,I.‘
‘Uc

Cl.

 

.1 v
05. t. u
c . fizu. I

. I:

'I

c .3 {lzvr‘llllblfvt 1.31:1.

 

.4.

Kurd:

.‘0

 

 

L’fi‘jl'
tiéifivf

0:.“

1
'I

- .l‘allzl .
1".“ I
if...)

«6‘.
.n 1

4

u? r
I I Ali-Pd: A

.3
'1:

«

Earl.

.33?
in

304.3” .,

.: 9.11} [.1

up,

,rpldp?

.

a. 71V o; LI .0.
. rlplulfv .o otnuu‘cho fiat!
J . pr

IKE-1.1 .
5 .

«aha: ffiufiru u... .

p v

I‘D

’-

{an

a
, a.
u.» .r: 34.4».

r. lfluue:

. (It. .
.1: b‘510.1-f‘
.1.O..vo.a.il.l I}!

"On.

Ill-til

. . )‘Ct’i”!
Up)???” 51% éfinfiuu : 4|!
I. I; l A D I
,Ihatl‘tl‘lifl§¢.‘r’ .‘ . o In... «lulu. I
b: ‘ ‘ \ l I A

v

3%..

 

“(£835

illlllmlIlllllllllliHlllflllllllllHMINIIHIIIIIIUIIHW

 

3 1293 00792
I _\
' LIBRARY
Michigan state
University

 

 

 

This is to certify that the

dissertation entitled

The Economics of Consumer Response
to Health-Risk Information in Food
presented by

Sedef Emine Akgungor

has been accepted towards fulfillment
of the requirements for

Ph.D. Mgmem Agricultural

 

 

Economics

(:3 <’”E?:>
“fig“ :29;/ M~M1¢'(-§

Major professor

Date‘3’7/6Vzmbé/L it; /9 9 (1

MS U is an Affirmative Action/Equal Opportunity Institution 0‘ 12771

 

 

PLACE IN RETURN BOX to removeth checkout from your record.
TO AVOID FINES return on or before date due.

DATE DUE DATE DUE DATE DUE

 

 

4

 

 

 

W

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MSU to An Affirmative ActiorVEquel Opportunity Institution
omens-9.1

 

THE ECONOMICS OF CONSUMER RESPONSE TO
HEALTH-RISK INFORMATION IN FOOD

By

Sedef Emine Akgungor

A Dissertation

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Agricultural Economics

1992

ABSTRACT
THE ECONOMICS OF CONSUMER RESPONSE TO HEALTH RISK
INFORMATION IN FOOD
By

Sedef Emine Akgiingér

This research extends previous research on the demand effects of health concerns
regarding Alar residues in apples. Following this previous research, an econometric
model for retail fresh apple demand is developed for the New York City (NYC) retail
apple market. However, a longer time series is used to estimate apple demand and two
improvements are made to the demand model. One of these improvements incorporates
the possibility that the national retail price and thus the NYC retail price may be
affected by health-risk information at the national level. Therefore, the NYC demand
equation is tested for simultaneity bias. The second improvement is in the modeling of
seasonality in per capita apple purchases and retail apple price variables.

The results indicate that simultaneity bias is not an issue in estimating the retail
apple demand in the NYC market. Therefore, the NYC apple demand is estimated by a
single equation. A multiplicative seasonal ARMA model appears to represent
seasonality in per capita apple purchases and retail apple price variables.

As found in the previous research, apple demand was found to shift downward
immediately following the initial announcement of health risk in July 1984. Demand
recovered fully when Alar was withdrawn from the market in June 1989. This finding
suggests that sales losses could have been avoided had the Government recalled Alar in
1984 since the majority of the drop in sales is due to the initial and sustained shift in
demand.

Following previous research, consumer’s willingness to pay to avoid Alar residues

in apples was calculated using the estimated demand model. Consumer’s marginal

Sedef Emine Akgflngdr
willingness to pay for risk reduction was calculated by dividing the annual willingness to
pay to avoid Alar by estimates of consumers’ perceived amount of risk avoided per year.
As found in previous research, the estimates of consumer willingness to pay to avoid
health risks suggest that consumers reacted to the health risks associated with Alar as

they have to other health risks.

ACKNOWLEDGEMENTS

There are many peOple who helped me to make my years at Michigan State
University most valuable. First, I thank Eileen van Ravenswaay, my major professor and
dissertation supervisor. Having the opportunity to work with her over the years was
intellectually rewarding and fulfilling. I owe her much gratitude for her guidance and
careful reading of the drafts of this dissertation. I also thank Dr. John Hoehn who
contributed much to the development of this research starting from the very early stages
of my dissertation work. Dr. Richard Baillie provided valuable contributions to the
development of the econometric model. I thank him for his insightful suggestions and
experience. I also want to thank Dr. Jeff Wooldridge for his prompt and useful
suggestions for the various specific econometric problems along the way.

