United States Office of Air Quality EPA-450/5-83-001c
Environmental Protection Planning and Standards August 1982
Agency Research Triangle Park NC 27711
Air
£EPA Benefit Analysis
of Alternative
Secondary
National Ambient
Air Quality
Standards
for Sulfur Dioxide
and Total
Suspended
Particulates
Volume III
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FINAL ANALYSIS
BENEFITS ANALYSIS OF ALTERNATIVE SECONDARY
NATIONAL AMBIENT AIR QUALITY STANDARDS FOR
SULFUR DIOXIDE AND TOTAL SUSPENDED PARTICULATES
VOLUME III
\
53S
L. ^^^^^^^^^^ /
^ PRO^C
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BENEFITS ANALYSIS PROGRAM
ECONOMIC ANALYSIS BRANCH
STRATEGIES AND AIR STANDARDS DIVISION
OFFICE OF AIR QUALITY PLANNING AND STANDARDS
U-S. ENVIRONMENTAL PROTECTION AGENCY
RESEARCH TRIANGLE PARK
NORTH CAROLINA 27711
AUGUST 1982
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FINAL ANALYSIS
BENEFITS ANALYSIS OF ALTERNATIVE SECONDARY
NATIONAL AMBIENT AIR QUALITY STANDARDS FOR
SULFUR DIOXIDE AND TOTAL SUSPENDED PARTICULATES
By:
Ernest H. Manuel, Jr.
Robert L. Horst, Jr.
Kathleen M. Brennan
William N. Lanen
Marcus C. Duff
Judith K. Tapiero
With the Assistance of:
Richard M. Adams
David S. Brookshire
Thomas D. Crocker
Ralph C. d'Arge
A. Myrick Freeman, III
Shelby D. Gerking
Edwin S. Mills
William D. Schulze
MATHTECH, Inc.
P.O. Box 2392
Princeton, New Jersey 08540
EPA Contract Number 68-02-3392
Project Officer:
Allen C. Basala
Economic Analysis Branch
Strategies and Air Standards Division
Office of Air Quality Planning and Standards
U.S. Environmental Protection Agency
Research Triangle Park, North Carolina 27711
August 1982
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PREFACE
This report was prepared for the U.S. Environmental Protection
Agency by MATHTECH, Inc. The report is organized into six volumes
containing a total of 14 sections as follows:
Volume I
Section 1:
Section 2:
Section 3:
Volume II
Sect ion 4:
Section 5:
Sect ion 6:
Volume III
Section 7:
Section 8:
Volume IV
Section 9:
Volume V
Section 10:
Section 11:
Volume VI
Section 12:
Section 13:
Section 14:
Executive Summary
Theory, Methods and Organization
Air Quality and Meteorological Data
Household Sector
Residential Property Market
Labor Services Market
Manufacturing Sector
Electric Utility Sector
Agricultural Sector
Extrapolations
Bibliography
Summary of the Public Meeting
Analysis of Pollutant Correlations
Summary of Manufacturing Sector Review
The analysis and conclusions presented in this report are those
of the authors and should not be interpreted as necessarily reflecting
the official policies of the U.S. Environmental Protection Agency.
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ACXNOWLEDQffiNTS
This report and the underlying analyses profited considerably
from the efforts of Allen Basala, who served as EPA Project Officer,
and V. Kerry Smith, who served as a reviewer for EPA. Allen provided
the initiative and on-going support to conduct an applied benefits
analysis. Kerry's technical insights and suggestions are reflected in
nearly every section of the report.
James Bain and Tom Walton of EPA, and Jan Laarman and Ray
Palmquist, who served as reviewers for EPA, also contributed
substantially to individual report sections through their advice and
comments during the course of the project. Also providing helpful
comments and assistance were Don Gillette, Fred Haynie, Neil Frank and
Larry Zaragosa, all with EPA.
Several other members of the Mathtech staff contributed to the
project during various stages of the work. They included Robert J.
Anderson, Jr., Neil Swan, John Keith, Donald Wise, Yaw Ansu, Gary
Labovich, and Janet Stotsky.
The production of the report was ably managed by Carol Rossell,
whose patience remained intact through countless drafts and deadlines.
Carol was assisted by Sally Webb, Gail Gay, and Deborah Piantoni.
Finally, we extend our appreciation to the many dozens of
individuals, too numerous to list here, who provided advice,
suggestions, and data during the course of the project.
111
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CONTENTS
7. THE MANUFACTURING SECTOR
Introduction 7-1
Overview 7-1
Objectives of the Study 7-6
Scope of the Study 7-8
Physical Effects of Air Pollution in the
Industrial Sector 7-11
Economic Effects of Air Pollution in the
Industrial Sector 7-16
The Economic Benefits of Improved Air Quality .. 7-26
Overview of Succeeding Sections 7-33
The Basic Model 7-34
Production Relationships 7-34
Cost Relationships 7-36
Input Demand Relationships 7-40
Properties of the Basic Model 7-41
Assumptions and Restrictions on the Model 7-44
Data and Data Sources 7-49
Selection of Industries 7-50
Data on Labor Inputs and Costs 7-55
Data on Capital Inputs and Costs 7-59
Data on Materials Inputs and Costs 7-77
Data on Manufacturing Output and Output Prices . 7-88
Air Pollution and Climatological Variables 7-105
Empirical Results 7-109
Equations to be Estimated 7-109
Estimation Results: Format 7-114
Estimation Results: SIC 201 7-122
Estimation Results: SIC 202 7-134
Estimation Results: SIC 265 7-141
Estimation Results: SIC 344 7-149
Estimation Results: SIC 346 7-158
Estimation Results: SIC 354 7-165
IV
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CONTENTS (continued)
7. MANUFACTURING SECTOR (continued)
Benefits Calculations for Selected Industries 7-173
Air Quality Scenarios 7-173
Economic Scenarios 7-177
Estimated Benefits 7-180
Plausibility of the Benefits Estimates 7-186
Plausibility of the Underlying Economic Models . 7-186
Plausibility of the Implied Pollution Effects .. 7-188
The Pattern of Pollution Effects 7-192
The Effect of Pollution Control Costs 7-195
Summary and Conclusions 7-202
References 7-205
Appendix: Final Models 7-211
8. ELECTRIC UTILITIES
Introduction 8-1
Theory 8-7
Cost Function Estimation Results 8-14
Data , 8-15
Functional Form 8-18
Empirical Results for Full Sample 8-22
Subsample Results 8-34
Estimation Results for Total O&M Cost 8-44
Summary of Estimation Results 8-47
Benefits Estimates 8-48
Baseline Estimates 8-48
Adjustments to the Baseline Estimates 8-53
Geographical Distribution of Benefits 8-56
Reasonableness of the Estimates 8-58
Conclusions 8-60
References 8-62
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FIGURES
Number Page
7-1. Locational effects of air pollution 7-19
7-2. Increase in consumers' surplus 7-28
7-3. Increase in producers' surplus 7-29
7-4. Increase in consumers' and producers' surplus 7-30
7-5. Equilibrium output price for a competitive industry . 7-93
7-6. SNAAQS air quality scenarios 7-176
VI
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TABLES
Number Page
7-1. . Estimated Benefits of SNAAQS Attainment for SC^
and TSP 7-3
7-2. SIC Classifications for the Manufacturing Sector .... 7-10
7-3. Industries Considered in the Analysis 7-12
7-4. Physical Effects of Sulfur Oxides and Particulate
Matter on Materials 7-14
7-5. Literature Estimates of (Materials Damage from
Sulfur Oxides and Particulates 7-21
7-6. The 30 Top-Ranked Industries in Gross Book Value of
Depreciable Assets in Buildings and Structures
(1976) Out of 140 3-Digit SIC Industries 7-54
7-7. Existence of Multi-Plant Companies in 1972 7-57
7-8. Summary of Characteristics of Materials Price
Indices 7-89
7-9. Matching of Industries and Producer Price Index
Components 7-96
7-10. Estimated Equilibrium Output Price Equations 7-98
7-11. Predicted Equilibrium Prices for SIC 344 in 1972 .... 7-103
7-12. Extent of Missing Air Quality Data 7-109
7-13. Summary Data for SIC 201 (Meat Products) 7-123
7-14. Estimated Model Characteristics for SIC 201 7-125
7-15. Comparative Estimates of Price Elasticities and
Elasticities of Substitution for SIC 20 7-128
7-16. Significance Tests for SIC 201 7-132
7-17. Summary Data for SIC 202 (Dairy Products) 7-135
VII
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TABLES (continued)
Number
7-18.
7-19.
7-20.
7-21.
7-22.
7-23.
7-24.
7-25.
7-26.
7-27.
7-28.
7-29.
7-30.
7-31.
7-32.
7-33.
7-34.
7-35.
7-36.
7-37.
7-38.
Estimated Model Characteristics for SIC 202
Significance Tests for SIC 202
Summary Data for SIC 265 (Paperboard Containers
and Boxes )
Estimated Model Characteristics for SIC 265
Comparative Estimates of Price Elasticities and
Elasticities of Substitution for SIC 26
Significance Tests for SIC 265
Summary Data for SIC 344 (Fabricated Structural
Metal Products )
Estimated Model Characteristics for SIC 344
Comparative Estimates of Price Elasticities and
Elasticities of Substitution for SIC 34
Significance Tests for SIC 344
Summary Data for SIC 346 (Metal Forgings and
Stampings )
Estimated Model Characteristics for SIC 346
Significance Tests for SIC 346
Summary Data for SIC 354 (Metalworking Machinery) ...
Estimated Model Characteristics for SIC 354
Comparative Estimates of Price Elasticities and
Elasticities of Substitution for SIC 35
Estimated Benefits of SNAAQS Attainment for S02
and TSP
Relative Coverage of Individual Industries
Geographic Distribution of Estimated Benefits
Air Pollution Control Costs in 1973
Page
7-137
7-139
7-142
7-144
7-146
7-148
7-151
7-152
7-155
7-157
7-160
7-161
7-163
7-166
7-167
7-169
7-171
7-182
7-183
7-185
7-197
Vlll
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TABLES (continued)
Number Page
7-39. Relationship Between Air Pollution Control Cost
and Ambient Air Pollution 7-201
8-1. Estimated Benefits to Privately-Owned, Fossil
Fuel-Fired, Steam-Electric Plants 8-6
8-2. Maintenance Cost Function Estimation Results
(Total maintenance cost is dependent variable) 8-23
8-3. Maintenance Cost Function Estimation Results
(Maintenance of structures is dependent variable) ... 8-26
8-4. Maintenance Cost Function Estimation Results
(Maintenance of boiler plant is dependent variable) . 8-28
8-5. Maintenance Cost Function Estimation Results
(Maintenance of electric plant is dependent
variable) 8-30
8-6. Estimation Results with Interaction Term 8-31
8-7. Maintenance Cost Function Results for Fuel
Subsamples 8-36
8-8. Maintenance Cost Function Results for Utilization
Rate Subsamples 8-38
8-9. Maintenance Cost Function Results for Vintage
Subsamples 8-39
8-10. Maintenance Cost Function Results for Capacity
Subsamples 8-41
8-11. Estimated Elasticities for Sulfur Oxides 8-43
8-12. Total Cost Function Estimation Results 8-46
8-13. Estimated Elasticities 8-47
8-14. Baseline Estimates for Fossil-Fuel Steam-Electric
Cost Savings 8-54
8-15. Final Estimates for Fossil-Fuel Steam-Electric
Cost Savings 8-56
8-16. Geographical Distribution of Adjusted Baseline
Benefits 8-57
IX
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SECTION 7
MANUFACTURING SECTOR
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SECTION 7
THE MANUFACTURING SECTOR
INTRODUCTION
Overview
Air pollution can adversely affect the manufacturing sector by
increasing the incidence of materials damage and soiling. Examples
include corrosion of exterior metal structures such as storage tanks,
piping, fencing and machinery; and soiling or deterioration of
interior surfaces such as walls, windows, furniture and equipment.
The economic effect in each instance may include the following: (1)
an increase in the costs of production due to increased expenditures
for cleaning, maintenance and repairs, (2) an increase in the costs of
production due to substitution - of costlier materials which are more
resistant to damage, or (3) an increase in the costs of production due
to reduced performance from the affected equipment or structure.
In this section, an effort is made to estimate the economic
damages of air pollution, and hence the benefits of improved air
quality for a selected number of manufacturing industries. The
estimates are developed by comparing production costs among similar
types of manufacturing firms located in regions with different levels
of air quality. Analyses are included for six specific industries
using production cost and air quality data for the year 1972.
7-1
-------
An important step in the analysis is to control for factors,
other than air pollution, which may cause production costs to vary
among regions. These factors may include variations in: wage rates,
capital costs and/or capital investment in-place, and materials costs.
These factors are controlled for by including them in the analysis of
production cost variations.
Also taken into account in the analysis are variations in
climatological conditions which may influence costs directly (e.g.,
through variations in heating and air conditioning costs), and which
may also influence the extent to which ambient air pollution causes
physical and economic damage. The climatological factors considered
include ambient temperature and precipitation.
Based on the analyses reported in subsequent sections, estimates
of the benefits of air quality improvement have been developed. The
estimates represent the benefits of attaining alternative Secondary
National Ambient Air Quality Standards (SNAAQS) for sulfur dioxide
(SCu) and total suspended particulates (TSP) by the year 1987.
Estimates have been developed for three standards: the current TSP
standard (150 jug/m , 24-hour average), the current SC^ standard (1,300
3 3
Mg/m , 3-hour average), and an alternative S02 standard (260 /ug/m ,
24-hour average).
Table 7-1 presents the estimates for each of the six industries
considered in the study. Entries in the table are the discounted
7-2
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present value in 1980 of all future benefits over an infinite time
horizon. The estimates assume a 10 percent discount rate and are
expressed in 1980 dollars.
As shown in the table, benefits for the current S02 standard are
estimated to be zero in these six industries. However, positive
benefits are estimated for the other standards. In four of the
industries, it is estimated that attainment of the other standards
would reduce average total costs of production by 0.1 to 0.9 percent.
In a fifth industry, the estimate is 2.1 percent of total costs. In
the sixth industry, the available data did not allow an estimate to be
developed.
All of the benefits reported above are gross benefits of improved
air quality to these industries. The costs of pollution control that
might be incurred by these industries in order to attain the standards
are being estimated in a separate EPA study.
Data on industry characteristics and air quality are not
uniformly available for all geographic areas. Estimates shown in
Table 7-1 thus do not reflect complete coverage of all manufacturing
establishments in each of the industries. In terms of economic value,
the fraction of each industry included in the estimates of Table 7-1
ranged from 11 to 50 percent. Lack of air pollution data was
generally the more limiting factor. Lack of complete coverage means
that the estimates in Table 7-1 may understate the total benefits of
7-4
-------
attaining SNAAQS. However, the degree of understatement is not nearly
as severe as the percentages might seem to indicate. Monitoring sites
are presumably concentrated in areas where air pollution is a problem;
thus, areas without monitoring facilities are more likely than not to
be in compliance with SNAAQS already.
The estimated benefits of SNAAQS attainment show significant
geographic concentrations. This is a result of the geographic
distribution of the individual industries, the geographic patterns of
air quality, and the availability of data. For SICs 201, 202 and 265,
the estimated benefits are primarily concentrated in two Census
Divisions — the Mid-Atlantic Division (New York, New Jersey and
Pennsylvania) and the East North Central Division (Ohio, Indiana,
Illinois, Michigan and Wisconsin). For SIC 344, benefits occur in all
nine divisions. For SIC 354, most of the benefits are in the East
North Central Division with additional benefits in other divisions.
It should be noted that the geographic distribution of estimated
benefits is based on where the affected manufacturing establishments
are located. Many of these establishments may ship products, and
return profits, to customers and shareholders in other regions. To
the extent that these interregional relationships exist, other
geographic areas will also share in the benefits.
7-5
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Objectives of the Study
As discussed in a later section, there have been a number of
studies which have attempted to determine the economic costs of
materials damage due to air pollution. In general, these studies
proceed through four steps: (1) determining the physical change in a
structure or surface exposed to air pollution; (2) estimating the unit
cost of repairing the exposed material (e.g., repainting); (3)
estimating the total stock or inventory of materials exposed; and (4)
calculating economic damages by multiplying the unit repair cost times
the total materials stock. Estimates developed in this fashion have
the very attractive feature that the calculation of damages is
directly linked to the physical change caused by air pollution.
The methods employed in this study represent a considerable
departure from the more conventional approach outlined above. In
particular, the starting point for this study is the total cost of
production (capital, labor and materials) for firms producing similar
products, but located in different geographic areas with different
levels of air quality. Advanced statistical techniques are then used
to sort out the extent to which variations in cost among the firms can
be attributed to "economic" factors (e.g., wage rate variations), and
the extent to which the remaining variation can be attributed to
differences in local air quality and climatological conditions.
7-6
-------
There are several reasons why the approach described above has
been used in this study. First, it makes use of data which have not
previously been brought to bear on the problem of benefits analysis.
In particular, it makes use of data on the production costs actually
incurred by firms, as opposed to estimates of what typical maintenance
and repair costs might be. Second, underlying the statistical
analysis is an economic model of optimizing behavior by firms, which
provides a conceptually sound basis for benefits analysis. In
particular, the model allows for the possibility that firms may
substitute costlier but more damage resistant materials rather than
incur air pollution damages. It also allows for the possibility that
firms may find it economical to take no action and simply allow
structures and equipment to deteriorate at a faster rate. The main
drawback to the approach used in this study, of course, is that the
precise linkage between economic costs and physical damages is not
identified explicitly. Rather, the findings of the study would simply
be that there is a statistical association between costs of production
and levels of air quality.
A key objective of this study has been to determine whether
econometric techniques can provide new evidence on the extent of air
pollution-related materials damage. In particular, can these
techniques detect air pollution effects, given the aggregate kinds of
cost data available? Do they provide damage estimates which are
plausible and reasonably consistent with the more conventional
approaches? Are the methods and data requirements such that they
7-7
-------
could be extended beyond the selected sample of industries considered
in this study? And finally, given the estimates obtained, what do
they imply about the benefits of improvements in air quality?
Scope of the Study
This section on the manufacturing sector, and a subsequent
section on the electric utility sector, are parallel tests of the use
of econometric techniques to identify air pollution-related materials
damage. In economic terms, the manufacturing sector is far larger.
It accounts for about one-quarter of total gross national product
versus about two percent for the electric utility sector. This would
suggest giving priority attention to the manufacturing sector in the
analysis. Nonetheless, the economic data on electric utilities is far
superior, because they are subject to economic regulation and thus
must publicly report extensive financial information. Analysis of the
utility sector was thus undertaken in parallel, in the event that the
more aggregate data available for manufacturing firms did not allow
for a clear test of the methodology. The results of the manufacturing
sector analysis are reported in this section. The electric utility
analysis is discussed in Section 8.
Definition of the Manufacturing Sector—
In the Standard Industrial Classification (SIC) system, the
manufacturing sector is comprised of 20 major industry groups, each of
which is assigned a 2-digit code. For example, the paper industry is
7-8
-------
assigned SIC Code 26 and the chemical industry is SIC Code 28. Each
2-digit code is further subdivided into several 3-digit codes, and
many of the 3-digit codes are subdivided into 4-digit codes.
Corresponding to the 20 major industry groups at the 2-digit SIC level
are about 140 groups at the 3-digit SIC level and about 450 industries
at the 4-digit level. Codes of five to seven digits are used to
define individual products and product groups within each 4-digit SIC
industry. A brief illustration of the code definitions for the
manufacturing sector is provided in Table 7-2.
Industries Included in this Study—
Selection of the industries considered in this study required
joint consideration of several factors which are explained in more
detail in a later section. Briefly, however, these factor included:
• The level of industry disaggregation — Should the
analysis focus on industries at the 2-digit, 3-digit
or 4-digit SIC level?
• The level of geographic disaggregation — Should the
analysis focus on air quality differences at the level
of cities, counties, SMSAs (metropolitan areas) or
states?
• Industries likely to be affected — Which industries
are most likely to be affected by air pollution-
induced materials damage or soiling?
• Data availability — For which industries, and which
levels of disaggregation, are data likely to be
available from the relevant economic censuses?
As it turned out, data availability was the primary factor in
determining both the industries examined and the level of
7-9
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disaggregation at which the analysis was done. For example, analysis
at the city level would have allowed the economic data to be most
closely matched to air pollution monitoring sites. Analysis at the 4-
digit SIC level would have provided the most homogeneous groupings of
firms. And analysis of industries like petroleum refining, which have
extensive networks of exterior piping, tanks and towers exposed to air
pollution, would have been the most interesting. Data availability
considerations, however, suggested analysis at the county level using
3-digit SIC industries. And several key industries that we would like
to have studied could not be included.
Taking into account the factors and data constraints mentioned
above, thirteen 3-digit SIC industries were initially selected for
analysis. When data collection was completed, seven of the industries
proved to have very limited samples or other data problems, and
received only limited analysis. The industries initially selected,
and the industries for which detailed analyses were eventually
conducted, are listed in Table 7-3.
Physical Effects of Air Pollution in the Industrial Sector*
In a wide range of laboratory and field studies, it has been
established that sulfur oxides and suspended particulate matter cause
damage to materials. Sulfur oxides have been found to cause corrosion
* The discussion in this section draws upon material in Reference (1).
7-11
-------
TABLE 7-3. INDUSTRIES CONSIDERED IN THE ANALYSIS
2-digit 3-digit SIC code Value added
SIC code and definition in 1972**
20
26
28
30
33
34
35
36
37
201
202
* 208
—
265
—
* 281
—
* 307
—
* 331
* 332
__
344
346
—
354
—
* 367
—
* 371
———————
Meat products
Dairy products
Beverages
Paperboard containers and boxes
Industrial inorganic chemicals
Misc. plastics products
Blast furnaces, basic steel products
Iron and steel foundries
Fabricated structural metal products
Metal forgings and stampings
Metalworking machinery
Electronic components, accessories
Motor vehicles and equipment
4.96
4.05
6.69
3.60
3.34
6.00
12.12
3.48
6.74
5.06
4.90
5.31
22.06
* Limited analysis only.
** Billions of 1972 dollars.
Source: Bureau of the Census. 1972 Census of Manufactures. 1976.
7-12
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of metal surfaces and deterioration of fabrics, building stone, and
products made of paper, leather or plastic. Particulate matter causes
soiling of surfaces, and also soiling of fabrics and exterior paints.
Particulate matter has also been found to cause degradation and
failure of electrical components and equipment. In concert with other
environmental factors, airborne particles can also lead to corrosion
of metals. A summary of the physical effects of sulfur oxides and
particulates on materials is provided in Table 7-4.
Given the types of physical effects listed above, it is likely
that ambient pollutant concentrations will affect individual
industrial establishments in different ways. Metal corrosion, for
example, is likely to be most significant among industrial firms
characterized by external metal structures. Examples include
petroleum refineries and petrochemical complexes which have wide
ranging networks of metal storage tanks, piping, and processing
towers. Another example is the electric utility industry which has
networks of metal transmission towers, external power transformers and
pole-line hardware. On the other hand, chain link fencing, gutters
and metallic building accessories, which are susceptible to corrosion
even after zinc-coating, are likely to be in widespread use throughout
industry.
Another factor which may lead to differing impacts among
industries is the varying extent to which industries require clean
working environments. Companies which manufacture or use electronic
7-13
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equipment such as semiconductor manufacturers, or users of electronic
computers, require very clean conditions to prevent component or
equipment failure. It has been noted that such firms often must
install air filtering equipment, even in relatively clean areas, in
order to achieve sufficient protection. Nonetheless, the degree of
filtering required, and indeed the need for air filtering among other
industries, may be influenced by the level of ambient particulate
concentrations.
The state of research on soiling and materials damage appears to
be at a stage where many of the physical mechanisms of damage have
been identified. The role of environmental factors such as relative
humidity, precipitation, and temperature in influencing the rate of
damage to metals have also received research attention. Less well
known at this point is the total extent of soiling and materials
damage either in physical or economic terms. In large part, this
stems from a lack of information as to the total inventory of
materials in place. A number of investigations are now underway,
however, in an effort to develop methods for estimating the quantity
and geographical distribution of materials.*
While the discussion to this point has focused solely on soiling
and materials damage, other physical effects may also occur in the
industrial sector. For example, to the extent that air pollution
* See, for example, McFadden and Koontz (2).
7-15
-------
affects vegetation, then damage to ornamental planting (lawns, shrubs,
trees) may occur at industrial sites. Affects on visibility may also
reduce the aesthetic values at a particular site. However, it seems
unlikely that vegetative or aesthetic effects will be detectable as
changes in industrial productivity or production costs. We note,
therefore, that our analysis is likely to miss these benefit
categories and thus potentially understate the total benefits of
improved air quality.
Economic Effects of Air Pollution in the Industrial Sector
Economic Consequences of Physical Damages—
The physical effects of air pollution summarized in the previous
section may have economic consequences. The specific economic
effects, however, will depend in large part on how industrial firms
respond to the physical damage. Consider, for example, a piece of
equipment or a structure whose performance or service life is reduced
in the presence of high ambient concentrations. In this situation,
firms may respond in at least five different ways which we summarize
briefly below.
Ignorance—One possibility is that the firm may not be aware of
the physical damage and continues with business as usual. If the
machine's performance is reduced, however, the economic effect will be
lower productivity and thus higher unit costs of production. Thus,
even though the firm may be ignorant of the damage taking place, the
7-16
-------
damage would have economic effects which are in theory observable in
the firm's economic performance.
Inaction—A second possibility is that the firm is aware of the
damage-induced reduction in performance and chooses to do nothing
about it. That is, the loss of performance may be sufficiently small
that it is not economical to undertake repair activities. As in the
ignorance case, productivity will nonetheless fall and unit costs will
rise, so that the economic effects will in theory be observable.
Maintenance—A third possibility is that the firm takes positive
steps to maintain the machine (or structure) at a high level of
performance. These steps may include purifying the air, cleaning and
repair activity, or more frequent replacement of the machine itself.
In this situation, the machine's performance may be maintained at a
high level, but at a cost in larger expenditures for protection,
maintenance or replacement. Since this course of action has involved
a change in the level and pattern of expenditures, the effect is again
observable in principle.
Substitution—A fourth possibility is that the firm may
substitute a costlier machine (or material) which is more resistant to
damage. For example, one might substitute galvanized steel for
untreated steel or sealed equipment for equipment with exposed
internal parts. Again, since substitution may involve an increase in
costs, this mode of behavior should also be observable.
7-17
-------
Location—A fifth possibility is that firms, knowing of pollution
damages, may relocate to cleaner areas, or locate in cleaner areas in
the first place. For example, firms may locate outside of polluted
center cities, balancing off higher transportation costs against lower
pollution costs. In this case, the costs of pollution may also be
reflected in changes in the price of fixed factors, such as land, as
well as in expenditures for maintenance and repair.
Consider the following illustrative situation as shown in Panel A
of Figure 7-1. In Panel A we assume that there is one factor of
production (land) and that all trade occurs in the center city. In
the center city, production costs include land costs and pollution
costs, the sum of which is also equal to the demand price. As one
moves out from the city, both land costs and pollution costs decline
and at a faster rate than the increase in transportation costs.
Hence, firms which locate outside the center city have the opportunity
to earn rents (above normal profits). The rents are shown as the
shaded area in Panel A.
Over time, however, land prices outside the city will be bid
upwards by firms seeking to share in the rents. Eventually, as shown
in Panel B, the bidding for land will transfer all the rents to
landowners, until the sum of production and transportation costs is
7-18
-------
Panel A
Center
city
J
$
D
B
Panel B
Demand price
New total production St transportation, cost
J
H1
Figure 7-1. Locational effects of air pollution.
7-19
-------
uniform at all locations.* Note that the land rents in Panel B, area
CFF1, are comparable in magnitude to the rents in Panel A, area DHJ.
The extent of pollution costs in the above situation can be
observed in several ways. First, to the extent tnat firms originally
owned the land outside the center city, they would be the recipients
of the rents and these rents would show up in the firms' economic
performance. Alternatively, if firms were not the original
landowners, but instead bought in at the higher land prices, then
pollution costs would be observable in the firms' capital expenditures
for land. That is, variations in expenditures for land, not explained
by differences in transportation cost or other site advantages, will
reflect variations in pollution costs.
Previous Studies of Economic Damages—
Previous studies of the economic damages to materials provide a
very wide range of estimates. A summary of several of these estimates
is shown in Table 7-5, excluding those studies which considered
primarily materials damages to households. The dollar figures shown
generally represent annual damages and have been adjusted from the
year of the study to 1980 dollars using the implicit GNP price
deflator for non-residential gross fixed investment. The wide
variation in estimates ($100 million to $80 billion) is to some extent
* We have assumed in Panel B that the firms are not themselves
polluters and hence do not alter the geographic pattern of air
quality or pollution costs.
7-20
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7-21
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due to the differing scopes of the individual studies. For example,
some studies were concerned with only certain industries, while others
appear also to include other sources of damage and other economic
sectors in addition to PM and SO and the industrial sector. The wide
A
variation also reflects, however, the degree of uncertainty about the
true extent of materials damage.
No studies of economic damages from air pollution exist using
methods comparable to those employed in this study. Perhaps the
closest in approach are the various comparative studies which have
examined the extent to which variations in residential property values
can be attributed to air pollution. These studies are reviewed in
detail in Section 5 and reflect, in part, some degree of soiling and
materials damage to households. No studies are known which have
developed comparable estimates for air pollution effects on non-
residential property values.
Other Economic Effects of Air Pollution on the Industrial Sector—
The previous discussion has emphasized economic effects due to
materials damage caused by air pollution. Industrial firms are also
affected by air pollution in less direct ways. For example, firms
located in areas with heavy air pollution may find that higher than
average wage rates are required to attract workers to the firm.
Second, firms located in polluted areas may face more stringent air
quality regulations, thus requiring increased capital and operating
7-22
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expenditures for air pollution control. Both of these issues are
discussed briefly below.
Wage Premiums—Several recent studies have found that wage rates
tend to be higher in areas with heavy air pollution compared to areas
with better air quality. The most recent of these was conducted as
part of this study and is reported in Section 6. As reported there,
the correlation between wage rates and ambient pollutant
concentrations remains, even after controlling for other potential
wage determinants such as age, sex, race, education, occupation,
climate, local cost of living differences, and several other factors.
The specific findings are that the elasticity of wage rates with
respect to ambient TSP concentrations is 0.20, for pollution levels
near the national secondary standard, and 0.13 for the national
primary standard. This result was found to be statistically
significant. Estimates for SC^ and NO were not significant.
The hypothesis advanced to explain the observed wage effects is
that workers demand a premium for taking jobs in areas with less
desirable air quality; or conversely, workers will accept lower wage
rates in areas with better air quality. The elasticity estimates
above suggest that wage rate variations can be appreciable. For
example, two identical firms located in cities which are identical
except that the first city meets only the primary standard, while the
7-23
-------
second city meets the stricter secondary standard, would find that
wage rates in the second city are about 3.3 percent lower on average.*
In the remainder of the analysis for the manufacturing sector,
the issue of wage premiums is not considered explicitly. We merely
note that the phenomenon exists and may thus account for some of the
observed variation in wage rates, and thus in production costs, among
firms.
Air Pollution Control Costs—In addition to being affected by air
pollution, manufacturing firms in many instances also contribute to
air pollution, and also make expenditures to control their own sources
of pollution. For example, in 1978 the manufacturing sector made
capital expenditures of $1.06 billion and $288 million for control of
particulates and sulfur oxides, respectively (3). During that same
year, those firms removed 40.1 million tons of particulates and 8.7
million tons of sulfur oxides (4).
The fact that manufacturing firms are both affected by air
pollution and make expenditures to control air pollution poses a
difficult problem for this type of study. In particular, if local air
pollution control regulations are correlated with local air quality
conditions, then variations in production costs among firms could
arise both from control cost variations and from materials damage
* Calculated using the arithmetic mean of the elasticities at the two
points.
7-24
-------
variations, as well as from the other economic factors (e.g., wage
rates). In this case, statistical separation of 'the two sources of
variation can be difficult.
In the electric utility sector analysis, the problem of control
costs is addressed directly. This was considered necessary because in
that industry, control costs are a major component of total production
costs. The details of the steps taken to account for air pollution
control activities in that sector are described in Section 8.
In the manufacturing sector analysis, the issue of control costs
is believed to be less of a problem. In the initial group of 13
industries selected for analysis, control costs are a major factor in
some of the industries (e.g., the steel industry). In the six
industries subjected to detailed analysis, however, control costs are
much less significant. While exact figures are not available, it
appears that annual expenditures for control of particulates and
sulfur oxides were a small fraction of total annual expenditures for
the year under analysis — about 0.04 percent or less.* In contrast,
our estimates of the economic effects of air pollution were found to
be on the order of 0.10 percent or more of total costs. We thus do
not believe our estimates are appreciably influenced by control costs.
* Specific details are presented in a later section.
7-25
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The Economic Benefits of Improved Air Quality
A Brief Review of the Theory*—
As noted in the previous section, manufacturing firms located in
regions with differing air quality may find their economic situation
affected in at least three ways. Firms in areas with high ambient
concentrations may experience: higher wage rates, more stringent air
pollution control requirements, and more soiling and materials damage.
In this section, the focus will be on economic benefits which arise
from reductions in soiling or materials damage.
As also noted previously, a reduction in soiling or materials
damage can yield cost savings to a firm in a variety of ways. These
may include a reduction in maintenance and repair costs, reduced
requirements for use of damage-resistant materials, or improved
performance or longevity for structures and equipment. Regardless of
the specific source of cost savings, the net result is a contribution
of economic benefits to society. Depending on several factors to be
discussed shortly, these economic benefits (cost savings) may be
passed on to consumers in the form of product price reductions;** they
may be retained by the firm in the form of larger profits; or
consumers and firms may jointly share in the benefits.
* A broader discussion of the theory underlying benefits analysis can
be found in Section 2 of this report.
** The term "consumer" as used here means the purchaser of the firm's
output. Consumers may thus include both households, or other firms
which use the firm's product as an input. In the latter case, the
product is commonly referred to as an "intermediate good".
7-26
-------
The potential distribution of benefits between consumers and
firms can be illustrated graphically. The three possibilities are
outlined in Figures 7-2 to 7-4. In Figure 7-2, the industry is
assumed to be competitive and all factors of production (inputs to the
firm) are assumed to be infinitely elastic (available in any quantity
at the same unit price). These two assumptions imply that price (P)
equals marginal cost (MC) and is constant at all levels of output (Q).
In the figure, the marginal cost (supply) curve is thus a horizontal
line. Under these assumptions, an improvement in air quality (a
reduction in ambient concentrations from S to S') reduces costs of
production as shown by the downward shift in the marginal cost curve
from MC(S) to MC(S'). The cost savings in this case are passed on
to consumers in the form of a price reduction. The magnitude of
economic benefits generated by this price reduction is given by the
shaded area in the figure, a quantity referred to as the change in
"consumers' surplus".* For illustrative purposes, we have assumed in
the figure that the pollutant is SC^.
In Figure 7-3, a second possibility is illustrated. In this
instance, the assumption is that there is at least one factor of
production whose supply is inelastic (e.g., land or a mineral
* Consumers' surplus can be defined as the difference between what
consumers would be willing to pay for the product, compared to what
they actually pay. In the figure, this is given by the triangular
area above the marginal cost curve (price line) and to the left of
the demand curve. With the reduction in price, the consumers'
surplus increases by the amount represented by the shaded area. See
Section 2 for a more complete discussion of this concept.
7-27
-------
Reduction in ambient concentrations produces cost savings
which are passed on to consumers as price reductions:
MC(S)
MC(S')
benefits (increase in
consumers' surplus)
i
demand
S = ambient S02 concentration, S' < S.
Assumptions: (1) Industry is competitive.
(2) Firms have constant costs (supply of factors
is infinitely elastic).
Figure 7-2. Increase in consumers' surplus.
7-28
-------
Reduction in ambient concentrations produces cost savings
which increase profits and the income of fixed factors:
MC(Q,S)
MC(Q,S')
benefits (increase in
producers' surplus)
S = ambient SO- concentration, S' < S.
Assumption: (1) Inelastic supply of some factors of production,
Figure 7-3. Increase in producers' surplus.
7-29
-------
Reduction in ambient concentrations produces cost savings
which are shared between consumers and producers:
MC(Q, S)
MC(Q, S')
benefits (increase
in consumers' and
producers' surplus)
S = ambient S02 concentration, S1 < S.
Figure 7-4. Increase in consumers' and producers' surplus.
7-30
-------
resource). This assumption leads to an upward sloping marginal cost
curve MC(Q,S), which depends on both the level of output Q and ambient
concentrations S. It is also assumed in Figure 7-3 that demand is
infinitely elastic. Under these two assumptions, a reduction in
ambient concentrations produces a cost savings which accrues in the
form of increased income for the fixed factor (i.e., above normal
profits). More specifically, the cost savings produces an increase in
producers' surplus.*
Figure 7-4 illustrates still a third possibility. In this case,
supply and demand conditions are such that the cost savings are shared
by both consumers and firms. That is, in this case there is an
increase in both consumers' and producers' surplus as a result of cost
savings from the lower ambient concentrations.
