
2
2
2
2
o
3
o
3
o
3
4
6
15
25
30
Sensitivity Calculation: Ozone-Related Mortality
Epidemiological studies suggest that there may be a link between ozone exposures and premature
mortality, however possible confounding with PM-related mortality precludes its inclusion in the primary
analysis. As an alternative, an ozone-related mortality meta-analysis was conducted to provide an
alternative calculation of mortality incidence. Using a random-effects pooling procedure, we take the
incidence estimates of four U.S. ozone-related mortality studies ~ Ito and Thurston (1996), Kinney et al.
(1995), Moolgavkar et al. (1995), and Samet et al. (1997) ~ and estimate the mortality incidence changes
for a given rule. For a complete discussion of ozone mortality and the pooling procedure, see the TSD for
the proposed Tier II rule (Abt Associates, 1999).
4.1.4 Valuing Premature Mortality
Two methods for valuing avoided premature mortality are presented in this analysis. The first is
the "statistical lives lost" approach. Using this approach, the value of a statistical death is estimated to be
$5.9 million (in 1997 $). The second valuation approach is the "statistical life years lost" approach. Using
this approach, the value of an avoid premature death depends on the age at which the individual dies. The
average value for an avoided PM-related premature death, however, is $2.8 million (in 1997 $)
(representing an average of 24 years of life saved, based on 1997 life expectancy estimates). In each case,
we assume for this analysis that some of the incidences of premature mortality related to PM exposures
occur in a distributed fashion over the five years following exposure (the five-year mortality lag). To take
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this into account in the valuation of reductions in premature mortalities, we apply an annual five percent
discount rate to the value of premature mortalities occurring in future years.26
Statistical Lives Lost
The "statistical lives lost" value of $5.9 million represents an intermediate value from a variety of
estimates that appear in the economics literature, and is a value that EPA has frequently used in RIAs for
other rules. This estimate is the mean of a distribution fitted to the estimates from 26 value-of-life studies
identified in the §812 study as "applicable to policy analysis." The approach and set of selected studies
mirrors that of Viscusi (1992) (with the addition of two studies), and uses the same criteria used by Viscusi
in his review of value-of-life studies. The $5.9 million estimate is consistent with Viscusi's conclusion
(updated to 1997 $) that "most of the reasonable estimates of the value of life are clustered in the $3.7 to
$8.6 million range." Uncertainty associated with the valuation of premature mortality is expressed through
a Weibull distribution with a standard deviation of $3.98 million (lEc 1992, p. 2).
Five of the 26 studies are contingent valuation (CV) studies, which directly solicit WTP
information from subjects; the rest are wage-risk studies, which base WTP estimates on estimates of the
additional compensation demanded in the labor market for riskier jobs. The 26 studies are listed in Exhibit
4-5. The references for all but Gegax et al. (1985) and V.K. Smith (1983) may be found in Viscusi (1992).
Although each of the studies estimated the mean WTP (MWTP) for a given reduction in mortality risk, the
amounts of reduction in risk being valued were not necessarily the same across studies, nor were they
necessarily the same as the amounts of reduction in mortality risk that would actually be conferred by a
given reduction in ambient concentrations. The transferability of estimates of the value of a statistical life
from the 26 studies to this analysis rests on the assumption that, within a reasonable range, WTP for
reductions in mortality risk is linear in risk reduction, or equivalently, that the marginal willingness to pay
curve is horizontal within a reasonable range. For example, suppose a study estimates that the average
WTP for a reduction in mortality risk of 1/100,000 is $30. Suppose, however, that the actual mortality
risk reduction resulting from a given air quality improvement is 1/10,000. If WTP for reductions in
mortality risk is linear in risk reduction, then a WTP of $30 for a reduction of 1/100,000 implies a WTP of
$300 for a risk reduction of 1/10,000 (which is ten times the risk reduction valued in the study). Under the
assumption of linearity, the estimate of the value of a statistical life does not depend on the particular
amount of risk reduction being valued.
26The choice of a five percent discount rate is based on the technical recommendation of the SAB for computing the value
of a statistical life-year (EPA-SAB-COUNCIL-ADV-00-002, 1999).
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Exhibit 4-5 Summary of Mortality Valuation Estimates
Study
Kneisner and Leeth (1991) (US)
Smith and Gilbert (1984)
Dillingham (1985)
Butler (1983)
Miller and Guria (1991)
Moore and Viscusi (1988)
Viscusietal. (1991)
Gegaxetal. (1985; 1991)
Marin and Psacharopoulos (1982)
Kneisner and Leeth (1991) (Australia)
Gerking et al. (1988)
Cousineau et al. (1988; 1992)
Jones-Lee (1989)
Dillingham (1985)
Viscusi (1978; 1979)
R.S. Smith (1976)
V.K. Smith (1983)
Olson (1981)
Viscusi (1981)
R.S. Smith (1974)
Moore and Viscusi (1988)
Kneisner and Leeth (1991) (Japan)
Herzog and Schlottman (1987; 1990)
Leigh and Folson (1984)
Leigh (1987)
Garen(1988)
Type of Estimate
Labor Market
Labor Market
Labor Market
Labor Market
Contingent Valuation
Labor Market
Contingent Valuation
Contingent Valuation
Labor Market
Labor Market
Contingent Valuation
Labor Market
Contingent Valuation
Labor Market
Labor Market
Labor Market
Labor Market
Labor Market
Labor Market
Labor Market
Labor Market
Labor Market
Labor Market
Labor Market
Labor Market
Labor Market
Valuation (millions 1997 S)
0.7
0.9
1.1
1.4
1.5
3.1
3.3
4.1
3.4
4.1
4.2
4.4
4.7
4.9
5.0
5.6
5.8
6.4
8.0
8.8
9.0
9.3
11.2
11.9
12.8
16.6
Source: Viscusi (1992, Table 4.1).
Although the particular amount of mortality risk reduction being valued in a study may not affect
the transferability of the WTP estimate from the study to this analysis, the characteristics of the study
subjects and the nature of the mortality risk being valued in the study could be important. Certain
characteristics of both the population affected and the mortality risk facing that population are believed to
affect the MWTP to reduce the risk. The appropriateness of the MWTP estimates from the 26 studies for
valuing the mortality-related benefits of reductions in ambient air concentrations therefore depends not only
on the quality of the studies (i.e., how well they measure what they are trying to measure), but also on (1)
the extent to which the subjects in the studies are similar to the population affected by changes in ambient
air concentrations and (2) the extent to which the risks being valued are similar.
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Focusing on the wage-risk studies, which make up the substantial majority of the 26 studies relied
upon, the likely differences between (1) the subjects in these studies and the population affected by changes
in air concentrations and (2) the nature of the mortality risks being valued in these studies and the nature of
air pollution-related mortality risk are considered. The direction of bias in which each difference is likely to
result is also considered.
Compared with the subjects in wage-risk studies, the population believed to be most affected by air
pollution (i.e., the population that would receive the greatest mortality risk reduction associated with a
given reduction in air concentrations) is, on average, older and probably more risk averse. For example,
citing Schwartz and Dockery (1992) and Ostro et al. (1996), Chestnut (1995) estimated that approximately
85 percent of those who die prematurely from ambient air pollution-related causes are over 65. The
average age of subjects in wage-risk studies, in contrast, is well under 65.
There is also reason to believe that those over 65 are, in general, more risk averse than the general
population while workers in wage-risk studies are likely to be less risk averse than the general population.
Although Viscusi's (1992) list of recommended studies excludes studies that consider only much-higher-
than-average occupational risks, there is nevertheless likely to be some selection bias in the remaining
studies that is, these studies are likely to be based on samples of workers who are, on average, more risk-
loving than the general population. In contrast, older people as a group exhibit more risk averse behavior.
In addition, it might be argued that because the elderly have greater average wealth than those
younger, the affected population is also wealthier, on average, than wage-risk study subjects, who tend to
be blue collar workers. It is possible, however, that among the elderly it is largely the poor elderly who are
most vulnerable to air pollution-related mortality risk (e.g., because of generally poorer health care). If this
is the case, the average wealth of those affected by a reduction in air concentrations relative to that of
subjects in wage-risk studies is uncertain.
The direction of bias resulting from the age difference is unclear, particularly because age is
confounded by risk aversion (relative to the general population). It could be argued that, because an older
person has fewer expected years left to lose, his WTP to reduce mortality risk would be less than that of a
younger person. This hypothesis is supported by one empirical study, Jones-Lee et al.(1985), that found
the value of a statistical life at age 65 to be about 90 percent of what it is at age 40. Citing the evidence
provided by Jones-Lee et al., Chestnut (1995) assumed that the value of a statistical life for those 65 and
over is 75 percent of what it is for those under 65.
The greater risk aversion of older people, however, implies just the opposite. Citing Ehrlich and
Chuma (1990), Industrial Economics Inc. (1992) noted that "older persons, who as a group tend to avoid
health risks associated with drinking, smoking, and reckless driving, reveal a greater demand for reducing
mortality risks and hence have a greater implicit value of a life year." That is, the more risk averse
behavior of older individuals suggests a greater WTP to reduce mortality risk.
There is substantial evidence that the income elasticity of WTP for health risk reductions is
positive (Alberini et al., 1997; Gerking et al., 1988; Jones-Lee et al., 1985; Loehman et al., 1982; Mitchell
et al., 1986), although there is uncertainty about the exact value of this elasticity). Individuals with higher
incomes (or greater wealth) should, then, be willing to pay more to reduce risk, all else equal, than
individuals with lower incomes or wealth. Whether the average income or level of wealth of the population
affected by ambient air pollution reductions is likely to be significantly different from that of subjects in
wage-risk studies, however, is unclear.
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Finally, although there may be several ways in which job-related mortality risks differ from air
pollution-related mortality risks, the most important difference may be that job-related risks are incurred
voluntarily whereas air pollution-related risks are incurred involuntarily.
There is some evidence that people will pay more to reduce involuntarily incurred risks than risks
incurred voluntarily (e.g., Violette and Chestnut, 1983). Job-related risks are incurred voluntarily whereas
air pollution-related risks are incurred involuntarily. If this is the case, WTP estimates based on wage-risk
studies may be downward biased estimates of WTP to reduce involuntarily incurred ambient air pollution-
related mortality risks.
The potential sources of bias in an estimate of MWTP to reduce the risk of air pollution related
mortality based on wage-risk studies are summarized in Exhibit 4-6. Although most of the individual
factors tend to have a downward bias, the overall effect of these biases is unclear.
Exhibit 4-6 Potential Sources of Bias in Estimates of Mean WTP to Reduce the Risk of PM Related
Mortality Based on Wage-Risk Studies
Factor
Age
Degree of Risk Aversion
Income
Risk Perception: Voluntary vs. Involuntary risk
Likely Direction of Bias in Mean WTP Estimate
Uncertain
Downward
Downward, if the elderly affected are a random sample of the elderly. It is
unclear, if the elderly affected are the poor elderly.
Downward
Alternative Calculation: Statistical Life-Years Lost
In an alternative calculation, we value statistical life-years, rather than valuing statistical lives.
Moore and Viscusi (1988) value a statistical life-year lost, by assuming that the WTP to save a statistical
life is the value of a single year of life times the expected number of years of life remaining for an
individual. They suggest that a typical respondent in a mortal risk study has a life expectancy of an
additional 35 years. Using a mean estimate of $4.8 million (1990 $) to save a statistical life, their
approach yields an estimate of $137,000 per life-year lost or saved, assuming no discounting. If an
individual discounts future additional years using a standard discounting procedure, the value of each life-
year lost must be greater than the value assuming no discounting. Using a 35 year life expectancy, a $4.8
million value of a statistical life, and a five percent discount rate, the implied value of each life-year lost is
$293,000 (1990 $). This is $360,000 in 1997 dollars.
This analysis assumes a value of a statistical life year lost of $360,000 and a five percent discount
rate, consistent with the "statistical lives lost" value of $5.9 million. In addition, the "statistical lives lost"
analysis must accommodate the five-year lag structure. For each person dying at a given age, using the
expected number of years remaining for that age, based on 1997 life expectancy tables (National Center for
Health Statistics, 1999, Table 5), and a VSLY of $360,000, we calculate the present discounted value
(discounted back to the beginning of the year of death) for that person. All values are then discounted back
to the beginning of 2030, whether the individual dies in 2030 or in a subsequent year. The present
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discounted value (discounted back to the beginning of 2030) of an avoided premature mortality will vary
from one individual to another, depending on the age of the individual at death and on the extent of lag
between exposure and death. The age at death determines the expected number of life years lost, while the
extent of lag between exposure and death determines the amount of discounting needed. The average value
of an avoided incidence of PM-related premature mortality, however, is $2.8 million (in 1997 $),
corresponding to 24 years of life.
4.2 CHRONIC ILLNESS
Onset of bronchitis and asthma, two chronic illnesses, have both been associated with exposure to
air pollutants. Three studies have linked the onset of chronic bronchitis in adults to particulate matter; one
study has linked the onset of chronic asthma in adults to ozone. These results are consistent with research
that has found chronic exposure to pollutants leads to declining pulmonary functioning (Abbey et al., 1998;
Ackermann-Liebrich et al., 1997; Betels et al., 1991).
4.2.1 Chronic Bronchitis
We estimate the changes in the new cases of chronic bronchitis using the studies by Schwartz
(1993), Abbey et al. (1993), and Abbey et al. (1995b). The Schwartz study is somewhat older and uses a
cross-sectional design, however, it is based on a national sample, unlike the Abbey et al. studies which are
based on a sample of California residents. We first pool the estimates from the two studies by Abbey et al.
- since they are based on the same sample population and simply use different measures of PM - and then
pool this estimate with that from Schwartz.
Three studies that have estimated C-R functions for PM and chronic bronchitis were pooled in this
analysis. These studies are listed in Exhibit 4-7.
Exhibit 4-7 Chronic Bronchitis Studies
Location
California
California
United States
Study
Abbey et al. (1993)
Abbey etal. (1995b)
Schwartz (1993)
Pollutants Used in Final Model
PM10
PM2.5
PM10
Age of Study
Population
>26
>26
>29
Schwartz (1993) examined survey data collected from 3,874 adults ranging in age from 30 to 74,
and living in 53 urban areas in the U.S. The survey was conducted between 1971 and 1975, as part of the
National Health and Nutrition Examination Survey, and is representative of the non-institutionalized U.S.
population. Schwartz (1993, Table 3) reported chronic bronchitis prevalence rates in the study population
by age, race, and gender. Non-white males under 52 years old had the lowest rate (1.7%) and white males
52 years and older had the highest rate (9.3%). The study examined the relationship between the prevalence
of reported chronic bronchitis and annual levels of total suspended particulates (TSP), collected in the year
prior to the survey.
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Abbey et al. (1993) surveyed 3,914 adult Seventh Day Adventists living in California, and
estimated the relationship between annual mean ambient TSP, ozone and SO2 and the onset of certain
chronic respiratory symptoms (including airway obstructive disease (AOD), chronic bronchitis, and
asthma) that were not present at the beginning of the study. The initial survey was conducted in 1977 and
the final survey in 1987. To ensure a better estimate of exposure, the study participants had to have been
living in the same area for an extended period of time. TSP was significantly linked to new cases of AOD
and chronic bronchitis, but not to asthma or the severity of asthma. Ozone was not linked to the incidence
of new cases of any endpoint, but ozone was linked to the severity of asthma. No effect was found for SO2.
A later study by Abbey et al. (1995b) examined the relationship between estimated PM25 (annual
mean from 1966 to 1977), PM10 (annual mean from 1973 to 1977) and TSP (annual mean from 1973 to
1977) and the same chronic respiratory symptoms in a sample population of 1,868 Californian Seventh-
Day Adventists. The initial survey was conducted in 1977 and the final survey in 1987. To ensure a better
estimate of exposure, the study participants had to have been living in the same area for an extended period
of time. In single-pollutant models, there was a statistically significant PM25 relationship with development
of chronic bronchitis, but not for AOD or asthma; PM10 was significantly associated with chronic
bronchitis and AOD; and TSP was significantly associated with all cases of all three chronic symptoms.
Other pollutants were not examined.
Alternative Calculation: Chronic Bronchitis Reversals
In developing the C-R functions for chronic bronchitis, it is necessary to estimate its annual
incidence rate. The annual incidence rate is derived by taking the number of new cases (234), dividing by
the number of individuals in the sample (3,310), as reported by Abbey et al.(1993, Table 3), dividing by
the ten years covered in the sample, and then multiplying by one minus the reversal rate (the percentage of
reversals is estimated to be 46.6% based on Abbey et al. (1995a, Table 1)). Reversals refer to those cases
of chronic bronchitis that were reported at the start of the Abbey et al. survey, but were subsequently not
reported at the end of the survey. Since we assume that chronic bronchitis is a permanent condition, we
subtract these reversals. Nevertheless, reversals may likely represent a real effect that should be included
in the analysis. To allow for this possibility, we present an estimate of reversals in an alternative
calculation in which reversals are considered to be chronic bronchitis cases of the lowest severity level, as
described below.
Valuing Chronic Bronchitis
PM-related chronic bronchitis is expected to last from the initial onset of the illness throughout the
rest of the individual's life. WTP to avoid chronic bronchitis would therefore be expected to incorporate
the present discounted value of a potentially long stream of costs (e.g., medical expenditures and lost
earnings) and pain and suffering associated with the illness. Two studies, Viscusi et al. (1991) and
Krupnick and Cropper (1992), provide estimates of WTP to avoid a case of chronic bronchitis.
The Viscusi et al. (1991) and the Krupnick and Cropper (1992) studies were experimental studies
intended to examine new methodologies for eliciting values for morbidity endpoints. Although these studies
were not specifically designed for policy analysis, we believe the studies provide reasonable estimates of the
WTP for chronic bronchitis. As with other contingent valuation studies, the reliability of the WTP
estimates depends on the methods used to obtain the WTP values. The Viscusi et al. and the Krupnick and
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Cropper studies are broadly consistent with current contingent valuation practices, although specific
attributes of the studies may not be.
The study by Viscusi et al. uses a sample that is larger and more representative of the general
population than the study by Krupnick and Cropper (which selects people who have a relative with the
disease). Thus, the valuation for the high-end estimate is based on the distribution of WTP responses from
Viscusi et al. The WTP to avoid a case of pollution-related chronic bronchitis (CB) is derived by starting
with the WTP to avoid a severe case of chronic bronchitis, as described by Viscusi et al. (1991), and
adjusting it downward to reflect (1) the decrease in severity of a case of pollution-related CB relative to the
severe case described in the Viscusi et al. study, and (2) the elasticity of WTP with respect to severity
reported in the Krupnick and Cropper study. Because elasticity is a marginal concept and because it is a
function of severity (as estimated from Krupnick et al., 1992), WTP adjustments were made incrementally,
in one percent steps. A severe case of CB was assigned a severity level of 13 (following Krupnick and
Cropper). The WTP for a one percent decrease in severity is given by:
where sev is the original severity level (which, at the start, is 13) and e is the elasticity of WTP with respect
to severity. Based on the regression in Krupnick and Cropper (1992) (see below), the estimate of e is
0.18*sev. At the mean value of sev (6.47), e = 1.16. As severity decreases, however, the elasticity
decreases. Using the regression coefficient of 0.18, the above equation can be rewritten as:
WTP(,99sev = WTPsev (1 - 0.01 0.1 Ssev) .
For a given WTPsev and a given coefficient of sev (0.18), the WTP for a 50 percent reduction in severity
can be obtained iteratively, starting with sev =13, as follows:
WTPUS7 = WTP099,3 = WTP13 (1 - 0.01 -0.18-13)
WTPU74 = WTP099,2gl = WTPug7 -(1- 0.01-0.18-12.87)
261 = ^^0.99.12.74 = ^2.74 ' (1 ~ 0.01 0.1 8 12.74)
and so forth. This iterative procedure eventually yields WTP6 5, or WTP to avoid a case of chronic
bronchitis that is of "average" severity.
The derivation of the WTP to avoid a case of pollution-related chronic bronchitis is based on three
components, each of which is uncertain: (1) the WTP to avoid a case of severe CB, as described in the
Viscusi et al. (1991) study, (2) the severity level of an average pollution-related case of CB (relative to that
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of the case described by Viscusi et al), and (3) the elasticity of WTP with respect to severity of the illness.
Because of these three sources of uncertainty, the WTP is uncertain. Based on assumptions about the
distributions of each of the three uncertain components, a distribution of WTP to avoid a pollution-related
case of CB was derived by Monte Carlo methods. The mean of this distribution, which was about
$319,000, is taken as the central tendency estimate of WTP to avoid a pollution-related case of CB. Each
of the three underlying distributions is described briefly below.
1. The distribution of WTP to avoid a severe case of CB was based on the distribution of WTP
responses in the Viscusi et al. (1991) study. Viscusi et al. derived respondents' implicit WTP to avoid a
statistical case of chronic bronchitis from their WTP for a specified reduction in risk. The mean response
implied a WTP of about $1,228,000 (1997 $)27; the median response implied a WTP of about $651,000
(1997 $). However, the extreme tails of distributions of WTP responses are usually considered unreliable.
Because the mean is much more sensitive to extreme values, the median of WTP responses is often used
rather than the mean. Viscusi et al. report not only the mean and median of their distribution of WTP
responses, however, but the decile points as well. The distribution of reliable WTP responses from the
Viscusi et al. study could therefore be approximated by a discrete uniform distribution giving a probability
of 1/9 to each of the first nine decile points. This omits the first five and the last five percent of the
responses (the extreme tails, considered unreliable). This trimmed distribution of WTP responses from the
Viscusi et al. study was assumed to be the distribution of WTPs to avoid a severe case of CB. The mean
of this distribution is about $884,000 (1997 $).
2. The distribution of the severity level of an average case of pollution-related CB was modeled as
a triangular distribution centered at 6.5, with endpoints at 1.0 and 12.0. These severity levels are based on
the severity levels used in Krupnick and Cropper (1992), which estimated the relationship between
ln(WTP) and severity level, from which the elasticity is derived. The most severe case of CB in that study
is assigned a severity level of 13. The mean of the triangular distribution is 6.5. This represents a 50
percent reduction in severity from a severe case.
3. The elasticity of WTP to avoid a case of CB with respect to the severity of that case of CB is a
constant times the severity level. This constant was estimated by Krupnick and Cropper (1992) in the
regression of ln(WTP) on severity, discussed above. This estimated constant (regression coefficient) is
normally distributed with mean = 0.18 and standard deviation = 0.0669 (obtained from Krupnick and
Cropper).
The distribution of WTP to avoid a case of pollution-related CB was generated by Monte Carlo
methods, drawing from the three distributions described above. On each of 16,000 iterations (1) a value
was selected from each distribution, and (2) a value for WTP was generated by the iterative procedure
described above, in which the severity level was decreased by one percent on each iteration, and the
corresponding WTP was derived. The mean of the resulting distribution of WTP to avoid a case of
pollution-related CB was $319,000.
This WTP estimate is reasonably consistent with full COI estimates derived for chronic bronchitis,
using average annual lost earnings and average annual medical expenditures reported by Cropper and
Krupnick (1990) Using a 5 percent discount rate and assuming that (1) lost earnings continue until age 65,
(2) medical expenditures are incurred until death, and (3) life expectancy is unchanged by chronic
27There is an indication in the Viscusi et al. (1991) paper that the dollar values in the paper are in 1987 dollars. Under this
assumption, the dollar values were converted to 1997 dollars.
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bronchitis, the present discounted value of the stream of medical expenditures and lost earnings associated
with an average case of chronic bronchitis is estimated to be about $109,000 for a 30 year old, about
$105,000 for a 40 year old, about $96,000 for a 50 year old, and about $55,000 for a 60 year old. A WTP
estimate would be expected to be greater than a full COI estimate, reflecting the willingness to pay to avoid
the pain and suffering associated with the illness. The WTP estimate of $319,000 is from 2.9 times the full
COI estimate (for 30 year olds) to 5.8 times the full COI estimate (for 60 year olds). The midpoint of the
COI estimates across the range of ages of $82,000 per case is used as an alternative valuation estimate for
reduced incidence of chronic bronchitis.
Alternative Calculation: Valuing Chronic Bronchitis Reversals
In an alternative calculation, we estimate chronic bronchitis reversals and value them using the
same method used to value cases of chronic bronchitis. However, instead of allowing the severity level to
range from one to 13, we value all reversals at a severity level of one. This yields a WTP estimate of
$140,000 for each chronic bronchitis reversal.
4.2.2 Chronic Asthma
In a number of studies ozone, PM, and even CO have been linked to acute asthmatic complaints
(e.g., Ostro et al., 1995; Sheppard et al, 1999; Whittemore et al., 1980), however there is more limited
evidence regarding the link between air pollution and the development of asthma. The best evidence points
to ozone. Abbey et al. (1991; 1993) reported a significant link between ozone and the development of
asthma, and Portney and Mullahy (1990) found ozone linked to sinusitis and hay fever. A review of
research data by the EPA (1996a, p. 9-35) concluded that prolonged ozone exposure causes structural
changes in several regions of the respiratory tract, and the available epidemiological studies are suggestive
of a link between chronic health effects in humans and long-term ozone exposure. And most recently, a
study by McDonnell et al. (1999) carefully measured ozone exposure over 15 years, and found ozone
exposure was linked to the onset of asthma in adult males.
The McDonnell et al. (1999) study used the same cohort of Seventh-Day Adventists as Abbey et
al. (1991; 1993), and examined the association between air pollution and the onset of asthma in adults
between 1977 and 1992. Males who did not report doctor-diagnosed asthma in 1977, but reported it in
1987 or 1992, had significantly higher ozone exposures, controlling for other covariates; no significant
effect was found between ozone exposure and asthma in females. No significant effect was reported for
females or males due to exposure to PM, NO2, SO2, or SO4.
Valuing Chronic Asthma
Two studies have estimated WTP to avoid chronic asthma in adults. Blumenschein and
Johannesson (1998) used two different contingent valuation (CV) methods, the dichotomous choice method
and a bidding game, to estimate mean willingness to pay for a cure for asthma. The mean WTP elicited
from the bidding game was $189 per month, or $2,268 per year (in 1996$). The mean WTP elicited from
the dichotomous choice approach was $343 per month, or $4,116 per year (in 1996$). Using $2,268 per
year, a five percent discount rate, and 1997 life expectancies for males in the United States (National
Center for Health Statistics, 1999, Table 5), the present discounted value of the stream of annual WTPs is
about $35,000 (in 1997 $).
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O'Conor and Blomquist (1997) estimated WTP to avoid chronic asthma from estimates of risk-risk
tradeoffs. Combining the risk-risk tradeoffs with a statistical value of life, the annual value of avoiding
asthma can be derived. Assuming a value of a statistical life of $6 million, they derived an annual WTP to
avoid asthma of $1500 (O'Connor etal., 1997, p. 677). For a value of a statistical life of $5,894,400 (in
1997 $), the corresponding implied annual value of avoiding chronic asthma, based on O'Conor and
Blomquist would be $1,474. Assuming a five percent discount rate and 1997 life expectancies for males in
the United States, the present discounted value of the stream of annual WTPs would be about $22,000 (in
1997 $).
Following the method used for the §812 Prospective analysis, the uncertainty surrounding the WTP
to avoid a case of chronic asthma among adult males was characterized by a triangular distribution on the
range determined by the two WTP estimates. The range used in the §812 Prospective analysis was
[$19,000, $30,000], centered at $25,000 (in 1990 $). In the current analysis these dollar values are
converted to 1997 $ using the CPI-U for "all items."
4.3 HOSPITAL ADMISSIONS
We estimate impact of ozone and PM on both respiratory and cardiovascular hospital admissions.
In addition, we estimate the impact of these pollutants on emergency visits for asthma.
4.3.1 Respiratory and Cardiovascular Hospital Admissions
Respiratory and cardiovascular hospital admissions are the two broad categories of hospital
admissions that have been related to exposure to PM and ozone. For both PM-related and ozone-related
hospital admissions there are multiple epidemiological studies that have estimated C-R functions that can
be used in this analysis. The respiratory and the cardiovascular hospital admissions studies are listed in
Exhibits 4-8 and 4-9, respectively. (Again, Appendices B and C provide details on each study.) Although
the benefits associated with respiratory and cardiovascular hospital admissions are estimated separately in
the analysis, the methods used to estimate changes in incidence and to value those changes are the same for
both broad categories of hospital admissions. The two categories of hospital admissions are therefore
discussed together in this section.
Although separate analyses are carried out for PM-related and ozone-related hospital admissions,
the method of pooling multiple studies is the same in both cases. To estimate the incidence and monetary
value of avoided hospital admissions, we pool the incidences and the monetary values corresponding to the
incidence estimates from a variety of U.S. and Canadian studies, using a random effects weighting
procedure. These studies differ from each other in two important ways: (1) Some studies considered people
of all ages while others considered only people ages 65 and older; and (2) The ICD codes included in
studies of respiratory hospital admissions and air pollution vary substantially.
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Exhibit 4-8 Respiratory Hospital Admission Studies
Location
Toronto, Canada
Toronto, Canada
Toronto, Canada
Minneapolis-St.
Paul, MN
Minneapolis-St.
Paul, MN
Birmingham,
AL
Detroit, MI
Spokane, WA
New Haven, CT
Tacoma, WA
Seattle, WA
Study
Burnett etal. ( 1997)
Burnett etal. ( 1999)
Thurston et al. (1994)
Moolgavkar et al.
(1997)
Schwartz (1994c)
Schwartz (1994a)
Schwartz (1994b)
Schwartz (1996)
Schwartz (1995)
Schwartz (1995)
Sheppard et al.
(1999)
Endpoints Estimated
(ICD code)
all respiratory (464-466, 480-
486, 490-494, 496)
asthma (493); respiratory
infection (464, 466, 480-487,
494); COPD (490-492, 496)
all respiratory (466, 480-482,
485, 490-493)
pneumonia (480-487); COPD
(490-496)
pneumonia (480-486); COPD
(490-496)
pneumonia (480-487); COPD
(490-496)
pneumonia (480-486); non-
asthma COPD (491-492, 494-
496)
all respiratory (460-519)
all respiratory (460-519)
all respiratory (460-519)
asthma (493)
Pollutants Used in Final Model
PM10.2.5, 03
O3, PM10.2 5 (asthma); O3, PM2 5
(respiratory infection); O3, PM10.
2.5 (COPD).
O3, PM2 5
O3, PM10 (pneumonia); O3, PM10
(COPD)
O3, PM10 (pneumonia); PM10
(COPD)
PM10
03,PM10
PM10
03,PM10
03,PM10
PM25
Age of
Study
Population
all ages
all ages
all ages
>64
>64
>64
>64
>64
>64
>64
<65
Exhibit 4-9 Cardiovascular Hospital Admission Studies
Location
Toronto, Canada
Toronto, Canada
Detroit, MI
Eight U.S. counties
1/88-12/90
Tucson, AZ
1/88-12/90
Study
Burnett etal. (1997)
Burnett etal. (1999)
Schwartz and Morris
(1995)
Schwartz (1999)
Schwartz (1997)
Endpoints Estimated
(ICD code)
cardiac (410-414, 427-428)
dysrhythmias (427);
ischemic heart disease (410-414);
congestive heart failure (428)
cardiovascular disease (390-429)
cardiovascular disease (390-429)
Pollutants Used
in Final Model
03,PM10.2.5
PM2 5, 03
PM10
PM10
PM10
Age of Study
Population
all ages
all ages
>64
>64
>64
The broadest classification includes ICD codes 460-519 (e.g., Schwartz, 1996). Other studies,
however, considered only subsets of the broader classification. For example, Burnett et al. (1997) consider
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ICD-9 codes 466, 480-486, 490-494, and 496. It is unclear what the correct set of ICD codes is. If the
broadest category (460-519) is too broad, including respiratory illnesses that are not linked to air pollution,
we would expect the estimated pollutant coefficients to be biased downward; however, they would be used
in combination with a larger baseline incidence in estimating changes in respiratory hospital admissions
associated with changes in pollutant concentrations. If the broadest category is correct (i.e., if all the
respiratory illnesses included are actually associated with air pollution), then studies using only subsets of
ICD codes within that category would presumably understate the change in respiratory hospital admissions.
It is likely, however, that all the studies have included the most important respiratory illnesses, and that the
impact of differences in the definition of "all respiratory illnesses" may be less than that of other study
design characteristics. We therefore treat each study equally, at least initially, in the pooling process,
assuming that each study gives a reasonable estimate of the impact of air pollution on respiratory hospital
admissions. The pooling process involves several steps.
1. For each study, develop a study-specific distribution of pollutant coefficients.28 If separate non-
overlapping sets of illnesses were considered in the study, develop a distribution for each set.
The value of the pollutant coefficient in a C-R function is estimated. Because of the statistical
uncertainty surrounding the estimated coefficient, the C-R function is uncertain. We assume a normal
distribution of the pollutant coefficient in the C-R function, with mean equal to the estimated coefficient
reported in the study and standard deviation equal to the reported standard error of that estimate. If
separate models were estimated for separate non-overlapping sets of illnesses (e.g., Burnett et al., 1999)
estimated three separate models: one for asthma (ICD code 493), one for "respiratory infection" (ICD
codes 464, 466, 480-487, and 494), and one for COPD (ICD codes 490-492, 496)), we develop a
distribution of coefficients for each non-overlapping hospital admissions category.
2. For each study, develop a distribution of unit monetary values. If separate non-overlapping sets of
respiratory illnesses were considered in the study, develop a distribution of unit monetary values for each
set.
The monetary value of an avoided hospital admission depends on the particular type of illness (i.e.,
the ICD code) and the length of stay in the hospital, which itself varies with the type of admission. The
monetary value of a set of hospital admissions (i.e., a set of ICD codes) is estimated as a weighted average
of the individual ICD-code-specific values in the set. The valuation of hospital admissions is described
more fully below.
3. For each study, develop a distribution of incidence changes and a distribution of monetary benefits
resulting from a given change in pollutant concentrations.
On each iteration of a Monte Carlo procedure, for each non-overlapping hospital admissions
category considered in the study,
we randomly select a pollutant coefficient from the distribution of coefficients.
Given the coefficient and the pollutant change, we calculate the incidence change.
We randomly select a unit dollar value from the corresponding dollar distribution;
The benefit is the product of the incidence change and the unit dollar value.
* "Pollutant" can refer either to PM or to ozone.
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If the study has considered several non-overlapping hospital admissions categories, we sum the
incidences and the dollar benefits across categories. For example, we estimated and summed the incidences
for the three separate models estimated by Burnett et al. (1999). A series of many (e.g., 5000) iterations
therefore produces (1) a series (distribution) of incidence changes for each non-overlapping hospital
admissions category considered by the study as well as for all categories combined, and (2) a distribution of
the dollar benefits associated with hospital admissions that would be predicted by the study.
4. Aggregate estimates across non-overlapping age categories.
Several studies estimated C-R functions for respiratory admissions for people ages 65 and older.
One study, Sheppard et al. (1999), estimated a C-R function for asthma only for people under 65. Using a
Monte Carlo procedure, we aggregate the results from the Sheppard study with those from each of the
over-65 respiratory admissions studies.
5. Pool estimates of respiratory hospital admissions changes.
The study-specific incidence estimates are then pooled using a random effects pooling procedure,
as described above. The study-specific dollar benefits estimates are similarly pooled.
Valuing Respiratory and Cardiovascular Hospital Admissions
Society's WTP to avoid a hospital admission includes medical expenses, lost work productivity,
the non-market costs of treating illness (i.e., air, water and solid waste pollution from hospitals and the
pharmaceutical industry), and the pain and suffering of the affected individual as well as of that of
relatives, friends, and associated caregivers.29
Because medical expenditures are to a significant extent shared by society, via medical insurance,
Medicare, etc., the medical expenditures actually incurred by the individual are likely to be less than the
total medical cost to society. The total value to society of an individual's avoidance of hospital admission,
then, might be thought of as having two components: (1) the cost of illness (COI) to society, including the
total medical costs plus the value of the lost productivity, as well as (2) the WTP of the individual, as well
as that of others, to avoid the pain and suffering resulting from the illness.
In the absence of estimates of social WTP to avoid hospital admissions for specific illnesses
(components 1 plus 2 above), estimates of total COI (component 1) are typically used as conservative
(lower bound) estimates. Because these estimates do not include the value of avoiding the pain and
suffering resulting from the illness (component 2), they are biased downward. Some analyses adjust COI
estimates upward by multiplying by an estimate of the ratio of WTP to COI, to better approximate total
WTP. Other analyses have avoided making this adjustment because of the possibility of over-adjusting ~
29 Some people take action to avert the negative impacts of pollution. While the costs of successful averting behavior should
be added to the sum of the health-endpoint-specific costs when estimating the total costs of pollution, these costs are not associated
with any single health endpoint It is possible that in some cases the averting action was not successful, in which case it might be
argued that the cost of the averting behavior should be added to the other costs listed (for example, it might be the case that an
individual incurs the costs of averting behavior and in addition incurs the costs of the illness that the averting behavior was intended to
avoid). Because averting behavior is generally not taken to avoid a particular health problem (such as a hospital admission for
respiratory illness), but instead is taken to avoid the entire collection of adverse effects of pollution, it does not seem reasonable to
ascribe the entire costs of averting behavior to any single health endpoint.
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that is, possibly replacing a known downward bias with an upward bias. The previous RIAs for PM and
ozone, as well as the revised RIA for ozone and PM NAAQS, did adjust the COI estimate upward. The
COI values used in this benefits analysis will not be adjusted to better reflect the total WTP.
Following the method used in the §812 analysis (U.S. EPA, 1999a), ICD-code-specific COI
estimates used in our analysis consist of two components: estimated hospital charges and the estimated
opportunity cost of time spent in the hospital (based on the average length of a hospital stay for the illness).
The opportunity cost of a day spent in the hospital is estimated as the value of the lost daily wage,
regardless of whether or not the individual is in the workforce. This is estimated at $102 (U.S. Bureau of
the Census, 1992).
For all hospital admissions included in this analysis, estimates of hospital charges and lengths of
hospital stays were based on discharge statistics provided by Elixhauser et al. (1993). The total COI for an
ICD-code-specific hospital stay lasting n days, then, would be estimated as the mean hospital charge plus
$102*n. Most respiratory hospital admissions categories considered in epidemiological studies consisted of
sets of ICD codes. The unit dollar value for the set of ICD codes was estimated to be a weighted average
of the ICD-code-specific values, where the weights are the relative frequencies of hospital discharges (in
Elixhauser et al. (1993)) of each ICD code in the set. The study-specific values for valuing respiratory and
cardiovascular hospital admissions are shown in Exhibits 4-10 and 4-11, respectively.
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Exhibit 4-10 Unit Values for Respiratory Hospital Admissions
Study
Burnett etal. (1997)
Toronto, Canada
Burnett etal. (1999)
Toronto, Canada
Thurston et al. (1994)
Toronto, Canada
Moolgavkar et al. (1997)
Minneapolis-St. Paul, MN
Schwartz (1994c)
Minneapolis-St. Paul, MN
Schwartz (1994a)
Birmingham, AL
Schwartz (1994b)
Detroit, MI
Schwartz (1996)
Spokane, WA
Schwartz (1995)
New Haven, CT
Schwartz (1995)
Tacoma, WA
Sheppard et al. (1999)
Seattle, WA
Endpoints Estimated
(ICD code)
all respiratory (464-466, 480-486, 490-494,
496)
asthma (493)
respiratory infection (464, 466, 480-487, 494)
COPD (490-492, 496)
all respiratory (466, 480-482, 485, 490-493)
pneumonia (480-487)
COPD (490-496)
pneumonia (480-486)
COPD (490-496)
pneumonia (480-487)
COPD (490-496)
pneumonia (480-486)
non-asthma COPD (491-492, 494-496)
all respiratory (460-519)
all respiratory (460-519)
all respiratory (460-519)
asthma (493)
COI"
(1997 S)
$ 9,914
$ 6,301
$ 10,720
$ 10,479
$ 9,652
$ 11,429
$ 8,634
$ 11,571
$ 8,634
$ 11,429
$ 8,634
$ 11,571
$ 11,893
$ 10,326
$ 10,326
$ 10,326
$ 6,301
1 The unit value for a group of ICD-9 codes is the weighted average of ICD-9 code-specific values, from Elixhauser et al. (1993).
