X-/EPA
United States
Environmental Protection
Agency
Office of Air Quality
Planning and Standards
Research Triangle Park NC 27711
EPA-450/5-83-001d
August 1982
Air
Benefit Analysis
of Alternative
Secondary
Ambient Air
Quality
Standards
for Sulfur Dioxide
and Total
Suspended
Particulates
Volume IV
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FINAL ANALYSIS
BENEFITS ANALYSIS OF ALTERNATIVE SECONDARY
NATIONAL AMBIENT AIR QUALITY STANDARDS FOR
SULFUR DIOXIDE AND TOTAL SUSPENDED PARTICULATES
VOLUME IV
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
U.S. Environmental Protection Agency
Region V, Libra; y
AUGUST 1982 230 Sot,;.-: Cw..-n S'r
Chicago, Illinois 6CS04
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04S. Environmental Protection Agency
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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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U.S. Environmental
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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
Section 4:
Section 5:
Section 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
Extrapola t ions
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.
11
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ACKNOWLEDGMENTS
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
9. AGRICULTURAL SECTOR
Introduction 9-1
Summary of Results 9-1
Background 9-3
Overview of the Agricultural Model 9-6
Market-Clearing Identity 9-15
Scope of Analysis 9-15
Plan of Presentation 9-17
Literature Review 9-17
Laboratory and Field Studies 9-19
Factors Which Affect the Response of Plants
to Air Pollution 9-21
Assessment of Crop Losses 9-24
Economic Studies 9-34
Methodology 9-36
Yield Functions 9-36
Supply and Demand Relationships 9-43
Estimation of the Economic Impact of a
Change in S02 9-55
Air Pollution Variables 9-66
Climatological Variables 9-69
Crop Production Variables 9-71
Aggregate Time Series Data 9-77
Yield Equation Results 9-80
Cotton 9-81
Soybeans 9-90
Summary of Results 9-98
Benefits Estimation 9-102
Supply and Demand Equations 9-106
Demand Equations 9-111
Calculation of Benefits 9-120
Comparison with Other Studies 9-121
IV
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CONTENTS (continued)
Conclusions 9-123
Refinements 9-128
Concluding Remarks 9-129
References 9-130
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FIGURES
Number Page
9-1. Demand and supply curves for crop i 9-7
9-2. Effect of a change in supply on crop price 9-8
9-3. Acreage supply curve for crop i 9-47
9-4. Supply curve for crop i 9-49
9-5. Demand curve for crop i 9-54
9-6. Long-run equilibrium for crop i 9-56
9-7. Effect of a change in SO2 in the market for crop i .. 9-58
9-8. Change in economic surplus in year t+1 9-60
9-9. Change in economic surplus in year t+2 9-62
9-10. Change in economic surplus in the presence of
long-run equilibrium 9-64
VI
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TABLES
Number Page
9-1. Benedict et al. Loss Estimates 9-30
9-2. States Included in Agricultural Data Sets 9-65
9-3. Air Pollution Variables 9-67
9-4. Climatological Variables 9-70
9-5. Crop Production Variables 9-72
9-6. States Included in Agricultural Regions of the
United States 9-74
9-7. Aggregate Time Series Data 9-78
9-8. Yield Functions for Cotton Sample 9-82
9-9. Regional Yield Functions for Cotton Sample 9-85
9-10. Yield Functions for Soybean Sample 9-91
9-11. Regional Yield Functions for Soybeans 9-94
9-12. Average Yield of Soybeans in the United States
Under Alternative SC>2 Levels 9-107
9-13. Soybean Acreage Response Equation 9-108
9-14. Soybean Domestic Demand Equation 9-112
9-15. Soybean Export Demand Equation 9-113
9-16. Soybean Stock Demand Equation 9-114
Vll
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SECTION 9
AGRICULTURAL SECTOR
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SECTION 9
AGRICULTURAL SECTOR ANALYSIS
INTRODUCTION
Summary of Results
In this section we examine the economic benefits of achieving
alternative secondary national ambient air quality standards (SNAAQS)
for sulfur dioxide (SO2) for two economically important crops in the
agricultural sector: cotton and soybeans. Economic benefits are
measured within the framework of the crop production process.
Individual crop yield functions are developed using actual crop
production data on a county basis. These functions relate yield to
the amount of inputs used in the crop production process. Inputs into
this process include both economic and climatological factors, with
the ambient level of S02 being considered a negative input. These
yield functions are estimated in order to test the hypothesis that
ambient £©2 levels have a deleterious effect on the yield of cotton
and soybeans. The results of these estimations are then integrated
with estimated market supply and demand equations in order to measure
the economic benefits of the reductions in S02 levels to alternative
secondary national ambient air quality standards.
9-1
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Based on our sample of cotton-producing counties in Alabama,
Arizona, California, Mississippi, New Mexico and Texas, a significant
negative relationship between S02 and cotton yield has not been found.
Consequently, the calculation of the economic benefits of meeting the
secondary standard for SCU for cotton is not warranted.
Our soybean sample consists of a subset of the soybean-producing
counties in Alabama, Georgia, Illinois, Indiana, Iowa, Kentucky,
Michigan, Minnesota, Mississippi, Ohio, Texas and Wisconsin. A
significant negative relationship between ambient 809 levels and
soybean yield has been found to exist for the sample counties in the
states of Illinois, Indiana, Iowa and Ohio. Incorporating the results
of the soybean yield functions for these states with our estimated
demand and supply functions, the economic benefits of the
implementation of SNAAQS are calculated based on the S02 and soybean
production levels existing in the sample counties of these states in
1977. Approximately 40 percent of these sample counties exceeded an
alternative secondary standard of 260 ng/m for the 24-hour maximum in
1977. The discounted present value in 1980 of the economic benefits
of the reduction in S02 levels in these counties to this alternative
secondary standard by 1988 are estimated to be $21.6 million in 1980
dollars. This assumes an infinite time horizon and a 10 percent
discount rate.
9-2
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Background
It is generally accepted that air pollution can have a negative
influence on plants. Numerous studies have examined the response of
plants to various levels of air pollution concentrations through the
use of controlled experiments and have found that air pollution can
have a deleterious impact on plant growth and yield. These studies
have been extremely useful in identifying the physical effects of air
pollution on plants. They are unable, however, to assess the economic
impact of ambient air pollution on agricultural crop production. In
order to accurately measure the benefits of any air pollution control
program, it is the economic effects of air pollution that must be
taken into account. Since the purpose of this section is to measure
the benefits associated with the implementation of alternative
secondary national ambient air quality standards (SNAAQS) in the
agricultural sector, it is the economic impacts of these standards
that we will address.
In the past, most studies that have evaluated the economic losses
in the agricultural sector due to air pollution have relied on the
results of controlled laboratory and field studies or field surveys.
Their emphasis has been primarily on the categorization and estimation
of the physical effects of air pollution on crop production. They
are, however, only rudimentary approaches to an accurate assessment of
the economic losses in the agricultural sector for several reasons.
9-3
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The applicability of controlled laboratory studies to actual crop
production conditions is questionable due to the differences in the
controlled and ambient environment. Both environmental and economic
conditions will affect the relationship between the plant and air
pollution that is exhibited in a controlled environment. Most
laboratory experiments are performed under ideal climatological
conditions and are therefore not representative of the conditions
under which a crop is grown. Although field experiments replicate the
climatological conditions influencing the crop, they do not take into
account the economic conditions that influence crop production. For
example, a producer, realizing that air pollution affects his crop,
may decide to apply more fertilizer to mitigate the effects of air
pollution. Using the dose-response relationship exhibited in a field
experiment to estimate the effect of a certain level of air pollution
will result in an overestimate of damages in this case.
The attempt of field surveys to directly measure the effects of
ambient air pollution on crop production is hampered by the difficulty
researchers face in isolating the effects of air pollution from all of
the other factors that influence crop production. The assessment of
crop damages depends, in large part, on the degree of researcher
training. Subjective judgments on the part of the researcher are
sometimes necessary, thus preventing a standardized methodology from
being developed. Reductions in crop production that result from
damages that are not visible (e.g., reduced photosynthetic capability
that results in reduced crop yield) will probably not be assessed
9-4
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accurately in the field surveys. Unlike the studies utilizing the
results of laboratory and field experiments, mitigative actions on the
part of the producer may be identified in the field survey.
Economic losses in both of these types of studies are generally
calculated by multiplying the estimated reduction in production by an
average crop price. Although the researchers are aware of the
possible impact that changes in production can have on product price,
their methodologies are unable to incorporate this effect into their
loss estimates.
In measuring the economic impact of air pollution on agricultural
production, it is necessary to couch the analysis within the framework
of the agricultural production process. The producer, as the decision
maker in this process, is concerned with transforming inputs into
agricultural outputs for the purpose of generating a profit. Included
as inputs in this production process are factors over which the
producer does and does not have control. Clearly, air pollution is a
factor over which the producer does not have control.
Assuming for the moment that air pollution enters into the
production process as a negative input (i.e., air pollution has a
deleterious effect on crop output), the producer has several options
open to him:
He can try to ameliorate the effects of air pollution
on his crop through the application of additional
9-5
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amounts of other inputs such as lime. This may enable
him to produce the same level of output but at a
higher cost.
• He can shift to a cultivar that is more resistant to
pollution. If the pollution-resistant cultivar is
more expensive than the original cultivar, this will
also tend to increase the costs of production.
• He can shift from production of the pollution-
sensitive crop to a crop that is less sensitive. This
shift is likely to result in revenues that are higher
in comparison to the revenues associated with the crop
that is pollution-sensitive, but lower in comparison
to the revenues associated with the production of the
original crop without air pollution.
• He can do nothing. This will result in a lower level
of output and a possible decrease in revenue.
Obviously, the adjustments that the producer does or does not
make regarding this negative input may influence both the net revenues
that the producer receives and the amount of the output produced.
These agricultural adjustments may also have an adverse effect on
consumers through their impact on crop price. Consequently, an
accurate assessment of the economic effects of air pollution on crop
production must measure the effects in both the producer and consumer
sectors. It is our intent in this section to develop a model that
takes both of these factors into account.
Overview of the Agricultural Model
In simple form, the economic effects of a change in air quality
on the production of an agricultural crop can be seen by examining the
demand and supply curves for the crop. As can be seen in Figure 9-1,
9-6
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pi
pi
B
0
Qi
S(q±)
Qi
Figure 9-1. Demand and supply curves for crop i.
the supply curve for crop i, S(q^), reflects the amount of the crop
that is supplied at alternative price levels. It is upward sloping,
indicating that the supply of the crop increases as price increases.
The demand curve D(q^), which is negatively sloped, shows the amount
of the crop that is demanded at alternative price levels. The demand
curve indicates that demand for the crop decreases as price increases.
Equilibrium price, P-, and quantity, Q>, are obtained when sellers are
willing to sell and buyers are willing to buy the same quantity at the
same price.
The hypothesis that air pollution has a deleterious effect on
crop supply will be tested in this analysis. Assuming that such a
relationship is found, the improvement in air quality that will result
9-7
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from the implementation of SNAAQS will cause an increase in the amount
of the crop that can be supplied at alternative price levels. This
increase can be represented by the shift in the supply curve from
S(qi) to Sfq.p1 in Figure 9-2.
Given the increase in supply due to the improvement in air
quality, price will drop and a new equilibrium price is established at
i i
Pj_. Equilibrium quantity increases from Q^ to Q^.
The economic benefits of this increase in crop supply can be
estimated by comparing the economic surplus that exists with and
without the change in air quality. The area above the price of crop i
and beneath the demand curve is called "consumer surplus". Consumer
P.
Pi
P. '
B
C
D(q±)
0
Qi
Figure 9-2. Effect of a change in supply on crop price,
9-8
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surplus represents the amount that consumers would be willing to pay
for a particular quantity over and above the market price. It is a
measure of the net benefits consumers derive from purchasing the crop.
With equilibrium price and quantity at P^ and Q^, respectively, total
expenditure on the crop would be P^ • Q^_. Consumer surplus, or the
amount consumers would be willing to pay in excess of P^ • Q^, is
equal to P^FA. "Producer surplus," on the other hand, is represented
by the area beneath the price of crop i and above the supply curve.
It is a measure of the net benefits producers receive from supplying
the crop at the market price. At the equilibrium price, P^, and
quantity, Q-, the producers' gross receipts are equal to P- • Q- and
are represented by the area P-FQ-0. Based on the supply curve S(q-),
producers would be willing to accept receipts equal to the area BFQ^O
for Q-. Producer surplus, therefore, is equal to the area P-FB.
Economic surplus, or the net benefit of supplying Q- at a price equal
to PJ_, is equal to the sum of consumer and producer surpluses. This
is equivalent to the area AFB in Figure 9-2.
Given that the implementation of SNAAQS will result in a shift of
the supply curve of crop i from S(q^) to S(q^) , economic surplus
increases to the area AGC. The economic benefits of this increase in
supply is equal to the difference in economic surplus with and without
the air quality change. In Figure 9-2, this is equivalent to the area
BFGC, which can be obtained by integrating over the area:
9-9
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BFGC = I [D(qi) - S(qi)']dq- f [Dtq^ - S(qi)]dq (9.1)
From the above discussion, it is clear that in order to measure
the economic impact of an improvement in air quality on crop
production, the supply and demand curves for the crop must be
estimated. A brief discussion of the crop supply and demand curves
that are estimated in this section follows.
Supply Equations—
In this analysis, the supply curve of an agricultural crop is
obtained from the estimation of two functions: an acreage response
function and a yield function. The acreage response function reflects
the relationship between the number of acres that are planted in a
particular year and the variables affecting that decision. In
general, it is of the form:
(9.2)
where ACPL^ = the number of acres planted of crop i.
P| = the expected price of the crop.
P| = the expected price of substitute crops in
production.
G- = government support programs for the crop.
9-10
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The acreage response equation is estimated using annual time series
data on the national level from 1955 to 1977.
The number of acres harvested of crop i (ACHR-) is assumed to be
a fixed percentage of the number of acres planted of crop i.
The yield function reflects the physical production process that
occurs after the crop has been planted. Explicit in this function are
factors over which the producer does and does not have control. As
such, it is able to examine the impact of air pollution on the crop
production process. The yield function for the it" crop in a
particular year can be represented by:
YLDi = f(Ii, Et) (9.3)
where YLD^ = the yield or output per acre of the i crop,
Ij_ = inputs used in the production process (labor,
fertilizer, machinery, etc.), and
E- = the environmental factor affecting Y. (temperature,
rain, air pollution, etc.).
It is posited that air pollution enters this process as a
negative input and therefore has a negative influence on crop
production.
The yield equation is designed to be estimated using actual crop
production and ambient air quality data on a site-specific basis and
9-11
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therefore avoids the problems associated with extrapolating the
results of controlled studies to the ambient environment. By
including environmental variables in the yield equation, the
possibility that environmental factors may influence the
susceptibility of the crop to air pollution is specifically taken into
account. The inclusion of economic variables enables the yield
equation to reflect the fact that producers can also influence the
yield of the crop through the decisions they make regarding the use of
labor, machinery, fertilizer, etc.
The total production of crop i can be found by multiplying the
number of acres harvested by the average yield per harvested acre:
Q? = ACHRi • YLl^ (9.4)
The total supply, or quantity available, of the crop in a
c
particular year is equal to the quantity produced in that year (Q^)
plus the quantity of the crop left over from the previous year
SUPPLYi = Q? + Q?(-l) (9.5)
It should be mentioned that this model, as currently developed,
is unable to directly reflect the possibility that producers may
respond to the effects of air pollution on a particular crop by
decreasing the number of acres of the pollution sensitive crop that is
9-12
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planted. In addition, it is unable to reflect the impact that air
pollution may have on the quality of the crop.
Demand Equations—
In this section, it is assumed that crop demand consists of three
components: domestic demand, export demand, and stock demand.* Like
the supply equation, annual time series data from 1955 to 1977 are
used to estimate the demand equations. The general form of these
three equations are:
Domestic demand—
dj = m(Pif PJ, Zj_) (9.6)
where Q^ = the amount of crop i demanded domestically.
P^ = the price of the crop.
P- = a vector of prices of other goods that affect the
demand for i (e.g., the price of a substitute crop in
consumption).
Z^ = a vector of other variables affecting the demand for
i (e.g., population, number of livestock).
Export demand—
Q* = x(Pi, P , XR, of, Ti, Vi) (9.7)
* If a significant portion of the crop is imported into the United
States, the export demand equation will be estimated as a net export
demand equation (i.e., EXPORTS - IMPORTS).
9-13
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where Q = the amount of the crop exported from the United
States.
P^ = the price of the crop in the United States.
P = a vector of prices of other goods that affect the
export demand for i (e.g., the price of a substitute
crop in consumption).