Calculation of Economic Benefits—
As the brief discussion in the previous section indicates,
calculation of economic benefits requires two sets of information:
knowledge of supply and demand conditions in the markets supplied by
the industries under consideration; and knowledge of the effect of air
pollution on costs of production. Given this information, the
* Producers' surplus can be defined as the difference between what
consumers pay for the product, compared to what it costs to produce
the product. Producers' surplus is given by the area below the
market price line (D) and to the left of the marginal cost curve.
With the reduction in costs, and no corresponding reduction in
selling price, producers' surplus increases by the amount shown as
the shaded area.
7-31
-------
economic benefits of an improvement in air quality are easily derived.
Consider the general case depicted previously in Figure 7-4. For this
case, let
Q = level of output
S = ambient concentration of pollutants (e.g., 802)
C(Q,S) = total costs of production, given Q and S
P (Q) = demand price at output Q (curve D in the figure).
Then the economic benefits of the reduction from S to S' are given by
the sum of
[C(Q1,S) - C(Q1,S')] (7.la)
which is the cost savings in producing the original level of output
Qlf plus
V
/
PD(Q)dQ - IC(Q2,S') -
which is the added surplus due to the expansion of output from Q-^ to
Q2. The expansion in output occurs because, with the reduction in
price, consumers increase their purchases of Q. The two quantities
above correspond in Figure 7-4 to the shaded areas to the left and
right of the vertical line at Q-j_, respectively.
7-32
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Note that in the two quantities defined above, calculation of the
first quantity requires knowledge of the cost function only.
Calculation of the second quantity requires knowledge of both the cost
function and the demand function. In this study, time and resources
did not permit estimation of the demand functions, and thus benefits
reflected in the second area are omitted from the estimates reported
later. If demand is relatively insensitive to price, then the degree
to which benefits are underestimated will be small.
It should also be noted at this point that the general formula
derived above represents the benefits accruing during a particular
point in time — i.e., during one year. A permanent reduction in
ambient concentrations from S to S1, however, would confer benefits
each year into the future. To calculate the value of the entire time
stream of benefits requires using the formula above to calculate the
benefits in each future year, and then applying an appropriate
discount rate to calculate the discounted present value of all future
benefits. The details of this procedure are described in a later
section.
Overview of Succeeding Sections
The remainder of Section 7 is concerned with empirically
implementing the concepts described previously and evaluating the
results. The development proceeds in six subsections. The first
subsection develops the underlying economic model of the firm and
7-33
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specifies the functional form for the cost function. The second
subsection outlines the data used in the model and the assumptions
underlying construction of the various data series. In the third
subsection, the estimated cost functions for each industry are
presented and evaluated. For those industries in which the estimated
cost functions appear plausible, economic benefits of air quality
improvements are calculated and presented in the fourth subsection. A
fifth subsection assesses the plausibility of the estimated benefits,
while the sixth subsection provides a summary and conclusions.
THE BASIC MODEL
Production Relationships
The starting point for analysis of economic behavior by
manufacturing firms is a production function
Q = f(L]_, ..., Lj^, K-jy ..., Kg, M^/ ..., MM' Z-^, ..., ^"2,^ (7*2)
which indicates the quantity of manufactured output (Q) that can be
produced with given input of labor (L^), capital (K^), materials (M^),
and other fixed factors (Z-) such as climate and air quality. For
example, the various labor inputs might include skilled and unskilled
production workers and supervisory personnel. The capital inputs
might include structures and equipment. The materials inputs might
include raw materials, supplies and energy.
7-34
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The production function is said to be weakly separable in the
aggregate inputs L, K, M, and Z if it can be written
Q = f(L, K, M, Z) (7.3)
where L = L(L1, ... , LL), K = K^, ... , KK), M = M(M]_, ... , MM)
and Z = Z(Z]_, ... , Zz). Weak separability implies that the cost-
minimizing (or profit-maximizing) mix of inputs within each aggregate
input is independent of the level and mix of inputs within each other
aggregate input (5). For example, the mix of production workers and
supervisory personnel is independent of the mix of different materials
inputs. However, the total labor input and total materials input are
not independent of one another.
If some inputs are always used in fixed proportion to total
output, then the weakly separable production function can be written
Q = min[g(Lx, K, M, Z), al^] (7.4)
where L^ is the input used in fixed proportion a of total output, and
L1 is the aggregate L(L-j_, ... , LL) with the ith labor input removed.
If the firm is efficient, then the production function (7.4) can also
be written as
Q = g(Lx, K, M, Z) , (7.5)
7-35
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or as
Q = aLj_ . (7.6)
In this case, there is said to be perfect complementarity between
input L^ and the other inputs (6).
In the next section, the assumption of weak separability is
imposed on the capital, labor and materials inputs. This assumption
is required because of data limitations. The assumption that non-
production labor is a perfect complement to all other inputs is also
assumed for the same reason. Note that the assumption of weak
separability means that we cannot identify the effect of pollution on
the mix of capital inputs or the mix of materials inputs. Only the
effect on total use of capital or total use of materials can be
identified.
Cost Relationships
Under the assumptions of weak separability between capital,
labor and materials inputs, and perfect complementarity between non-
production workers and all other inputs, the production function can
be written as
Q = ML1, K, M, Z-L, ... , Zz) (7.7)
where the arguments of the function h(*) are defined as before.
7-36
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If one can assume that the prices of inputs and the level of
output are exogenously determined, and that firms behave so as to
minimize the costs of producing output Q, then the theory of duality
between cost and production implies that there exists a cost function
C(') which provides an equivalent dual representation of the firm (7).
In particular, if the function h(-) in Equation (7.7) possesses
certain regularity properties (e.g., continuity), then an equivalent
representation for the production technology is a cost function of the
form
C = C(PL, PK, PM, Q, Zlf ... , Zz) (7.8)
The function C(*) represents the minimum total cost of producing
output Q, given input prices P, / PK and ?„ for the aggregate inputs
L1, K and M, and given the fixed inputs Z-,, ... , Z™. The remainder
of Section 7 is concerned with developing empirical estimates of the
cost functions for each of the manufacturing industries described in
an earlier section.
As a starting point, it is necessary to assume a specific
functional form for the cost function. In this study, a
transcendental logarithmic function (translog) is used because it is a
very general functional form which therefore imposes fewer
restrictions on the cost function (8). The translog is basically a
second-order expansion of log C in powers of the logarithm of each
7-37
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argument of C.* In the most general form, the translog expansion
corresponding to the cost function (7.8) is given by
log C = an + E a. log p. + 1/2 I a•^ log P. log P^
*J 1- -L i- J J. j
+ b0 log Q + 1/2 b00(log Q)2 + E bQi log Q log ?i
(7.9)
+ E c^.i log P^ log Z- + E d^ log Z;
+ 1/2 E dj_j log Z^ log Z^ + E eQi log Q log Z^
The properties of the translog expansion are most easily
understood by looking at various simplified versions. For example, if
all a.j_^ = bQQ = bQj_ = c^ = d^ = 6^- = BQ^ = 0, then the function C
can be written (after exponentiation) as
a a a a
C = e ° PLl PK2 PM3 Qb (7.10)
which is simply the Cobb-Douglas cost function. In this form, all of
the exponents can be interpreted as elasticities. Thus, a one percent
increase in P^ would result in an a-, percent increase in total cost, a
one percent increase in output would cause a b percent increase in
total cost, and so on. If in addition b = 1, then the cost function
would exhibit constant returns to scale (no scale economies or
diseconomies). Also, if a^ + a2 + a-j = 1, the cost function would be
* In this report, log x is the natural logarithm of x.
7-38
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homogeneous of degree one in prices; that is, if all input prices were
to increase by 10 percent, then total cost would increase by 10
percent.
The other terms in the translog expansion allow for interactions
between inputs, and adjustments to the arbitrary scaling parameter
a
e . The effects of these additional terms can be interpreted as
follows:
The a.• allow the elasticities of substitution between
inputs^ to differ from 1.0 as implied in the simpler
Cobb-Douglas form. In a cost function with only two
inputs, the elasticity of substitution is the rate at
which one input is substituted for the other in
response to relative price changes between the two
inputs. With more than two inputs, the elasticity of
substitution is usually defined in terms of a scaled
cross-price elasticity of demand [see Equation (7.17)
for the description in terms of a neoclassical cost
function].
The boi allow for the possibility that the effect of
an input price change on total cost may depend on the
size of the firm, or equivalently, that the
appropriate mix of inputs may depend on firm size.
The d^ allow for the possibility that fixed factors,
such as climate and air quality, may influence overall
efficiency of production.
The d. . allow interaction between the effects of the
fixecT^factors, as for example, between ambient
temperature and ambient pollution.
The c . . allow for the possibility that the effect of
the ri-xed factors may depend on input prices, or
equivalently, on the mix of inputs. As an example,
capital-intensive firms may be more affected by air
pollution than labor-intensive firms.
The Cj- allow for interaction between the fixed
factors-1 and firm size.
7-39
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Most of the statistical analyses reported later make use of
various simplified forms of the translog expansion given by (7.9).
Input Demand Relationships
Given a minimum cost function of the form (7.8), it has been
proven that the input demand for each of the variable factors can be
found by partial differentiation of the total cost function with
respect to the price of each input [Shephard's Lemma (9)]. Thus the
demand for input i, X^, is given by
X^_ = 3C/3Pi , (7.11)
where i = L, K, M. Combining this result with the property of
logarithms indicates that the share of total cost, S-, accounted for
by input i, is given by
3 In C/a In Pi = Xi(Pi/C)
= PJ.XJ/C (7.12)
= Si
For the translog cost function given by (7.9), Equation (7.12)
implies:
7-40
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pixi
Si = —— = ai + I ai-j log p. + boi log Q + E c^ log Z- (7.13)
C
for i = L, K, M.
An important property of the translog total cost function and the
translog cost share equations is that while they are non-linear in the
price variables and fixed inputs, they are linear in all of the
unknown parameters (e.g., the a^, a^_i, etc.) that must be estimated.
Properties of the Basic Model
From the translog cost function, a variety of useful properties
of the model can be derived in terms of the unknown parameters to be
estimated (10). For example, the elasticities of substitution between
variable inputs i and j (6^-) are given by
(ai;j + S^/S^ for i^j (7.14)
and
si - si)/si - (7.15)
As mentioned earlier, d— measures the rate at which firms substitute
input i for input j in response to changes in the relative prices of
the two inputs.
7-41
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Another measure of price responsiveness is the own price
elasticity of demand, namely, the percentage change in demand for an
input, in response to a percentage change in the price of the input.
For the translog cost function, the own price elasticity of demand
(Eii) is given by
3Xi
The cross-price elasticity of demand (E) is given by
x
The cross-price elasticity measures the percentage change in the use
of input i in response to a percentage change in the price of input j.
Another property which is of interest is the existence of
economies (or diseconomies) of scale. Roughly speaking, scale
economies exist if an increase in output can be made with a less than
proportional increase in total cost. For the translog cost function,
a commonly used measure of scale economies is (11):
SCE = 1-3 log C/6 log Q
(7.18)
= 1 - (bQ + bOQ log Q H- E bQi log PL + I eQi log Zi)
7-42
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In this case, values of SCE = 0 would imply constant returns to scale,
SCE > 0 implies economies of scale, and SCE < 0 implies diseconomies
of scale. Note that since SCE depends on the level of output Q, it is
possible for economies of scale to exist at some levels of output
while disappearing at others.
The effects of air quality or climate on total cost can also be
expressed in elasticity form. For example, if Z-, is the ambient
concentration of SC^, then the elasticity of total cost with respect
to a change in ambient S02 is given by
6C zl
az ' c
= 3 log C/a log Z-, (7.19)
I Cu log Pj_ + d1 + I dj. log Z. + eQ1 log Q
i j
Note the role of the various terms in Equation (7.19). As
observed earlier, the term d-, allows for the possibility that SOp
causes an overall loss of efficiency which is neutral with respect to
inputs. That is, SC^ may cause total costs to increase but with no
effect on the share of total cost accounted for by each input. The
C.Q, on the other hand, allow for non-neutral efficiency losses. That
is, since the C.Q terms also appear in the input cost share equations,
they allow for the possibility that increased S02 may increase the
cost share for some inputs. As an example, if the response to
7-43
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pollution is to employ structures which are more resistant to
pollution damage, one would expect to see the cost share for capital
increase, while the cost shares for labor and materials would
decrease.* Note that a decrease in the cost share for an input does
not necessarily imply that use of the input decreases. It might
happen, for example, that the cost of all inputs increase, but at
different rates, so that some cost shares increase while others
decrease.
Assumptions and Restrictions on the Model
In using a specific functional form for the cost function, it is
important to keep in mind the various hypotheses and assumptions
underlying the analysis. These include the so-called "maintained
hypotheses" which are assumed by the model and cannot be tested
directly, and other hypotheses which can be tested (12). For the
model used in this analysis, some of the more important maintained
hypotheses are
• Firms exhibit cost-minimizing behavior
• The underlying production function is weakly separable
in the aggregate inputs L, K, and M.
• Non-production worker labor input exhibits perfect
complementarity with all other inputs.
* In this study, "materials" refers to parts, supplies, fuels, etc.
which are consumed during the manufacturing process. Structures and
equipment, which are durable assets, are included as the capital
input.
7-44
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• All input prices, output price, and the level of
output are exogenous to the firm.
• All climate and air quality conditions are exogenous
to the firm.
• Interaction effects of third-order and higher are
negligible.
With the data available for this study, it is not generally possible
to test formally any of the above assumptions. The empirical results
obtained in the study are thus conditional on the assumptions being
valid. Fortunately, most of them appear reasonable and represent
conventional practice.
There are a variety of assumptions which can be tested directly,
however. For example, a test of the hypothesis that SC^ has no effect
on production costs can be made by testing whether the coefficients in
the terms involving Z-^ are statistically different from zero. In a
later section, tests of this types are carried out.
One problem of a practical nature which arises in this study is
the availability of degrees of freedom for conducting the various
statistical tests. The general translog cost function given
previously as Equation (7.9) incorporates 54 unknown parameters
(assuming four fixed inputs: S02, TSP, temperature, and rainfall).
Yet for only three of the 13 industries under study are more than 30
degrees of freedom available. This means that some additional
assumptions, in the form of restrictions on the unknown parameters,
7-45
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must be incorporated. The various possibilities include the
following:
• a^ = a^ and d— = d^ (Al)
• boi = 0 for all i (A3)
• b0 = 1, b00 = boi = eoi = 0 for all i (A4)
Assumption (Al) is commonly referred to as symmetry, and implies
that the values of the cross-partial derivatives
32 log C , a2 log C
and
3 log Pi 3 log Pj a log Z^ 6 log Z•
are independent of the ordering of the indices. Since this would seem
to be a very unrestrictive assumption, it is imposed throughout the
empirical analysis, thus eliminating nine unknown parameters.
Assumption (A2) imposes homogeneity of degree 1 on the input
prices for all variable inputs (L, K, M). That is, it says that if
all input prices are multiplied by a constant 3, then total cost would
also be multiplied by 13. This assumption follows directly from the
assumption of cost-minimizing behavior by firms. Assumption (A2)
eliminates nine parameters in addition to those eliminated by (Al).
7-46
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Assumption (A3) imposes homotheticity on the underlying
production structure. One implication of homotheticity is that the
effect of a price change on total cost is independent of the firm's
level of output. This is clearly a stronger assumption than (A2).
Assumption (A3) is not imposed in the analysis, and instead can be
examined on an industry-by-industry basis as to plausibility.
Assumption (A4) would make total cost homogeneous of degree 1 in
output, or equivalently, impose constant returns to scale on the
production structure. As in the case of Assumption (A3), this
assumption is also not imposed globally in the analysis.
With Assumptions (Al) and (A2) being the only assumptions imposed
a_ priori on all industries, a total of 54 - 18 = 36 parameters remain
in the translog cost function to be estimated. For most of the
industries, this is still too large a number, given the degrees of
freedom available. Thus, various combinations of restrictions on the
coefficients involving the fixed inputs (the climate and air quality
variables) must also be considered. In the empirical analysis, the
assumptions have been imposed in the following sequence, until the
number of unknown parameters is less than the available degrees of
freedom:
• di;j_ = 0 for i = SO2, TSP (Bl)
• c.j_j = 0 for all i and for j = RAIN (B2)
• dij = 0 for i = TEMP, j = RAIN (B3)
7-47
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eoi = 0 for all i (B4)
d = 0 for i = TEMP, RAIN (B5)
Assumption (Bl) says that the elasticity of total cost with
respect to TSP and S0_ is independent of the ambient concentration of
S02 and TSP, although it may depend on other factors. One implication
of (Bl) is that the relationship between cost and TSP or S02 is
monotonic. Assumption (B2) says that variations in ambient rainfall
do not affect input cost shares. Ambient temperature variations may
affect input cost shares, however, due to variations in heating, air
conditioning, or refrigeration loads; thus the c^. for j = TEMP are
retained.
Assumption (B3) imposes the restriction that the effects of
temperature and rainfall on total cost do not interact with one
another. Assumption (B4) says that the effects of the fixed factors
are independent of firm size. Assumption (B5) in analagous to (Bl)
but concerns the fixed inputs temperature and rainfall. (B5) is
potentially a strong assumption since one might expect that the
relationship is not monotonic, but rather that "optimal" levels of
temperature and rainfall exist. This is thus the last a_ priori
assumption imposed.
In the six industries subjected to detailed analysis,
restrictions other than (Bl) to (B5) can be tested directly rather
7-48
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than imposed a priori. The details of these tests are described
later.
DATA AND DATA SOURCES
In the planning stages for this study, it had been our
expectation that data from the most recent (1977) Census of
Manufacturing could be used. Publication timetables for the 1977
Census were delayed considerably, however, and its use proved
impossible. Opportunities for use of a prepublication special
tabulation were also not available; we were advised by Bureau of
Census personnel that a special tabulation of the type we required
could not be initiated for another six months or more. As a result,
it proved necessary to rely on the previous census conducted in 1972.
As it turns out, there are two distinct advantages to working
with the 1972 data rather than the 1977 data. First, it is generally
the case that air quality has improved during the 1972 to 1977 period.
Use of the 1972 data thus offered the possibility that cross-sectional
variation in air quality might be larger than in 1977, which would
make the 1972 data better for statistical analysis purposes. Second,
in 1972 the state and Federal air pollution control programs were far
less advanced than they were in 1977, as were air pollution control
activities within the manufacturing sector. As an example, flue gas
desulfurization processes for SOX control were not yet in widespread
use (see the electric utility sector analysis in Section 8 on this
7-49
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point). There is thus reason to believe that the problem mentioned in
an earlier section — that production cost variations among different
regions could be due to control cost variations as well as to vari-
ations in air pollution materials damage — would be less of a problem
in 1972 than in 1977.
Use of data from sources'other than the Census of Manufacturing
was considered but determined to be impractical. For example,
financial data reported to the Securities and Exchange Commission is
generally on a company-wide basis, or, at best, for major product
groups within a company. These kind of data are seldom made available
for individual manufacturing plants within a company and thus could
not be matched with air pollution data on a geographic basis. Sources
other than the Census of Manufacturing were thus not pursued further.
Selection of Industries
The Level of Disaggregation—
As noted in a previous section, an early decision point in the
study was selection of the appropriate levels of geographic and
industry detail. Clearly, the best situation would be to use data for
individual manufacturing establishments, matched to air quality data
from a nearby monitoring site. In fact, however, what was actually
used was data for counties at the 3-digit SIC level.
7-50
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The constraint on data detail is the Bureau of Census publication
policy. The Bureau, by law, cannot publish data on individual firms
or establishments. In addition, they withhold from publication data
on groups of establishments when either: (1) the operations of an
individual establishment might be revealed (i.e., there must be a
minimum of three or more firms in the group); or (2) the level of
employment is below a cut-off value. For example, data are 'typically
published only for larger cities and counties and for larger
industries. This means that in the 1972 Census, the following options
were available: (1) data for selected 2-digit SIC industries in
selected cities; (2) data for selected 2-digit and 3-digit SIC
industries in selected counties; and (3) data for selected 2-digit, 3-
digit, and 4-digit industries in selected SMSAs (metropolitan areas).
We rejected the use of 2-digit SIC industry data as being far too
aggregate in most industries. At the 2-digit SIC level, regional
variations in industry composition undoubtedly produce larger
variations in average production costs than the magnitude of the
variation in air pollution damages. Hence, the latter would be
difficult, if not impossible, to detect. This left as options the use
of 3-digit SIC data for counties or 3-digit or 4-digit SIC data for
SMSAs. We decided to use the county data, based on the observation
that air quality can vary quite a lot within a county, and thus even
more so within an SMSA. Use of the county data would thus provide a
closer match between the economic data and air quality data. In
retrospect, the other two options would still be worthy of further
7-51
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study — the 4-digit SIC data for SMSAs because of the finer industry
detail, and the 3-digit SIC data for SMSAs because data are available
in this form for the inter-census years 1973 to 1976, and thus
additional degrees of freedom (observations) would be available for
the analysis.
Selection of 3-Digit SIC Industries—
Given the decision to use county-wide data for 3-digit SIC
industries, the next step was to select specific industries for study.
Because of the data required for study of an individual industry, it
was not possible to cover all 143 industries at the 3-digit SIC level.
It was decided that data collection would be initiated for between 10
and 15 industries, in the hope that reasonable sample sizes might then
prove available for at least half that many.*
Under the assumption that air pollution would have the largest
impact on those industries with extensive exterior structures, the 143
industries were ranked according to the gross book value of assets in
* It is not easy to determine in advance of actual data collection how
big the sample will be for each industry. For example, data .on
labor hours and wages are obtained from the 1972 Census. However,
data on capital stock in place must be constructed from capital
expenditure data obtained from the earlier censuses. The sample
size for 1972 seldom proved to be a good indicator of data
availability in earlier censuses. A typical example is SIC 332 —
the iron and steel foundry industry. In 1972, data on this industry
were available from 40 counties. However, when these same counties
were checked in the earlier censuses, capital expenditure data were
available for only 17, 14, and 17 counties in 1967, 1963 and 1958,
respectively. Only two counties had data available in all four
censuses.
7-52
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buildings and structures. The 30 highest-ranked industries are listed
in Table 7-6. A striking feature of the list is the concentration of
total capital investment in a few industries. Five industries out of
143 account for almost 25 percent of the manufacturing sector's assets
in buildings and structures. Twenty-one industries represent nearly
50 percent.
Also shown in the table is the percent of each industry's payroll
that went for maintenance and repair activities by personnel in that
industry. These data are for the year 1957 (the most recent year
available) and do not include the cost of supplies and materials or
the cost of maintenance and repair performed by outside contractors.
Between 1957 and 1972 the definitions for a number of the industries
changed so the data are not exactly comparable. For example, SIC 281
formerly included both organic and inorganic industrial chemical
manufacturing, whereas now only the latter is included in that
industry (most of the remainder was shifted to SIC 286).
In selecting industries from the list in Table 7-6, our objective
was to pick the highest ranked industries for which sufficient county-
level data were also available. An inspection of data available in
1972 unfortunately eliminated some of the most interesting industries.
For example, SIC 291 (petroleum refining) is the most highly ranked,
both in terms of the value of assets in buildings and structures, and
in the proportion of total payroll devoted to maintenance and repair.
Unfortunately, very few counties in the U.S. have more than one
7-53
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TABLE 7-6.
THE 30 TOP-RANKED INDUSTRIES IN GROSS BOOK VALUE
OF DEPRECIABLE ASSETS IN BUILDINGS AND STRUCTURES
(1976) OUT OF 140 3-DIGIT SIC INDUSTRIES
Gross book value
SIC
code
291
331*
371*
286
208*
282
372
283
353
307*
344*
335
201*
262
366
271
367*
203
333
204
346*
356
281*
332*
386
265*
202*
349
354*
373
Number of
establishments
413
1,151
3,497
773
3,034
597
1,032
1,054
2,617
8,100
10,402
931
4,042
355
1,976
7,871
3,134
2,138
216
2,817
3,201
3,302
1,179
1,366
614
2,650
3,597
5,099
9,552
2,167
Total
($ millions) •
9,008.0
5,747.4
4,615.7
2,760.9
2,408.9
2,306.6
2,003.5
1,901.3
1,889.0
1,767.4
1,709.8
1,689.5
1,600.1
1,597.6
1,553.6
1,540.0
1,487.2
1,433.9
1,400.9
1,396.8
1,346.9
1,323.1
1,319.5
1,227.6
1,202.7
1,152.9
1,065.8
1,063.6
1,042.5
1,015.5
As a percent of all ITS
itanufactunng
i
Individual Cumulative
8.3
5.6
4.5
2.7
2.3
2.3
2.0
1.9
1.8
1.7
1.7
1.6
1.6
1.6
1.5
1.5
1.5
1.4
1.4
1.4
1.3
1.3
1.3
1.2
1.2
1.1
1.0
1.0
1.0
1.0
3.8
14.4
18.9
21.6
23.9
26.2
28.1
30.0
31.8
33.6
35.2
36.9
38.4
40.0
41.5
43.0
44.5
45.9
47.2
48.6
49.9
51.2
52.5
53.7
54.9
56.0
57.1
58.1
59.1
60.1
own uayt^j-j. mt
aintenance & repair
as a % of total
payroll in 1957**
25.7
21.1
8.5
16.5
5.2
12.3
3.2
NA
4.0
4.2
2.9
10.2
4.1
14.4
3.5
2.1
NA.
5.2
NA
NA
4.1
3.2
15.0
6.6
3.5
3.9
5.2
2.6
4.1
* Industries selected for data collection.
** Changes occurred in some industry definitions between 1958
and 1972. Percent figures shown in the table are therefore
only approximate in some cases.
Sources: Bureau of the Census. 1976 Annual Survey of
Manufactures (asset data).
Bureau of the Census. 1976 County Business Patterns
(number of establishments).
Bureau of the Census. 1957 Census of Manufactures
(maintenance data).
7-54
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refinery present so that data on costs of operations for this industry
are almost non-existent at the county level in the 1972 Census. A
good indication of the problem is the small number of establishments
in this industry. As shown in Table 7-6, there were only 413
establishments classified in this industry in 1976, whereas there are
more than 3,000 counties in the United States.
The 13 industries ultimately selected were listed previously in
Table 7-3, along with industry definitions, and are also indicated in
Table 7-6 by an asterisk.
Data on Labor Inputs and Costs
The Census of Manufacturing distinguishes between two labor
categories: production workers and all other employees. Production
workers include workers up through the working foreman level, employed
in such activities as fabrication, processing, assembly, inspection,
shipping and receiving, and maintenance and repair. "All other"
includes factory supervision above the working foreman level and other
activities such as sales, delivery, advertising, clerical, finance,
personnel, professional, and executive functions.
In aggregate time-series econometric studies of the manufacturing
sector, consideration of both labor categories has become more widely
practiced. For cross-sectional studies, particularly a county-level
study such as this one, the advisability of including both labor
7-55
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categories is far less clear. One problem, which affects both time-
•
series and cross-sectional studies, is definitional. The data
available on production workers includes: number of employees,
manhours, and wages; for all other employees the only information
available is the number of employees and the payroll. Thus, for the
first labor category, a natural measure of labor input is manhours and
a natural measure of the price of labor is the average hourly wage.
For non-production workers, one must use the number of employees as
the labor quantity, and average annual payroll per employee as the
labor price, or else arbitrarily define say 2,000 hours as a standard
year in order to get labor hours and wage rates. The problem with
either approach for non-production workers is that no account is taken
of part-time employees or variations in the length of the work week.
A second, more serious problem arises in the treatment of non-
production employees in cross-sectional studies. Consider a company
with two manufacturing plants producing similar products but in
different geographic locations. For efficiency reasons, it may be the
case that the company has consolidated most of the executive,
professional and administrative activities in one location, even
though production and production supervision are present in both
locations. In this situation, including the non-production workers in
the analysis would result in one of the plants showing a
disproportionately large labor input, even though both plants may
produce the same quantity of manufactured output.
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One crude measure of the problem is the ratio of the number of
establishments in an industry to the number of companies in an
industry. As shown in Table 7-7, this ratio varies from 1.044 to
3.041 in the 13 industries included in this study. In view of the
evidence that multiplant companies are evident in a number of the
industries, and because of the other definitional problems, we have
excluded non-production workers from the analysis. Thus, the measure
of labor input used in this study is production worker manhours and
the price of labor is taken to be the average hourly wage rate,
computed by dividing total production worker wages by total production
worker hours.* As noted in an earlier section, an assumption which
would be consistent with this approach is that non-production worker
inputs and all other inputs are perfect complements, i.e., the input
of non-production labor is a fixed proportion of total output.
TABLE 7-7. EXISTENCE OF MULTI-PLANT COMPANIES IN 1972
SIC
201
202
208
265
281
307
331
___________
Establishments
per company
1.13
1.29
1.22
1.57
3.04
1.13
1.51
SIC
332
344
346
354
367
371
Establishments
per company
1.15
l.OS
1.08
1.04
1.17
1.20
* In one industry (SIC 354) we found it necessary to use total payroll
data. See the later section on output prices.
7-57
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One final issue concerning the labor data is the problem of
supplemental labor costs. Supplemental labor costs include the
employers' contributions towards social security, unemployment
compensation, workman's compensation, life and health insurance,
pension programs and so forth. These payments were about 13.5 percent
of actual payroll across all manufacturing industries in 1972.
Consideration of supplemental labor costs is important because they
represent part of the true cost of using labor in the manufacturing
process. Their consideration is particularly important in time series
studies because supplementals have been an increasing percentage of
labor costs over the past several decades.
Omission of supplemental labor costs in a cross-sectional study,
as was necessitated here, is perhaps less serious. Omission would be
serious only if supplementals, as a percent of wages, varied
geographically within an individual industry. Omission would be less
serious if supplementals primarily vary over time (e.g., due to
changes in the required social security contribution) or across
industries (e.g., unionized industries versus non-unionized
industries). While we expect that the variation is more important
over time and across industries than across regions in the same
industry, it has not been possible to verify this assumption. The
Census Bureau in the past has published data on supplemental labor
costs in two forms only — for individual industries on a national
basis and for individual states on an all manufacturing basis.
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Supplemental labor costs for individual industries at either the
state, SMSA or county level were not published for 1972.
Data on Capital Inputs and Costs
The treatment of capital in econometric studies of manufacturing
is perhaps one of the most difficult issues in both theoretical and
practical terms. Among the theoretical issues are: the definition of
capital (e.g., physical capital versus "working" capital), the units
of measurement for physical capital, the relevance of net versus gross
capital, the appropriate procedure for determining net capital, the
treatment of capital as a variable input or as a fixed input in the
short-run, and the effect of changes in the utilization of capital.
The practical problems include differing availability of data to
implement the various theoretical approaches suggested, and for cross-
sectional studies, the almost total lack of region-specific data
altogether.
A variety of methods and data sources have been used in the
treatment of capital in previous cross-sectional studies of the U.S.
manufacturing sector. Representative examples are the 1965 study by
Hildebrand and Liu (13) and the 1972 study by Moroney (14). Both
studies used data from the 1958 Census of Manufacturing which included
1957 data on the gross and net book value of depreciable assets for 2-
7-59
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digit SIC industries at the state level.* Neither study considered
air pollution effect, and more recent data on net book value has not
been published by the Census Bureau. A 1980 study by Field and
Grebenstein (15) made use of 1964 data on gross book value published
by the Census Bureau in 1972 for 2-digit industries at the state
level. Air pollution was not considered. Many other cross-sectional
studies of the U.S. manufacturing sector were conducted in the 1960's
and 1970's using analytical approaches which did not require data on
capital stocks. Particularly common were studies based on the CES
(constant elasticity of substitution) production function, many of
which are reviewed in a 1976 survey by Caddy (16). None of these
studies dealt with air pollution.
The Basic Approach of this Study—
In order to estimate the translog cost function defined
previously, two capital-related items are required. These include a
price for capital services, and the annual cost or outlay for capital
services. The fact that cost divided by price equals quantity means
that a quantity concept is also defined.
The remainder of this subsection is concerned with the procedures
used to develop estimates of capital stocks and capital service prices
for each industry and county. Attention is restricted to capital
* The data included gross book value of depreciable assets, the value
of accumulated depreciation charged against those assets, and the
value of rental payments for plant and equipment.
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assets in the form of physical capital. Physical capital is defined
to include buildings, structures, machinery and equipment (hereafter
simply referred to as structures and equipment), but not land. Land
is excluded because it is not generally viewed as a depreciable asset.
The analysis also includes only chose capital assets which are owned.
Data on rented capital assets were not available in appropriate form.
For example, the Bureau of the Census has published 1972 data on
rental payments for physical assets in two forms: on a national basis
for 4-digit SIC industries and on a state basis for all manufacturing.
Rental payments by 3-digit industries are not available for states or
sub-state areas.
The exclusion of rental payments will be a serious problem only
if there is variation across states in the use of rented assets within
an industry. We have no reason to expect that such variation exists.
Unfortunately, as in the case of supplemental labor costs, the data
are not available to determine the actual extent of the variation.
Calculation of Net Capital Stocks—
The net value of capital stocks (assets in-place) were calculated
for each industry and county using the perpetual inventory formula
Kijt
where K^ -t is the net value of the capital stock in industry i, and
*
county j at the end of year t; Ij_jt is gross capital expenditure (in
7-61
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1972 dollars) in industry i, county j, and year t; and A is the annual
rate of depreciation (or replacement). Equation (7.28) says that the
current net value of the capital in place is the sum of the
depreciated values of past annual capital expenditures. This is more
easily seen by rewriting (7.28) after making successive substitutions
for
Kijt
(7.29)
_ i i
(1 - A
where KQ = K^-t-(n+l) • Tne depreciation factor A assigns
exponentially decreasing weight to capital expenditures made in
earlier years.*
* There is some controversy in the literature as to the appropriate
aggregation procedure for net capital stocks. The perpetual
inventory method using exponentially decreasing weights as in
Equation (7.28) is the most widely used method. It basically
attempts to measure the rates of addition to and decline in the
economic value of assets. With exponential depreciation, most of
the decline in value occurs in the early years of the asset's
lifetime. For a comprehensive application of this approach to U.S.
time series data, see Reference (17). An interesting alternative
approach based on changes in the "efficiency" of assets rather than
their economic value is available in Reference (18). In this latter
approach, the perpetual inventory technique is still employed but
depreciation rates are not exponential. In the efficiency approach,
the assumption is that assets retain most of their "serviceability"
until near the end of their economic lifetime, at which time most of
the depreciation (in this case, loss of serviceability) occurs. In
the present study, the exponential depreciation method has been
employed. Since the objective of the study is to estimate
production costs, and the appropriate "cost" of capital is its value
in alternative uses, it was decided to use exponential depreciation
as being a better measure of net value.
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Implementation of Equation (7.28) requires data on annual capital
expenditures, a price index for capital expenditures to convert the
historical dollar expenditure stream to 1972 dollars, and an estimate
of the initial net capital stock in some benchmark year. These items
are discussed in the following three subsections.
Annual Capital Expenditure Data—For a variety of reasons, it was
decided that the end of the year 1953 would be the benchmark. This
meant that capital expenditure data were required for each 3-digit SIC
industry and county in the sample for every year 1954 to 1972 (a total
of more than 10,000 data points!). Unfortunately (or fortunately),
the Bureau of the Census publishes capital expenditure data at the 3-
digit SIC level for counties only in census years (1958, 1963, 1967
and 1972). Thus, a procedure for estimating capital expenditures
during the inter-census years was required. The procedure used was to
determine for each successive pair of census years the fraction of the
total capital expenditures in an industry accounted for by each county
containing that industry. The capital expenditures for that county
and industry in the intervening years were then estimated by
interpolating the census year fractions and then applying the
interpolated values to the published total for that industry in the
intervening years.
More formally, let Iijt and Ij_jt4.n be the capital expenditures in
industry i, county j and census years t and t-t-n. Let Ij,ut be the
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national total capital expenditures for industry i in year t. Then
compute
!3ijt+n "" I/I-- ' (7.31)
and interpolate between P.; and P^+ according to
f (k/n)(Pijt+n - Pijt) . (7.32)
Finally, calculate the estimated capital expenditures in year t+k from
A A
Iijt4-k = !3ijt4-kIiUt+k ' (7.33)
where I-^ut+k ^s a Polished value. This procedure fills in all of the
missing years between 1958 and 1972. For the years 1954 to 1957, the
values of Pjit in 1958 were applied to industry totals for those
years.
The investment series constructed according to Equation (7.33)
includes capital expenditures for both structures and equipment.
Although a breakdown between the two categories is available annually
for each industry on a national basis, no breakdown is published by
industry, for states, SMSAs or counties.
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In a large number of instances, capital expenditure data for
census years before 1972 were not available for e.ach industry and
county included in the data set for 1972. Consideration was given to
eliminating from the data set any industry-county pair which did not
have data for each of the four census years. However, this would have
so reduced the sample size for each industry that only four industries
would have possessed sample sizes of 20 or more observations. As an
alternative, it was decided that industry-county pairs would be
included if they met either of the following criteria: (1) data were
available in each of the four census years, or (2) data were available
in each of the two most recent census years (1972 and 1967) and at
least one of the earlier two years (1958 or 1963). With this less
stringent selection procedure, seven of the original 13 industries
possessed a sample size of 20 or more.