The weights are the relative frequencies of hospital discharges in Elixhauser et al. for each ICD-9 code in the group. The
monetized benefits of non-overlapping endpoints within each study were aggregated. Monetized benefits for asthma among
people age <65 (Sheppard et al., 1999) were aggregated with the benefits in studies of people age >64.
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Exhibit 4-11 Unit Values for Cardiovascular Hospital Admissions
Study
Burnett etal. ( 1997)
Toronto, Canada
Burnett etal. (1999)
Toronto, Canada
Schwartz and Morris (1995)
Detroit, MI
Schwartz (1999)
Eight U.S. counties
1/88-12/90
Schwartz (1997)
Tucson, AZ
1/88-12/90
Endpoints Estimated
(ICD code)
cardiac (410-414, 427-428)
dysrhythmias (427)
ischemic heart disease (410-414)
congestive heart failure (428)
cardiovascular disease (390-429)
cardiovascular disease (390-429)
COI"
(1997 S)
$ 13,430
$ 6,483
S 16,142
$ 11,933
S 13,440
$ 13,440
1 The unit value for a group of ICD-9 codes is the weighted average of ICD-9 code-specific values, from Elixhauser et al. (1993).
The weights are the relative frequencies of hospital discharges in Elixhauser et al. for each ICD-9 code in the group.
The uncertainty surrounding cost-of-illness estimates for hospital admissions was based on the estimated
means and standard errors of those means for hospital charges as reported in Elixhauser et al. (1993). For
a hospital admission defined by a single ICD code (e.g., hospital admissions for congestive heart failure ~
ICD-9 code 428), the uncertainty distribution of cost was characterized as a normal distribution with mean
equal to the mean hospital charge for that ICD code and standard deviation equal to the standard error of
that mean, as reported in Elixhauser et al. (1993).
For a hospital admission endpoint defined by a group of ICD codes, the uncertainty distribution of
cost was defined by considering the cost to be a linear combination of the ICD code-specific costs, where
the coefficient for each ICD code-specific cost is the relative frequency of hospital discharges for that ICD
code in the group. The cost of a hospital admission for an illness category defined by a group of ICD codes
(e.g., cardiovascular disease, defined as ICD codes 390-429), Y, is given by:
i=\
where Xj is the hospital charge associated with the ith ICD code in the group, and aj is the relative frequency
(in Elixhauser et al. (1993)) of hospital discharges for the ith ICD code in the group. If each of the X's is
distributed as a normal random variable, then Y is also a normal random variable, with mean equal to:
and variance equal to
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The standard deviation of the distribution of Y would just be the square root of the variance.
4.3.2 Asthma-Related Emergency Room (ER) Visits
We use four C-R functions to estimate the effects of PM and ozone exposure to asthma-related ER
visits. Three predict ozone-related asthma ER visits, while a fourth predicts asthma-related ER visits based
on exposures to PM. Ozone-related asthma ER visits are based on epidemiological studies by Cody et al.
(1992), Weisel et al. (1995), and Stieb et al. (1996). The first two studies, Cody et al. and Weisel et al.,
were conducted in Northern New Jersey. The Cody et al. study examined asthma-related ER visits over a
16 month period between May, 1988 and August, 1989, and found that ozone was linked to asthma-related
ER visits. No significant effect was seen for PM10 or SO2. Using a one-pollutant model, Weisel et al. also
found ozone linked to asthma-related ER visits in an all-age 1990 population for eight New Jersey counties.
Finally, Stieb et al. examined asthma-related ER visits over an eight year period from May through
September in St. John, New Brunswick, Canada. Ozone was linked to ER visits within the all-ages
population, especially when ozone levels exceeded 75 ppb. No significant effect was seen for the other
pollutants.
Schwartz et al. (1993) failed to find a significant relationship between asthma-related ER visits and
ozone. In this study of Seattle residents, Schwartz et al. instead found PM10 to be significantly related to
asthma-related ER visits. The four studies are listed in Exhibit 4-12 below.
Exhibit 4-12 Asthma-Related Emergency Room Visit Studies
Location
central and northern NJ
central and northern NJ
Seattle, WA
St. John, New Brunswick,
Canada
Study
Cody et al. (1992)
Weisel etal. (1995)
Schwartz etal. (1993)
Stieb et al. (1996)
Pollutants Used in Final Model
03
03
PM10
03
Study Population
all ages
all ages
<65
all ages
Because we are estimating ER visits as well as hospital admissions for asthma, we must avoid
counting twice the ER visits for asthma that are subsequently admitted to the hospital. To avoid double-
counting, the baseline incidence rate for emergency room visits is adjusted by subtracting the percentage of
patients that are admitted into the hospital. Three studies provide some information to do this: Richards et
al. (1981, p. 350) reported that 13% of children's ER visits ended up as hospital admissions; Lipfert (1993,
p. 230) reported that ER visits (for all causes) are two to five times more frequent than hospital admissions;
Smith et al. (1997, p. 789) reported 445,000 asthma-related hospital admissions in 1987 and 1.2 million
asthma ER visits. The study by Smith et al. seems the most relevant since it is a national study and looks
at all age groups. Assuming that air-pollution related hospital admissions first pass through the ER, the
reported incidence rates suggest that 37% (=445,000/1,200,000) of ER visits are subsequently admitted to
the hospital, or that ER visits for asthma occur 2.7 times as frequently as hospital admissions for asthma.
The baseline incidence of asthma ER visits is therefore taken to be 2.7 times the baseline incidence of
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hospital admissions for asthma. To avoid double-counting, however, only 63% of the resulting change in
asthma ER visits associated with a given change in pollutant concentrations is counted in the ER visit
incidence change.
Valuing Asthma-Related Emergency Room (ER) Visits
The value of an avoided asthma-related ER visit was based on national data reported in Smith et
al. (1997). Smith et al. reported that there were approximately 1.2 million asthma-related ER visits made
in 1987, atatotal cost of $186.5 million, in 1987$. The average cost per visit was therefore $155 in
1987$, or $279.55 in 1997 $ (using the CPI-U for medical care to adjust to 1997 $). The uncertainty
surrounding this estimate, based on the uncertainty surrounding the number of ER visits and the total cost
of all visits reported by Smith et al. was characterized by a triangular distribution centered at $279.55, on
the interval [$207.50, $387.63].
4.4 ACUTE ILLNESSES AND SYMPTOMS NOT REQUIRING HOSPITALIZATION
We consider in this section a number of acute symptoms that do not require hospitalization, such
as acute bronchitis, and upper and lower respiratory symptoms. Several of these illnesses and symptoms
were considered in the §812 Prospective analysis as well. The unit values and the uncertainty distributions
for those acute illnesses and symptoms that were also considered in the §812 Prospective analysis were
obtained by adjusting the unit values used in that analysis from 1990 $ to 1997 $ by multiplying by 1.228
(based on the CPI-U for "all items").
4.4.1 Acute Bronchitis
Dockery et al. (1996) examined the relationship between PM and other pollutants on the reported
rates of asthma, persistent wheeze, chronic cough, and bronchitis, in a study of 13,369 children ages 8-12
living in 24 communities in U.S. and Canada. Health data were collected in 1988-1991, and single-
pollutant models were used in the analysis to test a number of measures of particulate air pollution.
Dockery et al. found that annual level of sulfates and particle acidity were significantly related to
bronchitis, and PM2 5 and PM10 were marginally significantly related to bronchitis.
Valuing Acute Bronchitis
Estimating WTP to avoid a case of acute bronchitis is difficult for several reasons. First, WTP to
avoid acute bronchitis itself has not been estimated. Estimation of WTP to avoid this health endpoint
therefore must be based on estimates of WTP to avoid symptoms that occur with this illness. Second, a
case of acute bronchitis may last more than one day, whereas it is a day of avoided symptoms that is
typically valued. Finally, the C-R function used in the benefit analysis for acute bronchitis was estimated
for children, whereas WTP estimates for those symptoms associated with acute bronchitis were obtained
from adults.
With these caveats in mind, the values used for acute bronchitis in this analysis were obtained by
adjusting the values used in the §812 Prospective analysis from 1990 $ to 1997 $ by multiplying by 1.228.
WTP to avoid a case of acute bronchitis was estimated as the midpoint between a low estimate and a high
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estimate. The low estimate is the sum of the midrange values recommended by lEc (1994) for two
symptoms believed to be associated with acute bronchitis: coughing and chest tightness. The high estimate
was taken to be twice the value of a minor respiratory restricted activity day. The unit value is the
midpoint between the low and high estimates. The low, high, and midpoint estimates used in the §812
Prospective analysis were $13, $77, and $45, respectively, in 1990 $. The corresponding values in 1997 $
are $15.96, $94.56, and $55.26, respectively.
4.4.2 Upper Respiratory Symptoms (URS)
Using logistic regression, Pope et al. (1991) estimated the impact of PM10 on the incidence of a
variety of minor symptoms in 55 subjects (34 "school-based" and 21 "patient-based") living in the Utah
Valley from December 1989 through March 1990. The children in the Pope et al. study were asked to
record respiratory symptoms in a daily diary, and the daily occurrences of URS and LRS, as defined above,
were related to daily PM10 concentrations. Pope et al. describe URS as consisting of one or more of the
following symptoms: runny or stuffy nose; wet cough; and burning, aching, or red eyes. Levels of ozone,
NO2, and SO2 were reported low during this period, and were not included in the analysis.
The sample in this study is relatively small and is most representative of the asthmatic population,
rather than the general population. The school-based subjects (ranging in age from 9 to 11) were chosen
based on "a positive response to one or more of three questions: ever wheezed without a cold, wheezed for
3 days or more out of the week for a month or longer, and/or had a doctor say the 'child has asthma' (Pope
et al., 1991, p. 669)." The patient-based subjects (ranging in age from 8 to 72) were receiving treatment
for asthma and were referred by local physicians. Regression results for the school-based sample (Pope et
al., 1991, Table 5) show PM10 significantly associated with both upper and lower respiratory symptoms.
The patient-based sample did not find a significant PM10 effect. The results from the school-based sample
are used here.
Valuing URS
Willingness to pay to avoid a day of URS is based on symptom-specific WTPs to avoid those
symptoms identified by Pope et al. as part of the URS complex of symptoms. Three contingent valuation
(CV) studies have estimated WTP to avoid various morbidity symptoms that are either within the URS
symptom complex defined by Pope et al. (1991) or are similar to those symptoms identified by Pope et al.
In each CV study, participants were asked their WTP to avoid a day of each of several symptoms. The
WTP estimates corresponding to the morbidity symptoms valued in each study are presented in Exhibit 4-
13. The three individual symptoms listed in Exhibit 4-13 that were identified as most closely matching
those listed by Pope, et al. for URS are cough, head/sinus congestion, and eye irritation, corresponding to
"wet cough," "runny or stuffy nose," and "burning, aching or red eyes," respectively. A day of URS could
consist of any one of the seven possible "symptom complexes" consisting of at least one of these three
symptoms. Using the symptom symbols in Exhibit 4-13, these seven possible symptom complexes are
presented in Exhibit 4-14. It is assumed that each of these seven URS complexes is equally likely.30 The
point estimate of MWTP to avoid an occurrence of URS is just an average of the seven estimates of
MWTP for the different URS complexes - $18.70, or about $19 in 1990 $. This is $23.33 (=$19* 1.228)
30 With empirical evidence, we could presumably improve the accuracy of the probabilities of occurrence of each type of
URS. Lacking empirical evidence, however, a uniform distribution seems the most reasonable "default" assumption.
Abt Associates Inc. 4-27 December 1999
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in 1997 $. In the absence of information surrounding the frequency with which each of the seven types of
URS occurs within the URS symptom complex, an uncertainty analysis for WTP to avoid a day of URS is
based on a continuous uniform distribution of MWTPs in Exhibit 4-14, with a range of [$7, $33], or
[$8.60, $40.52] in 1997 $.
Exhibit 4-13 Median WTP Estimates and Derived Midrange Estimates (in 1997 $)
Symptom "
Throat congestion
Head/sinus congestion
Coughing
Eye irritation
Headache
Shortness of breath
Pain upon deep inhalation (PDI)
Wheeze
Coughing up phlegm
Chest tightness
Dickie et al. (1987)
4.63
5.40
1.55
-
1.55
0.00
5.42
3.09
3.38"
7.74
Tolley et al. (1986)
20.08
21.63
17.00
19.30
30.90
-
-
-
-
-
Loehman et al. (1979)
-
10.07
6.12
-
-
12.98
-
-
-
-
Mid-Range Estimate
12.28
12.28
8.60
19.30
12.28
6.14
5.42
3.09
3.38
7.74
1 All estimates are WTP to avoid one day of symptom. Midrange estimates were derived by lEc (1993).
b 10% trimmed mean.
Exhibit 4-14 Estimates of MWTP to Avoid Upper Respiratory Symptoms (1997 $)
Symptom Combinations Identified as URS by Pope et al. (1991)
Coughing
Head/Sinus Congestion
Eye Irritation
Coughing, Head/Sinus Congestion
Coughing, Eye Irritation
Head/Sinus Congestion, Eye Irritation
Coughing, Head/Sinus Congestion, Eye Irritation
MWTP to Avoid
Symptom(s)
$8.60
$12.28
$19.30
$20.88
$27.90
$31.58
$40.18
Average: $22.96
Based on values reported in Exhibit 4-13.
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December 1999
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It is worth emphasizing that what is being valued here is URS as defined by Pope et al. (1991).
While other definitions of URS are certainly possible, this definition of URS is used in this benefit analysis
because it is the incidence of this specific definition of URS that has been related to PM exposure by Pope
etal.
4.4.3 Lower Respiratory Symptoms (LRS)
Schwartz et al. (1994) used logistic regression to link lower respiratory symptoms in children with
SO2, NO2, ozone, PM10, PM2 5, sulfate and H+ (hydrogen ion). Children were selected for the study if they
were exposed to indoor sources of air pollution: gas stoves and parental smoking. The study enrolled 1,844
children into a year-long study that was conducted in different years (1984 to 1988) in six cities. The
students were in grades two through five at the time of enrollment in 1984. By the completion of the final
study, the cohort would then be in the eighth grade (ages 13-14); this suggests an age range of 7 to 14.
In single pollutant models SO2, NO2, PM2 5, and PM10 were significantly linked to cough. In two-
pollutant models, PM10 had the most consistent relationship with cough; ozone was marginally significant,
controlling for PM10. In models for upper respiratory symptoms, they reported a marginally significant
association for PM10. In models for lower respiratory symptoms, they reported significant single-pollutant
models, using SO2, O3, PM2 5, PM10, SO4, and H+.
Valuing LRS
The method for deriving a point estimate of mean WTP to avoid a day of LRS is the same as for
URS. Schwartz et al. (1994, p. 1235) define LRS as at least two of the following symptoms: cough, chest
pain, phlegm, and wheeze. The symptoms for which WTP estimates are available that reasonably match
those listed by Schwartz et al. for LRS are cough (C), chest tightness (CT), coughing up phlegm (CP), and
wheeze (W). A day of LRS, as defined by Schwartz et al., could consist of any one of the 11
combinations of at least two of these four symptoms, as displayed in Exhibit 4-15.31
31 Because cough is a symptom in some of the URS clusters as well as some of the LRS clusters, there is the possibility of a
very small amount of double counting - if the same individual were to have an occurrence of URS which included cough and an
occurrence of LRS which included cough both on exactly the same day. Because this is probably a very small probability occurrence,
the degree of double counting is likely to be very minor. Moreover, because URS is applied only to asthmatics ages 9-11 (a very small
population), the amount of potential double counting should be truly negligible.
Abt Associates Inc. 4-29 December 1999
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Exhibit 4-15 Estimates of MWTP to Avoid Lower Respiratory Symptoms (1997 $)
Symptom Combinations Identified as LRS by Schwartz et al. (1994)
Coughing, Chest Tightness
Coughing, Coughing Up Phlegm
Coughing, Wheeze
Chest Tightness, Coughing Up Phlegm
Chest Tightness, Wheeze
Coughing Up Phlegm, Wheeze
Coughing, Chest Tightness, Coughing Up Phlegm
Coughing, Chest Tightness, Wheeze
Coughing, Coughing Up Phlegm, Wheeze
Chest Tightness, Coughing Up Phlegm, Wheeze
Coughing, Chest Tightness, Coughing Up Phlegm, Wheeze
MWTP to Avoid
Symptom(s)
$16.33
$11.97
$11.69
$11.11
$10.83
$6.47
$19.71
$19.43
$15.07
$14.21
$22.80
Average: $14.51
Based on values reported in Exhibit 4-13.
We assumed that each of the eleven types of LRS is equally likely.32 The mean WTP to avoid a
day of LRS as defined by Schwartz et al. (1994) is therefore the average of the mean WTPs to avoid each
type of LRS, -$11.82, which rounds to $12.00. This is $14.74 (=1.228*$12.00) in 1997$. This is the
point estimate used in the benefit analysis for the dollar value for LRS as defined by Schwartz et al. The
WTP estimates are based on studies which considered the value of a day of avoided symptoms, whereas the
Schwartz et al. study used as its measure a case of LRS. Because a case of LRS usually lasts at least one
day, and often more, WTP to avoid a day of LRS should be a conservative estimate of WTP to avoid a
case of LRS.
In the absence of information about the frequency of each of the seven types of LRS among all
occurrences of LRS, the uncertainty analysis for WTP to avoid a day of URS is based on a continuous
uniform distribution of MWTPs in Exhibit 4-13, with a range of [$5, $19], or [$6.14, $23.33] in 1997 $.
This is the same procedure as that used in the URS uncertainty analysis.
As with URS, it is worth emphasizing that what is being valued here is LRS as defined by
Schwartz et al. (1994). While other definitions of LRS are certainly possible, this definition of LRS is
used in this benefit analysis because it is the incidence of this specific definition of LRS that has been
related to PM exposure by Schwartz et al.
32 As with URS, if we had empirical evidence we could improve the accuracy of the probabilities of occurrence of each type
of LRS. Lacking empirical evidence, however, a uniform distribution seems the most reasonable "default" assumption.
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Issues in the Valuation of URS and LRS
The point estimates derived for mean WTP to avoid a day of URS and a case of LRS are based on
the assumption that WTPs are additive. For example, if WTP to avoid a day of cough is $8.60, and WTP
to avoid a day of shortness of breath is $6.14, then WTP to avoid a day of both cough and shortness of
breath is $14.74. If there are no synergistic effects among symptoms, then it is likely that the marginal
utility of avoiding symptoms decreases with the number of symptoms being avoided. If this is the case,
adding WTPs would tend to overestimate WTP for avoidance of multiple symptoms. However, there may
be synergistic effects- that is, the discomfort from two or more simultaneous symptoms may exceed the
sum of the discomforts associated with each of the individual symptoms. If this is the case, adding WTPs
would tend to underestimate WTP for avoidance of multiple symptoms. It is also possible that people may
experience additional symptoms for which WTPs are not available, again leading to an underestimate of the
correct WTP. However, for small numbers of symptoms, the assumption of additivity of WTPs is unlikely
to result in substantive bias.
There are also three sources of uncertainty in the valuation of both URS and LRS: (1) an
occurrence of URS or of LRS may be comprised of one or more of a variety of symptoms (i.e., URS and
LRS are each potentially a "complex of symptoms"), so that what is being valued may vary from one
occurrence to another; (2) for a given symptom, there is uncertainty about the mean WTP to avoid the
symptom; and (3) the WTP to avoid an occurrence of multiple symptoms may be greater or less than the
sum of the WTPs to avoid the individual symptoms.
Information about the degree of uncertainty from either the second or the third source is not
available. The first source of uncertainty, however, is addressed because an occurrence of URS or LRS
may vary in symptoms. For example, seven different symptom complexes that qualify as URS, as defined
by Pope et al. (1991), were identified above. The estimates of MWTP to avoid these seven different kinds
of URS range from $8.60 (to avoid an occurrence of URS that consists of only coughing) to $40.52 (to
avoid an occurrence of URS that consists of coughing plus head/sinus congestion plus eye irritation).
There is no information, however, about the frequency of each of the seven types of URS among all
occurrences of URS.
Because of insufficient information to adequately estimate the distributions of the estimators of
MWTP for URS and LRS, as a rough approximation, a continuous uniform distribution over the interval
from the smallest point estimate to the largest is used. As was mentioned in the two previous sections, the
interval for URS is [$8.60, $40.52], and for LRS, the interval is [$6.14, $23.33].
Alternatively, a discrete distribution of the seven unit dollar values associated with each of the
seven types of URS identified could be used. This would provide a distribution whose mean is the same as
the point estimate of MWTP. A continuous uniform distribution, however, is probably more reasonable
than a discrete uniform distribution. The differences between the means of the discrete uniform
distributions (the point estimates) and the means of the continuous uniform distributions are relatively
small, as shown in Exhibit 4-16.
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Exhibit 4-16 Comparison of the Means of Discrete and Continuous Uniform Distributions of MWTP
Associated with URS and LRS (1990 $)
Health Endpoint
URS (Pope et al., 1991)
LRS (Schwartz et al., 1994)
Mean of Discrete Uniform
Distribution (Point Est.)
18.70
11.82
Mean of Continuous Uniform
Distribution
19.86
11.92
4.4.4 "Any of 19 Respiratory Symptoms" and Minor Restricted Activity Days (MRADs)
Two studies, one by Ostro and Rothschild (1989b) and the other by Krupnick et al. (1990), cover a
variety of minor symptoms. To avoid double counting, we treat these two studies as alternative measures
of the same health effect, and pool the incidence estimates. The method of pooling incidence and benefits
estimates is the same as that used for hospital admissions and is described above in the section on
respiratory and cardiovascular hospital admissions.
Ostro and Rothschild (1989b) estimated the impact of PM25 on the incidence of minor restricted
activity days (MRAD) in a national sample of the adult working population, ages 18 to 65, living in
metropolitan areas. We developed separate coefficients for each year in the analysis (1976-1981), which
were then combined for use in this analysis. The coefficient used in the C-R function is a weighted average
of the coefficients in Ostro (Ostro, 1987, Table IV) using the inverse of the variance as the weight.
Krupnick et al. (1990) estimated the impact of coefficient of haze (COH, a measure of particulate
matter concentrations), ozone and SO2 on the incidence of any of 19 symptoms or conditions in the adult
population, ages 18 to 65,33 They used a logistic regression model that takes into account whether a
respondent was well or not the previous day. A key difference between this and the usual logistic model is
that the model they used includes a lagged value of the dependent variable. This makes the derivation of a
C-R function somewhat more complicated than the usual logistic regression.34
The presence of "any of 19 acute respiratory symptoms" is a somewhat subjective health effect
used by Krupnick et al. (1990). Moreover, not all 19 symptoms are listed in the Krupnick et al. study. It is
therefore not clear exactly what symptoms were included in the study. Even if all 19 symptoms were
known, it is unlikely that WTP estimates could be obtained for all of the symptoms. Finally, even if all 19
symptoms were known and WTP estimates could be obtained for all 19 symptoms, the assumption of
additivity of WTPs becomes tenuous with such a large number of symptoms. The likelihood that all 19
symptoms would occur simultaneously, moreover, is very small.
In addition to the overlapping health effects present in both of these endpoints, the Ostro and
Rothschild (1989b) study, as well as the Krupnick et al. (1990) study, overlap with a smaller subset of
"Krupnick et al. (1990) list 13 specific "symptoms or conditions": head cold, chest cold, sinus trouble, croup, cough with
phlegm, sore throat, asthma, hay fever, doctor-diagnosed ear infection, flu, pneumonia, bronchitis, and bronchiolitis. The other six
symptoms or conditions are not specified.
34Details of the derivation of the C-R function based on the model used by Krupnick et al. (1990) are presented in Abt
Associates (1999, p. A-40).
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health effects predicted by other studies. In particular, two studies predict asthma attacks (Whittemore and
Korn (1980)) and moderate or worse asthma (Ostro et al. (1991)) (both discussed later in the text). These
endpoints are included in the array of health effects covered by the pooled "any of 19"/MRAD incidence
estimate, and would thus constitute a double counting of benefits if included in the primary analysis.
Instead, asthma attack incidence and moderate or worse asthma incidence are presented as supplemental
calculations to the pooled incidence estimate of "any of 19 symptoms" and MRADs.
Valuing "Any of 19 Respiratory Symptoms"
The unit value and uncertainty distribution for "any of 19 respiratory symptoms" for this analysis
were obtained by adjusting the (rounded) values in 1990 $ used in the §812 Prospective analysis to 1997 $
by multiplying by 1.228. Acute respiratory symptoms must be either upper respiratory symptoms or lower
respiratory symptoms. In the absence of further knowledge about which of the two types of symptoms is
more likely to occur among the "any of 19 acute respiratory symptoms," we assumed that they occur with
equal probability. Because this health endpoint may also consist of combinations of symptoms, it was also
assumed that there is some (smaller) probability that upper and lower respiratory symptoms occur together.
To value avoidance of a day of "the presence of any of 19 acute respiratory symptoms" we therefore
assumed that this health endpoint consists either of URS, or LRS, or both. We also assumed that it is as
likely to be URS as LRS and that it is half as likely to be both together. That is, it was assumed that "the
presence of any of 19 acute respiratory symptoms" is a day of URS with 40 percent probability, a day of
LRS with 40 percent probability, and a day of both URS and LRS with 20 percent probability. Using the
point estimates of WTP to avoid a day of URS and LRS derived above, the point estimate of WTP to avoid
a day of "the presence of any of 19 acute respiratory symptoms" is:
(0.40)($18.70) + (0.40)($11.82) + (0.20)($18.70 + $11.82) = $18.31, or about $18 (1990 $) .
This is $22.10 (=$18*1.228) in 1997 $. Because this health endpoint is only vaguely defined, and because
of the lack of information on the relative frequencies of the different combinations of acute respiratory
symptoms that might qualify as "any of 19 acute respiratory symptoms," the unit dollar value derived for
this health endpoint must be considered only a rough approximation.
The sources of uncertainty in the valuation of LRS and URS described above similarly exist in the
valuation of this health endpoint. In particular, (1) "the presence of any of 19 acute respiratory symptoms"
may be comprised of one or more of a variety of symptoms, so that what is being valued may vary from
one occurrence to another; (2) for a given symptom, there is uncertainty about the mean WTP to avoid the
symptom; and (3) the WTP to avoid an occurrence of multiple symptoms may be greater or less than the
sum of the WTPs to avoid the individual symptoms.
To characterize the uncertainty surrounding the estimated value of avoiding "any of 19 acute
respiratory symptoms," we used the distributions described above for the input components, URS and
LRS. On each iteration of a Monte Carlo procedure, URS was chosen with 40 percent probability, LRS
was chosen with 40 percent probability and URS+LRS was chosen with 20 percent probability. Given the
choice, a dollar value was randomly selected from the appropriate distribution. For example, if URS was
selected, a dollar value was selected from the continuous uniform distribution for URS.
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Valuing Minor Restricted Activity Days (MRADs)
The unit value and uncertainty distribution for MRADs for this analysis were obtained by
adjusting the (rounded) values in 1990 $ used in the §812 Prospective analysis to 1997 $ by multiplying by
1.228. No studies are reported to have estimated WTP to avoid a minor restricted activity day (MRAD).
However, lEc (1993) has derived an estimate of WTP to avoid a minor respiratory restricted activity day
(MRRAD), using WTP estimates from Tolley et al. (1986) for avoiding a three-symptom combination of
coughing, throat congestion, and sinusitis. This estimate of WTP to avoid a MRRAD, so defined, is
$38.37 (1990 $), or about $38. Although Ostro and Rothschild (1989b) estimated the relationship between
PM25 and MRADs, rather than MRRADs (a component of MRADs), it is likely that most of the MRADs
associated with exposure to PM2 5 are in fact MRRADs. For the purpose of valuing this health endpoint,
then, we assumed that MRADs associated with PM exposure may be more specifically defined as
MRRADs, and therefore used the estimate of mean WTP to avoid a MRRAD.
Any estimate of mean WTP to avoid a MRRAD (or any other type of restricted activity day other
than WLD) will be somewhat arbitrary because the endpoint itself is not precisely defined. Many different
combinations of symptoms could presumably result in some minor or less minor restriction in activity.
Krupnick and Kopp (1988) argued that mild symptoms will not be sufficient to result in a MRRAD, so that
WTP to avoid a MRRAD should exceed WTP to avoid any single mild symptom. A single severe
symptom or a combination of symptoms could, however, be sufficient to restrict activity. Therefore WTP
to avoid a MRRAD should, these authors argue, not necessarily exceed WTP to avoid a single severe
symptom or a combination of symptoms. The "severity" of a symptom, however, is similarly not precisely
defined; moreover, one level of severity of a symptom could induce restriction of activity for one individual
while not doing so for another. The same is true for any particular combination of symptoms.
Given that there is inherently a substantial degree of arbitrariness in any point estimate of WTP to
avoid a MRRAD (or other kinds of restricted activity days), the reasonable bounds on such an estimate
must be considered. By definition, a MRRAD does not result in loss of work. WTP to avoid a MRRAD
should therefore be less than WTP to avoid a WLD. At the other extreme, WTP to avoid a MRRAD
should exceed WTP to avoid a single mild symptom. The highest lEc midrange estimate of WTP to avoid
a single symptom is $15.72 (1990 $), or about $16, for eye irritation. The point estimate of WTP to avoid
a WLD in the benefit analysis is $83 (1990 $). If all the single symptoms evaluated by the studies are not
severe, then the estimate of WTP to avoid a MRRAD should be somewhere between $16 and $83.
Because the lEc estimate of $38 falls within this range (and acknowledging the degree of arbitrariness
associated with any estimate within this range), the lEc estimate is used as the mean of a triangular
distribution centered at $38, ranging from $16 to $61. Adjusting to 1997 $, this is a triangular distribution
centered at $46.66, ranging from $19.65 to $74.91.
4.4.5 Shortness of Breath
Using logistic regression, Ostro et al. (1995) estimated the impact of PM10, ozone, NO2, and SO2
on the incidence of coughing, shortness of breath, and wheezing in 83 African-American asthmatic children
aged 7-12 living in Los Angeles from August through September 1992. Regression results show both PM10
and ozone significantly linked to shortness of breath; the beginning of an asthma episode was also
significantly linked to ozone. Results for single-pollutant models only were presented in the published
paper.
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Valuing Shortness of Breath
A point estimate of mean WTP to avoid a day of shortness of breath was derived as the mean of
the median estimates from two studies that evaluated this symptom. The median estimate from Dickie et al.
(1987), was $0.00; the median estimate from Loehman et al. (1979) was $10.57, or about $10.60 (1990 $).
The mean of these two medians is $5.30, or $6.51 in 1997 $. In the absence of sufficient information to
characterize the distribution of MWTP to avoid a day of shortness of breath, this distribution is roughly
approximated by a continuous distribution on the interval from the low estimate to the high estimate -
[$0.00, $10.60] in 1990 $, or [$0.00, $13.02] in 1997 $.
4.4.6 Work Loss Days (WLD)
Ostro (1987) estimated the impact of PM25 on the incidence of work-loss days (WLDs), restricted
activity days (RADs), and respiratory-related RADs (RRADs) in a national sample of the adult working
population, ages 18 to 65, living in metropolitan areas. The annual national survey results used in this
analysis were conducted in 1976-1981. Ostro reported that two-week average PM25 levels were
significantly linked to work-loss days, RADs, and RRADs, however there was some year-to-year
variability in the results. Separate coefficients were developed for each year in the analysis (1976-1981);
these coefficients were pooled. The coefficient used in the concentration-response function used here is a
weighted average of the coefficients in Ostro (1987, Table III) using the inverse of the variance as the
weight.
Valuing WLD
Willingness to pay to avoid the loss of one day of work was estimated by dividing the median
weekly wage for 1990 (U.S. Bureau of the Census, 1992) by five (to get the median daily wage). This
values the loss of a day of work at the national median wage for the day lost. To account for regional
variations in median wages, the national daily median wage was adjusted on a county-by-county basis
using a factor based on the ratio of national median household income divided by each county's median
income. Each county's income-adjusted willingness to pay to avoid the loss of one day of work was then
used to value the number of work loss days attributed to that county. Valuing the loss of a day's work at
the wages lost is consistent with economic theory, which assumes that an individual is paid exactly the
value of his labor.35
The use of the median rather than the mean, however, requires some comment. If all individuals in
society were equally likely to be affected by air pollution to the extent that they lose a day of work because
of it, then the appropriate measure of the value of a work loss day would be the mean daily wage. It is
highly likely, however, that the loss of work days due to pollution exposure does not occur with equal
probability among all individuals, but instead is more likely to occur among lower income individuals than
among high income individuals. It is probable, for example, that individuals who are vulnerable enough to
the negative effects of air pollution to lose a day of work as a result of exposure tend to be those with
generally poorer health care. Individuals with poorer health care have, on average, lower incomes. To
estimate the average lost wages of individuals who lose a day of work because of exposure to PM
35 The estimate of the value of work loss days avoided could be improved if, instead of a single national wage rate, state-
specific or county-specific wage rates were used.
Abt Associates Inc. 4-35 December 1999
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pollution, then, would require a weighted average of all daily wages, with higher weights on the low end of
the wage scale and lower weights on the high end of the wage scale. Because the appropriate weights are
not known, however, the median wage was used rather than the mean wage. The median is more likely to
approximate the correct value than the mean because means are highly susceptible to the influence of large
values in the tail of a distribution (in this case, the small percentage of very large incomes in the United
States), whereas the median is not susceptible to these large values. The median daily wage in 1990 was
$83, or $101.92 in 1997 $. This is the value that was used to represent work loss days (WLD). An
uncertainty distribution for this endpoint was unavailable, therefore the same central estimate ($101.92)
was used to value incidence changes at the fifth, mean, and ninety-fifth percentiles.
4.4.7 Worker Productivity
To monetize benefits associated with increased worker productivity resulting from improved ozone
air quality, we used information reported in Crocker and Horst (1981) and summarized in EPA (1994).
Crocker and Horst examined the impacts of ozone exposure on the productivity of outdoor citrus workers.
The study measured productivity impacts as the change in income associated with a change in ozone
exposure, given as the elasticity of income with respect to ozone concentration (-0.1427).36 The reported
elasticity translates a ten percent reduction in ozone to a 1.4 percent increase in income. Given the median
daily income for outdoor workers engaged in strenuous activity reported by the 1990 U.S. Census, $89.64
per day (1997 $), a ten percent reduction in ozone yields about $1.26 in increased daily wages. The median
daily income for outdoor workers is a national estimate, however. We adjust this estimate to reflect
regional variations in income using a factor based on the ratio of national median household income divided
by a county's median household income. No information was available for quantifying the uncertainty
associated with the central valuation estimate. Therefore, no uncertainty analysis was conducted for this
endpoint.
4.4.8 Supplemental Endpoints: Acute Illnesses And Symptoms Not Requiring Hospitalization
The benefits associated with several endpoints are estimated separately but are not included in the
total benefits estimates because of the possibility of double counting of benefits. Two studies estimate the
incidence of asthma (which overlap with the pooled measure of "any of 19 symptoms" and MRADs) and
one study estimates the incidence of restricted activity days (which overlaps with measures of work loss
days and MRADs).
Asthma Attacks
Whittemore and Korn (1980) examined the relationship between air pollution and asthma attacks in
a survey of 443 children and adults, living in six communities in southern California during three 34-week
periods in 1972-1975. The analysis focused on TSP and ozone. Respirable PM, NO2, SO2 were highly
correlated with TSP and excluded from the analysis. In a two pollutant model, daily levels of both TSP and
Ox were significantly related to reported asthma attacks. The value of an asthma attack is assumed to be
the same as for a day in which asthma is moderate or worse.
36 The relationship estimated by Crocker and Horst (1981) between wages and ozone is a log-log relationship. Therefore
the elasticity of wages with respect to ozone is a constant, equal to the coefficient of log ozone in the model.
Abt Associates Inc. 4-36 December 1999
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Valuing Asthma Attacks
The value of avoiding an asthma attack is estimated as the mean of four WTP estimates obtained
in a study by Rowe and Chestnut (1986). The four WTP estimates correspond to four severity definitions
of a "bad asthma day." The mean of the four average WTPs is $32 (1990 $), or $39.30 in 1997 $. The
uncertainty surrounding this estimate was characterized by a continuous uniform distribution on the range
defined by the lowest and highest of the four average WTP estimates from Rowe and Chestnut, [$12, $54],
or [$14.74, $66.31] in 1997$.
Moderate or Worse Asthma
Ostro et al. (1991) examined the effect of air pollution on asthmatics, ages 18 to 70, living in
Denver, Colorado from December 1987 to February 1988. The respondents in this study were asked to
record daily a subjective rating of their overall asthma status each day (0=none, l=mild, 2=moderate,
3=severe, 4=incapacitating). Ostro et al. then examined the relationship between moderate (or worse)
asthma and H+, sulfate, SO2, PM25, estimated PM25, PM10, nitrate, and nitric acid. Daily levels of H+ were
linked to cough, asthma, and shortness of breath. PM25 was linked to asthma. SO2 was linked to shortness
of breath. No effects were seen for other pollutants.
Valuing Moderate or Worse Asthma
The unit value and uncertainty distribution for moderate or worse asthma were assumed to be the
same as for an asthma attack (see above), based on four WTP estimates from Rowe and Chestnut (1986).
The mean of the four average WTPs is $32 (1990 $), or $39.30 in 1997 $. The uncertainty surrounding
this estimate was characterized by a continuous uniform distribution on the range defined by the lowest and
highest of the four average WTP estimates from Rowe and Chestnut, [$12, $54], or [$14.74, $66.31] in
1997 $.
Although subjects' assessment of what constitutes a "bad asthma day" varied considerably in the
Rowe and Chestnut (1986) study, the subjective assessment of an asthma day being bad is very similar to
the subjective assessment of an asthma day being "of moderate or worse status" in the Ostro et al. (1991)
study, in which subjects were also asked their subjective assessments.
Restricted Activity Days (RADs)
Ostro (1987) estimated the impact of PM25 on the incidence of work-loss days (WLDs), restricted
activity days (RADs), and respiratory-related RADs (RRADs) in a national sample of the adult working
population, ages 18 to 65, living in metropolitan areas. The annual national survey results used in this
analysis were conducted in 1976-1981. Ostro reported that two-week average PM25 levels were
significantly linked to work-loss days, RADs, and RRADs, however there was some year-to-year
variability in the results. Separate coefficients were developed for each year in the analysis (1976-1981);
these coefficients were pooled. The coefficient used in the concentration-response function used here is a
weighted average of the coefficients in Ostro (1987, Table III) using the inverse of the variance as the
weight.
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The health effects included in the definition of RADs overlap with health effects included in both
measures of work loss days and minor restricted activity days. To include both of these endpoints along
with restricted activity days would lead to a double-counting of benefits, therefore restricted activity days
are presented as a supplemental calculation of incidence only.
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WELFARE BENEFITS
This analysis considers four types of benefits that are loosely termed "welfare" benefits. These
include visibility improvements, reductions in agricultural crop damage, reduced household soiling, and
reduced nitrogen deposition into estuaries. We consider each in turn.
5.1 VISIBILITY BENEFITS
Visibility degradation estimates used in this analysis are generated by the CRDM SR Matrix.
Because these air quality-related changes in visibility are directly used in the benefits analysis, the
methodology for predicting visibility changes is not discussed here. The visibility estimation methodology
is described in detail in Pechan-Avanti (1999).