XR = the exchange rate between the United States and the
importing country.
Q| = the amount of the crop produced outside of the United
States.
T^ = the cost of transporting the agricultural crop from
the United States to the importing country.
V^ = a vector of other variables affecting the exports of
i (e.g., United States foreign aid policy, population
of importing counties, number of livestock in
importing countries).
Stock demand —
= k Pif Pf, Qf, Q^(-l), q," Gi (9.8)
where Q^ = the amount of the crop held in stock.
P^ = the actual price of the crop.
P| = the expected price of the crop.
Q| = the quantity produced of the crop.
Q^(-l) = the amount of the stock held in the previous year.
C^ = the cost of holding stocks of the crop.
G. = the capacity constraints of processing the crop into
a final good.
Total demand in a particular year is equal to the sum of the
components of demand:
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DEMAND = Q" + Q* + Qf (9.9)
Market-Clearing Identity
In order to ensure that the market for the crop clears (i.e.,
SUPPLY = DEMAND), the estimated supply and demand components are
subject to the following market-clearing identity:
Qf + Qf(-l) = d£ + Qf + Qf (9.10)
Scope of Analysis
Agricultural production is an important part of the United States
economy and plays a significant role in the economies of many foreign
countries. It is not possible at this time to analyze the effects of
air pollution on the entire agricultural sector since the sector is
highly complex, composed of the production of many different crops and
species whose susceptibility to air pollution vary over a considerable
range. For this study, we concentrate on two crops that the
literature has shown to be susceptible to air pollution under
controlled conditions: cotton and soybeans. In addition to being
susceptible to air pollution, these crops are economically important
crops, ranking fifth and second, respectively, in terms of crop value
within the U.S. in 1977.
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Although the alternative secondary standards used in this study
are set in terms of total suspended particulate matter (TSP) and
sulfur dioxide (SC^K we will only consider the effects of SC>2 on
cotton and soybean production in this analysis. Particulate matter is
a generic term for a pollutant whose composition varies significantly.
Depending on its composition, this pollutant can have a negative
effect on plants (see Literature Review). In general, however, most
particulate matter is not considered to be phytotoxic. Since the
available particulate matter data are not broken down by composition,
and since the generic form of particulate matter is not considered to
be harmful to plants, the effect of TSP on crop yield is not examined
in this analysis.
To enable us to capture the effect of year-to-year variations in
S02 on crop yield, our yield equations are estimated using county air
pollution and crop production data from 1975 to 1977.
The analysis will include all areas producing cotton and soybeans
for which adequate air quality and farm production data are available.
Our cotton sample includes counties in the states of Alabama, Arizona,
California, Mississippi, New Mexico, and Texas. These states
accounted for approximately 80 percent of the U.S. cotton production
in 1977. The soybean sample includes counties in the states of
Alabama, Georgia, Illinois, Indiana, Iowa, Kentucky, Michigan,
Minnesota, Mississippi, Ohio, Texas, and Wisconsin. These states
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accounted for approximately 69 percent of the U.S. soybean production
in 1977.
Plan of Presentation
The subsections of the remainder of the Agricultural section are
organized in the following manner:
• Literature Review
• Methodology
• Data
• Yield Equation Results
• Benefit Estimation
• Conclusions
LITERATURE REVIEW
The effects of air pollution on vegetation have been the subject
of extensive study by plant pathologists and biologists for a number
of years. In general, these studies have found that various types and
levels of air pollution can have a deleterious effect on plants. The
purpose of this subsection is to highlight some of the findings of the
studies which investigate the effects of TSP and SC>2 on vegetation and
to illustrate briefly the confounding factors implicit in the
measurement of these effects. In addition, special attention will be
given to those studies that have quantified, in dollar terms, the
9-17
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effects of air pollution on vegetation. For a comprehensive review of
the literature on the physical effects of air pollution on vegetation,
the interested reader is directed to the studies by Jacobson and
Hill (1), Treshow (2), Naegele (3), and Mudd and Kozlowski (4).
Before reviewing the studies which examine the effects of TSP and
SC>2 on vegetation, it is helpful to understand the types of injuries
plants may sustain as a result of air pollution exposure.
The deleterious effects of air pollution can be broadly
classified into two groups: (1) visible and (2) subtle injury. Plant
injury evidenced by discoloration and/or lesions of the leaves, stems,
or roots are examples of visible injury. Subtle injury, on the other
hand, tends to be more difficult to detect. Examples of subtle injury
are reductions in photosynthetic capability, growth, weight,
flowering, and the amount or quality of yield. Increased
susceptibility to insects and disease is another form of subtle
injury. The fact that injury is not always apparent does not indicate
that it is unimportant. In evaluating the economic damages of the
effects of air pollution on agricultural crops, subtle injury that
results in a reduction in yield may comprise a significant portion of
economic damages.*
* One facet of potential pollution effects not encompassed by yield
reduction is the change in the taste or other quality attributes of
the crop.
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Laboratory and Field Studies*
Particulate Matter—
Relatively few studies have been done that examine the effects of
particulate matter on plants. The pollutant called "particulate
matter" is composed of many different elements whose distribution
varies, depending on the source of the pollutant. At the present
time, particulate matter is generally not considered to be harmful to
plants and is therefore not considered to be a phytotoxic pollutant of
major importance.
Studies that have examined the effects of particulate matter on
plants have concentrated on the effects of dust accumulation on the
plant itself rather than the accumulation of dust in the soil. In
some cases, plant injury has been shown to occur from the deposition
of particulate matter which is contained in waste gases of cement
kilns. It has been found that the stomata of a number of plants may
become clogged, resulting in a reduction in photosynthesis (7,3). The
conclusions that can be drawn from such studies are limited, however,
because the composition of the dusts in these studies varies
significantly.
Heavy metals such as lead, manganese, zinc, nickel, boron,
beryllium, and cadmium are phytotoxic elements that may be found in
* This summary relies on information contained in References (1), (2),
(3), (4), (5), and (6).
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particulate matter. Some studies that have examined the effects of
these metals on plants have found that plant injury may occur where
accumulated amounts of these metals are found in the soil where the
plant is grown (8,9).
Sulfur Dioxide—
Sulfur dioxide (SCU) enters the plant through the stomata. Once
inside the plant, SC^ reacts with water to form a sulfite ion which is
oxidized by the plant to produce a sulfate ion. This ion can then be
used by the plant for its sulfur requirements. Injury from SCu will
occur if the amount of the sulfite and sulfate ions present in the
plant cells exceed that which can be oxidized and assimilated. Injury
may appear as chlorosis or necrosis of the leaves (10). Chronic
injury may resemble senescence (1).
Invisible injury from SC>2 has also been found to occur. Thomas
and Hill (11) found a reduction in the uptake of CO 2 by the plant as
the result of SC>2 exposure. Changes in stomatal resistance, and
therefore photosynthetic capabilities, have been found in plants
exposed to SC>2 (12). Some studies have found that reduced
photosynthetic rates lead to reduced yield (13). Miller and
Sprugel (14) and Sprugel et al. (15) have found that reductions in the
yield of soybeans can occur from exposure to various concentrations of
SC>2 without visible injury to the soybean plants. Brisley e_t al. (10)
have found that cotton yield in terms of the number of bolls decreased
as the result of S02 exposure.
9-20
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It has also been found that plants can be positively affected by
S02 under certain circumstances. Plants grown in sulfur-deficient
soil that are subsequently exposed to S02 have been found to use the
atmospheric S02 for their sulfur requirements. As compared to plants
of the same species grown under the same conditions but without S02
exposure, the S02~exposed plants had greater yields (16,17). Noggle
and Jones (18) found that cotton located close to certain coal-fired
power plants produced more biomass than cotton grown at a distance
from the power plants.
Factors Which Affect the Response of Plants to Air Pollution
The majority of studies which examine the effect, of air pollution
on plants has been conducted in greenhouses and growth chambers. The
plants are generally grown under optimal conditions (i.e., adequate
moisture, temperature, and nutrients) which do not tend to replicate
actual field conditions. Even open-topped field chambers, a
substantial improvement over greenhouses and growth chambers, have
been criticized because the air velocity throughout the chambers is
less than that in the field (19). In this section we will briefly
discuss the factors which tend to affect the response of plants to air
pollution. Given the lack of studies on the effects of particulate
matter on plants, we will concentrate on studies which examine the
factors that affect the response of plants to S02-
9-21
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Length and Concentration of Exposure—
The length and concentration of exposure to air pollution are
extremely important in analyzing plant susceptibility. Equal doses of
pollution do not result in equal plant response if the concentration
and duration of the exposures differ. In general, plants are more
susceptible to high doses of pollution over a short period of time
than an equal amount of pollution in low doses over a longer period of
time (20).
Temperature—
The temperature at which plants are grown and the temperature at
which they are exposed to air pollution affects the susceptibility of
plants to air pollution. This relationship, however, is dependent
upon plant species (21). In general, plant sensitivity to S02
increases with increasing temperatures (22).
Humidity—
Increasing relative humidity tends to increase the susceptibility
of plants to SC>2 (23). Susceptibility varies, however, depending on
the plant species and level of humidity.
Light-
Since SOo enters the plant through the stomata, plants with open
stomata are more susceptible to SC>2 than plants with closed stomata.
Light is an important factor which can influence the opening and
closing of the stomata and consequently will affect the susceptibility
9-22
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of plants to S02. Plants, are-more susceptible to S02 in the daylight
than in the dark (24).
Soil Moisture—
Soil moisture, like light, influences stomatal opening and
therefore is an important factor in determining plant sensitivity.
Plants grown under water-stress conditions tend to be less susceptible
to S02 than plants grown with a sufficient water supply (23). A study
by the National Academy of Sciences (25) found, however, that sudden
changes in soil moisture do not have much influence on plant
sensitivity to SC^.
Soil Fertility—
As mentioned previously, plants exposed to SOn that are grown in
sulfur-deficient soils have been found to have greater yields than
plants grown under similar conditions without SC>2 exposure.
Setterstrom and Zimmerman (23) have found that soil nutrient
deficiencies increased the susceptibility of alfalfa to S02.
Genetic Factors—
Genetic factors play an important role in determining the
susceptibility of plants to air pollution. Different plants have been
shown to exhibit differing degrees of sensitivity to air pollution.
Cultivars of a particular species have also been found to vary in
susceptibility to air pollution (26,27).
9-23
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Stage of Development—
The sensitivity of plants to air pollution is affected by the age
of the plant during exposure. Setterstrom and Zimmerman (23) and
Webster (28) have found that developing and older leaves tend to be
more resistant to SCu.
Plant Disease—
Susceptibility to disease resulting from air pollution exposure
varies, depending on the plant and the disease. Both increased and
decreased incidence of disease have been found in plants exposed to
air pollution (29).
Interaction With Other Pollutants—
The response of plants to simultaneous exposure to two or more
air pollutants varies. Plant response in these instances can be less
than additive, additive, or synergistic. Reinert et al. (30) have
reviewed the literature in this area.
Assessment of Crop Losses
The studies reviewed in the last section have concentrated on the
biological and physiological responses of plants to air pollution.
These studies have been instrumental in uncovering the physical
effects (visible and subtle) of air pollution but cannot provide any
information on the economic impact of these effects. Researchers have
attempted to quantify these effects in a number of ways. The effects
9-24
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of air pollution on plants have generally been quantified through:
(1) field surveys of crops exposed to air pollution; (2) development
of dose-response functions from the results of laboratory and field
studies; or (3) economic studies. It is these studies that we will
now review.*
Field Surveys—
Middleton and Paulus (33) were among the first researchers to
undertake a survey designed to identify crops injured from air
pollution, the location of the injury, and the pollutant causing the
injury. Similar surveys were done by Lacasse et al. (34) in 1969, and
Lacasse (35) in 1970 in Pennsylvania. Trained researchers were used
to identify and evaluate air pollution damage to commercial and non-
commercial plants in order to estimate the total cost of agricultural
losses due to air pollution in Pennsylvania. One of the objectives of
these studies was to determine the ranking of pollutants in terms of
their effect on vegetation. It was also hoped that the surveys would
provide a basis for estimating the nationwide impact of air pollution
on vegetation.
Direct losses from air pollution were estimated to be in excess
of $3.5 million, with indirect losses of $8 million in the 1969 study.
Direct losses of $218,306 and indirect losses of $4,000 were estimated
* The summary of the studies assessing the economic effects of air
pollution on plants through the survey methodology relies on
information contained in References (31) and (32).
9-25
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in the 1970 study. Lacasse reported that better air quality in 1970
accounted for the difference in the estimates of the agricultural
losses for the two years.
The Lacasse surveys are useful because they provide additional
knowledge on the relationship between air pollution and plants and
give some idea of the magnitude of the air pollution problem in
Pennsylvania in 1969 and 1970. The surveys can be criticized because
the damage estimates are based on a non-standardized method of
translating physical damage into economic damage. Although the damage
estimates were made by trained researchers, it is likely that some
subjective judgments were made. Another criticism of the study
regards the definition of direct and indirect losses. Direct losses
to growers included only production costs. Losses in growers' profits
resulting from air pollution were considered to be indirect losses,
although it would have been more appropriate to include this in the
direct loss category. In addition, the loss estimates for non-
commercial vegetation are questionable since the effect of air
pollution on these types of plants is not clearly understood and there
is some question as to what value should be attached to these plants.
Several other studies have estimated the dollar losses that
result from the exposure of vegetation to air pollution using methods
similar to Lacasse. Millecan (36) examined the effect of air
pollution on agricultural crops in California in 1970 through a
survey. Loss estimates were calculated for 15 counties in the state
9-26
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and were estimated to be over $26 million. Except for citrus and
grapes, these loss estimates did not include estimates for subtle
damages such as reductions in growth or yield. The loss estimates
also did not include losses to forests and landscapes. Ozone was the
pollutant found to be the most damaging.
Feliciano (37) reported that agricultural losses due to air
pollution in New Jersey in 1971 were $1.19 million. An attempt was
made to standardize the estimation of loss from crop damage
information using Millecan's "Rule of Thumb" valuation method (36)
(i.e., 1-5 percent injury of the plant leaves of the crop would be
estimated as a 1 percent loss, 6-10 percent injury was estimated as a
2 percent loss, 11-15 percent injury translated into a 4 percent loss,
and 16-20 percent injury resulted in an 8 percent loss). Like the
Lacasse surveys, no account was made for losses that may have occurred
without visible injury to the plant and profit losses were not
included in the loss estimates.
Pell (38) did a follow-up study to the Feliciano study in New
Jersey in 1972. Direct losses were estimated to be approximately
$130,000. The lack of soil moisture in 1972 was cited as the reason
for the difference in loss estimates.
Naegele et al. (39) estimated direct losses to be $1.1 million in
New England for the 1971-1972 growing season. Losses were based on
surveys in 40 counties of the six New England states. This study
9-27
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included profit losses in the direct loss estimates. Oxidant air
pollution was found to be the most damaging.
Millecan (40) conducted another survey in California in order to
estimate air pollution damages from 1970-1974. Four types of crops
were covered: fruits and nuts, field crops, vegetables, and nursery
and cut flowers. An improved standardized method for estimating
losses was developed in this study. Losses from the exposure of
alfalfa to air pollution were calculated from a crop-dose conversion
scale. This scale ensured that equal exposure to air pollution would
result in equal loss estimates. Losses ranged from $16.1 million in
1970 to $55.1 million in 1974. It was acknowledged that the dollar
value of these loss estimates could differ from year to year due to
increases in the prices and quantities of the crops under study, and a
better understanding and reporting of the effects of air pollution, as
well as increases in the level of pollution.
Dose Response Function Studies—
In an attempt to standardize the methods for translating physical
damages into economic losses, numerous studies have developed crop
loss equations. These equations enable the researcher to predict the
economic value of plant damage from the dose of air pollution.
Obviously, the accuracy of the economic losses predicted from these
equations depends on how well the crop loss equation is specified.
9-28
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One of the first studies that used a crop loss equation to
estimate economic losses was Benedict et al. (41,42). This study was
conducted to provide comprehensive estimates of the economic losses to
agriculture in the United States. A crop loss equation was developed
from information regarding the air pollution concentrations of fuel
emissions throughout the country and the sensitivity of specific types
of vegetation to air pollution. This equation was developed in order
to estimate losses from exposure to emissions of oxidants, sulfur
dioxide, and fluorides. Counties where air pollution was considered
to be a problem were selected to be studied. The "relative potential
severity" of oxidant and sulfur dioxide pollution was estimated based
on fuel consumption data, a pollution concentration rate factor, a
factor representing the total area in the county, and the number of
days likely in an air pollution episode. The relative sensitivity of
the commercial crops, forests, and ornamental plantings was
extrapolated from information contained in the literature. Crop value
was estimated based on the Census of Agriculture and state and county
reports. Forest values were based on Federal and state information.