For those industry-county pairs missing data for one of the
earlier census years, capital expenditure estimates were developed by
expanding the time period over which the estimation procedure in
Equation (7.33) was used. The additional measurement error introduced
by this procedure is heavily discounted by the exponential
depreciation schedule. For example, assuming a depreciation rate of
0.10 per year (X = 0.10), a dollar of investment in 1963 would
contribute only $0.38 to the 1972 net capital stock value and a dollar
in 1958 would contribute only $0.23. Thus, any errors in estimates
for the earlier years have only a small effect on the final estimate
of total net value in 1972.
7-65
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Price Indexes for the Investment Series—The investment series
constructed above is in historical dollars. Since it is desirable
that the net value of the capital stock be estimated from a consistent
investment data series, we converted the capital expenditure data in
each year to 1972 dollars. This was done using the relationship
^F <7.34)
^t
where I;-;* is capital expenditures in year t in historical dollars,
Ij_^t is capital expenditure in year t in 1972 dollars and Pfc is a
price index for capital expenditures in year t (Pi 972 = 1-00). Values
for Pfc, for each industry, were computed from Reference (19). This
reference contains U.S. annual capital expenditure data for individual
industries, measured in both historical and 1972 dollars. Values for
?t were calculated as the ratio of the historical series to the series
in 1972 dollars, for total investment in structures and equipment.
Benchmark Values for Net Capital Stock—Recall that the perpetual
inventory formula can be written in the form
Kijt
(7.35)
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This section is concerned with estimating the benchmark value of the
capital stock, KQ . Recall that the benchmark year is the end of 1953.
Because of the exponential depreciation, capital expenditures
before 1954 make only a minor contribution to the net value of the
capital stock in 1972. The following simple procedure was therefore
used to calculate the benchmark value. Let IQ be the 1954 capital
investment in a given industry and county (dropping the ijt subscripts
for convenience). The value of Ig is determined using Equation
(7.33). Assume, further, that capital investment in this industry and
county grew at a rate a per year during the years prior to 1954. In
this case, the net value of the capital stock at the end of 1953,
using the recursion formula, is given by
00
i"1
K0 = (1 - A)"1I0/(l + a) (7.36)
i=l
which equals
I0/(cc + X) . (7.37)
The contribution of this capital stock to the net value in 1972 is
given by
(1 - A)19I0/(a + X)
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The value of a. was assumed to be 0.05. Because of the weighting
1 q
factor (1 - X) , the net value of the total capital stock in 1972 is
not very sensitive to the assumed value of a.
Price of Capital Services—
The price of capital services in this study is a modified version
of the concept used in Field and Grebenstein (20), which in turn was
derived from Christensen and Jorgenson (21), and Hall and Jorgenson
(22). A similar approach can also be found in Coen (23). The basic
idea behind the concept used in this study is as follows. In the
previous section, a procedure for calculating the net value of capital
assets was presented. Let this value in industry i and county j be
denoted VK^-. As a measure of value, VK|- incorporates both price and
quantity attributes. In particular, it reflects the prices at which
the various capital assets were purchased. However, it does not
reflect the price or cost of using these assets per unit of time. It
is the latter items which are required since the translog cost
function to be estimated is the cost of production per year. For this
purpose, we employ the concept of a service price of capital which has
an explicit time dimension. The service price of capital in this
instance is the annual price for use of an asset whose life extends
over many years. Because of the time dimension associated with this
price, it is often referred to as a rental price, as if the asset were
to be rented for one year.
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To be more specific, the capital services price is defined to be
the implicit rental value of the capital services derived from an
asset, taking into account the price of the asset, the rate of
depreciation of the asset, the corporate tax structure and the
discount rate (cost of money). In the notation of this study, the
service price of capital, PK, is defined to be
PA
= P __ ,r
A 1 - U
(7.38)
where P, is an index of asset prices, u is the effective tax rate on
corporate income, D is the discounted present value of depreciation
deductions for income tax purposes on one dollar of investment, r is
the cost of money, and A is the rate of depreciation for physical
assets.
The link with the net value of the capital stock can now be
completed. If PA is an index of asset prices, then the quantity of
capital stock in place, K, is simply
K = VK/PA • (7.39)
The annual outlay for capital services is then the price of capital
services times the quantity of capital services, or
7-69
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(r
(7.40)
1 - uD
1 - u
(r + X)(VK)
The remainder of this subsection discusses the methods and data
sources for calculating the variables in Equation (7.38). Of
particular importance is the problem of incorporating regional and
industry variations in these variables.
Cost of Money (r)—The appropriate value for the cost of money is
the weighted average cost of money from debt and equity sources. In
general, one would expect this cost to vary from industry to industry,
and from company to company within an industry, depending upon
relative degrees of perceived investment risk. It is also possible
that costs of money will vary across different states; however, the
relative mobility of capital funds, and arbitrage opportunities, tend
to minimize regional variation. In this study we have assumed that
regional variations in the cost of money are negligible.*
* Field and Grebenstein (25), who use a similar approach, incorporate
regional variations in r. They use as the regional cost of money
the average bank rates on long-term business loans in the various
Federal Reserve Board (FRB) regions. Our suspicion is that the
regional variations observed in the FRB data are due more to
regional differences in industry composition than to any regional
variations in the cost of money.
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In the matter of industry variations in the cost of money, we
considered a number of approaches, none of which seemed fully
satisfactory. For example, a few years ago the U.S. E.P.A. funded a
study to estimate the weighted average cost of money in selected
industries (24). However, the industries selected were those with
large capital investments in pollution control activities and did not
match with the seven industries considered in this study.
Ultimately, we decided to use the average yield on industrial
bonds in 1972 as the value of r, as reported in the Federal Reserve
Bulletin (26). This value was 0.0735. At a later stage in the
analysis, overall values of ?„ are adjusted to reflect industry
differences. These adjustments are discussed in a later subsection.
Depreciation Deductions (D) — It has been shown elsewhere (27)
that the present value of depreciation deductions allowable against
corporate income taxes is given by
D = (2/rn)(l - (l/rn)(l - e~rn)) (7.41)
where n is the life of the asset for income tax purposes. This
formula assumes that firms use sum-of-years digits depreciation for
tax purposes, a reasonable assumption since it is one of the popular
methods of accelerated depreciation. For this study, an average tax
life of 20 years was assumed, this being about midway between the
allowable tax lives for structures and equipment.
7-71
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Effective Corporate Income Tax Rate (u)—The effective corporate
income tax rate is intended to reflect both Federal and state tax
rates, net of investment tax credits and other deductions. Following
the Field and Grebenstein approach, the effective tax rate in state j,
u.i, is calculated from
= (FCTj + SCTj)/TYj (7.42)
and
TY- = (FCT^)(TY)/I FCT^ (7.43)
j
where FCT^ is the dollar amount of Federal corporate income taxes
collected in state j, as reported in (28).
SCT- is the dollar amount of state corporate income taxes
collected in state j, as reported in (29).
TY is total corporate profits before income taxes, as
reported in (30).
Depreciation Rate (X.)—The depreciation rate X is used both in
the capital services price, P~, and in calculating the net value of
capital assets, VK. Recall that X is a measure of the rate of
economic depreciation.
Initial consideration was given to estimating X for each industry
based on the data mentioned earlier that was available in the 1958
Census. That data included estimates of gross book value, accumulated
7-72
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depreciation, and current depreciation charges for the year 1957.
However, this approach was not pursued in view of the likelihood that
the 1958 Census depreciation data reflect straight-line depreciation
for financial reporting purposes and thus bear little resemblance to
economic depreciation.
Ultimately it was decided that an "average" of the depreciation
rates reported for non-residential structures (0.056) and producers'
durables (0.138) in Christensen and Jorgenson (31) would be used.
These values are weighted average depreciation rates for 20 types of
non-residential structures and 52 categories of producers' durables.
The depreciation rate in each category assumes double-declining
balance depreciation over the mean service life for assets in each
category. The value used in the present study is X = 0.10, which
gives somewhat more weight to producers' durables than to structures.
This is based on the observation that machinery and equipment account
for between 60 and 80 percent of the 1972 total gross book value in
the various industries included in this study.
Asset Prices (P^)—Recall that in constructing estimates of net
capital stock value, adjustments were made to the annual capital
expenditure data to reflect variations in asset prices over time. No
adjustments, however, were incorporated to reflect regional variations
in asset prices. Since these variations, if significant, would
influence the relative use of capital vis-a-vis other inputs on a
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regional basis, an effort was made to develop an approximate index of
regional asset prices.
The basic idea behind the approach was as follows. First, the
Producer Price Index component for machinery and equipment (32) was
regressed on average hourly wage rates, capital services prices, and a
specially-constructed price index for materials. The regression used
a Cobb-Douglas unit cost function specification. It was estimated on
U.S. time series data for 1958 to 1972, using wage and materials data,
for industries SIC 35 and SIC 36, the machinery and equipment
industries corresponding to the Producer Price Index component. The
estimated equation, and corresponding data for each state in 1972,
were then used to predict asset price variations across states. The
asset price predicted for a state was then used for each sampled
county in the state. The price variations across states are
normalized to an index value of 1.0 for the U.S. in 1972.*
* It might appear that this procedure requires knowledge of the
capital services price in a state, and thus the asset price in a
state, in order to predict the asset price in a state. In fact this
is not the case. Let PK, PA and R be defined as before, and let PL
and PM be labor and materials prices, respectively. In this case,
the asset price equation estimated is
log PA = aQ + a^ log PL + a2 log PK + a-j log P
M
where a^, ... , a, are the coefficients of the regression equation.
Making the substitution PK = PA • R, and rearranging terms, yields
(1 - a2) log PA = aQ + a-j_ log PL + a2 log R + a3 log P^
Thus PA can be predicted without prior knowledge of P*.
Furthermore, since it is variation in PA across states which
matters, the factor (1 - a2) can be dropped in calculating the index
value for each state.
7-74
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The approach described above does have its shortcomings. First,
the index reflects variation in machinery and equipment prices only,
to the exclusion of structures. However, as noted earlier, machinery
and equipment account for 60 to 80 percent of gross asset value in
these industries. Second, the index reflects price variation across
states in 1972, while capital stocks include assets purchased over a
period of years. This could present a problem if the pattern of
regional asset price variation has changed considerably over time.
However, even if the pattern has changed, recall that the use of
exponential depreciation gives the largest weight to capital
expenditures made in 1972 and the immediately preceding years. Thus
differences in the regional pattern of asset prices in earlier years
are of lesser importance.
A third issue which arises is how equipment sales between states
might affect the actual equilibrium asset price in each state,
relative to the predicted price via the above approach. Since this
issue also arises in the procedure used for estimating industry output
prices, it will be discussed later in that section, as will the
estimated asset price equation.
Capital Services in Summary—
Since much ground has been covered in this section, it will be
helpful to summarize briefly. The price of capital services used in
the translog cost function is the variable, PR, defined as
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•K
= (Pa)(R) (7.44)
where
R = } " UD (r + X) . (7.45)
1 - u
The annual cost of capital services used in the translog cost function
is calculated as
(PK)(K) = (PK)(VK)/PA
(7.46)
= (R)(VK)
where VK is the net value of capital assets in place. The quantity VK
is calculated from the recursion formula
VKt = ij! + (1 - X)VKt-1 . (7.47)
The values of P« and (R)(VK) are allowed to vary across industries and
states due to variations in the values of P., VK and u. A minor
adjustment is also made in the value of R, on an industry-by-industry
basis, to achieve consistency in the scaling of the capital service
price with the industry output price.
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Data on Materials Inputs and Costs
In the many previous cross-sectional econometric studies of U.S.
manufacturing, very little attention has been given to the issue of
materials inputs other than energy. The constraint in most cases is
the absence of systematic price data for materials on a regional
basis. The 1972 Census of Manufacturing, as an example, provides
regional data on the total cost of materials but no data on regional
materials prices. As a result, most previous cross-sectional studies
have used variations of the two-factor model where capital and labor
are the two factor inputs, and value added is the measure of output.
As noted earlier, value added is the dollar difference between the
value of shipments and the cost of materials, adjusted for inventory
changes.
It was decided during this study that the conventional two-factor
model, and the use of value added as an output measure, would be
unsatisfactory. One reason is that recent studies (33) of the
manufacturing sector using time-series data, and incorporating
materials inputs, have found that the assumptions required for a value
added specification to be valid are not consistent with actual data.
A second reason is that air pollution could conceivably affect the
relative use of materials on a regional basis. As defined by the
Bureau of the Census, "materials" includes all inputs to the
manufacturing process except labor, capitalized assets and land,
purchased services, and certain overhead costs such as rent and
7-77
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royalties.* Specifically included are parts and supplies used for
maintenance and repair activities which *are not capitalized. While
air pollution effects on materials were expected to be small, and
difficult to detect, they could not be ruled out in advance.
Recall from the previous section that missing data on historical
capital expenditures reduced the original group of 13 industries to a
group of seven. The seven included:
SIC 201 Meat Products
SIC 202 Dairy Products
SIC 208 Beverages
SIC 265 Containers and Boxes
SIC 344 Fabricated Structural Metal Products
SIC 346 Metal Forgings and Stampings
SIC 354 Metalworking Machinery
For six of these industries, regional materials price data of varying
degrees of quality were located and price indices developed. For the
seventh industry (SIC 208), no suitable data were identified. The
remainder of this section is concerned with the methods and data used
in constructing regional materials price indices for the six
industries other than SIC 208.
* The Bureau's definition of materials includes: raw materials,
parts, supplies, containers, etc.; fuels and electricity; products
bought for resale; and products manufactured by others under
contract.
7-78
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The Basic Approach—
All of the materials price indices in this study are applications
of the price index concepts described in Diewert (34). The idea
behind the index procedure is the following. Suppose there are n
different materials in the manufacturing process, each with its own
price. If one wanted to represent these prices by a single aggregate
price, so that price variations across regions or over time could be
more easily compared, what is an appropriate aggregation procedure?
One approach, as shown by Diewert, is an index defined in its most
general form as follows:
n
log(pVP°) = (1/2)S + s Iogp/P (7.48)
where the subscript i runs from 1 to n, the number of commodities
included in the index; the superscript j runs across regions (or
across years); the P^ are the prices of the individual commodities in
region j; the S^ are the shares of total cost accounted for by each
commodity i in region j; and P^ denotes the value of the index
relative to a base year or base region denoted by the superscript 0.*
In effect, the formula states that the aggregate price index can be
constructed as a cost-weighted average of the logarithms of the ratios
of each commodity price to a corresponding base price.
* The index formula given by Equation (7.48) is typically referred to
as the Fisher-Tornqvist approximation to a Divisia index. Hulten
(35) has shown that the Divisia index is the best index method.
7-79
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In this study, two types of materials price indices were required
— an index over time, which is used in developing industry output
price estimates; and an index across regions, which is used in the
estimation of the translog cost function. In developing the time
series indices, the available data allow Equation (7.48) to be used in
its most general form. In the regional (state) indices, the available
data require the assumption that SJJ = S^, in which case Equation
(7.48) simplifies to
n
Si
In this form the cost-shares are taken to be the national average cost
shares for each commodity i.
SIC 201 (Meat Products)—
For the meat products industry in 1972, the total cost of
materials was $26.6 billion, or 85 percent of the value of shipments
that year. Most of this cost was for the acquisition of livestock, and
meat. The three largest items of cost were cattle, hogs, and
chickens, which together accounted for more than 64 percent of total
materials cost. Price indices involving these three commodities were
thus constructed.
The time series index for this industry on a national basis was
constructed for the time period 1958 to 1972, with 1972 defined as the
7-80
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base year. Cost shares for the three livestock products were
published for SIC 201 in each of the census years 1958, 1963, 1967 and
1972 (36). Cost shares for the intervening years were estimated by
linear interpolation. Prices for each type of livestock in each year
were taken from publications of the U.S. Department of Agriculture
(37). It was decided that use of prices from the latter source would
be preferable since the data were available for each year. Average
unit costs could have been calculated from total cost and quantity
data in each of the four censuses; however, unit cost data would not
have been available for the inter-census years. We judged that inter-
polation of prices was less justifiable than interpolation of the cost
shares since the former appeared to be more volatile.
The cross-sectional price index for states in 1972 was
constructed using similar data. The cost shares for each type of
livestock in each state were assumed to be equal to the national
average cost shares for the industry as a whole. Prices in each state
for each type of livestock were taken from the same source as in the
time series index.
SIC 202 (Dairy Products)—
The dairy products industry in 1972 consumed $12.3 billion of
materials or more than 75 percent of the value of shipments. The
purchase of whole milk accounted for half of the cost, followed at a
considerable distance by cheese and cream. Because milk was such a
dominant cost item, and since price data of comparable quality were
7-81
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not available for the other items, the index for this industry is
based on milk prices alone.
With only a single commodity, no cost share data were required in
constructing either the time series or cross-sectional price indices
(i.e., the cost share for milk in the index is 1.0). The price data
for milk, both for the period 1958 to 1972, and for each state in
1972, were taken from Department of Agriculture publications (38).
SIC 265 (Containers and Boxes)—
The cost of materials in the container and box industry was $4.5
billion in 1972 or nearly 56 percent of the value of shipments. By
far the largest cost item was the consumption of paperboard. Although
exact data are not available, it appears that paperboard accounted for
perhaps $2.5 to $3.0 billion of total materials cost, or 50 to 70
percent. The next largest item appears to have been paper, and
although exact data are not available, paper's share of total
materials cost was probably 10 percent or less. In view of the
dominant role of paperboard as a materials input for this industry,
and given the lack of exact data on cost shares for individual
materials, it was decided to use the price of paperboard as the basis
for a price index.
Time series prices for paperboard nationally were calculated by
dividing the total value of paperboard shipped, from Reference (39),
by the total quantity of paperboard production, from Reference (40).
7-82
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The time series in this industry covers the period 1963 to 1972. The
Census Bureau changed the definition of paperboard in 1963 so that
data before that time are not directly comparable with the more recent
data.
Average paperboard prices by state for 1972 were calculated using
the same method and data sources as in the time series index. In this
case, however, value of shipments data on paperboard were more
difficult to obtain. The problem was that shipments data for certain
types of paperboard were withheld from publication by the Census
Bureau for certain states. Thus the total value of shipments of
paperboard for these states could only be determined within certain
ranges. Fortunately, through a tedious process of working with
published totals for larger geographic areas and U.S. totals for each
type of paperboard, it was possible to narrow these ranges to within
tolerable limits for those states included in the sample. It would
have been preferable to include individual types of paperboard in the
index, rather than simply total paperboard, but this was not possible
because of the problem described above.
SIC 344 (Fabricated Structural Metal Products)—
In this industry, the cost of materials was $7.5 billion in 1972,
or 53 percent of the total value of shipments. Carbon steel and
aluminum accounted for 48 percent of total materials cost, followed at
a considerable distance by alloy and stainless steels. Materials not
specifically identified accounted for most of the remainder.
7-83
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The price indices for this industry incorporate five materials —
three types of carbon steel products (sheet/strip, plates, and
structural shapes) and two types of aluminum products
(sheet/plate/foil and extruded shapes). These are the dominant
materials used, in terms of total cost, and together accounted for
about 38 percent of total materials cost. While this percent coverage
is somewhat lower than in the industries described previously, price
behavior among these products is also likely to be indicative of price
behavior among the other steel and aluminum products not included in
the index. Thus, as a measure of price variation, the index is likely
to be somewhat better than the percent figure noted above.
The time series index was calculated using cost and quantity
information available for SIC 344 in the four census years 1958, 1963,
1967 and 1972 (41). Prices for these years were calculated as total
cost divided by total quantity, for each material in the index. Since
comparable price and cost share data were not available for the
intervening years, index values for these years were obtained as
follows. The index values calculated for the four census years were
regressed in pairs against the producer price index component for
steel mill products (42) in the corresponding years. The fitted
regression equations were then used to interpolate the missing index
years based on the value of the producer price index component in
these years. The final index thus covered the period 1958 to 1972.
7-84
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The cross-sectional price index for 1972 was constructed using
the same census data. The cost shares for each type of metal for each
state were assumed to be equal to the national average cost shares for
SIC 344 as a whole in 1972. Prices for each metal in each state,
relative to the national averages, were assumed to be in the same
relationship as existed in 1963. That was unfortunately the last year
that the Census Bureau published metal cost and quantity information
at the state level.* As in the case of the time series index, prices
were calculated as total cost divided by total quantity.
SIC 346 (Metal Forgings and Stampings)—
The total cost of materials in this industry in 1972 was $4.9
billion or 50 percent of the value of shipments. As in the case of
SIC 344, the dominant materials used were steels and aluminum, which
together accounted for about 64 percent of total materials cost. Much
of this, in turn, was accounted for by carbon steel alone, and in
particular by carbon steel sheet and strip.
Because of the similarity in materials use between SIC 344 and
SIC 346, the price indices for the latter were constructed using the
same methods and data sources as described for SIC 344. The primary
difference is in the cost shares for the five metals included in the
* A number of trade publications (e.g., Iron Age) have more recent
price data on a regional basis. However, these data are generally
list prices and thus do not reflect premiums, discounts, taxes or
transportation costs. In contrast, the Census data are actual
delivered costs and are. available for more geographic areas. In
view of this, the Census data were used in this study.
7-85
-------
index. This naturally leads to slightly different index values, both
for the time-series and cross-sectional cases.
SIC 354 (Metalworking Machinery)—
Industry SIC 354 consumed $2.4 billion in materials or 34 percent
of the value of shipments in 1972. The largest materials inputs in
terms of cost were carbon and alloy steels; iron, steel, and aluminum
castings; and motors, generators and bearings. Based on cost share
rankings, an index consisting of five materials was decided upon. The
five materials included alloy steel bars, iron castings, carbon steel
bars, carbon steel plate, and aluminum castings. These items
accounted for 15 percent of total materials costs and should also
reflect price variations among other metal products used by the
industry. It is not possible to develop a much broader index for this
industry because a significant fraction of materials inputs are not
identified in the census. Fortunately, however, materials cost as a
percent of total production costs are quite low in this industry
compared to the five discussed previously.
Both the time series and cross-sectional price indices for this
industry were developed using the same methods and data sources as
used for SIC 344. The primary differences are in the specific
materials included in the index, and in their cost shares. Thus the
index values are different from those of SIC 344 both in the time
series and cross-sectional cases.
7-86
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SIC 35 and SIC 36—
In the earlier section on capital inputs, a procedure for
developing regional prices for capital assets was described. One
input to the price estimating procedure was a materials price for the
machinery and equipment industries (specifically, SIC 35 and SIC 36).
Both a time series and cross-sectional materials price index were
used. These were developed using the data sources and methods
described in the immediately preceding section.
Industries SIC 35 and SIC 36 consumed materials with a total
value of $52.5 billion in 1972, or 44 percent of the total value of
shipments. The dominant materials were carbon steels, castings,
copper and steel alloys, and aluminum. Together these items and other
metal products accounted for more than 20 percent of total materials
cost in the two industries. Much of the remaining materials cost was
not specifically identified by kind in the census.
An index consisting of seven different materials was constructed
for these two industries. Included in the index were carbon steel
(bars, sheet and plate), alloy steel bars, aluminum sheet/plate/foil,
and iron and steel castings. Together these seven items represented
about 10 percent of total materials cost and should also reflect price
variation by the other metal products used in these industries. The
time series and cross-sectional indices were constructed using the
methods and data sources described previously for SIC 344.
7-87
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Materials Prices in Summary—
The characteristics of the materials price indices used for each
industry are summarized in Table 7-8. The first three columns in the
table are self-explanatory. The second three columns reflect the
degree of coverage provided by the price indices. The first column
indicates the percent of total materials cost accounted for by
commodities included in the index. The second column is an estimate
of the additional materials cost not directly included in the index
but likely to exhibit similar price behavior. For example, in SIC
201, the index includes cattle, hogs and chickens; other commodities
likely to exhibit similar price behavior are calves, beef and pork.
These latter items and others account for an additional 10 to 20
percent of materials cost.
The final two columns in the table represent our judgment
concerning the relative quality of the various price indices. The
judgments take into account index coverage, quality of underlying data
and reasonableness of underlying assusmptions.
Data on Manufacturing Output and Output Prices
Econometric studies of the manufacturing sector have generally
employed either value added or value of production as a measure of the
quantity of manufactured output. Recall from before that value added
is defined to be value of shipments, less the cost of materials, and
adjusted for changes in inventories. Value of production is defined
7-88
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7-89
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as the value of shipments, adjusted for changes in inventories. The
two concepts thus differ from one another by the cost of materials.
As noted previously, we decided that value of production would be the
more correct measure of output, and thus it is the concept employed in
this study. In later sections, the value of output (i.e., the value
of production) is denoted by VQ.
As a measure of the value of production, VQ reflects both price
and quantity effects (this is also true, of course, for value added
measures). That is, two firms may differ in the value of production
either because one firm produced a larger quantity of output, or
because the firm's output sold at a higher price, or both. This
distinction between the price and quantity of output is critically
important in this study. Since the hypothesis being considered is
that pollution increases the costs of production, then the implication
is that the effects of pollution may show up as a change in the market
price of output. This is the phenomenon depicted previously in
Figures 7-2 and 7-4. It is also possible that pollution may affect
costs, but have no effect on market price, which is the case
illustrated in Figure 7-3. Since it is not possible to know in
advance which of these situations is likely to occur in each industry
and county, both possibilities are allowed for in the analysis.
The implication of the above discussion is that in estimating the
cost function for each industry, it is essential that output be
7-90
-------
measured in quantity terms rather than in value terms. Recall that
the cost function is assumed to be of the form
C = C(P, Q, Z) (7.50)
where C is total cost, P is a vector of input prices, Q is the
quantity of output, and Z is a vector of air quality and climate
variables. The hypothesis to be tested is that variations in total
cost which are not explained by variations in P and Q may be explained
by variations in Z. If one were instead to estimate the function
C = C(P, VQ, Z) , (7.51)
where VQ has replaced Q, then the variable VQ would already
incorporate the cost/price effects one is looking for since VQ
incorporates both price and quantity. The coefficient estimates for
the P and Z variables would as a result be biased and inconsistent
(43). That is, one would not be able to detect accurately the effect
of Z on production cost.
In order to determine the quantity of production in each region
(county), given the value of production in each region, what is needed
is an index of regional output prices. Given such an index, PQ, one
can then define a quantity measure, Q, by the relationship
Q = VQ/PQ . (7.52)
7-91
-------
The remainder of this subsection is concerned with how these output
price indices were developed tor each industry. Because the output
price in each region will depend on the equilibrium conditions between
supply and demand for industry output, the requirement is for an index
of regional equilibrium output prices.
The Concept of an Equilibrium Output Price—
The concept of an equilibrium output price can be illustrated as
shown in Figure 7-5. In the figure, P (Q) is the supply curve for a
competitive industry. It represents the minimum price, P, which is
required to enable firms in the industry to produce at each level of
output, Q. In the long-run, this curve will be determined by the
properties of the long-run average cost curves of firms in the
industry. Also shown in the figure is P (Q), the demand curve for
products made by that industry. This curve represents the maximum
price that consumers of those products are willing to pay at each
level of output Q. The intersection of the two curves determines the
equilibrium price, PQ, and the equilibrium quantity, QQ, for that
industry. At the intersection point (QQ/PQ)? tne quantity supplied
and the quantity demanded are equal.
In this simplified definition of an equilibrium output price, it
can be seen that changes in the equilibrium price can result either
from shifts in the supply curve, shifts in the demand curve, or both.
Thus, in comparing equilibrium prices among different regions,
differences in price could be due to both of these factors. For
7-92
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Price
PS(Q)
Quantity
Figure 7-5. Equilibrium output price for a competitive industry.
7-93
-------
example, input prices may be higher in one region than in another so
that the supply curve for the first region would lie above that for
the second region at every level of output. Similarly, the price of
substitutes for the industry's output may be higher in one region so
that the demand curve in that region is higher at every level of
output.
Other factors can also influence regional equilibrium prices
(44). Examples include imperfectly competitive markets, which may
allow price to deviate from the competitive equilibrium; and trade
between regions, which means that supply and demand relationships in a
given region are influenced by consumers and producers outside the
region, and by transportation costs between regions.
Overview of the Estimating Procedure—
The output price indices used in this study were developed using
the following procedure. First, for each 3-digit SIC under
consideration, we identified the component of the Producer Price Index
most closely related to it. Components of the Producer Price Index
are national indices of commodity prices, f.o.b. the manufacturer
(45). Annual values of the Producer Price Index components over the
period 1958 to 1972 were then regressed on four variables covering the
same time period: the national average hourly wage rate in each 3-
digit SIC, a capital services price for the 2-digit SIC containing
each 3-digit SIC, the time-series materials price index for each
industry discussed in the previous section, and a time trend variable.
7-94
-------
These regressions are reported in a later section. In general, the
Producer Price Indices are based on actual transaction prices (46),
net of all discounts and rebates, and hence reflect equilibrium price
conditions.
Given the regression equations, equilibrium prices for each
region in 1972 were predicted using corresponding data for each
region. These data include wage rates, capital service prices, and
the materials price indices described previously. For this study, we
used states as the regions, so that counties within a given state are
all assumed to possess the same equilibrium price. The use of states
as regions was a compromise. On the one hand, we considered counties
to be too small an area since prices in adjacent counties are likely
to be similar. Multistate regions, on the other hand, were considered
to be too large. It would be preferable to define the size of regions
for each industry based on a detailed study of trading patterns in
each industry. However, time did not permit this additional
refinement.
The Producer Price Index components used for each industry are
listed in Table 7-9. The match between industries and indices is
quite good for SICs 201, 202, 344, 354, and for SICs 35 and 36 — the
machinery and equipment industries. For industry SIC 265, the
products of the industry are a subset of the products included in the
corresponding Producer Price Index. For SIC 346, the match is perhaps
7-95
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the least satisfactory of the six industries since the index is a
"miscellaneous" category.
Estimation Results—
The equilibrium output price equations were estimated using a
variety of different functional forms since there is little a_ priori
evidence as to the appropriate form. We have earlier assumed that the
total cost function for the average firm can be approximated as a
translog function, which (under competition) implies a particular form
for the supply price of the firm. However, the equilibrium output
price for a regional market will be jointly determined by the supply
price for all of the firms competing in that market, together with the
demand functions for all consumers in that market. The appropriate
functional form is thus not readily apparent.
The final estimated equilibrium output price equations for each
industry are provided in Table 7-10. Also shown in the table is the
estimated equation for the price of physical assets as discussed in an
earlier section. The basic functional form in each case is a Cobb-
Douglas unit cost function of the form:
log PQ = aQ + aj_ log PL + a2 log PK + a3 log PM
(7.53)
+ b • T
where PQ = value of the Producer Price Index component (1967 =
100.0) from Reference (45).
7-97
-------
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7-98
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PL = national average hourly wage rate for production workers
in the corresponding 3-digit SIC ($/hour) from Reference
(47).
PR = capital services price for the corresponding 2-digit SIC
from Reference (48).
PM = materials price index for the corresponding 3-digit SIC
(1972 = 1.00) as described previously.
T = time.
The various specifications that were estimated included:
• Equation (7.53) as defined previously.
• Equation (7.53) with the assumption of linear
homogeneity imposed (b^ + ^ + 03 = 1).
• Equation (7.53) with the time variable omitted.
• Generalizations of Equation (7.53) incorporating
second-order and interaction terms between the various
prices.
The results shown in the table are the best among the various
specifications examined, in terms of overall plausibility and
goodness-of-fit with the data. In general, the specifications
involving quadratic and interaction terms led to unstable coefficient
estimates due to collinearity among the variables; none of these
specifications were thus used.
Overall the price equations appear quite satisfactory. The
equations fit the data very well as evidenced by the adjusted R
statistics, and the small standard errors of regression. The
coefficients also appear quite plausible and generally reflect the
7-99
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relative magnitude of each input's contribution to total cost in each
industry. Also as expected, the poorest fit is for SIC 346, the
industry for which the associated Producer Price Index component was
less than ideal.
The Durbin-Watson statistics indicate that serial correlation of
the error terms exists in the estimated equations for a few of the
industries. Generally, one can reduce this problem by taking the
serial correlation into account during estimation (49). It is not
practical to do this in this case, however, because most of the
various corrective actions result in an estimated equation with a
lagged dependent variable (last year's output price). Such an
equation would be useless in this study since neither 1972 nor 1971
prices are known on a regional basis. Fortunately, it is the case
that serial correlation affects only the estimated standard errors of
an equation but does not bias the coefficient estimates (50). No
correction for serial correlation was therefore attempted.
Another potential source of bias would be the use of Equation
(7.53) to predict PQ rather than log PQ. Although the constant term
estimated in the log form of the equation will be unbiased, when
exponentiated it will be a downward biased estimate of the constant
term in the equation for PQ. Fortunately, this is not a problem here
because it is actually log PQ that is needed for the translog cost
function. That is, we use log PQ to calculate log Q from:
7-100
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log Q = log(VQ/PQ) = log VQ - log PQ.
Among the six industries, there was one unusual result. In SIC
354 (Metalworking Machinery), the coefficient b^ on wage rate was
consistently negative, counter to expected results. A more plausible
result was obtained using the average annual payroll (in $1000s) per
employee, for both production and non-production workers combined.
The equation for SIC 354 in the table uses this variable. Recall that
in a previous section it was argued that excluding non-production
workers seemed more appropriate because of the problem of multiplant
companies. Interestingly enough, reference to the earlier Table 7-7
indicates that SIC 354 is the one industry with the lowest ratio of
manufacturing establishments per company (1.04). Use of all employees
in this industry thus seemed reasonable.
Interpretation of the Predicted Regional Output Prices—
In terms of the factors likely to influence regional equilibrium
output prices, the estimated equations incorporate some factors but
not others. The equations will reflect variations in input prices on
the supply side, clearly the most important effect. Furthermore, even
though the estimated equations do not include any demand side
variables, the estimated coefficients in the equations will be biased
in the direction of the correlation between the included supply side
7-101
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variables and the omitted demand side variables.* Thus to the extent
that regional supply and demand determinants are correlated, and
regional demand conditions are "similar" to national demand
conditions, the predicted regional equilibrium prices will reflect
some demand side effects, albeit imperfectly.
The most important factor not likely to be well represented in
the predicted prices is the effect of interregional trade. In
general, trade between regions would have the effect of reducing
regional price variations to limits defined by the unit cost of
transporting products between regions. The accuracy of the predicted
regional prices thus depends on whether the predicted variations in
price are larger or smaller than actual transportation costs. That
is, if the predicted price difference between two adjacent states is
less than or equal to the unit transportation cost between the two
states, then the predicted price difference is probably reasonable.
On the other hand, if the predicted difference is larger than the unit
transportation cost, it is likely that the predicted difference will
overstate the actual difference.
* Consider the simple case where the "true" equilibrium price is given
by P = aX + ,3Y where X is a supply side variable and Y is a demand
side variable. Suppose that the equation actually estimated is P =
aX were the demand side variable has been omitted. In this case, it
can be shown (51) that the estimated coefficient a1 will be related
to the true coefficients a and U in the following way:
a1 = a + (3 • Cov(X,Y)/Var(X) ,
where Cov and Var stand for covariance and variance, respectively.
Thus, even though the estimated coefficient is biased, the effect of
the bias should be to improve the usefulness of the equation for
forecasting purposes.
7-102
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Although a complete analysis of the interregional trade effect
was not possible within the time available for this study, the
plausibility of the predicted output prices for one industry (SIC 344)
was reviewed in some detail. Listed in Table 7-11 are the predicted
1972 equilibrium prices for SIC 344 (Fabricated Structural Metal
Products) for the states containing the counties used in estimating
the total cost function for this industry. States are grouped in the
table based on geographic distances.
As can be seen in the table, the price variation between adjacent
states is generally between one and three percent. Massachusetts,
relative to the rest of New England, shows a somewhat larger
TABLE 7-11. PREDICTED EQUILIBRIUM PRICES FOR SIC 344 IN 1972
(fabricated structural metal products)
— _ _.^ _» ._ _ . _. « ^ — —.•^ « __ _ « « — ^ -»_ ___*_
Connecticut
Massachusetts
Rhode Island
New York
New Jersey
Pennsylvania
Maryland
District of Columbia
Ohio
Indiana
Michigan
Illinois
Kentucky
1.345
1.436
1.318
1.284
1.319
1.239
1.262
1.555
1.211
1.208
1.245
1.217
1.189
Minnesota
Wisconsin
Missouri
Alabama
Georgia
Louisiana
Texas
Colorado
Washington
California
1.333
1.241
1.269
1.188
1.169
1.215
1.181
1.363
1.414
1.379
Index base year: 1967 = 1.000 for U.S,
7-103
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variation, and the District of Columbia seems high. But in most other
cases the variations are quite small.
For comparison purposes, average product prices in this industry
were on the order of $500 per ton in 1972 (52). A one to three
percent variation would thus amount to about $5 to $15 per ton. Since
the transportation cost for rail shipments by this industry in 1972
was about $0.03 per ton-mile (53), a $5 to $15 per ton variation in
product prices could be accommodated within shipping distances on the
order of 150 to 500 miles. This is approximately the distance between
states listed in each group in Table 7-11. Hence, at least for this
industry, the predicted equilibrium output price variations appear
quite plausible.
As a final note, it should be pointed out that the equilibrium
output prices will not reflect air quality differences across regions.
This is because air quality is not incorporated into the national time
series regression equations since "national" measures of air quality
variations are not well defined. This omission may not be too serious
if other variables in the equation have picked up some of the pollu-
tion effect in the same way that omitted demand effects may have been
picked up, as explained previously. For example, effects may show up
in the wage rate coefficient to the extent that wage rates and pollu-
tion levels are correlated. The effect, if any, of omitting air
quality would be to impart a downward bias to the pollution
7-104
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coefficients in the cost function for firms, thus making it more
difficult to identify the effect of pollution on production costs.