Economic benefits may result from two broad categories of visibility changes: (1) changes in
"residential" visibility - i.e., the visibility in and around the locations where people live; and (2) changes in
"recreational" visibility at Class I areas - i.e., visibility at Class I national parks and wilderness areas.37 In
this analysis, only recreational benefits are included in the primary presentation of benefits; residential
benefits are presented as an alternative calculation of visibility benefits.
Within the category of recreational visibility, further distinctions have been made. There is
evidence (Chestnut and Rowe, 1990) that an individual's WTP for improvements in visibility at a Class I
area is influenced by whether it is in the region in which the individual lives, or whether it is somewhere
else. In general people appear to be willing to pay more for visibility improvements at parks and
wilderness areas that are "in-region" than at those that are "out-of-region." This is plausible, because
people are more likely to visit, be familiar with, and care about parks and wilderness areas in their own part
of the country.
To value estimated visibility changes, we are using an approach consistent with economic theory.
Below we discuss an application of the Constant Elasticity of Substitution (CES) utility function
approach38 to value both residential visibility improvements and visibility improvements at Class I areas in
the United States. This approach is based on the preference calibration method developed by Smith et al.
(1999). The presentation of this methodology is organized as follows. The basic utility model is presented
in Section 5.1.1. In Section 5.1.2 we discuss the measurement of visibility, and the mapping from
environmental "bads" to environmental "goods." In Sections 5.1.3 and 5.1.4 we summarize the
information that is available to estimate the parameters of the model corresponding to visibility at in-region
and out-of-region Class I areas, and visibility in residential areas, respectively, and we describe the
methods used to estimate these parameters. Section 5.1.5 synthesizes the results.
37 Hereafter referred to as Class I areas, which are defined as areas of the country such as national parks, national wilderness
areas, and national monuments that have been set aside under Section 162(a) of the Clean Air Act to receive the most stringent degree
of air quality protection. Class I federal lands fall under the jurisdiction of three federal agencies, the National Park Service, the Fish
and Wildlife Service, and the Forest Service.
38 The Constant Elasticity of Substitution utility function has been chosen for use in this analysis due to its flexibility when
illustrating the degree of substitutability present in various economic relationships (in this case, the tradeoff between income and
improvements in visibility).
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5.1.1 Basic Utility Model
We begin with a CES utility function in which a household derives utility from
(1) "all consumption goods," X,
(2) visibility in the residential area in which the household is located ("residential visibility"),39
(3) visibility at Class I areas in the same region as the household ("in-region recreational
visibility"), and
(4) visibility at Class I areas outside the household's region ("out-of-region recreational
visibility").
There are a total of six regions being considered, so there are 5 regions for which any household is out-of-
region. The utility function of a household in the nth residential area and the ith region of the country is:
Um = (X* + 9Z? + £ rtkQl + 11 SJkQ!kf ,
k=l j*i k=l
9>0, jlk >0,V i, k, Sjk > 0, Vj, k, p < 1.
where
Zn = the level of visibility in the nth residential area;
Qlk = the level of visibility at the kth in-region park (i.e., the kth park in the ith region);
Qjk = the level of visibility at the kth park in the jth region ( for which the household is out-of-
region), j#i;
N; = the number of Class I areas in the ith region;
Nj = the number of Class I areas in the jth region (for which the household is out-of-region), j *i;
and
6, the y's and 8's are parameters of the utility function corresponding to the visibility levels at residential
areas, and at in-region and out-of-region Class I areas, respectively. In particular, the y^'s are the
parameters corresponding to visibility at in-region Class I areas; the 8/s are the parameters corresponding
to visibility at Class I areas in region 1 (California), if i# 1; the 62's are the parameters corresponding to
visibility at Class I areas in region 2 (Colorado Plateau), if i#2, and so forth. Because the model assumes
that the relationship between residential visibility and utility is the same everywhere, there is only one 6.
The parameter p in this CES utility function is an important determinant of the slope of the marginal WTP
curve associated with any of the environmental quality variables. When p=l, the marginal WTP curve is
horizontal. When p
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where m is income, and p is the price of X. Without loss of generality, set p = 1. The only choice variable
is X. The household maximizes its utility by choosing X=m. The indirect utility function for a household
in the nth residential area and the ith region is therefore
where Q denotes the vector of vectors, Qb Q2, Q3, Q4, Q5, and Q6, and the unsubscripted y and d denote
vectors as well.
Given estimates of p, 6, the y's and the 6's, the household's utility function and the corresponding
WTP functions are fully specified. The household's WTP for any set of changes in the levels of visibility at
in-region Class I areas, out-of-region Class I areas, and the household's residential area can be shown to
be:
WTPJ^Z, A0; = ni - [nf + B(Zln - Z'J + £ rik(QL ~ QSJ + 1 1 SJk(Q>Jk - Qpljk)]1/p
The household's WTP for a single visibility improvement will depend on its order in the series of visibility
improvements the household is valuing. If it is the first visibility improvement to be valued, the
household's WTP for it follows directly from the previous equation. For example, the household's WTP
for an improvement in visibility at the first in-region park, from Qn = Q0ll to Qn = Qm, is
WTP(kQn) = m-[mp + 7n(Q0pn - Q^}fp ,
if this is the first (or only) visibility change the household values.
5.1.2 Measure of Visibility: Environmental "Goods" Versus "Bads"
In the above model, Q and Z are environmental "goods." As the level of visibility increases, utility
increases. The utility function and the corresponding WTP function both have reasonable properties. The
first derivative of the indirect utility function with respect to Q (or Z) is positive; the second derivative is
negative. WTP for a change from Q0 to a higher (improved) level of visibility, Qb is therefore a concave
function of Qb with decreasing marginal WTP.
The measure of visibility that is currently preferred by air quality scientists is the deciview, which
increases as visibility decreases. Deciview, in effect, is a measure of the lack of visibility. As deciviews
increase, visibility, and therefore utility, decreases. The deciview, then, is a measure of an environmental
"bad." There are many examples of environmental "bads" - all types of pollution are environmental
"bads." Utility decreases, for example, as the concentration of particulate matter in the atmosphere
increases.
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One way to value decreases in environmental bads is to consider the "goods" with which they are
associated, and to incorporate those goods into the utility function. In particular, if B denotes an
environmental "bad," such that:
dV
and the environmental "good," Q, is a function of B,
Q = F(B} ,
then the environmental "bad" can be related to utility via the corresponding environmental "good":40
V=V(m,Q)=V(m,F(B'j) .
The relationship between Q and B, F(B), is an empirical relationship that must be estimated.
There is a potential problem with this approach, however. If the function relating B and Q is not
the same everywhere (i.e., if for a given value of B, the value of Q depends on other factors as well), then
there can be more than one value of the environmental good corresponding to any given value of the
environmental bad, and it is not clear which value to use. This has been identified as a problem with
translating deciviews (an environmental "bad") into visual range (an environmental "good"). It has been
noted that, for a given deciview value, there can be many different visual ranges, depending on the other
factors that affect visual range - such as light angle and altitude. We note here, however, that this problem
is not unique to visibility, but is a general problem when trying to translate environmental "bads" into
"goods."41
In order to translate deciviews (a "bad") into visual range (a "good"), we use a relationship derived
by Malm and Pitchford (1994) in which
DV= 10*l
where DV denotes deciview and VR denotes visual range (in kilometers). Solving for VR as a function of
DV yields
40 There may be more than one "good" related to a given environmental "bad." To simplify the discussion, however, we
assume only a single "good."
41 Another example of an environmental "bad" is particulate matter air pollution (PM). The relationship between survival
probability (Q) and the ambient PM level is generally taken to be of the form
Q=l-aeppM.
where a denotes the mortality rate (or level) when there is no ambient PM (i.e., when PM=0). However, a is implicitly a function of
all the factors other than PM that affect mortality. As these factors change (e.g., from one location to another), a will change (just as
visual range changes as light angle changes). It is therefore possible to have many values of Q corresponding to a given value of PM,
as the values of a vary.
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-0.1DV
VR=391* e
This conversion is based on specific assumptions characterizing the "average" conditions of those factors,
such as light angle, that affect visual range. To the extent that specific locations depart from the average
conditions, the relationship will be an imperfect approximation.42
5.1.3 Estimating the Parameters for Visibility at Class I Areas: the y's and 5's
As noted in Section 2, if we consider a particular visibility change as the first or the only visibility
change valued by the household, the household's WTP for that change in visibility can be calculated, given
income (m), the "shape" parameter, p, and the corresponding recreational visibility parameter. For
example, a Southeast household's WTP for a change in visibility at in-region parks (collectively) from Qj =
Q01 to Qj = Qn is:
WTP(DQ1)= m- [mr + gl(Qr01 - Qrn)]1/r
if this is the first (or only) visibility change the household values.
Alternatively, if we have estimates of m as well as WTP/11 and WTPj0"' of in-region and out-of-
region households, respectively, for a given change in visibility from Q01 to Qn in Southeast parks, we can
solve for YI and 6j as a function of our estimates of m, WTP/11 and WTPj0"', for any given value of p.
Generalizing, we can derive the values of y and 6 for the jth region as follows:
(m-WTPm)p -mp
(QP0] - QP13)
and
(m - WTPout)p - mp
*, = '
Chestnut and Rowe (1990) and Chestnut (1997) estimated WTP (per household) for specific
visibility changes at national parks in three regions of the United States - both for households that are in-
region (in the same region as the park) and for households that are out-of-region. The Chestnut and Rowe
study asked study subjects what they would be willing to pay for each of three visibility improvements in
the national parks in a given region. Study subjects were shown a map of the region, with dots indicating
the locations of the parks in question. The WTP questions referred to the three visibility improvements in
all the parks collectively; the survey did not ask subjects' WTP for these improvements in specific parks
individually. Responses were categorized according to whether the respondents lived in the same region as
42 Ideally, we would want the location-, time-, and meteorological condition-specific relationships between deciviews and
visual range, which could be applied as appropriate. This is probably not feasible, however.
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the parks in question ("in-region" respondents) or in a different region ("out-of-region" respondents). The
areas for which in-region and out-of-region WTP estimates are available from Chestnut and Rowe (1990),
and the sources of benefits transfer-based estimates that we employ in the absence of estimates, are
summarized in Exhibit 5-1. In all cases, WTP refers to WTP per household.
Exhibit 5-1 Available Information on WTP for Visibility Improvements in National Parks
Region of Park
1. California
2. Colorado Plateau
3. Southeast United States
4. Northwest United States
5. Northern Rockies
6. Rest of United States
Region of Household
In-Region"
WTP estimate from study
WTP estimate from study
WTP estimate from study
Out-of-Regionb
WTP estimate from study
WTP estimate from study
WTP estimate from study
(based on benefits transfer from California)
(based on benefits transfer from Colorado Plateau)
(based on benefits transfer from Southeast U.S.)
1 In-region" WTP is WTP for a visibility improvement in a park in the same region as that in which the household is located. For
example, in-region WTP in the "Southeast" row is the estimate of the average Southeast household's WTP for a visibility
improvement in a Southeast park.
b Out-of-region" WTP is WTP for a visibility improvement in a park that is not in the same region in which the household is
located. For example, out-of-region WTP in the "Southeast" row is the estimate of WTP for a visibility improvement in a park in
the Southeast by a household outside of the Southeast.
In the primary calculation of visibility benefits for this analysis, only visibility changes at parks
within visibility regions for which a WTP estimate was available from Chestnut and Rowe (1990) are
considered (for both in- and out-of-region benefits). Primary estimates will not include visibility benefits
calculated by transferring WTP values to visibility changes at parks not included in the Chestnut and Rowe
study. Transferred benefits at parks located outside of the Chestnut and Rowe visibility regions will,
however, be included as an alternative calculation.
The values of the parameters in a household's utility function will depend on where the household
is located. The region-specific parameters associated with visibility at Class I areas (that is, all parameters
except the residential visibility parameter) are arrayed in Exhibit 5-2. The parameters in columns 1-3 can
be directly estimated using WTP estimates from Chestnut and Rowe (1990) (the columns labeled "Region
1," "Region 2," and "Region 3").
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December 1999
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Exhibit 5-2 Summary of Region-Specific Recreational Visibility Parameters to be Estimated in
Household Utility Functions
Region of
Household
Region 1
Region 2
Region 3
Region 4
Region 5
Region 6
Region of Park
Region 1
a
11
h
sl
sl
sl
ST
Region 2
62
12
62
f,2
62
6,
Region 3
S3
S3
T3
S3
S3
»!
Region 4
84
84
84
Y4
84
84
Region 5
85
85
85
85
Y5
85
Region 6
86
86
86
86
86
Y6
1 The parameters arrayed in this table are region-specific rather than park-specific or wilderness area-specific. For example, ^ is the
parameter associated with visibility at" Class I areas in region 1" for a household in any region other than region 1. The benefits
analysis must derive Class I area-specific parameters - e.g., 8lk, for the kth Class I area in the first region.
For the three regions covered in Chestnut and Rowe (1990) (California, the Colorado Plateau, and
the Southeast United States), we can directly use the in-region WTP estimates from the study to estimate
the parameters in the utility functions corresponding to visibility at in-region parks (YI); similarly, we can
directly use the out-of-region WTP estimates from the study to estimate the parameters for out-of-region
parks (6j). For the other three regions not covered in the study, however, we must rely on benefits transfer
to estimate the necessary parameters.
While Chestnut and Rowe (1990) provide useful information on households' WTP for visibility
improvements in national parks, there are several significant gaps remaining between the information
provided in that study and the information necessary for the benefits analysis. First, as noted above, the
WTP responses were not park-specific, but only region-specific. Because visibility improvements vary
from one park in a region to another, the benefits analysis must value park-specific visibility changes.
Second, not all Class I areas in each of the three regions considered in the study were included on the maps
shown to study subjects. Because the focus of the study was primarily national parks, most Class I
wilderness areas were not included. Third, only three regions of the United States were included, leaving
the three remaining regions without direct WTP estimates.
In addition, Chestnut and Rowe (1990) elicited WTP responses for three different visibility
changes, rather than a single change. In theory, if the CES utility function accurately describes household
preferences, and if all households in a region have the same preference structure, then households' three
WTP responses corresponding to the three different visibility changes should all produce the same value of
the associated recreational visibility parameter, given a value of p and an income, m. In practice, of course,
this is not the case.
In addressing these issues, we take a three-phase approach:
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(1) We estimate region-specific parameters for the region in the modeled domain covered by
Chestnut and Rowe (1990) (California, the Colorado Plateau, and the Southeast) - YI, Y2> and j3 and 81; 62
and 63. (2) We infer region-specific parameters for those regions not covered by the Chestnut and Rowe
study (the Northwest United States, the Northern Rockies, and the rest of the U.S.) - yA, YS, and Ye and 64,
65, and 66 (3) We derive park- and wilderness area-specific parameters within each region (Ylk and 6lk, for
k=l, ..., N]; Y2k and 62k, for k=l, ..., N2; and so forth).
The question that must be addressed in the first phase is how to estimate a single region-specific in-
region parameter and a single region-specific out-of-region parameter for each of the three regions covered
in Chestnut and Rowe (1990) from study respondents' WTPs for three different visibility changes in each
region. All parks in a region are treated collectively as if they were a single "regional park" in this first
phase. In the second phase, we infer region-specific recreational visibility parameters for regions not
covered in the Chestnut and Rowe study (the Northwest United States, the Northern Rockies, and the rest
of the U.S.). As in the first phase, we ignore the necessity to derive park-specific parameters at this phase.
Finally, in the third phase, we derive park- and wilderness area-specific parameters for each region.
Estimating Region-Specific Recreational Visibility Parameters for the Region Covered in the
Chestnut and Rowe Study (Regions 1, 2, and 3)
Given a value of p and estimates of m and in-region and out-of-region WTPs for a change from Q0
to Q! in a given region, the in-region parameter, Y, and the out-of-region parameter, 6, for that region can
be solved for. Chestnut and Rowe (1990), however, considered not just one, but three visibility changes in
each region, each of which results in a different calibrated Y and a different calibrated 6, even though in
theory all the y's should be the same and similarly, all the 8's should be the same. For each region,
however, we must have only a single Y and a single 6.
Denoting y j as our estimate of Y for the j* region, based on all three visibility changes, we chose
y j to best predict the three WTPs observed in the study for the three visibility improvements in the jth
region. First, we calculated y j;, i=l, 2, 3, corresponding to each of the three visibility improvements
considered in the study. Then, using a grid search method beginning at the average of the three y j; 's , we
chose y j to minimize the sum of the squared differences between the WTPs we predict using y j and the
three region-specific WTPs observed in the study. That is, we selected y j to minimize:
where WTP^ and WTP^ y j) are the observed and the predicted WTPs for a change in visibility in the jth
region from Q0 = Q0i to Q]= QH, i=l, ..., 3. An analogous procedure was used to select an optimal 6, for
each of the three regions in the Chestnut and Rowe study.
Inferring Region-Specific Recreational Visibility Parameters for Regions Not Covered in the
Chestnut and Rowe Study (Regions 4, 5, and 6)
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One possible approach to estimating region-specific parameters for regions not covered by
Chestnut and Rowe (1990) (y4, YS, and Ye and 64, 65, and 66) is to simply assume that households' utility
functions are the same everywhere, and that the environmental goods being valued are the same - e.g., that
a change in visibility at national parks in California is the same environmental good to a Californian as a
change in visibility at national parks in Minnesota is to a Minnesotan.
For example, to estimate 64 in the utility function of a California household, corresponding to
visibility at national parks in the Northwest United States, we might assume that out-of-region WTP for a
given visibility change at national parks in the Northwest United States is the same as out-of-region WTP
for the same visibility change at national parks in California (income held constant). Suppose, for
example, that we have an estimated mean WTP of out-of-region households for a visibility change from Q01
to Qn at national parks in Califonia (region 1), denoted WTPj0"1. Suppose the mean income of the out-of-
region subjects in the study was m. We might assume that, for the same change in visibility at national
parks in the Northwest United States, WTP4out = WTPj0"1 among out-of-region individuals with income m.
We could then derive the value of 64, given a value of p as follows:
<54 =
where Q04 = Q0i and Q14 = Qn, (i.e., where it is the same visibility change in parks in region 4 that was
valued at parks in the region 1).
This benefits transfer method assumes that (1) all households have the same preference structures
and (2) what is being valued in the Northwest United States (by a California household) is the same as
what is being valued in the California (by all out-of-region households). While we cannot know the extent
to which the first assumption approximates reality, the second assumption is clearly problematic. National
parks in one region are likely to differ from national parks in another region in both quality and quantity
(i.e., number of parks).
One statistic which is likely to reflect both the quality and quantity of national parks in a region is
the average annual visitation rate to the parks in that region. A reasonable way to gauge the extent to
which out-of-region people would be willing to pay for visibility changes in parks in the Northwest United
States versus in California might be to compare visitation rates in the two regions.43 Suppose, for example,
that twice as many visitor-days are spent in California parks per year as in parks in the Northwest United
States per year. This could be an indication that the parks in California are in some way more desirable
than those in the Northwest United States and/or that there are more of them ~ i.e., that the environmental
goods being valued in the two regions ("visibility at national parks") are not the same.
A preferable way to estimate 64, then, might be to assume the following relationship:
WTP4°"' n4
WTP* = ^
43 We acknowledge that reliance on visitation rates does not get at nonuse value.
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(income held constant), where nj = the average annual number of visitor-days to California parks and n4
the average annual number of visitor-days to parks in the Northwest United States. This implies that
774
for the same change in visibility in region 4 parks among out-of-region individuals with income m. If, for
example, nj = 2n4, WTP4out would be half of WTPj0"1. The interpretation would be the following:
California national parks have twice as many visitor-days per year as national parks in the Northwest
United States; therefore they must be twice as desirable/plentiful; therefore, out-of-region people would be
willing to pay twice as much for visibility changes in California parks as in parks in the Northwest United
States; therefore a Californian would be willing to pay only half as much for a visibility change in national
parks in the Northwest United States as an out-of-region individual would be willing to pay for the same
visibility change in national parks in California. This adjustment, then, is based on the premise that the
environmental goods being valued (by people out-of-region) are not the same in all regions.
The parameter 64 is estimated as shown above, using this adjusted WTP4out. The same procedure is
used to estimate 65 and 66 We estimate y/i, Ys, and Ye in an analogous way, using the in-region WTP
estimates from the transfer regions, e.g.,
WTP =
Estimating Park- and Wilderness Area-Specific Parameters
As noted above, Chestnut and Rowe (1990) estimated WTP for a region's national parks
collectively, rather than providing park-specific WTP estimates. The y's and 8's are therefore the
parameters that would be in household utility functions if there were only a single park in each region, or if
the many parks in a region were effectively indistinguishable from one another. Also noted above is the
fact that the Chestnut and Rowe study did not include all Class I areas in the regions it covered, focusing
primarily on national parks rather than wilderness areas. Most Class I wilderness areas were not
represented on the maps shown to study subjects. In California, for example, there are 31 Class I areas,
including 6 national parks and 25 wilderness areas. The Chestnut and Rowe study map of California
included only 10 of these Class I areas, including all six of the national parks. It is unclear whether
subjects had in mind "all parks and wilderness areas" when they offered their WTPs for visibility
improvements, or whether they had in mind the specific number of (mostly) parks that were shown on the
maps. The derivation of park- and wilderness area-specific parameters depends on this.
Derivation of Region-specific WTP for National Parks and Wilderness Areas
If study subjects were lumping all Class I areas together in their minds when giving their WTP
responses, then it would be reasonable to allocate that WTP among the specific parks and wilderness areas
in the region to derive park- and wilderness area-specific y's and 8's for the region. If, on the other hand,
study subjects were thinking only of the (mostly) parks shown on the map when they gave their WTP
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response, then there are two possible approaches that could be taken. One approach assumes that
households would be willing to pay some additional amount for the same visibility improvement in
additional Class I areas that were not shown, and that this additional amount can be estimated using the
same benefits transfer approach used to estimate region-specific WTPs in regions not covered by Chestnut
and Rowe( 1990).
However, even if we believe that households would be willing to pay some additional amount for
the same visibility improvement in additional Class I areas that were not shown, it is open to question
whether this additional amount can be estimated using benefits transfer methods. A third possibility, then,
is to simply omit wilderness areas from the benefits analysis. For this analysis we calculate visibility
benefits assuming that study subjects lumped all Class I areas together when stating their WTP, even if
these Class I areas were not present on the map.
Derivation of park- and wilderness area-specific WTPs, given region-specific WTPs for national
parks and wilderness areas
The first step in deriving park- and wilderness area-specific parameters is the estimation of park-
and wilderness area-specific WTPs. To derive park and wilderness area-specific WTPs, we apportion the
region-specific WTP to the specific Class I areas in the region according to each area's share of the
region's visitor-days. For example, if WTP/" and WTP]0"' denote the mean household WTPs in the
Chestnut and Rowe (1990) study among respondents who were in-region-1 and out-of-region-1,
respectively, nlk denotes the annual average number of visitor-days to the kth Class I area in California,
and nj denotes the annual average number of visitor-days to all Class I areas in California (that are
included in the benefits analysis), then we assume that
l = * WTP;m ,
n,
and
Using WTP/11 and WTPj°ut, either from the Chestnut and Rowe study (for j = 1, 2, and 3) or derived by the
benefits transfer method (for j = 4, 5, and 6), the same method is used to derive Class I area-specific WTPs
in each of the six regions.
While this is not a perfect allocation scheme, it is a reasonable scheme, given the limitations of
data. Visitors to national parks in the United States are not all from the United States, and certainly not all
from the region in which the park is located. A very large proportion of the visitors to Yosemite National
Park in California, for example, may come from outside the U.S. The above allocation scheme implicitly
assumes that the relative frequencies of visits to the parks in a region from everyone In the world is a
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reasonable index of the relative WTP of an average household in that region (WTPjm) or out of that region
(but in the U.S.) (WTPj°ut) for visibility improvements at these parks.44
A possible problem with this allocation scheme is that the relative frequency of visits is an
indicator of use value but not necessarily of nonuse value, which may be a substantial component of the
household's total WTP for a visibility improvement at Class I areas. If park A is twice as popular (i.e., has
twice as many visitors per year) as park B, this does not necessarily imply that a household's WTP for an
improvement in visibility at park A is twice its WTP for the same improvement at park B. Although an
allocation scheme based on relative visitation frequencies has some obvious problems, however, it is still
probably the best way to allocate a collective WTP.
Derivation of park- and wilderness area-specific parameters, given park- and wilderness area-specific
WTPs
Once the Class I area-specific WTPs have been estimated, we could derive the park- and
wilderness area-specific y's and 6's using the method used to derive region-specific y's and 6's. Recall that
that method involved (1) calibrating y and 6 to each of the three visibility improvements in the Chestnut and
Rowe study (producing three y's and three 6's), (2) averaging the three y's and averaging the three 6's, and
finally, (3) using these average y and 6 as starting points for a grid search to find the optimal y and the
optimal 6 - i.e., the y and 6 that would allow us to reproduce, as closely as possible, the three in-region and
three out-of-region WTPs in the study for the three visibility changes being valued.
Going through this procedure for each national park and each wilderness area separately would be
very time consuming, however. We therefore used a simpler approach, which produces very close
approximations to the y's and 6's produced using the above approach. If:
WTPjin = the in-region WTP for the change in visibility from Q0 to Qj in the jth region;
WTPjkm= the in-region WTP for the same visibility change (from Q0 to Qj) in the kth Class I
area in the jth region (= sjk*WTPjin, where sjk is the kth area's share of visitor-days
in the jth region);
m = income;
YJ* = the optimal value of y for the jth region; and
Yjk = the value of yjk calibrated to WTPjkm and the change from Q0 to Qj;
then45:
44 This might be thought of as two assumptions: (1) that the relative frequencies of visits to the parks in a region from
everyone in the worldis a reasonable representation of the relative frequency of visits from people in the UnitedStates - i.e., that the
parks that are most popular (receive the most visitors per year) in general are also the most popular among Americans; and (2) that the
relative frequency with which Americans visit each of their parks is a good index of their relative WTPs for visibility improvements at
these parks.
45 YJ* is only approximately equal to the right-hand side because, although it is the optimal value designed to reproduce as
closely as possible all three of the WTPs corresponding to the three visibility changes in the Chestnut and Rowe study, YJ* will not
exactly reproduce any of these WTPs.
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. (m - WTP'")P - mp
7^ i
/ ~
and
- mp
(Qpo-Q!)
which implies that:
where:
(m - WTP'")P - mp
We use the adjustment factor, a^, to derive Yjk from YJ*, for the kth Class I area in the jth region. We use
an analogous procedure to derive 6jk from 6j* for the kth Class I area in the jth region (where, in this case,
we use WTPj°ut and WTPjkout instead of WTP/" and WTPjkm).46
5.1.4 Estimating the Parameter for Visibility in Residential Areas: e
The estimate of 6 is based on McClelland et al. (1991), in which household WTP for improvements
in residential visibility was elicited from respondents in Chicago and Atlanta. A notable difference between
the Chestnut and Rowe study and the McClelland study is that, while the former elicited WTP responses
for three different visibility changes, the latter considered only one visibility change. The estimation of 6
was therefore a much simpler procedure, involving a straightforward calibration to the single income and
WTP in the study:
(m - WTP)P - mp
(Zp - Zp)
5.1.5 Putting it All Together: the Household Utility and WTP Functions
46 This method uses a single in-region WTP and a single out-of-region WTP per region. Although the choice of WTP will
affect the resulting adjustment factors (the ajk's) and therefore the resulting yjk's and 8jk's, the effect is negligible. We confirmed this
by using each of the three in-region WTPs in California and comparing the resulting three sets of yjk's and 8jk's, which were different
from each other by about one one-hundredth of a percent.
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Given an estimate of 6, derived as shown in Section 5, and estimates of the y's and 6's, derived as
shown in Section 4, based on an assumed or estimated value of p, the utility and WTP functions for a
household in any region are fully specified. We can therefore estimate the value to that household of
visibility changes from any baseline level to any alternative level in the household's residential area and/or
at any or all of the Class I areas in the United States, in a way that is consistent with economic theory. In
particular, the WTP of a household in the ith region and the nth residential area for any set of changes in
the levels of visibility at in-region Class I areas, out-of-region Class I areas, and the household's residential
area (given by equation (24)) is:
WTPJLZ.LQ) = m-fmp + 9(Z?n - Z'J + f r,k(QL ~ Q$J + It 8]k(Q?]k - Q?]k)f/p .
k=l j*i k=l
The national benefits associated with any suite of visibility changes is properly calculated as the
sum of these household WTPs for those changes. The benefit of any subset of visibility changes (e.g.,
changes in visibility only at Class I areas in California) can be calculated by setting all the other
components of the WTP function to zero (that is, by assuming that all other visibility changes that are not
of interest are zero). This is effectively the same as assuming that the subset of visibility changes of
interest is the first or the only set of changes being valued by households. Estimating benefit components in
this way will yield slightly upward biased estimates of benefits, because disposable income, m, is not being
reduced by the WTPs for any prior visibility improvements. That is, each visibility improvement (e.g.,
visibility at Class I areas in the California) is assumed to be the first, and they cannot all be the first. The
upward bias should be extremely small, however, because all of the WTPs for visibility changes are likely
to be very small relative to income.
5.2 AGRICULTURAL BENEFITS
Changes in ozone concentrations are known to affect agricultural production, affecting agricultural
crops to different degrees depending on their sensitivity. Estimating the economic benefits associated with
these changes in production requires several steps. Estimated changes in ozone concentrations are
combined with experimental dose-response functions to estimate crop yield changes. The effect of yield
changes on agricultural cropping decisions and resulting production and prices are then evaluated using a
model of the agricultural sector, resulting in estimates of changes in farm income and consumer welfare.
Each of the steps involved in this analysis is described in more detail in the following sections. Section
5.2.1 describes the source of exposure-response functions and the selection of an index of ozone exposure.
Section 5.2.2 describes the derivation of estimated ozone concentrations under alternative regulatory
profiles. The method for estimating yield changes is described in Section 5.2.3, and the agricultural model
used to estimate the impact of changes in yield is discussed in Section 5.2.4. The results are presented in
Chapter 6.
5.2.1 Exposure-Response Functions
Experimental data to evaluate the response of crops to ozone has been collected for a limited
number of crops under the National Crop Loss Assessment Network (NCLAN) program. The objective of
this program was to employ a consistent experimental methodology to provide comparable results across
crops. The crops included in the NCLAN experiments are corn, cotton, peanuts, sorghum, soybeans,
winter wheat, potatoes, lettuce, kidney beans, tomatoes, and hay. For many crops, the NCLAN program
evaluated the effects of ozone on several different cultivars. Although not necessarily representative of the
full range of variability in crop response, the results for different cultivars do permit identification of a
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range of responsiveness. The most tolerant and responsive functions are used to represent minimum and
maximum impacts, within the limits of available data.
In its analysis of the welfare benefits associated with ozone National Ambient Air Quality
Standards (NAAQS), U.S. EPA elected to represent crop exposure to ozone as a cumulative index (U.S.
EPA, 1996b). The index selected is the SUM06 index, which sums the ozone concentration for every hour
that exceeds 0.06 ppm, within a 12-hour period from 8:00 A.M. to 8:00 P.M.
Use of cumulative exposure-response functions is relatively recent, and few experiments have been
designed or reported in terms of the SUM06 index. Because the NCLAN program used a consistent
protocol and developed a database of experimental conditions and results for all of its studies, U.S. EPA's
Environmental Research Laboratory (ERL) was able to use original data from NCLAN studies to develop
SUM06 exposure response functions for most NCLAN crops47 (Lee and Hogsett, 1996). In addition, the
agricultural model used in this analysis does not reflect non-commodity crops such as lettuce and kidney
beans (described below). Exhibit 5-3 presents the exposure-response functions used in this analysis.
Exhibit 5-3 Ozone Exposure-Response Functions for Selected Crops (SUM06)
Ozone Index
SUM06
SUM06
SUM06
SUM06
SUM06
SUM06
SUM06
SUM06
SUM06
SUM06
SUM06
SUM06
Quantity
Max
Max
Max
Max
Max
Max
Min
Min
Min
Min
Min
Min
Crop
Cotton
Field Corn
Grain Sorghum
Peanut
Soybean
Winter Wheat
Cotton
Field Corn
Grain Sorghum
Peanut
Soybean
Winter Wheat
Function
l-exp(-(index/78)A1.311)
l-exp(-(index/92.4)A2.816)
l-exp(-(index/177.8)A2.329)
l-exp(-(index/99.8)A2.219)
l-exp(-(index/131.4)Al)
l-exp(-(index/27.2)A1.0)
l-exp(-(index/l 16.8)A1 .523)
l-exp(-(index/94.2)A4.307)
l-exp(-(index/177.8)A2.329)
l-exp(-(index/99.8)A2.219)
l-exp(-(index/299.7)Al .547)
l-exp(-(index/72.1)A2.353)
Median
Experimental
Duration (Days)
119
83
85
112
104
58
119
83
85
112
104
58
Median
Duration
(Months)
4
3
3
4
3
2
4
3
3
4
3
2
Source: Lee and Hogsett (1996)
47Data were not sufficient to develop functions for tomatoes or hay.
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The form of these functions is a Weibull specification transformed to predict a yield loss relative to
conditions of "clean air", or a zero SUM06 value. The resulting equation is in the form of:
Y = 1- g[-(SUM06/B)"C]
where:
Y = predicted relative yield loss (PRYL), expressed as a decimal value (i.e.,
not multiplied by 100 to report as a percent loss), and relative to a zero
SUM06 (or clean air) condition
SUM06 = cumulative SUM06 ozone statistic at a specified level of spatial
representation, in ppm
B, C = statistically estimated parameters, unitless.
Application of Exposure Response Functions to a Non-Zero Baseline
There is an issue associated with applying the yield loss functions to analysis of alternative
regulatory profiles. The functions provide a predicted yield loss relative to "clean" air, while regulatory
analysis needs to compare regulatory options to a baseline, non-zero ozone condition. Therefore, the yield
change resulting from the regulatory scenario is evaluated as the yield loss relative to clean air under the
regulatory scenario being evaluated compared to the yield loss under baseline conditions.
To address this issue, the change in yield under clean air conditions can be divided by the baseline
yield. If yield under clean conditions is 100 percent of possible yield, then baseline yield in this context is 1
minus baseline yield loss. Thus the change in yields relative to the baseline can be given as:
(PRYLbaselme - PRYLcontrol)/(l-PRYLbaselme).
Ozone Index Computation
In order to accurately reflect changes in yields using exposure response functions, they must be
applied in a way that is consistent with the experimental conditions used to generate the functions.
Specifically, the ozone index, in this case the SUM06 index, needs to be consistent with ozone exposure
used in the experimental derivation of the function. For example, if the function is a 12-hour exposure
function, then the index used must be a 12-hour index. Another component of the experimental exposure is
the duration of the experiment. A precise reflection of experimental conditions would require that the ozone
index should be calculated for the same number of days as used in the experiment for each crop. However,
in the benefits analysis for the 1997 ozone NAAQS RIA, it was determined that the median duration of all
NCLAN experiments for a given crop provided a statistically sound reflection of duration for the purposes
of estimating SUM06 indices for estimating agricultural benefits (Mathtechl997). The median durations
for each crop are reported in Exhibit 5-3 in both days and months. The ozone NAAQS analysis
constructed the ozone index based on the nearest number of months; this analysis constructed the index
based on the number of days.
Finally, because growing seasons vary throughout the U.S., the exposure needs to reflect the
months in which a crop would be grown in a given location. To calculate the SUM06 index for the
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appropriate growing season, state-level data on planting and harvesting dates was used in this analysis48
(U.S. Department of Agriculture, 1984; U.S. EPA, 1993). To calculate the cumulative SUM06 index, the
experimental duration for each crop was anchored on that crop's harvest date in each state in order to most
closely approximate the relevant period of exposure for yield analysis. The harvest date was assumed to be
the first day in the month of harvest, so that the SUM06 index includes the months up to but not including
the harvest month.
The baseline and control ozone data for this analysis were developed from monthly SUM06 values,
requiring several steps in the calculation of a duration-based index. First, starting at the month before the
harvest month, each full month of SUM06 data was summed. The ozone value for the first month of the
duration period was calculated as the fraction of the remaining days in the duration period to the number of
days in the month. For example, soybeans have a 104-day duration, translating to 3 full months plus a
fraction of the first month in the growing season. If soybeans are harvested in October in a given state,
three full months of data starting in September are summed (91 days), along with 13 days of June, or 0.43
of the June SUM06 data, to obtain the 104-day SUM06 index. This approach implicitly assumes an equal
average daily SUM06 within each bi-monthly period. The index was calculated on a county level
assuming all counties reflect the state-level growing seasons.
While the ozone data in this analysis were modeled from May through September, the growing
season for some crops includes April, October, and November. To estimate SUM06 values for these
unmodeled months, base-year ozone values were used. For the Western U.S., the available data were
historical monitor-level ozone values for 1995, and for the Eastern U.S., we used data from 1996.
5.2.2 Estimation of Yield Changes
In this analysis, use of a single exposure response function to estimate changes in yields implies
that all producers are using a single cultivar of a given crop. This, combined with the limited number of
cultivars evaluated in the NCLAN program, introduces an unquantifiable uncertainty into the estimation of
yield changes. The most sensitive cultivar was used to represent the upper bound of the range that could be
estimated, and the least sensitive cultivar was used to represent the lower bound of that range.
Using the exposure response functions and the SUM06 ozone indices, county-level yield changes
were estimated between each regulatory profile and the baseline. County level yield changes were then
aggregated to the state level using 1997 data on county level production as weights (U.S. Department of
Agriculture, 1988a): the resulting state-level yield changes were used for quality control purposes. The
model used to estimate changes in the agricultural sector resulting from yield changes (described in Section
3.4, below) requires a national level yield change; this was calculated in the same manner as was the
change in state-level yields.
5.2.3 AGSIM© MODEL
AGSIM© is an econometric-simulation model that is based on a large set of statistically estimated
demand and supply equations for agricultural commodities produced in the United States. This model has
48Peanut emergence and harvest dates were taken from the U.S. EPA PRZM-2 Model data.
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been peer-reviewed and utilized in many pesticide and other major agricultural policy evaluations (Taylor
etal, 1993).
The model is capable of analyzing the effects of changes in policies that affect crop yields or
production costs. This is achieved by estimating how farmers will adjust crop acreage between
commodities when relative profitability changes as a result of policy-induced crop yield and/or production
cost changes. Acreage and yield changes from various scenarios will affect total production of crops,
which simultaneously affects both commodity prices and consumption. Commodity price changes, in turn,
affect profitability and cropping patterns in subsequent years. Federal farm program and conservation
reserve effects are also incorporated into the model. The model has been adapted to reflect the projections
to 2010 from the last future year for which baseline forecasts are available: 2007. Although ozone impacts
will be experienced far in the future, it was not possible to forecast the AGSIM© model far beyond USDA
baseline forecasts that extend to 2007. Therefore, the 2030 ozone conditions were modeled using the 2010
version of the model.
Model Specification
AGSIM© is based on a set of dynamic supply and demand equations for major crops.
Commodities are generally linked on both the supply side and demand side of markets. Crops included in
the model are corn, grain sorghum, barley, oats, wheat, soybeans, cotton, hay, peanuts and rice. The
simulation component of the model finds the set of prices for all commodities endogenous to the model that
simultaneously clear all markets in each year over the simulation period. Dynamics are incorporated into
the econometric specification and thus incorporated into the simulation model. All equations in the model
were econometrically estimated, except a few policy equations that were based on legislated formula.