Ornamental plants were valued at maintenance and replacement costs.
Using the above information, economic losses for plant j in county i
were calculated according to the following loss equation:
Plant Loss — = Plant Value — • Plant Sensitivity'
Pollution Potential^
9-29
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Aggregate losses were obtained by summing over all plants and
counties. For 1964, total losses to crops and ornamentals in 687 of
the 3078 counties in the United States from oxidantsr sulfur dioxide,
and fluorides was $131.8 million. Total losses in 1969 were estimated
to be $134.6 million. These loss estimates accounted for 0.99 percent
and 1.84 percent of the total crop value in the counties included in
the study in 1969 and 1974, respectively. As Table 9-1 shows, losses
due to oxidant pollution made up the major portion of the total losses
in both years.
As part of the National Crop Loss Assessment Network program
(NCLAN), Moskowitz e_t ?1. (43) updated the Benedict e_t a_l. model to
estimate agricultural losses due to oxidants in 1969 and 1974.
Basically the same methodology was used with updated information on
emissions and crop values. In 1969 dollars, the total annual losses
from oxidant pollution were estimated to be $130.0 million and $290.0
million in 1969 and 1974, respectively. These losses account for 1.2
TABLE 9-1. BENEDICT ET AL. LOSS ESTIMATES
(in million $)
1964
Crops
Ornamentals
1969
Crops
Ornamental's
Oxidants
78.0
43.0
Oxidants
77.3
42.8
Sulfur Dioxide
3.3
3.0
Sulfur Dioxide
4.97
2.70
Fluorides
4.3
0.2
Fluorides
5.25
1.70
9-30
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percent of the vegetation value in the counties studied in 1969 and
2.2 percent in 1974.
As in the studies which use surveys to estimate the economic
losses to vegetation, these studies are useful because they provide
information on the air pollution-plant relationship and give some idea
of the magnitude of the air pollution problem throughout the United
States. They can be criticized, however, for the following reasons:
(1) loss estimates were not based on actual pollution levels within
each county but on a "potential pollution" level that was calculated
from fuel consumption and meteorological data, (2) sensitivity of
plants to air pollution were extrapolated from studies that measured
the response of plants to air pollution in environments that differed
significantly from the environments in which the plants are typically
grown, and (3) the possibility that reductions in crop output would
lead to higher output prices was not considered.
Oshima (44) and Oshima et. al. (45) estimated crop loss functions
for crops grown under conditions that closely approximated ambient air
quality conditions in several areas of Southern California. Crop loss
equations, as a function of oxidant pollution, were estimated for
alfalfa, cotton, and tomatoes.
Liu and Yu (46) estimated crop loss as a function of an oxidant
index, sulfur dioxide level, crop value, and several climatological
variables for ten crop categories. Since data on crop loss
9-31
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information were not available, Liu and Yu used the crop loss
estimates calculated by Benedict et al. (41,42). As previously
discussed, these estimates are subject to criticism.
Armentano (19), in a study of the Ohio River Basin, estimated
crop loss functions for oxidants and sulfur dioxide based on a review
of the literature. The crops included in the analysis were soybeans,
corn, and wheat. Crop loss functions were derived using the results
of studies primarily conducted in the field. Air pollution
concentrations around coal-fired electrical generating stations in the
Ohio River Basin were estimated using a plume dispersion model based
on air quality variables. The calculation of losses for each crop
were done by Miller and Usher (19) and proceeded in the following
manner:
(1) Air quality concentrations around the generating
stations impacting the acres on which the crop was
grown were estimated from a dispersion model.
(2) Using a crop loss function that was developed from the
literature, the percentage loss in crop yield
associated with this air pollution concentration was
determined.
(3) Because the crop production observed in the Ohio River
Basin reflects the effect of air pollution, estimates
for the probable clean air production (i.e., the
probable production under the assumption that there is
no £©2 in the atmosphere) were made based on the
following formula:
Probable Clean Air Production =
Average Production From 1975-1977
100 - % Loss in Production Due to Pollution
x 100
9-32
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(4) Crop loss, in terms of bushels, for each impacted area
was estimated as the difference between the probable
clean air production and the observed level of
production.
(5) Total crop losses for each crop for the area around
coal-fired electrical generating stations in the Ohio
River Basin were estimated as the summation of the
individual impacted areas.
Recognizing that the decrease in production due to air pollution
will probably impact product prices, Miller and Usher did not attempt
to place a dollar value on crop losses. An increase in soybean yield
of 681,285 bushels resulting from the abatement of direct SC^ impact
from coal-fired electrical generating stations in 1985 were estimated
for the states of Illinois, Indiana, Kentucky, Ohio, Pennsylvania and
West Virginia. It is questionable, however, whether the estimated
bushel losses can be considered to reflect losses accurately since the
loss functions on which the estimates are based do not take into
account the actions a farmer may take to mitigate the effects of air
pollution. For example, a farmer may have switched to a pollution-
resistant cultivar or changed fertilization practices in order to
diminish the effect of air pollution on his crop. In this case, the
production estimates used reflect the production after the farmer has
adjusted to air pollution and consequently may result in
underestimates of the effects of air pollution on the crop. In
addition, the estimates do not reflect the possible costs of
adjustment that are incurred by the farmer in order to mitigate the
effects of pollution.
9-33
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Economic Studies
Recently, more attention has been given to the incorporation of
both economic and environmental factors in determining the impact of
air pollution on crops. Adams et al. (31) were the first researchers
to incorporate both of these factors into the development of their
model of the assessment of oxidant pollution damages in Southern
California, The impact of a change in quantity on product price was
specifically examined. Using the equations developed by Larsen and
Heck (47) to estimate percentage leaf damage as a function of ozone
concentration and Millecan's "Rule of Thumb" method for translating
leaf damage into yield reduction estimates, yield reductions for all
crops included in the study except cotton were estimated. The yield
reductions for cotton were estimated using the yield loss equation for
cotton developed by Oshima et_ al. (45). Through the estimation of a
price forecasting equation, the change in price resulting from a
change in the quantity produced of each crop was obtained. Consumer
losses of $14.8 million per year from 1972 to 1976 were estimated to
have occurred due to the exposure of certain vegetable and field crops
to ozone.
Although the Adams et al. study is an improvement over other
studies trying to assess the economic damages of air pollution in that
it takes account of price changes resulting from air pollution
damages, it still does not take into account the actions that the
producer may take to offset the effects of pollution. In addition,
9-34
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the estimated yield reductions resulting from exposure to ozone based
on Millecan's "Rule of Thumb" method are somewhat arbitrary.
Leung et al. (48) also incorporated both environmental and
economic factors into the development of a model that assessed the
impact of ozone on crop yield in the California South Coast Air Basin.
In the interim report, crop production equations were developed for
five crops: strawberry, tomato, lemon, navel orange, and Valencia
orange. Production was estimated to be a function of ozone,
temperature, and rainfall. Significant negative relationships were
found to exist between ozone and yield for the five crops.
One of the problems apparent in the implementation of the
methodologies which incorporate both economic and environmental
factors is the lack of data. Both Adams gt al. and Leung et al. could
not incorporate information on the producer's use of inputs (e.g.,
fertilizer, machinery, and labor) into the estimation of their models.
Finally, Stanford Research Institute (49) estimated the benefits
of meeting SNAAQS in the agricultural sector. Crop damage functions
developed primarily from field studies were used to estimate the
percentage reduction in yield resulting from crop exposure to air
pollution in counties exceeding the secondary standard in 1980. The
yield reduction functions did not incorporate any information on
environmental conditions and therefore are not likely to represent the
reduction in yield resulting from exposure to air pollution if
9-35
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environmental conditions are different from those in the field
studies. These functions were developed for economically important
agricultural crops and were combined with information on crop
production and price to calculate the cost of damage to these crops:
Cost of damage = reduction in yield • production • price
The benefits of implementing SNAAQS were estimated to be $1.78
billion in 1980 dollars. The reduction in sulfur dioxide accounted
for benefits of $34 million with the remainder of the benefits being
attributed to the reduction in oxidants.
METHODOLOGY
The problem, as stated in the introduction to this section, is to
try to provide an accurate assessment of the agricultural economic
benefits that are associated with the implementation of alternative
SNAAQS. In this subsection, we explain the methodological framework
that is used to examine the economic effects of S02 on the two crops
we have chosen to study in this sector: cotton and soybeans.
Yield Functions
The process by which a producer transforms inputs into outputs
can be expressed in terms of a production function. The production
function is a mathematical expression that relates the quantities of
9-36
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the inputs the producer employs with the quantities of the outputs he
produces. For the farmer, inputs can be considered to be land, labor,
equipment, fertilizer, insecticide, and seed. In agricultural
production, this process is also heavily influenced by factors over
which the producer does not have control: temperature, rainfall,
ambient air quality, etc.
Typically, most farmers produce more than one output. The
production processes of these farms can be represented by the implicit
production function,
f(Qx, ... , Qn; Xx, ... , Xjjj) = 0 (9.11)
This implicit function relates all of the output produced (Q's) to all
of the inputs used (X's). The production function of any one output,
i, by fanner j can be expressed by the explicit function:
(9.12
In this study, we estimate this function in terms of a yield
response function by using actual crop production data. Air pollution
enters into this function as a negative input. (Improvements in air
quality, on the other hand, may be viewed as a positive input.) It is
assumed that the farmer does not have any control over the quantity
and timing of use of this negative input. Because of the
unavailability of data on the farm level, the county is used as the
9-37
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unit of observation. Specifically, the yield of crop i for county j
is hypothesized to be a function of a set of physical and economic
variables:
YLDij = f(Lij' Kij' Fij' Jij' Sij' Mi j' Tij' Hij'
Rij' S02ij' Eij)
where Y^D^^ = yield of crop i for county j.
Lj_.; = labor.
K^ = capital machinery and equipment.
F^J. = fertilizer.
1-^ = insecticide.
S.J. = seed.
M- • = management.
T^ • = temperature.
H. • = humidity.
^.i
= rain.
= ambient level of sulfur dioxide.
= other environmental variables affecting yield such
as light duration and intensity, and other
pollutants.
The first-order partial derivatives of yield with respect to the
economic inputs and the climatological variables of temperature and
rain are expected to be positive (e.g., 6YLD^^/8L^.: > 0). It is our
hypothesis that SC^ has a deleterious effect on crop yield.
Consequently, the first-order partial derivative of crop yield with
9-38
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respect to this variable is expected to be negative (i.e.,
3YLD-./8S02.• < 0). The first derivative of yield with respect to the
other environmental variables is uncertain. (See Literature Review.)
Assume for the moment that a significant negative relationship is
found to exist between S02 and crop yield (i.e., dYLD^/dSC^— < 0).
The increase in yield resulting from an incremental improvement in the
level of S02 can then be calculated:
/aYLD^
J ' ' "^^j (9.14)
In this case, Equation (9.14) could be used to calculate the physical
improvement in yield resulting from an improvement in the level of
S02.
Functional Forms —
A number of different functional forms of these yield functions
will be estimated in order to reflect the various relationships that
may exist between crop inputs and output. These functions are briefly
summarized as follows, using labor (L^-), rain (R^-p, and S02— as
representative inputs:
Linear —
YLDij = a0 + a^j + a2Rij + a3S02ij (9.15)
9-39
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This function assumes that the relationship between crop yield and the
inputs is linear and implies that the marginal productivity of each
input is constant. That is, the partial derivative of yield with
respect to any one of the inputs is constant, regardless of the level
of the input used. With respect to S02/ this can be stated as:
9so2ij
The linear function also implies that the elasticity of substitution
between factor inputs is infinity. This means that any input can be
easily substituted by another input. This may not be possible with
respect to the negative input of S02 since it may not be possible to
offset totally the effects of SC>2 by the additional use of other
inputs.
Quadratic —
+ a5S02ij + a6(S02ij)2
The quadratic function implies that the marginal productivity of each
input depends upon the level of each input used. The marginal
productivity of S02 in the quadratic yield function is equal to:
9-40
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If both a^ and ctg are negative, this means that the deleterious effect
of S02 on crop yield increases as the level of SC^ increases.
Logarithmic —
a a a
YLD = CXL 2S02 * (9.19)
This function can be equivalently written as
log (YLD,;:) = cxn + a-, log)L^ + a->
J J (9.20
+ a3 log(S02ij)
This yield function implies that the marginal productivity of the
positive factor inputs increase at a decreasing rate as the amount of
2 7
input used increases (i.e., d YLD^/dL^.^ < 0). This is reasonable
since the farmer is faced with a fixed amount of land and increasing
the application of inputs to a fixed amount of land will tend to
result in smaller and smaller increases in the yield of the crop.
The marginal product of the negative input S02 is equal to:
dYLDj YLD^
—
Assuming that cx3 is negative, this yield function implies that the
marginal productivity of SC>2 decreases at a decreasing rate as the
level of S02 increases (i.e., d2YLDi j/6S02i j2 > 0). In other words,
9-41
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the marginal crop damage due to SC^ decreases as the level of SCU
increases. This may not be realistic since since crop damage tends to
be more serious for higher levels of pollution.
Linear Interaction-
YLD— = a0 + oc1Lij + a2%j + a3S02ij
(9.22)
+ a,(R^ • S02,,)
Since evidence exists that the susceptibility of plants to air
pollution may be influenced by the environmental conditions under
which the plant is grown, this equation will be estimated in order to
test for "interaction" effects between SO- and climatological
variables. This effect can be clearly seen by taking the first
partial derivative of yield with respect to S02:
In this interaction equation, the change in yield due to a change in
the level of SC>2 is also dependent upon the level of rain.
This function can also be used to test the possibility that
farmers may take mitigative actions, such as the application of more
fertilizer, to offset the effects of SCU on their crop. For example,
a variable expressing the interaction between SC and fertilizer
9-42
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(502^ • FJX) in the yield equation would be able to indicate that the
change in yield due to a change in the level of SC^ is dependent on
the amount of fertilizer used.
Separate yield functions for soybeans and cotton will be
estimated using regression analysis and cross-sectional and time
series data on a county basis from 1975 to 1977. These functions
provide the means of estimating the physical impact of S02 on crop
yield.
Supply and Demand Relationships
The yield function is designed to estimate the physical
relationship between inputs and outputs. This function is only one
element in the process that determines how much of a crop is supplied
in a particular year. It does not provide any information on how the
price of a crop will be affected by a change in yield. In order to
estimate the economic effects of a change in SC>2 in the agricultural
sector, the physical effects of a change in crop yield must be
integrated with information on how crop price responds to such
changes. For the purposes of this study, the estimation of the
economic effects of the implementation of alternative SNAAQS is done
through the estimation of a system of crop supply and demand
equations.
9-43
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Supply Equations—
As mentioned in the introduction, the supply of a crop can be
considered to consist of two parts: stocks in year t-1, and
production in year t*. For agricultural commodities, "crop
production" in any year is generally expressed in terms of an acreage
response function.** It is assumed that the aggregate number of acres
planted of a particular crop i in year t is a function of the price at
which the crop is expected to be sold when harvested (P®t)/ the
expected price of substitute crops in production (Pf^)/ an|3 a variable
representing government support programs for crop i (Gj_t). The
general form of the acreage response equation we use to estimate the
effect of SO2 on crop supply will therefore be:
ACPLH^ = g(p? , P« Git\ (9.24)
it t,
where ACPL^t = the aggregate number of acres planted of crop i
in year t.
priori, it is expected that the following relationships hold:
dACPLit
> 0
* The equation used to estimate stocks is discussed in the demand
equation subsection.
** See Houck, Ryan, and Subotnik (50), Adams (51), and Maumes and
Meyers (52).
9-44
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and
dACPLit
< 0
The relationship between ACPL^t and G^t is undetermined a priori. An
increase in the government's price support could be interpreted as a
reduction in the price risk associated with the crop and consequently
would cause an increase in acres planted. It is also possible that
farmers may interpret the increase in the support price as an indica-
tion of a poor market for their crop and therefore would cause a
decrease in acres planted.
For this analysis, expected prices in year t are assumed to be
equal to the prices received in year t-1, P^-l* ^n °ther words,
producers base their planting decisions in year t on the price
received for the crop in year t-1. Since producers react to past
prices, this equation can be called a supply recursive equation.
The parameters of this equation will be estimated by ordinary
least squares. The data used to estimate this equation will consist
of annual time series data on the national level from 1955 to 1977.
The number of acres harvested of crop i in year t (ACHR-t) is
assumed to be a constant percentage of the number of acres planted:
9-45
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ACHRit = b • ACPLit (9.25)
where b = the percentage of acres planted that are harvested
estimated from historical data.