Air Pollution and Climatological Variables
The data and data sources for air pollution and climate are
discussed in detail in Section 3 and hence will be reviewed only
briefly here.
Air Pollution Variables—
The air pollution variables considered in the manufacturing
sector analysis included both ambient concentrations of sulfur dioxide
(SCU) and ambient concentrations of total suspended particulates
(TSP). The current secondary national ambient air quality standards
(SNAAQS) for both of these pollutants are stated in terms of maximum
allowable concentrations, not to be exceeded more than once per year.
For shorthand, we refer to this measure of air pollution as the "2nd
High".
For both SCU and TSP, we have used measurements based on a 24-
hour averaging time. This is the averaging time used in the current
TSP standard. The current SCU standard is based on a 3-hour averaging
time, apparently to prevent vegetation damage (see Section 3 of this
report). Since longer averaging times are believed to be more
appropriate for soiling and materials damage, we have used a 24-hour
7-105
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averaging time for SC^ rather than the 3-hour measure. Thus, a 24-
hour averaging time is used for both SC^ and TSP in this study.
In a given county there is often more than one monitoring station
for air pollution. In these counties we have thus defined two
measures of air pollution for each pollutant:
SOXA2HI — the average of the 2nd High readings across
all sites, for SCu •
SOXX2HI — the maximum of the 2nd High readings across
all sites, for S02.
TSPA2HI — the average of the 2nd High readings across
all sites, for TSP.
TSPX2HI — the maximum of the 2nd High readings across
all sites, for TSP.
The cost functions reported in a later section consider all four
possible combinations of these measures for the two pollutants.
Climate Variables—
Two climate variables are considered in the study. These
include:
• TEMP — the average annual temperature in the county.
• RAIN — the average annual rainfall in the county.
While it would have been desirable to consider additional climate
variables such as humidity, and other measures of temperature and
7-106
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rairjfall besides the annual mean, the limited sample sizes available
for each industry required limiting the number of climate variables.
Highest priority was given to temperature because of the _a priori
expectation that temperature would influence regional production costs
due to variations in heating, air-conditioning, and refrigeration
loads. In choosing between rainfall and humidity, priority was given
to the rainfall variable based on preliminary results from the
electric utility sector analysis (see Section 8). That analysis found
that rainfall was far more significant than humidity as an explanatory
variable. Hopefully, at some later date it will be possible to
consider additional climate variables. In particular, it would be
useful to give some attention to humidity because of the finding in
various dose-response studies that humidity accelerates atmospheric
corrosion of metals. Other measures of temperature, such as heating
and cooling degree days, would also be of interest as an alternative
to the annual mean.
Missing Pollutant Data—
In a number of counties for which price and cost data were
available, data on ambient air quality were not available. There are
a variety of ways to deal with the problem of missing data. The
easiest is simply to eliminate the problem counties from the data set.
However, this results in a loss of the information available about the
economic variables. More importantly for this study, dropping
observations further reduces the already small sample sizes.
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One commonly used approach for dealing with missing data is to
replace the missing values with the mean value across the observations
for which the data are complete. For example, consider the two
variable equation, Y = a + (3X, estimated using ordinary least squares
(OLS). In this case, it is easy to show that the estimator of p> will
be unbiased if all observations on Y are complete and missing
observations on X are replaced by the mean of the known values of X
(54).
In more general situations, the effect of using the sample means
to fill in missing data is not as well known. For example, the
extension of this approach to iterative Zellner estimation techniques,
as employed in this study, does not appear to have been investigated.
Consequently, in industries where sufficient data were available, we
estimated the equations both with and without the missing
observations. Since the results based on the complete observations
are probably more valid, they are given greater emphasis in later
sections.
The extent of the missing data problem is summarized in Table
7-12. As can be seen, there is more of a problem with SO2 than with
TSP. The table also makes clear that dropping the observations with
missing air pollution data is particularly painful.*
* Note that use of mean values to fill in missing capital stock data
would not be of any value because VK appears only on the left-hand
side of the equation system, as part of total cost, C.
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TABLE 7-12. EXTENT OF MISSING AIR QUALITY DATA
Missing observations
SIC
code
201
202
265
344
346
354
Original*
sample size
60
64
78
124
54
58
Final**
sample size
31
44
25
57
22
28
in final
so2
17
17
6
21
5
6
sample
TSP
10
10
1
3
0
1
* Number of counties with complete economic data for 1972.
** Sample available after deleting counties with inadequate capital
expenditure data for years prior to 1972.
EMPIRICAL RESULTS
Equations to be Estimated
The data described in the previous section can be used to
estimate the coefficients of the total cost function given previously
as Equation (7.9). It is possible to estimate the cost function
directly, using ordinary least squares (OLS) regression techniques.
However, this approach would not make full use of the information
available in the data. In particular, it would not take into account
the known relationship between the total cost of production and the
7-109
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share of total cost accounted for by each input (labor, capital,
materials). Recall that if the total cost function is given by
Equation (7.9), then the cost share for each input is given by
Equation (7.13). Considerable gains in efficiency (precision of the
coefficient estimates) can be obtained when the total cost function
and the cost share equations for each input are estimated
simultaneously as a system. The gain in efficiency occurs because the
inclusion of the cost share equations has the effect of adding
additional degrees of freedom to the problem, without adding any
additional unrestricted coefficients.* All of the coefficients in the
cost share equations already appear in the total cost function.
Following Christensen and Greene (55), the statistical properties
of the cost function are specified by the addition of a random error
term to the equation, and similarly to each cost share equation. The
conventional interpretation is that these represent random errors in
cost-minimizing behavior. Since the cost share equations are obtained
by differentiation of the total cost function, the error term for the
latter does not appear in the cost share equations. The error terms
in the system are assumed to be jointly normally distributed with non-
zero correlations between equations but zero correlation across
different observations (counties). As noted above, these assumptions
represent conventional practice. The assumptions imply that one of
* In particular, if there are N data points and M cost share
equations, then the degrees of freedom available would become
(N)(1+M) rather than N.
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cost share equations must be deleted from, the system to prevent
singularity of the covariance matrix of the system.*
In general, the coefficient estimates will depend on which cost
share equation is deleted. It has been shown, however, that use of
maximum likelihood estimation will result in coefficient estimates
which are invariant to the cost share equation deleted (56). It has
also been shown that use of iterative Zellner estimation is
asymptotically equivalent to maximum likelihood estimation (57). We
have thus used iterative Zellner estimation techniques and, without
loss of generality, the capital cost share equation is deleted from
the system.**
Recall from an earlier section that the general translog cost
function with three input prices and four fixed inputs incorporates 54
unknown coefficients. Since this exceeds the number of observations
available for all but one of the industries under study, we imposed
certain restrictions on the coefficients to reduce their number.
Restrictions which were imposed on all of the industries included two
denoted previously as assumptions Al and A2. Assumption Al imposes
* The covariance matrix becomes singular because the error terms for
the cost share equations must sum to zero for each firm.
** Although iterative Zellner estimation is asymptotically equivalent
to maximum likelihood estimation, in finite sample sizes there may
be numerical differences in the coefficient estimates. Since
iterative Zellner estimation is computationally expensive, we have
not attempted re-estimation of the equation systems to check the
sensitivity of our results to the deletion of alternative cost
share equations.
7-111
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symmetry on the second derivatives of the total cost function.
Assumption A2 imposes homogeneity of degree 1 (PLH) on the input
prices for the three variable inputs (labor, capital and materials).*
Both of these assumptions are quite commonly made and reduce the
number of unknown coefficients from 54 to 36.
Four additional restrictions imposed on all industries were
denoted previously as Bl, B2, B3, and a modified version of B4. Bl
restricts the second derivatives of (log) total cost with respect to
(log) S02 and TSP to be zero. This implies that the elasticity of
total cost with respect to S02 and TSP is independent of the ambient
concentration, although it may of course be influenced by other
factors. Assumption B2 assumes that input cost shares are unaffected
by variations in rainfall, even though total cost may be affected.
Assumption B3 assumes that total cost is unaffected by interactions
between temperature and rainfall, even though they may influence cost
individually or through interactions with other variables. In the
modified version of B4, we assume that total cost is unaffected by
interactions between temperature and the size of manufacturing firms,
or between rainfall and firm size. We continue to allow for the
* Recall that in estimating the output price equations, PLH was not
imposed. This was because the output price for an industry will
depend on several prices in addition to those included in the output
price equations. Two examples are the price of purchased services
and the price of non-production worker labor. Imposition of PLH on
the total cost function is reasonable, however, because we have
defined "total" cost to be the sum of production worker labor cost,
the cost of physical capital services, and the cost of materials.
All three of these items are represented by prices in the cost
function.
7-112
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possibility that the effect of SC>2 and TSP may vary with firm size.
All of these assumptions also appear quite reasonable.
The additional assumptions Bl, B2, B3 and modified B4 reduce the
number of unknown coefficients from 36 to 29. All of these
constraints were imposed a_ priori on all of the industries under
study.
One additional adjustment was also made to the equations before
estimation. Recall that the total cost function is based on the
assumption of cost-minimizing behavior on the part of individual
firms. It is therefore more appropriately estimated using data on
individual firms. However, the data available from the Census of
Manufacturing are county totals for all of the firms in each county.
To reduce the potential problems introduced by the aggregation of data
across firms, we divided total cost, C, and total quantity of output,
Q, in each county by the number of establishments, N, in the county.
This does not completely solve the problem of aggregation but may
reduce its importance. Strictly speaking, then, the cost function is
hypothesized to represent the production structure for the "average"
establishment in a county.
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Estimation Results; Format
Introduction—
In an initial round of estimation for each industry, we employed
models incorporating the coefficient constraints outlined above. We
also used data sets with missing air quality observations replaced by
sample means. With a few exceptions, the results seemed plausible
when the properties of the estimated equations were evaluated at the
sample means. In particular, as implied by the partial derivatives of
the total cost function, the effects of changes in input prices,
output, and air quality were about as expected. Further inspection,
however, revealed the following disturbing properties. As one moved
away from the sample means, i.e., evaluated the partial derivatives at
each observation, the values of the partial derivatives for the non-
economic variables often diverged dramatically from their mean values.
In many cases, the derivatives of the air quality variables actually
changed signs. At some observations, it would happen that large
positive derivatives for one pollution variable were being offset by
large negative ones for the other.
Considerable experimentation led us to conclude that with the
large number of coefficients, and the high degree of collinearity
among the variables, the overall equation systems were experiencing
numerical instability. The problems in particular seemed to be
associated with the quadratic and interaction terms involving the air
quality and climate variables, namely the d. terms in Equation (7.9).
7-114
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The cL-; terms apparently cause problems for two reasons. First, the
simple correlations between these variables are often quite high
(especially SC>2 and RAIN). Thus, collinearity among cross-product
terms involving these variables is extremely high. Second, none of
the d. • coefficients appear in the cost share equations — only in the
total cost function. This is in contrast to the interaction terms
among the economic variables which in all but two instances always
appear in at least two equations. Thus, the additional structure
imposed on the economic coefficients via the cost share equations,
which mitigates collinearity among those variables, is not similarly
imposed on the dj • variables.
Following the initial round of estimation, we thus experimented
with simpler models in which additional constraints were imposed on
the air quality and climate coefficients. In particular, coefficients
other than the d- and the c^ were assumed to be zero.* The d.
coefficients are the first-order terms involving air quality and
climate. The c^_- are interaction terms between input prices and the
air quality and climate variables. These coefficients thus allow for
overall effects on cost as well as for differential effects on the
individual inputs. Specifically excluded were the d-^ terms and the
eQ^ terms, neither of which appear except in the total cost function.
We generally found that in the reduced models, there was much less of
* In industries with sufficient observations, it is possible to test
this assumption directly. See, for example, the results for SIC
201, which are consistent with this assumption.
7-115
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a tendency for the partial derivatives of total cost to diverge wildly
at individual observations.
Reported Results—
Because the volume of computer output from all of the above was
quite considerable, the following sections provide only a condensed
summary. In particular, for each industry, the following results are
generally reported:
• Estimation results for the complete model (d^ and CQ^
terms included) for one combination of the four
alternative measures of air quality (SOXX2HI, SOXA2HI,
etc.).
• Estimation results for the reduced model (d. ^ and eni
i I w J.
terms excluded) for the same measures of air quality.
• Estimation results for the reduced model when
restricted to observations with complete air quality
data.
The information provided for each industry is contained in a
summary table. The table allows easy comparison of the different
models in terms of various economic parameters calculated from the
estimated coefficients. The parameters include:
• Price elasticities of demand for the variable inputs
• Elasticities of substitution between the variable
inputs (^i-i).
• The degree of scale economies (SCE).
• The ratio of predicted labor demand to actual labor
demand (L'/L).
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• The effect on total cost from a unit increment in each
of the climate and air quality variables (MTCSOX,
etc.).
• The logarithm of the determinant of the inverse of the
residual covariance matrix (LDET).
The first three groups of parameters above are calculated using
Equations (7.14)^0 (7.18) presented earlier, and are evaluated at the
sample means. These three sets of parameters provide one plausibility
check on the estimated equations because somewhat comparable estimates
for these parameters exist in the open literature. The exact degree
to which we should expect comparability is not clear. As noted
previously, to our knowledge, no econometric study of U.S.
manufacturing has previously been conducted using county level data,
using 3-digit SICs on a cross-sectional basis, or which incorporates
materials inputs on a cross-sectional basis. Nonetheless, we should
expect some degree of comparability with the existing, more
aggregated, studies. We thus provide a comparison of our results with
those from the one existing study which is most closely comparable
(58). The latter was a study of 2-digit SIC manufacturing, estimated
with aggregate U.S. time series data, and incorporating four inputs
(labor, capital, materials and energy).
The fourth parameter above (L'/D is a similar type of
plausibility check. It is calculated as follows. From Equation
(7.12), the derived demand for labor is given by:
7-117
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L = 6C/3PL
= (3 log C/3 log PL)(C/PL)
= (C/PL)ja1 + I a-^ log Pj + bQ1 log Q
\
+ £ cXj log Z_j
When this equation is evaluated using the estimated coefficients, it
provides a prediction of the demand for labor, denoted L1. Since the
quantity of labor demanded is implied by the model, but is not one of
the directly estimated equations (labor's cost share is directly
estimated), then a comparison of L' with actual labor demand L
provides an additional test of the model's plausibility. The ratio
L'/L in the summary tables is calculated from
L'/L = (3 log C/3 log PL)(C/PL)/L
= (3 log C/3 log PL)(C/PLD
(7.54)
= (3 log C/3 log PL)/ML
+ I a-^ log P. -f bQ1 log Q -t- I c^ log Z^|/ML
j j 7
where ML is the cost share for labor at the sample mean and the other
variables are also evaluated at the sample mean. Note that a more
rigorous test of the model would be to calculate this ratio at each
observation in the sample, rather than just at the sample mean.
7-118
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However, because of the many additional computations involved, this
additional effort was not undertaken.
The fifth item in the summary tables is the estimated effect on
total cost from a unit increment in each of the climate and pollution
variables. For example, the marginal change in total cost from a one
Aig/m change in the ambient concentration of SOo is calculated from
MTCSOX = 3C/3 S02
= (3 log C/3 log S02)(C/S02) (7.55)
= (C/S02)(E ci;L log Pi + dx + I dj, log Z. + eQ1 log Q)
\i j /
where the expression in the second parentheses is simply Equation
(7.19), the elasticity of total cost with respect to a change in SO .
X
Equation (7.55) is evaluated using the estimated coefficients, the
exogenous variables set to the sample means, and actual total cost at
the sample mean. The values shown in the table are in thousands of
dollars per unit change. The units for SCU and TSP are fj-g/m. ,
temperature is in degrees Celsius, and rainfall is in millimeters per
year.
Significance Tests—
The sixth and final item in the summary tables (LDET) is used in
testing various hypotheses about the statistical significance of the
estimated coefficients. Roughly speaking, the larger the value of
7-119
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LDET, the smaller the unexplained variation in the estimated equation
system. Tests of hypotheses about the statistical significance of
coefficients can be made by comparing the values of LDET for models
with and without the particular coefficients. Specifically, suppose
there is a subset of M coefficients to be tested for significance;
that is, can the restriction that the M coefficients are equal to zero
be imposed? Since the iterative Zellner procedure provides maximum
likelihood estimates, the appropriate test is based on the likelihood
ratio (59). The likelihood ratio, X, is given by
(det SR/det
where det SR and det Sy are the determinants of the residual
covariance matrix in the restricted and unrestricted cases. N is the
number of observations (in this case, the number of counties). The
quantity -2 log X follows a chi-squared distribution asymptotically.
The test statistic is thus given by
X2 = N(LDET0 - LDETR) , (7.56)
which makes use of the fact that LDET = log det S = -log det S.
A second summary table provided for each industry contains tests
of coefficients based on Equation (7.56). In developing test
statistics for the pollutant variables, the value of N used in
Equation (7.56) will not generally be as large as the number of
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counties in the sample. Recall that for some counties, data on one or
both of the pollutants was unavailable and the sample means were used
as a substitute. The correct value of N in Equation (7.56) in these
cases is the number of counties for which data were actually
available.
The missing observations also mean that the residual covariance
matrix, S, produced by the estimation routine is somewhat misleading.
The matrix S is of the form
S =
where N is the number of observations and W is the matrix of residuals
from the estimated equation system. In using S to make tests
concerning variables with missing observations, it would appear that
an adjustment to S is also required. Fortunately, this is not the
case. This occurs because in calculating the expression in
parentheses in Equation (7.56), the effect of N on S cancels out.
In particular, note that
LDET = log det S-1
= log det(NW~1)
= log(Nk det W'1)
= log Nk -I- log det W'1 ,
7-121
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where k is the order of the matrix W. Applying this result yields
LDET
R
= (log Nk + log det W^1) - (log Nk + log det
= log det W^1 - log det
Thus, since the value of N does not affect the calculation of this
part of Equation (7,56), no additional adjustments are necessary to
account for the missing observations.
Estimation Results; SIC 201
SIC 201, the meat products industry, includes meatpacking plants,
poultry dressing plants, and establishments which manufacture prepared
meat and poultry products using carcasses purchased from other
establishments. For comparative purposes, it will be useful later to
have certain summary data for this industry. These data are provided
in Table 7-13. As can be seen in the table, the establishments
included in the sample used for estimation appear on average
representative of the cost characteristics of the industry as a whole.
Establishments in this industry are characterized by very high
materials cost as a proportion of total cost. Labor and capital
services account for a small fraction of total cost. Note also that
even though the sample includes only one percent of all U.S. counties,
these counties account for 18 percent of the industry's output.
7-122
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TABLE 7-13. SUMMARY DATA FOR SIC 201 (MEAT PRODUCTS)*
1
2
3
4
5
6
7
8
Number of establishments
Value of output per establishment**
Value added per establishment
Avg. cost of production worker
labor per establishment
Avg. cost of capital services per
establishment
Avg. cost of materials per
establishment
Avg. total cost per establishment"1"
Number of counties
Counties in
the sample
757
7.66
1.24
0.55
0.16
6.42
7.14
31
All U
count
4,437
7
1
0
NA
6
NA
3,141
.S.
ies
.12
.12
.43
.00
* All data are for 1972 in millions of 1972 dollars.
** Defined to be the sum of items 3 and 6.
+ Defined to be the sum of items 4, 5, and 6.
NA = Not available.
7-123
-------
Table 7-14 provides summary oharacteristi.es for several of the
alternative model specifications estimated. Model 1 includes only the
10 basic economic variables.* Model 2 is the complete model with 29
unknown coefficients. The particular version shown in the table
employs the maximum 2nd High measure for both pollutants (X2HI).
Versions containing the average 2nd High (A2HI) were also estimated
but resulted in lower likelihood ratios. Model 3 is the reduced model
containing 20 coefficients (all dj_ • and e^. eliminated). For
comparison purposes, it employs the same pollution measures. Models 4
and 5 are smaller versions of the reduced model estimated over the
observations with complete air quality data. Because there are fewer
complete observations for SC^, Model 4 includes only TSP. In Model 5,
only SC>2 is included because the available sample size does not allow
both pollutants to be considered.
Economic Properties of the Estimated Models—
Looking first at the price elasticities, it can be seen that the
own price elasticities are all negative in all specifications, as
would be expected from economic theory. Across the different models,
the own price elasticity for materials (EMM) is rather stable, except
in the reduced data set of Model 5. A similar pattern holds for the
own elasticity for labor (E). The magnitude of E in contrast
* If all air quality and meteorological variables are eliminated from
Equation (7.9), 18 unknown coefficients would remain (the a., a^-f
bg, bgQ, bQ^ terms). The assumptions of symmetry (Al) and linear
homogeneity in the input prices (A2) reduce the number from 18 to
10.
7-124
-------
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7-125
-------
appears less stable. The cross-price elasticities between labor and
materials, and between capital and materials are positive, which is
evidence of substitutability between these inputs. The negative
cross-elasticities between labor and capital are evidence of
comp1erne ntar i ty.
The elasticities of substitution follow the same pattern as do
the price elasticities. Own elasticities for labor and materials are
both quite stable across models (except Model 5) although labor's
seems large. Elasticities involving capital are less stable and quite
large in magnitude. The magnitude and instability of the capital
elasticities is in part related to the very small share of total cost
accounted for by capital. On average, the cost share for capital is
about two percent. In view of the form of Equation (7.15) for
calculating ^^K' one can see that ^KK w^^^ 'De very sensitive to even
small changes in the estimated coefficient &vv*
The parameter SCE in all of the models suggests the absence of
economies of scale in this industry. The ratio L'/L suggests that the
models' implied prediction of the derived demand for labor is very
close to the actual demand at the sample mean.
Although there are no directly comparable studies available for
this industry, some results are available for SIC 20, the 2-digit
industry containing SIC 201. SIC 201 comprises about 14 percent of
SIC 20 in terms of value added. The available results are from a
7-126
-------
study using time-series data for the U.S. over the period 1947 to 1971
(58). The four inputs included in the study were labor, capital,'
materials and energy, and the underlying model incorporates dynamic
adjustment behavior unlike the present study.
The (long-run) price elasticities reported in the above study are
shown in Table 7-15. Also shown in the table are the implied
elasticities of substitution. The latter were not reported but can be
calculated using our Equations (7.16) and (7.17), the reported price
elasticities and the reported input cost shares. We have used cost
shares for the year 1958 in the calculation since this is
approximately the midpoint in the sample.
In comparing Tables 7-14 and 7-15, several general patterns
emerge. Our estimated price elasticities involving labor and capital
are much higher; those involving materials are quite close. The rank
ordering among the elasticities based on relative magnitudes is
similar and the sign pattern is identical. In particular, note that
both studies find evidence of complementarity between labor and
capital. Generally, these same patterns also hold true for the
elasticities of substitution. Note also that the own elasticity of
substitution for energy in Table 7-15 exhibits the same problem as OKK
in Table 7-14. Namely, because of the very small cost share, the
implied own elasticity of substitution is extremely large.
7-127
-------
TABLE 7-15. COMPARATIVE ESTIMATES OF PRICE ELASTICITIES AND
ELASTICITIES OF SUBSTITUTION FOR SIC 20
Price elasticities
ELL -0.16
EKL -0.07
EML °'05
EEL ° • 45
EEK 0.14
EEM -0.01
-------
Implied Effects of Air Quality and Climate—
The bottom rows of Table 7-14 indicate the implied effect on
total cost, due to a unit change in the air quality and climate
variables. The implied effect of a one /ug/m increase in ambient SC>2
ranges from $120 to $880, depending on the model and the data set.
Referring back to Table 7-13, one can see that a change of $700 would
be about 0.01 percent of average total cost. The implied effect of a
similar increase in TSP concentrations ranges from $-2,430 to $+680,
again depending on the model and data. Although the apparent effect
of TSP in one instance is negative, the coefficients for TSP are not
statistically significant.
The table suggests that the largest cost effects are associated
with changes in temperature. The implied effect of a 1°C increase in
annual average temperature ranges from $-17,000 to $+55,000. The mean
temperature in the sample, however, is 12.7°C so that a 1°C change is
close to an eight percent deviation from the mean. The implied effect
of rainfall is quite small and also varies across the models.
In general, the cost effects implied by Models 3, 4 and 5 are
quite similar to one another, even though each one is based on a
different data set. In contrast, the estimates from Model 2 (the
complete model with 29 coefficients) differ substantially. As
indicated previously, we found this divergent behavior to be a problem
in general with the larger models which incorporated all of the dj_ •
variables. As a further indication of the problem, in Model 2 the
7-129
-------
elasticity of total cost with respect to S02 is 0.049, at the sample
mean. The elasticity is the percentage increase in cost due to a
percentage increase in SC^ concentrations. When evaluated at each
individual observation, however, the elasticity ranged from -0.075 to
+0.231. With TSP, the range was from -0.380 to +0.125 around the
sample mean of -0.09. At the six observations where TSP turned
positive, S02 turned negative.
If these instabilities had arisen in only one of the industries,
we could probably have attributed it to the data. However, when it
arose in all of the industries, despite the differences in data, we
began to suspect the model. It was at that point that we decided to
drop the d^j variables and proceed instead with the reduced model.
Significance Tests—
In comparing the performance of Models 1 through 5, the previous
sections suggest that there are only minor differences among the
models in terms of implied economic characteristics such as the price
elasticities of demand. There are differences between the models in
terms of the implied effect of air quality and climate. In
particular, Model 2 differs considerably from Models 3-5. As
indicated previously, we believe this results in large part from
numerical problems with Model 2. Nonetheless, it is possible to test
formally the desirability of dropping the additional nine variables in
moving from Model 2 to Model 3. The chi-squared statistic is
7-130
-------
(13)(24.0004 - 23.1506) = 11.047 with nine degrees of freedom.* The
associated Level of significance is 0.27, indicating that the null
hypothesis (that the nine coefficients are zero) cannot be rejected.**
Further discussion will thus be based on Model 3.
In the case of Model 3, somewhat more discriminating tests of
individual groups of coefficients are summarized in Table 7-16. The
model numbers in the table correspond to versions of Model 3 with
different sets of coefficients restricted to be zero. The first row
in the body of the table contains the chi-squared statistics for a
series of tests on Model 3. Under each statistic in parentheses are
the number of observations (adjusted downward to account for missing
air quality data) and the degrees of freedom available for each test.
The significance levels for all of the tests fail to reject the null
hypothesis.
Given that neither SC^f TSP nor RAIN are significant (although
TEMP is), it is efficient to re-estimate the model and re-perform each
test. The second row in the table is a test of the null hypothesis
that SC>2 is not significant, given a model with TSP and RAIN excluded.
The significance level in this case is 0.16. The third row repeats
the same procedure for TSP and obtains a significance level of 0.57.
* Only 13 complete observations are in the sample.
** In hypothesis testing, values of 0.10, 0.05, or 0.01 are typically
used in deciding whether a null hypothesis should be rejected,
i.e., whether a coefficient is "significant". In this analysis,
0.10 is used. The terminology "significant at the 0.10 level" and
"significant at the 10 percent level" are used interchangeably.
7-131
-------
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indicative that the association between TEMP and costs of production
is highly significant.
Significance tests based on Models 4 and 5 were also conducted
for TSP and SC^. In the case of Model 4, TSP was not statistically
significant. In Model 5, the level of significance for SC>2 was 0.12.
Similar tests based on these models and employing A2HI measures of
pollution were also not significant.
Conclusions for SIC 201—
Within the limits of the models and data available for this
industry, we find no evidence that higher levels of ambient TSP
concentrations are associated with higher costs of production. One
possible explanation for this finding is that in a food processing
industry, cleaning activities are undertaken routinely and
systematically. The effect of additional soiling due to TSP may thus
have little or no noticeable affect on cleaning frequency or
difficulty. Another possible explanation is that the available data
simply do not allow such effects to be detected. The sample size
available for this industry is small, and like all of the industries,
the cost categories are quite aggregate.
In the case of SC^, there is somewhat more evidence of an effect.
A significance level of 0.16 was identified with Model 3D. For Model
5 it was 0.12. And tests based on Model 2 found a significance level
7-133
-------
of 0.09. Although the latter meets our criteria of "significance", we
do not consider Model 2 reliable for reasons stated earlier. It is
possible that with additional data on ambient SO^ concentrations, a
more conclusive result could be established for this industry. As it
is, with only 14 observations on S02r and 12 degrees of freedom taken
up by economic and climate variables, the levels of significance
obtained are probably better than could be expected.
Estimation Results: SIC 202
SIC 202 is the dairy products industry. It includes
establishments which manufacture creamery butter, natural and
processed cheese, condensed and evaporated milk, ice cream, and other
frozen desserts. It also includes establishments which process fluid
milk and cream for wholesale or retail distribution. Diary farms,
including those with milk processing and bottling facilities, are
classified in SIC 024 and are thus not considered in this analysis.
Relevant summary data for this industry are provided in Table
7-17. As in the case of SIC 201, the cost of materials is the
dominant component of total production cost, followed by labor and
capital services. Establishments included in the sample are on
average slightly larger than is the case for the industry as a whole.
The 44 counties in the sample account for about 26 percent of total
output in the industry.
7-134
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TABLE 7-17. SUMMARY DATA FOR SIC 202 (DAIRY PRODUCTS)*
Counties in All U.S.
the sample counties
1.
2.
3.
4.
5.
6.
7.
8.
Number of establishments
Value of output per establishment**
Value added per establishment
Avg. cost of production worker
labor per establishment
Avg. cost of capital services per
establishment
Avg. cost of materials per
establishment
Avg. total cost per establishment"1"
Number of counties
896
4.73
1.21
0.23
0.14
3.52
3.90
44
4,590
3
0
0
NA
2
NA
3,141
.56
.88
.16
.68
* All data are for 1972 in millions of 1972 dollars.
** Defined to be the sum of items 3 and 6.
+ Defined to be the sum of items 4, 5, and 6.
NA = Not available.
7-135
-------
Summary characteristics for several of the model specifications
estimated for this industry are provided in Table 7-18. Model 1 is
the basic model with the 10 economic variables. Model 2 is the
complete model with 29 variables, using the maximum 2nd High measure
for both TSP and S02. Both Models 1 and 2 were estimated over the
full sample containing missing air quality data. Model 3 is the
reduced model with the djj and eQ^ coefficients deleted. It also uses
the maximum 2nd High measures and was estimated over the data set with
complete air quality data. Model 4 is the same as Model 3 except that
all TSP variables have been deleted.
Economic Properties of the Estimated Models—
A comparison of Table 7-18 with the corresponding Table 7-14 for
SIC 201 is instructive. It indicates that the estimated price
elasticities for SIC 202 are generally smaller, as are the estimated
elasticities of substitution. In that respect, they compare more
favorably with the time series estimates for SIC 20 provided earlier
in Table 7-15. We also observe that for SIC 202, the own price
elasticities are all negative, as would be expected. The cross-price
elasticities are all positive. Note that the latter is in contrast to
the earlier tables which found evidence of labor-capital
complementarity. It thus points out the difficulties in comparing
results at the 2-digit SIC and 3-digit SIC levels. The aggregation in
the former tends to mask apparent differences in the latter.
7-136
-------
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7-137
-------
The evidence for scale economies in this industry is mixed. Two
of the models find slight evidence of scale economies, while the other
two do not. All four models predict the derived demand for labor very
accurately at the sample mean.
In terms of the economic properties, the models for SIC 202 all
appear quite plausible.
Implied Effects of Air Pollution and Climate—
In comparing the three models which contain air quality and
climate variables, the similarity of the implied effect of S02 is
quite striking. Estimates of the effect on total cost, from a one
Mg/m3 increase in ambient SCU/ range from $560 to $710. This is
within the range observed for SIC 201, although average total costs in
that industry were higher. A change of $600 would represent an
increase of about 0.015 percent of average total cost for an
establishment in SIC 202.
For TSP, the implied effects on cost are disconcerting. It seems
unrealistic to expect that increases in ambient TSP would reduce
production costs. Yet this is what Models 2 and 3 imply, and the
coefficients for TSP are statistically significant. The
implausibility of the results for TSP led us to estimate Model 4,
which is the same as Model 3 except that the TSP variables have been
omitted.
7-138
-------
The implied effect of rain and temperature on this industry is
that costs tend to be lower in areas with warmer temperatures and more
rainfall. The magnitudes of the implied effect seem large, but of the
same order as found in SIC 201, with opposite signs. One explanation
could be differences in the relative requirements for space heating of
buildings and refrigeration of products.
Significance Tests—
For purposes of statistical testing, Model 4 will be used. Tests
based on this model are summarized in Table 7-19, which follows the
same format as the corresponding table for SIC 201. Recognize,
however, that these tests are based on the assumption that it is valid
to delete TSP from Model 3 in view of the implausibility of the sign
for TSP; i.e., the negative sign is probably a spurious correlation.
TABLE 7-19. SIGNIFICANCE TESTS FOR SIC 202*
Model number
4A
LDET =
Model 4
21.7526
w/o
for
4B
w/o
SO-,
21.7415
21.6269
Model 4:
Model 4A:
0.300
(27,2)
3.394
(27,3)
3.094
(27,1)
* Based on the sample containing complete air quality data (N = 27)
7-139
-------
The first row in the body of Table 7-19 consists of tests against
Model 4. The first entry in the row indicates that the GJ_- terras for
SOo are not significant. Hence, it is not too surprising that when
the dj_ and Cj. terms together are dropped from Model 4, the null
hypothesis cannot be rejected. This result is confirmed by the second
entry in the row. However, in view of the lack of significance for
the c^ terms, it is efficient to re-estimate the model without them
and then re-perform the test. The re-estimated model is shown as
Model 4A. The second row indicates that when SO2 is dropped out of
Model 4A, the null hypothesis can be rejected. The level of
significance for SC>2 in this case is 0.079.
Conclusions for SIC 202—
The estimation results for SIC 202 are similar in many respects
to those for SIC 201. The implied economic characteristics seems
reasonable, and compare favorably with an independent study using
different data and models. Some of the calculated parameters
involving capital are considerably larger than might be expected and
are due no doubt in part to the difficulties in accurately
constructing capital services and service price data.
In neither SIC 201 nor 202 do the data suggest a positive
relationship between TSP concentrations and production cost. In fact,
a negative relationship was identified in SIC 202 but disregarded as
implausible. We hypothesized that as food processing industries,
cleaning activities are done so routinely and systematically, for
7-140
-------
other reasons, that the added soiling from TSP is probably not
noticed.
In the case of SC>2f there is evidence of a positive association
with total costs of production. The implied effects are very small —
on the order of a few hundred dollars per A^g/m3 of SC- We estimate
that a one Mg/m reduction in ambient SC>2 would reduce total costs of
production by about 0.01 to 0.015 percent at the sample mean. In the
case of SIC 201, the effect of SC^ is not statistically significant,
but comes quite close (0.12). For SIC 202, the effect was found to be
significant at about the 0.08 level.
Estimation Results; SIC 265
SIC 265 includes establishments using purchased paperboard to
manufacture paperboard boxes, corrugated and solid-fiber boxes,
sanitary food containers, and fiber cans, tubes and drums.
Establishments which manufacture these products and which also produce
the paperboard are included in SIC 263 and are thus not considered in
this analysis.
Relevant summary data for this industry are provided in Table
7-20. In comparison with the food industries discussed previously,
labor and capital costs comprise a larger proportion of total cost in
this industry. As can also be seen, establishments included in the
sample are representative, on average, of the cost characteristics of
7-141
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TABLE 7-20. SUMMARY DATA FOR SIC 265 (PAPERBOARD CONTAINERS
AND BOXES)
1.
2.
3.
4.
5.
6.
7.
8.
Number of establishments
Value of output per establishment**
Value added per establishment
Avg. cost of production worker
labor per establishment
Avg. cost of capital services per
establishment
Avg. cost of materials per
establishment
Avg. total cost per establishment"1"
Number of counties
Counties in
the sample
744
3.00
1.42
0.51
0.12
1.58
2.21
25
All U.
count i
2,739
2.
1.
0.
NA
1.
NA
3,141
S.
es
97
31
48
66
* All data are for 1972 in millions of 1972 dollars.
** Defined to be the sum of items 3 and 6.
+ Defined to be the sum of items 4, 5, and 6.
NA = Not available.
7-142
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the industry as a whole. The sample includes counties producing more
than 27 percent of the industry's total output, even though only 25
counties are included in the sample.
Summary characteristics for several of the model specifications
estimated for this industry are provided in Table 7-21. As before,
Model 1 includes only the 10 economic variables. The other model
definitions for this industry differ from the earlier industries
because the available sample size did not allow estimation of the
"complete" model with 29 coefficients. The "complete" model (Model 2)
in this case excludes coefficients d-^/ d^, ^23 an(^ ^24* Versions
excluding other combinations of the dj_j terms gave generally inferior
results. The pollutant measures in this model are the average 2nd
High for SC^ and the maximum 2nd High for TSP, selected on the basis
of likelihood ratios.
The "reduced" model for this industry also differs from the
earlier industries. Instead of 20 coefficients, the reduced model
contains only 18 to accommodate the size of the sample containing
complete air quality data. Experimentation with dropping the c-. for
S02 versus the c.^ for TSP, to reduce the model to 18 coefficients,
led us to conclude that the latter was more reasonable. Model 3 is
thus the "reduced" model as defined in the other industries, less the
c terms for TSP.