Supply Components
The crop supply component of AGSIM© is based on a set of supply equations for the major field
crops produced in the United States. Effects of farm programs, specifically the 1985 Food Security Act
(FSA), the 1990 Food Agricultural Conservation and Trade Act (FACTA), and the 1996 Federal
Agricultural Improvement and Reform Act (FAIR), are reflected in the econometric specification of the
supply component of the model, and thus are included in the simulation model.
Ex ante simulation of environmental policy will likely involve an assumption of continuation of the
1996 FAIR Act indefinitely. However, since most of the historical observations on which supply equations
were econometrically estimated occurred under different programs, it is important to consider how
historical equations reflect the 1996 FAIR Act. The basic philosophy that guided inclusion of farm
program features into the supply component of the model follow. First, beginning with the 1985 FSA,
continuing with the 1990 FACTA, and now with the 1996 FAIR Act, North American Free Trade
Agreement (NAFTA) and the General Agreement on Tariffs and Trade (GATT), farm and international
trade policy has moved U.S. agriculture to a market orientation. Although the 1985 FSA and the 1990
FACTA had price support and acreage diversion features, they embodied a strong market orientation. For
all major program crops (in AGSIM©), the acreage devoted to the crop exceeded the acreage under
government programs. Thus, at the margin, market prices (and not support prices) influenced crop
acreage. Another way of looking at this is that farm programs have influenced crops at the intra-margin,
while the market has influenced crops at the margin. Thus, after accounting for acreage diverted under
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farm programs, expected prices determine acreage. For these reasons, AGSIM© should be valid for
simulating agricultural markets under the market conditions established under the 1996 FAIR Act.
Sets of equations that comprise the supply component of the current version of the model include:
(1) acreage planted to each crop, (2) acreage harvested of each crop, (3) acreage in annual set-aside or
acreage reduction programs (ARP) by crop, (4) acreage in cultivated summer fallow, (5) crop yields per
harvested acre, (6) rate of participation in Federal farm programs by crop, and (7) annual set-aside rates by
crop under past farm programs, as related to stock levels (historically legislated) and thus related to market
price. Identities in the model are: (a) production is the product of acreage harvested and yield per harvested
acre, and (b) the quantity supplied equals the quantity demanded for each commodity (market clearing).
Specification of each of these sets of equations follows.
Acreage Planted Equations. Acreage planted is the key behavioral relationship in the supply
component of the model. Acreage planted of a particular crop depends on expected per-acre net returns for
that crop, expected per-acre net returns for competing crops, and farm program variables. In algebraic (and
Fortran) form, the acreage planted equation is:
(1) acresp(ic,it,irun) = bc(ic) + bap(ic)*acresp(ic,it-l,irun) + bcrp(ic)*acrp(ic,it,irun) +
bdiv(ic)*acrediv + brm(ic)*rerntm(ic,it,irun) +
ber(ic)*rerentnp(it,irun) + byr(ic)*time(it) + bd83(ic)*dumb83(it)
where:
acresp(ic,it,irun) = acreage planted to the ic* crop in the it* year and in simulation
"irun",
acrp(ic,it,irun) = acreage of crop "ic" that was placed in the conservation reserve
program,
acrediv = acreage diverted under annual set-aside programs,
rerentm(ic,it,irun) = real expected per acre returns over variable costs for the icth crop,
rerentnp(it,irun) = real expected per acre returns over variables costs computed as a
weighted average49 of rerentm(ic,it,irun) over all endogenous
crops,
time(it) = a time-trend variable, and
dumb83(it) = a binary dummy variable to account for the PIK program in crop
year 1983.
The remaining variables in equation (1) represent estimated coefficients. A single run of AGSIM
involves two simulations, one for the baseline (irun=0) and one for the policy scenario (irun=l). These two
simulations are then compared to estimate the economic impacts of the policy scenario.
Expected returns over variable costs, rerentm(ic,it,irun), is defined as:
(la) rerntm(ic,it,irun) = rp(ic,it-l,irun)*ey(ic,it,irun) - rcost(ic,it,irun)
where:
49Weights used in computing a composite expected return variable were the acreage harvested of each crop the previous
year divided by total acreage harvested the previous year.
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rp(ic,it-l,irun) = real price the previous crop year (actual or simulated, depending on the
time period),
ey(ic,it,irun) = expected crop yield, and
rcost(ic,it,irun) = real variable production cost.
Expected yield is based on trend-line regressions:
(Ib) ey(ic,it,irun) = [cint(ic) + by(ic)*time(it)]
where:
cint(ic) and by(ic) are estimated coefficients.
In the policy run, expected yield is adjusted for exogenously specified percentage yield changes ("dyld"):
(Ic) ey(ic,it,irun) = [cint(ic) + by(ic)*time(it)]*(1.0 + dyld(ic,it)/100.)
Changes in real variable costs of production can also be exogenously specified for the policy
simulation run. Thus, yield and cost changes directly impact acreage planted through equation (1), and
indirectly impact acreage planted because of the resulting impact on prices in equation (la) and thus in
equation (1).
Given signs and magnitudes of estimated coefficients in equation (1), an increase in expected
returns of the icth crop will increase acreage planted of that crop, while an increase in expected returns of
other endogenous crops will decrease acreage of the icth crop. The estimated coefficient on lagged acreage
planted in equation (1) is positive and less than one in value for all crops, which means that acreage planted
is dynamically stable. The estimated coefficient on the set-aside acreage is negative and less than one in
absolute value for all crops except oats, which reflects acreage slippage in the ARP program. Oats were
typically planted to set-aside acreage, thus the estimated coefficient on set-aside acreage is positive in the
oats equation, as expected. Further comments will be made on the acreage diverted effects on planted
acreage after participation rate and acreage diverted equations, which are endogenous, are presented below.
Acreage Harvested Equations. Acreage harvested depends primarily on acreage planted:
(2) acresh(ic,it,irun) = bch(ic) + baph(ic)*acresp(ic,it,irun) + byrh(ic)*time(it) +
bdvh(ic) * acrediv
where:
acresh(ic,it,irun) = the acreage harvested of the ic* crop in the it* year and in
simulation "irun",
and other variables are as defined previously.
The estimated coefficient baph(ic) is positive and less than one, indicating that not all planted
acreage is harvested, as expected. The coefficient bdvh(ic) on the acreage diverted variable is non-zero for
oats only, in which case it is negative. This adjusts oat acreage harvested for the complexity of oats being
planted (but not harvested) on ARP acreage. A time-trend variable for corn and grain sorghum, but not
other crops shows how harvested acreage as a percentage of planted acreage has been increasing slightly
overtime.
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Participation Rate in Farm Programs. Participation rates in the annual set-aside programs under
the 1985 FSA and the 1990 FACTA were endogenized in the model with the set of equations:
(3) part(ic,it,irun) = bcp(ic) + brmp(ic)*rerntm(ic,it,irun) + brpp(ic)*rerntp(ic,it,irun) +
byr(ic)*time(ic) + bpart(ic)*part(ic,it-l,irun) + bedpp(ic)*redp(ic,it,irun)
+ bd83p(ic)*dumb83(it)
where:
part(ic,it,irun) = the participation rate in the farm program for the icth crop in the itth year
and in simulation "irun",
rerntp(ic,it,irun)= real expected returns over variable costs based on the support (target)
price for that crop,
redp(ic,it,irun) = real effective acreage diversion payment rate,
and other variables are as defined previously.
Estimated coefficients brpp(ic) are non-negative, indicating that an increase in expected returns
based on support price will increase participation, while estimated coefficients brmp(ic) are non-positive,
indicating that an increase in expected returns based on expected market price will decrease participation.
Lagged participation rate in equation (3) shows strong dynamics with respect to farm program
participation.
Acreage Diverted under Farm Programs. Acreage diverted under annual set-aside (or ARP)
programs is modeled as:
(4) adiv(ic,it,irun) = bcd(ic) + bd83d(ic)*dumb83(it) + bedpd(ic)*redp(ic,it,irun) +
byrd(ic)*time(it) + bpsa(ic)*sa(ic,it,irun)*part(ic,it,irun)
where:
adiv(ic,it,irun) = acreage diverted under annual diversion programs for the icth crop in the
it* year and in simulation "irun",
sa(ic,it,irun) = the set-aside rate specified by the Secretary of Agriculture under 1985
FSA and 1990 FACTA,
and other variables are as defined previously.
Acreage slippage (with respect to historical set-aside) in farm programs is implicit in the model
specification, and results from the complex simultaneity of farm program variables in sets of equations (1),
(3), and (4).
Acreage in Cultivated Summer Fallow. Acreage in cultivated summer fallow is modeled by the
equation:
(5) afl(it,irun) = bcfl + bafl*afl(it-l,irun)+ berfl*rerentnp(it,irun)+ byrfl*time(it) +
bd83fl*dumb83(it)
where:
afl(it,irun) = acreage fallowed in year it in simulation run "irun".
Abt Associates Inc. 5-21 December 1999
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Although the acreage in cultivated summer fallow is highly inelastic, this equation shows that an
increase in expected returns based on expected market price results in a small decrease in acreage fallowed.
Demand Components
The crop demand component of AGSIM© is based on a set of demand equations for each crop for
utilization categories of (a) imports, (b) exports,(c) livestock feed, (d) food, fiber, ethanol production and
other domestic uses, (e) ending stocks, and (f) residual use. Each demand component depends on current
market price for that commodity and, where relevant, prices of other commodities. The model specification
of each utilization category follows.
Imports. Imports of agricultural commodities are modeled by the set of equations:
(6) qd(ic,it,irun,l) = bim(l,ic) + bim(2,ic)*rp(ic,it,irun)*xrate(ic,it-l,irun)
+ bim(3,ic)*qd(ic,it-l,irun,l) + bim(4,ic)*time(it) +
bim(5,ic)*uspop(it,irun)
where:
qd(ic,it,irun,l) = the quantity of crop ic imported in year it in simulation run
"irun",
rp(ic,it,irun) = real market price,
xrate(ic,it-l,irun) = the real trade-weighted exchange rate,
uspop(it,irun) = the United States population,
and bim(j,ic) are estimated coefficients. Lagged imports in equation (6) reflects dynamic adjustments.
Exports. Exports of agricultural commodities are modeled by the set of equations:
(7) qd(ic,it,irun,2) = bex(l,ic) + bex(2,ic)*rp(ic,it,irun)*xrate(ic,it-l,irun) + bex(3,ic)*
qd(ic,it-l,irun,2) + bex(4,ic)*time(it) + bex(5,ic)*wpop(it,irun)
where:
qd(ic,it,irun,2) = the quantity of crop ic exported in year it in simulation run "irun", and
wpop(it,irun) = world population.
Feed, Fiber and Crushing Use. Domestic utilization of crops for feed, fiber or crushing
(depending on the crop) is modeled by the set of equations:
(8) qd(ic,it,irun,3) = bfd(l,ic) + Xjcbfdcross(ic,jc)*rp(jc,it,irun)+ bfd(2,ic)*qd(ic,it-l,irun,3) +
bfd(3,ic)*time(it)
where:
qd(ic,it,irun,3) = utilization for feed, fiber or crushing.
Note that cross-price effects are incorporated into this set of equations through the set of estimated
coefficients bfdcross(icjc). Symmetry of cross-price effects, consistent with microeconomic theory, was
imposed on estimation so that bfdcross(icjc) = bfdcross(jc,ic) for ic * jc. Own-price effects are all
negative, as expected.
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Domestic Food Use. The set of equations to represent domestic food use is:
(9) qd(ic,it,irun,4) = bfo(l,ic) + bfo(2,ic)*rp(ic,it,irun) +bfo(3,ic)*qd(ic,it-l,irun,4) +
bfo(4,ic)*time(it) + bfo(5,ic)*uspop(it,irun) + bfo(6,ic)*rdincome(it,irun)
where:
rdincome(it,irun) = real per-capita disposable income in the United States,
and other variables are as defined previously. In the case of peanuts, the real market price is replaced by
the fixed quota price that applies to all domestically consumed peanuts. This quota price for peanuts
applies to the 1985 FSA, the 1990 FACTA, and continues with the 1996 FAIR Act.
Ending Stocks. Ending stocks are viewed as another component of demand. Although
commodities are often held to maintain pipeline inventories, commodities are also held for speculative
purposes. Thus, stock levels respond strongly to prices, so the stock relationships were specified and
estimated as
(10) qd(ic,it,irun,5) = bst(l,ic) + bst(2,ic)*rp(ic,it,irun) + bst(3,ic)*qd(ic,it-l,irun,5) +
bst(4,ic)*time(it)
where qd(ic,it,irun,5) is ending stocks in year t.
Residual Use. For some crops (rice, peanuts, and cottonseed), supply and utilization data show a
residual category, which is modeled as,
(11) qd(ic,it,irun,6) = brs(l,ic) + brs(2,ic)*rp(ic,it,irun) + brs(3,ic)*time(it)
where:
qd(ic,it,irun,6) = residual use.
Although quantities in this residual use category are never used, the level of the residual does
respond negatively to the real price, and is thus viewed as another utilization (demand) category.
Market Clearing Identities
In supply and demand specification outlined above, supply generally depends on past prices, while
demand depends on current prices. In simulating these econometrically estimated equations into the future,
simulated prices are solved by simultaneously solving the market clearing identities
(12) qs(ic,it,irun)+qd(ic,it-l,irun,5) = qd(ic,it,irun,l) + qd(ic,it,irun,2) + qd(ic,it,irun,3) +
qd(ic,it,irun,4) + qd(ic,it,irun,5) + qd(ic,it,irun,6)
where:
qs(ic,it,irun) = the quantity produced of crop ic in year it in simulation "irun".
Abt Associates Inc. 5-23 December 1999
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Production is defined to be qs(ic,it,irun) = acresh(ic,it,irun)*ey(ic,it,irun). The left hand side of the
equal sign in (12) gives total supply (production plus beginning stocks), while the right-hand side of (12)
gives total utilization, including ending stocks.
In the simulation model this set of simultaneous equations are numerically solved to get the market
clearing prices in a given year. This process is continued, considering the dynamics of the model,
indefinitely into the future.
Historical Observation Period
Many econometric relationships in the model were estimated with data for the 1975-1995 time
period. However, where structural change was apparent, such as with stock holding behavior and
international trade, some of the early years were dropped from statistical analysis so that the simulation
model would better reflect the future.
Alternative Specifications Considered
Many different specifications of how farm programs influence crop acreage have been considered
in the evolution of AGSIM©, including: (a) acreage depends on support price, (b) acreage depends on the
maximum of expected market price and support price, (c) acreage depends on a weighted average of
support and expected market prices, with weights based on program and non-program acreage of the crop,
and (d) acreage depends on expected market price. Models for expected market price have considered
complex distributed lags that go back several years in time, to a simple model that expected market price is
actual price the previous year. Acreage equations have also been specified to depend on expected returns
of: (1) all competing individual crops with no parameter restrictions, (2) all competing individual crops
with full symmetry of cross-effects imposed on estimation, (3) major competing individual crops, and (4) a
weighted average of all expected returns for all other crops. Many different ways of incorporating
participation rates and acreage diverted into the model have also been considered. Several alternative
functional forms (linear, log-linear, nonlinear share equations, asymptotic) have also been considered.
Theoretical specifications considered have ranged from ad hoc models to very tightly specified and detailed
theoretical economic models based on complex assumptions. The present model draws from economic
theory (e.g. symmetry of cross-price effects in demand and homogeneity of degree zero of all supply and
demand equations with respect to prices), but does not specify the model so tightly with untested
assumptions and functional forms that empirical data has almost no role in the resulting estimates.
Alternative estimation techniques, ranging from simultaneous equations techniques, to Zellner's seemingly
unrelated regressions, to ordinary least squares regression have been used. The current version of
AGSIM© reflects a degree of subjective judgement of what best reflects supply and demand of agricultural
commodities based on microeconomic theory, traditional statistical criteria, and substantive direct contact
with farmers and ranchers in most regions of the United States.
Baseline
The current version of AGSIM© is designed to estimate changes in the agricultural sector resulting
from pesticide or other policy. Changes in economic variables are computed by comparing a policy
simulation of the model with a baseline simulation of the model. For ex post (retrospective) evaluations,
the baseline reflects actual farm programs, prices, acreages, etc. However, for ex ante evaluations,
Abt Associates Inc. 5-24 December 1999
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AGSIM© is calibrated to an external baseline. The calibration is done by comparing an internally
generated baseline to the external baseline and computing adjusted intercepts for all of the relevant demand
and supply relationships in AGSIM©.
For the 1999 version of AGSIM© the externally specified year 2010 baseline is forecasted from
the 2007 baseline reported by USDA (1988b). A few endogenous variables in AGSIM© were not included
in the USDA baseline. In those cases, the 1997 FAPRI baseline was used (FAPRI, 1997).
It should be noted that the baseline is not especially critical to estimates of changes in the
agricultural sector, except for the case of price support policy, which is not relevant here. That is,
sensitivity analyses with previous versions of AGSIM© have shown that estimates of changes in variables
are not very sensitive to baseline absolute values of variables. Use of the USDA baseline to the extent
possible assures consistency with other governmental mandated agricultural policy analyses.
Regional Effects Sub-Model
AGSIM© subroutines are also available to combine AGSIM© output with production cost
information to estimate net farm income impacts for the policy scenario at the regional level (or farm,
representative farm, area or state level). Required information for this type of evaluation includes for each
farm or area: (a) yield and cost changes (which often differ from the national yield and cost changes for the
policy scenario), (b) baseline production costs, and(c) acreages of each crop. This information is combined
with price impacts estimated with AGSIM©, and regional supply elasticities from a prior version of
AGSIM© (or from other sources) to estimate net farm income changes for the farms or areas considered.
The conceptual foundation for regional evaluation in this version of AGSIM© begins with a net
farm income formula,
where:
nir = net farm income in region ir,
Aic,ir = acreage harvested of the ic* crop in that region, and
R1C ir = per-acre net return in that region.
Based on equation (13), it can be shown that the theoretically appropriate formula for computing
net farm income changes for different regional situations is:
(14)
( }
A 7 ~ ll^c,irll AD A 7 ZI ^c.irzI A 7
AZ ic jc \K-ir AZ jc jc AZ
where:
A represents a discrete change,
AZ represents the discrete policy change,
ic and jc are crop indices,
and other variables are as previously defined.
Abt Associates Inc. 5-25 December 1999
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Equation (14) can be expressed in acreage elasticity (with respect to per-acre income) form,
(is) ~ yR v£ JL + yA v,
' AZ = ^ '^y^A^ AZ + ^ ^r2- AZ
elclJ ir = elasticity of acreage of the icth crop in the irth region with respect to per-
where:
elcljir = elasticity of acreage
acre income of the jcth crop in that region.
The term AR1C1J/AZ in equations (14) and (15) can be further expanded to give
Formula (15) along with (16) can be empirically implemented to estimate the change in regional
(or farm, representative farm, area or state level) farm income with the following information for each
region: (a) crop budgets, (b) the change in yield and cost associated with the policy in question, price
impacts estimated with AGSIM©, and externally specified (from an older version of AGSIM©, from
subjective estimates, or from the literature) elasticities.
The first term on the right-hand side of (14) and (15) represents the change in net income resulting
from increased or decreased acreage, while the last term on the right-hand side of (14) and (15) represents
the change in net farm income on existing acreage of crops in the region. Since acreage response is
generally inelastic, the last term on the right-hand side of (14) and (15) dominates the change in net farm
income in a region; thus, elasticities generally will not have a major impact on regional net farm income
changes estimated with the above approach.
AGSIM© Output
The major outputs from AGSIM© are changes in crop acreage, production, price, income, foreign
consumer benefits, domestic consumer benefits, and farm program costs. The traditional method of
economic welfare analysis (which is based on the concept of economic surplus) of policy changes is used to
compute the sum of changes in producer surplus (net farm income) plus changes to all consumers (changes
in consumers surplus) plus any changes in farm program payments (zero under 1996 FAIR). To avoid the
possibility of inappropriately comparing a baseline with a policy scenario that was actually based on
another baseline, a single run of AGSIM© produces both the baseline tables and the policy scenario tables,
then computes economic surplus and price changes based on these two runs of the model.
Output from each run of the model includes two sets of tables for each crop; one set of tables for
supply variables and another set of tables for supply and utilization variables. Each table includes
historical statistics as well as simulations into the future. These tables are constructed for the baseline and
the policy scenario.
Abt Associates Inc. 5-26 December 1999
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5.3 CONSUMER CLEANING COST SAVINGS
Particulate matter air pollution has been shown to result in dirtier clothes, which in turn results in
higher annual cleaning costs for consumers. One benefit of reduced particulate matter, then, is the
consequent reduction in cleaning costs for consumers. Several studies have provided estimates of the cost
to households of PM soiling. The study that is cited by ESEERCO (1994) as one of the most sophisticated
and is relied upon by EPA in its 1988 Regulatory Impact Analysis for SO2 is Manuel et al. (1982). Using
a household production function approach and household expenditure data from the 1972-73 Bureau of
Labor Statistics Consumer Expenditure Survey for over twenty cities in the United States, Manuel et al.
estimated the annual cost of cleaning per (Jg/m3 PM per household as $1.55 ($0.59 per person times 2.63
persons per household). This estimate is low compared with others (e.g., estimates provided by Cummings
et al. (1985) and Watson and Jaksch (1982) are about eight times and five times greater, respectively). The
ESEERCO report notes, however, that the Manuel estimate is probably downward biased because it does
not include the time cost of do-it-yourselfers. Estimating that these costs may comprise at least half the cost
of PM-related cleaning costs, they double the Manuel estimate to obtain a point estimate of $3.10 (reported
by ESEERCO in 1992 dollars as $2.70).
The Manuel et al. (1982) study measured particulate matter as TSP rather than PM10 or PM2 5. If
a one (jg/m3 increase in TSP causes $1.55 worth of cleaning expenses per household, the same unit dollar
value can be used for PM10 (or PM25) only if particle size doesn't matter ~ i.e., only if particles of all sizes
are equally soiling. Suppose, for example, that PM10 is 75% of TSP and that all particles are equally
soiling. Then 75% of the damage caused by a one (Jg/m3 increase in TSP is due to PM10. This is
(0.75)($1.55) = $1.16. However, this corresponds to a 0.75 (Jg/m3 increase in PM10. A one pg/m3 increase
in PM10 would therefore yield a dollar soiling damage of $1.16/0.75 = $1.55.
Suppose, however, that only PM10 matters. Then the $1.55 underestimates the impact of a one
(jg/m3 increase in PM10, because it corresponds to a less than one (jg/m3 increase in PM10 (e.g., a 0.75
(jg/m3 increase in PM10). In this case, the correct unit value per unit of PM10 would be ($1.55)70.75 =
$2.07. If only PM10 matters, then either (1) the dollar value can be adjusted by dividing it by the
percentage of TSP that is PM10 and PM10 can be used in the soiling damage function, or (2) the dollar value
can be left unadjusted and TSP, rather than PM10, can be used in the soiling damage function.
Finally, it is possible that, while both PM10 and PM25 are components of TSP that cause consumer
cleaning costs, the remaining portion of TSP has a greater soiling capability than either the PM10 or PM25
component. In this case, using either PM10 or PM2 5 air quality data with a household soiling function
based on TSP would yield overestimates of the PM10- or PM25-related consumer cleaning costs avoided by
reductions in concentration of these pollutants.
There is, however, insufficient information on the relative soiling capabilities of the different
components of TSP. This analysis assumes that all components of TSP have an equivalent soiling
capacity.
Abt Associates Inc. 5-27 December 1999
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5.4 NITROGEN DEPOSITION
Excess nutrient loads, especially that of nitrogen, are responsible for a variety of adverse
consequences to the health of estuarine and coastal waters, especially in the eastern United States. These
effects include toxic and/or noxious algal blooms such as brown and red tides, low (hypoxic) or zero
(anoxic) concentrations of dissolved oxygen in bottom waters, the loss of submerged aquatic vegetation due
to the light-filtering effect of thick algal mats, and fundamental shifts in phytoplankton community
structure. In order to model the impacts of nitrogen deposition on eastern estuaries, 10 eastern case study
estuaries and two Gulf Coast estuaries have been chosen because of the availability of necessary data and
their potential representativeness. Estimating nitrogen deposition in these 12 estuaries involves: (1)
assigning county-level NOX emissions to watershed-specific airsheds; and (2) calculating the change in
nitrogen deposition to each estuary using both local area and broader regional deposition estimates to the
watershed (kg of nitrogen deposited/ton of NOX emitted). The nitrogen deposition rate estimates were
derived by Pechan-Avanti (1999) using a methodology developed for the 1997 PM/Ozone/Regional Haze
NAAQS PJA (U.S. EPA, 1997c).50
The benefits to surrounding communities of reduced nitrogen loadings are not included in the
primary analysis. Instead, benefits attributed to the 12 case study estuaries are included as an alternative
estimate of welfare benefits. The extrapolation of these benefits to 43 Eastern nutrient-sensitive estuaries is
presented as a sensitivity analysis. Benefits due to reduced nitrogen deposition in the West are expected to
be minimal, and are not calculated in this analysis.
Direct C-R functions relating deposited nitrogen and reductions in estuarine benefits are not
available. The preferred WTP based measure of benefits depends on the availability of these C-R functions
and on estimates of the value of environmental responses. Because neither appropriate C-R functions nor
sufficient information to estimate the marginal value of changes in water quality exist at present, an
avoided cost approach is used instead of WTP to generate estuary related benefits. This analysis uses the
following data for each estuary: (1) total nitrogen load from all sources; (2) direct nitrogen load from
atmospheric deposition to the estuary surface; (3) indirect nitrogen load from atmospheric deposition to the
estuary watershed and subsequent pass-through to the estuary itself; (4) established nitrogen thresholds
and reduction goals adopted by the community; and (5) costs associated with using agreed upon non-point
water pollution control technologies.
Atmospheric nitrogen reductions are valued in this analysis on the basis of avoided costs associated
with agreed upon controls of nonpoint water pollution sources. Benefits are estimated using an average,
locally-based cost for nitrogen removal from water pollution (U.S. EPA, 1998). Valuation reflects water
pollution control cost avoidance based on average cost/pound of current non-point source water pollution
controls for nitrogen in three case study estuaries: Albemarle/Pamlico Sounds, Chesapeake Bay, and
Tampa Bay. Taking the weighted cost/pound of these available controls assumes States will combine low
cost and high cost controls.
In a recent advisory statement, the EPA's Science Advisory Board (SAB) was charged with
reviewing the benefits methodology for the §812b report on the benefits and costs of the Clean Air Act
Amendments. The SAB raised concerns about the use of the avoided cost approach to value reduced
ecosystem damages. Specifically, they identified a key requirement which should be met in order for
50Further details on the estimation of nitrogen deposition are provided by EPA (1997b). Revisions to this methodology are
described in U.S. EPA (1999)
Abt Associates Inc. 5-28 December 1999
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avoided costs to approximate environmental benefits. This requirement is that there is a direct link between
implementation of the air pollution regulation and the abandonment of a separate costly regulatory program
by some other agency, i.e. a state environmental agency. Reductions in nitrogen deposition are expected to
impact estuaries all along the eastern seaboard and the Gulf Coast. Many of the estuaries in these areas are
currently being targeted by nitrogen reduction programs due to current impairment of estuarine water
quality by excess nutrients. Some of the largest of these estuaries, including the Chesapeake Bay, have
established goals for nitrogen reduction and target dates by which these goals should be achieved. Using
the best and most easily implemented existing technologies, many of the estuaries will not be able to
achieve the stated goals by the target dates. Meeting these additional reductions will require development
of new technologies, implementation of costly existing technologies (such as stormwater controls), or use of
technologies with significant implementation difficulties, such as agricultural best management practices
(BMPs). Reductions in nitrogen deposition from the atmosphere will directly reduce the need for these
additional costly controls. Thus while the final Tier II rule does not eliminate the need for nutrient
management programs already in place, it may substitute for some of the incremental costs and programs
(such as an agricultural BMP program) necessary to meet the nutrient reduction goals for each estuary.
It should be noted that avoided cost is only a proxy for benefits, and should be viewed as inferior to
WTP based measures. Current research is underway to develop other approaches for valuing estuarine
benefits, including contingent valuation and hedonic property studies. However, this research is still
sparse, and does not contain sufficient information on the marginal WTP for changes in concentrations of
nitrogen (or changes in water quality or water resources as a result of changes in nitrogen concentrations).
The fixed capital costs for non-point controls in the case study estuaries ranges from $0.75 to
$55.59 per pound for agricultural and other rural best management practices and from $42.98 to $175.16
per pound for urban nonpoint source controls (stormwater controls, reservoir management, onsite disposal
system changes, onsite BMPs). Using these as a base, the total fixed capital cost per pound (weighted by
the ratio of the controlled nitrogen load to the estuary goal) is calculated for each of the case-study
estuaries and applied in the valuation of their avoided nitrogen load controlled. The weighted capital costs
per pound for the case-study estuaries are $40.95 for Albemarle-Pamlico Sounds, $26.79 for Chesapeake
Bay, and $108.36 for Tampa Bay51. For the purposes of this analysis, EPA assumes that estuaries that
have not yet established nutrient reduction goals will utilize the same types of nutrient management
programs as projected for the case study estuaries. For the other nine estuaries, an average capital cost per
pound of nitrogen (from the three case-estuaries) of $58.70/lb is calculated and applied; this cost may
understate or overstate the costs associated with reductions in these other estuaries. The other nine
estuaries generally represent smaller, more urban estuaries (like Tampa Bay), which typically have fewer
technical and financial options available to control nitrogen loadings from nonpoint sources. This may
result in higher control costs more similar to the Tampa Bay case. On the other hand, these estuaries may
have opportunities to achieve additional point source controls at a lower cost. Also, increased public
awareness of nullification issues and technological innovation may, in the future, result in States finding
lower cost solutions to nitrogen removal.
The benefits analysis assumed that the ten included East Coast estuaries are highly or moderately
nutrient sensitive, and they represent approximately 45.46 percent of all estuarine watershed areas along
51 The value for Tampa Bay is not a true weighted cost per pound, but a midpoint of a range of $71.89 to $144.47
developed by Apogee Research for the control possibilities (mostly urban BMPs) in the Tampa Bay estuary.
Abt Associates Inc. 5-29 December 1999
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the East Coast.52 Because data provided by the National Oceanic and Atmospheric Administration
(NOAA) indicate that approximately 92.6 percent of the watershed and surface area of East Coast
estuaries are highly or moderately nutrient sensitive, it is reasonable to expect that East Coast estuaries not
included in this analysis would also benefit from reduced deposition of atmospheric nitrogen. Therefore,
we scaled-up total benefits from the ten representative East Coast estuaries to include the remainder of the
nutrient sensitive estuaries along the East Coast on the basis of estuary watershed plus water surface area.
Since the ten estuaries are assumed to be nutrient sensitive and account for 48 percent of total eastern
estuarine area, we scaled-up estimates by multiplying the estimate for the ten East Coast estuaries by 2.037
(equal to 92.6 percent divided by 45.46 percent). We then added this figure to the benefits estimated for
the two Gulf Coast estuaries for a total benefits estimate for nitrogen deposition.
The analysis then annualized all capital cost estimates based on a seven percent interest rate and a
typical implementation horizon for control strategies. Based on information from the three case study
estuaries, this typically ranges from five to ten years. EPA has used the midpoint of 7.5 years for
annualization, which yields an annualization factor of 0.1759. Non-capital installation costs and annual
operating and maintenance costs are not included in these annual cost estimates. Depending upon the
control strategy, these costs can be significant. Reports on the Albemarle-Pamlico Sounds indicate, for
instance, that planning costs associated with control measures comprises approximately 15 percent of
capital costs. Information received from the Association of National Estuary Programs indicates that
operating and maintenance costs are about 30 percent of capital costs, and that permitting, monitoring, and
inspections costs are about one to two percent of capital costs. For these reasons, the annual cost estimates
may be understated.
52 There are 43 East Coast estuaries of which ten were in the sample, and 31 Gulf of Mexico estuaries of which two are in
the sample.
Abt Associates Inc. 5-30 December 1999
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RESULTS
This chapter provides estimates of the magnitude and value of changes in selected health and
welfare endpoints associated with Tier II-related changes in ambient Ozone and PM concentrations. The
total dollar benefits associated with a given endpoint depend on how much the endpoint will change (e.g.,
how many premature deaths will be avoided) and how much each unit of change is worth (e.g., how much a
premature death avoided is worth).
To place estimated incidence changes into context with predicted baseline incidence, Exhibit 6-1
displays the baseline incidence figures for those endpoints for which one can be calculated. Due to the
nature of the endpoints, baseline incidence can only be calculated for Ozone- and PM-related health effects.
In addition to baseline incidence, for each health effect, both the mean estimated incidence change and
corresponding percent change between post-control incidence reductions and the predicted incidence
baseline is presented.
Exhibits 6-2 and 6-3 present the primary incidence and benefit estimates associated with the
primary scenario. A 5th percentile, mean, and 95th percentile estimate for both incidence and benefits is
presented for each endpoint, as well as the simple mean benefit (calculated by multiplying the mean
estimate of incidence by the corresponding mean valuation). Total benefits are also displayed, calculated
by simply summing the simple mean of each endpoint.
Exhibit 6-4 displays alternative incidence and benefit calculations to those included in the primary
analysis. Where possible, a 5th percentile, mean, and 95th percentile estimate for incidence and/or benefits
is presented for each alternative endpoint. Exhibit 6-5 presents the aggregate uncertainty results (5th, mean,
and 95th percentiles) for PM- and ozone-related benefits, as well as for total benefits (PM + ozone).
Abt Associates Inc. 6-1 December 1999
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Exhibit 6-1 Baseline Percentages
Endpoint
Reference
2030 Control
Mean
Scenario
% of Baseline
PM-RELATED BASELINE PERCENTAGES
Ages 30+
Chronic Bronchitis
Respiratory-Related
Cardiovascular-Related
Asthma-Related ER Visits
Acute Bronchitis
Upper Respiratory Symptoms
Lower Respiratory Symptoms
Shortness of Breath
Work Loss Days
MRAD/Any-of-19
Pope etal. (1995)
Pooled Analysis
Pooled Analysis
Pooled Analysis
Schwartz etal. (1993)
Dockery et al. (1996)
Pope etal. (1991)
Schwartz etal. (1994)
Ostro etal. (1995)
Ostro(1987)
Pooled Analysis
4,307
2,296
1,162
485
899
7,933
86,476
87,123
17,434
682,898
3,628,527
0.161%
0.308%
0.028%
0.008%
0.088%
0.732%
0.067%
0.512%
0.280%
0.133%
0.214%
OZONE-RELATED BASELINE PERCENTAGES
Chronic Asthma
Respiratory-Related Hospital Admissions
Dysrhythmias Hospital Admissions
Asthma-Related ER Visits
MRAD/Any-of-19
McDonnell et al. (1999)
Pooled Analysis
Burnett etal. (1999)
Pooled Analysis
Pooled Analysis
432
1,012
269
346
2,226,463
0.196%
0.024%
0.033%
0.034%
0.132%
Abt Associates Inc.
6-2
December 1999
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Exhibit 6-2 Estimated PM-Related Health and Welfare Benefits Associated with Air Quality Changes Resulting from the Final Tier II Rule
2030 Control Scenario
Endpoint Reference
MORTALITY
Ages 30+ Pope et al. (1995)
CHRONIC ILLNESS
Chronic Bronchitis Pooled Analysis
HOSPITALIZATION
Respiratory-Related Pooled Analysis
Cardiovascular-Related Pooled Analysis
Asthma-Related ER Visits Schwartz et al. (1993)
MINOR ILLNESS
Acute Bronchitis Dockery et al. (1996)
Upper Respiratory Symptoms Pope et al. (1991)
Lower Respiratory Symptoms Schwartz et al. (1994)
Shortness of Breath Ostro et al. (1995)
Work Loss Days Ostro (1987)
MRAD/Any-of- 1 9 Pooled Analysis
WELFARE EFFECTS
Recreational Visibility Based on Chestnut and Rowe (1990)
TOTAL PRIMARY PM-RELATED BENEFITS
Avoided Incidence (cases/year)
5th %ile Mean 95th %ile
2,671 4,307 5,891
610 2,296 4,066
364 1,162 2,052
141 485 1,062
406 899 1,424
-40 7,933 16,313
25,475 86,476 144,578
39,947 87,123 131,148
4,697 17,434 29,508
597,804 682,898 771,811
3,034,085 3,628,527 4,177,213
Direct Economic Valuation
Monetary Benefits (millions 1997$)
5th %ile Mean 95th %ile
$3,193 $23,370 $57,022
$58 $727 $2,463
$4 $11 $18
$2 $7 $15
$0.1 $0.3 $0.4
<$0.1 $0.4 $1.1
$0.5 $2 $4
$0.4 $1 $2
<$0.1 $0.1 $0.3
$61 $70 $79
$97 $173 $253
$371
$4,510 - $58,675
Simple
Mean
$23,375
$728
$11
$7
$0.3
$0.4
$2
$1
$0.1
$70
$173
$371
$24,739
Abt Associates Inc.
6-3
December 1999
-------
Exhibit 6-3 Estimated Ozone-Related Health and Welfare Benefits Associated with Air Quality Changes Resulting from the Final Tier II
Rule 2030 Control Scenario
Endpoint Reference
CHRONIC ILLNESS
Chronic Asthma McDonnell et al. (1999)
HOSPITALIZATION
Respiratory-Related Pooled Analysis
Cardiovascular-Related
Dyrhythmias Burnett et al . ( 1 999)
Asthma-Related ER Visits Pooled Analysis
MINOR ILLNESS
MRAD/Any-of- 1 9 Pooled Analysis
WELFARE EFFECTS
Decreased Worker Productivity Crocker & Horst ( 1 98 1 ) and EPA
(1994)
Agriculture
TOTAL PRIMARY OZONE-RELATED BENEFITS
Avoided Incidence (cases/year)
5th %ile Mean 95th %ile
98 432 757
165 1,012 1,826
-11 269 538
109 346 551
1,014,435 2,226,463 3,414,837
Direct Economic Valuation
Direct Economic Valuation
Monetary Benefits (millions 1997$)
5th %ile Mean 95th %ile
$3 $13 $23
$2 $11 $21
$0 $2 $4
$0.0 $0.1 $0.2
$39 $101 $182
$142
$217
$278 - $688
Simple
Mean
$13
$11
$2
$0.1
$101
$142
$217
$486
Abt Associates Inc.
6-4
December 1999
-------
Exhibit 6-4 Alternative Benefit Calculations for the Tier II 2030 Control Scenario
Endpoint Reference/ Alternative Valuation
PM-RELATED ALTERNATIVE CALCULATIONS
Mortality
Ages 30+ Dockery et al . ( 1 993)
Life Years Lost, Ages: Pope et al. (1995)
30-34
35-44
45-54
55-64
65-74
75-84
85+
Chronic Bronchitis Reversals
Chronic Bronchitis Cost-of-Illness Valuation
Visibility
Recreational All U. S . Class I Areas
Eastern U.S.
Residential Continental U.S.
Household Soiling Damage ESEERCO ( 1 994)
Nitrogen Deposition 12 Estuaries
Avoided Incidence (cases/year)
5th %ile Mean 95th %ile
4,472 9,820 15,479
1,108 1,822 2,496
3,603 5,925 8,116
4,215 6,933 9,496
6,516 10,717 14,679
8,576 14,105 19,319
6,803 11,188 15,324
3,789 6,232 8,536
532 2,002 3,527
610 2,296 4,066
Direct Economic Valuation
Direct Economic Valuation
Direct Economic Valuation
Direct Economic Valuation
Direct Economic Valuation
Monetary Benefits (millions 1997$)
5th %ile Mean 95th %ile
$6,864 $53,577 $134,024
$11,949
-
-
-
-
-
-
.