The general form of the acreage response curve is shown in Figure 9-3.
Obviously, the acreage response curve shown in Figure 9-3 does
not reflect the true supply of the crop in a particular year because
crop yield and stocks left over from the previous year are not taken
into account. The total production of crop i can be obtained by
multiplying the number of acres harvested of crop i by the average
yield of crop i estimated from Equation (9.13):
Q?t = ACHRit • YLDit (9.26)
where Q^t = the quantity of crop i produced in year t.
YLD-1 = the average yield per harvested acre of crop i in
year t.
Total supply of crop i in year t (S(q)) is equal to the sum of
the total production of crop i in year t (Qft)r the commercial stocks
rr
of crop i in year t-1 (Q^t(-D), and the stocks held by the Commodity
Credit Corporation:
S(q) = Qft
9-46
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Figure 9-3. Acreage supply curve for crop i,
9-47
-------
The supply curve for crop i is shown in Figure 9-4.
Demand Equations—
In this analysis, crop demand will be estimated by a system of
demand equations.* This system consists of three equations: domestic
demand, export demand, and stock demand. Domestic demand for crop i
in year t (Qit) is assumed to be a function of crop price (pit)f a
vector of the prices of goods that are substitutes in consumption for
crop i (p-}t)r and a vector of other variables — such as population —
that affect the domestic demand for i (Zj_t). The general form of the
domestic demand equation is:
Q5t = m(Pit, Pjt, Zit) (9.28)
where sQit/aPit < 0;
dQit/dPjt
and 6Q:-;t/9Z^t > ^ ^or variables such as population.
Export demand for crop i in year t (Q^t) is assumed to be a
function of crop i's price in the United States (P-;-^' a vector of the
prices of goods that are substitutes in consumption for the crop
(Pai.)f the quantity of the crop produced outside of the United States
* See the studies by Houck, Ryan and Subotnik (50), Baumes and
Meyers (52), and Womack (53) for further information on the
estimation of demand systems for agricultural commodities.
9-48
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S(q)
Qit
Figure 9-4. Supply curve of crop i,
9-49
-------
p
(QjV), the costs of transporting the crop from the United States to
the importing country (Tj_t)f the exchange rate between the United
States and the importing country (XRt) (i.e., the amount of foreign
currency obtainable per U.S. dollar), and a vector of other variables
— such as population in the importing country — which affect the
export demand for i (V^t). The general form of the export demand
equation is:
= x(Pit, Pqt, Qt, Tit, XRt, Vit) (9.29)
where 9Qit/dPit < 0;
9Qit/3Qit
dQit/dTit < 0;
< 0;
and dQ*t/6Vit > 0 for variables such as population.
Since the two crops we examine in this analysis can be stored for
an extended period of time without perishing, it is necessary to
estimate a stock demand equation. The general form of the stock
demand equation is:
' cit' Off Qi
9-50
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where Q^t = the commercial stocks of crop i held in year t
[i.e., the total quantity of stocks held excluding
those stocks owned by the Commodity Credit
Corporation (CCC)].
P-t = price of crop i in year t.
pf . ,, = the expected price of crop i in year t+1.
J. , U ' J.
C.j_t = the opportunity cost of holding stocks of the crop
(e.g., the interest rate).
Q|t = the quantity produced of crop i.
Q^ t_2_ = the commercial stocks held in year t-1.
Gj_t = the capacity constraints of processing the crop into
a final good.
This stock equation reflects three motives for holding stocks:
speculation, transaction, and precaution (60). Speculative holdings
of a crop take place if there is an expectation that future prices of
the crop will exceed the current price of the crop plus the costs of
holding the crop as a stock. The variables P-t and P^ t+-]_ are
included to reflect the speculative motive for holding stocks. C-. is
included to reflect the fact that the opportunity cost of holding the
stock influences the amount of the stock that is held. It is expected
that:
aoft/apit < o
-,nK
oUjj
and
•^ i^\JA.
9-51
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Stocks are held for transaction purposes because of the nature of
the agricultural production process. Crop harvesting is cyclical,
occurring only in the fall, while consumption remains relatively
constant throughout the year. It is therefore necessary to hold some
level of stocks throughout the year. It is assumed that stocks held
for transaction purposes are a percentage of the amount of the crop
c
produced (Q^t). In addition, it is assumed that the level of stocks
in year t are related to the level of stocks in year t-1 (Q^ t-1^*
The following relationships are expected to hold:
and
Stocks of the crop may also be held due to capacity constraints.
Due to the cyclical nature of crop production, backlogs in the
processing of the crop may result in more of the crop being held in
stock. The variable used to reflect the capacity is G^,. A priori,
it is expected that:
9-52
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The probability of the occurrence of unforeseen circumstances may
cause some level of stocks to be held as a precaution against these
occurrences. For example, a certain level of stocks may be held
because of the impact that changes in the weather may have on crop
production. For this study, it is assumed that the precautionary
demand for stocks is a relatively small component of total stock
demand and is therefore assumed to be reflected in the constant term
of the stock demand equation.
Because crop price and quantity demanded are determined
simultaneously, the parameters of this system of demand equations will
be estimated using two-stage least squares. Like the supply
equations, these demand equations will be estimated using aggregate
annual time series data from 1955 to 1977.
The general form of the crop remand curve depicting the
relationship between crop price and quantity demanded is shown in
Figure 9-5. D(q) is equal to the horizontal summation of the
domestic, export, and stock demand curves.
D(q) = of* + dL + Q^ + Q?fC (9.31)
A. U. i U J.L. i L.
where QV^ = stocks of crop i owned by the Commodity Credit
Corporation in year t.
9-53
-------
pit
D(g)
Qit
Figure 9-5. Demand curve for crop i
9-54
-------
Market Clearing Identity —
Once the parameters of the supply and demand equations have been
estimated, the system can be solved for market quantity and price.
Since the supply of the crop is assumed to be a function of crop price
in year t-1, crop supply in year t enters the demand system as
predetermined. The components of demand and crop price in year t can
be solved for simultaneously, based on the market clearing identity:
oft + °i,t-i + Q??t-i = Qi
Estimation of the Economic Impact of a Change in SC^
The mechanism by which a change in the level of SC^ influences
the market for a particular crop can be shown graphically by
considering the following scenario. Assume that in the presence of a
certain level of SCU, long-run market equilibrium for crop i is
established in year t at price P and quantity Q.* This is shown in
Figure 9-6.
Assume that the concentration of S02 permanently decreases and
that this improvement in air quality has a positive impact on the
* In order to facilitate the graphical presentation, we have assumed
that long-run equilibrium in the market for crop i has been
established prior to the change in air quality. In the actual
calculation of benefits, however, we have made no assumptions
regarding the existence of long-run equilibrium in the market for
crop i.
9-55
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pi
S(q)
D(q)
Qi
Figure 9-6. Long-run equilibrium for crop i,
9-56
-------
crop's yield in the counties growing the crop in year t+1. This
impact can be estimated from our yield equation. Equation (9.14) can
be used to calculate the change in yield in each county j that will
i
result from a reduction in S02 in year t+1 from SC>2 to SQ>:
= 6YLDij/aS02ij(S02ij - S02ij) (9.33)
The increase in yield in each county will result in an increase
in the average yield of the crop and, consequently, an increase in
crop supply. This increase is shown by the parallel shift of the
i
supply curve from S(q) to S(q) in Figure 9-7. Since it is assumed
that crop supply in any year is a function of the price received for
the crop in the previous year, the decrease in the level of SC>2 will
result in Q^ of the crop being supplied in year t+1. In order to sell
the quantity Q-j_, price in year t+1 must drop to P-^. This lower price
in year t+1 will induce a lower quantity of the crop to be supplied in
year t+2 (i.e., Q2). This smaller supply induces a price increase
from P^ to ?2 in year t+2. Assuming that the demand curve is more
elastic than the supply curve and assuming that no other changes
occur, this dynamic process will continue in the typical cobweb
fashion until a new long-run equilibrium is reached at P and Q .
Note that equilibrium price decreases and equilibrium quantity
increases because of the improvement in the level of SCU.
The economic impact of this change in the level of S02 can be
estimated by comparing the economic surpluses that exist in the market
9-57
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pi
p
p.
S(q)
1 (q)
D(q)
Q QoCTQ,
Figure 9-7. Effect of a change in S02 in the
market for crop i.
9-58
-------
for crop i with and without the change in yield. As mentioned in the
introduction, economic surplus consists of two parts: consumer and
producer surpluses. Consumer surplus is equal to the area under the
demand curve that is above the equilibrium price of the crop. The
consumer surplus prior to the air quality change is equal to the area
ABP in Figure 9-8. Producer surplus, on the other hand, represents
the net return to factor owners or the amount they receive for
producing a certain quantity over and above the cost of producing that
quantity. For the original level of S02r this is represented by the
area PBC. The sum of the consumer and producer surpluses is equal to
the area ABC. Due to the change in S02c quantity Q-^ will be supplied
at price P^ in year t+1. As shown in Figure 9-8, consumer surplus
increases to the area AHP-|_ at this price and quantity. Similarly, a
producer surplus equal to the area P-^FD exists in year t+1. However,
producers also incur a loss in year t+1 due to the change in air
quality. This loss is equal to the area beneath the supply curve and
above the price received for the crop. In Figure 9-8, this is equal
to the area GHF. Part of the loss, the area IHF, is simply a transfer
from producers to consumers. Consequently, the societal loss is equal
to the area GHI. Net economic surplus in this case is equal to the
area AID minus the area GHI. The net benefits to society in year t+1
of the improvement in the level of S02 is equal to the difference in
economic surplus with and without the air quality change. In Figure
9-8, this is equal to the slashed area BIDC minus the dotted area GHI.
This area can be found by evaluating the integral:
9-59
-------
p.
A
D
S(q)
S' (q)
D(q)
Q Q* Q-
Qi
Figure 9-8. Change in economic surplus in year t+1,
9-60
-------
Q . 9i
BIDC - GHI = J [D(q) - S (q)]dq - I [S (q) - D(q)]dq
0 Q*
(9.34)
Q
I [D(q) - S(q)]dq
0
Since it is assumed that the lower level of SC>2 will be
maintained in the future, benefits will continue to accrue in future
crop years. Due to the dynamic nature of the model, benefits in
successive years will not be equal to the benefits in year t+1.
Figure 9-9 will be used to show the benefits in year t+2 of the
reduction in SC>2. Since it is assumed that producers base their
planting decisions on the price they received for their crop in the
previous year, the lower price that prevailed in year t+1 will result
in Q2 being supplied in year t+2. Demanders are willing to pay ?2 for
the quantity ^ and consequently price rises to ?2. Economic surplus
in year t+2 is equal to the sum of consumer surplus — the area AH?2
— and producer surplus — the area HFDP2. This sum is equivalent to
the area AHFD. Like the previous year, the net benefit in year t+2 of
the reduction in SC>2 is equal to the difference in consumer surplus
with and without the air quality change (the shaded area BHFDC in
Figure 9-9). By integrating over this area, this is equal to:
Q2 , Q
BHFDC = I [D{q) - S (q)]dq- I [D(q) - S(q)]dq (9.35)
0 0
9-61
-------
p.
D
S(q)
S' (q)
D(q)
Q Q2Q
Qi
Figure 9-9. Change in economic surplus in year t+2.
9-62
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Benefits will be calculated according to Equations (9.34) and
(9.35) for ensuing years until long-run equilibrium is reached. Once
this equilibrium is reached, the net benefits will remain the same in
future years. This can be seen in Figure 9-10. At long-run
* *
equilibrium P and Q , net benefits are equal to the the shaded area
BIDC:
Q , Q
BIDC = I [D(q) - S (q)]dq - J [D(q) - S(q)]dq (9.36)
0 0
The total benefits of the reduction in SOn can be found by taking
the sum of the discounted present value of these calculated benefits
in each year.
DATA
The yield functions discussed in the last subsection will be
estimated for .both cotton and soybeans using cross-sectional and time
series data from 1975 to 1977. As mentioned previously, the cotton
data set includes six cotton-producing states. These states accounted
for approximately 80 percent of U.S. cotton production in 1977. The
soybean data set includes twelve soybean-producing states; these
states accounted for approximately 69 percent of U.S. soybean
production in 1977. A list of the states included in each of these
data sets is found in Table 9-2.
9-63
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S(q)
S' (q)
Figure 9-10.
Change in economic surplus in the
presence of long-run equilibrium.
9-64
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Ideally, we would have liked to have estimated our yield
functions using the farm as the unit of observation. Unfortunately,
farm level production data could not be obtained for this analysis.
Data on farm production was found disaggregated to the county level;
hence, the county is the unit of observation. The use of county level
data may tend to obscure the relationship we are trying to uncover if
significant variations in S02 and yield exist within the county.
The number of observations available for the estimation of the
yield equation for each crop was constrained by whether there were
reliable economic and environmental data for the counties producing
the crop. By far, the most constraining factor was the availability
of reliable data for SC^. Some counties had more than one monitoring
station with readings for SC^, some had only one, and some had none.
TABLE 9-2. STATES INCLUDED IN AGRICULTURAL DATA SETS
Cotton Soybeans
Alabama Alabama
Arizona Georgia
California Illinois
Mississippi Indiana
New Mexico Iowa
Texas Kentucky
Michigan
Minnesota
Mississippi
Ohio
Texas
Wisconsin
9-65
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Consequently, our sample is not random since counties that produced
the crop but did not have a reliable SOn reading had to be excluded
from the analysis. This reduced the size of the data set
significantly. The soybean data set includes 494 observations (about
164 counties), while the cotton data set includes 84 observations
(about 28 counties). Over the three-year period of this analysis,
these counties accounted for approximately 14 percent of the United
States production of soybeans and approximately 15 percent of the
United States production of cotton.
Air Pollution Variables
Sulfur Dioxide—
Table 9-3 lists the sulfur dioxide (S02) variables included in
this part of the study. Note that these variables are measured at the
county level and are available for the second quarters of 1975, 1976,
and 1977. Variables on both average 'and maximum readings are used in
this study in order to measure the effect of long-term (average) and
acute (maximum) levels of SC^ on crop yield. Second quarter data were
used to control for the seasonal nature of agricultural crop
production.*
* There is evidence that plants are more susceptible to air pollution
directly before flowering and pod growth (54). If this is the case
for soybeans and cotton, third quarter averages would be a better
measure to use in order to determine the sensitivity of plants to
air pollution exposure. Hence, the use of second quarter data may
understate the effect of pollution on yield.
9-66
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TABLE 9-3. AIR POLLUTION VARIABLES
Variable
Definition
AMEAN.
XMEAN.
A2HI-
X2HIj
RATIOX-
RATIOA.;
The average of the second quarter* arithmetic 24-
hour means of SO? for the monitoring stations within
county j (in pq/m ).
The maximum of the second quarter arithmetic 24-hour
means of £©2 for. the monitoring stations within
county j (in /ug/m ) .
The average of the second highest 24-hour S02
reading for the monitoring stations within county 3
for the second quarter (in
The maximum of the second highest 24-hour S02
reading for the monitoring stations within county 3
for the second quarter ( in
The ratio of the average of the second highest 24-
hour reading to the average of the second quarter
arithmetic means of S02 -for the monitoring stations
within county j (in ^g/m ) ; i.e., A2HI^/AMEANjL.
The ratio of the maximum of the second quarter
second highest 24-hour S02 reading to the maximum of
the second quarter arithmetic 24-hour mean of S02
for the monitoring stations within county j (in
3); i.e., X2HIi/AMEANi.
* The second quarter refers to the months April through June.
Source: SAROAD Data Base, 1975-1977.
Use of these air pollution variables is likely to be only an
approximation of the ambient air quality within each county since no
attempt was made to reflect the dispersion of air pollution from the
monitoring stations to the surrounding areas. Since there is evidence
that plants are more susceptible to air pollution during daylight
hours (24), daytime S02 readings would have been more appropriate to
9-67
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use instead of the 24-hour readings. These data were not available at
the time the study was undertaken, however.
As discussed in Section 3, the S02 data available to us came from
two types of monitoring methods: non-continuous and continuous. It
has been found that the non-continuous method can lead to biased
estimates of the level of SC>2 because it does not control for
temperature. A correction factor was developed in order to remove
this bias from the SCU data measured by non-continuous methods (see
Section 3 for the details regarding this conversion).
Other Pollutants—
As mentioned in the Literature Review subsection, the
susceptibility of plants to S02 may vary depending on the presence of
other pollutants in the atmosphere. For example, it has been found
that soybeans exposed to both SC>2 and ozone have exhibited greater
than additive growth effects (55), but less than additive foliar
injury effects (56). Tingey et al. (57) found that although soybeans
showed no evidence of injury when exposed to levels of either SC>2 or
nitrogen dioxide (NC^)/ injury occurred when soybeans were exposed to
both of these pollutants.