7-143
-------
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7-144
-------
Economic Properties of the Estimated Models—
Of the industries reviewed so far, the models for SIC 265 appear
the most reasonable. As indicated in Table 7-21, all of the economic
parameters, with the exception of 3KK, are smaller in magnitude. Even
Grrrr is reduced in magnitude compared to the earlier industries. All
of the own-price elasticities are negative as expected. All of the
cross-price elasticities are positive, except EKL and ELK in Model 1.
The models predict the derived demand for labor very closely at the
sample mean. Little evidence of scale economies is present.
The models also compare favorably with the results available in
Reference (58) as shown in Table 7-22. Given the differences in
methods, data sources, and cost category definitions, the similarities
are striking. Two obvious differences do stand out. Our models
(Model 1 only) suggest some evidence of labor-capital complementarity.
Table 7-22 suggests labor-materials complementarity. This difference
may simply be due to the fact that Table 7-22 reflects characteristics
for all of SIC 26, whereas our models are for a small subset of that
industry.
Implied Effects of Air Quality and Climate—
Models 2 and 3 both predict similar effects on total cost from
changes in air quality and climate. For S02/ the implied effect is a
$400 to $440 increase in total cost for a one ,ug/m increase in
ambient SC>2' This would represent slightly less than an 0.02 percent
increase in total cost. For TSP, the range is $130 to $290 or about
7-145
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TABLE 7-22. COMPARATIVE ESTIMATES OF PRICE ELASTICITIES AND
ELASTICITIES OF SUBSTITUTION FOR SIC 26
Price elasticities
ELL -0-69 ELK 0.82 ELM -0.24
EKL o.4i EKK -0.50 EKM o.is
EML -0.12 Em 0.15 E^ -0.07
1.01 ELE 0.12 EEE -0.73
-1.02 EKE -0.06
0.74 Eflg 0.04
Elasticities of substitution
-3.68 3m 0.37 3EE -31.60
-1.33 Gm -0.60 dL£ 5.17
2.18 Cm -0.16 d^ -2.61
C3.«, 1.78
Source: Reference (58). Price elasticities were reported directly.
Elasticities of substitution have been calculated based on
other data reported in the study.
7-146
-------
0.01 percent of total cost. The standard errors on the TSP
coefficients, however, are large.
The implied effects of temperature changes are somewhat larger
than $12,000 to $20,000 per degree. As noted previously, this is due
in part to the fact that a 1°C temperature change is a much larger
deviation in percentage terms away from the mean. The implied effects
of rainfall are small.
Significance Tests—
Tests of statistical significance based on Model 3 are organized
in Table 7-23, following the format of earlier tables. Model 3 is the
model discussed previously, namely, the regular "reduced" model with
the Cji terms involving TSP deleted. Model 3A is the same model but
with the Cji terms for SC>2 deleted instead.
A test of the validity of dropping the Cj_- terms for TSP requires
a comparison of Models 3A and 3B. The chi-squared statistic of 2.894,
with 2 degrees of freedom, indicates that it is valid. A similar test
for SC>2 is based on a comparison of Model 3 and Model 3B. The
statistic of 1.041 indicates the c^- for SO2 can also be dropped.
Note that with 19 observations, it is not possible to conduct these
tests using the same model since 20 unknown coefficients are involved.
Given the results for the first two tests, attention can now be
restricted to Model 3B which omits the c^- terms for both TSP and S02.
7-147
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statistic of 5.979 indicates that the remaining S02 variable is
significant at the 0.014 level. The test statistic for the remaining
TSP variable indicates that TSP is not significant.
Conclusions for SIC 265 —
Available data for this industry indicate a positive and
statistically significant association between ambient S02
concentrations and total production costs — higher concentrations are
associated with higher costs. The magnitude of the effect is small —
about $400 per /ug/m change. For the average firm in the industry,
this would represent about 0.015 percent of average total cost.
The data do not suggest a relationship between ambient TSP
concentrations and costs of production.
The estimates for this industry are based on a model which has
very plausible economic characteristics that also compare reasonably
well with an independent study using entirely different data and
models.
Estimation Results; SIC 344
SIC 344 includes establishments which manufacture fabricated
structural metal products. Examples include structural metal for
buildings, bridges and ships; metal doors, frames and trim; fabricated
7-149
-------
plate work such as boilers and storage tanks; sheet metal work; and
architectural metal. Establishments which primarily produce ferrous*
and non-ferrous metals from metal ores and scrap, for sale to
industries such as SIC 344, are classified in SIC 33 and thus are not
considered in this analysis.
Summary data for SIC 344 are provided in Table 7-24. The sample
consists of 57 counties containing establishments which produce about
38 percent of the industry's total output. The average establishment
in the sample had total production costs of $1.09 million in 1972,
more than 70 percent of which represented materials costs. Estab-
lishments included in the sample are slightly larger on average than
is the case in the industry as a whole.
Table 7-25 summarizes the characteristics of several of the
models estimated for this industry. Model 1 is defined as before.
Model 2 is the complete model estimated over the data set containing
missing air quality data. Model 3 is the reduced model estimated over
the data set with complete air quality data. Models 1A and 3A are the
same as Models 1 and 3 but with the observation for the District of
Columbia deleted (the reason for this is discussed subsequently).
Model 4 is the same as Model 3A but with the SO., variables deleted.
All models employ the average 2nd High measures for both pollutants.
A problem present in Models 1 through 3 is that the own-price
elasticity for materials has the incorrect sign. In Model 3 this is
7-150
-------
TABLE 7-24. SUMMARY DATA FOR SIC 344 (FABRICATED STRUCTURAL
METAL PRODUCTS)
1.
2.
3.
4.
5.
6.
7.
8.
Number of establishments
Value of output per establishment**
Value added per establishment
Avg. cost of production worker
labor per establishment
Avg. cost of capital services per
establishment
Avg. cost of materials per
establishment
Avg. total cost per establishment"1"
Number of counties
Counties in
the sample
3,447
1.54
0.75
0.26
0.05
0.79
1.09
57
All U.S.
counties
10,351
1.38
0.65
0.22
NA
0.73
NA
3,141
* All data are for 1972 in millions of 1972 dollars.
** Defined to be the sum of items 3 and 6.
+ Defined to be the sum of items 4, 5, and 6.
NA = Not available.
7-151
-------
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7-152
-------
also true for the own-price elasticity of labor. Examination of the
underlying data revealed that the problem appeared to be with the
observation for the District of Columbia (DC). As noted previously in
Table 7-11, the output price for DC is somewhat of an outlier.
Further analysis indicated that this was due to the fact that the
calculated wage rate for DC was an even more severe outlier (4.4
standard deviations from the sample mean). When this observation was
eliminated from the data, the incorrect signs on the price elastici-
ties disappeared. This can be observed in Models 1A, 3A and 4.
It is generally not good practice to exclude arbitrarily observa-
tions that are outliers since they may contain important information.
In this case, however, two factors argue for the exclusion of the DC
data. First, in terms of labor hours, DC is the smallest observation
in the sample. Thus, it is the most susceptible to measurement error
introduced by Census Bureau roundoff in reporting of data. Labor
hours, for example, are reported to the nearest 100,000 hours and
thus, in the case of DC, are reported to only one significant digit.
Measurement error can produce biased and inconsistent coefficient
estimates.
The second reason for excluding the DC data is that the models
without it are simply more plausible and acceptable in terms of their
basic economic properties. Own-price elasticities should be negative,
as they are in Models 1A, 3A and 4 which omit the DC data. One or
more of the own-price elasticities is positive in Models 1 through 3
7-153
-------
which include the DC data. In view of these two reasons, the focus of
the remaining discussion will be on the models without the DC data.
Economic Properties of the Estimated Models—
With the DC observation omitted, the models for this industry
appear quite good. The estimated parameters are quite stable across
models. All of the estimated price elasticities seem to be of
reasonable magnitude. All of the own price elasticities have the
correct sign, as is the case with the elasticities of substitution.
Most of the latter are also reasonable in magnitude.
There is little evidence of scale economies in this industry — a
finding which is consistent with the fact that the industry is
comprised of more than 10,000 establishments averaging about $1.5
million per year in output. The models also predict the demand for
labor very well at the sample mean.
Table 7-26 provides comparative results for SIC 34 from reference
(58). Aside from the usual variability in magnitudes between the two
studies, there are considerable similarities. The elasticity of sub-
stitution between labor and capital, for instance, is remarkably
similar. It is also interesting that both studies find the own-price
elasticity for materials to be near zero. Differences in the defini-
tion of labor, and consequently the cost shares for labor and capital,
lead to differing magnitudes for the labor and capital price elastici-
ties. Note also that we show some evidence of capital-materials
7-154
-------
TABLE 7-26. COMPARATIVE ESTIMATES OF PRICE ELASTICITIES AND
ELASTICITIES OF SUBSTITUTION FOR SIC 34
ELL
EKL
EML
EEL
EEK
EEM
°LL
dKK
dLK
-1.18
1.05
-0.01
3.05
-2.82
0.03
-4.08
-3.71
3.90
Price elasticities
ET-K 1.09 ETM
LjJS. LiiYl
E™ -0.97 EKM
t\j\ IMVI
EMK o.oi EMM
ETP 0.10 EPP
Ljd >f r/
EKE -0.09
EME °'00
Elasticities of substitution
dKM °'02 dEE
d^ -0.02 dLE
0^ -0.00 dKE
°ME
-0.01
0.01
-0.00
-0.25
-26.74
10.45
-10.00
0.06
Source: Reference (58). Price elasticities were reported directly.
Elasticities of substitution have been calculated based on
other data reported in the study.
7-155
-------
complementarity, whereas the latter evidences labor-materials comple-
mentarity. As in the other industries, the differences are likely due
to the fact that SIC 344 is but one of nine industries in SIC 34.
Implied Effects of Air Pollution and Climate—
In this industry there was some variability among the models as
to the effect of SO-. For example, in Model 2 the implied effect is
an increase in total cost of $120 per ug/m increase in ambient 302-
In Model 3A, the reduced model, the implied effect is in the opposite
direction, and statistically significant. However, the implied effect
is also very small, about $20. Model 4 is a re-estimated version of
Model 3A with SC>2 deleted.
For TSP, the implied effects are more stable. All models suggest
that higher TSP leads to higher cost, with effects ranging from $90 to
$340 per ug/m . This would represent 0.008 to 0.031 percent of
average total cost. Note that the relationship between cost and TSP
is positive whether or not the data for DC are included.
Temperature and rain have only a small implied effect on cost in
this industry, in comparison with the other industries reviewed so
far.
Significance Tests—
For testing the statistical significance of the association
between TSP and costs of production, we employ Models 3A and 4. The
7-156
-------
tests are organized in Table 7-27. The first row in the table
consists of tests with Model 3A. The test statistics indicate that
S02 is significant at the 0.02 level and TSP at the 0.11 level. The
second row in the table is based on Model 4 (Model 3A with SC>2
deleted). The test statistic in this case indicates that TSP is
significant at about the 0.106 level.*
Conclusions for SIC 344—
The models for this industry appear quite good when the data for
DC are excluded. The exclusion is done for reasons noted previously.
TABLE 7-27. SIGNIFICANCE TESTS FOR SIC 344**
Model
3A 4
w/o
Model 3A S02
LDET = 20.8348 20.5533
Model 3A: 9.853
(35,3)
Model 4:
number
5
w/o
TSP
20.6642
5.971
(35,3)
6
w/o
S02,TSP
20.3788
6.108
(35,3)
* When the observation for DC is included, the significance level is
0.008.
** Based on data set containing complete air quality data and
excluding data for the District of Columbia (N = 35).
7-157
-------
The implied economic characteristics (e.g., estimated price elastici-
ties) are stable across different models, reasonable in magnitude, and
comparable in most respects to an independent study in the open
literature.
The implied effects of TSP are also stable across models and of
plausible magnitude. TSP is of borderline statistical significance
when the DC data are excluded, and highly significant when they are
included. The models suggest that a one ug/m increase in TSP would
increase total production costs by 90 to 340 dollars. This is 0.008
to 0.031 percent of total cost.
The implied effects of SO- are less stable across models, ranging
from negative to positive effects on total cost. In view of this, the
S02 variables were deleted from the final model.
Estimation Results: SIC 346
SIC 346 includes establishments which manufacture metal forgings
or metal stampings for sale or transfer to others. Establishments
which produce forgings and stampings, and use them in the manufacture
of other end products, are classified in other industries based on the
specific end products produced. Example products of SIC 346 are
gears, wheels, and crankshafts not made in rolling mills; auto body
parts; metal caps and closures; and porcelain enameled applicance
parts.
7-158
-------
Summary economic data for SIC 346 are provided in Table 7-28.
The average establishment in the sample has total production costs of
about $2 million per year, with materials accounting for more than 60
percent of total cost. The 22 counties included in the sample contain
establishments producing about 35 percent of total output in the
industry.
Table 7-29 summarizes the economic properties of several of the
models estimated for this industry. Model 1 is the basic model with
no air quality or climate variables. Model 2 is a smaller version of
the complete 29 variable model in order to accommodate the available
sample size. It is essentially the reduced model with one additional
variable, the eg- term, included. It was estimated over the data set
with missing air quality data.
Model 3 was estimated over the data set with complete air quality
data. In order to accommodate the available sample size, it includes
only the reduced model variables for temperature and rainfall, and the
d^ variables for SO2 and TSP. Model 4 is the same as Model 3 but with
TSP deleted. All three models use the maximum 2nd High measure for
both SO2 and TSP.
Economic Properties of the Estimated Models—
Compared to the models for the previous metal products industry
(SIC 344), the models for this industry appear less satisfactory. The
own price elasticity for capital is extremely large, particularly in
7-159
-------
TABLE 7-28. SUMMARY DATA FOR SIC 346 (METAL FORCINGS AND STAMPINGS)
1.
2.
3.
4.
5.
6.
7.
8.
Number of establishments
Value of output per establishment**
Value added per establishment
Avg. cost of production worker
labor per establishment
Avg. cost of capital services per
establishment
Avg. cost of materials per
establishment
Avg. total cost per establishment"1"
Number of counties
==== = ======:==:==============:=:========:==
Counties in
the sample
1,242
2.84
1.46
0.62
0.07
1.38
2.07
22
All U.S.
counties
3,188
3.14
1.59
0.67
NA
1.55
NA
3,141
* All data are for 1972 in millions of 1972 dollars.
** Defined to be the sum of items 3 and 6.
+ Defined to be the sum of items 4, 5, and 6.
NA = Not available.
7-160
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the models containing air quality and climate variables. Similar
behavior is observed in the cross-price elasticity between capital and
materials, and in the corresponding elasticities of substitution. The
other price elasticities are of more reasonable magnitude but in some
instances are not very stable across models. The scale economies and
labor demand parameters in contrast are reasonably similar across
models.
We can also refer back to Table 7-26 which provided independent
parameter estimates for SIC 34. A comparison between the two sets of
estimates indicates a number of dissimilarities. As noted previously
in the other industries, however, this could be due to the aggregation
present in estimates for a 2-digit SIC industry.
Implied Effects of Air Pollution and Climate—
It was generally found to be the case that in the models for this
industry, the implied effects of SO- varied considerably across
models. This is the pattern indicated in Table 7-29 where the sign on
SO- changes from positive to negative in different models. In
contrast, the sign on TSP was more stable, but usually negative. When
TSP was deleted from Model 3, the sign on S02 also went negative, as
shown in Model 4. The signs for temperature and rain were almost
always positive and showed less variability in magnitude.
7-162
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Significance Tests—
Using Model 3, the statistical significance of the S02 and TSP
variables can be determined. The appropriate calculations are
provided in Table 7-30. The chi-squared statistics indicate that
neither the S02 nor TSP coefficient is statistically significant.
Conclusions for SIC 346—
The available data for this industry provide no evidence that
either S0_ nor TSP affects costs of production. The available data,
however, were quite limited. This industry had the smallest sample
size among the six industries analyzed in detail.
t
We note also that the economic characteristics of the estimated
models for this industry were perhaps not as satisfactory as in the
other industries studied. In addition to the smaller sample size, we
suspect two other factors may have contributed to the lesser results.
TABLE 7-30. SIGNIFICANCE TESTS FOR SIC 346*
Model number
3 3A
w/o
Model 3 SO2
LDET = 21.5038 21.4976
Model 3: 0.105
(17,1)
. — —_____._-. _ — __
4
w/o
TSP
21.3682
2.305
(17,1)
Based on the sample containing complete air quality data (N = 27]
7-163
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First, recall that this was the industry for which the output price
index was the least satisfactory. Among the six industries, the
output price equation for this industry had the poorest fit to the
historical data. In part we attributed this to the Producer Price
Index component matched to this industry.
A second possible source of difficulties has not previously been
mentioned. Namely, the definition for SIC 346 was changed between
1967 and 1972, with the addition of industries previously classified
in SIC 339. While this change would not affect the 1972 economic data
used, it would affect the historical capital expenditure data used in
constructing capital stock estimates. This may explain the unusual
behavior of the price elasticities involving capital.*
In conclusion, given the small sample size for this industry, and
the apparent problems with the basic economic data, it is not
surprising that the models did not behave as well as in the other
industries. It is therefore possible that air quality effects may be
present in this industry but that problems in the data make them
considerably more difficult to detect.
* Among the other five industries, SIC 201 also changed definitions
between 1967 and 1972. Perhaps not coincidentally, pollution
effects in that industry were not statistically significant either.
The other four industries did not change definitions during the
historical period 1958-1972.
7-164
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Estimation Results; SIC 354
SIC 354 includes establishments which manufacture metalworking
machinery and equipment. Example product categories are metal cutting
tools, metal forming tools, machine tool accessories, and rolling
machinery and equipment for metal production.
Summary data for this industry are provided in Table 7-31.
Recall that in this industry, the labor cost category includes all
employees, in addition to production workers. This is reflected in
the table. In this industry, labor costs are the largest component of
cost, followed by materials and capital. As the table also indicates,
the sample for this industry includes 28 counties which together
account for nearly 56 percent of the industry's total output.
Summary characteristics for several of the models estimated for
this industry are provided in Table 7-32. Model 1 is the basic model.
Model 2 is the complete model, estimated over the data set with
missing air quality data. Since only 28 counties were available for
this industry, the "complete" model in this case must omit two
variables in order to accommodate the sample size. The omitted
variables are d^3 and d. ., the quadratic terms for temperature and
rain. The pollutant measures used are the maximum 2nd High for S02
and the average 2nd High for TSP, selected on the basis of the likeli-
hood ratios.
7-165
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TABLE 7-31. SUMMARY DATA FOR SIC 354 (METALWORKING MACHINERY)
1.
2.
3.
4.
5.
Number of establishments
Value of output per establishment**
Value added per establishment
Avg. payroll per establishment
Avg. cost of capital services per
Counties in
the sample
3,825
1.07
0.77
0.45
0.06
— — — :
All U.S.
counties
9,652
0.76
0.51
0.30
NA
establishment
6. Avg. cost of materials per 0.30 0.25
establishment
7. Avg. total cost per establishment"1" 0.81 NA
8. Number of counties 28 3,141
* All data are for 1972 in millions of 1972 dollars.
** Defined to be the sum of items 3 and 6.
+ Defined to be the sum of items 4, 5, and 6.
NA = Not available.
7-166
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TABLE 7-32.
ESTIMATED MODEL CHARACTERISTICS FOR SIC 354
(Metalworking Machinery)
Elasticities
($1,000)
Log determinant of S
Model number
Model version
No. of observations
No. of variables
SO_ measure
TSP measure
R
E~~
HWT
ETV
'ItlGS fit-.-.
SIR
gMK
EKM
TM
°LL
d
.KK
:ies 0
:ution d '
•<3
°MM
lomies SCE
lemand L'/L
KTCSQX
. cost MTCTSP
MTCTEMP
MTCRAIN
)f S"1 LDET
1
Basic
28
10
—
—
-0.46
-0.09
0.65
-0.01
-0.67
0.17
0.47
0.75
-0.83
-0.86
-7.61
-0.17
1.98
1.23
-2.17
0.06
1.00
_
—
—
—
19.1339
2
Complete
28
27
X2HI
A2HI
-0.65
0.44
0.81
0.07
-2.20
0.40
0.58
1.75
-1.21
-1.23
-25.10
0.83
4.60
1.52
-3.16
0.11
1.00
-0.01
0.53
-8.05
-0.09
21.5807
3
Reduced
22
20
X2HI
A2HI
-0.46
0.20
0.60
0.03
-1.00
0.19
0.42
0.81
-0.80
-0.85
-11.27
0.37
2.15
1.13
-2.12
0.12
1.00
-0.04
0.18
-8.58
-0.02
21.5146
4
Reduced
22
17
—
A2HI
-0.45
0.22
0.59
0.04
-1.06
0.20
0.41
0.83
-0.79
-0.84
-11.87
0.42
2.22
1.10
-2.11
0.12
1.00
_
0.15
-8.67
-0.02
21.2762
7-167
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Model 3 in Table 7-32 is the normal reduced model, estimated
using only the observations with complete data. Model 4 is the same
as Model 3 but with the S02 variables eliminated.
Economic Properties of the Estimated Models—
The economic properties of the models for this industry are very
stable and of reasonable magnitude across all versions. There is a
sign change on the cross-price elasticity between labor and capital in
Model 1 compared to the other models. The coefficients for Model 2
are somewhat larger than in the other four models. Aside from these
differences, the estimated results are very similar.
All of the models suggest evidence of scale economies in this
industry. This would be consistent with the observation made earlier
that most companies in this industry have only one manufacturing
establishment rather than multi-plant operations.
Table 7-33 provides comparative results for SIC 35 as reported in
Reference (58). Most of the labor- and capital-related price elasti-
cities reported in that study are larger than our estimates. Most of
the materials-related elasticities are smaller. Industry SIC 354,
however, is but one of nine industries in SIC 35 and thus the level of
aggregation present in Table 7-33 makes exact comparisons difficult.
7-168
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TABLE 7-33. COMPARATIVE ESTIMATES OF PRICE ELASTICITIES AND
ELASTICITIES OF SUBSTITUTION FOR SIC 35
ELL -2.56
EKL 2'10
EML -° • °8
EEL 1 . 16
EEK -1-19
EEM 0.04
OLL -8.50
dKK -6.41
^LK 7'39
Price elasticities
ELK 2.63 ELM -0.09
EKK -2-15 EKM °-08
F n OQ F -o nn
£JT»«V U • U .7 ^MM VJ • U U
rlJA iYli 1
EL£ 0.03 EEE -0.01
EK£ -0.02
EME °-°°
Elasticities of substitution
dKM 0.24 cipp -1.58
3\i 1 £j£j
<3TM -0.27 dTp 3.69
i_U 1 J^fj
0,^ -0.01 dKE -3.20
Source: Reference (58). Price elasticities were reported directly.
Elasticities of substitution have been calculated based on
other data reported in the study.
7-169
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Implied Effects of Air Quality and Climate—
In most of the models estimated for SIC 354, the relationship
between SO- and costs of production was negative at the sample mean,
with positive values at some observations. This is reflected in
Models 2 and 3, and is similar to what was found in SIC 344. Signifi-
cance tests based on Model 3 indicated that the implied effect of S02
was not statistically significant. The S02 variables were thus
deleted and the model was re-estimated. The re-estimated version is
shown in Table 7-32 as Model 4. Note that the deletion of the SO,,
variables did not lead to any appreciable differences between Models 3
and 4.
The implied effect of TSP in the various models ranges from $150
to $530 per ug/m3. The implication is that a unit increase in ambient
TSP concentrations would increase total costs of production by a few
hundred dollars. A $200 increase would represent about an 0.025
percent increase in total cost for the average establishment in the
sample.
The implied effects of temperature and rain in this industry are
small and consistent across the models. The implication is that costs
are lower in areas with warmer climates and more rainfall.
Presumably, this could reflect reduced space heating requirements.
7-170
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Significance Tests—
The statistical significance of the air quality effects are
studied in Table 7-34, using Model 3 as the initial base. The first
row in the table considers the SO- and TSP variables. The chi-squared
statistic for the SO variables is 5.245 which corresponds to a 0.15
level of significance. This indicates that S02 can be deleted from
the model. In contrast, the TSP variables are significant at the
0.042 level.
The second row in the table considers Model 4, which is simply
Model 3 with the S02 variables deleted. The test statistic in this
case is 7.465 which indicates that the TSP terms are significant at
the 0.0585 level.
TABLE 7-34. SIGNIFICANCE TESTS FOR SIC 354*
Model
3 4
w/o
Model 3 SO2
LDET = 21.5146 21.2762
Model 3: 5.245
(22,3)
Model 4 :
number
3A 5
w/o w/o
TSP SO2,TSP
21.1428 20.9369
8.180
(22,3)
7.465
(22,3)
* Based on the sample containing complete air quality data (N = 22)
7-171
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The small sample size did not allow testing of the equations over
alternative subsamples of the data. However, the data were examined
for outlying observations. This revealed that the observation for
Maricopa County (Phoenix), Arizona, had a TSP value that was 3.55
standard deviations from the mean of the sample counties. Re-
estimation of Model 4 without this observation caused the significance
level to change from 0.0585 to 0.281, and the elasticity of total cost
with respect to TSP declined by about half. Examination of the
original TSP data for the county indicated that it was based on the
average of data from seven separate particulate monitors. Thus, the
observation, although influential, nonetheless appeared valid. No
other outlying data were observed. The original version of Model 4
incorporating Maricopa County was thus retained.
Conclusions for SIC 354—
The estimated models for SIC 354 perform well in terms of their
implied economic properties. The estimated economic parameters are of
reasonable magnitude, consistent with economic theory, and relatively
insensitive to changes in data or equation specification.
The air quality effects implied by the models are less stable.
The implied effect of SCL is small, frequently negative, and statis-
tically insignificant. The implied effects of TSP are generally
positive (higher TSP leads to higher costs) and statistically signifi-
cant. In the most plausible specification, the implied effect of TSP
is about $150 per ug/m3 change in the ambient concentration.
7-172
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BENEFITS CALCULATIONS FOR SELECTED INDUSTRIES
The statistical analyses discussed in the previous sections
suggest that for certain industries and pollutants, there is a
positive association between costs of production and the level of
ambient air pollution — higher pollution levels are associated with
higher costs. In this section, the benefits (cost savings) associated
with improvements in air quality are calculated for those industries
and pollutants. Calculations are included for those industries where
the estimated cost function appear plausible. Recall that benefits
are calculated by measuring the cost savings due to improved air
quality [see Equation (7.1.a)].
Air Quality Scenarios
As discussed in Section 3 of this report, the current secondary
standard for TSP is 150 ug/m , based on a 24-hour averaging time. The
primary standard for TSP at this averaging time is 260 ug/m^. As
discussed below, the economic benefits of the TSP secondary standard
are calculated by estimating the costs of production under each of two
air quality scenarios — one in which the secondary standard is
attained by 1987, and one in which only the primary standard is
attained.
In the case of S02/ the current secondary standard is 1,300
ug/m , based on a 3-hour averaging time. There is no primary standard
7-173
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with this averaging time although primary standards do exist at longer
averaging times (24 hours and annual average). In part because of the
above, and also because longer averaging times are believed to be more
appropriate for soiling and materials damage, the models in this
sector are based on a 24-hour averaging time (the 3-hour standard was
apparently chosen to prevent vegetation damage — see Section 3 of
this report).
In view of the above situation for SC^/ we calculate benefits for
two SO2 standards — the current 3-hour standard and an alternative
24-hour standard. In both cases, benefits are calculated according to
the same scenario as described for TSP — attainment of the secondary
standard by 1987 versus attainment of the primary standard only. For
the 24-hour averaging time, the current primary standard is 365 ug/m3
and the alternative secondary standard is 260 ug/m3. For the current
3-hour secondary standard, there is no corresponding primary standard.
Hence, to calculate benefits, we first calculate the 24-hour equiva-
lent of the current 3-hour standard.* Benefits are then calculated
assuming attainment of the "equivalent" 24-hour secondary standard
versus attainment of the current 24-hour primary standard.
* The procedure used to calculate the 24-hour equivalent standard is
described in Section 3 of this report. Basically, it involves
predicting what air quality would be on a 24-hour basis, given
attainment of the 3-hour standard. Since the prediction depends on
the time distribution of air pollution in each county, the
equivalent standard will vary from county to county.
7-174
-------
For each of the pollutants and standards, the same two basic
scenarios are employed:
• Attainment of the primary standard (PNAAQS) only by
1985 — the baseline scenario.
• Attainment of the primary standard by 1985 and the
secondary standard (SNAAQS) by 1987 — the alternate
scenario.
The two scenarios can be illustrated as shown in Figure 7-6.
Three possible cases are illustrated:
• Case A — counties current (1978) out of compliance
with both standards.
• Case B — counties currently in compliance with the
primary standard but not the secondary standard.
• Case C — counties currently in compliance with both
standards.
The baseline scenario for the three cases can be summarized as
follows. All Type A counties are assumed to achieve PNAAQS compliance
by 1985, with no further change in air quality thereafter. Type B and
C counties, which are already in PNAAQS compliance, as assumed to
remain unchanged in the future. Note that this is a conservative
assumption which may lead to understating actual benefits. That is,
in the absence of SNAAQS, air quality in Type C (and B) counties may
deteriorate to the primary standard rather than remaining unchanged
for current levels.
7-175
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1
1
<\
1
1
<
-
03
1
1
i
|
1
1
03
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00
CO • •
CTi CO 00
rH O O
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H -H -H 0)
rH • fH • D
CU
-------
The alternate scenario follows the baseline scenario through 1985
where PNAAQS compliance is required. By 1987, all counties are
assumed to be in compliance with SNAAQS. In the interim 2-year
period, air quality is assumed to change by equal amounts each year.
In 1988 and thereafter, air quality is assumed to remain at 1987
levels. Note that the alternate scenario is also conservative since
SNAAQS compliance by Type A and B counties may also improve air
quality in some of the nearby Type C counties.
In counties for which 1978 air quality data were not available,
we assumed that the SNAAQS were met and set the air qualities to
SNAAQS levels. Clearly, no benefits can accrue when air quality is
assumed to be at the SNAAQS level already, so this assumption has no
direct effect on the benefits calculation.
Economic Scenarios
In this subsection, we discuss the economic scenario assumed for
the benefits calculations. Input prices, i.e., wage rates, the price
of capital services, and materials prices (PT, PT, and ?„), are assumed
ij K M
to remain constant in 1980 dollars. This is equivalent to assuming
that input prices will increase at the general rate of inflation.
Although wage rates may fall slightly as air quality improves, this
effect is not incorporated in this analysis. As discussed in an
earlier subsection, this omission will lead to understating actual
7-177
-------
benefits. Wage effects due to air quality are considered in Section 6
of this report.
In order to calculate benefits, one must first make a forecast of
how industry output is likely to change in the future. This must be
done because costs of production depend on output levels as well as on
input prices. For the forecast of industry output, we used national
forecasts from the Wharton Annual Model, a well-known product of
Wharton Econometric Forecasting Associates. The Wharton Model
provides long-term macroeconomic forecasts based on a linkage between
the national income accounts and interindustry accounts within the
framework of a macro-model. One of the various forecasted quantities
of the Wharton model is a national forecast of gross product
originating in constant dollars for each 2-digit SIC. Gross product
originating (GPO) is one alternative measure of output. We have
assumed that the relative growth in 3-digit SIC output is identical to
the relative growth in 2-digit SIC GPO predicted by the Wharton model.
This assumption is used for the period 1980 to 2000, which is the
period covered by the Wharton forecast. A mean growth rate based upon
the last 5-year period 1996 to 2000 was used to extrapolate output
growth beyond the year 2000. In each county, the level of manufac-
turing output is assumed to reflect the same proportional share of
future national output that existed in the base year 1972.
Finally, it is noted that growth can occur in two ways — through
increases in the number of manufacturing facilities and through
7-178
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increases in capacity at existing facilities. A parameter, e, where 0
<_ c <_ I/ is introduced to allocate the county-wide growth to each of
these two factors. Defining:
N-t = number of establishments in industry i, year t and
county c
s'tc = outPut °f an "average" establishment in industry i,
year t and county c
= output of industry i, in year t, in county c
^t = gross product originating (Wharton Model) for industry
i, year t,
the economic scenario can be summarized by the following
GPOit
— -
GPOi72
Q
i72c
"c
Nitc - (;TT— ' Ni72c
GPOi72
- Nitc • Sitc
The growth allocation parameter, c, could have been indexed by i, t
and c, but there is little justification for doing this. In calcula-
ting the estimated benefits, we assume c = 1/2, which allows an equal
7-179
-------
split in growth due to increases in plant size and in the number of
plants.
Finally, in calculating the discounted present value (DPV) of
benefits, as presented in the next subsection, three different
discount rates are used. These rates, chosen to exercise the benefits
model under different conditions, are set at 2, 4 and 10 percent.
Estimated Benefits
Benefits in each year, beginning with 1986, are calculated by
evaluating Equation (7.la) in each county, under the scenarios out-
lined previously. The function C in the equation is the cost function
estimated for each industry, as discussed in the earlier sections.
The specific equations are contained in the Appendix to this section.
Annual benefits are calculated for each year out to the year 2050.
Total benefits in all future years beyond 2050 are approximated by the
quantity (B205o^r' wnere B2050 is the benefits estimate for the year
2050 and r is the discount rate. All benefits are then converted to
1980 discounted present values in 1980 dollars.
National Totals—
Table 7-35, which is a repeat of Table 7-1, provides the details
of the estimated benefits for each industry and pollutant. The values
shown in the table are discounted present values in 1980, expressed in
billions of 1980 dollars. The estimates are based on a discount rate
7-180
-------
of 10 percent and an infinite time horizon. Note that the estimated
benefits for the current 3-hour SO- standard are zero, while those for
the other standards range from $511 million to $3.9 billion.*
For comparison purposes, Table 7-35 also shows the discounted
present value of total production costs in all counties used in the
benefits calculation. Comparison of the two sets of numbers indicates
that attainment of SNAAQS would reduce average total costs of
production by 0.1 percent to 2.1 percent, depending on the industry
and pollutant.
Geographical Coverage of the Estimates—
As noted previously, data are not available for all U.S. counties
containing the industries studied. The estimates shown in Table 7-35
thus do not reflect complete coverage of all manufacturing estab-
lishments in each industry and thus may understate actual benefits.
Table 7-36 indicates the degree of coverage for each industry in terms
of value added by manufacture. As an example, for SIC 201, the
counties included in the benefits calculation contained establishments
producing 26.6 percent of total industry value added (Column A).
However, data on SC> concentrations were not available for all of
* Benefits for the 24-hour equivalent of the current 3-hour S02
secondary standard are approximately zero because the primary 24-
hour standard is binding in all but five counties, and in these
counties, the economic value of the relevant industries (SlCs 201,
202, 265) is generally small or negligible. Because of the small
economic value, the Census did not publish detailed economic data
for some of the counties.
7-181
-------
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7-182
-------
TABLE 7-36. RELATIVE COVERAGE OF INDIVIDUAL INDUSTRIES
(in terms of value added by manufacture)
SIC
201
202
265
344
346
354
Relevant
pollutant
so2
so2
S02
TSP
—
TSP
A
26.6
33.8
55.0
51.2
—
56.0
B
10.9
12.6
26.3
46.2
—
49.6
C
4.8
5.8
20.2
7.5
—
15.0
D
6.1
6.8
6.1
38.6
—
34.5
Key: A = Percent of industry for which economic data are available.
B = Percent of industry for which both economic data and air
quality data are available.
C = Percent of industry with both economic and air quality
data available, but compliance with SNAAQS (24-hour
standards) had already been achieved by 1978.
D = Same as C but not in compliance by 1978.
these counties; as shown in Column B, counties for which we had both
economic data and S02 data represented 10.9 percent of total value
added. Columns C and D show the allocation of the 10.9 percent
between counties already in compliance with SNAAQS (24-hour standards)
in 1978 and counties not in compliance.
The lack of complete data for each industry means that benefits
shown in Table 7-35 are likely to be understated. However, the degree
7-183
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of understatement may not be as severe as the percent coverage figures
in Table 7-36 might seem to indicate. Air quality monitoring stations
are presumably concentrated in areas where air pollution is a problem;
thus areas without monitoring facilities are more likely than not to
be in compliance with SNAAQS already.
Geographic Distribution of Benefits—
The geographic distribution of benefits for each industry is
shown in Table 7-37. Benefits are shown for the current TSP standard
and the alternative SO standard. As can be seen, there are signifi-
cant geographic concentrations. This pattern is the result of three
factors: the geographic distribution of the individual industries;
the geographic pattern of air quality; and the availability of both
economic data and air quality data. For SICs 201, 202 and 265, the
estimated SO- benefits are concentrated in two Census Divisions — the
Mid-Atlantic Division (New York, New Jersey and Pennsylvania) and the
East North Central Division (Ohio, Indiana, Illinois, Michigan and
Wisconsin). The TSP benefits in SIC 344 and SIC 354 are more broadly
distributed.
The geographic distribution of estimated benefits shown in Table
7-37 is based on where the affected manufacturing facilities are
located. However, it is important to recognize that many of these
establishments may ship products, and return profits, to customers and
shareholders in other regions. To the extent that these interregional
relationships exist, other regions will also share in the benefits.