$16 $281 $973
$188
$553
$423
$557
$61 $111 $201
$161
Simple
Mean
$53,297
$11,949
-
-
-
-
-
-
-
$281
$188
$553
$423
$557
$111
$161
Abt Associates Inc.
6-5
December 1999
-------
Exhibit 6-5 Measures of Aggregate Uncertainty in the Benefits Analysis
Benefits Aggregation
Total Ozone-Related Benefits
Total PM-Related Benefits
Total Tier II Primary Analysis Benefits (Ozone + PM)
Monetary Benefits (millions 1997$)
5th %ile Mean 95th %ile
$278 $485 $688
$4,510 $24,973 $58,675
$4,971 $25,458 $59,133
Simple Mean
$486
$24,739
$25,225
Abt Associates Inc.
6-6
December 1999
-------
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APPENDIX A: RESULTS FOR SUPPLEMENTARY CALCULATIONS AND SENSITIVITY ANALYSES
Exhibit A-l Supplemental Benefit Estimates for the Final Tier II Rule 2030 Control Scenario
Endpoint Reference Pollutant
Short- Term Mortality Schwartz etal. (1996) PM
Post-Neonatal Mortality Woodruff et al . ( 1 997) PM
Cardiac Burnett etal. (1997) Ozone
Moderate/Worse Asthma Ostro etal. (1991) PM
Asthma Attacks Whittemore and Korn (1980) PM
Asthma Attacks Whittemore and Korn (1980) Ozone
Restricted Activity Days Ostro (1987) PM
Avoided Incidence (cases/year)
5th %ile Mean 95th %ile
983 1,158 1,322
7 13 20
5,266 9,699 13,873
15,895 79,422 142,473
29,560 76,866 127,718
64,505 188,069 311,118
1,726,662 1,923,255 2,120,714
Monetary Benefits (millions 1997$)
5th %ile Mean 95th %ile
$980 $6,318 $14,493
$9 $71 $176
$71 $130 $188
$0 $3 $7
$1 $3 $6
$2 $8 $15
Simple
Mean
$6,283
$71
$130
$3
$3
$7
Abt Associates Inc.
A-l
December 1999
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Exhibit A-2 Sensitivity Analysis Results for the Tier II 2030 Control Scenario
Endpoint Reference/ Alternative Valuation
Avoided Incidence (cases/year)
5th %ile Mean 95th %ile
Monetary Benefits (millions 1997$)
5th %ile Mean 95th %ile
Simple
Mean
MORTALITY
Mortality Lags:
No Lag
8 Year Incidence Occurs 8th Year
1 5 Year Incidence Occurs 1 5th Year
1 5 Year Incidence Skewed Early
1 5 Year Incidence Skewed Late
4,307
4,307
4,307
4,307
4,307
$25,387
$18,042
$12,822
$22,656
$14,753
-
-
-
-
-
WELFARE EFFECTS
Nitrogen Deposition All Eastern Estuaries
Direct Economic Valuation
$307
$307
Abt Associates Inc.
A-2
December 1999
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Exhibit A-3 Sensitivity Analysis: Effect of Thresholds on Estimated PM-Related Mortality Based on Pope et al. (1995)
5000
o"
2 4000
g 3000
g 2000
2
"S
1000
0
0
10
15 20 25 30
35
40 45
Assumed Effect Threshold (Annual Mean PM2.5 (ug/m3))
Abt Associates Inc.
A-3
December 1999
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Exhibit A-4 Underlying Estimates and Weights for Pooled Estimate of PM-Related Respiratory Hospital Admissions
Study
Burnett et al. (1997), Toronto
Burnett et al. (1999), Toronto
Thurston et al. (1994), Toronto
Moolgavkar et al. (1997), Twin Cities
Schwartz (1994c), Twin Cities
Schwartz (1994a), Birmingham
Schwartz (1994b), Detroit
Schwartz (1996), Spokane
Schwartz (1996), New Haven
Schwartz (1996), Tacoma
Ages
affected
all ages
all ages
all ages
>64
>64
>64
>64
>64
>64
>64
Study
weights
0.03
0.01
0.02
0.19
0.12
0.18
0.23
0.14
0.06
0.03
Pooled estimate of respiratory hospital admissions
5th %ile
-34
1,310
-457
307
1,037
853
661
827
499
343
362
mean
32
2,495
667
751
1,624
1,308
1,031
1,364
1,400
1,699
1,162
95th %ile
95
4,491
1,743
1,277
2,271
1,852
1,524
1,947
2,319
3,079
2,052
Abt Associates Inc.
A-4
December 1999
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Exhibit A-5 Underlying Estimates and Weights for Pooled Estimate of Ozone-Related Respiratory Hospital Admissions
Study
Burnett et al. (1997), Toronto
Burnett et al. (1999), Toronto
Thurston et al. (1994), Toronto
Moolgavkar et al. (1997), Twin Cities
Schwartz (1994c), Twin Cities
Schwartz (1994b), Detroit
Schwartz (1996), New Haven
Schwartz (1996), Tacoma
Ages
affected
all ages
all ages
all ages
>64
>64
>64
>64
>64
Study
weights
0.01
0.01
0.01
0.33
0.28
0.26
0.08
0.02
Pooled estimate of respiratory
hospital admissions
5th %ile
4,040
1,065
89
509
-20
909
155
1,147
165
mean
6,148
1,508
1,170
948
467
1,399
994
2,691
1,012
95th %ile
8,258
1,955
2,317
1,382
965
1,893
1,847
4,280
1,826
Exhibit A-6 Underlying Estimates and Weights for Pooled Estimate of PM-Related Cardiovascular Hospital Admissions
Study
Burnett et al. (1997), Toronto
Burnett et al. (1999), Toronto
Schwartz and Morris (1995), Detroit
Schwartz (1999), 8 US Counties
Schwartz (1997), Tucson
Ages
Affected
all ages
all ages
>64
>64
>64
Study
Weights
0.33
0.03
0.30
0.25
0.09
Pooled estimate of cardiovascular hospital admissions
5th %ile
117
-44
213
472
307
141
Mean
229
346
421
751
1,035
485
95th %ile
347
755
628
1,041
1,765
1,062
Abt Associates Inc.
A-5
December 1999
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Exhibit A-7 Underlying Estimates and Weights for Pooled Estimate of Ozone-Related Asthma ER Visits
Study
Cody et al. (1992)
Weiseletal. (1995)
Stieb et al. (1996)
Ages
Affected
>26
>26
>29
Study
Weights
0.49
0.49
0.02
Pooled estimate of asthma ER
5th %ile
139
545
375
109
mean
345
754
2,931
346
95th %ile
540
950
5,341
551
Exhibit A-8 Underlying Estimates and Weights for Pooled Estimate of PM-Related Chronic Bronchitis Studies
Study
Abbey et al. (1993)
Abbey etal. (1995b)
Schwartz (1993)
Ages
Affected
>26
>26
>29
Study
Weights
0.32
0.16
0.52
Pooled estimate of chronic bronchitis
5th %ile
275
356
929
610
mean
2,025
2,819
2,310
2,296
95th %ile
3,670
5,134
3,609
4,066
Exhibit A-9 Underlying Estimates and Weights for Pooled Estimate of PM-related MRAD and Any-of-19 Studies
Study
Krupnick et al. (1990)
Ostro and Rothschild (1989b)
Ages
Affected
18-65
18-65
Study
Weights
0.004
0.996
Pooled estimate of MRAD Any of 19
5th %ile
1,808,712
3,066,913
3,034,085
mean
10,720,334
3,615,693
3,628,527
95th %ile
19,313,814
4,177,213
4,177,213
Abt Associates Inc.
A-6
December 1999
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Exhibit A-10 Underlying Estimates and Weights for Pooled Estimate of Ozone-related MRAD and Any-of-19 Studies
Study
Krupnick et al. (1990)
Ostro and Rothschild (1989b)
Ages
Affected
18-65
18-65
Study
Weights
0.04
0.96
Pooled estimate of MRAD Any of 19
5th %ile
821,285
1,014,435
1,014,435
mean
6,019,281
2,061,615
2,226,463
95th %ile
11,145,526
3,118,562
3,414,837
Abt Associates Inc.
A-7
December 1999
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APPENDIX B: OZONE CONCENTRATION-RESPONSE FUNCTIONS
Note that AO3 is defined as (O3 baSeime - O3 control), and that the change is defined as: (incidencecontrol -
incidencebaselme).
B.I SHORT-TERM OZONE-RELATED MORTALITY (FOUR U.S. STUDIES)
Four studies were used to estimate the possible relationship between ozone and increased mortality.
B.I.I Short-Term Mortality (U.S.) (Ito et al., 1996)
Ito and Thurston (1996) examined the relationship between daily non-accidental mortality and air
pollution levels in Cook County, Illinois from 1985 to 1990. They examined daily levels of ozone, PM10,
SO2, and CO, and found a significant relationship for ozone and PM10 with both pollutants in the model; no
significant effects were found for SO2 and CO. The ozone coefficient is estimated from a model with PM10.
The C-R function to estimate the change in short-term mortality associated with a change in ozone
is:
l^NonaccidentalMortality = -\yQ- (e~^0i - \)\-pop,
where:
y0 = county-level daily incidence for non-accidental deaths per person of any age
p = ozone coefficient = 0.000634 (Ito, 1998)53
AO3 = change in daily one-hour maximum ozone concentration (ppb)
pop = population of all ages
p = standard error of (3 = 0.000251 (Ito, 1998).
Incidence Rate. To estimate county-specific baseline mortality incidence, this analysis used the average
annual county mortality rate from 1994 through 1996 (U.S. Centers for Disease Control, 1999).
53The published paper has an incorrect coefficient and standard error; updated estimates were obtained from the author.
Abt Associates Inc. B-l December 1999
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B.1.2 Short-Term Mortality (U.S.) (Kinney et al., 1995)
Kinney et al. (1995) examined the relationship between daily non-accidental mortality and air
pollution levels in Los Angeles, California from 1985 to 1990. They examined ozone, PM10, and CO, and
found a significant relationship for each pollutant in single pollutant models. The effect for ozone dropped
to zero with the inclusion of PM10 in the model, while the effect for CO and PM10 appeared independent of
each other and were of a similar magnitude.
The C-R function to estimate the change in short-term mortality associated with a change in ozone
is:
l^NonaccidentalMortality = -\y0- (e~^0i - \)\-pop,
where:
y0 = county-level daily incidence for non-accidental deaths per person of any age
p = ozone coefficient = 0
AO3 = change in daily 1-hour maximum ozone concentration (ppb)
pop = population of all ages
= standard error of p = 0.000214
Incidence Rate. To estimate county-specific baseline mortality incidence, this analysis used the average
annual county mortality rate from 1994 through 1996 (U.S. Centers for Disease Control, 1999).
Coefficient Estimate (p). In a model with PM10, the ozone coefficient (p) for non-accidental mortality is
estimated from the relative risk (1.00) associated with a change in daily one-hour maximum ozone of 143
ppb (Kinney et al., 1995, Table 2 and Figure 3):
Standard Error ( p). The standard error ( p) was calculated as the average of the standard errors implied
by the reported lower and upper bounds of the relative risk (Kinney et al., 1995, Table 2 and Figure 3):
ln(1.06)
( In(l.OO) ln(0.94)^
= 0.000214.
Abt Associates Inc. B-2 December 1999
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B.1.3 Short-Term Mortality (U.S.) (Moolgavkar et al., 1995)
Moolgavkar et al. (1995) examined the relationship between daily non-accidental mortality and air
pollution levels in Philadelphia, Pennsylvania from 1973 to 1988. They examined ozone, TSP, and SO2 in
a three-pollutant model, and found a significant relationship for ozone and SO2; TSP was not significant.
The C-R function to estimate the change in short-term mortality associated with a change in ozone
is:
I^NonaccidentalMortality = -\yQ- (e~^'^ - \)\-pop,
where:
y0 = county-level daily incidence for non-accidental deaths per person of any age
p = ozone coefficient = 0.000611
AO3 = change in daily average ozone concentration (ppb)
pop = population of all ages
p = standard error of p = 0.000216
Incidence Rate. To estimate county-specific baseline mortality incidence, this analysis used the average
annual county mortality rate from 1994 through 1996 (U.S. Centers for Disease Control, 1999).
Coefficient Estimate (p). Based on a model with TSP and SO2, the coefficient (p) for non-accidental
mortality is estimated from the relative risk (1.063) associated with a change in daily average ozone of 100
ppb (Moolgavkar et al., 1995, Table 5):
Standard Error ( p). The standard error ( p) was calculated as the average of the standard errors implied
by the reported lower and upper bounds of the relative risk (Moolgavkar et al., 1995, Table 5):
fln(1.108)
IPO IPO
ln(1.063)
a, = " = O.OOQ216.
Abt Associates Inc. B-3 December 1999
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B.1.4 Short-Term Mortality (U.S.) (Samet et al., 1997)
Samet et al. (1997) examined the relationship between daily non-accidental mortality and air
pollution levels in Philadelphia, Pennsylvania from 1974 to 1988. They examined ozone, TSP, SO2, NO2,
and CO in a five-pollutant model, and found a significant relationship for each pollutant.
The C-R function to estimate the change in short-term mortality associated with a change in ozone
is:
I^Nonaccidental Mortality = -\yQ- (e~^'^ - \)\-pop,
where:
y0 = county-level daily incidence for non-accidental deaths per person of any age
p = ozone coefficient = 0.000936
AO3 = change in daily average ozone concentration (ppb)
pop = population of all ages
p = standard error of p = 0.000312
Incidence Rate. To estimate county-specific baseline mortality incidence, this analysis used the average
annual county mortality rate from 1994 through 1996 (U.S. Centers for Disease Control, 1999).
Coefficient Estimate (p). In a model with TSP, SO2, NO2, and CO, the ozone coefficient (p) for non-
accidental mortality is estimated from the relative risk (1.0191) associated with a change in the two-day
average ozone level of 20.219 ppb (Samet et al., 1997, Table 9):
= 0.000936.
(20.219)
Standard Error ( p). The standard error ( p) was calculated using the reported t-value (t=3) (Samet et al.,
1997, Table 9):
.000936
<7« = = 0.000312.
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B.2 CHRONIC ILLNESS
= population of In recent years, a number of studies have investigated the possible link between ozone and
the development of chronic illness. Abbey et al. (1991; 1993) reported a significant link between ozone and
the development of asthma, and Portney and Mullahy (1990) found ozone linked to sinusitis and hay fever.
A review of research data by EPA (1996a, p. 9-35) concluded that prolonged ozone exposure causes
structural changes in several regions of the respiratory tract, and the available epidemiological studies are
suggestive of a link between chronic health effects in humans and long-term ozone exposure. Most
recently, a study by McDonnell et al. (1999) carefully measured ozone exposure for Seventh Day
Adventists living in California.
B.2.1 Asthma Adult Onset (McDonnell et al., 1999)
The McDonnell et al. (1999) study used the same cohort of Seventh-Day Adventists as Abbey et
al. (1991; 1993), and examined the association between air pollution and the onset of asthma in adults
between 1977 and 1992. Males who did not report doctor-diagnosed asthma in 1977, but reported it in
1987 or 1992, had significantly higher ozone exposures, controlling for other covariates; no significant
effect was found between ozone exposure and asthma in females. No significant effect was reported for
females or males due to exposure to PM, NO2, SO2, or SO4.
The C-R function to estimate the change in chronic asthma is:
A Chronic Asthma = -
pop,
where:
y0 = annual asthma incidence rate per person (McDonnell et al., 1999, Table 4) = 0.00219
p = estimated O3 coefficient (McDonnell et al., 1999, Table 5) = 0.0277
AO3 = change in annual average 8-hour O3 concentration54
pop = population of non-asthmatic males ages 27 and older55 = 96.66% of males 27+
p = standard error of p (McDonnell et al., 1999, Table 5) = 0.0135
Incidence Rate. The annual incidence rate is derived by taking the number of new cases (32), dividing by
the number of individuals in the sample (972), as reported by (McDonnell et al., 1999, Table 4), and then
dividing by the 15 years in the sample.
54The eight-hour ozone concentration is defined as 9:00 A.M. to 4:59 P.M. The study used the 1973-1992 mean 8-hour
average ambient ozone concentration (McDonnell et al., 1999, p. 113).
55The population weighted average incidence of asthma in males 27 and older is 3.34 percent. Population data from U.S.
Census Bureau (1997, Table 14); asthma prevalence for males from Collins (1997, Table 9).
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B.3 HOSPITAL ADMISSIONS
B.3.1 Hospital Admissions for Asthma (Burnett et al., 1999, Toronto)
Burnett et al. (1999) examined the relationship between air pollution and hospital admissions for
individuals of all ages in Toronto, Canada froml980 to 1994. They estimated multiple pollutant models,
where pollutants for best fitting model were chosen using stepwise regression based on AIC criterion.
Asthma admissions were linked to O3, CO, and PM2 5_10. This C-R function is based on the results of this
three-pollutant model.
The C-R function to estimate the change in hospital admissions for asthma associated with daily
changes in ozone is:
A Asthma Admissions = - [y0 (e'^03 - !)] pop,
where:
y0 = daily hospital admission rate for asthma per person = 4.75 E-6
p = ozone coefficient = 0.00250
AO3 = change in daily average ozone concentration (ppb)
pop = population of all ages
p = standard error of p = 0.000718
Incidence Rate. Hospital admissions for obstructive lung disease (ICD-9 codes: 490-492, 496) are based
on first-listed discharge figures for the latest available year, 1994. The rate equals the annual number of
first-listed diagnoses for discharges (0.547 million) divided by the 1994 population (260.372 million), and
then divided by 365 days in the year. The discharge figures are from Graves and Gillum (1997, Table 1),
and the population data are from U.S. Bureau of the Census (1997, Table 14).
Coefficient Estimate (p). The estimated coefficient (p) is based on a 4.99 percent increase in admissions
due to a ozone change of 19.5 ppb (Burnett et al., 1999, Tables 1 and 5). This translates to a relative risk
of 1.0499. The coefficient is calculated as follows:
m(1.0499)
1 = \95 =0.00250.
Standard Error ( p). The standard error ( p) was calculated using the t-value (t=3.48) (Burnett, 1999):
0.00250
-= 0.000718.
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B.3.2 Hospital Admissions for Obstructive Lung Disease (Burnett et al., 1999, Toronto)
Burnett et al. (1999) examined the relationship between air pollution and hospital admissions for
individuals of all ages in Toronto, Canada froml980 to 1994. They estimated multiple pollutant models,
where pollutants for the best fitting model were chosen using stepwise regression based on AIC criterion.
Admissions for chronic obstructive pulmonary disease (COPD) were linked to O3 and PM2 5_10. This C-R
function is based on the results of this two-pollutant model.
The C-R function to estimate the change in hospital admissions for obstructive lung disease
associated with daily changes in ozone is:
A Obstructive Lung Disease Admissions = - I y0 (e^'A°3 - 1)1 pop ,
where:
y0 = daily hospital admission rate for obstructive lung disease per person = 5.76 E-6
p = ozone coefficient = 0.00303
AO3 = change in daily average ozone concentration (ppb)
pop = population of all ages
p = standard error of p = 0.00 110
Incidence Rate. Hospital admissions for respiratory infection (ICD-9 codes: 464, 466, 480-487, 494) are
based on first-listed discharge figures for the latest available year, 1994. The rate equals the annual
number of first-listed diagnoses for discharges (1.485 million) divided by the 1994 population (260.372
million), and then divided by 365 days in the year. The discharge figures are from Graves and Gillum
(1997, Table 1), and the population data are from U.S. Bureau of the Census (1997, Table 14).
Coefficient Estimate (p). The estimated coefficient (p) is based on a 6.08 percent increase in admissions
due to a ozone change of 19.5 ppb (Burnett et al., 1999, Tables 1 and 5). This translates to a relative risk
of 1.0608. The coefficient is calculated as follows:
m(1.0608)
1= =0.00303.
Standard Error ( p). The standard error ( p) was calculated using the t-value (t=2.74) (Burnett, 1999):
0.00303
2.74
=°-00110-
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B.3.3 Hospital Admissions for Respiratory Infection (Burnett et al., 1999, Toronto)
Burnett et al. (1999) examined the relationship between air pollution and hospital admissions for
individuals of all ages in Toronto, Canada from 1980 to 1994. They estimated multiple pollutant models,
where pollutants for the best fitting model were chosen using stepwise regression based on AIC criterion.
Respiratory infection admissions were linked to O3, NO2, and PM2 5. This C-R function is based on the
results from this three-pollutant model.
The C-R function to estimate the change in hospital admissions for respiratory infection associated
with daily changes in ozone is:
A Re spiratory Infection Admissions = - I y0 (e~^°3 - \)\- pop,
where:
y0 = daily hospital admission rate for respiratory infection per person =1.56 E-5
p = ozone coefficient = 0.00198
AO3 = change in daily average ozone concentration (ppb)
pop = population of all ages
p = standard error of p = 0.000520
Incidence Rate. Hospital admissions for respiratory infections (ICD-9 codes: 464-466, 480-486, 490-
494, 496) are based on first-listed discharge figures for the latest available year, 1994. The rate equals the
annual number of first-listed diagnoses for discharges (2.452 million) divided by the 1994 population
(260.372 million), and then divided by 365 days in the year. The discharge figures are from Graves and
Gillum (1997, Table 1), and the population data are from U.S. Bureau of the Census (1997, Table 14).
Coefficient Estimate (p). The estimated coefficient (p) is based on a 3.93 percent increase in admissions
due to a ozone change of 19.5 ppb (Burnett et al., 1999, Tables 1 and 5). This translates to a relative risk
of 1.0393. The coefficient is calculated as follows:
m(1.0393)
ft = - - -= 0.00198 .
Standard Error ( p). The standard error ( p) was calculated using the t-value (t=3.80) (Burnett, 1999):
0.00198
3.80
=a°00520-
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B.3.4 Hospital Admissions for All Respiratory (Burnett et al., 1997, Toronto)
Burnett et al. (1997) examined the relationship between air pollution and hospital admissions for
individuals of all ages in Toronto, Canada during the summers of 1992-1994. All respiratory admissions
were linked to coefficient of haze (COH) and O3; other PM measures were less strongly linked. In two
pollutant models, they found that CO, NO2, and SO2 were not significant, controlling for COH. They
found that O3 was still significant, controlling for COH. This C-R function is based on the results from the
four-pollutant model (PM25_10, O3, NO2, and SO2) to estimate all respiratory incidence.
The C-R function to estimate the change in all respiratory hospital admissions associated with
daily changes in ozone is:
Mil Re spiratory Admissions = - |y0 (e~l 3 - 1JJ pop,
where:
y0 = daily hospital admission rate for all respiratory admissions per person = 2.58 E-5
P = O3 coefficient = 0.00498
AO3 = change in daily 12-hour average O3 concentration (ppb)56
pop = population of all ages
p = standard error of p = 0.00106
Incidence Rate. Hospital admissions for all respiratory causes (ICD-9 codes: 464-466, 480-486, 490-494,
496) are based on first-listed discharge figures for the latest available year, 1994. The rate equals the
annual number of first-listed diagnoses for discharges (2.452 million) divided by the 1994 population
(260.372 million), and then divided by 365 days in the year. The discharge figures are from Graves and
Gillum (1997, Table 1), and the population data are from U.S. Bureau of the Census (1997, Table 14).
Coefficient Estimate (p). The estimated coefficient (p) is based on a relative risk of 1.059 due to a change
of 11.50 ppb in the daily average for O3 (Burnett et al., 1997, Tables 2 and 6). The coefficient is
calculated as follows:
ln(L059)
-=0.00498.
Standard Error ( p). The standard error ( p) was calculated using the t-value (t=4.71) (Burnett et al.,
1997, Table 6)
.00498
0B = = 0.00106.
1 4.71
56 Burnett et al. (1997, Table 2 and p. 614) reported using the daytime average ozone level from 8 A.M. to 8 P.M.
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B.3.5 Hospital Admissions for All Respiratory (Thurston et al., 1994, Toronto)
Thurston et al. (1994) examined the relationship between air pollution and hospital admissions for
individuals of all ages in Toronto, Canada, for six weeks in July and August 1986-1988. In single-pollutant
models, ozone and various measures of PM were linked to all respiratory admissions. In two-pollutant
models, ozone was still significant, but measures of PM were often not significant; only H+ was significant.
This C-R function is based on the results of a two-pollutant model (PM25 and ozone).
The C-R function to estimate the change in all respiratory hospital admissions associated with
daily changes in ozone is:
A All Respiratory Admissions - /3 A<93 pop,
where:
p = ozone coefficient = 1.68 E-8
AO3 = change in daily one-hour maximum ozone concentration (ppb)
pop = population of all ages
p = standard error of (3 = 9.71 E-9 .
Coefficient Estimate (p). Based on a linear model with PM2 5, the one-hour maximum ozone coefficient
comes from an estimated coefficient of 0.0404, which estimates admissions per ppb of ozone (Thurston et
al., 1994, Table 3).57 The population of Toronto was estimated to be 2.4 million (U.S. EPA, 1997a, Table
D-7). We estimated a coefficient estimating admissions per person per ppb of ozone as follows:
0.0404
Standard Error ( p). The standard error ( p) was calculated in a similar fashion (Thurston et al., 1994,
Table 3):
57The 812 Retrospective analysis (U.S. EPA, 1997a, Table D-7) used an ozone coefficient based on a model with PM10.
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B.3.6 Hospital Admissions for Pneumonia (Moolgavkar et al., 1997, Minneapolis)
Moolgavkar et al. (1997) examined the relationship between air pollution and hospital admissions
for individuals 65 and older in Minneapolis-St. Paul, Minnesota, from January 1986 to December 1991. In
a four pollutant model examining pneumonia admissions in Minneapolis, ozone was significant, while NO2,
SO2, and PM10 were not significant. This C-R function is based on the results from the four-pollutant
model to estimate pneumonia incidence.
The C-R function to estimate the change in hospital admissions for pneumonia associated with
daily changes in ozone is:
/^Pneumonia Admissions = - \y0 (e~^'^°3 - \)\ pop ,
where:
y0 = daily hospital admission rate for pneumonia per person = 5.30 E-5
p = O3 coefficient = 0.00370
AO3 = change in daily average O3 concentration (ppb)
pop = population of ages 65 and older
p = standard error of p = 0.00103
Incidence Rate. Hospital admissions for pneumonia (ICD-9 codes: 480-487) are based on first-listed
discharge figures for the latest available year, 1994. The rate equals the annual number of first-listed
diagnoses for discharges (0.642 million) divided by the 1994 population of individuals 65 years and older
(33.162 million), and then divided by 365 days in the year. The discharge figures are from Graves and
Gillum (1997, Table 1), and the population data are from U.S. Bureau of the Census (1997, Table 14).
Coefficient Estimate (p). The estimated coefficient (p) is based on a 5.7 percent increase in admissions
due to a O3 change of 15 ppb (Moolgavkar et al., 1997, Table 4 and p. 366); the model with a 130 df
smoother was reported to be optimal (p. 368). This translates to a relative risk of 1.057. The coefficient
is calculated as follows:
. 0003,0.
Standard Error ( p). The standard error ( p) was calculated as the average of the standard errors implied
by the reported lower and upper bounds of the relative risk (Moolgavkar et al., 1997, Table 4):
( ln(1.089) ln(1.057)
~~
ln(1.057) ln(1.025)
~~~
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-^ = 0.00103.
B.3.7 Hospital Admissions for COPD (Moolgavkar et al., 1997, Minneapolis)
Moolgavkar et al. (1997) examined the relationship between air pollution and hospital admissions
for individuals 65 and older in Minneapolis-St. Paul, Minnesota, from January 1986 to December 1991.
No significant effect found for any pollutant; the effect for ozone was marginally significant. This C-R
function is based on the results from a three-pollutant model (O3, CO, PM10) to estimate COPD incidence.
The C-R function to estimate the change in hospital admissions for COPD associated with daily
changes in ozone is:
A COPD Admissions = -[y0- (V3 A°3 - i;] pop,
where:
y0 = daily hospital admission rate for COPD per person = 3.75 E-5
P = O3 coefficient = 0.00274
AO3 = change in daily average O3 concentration (ppb)
pop = population of ages 65 and older
p = standard error of p = 0.00170
Incidence Rate. Hospital admissions for COPD (ICD-9 codes: 490-496) are based on first-listed
discharge figures for the latest available year, 1994. The rate equals the annual number of first-listed
diagnoses for discharges (0.454 million) divided by the 1994 population of individuals 65 years and older
(33.162 million), and then divided by 365 days in the year. The discharge figures are from Graves and
Gillum (1997, Table 1), and the population data are from U.S. Bureau of the Census (1997, Table 14).
Coefficient Estimate (p). The estimated coefficient (p) is based on a 4.2 percent increase in admissions
due to a O3 change of 15 ppb (Moolgavkar et al., 1997, Table 4 and p. 366); the model with a 100 df
smoother was reported to be optimal (p. 368). This translates to a relative risk of 1.042. The coefficient
is calculated as follows:
ln(L042)
J3= =0.00274.
Standard Error ( p). The standard error ( p) was calculated as the average of the standard errors implied
by the reported lower and upper bounds of the relative risk (Moolgavkar et al., 1997, Table 4):
(ln(1.094) ln(1.042)
ln(1.042) ln(0.99)
15 "
1.96 1.96
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= 0.00170.
B.3.8 Hospital Admissions for Pneumonia (Schwartz, 1994c, Minneapolis)
Schwartz (1994c) examined the relationship between air pollution and hospital admissions for
individuals 65 and older in Minneapolis-St. Paul, Minnesota, from January 1986 to December 1989. In a
two-pollutant model, Schwartz found PM10 significantly related to pneumonia; ozone was weakly linked to
pneumonia. This C-R function is based on the results of the two-pollutant model (PM10, O3) to estimate
pneumonia incidence.
The C-R function to estimate the change in hospital admissions for pneumonia associated with
daily changes in ozone is:
/^Pneumonia Admissions = - \y0 (e~^'^°3 - \)\ pop ,
where:
y0 = daily hospital admission rate for pneumonia per person = 5.30 E-5
p = O3 coefficient = 0.00280
AO3 = change in daily average O3 concentration (ppb)
pop = population of ages 65 and older
p = standard error of p = 0.00172
Incidence Rate. Hospital admissions for pneumonia (ICD-9 codes: 480-487) are based on first-listed
discharge figures for the latest available year, 1994. The rate equals the annual number of first-listed
diagnoses for discharges (0.642 million) divided by the 1994 population of individuals 65 years and older
(33.162 million), and then divided by 365 days in the year. The discharge figures are from Graves and
Gillum (1997, Table 1), and the population data are from U.S. Bureau of the Census (1997, Table 14).
Coefficient Estimate (p). Based on a model with ozone, the coefficient (p) is estimated from the relative
risk (1.15) associated with a 50 ppb change in the daily average ozone level (Schwartz, 1994c, Table 4 and
p. 369):
.
j8 = = 0.00280.
Standard Error ( p). The standard error ( p) was calculated as the average of the standard errors implied
by the reported lower and upper bounds of the relative risk (Schwartz, 1994c, Table 4):
ln(1.36)
ln(0.97)
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=0.00172.
B.3.9 Hospital Admissions for Pneumonia (Schwartz, 1994b, Detroit)
Schwartz (1994b) examined the relationship between air pollution and hospital admissions for
individuals 65 and older in Detroit, Michigan, from January 1986 to December 1989. In a two-pollutant
model, Schwartz found both PM10 and ozone significantly linked to pneumonia and COPD; no significant
link to asthma admissions was found for either pollutant. We use the results of this two-pollutant model.
The C-R function to estimate the change in hospital admissions for pneumonia associated with
daily changes in ozone is:
/^Pneumonia Admissions = - \y0 (e~^'^°3 - \)\ pop,
where:
y0 = daily hospital admission rate for pneumonia per person = 5.18 E-5
p = O3 coefficient (Schwartz, 1994b, Table 4) = 0.00521
AO3 = change in daily average O3 concentration (ppb)
pop = population of ages 65 and older
p = standard error of p (Schwartz, 1994b, Table 4) = 0.0013
Incidence Rate. Hospital admissions for pneumonia (ICD-9 codes: 480-486) are based on first-listed
discharge figures for the latest available year, 1994. The rate equals the annual number of first-listed
diagnoses for discharges (0.627 million) divided by the 1994 population of individuals 65 years and older
(33.162 million), and then divided by 365 days in the year. The discharge figures are from Graves and
Gillum (1997, Table 1), and the population data are from U.S. Bureau of the Census (1997, Table 14).
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B.3.10 Hospital Admissions for COPD (Schwartz, 1994b, Detroit)
Schwartz (1994b) examined the relationship between air pollution and hospital admissions for
individuals 65 and older in Detroit, Michigan, from January 1986 to December 1989. In a two-pollutant
model, Schwartz found both PM10 and ozone significantly linked to pneumonia and COPD; no significant
link to asthma admissions was found for either pollutant. We use the results of this two-pollutant model.
The C-R function to estimate the change in hospital admissions for COPD associated with daily
changes in O3 is:
A COPD Admissions = -[y0- (V3 A°3 - i;] pop,
where:
y0 = daily hospital admission rate for COPD per person = 3.05 E-5
p = O3 coefficient (Schwartz, 1994b, Table 4) = 0.00549
AO3 = change in daily average O3 concentration
pop = population of ages 65 and older
= standard error of p (Schwartz, 1994b, Table 4) = 0.00205
Incidence Rate. Hospital admissions for COPD (ICD-9 codes: 491-492, 494-496) are based on first-
listed discharge figures for the latest available year, 1994. The rate equals the annual number of first-listed
diagnoses for discharges (0.369 million) divided by the 1994 population of individuals 65 years and older
(33.162 million), and then divided by 365 days in the year. The discharge figures are from Graves and
Gillum (1997, Table 1), and the population data are from U.S. Bureau of the Census (1997, Table 14).
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B.3.11 Hospital Admissions for All Respiratory (Schwartz, 1995, New Haven)
Schwartz (1996) examined the relationship between air pollution and hospital admissions for
individuals 65 and older in New Haven, Connecticut, from January 1988 to December 1990. In single-
pollutant models, PM10 and SO2 were significant, while ozone was marginally significant. In two-pollutant
models, ozone was significant in one of two models, and had stable coefficient estimates; PM10 was
significant in two of two models, but had less stable estimates. SO2 was significant in one of four models.
The C-R function in this analysis is based on a two-pollutant model with ozone and PM10.
The C-R function to estimate the change in all respiratory hospital admissions associated with
daily changes in ozone is:
A All Re spiratory Admissions = -\y0-(e ^A°3 - \)\-pop,
where:
y0 = daily hospital admissions for all respiratory conditions per person 65 and older = 1.187 E-4
p = ozone coefficient = 0.00265
AO3 = change in daily average ozone concentration (ppb)
pop = population of ages 65 and older
p = standard error of p = 0.00140
Incidence Rate. All respiratory hospital admissions (ICD-9 codes: 460-519) are based on first-listed
discharge figures for the latest available year, 1994. The rate equals the national annual number of first-
listed diagnoses for discharges (1.437 million) divided by the 1994 U.S. population of individuals 65 years
and older (33.162 million), and then divided by 365 days in the year. The discharge figures are from
Graves and Gillum (1997, Table 1), and the population data are from U.S. Bureau of the Census (1997,
Table 14).
Coefficient Estimate (p). Based on a model with PM10, the coefficient (p) is estimated from the relative
risk (1.07) associated with a change in ozone exposure of 50 (jg/m3 (Schwartz, 1995, Table 3 and p.
535):58
inn rm
= 0.00265.
1.96.
58A conversion of 1.96 ug/m3 per ppb is used, based on a density of ozone of 1.96 grams per liter (at 25 degrees Celsius).
Since there are 1000 liters in a cubic meter and a million ug in a gram, this density means that there are 1.96 billion ug of ozone in a
cubic meter of ozone. If a cubic meter has just one ppb of ozone, then this means that this particular cubic meter has 1.96 ug of ozone
(i.e., one ppb = 1.96 ug/m3).
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Standard Error ( p). The standard error ( p) was calculated as the average of the standard errors implied
by the reported lower and upper bounds of the relative risk (Schwartz, 1995, Table 3).
V 50 71.96 50/1.96 _..,,
- - = ao°144
(ln(1.07) In(l.OO)
a -g = 0.0014Q.
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B.3.12 Hospital Admissions for All Respiratory (Schwartz, 1995, Tacoma)
Schwartz (1996) examined the relationship between air pollution and hospital admissions for
individuals 65 and older in Tacoma, Washington, from January 1988 to December 1990. In single-
pollutant models, PM10, ozone, and SO2 were all significant. In two-pollutant models, ozone was
significant in two of two models, and had stable coefficient estimates; PM10 was significant in one of two
models, but had less stable estimates; SO2 was not significant in either of the two-pollutant models. The
C-R function in this analysis is based on a two-pollutant model with ozone and PM10.
The C-R function to estimate the change in hospital admissions for all-respiratory causes
associated with daily changes in ozone is:
A All Re spiratory Admissions = -\y0- (e /j'A°3 - \)\ pop,
where:
y0 = daily hospital admissions for all respiratory conditions per person 65 and older = 1.187 E-4
p = ozone coefficient = 0.00715
AO3 = change in daily average ozone concentration (ppb)
pop = population of ages 65 and older
p = standard error of p = 0.00257
Incidence Rate. All respiratory hospital admissions (ICD-9 codes: 460-519) are based on first-listed
discharge figures for the latest available year, 1994. The rate equals the national annual number of first-
listed diagnoses for discharges (1.437 million) divided by the 1994 U.S. population of individuals 65 years
and older (33.162 million), and then divided by 365 days in the year. The discharge figures are from
Graves and Gillum (1997, Table 1), and the population data are from U.S. Bureau of the Census (1997,
Table 14).
Coefficient Estimate (p). Based on a model with PM10, the coefficient (p) is estimated from the relative
risk (1.20) associated with a change in ozone exposure of 50 (jg/m3 (Schwartz, 1995, Table 6 and p.
535):59
inn ?.m
= 0.00715.
1.96
59A conversion of 1.96 ug/m3 per ppb is used, based on a density of ozone of 1.96 grams per liter (at 25 degrees Celsius).
Since there are 1000 liters in a cubic meter and a million ug in a gram, this density means that there are 1.96 billion ug of ozone in a
cubic meter of ozone. If a cubic meter has just one ppb of ozone, then this means that this particular cubic meter has 1.96 ug of ozone
(i.e., one ppb = 1.96 ug/m3).
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Standard Error ( p). The standard error ( p) was calculated as the average of the standard errors implied
by the reported lower and upper bounds of the relative risk (Schwartz, 1995, Table 6):
(ln(1.37)
ln(1.20)
, 0.00257.
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B.3.13 Hospital Admissions for Cardiac (Burnett et al., 1997, Toronto)
Burnett et al. (1997) examined the relationship between air pollution and hospital admissions for
individuals of all ages in Toronto, Canada during the summers of 1992-1994. COH and ozone were
significantly linked to cardiac admissions; other PM measures less strongly linked. In two-pollutant
models, they found CO, NO2, and SO2 were not significant, when controlling for COH. Ozone was
significant, controlling for COH. In four-pollutant models, COH and O3 were both significant; no effect
for NO2 and SO2. The C-R function in this analysis is based on a two-pollutant model with ozone and
PM2.5.10.
The C-R function to estimate the change in cardiac hospital admissions associated with daily
changes in ozone is:
A Cardiac Admissions=-1 y0 (V^'A°3 - \) I pop,
where:
y0 = daily hospital admission rate for cardiac problems per person = 3.81 E-5
p = O3 coefficient = 0.00531
AO3 = change in daily 12-hour average O3 concentration (ppb)60
pop = population of all ages
p = standard error of p = 0.00142
Incidence Rate. Hospital admissions for cardiac (ICD-9 codes: 410-414, 427-428) are based on first-
listed discharge figures for the latest available year, 1994. The rate equals the annual number of first-listed
diagnoses for discharges (3.617 million) divided by the 1994 population (260.372 million), and then
divided by 365 days in the year. The discharge figures are from Graves and Gillum (1997, Table 1), and
the population data are from U.S. Bureau of the Census (1997, Table 14).