Although it would have been desirable to include measures of
other pollutants such as ozone and nitrogen dioxide as variables in
our yield equations, these pollutants could not be incorporated into
the present analysis. Data on nitrogen dioxide were not available
9-68
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when the analysis was undertaken. Although data on ozone were
available at the county level, the number of counties that had valid
observations on both S02 and ozone led to a significant reduction in
the size of our sample. It was therefore decided not to include ozone
in the estimation of our yield equations.
It should be mentioned that if S02 is correlated with the
pollutants that are excluded from the yield equations, the estimated
relationship between SCU and crop yield may be biased. If the
presence of both S02 and another pollutant tend to have a less than
additive effect on the yield of cotton and/or soybeans, estimating a
yield equation without including both pollutants may result in an
underestimate of the isolated effect of S02 on the crop. On the other
hand, estimation of the yield equation with only S02 may result in an
overestimate of the isolated effect of S02 on crop yield if the
exposure of the crop to both S02 and another pollutant has a greater
than additive effect on yield.
Climatological Variables
As explained in the Literature Review subsection, the
susceptibility of plants to SO2 is influenced by a number of
climatological factors. Humidity, temperature, rain, wind, and light
intensity are examples of the climatological varibles influencing the
susceptibility of plants to S02. Data on both rain and temperature
9-69
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were available at the county level. Data on the other climatological
factors that influence plant susceptibility were not available on the
county level when the analysis was undertaken. Consequently,
temperature and rain are the only climatological variables included in
the model at this time. The definitions of these two variables are
given in Table 9-4.
Like the exclusion of other pollutants from the estimation of the
yield equations, the exclusion of relevant climatological variables
may also tend to result in biased estimates of the relationship
between SC>2 and crop yield. It is possible, however, that rain and
temperature may be good surrogates for some of the excluded
climatological variables such as humidity and light intensity.
TABLE 9-4. CLIMATOLOGICAL VARIABLES
Variable Definition
Average temperature in degrees Celsius during April,
May and June as reported by one monitoring station
within county j.*
RAIN- Average rainfall in centimeters during April, May
and June as reported by one monitoring station
within county j.
* The monitoring stations for temperature and rain are not necessarily
located in the same place as the monitoring stations for S02«
Source: U.S. National Oceanic and Atmospheric Administration, Annual
Summary, various states, 1975-1977.
9-70
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Crop Production Variables
The crop production variables used in the specification of our
yield equation are listed in Table 9-5. Information on the use of
inputs (labor, fertilizer) by farmers producing soybeans could not be
obtained on a county level; consequently, state and regional data had
to be used as proxies for the county level use of inputs (see Table
9-6 for the states included in the agricultural regions of the U.S.).
The total number of hours used for farmwork in the production of oil
crops (soybeans and flaxseed) was used as a proxy for the labor input.
This variable was available at the regional level, hence only regional
variations in the use of this input were measured. Data on the use of
fertilizer (nitrogen, phosphorous, and potash) were available at the
state level from the 1976 to 1978 issues of Fertilizer Situation of
the Economic Research Service (61).
It should be mentioned that the fertilizer data are, at best,
gross approximations of the county-level use of fertilizer. The
information obtained from Fertilizer Situation are based on a survey
of selected cotton- and soybean-producing fields in certain states.
Only information on the amount of fertilizer applied per acre
receiving fertilizer in the survey is available. It is not clear that
a random sample of farms is included in the survey, and consequently
this amount may not be indicative of fertilizer application by the
remainder of the cotton- and soybean-producing farms in the state. In
addition, since there is a large variation in the fertility of the
9-71
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TABLE 9-5. CROP PRODUCTION VARIABLES
Variable
Definition
Level
YLDj
YLDCj
ACHR.
ACHRCj
PROD.
PRODC-
Yield of soybeans in county j; yield is
expressed in terms of bushels produced
per acre. Source: Reference (58).
Yield of cotton in county j ; yield is
expressed in terms of pounds produced
per acre. Source: Reference (58).
Number of acres of soybeans harvested.
Source: Reference (58).
Number of acres of cotton harvested .
Source: Reference (58).
Number of bushels of soybeans produced.
Source: Reference (58).
Number of bales of cotton produced.
C ^~M T v^ t-\ * 'D/r* f c\ ^r*f\^r\ r^f^\ ( El Q \
County
County
County
County
County
County
LABOR*
LABORC
LIME
NITROGEN
P2°5
Total number of farmwork hours used in
the production of oil crops (soybeans
flaxseed). Source: Reference (59).
Total number of farmwork hours used in
the production of cotton. Source:
Reference (59).
Tons of agriculture limestone used.
Source: Reference (60).
Number of pounds of nitrogen applied
per soybean acre receiving any
fertilizer. Reference (61)
Number of pounds of phosphorous applied
per soybean acre receiving any
fertilizer. Source: Reference (61).
Agricultural
region
Agricultural
region
State
State
State
* Information on this variable is not available for the state of
Mississippi.
(continued)
9-72
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TABLE 9-5 (continued)
Variable
Definition
Level
K2°
NITROGENC
P2o5c
K2OC
PRICE
IRRIGj
Number of pounds of potash applied per State
soybean acre receiving any fertilizer.
Source: Reference (61).
Number of pounds of nitrogen applied State
per cotton acre receiving any
fertilizer. Source: Reference (61).
Number of pounds of phosphorous applied State
per cotton acre receiving any
fertilizer. Source: Reference (61).
Number of pounds of potash applied per State
cotton acre receiving any fertilizer.
Source: Reference (61).
Average price per bushel of soybeans State
received by farmers. Source:
Reference (62).
A 0-1 dummy variable reflecting the County
presence of irrigation in county j. If
the county irrigates the crop, IRRIG^
is equal to 1; otherwise it is equal to
0.
9-73
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TABLE 9-6. STATES INCLUDED IN AGRICULTURAL REGIONS OF
THE UNITED STATES
Northeast
Mountain
Maine
New Hampshire
Vermont
Massachusetts
New York
Connecticut
Rhode Island
New Jersey
Pennsylvania
Arizona
Colorado
Idaho
Montana
Nevada
New Mexico
Utah
Wyoming
Southeast
Alabama
Georgia
South Carolina
Florida
Lake States
Michigan
Minnesota
Wisconsin
Corn Belt
Illinois
Indiana
Iowa
Missouri
Ohio
Delta States
Arkansas
Louisiana
Mississippi
Southern Plains
Oklahoma
Texas
Mountain
Arizona
Colorado
Idaho
Montana
Nevada
New Mexico
Utah
Wyoming
Northern Plains
Kansas
Nebraska
North Dakota
South Dakota
Pacific
California
Oregon
Washington
9-74
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soil within each state, the use of state-level data is likely to be a
poor approximation of the use of fertilizer by the counties within the
state.
Data on the agricultural consumption of lime by state was used as
a proxy for the county-level use of lime by farmers producing cotton
and soybeans. Like the fertilizer data, this is a gross approximation
of the county-level use of lime. However, since lime is used to
control the pH levels of the soil and since there are distinct
regional differences in the pH levels of the soil throughout the
country, this variable may be useful in controlling for the
interregional differences in the use of lime. In addition, it is
important to include this variable in the estimation of our yield
functions because of its possible relationship to SCu. For example,
soils in the midwestern states tend to be relatively acidic (pH range
is approximately 4 to 6) and farmers in these states apply lime to
reduce the acidity of these soils. Since the existence of certain
levels of SC>2 in the atmosphere can result in increased acidity of the
soil, farmers may increase their application of lime in order to
mitigate the effects of SO-. Consequently, it is important to control
for the mitigative actions of the farmer when estimating the yield
function. Leaving this variable out of the equation may result in an
underestimate of the effect of SCu on crop yield.
As Table 9-5 shows, only information on the use of labor and
fertilizer by farms producing soybeans and cotton could be obtained
9-75
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for our analysis. Information on the use of other inputs such as
herbicides, pesticides, and seed was not available. If the use of
these inputs changes as a result of the exposure of the crop to S02,
omission of these variables may result in biased estimates of the
relationship between SC>2 and crop yield. This bias can be shown (63)
to be equal to:
= aS02 + ax " Cov(S02,X) (9.37)
where E(as02^ = tne exPected value of the predicted
coefficient of SC^.
otcm = the "true" coefficient of SO->.
ax = the "true" coefficient of the excluded
variable.
Cov(S02,X) = the correlation between 302 an(^
excluded variable.
In other words, the direction of the bias of the coefficient of
862 resulting from the exclusion of a relevant explanatory variable in
the yield equation depends upon the sign of the coefficient of the
excluded variable and the correlation between SCu and the excluded
variable. For example, if the use of pesticides has a positive effect
on yield and the use of this input increases as a result of crop
exposure to S02f the estimated coefficient of S02 will be biased
toward zero, thus underestimating the true impact of SCu on crop
yield. Alternatively, if the use of pesticides decreases as a result
of crop exposure to S02, the estimated coefficient of SC^ will be
biased away from zero. Since evidence exists that plants can either
9-76
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be more or less susceptible to disease and insects as a result of
exposure to S02/ the direction of the bias of the SO2 coefficient
resulting from the omission of variables such as herbicide and
pesticide application is unclear.
It should be mentioned that the use of different cultivars by
farmers could not be incorporated into the model. Although
information on the use of the three leading soybean cultivars in each
state was available from Crop Production of the Crop Reporting Board,
USDA (64), these varieties were generally not used for more than 50
percent of the total number of acres harvested. No one cultivar
clearly dominated the production in any one state, and the county-
level use of these cultivars could not be identified from the
available data.
Aggregate Time Series Data
Time series data on the variables used to estimate the acreage
response and demand equations were obtained from various issues of
Agricultural Statistics (65), Fats and Oil Situation (66), Monthly
Bulletin of Agricultural Economics and Statistics (67), International
Financial Statistics Yearbook (68), and The Wharton EFA Annual Model
(69). These data are listed in Table 9-7 and were collected for the
1955 to 1977 time period. For reasons that will be explained when we
9-77
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Variable
TABLE 9-7. AGGREGATE TIME SERIES DATA
~ 2z?«~« wSmzz£~~——s!z~«——•———H««W«w«———^^?£^~*~ •
Definition
ACREP
ACREH
YLDYR
BUSHELU
BUSHELW
QDOM
QEXP
STOCK
STOCK(-1)
STOCKC
STOCKC(-l)
STOCKM
PSOY
TRANS
Soybean acres planted in crop year t (million
acres). Source: Reference (65).
Soybean acres harvested in crop year t (million
acres). Source: Reference (65).
Average yield of soybeans in crop year t (bushels
per harvested acre). Source: Reference (65).
Bushels of soybeans produced in the U.S. in crop
year t (million bushels). Source: Reference (65).
Bushels of soybeans produced in the rest of the
world (i.e., outside of the U.S.) in crop year t
(million bushels). Source: Reference (65).
Domestic disappearance of soybeans in crop year t
(million bushels). Source: Reference (65).
Net exports of soybeans in crop year t (million
bushels). Source: Reference (65).
Commercial stocks of soybeans held at beginning of
crop year t (million bushels). Source: Reference
(66).
Commercial stocks of soybeans held at beginning of
crop year t-1 (million bushels). Source: Reference
(66).
Stocks of soybeans held by the CCC at the beginning
of crop year t (million bushels). Source:
Reference (66).
Stocks of soybeans held by the CCC at the beginning
of crop year t-1 (million bushels). Source:
Reference (66).
Stocks of soybean cake and meal (1,000 tons).
Average U.S. price per bushel of soybeans received
by farmers in crop year t (dollars). Source:
Reference (66).
PSOYUK minus PSOYUSA.
(continued)
9-78
-------
Variable
TABLE 9-7 (continued)
Definition
PSOY(-l)
PCTN(-l)
PWHT(-l)
PCRN
PFISH
PGNUT
PSOYUK
EXC
INT
POP
GOV(-i;
TREND
DUM74
Average U.S. price per bushel of soybeans received
by farmers in crop year t-1 (dollars). Source:
Reference (65).
Average U.S. price per pound of cotton received by
farmers in crop year t-1 (cents). Source:
Reference (65).
Average U.S. price per bushel of wheat received by
farmers in crop year t-1 (dollars). Source:
Reference (65).
Average U.S. price per bushel of corn received by
farmers in crop year t (dollars). Source:
Reference (65).
Wholesale price per ton of fish meal in year t;
Menhaden 60% protein 100 Ib. bags F.O.B. East Coast
Plants (dollars). Source: Reference (67).
Import price per kilogram of Senegal groundnuts in
France (cents) in year t. Source: Reference (67).
Import price of a bushel of U.S. soybeans in the
United Kingdom in crop year t (dollars). Source:
Reference (67).
Exchange rate between the United States and Germany
in year t (deutche marks per U.S. dollar). Source:
Reference (68).
User cost of capital in the agricultural sector in
year t. Source: Reference (69).
People eating from civilian food supplies in year t
(millions). Source: Reference (65).
0-1 dummy variable indicating the presence of
government support in crop year t-1. Equal to 1 if
5 percent of the total number of bushels were
acquired by the CCC in crop year t-1; 0 otherwise.
Linear time trend variable where 1955 = 1, 1956 = 2,
1957 = 3, etc.
Dummy variable equal to 1 in 1974; 0 elsewhere.
9-79
-------
present the results of our yield equations, these data were collected
only for soybeans.
Data on commodities in the agricultural sector are reported on a
crop-year basis. A crop-year is from September 1 to August 31 of the
following calendar year.
All prices used in the estimation of the supply and demand
equations have been deflated by the Consumer Price Index (70) and are
expressed in terms of 1967 dollars.
YIELD EQUATION RESULTS
The estimation results of the yield functions for cotton and
soybeans will be presented in this subsection. A detailed explanation
of the equations for each of these crops will be followed by a brief
summary of the conclusions that can be drawn from this subsection
regarding the effect of ambient SC>2 on cotton and soybeans. In the
next subsection, these results will be used to estimate the economic
benefits of attaining SNAAQS.
The statistics that are reported for each equation are:
1) The estimated coefficient and standard error of each
variable included in the equation.
2) The number of observations (NOB) used to estimate the
equation.
9-80
-------
• • *?
3) The corrected coefficient of determination (R ) which
is a measure of the percentage of the variation in the
dependent variable that is explained by the variation
in the independent variables adjusted for the degrees
of freedom.
4) The F-statistic which is used to test the hypothesis
that none of the explanatory variables is signifi-
cantly different from zero.
5) The elasticity of yield with respect to the air pollu-
tion variable (eSO2).
The Durbin-Watson statistic is not reported since serial correlation
is not likely to be a problem in the pooled time series cross-
sectional data set we are using. Durbin-Watson statistics indicating
the presence of serial correlation would be a function of the manner
in which the data are entered (i.e., alphabetically by state). Since
the Durbin-Watson statistic could be changed simply by rearranging the
way in which the data are entered, we have not reported this statistic
in order to avoid confusion.
Cotton
The yield functions estimated for the cotton-producing states
included in the study are shown in Equations (1) and (2) of Table 9-8.
As can be seen in this equation, all of the variables except IRRIG are
in logarithmic form. This is because IRRIG is a dummy variable
indicating the presence of irrigation in the county. If any of the
acres growing cotton within the county are irrigated, the dummy
variable is equal to one. Otherwise, it is equal to zero.
9-81
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TABLE 9-8. YIELD FUNCTIONS FOR COTTON SAMPLE
(standard error in parentheses)
Variable
Constant
log(AMEAN)
log(X2HI)
log (TEMP)
IKRIG
log(NITROGENC)
log (LIME)
log(LABORC)
No. of observations
F
R2
'S02
==— — — — — _____ — _.
Equation 1
-2.250
U. 946)
-0.050
(0.080)
0.730*
(0.398)
0.538**
(0.110)
0.995**
(0.132)
0.089
(0.071)
0.202*
10.095)
84
16.491
0.528
-0.050
= = — = =—=:=:= — — -s s—
Equation 2
-2.452
(1.984)
0.016
(0.069)
0.794*
(0.389)
0.507**
(0.110)
1.006**
(0.146)
0.066
(0.075)
0.209*
(0.100)
83
15.492
0.515
0.016
**
* Significant at the 5 percent level.
Significant at the 1 percent level.
9-82
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The R2 of Equation -(1) is 0.528. All of the coefficients of the
economic variables included in the equation are of the expected signs.