7-184
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TABLE 7-37. GEOGRAPHIC DISTRIBUTION OF ESTIMATED BENEFITS*
(discounted present values for 1980 in
billions of 1980 dollars)**
census Q J.V is ion
New England
Mid-Atlantic
East North Central
West North Central
South Atlantic
East South Central
West South Central
Mountain
Pacific
Industry/pollutant
201+ 202 265 344+ 346
(S02) (S02) (S02) (TSP)
0.052
0.110 0.121 0.043 0.668
0.055 0.135 0.046 1.097
0.235
0.036
0.178
0.403
0.083
0.202
354
(TSP)
0.004
0.101
0.804
0.008
—
—
0.002
0.002
—
Totals 0.165 0.257 0.088 2.955 — 0.920
* Based on the location of affected manufacturing facilities.
Details may not add to totals due to independent round-off errors.
** At a discount rate of 10 percent.
+ The pollution variables for these industries were statistically
significant in some cases but not in the final model version
chosen.
— Equals 0.0.
7-185
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PLAUSIBILITY OF THE BENEFITS ESTIMATES
As noted in the introduction to this section, there is consider-
able evidence from laboratory and field studies indicating that sulfur
oxides and particulate matter cause materials damage and soiling.
There seems to be little disagreement, therefore, that improved air
quality would yield economic benefits to society. The uncertainty
lies in the magnitude of these benefits and their relationship to air
pollution control costs.
A variety of studies have made estimates of soiling and materials
damage, typically using estimated dose-response relationships, and
used these damage estimates to predict benefits. The purpose of this
study has been to estimate benefits using an altogether different
methodology and data set. The question we can ask at this point is
whether the benefits estimates obtained from this new methodology are
plausible. The purpose of this subsection is to consider the question
of plausibility from several perspectives.
Plausibility of the Underlying Economic Models
The benefits estimated in the previous subsection are based on
economic models of optimizing behavior by industrial firms. Similar
models have been widely used and tested in other applications. One
measure of plausibility then is the extent to which the models we have
7-186
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used to predict benefits are reasonable, and consistent with the
earlier models, in terms of their basic economic properties.
In reporting the estimation results for each industry, attention
was given to the estimated economic properties. A reasonable
assessment would be that the models performed moderately well but not
spectacularly. In all six industries, the own-price elasticities of
demand were negative, as would be expected, and of reasonable magni-
tude for labor and materials. The magnitudes were generally larger
for capital and greater than 1.0 in absolute value in five of the six
industries (the exception was SIC 344 — the worst was SIC 346). The
own-partial elasticities of substitution followed a similar pattern —
generally reasonable results for labor and materials, and rather large
values for capital. In general, the poorer results with capital were
attributed to the approximations involved in constructing estimates of
capital stocks and capital services prices.
The estimated economic elasticities in each industry were also
compared with results from an independent study. Given the signifi-
cant differences between the two studies in methods, data, and the
level of aggregation, the results compared favorably. The major
differences tended to arise in the estimated magnitudes and in the
signs on some of the cross-price elasticities.
On the basis of these considerations, the previous conclusion
seems warranted — the economic properties of the models are
7-187
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moderately good but not spectacular. The weakest models were probably
those in SIC 346, due undoubtedly to the small sample size and a
number of specific data problems with that industry cited earlier. It
is not too surprising, therefore, that no pollution effects could be
detected in SIC 346.
Plausibility of the Implied Pollution Effects
A second test of plausibility is the reasonableness of the
economic effect of pollution implied by the models. Reasonableness in
this instance is a relative question. That is, a finding that pollu-
tion increases production costs by, say, 50 percent would be
unreasonable; if the effect were this large, we would expect to see
firms relocating just to avoid air pollution. On the other hand, if
the effect were, say, 0.1 percent, then in the absence of other
information, we could probably agree that the effect is "reasonable".
Between these two extremes, however, a judgment becomes more difficult
to make .
in general, across industries, the implied effect of a one
increase in either TSP or S02 was on the order of $100 to $500. In
comparison with costs of production, these figures correspond to a
range on the order of 0.005 to 0.04 percent, depending on the
industry. SIC 201 was at the lower end; SIC 344 was at the upper end.
Clearly, these numbers are quite small.
7-188
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The figures above represent the cost of a unit change in air
pollution and* are therefore sensitive to the units used in measuring
pollution. An alternative comparison that can be made is between
costs of production and the costs of pollution if air quality were at
PNAAQS levels rather than at SNAAQS levels. This is approximately
equivalent to comparing the benefits of SNAAQS to the total costs of
production, as indicated previously in Table 7-35.* In the discussion
of that table, it was noted that benefits ranged from 0.1 percent to
2.1 percent of total costs. The number at the lower end of the range
seems very reasonable; the one at the upper end (SIC 344) is more
difficult to judge in the absence of other information.
Unfortunately, there are no independent estimates which provide
an accurate standard of comparison for the above results. For
example, it is difficult to compare these results with the various
studies based on physical damage functions. To apply the latter
technique to estimating benefits for one of our industries would
require determining the stock of all affected materials in each
industry. Even if stocks could be estimated, the benefits estimates
would still very likely be different. The existing damage functions
in the literature tend to capture only direct materials affects (e.g.,
corrosion). It is not clear that they identify soiling effects or the
differential cost of damage-resistant materials. They almost
* The equivalence is only approximate because some counties in Table
7-35 already had better than PNAAQS air quality.
7-189
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certainly would not identify efficiency losses such as reduced
serviceability of equipment.
For the same reasons as above, it is difficult to compare our
results with the estimates of maintenance cost by industry in 1957
provided earlier in Table 7-6. For the six industries under consid-
eration, the percent of total payroll devoted to maintenance and
repair ranged from 2.9 percent to 4.1 percent, as indicated in the
earlier table. Our benefits estimates, in comparison, range from 0.1
percent to 2.1 percent. The difficulty in comparing the two sets of
numbers is that the former also includes maintenance and repair
unrelated to air pollution and does not include materials or capital.
The latter also includes air pollution effects which may not be mani-
fested in, or classified as, maintenance and repair activities.
Examples may include reduced serviceability of equipment, the differ-
ential cost of damage-resistant materials, the cost of air filtration
systems and other protective measures.
In the absence of clear evidence either confirming or refuting
our benefits estimates, we contacted a small number of companies to
see if additional clarification could be obtained. Since the estimate
for SIC 344 is the largest in percentage terms, effort was focused on
that one industry. Recall that benefits in this industry arise from
reduced TSP.
7-190
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Two metal fabricating companies and one air filtration system
manufacturer were contacted and queried as to the impact of dust and
particles on metal fabricating operations. They volunteered the
following information:
Welding, which is an integral part of many metal
fabricating operations, was said to be greatly
affected by dust and other contaminants. In
particular, the presence of contaminants on the
welding surface will affect the strength and integrity
of a welded joint. One protective measure taken is
the use of dust control systems at each welding
station both to reduce contamination and to control
by-products of the welding operation. Blowers and
ventilation systems are also used to control dust,
much of which can be generated by other operations in
the plant (e.g., grinding).
Power sources (e.g., transformers) for the plant can
be affected by dust and typically must be cleaned a
couple of times each year.
Optical tape readers and magnetic tape readers used in
numerical control of machine tool operations are
highly sensitive to dust. Exposure can occur whenever
the readers are opened to change the tapes.
Metal inventories are typically covered or kept
indoors to keep the metal surfaces in good condition
before use. This is done even in plants which operate
on a job or order basis and which thus have short
duration inventories (4 to 5 weeks) purchased on an
as-needed basis. Metal inventories not handled in
this way can require sandblasting before use.
One particularly striking feature about the examples supplied is
that the physical effects involved are not exclusively corrosion.
Rather, soiling and contamination are also significant mechanisms.
Within the physical damage function literature, these effects have
been much less widely studied in the industrial context in comparison
7-191
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with paint and metal corrosion studies.* It is therefore possible
that the TSP effects identified in this industry represent a benefits
category which have been largely overlooked in the past. Clearly, if
TSP can soil household surfaces, it must also do the same to
industrial surfaces.
The above examples, however, do not provide any guidance as to
the magnitude of the TSP effect in this industry — they are merely
suggestive of some of the physical mechanisms of damage. Hence, it
still remains difficult to judge whether the benefits number for this
particular industry (SIC 344) is reaonable in magnitude.
The Pattern of Pollution Effects
One very interesting pattern to emerge from this study is the
specific pollutant associated with each industry. Our a. priori expec-
tation had been that TSP would show up as significant in those
industries where cleanliness was important; i.e., the food processing
industries, SICs 201 and 202. Similarly, we expected SO2 to show up
in the metal-fabricating and machinery-producing industries, SICs 344,
346 and 354. In fact, precisely the opposite pattern emerged. SO-/
* Note, for example, that existing studies of TSP-related soiling
damage are almost exclusively concerned with households. For
example, in the recent SRI study (60) for the National Commission on
Air Quality, estimates of soiling effects include households only.
Most of the studies referenced in EPA's Criteria Document (61) also
deal primarily with household soiling.
7-192
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but not TSP, was found in the food industries; TSP but not S02 was
found in the metal fabricating and machinery industries. This
unexpected pattern is discussed further below.
The Food Processing Industries—
In reviewing the results for the food processing industries, we
hypothesized the following explanation. In these industries, cleanli-
ness and sanitation requirements may lead to such routine and
systematic cleaning practices, for other reasons, that the additional
soiling due to TSP is not important. If this is the case, then only
SO- effects may lead to any detectable differences across individual
establishments. A review of some of the Federal regulations
pertaining to the food industries supports this hypothesis. For
example, the Food and Drug Administration has established regulations
dealing specifically with sanitation and cleaning in the food manufac-
turing and processing industries (21 CFR 110). The regulations
contain requirements such as the following:
• "Cleaning operations shall be conducted in such a
manner as to minimize the danger of contamination of
food and food-contact surfaces."
• "All utensils and product-contact equipment shall be
cleaned as frequently as necessary to prevent
contamination of food and food products."
• "... the contact surfaces of such equipment and
utensils shall be cleaned and sanitized on a
predetermined schedule using adequate methods for
cleaning and sanitizing" (62).
7-193
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The implication of these requirements is that they may result in
routine, standardized cleaning practices. If that is the case, then
variations in cleaning across establishments will be small and TSP
effects will be obscured and difficult to detect from a one-year
cross-section of data. The effects of SO-? on the other hand, may
still be detectable. For example, if the effects of S02 are corrosion
related, they may not be ameliorated by routine cleaning. In this
case, SO- effects may vary cross-sectionally with air quality and be
detectable by statistical analysis. Thus, the finding of SCL effects
in the food industries, but no TSP effects, may be a reasonable
result.
The Metal Fabricating and Machinery Industries—
In the case of the metal fabricating and machinery-producing
industries, the finding was one of TSP effects but no SO- effects. A
^
number of examples were identified previously as to how the TSP
effects may be manifested. The question remaining, however, is why
there were no SO- effects identified. One possibility, of course, is
that the effects are very small and not readily detectable with aggre-
gate economic data. The other possibility is that these industries
are well aware of atmospheric corrosion effects on metals, since they
work with metals on a day-to-day basis. In this case, there may be
standard industry practices to prevent corrosion. One example of this
in SIC 344 was cited earlier — the practice of keeping metal
inventories covered or indoors, specifically to protect the metal
surfaces. Standard practices of this sort would reduce the variation
7-194
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in corrosion damages across different establishments. In this case,
corrosion damages would not be detectable from a one-year cross-
section of data. Pooled time-series cross-sections would be required.
The Effect of Pollution Control Costs
At an earlier point in this section, it was noted that some
manufacturing firms are also sources of air pollution. These firms
may therefore be required to install pollution control equipment to
comply with local air quality regulations. In this case, geographic
variations in production costs among firms could arise both from
control cost variations and from variations in the soiling and
materials damage due to air pollution, as well as from other economic
factors such as wage rate differences.
In this study, the influence of wage rate variations and other
economic factors have been taken into account by incorporating prices
into the statistical model. The influence of control costs, however,
has not been specifically addressed because the requisite data are not
available. The question arises, therefore, as to whether the models
are merely picking up the effects of control cost variations, rather
than the effect of air pollution soiling and materials damage, or
possibly both effects together. One might expect this to be a problem
if local air pollution control regulations are correlated with local
air quality. That is, in areas with poor air quality, the situation
may be: (1) air pollution damages are larger, (2) air quality control
7-195
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regulations are stricter, and (3) air pollution control costs are
larger.
Average Air Pollution Control Costs—
The data required to test the above hypothesis are not available
— otherwise they would have been incorporated in the models already.
Somewhat more indirect tests can be made, however, using data which
the Census Bureau began collecting in 1973 (63). Table 7-38 displays
some of these data for the six industries under consideration. The
first two columns show the total capital expenditures for these
industries. The next four columns show the capital expenditures for
air pollution control, by type of pollutant. These figures include
the cost for both end-of-line control and changes in production
processes. The seventh column shows the annual cost of air pollution
control for all pollutants; no breakdown is available for individual
pollutants. Included in the annual cost figure are the following
items: depreciation, labor, equipment leasing, materials supplies,
services, the incremental cost of cleaner fuels, increased fuel or
power consumption due to control equipment, and other.
The last two columns in the table provide a comparison between
the costs of air pollution control and the value of shipments. Note
that costs range from 0.007 percent to 0.04 percent, depending on the
industry. In each case, these percent figures are an order of magni-
tude smaller than the estimated benefits of SNAAQS attainment
presented earlier in Table 7-35. This is despite the fact that the
7-196
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control cost figures include the costs for all pollutants, while the
benefits figures are for single pollutants.* These comparisons thus
provide no evidence to indicate that the statistical models are
picking up air pollution control costs rather than air pollution
damages. That is, the economic effects identified by the models are
much larger on average than the costs of air pollution control.
Variations in Air Pollution Control Costs—
There is an alternative test of whether the pollution variables
in the models are actually picking up cost effects due to air pollu-
tion control requirements. This would involve testing whether
geographic variations in control cost are statistically associated
with geographic variations in air pollution. If such an association
were found, and if the marginal change in control cost due to a unit
change in air pollution were of the same magnitude as in the
previously estimated models, then we would have reason to conclude
that the models may be picking up control cost variations rather than
air pollution damages.
As noted previously, the data required to conduct the above test
are not available. No control cost data have been published for 3-
digit SlCs at the county level. The lowest level of aggregation
* Since 1973 was the first year of the survey, the Census Bureau
observed that some plants did not properly understand the purpose of
the survey, and therefore under-reported their pollution control
costs. To see if any of these industries were affected, we
recalculated these percent figures using 1974 survey data. None of
the figures were found to differ in any significant way.
7-198
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available is for 2-digit SICs at the SMSA level. The test described
above was therefore conducted using the 2-digit SIC data for SMSAs.
The results of this test are described below.
The data on pollution control costs described above were
assembled for those SMSAs for which control cost data were available
and for which SMSA air quality data had been developed as part of the
household sector analysis reported in Section 4. Generally, this
included most of the largest SMSAs in the country. The data used were
for 1973, the year closest to that used in the manufacturing sector
analysis (1972). Three industries were analyzed in detail, SICs 344,
346, and 354 (actually, the 2-digit SICs containing these industries),
since these industries had the largest pollution control costs rela-
tive to value of shipments. The cost of pollution control was taken
to be the "operating cost for air pollution control" as defined in the
table in the previous subsection.* The measure of air quality for
each industry was taken to be the same as that used in the final
economic model reported earlier for each industry.
Using the data described above, the following regressions
equations were estimated for each industry:
APCCOST VS
= a + b • — + c • TSPA2HI
N N
* Recall that this figure includes depreciation and therefore reflects
both capital and operating costs.
7-199
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APCCOSZ = a + b • S + c - TSPA2HI + d - S • TSPA2HI
N N N
where APCCOST = air pollution control cost
N = number of estblishirents
VS = value of shipments
TSPA2HI = ambient TSP concentration.
The idea behind these equations is that control cost per establishment
will increase with the size of the establishment and possibly with the
level of air pollution. If the latter proved to be true, we would
have some cause to reconsider the earlier results.
The results of the above regressions are provided in Table 7-39.
In the first equation for SIC 34, the coefficient for TSP is not
significant. In the second equation, the TSP coefficients are signi-
ficant, but the implied effect of air pollution at the sample mean is
negative. The third and fourth equations indicate similar results —
either the pollution variable is not significant or the implied
effect at the sample mean is negative. In the results for SIC 35,
none of the pollution variable coefficients are significant.
One conclusion to be drawn from the above analysis is that these
data do not provide any indication that pollution control costs were
7-200
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TABLE 7-39.
RELATIONSHIP BETWEEN AIR POLLUTION CONTROL COST
AND AMBIENT AIR POLLUTION
(t-statistics are shown in parentheses)
SIC
code
34
34
34*
34*
35
35
E
*
N
Adj. R2
Cond(x)
Estimated coefficients Regression
statistics
Constant VS/N TSP (TSP)(VS/N) N Adj. R2 Cond(x)
-1.2E-3 9.1E-4 1.9E-6 17 0.525
(-0.96) (3.80) (0.23)
8.5E-3 -2.5E-3 -6.0E-5 2.0E-5 17 0.748
(3.05) (-2.62) (-3.35) (3,66)
4.42 3.07 -2.82 17 0.458
(0.51) (3.87) (-1.60)
31.81 -26.47 -8.30 5.84 17 0.524
(1.78) (-1.54) (-2.31) (1.72)
-1.4E-4 6.0E-4 -2.3E-6 14 0.259
(-0.20) (2.45) (-0.50)
-1.5E-3 1.1E-3 6.5E-6 -3.5E-6 14 0.205
(-0.54) (1.04) (0.36) (-0.51)
= Exponential notation; i.e., l.OE-3 = 1.0 x 10 .
= All variables in log form. This form not estimable for SIC
SMSA had a zero value for pollution control cost.
= Number of observations.
2
= R adjusted for degrees of freedom.
= Condition number for the x matrix. Values greater than 100
10.2
50.5
62.9
204.5
9.2
54.0
35 since one
indicate high
collinearity anong the independent variables and thus imprecise
coefficient estimates.
7-201
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higher in areas with higher air pollution.* Hence, these data do not
provide any basis for concluding that air pollution control costs,
rather than air pollution damages, were the reason for the earlier
finding of higher production costs in polluted areas.
SUMMARY AND CONCLUSIONS
The purpose of this analysis has been to estimate the benefits
arising in the manufacturing sector from an improvement in air
quality. The study has focused on benefits in the form of reduced
materials damage and soiling. Six specific industries, accounting for
about 8 percent of the value added in the manufacturing sector, were
studied in detail. For these industries, it is estimated that attain-
ment of alternative secondary national ambient air quality standards
for S02 and TSP could yield benefits (cost savings) ranging as high as
2.6 percent of average total production costs.
The estimated cost savings represent gross benefits to these
industries from attainment of the standards. The costs of air pollu-
tion control equipment that these industries and others may incur to
attain the standards are being estimated in a separate EPA study.
* The finding of no association, or of a negative association, between
control costs and air pollution can be explained in a variety of
ways. These include: (1) data limitations and (2) the possibility
that ambient concentrations are higher in some areas precisely
because control expenditures are lower in those areas.
7-202
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The benefits described above were estimated using statistical
models of production costs in each of the industries. In many
respects, this approach represents a considerable advancement in the
empirical measurement of air quality benefits in this sector.
Important characteristics of the models used are that they: (1) yield
estimates consistent with the theoretical definition of benefits, (2)
allow for behavioral adjustments on the part of affected firms, (3)
use real world data rather than extrapolations from controlled labora-
tory experiments, (4) identify a broader range of air pollution
effects compared to more conventional approaches, and (5) appear
plausible and robust according to a variety of criteria.
As with most statistical analyses, the findings of this study are
in the form of identified statistical associations. In this case, the
findings were that total costs of production in certain industries are
positively associated with local ambient TSP/SCU concentrations, after
accounting for other sources of cost variation (e.g., input prices,
in-place capital, and climate). These findings are, of course,
contingent upon the assumptions made in the analysis and do not prove
the existence of a cause-and-effeet relationship. However, we believe
that the physical evidence from other studies, and the supporting
anecdotal evidence collected as a small part of this study, are
consistent with the kinds of air pollution effects identified here.
In view of this, we believe that the findings of this study are
suggestive of a cause-and-effect relationship.
7-203
-------
An effort was made to isolate one potentially important source of
spurious correlation. This was the possibility that production costs
in polluted areas might be higher because air pollution control regu-
lations are stricter, and thus pollution control costs are higher. An
examination of available pollution control cost data yielded no
evidence to suggest that our analysis had been affected in this way.
As a final note, it should be stressed that the estimates
reported in this study are in several respects conservative estimates
of the potential benefits to the manufacturing sector from improved
air quality. First, as noted previously, this analysis has focused on
six specific industries representing less than 10 percent of all
manufacturing activity. Second, several industries not considered in
the analysis, because of data limitations, may account for a dispro-
portionately large share of benefits. One example is the petroleum
refining industry, which is characterized by wide-ranging networks of
metal storage tanks, piping, and processing towers exposed to atmos-
pheric pollution.
Third, not included in the estimated benefits is the affect that
improved air quality may have on wage rates, and thus labor costs in
the manufacturing sector. Evidence suggests that workers receive a
wage premium for jobs in heavily polluted areas (see Section 6).
Thus, improvements in air quality may yield additional savings in
labor costs which are not reflected in the benefits reported earlier.
7-204
-------
REFERENCES
1. U.S. Environmental Protection Agency, Environmental Criteria and
Assessment Office, Office of Health and Environmental Assessment,
Office of Research and Development. Effects on Materials.
Chapter 10 in: Air Quality Criteria for Particulate Matter and
Sulfur Oxides, Volume III: Welfare Effects. April and October
1980 drafts.
2. McFadden, J. E. and M. D. Koontz. Sulfur Dioxide and Sulfates
Materials Damage Study. GEOMET, Inc., EPA Contract No. 68-02-
2943. February 1980.
3. U.S. Department of Commerce, Bureau of the Census. Pollution
Abatement Costs and Expenditures, 1978. MA-200(78)-2,
U.S. Government Printing Office, Washington, DC, 1980. p. 10.
4. Ibid, p. 24.
5. An example application of the weak separability assumption
applied to the manufacturing sector is: Fuss, Melvyn A. The
Demand for Energy in Canadian Manufacturing. Journal of
Econometrics, 5:89-116, 1977.
6. A discussion of the implications of perfect complementarity for
analysis of production can be found in: Denny, Michael and J.
Douglas May. Homotheticity and Real Value-Added in Canadian
Manufacturing. Chapter III.3 in: Fuss, Melvyn and Daniel
McFadden (eds.). Production Economics: A Dual Approach to
Theory and Applications (2 Vols.). North-Holland Publishing
Company, Amsterdam, 1978.
7. For a discussion of this application of duality see: Fuss
(1977), op. cit. A more general reference is: Shephard, R. W.
Cost and Production Functions. Princeton University Press,
Princeton, New Jersey, 1953 and 1970.
8. See, for example, Christensen, Laurits R., Dale W. Jorgenson and
Lawrence J. Lau. Transcendental Logarithmic Production
Frontiers. Review of Economics and Statistics, 55:28-45, 1973.
9. Diewert, W. E. An Application of the Shephard Duality Theorem:
A Generalized Leontief Production Function. Journal of Political
Economy, 79:481-507, 1971.
10. The elasticities of substitution and price elasticities of demand
for the translog cost function can be found in: Berndt, Ernst R.
and David 0. Wood. Technology, Prices, and the Derived Demand
for Energy. Review of Economics and Statistics, 57:259-263,
1975.
7-205
-------
11. This definition for scale economies can be found in:
Christensen, Laurits R. and William H. Greene. Economies of
Scale in U.S. Electric Power Generation. Journal of Political
Economy, 84:655-676, 1976.
12. An excellent discussion of systematic testing of hypotheses in
econometric studies of production can be found in Fuss, Melvyn,
Daniel McFadden, and Yair Mundlak. A Survey of Functional Forms
in the Economic Analysis of Production. Chapter II.1 in: Fuss
and McFadden (1978), op. cit.
13. Hildebrand, George H. and Ta-Chung Liu. Manufacturing Production
Functions in the United States, 1957: An Interindustry and
Interstate Comparison of Productivity. The New York State School
of Industrial and Labor Relations, Ithaca, New York, 1965.
14. Moroney, J. R. The Structure of Production in American
Manufacturing. The University of North Carolina Press, Chapel
Hill, North Carolina, 1972.
15. Field, Barry C. and Charles Grebenstein. Capital-Energy
Substitution in U.S. Manufacturing. Review of Economics and
Statistics, 62:207-212, 1980.
16. Caddy, Vern. Empirical Estimation of the Elasticity of
Substitution. Preliminary Working Paper No. OP-09. Industries
Assistance Commission, Melbourne, 1976.
17. Christensen, Laurits R. and Dale W. Jorgenson. The Measurement
of U.S. Real Capital Input, 1929-1967. The Review of Income and
Wealth, 15:293-320, 1969.
18. U.S. Department of Labor, Bureau of Labor Statistics. Capital
Stock Estimates for Input-Output Industries: Methods and Data.
Bulletin 2034. U.S. Government Printing Office, Washington, DC,
1979.
19. Ibid. Appendix C.
20. Field and Grebenstein (1980), op. cit.
21. Christensen and Jorgenson (1969), op. cit.
22. Hall, Robert E. and Dale W. Jorgenson. Tax Policy and Investment
Behavior. American Economic Review, 57:391-414, 1967.
23. Coen, Robert M. Effects of Tax Policy on Investment in
Manufacturing. Papers and Proceedings of the American Economic
Association, 58:200-211, 1968.
7-206
-------
24. Pogue, Gerald A. Estimation of the Cost of Capital for Major
United States Industries with Application to Pollution-Control
Investments. EPA-230/3-76-001, 1975.
25. Field and Grebenstein (1980), op. cit.
26. Board of Governors of the Federal Reserve System. Federal
Reserve Bulletin. Volume 62, 1976. p. A28.
27. See, for example, Hall, Robert E. and Dale W. Jorgenson, gp_. cit.
pp 394-395.
28. U.S. Internal Revenue Service. Report of the Commissioner of
Internal Revenue, 1972-73. p. 122. Data are reported on a
fiscal year basis; data used in this study are for FY 1973,
covering the period July 1972 to June 1973.
29. U.S. Department of Commerce, Bureau of the Census. Statistical
Abstract of the United States, 1974. U.S. Government Printing
Office, Washington, DC, 1975. p. 418. Data are reported on a
fiscal year basis; data used in this study are for FY 1973,
covering the period July 1972 to June 1973.
30. U.S. Department of Commerce, Bureau of Economic Analysis. Survey
of Current Business. January 1976. p. 52. For consistency with
the data on state and Federal corporate income taxes referenced
above, an average of the figures for 1972 and 1973 was used.
31. Christensen and Jorgenson (1969), op. cit. p. 297.
32. U.S. Department of Labor, Bureau of Labor Statistics. Handbook
of Labor Statistics, 1978. Bulletin 2000. U.S. Government
Printing Office, Washington, DC, 1979. Index is BLS Code Number
11: Machinery and Equipment.
33. See, for example, Berndt and Wood (1975), op. cit.; and Denny and
May (1978), op. cit. The latter study is of Canadian
manufacturing.
34. Diewert, W. E. Exact and Superlative Index Numbers. Journal of
Econometrics, 4:115-145, 1976.
35. Hulten, Charles R. Divisia Index Numbers. Econometrica,
41:1017-25, 1973.
36. U.S. Department of Commerce, Bureau of the Census. Census of
Manufactures. Vol. II: Industry Statistics, was used for 1972
and 1967. Vol. I: Subject Statistics, was used for 1963 and
1958.
37. U.S. Department of Agriculture, Statistical Reporting Service,
Crop Reporting Board. Agricultural Prices. Various years.
7-307
-------
38. Ibid.
39. U.S. Department of Commerce, Bureau of the Census. Census of
Manufactures. Vol. II: Industry Statistics.
40. U.S. Department of Commerce, Bureau of the Census. Current
Industrial Reports. Series M26A. Various years.
41. U.S. Department of Commerce, Bureau of the Census. Census of
Manufactures. Vol. I: Subject Statistics, and Vol. II:
Industry Statistics.
42. U.S. Department of Labor, Bureau of Labor Statistics. Handbook
of Labor Statistics, op. cit. Index is BLS Code Number 10-13:
Steel Mill Products.
43. For an excellent discussion of this problem in the context of
Cobb-Douglas ans CES production structures, see Moroney, op.
cit., Chapters 2 and 3. The bias arises because use of VQ in
place of Q means in effect that measurement error is present in
the output variable.
44. Price determination in manufacturing industries has been studied
extensively. One recent example which considers price
determination using national data is Straszheim, Donald H. and
Mahlon R. Straszheim. An Econometric Analysis of the
Determination of Prices in Manufacturing Industries. Review of
Economics and Statistics, 58:191-201, 1976.
45. The details of the Producer Price Index are described in: U.S.
Department of Labor, Bureau of Labor Statistics. BLS Handbook of
Methods, Bulletin 1910. U.S. Government Printing Office,
Washington, DC, 1976, Chapter 14. The indices themselves are
available in the Bureau's publication: Handbook of Labor
Statistics, op. cit. The Bureau also publishes an industry price
index series for 4-digit SICs. Use of the latter would have been
preferable since they are organized around industries rather than
commodities. However, use of the industry price indices was not
possible, since complete coverage of the relevant 3-digit SIC
industries is not provided (only selected 4-digit SICs are
included), and many of the indices do not cover a long enough
time period for statistical estimation purposes.
46. Ibid, p. 110.
47. U.S. Department of Commerce, Bureau of the Census. Census of
Manufactures. And: Annual Survey of Manufactures. U.S.
Government Printing Office, Washington, DC. Various years.
48. Wharton EFA, Inc. The Wharton EFA Annual Model: Historical
Tables, 1955-1976. Data are for the user cost of capital.
7-208
-------
49. See for example, Kmenta, Jan. Elements of Econometrics.
MacMillan, New York, 1971.
50. Ibid. Section 8.2.
51. See for example, Pindyck, R. S. and D. L. Rubinfeld. Econometric
Models and Economic Forecasts. McGraw-Hill, New York, 1976. pp.
187-9.
52. Calculated as value of shipments divided by quantity of
shipments, for a sample of products for which quantity data in
tons were available. Source: 1972 Census of Manufactures, op.
cit., Vol. II. pp. 34C-22 to 34C-28.
53. The U.S. average revenue per ton mile for rail shipments of the
products of SIC 344 was 3.74 cents in 1975. This figure was
adjusted to 1972 using the ratio of the U.S. average for all
shipments in 1972 (2.012) and 1975 (2.490). All three figures
are from: U.S. Department of Transportation, Federal Railroad
Administration. 1975 Carload Waybill Statistics, 1976.
54. For a proof of this statement, see: Kmenta, J. (1971), op. cit.
Section 9-3
55. Christensen and Greene, op. cit. pp. 662-663.
56. Barten, A. P. Maximum Likelihood Estimation of a Complete System
of Demand Equations. European Economic Review, 1:7-73, 1969; as
cited in Christensen and Greene, op. cit.
57. Kmenta, J. and R. F. Gilbert. Small Sample Properties of
Alternative Estimators of Seemingly Unrelated Regressions.
Journal of the American Statistical Association, 63:1180-1200,
1968. And, Dhrymes, P. J. Equivalence of Iterative Aitken and
Maximum Likelihood Estimates for a System of Regression
Equations. University of Pennsylvania, unpublished, 1970; as
cited in Christensen and Greene, op. cit.
58. Berndt, E. R.f M. A. Fuss, and L. Waverman. Dynamic Adjustment
Models of Industrial Energy Demand: Empirical Analysis of U.S.
Manufacturing, 1947-1974. Economics Research Group Ltd. A
report prepared for the Electric Power Research Institute (EA-
1613), Palo Alto, CA, 1980.
59. Christensen and Greene, op. cit. p. 663.
60. John W. Ryan, e_t a_l. An estimate of the Non-Health Benefits of
Meeting the Secondary National Ambient Air Quality Standards.
SRI International, 1981. p. 35.
61. U.S. Environmental Protection Agency (1980), op cit. pp. 10-60
to 10-63.
7-209
-------
62. U.S. Office of the Federal Register. Code of Federal
Regulations. Title 21 (Food and Drugs), Part 110, April 1, 1980.
63. Pollution Abatement Costs and Expenditures, op. cit. Annual,
beginning with data for 1973.
7-Z10
-------
APPENDIX
FINAL MODELS
7-211
-------
SIC 201
(Model 5)
MODEL: siczoicc NOB = 14 NOUAR = 13 NOEQ = 3
OPT ALGORITHM: DAVIDON-FLETCHER-POUELL
OPT OPTIONS: RADIUS = i. CONCR - o.ooi ITER LIMIT = 10
INITIAL S MATRIX.1 RESIDUALS CALCULATED FROM INITIAL COEFFICIENT ESTIMATES
ITERATIVE 3SLS SELECTED? ITER LIMIT = 15 CONCR = 0,001
INITIAL H-INVERSE! DEFAULT START
COEF
D4
03
Dl
BOO
BO
P03
A13
B01
AO
All
A3
Al
A23
0.
0.
VALUE
.01599
,055122
0.022065
-0,114,479
1.22784
0.014412
0.001289
-0.009781
-0.188223
0.020634
0.926742
0.030261
0.036067
STD ERR
0.012033
0.03002
0.011846
0.04144S
0.067045
0.012881
0.027974
0.010251
0.094145
0.024903
0.048156
0.038511
0.009948
T-STAT
1.32688
1.83416
1.86267
-2.81524
18.3139
1.13441
0.04606
-0.954147
-1.99886
0.82855
19,2449
0.785775
3.62558
SINGLE EQUATION STATISTICS
EON 59
EON 60
EON 41
RSO !
0.02004 .'
0.043566 !
0.994924 !
= = = ==« = = =. = = = = • «-,;
CRSQ !
-0.273947 I
-0.243345 !
0.934019 !
SSR !
0,00777 A !
0.012418 !
0.029976 !
DU
1 .45391
1 .67763
2.46226
7-212
-------
SIC 202
(Model 4)
MODEL: siC202cc NOB = 27 NOVAR = 17 NOEQ = 3
OPT ALGORITHM: DAVIDON-FLETCHER-POWELL
OPT OPTIONS: RADIUS = i. CONCR = o.ooi ITER LIMIT
INITIAL s MATRIX: RESIDUALS CALCULATED IN 2 STAGE REGRESSION
ITERATIVE 3SLS SELECTED! ITER LIMIT = 20 CONCR = 0.001
INITIAL H-INVERSE: DEFAULT START
COEF
C13
Cll
D4
03
01
BOO
BO
B03
A13
B01
AO
All
A3
Al
A23
C31
C33
-0
VALUE
0.004429
0.002142
148168
0.108624
0.055398
0.032494
0.938742
0.018364
0.019939
0.002315
0.024699
0.002895
0.951407
0.073643
0.02612
0.003976
0.004735
STD ERR
0.00821
0.004182
0.036868
0.06611
0.039568
0.081639
0.098847
0.008118
0.016701
0.00464
0.18179
0.010428
0.051073
0.029719
0.02494
0.007343
0.014466
T-STAT
0.539444
0.512124
-4.01892
-1.64309
1.40008
0.398015
9.4969
2.26204
-1.19386
-0.498847
0.135863
0.277578
18.6283
2.47799
1.04731
-0.541556
-0.327287
SINGLE EQUATION STATISTICS
EON 59
EON 60
EON 61
RSO !
-0.044222 !
0.247026 !
0.973085 !
CRSO !
-0.292846 !
0.067747 !
0.930021 !
SSR !
0.005592 !
0.017258 !
0.32025 f
DU
2.66581
2.8255
2.306
7-213
-------
SIC 265
(Model 3)
MODEL: sic26scc NOB = 19 NOVAR = is NOEQ » 3
OPT ALGORITHM: DAVIDON-FLETCHER-POWELL
OPT OPTIONS: RADIUS = i. CONCR = o.ooi ITER LIMIT
INITIAL s MATRIX: RESIDUALS CALCULATED IN 2 STAGE REGRESSION
ITERATIVE 3SLS SELECTED! ITER LIMIT = 20 CONCR = 0.001
INITIAL H-INVERSE: DEFAULT START
10
COEF
C13
Cll
D4
D3
D2
Dl
BOO
BO
B03
A13
B01
AO
All
A3
Al
A23
C31
C33
VALUE
-0.056966
0.006643
-0.053662
0.166152
0.014679
0.04903
-0.524395
1.57907
0.068424
-0.088244
-0.047233
-1.10969
0.079713
0.727346
0.310779
0.028562
-O.010479
0.040971
STD ERR
0.
0.
0.
0.021254
0.012082
.015297
.059464
.022646
0.036463
0.110037
0.130604
0.021519
0.061654
0.022029
0.222091
0.065953
0.12209
0.13588
0.024214
0.011886
0.021012
T-STAT
-2.68018
0.549833
-3.50811
2.79415
0.648192
34464
76564
0905
3.17975
-1.43126
-2.14408
-4.99656
1.20864
5.95746
2.28716
1.17956
-0.881591
1.94986
1
-4
12
SINGLE EQUATION STATISTICS
t
EON 59 !
EON 60 !