Coefficient Estimate (p). The estimated coefficient (p) is based on a relative risk of 1.063 due to a O3
change of 11.50 ppb (Burnett et al., 1997, Tables 2 and 5). The coefficient is calculated as follows:
ln( 1.063)
Standard Error ( p). The standard error ( p) was calculated using the t-value (t=3.74) (Burnett et al.,
1997, Table 5)
.00531
=0.00142.
60 Burnett et al. (1997, Table 2 and p. 614) reported using the daytime average ozone level from 8 A.M. to 8 P.M.
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B.3.14 Hospital Admissions for Dysrhythmias (Burnett et al., 1999, Toronto)
Burnett et al. (1999) examined the relationship between air pollution and hospital admissions for
individuals of all ages in Toronto, Canada froml980 to 1994. They estimated multiple pollutant models,
where pollutants for best fitting model were chosen using stepwise regression based on AIC criterion.
Dysrhythmias admissions were linked to O3, CO, and PM2 5. This C-R function is based on the results of
this three-pollutant model.
The C-R function to estimate the change in hospital admissions for dysrhythmias associated with
daily changes in ozone is:
/^Dysrhythmias Admissions = - [y0 -(e~^^ - !)] pop,
where:
y0 = daily hospital admission rate for dysrhythmias per person = 6.46 E-6
p = ozone coefficient = 0.00168
AO3 = change in daily average ozone concentration (ppb)
pop = population of all ages
p = standard error of p = 0.00103
Incidence Rate. Hospital admissions for dysrhthmias (ICD-9 code: 427) are based on first-listed
discharge figures for the latest available year, 1994. The rate equals the annual number of first-listed
diagnoses for discharges (0.614 million) divided by the 1994 population (260.372 million), and then
divided by 365 days in the year. The discharge figures are from Graves and Gillum (1997, Table 1), and
the population data are from U.S. Bureau of the Census (1997, Table 14).
Coefficient Estimate (p). The estimated coefficient (p) is based on a 3.34 percent increase in admissions
due to a ozone change of 19.5 ppb (Burnett et al., 1999, Tables 1 and 5). This translates to a relative risk
of 1.0334. The coefficient is calculated as follows:
m(1.0334)
P= =0.00168.
Standard Error ( p). The standard error ( p) was calculated using the t-value (t=1.63) (Burnett, 1999):
0.00168
163
=0-00103-
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B.4 EMERGENCY ROOM VISITS
There is a wealth of epidemiological information on the relationship between air pollution and
hospital admissions for various respiratory and cardiovascular diseases; in addition, some studies have
examined the relationship between air pollution and ER visits. Because most ER visits do not result in an
admission to the hospital ~ the majority of people going to the ER are treated and return home we treat
hospital admissions and ER visits separately, taking account of the fraction of ER visits that do get
admitted to the hospital, as discussed below.
The only types of ER visits that have been explicitly linked to ozone in U.S. and Canadian
epidemiological studies are asthma visits. However, it seems likely that ozone may be linked to other types
of respiratory-related ER visits.
B.4.1 Emergency Room Visits for Asthma (Cody et al., 1992, Northern NJ)
Cody et al. (1992) examined the relationship between ER visits and air pollution for persons of all
ages in central and northern New Jersey, from May to August in 1988-1989. In a two pollutant model,
ozone was linked to asthma visits, and no effect was seen for SO2. PM10 considered in separate analysis,
because of limited (every sixth day) sampling; no significant effect was seen for PM10.
The C-R function to estimate the change in asthma ER visits associated with daily changes in
ozone is:
A Asthma ER Visits = A <93 pop- (\ - 0.37),
BasePop
where:
p = ozone coefficient (Cody et al., 1992, Table 6) = 0.0203
BasePop = baseline population in northern New Jersey61 = 4,436,976
AO3 = change in daily five-hour average ozone concentration (ppb)62
pop = population of all ages
p = standard error of p (Cody et al., 1992, Table 6) = 0.00717
Correction for Double Counting. Smith et al. (1997, p. 789) reported that in 1987 there were 445,000
asthma admissions and 1.2 million asthma ER visits. Assuming that all asthma hospital admissions pass
through the ER room, then 37% of ER visits end up as hospital admissions. This percentage is then
subtracted from the estimated change in asthma-related ER visits.
61The population estimate is based on the 1990 population for the eight counties containing hospitals or in the central core
of the study. Cody et al. (1992, Figure 1) presented a map of the study area; the counties are: Bergen, Essex, Hudson, Middlesex,
Morris, Passaic, Somerset, and Union.
62The coefficients in the study were based on the five-hour (10:00 am to 2:59 pm) ozone average in ppm; they have been
converted to ppb.
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B.4.2 Emergency Room Visits for Asthma (Weisel et al., 1995, Northern NJ)
Weisel et al. (1995) examined the relationship between ER visits and air pollution for persons of
all ages in central and northern New Jersey, from May to August in 1986-1990. A significant relationship
was reported for ozone.
The C-R function to estimate the change in asthma ER visits associated with daily changes in
ozone is:
A Asthma ER Visits = A O, pop- (I - 0.37),
BasePop 3 ^ ^ ' y
where:
p = ozone coefficient = 0.0443
BasePop = baseline population in northern New Jersey63 = 4,436,976
AO3 = change in daily five-hour average ozone concentration (ppb)64
pop = population of all ages
p = standard error of p = 0.00723
Correction for Double Counting. Smith et al. (1997, p. 789) reported that in 1987 there were 445,000
asthma admissions and 1.2 million asthma ER visits. Assuming that all asthma hospital admissions pass
through the ER room, then 37% of ER visits end up as hospital admissions. This percentage is then
subtracted from the estimated change in asthma-related ER visits.
Coefficient Estimate (p). The coefficient used in the C-R function is a weighted average of the coefficients
in Weisel et al. (1995, Table 2) using the inverse of the variance as the weight:
A.
= 0.0443.
1
z = 1986 ft
1990
Standard Error ( p). The standard error of the coefficient ( p) is calculated as follows, assuming that the
estimated year-specific coefficients are independent:
63The population estimate is based on the 1990 population for the eight counties containing hospitals or in the central core
of the study. Cody et al. (1992, Figure 1) presented a map of the study area; the counties are: Bergen, Essex, Hudson, Middlesex,
Morris, Passaic, Somerset, and Union.
64The coefficients in the study were based on the five-hour (10:00 am to 2:59 pm) ozone average in ppm; they have been
converted to ppb.
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= var
( 1990 0 \
Zri
2
!=1986 " ft
1990 i
y x
V!=1986 ^ft y1
/ 1990 0 "N
y Pi
^ffft
7
v y
1990
var
!=1986
This eventually reduces down to:
= I-= 0.00723.
V7
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B.4.3 Emergency Room Visits for Asthma (Stieb et al., 1996, New Brunswick)
Stieb et al. (1996) examined the relationship between ER visits and air pollution for persons of all
ages in St. John, New Brunswick, Canada, from May through September in 1984-1992. Ozone was
significantly linked to ER visits, especially when ozone levels exceeded 75 ppb.
The C-R function to estimate the change in asthma ER visits associated with daily changes in
ozone is:
A Asthma ER Visits = A O, pop- (I - 0.37),
BasePop 3 ^ ^ ' '
where:
p = ozone coefficient (Stieb et al., 1996, Table 2 linear model) = 0.0035
BasePop = baseline population in Saint John, New Brunswick (Stieb et al., 1996, p. 1354) =
125,000
AO3 = change in the daily one-hour maximum ozone concentration (ppb)
pop = population of all ages
p = standard error of p (Stieb et al., 1996, Table 2 linear model) = 0.0018
Correction for Double Counting. Smith et al. (1997, p. 789) reported that in 1987 there were 445,000
asthma admissions and 1.2 million asthma ER visits. Assuming that all asthma hospital admissions pass
through the ER room, then 37% of ER visits end up as hospital admissions. This percentage is then
subtracted from the estimated change in asthma-related ER visits.
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B.5 ACUTE MORBIDITY
B.5.1 Any of 19 Respiratory Symptoms: Krupnick (1990)
Krupnick et al. (1990) estimated the impact of air pollution on the incidence of any of 19
respiratory symptoms or conditions in 570 adults and 756 children living in three communities in Los
Angeles, California from September 1978 to March 1979. Krupnick et al. (1990) listed 13 specific
"symptoms or conditions": head cold, chest cold, sinus trouble, croup, cough with phlegm, sore throat,
asthma, hay fever, doctor-diagnosed ear infection, flu, pneumonia, bronchitis, and bronchiolitis. The other
six symptoms or conditions are not specified.
In their analysis, they included coefficient of haze (COH, a measure of particulate matter
concentrations), ozone, NO2, and SO2, and they used a logistic regression model that takes into account
whether a respondent was well or not the previous day. A key difference between this and the usual logistic
model, is that the model they used includes a lagged value of the dependent variable. In single-pollutant
models, daily O3, COH, and SO2 were significantly related to respiratory symptoms in adults. Controlling
for other pollutants, they found that ozone was still significant. The results were more variable for COH
and SO2, perhaps due to collinearity. NO2 had no significant effect. No effect was seen in children for any
pollutant. The results from the two-pollutant model with COH and ozone are used to develop a C-R
function.
The C-R function used to estimate the change in ARD2 associated with a change in daily one-hour
maximum ozone is based on Krupnick et al. (1990, p. 12):65
where:
P* = first derivative of the stationary probability = 0.000137
AO3 = change in daily one-hour maximum ozone concentration (ppb)66
pop = population aged 18-65 years old67
p = standard error of p* = 0.0000697
Coefficient Estimate (p*). The logistic regression model used by Krupnick et al. (1990) takes into account
whether a respondent was well or not the previous day. Following Krupnick et al. (p. 12), the probability
that one is sick is on a given day is:
probability(AKDT) = ^
65Krupnick and Kopp (1988, p. 2-24) and ESEERCO (1994, p. V-32) used the same C-R functional form as that used here.
66Krupnick et al. (1990) used parts per hundred million (pphm) to measure ozone; the coefficient used here is based on ppb.
67The coefficient estimates are based on the sample of "adults," and assumes that individuals 18 and older were considered
adult. According to Krupnick et al. (1990, Table 1), about 0.6 percent of the study sample was over the age of 60. This is a relatively
small fraction, so it is further assumed that the results do not apply to individuals over the age of 65.
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p, = probability (ARD2\sickness or not t _,) = B +B -AKDI +X-B >fori = *-*,!
1 /? "o "l f~ 1 "
where:
X = the matrix of explanatory variables
Po = the probability of sickness on day t, given wellness on day t-1, and
P! = the probability of sickness on day t, given sickness on day t-1.
In other words, the transition probabilities are estimated using a logistic function; the key difference
between this and the usual logistic model, is that the model includes a lagged value of the dependent
variable.
To calculate the impact of ozone (or other pollutants) on the probability of ARD2, it is possible, in
principle, to estimate ARD2 before the change in ozone and after the change:
MRD2 = ARD2after - ARD2before .
However the full suite of coefficient estimates are not available.68 Rather than use the full suite of
coefficient values, the impact of ozone on the probability of ARD2 may be approximated by the derivative
of ARD2 with respect to ozone:69
dprobability(ARDI) P0 (l - A) ' P ' \Pi + (* ~ Po}] ,
where p is the reported logistic regression coefficient for ozone. The change in the incidence of ARD2
associated with a given change in ozone is then estimated by:
3ARD2 &ARD2
dO3 = A<93
&ARD2
68The model without NO2 (Krupnick et al., 1990, Table V equation 3) was used in this analysis, but the full suite of
coefficient estimates for this model were not reported. Krupnick et al. (Table IV) reported all of the estimated coefficients for a model
of children and for a model of adults when four pollutants were included (ozone, COH, SO2, and NO2). However, because of high
collinearity between NO2 and COH, NO2 was dropped from some of the reported analyses (Krupnick et al., p. 10), and the resulting
coefficient estimates changed substantially (see Krupnick et al., Table V). Both the ozone and COH coefficients dropped by about a
factor of two or more.
69The derivative result is reported by Krupnick et al. (1990, p. 12).
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This analysis uses transition probabilities obtained from Krupnick et al. as reported by ESEERCO
(1994, p. V-32) for the adult population: pl = 0.7775 and p0 = 0.0468. This implies:
, 0.0468(!- 0.7775)-0.00055-[0.7775+ (l- 0.0468)]
(1- 0.7775 + 0.0468)2
Standard Error ( p). The standard error for the coefficient ( p) is derived using the reported standard
error of the logistic regression coefficient in Krupnick et al. (1990, Table V):
Bhigh = 0.00055+ (1.96- 0.00027) = 0.00108
0.0468 (1 - 0.7775) 0.00108 [0.7775 + (1 - 0.0468)1
=> A** = r^ '^r^ = 0.000268
"*"* (I- 0.7775 + 0.0468)2
$h,Kh-?> (0.000268-0.000137)
«».- = -isr= [^ =00000668
= 0.00055- (1.96- 0.00027) = 0.0000208
0.0468-(1- 0.7775)-0.0000208-[0.7775+ (l- 0.0468)1
B = ^-=517-10~
low (l- 0.7775 + 0.0468)2
B-B, (0.000137 +5.17-10"6)
p Plm = ± '-= 0.0000725
1.96 1.96
= O.OOOQ697.
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B.5.2 Minor Restricted Activity Days: Ostro and Rothschild (1989b)
Ostro and Rothschild (1989b) estimated the impact of PM25 on the incidence of minor restricted
activity days (MRADs) and respiratory-related restricted activity days (RRADs) in a national sample of the
adult working population, ages 18 to 65, living in metropolitan areas. The annual national survey results
used in this analysis were conducted in 1976-1981. Controlling for PM25, two-week average O3 has highly
variable association with RRADs and MRADs. Controlling for O3, two-week average PM25 was
significantly linked to both health endpoints in most years.
The study is based on a "convenience" sample of individuals ages 18-65. Applying the C-R
function to this age group is likely a slight underestimate, as it seems likely that elderly are at least as
susceptible to PM as individuals 65 and younger. The elderly appear more likely to die due to PM
exposure than other age groups (e.g., Schwartz, 1994d, p. 30) and a number of studies have found that
hospital admissions for the elderly are related to PM exposures (e.g., Schwartz, 1994a; Schwartz, 1994b).
Using the results of the two-pollutant model, we developed separate coefficients for each year in
the analysis, which were then combined for use in this analysis. The coefficient used in this analysis is a
weighted average of the coefficients (Ostro, 1987, Table IV) using the inverse of the variance as the weight.
The C-R function to estimate the change in the number of minor restricted activity days (MRAD)
associated with a change in daily O3 is:
t^MRAD = -[y0 (e^P'^ - 1)] pop,
where:
y0 = daily MRAD daily incidence rate per person = 0.02137
p = inverse-variance weighted O3 coefficient = 0.00220
AO3 = change in daily one-hour maximum ozone concentration (ppb)70
pop = adult population aged 18 to 65
p = standard error of (3 = 0.000658
Incidence Rate. The annual incidence rate (7.8) provided by Ostro and Rothschild (1989b, p. 243) was
divided by 365 to get a daily rate of 0.02137.
Coefficient Estimate (p). The coefficient used in the C-R function is a weighted average of the coefficients
in Ostro and Rothschild (1989b, Table 4) using the inverse of the variance as the weight:71
1981 O *
I
'^^ =0.00220.
The study used a two-week average pollution concentration; the daily rate used here is assumed to be a reasonable
approximation. The study used ozone measurements in ug/m3; a conversion of 1.96 ug/m3 = 1 ppb is assumed here.
"The calculation of the MRAD coefficient and its standard error is exactly analogous to the calculation done for the work-
loss days coefficient based on Ostro (1987).
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Standard Error ( p). The standard error of the coefficient ( p) is calculated as follows, assuming that the
estimated year-specific coefficients are independent:
= var
X^ Pi
Zj 2
z=1976 °ft-
1981 -,
y
/-^ _2
V A-
i=1976 ^ft
7
1981 f
X~>
Zj
!=1976 V
A
^/
This reduces down to:
(Jfl2 = ^ (Jfl = J = 0.000658.
7 V 7
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B.5.3 Asthma Attacks: Whittemore and Korn (1980)
Whittemore and Korn (1980) examined the relationship between air pollution and asthma attacks in
a survey of 443 children and adults, living in six communities in southern California during three 34-week
periods in 1972-1975. The analysis focused on TSP and oxidants (Ox). Respirable PM, NO2, SO2 were
highly correlated with TSP and excluded from the analysis. In a two pollutant model, daily levels of both
TSP and oxidants were significantly related to reported asthma attacks. The results from this model were
used, and the oxidant result was adjusted below so it may be used with ozone data.
The C-R function to estimate the change in asthma attacks associated with a change in daily ozone
is:
^Asthma Attacks = -
pop,
where:
y0 = daily incidence of asthma attacks = 0.027 (Krupnick, 1988, p. 4-6)
p = ozone coefficient = 0.00184
AO3 = change in daily one-hour maximum ozone concentration (ppb)
pop = population of asthmatics of all ages = 5.61% of the population of all ages (Adams and Marano,
1995 Table 57).
p = standard error of (3 = 0.000714
Incidence Rate. The annual rate of 9.9 asthma attacks per astmatic is divided by 365 to get a daily rate.
A figure of 9.9 is roughly consistent with the recent statement that "People with asthma have more than
100 million days of restricted activity" each year (National Heart, 1997). This 100 million incidence figure
coupled with the 1996 population of 265,557,000 (U.S. Bureau of the Census, 1997, Table 2) and the
latest asthmatic prevalence rate of 5.61% (Adams et al., 1995, Table 57), suggest an annual asthma attach
rate per asthmatic of 6.7.
Coefficient Estimate (p). Based on a model with TSP, the daily one-hour ozone coefficient is based on an
oxidant coefficient (1.66) estimated from data expressed in ppm (Whittemore et al., 1980, Table 5):72
1.66-1.11
72The study used oxidant measurements in ppm (Whittemore et al., 1980, p. 688); these have been converted to ozone
measurements in ppb, assuming ozone comprises 90% of oxidants (i.e., l.ll*ozone=oxidant). It is assumed that the harm of oxidants
is caused by ozone. The view expressed in the Ozone Staff Paper (U.S. EPA, 1996b, p. 164) is consistent with assuming that ozone is
the oxidant of concern at normal ambient concentrations: "Further, among the photochemical oxidants, the acute-exposure chamber,
field, and epidemiological human health data base raises concern only for O3 at levels of photochemical oxidants commonly reported
in ambient air. Thus, the staff recommends that O3 remain as the pollutant indicator for protection of public health from exposure to
all photochemical oxidants found in the ambient air."
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Standard Error ( p). The standard error ( p) is calculated from the two-tailed p-value (<0.01) reported by
Whittemore and Korn (1980, Table 5), which implies at-value of at least 2.576 (assuming a large number
of degrees of freedom).
B 0.184
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B.5.4 Worker Productivity: Crocker and Horst (1981)
To monetize benefits associated with increased worker productivity resulting from improved ozone
air quality, we used information reported in Crocker and Horst (1981) and summarized in EPA (1994).
Crocker and Horst examined the impacts of ozone exposure on the productivity of outdoor citrus workers.
The study measured productivity impacts as the change in income associated with a change in ozone
exposure, given as the elasticity of income with respect to ozone concentration (-0.1427).73 The reported
elasticity translates a ten percent reduction in ozone to a 1.4 percent increase in income. Given the median
daily income for outdoor workers engaged in strenuous activity reported by the 1990 U.S. Census, $89.64
per day (1997$), a ten percent reduction in ozone yields about $1.26 in increased daily wages. The median
daily income for outdoor workers is a national estimate, however. We adjust this estimate to reflect
regional variations in income using a factor based on the ratio of national median household income divided
by a county's median household income. No information was available for quantifying the uncertainty
associated with the central valuation estimate. Therefore, no uncertainty analysis was conducted for this
endpoint.
73 The relationship estimated by Crocker and Horst between wages and ozone is a log-log relationship. Therefore the
elasticity of wages with respect to ozone is a constant, equal to the coefficient of the log of ozone in the model.
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APPENDIX C: PARTICULATE MATTER C-R FUNCTIONS
Note that APM is defined for all of the concentration-response (C-R) functions ~ as PM
PMcontrol, and that the change is defined to be: - (incidencecontrol - incidencebaselme).
3.1 MORTALITY
There are two types of exposure to PM that may result in premature mortality. Short-term
exposure may result in excess mortality on the same day or within a few days of exposure. Long-term
exposure over, say, a year or more, may result in mortality in excess of what it would be if PM levels were
generally lower, although the excess mortality that occurs will not necessarily be associated with any
particular episode of elevated air pollution levels. In other words, long-term exposure may capture a facet
of the association between PM and mortality that is not captured by short-term exposure.
3.1.1 Mortality (Pope et al., 1995)
Pope et al. (1995) used a Cox proportional hazard model to estimate the impact of long-term PM
exposure. They followed 552,138 individuals ages 30 and over in 51 cities from September 1, 1982 to
December 31, 1989, and related their survival to median PM25 concentrations for 1979 to 1983. Pope et
al. (1995, Table 2) reported results for all-cause deaths, lung cancer (ICD-9 code: 162), cardiopulmonary
deaths (ICD-9 codes: 401-440 and 460-519), and "all other" deaths,74 and found that median PM25 is
significantly related to all-cause and cardiopulmonary mortality. Pope et al. included only PM, so it is
unclear to what extent it may be including the impacts of ozone or other gaseous pollutants.
Pope et al. (1995) is the better of the two published prospective cohort studies: it has a larger
population and includes more cities than the prospective cohort study by Dockery et al. (1993). Pope et
al.'s study has several further advantages. The population followed in this study was largely Caucasian
and middle class, decreasing the likelihood that interlocational differences in premature mortality were due
in part to differences in race, socioeconomic status, or related factors. In addition, the PM coefficient in
Pope et al. is likely to be biased downward, counteracting a possible upward bias associated with historical
air quality trends discussed earlier. One source of this downward bias is the generally healthier study
population, in comparison to poorer minority populations. Another source of downward bias is that
intercity movement of cohort members was not considered in this study. Migration across study cities
would result in exposures of cohort members being more similar than would be indicated by assigning city-
specific annual average pollution levels to each member of the cohort. The more intercity migration there
is, the more exposure will tend toward an intercity mean. If this is ignored, differences in exposure levels,
that are proxied by differences in city-specific annual average PM levels, will be exaggerated, and will
result in a downward bias of the PM coefficient (because a given difference in mortality rates is being
associated with a larger difference in PM levels than is actually the case).
74All-cause mortality includes accidents, suicides, homicides and legal interventions. The category "all other" deaths is all-
cause mortality less lung cancer and cardiopulmonary deaths.
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The C-R function to estimate the change in long-term mortality is:
kNonaccidental Mortality = -\y0- (e~ ^'APM2-5 - 1) pop ,
where:
y0 = county-level annual non-accidental death rate per person
P = PM25 coefficient = 0.006408
APM2 5 = change in annual median PM2 5 concentration
pop = population of ages 30 and older
= standard error of p = 0.001509
Incidence Rate. To estimate county-specific baseline mortality incidence among individuals ages 30 and
over, this analysis used the average annual county mortality rate from 1994 through 1996 (U.S. Centers for
Disease Control, 1999). Note that Pope et al. (1995) used all cause mortality when estimating the impact
of PM, however, it was decided to use non-accidental mortality in this analysis. Using non-accidental
mortality (rather than all-cause mortality) underestimates deaths averted by about 7 percent; this is
discussed in Abt Associates (1999, p. A-21).
Coefficient Estimate (p). The coefficient (p) is estimated from the relative risk (1.17) associated with a
change in median exposure going from 9 pg/m3 to 33.5 (Jg/m3 (Pope et al., 1995, Table 2).
(33.5-9)
Standard Error ( p). The standard error ( p) was calculated as the average of the standard errors implied
by the reported lower and upper bounds of the relative risk (Pope et al., 1995, Table 2).
= 0.001543
hlgh = =
'*'** 1.96 1.96
8Jow 1.96 1.96
fln(1.17) 111(1.09)^
-) = aooi475
w = 0.001509.
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3.1.2 Mortality (Dockery et al., 1993)
Dockery et al. (1993) examined the relationship between PM exposure and mortality in a cohort of
8,111 individuals aged 25 and older, living in six U.S. cities. They surveyed these individuals in 1974-
1977 and followed their health status until 1991. While they used a smaller sample of individuals from
fewer cities than the study by Pope et al., they used improved exposure estimates, a slightly broader study
population (adults aged 25 and older), and a follow-up period nearly twice as long as that of Pope et al.
(1995). Perhaps because of these differences, Dockery et al. study found a larger effect of PM on
premature mortality than that found by Pope et al.
The C-R function to estimate the change in long-term mortality is:
ANonaccidentalMortality = -\y0 -(e~/j'APM2-5 -1)1 -pop,
where:
y0 = county-level annual non-accidental death rate per person
P = PM25 coefficient = 0.0124
APM2 5 = change in annual mean PM2 5 concentration
pop = population of ages 25 and older
p = standard error of p = 0.00423
Incidence Rate. To estimate county-specific baseline mortality incidence among individuals ages 25 and
over, this analysis used the average annual county mortality rate from 1994 through 1996 (U.S. Centers for
Disease Control, 1999). Dockery et al. (1993, p. 1754) appear to have used all-cause mortality when
estimating the impact of PM, however, it was decided to use non-accidental mortality in this analysis.
Using non-accidental mortality (rather than all-cause mortality) underestimates deaths averted by about 7
percent; this is discussed in Abt Associates (1999, p. A-21).
Coefficient Estimate (p). The coefficient (p) is estimated from the relative risk (1.26) associated with a
change in mean exposure going from 11.0 (Jg/m3 to 29.6 (Jg/m3 (Dockery et al., 1993, Tables 1 and 5):
Standard Error ( p). The standard error ( p) was calculated as the average of the standard errors implied
by the reported lower and upper bounds of the relative risk (Dockery et al., 1993, Table 5):
(ln(1.47) ln(1.26)^
ln(1.26)
~i^"" ~iSU. = 0.00423
1.96 1.96
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Mg. =a00423-
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3.1.3 Neonatal Mortality (Woodruff et al., 1997)
In a study of four million infants in 86 U.S. metropolitan areas conducted from 1989 to 1991,
Woodruff et al. (1997) found a significant link between PM10 exposure in the first two months of an
infant's life with the probability of dying between the ages of 28 days and 364 days. PM10 exposure was
significant for all-cause mortality. PM10 was also significant for respiratory mortality in average birth-
weight infants, but not low birth-weight infants.
In addition to the work by Woodruff et al., work in Mexico City (Loomis et al., 1999), the Czech
Republic (Bobak and Leon, 1992), Sao Paulo (Pereira et al., 1998; Saldiva et al., 1994), and Beijing
(Wang et al., 1997) provides additional evidence that particulate levels are significantly related to infant or
child mortality, low birth weight or intrauterine mortality.
Conceptually, neonatal or child mortality could be added to the premature mortality predicted by
Pope et al. (1995), because the Pope function covers only the population over 30 years old.75 However, the
EPA Science Advisory Board recently advised the Agency not to include post-neonatal mortality in this
analysis because the study is of a new endpoint and the results have not been replicated in other studies
(U.S. EPA, 1999b, p. 12). The estimated avoided incidences of neonatal mortality are estimated and
presented as a sensitivity analysis, and are not included in the primary analysis.
The C-R function to estimate the change in infant mortality is:
AInfant Mortality = -
pop,
where:
y0 = county annual postneonatal76 infant deaths per infant under the age of one
P = PM10 coefficient = 0.00392
APM10 = change in annual average PM10 concentration77
pop = population of infants under one year old
p = standard error of p = 0.00122
Coefficient Estimate (p). The estimated logistic coefficient (p) is based on the odds ratio (= 1.04)
associated with a 10 jug/m3 change in PM10 (Woodruff et al., 1997, Table 3). The coefficient is calculated
as follows:
= 0.00392.
75 Predicted neonatal mortality could not be added to the premature mortality predicted by the daily (short-term exposure)
mortality studies, however, because these studies cover all ages.
76Post-neonatal refers to infants that are 28 days to 364 days old.
"Woodruff et al. (1997) used PM10 exposure in the first two months of an infant's life.
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Standard Error ( p). The standard error for the coefficient is calculated as the average of the standard
errors implied by the reported lower and upper bounds of the odds ratio (1.02 to 1.07) (Woodruff et al.,
1997, Table 3). This reproduces both the lower and upper bounds of the odds ratio:
111(1.04)^
~
~ = = O.OQ1451
8'lm 1.96 1.96
in(1.04)
=0.000991
= 0.00122.
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3.1.4 Short-Term Mortality (Schwartz et al., 1996)
Schwartz et al. (1996) pooled the results from six cities in the U.S. and found a significant
relationship between daily PM25 concentration and non-accidental mortality.78 Abt Associates Inc. (1996b,
p. 52) used the six PM2 5 relative risks reported by Schwartz et al. in a three-step procedure to estimate a
pooled PM2 5 coefficient and its standard error. The first step estimates a random-effects pooled estimate of
P; the second step uses an "empirical Bayes" procedure to reestimate the p for each study as a weighted
average of the p reported for that location and the random effects pooled estimate; the third step estimates
the underlying distribution of p, and uses a Monte Carlo procedure to estimate the standard error (Abt
Associates Inc., 1996a, p. 65).
The C-R function to estimate the change in mortality associated with daily changes in PM2 5 is:
kNonaccidentalMortality =-[y0-(e~^^M^ -1)] pop,
where:
y0 = county-level daily incidence for non-accidental deaths per person of any age
P = PM25 coefficient (Abt Associates Inc., 1996a, Exhibit 7.2) = 0.001433
APM2 5 = change in daily average PM2 5 concentration
pop = population of all ages
= standard error of p (Abt Associates Inc., 1996a, Exhibit 7.2) = 0.000129
78Schwartz et al. (1996, p. 929) defined non-accidental mortality as all-cause mortality less deaths due to accidents and other
external causes (ICD-9 codes: 800-999). Other external causes includes suicide, homicide, and legal intervention (National Center for
Health Statistics, 1994).
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3.2 CHRONIC MORBIDITY
Schwartz (1993) and Abbey et al. (1995b; 1993) provide evidence that PM exposure over a
number of years gives rise to the development of chronic bronchitis in the U.S., and a recent study by
McDonnell et al. (1999) provides evidence that ozone exposure is linked to the development of asthma in
adults. These results are consistent with research that has found chronic exposure to pollutants leads to
declining pulmonary functioning (Abbey et al., 1998; Ackermann-Liebrich et al., 1997; Detels et al.,
1991).79
We estimate the changes in the new cases of chronic bronchitis using the studies by Schwartz
(1993), Abbey et al. (1993), and Abbey et al. (1995b). The Schwartz study is somewhat older and uses a
cross-sectional design, however, it is based on a national sample, unlike the Abbey et al. studies which are
based on a sample of California residents. We first pool the estimates from the two studies by Abbey et al.
- since they are based on the same sample population and simply use different measures of PM - and then
pool this estimate with that from Schwartz.
3.2.1 Chronic Bronchitis (Schwartz, 1993)
Schwartz (1993) examined survey data collected from 3,874 adults ranging in age from 30 to 74,
and living in 53 urban areas in the U.S. The survey was conducted between 1974 and 1975, as part of the
National Health and Nutrition Examination Survey, and is representative of the non-institutionalized U.S.
population. Schwartz (1993, Table 3) reported chronic bronchitis prevalence rates in the study population
by age, race, and gender. Non-white males under 52 years old had the lowest rate (1.7%) and white males
52 years and older had the highest rate (9.3%). The study examined the relationship between the
prevalence of reported chronic bronchitis, asthma, shortness of breath (dyspnea) and respiratory illness80,
and the annual levels of TSP, collected in the year prior to the survey (TSP was the only pollutant
examined in this study). TSP was significantly related to the prevalence of chronic bronchitis, and
marginally significant for respiratory illness. No effect was found for asthma or dyspnea.
Schwartz (1993) examined the prevalence of chronic bronchitis, not its incidence. To use
Schwartz's study and still estimate the change in incidence, there are at least two possible approaches. The
first is to simply assume that it is appropriate to use the baseline incidence of chronic bronchitis in a C-R
function with the estimated coefficient from Schwartz's study, to directly estimate the change in incidence.
The second is to estimate the percentage change in the prevalence rate for chronic bronchitis using the
estimated coefficient from Schwartz's study in a C-R function, and then to assume that this percentage
change applies to a baseline incidence rate obtained from another source. (That is, if the prevalence
declines by 25 percent with a drop in PM, then baseline incidence drops by 25 percent with the same drop
in PM.) This analysis is using the latter approach, and estimates a percentage change in prevalence which
is then applied to a baseline incidence rate.
79 There are a limited number of studies that have estimated the impact of air pollution on chronic bronchitis. An important
hindrance is the lack of health data and the associated air pollution levels over a number of years.
80 Respiratory illness defined as a significant condition, coded by an examining physician as ICD-8 code 460-519.
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The C-R function to estimate the change in chronic bronchitis is:
^Chronic Bronchitis = -
pop,
where:
y0 = national chronic bronchitis prevalence rate for individuals 18 and older (Adams et al, 1995,
Table 62 and 78) =0.0535
z0 = annual bronchitis incidence rate per person (Abbey et al., 1993, Table 3) = 0.00378
p = estimated PM10 logistic regression coefficient = 0.0123
APM10 = change in annual average PM10 concentration
pop = population of ages 30 and older without chronic bronchitis = 0.9465*population 30+
p = standard error of p = 0.00434 .
Prevalence Rate. The national chronic bronchitis prevalence rate was not available for individuals 30 and
older. Instead, we used the prevalence rate for individuals 18 and older (Adams et al., 1995, Table 62 and
78). The 1994 national figures are the latest available, and are suggested here.
Incidence Rate. The annual incidence rate is derived by taking the number of new cases (234), dividing by
the number of individuals in the sample (3,3 10), as reported by Abbey et al.(1993, Table 3), dividing by
the ten years covered in the sample, and then multiplying by one minus the reversal rate (the percentage of
reversals is estimated to be 46.6% based on Abbey et al. (1995a, Table 1)). Using the same data base,
Abbey et al. (1995a, Table 1) reported the incidences by three age groups (25-54, 55-74, and 75+) for
"cough type" and "sputum type" bronchitis, but they did not report an overall incidence rate for bronchitis.
Coefficient Estimate (p). The estimated logistic coefficient (p) is based on the odds ratio (= 1.07)
associated with 10 (Jg/m3 change in TSP (Schwartz, 1993, p. 9). Assuming that PM10 is 55 percent of
TSP81 and that particulates greater than ten micrometers are harmless, the coefficient is calculated as
follows:
InflffJ)
Standard Error ( p) The standard error for the coefficient ( p) is calculated from the reported lower and
upper bounds of the odds ratio (1.02 to 1.12) (Schwartz, 1993, p. 9):
0.55- 10 0.55-lo nnn^A
- = ao°424
( ln(1.07)
- 0.00444
81The conversion of TSP to PM10 is from ESEERCO (1994, p. V-5), who cited studies by EPA (1986) and the California
Air Resources Board (1982).
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= O.OQ434.
Population. The study population in Schwartz (1993) includes 3,874 individuals over the age of 30, living
in 57 urban areas in the United States. To what extent the study should be applied to individuals under the
age of 30 is unclear, and no effect is assumed for these individuals.
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3.2.2 Chronic Bronchitis (Abbey et al., 1993, California)
Abbey et al. (1993) surveyed 3,914 adult Seventh Day Adventists living in California, and
estimated the relationship between annual mean ambient TSP, ozone and SO2 and the onset of certain
chronic respiratory symptoms (including airway obstructive disease (AOD), chronic bronchitis, and
asthma) that were not present at the beginning of the study. The initial survey was conducted in 1977 and
the final survey in 1987. To ensure a better estimate of exposure, the study participants had to have been
living in the same area for an extended period of time. TSP was significantly linked to new cases of AOD
and chronic bronchitis, but not to asthma or the severity of asthma. Ozone was not linked to the incidence
of new cases of any endpoint, but ozone was linked to the severity of asthma. No effect was found for SO2.
The C-R function to estimate the change in chronic bronchitis is:
^Chronic Bronchitis = -[y0 .(e-^PMl° - l)]-/?qp,
where:
y0 = annual bronchitis incidence rate per person (Abbey et al., 1993, Table 3) = 0.00378
P = estimated PM10 logistic regression coefficient = 0.00932
APM10 = change in annual average PM10 concentration
pop = population of ages 27 and older without chronic bronchitis82 = 0.9465*population 27+
p = standard error of p = 0.00475
Incidence Rate. The annual incidence rate is derived by taking the number of new cases (234), dividing by
the number of individuals in the sample (3,3 10), as reported by Abbey et al.(1993, Table 3), dividing by
the ten years covered in the sample, and then multiplying by one minus the reversal rate (estimated to be
46.6% based on Abbey et al. (1995a, Table 1)). Using the same data base, Abbey et al. (1995a, Table 1)
reported the incidences by three age groups (25-54, 55-74, and 75+) for "cough type" and "sputum type"
bronchitis, but they did not report an overall incidence rate for bronchitis.
Coefficient Estimate (p). The estimated coefficient (p) is based on the relative risk (= 1.36) associated
with 60 (jg/m3 change in TSP (Abbey et al., 1993, Table 5). Assuming that PM10 is 55 percent of TSP83
and that particulates greater than ten micrometers are harmless, the coefficient is calculated as follows:
Standard Error ( p). The standard error for the coefficient ( p) is calculated from the reported significance
level of p < 0.05 (Abbey et al., 1993, Table 5). We assume that p = 0.05, which implies that the standard
error is roughly one half of the coefficient value:
B 0.00932
82Using the same data set, Abbey et al. (1995a, p. 140) reported that the respondents in 1977 ranged in age from 27 to 95.
Chronic bronchitis prevalence from Adams and Marano (1995, Tables 62 and 78).
83The conversion of TSP to PM10 is from ESEERCO (1994, p. V-5), who cited studies by EPA (1986) and the California
Air Resources Board (1982).
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3.2.3 Chronic Bronchitis (Abbey et al., 1995b, California)
Abbey et al. (1995b) examined the relationship between estimated PM25 (annual mean from 1966
to 1977), PM10 (annual mean from 1973 to 1977) and TSP (annual mean from 1973 to 1977) and the
same chronic respiratory symptoms in a sample population of 1,868 Californian Seventh Day Adventists.
The initial survey was conducted in 1977 and the final survey in 1987. To ensure a belter estimate of
exposure, the study participants had to have been living in the same area for an extended period of time. In
single-pollutant models, there was a statistically significant PM2 5 relationship with development of chronic
bronchitis, but not for AOD or asthma; PM10 was significantly associated with chronic bronchitis and
AOD; and TSP was significantly associated with all cases of all three chronic symptoms. Other pollutants
were not examined.
The C-R function to estimate the change in chronic bronchitis is:
/^.Chronic Bronchitis = - \y0 (e~P'APMz 5 - 1) pop,
where:
y0 = annual bronchitis incidence rate per person (Abbey et al., 1993, Table 3) = 0.00378
p = estimated PM25 logistic regression coefficient = 0.0132
APM2 5 = change in annual average PM2 5 concentration
pop = population of ages 27 and older without chronic bronchitis84 = 0.9465*population 27+
p = standard error of p = 0.00680
Incidence Rate. The annual incidence rate is derived by taking the number of new cases (234), dividing by
the number of individuals in the sample (3,3 10), as reported by Abbey et al.(1993, Table 3), dividing by
the ten years covered in the sample, and then multiplying by one minus the reversal rate (estimated to be
46.6% based on Abbey et al. (1995a, Table 1)). Using the same data base, Abbey et al. (1995a, Table 1)
reported the incidences by three age groups (25-54, 55-74, and 75+) for "cough type" and "sputum type"
bronchitis, but they did not report an overall incidence rate for bronchitis.