As the t-statistic indicates, LIME is not significantly different from
zero.*
The coefficient of NITROGENC, significantly different from zero
at the 1 percent level, is extremely high, indicating that a 10
percent increase in the use of nitrogen will result in approximately a
10 percent increase in cotton yield. The magnitude of this sign may
be the result of the fact that NITROGENC may be correlated with
variables that are not included in the equation. Inclusion of other
fertilizer variables, however, did not affect the magnitude of the
sign. IRRIG, the dummy variable indicating the presence of
irrigation, is positive and significant at the 1 percent level. TEMP
also has a significant, positive effect on cotton yield.
The variable representing the exposure of cotton to SC^/ AMEAN,
is negative but not significant.** Alternative specifications did not
affect the sign or significance of this variable.
* Unless otherwise stated, significance levels are reported at the 5
percent and 1 percent levels. In general, when an independent
variable is said to be significantly different from zero, it means
that the variable can be considered to have a potential effect on
the dependent variable.
** Since evidence exists that SC>2 can either enhance or diminish crop
yield, we will use a two-tailed test when evaluating the
significance of the coefficient of SOo. One-tailed tests will be
used to evaluate the significance or the other input variables
since it is hypothesized that the partial derivatives of yields
with respect to these inputs are positive.
9-83
-------
In Equation (2), an alternative measure of SO 2 is used in the
yield equation. The coefficient of X2HI has a positive sign but is
not significant. The significance of the coefficients of all of the
other variables are relatively unchanged.
Other specifications of the yield functions for the cotton-
producing counties that were tried generally did not change the
reported results for SC^
Because there may be significant differences in the production
process throughout the country that cannot be controlled for in our
yield functions (i.e., soil conditions, cultural practices), we have
also estimated yield equations for regional subsets of the cotton-
producing states. Estimating yield equations may enable us to uncover
more reliable estimates of the true relationship between crop yield
and S02, since these excluded factors may not vary within a particular
agricultural region.
Equations (1) through (3) of Table 9-9 present the results of the
regional cotton yield equations for: (1) Arizona, New Mexico and
California, (2) Alabama and Mississippi, and (3) Texas. Except for
California, the states included in each region are based on the break-
down of agricultural regions listed in Table 9-6. California was
included in the Mountain Region since there were not enough observa-
tions to estimate a yield equation for this state independently.
9-84
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TABLE 9-9. REGIONAL YIELD FUNCTIONS FOR COTTON SAMPLE
(standard error in parentheses)
Variable
Constant
X2HI
A2HI
TEMP
RAIN
NITROGENC
LABORC
No. of observations
F
R2
cSOi
Equation 1
AZ, NM and CA
418.405
(385.846)
-0.177
(0.180)
—
-6.066
(17.630)
-3.079
(3.703)
5.760**
(1.515)
-9.128
(20.424)
33
7.109
0.488
0.074
Equation 2
AL and MS
-569.429*
(257.680)
—
-0.138
(0.127)
20.471*
(9.981)
-0.393
(0.750)
7.681**
(2.282)
—
33
6.772
0.419
0.052
**
Significant at the 5 percent level.
Significant at the 1 percent level.
(continued)
9-85
-------
TABLE 9-9 (continued)
Equation 3
Variable TX
Constant -5.992
(4.142)
log(A2HI) 0.349**
(0.090)
log(TEMP) 1.267
(0.756)
IRRIG 0.567**
(0.109)
log(NITROGENC) 1.108*
(0.509)
log(LIMEC) 0.166
(0.321)
No. of observations 33
F(5/27) - 8.634
R2 0.476
0.349
* Significant at the 5 percent level.
** Significant at the 1 percent level.
9-86
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Equation (1) shows a linear cotton yield specification for
_2
Arizona, New Mexico, and California. The R of this equation is
approximately 0.488. The only variable in this equation significantly
different from zero is NITROGENC. RAIN, TEMP, and LABORC are negative
although insignificant. The coefficient of X2HI, although negative,
is insignificant.
Alternative specifications of this regional yield equation were
tried (i.e., log-linear, quadratic), but did not significantly alter
the results for SC>2. The coefficients of the SO2 variables were
generally positive and insignificant in the log-linear specifications.
When the SCu variables were entered with an interaction term (e.g.,
X2HI • RAIN and X2HI • TEMP), the coefficients of these terms were
insignificant.
A regional production function for Arizona and New Mexico was
also estimated to see if the production function would be better
specified using a more homogeneous region. The results for S02 were
not significant in these specifications.
The linear yield equation generally behaved better than the log-
linear functions for the agricultural region including Alabama and
Mississippi. As Equation (2) shows, R2 is equal to 0.419 with TEMP
and NITROGENC being of the expected signs and significantly different
from zero. Surprisingly, the coefficient of RAIN is negative,
9-87
-------
although insignificant (cotton is not irrigated in Alabama and
Mississippi). The coefficient of the A2HI term is not significant.
Alternative measures of SCu were used in place of A2HI but were
not significant. Interaction terms between SC^ and the climate
variables did not improve the specifications and were not significant.
When the other fertilizer variables were entered into the equation,
they generally were not significant and had inconsistent signs.
The third regional equation specified for the cotton data set is
for Texas. Texas is the leading producer of cotton in the United
States (Agricultural Statistics, 1979). A complete set of observa-
tions, however, were only available for approximately 14 of the 152
cotton-producing counties in the state. As Equation (3) shows, A2HI,
IRRIG, and NITROGENC are significantly different from zero at the 1
percent level. A2HI is positive and, surprisingly, significant at the
1 percent level. The elasticity of yield with respect to A2HI is
0.349, which is extremely high relative to the other elasticities that
have been reported for the cotton yield equations.*
The coefficients of TEMP and NITROGENC seem to be extremely high
in this equation. It is interesting to note that LIMEC, although
positive, is not significantly different from zero. This may be due
* The elasticity is a measure of the percent change in one variable
that can be expected from the percent change in another variable;
i.e., [(8Y/Y)/(ax/X)].
9-88
-------
to the fact that the data used as proxies for these inputs are state-
specific. Consequently, only year-to-year variations in the use of
lime are measured by the variables in the Texas yield equation.
The sign and significance of X2HI were relatively constant over
all of the alternative specifications that were tried. When X2HI was
entered into the yield equations instead of A2HI, it was positive but
insignificant. XMEAN and AMEAN were negative but not significant.
The strong positive relationship exhibited between A2HI and crop yield
may be due to the soil composition in Texas. The soil in the
southwestern part of the country tends to be alkaline with pH levels
in the 7 to 8.5 range (as per conversation with state soil
scientists). In alkaline areas such as these, plants may have to rely
on the SCU in the atmosphere for their sulfur needs. Consequently, it
is possible that SCU may have a positive impact on crop yield. As
explained in the literature review, plants grown in sulfur-deficient
soils have been shown to metabolize S02 from the atmosphere for their
sulfur requirements (18). However, injury will occur if the amount of
the sulfur ions present in the plant cell exceed that which can be
oxidized and assimilated. In order to test for this possibility, a
quadratic S02 term was included in the specification of the yield
function. The linear term remained positive and significant in this
specification, while the square term, although negative, was
insignificant.
9-89
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Soybeans
The results of the yield equations estimated for the soybean-
producing counties are presented in Table 9-10. The results of a log-
linear yield equation are reported in Equation (1). Because of the
lack of data on the use of fertilizer and labor for all of the states
included in this analysis, this equation is based on 271 observations.
The coefficients of all of the economic variables except LIME and TEMP
are significantly different from zero. The signs of the coefficients
of NITROGEN and K20 do not conform with a_ priori expectations,
however. Besides the fact that the data used to reflect the use of
these fertilizers are gross approximations of county level use, the
perverse signs exhibited in Equation (1) may be due to the relation-
ship between fertilizer application and the inherent quality of
soybeans and the soil. Soybeans are known to be a nitrogen-fixing
plant, meaning that instead of taking nitrogen out of the soil for
their nutritional requirements, soybeans provide the soil with
nitrogen. Consequently, it is not surprising that nitrogen
application has a negative impact on soybean yield in Equation (1).
In addition, soils that are rich in nutrients will not need to be
fertilized as intensively as those soils that are lacking nutrients.
Thus, the relationship exhibited in Equation (1) does not necessarily
reflect a cause-and-effect relationship and does not mean that the
application of more K20 will result in lower soybean yields. It is
more likely that the application of larger amounts of this fertilizer
in certain regions indicates that the soil is inherently lacking the
9-90
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TABLE 9-10. YIELD FUNCTIONS FOR SOYBEAN SAMPLE
(standard error in parentheses)
Variable
Equation 1
Equation 2
Constant
log(X2HI)
2.075**
(0.427)
2.509**
(0.336)
-0.015
(0.018)
log(AMEAN)
log (TEMP)
log (RAIN)
log (NITROGEN)
P2°5
K20
log (LIME)
log ( LABOR)
No. of observations
F
R2
CS02
-0.015
(0.020)
0.077
(0.094)
0.110**
(0.036)
-0.146**
(0.057)
0.212*
(0.116)
-0.150*
(0.078)
0.008
(0.028)
0.184**
(0.050)
271
32.896
0.486
-0.015
_.
0.090
(0.066)
0.022
(0.036)
-0.007
(0.020)
0.183**
(0.019)
459
45.497
.0.327
-0.015
**
* Significant at the 5 percent level.
Significant at the 1 percent level.
9-91
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nutrients necessary to grow soybeans and the yields in these areas
will tend to be less than areas where the soil is inherently rich in
nutrients. Thus, 1^0 may be acting as a proxy for the presence of
poorer quality soils in certain states.
The coefficient of AMEAN is negative but not significant. When
the other S02 variables were used in Equation (1) in place of AMEAN,
they also were not significant.
Alternative specifications of the yield function were tried but
did not result in an improvement of the reported results.
Since the use of different amounts of fertilizer will tend to
diminish the variation in the fertility levels of the soils growing
soybeans, we have dropped these variables from Equation (1) under the
assumption that the fertility of the soils in which soybeans are grown
are basically the same due to fertilization. LIME was not dropped
from this equation because of the suspected relationship between
atmospheric SC>2 and the application of LIME (i.e., the pH level of
soil may be increased through the application of lime). This enables
us to include the states excluded from Equation (1) due to the lack of
fertilizer data. These results are shown in Equation (2). Compared
to Equation (1), the R is reduced significantly in this equation.
The coefficient of LABOR is positive and significant, and relatively
unchanged from Equation (1). The coefficient of X2HI is negative but
insignificant. It is interesting to note that the magnitude of the
9-92
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coefficient of X2HI is the same as the coefficient of AMEAN. The
remainder of the variables included in the equation were not
significant.
The equation was re-estimated using the different measures of S02
in place of X2HI. Although the coefficients of these variables were
negative, none of them were significant.
In order to determine whether regional differences were obscuring
the posited relationship between S02 and soybean yield, yield
equations were also estimated for specific agricultural regions.
Based on the regions listed in Table 9-10, regional yield functions
were estimated for: (1) Mississippi; (2) Illinois, Indiana, Iowa, and
Ohio; (3) Texas; (4) Alabama, Georgia, and Kentucky; and (5) Michigan,
Minnesota, and Wisconsin. The results of these estimations are
reported in Equations (1) through (5) of Table 9-11.
Equation (1) presents the results of the estimated yield function
for Mississippi. Although the coefficient of A2HI is negative, it is
insignificant. The F-test for this and alternative specifications of
the Mississippi yield equation indicated that none of the coefficients
in the equation were significantly different from zero.
Equation (2) presents the results of the equation estimated for
the Corn Belt Region (Illinois, Indiana, Iowa, and Ohio). The R2 of
this equation is relatively low (0.151) compared to the other regional
9-93
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TABLE 9-11. REGIONAL YIELD FUNCTIONS FOR SOYBEANS
(standard error in parentheses)
Variable
Constant
X2HI
A2HI
(X2HI • TEMP)
TEMP
RAIN
LIME
LABOR
No. of observations
F
R2
£.qn o
Equation 1
MS
13.882*
(8.439)
-0.007
(0.004)
-0.213
(0.249)
0.024*
(0.012)
1.495E-05**
(5.831E-06)
35
2.541
0.154
-0.040
=— — — — — — — ___.
Equation 2
IL, IN, IA, OH
7.130
(5.292)
-0.006**
(0.002)
0.479**
(0.162)
-0.001
(0.011)
4.483E-07*
(2.133E-07)
0.215**
(0.062)
234
9.312
0.151
-0.049
Equation 3
TX
-101.562**
(41.183)
0.882**
(0.249)
-0.038**
(0.011)
5.266**
(1.944)
0.070**
(0.023)
1.243E-04
(8.153E-05)
-4.650
(3.555)
19
3.539
0.458
-0.124
* Significant at the 5 percent level.
** Significant at the 1 percent level.
(continued)
9-94
-------
TABLE 9-11 (continued)
Variable
Constant
log(X2HI)
log(RATIOX)
log(X2HI) • log (RAIN)
log (TEMP)
log (RAIN)
log (LIME)
log (LABOR)
No. of observations
F
R2
£S02
Equation 4
AL, GA and KY
-12.749**
(3.498)
1.525*
(0.612)
-0.317*
(0.130)
0.256
(0.225)
1.841**
(0.690)
0.399**
(0.080)
0.202
(0.217)
108
12.740
0.397
0.064
Equation 5
MI, MN and WI
-4.252**
(1.610
-0.041
(0.084)
0.936**
(0.340)
-0.060
(0.113)
0.084
(0.054)
1.576**
(0.332)
98
6.957
0.235
-0.041
**
* Significant at the 5 percent level.
Significant at the 1 percent level.
9-95
-------
equations. Alternative specifications did not significantly improve
_2
the R , and the coefficient of RAIN is negative but not significant in
this equation. The coefficients of the other variables in the
equation have their expected signs and are significantly different
from zero. In addition, a significant negative relationship between
SC>2 and soybean yield in the Corn Belt Region is observed from the
results of this equation.
Alternative specifications and S02 measures that were tried
consistently revealed a significant negative relationship between S02
and YLD. The addition of the fertilizer variables into the equation
did not affect the size or significance of the coefficient of X2HI.
The results of the yield function estimated for Texas are shown
in Equation (3). A linear yield function gave the best results for
this state. Neither LIME nor LABOR are significantly different from
zero in this equation. The coefficients of the climatological
variables are positive and significant, however. Both X2HI and the
variable expressing the interaction between SC^ and temperature
(X2HI • TEMP) are significantly different from zero. Their signs
indicate that SC^ may have a positive impact on soybean yield for a
range of temperatures that are relatively low. As temperature
increases, however, this positive impact on yield diminishes and at
some point becomes negative. When evaluated at the mean of TEMP, the
partial derivative of YLD with respect to X2HI is -0.0185.
9-96
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Equation (4) of Table 9-11 presents the regression results for
the regional yield functions including the states of Alabama, Georgia
and Kentucky. Mississippi was not included in this set due to its
lack of data on LABOR. Due to an insufficient number of observations
on NITROGEN, P2°5' an<^ K2°' tiiese variables could not be included in
the equation. Since these variables do not tend to be correlated with
the S02 variables, their omission is not a serious concern.
As can be seen in Equation (4), all of the estimated coefficients
are significantly different from zero except for TEMP and LABOR. The
lack of significance of LABOR may be due in part to the lack of
variation in the variable across the regions included in this data
set. LIME has a positive sign and is strongly significant.
In addition to including X2HI and RAIN as separate variables, the
log-linear yield function reported in Equation (4) includes a term
that reflects the interaction between X2HI and RAIN. This variable is
included to test for the possibility that the effect of S02 on
soybeans may differ depending on the level of rain. As evidenced by
Equation (4), both of the terms, including X2HI, are significant.
Evaluated at the mean of RAIN, the elasticity of soybean yield with
respect to X2HI is 0.064 and significantly different from zero.
The results of the yield equation estimated for the Lake States
(Michigan, Minnesota and Wisconsin) are listed in Equation (5) of
Table 9-11. The R2 of this equation is 0.235. The only variables
9-97
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significantly different from zero in this equation are TEMP and LABOR.
Both of these variables are of their expected signs. The coefficient
of LABOR is extremely high, suggesting that it might be acting as a
proxy for another variable. Surprisingly, neither the coefficient of
LIME nor RAIN is significant. RATIOX is negative but insignificant.
The coefficients of the other S02 variables that were tried were
generally positive but were not significant. The alternative forms of
the yield function and alternative measures of S02 that were tried
also did not improve the results.
Summary of Results
Based on the results reported in Tables 9-8 and 9-9, we are
unable to assert that ambient S02 concentrations have a significant
negative impact on cotton yield in the counties in our study.
Although the results suggest that in some cases S02 may be negatively
related to cotton yield, these results were not significant. In fact,
the only significant relationship exhibited between S02 and YLDC was
found in the Texas yield function and indicated that SO2 had a
positive effect on cotton yield. The results of the yield functions
estimated for the cotton-producing counties are not too surprising for
a number of reasons.