Many thanks to the Department computer staff, especially to Margaret Beaver
who patiently answered my questions and problems on word processing.

I owe much thanks to Ege University, School of Agriculture, Department of
Agricultural Economics in Izmir, Turkey, for financially supporting me for my graduate
studies abroad.

The funding of this project was provided in part by the US. Environmental
Protection Agency Cooperative Agreement (#CR-815424-01-2), the Michigan
Agricultural Experiment Station Project #3800, and the Department of Agricultural
Economics, Michigan State University. Their financial support is greatly appreciated.

I would like to thank to my peer graduate students in the Department of

Agricultural Economics who helped me to feel much like at home here in the United

States. My special thanks go to Ellen Fitzpatrick and Lih-Chyun Sun whose friendship
and support I deeply value.

I thank Nuran Erol for her close and enduring friendship over the years.

The last word of thanks go to my family. I thank my parents, Saer and Uner
Birkan and my brother, Emre Birkan for their patience and encouragement. Lastly I
thank my husband, Kadir, for his endless support through this long and seemingly

endless journey.

TABLE OF CONTENTS

Page
List of Tables ........................................................ x
List of Figures ....................................................... xi
CHAPTER I

INTRODUCTION ................................................... 1
1.1 Background ............................................. 3
1.2 Problem Statement and Scope of Research ..................... 4
1.3 Importance of Research .................................... 5

1.4 Existing Empirical Evidence on the Impact of the Alar Incident on
Apple Purchases .......................................... 5
1.5 Research Objectives ....................................... 8
1.6 Research Procedures ..................................... 10
1.7 Description of the Data ................................... 12
1.8 Plan for the Presentation of the Research ..................... 12

CHAPTER II

CONCEPTUAL FRAMEWORK ....................................... 14
2.1 A Model of Consumption Choice ............................ 14

2.1.1 Definition of the Terms: Health Problem, Health Risk and
Health-Risk Perception .............................. 14
2.1.2 The Model of Consumption Choice .................... 21

vi

2.2 Specifying the Information Variables .........................
2.3 Hypotheses on Modelling the Information Effect ................

2.4 Methods for Valuing the Welfare Effects of the Health-Risk
Information ............................................

CHAPTER III

THE ECONOMETRIC MODEL .......................................
3.1 An Econometric Model for Apples ...........................
3.2 The Reduced-Form Equations and the Demand Equation .........

3.2.1 The Reduced-Form Equation for Per Capita Apple Purchases
in NYC Region ....................................

3.2.2 The Reduced-Form Equation for Deflated Retail Apple Price
in the NYC Region .................................

3.2.3 Interpretation of the Estimates for the Coefficients on the
Information Variables in the Reduced-Form Equations .....

3.2.4 Hypotheses on the Information Effect on Reduced-Form
Equations and Demand Equation ......................

3.3 Methods for Estimating the Reduced-Form Equations and the
Demand Equation .......................................

3.3.1 Specifying Time»Series Model for the 1n and the ln
Variables ........................................

3.3.2 The Estimation Procedure for the Demand Equation and
Methods to Detect Simultaneity Bias ...................

CHAPTER IV

THE ECONOMETRIC RESULTS ......................................

4.1

Specifying a Time-Series Model for the Quantity and the Price

Variables ..............................................

4.1.1 Methods for Determining a Stochastic Model for the Error

Term ...........................................
4.1.2 Identification .....................................
4.1.3 Estimation and Diagnostic Checking ....................

23
26

29

32
33
38

39

41

42

44

51

52

55

56

59

4.2 Checking for Sirnultaneity Bias in the Demand Equation .......... 61

4.3 The Information Effect on the NYC Region’s Apple Demand for the
January 1980-July 1989 Observation Period .................... 64

4.4 The Information Effect on the NYC Region’s Apple Demand for the
January 1980-July 1991 Observation Period .................... 72

4.5 The Information Effect on Quantity and Price in the Reduced-Form
Equations .............................................. 76

4.6 Estimating the Change in Revenue to the NYC Region Fresh Apple
Retailers .............................................. 84

4.7 Estimating the Change in Consumer Surplus Associated With the
Risk Information ........................................ 86

CHAPTER V

CONCLUSIONS, POLICY ISSUES, AND FURTHER RESEARCH ........... 90
5.1 Summary of Research Problem and Methods ................... 93
5.2 Summary of the Research Results ........................... 93