Coefficient Estimate (p). The estimated coefficient (p) is based on the relative risk (= 1.81) associated
with 45 /^g/m3 change in PM25 (Abbey et al., 1995b, Table 2). The coefficient is calculated as follows:
Standard Error ( p). The standard error for the coefficient ( p) is calculated from the reported lower and
upper bounds of the relative risk (0.98 to 3.25) (Abbey et al., 1995b, Table 2):
n(3.25)
45 45 . nnn^A
- = ao°664
84Using the same data set, Abbey et al. (1995a, p. 140) reported that the respondents in 1977 ranged in age from 27 to 95.
Chronic bronchitis prevalence from Adams and Marano (1995, Tables 62 and 78).
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ln(0.98)
V 45 45 ,
- - = ao°696
g, = = O.OQ680.
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3.3 HOSPITAL ADMISSIONS
There is a wealth of epidemiological information on the relationship between air pollution and
hospital admissions for various respiratory and cardiovascular diseases; in addition, some studies have
examined the relationship between air pollution and emergency room (ER) visits. Because most emergency
room visits do not result in an admission to the hospital ~ the majority of people going to the ER are
treated and return home ~ we treat hospital admissions and ER visits separately, taking account of the
fraction of ER visits that do get admitted to the hospital, as discussed below.
Hospital admissions require the patient to be examined by a physician, and on average may
represent more serious incidents than ER visits (Lipfert, 1993, p. 230). The two main groups of hospital
admissions estimated in this analysis are respiratory admissions and cardiovascular admissions. There is
not much evidence linking air pollution with other types of hospital admissions. The only types of ER
visits that have been linked to air pollution in the U.S. or Canada are asthma-related visits.
3.3.1 Hospital Admissions for Asthma (Burnett et al., 1999, Toronto)
Burnett et al. (1999) examined the relationship between air pollution and hospital admissions for
individuals of all ages in Toronto, Canada from 1980 to 1994. They estimated multiple pollutant models,
where pollutants for the best fitting model were chosen using stepwise regression based on AIC criterion.
Asthma admissions were linked to O3, CO, and PM2 5_10. This C-R function is based on the results based
on this three-pollutant model.
The C-R function to estimate the change in hospital admissions for asthma associated with daily
changes in PM10_25 is:
^Asthma Admissions = - [y0 (g'^4^" - 1)J pop ,
where:
y0 = daily hospital admission rate for asthma per person = 4.75 E-6
P = PM10_2 5 coefficient = 0.00321
APM10.2 5 = change in daily average PM10.2 5 concentration
pop = population of all ages
p = standard error of p = 0.00106
Incidence Rate. Hospital admissions for asthma (ICD-9 code: 493) are based on first-listed discharge
figures for the latest available year, 1994. The rate equals the annual number of first-listed diagnoses for
discharges (0.451 million) divided by the 1994 population (260.372 million), and then divided by 365 days
in the year. The discharge figures are from Graves and Gillum (1997, Table 1), and the population data
are from U.S. Bureau of the Census (1997, Table 14).
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Coefficient Estimate (p). The estimated coefficient (p) is based on a 4.00 percent increase in admissions
due to a PM10_25 change of 12.2 (jg/m3 (Burnett et al., 1999, Tables 1 and 5). This translates to a relative
risk of 1.04. The coefficient is calculated as follows:
= 0.00321.
Standard Error ( p). The standard error ( p) was calculated using the t-value (t=3.04) (Burnett, 1999):
.00321
=0.00106.
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3.3.2 Hospital Admissions for Obstructive Lung Disease (Burnett et al., 1999, Toronto)
Burnett et al. (1999) examined the relationship between air pollution and hospital admissions for
individuals of all ages in Toronto, Canada froml980 to 1994. They estimated multiple pollutant models,
where pollutants for best fitting model were chosen using stepwise regression based on AIC criterion.
Chronic obstructive pulmonary disease (COPD) was linked to O3 and PM2 5_10. This C-R function is based
on the results of this two-pollutant model.
The C-R function to estimate the change in hospital admissions for obstructive lung disease
associated with daily changes in PM10_25 is:
^.Obstructive Lung Disease Admissions = - I y0 (e ~^ 'APMl°-2 -5 - 1)1- pop,
where:
y0 = daily hospital admission rate for obstructive lung disease per person = 5.76 E-6
P = PM10_2.5 coefficient = 0.00310
A PM10.2 5 = change in daily average PM10.2 5 concentration
pop = population of all ages
p = standard error of p = 0.00163
Incidence Rate. Hospital admissions for obstructive lung disease (ICD-9 codes: 490-492, 496) are based
on first-listed discharge figures for the latest available year, 1994. The rate equals the annual number of
first-listed diagnoses for discharges (0.547 million) divided by the 1994 population (260.372 million), and
then divided by 365 days in the year. The discharge figures are from Graves and Gillum (1997, Table 1),
and the population data are from U.S. Bureau of the Census (1997, Table 14).
Coefficient Estimate (p). The estimated coefficient (p) is based on a 3.86 percent increase in admissions
due to a PM10_25 change of 12.2 (jg/m3 (Burnett et al., 1999, Tables 1 and 5). This translates to a relative
risk of 1.0386. The coefficient is calculated as follows:
ln(1.0386)
3= =0.00310.
Standard Error ( p). The standard error ( p) was calculated using the t-value (t=1.90) (Burnett, 1999):
.00310
=0.00163.
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3.3.3 Hospital Admissions for Respiratory Infection (Burnett et al., 1999, Toronto)
Burnett et al. (1999) examined the relationship between air pollution and hospital admissions for
individuals of all ages in Toronto, Canada froml980 to 1994. They estimated multiple pollutant models,
where pollutants for best fitting model were chosen using stepwise regression based on AIC criterion.
Respiratory infection admissions were linked to O3, NO2, and PM2 5. This C-R function is based on the
results of this three-pollutant model.
The C-R function to estimate the change in hospital admissions for respiratory infection associated
with daily changes in PM25 is:
A ^Respiratory Infection Admissions = - \y0 .(e~^PM2-5 - V)\- pop,
where:
y0 = daily hospital admission rate for respiratory infection per person =1.56 E-5
P = PM25 coefficient = 0.00328
APM2 5 = change in daily average PM2 5 concentration
pop = population of all ages
p = standard error of p = 0.000735
Incidence Rate. Hospital admissions for respiratory infection (ICD-9 codes: 464, 466, 480-487, 494) are
based on first-listed discharge figures for the latest available year, 1994. The rate equals the annual
number of first-listed diagnoses for discharges (1.485 million) divided by the 1994 population (260.372
million), and then divided by 365 days in the year. The discharge figures are from Graves and Gillum
(1997, Table 1), and the population data are from U.S. Bureau of the Census (1997, Table 14).
Coefficient Estimate (p). The estimated coefficient (p) is based on a 6.08 percent increase in admissions
due to a PM25 change of 18 (jg/m3 (Burnett, 1999, Tables 1 and 5). This translates to a relative risk of
1.0608. The coefficient is calculated as follows:
ln(1.0608)
J3= \ =0.00328.
18
Standard Error ( p). The standard error ( p) was calculated using the t-value (t=4.46) (Burnett, 1999):
.00328
4.46
=0.000735.
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3.3.4 Hospital Admissions for All Respiratory (Burnett et al., 1997, Toronto)
Burnett et al. (1997) examined the relationship between air pollution and hospital admissions for
individuals of all ages in Toronto, Canada during the summers of 1992-1994. All respiratory admissions
were linked to COH and O3; other PM measures were less strongly linked. In two pollutant models, they
found that CO, NO2, and SO2 were not significant, controlling for COH. They found that O3 was still
significant, controlling for COH. This analysis used the results from the four-pollutant model (PM2 5_10, O3,
NO2, and SO2) to estimate all respiratory incidence.
The C-R function to estimate the change in all respiratory hospital admissions associated with
daily changes in PM10_25 is:
spiratory Admissions = - \y0 ^e~/JAPMl(|-2-5 - \)\-pop,
where:
y0 = daily hospital admission rate for all respiratory causes per person = 2.58 E-5
P =PM10_2 5 coefficient = 0.00147
APM10_2 5 = change in daily average PM10_2 5 concentration
pop = population of all ages
p = standard error of p = 0.00179
Incidence Rate. Hospital admissions for all respiratory (ICD-9 codes: 464-466, 480-486, 490-494, 496)
are based on first-listed discharge figures for the latest available year, 1994. The rate equals the annual
number of first-listed diagnoses for discharges (2.452 million) divided by the 1994 population (260.372
million), and then divided by 365 days in the year. The discharge figures are from Graves and Gillum
(1997, Table 1), and the population data are from U.S. Bureau of the Census (1997, Table 14).
Coefficient Estimate (p). The estimated coefficient (p) is based on a relative risk of 1.007 due to a PM10_25
change of 4.75 (jg/m3 (Burnett et al., 1997, Tables 2 and 6). The coefficient is calculated as follows:
Standard Error ( p). The standard error ( p) was calculated using the t-value (t=0.82) (Burnett et al.,
1997, Table 6)
.00147
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3.3.5 Hospital Admissions for All Respiratory (Thurston et al., 1994, Toronto)
Thurston et al. (1994) examined the relationship between air pollution and hospital admissions for
individuals of all ages in Toronto, Canada, for six weeks in July and August 1986-1988. In single-pollutant
models, ozone and various measures of PM were linked to all respiratory admissions. In two-pollutant
models, ozone was still significant, but measures of PM were often not significant; only H+ was significant.
However, since H+ exposure information is not available, this analysis used the results from a two-pollutant
model (PM25 and O3) to estimate all respiratory incidence.
The C-R function to estimate the change in all respiratory hospital admissions associated with
daily changes in PM25 is:
A All Re spiratory Admissions = J3 APM2 5 pop,
where:
P = PM2 5 coefficient = 1.81 E-8
APM2 5 = change in daily average PM2 5
pop = population of all ages
p = standard error of p = 1.79 E-8 .
Coefficient Estimate (p). Based on a linear model with ozone, the daily average PM2 5 coefficient comes
from an estimated coefficient of 0.0434, which estimates admissions per (Jg/m3 of PM25 (Thurston et al.,
1994, Table 3). The population of Toronto was estimated to be 2.4 million (U.S. EPA, 1997a, Table D-7).
We estimated a coefficient estimating admissions per person per (jg/m3 of PM25 as follows:
0.0434
Standard Error ( p). The standard error ( p) was calculated in a similar fashion (Thurston et al., 1994,
Table 3):
0.0429
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3.3.6 Hospital Admissions for Pneumonia (Moolgavkar et al., 1997, Minneapolis)
Moolgavkar et al. (1997) examined the relationship between air pollution and hospital admissions
for individuals 65 and older in Minneapolis-St. Paul, Minnesota, from January 1986 to December 1991. In
a four pollutant model examining pneumonia admissions in Minneapolis, ozone was significant, while NO2,
SO2, and PM10 were not significant. This analysis used the results from the four-pollutant model to
estimate pneumonia incidence.
The C-R function to estimate the change in hospital admissions for pneumonia associated with
daily changes in PM10 is:
/^Pneumonia Admissions = - \y0 (e~^'^Mm - \)\ pop ,
where:
y0 = daily hospital admission rate for pneumonia per person = 5.30 E-5
P = PM10 coefficient = 0.000498
A PM10 = change in daily average PM10 concentration
pop = population of ages 65 and older
p = standard error of p = 0.000505
Incidence Rate. Hospital admissions for pneumonia (ICD-9 codes: 480-487) are based on first-listed
discharge figures for the latest available year, 1994. The rate equals the annual number of first-listed
diagnoses for discharges (0.642 million) divided by the 1994 population of individuals 65 years and older
(33.162 million), and then divided by 365 days in the year. The discharge figures are from Graves and
Gillum (1997, Table 1), and the population data are from U.S. Bureau of the Census (1997, Table 14).
Coefficient Estimate (p). The estimated coefficient (p) is based on a 1.00 percent increase in admissions
due to a PM10 change of 20 (jg/m3 (Moolgavkar et al., 1997, Table 4 and p. 366); the model with a 130 df
smoother was reported to be optimal (p. 368). This translates to a relative risk of 1.01. The coefficient is
calculated as follows:
Standard Error ( p). The standard error ( p) was calculated as the average of the standard errors implied
by the reported lower and upper bounds of the relative risk (Moolgavkar et al., 1997, Table 4):
( ln(1.03)
( In(l.Ol) ln(0.99)>|
"
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= 0.000505.
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3.3.7 Hospital Admissions for COPD (Moolgavkar et al., 1997, Minneapolis)
Moolgavkar et al. (1997) examined the relationship between air pollution and hospital admissions
for individuals 65 and older in Minneapolis-St. Paul, Minnesota, from January 1986 to December 1991.
No significant effect found for any pollutant; the effect for ozone was marginally significant. This
analysis used the results from a three-pollutant model (O3, CO, PM10) to estimate COPD incidence.
The C-R function to estimate the change in hospital admissions for COPD associated with daily
changes in PM10 is:
A COPD admissions = -[y0- (e^^M^ - 1)] pop,
where:
y0 = daily hospital admission rate for COPD per person = 3.75 E-5
P = PM10 coefficient = 0.000877
A PM10 = change in daily average PM10 concentration
pop = population of ages 65 and older
p = standard error of p = 0.000777
Incidence Rate. Hospital admissions for COPD (ICD-9 codes: 490-496) are based on first-listed
discharge figures for the latest available year, 1994. The rate equals the annual number of first-listed
diagnoses for discharges (0.454 million) divided by the 1994 population of individuals 65 years and older
(33.162 million), and then divided by 365 days in the year. The discharge figures are from Graves and
Gillum (1997, Table 1), and the population data are from U.S. Bureau of the Census (1997, Table 14).
Coefficient Estimate (p). The estimated coefficient (p) is based on a 1.77 percent increase in admissions
due to a PM10 change of 20 (jg/m3 (Moolgavkar et al., 1997, Table 4 and p. 366); the model with a 100 df
smoother was reported to be optimal (p. 368). This translates to a relative risk of 1.0177. The coefficient
is calculated as follows:
ln(1.0177)
8 = = 0.000877.
P 20
Standard Error ( p). The standard error ( p) was calculated as the average of the standard errors implied
by the reported lower and upper bounds of the relative risk (Moolgavkar et al., 1997, Table 4):
fln(1.049) ln(1.0177)^
- = 0.000773
196 196
fln(1.0177)
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= 0.000777.
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3.3.8 Hospital Admissions for Pneumonia (Schwartz, 1994c, Minneapolis)
Schwartz (1994c) examined the relationship between air pollution and hospital admissions for
individuals 65 and older in Minneapolis-St. Paul, Minnesota, from January 1986 to December 1989. In a
two-pollutant model, Schwartz found PM10 significantly related to pneumonia; ozone was weakly linked to
pneumonia. This analysis used the results of the two pollutant model (PM10, O3) to estimate pneumonia
incidence.
The C-R function to estimate the change in hospital admissions for pneumonia associated with
daily changes in PM10 is:
/^Pneumonia Admissions = - Iy0 (e~^'^Mm - \)\ pop ,
where:
y0 = daily hospital admission rate for pneumonia per person = 5.18 E-5
P =PM10 coefficient = 0.00157
A PM10 = change in daily average PM10 concentration
pop = population of ages 65 and older
p = standard error of p = 0.000677
Incidence Rate. Hospital admissions for pneumonia (ICD-9 codes: 480-486) are based on first-listed
discharge figures for the latest available year, 1994. The rate equals the annual number of first-listed
diagnoses for discharges (0.627 million) divided by the 1994 population of individuals 65 years and older
(33.162 million), and then divided by 365 days in the year. The discharge figures are from Graves and
Gillum (1997, Table 1), and the population data are from U.S. Bureau of the Census (1997, Table 14).
Coefficient Estimate (p). Based on a model with ozone, the coefficient (p) is estimated from the relative
risk (1.17) associated with a 100 (jg/m3 change in exposure (Schwartz, 1994c, Table 4 and p. 369):
Standard Error ( p). The standard error ( p) was calculated as the average of the standard errors implied
by the reported lower and upper bounds of the relative risk (Schwartz, 1994c, Table 4):
ln(1.33)
~ ft 100 " 100 . nnnn,c,
-= - - = ao°0654
ln(1.02)
= 0.000611.
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3.3.9 Hospital Admissions for COPD (Schwartz, 1994c, Minneapolis)
Schwartz (1994a) examined the relationship between air pollution and hospital admissions for
individuals 65 and older in Minneapolis, MN, from January 1986 to December 1989. In single-pollutants
models, Schwartz found PM10 significantly related to COPD, and ozone was not significantly linked to
COPD. This analysis used the results of the single-pollutant model to estimate COPD incidence.
The C-R function to estimate the change in hospital admissions for COPD associated with daily
changes in PM10 is:
A COPD Admissions = -[y0- (e-f*'*PMw - l)\ pop,
where:
y0 = daily hospital admission rate for COPD per person = 3.75 E-5
P = PM10 coefficient = 0.0045 1
A PM10 = change in daily average PM10 concentration
pop = population of ages 65 and older
p = standard error of p = 0.00138
Incidence Rate. Hospital admissions for COPD (ICD-9 codes: 490-496) are based on first-listed
discharge figures for the latest available year, 1994. The rate equals the annual number of first-listed
diagnoses for discharges (0.454 million) divided by the 1994 population of individuals 65 years and older
(33.162 million), and then divided by 365 days in the year. The discharge figures are from Graves and
Gillum (1997, Table 1), and the population data are from U.S. Bureau of the Census (1997, Table 14).
Coefficient Estimate (p). Based on a single-pollutant model, the coefficient (p) is estimated from the
relative risk (1.57) associated with a 100 (jg/m3 change in exposure (Schwartz, 1994c, Table 4 and p.
369):
Standard Error ( p). The standard error ( p) was calculated as the average of the standard errors implied
by the reported lower and upper bounds of the relative risk (Schwartz, 1994c, Table 4):
ln(2.06) ln(1.57)
100 " 100 nnm,Q
- = ao°139
ln(1.57) ln(1.20)
IPO " 100
= 0.00138.
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3.3.10 Hospital Admissions for Pneumonia (Schwartz, 1994a, Birmingham)
Schwartz (1994a) examined the relationship between air pollution and hospital admissions for
individuals 65 and older in Birmingham, Alabama, from January 1986 to December 1989. In single-
pollutants model, Schwartz found PM10 significantly related to pneumonia; ozone was not significantly
linked to pneumonia. This C-R function is based on the results of the single-pollutant model to estimate
pneumonia incidence.
The C-R function to estimate the change in hospital admissions for pneumonia associated with
daily changes in PM10 is:
^Pneumonia Admissions = - [y0 (e'^'^1^10 - IjJ pop,
where:
y0 = daily hospital admission rate for pneumonia per person = 5.30 E-5
P =PM10 coefficient = 0.00174
A PM10 = change in daily average PM10 concentration
pop = population of ages 65 and older
p = standard error of p = 0.000536
Incidence Rate. Hospital admissions for pneumonia (ICD-9 codes: 480-487) are based on first-listed
discharge figures for the latest available year, 1994. The rate equals the annual number of first-listed
diagnoses for discharges (0.642 million) divided by the 1994 population of individuals 65 years and older
(33.162 million), and then divided by 365 days in the year. The discharge figures are from Graves and
Gillum (1997, Table 1), and the population data are from U.S. Bureau of the Census (1997, Table 14).
Coefficient Estimate (p). Based on a model with ozone, the coefficient (p) is estimated from the relative
risk (1.19) associated with a 100 (jg/m3 change in exposure (Schwartz, 1994a, Table 4):
=0.00174.
Standard Error ( p). The standard error ( p) was calculated as the average of the standard errors implied
by the reported lower and upper bounds of the relative risk (Schwartz, 1994a, Table 4):
ln(1.32)
100 100 J nnnnc^n
- = ao°0529
ln(1.07)
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= 0.000536.
3.3.11 Hospital Admissions for COPD (Schwartz, 1994a, Birmingham)
Schwartz (1994a) examined the relationship between air pollution and hospital admissions for
individuals 65 and older in Birmingham, Alabama, from January 1986 to December 1989. In single-
pollutants model, Schwartz found PM10 significantly related to COPD; ozone was not significantly linked
to COPD. This C-R function is based on the results of the single-pollutant model to estimate COPD
incidence.
The C-R function to estimate the change in hospital admissions for COPD associated with daily
changes in PM10 is:
A COPD Admissions = -[>> (e^'APMl° - I)] pop,
where:
y0 = daily hospital admission rate for COPD per person = 3.75 E-5
P = PM10 coefficient = 0.00239
A PM10 = change in daily average PM10 concentration
pop = population of ages 65 and older
p = standard error of p = 0.000838
Incidence Rate. Hospital admissions for COPD (ICD-9 codes: 490-496) are based on first-listed
discharge figures for the latest available year, 1994. The rate equals the annual number of first-listed
diagnoses for discharges (0.454 million) divided by the 1994 population of individuals 65 years and older
(33.162 million), and then divided by 365 days in the year. The discharge figures are from Graves and
Gillum (1997, Table 1), and the population data are from U.S. Bureau of the Census (1997, Table 14).
Coefficient Estimate (p). Based on a model with ozone, the coefficient (p) is estimated from the relative
risk (1.27) associated with a 100 (jg/m3 change in exposure (Schwartz, 1994a, Table 5):
ln(1.27)
£ = ^=0.00239.
Standard Error ( p). The standard error ( p) was calculated as the average of the standard errors implied
by the reported lower and upper bounds of the relative risk (Schwartz, 1994a, Table 5):
ln(1.50) ln(1.27)
( ln(1.27)
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= O.OOQ838.
3.3.12 Hospital Admissions for Pneumonia (Schwartz, 1994b, Detroit)
Schwartz (1994b) examined the relationship between air pollution and hospital admissions for
individuals 65 and older in Detroit, Michigan, from January 1986 to December 1989. In a two-pollutant
model, Schwartz found both PM10 and ozone significantly linked to pneumonia and COPD; no significant
link to asthma admissions was found for either pollutant. We use the results of this two-pollutant model.
The C-R function to estimate the change in hospital admissions for pneumonia associated with
daily changes in PM10 is:
/^Pneumonia Admissions = - \yQ (e~^'^PMw - \)\ pop ,
where:
y0 = daily hospital admission rate for pneumonia per person = 5.18 E-5
p = PM10 coefficient (Schwartz, 1994b, Table 4) = 0.001 15
A PM10 = change in daily average PM10 concentration
pop = population of ages 65 and older
= standard error of p (Schwartz, 1994b, Table 4) = 0.00039
Incidence Rate. Hospital admissions for pneumonia (ICD-9 codes: 480-486) are based on first-listed
discharge figures for the latest available year, 1994. The rate equals the annual number of first-listed
diagnoses for discharges (0.627 million) divided by the 1994 population of individuals 65 years and older
(33.162 million), and then divided by 365 days in the year. The discharge figures are from Graves and
Gillum (1997, Table 1), and the population data are from U.S. Bureau of the Census (1997, Table 14).
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3.3.13 Hospital Admissions for COPD (Schwartz, 1994b, Detroit)
Schwartz (1994b) examined the relationship between air pollution and hospital admissions for
individuals 65 and older in Detroit, Michigan, from January 1986 to December 1989. In a two-pollutant
model, Schwartz found both PM10 and ozone significantly linked to pneumonia and COPD; no significant
link to asthma admissions was found for either pollutant. We use the results of this two-pollutant model.
The C-R function to estimate the change in hospital admissions for COPD associated with daily
changes in PM10 is:
A COPD admissions = - [y0 (e-f*-*PM - \j\ . pop ,
where:
y0 = daily hospital admission rate for COPD per person = 3.05 E-5
P = PM10 coefficient (Schwartz, 1994b, Table 4) = 0.00202
A PM10 = change in daily average PM10 concentration
pop = population of ages 65 and older
= standard error of p (Schwartz, 1994b, Table 4) = 0.00059
Incidence Rate. Hospital admissions for COPD (ICD-9 codes: 491-492, 494-496) are based on first-listed
discharge figures for the latest available year, 1994. The rate equals the annual number of first-listed
diagnoses for discharges (0.369 million) divided by the 1994 population of individuals 65 years and older
(33.162 million), and then divided by 365 days in the year. The discharge figures are from Graves and
Gillum (1997, Table 1), and the population data are from U.S. Bureau of the Census (1997, Table 14).
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3.3.14 Hospital Admissions for All Respiratory (Schwartz, 1996, Spokane)
Schwartz (1996) examined the relationship between air pollution and hospital admissions for
individuals 65 and older in Spokane, Washington, from January 1988 to December 1990. In single
pollutant models, Schwartz found that both PM10 and ozone were significant. In single pollutant models,
Schwartz found PM10 was marginally significantly linked to pneumonia and ozone was not significant; no
link was found to COPD for either pollutant. Two-pollutant models were not estimated because of limited
overlap between PM10 and ozone data.
The C-R function to estimate the change in all respiratory hospital admissions associated with
daily changes in PM10 is:
A All Re spiratory Admissions = - [_y0 (e~P'^PMw - 1)^- pop,
where:
y0 = daily hospital admission rate for all respiratory per person 65 and older = 1.187 E-4
P =PM10 coefficient = 0.00163
A PM10 = change in daily average PM10 concentration
pop = population of ages 65 and older
= standard error of p = 0.000470
Incidence Rate. All respiratory hospital admissions (ICD-9 codes: 460-519) are based on first-listed
discharge figures for the latest available year, 1994. The rate equals the annual number of first-listed
diagnoses for discharges (1.437 million) divided by the 1994 population of individuals 65 years and older
(33.162 million), and then divided by 365 days in the year. The discharge figures are from Graves and
Gillum (1997, Table 1), and the population data are from U.S. Bureau of the Census (1997, Table 14).
Coefficient Estimate (p). Based on a model with ozone, the coefficient (p) is estimated from the relative
risk (1.085) associated with a 50 (jg/m3 change in exposure (Schwartz, 1996, Table 3):
Standard Error ( p). The standard error ( p) was calculated as the average of the standard errors implied
by the reported lower and upper bounds of the relative risk (Schwartz, 1996, Table 3):
ln(1.085)
ln(1.085)
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= 0.000410.
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3.3.15 Hospital Admissions for All Respiratory (Schwartz, 1995, New Haven)
Schwartz (1996) examined the relationship between air pollution and hospital admissions for
individuals 65 and older in New Haven, Connecticut, from January 1988 to December 1990. In single-
pollutant models, PM10 and SO2 were significant, while ozone was marginally significant. In two-pollutant
models, ozone was significant in one of two models, and had stable coefficient estimates; PM10 was
significant in two of two models, but had less stable estimates. SO2 was significant in one of four models.
The C-R function in this analysis is based on a two-pollutant model with ozone and PM10.
The C-R function to estimate the change in all respiratory hospital admissions associated with
daily changes in PM10 is:
A All Re spiratory Admissions = - \yQ -(e ~^ 'APMw - l)^- pop,
where:
y0 = daily hospital admissions for all respiratory per person 65 and older = 1.187 E-4
P =PM10 coefficient = 0.00172
A PM10 = change in daily average PM10 concentration
pop = population of ages 65 and older
= standard error of p = 0.000930
Incidence Rate. All respiratory hospital admissions (ICD-9 codes: 460-519) are based on first-listed
discharge figures for the latest available year, 1994. The rate equals the national annual number of first-
listed diagnoses for discharges (1.437 million) divided by the 1994 U.S. population of individuals 65 years
and older (33.162 million), and then divided by 365 days in the year. The discharge figures are from
Graves and Gillum (1997, Table 1), and the population data are from U.S. Bureau of the Census (1997,
Table 14).
Coefficient Estimate (p). Based on a model with ozone, the daily average coefficient (p) is estimated from
the relative risk (1.09) associated with a change in PM10 exposure of 50 (jg/m3 (Schwartz, 1995, Table 3):
ln(1.09)
j3 = = 0.00172.
Standard Error ( p). The standard error ( p) was calculated as the average of the standard errors implied
by the reported lower and upper bounds of the relative risk (Schwartz, 1995, Table 3).
ln(1.20) ln(1.09)
( ln(1.09) ln(1.00)
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^^=0.000930.
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3.3.16 Hospital Admissions for All Respiratory (Schwartz, 1995, Tacoma)
Schwartz (1996) examined the relationship between air pollution and hospital admissions for
individuals 65 and older in Tacoma, Washington, from January 1988 to December 1990. In single-
pollutant models, PM10, ozone, and SO2 were all significant. In two-pollutant models, ozone was
significant in two of two models, and had stable coefficient estimates; PM10 was significant in one of two
models, but had less stable estimates; SO2 was not significant in either of the two-pollutant models. The
C-R function in this analysis is based on a two-pollutant model with ozone and PM10.
The C-R function to estimate the change in all respiratory hospital admissions associated with
daily changes in PM10 is:
A All Re spiratory Admissions = - \yQ -(e ~^ 'APMw - l)^- pop,
where:
y0 = daily hospital admissions for all respiratory conditions per person 65 and older = 1 . 187 E-4
P = PM10 coefficient = 0.00227
A PM10 = change in daily average PM10 concentration
pop = population of ages 65 and older
p = standard error of p = 0.00145
Incidence Rate. All respiratory hospital admissions (ICD-9 codes: 460-519) are based on first-listed
discharge figures for the latest available year, 1994. The rate equals the national annual number of first-
listed diagnoses for discharges (1.437 million) divided by the 1994 U.S. population of individuals 65 years
and older (33.162 million), and then divided by 365 days in the year. The discharge figures are from
Graves and Gillum (1997, Table 1), and the population data are from U.S. Bureau of the Census (1997,
Table 14).
Coefficient Estimate (p). Based on a model with ozone, the daily average coefficient (p) is estimated from
the relative risk (1.12) associated with a change in PM10 exposure of 50 (jg/m3 (Schwartz, 1995, Table 6):
£ = ^= 0.00227.
Standard Error ( p). The standard error ( p) was calculated as the average of the standard errors implied
by the reported lower and upper bounds of the relative risk (Schwartz, 1995, Table 6):
-....
= ao°144
ln(1.29)
fiugh ~ ft 50 " 50
- -
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^^=0.00145.
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3.3.17 Hospital Admissions for Asthma (Sheppard et al., 1999, Seattle)
Sheppard et al. (1999) studied the relation between air pollution in Seattle and nonelderly hospital
admissions for asthma from 1987 to 1994. They used air quality data for PM10, PM25, coarse PM25_10,
SO2, ozone, and CO in a Poisson regression model with control for time trends, seasonal variations, and
temperature-related weather effects. They found asthma hospital admissions associated with PM10, PM2 5,
coarse PM25.10, CO, and ozone. They did not observe an association for SO2. They found PM and CO to
be jointly associated with asthma admissions. The best fitting model was found using ozone. However,
ozone data was only available April through October, so they did not consider ozone further. The C-R
function in this analysis is based on a two-pollutant model with CO and PM2 5.
The C-R function to estimate the change in hospital admissions for asthma associated with daily
changes in PM25 is:
A Asthma Admissions = - \y0 (e"^425 - l) I pop,
where:
y0 = daily hospital admission rate for asthma per person = 4.52 E-6
P = PM25 coefficient = 0.00227
APM2 5 = change in daily average PM2 5 concentration
pop = population of ages less than 65
= standard error of p = 0.000948
Incidence Rate. Hospital admissions for asthma (ICD-9 code: 493) are based on first-listed discharge
figures for the latest available year, 1994. The rate equals the annual number of first-listed diagnoses for
discharges (0.375 million) divided by the 1994 population (227.210 million), and then divided by 365 days
in the year. The discharge figures are from Graves and Gillum (1997, Table 1), and the population data
are from U.S. Bureau of the Census (1997, Table 14).
Coefficient Estimate (p). Based on a model with CO, the daily average coefficient (p) is estimated from
the relative risk (1.03) associated with a change in PM25 exposure over the interquartile range of 8 to 21
Mg/m3 (Sheppard et al., 1999, Table 3 and p. 28):
ln(1.03)
ft = = 0.00227 .
Standard Error ( p). The standard error ( p) was calculated as the average of the standard errors implied
by the reported lower and upper bounds of the relative risk (Sheppard et al., 1999, p. 28):
( ln(1.06)
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ln(1.03)
a -= 13 13 .
L96 1.96
= 0.000948.
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3.3.18 Hospital Admissions for Cardiovascular (Schwartz, 1999, Eight Counties)
Schwartz (1999) examined the link between air pollution and cardiovascular admissions for
persons 65 and older in eight U.S. counties from 1988 to 1990. They limited the analysis to CO and PM10,
and found that in two-pollutant models both pollutants were significant. The C-R function in this analysis
is based on a two-pollutant model with CO and PM10.
The C-R function to estimate the change in cardiovascular hospital admissions associated with
daily changes in PM10 is:
^Cardiovascular Admissions = -Iy0 .(e~/3'&PMw - l)\- pop,
where:
y0 = daily hospital admission rate for cardiovascular disease per person 65 and older = 2.23 E-4
P = PM10 coefficient = 0.000737
APM10 = change in daily average PM10 concentration
pop = population of ages 65 and older
= standard error of p = 0.000170
Incidence Rate. Congestive heart failure hospital admissions (ICD-9 codes: 390-429) are based on first-
listed discharge figures for the latest available year, 1994. The rate equals the annual number of first-listed
diagnoses for discharges (2.695 million) divided by the 1994 population of individuals 65 years and older
(33.162 million), and then divided by 365 days in the year. The discharge figures are from Graves and
Gillum (Graves et al., 1997, Table 1), and the population data are from U.S. Bureau of the Census (1997,
Table 14).
Coefficient Estimate (p). In a two pollutant model with CO, the estimated coefficient (p) is based on a
1.86 percent increase in admissions due to a PM10 change of 25 (Jg/m3 (Schwartz, 1999, p. 20). 85 This
translates to a relative risk of 1.0186. The coefficient is calculated as follows:
, aooo737.
85This result is based on the five counties with a PMIO-CO correlation of less than 0.5.
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Standard Error ( p). The standard error ( p) was calculated as the average of the standard errors implied
by the reported lower and upper bounds of the relative risk (Schwartz, 1999, p. 20):
n(1.0271) ln(1.0186)
ln(1.0186) ln(1.0101)^
-=0.000171
1.96 1.96
= 0.000170.
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3.3.19 Hospital Admissions for Cardiovascular (Schwartz, 1997, Tucson)
Schwartz (1997) examined the relation between air pollution and cardiovascular admissions for
persons 65 and older in Tucson, Arizona from 1988 to 1990. They focused on ozone, CO, SO2, NO2, and
PM10. In a model with the two pollutants, CO and PM10 were both significant. No effect was seen for O3,
SO2, and NO2. The C-R function in this analysis is based on a two-pollutant model with CO and PM10.
The C-R function to estimate the change in daily cardiovascular hospital admissions associated
with daily changes in PM10 is:
^Cardiovascular Admissions = -Iy0 .(e~/3'&PMw - l)\- pop,
where:
y0 = daily hospital admission rate for cardiovascular disease per person 65 and older = 2.23 E-4
P =PM10 coefficient = 0.00102
APM10 = change in daily average PM10 concentration
pop = population of ages 65 and older
p = standard error of p = 0.000423
Incidence Rate. Congestive heart failure hospital admissions (ICD-9 codes: 390-429) are based on first-
listed discharge figures for the latest available year, 1994. The rate equals the annual number of first-listed
diagnoses for discharges (2.695 million) divided by the 1994 population of individuals 65 years and older
(33.162 million), and then divided by 365 days in the year. The discharge figures are from Graves and
Gillum (Graves et al., 1997, Table 1), and the population data are from U.S. Bureau of the Census (1997,
Table 14).
Coefficient Estimate (p). In a two pollutant model with CO, the estimated coefficient (p) is based on a
2.37 percent increase in admissions due to an interquartile PM10 change of 28 to 51 (Jg/m3 (Schwartz,
1997, Tables 1 and 4). This translates to a relative risk of 1.0237. The coefficient is calculated as follows:
ln(1.0237)
J3= =0.00102.
Standard Error ( p). The standard error ( p) was calculated as the average of the standard errors implied
by the reported lower and upper bounds of the relative risk (Schwartz, 1997, Table 4):
fln(I0472) ln(1.0237)1
l~ 0000.03
ln(I0237) ln(I0008y\
~~~
a, = " = O.OOQ423.
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3.3.20 Hospital Admissions for Cardiac (Burnett et al., 1997, Toronto)
Burnett et al. (1997) examined the relationship between air pollution and hospital admissions for
individuals of all ages in Toronto, Canada during the summers of 1992- 1994. COH and ozone were
significantly linked to cardiac admissions; other PM measures less strongly linked. In two-pollutant
models, they found CO, NO2, and SO2 were not significant, when controlling for COH. Ozone was
significant, controlling for COH. In four-pollutant models, COH and O3 were both significant; no effect
for NO2 and SO2. The C-R function in this analysis is based on a two-pollutant model with ozone and
PM2.5.10.
The C-R function to estimate the change in cardiac hospital admissions associated with daily
changes in PM10_25 is:
A Cardiac Admissions =- [y0 ^e~/JAPMio-" _ lj^. pop,
where:
y0 = daily hospital admission rate for cardiac problems per person = 3.81 E-5
P = PM10_2.5 coefficient = 0.00704
APM10_2.5 = change in daily average PM10_2 5 concentration
pop = population of all ages
p = standard error of p = 0.00215
Incidence Rate. Hospital admissions for cardiac (410-414, 427-428) are based on first-listed discharge
figures for the latest available year, 1994. The rate equals the annual number of first-listed diagnoses for
discharges (3.617 million) divided by the 1994 population (260.372 million), and then divided by 365 days
in the year. The discharge figures are from Graves and Gillum (1997, Table 1), and the population data
are from U.S. Bureau of the Census (1997, Table 14).
Coefficient Estimate (p). The estimated coefficient (p) is based on a relative risk of 1.034 due to a PM10_25
change of 4.75 (jg/m3 (Burnett et al., 1997, Tables 2 and 5). The coefficient is calculated as follows:
ln(1.034)
=0.00704.
Standard Error ( p). The standard error ( p) was calculated using the t-value (t=3.28) (Burnett et al.,
1997, Table 6)
.00704
^ = ^-=0.00215.
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3.3.21 Hospital Admissions for Ischemic Heart Disease (Schwartz et al., 1995)
Schwartz and Morris (1995) examined the relationship between air pollution and hospital
admissions for ischemic heart disease, dysrhythmias, and congestive heart failure in Detroit, Michigan,
from 1986 to 1989. In their analysis, they considered ozone, CO, SO2, and PM10. For ischemic heart
disease, they found no effect for SO2 and ozone; however, in a two-pollutant model, they found that PM10
and CO were both significant. They did not find any significant relation between air pollution and
dysrhythmias. For congestive heart failure, they found single-pollutant models with PM10 and CO were
both significant; SO2 and O3 were not significant. In two-pollutant models, they found that PM10 and CO
were both significant. The C-R function in this analysis is based on a two-pollutant model with CO and
PM10.