One reason for the lack, of significance between S02 and cotton
yield may result from the possibility that the S02 levels in the
counties included in this study are not high enough to have a
9-98
-------
deleterious effect on cotton yield. For example, the average of the
maximum of the annual average SCu readings (XMEAN) for the 84 counties
included in this study is 29.08 jag/m . Given that the soils in some
of the cotton-producing areas tend to be rather alkaline, it is
possible that the cotton plants are drawing on the SC>2 in the
atmosphere for their sulfur requirements and consequently would not be
negatively impacted by exposure to SC>2. In fact, as the results of
the Texas yield function show, it is possible that crop yield may
actually be enhanced due to the exposure to S02. This result is
consistent with studies which have found that plants grown in soils
deficient in sulfur can be positively affected by exposure to SC>2
(16,17). Since none of the sample cotton-producing counties in Texas
in 1977 had an S02 reading for A2HI that excluded 215 ng/m , the
relationship exhibited between S02 and cotton yield in Texas is
certainly reasonable.
Although the yield functions estimated for the entire soybean
data set did not find a significant negative relationship between S02
and soybean yield, certain regional yield functions that were
estimated indicated that such a relationship did exist on the regional
level. The significant differences in the relationship between S02
and soybean yield exhibited in the regional yield equations suggest
that various climatological and soil factors within each region may
play an important part in determining the susceptibility of soybeans
to air pollution.
9-99
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The yield functions estimated for Mississippi and the Lake States
Region (Michigan, Minnesota and Wisconsin) did not indicate that the
soybean yield and SC^ were negatively related. The results of the
yield equation for the Lake States Region are particularly surprising
since approximately 36 percent of the counties included in our sample
exceeded 260 ^g/m for the average of the second highest SC>2 readings
within a county (X2HI).
A significant relationship was found to exist between soybean
yield and S02 in the states of Alabama, Georgia and Kentucky. The
relationship exhibited in these states indicates that in the presence
of relatively large amounts of rain (123.08 centimeters), SOn can have
a deleterious effect on soybean yield. This result is somewhat
similar to the results of laboratory studies that have found that
plants are more susceptible to SO^ in the presence of adequate amounts
of soil moisture.
Significant negative relationships between soybean yield and
various measures of S02 were also found to exist for the Corn Belt
Region (Illinois, Indiana, Iowa and Ohio) and Texas, and this
relationship remained consistent in the alternative specifications
that were tried. Interestingly, the relationship between SC^ and
soybean yield in Texas was dependent on temperature.
The results of our estimation of regional yield functions for
both cotton and soybeans are certainly plausible given the data with
9-100
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which we were working. Since this analysis examines the effect of S02
on yields during 1975 to 1977, it is possible that farmers have had
time to adjust to past levels of S02 and that the yields in 1975 to
1977 reflect this adjustment. Changes in the amount of the crop
planted in a particular area and changes in the type of seed
(cultivar) used are examples of the adjustment that farmers may have
made to avoid the effects of S02 on their crops. Consequently, the
true effect on yield will be understated if these types of adjustment
to ambient SCU have already taken place. In addition, it is possible
that the air quality during the 1975 to 1977 time period has improved
so that the deleterious effects of S02 on cotton and soybean yields
are not discernible.
As mentioned in the Data subsection, the relationship between S02
and crop yield may be obscured because our data sets are comprised of
information on farm production and S02 aggregated to the county level.
The different effects of SO2 on yield within each county cannot be
identified in this analysis. This may be particularly relevant in
counties where the air quality varies significantly throughout the
county. For example, if certain farmers within a county experience
depressed yields because their farms are located downwind of a power
plant and farmers upwind of the plant are not affected by the plant's
emissions, the aggregation of yields to the county level will tend to
obscure the relationship between SO2 and yield.
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It is also possible that the relationship between S02 and crop
yield may be obscured due to the air quality data used in this
analysis. Evidence exists that certain plants are more susceptible to
air pollution during their flowering stages, which tend to occur
during the third quarter of the year (54). Use of the means and
second highest values of SCU during the second quarter of the year may
consequently underestimate the impact of SC>2 on crop yield.
Even with these data limitations, a significant negative
relationship between SC^ and soybean yield has been found to exist in
certain regions of the country. In the next subsection, we will use
the yield functions of these regions to estimate the change in yield
that can be expected from attainment of alternative SNAAQS. It is
important to note that based on these data limitations, these
estimates will be considered to be lower-bound estimates of the
benefits of attaining alternative SNAAQS.
BENEFIT ESTIMATION
In this subsection, we will estimate the benefits of attaining
alternative SNAAQS for those regions where our estimated yield
functions indicate that a significant negative relationship between
SC>2 and crop yield exists. Since such a relationship was not found
for any of the states included in the cotton sample, and in only some
of the states included in the soybean sample, agricultural benefits
9-102
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will be calculated only for the soybean-producing counties of Alabama,
Georgia, Kentucky, Illinois, Indiana, Iowa, Ohio and Texas.*
The scenario for reaching the secondary standard is identical to
the one used in the other sections of the report; i.e., the level of
SC>2 will improve by half of the amount necessary to reach the
secondary standard by the end of 1986 and by the remaining amount by
the end of 1987. It is also assumed that these improvements will be
instantaneous, occurring on the last day of 1986 and 1987. In the
agricultural sector this means that half of the improvement will occur
during the crop year of 1986 and the remaining half will occur during
the crop year of 1987. Once the secondary standard is attained at the
end of 1987, it is assumed that it will be maintained indefinitely
into the future. It is assumed for our analysis that any soybean-
producing county that was in excess of the primary standard in 1977
will be assumed to be meeting the primary standard in 1985, and
benefits will be estimated for the change in pollution from the
primary to the secondary standard. Benefit calculations for any
soybean-producing county that had a level of pollution in 1977 that
was less than the primary but more than the secondary standard will be
based on the change in pollution from the 1977 level to the secondary
standard. Any soybean-producing county that was meeting the secondary
* Although the significant positive relationship found to exist
between S02 and cotton yield for the sample counties in Texas
indicates that reductions in the level of S02 will result in
reductions in crop yield, the "negative" benefits (i.e., costs) in
these counties need not be calculated since none of these counties
exceeded the alternative SNAAQS in 1977.
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standard in 1977 is assumed to be meeting it in 1985.* Consequently,
under our assumptions there would be no economic benefits in these
counties resulting from the implementation of SNAAQS.
Benefits estimates will be based on compliance with these
alternative standards:
S02
Annual arithmetic mean
24-hour maximum*
3-hour maximum+
Alternative secondary
air quality standard
60
260
1,300
Given this scenario and the requirement that a significant
negative relationship exists between SC^ and soybean yield, our
benefit calculations will be limited to the soybean-producing counties
in Illinois, Indiana, Iowa and Ohio (hereafter referred to as the Corn
Belt Region).++ The counties in the other regions where a significant
relationship between S02 and soybean yield has been found to exist
* The other sections of this study base the estimated reduction in
pollution necessary to meet the secondary standard on 1978 pollu-
tion levels.
** The standards listed above are not, in all cases, part of the
current Federal regulations. The source of the standards shown
here is Stern et. _al_. (71), p. 159; and Air Quality Data, Annual
Statistics, 1977 (72).
+ This value is not to be exceeded more than once a year.
-H- The Corn Belt Region, as defined by the U.S. Department of
Agriculture, also includes the state of Missouri.
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would not experience an increase in soybean yield as a result of the
improvement in air quality.*
In order to calculate the economic benefits of increased soybean
yields, we have also assumed that the soybean market in 1977 can be
used to represent the soybean market over the period for which we will
calculate benefits. In other words, except for the level of S02, all
the factors influencing soybean yield, production, and price in 1977
are assumed to hold over the period of our analysis.**
Based on the above scenario, the physical increases in yield (in
terms of bushels) that can be expected from the implementation of
SNAAQS can be calculated using the relationship between yield and SCu
estimated in the soybean yield function for the Corn Belt Region (see
Equation (2) in Table 9-11). The improvement in yield for each county
exceeding the secondary standard in the Corn Belt Region can be
calculated from:
AYLD = 0.006 (AS02)
* See the Results subsection for explanation of the interaction
between climate and SCu in the production functions for Alabama,
Georgia, Kentucky and Texas.
** This may tend to underestimate the benefits of achieving SNAAQS
since the amount of acreage planted into soybeans has been
increasing over the past and is expected to continue to increase in
the future (73).
9-105
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where 0.006 = aYLD/3S02? the change in yield due to a change in
SC>2 that is estimated from the Corn Belt Region
yield function.
Table 9-12 lists the estimated increases in the average yield of
soybeans that can be expected from moving from the primary to the
alternative secondary standard.
Supply and Demand Equations
As mentioned in the Methodology subsection, it is necessary to
examine the estimated relationship between SCU and crop yield within
the framework of the soybean market. The estimated supply and demand
equations that will be used to calculate the benefits of implementing
alternative SHAAQS are reported in this subsection.
The statistics reported for these equations are the same as the
ones reported for the yield equations. Two additional statistics,
however, are reported for these equations. They are:
(1) The Durbin-Watson statistic (DW) which is used to test
for the existence of serial correlation among the
error terms.
(2) The correlation coefficient (X) between the error
terms in period t and period t-1 is reported when
serial correlation is suspected to be a problem.
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TABLE 9-12. AVERAGE YIELD OF SOYBEANS IN THE UNITED STATES
UNDER ALTERNATIVE SO2 LEVELS
Bushels
Average yield in the presence of the primary standard 30.587
Average yield after moving halfway to the alternative 30.591
secondary standard
Average yield after attaining the alternative secondary 30.596
standard
Supply—
Acreage Response Equation—The soybean acreage response equation
is reported in Table 9-13. The specification used in Table 9-13 is
similar to the acreage response equations developed for soybeans by
Houck et al. (50), Adams e_t al. (51), and Baumes and Meyers (52).
The variables used to reflect the price expectations of farmers
in year t are the prices of soybeans and substitute crops in
production in year t-1.
All of the price variables included in this equation have their
expected signs and are significantly different from zero. The price
of soybeans in year t-1 has a significant impact on the number of
soybean acres planted in year t, indicating that producers base their
planting decisions on the prices received for soybeans in the previous
year. Alternative lagged soybean price variables were tried, such as
PSOY(-2) and [PSOY(-l) - PSOY(-2], but were not significantly
9-107
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TABLE 9-13,
SOYBEAN ACREAGE RESPONSE EQUATION
(standard error in parentheses)
Variable ACREP
Constant
PSOY(-l)
PCTN(-l)
PWHT(-l)
TREND
GOV(-l)
No. of observations
F(5/17)
R2
DW
£PSOY(-1)
* Significant at the 5 percent level,
** Significant at the 1 percent level,
16.681**
(2.441)
6.794**
(1.051)
-0.189*
(0.075)
-3.860**
(1.045)
1.192**
(0.096)
0.655
(0.729)
23
330.051
0.987
1.95
0.512
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different from zero. The elasticity of soybean acres planted (ACREP)
with respect to PSOY(-l) is 0.512. This elasticity is larger than the
elasticity of 0.39 reported by Houck et_ al_. (74) and smaller than the
elasticity of 0.84 reported by Houck and Subotnik (75). It is
reasonably close to the elasticity of 0.56 reported by Gardner (76)
and within the range of elasticities of 0.21 to 0.97 reported by Adams
et al. (51).
The lagged price of cotton and wheat were included in the soybean
acreage response equation in order to control for the impact that the
prices of other crops that compete with soybeans for acreage have on
the quantity of soybean acreage planted. The coefficients of these
variables — both negative and significantly different from zero —
imply that farmers are responsive to the lagged prices of crops that
can be planted in place of soybeans. Wheat is a substitute crop for
soybeans in the Lake States agricultural region, while cotton is a
substitute crop in the agricultural regions comprising the Atlantic
and Delta States. Given the significant increase in the production of
soybeans relative to the production of cotton in the Delta States over
the period of this analysis, it is not surprising that the lagged
price o£ cotton has a significant impact on the number of acres of
soybeans planted. When the lagged price of corn, a major substitute
for soybeans in the Corn Belt Region, was included in Equation (9.13),
it was plausibly signed but insignificant. Equation (9.13) was also
estimated with the lagged price of wheat being replaced by the lagged
price of corn. Although the coefficient of the lagged price of corn
9-109
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was negative and significantly different from zero, the F-statistic
decreased to 269.007 and the Durbin-Watson statistic suggested that
serial correlation was a problem. Consequently, it was decided not to
use this specification.
The linear time trend variable (TREND) that is included to
reflect the secular trend in the number of soybean acres planted is
positive and significantly different from zero. GOV(-l), the dummy
variable indicating the presence of government support operations in
the year prior to the planting of soybeans, is positive but not
statistically different from zero.
«. 0
The R of the equation is 0.987, indicating that the estimated
equation fits the historical data quite well. The Durbin-Watson
statistic (DW) does not indicate that serial correlation is a problem
in this equation.
Acres Harvested—Over the period of this analysis (1955 to 1977),
approximately 98.6 percent of the soybean acreage planted has been
harvested. Therefore, we will use this percentage to estimate the
number of soybean acres harvested in each period.
9-110
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Demand Equations
The components of the demand for soybeans are reported in Tables
9-14 to 9-16. Due to the simultaneous determination of the price of
soybeans (PSOY) and the components of demand, these equations are
estimated using two-stage least squares.
Domestic Demand—
Table 9-14 reports the results of the domestic demand equation
for soybeans. Preliminary estimation of this equation suggested that
there was serial correlation of the error terms in successive years.
Consequently, the equation was re-estimated with the variables
transformed into generalized differences.*
All of the variables included in the equation exhibit their
expected signs and are statistically different from zero. The
elasticity of the domestic demand for soybeans with respect to its own
price, PSOY, is equal to -0.350. The price of corn (PCRN), a feed
grain consumed by livestock, is positive and significantly different
from zero. Although not a perfect substitute for soybeans in terms of
* The form of the generalized difference domestic demand equation is:
QDOM - X • QDOM(-l) = J3,(1-X) + P2 (PSOY - X • PSOY(-l)) + £3 (PCRN
- X • PCRN(-l)) + J34 (PFISH - X • PFISH(-l)) + &5 POP - X • (POP(-
D) + 13g(DUM74 - X • DUM74), where X is the estimated correlation
coefficient between the error terms in year t and t-1, and |3 is the
estimated coefficient of the variable. See Pindyck and Ruoinfeld
(77) and Cochrane and Orcutt (78) for an explanation of this
process.
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TABLE 9-14. SOYBEAN DOMESTIC DEMAND EQUATION
(standard error in parentheses)
Variable
QDOM
Constant
PSOY
PCRN
PFISH
POP
DUM74
No. of observations
F(5/17)
R2
DW
CPSOY
X
-2184.860**
(290.023)
-78.071**
(18.481)
96.545*
(46.286)
0.447*
(0.185)
14.853**
(1.512)
-109.139**
(29.448)
23
29.629
0.867
1.99
-0.350
0.8005
* Significant at the 5 percent level.
Significant at the 1 percent level.
**
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TABLE 9-15. SOYBEAN EXPORT DEMAND EQUATION
(standard error in parentheses)
Variable
QEXP
Constant
PSOY
PGNUT
PFISH
BUSHELW
TRANS
EXC
TREND
No. of observations
F(7/15)
R2
DW
''PSOY
-869.865**
(203.928)
-125.288**
(23.273)
5.596*
(2.606)
0.608**
(0.215)
-0.177**
(0.064)
-44.965*
(24.470)
-164.224**
(37.803)
21.614**
(2.841)
23
199.891
0.984
2.23
-1.175
**
Significant at the 5 percent level.
Significant at the 1 percent level.
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TABLE 9-16,
SOYBEAN STOCK DEMAND EQUATION
(standard error in parentheses)
Variable
STOCK
Constant
PSOY
PSOY(-l)
STOCKM
BUSHELU
INT
STOCK(-1)
No. of observations
F(6/14)
R2
DW
'PSOY
73.616**
(119.191)
-39.886**
(11.527)
42.771*
(13.618)
0.239*
(0.099)
0.054
(0.037)
-6.407
(7.315)
0.410**
(0.145)
21
13.227
0.786
1.66
-1.216
* Significant at the 5 percent level,
** Significant at the 1 percent level
9-114
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protein content, the sign and significance of this variable indicate
that higher corn prices will lead to the more intensive use of
soybeans as an animal feed. The price of fish meal (PFISH), a high-
protein livestock feed, is also positive and significantly different
from zero, indicating that fish meal is used as a substitute for
soybeans in consumption. A variable for livestock, representing one
of the primary demanders of soybeans, was also included in the
domestic demand equation. It did not conform to a. priori
expectations, and consequently was excluded from the final equation.