5.2.1 The Importance of Considering Seasonality when Estimating
the Regression Equation ............................. 93
5.2.2 Sirnultaneity Bias in the Demand Equation .............. 95
5.2.3 Information Effect ................................. 96
5.2.4 Own-Price Elasticities ............................... 97

5.2.5 Change in Total Apple Sales Associated with the Information
on Alar .......................................... 97

5.2.6 Change in Consumer Surplus Associated with Information on
Alar ............................................ 97
5.3 Policy Issues ............................................ 98
5.4 Needs for Future Research ................................ 100
APPENDIX A: DESCRIPTION OF DATA .............................. 102
APPENDIX B: THE DATA .......................................... 108
APPENDIX C: WEEKLY DATA ON EARNINGS ......................... 118

viii

APPENDIX D: DERIVATION OF THE REDUCED-FORM EQUATIONS FOR
45 AND p,’ ................................................. 131

APPENDIX B: THE ASYMPTOTIC COVARIANCE MATRIX FOR THE TWO-
STAGE LEAST SQUARES ESTIMATOR WITH SEASONAL ARIMA

ERRORS .................................................... 137
APPENDIX F: EHECTED VALUE OF THE CHANGE IN APPLE SALES

ASSOCIATED WITH HEALTH RISK INFORMATION ............... 146
APPENDIX G: EXPECTED VALUE OF THE CHANGE IN THE CONSUNIER

SURPLUS ASSOCIATED WITH HEALTH-RISK INFORMATION ...... 150
BIBLIOGRAPHY ................................................... 153

LIST OF TABLES

Page

Table 4.1. Estimate of Seasonal ARMA models for Per Capita Apple

Consumption and Retail Price of Apples in the NYC Region (January

1980-July 1989) ............................................... 60
Table 4.2. Estimate of the Demand Equation With Seasonal ARMA Errors With

and Without an Instrument for the Price Variable (January 1980-July

1991) ....................................................... 63
Table 4.3. Estimate of the Demand Equation With Seasonal ARMA Errors

(January 1980-July 1989) ........................................ 66
Table 4.4. Estimate of the Demand Equation With Seasonal ARMA Errors

(January 1980-July 1989) ........................................ 68
Table 4.5. Estimate of the Demand Equation With AR(1) Errors (January 1980-

July 1989) ................................................... 70
Table 4.6. Estimate of the Demand Equation With Seasonal ARMA Errors

Under Different Specifications for the Information Variable (January

1980-July 1991) ............................................... 73
Table 4.7. Estimate of the Reduced-Form Equation for Per Capita Apple

Purchases With Seasonal ARMA Errors ............................ 78
Table 4.8. Estimate of the Reduced-Form Equation for Retail Apple Price With

Seasonal ARMA Errors ......................................... 80
Table 4.9. Estimates of Total Apple Sales in the New York Region With and

Without the Effect of Alar for the July 1984-June 1989 Period (1983

Dollars) ..................................................... 87
Table 4.10. The Expected Value of the Annual Change in Consumer Surplus

Under Alternative Elasticity Estimates (1983 Dollars) .................. 89
Table 4.11. The Implicit Willingness to Pay for an Annual Reduction of One in

One Million (1 x 10‘) Risk of Cancer Death (1983 Dollars) ............. 91
Table 4.12. Definitions of the Variables Used in the Econometric Model ......... 92

LIST OF FIGURES

Page
Figure 3.1 Hypothesis I .............................................. 46
Figure 3.2 Hypothesis II .............................................. 47
Figure 3.3 Hypothesis 111, Case 1 ....................................... 48
Figure 3.4 Hypothesis 1]], Case 2 ....................................... 49
Figure 3.5 Hypothesis 111, Case 3 ....................................... 50
Figure 3.6 Hypothesis IV ............................................. 51
Figure 4.1. Estimates of the Apple Sales in the New York Region With and Without
the Risk Information (Model 4) ................................... 85
Figure 4.2. Estimates of the Apple Sales in the New York Region With and Without
the Risk Information (Model 5) ................................... 86
Figure A.1. Retail Fresh Apple Prices (1983 Dollars) and Per Capita Fresh Apple
Purchases in the NYC Region (Pounds) ............................ 107
Figure F .1. Change in Apple Sales Asociated With Health-Risk Information ...... 146
Figure G.1. Change in Consumer Surplus Associated with Health-Risk
Information .................................................. 150

CHAPTER I
INTRODUCTION

Consumer concerns about the safety of the food supply, especially about the
safety of pesticide residues in food, have been high during the past decade.1 These
concerns appear to be due to new information that consumers have received about the
potential health risks of pesticide residues in food. These risks are conveyed by new
information about the toxicity and presence of pesticide resides in food.