The C-R function to estimate the change in daily hospital admissions for ischemic heart disease
associated with daily changes in PM10 is:
hlschemic Heart Disease Admissions = - 1 y0 (e ~^ 'APMi° - \)\- pop,
where:
y0 = daily hospital admission rate for ischemic heart disease per person 65 and older = 9.96 E-5
P = PM10 coefficient= 0.000496
APM10 = change in daily average PM10 concentration
pop = population of ages 65 and older
p = standard error of p = 0.000220
Incidence Rate. Ischemic heart disease hospital admissions (ICD-9 codes: 410-414) are based on first-
listed discharge figures for the latest available year, 1994. The rate equals the annual number of first-listed
diagnoses for discharges (1.206 million) divided by the 1994 population of individuals 65 years and older
(33.162 million), and then divided by 365 days in the year. The discharge figures are from Graves and
Gillum (Graves et al., 1997, Table 1), and the population data are from U.S. Bureau of the Census (1997,
Table 14).
Coefficient Estimate (p). Based on a model with CO, the daily average coefficient (p) is estimated from
the relative risk (1.016) associated with a change in PM10 exposure over the interquartile range of 30 to 62
(jg/m3 (Schwartz et al., 1995, Tables 1 and 4):
n ₯1.016)
ff= =0.000496.
Standard Error ( p). The standard error ( p) was calculated as the average of the standard errors implied
by the reported lower and upper bounds of the relative risk (Schwartz et al., 1995, Table 4):
32 32
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fln(1.016)_ln(I002)
3232
a, = " = 0.000220.
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3.3.22 Hospital Admissions for Congestive Heart Failure (Schwartz et al., 1995)
Schwartz and Morris (1995) examined the relationship between air pollution and hospital
admissions for ischemic heart disease, dysrhythmias, and congestive heart failure in Detroit, Michigan,
from 1986 to 1989. In their analysis, they considered ozone, CO, SO2, and PM10. For ischemic heart
disease, they found no effect for SO2 and ozone; however, in a two-pollutant model, they found that PM10
and CO were both significant. They did not find any significant relation between air pollution and
dysrhythmias. For congestive heart failure, they found single-pollutant models withPM10 and CO were
both significant; SO2 and O3 were not significant. In two-pollutant models, they found that PM10 and CO
were both significant. The C-R function in this analysis is based on a two-pollutant model with CO and
PM10.
The C-R function to estimate the change in daily hospital admissions for congestive heart failure
associated with daily changes in PM10 is:
^Congestive Heart Failure Admissions = -\y0 .(e~l}APMw -I)]- pop,
where:
y0 = daily hospital admission rate for congestive heart failure per person 65 and older = 5.82 E-5
P =PM10 coefficient = 0.000741
APM10 = change in daily average PM10 concentration
pop = population of ages 65 and older
p = standard error of p = 0.0003 11
Incidence Rate. Congestive heart failure hospital admissions (ICD-9 code: 428) are based on first-listed
discharge figures for the latest available year, 1994. The rate equals the annual number of first-listed
diagnoses for discharges (0.705 million) divided by the 1994 population of individuals 65 years and older
(33.162 million), and then divided by 365 days in the year. The discharge figures are from Graves and
Gillum (Graves et al., 1997, Table 1), and the population data are from U.S. Bureau of the Census (1997,
Table 14).
Coefficient Estimate (p). Based on a model with CO, the daily average coefficient (p) is estimated from
the relative risk (1.024) associated with a change in PM10 exposure over the interquartile range of 30 to 62
(jg/m3 (Schwartz et al., 1995, Tables 1 and 6):
32
Standard Error ( p). The standard error ( p) was calculated as the average of the standard errors implied
by the reported lower and upper bounds of the relative risk (Schwartz et al., 1995, Table 6):
ln(1.044) ln(1.024)^
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ln(1.024) ln(1.004y\
= 0.000311.
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3.3.23 Hospital Admissions for Dysrhythmias (Burnett et al., 1999, Toronto)
Burnett et al. (1999) examined the relationship between air pollution and hospital admissions for
individuals of all ages in Toronto, Canada froml980 to 1994. They estimated multiple pollutant models,
where pollutants for best fitting model were chosen using stepwise regression based on AIC criterion.
Dysrhythmias admissions were linked to O3, CO, and PM2 5. This C-R function is based on the results of
this three-pollutant model.
The C-R function to estimate the change in hospital admissions for dysrhythmias associated with
daily changes in PM25 is:
^Dysrhythmias Admissions = - [y0 (e'*25 - 1) pop,
where:
y0 = daily hospital admission rate for dysrhythmias per person = 6.46 E-6
P = PM25 coefficient = 0.00136
APM2 5 = change in daily average PM2 5 concentration
pop = population of all ages
p = standard error of p = 0.000910
Incidence Rate. Hospital admissions for dysrhythmias (ICD-9 code: 427) are based on first-listed
discharge figures for the latest available year, 1994. The rate equals the annual number of first-listed
diagnoses for discharges (0.614 million) divided by the 1994 population (260.372 million), and then
divided by 365 days in the year. The discharge figures are from Graves and Gillum (1997, Table 1), and
the population data are from U.S. Bureau of the Census (1997, Table 14).
Coefficient Estimate (p). The estimated coefficient (p) is based on a 2.47 percent increase in admissions
due to a PM25 change of 18 (jg/m3 (Burnett, 1999, Tables 1 and 5). This translates to a relative risk of
1.0247. The coefficient is calculated as follows:
r 18
Standard Error ( p). The standard error ( p) was calculated using the t-value (t=1.49) (Burnett, 1999):
.00136
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3.4 EMERGENCY ROOM VISITS
There is a wealth of epidemiological information on the relationship between air pollution and
hospital admissions for various respiratory and cardiovascular diseases; in addition, some studies have
examined the relationship between air pollution and ER visits. Because most ER visits do not result in an
admission to the hospital ~ the majority of people going to the ER are treated and return home we treat
hospital admissions and ER visits separately, taking account of the fraction of ER visits that do get
admitted to the hospital, as discussed below.
The only types of ER visit that have been explicitly linked to ozone in U.S. and Canadian
epidemiological studies are asthma visits. However, it seems likely that ozone may be linked to other types
of respiratory-related ER visits.
3.4.1 Emergency Room Visits for Asthma (Schwartz et al., 1993, Seattle)
Schwartz et al. (1993) examined the relationship between air quality and emergency room visits for
asthma in persons under 65 and 65 and over, living in Seattle from September 1989 to September 1990.
Using single-pollutant models they found daily levels of PM10 linked to ER visits in individuals ages under
65, and they found no effect in individuals ages 65 and over. They did not find a significant effect for SO2
and ozone in either age group. The results of the single pollutant model for PM10 are used in this analysis.
The C-R function to estimate the change in daily emergency room visits for asthma associated with
daily changes in PM10 is:
A Asthma ERvisits = -[y0 (e~^^M^ _ l)\. pop ,
where:
y0 = daily ER visits for asthma per person under 65 years old = 7.69 E-6
P = PM10 coefficient (Schwartz et al., 1993, p. 829) = 0.00367
APM10 = change in daily average PM10 concentration
pop = population of ages 0-64
p = standard error of (3 (Schwartz et al., 1993, p. 829) = 0.00126
Incidence Rate. Smith et al. (1997, p. 789) reported that in 1987 there were 445,000 asthma admissions
and 1 .2 million asthma ER visits. Assuming that all asthma hospital admissions pass through the ER room,
then 37% of ER visits end up as hospital admissions. As described below, the 1994 asthma admission rate
for people less than 65 is 4.522 E-6. So one might assume, ER visits = (l/0.37)*asthma admission rate =
2.7*asthma admission rate = 1.22 E-5. Now, ER visits (subtracting out those visits that end up as
admissions)= 1.7*asthma admission rate = 7.69 E-6.
Asthma hospital admissions (ICD-9 code: 493) are based on first-listed discharge figures for the
latest available year, 1994. The rate equals the annual number of first-listed diagnoses for discharges
(0.375 million) divided by the 1994 population of individuals under 65 years old (227.21 million), and then
divided by 365 days in the year. The discharge figures are from Graves and Gillum (Graves et al., 1997,
Table 1), and the population data are from U.S. Bureau of the Census (1997, Table 14).
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3.5 ACUTE MORBIDITY
In addition to chronic illnesses and hospital admissions, there is a considerable body of scientific
research that has estimated significant relationships between elevated air pollution levels and other
morbidity health effects. Chamber study research has established relationships between specific air
pollution chemicals and symptoms such as coughing, pain on deep inspiration, wheezing, eye irritation and
headaches. In addition, epidemiological research has found air pollution relationships with acute infectious
diseases (e.g., bronchitis, sinusitis) and a variety of "symptom-day" categories. Some "symptom-day"
studies examine excess incidences of days with identified symptoms such as wheezing, coughing, or other
specific upper or lower respiratory symptoms. Other studies estimate relationships for days with a more
general description of days with adverse health impacts, such as "respiratory restricted activity days" or
work loss days.
A challenge in preparing an analysis of the minor morbidity effects is identifying a set of effect
estimates that reflects the full range of identified adverse health effects but avoids double counting. From
the definitions of the specific health effects examined in each research project, it is possible to identify a set
of effects that are non-overlapping, and can be ultimately treated as additive in a benefits analysis.
3.5.1 Acute Bronchitis C-R Function (Dockery et al., 1996)
Dockery et al. (1996) examined the relationship between PM and other pollutants on the reported
rates of asthma, persistent wheeze, chronic cough, and bronchitis, in a study of 13,369 children ages 8-12
living in 24 communities in U.S. and Canada. Health data were collected in 1988-1991, and single-
pollutant models were used in the analysis to test a number of measures of particulate air pollution.
Dockery et al. found that annual level of sulfates and particle acidity were significantly related to
bronchitis, and PM2^ and PM10 were marginally significantly related to bronchitis.86 They also found
nitrates were linked to asthma, and sulfates linked to chronic phlegm. It is important to note that the study
examined annual pollution exposures, and the authors did not rule out that acute (daily) exposures could be
related to asthma attacks and other acute episodes.
86 The original study measured PM215 however when using the study's results we use PM25. This makes only a negligible
difference, assuming that the adverse effects of PM2A and PM25 are comparable.
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Earlier work, by Dockery et al. (1989), based on six U.S. cities, found acute bronchitis and chronic
cough significantly related to PM15. Because it is based on a larger sample, the Dockery et al. (1996) study
is the better study to develop a C-R function linking PM2 5 with bronchitis. The C-R function to estimate
the change in acute bronchitis is:
y0
kAcute Bronchitis = 7^77 vn pop,
/i . \ _AWWo =-u . / U r r '
where:
y0 = annual bronchitis incidence rate per person = 0.044
p = estimated PM25 logistic regression coefficient = 0.0272
APM2 5 = change in annual average PM2 5 concentration
pop = population of ages 8-12
p = standard error of p = 0.0171
Incidence Rate. Bronchitis was counted in the study only if there were "reports of symptoms in the past
12 months" (Dockery et al., 1996, p. 501). It is unclear, however, if the cases of bronchitis are acute and
temporary, or if the bronchitis is a chronic condition. Dockery et al. found no relationship between PM and
chronic cough and chronic phlegm, which are important indicators of chronic bronchitis. For this analysis,
we assumed that the C-R function based on Dockery et al. is measuring acute bronchitis.
In 1994, 2,115,000 children ages 5-17 experienced acute conditions (Adams et al., 1995, Table 6)
out of population of 48.110 million children ages 5-17 (U.S. Bureau of the Census, 1998, Table 14), or 4.4
percent of this population. This figure is somewhat lower than the 5.34 percent of children under the age of
18 reported to have chronic bronchitis in 1990-1992 (Collins, 1997, Table 8). Dockery et al. (1996, p.
503) reported that in the 24 study cities the bronchitis rate varied from three to ten percent. Finally a
weighted average of the incidence rates in the six cities in the Dockery et al. (1989) study is 6.34 percent,
where the sample size from each city is used to weight the respective incidence rate (Dockery et al., 1989,
Tables 1 and 4).87 This analysis assumes a 4.4 percent prevalence rate is the most representative of the
national population. Note that this measure reflects the fraction of children that have a chest ailment
diagnosed as bronchitis in the past year, not the number of days that children are adversely affected by
acute bronchitis.88
Coefficient Estimate (p). The estimated logistic coefficient (p) is based on the odds ratio (= 1.50)
associated with being in the most polluted city (PM21 = 20.7 (jg/m3) versus the least polluted city (PM21 =
5.8 (jg/m3) (Dockery et al., 1996, Tables 1 and 4). The original study used PM2 b however, we use the
PM21 coefficient and apply it to PM2 5 data.
ln(1.50)
87The unweighted average of the six city rates is 0.0647.
88In 1994, there were 13,707,000 restricted activity days associated with acute bronchitis, and 2,115,000 children (ages 5-
17) experienced acute conditions (Adams et al., 1995, Tables 6 and 21). On average, then, each child with acute bronchitis suffered
6.48 days.
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Standard Error ( p). The standard error of the coefficient ( p) is calculated from the reported lower and
upper bounds of the odds ratio (Dockery et al., 1996, Table 4):
(ln(2.47)
V 14.9 14.9_=aoi71
196 196
ln(1.50)
B - B, V 149 149 )
196=
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3.5.2 Lower Respiratory Symptoms (Schwartz et al., 1994)
Schwartz et al. (1994) used logistic regression to link lower respiratory symptoms in children with
SO2, NO2, ozone, PM10, PM2 5, sulfate and H+ (hydrogen ion). Children were selected for the study if they
were exposed to indoor sources of air pollution: gas stoves and parental smoking. The study enrolled 1,844
children into a year-long study that was conducted in different years (1984 to 1988) in six cities. The
students were in grades two through five at the time of enrollment in 1984. By the completion of the final
study, the cohort would then be in the eighth grade (ages 13-14); this suggests an age range of 7 to 14.
In single pollutant models SO2, NO2, PM2 5, and PM10 were significantly linked to cough. In two-
pollutant models, PM10 had the most consistent relationship with cough; ozone was marginally significant,
controlling for PM10. In models for upper respiratory symptoms, they reported a marginally significant
association for PM10. In models for lower respiratory symptoms, they reported significant single-pollutant
models, using SO2, O3, PM2 5, PM10, SO4, and H+.
The C-R function used to estimate the change in lower respiratory symptoms is:
A Lower Respiratory Symptoms =- -/ \ y0 -pop.
where:
y0 = daily lower respiratory symptom incidence rate per person = 0.0012
p = estimated PM25 logistic regression coefficient = 0.01823
APM2 5 = change in daily average PM2 5 concentration
pop = population of ages 7-14
p = standard error of p = 0.00586
Incidence Rate. The proposed incidence rate, 0.12 percent, is based on the percentiles in Schwartz et al.
(Schwartz et al., 1994, Table 2). They did not report the mean incidence rate, but rather reported various
percentiles from the incidence rate distribution. The percentiles and associated values are 10th = 0 percent,
25th = 0 percent, 50th = 0 percent, 75th = 0.29 percent, and 90th = 0.34 percent. The most conservative
estimate consistent with the data are to assume the incidence is zero up to the 75th percentile, a constant
0.29 percent between the 75th and 90th percentiles, and a constant 0.34 percent between the 90th and 100th
percentiles. Alternatively, assuming a linear slope between the 50th and 75th, 75th and 90th, and 90th to 100th
percentiles, the estimated mean incidence rate is 0.12 percent,89 which is used in this analysis.
Coefficient Estimate (p). The coefficient p is calculated from the reported odds ratio (= 1.44) in a single-
pollutant model associated with a 20 ,ug/m3 change in PM25 (Schwartz et al., 1994, Table 5):
f=a*w=o.olsa.
20
Standard Error ( p). The standard error for the coefficient ( p) is calculated from the reported lower and
upper bounds of the odds ratio (Schwartz et al., 1994, Table 5):
89For example, the 62.5th percentile would have an estimated incidence rate of 0.145 percent.
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, hlgh
ft'lttgh 1.96 1.96
ln(1.44)
= 0.00597
a. = ^=0 =0.00574
1.96 1.96
. 0.00586.
Population. Schwartz et al. (1994, Table 5 and p. 1235) enrolled 1,844 children into a year-long study
that was conducted in different years in different cities; the students were in grades two through five and
lived in six U.S. cities. All study participants were enrolled in September 1984; the actual study was
conducted in Watertown, MA in 1984/85; Kingston-Harriman, TN, and St. Louis, MO in 1985/86;
Steubenville, OH, and Portage, WI in 1986/87; and Topeka, KS in 1987/88. The study does not publish
the age range of the children when they participated. As a result, the study is somewhat unclear about the
appropriate age range for the resulting C-R function. If all the children were in second grade in 1984 (ages
7-8) then the Topeka cohort would be in fifth grade (ages 10-11) when they participated in the study. It
appears from the published description, however, that the students were in grades two through five in
1984.90 By the completion of the study, some students in the Topeka cohort would then be in the eighth
grade (ages 13-14); this suggests an age range of 7 to 14.
90Neas et al. (1994, p. 1091) used the same data set; their description suggests that grades two to five were represented
initially.
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3.5.3 Upper Respiratory Symptoms (Pope et al., 1991)
Using logistic regression, Pope et al. (1991) estimated the impact of PM10 on the incidence of a
variety of minor symptoms in 55 subjects (34 "school-based" and 21 "patient-based") living in the Utah
Valley from December 1989 through March 1990. The children in the Pope et al. study were asked to
record respiratory symptoms in a daily diary. With this information, the daily occurrences of upper
respiratory symptoms (URS) and lower respiratory symptoms (LRS) were related to daily PM10
concentrations. Pope et al. describe URS as consisting of one or more of the following symptoms: runny
or stuffy nose; wet cough; and burning, aching, or red eyes. Levels of ozone, NO2, and SO2 were reported
low during this period, and were not included in the analysis. The sample in this study is relatively small
and is most representative of the asthmatic population, rather than the general population. The school-
based subjects (ranging in age from 9 to 11) were chosen based on "a positive response to one or more of
three questions: ever wheezed without a cold, wheezed for 3 days or more out of the week for a month or
longer, and/or had a doctor say the 'child has asthma' (Pope et al., 1991, p. 669)." The patient-based
subjects (ranging in age from 8 to 72) were receiving treatment for asthma and were referred by local
physicians. Regression results for the school-based sample (Pope et al., 1991, Table 5) show PM10
significantly associated with both upper and lower respiratory symptoms. The patient-based sample did
not find a significant PM10 effect. The results from the school-based sample are used here.
The C-R function used to estimate the change in upper respiratory symptoms is:
AUpper'^Respiratory Symptoms = -
pop,
where:
y0 = daily upper respiratory symptom incidence rate per person = 0.3419
p = estimated PM10 logistic regression coefficient (Pope et al., 1991, Table 5) = 0.0036
APM10 = change in daily average PM10 concentration
pop = asthmatic population91 ages 9 to 11 = 6.91% of population ages 9 to 11
p = standard error of p (Pope et al., 1991, Table 5) = 0.0015
Incidence Rate. The incidence rate is published in Pope et al. (Pope et al., 1991, Table 2). Taking a
sample-size-weighted average, one gets an incidence rate of 0.3419.
"Adams (1995, Table 57) reported that in 1994, 6.91% of individuals under the age of 18 have asthma.
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3.5.4 Any of 19 Respiratory Symptoms (Krupnick et al., 1990)
Krupnick et al. (1990) estimated the impact of air pollution on the incidence of any of 19
respiratory symptoms or conditions in 570 adults and 756 children living in three communities in Los
Angeles, California from September 1978 to March 1979. Krupnick et al. (1990) listed 13 specific
"symptoms or conditions": head cold, chest cold, sinus trouble, croup, cough with phlegm, sore throat,
asthma, hay fever, doctor-diagnosed ear infection, flu, pneumonia, bronchitis, and bronchiolitis. The other
six symptoms or conditions are not specified.
In their analysis, they included COH, ozone, NO2, and SO2, and they used a logistic regression
model that takes into account whether a respondent was well or not the previous day. A key difference
between this and the usual logistic model, is that the model they used includes a lagged value of the
dependent variable. In single-pollutant models, daily O3, COH, and SO2 were significantly related to
respiratory symptoms in adults. Controlling for other pollutants, they found that ozone was still
significant. The results were more variable for COH and SO2, perhaps due to collinearity. NO2 had no
significant effect. No effect was seen in children for any pollutant. The results from the two-pollutant
model with COH and ozone are used to develop a C-R function.
The C-R function used to estimate ARD2 is based on Krupnick et al. (1990, p. 12):92
where:
P* = first derivative of the stationary probability = 0.000461
APM10 = change in daily average PM10 concentration
pop = population of ages 18-65 (Krupnick et al., 1990, Table I)93
p = standard error of p* = 0.000239
Coefficient Estimate (p*). The logistic regression model used by Krupnick et al. (1990) takes into account
whether a respondent was well or not the previous day. Following Krupnick et al. (p. 12), the probability
that one is sick is on a given day is:
probability(ARD2) = ^
probability(ARD2\sicknessornott_l ) = p,=
92Krupnick and Kopp (1988, p. 2-24) and ESEERCO (1994, p. V-32) used the same C-R functional form as that used here.
93Krupnick et al. (1990, Table 1) reported the age distribution in their complete data, but they did not report the ages of
individuals that were considered "adult." This analysis assumes that individuals 18 and older were considered adult. Only a small
percentage (0.6%) of the study population is above the age of 60, so the C-R function was limited to the adult population up through
the age of 65.
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where:
X = the matrix of explanatory variables
Po = the probability of sickness on day t, given wellness on day t-1, and
P! = the probability of sickness on day t, given sickness on day t-1.
In other words, the transition probabilities are estimated using a logistic function; the key difference
between this and the usual logistic model, is that the model includes a lagged value of the dependent
variable.
To calculate the impact of COH (or other pollutants) on the probability of ARD2, it is possible, in
principle, to estimate ARD2 before the change in COH and after the change:
MRD2 = ARD2after - ARD2before .
However the full suite of coefficient estimates are not available.94 Rather than use the full suite of
coefficient values, the impact of COH on the probability of probability of ARD2 may be approximated by
the derivative of ARD2 with respect to COH:
dprobability(ARD2) P, (l- Pi] $CQH'[PI
where pCOH is the reported logistic regression coefficient for COH. Since COH data are not available for
the benefits analysis, an estimated PM10 logistic regression coefficient is used based on the following
assumed relationship between PM10, COH, and TSP:
COH = 0.116-TSP
PMW =0.55- TSP
COH = 0.2109 -PMW
PPM = 0.2109 PCOH = 0.2109 0.0088 = 0.001856.
This analysis uses pCOH = 0.0088 (Krupnick et al., 1990, Table V equation 3). The conversion
from COH to TSP is based on study-specific information provided to ESEERCO (1994, p. V-32). The
94The model without NO2 (Krupnick et al., 1990, Table V equation 3) was used in this analysis, but the full suite of
coefficient estimates for this model were not reported. Krupnick et al. (1990, Table IV) reported all of the estimated coefficients for a
model of children and for a model of adults when four pollutants were included (ozone, COH, SO2, and NO2). However, because of
high collinearity between NO2 and COH, NO2 was dropped from some of the reported analyses (Krupnick et al., p. 10), and the
resulting coefficient estimates changed substantially (see Krupnick et al., 1990, Table IV). Both the ozone and COH coefficients
dropped by about a factor of two or more.
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conversion of TSP to PM10 is from also from ESEERCO (1994, p. V-5), which cited studies by EPA
(1986) and the California Air Resources Board (1982).
The change in the incidence of ARD2 associated with a given change in COH is then estimated by:
9ARD2 _ AARD2
dPMw = APMW
AARD2 _ g.
APMW = PMw
This analysis uses transition probabilities obtained from Krupnick et al. as reported by ESEERCO
(1994, p. V-32), for the adult population: pj = 0.7775 and p0 = 0.0468. This implies:
0.0468 -A -0.7775) -0.00 1856 -[0.7775, +(1-0.0468)1
/WIO = - - - -1 - ,2 - ^ = 0.000461.
(1-0.7775 + 0.0468)
Standard Error ( ^. The standard error for the coefficient ( p) is derived using the reported standard
error of the logistic regression coefficient in Krupnick et al. (1990, Table V):
=* PPMM = 0.2109- /^^ = 0.2109- (0.0088 + (1.96- 0.0046)) = 0.003757
0.0468 (l - 0.7775) 0.003757 [0.7775 + A - 0.0468)1
= - * - -r2 - L .2 V - ^ = 0.000934
(1-0.7775 + 0.0468)
PPMW ugh ~ PPMW (0.000934 - 0.000461)
~L96~L96~
)8COHj/ow = 0.2109 (0.0088 - (l.96 0.0046)) = -4.555 10"5
0.0468 (l - 0.7775) (-4.555 10~5) [0.7775 + (l - 0.0468)1
_ V _ / L _ V _ il-_i 1-17.10"
, .2 ~
(1-0.7775 + 0.0468)
R_R (0.000461 + 1.132 -10
= P Plow = ± - '- = 0.000241
1.96 1.96
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= 0.000239
2
3.5.5 Shortness of Breath (Ostro et al., 1995)
Using a logistic regression estimation, Ostro et al. (1995) estimated the impact of PM10, ozone,
NO2, and SO2 on the incidence of coughing, shortness of breath, and wheezing in 83 African-American
asthmatic children ages 7-12 living in Los Angeles from August through September 1992. Regression
results show both PM10 and ozone significantly linked to shortness of breath; the beginning of an asthma
episode was also significantly linked to ozone. No effect was seen for NO2 and SO2. Results for single-
pollutant models only were presented in the published paper.
The C-R function to estimate the change in shortness of breath days is:
^.Shortness of Breath = -
pop,
where:
y0 = daily shortness of breath incidence rate per person (Ostro et al., 1995, p. 715) = 0.056
p = estimated PM10 logistic regression coefficient = 0.00841
APM10 = change in daily average PM10 concentration
pop = asthmatic African-American population ages 7 to 12 = 6.91% of African-American population
ages 7 to 12
p = standard error of p = 0.00363
Prevalence. Adams (1995, Table 57) reported that in 1994, 6.91% of individuals under the age of 18 have
asthma. It has been reported that African-Americans have a higher prevalence of asthma (e.g., see U.S.
EPA, 1996b). Ostro et al. (1995, p. 71 1) noted that "Although prevalence is only somewhat greater among
African- Americans than among whites, rates of morbidity are markedly higher." Indeed, the asthma rates
for whites and African- Americans were almost identical in 1994 (1995, Table 59), so no correction is made
to the estimated prevalence rate for asthma in African-Americans.
Coefficient Estimate (p). The estimated logistic coefficient (p) is based on the odds ratio of 1.60 (Ostro et
al., 1995, Table 3) associated with a change in mean PM10 of 55.87 /^g/m3 (Ostro et al., 1995, Table 2).
The coefficient is calculated as follows:
Standard Error ( p). The standard error for the coefficient ( p) is calculated from the reported lower and
upper bounds of the odds ratio (Ostro et al., 1995, Table 2):
ln(1.60)
a = ' "*" ' = _^^i - - = 0.003588
"'*** 1.96 1.96
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ty =0.003631.
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3.5.6 Moderate (or Worse) Asthma (Ostro et al., 1991)
Ostro et al. (1991) examined the effect of air pollution on asthmatics, ages 18 to 70, living in
Denver, Colorado from December 1987 to February 1988. The respondents in this study were asked to
record daily a subjective rating of their overall asthma status each day (0=none, l=mild, 2=moderate,
3=severe, 4=incapacitating). Ostro et al. then examined the relationship between moderate (or worse)
asthma and H+, sulfate, SO2, PM25, estimated PM25, PM10, nitrate, and nitric acid. Daily levels of H+ were
linked to cough, asthma, and shortness of breath. PM25 was linked to asthma. Sulfate was linked to
shortness of breath. No effects seen for other pollutants. The C-R function is based on a single-pollutant
linear regression model where the log of the pollutant is used.
The C-R function to estimate the change in the number of days with moderate (or worse) asthma is:
ADays Moderate I Worse Asthma = -{} In ^_^_
(.PM2.5, before)
where:
p = estimated PM25 coefficient (Ostro et al., 1991, Table 5) = 0.0006
PM2 5 = change in daily average PM2 5 concentration
pop = asthmatic population of all ages = 5.61% of the population of all ages (Adams et al., 1995 Table
57)
= standard error of p (Ostro et al., 1991, Table 5) = 0.0003
Coefficient Estimate (p). Two PM25 coefficients are presented, both equal 0.0006, however only one is
significant. The coefficient based on data that does not include estimates of missing PM2 5 values is not
significant ( p = 0.0053); the coefficient that includes estimates of missing PM25 values (estimated using a
function of sulfate and nitrate) is significant at p < 0.5 ( p = 0.0003). The latter coefficient is used here.
Population. The C-R function is applied to asthmatics of all ages, where it is assumed that 5.61 percent of
the population of all ages is asthmatic. This raises two issues: the age group for which the function should
be used, and the fraction of the population that is asthmatic. The study population consists of asthmatics
between the ages of 18 and 70. It seems reasonable to assume that individuals over the age of 70 are at
least as susceptible as individuals in the study population. It also seems reasonable to assume that
individuals under the age of 18 are also susceptible. For example, controlling for oxidant levels,
Whittemore and Korn (1980) found TSP significantly related to asthma attacks in a study population
comprised primarily (59 percent) of individuals less than 16 years of age.
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3.5.7 Minor Restricted Activity Days (Ostro et al., 1989b)
Ostro and Rothschild (1989b) estimated the impact of PM25 on the incidence of minor restricted
activity days (MRADs) and respiratory-related restricted activity days (RRADs) in a national sample of the
adult working population, ages 18 to 65, living in metropolitan areas. The annual national survey results
used in this analysis were conducted in 1976-1981. Controlling for PM25, two-week average O3 has highly
variable association with RRADs and MRADs. Controlling for O3, two-week average PM25 was
significantly linked to both health endpoints in most years.
The study is based on a "convenience" sample of individuals ages 18-65. Applying the C-R
function to this age group is likely a slight underestimate, as it seems likely that elderly are at least as
susceptible to PM as individuals 65 and younger. The elderly appear more likely to die due to PM
exposure than other age groups (e.g., Schwartz, 1994d, p. 30) and a number of studies have found that
hospital admissions for the elderly are related to PM exposures (e.g., Schwartz, 1994a; Schwartz, 1994b).
Using the results of the two-pollutant model, we developed separate coefficients for each year in
the analysis, which were then combined for use in this analysis. The coefficient used in this analysis is a
weighted average of the coefficients (Ostro, 1987, Table IV) using the inverse of the variance as the weight.
The C-R function to estimate the change in the number of minor restricted activity days (MRAD) is:
AMRAD = Ay pop = -[y0 (e-^PM" -1)] pop,
where:
y0 = daily MRAD daily incidence rate per person = 0.02137
p = inverse-variance weighted PM25 coeffcient = 0.00741
APM2 5 = change in daily average PM2 5 concentration95
pop = adult population ages 18 to 65
p = standard error of p = 0.0007
Incidence Rate. The annual incidence rate (7.8) provided by Ostro and Rothschild (1989b, p. 243) was
divided by 365 to get a daily rate of 0.02137.
Coefficient Estimate (p). The coefficient is a weighted average of the coefficients in Ostro and Rothschild
(1989b, Table 4) using the inverse of the variance as the weight:
( 1981 r>
V;=1976ft
^fJL =0.00741.
95The study used a two-week average pollution concentration; the daily rate used here is assumed to be a reasonable
approximation.
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Standard Error ( p). The standard error of the coefficient ( p) is calculated as follows, assuming that the
estimated year-specific coefficients are independent:
= var
This reduces down to:
/ 1981 n \
V #
! = 1976 Gfii
1981 i
% i
Vz = 1976 ^ft )
I 19S1 ft 1
y^ A
, aft
7
v /
var
A
!=1976
al = - => a = = 0.00070 .
r
K
r
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3.5.8 Work Loss Days (Ostro, 1987)
Ostro (1987) estimated the impact of PM25 on the incidence of work-loss days (WLDs), restricted
activity days (RADs), and respiratory-related RADs (RRADs) in a national sample of the adult working
population, ages 18 to 65, living in metropolitan areas. The annual national survey results used in this
analysis were conducted in 1976-1981. Ostro reported that two-week average PM25 levels were
significantly linked to work-loss days, RADs, and RRADs, however there was some year-to-year
variability in the results. Separate coefficients were developed for each year in the analysis (1976-1981);
these coefficients were pooled. The coefficient used in the concentration-response function used here is a
weighted average of the coefficients in Ostro (1987, Table III) using the inverse of the variance as the
weight.
The study is based on a "convenience" sample of individuals ages 18-65. Applying the C-R
function to this age group is likely a slight underestimate, as it seems likely that elderly are at least as
susceptible to PM as individuals 65 and younger. The elderly appear more likely to die due to PM
exposure than other age groups (e.g., Schwartz, 1994d, p. 30) and a number of studies have found that
hospital admissions for the elderly are related to PM exposures (e.g., Schwartz, 1994a; Schwartz, 1994b).
On the other hand, the number of workers over the age of 65 is relatively small; it was under 3% of the
total workforce in 1996 (U.S. Bureau of the Census, 1997, Table 633).
The C-R function to estimate the change in the number of work-loss days is:
kWLD =&y-pop=- [j0 (e-^PM" -1)] pop,
where:
y0 = daily work-loss-day incidence rate per person = 0.00648
p = inverse-variance weighted PM2 5 coefficient = 0.0046
APM2 5 = change in daily average PM2 5 concentration96
pop = population of ages 18 to 65
p = standard error of p = 0.00036
Incidence Rate. The estimated 1994 annual incidence rate is the annual number (376,844,000) of WLD
per person in the age 18-64 population divided by the number of people in 18-64 population (159,361,000).
The 1994 daily incidence rate is calculated as the annual rate divided by 365,97 Data are from U.S. Bureau
of the Census (1997, Table 14) and Adams (1995, Table 41).
96The study used a two-week average pollution concentration; the daily rate used here is assumed to be a reasonable
approximation.
97Ostro (1987) analyzed a sample aged 18 to 65. It is assumed that the age 18-64 rate is a reasonably good approximation
to the rate for individuals 18-65. Data are from U.S. Bureau of the Census (1997, Table 14) and Adams (1995, Table 41).
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Coefficient Estimate (p). The coefficient used in the C-R function is a weighted average of the coefficients
in Ostro (1987, Table III) using the inverse of the variance as the weight:
( 1981 n
Z 2
z=1976
1981
iysi i
z -7-
i = 1976°ft
= 0.0046.
Standard Error ( p). The standard error of the coefficient ( p) is calculated as follows, assuming that the
estimated year-specific coefficients are independent:
= var
v ft
L 2
r= 1976° ft
1981 ,
V 1
^ rr?
v ft
2, 2
r=1976°A
7
1981
varl
Z=1976
\i=l916^^J \
This eventually reduces down to:
l_
7
= 1 = 0.00036.
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3.5.9 Restricted Activity Days (Ostro, 1987)
Ostro (1987) estimated the impact of PM25 on the incidence of work-loss days (WLDs), restricted
activity days (RADs), and respiratory-related RADs (RRADs) in a national sample of the adult working
population, ages 18 to 65, living in metropolitan areas. The annual national survey results used in this
analysis were conducted in 1976-1981. Ostro reported that two-week average PM25 levels were
significantly linked to work-loss days, RADs, and RRADs, however there was some year-to-year
variability in the results. Separate coefficients were developed for each year in the analysis (1976-1981);
these coefficients were pooled. The coefficient used in the concentration-response function used here is a
weighted average of the coefficients in Ostro (1987, Table III) using the inverse of the variance as the
weight.
The study is based on a "convenience" sample of individuals ages 18-65. Applying the C-R
function to this age group is likely a slight underestimate, as it seems likely that elderly are at least as
susceptible to PM as individuals 65 and younger. The elderly appear more likely to die due to PM
exposure than other age groups (e.g., Schwartz, 1994d, p. 30) and a number of studies have found that
hospital admissions for the elderly are related to PM exposures (e.g., Schwartz, 1994a; Schwartz, 1994b).
The C-R function to estimate the change in the number of restricted activity days (RAD) is:
ARAD = Ay.pop=- [y0 (e^M^ - 1)] pop,
where:
y0 = daily RAD incidence rate per person = 0.0177
p = inverse-variance weighted PM25 coeffcient = 0.00475
APM2 5 = change in daily average PM2 5 concentration98
pop = adult population ages 18 to 65
= standard error of p = 0.00029
Incidence Rate. The estimated daily RAD incidence rate is the 1994 annual number of RAD for the
population aged 18-64 in the nation (1,029,419,000), divided by the number of people aged 18-64 in the
nation (159,361,000), and then divided by 365." RAD estimates are from Adams (1995, Table 21), and
the 1994 population estimate is from U.S. Bureau of the Census (1997, Table 14).
Coefficient Estimate (p). The coefficient used in the C-R function is a weighted average of the coefficients
in Ostro (1987, Table III) using the inverse of the variance as the weight:
98The study used a two-week average pollution concentration; the daily rate used here is assumed to be a reasonable
approximation.
"Ostro (1987) analyzed a sample aged 18 to 65. It is assumed that the age 18-64 rate is a reasonably good approximation.
This may be a slight underestimate, since the 65 and over rate is significantly higher than the rest of the adult population (Adams et
al., 1995, Table 16). RAD estimates are from Adams and Marano (Table 21), and the 1994 population estimate is from U.S. Bureau
of the Census (1997, Table 14).
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( 1981
i=1976 a/}j
1981 i
S^r
V;=1976
= 0.00475.
Standard Error ( p). The standard error of the coefficient ( p) is calculated as follows, assuming that the
estimated year-specific coefficients are independent:
f 1981 n \ f 1981 n \
= var
\-^ Pi
i=l976 °ft
1981 i
V
y A
! = 1976 ^ft-
7
1981
var
A
This eventually reduces down to:
!=1976
; = - => aB = l- = 0.00029.
n/ " Al n/
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3.5.10 Asthma Attacks: Whittemore and Korn (1980)
Whittemore and Korn (1980) examined the relationship between air pollution and asthma attacks in
a survey of 443 children and adults, living in six communities in southern California during three 34-week
periods in 1972-1975. The analysis focused on TSP and ozone. Respirable PM, NO2, SO2 were highly
correlated with TSP and excluded from the analysis. In a two pollutant model, daily levels of both TSP and
Ox were significantly related to reported asthma attacks.
The C-R function to estimate the change in the number of asthma attacks is:
hasthma attacks = -
pop,
where:
y0 = daily incidence of asthma attacks = 0.027 (Krupnick, 1988, p. 4-6)
P =PM10 coefficient = 0.00144
APM10 = change in daily PM10 concentration
pop = population of asthmatics of all ages = 5.61% of the population of all ages (Adams et al., 1995
Table 57).
p = standard error of p = 0.000556
Incidence Rate. The annual rate of 9.9 asthma attacks per astmatic is divided by 365 to get a daily rate.
A figure of 9.9 is roughly consistent with the recent statement that "People with asthma have more than
100 million days of restricted activity" each year (National Heart, 1997, p. 1). This 100 million incidence
figure coupled with the 1996 population of 265,557,000 (U.S. Bureau of the Census, 1997, Table 2) and
the latest asthmatic prevalence rate of 5.61% (Adams et al., 1995, Table 57), suggest an annual asthma
attach rate per asthmatic of 6.7.
Coefficient Estimate (p). Based on a model with ozone, the coefficient is based on a TSP coefficient
(0.00079) (Whittemore et al., 1980, Table 5). Assuming that PM10 is 55 percent of TSP100 and that
particulates greater than ten micrometers are harmless, the coefficient is calculated as follows:
0.00079
/? = = 0.00144.
0.55
Standard Error ( p). The standard error ( p) is calculated from the two-tailed p-value (<0.01) reported by
Whittemore and Korn (1980, Table 5), which implies at-value of at least 2.576 (assuming a large number
of degrees of freedom).
B 0.144
an = = = 0.000556.
ft t 2.576
100The conversion of TSP to PM10 is from ESEERCO (1994, p. V-5), who cited studies by EPA (1986) and the California
Air Resources Board (1982).
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