EQN 61 i
RSO
0.592409
0.551438
0.975898
CRSQ I
0.435643 !
0.378914 !
0.56617 !
SSR t
0.013129 !
0.012848 !
0.040331 !
nu
2.41964
2.61386
2 . OOO56
7-214
-------
SIC 344
(Model 4)
MODEL: siC344cc NO* = 35 NOVAR * 17 NOEO » 3
OPT ALGORITHMS DAVIDGN-FLETCHER-POWELL
OPT OPTIONS? RADIUS » 1. CONCR « 0.001 ITER LIMIT
INITIAL s MATRIX: RESIDUALS CALCULATED IN 2 STAGE REGRESSION
ITERATIVE 3SLS SELECTED: ITER LIMIT = IS CONCR - 0.001
INITIAL H-INVERSE: DEFAULT START
10
COEF
C13
C12
D4
D3
D2
BOO
BO
B03
A13
B01
AO
All
A3
Al
A23
C32
C33
VALUE
-0.033239
0.024791
0.055082
0.077029
0.053408
0.020619
1.10556
0.077057
-0.154229
-0.069934
-0.622765
0.125884
0.785412
0.190601
-0.026183
-0.034544
0.046975
STD ERR
0.
0.
0.020766
0.022942
.031764
.056576
0.0621
0.097649
0.041859
0.017442
0.045073
0.015405
0.198932
0.040335
0.122274
0.097118
0.043553
0.025946
0.023456
T-STAT
-1.6006
1.08058
1,7341
1.36151
0.860038
0.211152
26.4112
4.41781
-3.42175
-4.53975
-3.13053
3.12093
6.42338
1.96258
-0.601175
-1.33139
2.00271
SINGLE EQUATION STATISTICS
!
EON 59 !
EON 60 !
EQN 61 !
RSO
0.526163
0.546438
0.980194
CKSU
0.444467
0.468238
0 . 962588
SSR
0.044039
0.056314
0.136196
DU
2.06003
2.06482
2.72023
7-215
-------
SIC 354
(Model 4)
MODEL: SIC354CC NOB = 22 NOVAR * \7 NOEQ » 3
OPT ALGORITHM: HAVIDON-FLETCHER-POUELL
OPT OPTIONS: RADIUS =• i. CONCR =« o.ooi ITER LIMIT
INIJIAL s MATRIX: RESIDUALS CALCULATED IN 2 STAGE REGRESSION
ITERATIVE 3SLS SELECTED: ITER LIMIT - 15 CONCR - 0,001
INITIAL H-INVERSE: DEFAULT START
10
COEF
D4
D3
D2
C13
C12
BOO
BO
BOS
A13
B01
AO
All
A3
Al
A23
C32
C33
VALUE
O.048762
0.108449
0.064971
O.029043
057925
016255
894938
034914
0,020913
O.015402
813007
0.00696
0,382423
0,492803
040735
066223
0.
0,
0.
0,
-0
0,
-0.
0.035415
STD ERR
0.033055
0.093383
0.073244
0.025298
0.020982
0.06661
0.061322
0,017135
0.034567
0,012328
0.347098
0.024536
0.165675
0.104719
0.060365
0.029149
0.035181
T-STAT
-1.4752
-1,16133
-0,887051
-1.14805
2,76077
0,244036
14,5941
2.03761
0,604997
-1.24939
-2.3423
0.283645
2,30827
4,70595
0,674809
-2,27192
1.00664
SINGLE EQUATION STATISTICS
1
! EON 59
! EGN 60
! EGN 61
RSQ
0.241375
0.323859
0.990813
CRSQ !
0.004305 !
0,112566 i
0.961413 !
SSR !
0,017166 i
0.033052 !
0.061161 !
DU
2.47183
2.32377
2.1447
7-216
-------
SECTION 8
ELECTRIC UTILITY SECTOR
-------
SECTION 8
ELECTRIC UTILITIES
INTRODUCTION
Electric utilities in the United States generate the majority of
their electricity through the combustion of fossil fuels including
coal, oil and natural gas. As a result of this combustion, electric
utilities are a major source of sulfur dioxide, particulates, and
other emissions. At the same time, however, electric utilities have a
large investment in plant and equipment which (potentially) may be
affected by corrosive elements in the atmosphere.
This dual role of the electric utility (both a source of
emissions and a receptor for the resulting air pollution) means that
air quality regulations may both impose costs and confer benefits on
the utility sector. The purpose of this analysis is to estimate the
benefits to the utility industry from improvements in ambient air
quality. The costs of air pollution controls required to bring about
the improved air quality are being estimated in a separate EPA study.
The benefits estimated below are based upon a statistical model
of the costs of maintenance (and operation) at electric utility
plants. Thus, the results are based on an approach which differs
significantly from the more common dose-response (damage function)
8-1
-------
studies. One advantage of a statistical study is that it permits us
to draw conclusions about the "average" plant rather than relying on
*
experimental controls to ensure that the study results can be applied
to plants not included in the experiment. Of course, there are
disadvantages also to statistical studies. In order for the model to
be reasonably tractable computationally, it is necessary to make
simplifying assumptions which in some cases depart from reality. In
addition, it is often the case that data for the variables included in
the theoretical model are not available. In that case, surrogates
must be used and, as a result, the conclusions of the study depend on
the choice of these surrogates. For these reasons, we have attempted
to examine the sensitivity of our results to at least some of the more
important assumptions we have made. These analyses make it possible
for the reader to draw inferences about the robustness of the results.
We have limited our statistical analysis to the production of
electric power by privately-owned steam-electric utility plants. We
have considered only those plants which produce electricity by the use
of fossil fuels (coal, oil and natural gas).* It is this segment of
the industry that not only may suffer from the effects of worsened air
quality, but also contributes significantly to the air pollution in
the local region.
* Excluded from the statistical analysis, therefore, are nuclear
plants, hydroelectric plants, gas turbine plants, and internal
combustion plants.
8-2
-------
We have further restricted our statistical analysis to the
production or generation phase of electric power. The effects of air
quality on the costs of transmission or distribution are not
considered here. The reason for this was primarily one of data
availability. While electricity generation takes place at a point,
and therefore, the air quality related to it is measurable,
transmission often is accomplished over relatively long distances
making it subject to varying levels of air quality. To test
statistically for an adverse effect of air quality on transmission
would require that an arbitrary assignment of varying levels of air
quality be applied to the capital equipment employed.* For the same
reason, the effect of air quality on the costs of electricity
distribution was not assessed as a part of the statistical analysis.
Rough estimates of benefits for transmission and distribution are
developed, however, in Section 10 of this report.
The plants used in our final sample include approximately 120
plants throughout the country that are privately owned and fired by
fossil fuels. These plants constituted approximately 22 percent of
the installed generating capacity and 22 percent of the total
generation of electricity in 1972, the year analyzed. Since they were
not selected as a random sample from a larger population (the choice
* It is possible to consider the effects of air pollution on
individual components of the transmission network. For example,
individual transmission towers can be matched to local air quality
and a valid statistical analysis conducted. For an example of this
approach, see Haynie (1).
8-3
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was restricted primarily by air quality data availability), the
extension of the results from the statistical analysis to other plants
depends on the extent to which the plants in our sample are
representative of other plants. For this reason, we estimated total
benefits in many ways in order to put bounds on the likely effect.
The general approach followed is to estimate statistically an
equation which relates the cost of producing a given level of output
to specified values of other variables such as input prices. In this
analysis, we are primarily concerned with the cost of maintenance.
Thus, we relate total maintenance costs of the individual plants to
selected variables thought to affect the cost. In addition to air
quality, the variables used include capacity, age of plant,
utilization rate, rainfall, sulfur content of fuel, selected prices,
and other variables which attempt to capture effects other than those
associated with air quality. From the results of these statistical
analyses, we estimate the effect on costs from a change in air quality
holding other factors constant. These changes are then applied to
those plants in counties where an improvement in air quality is
required in order for the county to be in compliance with the
Secondary National Ambient Air Quality Standards (SNAAQS).
There are two important factors that, in the case of electric
utilities, may be important in our analysis. The first is that, as
noted above, the generating plant may be affected by pollution as well
as being a source of pollution. Therefore, there is the danger that
8-4
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any positive association between maintenance costs and the level of
ambient air quality is spurious. Instead of reflecting the damages
done by corrosive elements in the air, the results may reflect the
increased amounts of maintenance that may be required to comply with
local air quality regulations — regulations that may be stricter in
"dirty" areas than in "clean" areas.
The second limitation was also alluded to above. As a major
contributor to local air pollution, the operators of the plant take
into account in their production decisions the effects of air quality
on their costs and thus may try to offset these effects by emitting at
lower levels. The result is that there is some question as to whether
the level of air quality can appropriately be taken as given (i.e.,
exogenous). The use of the statistical techniques employed in this
analysis require that the independent variables can be assumed
exogenous. To the extent that this is not true for the plants we have
used in this study, the estimated effects of air quality may be
biased. We discuss both of these limitations in the sections that
follow.
Given the above limitations and the detailed assumptions
discussed in the body of this chapter, we find that the cost of
electricity generation is positively related to the ambient level of
SC^. We estimate the discounted present value in 1980 of the benefits
associated with the attainment of alternative secondary standards for
S02 to be between $0.0 and $123.6 million (1980 dollars). As shown in
8-5
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Table 8-1, benefits associated with attainment of the current 3-hour
secondary standard are estimated to be zero. Benefits for an
alternative 24-hour secondary standard of 260 ^g/m are estimated to
be $123.6 million. Benefits for an alternative secondary standard of
60 Mg/m (annual arithmetic mean) are estimated to be $68.7 million.
These estimates represent savings in operation and maintenance (O&M)
costs. Savings in maintenance cost alone are about 40 percent of the
above estimates.
The relationship between the cost of electricity generation and
the ambient level of TSP concentrations was generally positive but not
statistically significant at the 5 percent level.
TABLE 8-1. ESTIMATED BENEFITS TO PRIVATELY-OWNED, FOSSIL FUEL-FIRED,
STEAM-ELECTRIC PLANTS*
Savings
category
Current
3- hour**
SO2 Standard
Alternative
24-hour
Alternative
annual mean
Maintenance 0.0 55.76 26.19
Operation and
maintenance 0.0 123.63* 68.66
* Millions of 1980 dollars discounted to 1980 with a discount rate of
10 percent.
** 24-hour equivalent of the current 3-hour standard (1300 /j.g/m ).
-i- This estimate is based on a coefficient with a significance level
of 0.13. The other estimates are based on coefficients significant
at the 0.05 level.
8-6
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The remainder of Section 8 is divided into four major sections.
The theory underlying the statistical analyses is discussed in the
following section. In the second section, the empirical results from
the cost equation estimation are presented and discussed. Additional
results are also presented there in order to provide some evidence on
the sensitivity of the results obtained to selected assumptions. The
third section contains a detailed discussion of the estimation of the
benefits in the electric utility sector related to improvements in the
air quality required to comply with selected regulations. Our
conclusions are presented in the fourth section.
THEORY
The theory on which our estimation results are based is discussed
in this section. (See Section 2 above for a discussion of the theory
of benefits estimation.)
The focus of this analysis is somewhat different from that
underlying many of the previous economic analyses of electricity
generation.* Rather than analyzing the process of electricity
generation, we are primarily interested in the effect of one factor —
* Cowing and Smith (2) provide a review of econometric analyses of
electric utility production and cost functions. Because of the
large data base available, many of these studies use electricity
generation for the econometric tests. It is this literature that is
summarized in the Cowing and Smith review.
8-7
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air quality. Although the two are interrelated, the problem being
investigated leads us to emphasize one particular portion of the
production process. Thus, we develop relatively more detailed models
for certain portions of the production process than previous studies.
Rather than including factors other than fuel, labor, and capital in
the error term, as have most other studies (since the problem under
investigation was different), we explicitly include other factors such
as air quality in the equation to be estimated. At the same time, we
consider primarily the maintenance costs rather than the total costs
of production.
The utility is assumed to face a production function for
electricity generation of the following form:
Q = f1(L,F,Ke) (8.1)
where Q represents output, L represents labor, F represents fuel, and
Ke represents "effective" capital. At this point, the particular
functional form (e.g., Cobb-Douglas, etc.) is not specified.
Effective capital represents the productive capability of the plant
after taking account of the effects of corrosion. The effective level
of capital is related to air quality in the following way:
Ke = f2(M,S,R,K) (8.2)
8-8
-------
where M represents maintenance resources, S represents air quality, R
represents weather variables (such as precipitation), and K represents
gross capital.
Air quality in a region is assumed to be generated according to:
S = f3(E0,EM,W) (8.3)
where E represents emissions of the pollutant from the plant, £„
represents emissions from other sources, and W represents appropriate
weather variables. Finally, "own" emissions (EQ) are generated
according to:
E0 = f4(Q,Cv) (8.4)
where Cv represents air pollution control resources (e.g., sulfur
content of fuel) selected by the plant.
In our analysis, we take gross capital as fixed. That is, the
analysis is of an ex post production process. (Although not of major
importance for the period used in the empirical analysis, any fixed
air quality control resources — e.g., flue-gas desulfurization
systems — are also taken as fixed.) This assumption is reasonable
given the plants used in the empirical analysis. Further, it implies
that the capital bias induced by rate-of-return regulation need not be
considered in this analysis. This approach also implies that some of
8-9
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the costs incurred by the firm because of ambient air quality will not
be included in our estimates. Specifically, a firm might use
different methods of construction or different materials in
construction to partially offset the maintenance costs affected by air
quality. Because the capital is taken as fixed, such preventative
expenditures will not be captured in our analysis. Hence, benefits
estimates may be understated.
Inspection of Equations (8.1) to (8.4) indicates how
consideration of the plant's emissions causes problems for the
derivation of the cost function. In general, the (ex post) cost
function for the plant is found by solving the following optimization
problem:
minimize prL + pMM + p F + pvC
L,M,F,CV U " V (8.5)
subject to Equations (8.1) to (8.4)
where, in (8.5), the p^ represent the prices of the (variable) inputs:
labor, maintenance, fuel, and control resources. Even for relatively
simple forms of the equations, the solution to (8.5) does not lead to
a closed form solution for the cost function. The problem is that,
through its actions, the plant can influence air quality so that the
firm has, as one of its inputs, its own output (suitably transformed).
In order to make the problem tractable, additional assumptions were
made.
8-10
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The existence of air quality regulations, implemented by the use
•
of emission constraints, may affect the firms' choices. To see this,
we add:
Ec >_ f4(Q,Cv) (8.6)
where E_ is the maximum level of emissions allowed (by regulation) for
c
a given level of output. (Nothing below is altered if we write the
constraint in terms of the amount of fuel consumed.) Constraint (8.6)
will be binding if it forces a plant to emit at a lower level than it
otherwise would for a given output.* In this case, (8.6) becomes:
Ec = f4(Q,Cv) (8.6')
* A second implication of this assumption is that, if the constraint
is binding, the firm would be willing to pay some positive amount
for relaxation of the constraints. An example of such willingness-
to-pay might be lobbying efforts by utilities for relaxation of air
quality regulations. The following quotation is appropriate in this
context:
Electric utilities, particularly those near deepwater ports,
started to convert from coal to oil and to build new oil-
fired units. This process was accelerated more recently
with the promulgation of strict sulfur (sic) oxide emission
control regulation. In the absence of a satisfactory,
commercially acceptable technology for the removal of sulfur
oxides from flue gases, and with the growing shortage in the
supply of natural gas, the use of desulfurized or naturally
low-sulfur oil offered the most viable solution to the
sulfur oxide pollution problem along the entire East Coast."
[FPC (3)]
8-11
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If (8. 6') holds, then, for a given level of output, GV is determined
for the plant and, holding outside factors such as exogeneous
emissions and weather constant (and imposing certain requirements on
the functional form), it determines the level of air quality through
equations (8.3) and (8.4). We assume throughout this analysis that
constraint (8. 6') does, in fact, hold.
An alternative would be to focus on the level of air quality
exogenously determined. In other words, we could "net out" the
portion of ambient air quality due to the firm. The difficulty with
this approach for our analysis (ignoring the problems associated with
determining the exogenous level of air quality) is that it is total
air quality which the firm must make expenditures to offset (if there
is an effect) and we would have to net out the plant's costs
associated with its air quality to develop measures of the effect of
air quality.
Given the above assumptions, the plant's cost minimization
problem becomes:
minimize pLL + pMM -f pFF
L,M,F (8.5')
subject to Equations (8.1) to (8.4) and (8.61).
Solving (8.5') provides the cost function for the firm. It will be of
the form:
8-12
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C = gdppfpK^CR) (8.7)
Equation (8.7) shows that the operations and maintenance (O&M) costs
for the firm are a function of input prices (assumed exogeneous),
capital, air quality, control resources, and precipitation (or other
weather variables). Since all of the independent variables are, by
assumption, exogenous, we can estimate the effect of air quality on
O&M costs by estimating Equation (8.7) given an assumed functional
form. We discuss alternative functional forms below.
From Equation (8.2), we see that air quality affects costs
through its effect on capital stock and thus on maintenance cost. The
effect of air quality on maintenance cost can be determined explicitly
using the total cost function given by Equation (8.7). In particular,
it has been proven that the input demand for each variable factor
(such as maintenance) can be found by partial differentiation of the
total cost function with respect to the price of each input
(Shephard's Lemma). Thus, the cost of maintenance, M*, is given by:
M* = pM = P dC/d (8.8)
Substituting in Equation (8.7) for C gives:
M* = PM 3g(PL/PF/PM/K,S,Cv,R)/3pM
= h(pL,pF,pM,K/S,Cv,R) (8.9)
8-13
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As with total operation and maintenance cost, the effect of air
quality on maintenance cost can be determined by estimating Equation
(8.9) for a given functional form.
In the following section, the results of our empirical analysis
of the cost functions are discussed. Although most of the discussion
concerns the maintenance cost function, results pertaining to total
O&M costs are also provided. Clearly, the results of our empirical
analysis depend on the model developed here and on the assumptions
underlying the model. Certain assumptions are required in all
empirical studies since the available data are limited. In the
discussion below, we attempt to test, to some extent, the sensitivity
of results to certain assumptions so that the robustness of the
results may be assessed.
COST FUNCTION ESTIMATION RESULTS
Before estimating the benefits associated with improved ambient
air quality, it is necessary to estimate the cost function relating
the costs incurred by the firm to the level of air quality. In this
section, we discuss the results of our estimation of this cost
function for the generation of electricity. The data used in the
estimation process are described in the first subsection. In the
second subsection, the functional form used is discussed. The results
for the full sample of plants for which data are available are
reported in the third subsection. In the fourth subsection, the
8-14
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sample is divided into subsamples to investigate further the effect of
•
air quality. The cost function for each of these subsamples is then
estimated and the result compared to that found for the full sample.
A fifth subsection presents a discussion of the extent to which
individual plants affect local air quality. That section contains the
results of estimating the emissions and air quality functions
discussed previously. A sixth subsection summarizes the results of
the empirical analysis.
Data
The estimation of the cost function is discussed below. The data
used in the estimation can be classified into four main groups: air
quality data, meteorological data, physical data, and cost data. The
source and description of the air quality and meteorological data are
provided in Section 3 of this report. Two Federal Power Commission
(FPC) reports* were the sources of the remaining data. Each of the
data items used in the estimation process are discussed separately.
Maintenance Cost—
The "Expenses" volume provides data on maintenance expenses in
five categories:
The two publications were FPC (4) and FPC (5), referred to below as
"Exnenses" and "Shai-i ct-i rs" .
"Expenses" and "Statistics".
8-15
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• Maintenance Supervision and Engineering
• Maintenance of Structures
• Maintenance of Boiler Plant
• Maintenance of Electric Plant
• Maintenance of Steam Plant.
Wages—•
One of the data items utilized in the estimation of the cost
function is the wage rate at the plant. Unfortunately, these data are
not published. The wage series was compiled as follows. From the
"Statistics" volume, we obtained total wages paid to production (i.e.,
generation) employees for each utility with one or more plants in the
sample. This number was divided by total production employees (steam-
electric, hydroelectric, and nuclear plants) at each utility,
available from FPC documents such as "Expenses". Note that this
approach implicitly assumes no systematic difference in average wages
across types of generation facilities within a given utility.
Although it might be expected that, for example, nuclear steam-
electric employees are paid differently than fossil steam-electric
employees, fossil steam-electric power is the predominant mode of
generation.
Fuel Prices—
Fuel price also enters the estimating equation as described
previously. A weighted average fuel price was computed based on
8-16
-------
number of Btu's consumed by fuel type (coal, oil, natural gas). These
data are provided in "Expenses".
Capacity and Age of Plant—
The installed generating capacity for each plant was obtained
from "Expenses". The date of initial installation was taken from
"Expenses". Although this assumes that all capacity was installed at
this date, a later section attempts to assess the sensitivity of the
results to this assumption. This assessment is based on age and
capacity data taken from Cowing and Smith (6).
Utilization Rate—
The utilization rate was calculated for each plant by dividing
net generation by capacity multiplied by 8,760 hours. These data were
taken from "Expenses".
Sulfur Content of Fuel—
The sulfur content of fuel consumed was computed from the data in
FPC (7), hereafter referred to as "Air Data". Data in that volume
include the sulfur content and quantity of fuel for coal, oil, and
natural gas. Sulfur content was taken to be a simple weighted
average.
Total Stack Height—
FPC (Air Data) was also the source for data on stack height.
Included there was the number of stacks at each plant, and the minimum
8-17
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and maximum height. Total stack height was taken to be the number of
stacks multiplied by the average of the minimum and maximum height.
Functional Form
Recall from the theory section above that the cost function was
not specified as to its form. In this subsection, we specify the
equations used in the primary portion of the analysis. In a later
subsection, where we discuss the appropriateness of the functional
forms used, we will be concerned solely with the maintenance cost
function. Thus, our results will be directed toward determining the
effect on maintenance cost resulting from a change in air quality.
Equation (8.9) of the previous section indicated the general form
of the maintenance function as:
M* = h(pL,pF,pM,S,R,K,Cv) (8.10)
where the p's are input prices, K represents "gross" capital, S
represents air quality, Cy represents control resources, and R
represents relevant weather variables. M* is total maintenance cost.
For the major part of our analysis, we assume that the Equation (8.10)
can be represented as a Cobb-Douglas cost function. Thus, we have
that Equation (8.10) can be written as:
8-18
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M* = a PL PF PM S R K UCV (8.11)
where a and the ji^'s are parameters.
The Cobb-Douglas form is quite restrictive in that it implies a
great deal about the underlying technology. However, it is important
to remember that we are estimating the cost function for a specific
portion of the underlying total cost function. Thus, even if the
total (O&M) cost function were not Cobb-Douglas (and recent empirical
work suggests that it is not), we cannot necessarily reject the
hypothesis that the maintenance cost function is approximately Cobb-
Douglas. Naturally, however, these results on the total O&M function
are reason enough to evaluate the possibility that the maintenance
cost function also cannot be adequately represented as a Cobb-Douglas.
This issue is addressed in a later section below.
Although the form of the maintenance cost function was specified
above, Equation (8.11) cannot yet be estimated. What remains is to
specify the variables for which data is available that will serve as
the surrogates for the independent variables given in Equation (8.11).
Unfortunately, data are not available for the price of maintenance
services. For this variable, we use two surrogate variables: the
wage rate and fuel price, which coincidentally already appear in the
equation. Capital is measured by several variables: capacity, age of
plant, and capacity utilization rate. Air quality is measured in
terms of sulfur dioxide (S02) and total suspended particulates (TSP).
8-19
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Various measures of these variables are used in the analyses. Weather
variables are summarized by rainfall.*
Two surrogates are used for control resources: stack height and
sulfur content of the fuel. Higher stacks and the increased use of
low sulfur fuel were common responses to air quality regulations.
Further, higher stacks would be expected to affect directly the
plant's maintenance costs. Although the sulfur content of fuel may
have a less direct effect on maintenance costs, it serves as a
surrogate for other, unobservable, control expenditures.**
Larger control systems were considered (e.g., flue gas
desulfurization systems), but there were so few installed in 1972 that
statistical estimation of the maintenance cost equation precluded
their use.
* Humidity was considered in preliminary regression results, based on
SMSA data, and it was found that humidity did not significantly
affect cost.
** Utility plants report "annual air quality control expenses."
However, the type of expense included is ambiguous. For example, a
footnote to the table in which this number is reported states that
the figure may or may not include the cost of low sulfur fuel. The
expenses appear to relate primarily to the collection of ash by the
plant.
8-20
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Given the above discussion, the basic equation measured is:
log(M*) = A + B * log(WAGE RATE) + C * log(FUEL PRICE)
+ D * log (CAPACITY) -HE* log (AGE OF PLANT)
+ F * log(UTILIZATION RATE) + G * log (RAIN) (
+ H * log(S02) + J * log(TSP)
+• K * log (SULFUR CONTENT) + L * log(STACK HEIGHT)
In the next two subsections, Equation (8.12) is estimated for various
measures of air quality and for alternative measures of maintenance
costs (see the first subsection for a discussion of the alternative
ways in which maintenance cost is measured).
Based on existing information concerning air quality's effect on
maintenance cost, we expect that all coefficients, with the possible
exception of F (utilization rate), will be positive. The ambiguity
that the utilization rate induces is that the firm's utilization of
the equipment would be expected to increase maintenance requirements.
At the same time, firms with low utilization may have low utilization
since the equipment is shut down for maintenance.
Since these hypotheses are one-sided, we will employ one-sided
significance tests in what follows.
8-21
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Empirical Results for Full Sample
In this section, the results of the maintenance cost function
estimation using the full sample of plants available are discussed.
Estimation results for the total maintenance cost function are shown
in Table 8-2. In Table 8-2, the parameter estimates are given for
four alternative measurement methods for S02 (average annual mean,
maximum second high, average second high, maximum annual mean).*
Column 1 provides the results for the average annual mean. As shown,
the parameter estimates have the expected sign or are insignificant.
Interestingly, the coefficient on the age variable is insignificant,
perhaps suggesting that plants are maintained at a reasonably constant
level. The coefficients on fuel price, capacity, utilization rate,
rain, SC>2 sulfur content of fuel, and stack height are all significant
at the 5 percent level.** These results imply that a 10 percent
reduction in the level of S02 (measured as the average annual mean)
reduces maintenance costs by approximately 2.78 percent.
In column 2, the estimated cost function for total maintenance
cost is shown where the SCU measure is the maximum second high in the
county. As shown in the table, when S02 is measured in terms of the
* See Section 3 for a discussion of the air quality data.
** The coefficient on the TSP measure is positive but not
statistically significant at the 5 percent level. This finding
generally occurs throughout the analysis for particulates.
8-22
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TABLE 8-2. MAINTENANCE COST FUNCTION ESTIMATION RESULTS
(t-statistics in parentheses)
Total maintenance cost is dependent variable
Sulfur dioxide measure
Variable
Constant
Wage rate
Fuel price
Capacity
Age of plant
Utilization rate
Rainfall
so2
TSP
Sulfur content
Stack height
Number of obs.
F
R2
Avg . annual
mean
-3.25*
(-1.80)
0.073
(0.547)
0.510**
(3.29)
0.565**
(7.32)
-0.050
(-0.77)
0.263**
(2.55)
0.173*
(1.79)
0.278*
(1.85)
0.039
(0.240)
0.051*
(1.87)
0.336**
(3.28)
122
30.258
0.71
Maximum 2
high
-4.49**
(-2.75)
0.154
(1.23)
0.522**
(3.23)
0.559**
(7.18)
-0.040
(-0.603)
0.246*
(2.36)
0.232**
(2.57)
0.83
(1.05)
0.164
(1.13)
0.062*
(2.35)
0.343**
(3.29)
122
29.421
0.70
Average 2
high
-4.45**
(-2.65)
0.099
(0.730)
0.619**
(3.89)
0.544**
(7.09)
-0.048
(-0.74)
0.276**
(2.77)
0.223**
(2.40)
0.201*
(1.76)
0.121
(0.792)
0.045*
(1.66)
0.316**
(3.15)
109
30.726
0.73
Max. annual
mean
-3.55*
(-1.94)
0.110
(0.836)
0.506**
(3.16)
0.561**
(7.24)
-0.050
(-0.753)
0.252**
(2.43)
0.199*
(2.08)
0.178
(1.43)
0.076
(0.474)
0.058*
(2.18)
0.336**
(3.25)
122
29.762
0.70
* Significant at the 5 percent level (one-sided test).
** Significant at the 1 percent level (one-sided test).
8-23
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maximum second high, the coefficient on S02 becomes insignificantly
different from zero. The other variables that were significant in
column 1 are not appreciably different with the new air quality
measure. In column 3, we see the results of the estimation when the
SO2 measure is the average second high reading for the county. Again,
the coefficient on the SCU variable is significant at the 5 percent
level and close to the value when the average annual mean reading was
used as the measure (column 1). The other variables continue to have
relatively stable coefficients. Finally, in column 4, the cost
function is estimated using the maximum annual mean reading for SO2.
As in the case where the maximum second high was used, the coefficient
on SCU is no longer statistically significant.
Summarizing the results of Table 8-2, maintenance costs appear to
be positively, and significantly, related to the level of SO2 as long
as it is measured in terms of the average for all sites in an area
(whether the average mean reading or the average second high). This
is what we would expect unless the location of the plant was
systematically located in the highest S02 areas. Particulates do not
appear to affect maintenance costs.* In addition, the estimates of
the remaining parameters do not appear to be significantly affected by
the particular measure of air quality used in the estimation.
* Equation (8.12) was estimated using the maximum second high reading
for TSP, the maximum geometric mean, and the average second high.
(The average annual mean for S02 was used in each of the
regressions.) In no case was the coefficient for TSP statistically
significant at the 5 percent level (the maximum t-statistic was
0.40). The coefficient on S02 was 0.27 or 0.28 in each case.
8-24
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Utilities report maintenance costs broken down by category of
maintenance. This separation can be used to assess, to some extent,
the reasonableness of the results obtained above. We use three of
these categories (maintenance of structures, maintenance of boiler
plant, and maintenance of electric plant) to further investigate the
effect of sulfur oxides on maintenance costs.
Table 8-3 presents the results for the estimation of the cost
function where maintenance of structures is the dependent variable.
Again, separate results are given for each of the possible measures of
air quality. Looking at column 1, where the regression uses average
annual mean as the SC>2 measure, we see that certain results change.
Specifically, the utilization rate, which was very significant when
total maintenance cost was the dependent variable, is no longer
significant. This seems reasonable since the relative use of the
plant in terms of electricity generation should have little effect on
the structures associated with the plant. It also shows that sulfur
content of fuel is not significant, again something that would be
expected. Finally, when the dependent variable is maintenance of
structures, the effect of SO2 is much more significant (at least when
measured by the average annual mean). Further, the coefficient of
0.73 suggests a rather strong result.
When the maximum second high measure is used, the results are
little changed except that the coefficient on the SCU term is no
longer significant, a result consistent with that found in Table 8-2
8-25
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TABLE 8-3. MAINTENANCE COST FUNCTION ESTIMATION RESULTS
(t-statistics in parentheses)
Maintenance of structures is the dependent variable
Sulfur dioxide measure
Variable
Constant
Wage rate
Fuel price
Capacity
Age of plant
Utilization rate
Rainfall
S02
TSP
Sulfur content
Stack height
Number of obs.
F
R2
Avg . annual
mean
-8.72**
(-2.45)
0.065
(0.245)
0.684*
(2.23)
0.521**
(3.42)
0.099
(0.769)
0.130
(0.883)
0.092
(0.480)
0.730**
(2.45)
0.132
(0.413)
-0.030
(-0.556)
0.386*
(1.91)
122
8.504
0.38
Maximum 2
high
-12.35**
(-3.77)
0.298
(1.19)
0.770*
(2.38)
0.501**
(3.22)
0.129
(0.980)
0.138
(0.665)
0.280
(1.55)
0.133
(0.837)
0.478
(1.64)
0.004
(0.070)
0.423*
(2.03)
122
7.613
0.35
Average 2d
high
-10.42**
(-2.92)
0.114
(0.394)
0.698*
(2.06)
0.534**
(3.26)
0.082
(0.595)
0.186
(0.872)
0.129
(0.649)
0.608**
(2.51)
0.217
(0.666)
-0.038
(-0.666)
0.354*
(1.65)
109
7.829
0.39
Max . annual
mean
-9.14**
(-2.52)
0.142
(0.547)
0.650*
(2.06)
0.512**
(3.34)
0.098
(0.754)
0.151
(0.739)
0.140
(0.741)
0.519*
(2.11)
0.200
(0.627)
-0.013
(-0.254)
0.380*
(1.85)
122
8.239
0.37
**
Significant at the 5 percent level (one-sided test).
Significant at the 1 percent level (one-sided test).
8-26
-------
above. Other coefficients, however, appear to exhibit the same sort
of stability as before. Using the average second high as the measure
changes little except that the S02 coefficient is again significant.
Finally, when the maximum annual mean is used, there is virtually no
change.
The largest single maintenance item is maintenance of boiler
plant. In Table 8-4, the regression results when maintenance of
boiler plant is the dependent variable are presented. The format of
Table 8-4 is the same as for the previous tables. Looking first at
column 1 where the average annual mean of SC>2 is used, the results
appear to be fairly similar to previous results with some exceptions.
First, the coefficient on the wage rate variable is significant in
this case. Sulfur dioxide and rain both contribute to increased
costs. The estimated elasticity of maintenance costs with respect to
SC>2 is 0.34, a value consistent with the other results. The corrected
2
R is comparable to that obtained when total maintenance costs were
used as the dependent variable. This probably reflects the fact that
maintenance of boilers is a substantial portion of total maintenance
costs.
Looking across the remaining columns, it again seems that using
maximum readings of SC>2 (both mean and second high), rather than
averages for counties leads to a loss of explanatory power for the S02
variable. The estimated elasticities for SC>2 are essentially the same
8-27
-------
TABLE 8-4. MAINTENANCE COST FUNCTION ESTIMATION RESULTS
(t-statistics in parentheses)
Maintenance of boiler plant is dependent variable
Sulfur dioxide measure
Variable
Constant
Wage rate
Fuel price
Capacity
Age of plant
Utilization rate
Rainfall
so2
TSP
Sulfur content
Stack height
Number of obs.
F
R2
Avg . annual
mean
-7.04**
(-3.49)
0.258*
(1.72)
0.353*
(2.04)
0.643**
(7.45)
-0.009
(-0.126)
0.337**
(2.92)
0.340**
(3.13)
0.340*
(2.02)
0.111
(0.610)
0.152**
(4.99)
0.304**
(2.66)
122
39.064
0.76
Maximum 2
high
-8.65**
(-4.71)
0.362**
(2.57)
0.381*
(2.10)
0.634**
(7.26)
0.004
(0.058)
0.317**
(2.71)
0.420**
(4.15)
0.081
(0.908)
0.268
(1.64)
0.167**
(5.60)
0.317
(2.71)
122
37.645
0.75
Average 2
high
-8.31**
(-4.32)
0.295*
(1.90)
0.427*
(2.34)
0.628**
(7.13)
-0.005
(-0.067)
0.345**
(3.01)
0.380**
(3.56)
0.266*
(2.03)
0.193
(1.10)
0.148**
(4.77)
0.283**
(2.46)
109
38.514
0.78
Max. annual
mean
-7.53**
(-3.66)
0.309*
(2.10)
0.354*
(1.97)
0.637**
(7.33)
-0.007
(-0.098)
0.323**
(2.78)
0.377**
(3.52)
0.201
(1.44)
0.166
(0.917)
0.162**
(5.39)
0.307**
(2.65)
122
38.192
0.75
* Significant at
** Significant at
the 5 percent
the 1 percent
level (one-sided test).
level (one-sided test).
8-28
-------
when the average of the mean readings is used or the average of the
second high readings is used.
The last dependent variable considered is maintenance of electric
plant. In Table 8-5, the results of the cost function estimation for
this dependent variable are given. Neither rainfall nor SC>2 is
significantly associated with the maintenance cost for electric plant.
This could be caused by the relatively small level for this cost or
reflect the fact that electric plant is kept relatively protected from
the corrosive effects of the outside environment.
These results suggest that there is a positive and significant
relationship between the ambient level of SC^/ appropriately measured,
and the costs plants incur for maintenance. One possibility, not
estimated in the regressions described so far, is that it is the
interaction between rain and SC>2 that is important in causing
corrosion. One specification that can be used to test for this is to
replace the separate rain and sulfur dioxide terms with a single
(multiplicative) term. Note that this implicitly restricts the
coefficient on the rain variable and the SO- variable to be the same.
(When both the single terms for rain and S02 and the interaction terms
are included in the regression, the collinearity among the variables
becomes extremely large.) The results for the four possible dependent
variables are presented in Table 8-6. In Table 8-6, the average
annual mean is used for the S02 variable, but using the other measures
leads to the same relationships as found in Tables 8-2 through 8-5.
8-29
-------
TABLE 8-5. MAINTENANCE COST FUNCTION ESTIMATION RESULTS
(t-statistics in parentheses)
Maintenance of electric plant is dependent variable
Sulfur dioxide measure
Variable
Constant
Wage rate
Fuel price
Capacity
Age of plant
Utilization rate
Rainfall
so2
TSP
Sulfur content
Stack height
Number of obs.