An example of this is the Alar incident. Alar is a growth regulator primarily used
on apples. In 1984, the Environmental Protection Agency (EPA) announced that it
would reevaluate its risk assessment for Alar because of the evidence that Alar and its
derivative UDMH cause cancer in laboratory animals. The toxicity of Alar was debated
for five years by the experts, the food industry, the government and the producer of Alar,
Uniroyal. The news media widely reported this dispute and thus caused a large impact
on consumer purchases of apples.2 Alar was taken off the market by Uniroyal in June

of 1984, and subsequently banned for use in apple production by the EPA.

 

1Julie A. Caswell, ed., W (New York. Elseiver Science
Publishing Co.,1991).

2Eileen van Ravenswaay and John P. Hoehn, ”The Impact of Health Risk
Information on Food Demand: A Case Study of Alar and Apples," in W
SALE. ed. Julie A. Caswell (New York. Elseiver Science Publishing Co.,1991),p.p 155-
174; A. Desmond O’Rourke, "Anatomy of a Disaster,” Agribusiness 6 (1990), pp. 417-
424; Boyd M. Buxton, "Economic Impact of Consumer Health Concerns About Alar on

APP1$"EMLWMWK "IFS-250 Economic
Research Service, United States Department of Agriculture (August 1989), pp. 85-88.

1

2

van Ravenswaay and Hoehn (1991) found that the demand for apples in the New
York-Newark (NYC) metropolitan area1 declined after the disclosure of health-risk
information associated with lifetime consumption of apples treated with Alar. They
examined the effect of the Alar incident on apple purchases until July 1989, one month
after Uniroyal removed the chemical from the market. They were therefore unable to
detect whether the Alar controversy caused any long-term effects to the NYC apple
market.

After the withdrawal of Alar from the market several alternative scenarios
regarding apple demand in the NYC market could have followed. One is that the
demand for apples may have recovered fully when consumers received information that
Alar was no longer on the market. This would imply that consumers responded swiftly
to the information available to them. Another alternative is that it may have taken
several periods of demonstrated product safety until consumers believed the apples were
safe to eat. The last alternative is that the demand for apples never shifted back to the
pre-product warning levels such that there remains a permanent effect in the NYC
region apple market. This would have occurred if consumers who have shifted away
from apple consumption to apple substitutes during the Alar scare did not return to
consuming apples because of their lack of confidence in the apple market or simply
because they become accustomed to consuming apple substitutes. It is not possible to
determine which scenario applies to the NYC apple market unless we include the
months after the chemical was removed from the market. To find out the long-term
effects of the Alar incident, this research extends the previous research by van
Ravenswaay and Hoehn (1991) by increasing the observation period to the months after

the withdrawal of Alar from the market. This research also examines some particular

 

1During the presentation of the research, the expressions ”NYC region" and "NYC
market" will be used to represent the region that covers the New York-Newark
metropolitan area.

3
problems in econometric modeling, including seasonality and sirnultaneity bias, which are

discussed in more detail below.

1.1 ac ou

The Alar controversy began in July of 1984 when the EPA announced that Alar,
the trade name for the chemical Daminozide, and its derivative UDMH were potential
carcinogens. The EPA’s decision not to ban Alar from the market at that time
stimulated a debate between Government officials, consumer groups, and industry about
the health risks of Alar. The debate continued through June 1989, when the chemical
was removed from the market by Uniroyal, the manufacturer of Alar. The public debate
was most controversial between February 1989 through June 1989; the news coverage of
the Alar controversy was also its heaviest then. In February 1989, EPA announced that
it would ban Alar within the next 18 months, when the tests were complete. During the
following days, consumer groups criticized EPA for not banning Alar promptly. Later
that month, a CBS Mm program focused on the findings of the Natural Resources
Defense Council (NRDC) on the cancer risks to children from Alar and other pesticides
in food.1 During this month, the NRDC announced its risk estimate from Alar, and the
EPA released a revised risk estimate.2

Uniroyal stopped most of its overseas sales of Alar in October 1989. The
company claims that it continues to believe in the safety of Alar, but the domestic

market for Alar had deteriorated so much that it was uneconomical to continue

 

lBradford H. Sewell and Robin M. Whyatt, "Intolerable Risk: Pesticides in Our
Children’s Food" (Washington, DC: Natural Resources Defense Council, 1989).

2For the chronology of the Alar incident from July 1984 through June 1989 see
Eileen van Ravenswaay and John Hoehn, 1991. This chronology is based on the review
of articles on Alar in the New York Times during that period.