Since soybeans are also consumed by humans (e.g., soybean oil,
processed foods), various variables, such as the consumption of fats
and oils by humans, were included to reflect this component of demand.
These variables were generally not significantly related to domestic
soybean demand. As seen in Table 9-14, POP, a variable measuring the
number of people eating from civilian food supplies, is positive and
significantly related to domestic demand.
The coefficient of DUM74, representing the unusual conditions of
the soybean market in 1974 (i.e., smaller acreage and sharply reduced
yields) is negative and statistically significant.
Export Demand—
The export demand equation for soybeans is reported in Table 9-
15. Like the acreage response equation, the percent of variation in
9-115
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export demand (QEXP) explained by the variables included in this
— 2
equation is extremely high (R = 0.984). The Durbin-Watson test for
serial correlation was in the indeterminate range for this equation.
Consequently, no corrective measures were taken.
The relationship between QEXP and PSOY is negative and
significant. The elasticity of QEXP with respect to PSOY is -1.175.
This is much higher than the "own-price" elasticity reported for the
domestic demand equation. This is to be expected since importing
countries are more likely to substitute soybeans from other countries
(e.g., Brazil, Nigeria) for U.S. soybeans than U.S. demanders. The
elasticity reported in Table 9-15 is higher than the -0.54 export
elasticity of demand reported by Houck et al. (50). It is lower,
however, than the export demand elasticity of -1.99 reported by Baumes
and Meyers (52).
The coefficients of the variables measuring the effect of the
prices of substitute goods in consumption, PGNUT and PFISH, are both
positive and statistically significant.
BUSHELW, the number of bushels of soybeans produced by the rest
of the world, has a significant negative impact on the export demand
for soybeans. TREND, the variable representing the upward trend in
soybean exports over time, is positive and significantly different
from zero.
9-116
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Since the export demand for soybeans also depends on the cost of
transporting soybeans from the United States to the importing
countries, a variable reflecting this cost is also included in the
export demand equation. A variable reflecting the actual cost of
soybean shipment was not available when the export demand equation was
estimated; therefore, the difference between the price of soybeans in
the United Kingdom and the United States (TRANS) was used as a proxy
for transport cost. Since Western Europe imports a significant amount
of soybeans, it was felt that TRANS would be an appropriate proxy. As
Equation (9.15) shows, TRANS is negative and significant.
The export demand for soybeans will also be influenced by the
exchange rate between the U.S. and foreign currencies. Since West
Germany is a primary demander of soybeans, and since the currencies of
Western European counties, with the exception of the English pound,
move somewhat in tandem with the West German deutsche mark, the
exchange rate between the deutsche mark and U.S. dollar (EXC) was used
as a proxy for the exchange rates between the United States and
importing counties. Time did not permit development of a broader
measure of exchange rates.
The coefficient of EXC, positive and significant, indicates that
soybean export demand is quite sensitive to changes in the exchange
rate. The elasticity of export demand with respect to the deutsche
mark-U.S. dollar exchange rate is -1.98. This is higher than -1.39
elasticity of the exchange rate variable in the study of the soybean
9-117
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market by Baumes and Meyers (52). Although it seems likely that the
export demand for soybeans would be responsive to changes in the
exchange rate since importing countries can buy soybeans from a number
of different exporting countries, the price elasticity of this
equation is somewhat unrealistic.
Stock Demand—
Table 9-16 reports the results for the soybean stock demand
equation. Because ordinary least squares will result in biased and
inconsistent coefficient estimates when some of the variables included
in the equation are lagged endogenous variables, it could not be used
to estimate the stock demand equation since both PSOY(-l) and
STOCK(-1) are lagged endogenous variables. Using a technique
developed by Fair (79), an instrumental variable for the endogenous
variable in the equation (PSOY) was created and the equation was
estimated using generalized least squares.
The coefficient of PSOY conforms to a_ priori expectations,
indicating the people will hold fewer stocks of soybeans as the market
price for soybeans rises. The elasticity of stock demand with respect
to PSOY is quite high, -1.216. This is much larger than the stock
demand elasticity of approximately -0.06 reported by Houck et al.
(50^, but lower than the elasticity of -2.29 reported by Baumes and
Meyers (52).
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PSOY(-l) is included in the equation in order to reflect the
speculative demand for soybeans. It is positive and significant,
indicating that higher prices for soybeans in year t-1 will result in
more soybean stocks being held in year t. The price of soybeans in
year t+1 [PSOY( + 1)] was also included in order to reflect the
possibility that stockholders base their expectations on future
prices. The coefficient of this variable was implausibly signed and
not significantly different from zero.
The coefficient of stocks in year t-1 is positive and
significantly related to soybean stock holdings in year t. BUSHELU,
the variable reflecting the transaction demand for soybean stocks,
although positive, is not significantly different from zero.
Similarly, the coefficient of the variable reflecting the opportunity
cost of holding stocks (INT), although conforming to a_ priori
expectations, is not significant.
Since soybeans are processed into soybean oil and meal, STOCKM is
included as a proxy for the capacity constraints of processing
soybeans into final products. STOCKM represents the stocks of soybean
cake and meal that are held in year t. The coefficient of this
variable conforms to the expectation that higher amounts of soybean
meal stocks that are held will result in higher levels of soybean
stocks.
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Calculation of Benefits
In order to calculate the economic benefits of the attainment of
alternative secondary national ambient air quality standards, the
soybean model is simulated over the period in which benefits are
expected to occur using the supply and demand equations reported in
Tables 9-13 through 9-16 of this subsection. The model is simulated
under two scenarios — one assuming that the SC>2 levels existing in
1977 will prevail indefinitely into the future, and one assuming that
the alternative secondary standards listed in Table 9-12 will be met
by 1987. Benefits are then calculated according to the procedure
discussed in the Methodology subsection (see specifically Equations
9.34 through 9.36.)
Using a 10 percent discount rate, the economic benefits in the
soybean market of reducing the maximum of the second highest 24-hour
SC>2 reading within a county to 260 ^g/m are estimated to be $21.6
million in 1980 dollars. The economic benefits of meeting the
secondary standard in terms of the 24-hour equivalent of the maximum
of the second highest 3-hour SC>2 reading are estimated to be $0.18
million. These benefits are much lower than the benefits estimated
using the 24-hour SCu readings since only one county in our sample
exceeded the 24-hour equivalent of the 3-hour secondary standard in
1977. Both estimates are discounted present values in 1980 and assume
an infinite time horizon.
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It should be mentioned that these benefit estimates are based on
a sample of counties that accounted for approximately 17.6 percent of
the soybean production within the Corn Belt Region in 1977.
Consequently, these benefits are not indicative of the benefits that
would be realized for the entire Corn Belt Region if there are any
soybean-producing counties in this region that exceed the alternative
secondary standard but are not included in our sample.
Our estimates indicate that the implementation of the 24-hour
secondary standard for SC>2 would result in an annual increase in
production of 500,000 bushels of soybeans.
Comparison With Other Studies
To date, we have found only two studies that have specifically
analyzed the economic impact of SCU on soybean production. As
mentioned in the Literature Review, Armentano and Miller and Usher
(19) estimated the impact of emitted S02 from coal-fired electrical
generating stations in the Ohio River Basin Area Energy Study (ORBES).
Specific estimates of the impact of these emissions on soybeans were
made for the states of Illinois, Indiana, Kentucky and Ohio. They
calculated that there would be a probable gain of 651,690 bushels of
soybeans due to the total abatement of SO^ emissions from 31
generating stations in 1976.
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Stanford Research Institute (49) estimated that the implementa-
tion of SNAAQS would result in annual benefits of $1.78 billion (1980
dollars) in the agricultural sector. Although the benefits of the
increased production of soybeans resulting from the reduction of S02
to the secondary standard were not specifically reported in the study,
annual benefits of the increased production of soybeans of
approximately $4.8 million are implied based on information in the
report. If one assumes that this level of annual benefits continued
into the indefinite future, then the equivalent discounted present
value at a 10 percent discount rate would be $48 million. Thus, our
estimate is about one-half as large.
Although our estimates are quite reasonable with respect to these
studies, they are not strictly comparable with these studies for the
following reasons:
Different methodologies - Both Miller and Usher and
SRI use crop loss functions in order to calculate
benefits. Consequently, their estimates do not
reflect the effects of changes in crop yield on price.
Different time periods - The SRI study is based on air
quality data from 1974 to 1978, while the ORBES study
includes 1976 air quality data. The benefits in this
study are based on 1977 data.
Different sample - SRI included all counties that
exceeded the secondary standard for SC>2 in 1980. The
ORBES sample included all counties impacted by 31
coal-fired generating sations within Illinois,
Indiana, Kentucky and Ohio. Our benefits estimates
are based on 17 percent of the soybean-producing
counties within the Corn Belt Region.
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Different scenarios - ORBES uses a clean air scenario
to measure the impact of S02 on soybeans. SRI assumes
that the secondary standard is met in 1980. Our
scenario calls for equal reductions in the level of
S02 in 1986 and 1987.
CONCLUSIONS
In this section we have analyzed the economic impact of achieving
secondary national ambient air quality standards for two economically
important crops in the agricultural sector: cotton and soybeans.
Economic benefits were measured within the framework of the crop
production process. Individual crop yield functions were developed
which relate the quantity of output produced to the amount of inputs
used. Inputs into the crop production process included both economic
and climatological factors with the ambient level of S02 being
considered a negative input. These yield functions were estimated in
order to test the hypothesis that ambient S02 levels have a
deleterious effect on the yield of cotton and soybeans. The results
of these estimations were integrated with market supply and demand
relationships in order to measure the impact of S02 on crop price.
This model has several conceptual advantages over previous
studies that have estimated the effect of S02 on crops. First, subtle
injury from SO2 that results in reduced yield is capable of being
measured. Many past studies have based their crop loss estimates on
only the visible damage that occurs as a result of exposure to S02.
9-123
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This approach tends to underestimate economic losses since crop yield
may be adversely affected as a result of subtle injury.
Second, since the yield functions estimated in this section
measure the effects of SC^ on each crop using actual crop production
data, the problems inherent in the extrapolation of the results of
controlled experiments to field conditions are avoided. This is
particularly important in the measurement of the impact of SC>2 on crop
production because the susceptibility of plants to ambient levels of
S02 can vary significantly due to climatological factors. Rain and
temperature are the two climatological factors specifically controlled
for in our analysis.
In addition, actions taken by the farmer that involve the use of
different amounts of inputs in order to mitigate the effects of SOn
are capable of being taken into account in this model. Past studies
have not been able to incorporate the effects of these countermeasures
on crop damage and consequently may result in overestimates of actual
crop damages. Conversely, some studies tend to underestimate losses
since their estimates are based on crop production after adjustments
to existing pollution levels have taken place.
Although the model is able to take into account the
countermeasures undertaken by the farmer in order to avoid the effect
of SC>2 once the crop is planted, it is unable to reflect the farmer's
decision process regarding "how much" and "what" crops to produce.
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Consequently, the possibility that a farmer chooses not to produce a
particular crop because of the effects of S02 on the crop cannot be
reflected. This may tend to underestimate the actual economic damage
if a portion of the acreage planted of a crop is taken out of produc-
tion due to SO^. Obviously, this is one of the limitations of the
model as it is currently structured.
A third advantage of the model presented in this section is that
the crop yield functions are brought into a more general framework
which specifies the crop's supply and demand relationships. This
implies that the effects of S02 on crop price can be measured. These
effects must be measured in order to accurately estimate the economic
impact of SOo on crop production. This is a major conceptual
advantage of this model over models that estimate the impact of S02 on
crop production in dollar terms without taking these price effects
into account.
Using pooled cross-sectional county level data from 1975 to 1977,
the hypothesis that SC^ has a deleterious effect on crop yield was
tested through the estimation of the crop yield functions. The
existence of a significant negative relationship between ambient SC>2
and cotton yield could not be supported based on our sample data.
Given the location of the cotton-producing counties included in our
sample, this result is not surprising. These counties are located in
areas where the soil tends to be alkaline, and it is conceivable that
the cotton plants are utilizing atmospheric SO 2 for their sulfur
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requirements. Although there was not any evidence that ambient SC>2
has a deleterious effect on soybeans on the national level, our
results indicated that such a relationship does exist for certain
regions of the country. A negative relationship between ambient SC>2
and soybean yield was found for the states of Illinois, Indiana, Iowa,
Ohio and Texas.
These results are plausible considering the time period of our
analysis. Since our data set included crop production and air quality
data from 1975 to 1977 and air pollution problems have existed prior
to 1975, it is quite possible that farmers have adjusted their
cropping patterns to mitigate the effects of SO 2 on their crops.
Consequently, this study reflects the relationship between ambient SC^
and cotton and soybean yield with respect to cropping patterns that
most likely have been changed due to past ambient air quality. In
addition, since air quality has been improving over the past decade,
the deleterious effects of ambient SC>2 on crop yield from 1975 to 1977
may not have been as severe as they were in the late 1960's.
It must be kept in mind, however, that the relationship between
SC>2 and crop yield exhibited in this analysis may tend to
underestimate actual damage occurring in some locations because our
data sets are comprised of farm production and air quality data
aggregated to the county level. Intra-county variations in yield due
to variations in SCU levels cannot be measured in this analysis.
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Consequently, the impact of SC>2 on cotton and soybean yields may tend
to be underestimated.
Although evidence exists that greater reductions in plant yield
occur from exposure to SCu during the early stages of growth than
during later stages (80), there is also evidence that plants are
susceptible immediately before flowering and during pod growth (54).
If cotton and soybeans tend to be more susceptible to S02 during the
later stages of growth, the use of S02 data from March, April and June
may underestimate the true relationship between SC>2 and crop yield.
The use of 24-hour means and second highest values may also tend
to obscure the relationship between SC>2 and soybean and cotton yield
since evidence exists that plants are more susceptible to SC^ during
daylight hours (24). Information on SC>2 levels during the daylight
hours were not available for this analysis, however.
Incorporating the results of our yield functions within the
framework of the demand and supply for the crop, the economic benefits
of the implementation of alternative SNAAQS were calculated based on
SC>2 levels and farm production existing in 1977. Since none of the
counties in our Texas sample exceeded the secondary standard of 260
Mg/m for the 24-hour maximum of SC>2 in 1977, our estimates are based
on the economic benefits for the soybean-producing counties in the
states of Illinois, Indiana, Iowa and Ohio that are included in our
sample. Approximately 40 percent of these sample counties exceeded
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the alternative secondary standard in 1977. The discounted present
value of the economic benefits of the reduction in SC>2 levels in these
counties to the proposed secondary standard of 260 M9/m are estimated
to be $21.6 million in 1980 dollars at a 10 percent discount rate.
Only one county in our sample exceeded the secondary standard for the
24-hour equivalent of the maximum of the second highest 3-hour S02
reading. Benefits are estimated to be $0.18 million for this county.
Refinements
It is clear from this study that the economic impacts of air
pollution on agricultural crops must be analyzed within the framework
of the production process. Various data limitations, however,
prevented this production process from being completely modeled for
the crops included in this study. This limits the conclusions that
can be drawn regarding the impact of SC^ on cotton and soybeans. If
these data limitations exist for other crops, the conclusions that can
be drawn using this model to estimate the economic impact of air
pollution control on other crops will also be limited.
A possible way of circumventing the data problems associated with
the estimation of the yield function would be to analyze the economic
impact of pollution on agricultural production through the estimation
of a cost function. In this approach, the costs of crop production
are assumed to be a function of ambient air quality. This approach
would be similar to the one used in Section 7 of this study.
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During our analysis, we found that data exists on the prices of
the factor inputs used by farmers. If data on the costs of production
are also available, this approach would be a viable alternative to the
crop yield function approach in the estimation of the economic
benefits of air pollution control.
Concluding Remarks
Given the data limitations encountered in this study, the
estimated economic benefits of increased soybean production from the
implementation of alternative SNAAQS, while conditional, seem
reasonable. They indicate that soybean production in certain regions
of the country are negatively impacted by SC^. The areas where these
negative impacts were found correspond to the areas that are known to
have air quality problems.
The methodology developed in this subsection can be a useful tool
in measuring the economic impacts of air pollution control in the
agricultural sector. It can be used to investigate the impact of
these controls on all agricultural commodities. Although the
methodology is sound, its use at the present time is somewhat limited
due to the sparse data. As this analysis shows, both better air
quality and farm production data are needed before any definitive
statements can be made regarding the true economic impact of SOo on
agricultural crop production.
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U.S. Environmental Protection Agency
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230 Soulh D—if-rn Street _y
Chicago, Illinois 60604^.^^
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