F
R2
Avg. annual
mean
-2.88
(-1.02)
0.036
(0.173)
0.737**
(3.04)
0.475**
(3.94)
-0.070
(-0.691)
0.400**
(2.49)
0.068
(0.446)
0.089
(0.380)
-0.144
(-0.569)
-0.064
(-1.50)
0.407**
(2.55)
122
9.101
0.401
Maximum 2
high
-3.09
(-1.22)
0.051
(0.265)
0.711**
(2.85)
0.475**
(3.95)
-0.068
(-0.667)
0.393**
(2.45)
0.068
(0.490)
0.072
(0.584)
-0.112
(-0.502)
-0.063
(-1.53)
0.399**
(2.48)
122
9.137
0.40
Average 2"
high
-3.93
(-1.44)
0.081
(0.368)
0.876
(3.39)
0.399
(3.21)
-0.070
(-0.672)
0.411**
(2.54)
0.132
(0.873)
0.008
(0.041)
-0.061
(-0.245)
-0.068
(-1.55)
0.417**
(2.56)
109
7.734
0.38
Max . annual
mean
-3.00
(-1.05)
0.049
(0.240)
0.737**
(2.97)
0.474**
(3.93)
-0.070
(-0.685)
0.397**
(2.47)
0.077
(0.517)
0.054
(0.281)
-0.130
(-0.521)
-0.062
(-1.48)
0.407**
(2.54)
122
9.090
0.40
**
Significant at the 5 percent level (one-sided test).
Significant at the 1 percent level (one-sided test).
8-30
-------
TABLE 8-6. ESTIMATION RESULTS WITH INTERACTION TERM
(t-statistics in parentheses)
Variable
Constant
Wage rate
Fuel price
Capacity
Age of plant
Utilization rate
Rain * S02
TSP
Sulfur content
Stack height
Number of obs.
F
R2
Dependent variable
Total
maint.
-3.81**
(-2.78)
0.101
(0.837)
0.528**
(3.50)
0.563**
(7.33)
-0.048
(-0.740)
0.260**
(2.54)
0.211**
(3.67)
0.082
(0.609)
0.053*
(1.98)
0.341**
(3.36)
122
33.825
0.71
Maint. of
structures
-12.15**
(-4.44)
0.234
(0.971)
0.788**
(2.63)
0.511**
(3.34)
0.114
(0.881)
0.165
(0.805)
0.321**
(2.80)
0.394
(1.47)
-0.017
(-0.315)
0.418*
(2.07)
122
9.104
0.38
Maint. of
boiler plant
-7.04**
(-4.59)
0.258*
(1.91)
0.353*
(2.10)
0.643**
(7.49)
-0.009
(-0.128)
0.337**
(2.94)
0.340**
(5.29)
0.111
(0.735)
0.152**
(5.08)
0.304**
(2.68)
122
43.795
0.76
Maint. of
elec. plant
-3.00
(-1.40)
0.042
(0.223)
0.741**
(3.15)
0.475**
(3.96)
-0.070
(-0.691)
0.400**
(2.50)
0.075
(0.839)
-0.135
(-0.641)
-0.064
(-1.52)
0.408**
(2.58)
122
10.203
0.41
* Significant at the 5 percent level (one-sided test).
** Significant at the 1 percent level (one-sided test).
8-31
-------
Looking at columns 1 and 3, we see that the estimated coefficients
obtained for the interaction term are roughly the same magnitude but
are more significant when the coefficients are estimated separately.
This reflects the fact that, given the restrictions hold, the
parameter estimates are more efficient.
Based upon the full-sample results, there appears to be a
positive and significant effect on the costs of maintenance due to air
quality (in terms of 302). The degree and significance of this effect
appears to differ depending on the particular component of maintenance
cost being estimated. This variation is in ways that we would expect
if the level of air quality does have a physical effect on capital
equipment. That is, if the level of SC>2 was simply a surrogate for
some unknown variable, it is unlikely that this other variable would
affect different maintenance components in exactly the way that S02
would be expected to. While we can never "prove" that it is the air
quality which "causes" the increase in maintenance costs, these
additional tests strengthen the original findings.
Before discussing the results for individual subsamples, it may
be useful to discuss a potential problem with the variable being used
to indicate age of plant. The age of plant proxy used in the
regressions described above was taken to be the initial date of plant
operation. Clearly, this may not be accurate since new units are
added over time. To investigate the potential effect this could have
on our results, we used the data contained in the Cowing and Smith
8-32
-------
data base referenced earlier (6). With these data, a capacity
weighted age of plant was measured. That is, the capacity of
individual units were used as weights on the dates of installation of
those units in order to determine an average age of the existing
plant. Because of differences in coverage, there were 62 plants in
common between the Cowing-Smith data and the sample used in our
analyses above. The cost function for total maintenance was rerun
with and without the restriction on the coefficients for SC^ and rain.
Without the restriction, the result was:
log(MAINT) = -3.55 - 0.019 log(WAGE) + 0.602* log(FUEL PRICE)
(1.27) (-0.08) (2.44)
-I- 0.538**log(CAPACITY)- 0.0291og(AGE OF PLANT)
(3.90) (-0.224)
+ 0.632** log(UTILIZATION) + 0.181 log(RAIN)
(3.01) (1.37)
+ 0.388 log(S02) + 0.125 log(TSP)
(1.50) (0.466)
4- 0.077 log (SULFUR CONTENT)
(1.36)
+ 0.415** log(STACK HEIGHT)
(2.46)
I2 = 0.71 F = 16.19
U33
-------
If the equation is estimated with the interaction term, the result is:
log(MAINT) = -4.36 + 0.019 log(WAGE) + 0.626** log(FUEL PRICE)
(-1.93) (0.094) (2.60)
+ 0.549** log (CAPACITY) - 0.016 log(AGE OF PLANT)
(4.04) (-0.127)
4- 0.632** log (UTILIZATION) + 0.233** log(RAIN*S02)
(3.03) (2.82)
+ 0.193 log(TSP) + 0.085 log(SULFUR CONTENT)
(0.831) (1.58)
-I- 0.415** log (STACK HEIGHT)
(2.48)
R2 = 0.72 F = 18.222
These results suggest that the use of initial plant operation does not
materially affect the results. Since the date of original operation
is available for a larger number of plants, we continue to use that in
the remaining analyses. In the next section, we look at subsamples of
the data selected by values of certain characteristics of the plants
to determine if there are significant differences in the effects of
air quality among different groups of plants.
Subsample Results
Although the use of plant data rather than firm data is useful in
reducing heterogeneity in the observations, substantial variation
remains in terms of various operating characteristics. In this
section, the full sample is divided into various categories based on
their individual characteristics. The maintenance cost function is
8-34
-------
then estimated for each of these subsamples and the results presented.
For each of the subsamples, the sulfur dioxide measure is the average
annual mean. We continue to include the annual geometric mean reading
for TSP in the equation.
The subsamples were generated by categorizing plants in terms of
four characteristics: type of fuel used; utilization rate; vintage;
and size. Each was considered to be a potentially important
characteristic in terms of its effect on our results.
In Table 8-7, the maintenance cost function estimation results
for the fuel-type subsamples are shown. The subsamples considered
were coal only, oil only, and gas only.* Since each represents a
different technology, it might be expected that ambient air quality
affects them in differing ways. For ease of comparison, the results
for the full sample are given in the last column.
A problem with the subsample cost functions is that with the
smaller sample and the reduced variation in one of the independent
variables, the standard errojrs of the coefficients become relatively
large. Therefore, these results must be interpreted with some
caution. Looking at the results in Table 8-7, we see that the
estimated coefficient on the SC^ variable varies considerably from one
* The plants were placed into one of the three fuel-types if that fuel
constituted 95 percent or more of the total fuel consumed by the
plant.
8-35
-------
TABLE 8-7. MAINTENANCE COST FUNCTION RESULTS FOR FUEL SUBSAMPLES
(t-statistics in parentheses)
Variable
Constant
Wage rate
Fuel price
Capacity
Age of plant
Utilization rate
Rain
so2
TSP
Sulfur content
Stack height
Number of obs.
F
R2
Coal only
-14.34*
(-2.35)
0.544*
(1.81)
1.107
(1.46)
0.047
(0.250)
-0.125
(-1.27)
0.434**
(2.62)
0.822
(1.44)
-0.473
(-1.37)
0.843*
(1.85)
0.640**
(2.44)
0.697**
(3.40)
33
5.199
0.57
Oil only
0.915
(0.196)
-0.021
(-0.076)
-0.197
(-0.206)
0.642**
(3.59)
0.066
(0.370)
-0.013
(-0.041)
-0.015
(-0.040)
-0.519
(-1.16)
-0.137
(-0.232)
-0.330
(-1.25)
0.293
(1.30)
28
6.649
0.68
: ============
Gas only
-14.05
(-1.34)
0.357
(0.799)
4.61*
(2.24)
0.584**
(2.56)
0.337
(1.11)
-0.735
(-1.60)
1.75*
(2.17)
-6.17
(-1.76)
0.938
(1.38)
-0.217
(-1.32)
-0.096
(-0.260)
18
6.638
0.77
Baseline
-3.25*
(-1.80)
0.073
(0.547)
0.510**
(3.29)
0.565**
(7.32)
-0.050
(-0.771)
0.263**
(2.55)
0.173*
(1.79)
0.278*
(1.85)
0.039
(0.241)
0.051*
(1.87)
0.336**
(3.28)
122
30.258
0.71
* Significant at the 5 percent level (one-sided test).
** Significant at the 1 percent level (one-sided test).
8-36
-------
sample to the next. In all three samples, the sign on the coefficient
is theoretically incorrect, but none of the coefficients is
significant. A probable cause of the instability of the coefficient
estimates in the fuel-type subsamples is the reduced variation in the
data. This problem is exaggerated by the small sample size for the
gas subsample.
Next, the full sample was divided according to the rate of
utilization of the equipment. The three subsamples are: less than 45
percent; 45 to 60 percent; and greater than 60 percent. The choice of
these limits was designed to give reasonably equal-sized groups. The
results are shown in Table 8-8. As shown in the table, the
coefficient estimates are much more stable than for the fuel-type
subsamples. The only sample for which the coefficient on the S02
variable is significant is the low utilization rate. However, the
magnitude of the coefficient for the other two samples is reasonably
consistent with that found earlier.
For the two lower utilization rate samples, the coefficient on
utilization rate is not significant, suggesting that within these
groups, utilization rate does not affect maintenance cost. For the
high utilization rate groups, this is not true.
Plants were next divided by vintages to correspond to previous
findings [see, e.g., Bich and Smith (8)]. The results of the
estimation by vintage groups is shown in Table 8-9. The three
8-37
-------
TABLE 8-8. MAINTENANCE COST FUNCTION RESULTS FOR UTILIZATION RATE
SUBSAMPLES
(t-statistics in parentheses)
Variable
Constant
Wage rate
Fuel price
Capacity
Age of plant
Utilization rate
Rain
so2
TSP
Sulfur content
Stack height
Number of obs.
F
R2
Utilization
< 0.45
1.08
(-0.321)
-0.416
(-1.61)
0.857**
(3.84)
0.431**
(3.63)
0.066
(0.426)
0.151
(1.03)
-0.075
(-0.433)
0.656*
(2.30)
0.065
(0.187)
-0.054
(-1.34)
0.236
(1.27)
35
7.105
0.64
0.45 to 0.60
-2.89
(-1.30)
0.361*
(2.24)
0.335
(1.46)
0.803**
(6.45)
-0.020
(-0.265)
0.002
(0.004)
0.162
(1.26)
0.269
(1.37)
-0.201
(-0.967)
0.089*
(2.32)
-0.088
(-0.560)
48
19.642
0.80
> 0.60
-2.75
(-0.751)
-0.150
(-0.591)
0.511*
(1.68)
0.670**
(4.52)
0.210
(1.49)
1.07**
(2.70)
0.052
(0.286)
0.392
(1.35)
0.035
(0.118)
0.072
(1.47)
0.469**
(2.42)
39
14.699
0.78
Baseline
-3.25*
(-1.80)
0.073
(0.547)
0.510**
(3.29)
0.565**
(7.32)
-0.050
(-0.771)
0.263**
(2.55)
0.173*
(1.79)
0.278*
(1.85)
0.039
(0.241)
0.051*
(1.87)
0.336**
(3.28)
122
30.258
0.71
======================================================================
* Significant at
** Significant at
the 5 percent
the 1 percent
level (one-sided
level (one-sided
test) .
test) .
8-38
-------
TABLE 8-9. MAINTENANCE COST FUNCTION RESULTS FOR VINTAGE SUBSAMPLES
(t-statistics in parentheses)
var iaDj.e
Constant
Wage rate
Fuel price
Capacity
Age of plant
Utilization rate
Rain
so2
TSP
Sulfur content
Stack height
Number of obs.
F
R2
_____ =_ _ .
Pre-1947
-3.73
(-1.54)
0.219
(1.23)
0.409*
(2.03)
0.553**
(5.53)
0.083
(0.346)
0.173
(1.47)
0.218
(1.21)
0.320*
(2.00)
-0.074
(-0.379)
0.020
(0.625)
0.188
(1.40)
54
13.089
0.70
Vintage
1948-1960
-4.63
(-1.15)
-0.187*
(-0.805)
0.795**
(2.99)
0.635**
(5.00)
0.372
(1.11)
0.4918
(2.19)
0.191
(1.16)
0.028
(0.098)
0.573*
(1.82)
0.077
(1.58)
0.302*
(1.74)
52
12.248
0.69
1961-1972
-6.39
(-0.684)
0.693
(1.22)
0.099
(0.086)
0.149
(0.241)
-0.056
(-0.164)
-0.790
(-0.761)
0.477
(0.880)
0.630
(0.691)
-0.852
(-1.41)
-0.054
(-0.266)
0.537
(0.760)
16
5.985
0.77
Baseline
-3.25*
(-1.80)
0.073
(0.547)
0.510**
(3.29)
0.565**
(7.32)
-0.050
(-0.771)
0.263**
(2.55)
0.173*
(1.79)
0.278*
(1.85)
0.039
(0.241)
0.051*
(1.87)
0.336**
(3.28)
122
30.258
0.71
* Significant at the 5 percent level (one-sided test).
** Significant at the 1 percent level (one-sided test).
8-39
-------
vintages considered were pre-1947; 1948 to 1960; and 1961 to 1972.
Again, the estimates appear to be more stable than for the fuel-type
subsample results. For the sulfur dioxide term, only the coefficient
estimated for the oldest vintage group is significant. The
coefficients on the variables found to be significantly related to
maintenance cost when the full sample was used appear to remain fairly
stable. For the newer vintages, the coefficient on the SO 2 term are
no longer statistically significant. Although not tested in this
analysis, such a result might be expected if newer vintage plants
incorporated in their construction protection against the effects of
corrosion.
The final subsample analyzed here was based on the size of the
plant. Thus, plants were placed in one of three groups, depending on
their capacity. The three groups were: less than 300 MW; 300 to 700
MW; and greater than 700 MW. This classification was used to
approximately equate the number of plants in each subsample. Table 8-
10 presents the regression results for this subsample. As shown
there, the coefficient on the SO2 term was positive for each of the
subsamples, but in none of them was the coefficient significant.
Capacity itself continues to be strongly related to maintenance costs
even in these subsamples based on capacity.
The results summarized above for the individual subsamples were
all based on the unrestricted form of the estimating equation. In
other words, the coefficient on S02 and rain were not restricted to be
8-40
-------
TABLE 8-10. MAINTENANCE COST FUNCTION RESULTS FOR CAPACITY SUBSAMPLES
(t-statistics in parentheses)
Variable
Constant
Wage rate
Fuel price
Capacity
Age of plant
Utilization rate
Rain
so2
TSP
Sulfur content
Stack height
Number of obs.
F
R2
< 300 MW
-0.131
(-0.027)
-0.333
(-0.946)
0.245
(0.748)
0.631**
(2.47)
0.032
(0.113)
0.335
(1.52)
0.108
(0.420)
0.488
(1.59)
0.162
(0.406)
0.087
(1.25)
0.398*
(1.70)
38
4.217
0.47
Capacity
300-700 MW
-5.09*
(-1.96)
0.072*
(0.347)
0.812**
(3.58)
0.652**
(2.90)
-0.043
(-0.400)
0.2128
(0.951)
0.194
(1.26)
0.170
(0.790)
0.202
(1.03)
0.027
(0.755)
0.289*
(2.03)
50
9.893
0.64
> 700 MW
-11.66*
(-2.09)
0.733*
(0.231)
0.394
(1.11)
1.13**
(3.34)
-0.031
(-0.252)
0.574*
(1.87)
0.266
(1.42)
0.231
(0.710)
-0.075
(-0.180)
0.012
(0.202)
0.146
(0.500)
34
5.473
0.58
Baseline
-3.25*
(-1.80)
0.073
(0.547)
0.510**
(3.29)
0.565**
(7.32)
-0.050
(-0.771)
0.263**
(2.55)
0.173*
(1.79)
0.278*
(1.85)
0.039
(0.241)
0.051*
(1.87)
0.336**
(3.28)
122
30.258
0.71
**
Significant at the 5 percent level (one-sided test).
Significant at the 1 percent level (one-sided test).
8-41
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equal. The coefficients will still be unbiased, but, if the
restrictions are valid, the coefficients will not be efficient. Thus,
some of the results above, which in many instances were statistically
insignificant, may, in fact, given the restrictions, be significant.
In Table 8-11, the results of the subsample results are summarized by
comparing the estimated coefficient on the SOj term for the restricted
and unrestricted cases. As shown in Table 8-11, the effect of
imposing the restriction tends to lead to more significant estimates.
Only for the fuel subsample are there no significant coefficients.
Again, with perhaps two exceptions, the coefficients estimated by
imposing the restrictions are reasonably close to those obtained with
the full sample.
The estimation of the maintenance cost functions using subsamples
based on various operating characteristics of the plants has given
somewhat ambiguous results. Although the signs on the coefficient
relating air quality to maintenance costs generally are correct, the
coefficients themselves tend to be statistically insignificant.
Unfortunately, it is not clear whether that is a result of true
underlying differences in the effects of air quality based on the
different characteristics or a reflection of the small samples and the
collinearity among the explanatory variables. It is interesting that
when the coefficients are estimated with the restrictions on the rain
and SC>2 coefficients imposed, the results correspond to that of the
full sample quite closely.
8-42
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TABLE 8-11. ESTIMATED ELASTICITIES FOR SULFUR OXIDES
(t-statistics in parentheses)
Restricted coefficient No restrictions
FUEL
Coal only -0.089 -0.473
(-0.311) (-1.37)
Oil only 0.227 -0.519
(1.23) (-1.16)
Gas only 0.469 -6.17
(0.908) (-1.76)
UTILIZATION RATE
Less than 0.45 0.179* 0.656*
(1.73) (2.30)
0.45 to 0.60 0.200** 0.269
(2.48) (1.37)
Greater than 0.60 0.174* 0.392
(1.89) (1.35)
VINTAGE
Pre-1947 0.273** 0.320*
(2.93) (2.00)
1948-1960 0.135 0.028
(1.52) (0.098)
1961-1972 0.532** 0.630
(2.76) (0.692)
CAPACITY
Less than 300 MW 0.275* 0.488
(1.94) (1.59)
300 to 700 MW 0.185* 0.170
(2.02) (0.790)
Greater than 700 MW 0.255* 0.231
(2.15) (0.710)
FULL SAMPLE 0.211** 0.278*
(3.66) (1.85)
* Significant at the 5 percent level (one-sided test).
** Significant at the 1 percent level (one-sided test).
8-43
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Estimation Results for Total O&M Cost
Up to this point, all of the results presented were for the
maintenance cost equation. Those results allow us to identify the
relationship between air quality and maintenance cost. Recall,
however, that the maintenance cost equation was derived from a total
cost function incorporating both operation and maintenance (O&M). By
estimating the latter equation, we can provide a cross-check on the
earlier results since the dollar effect of S02 on O&M cost should be
at least as large as the effect on maintenance cost alone. In
addition, if the O&M effect is found to be strictly larger, this would
suggest that pollution may have effects which are not fully offset by
increased maintenance activity.
One problem with estimating the total cost equation is that
previous research suggests that the Cobb-Douglas functional form may
not be appropriate (even though it may be appropriate for maintenance
cost). Yet with the number of variables included in our total cost
equation, more general functional forms such as the translog (see
Section 7) are not particularly attractive either, when ordinary least
squares regression is involved. The problem is that the number of
independent variables becomes very large. In this case, multi-
collinearity can result and lead to very large standard errors.
Rather than omit estimation of the total cost equation entirely,
it was decided to use the more restrictive Cobb-Douglas functional
8-44
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form, recognizing that it may not be entirely appropriate. The
results obtained when the total cost function was estimated are shown
in Table 8-12. Notice in the table that when air quality is measured
in terms of annual mean, the level of SCu is positively related to
cost. When air quality is measured by average second high, the
association is still positive but the significance level is only 0.13.
It is interesting to compare the results for the total cost
equation with the earlier results for the maintenance cost equation.
For the Cobb-Douglas functional form, the coefficients in the
equations are elasticities. An elasticity is the percent change in
the dependent variable (e.g., cost) associated with a one percent
change in an independent variable (e.g., 302). The elasticities for
SC>2 in the two equations are shown in Table 8-13 for each of the
measures of SC^.
Using the elasticities and the variable means, the marginal costs
of pollution can be calculated. The marginal costs are related to the
elasticities in the following way:
MC = ac/aso2 = (c/so2)c ,
8-45
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TABLE 8-12,
TOTAL COST FUNCTION ESTIMATION RESULTS
(t-statistics in parentheses)
Total O&M is the dependent variable
Variable
Constant
Wage rate
Fuel price
Capacity
Age of plant
Utilization
Rain
SO 2
TSP
Sulfur content
Stack height
Number of obs.
F
R2
Sulfur
Annual mean
0.037
(0.063)
0.045
(1.02)
0.807**
(15.8)
0.741**
(29.5)
-0.010
(-0.44)
0.608**
(18.1)
0.033
(1.02)
0.110*
(2.24)
0.053
(1.00)
0.011
(1.23)
0.144**
(4.32)
121
313
0.96
dioxide measure
Average 2 high
-0.502
(-0.88)
0.082*
(1.78)
0.829**
(15.11)
0.745**
(28.5)
-0.009
(-0.40)
0.611**
(18.1)
0.055*
(1.74)
0.043
(1.11)
0.092*
(1.77)
0.014
(1.56)
0.137**
(4.00)
108
297
0.97
**
Significant at the 5 percent level (one-sided test).
Significant at the 1 percent level (one-sided test).
8-46
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TABLE 8-13. ESTIMATED ELASTICITIES
SO2 measure
Dependent variable Annual mean Average second high
Maintenance 0.278* 0.201*
0 & M 0.110* 0.043
* Significant at the 5 percent level.
where & is the elasticity of maintenance cost with respect to SC^. At
the sample mean, and using the annual mean measure of S02/ the
marginal costs are (in $l,000's):
MCM = (1555.03/40.8977)(0.27812) = 10.6
MC0&M = (14839.3/40.8977)(0.10995) = 39.9
Thus, the effect on O&M cost from a unit change in pollution is larger
than the effect on maintenance cost, as would be expected. At the
sample mean, the difference is about four to one. Notice also that
the marginal costs are quite small as a percent of average cost —
about 0.68 percent for maintenance and 0.27 percent for O&M.
Summary of Estimation Results
These results suggest that S02, measured either by annual
arithmetic mean or average second high, is associated with higher
maintenance cost and, in the case of the annual mean, operations and
maintenance cost as well.
8-47
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BENEFITS ESTIMATES
The statistical results presented and discussed in the previous
section suggest that higher levels of ambient sulfur dioxide are
associated with higher costs for generating plants. In this section,
we estimate the cost savings (benefits) associated with attainment of
the secondary standards using these statistical results. Benefits are
derived in several categories because of the limitations imposed by
data availability.
In the first subsection, we calculate what we term "baseline
benefits" — benefits associated with existing fossil-fuel fired
steam-electric power plants. In the second subsection, these baseline
estimates are adjusted to account for growth in new generating
capacity.
Baseline Estimates
As noted in Section 3 of this report, the current secondary
standard for SCU is stated in terms of a 3-hour averaging time and was
apparently based on vegetation effects. All of the significant
effects identified in this analysis of the electric utility sector are
based on either a 24-hour averaging time or an annual average. We
thus develop three separate estimates of benefits — one based on an
alternative standard of 60 jug/ra (annual average), one based on an
8-48
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alternative standard of 260 Mg/m (average 24-hour second high), and
one based on the 24-hour "equivalent" of the current 3-hour standard.*
The air quality data discussed in Section 3 were used to identify
the counties not currently (1978) in attainment with the above
standards. Data in reference (9) were used to identify the fossil-
fuel fired steam-electric plants in the non-attainment counties. A
total of 10 counties containing at least one plant, and containing a
total of 18 plants, currently exceed the annual average standard. A
total of 22 counties with 41 plants exceed the 24-hour standard. No
counties with power plants are affected by the "equivalent"
standard.** For each of the pertinent plants, total operations and
maintenance (O&M) and total maintenance costs for 1977 were obtained
from FPC (10).
* The procedure used to develop the 24-hour equivalent standard is
described in Section 3. A 24-hour equivalent must be used since
there is no primary standard with a 3-hour averaging time; hence, a
scenario based on improving air quality from the primary standard
to the secondary standard cannot be defined. There is, however, a
24-hour primary standard (365 Mg/m ).
** Two counties with a total of three power plants have at least one
monitoring site where the 24-hour equivalent of the 3-hour
secondary standard is below the 24-hour primary standard. In all
other counties with fossil-steam plants, the 24-hour equivalent
secondary standard is above the 24-hour primary standard and thus
the primary standard is binding. In the remaining two counties,
where the average across all sites in the county is taken, as
required by the model, the average also exceeds the primary
standard. Hence, the current 3-hour standard is irrelevant for
this analysis.
8-49
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It was assumed that air quality in the county in 1985 would be
the lesser of the current level or the primary standard (annual
arithmetic mean of 80 M9/m and average 24-hour second high of 365
Mg/m ). The attainment of the secondary standard is assumed to take
place over the two-year period 1986-1987. The reduction is assumed to
be linear. Thus, for example, if the annual mean is 64 in some
county, then the level for 1986 is assumed to be 62 and for 1987 and
thereafter it is assumed to be 60.
Recall that the estimated cost function was of the form
C =
For the purposes of the baseline estimates, we assume that all factors
other than air quality remain constant. Then, we can write the cost
function for plants in a given county as
C. = KxJ
L. I-
where Ct is cost, xfc is air quality with exponent p>, and K is some
constant. The t subscripts refer to time periods. Given air quality
estimates at time t+1, we can then estimate Ct+j_ as
8-50
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Equation (8.13) thus provides the basis for calculating the cost
savings that would occur as air quality progresses toward the
secondary standard.
An example will illustrate the procedure in more detail. Suppose
a particular power plant has annual maintenance costs of 1,000 (in
$l,000's) in 1977 and current (1978) air quality is 82 Mg/m3 measured
as an annual mean. We assume that except for general inflation, and
the improvement in air quality from 82 to 80 (the primary standard),
that maintenance costs are unchanged between 1977 and 1985. Thus,
maintenance costs in 1985, stated in 1980 dollars, are:
(1000)(80/82)°-27812 (177.40/141.61) = 1244.2
The adjustments shown are to account for the improvement in air
quality to the primary standard (which reduces maintenance cost), and
to change in price levels from 1977 dollars to 1980 dollars as
measured by the implicit GNP price deflator.
Now between 1985 and 1987, air quality progresses toward the
secondary standard (60). The savings in maintenance as a result,
measured in 1980 dollars, is equal to
;i244.2)[l-(70/80)°'27812] = 45.4
8-51
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in 1986. This savings is also realized in 1987, together with
additional savings of
(1244.2 - 45.4)[l-(60/70)°-27812J = 50.3
Thus, total savings in 1987 are 45.4 4- 50.3 = 95.7.
In 1988 and thereafter, air quality is assumed to remain at the
secondary standard so that the savings of 95.7 continues to be
realized each year. The discounted present value in 1980 of all
future benefits is thus given by
N
(45.4)(l+r)~6 + (95.7)(l+r)~7 + I (95.7) (H-r)~(7+l)
i=l
where r is the discount rate and N is the length of the future time
horizon in years.
The benefits reported in the following paragraphs are separately
estimated for discount rates of 2, 4 and 10 percent. In selecting a
value for N, the length of time horizon, several options were
considered. One approach was to set the N for each plant equal to an
estimate of the remaining useful plant life based on the installation
date of each plant. Another was to assume an average remaining life
for each plant. However, both of these approaches ignore the fact
that replacement capacity must be provided when the plants are
retired. An alternative assumption, then, is that existing sites
8-52
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(i.e., counties) continue to be the location of power generating
activity, with replacement capacity being installed at certain
intervals. It was the latter assumption that was adopted as being
more realistic, and thus an infinite time horizon was used.*
Table 8-14 summarizes the benefits estimates for the different
S02 standards and discount rates. The top half of the table shows the
cost savings (benefits) in maintenance alone. The bottom half shows
the corresponding figures for operation and maintenance together.
Note that benefits are very sensitive to the assumed discount rate and
that benefits for the 3-hour standard are zero.
Adjustments to the Baseline Estimates
The benefits reported in Table 8-14 reflect only existing power
plants and replacement capacity for those plants. Demand for
electricity is projected to grow substantially over current levels,
however, and new capacity will be required to supply that demand. It
is also the case that some of this new capacity is likely to be
installed in the counties we have been considering. Under the
* To evaluate the sensitivity of the results to this assumption,
sample calculations were made using N = 15. This value was chosen
under the assumption that plants existing in 1977 would be 20 years
old in 1985 and have a useful life of 30 to 40 years. Compared to
the assumption of perpetual replacement (infinite N), benefits with
N = 15 are about 80 percent as large when a 10 percent discount rate
is used, and about 30 percent as large when a 2 percent discount
rate is used.
8-53
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TABLE 8-14. BASELINE ESTIMATES FOR FOSSIL-FUEL STEAM-ELECTRIC
COST SAVINGS*
=======:=====:== = = =:=====
Savings category/
discount rate
Maintenance
10 percent
4 percent
2 percent
O&M
10 percent
4 percent
2 percent
Current
3-hour**
0.0
0.0
0.0
0.0
0.0
0.0
S02 standard
Alternative
24-hour
49.99
178.09
403.57
110.85
394.66
894.15
Alternative
annual mean
23.48
83.62
189.45
61.55
219.22
496.70
* Millions of 1980 dollars discounted to 1980.
** 24-hour equivalent of the current 3-hour standard.
8-54
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assumption that these new plants will also benefit from the improved
air quality, these additional benefits must be incorporated into the
previous estimates.
A recent DOE forecast suggests that fossil steam-electric
generation will grow from 5.4 x 1015 Btu (in 1978) to 8.6 x 1015 by
the year 2020 (13). This is the "middle" forecast and may even be
viewed as conservative since it assumes more than a sixfold increase
in nuclear generation over the same time period. Nonetheless, we will
use the forecast as is and note that the implied average annual growth
rate is 1.11 percent per year.
It is difficult to know how much of the new capacity is likely to
be located in the counties currently under consideration in the
analysis. A not unreasonable assumption is that they would capture
the same proportion of national growth as they did in the past. To be
conservative, we will assume that they grow at only half the national
rate (which could occur if air quality conditions impede the location
of new plants in these counties). In this case, maintenance and O&M
costs in those counties would grow at 0.56 percent per year (assuming
no technological breakthrough in maintenance practice). In the
context of the earlier example calculation, benefits would now become
(1.0056)8(45.4)(l+r)"6 + (1.0056)9(95.7)(1+r)"7
N
-I- t (1.0056)9+1(95.7)(H-r)~(7 + i)
8-55
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Table 8-15 presents the baseline benefits adjusted for growth in
the manner described above, for a discount rate of 10 percent. On
average, the adjustment for new capacity additions increases benefits
by about 10 percent over the baseline estimates.
Geographical Distribution of Benefits
The benefits shown previously in Tables 8-14 and 8-15 were based
on plants located in specific counties. Hence, it is possible to
determine the origin of these benefits on a geographical basis. The
geographical breakdown is provided in Table 8-16 for the adjusted
baseline benefits using a 10 percent discount rate. Note that for the
alternative standard based on the annual mean, benefits are heavily
concentrated in the Mid-Atlantic and East North Central regions. With
the 24-hour alternative standards, large benefits also arise in the
TABLE 8-15. FINAL ESTIMATES FOR FOSSIL-FUEL STEAM-ELECTRIC
COST SAVINGS*
Savings
category
Maintenance
O&M
Current
3-hour**
0.0
0.0
S02 standard
Alternative
2 4 -hour
55.76
123.63
Alternative
annual mean
26.19
68.66
* Millions of 1980 dollars discounted to 1980 with a discount rate of
10 percent.
** 24-hour equivalent of the current 3-hour standard.
8-56
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TABLE 8-16. GEOGRAPHICAL DISTRIBUTION OF ADJUSTED BASELINE BENEFITS*
S00 standard
Savings category/
census division
Current
3-hour
Alternative
24-hour
Alternative
annual mean
Maintenance
New England
Mid-Atlantic
E. North Central
W. North Central
South Atlantic
E. South Central
W. South Central
Mountain
Pacific
U.S. Total
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.04
6.8
34.3
2.2
8.7
2.8
0.0
0.8
0.0
55.8
0.0
14.6
9.6
0.4
0.0
0.6
0.0
1.0
0.0
26.2
O&M
New England
Mid-Atlantic
E. North Central
W. North Central
South Atlantic
E. South Central
W. South Central
Mountain
Pacific
U.S. Total
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.1
15.9
60.8
5.0
34.3
5.5
0.0
2.1
0.0
123.6
0.0
38.0
22.1
0.9
0.0
3.2
0.0
4.4
0.0
68.7
Millions of 1980 dollars discounted to 1980 with a 10 percent
discount rate. Details may not add to totals due to independent
round-off errors.
8-57
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South Atlantic region. Benefits also occur in other regions to a
lesser extent with either standard.
Reasonableness of the Estimates
Although this study has been concerned with estimating the
economic.damages suffered by generation plants as a result of air
pollution, it was noted that, as emitters, the generation plants also
contributed to local air pollution. If the assumption of cost
minimizing behavior is assumed to hold, do the benefits estimated
above seem "reasonable"? That is, are the benefits sufficiently small
that one would not expect utilities to undertake voluntarily more
extensive pollution control activities? On a national basis this is
clearly the case. Even without knowing what the utility control costs
might be, it would seem likely that they are far larger, in discounted
present value terms, than the benefits reported previously in Tables
8-14 and 8-15.
Benefits are also small even for those plants that would
experience cost savings from improved air quality. Average benefits
per plant per year (at the 10 percent discount rate), among those
plants which benefit, range from $120,000 to $340,000 depending on the
alternative standard and the cost category. These represent savings
of about 4 percent in maintenance cost or 1 percent in O&M cost. This
is not large relative to the capital and O&M cost (and low sulfur fuel
premiums) that might be required to achieve the required reduction in
8-58
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ambient air quality. This is especially true since these benefiting
plants are only one, albeit important, source of emissions within
their local areas.
We also attempted to elicit some comments about the results of
our study from utilities. We contacted by telephone four utilities —
two of which responded. Both individuals who responded were
associated with the maintenance engineering departments of their
respective utilities. In general, both were pessimistic about
isolating, for their plants, the effects of air quality by itself. A
common reason given was that a major cost associated with corrosion
problems was painting, and that was done in response to corrosion
whatever the cause. An interesting point made, however, was that for
scheduling purposes, painting was done routinely rather than in
response to a specific problem. This would suggest that plants owned
by the same utility but being located in different areas and subject
to different air quality would not necessarily reflect different
maintenance costs if painting were done on a common schedule. Such an
operation would tend to bias against finding a significant effect of
air pollution.
One individual also volunteered an interesting example of what
was apparently an air pollution problem. He indicated that some years
ago a chemical company was located near one of their plants.
Corrosion at that particular plant was found to be more severe than at
8-59
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others owned by the utility. Later, when the chemical company ceased
operations, the unusual corrosion problems disappeared.
CONCLUSIONS
This analysis has been concerned with the relationship between
ambient air pollution and the cost of maintenance and O&M for
privately-owned, fossil fuel-fired, steam-electric power plants. The
major finding is that the costs of maintaining and operating a power
plant are positively associated with the ambient S02 concentration in
the vicinity of the plant, taking into account other sources of cost
variation (e.g., input price and pollution control variations). The
association between costs and the ambient TSP concentration was
generally positive but not statistically significant at the 5 percent
level. These findings are, of course, contingent upon the assumptions
made and the methods employed in the study.
As with most statistical analyses, evidence of association does
not prove the existence of a cause-and-effect relationship. However,
given the physical evidence from other studies (see Section 7 for
references) suggesting that ambient SO2 does have adverse effects on
metals and other materials, the findings of this study are suggestive
of a cause-and-effect relationship. In view of this, the estimated
models have been used to predict the savings in maintenance and
operating costs that are likely to result from attainment of
alternative secondary ambient air quality standards for S02- These
8-60
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savings range from $0.0 to $124 million, depending on the cost
category and alternative standard.
The savings estimated above represent the gross benefits of
attainment that would be realized at the individual power plants. The
costs of pollution controls that may be required to attain the
secondary standards are being estimated in a separate EPA study.
8-61
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DATF HUE
------- |