4

production for the overseas market alone.1 In November 1990, almost two years after
the N RDC’s report, a group of apple growers filed a law suit against CBS for airing the
program that reported the NRDC’s findings in March 1989 and against NRDC for
declaring misleading statements to the public. The industry’s estimate of the sales losses
to the growers after February 1989 was $100 million.2

As seen from the chronology, there are three major events that mark the Alar
incident. The first is the EPA’s initial announcement in July 1984 that Alar was a
potential carcinogen. The second is the events surrounding the publicity of the NRDC’s
and EPA’s findings and the W program in February 1989. The third is the
voluntary ban on Alar use in June 1989 followed by the Government ban. To understand
the long-term effects of the Alar controversy on apple purchases, it is necessary to look
at apple demand patterns after 1989, the date when the chemical was removed from the

market.

12 W11

This research analyzed how health-risk information about food afi'ects food
purchases over time by systematically identifying measures of the presence or absence of
risk information in the market and incorporating these variables into an econometric
demand model. Using the econometric model, estimates of how consumers value
improvements in the safety of the food supply were developed. More specifically, this
research investigated the long-term effect of the Alar incident on fresh apple purchases
in the NYC retail apple market, and examined what consumers were willing to pay to

avoid health risks associated with the consumption of Alar treated apples.

 

1Allan R. Gold, ”Company Ends Use of Apple Chemical,” We; 18
October 1989, p. A18.

2"After Scare, Suit by Apple Farmers," W 29 November 1990, p. A22.

5
One of the major reasons that we chose the NYC metropolitan area is to be
able to follow up on the findings of van Ravenswaay and Hoehn (1991) by extending
their data set through July 1991 to examine the demand patterns after Alar was removed
from the market. The NYC market was originally chosen by van Ravenswaay and

Hoehn (1991) due to the availability of the most comprehensive price data.

1.3 Wasatch

The findings from this study have significant implications for the government and
the food industry. An understanding of how consumers have reacted to the Alar incident
and how the demand patterns have changed after risk was eliminated from the market
provides guidance to policy makers in responding to consumer fears in similar health-
scare events. The food industry also benefits from such knowledge in developing
strategies to prepare for similar incidents. An estimate of the economic consequences of
the Alar event provides an important piece of evidence for the apple industry in
quantifying the revenue losses associated with the controversy on Alar. Another finding
from this study is an estimate of the consumer’s willingness to pay to avoid Alar residues
in apples. From that willingness to pay estimate, it is possible to assess consumer’s
valuation of risk-reduction benefits. This piece of information is valuable for policy

makers in evaluating policy alternatives concerning food safety improvements.

1.4 -A, 1‘ 110_!.¥€-'."l';'11‘H.221. rs; .19"!°lé'fi‘

Buxton (1989) examined the impact of the Alar incident on Washington State red

delicious FOB prices. He compared the actual weekly FOB prices during the 1988-1989

marketing season with the expected prices that usually occur over a typical season. The

6

typical season price pattern was calculated based on the FOB prices for Washington
State red delicious apples at the Wenatchee shipping point. The seasonal index was
estimated by removing trend, cyclical and irregular price changes from the actual price
series for the period of January 1983-March 1989. The author found that the FOB
prices of red delicious apples fell after February 1989, the time that the news coverage
on Alar was the most intense. The findings suggest that over the period starting in late
February through the second week in September, the total revenue loss for the growers
of red delicious apples in Washington was $140 million in 1989 dollars. The author also
reports that the retail prices did not reflect the full decline in the FOB prices which
made it harder to market apples remaining in storage.

O’Rourke (1991) examined the impact of the Alar incident on Washington State
FOB shipping point apple prices. Washington State is considered the major supplier of
apples to the U.S. market. Therefore, the impact of the Alar incident on the
Washington State apple industry may be a good proxy for its impact on the US
wholesale apple market. The author used existing price forecasting models developed by
the Washington Growers Clearing Association for Red Delicious, Golden Delicious and
Granny Smith apples, and projected what the FOB shipping point apple prices would
have been had the Alar incident not occurred. The method he used in calculating the
revenue change to the apple growers is to subtract the observed values of the actual
1988-1989 average FOB shipping point prices from the apple prices that were projected
from the price forecasting models. His findings suggest that the apple industry lost $130
million in the 19884989 marketing season (in 1989 dollars). Red delicious was the
variety most affected by the Alar scare.

van Ravenswaay and Hoehn (1991) examined the effect of the Alar scare in the
NYC retail fresh apple market. The authors used a single-equation demand model to
estimate demand for apples in the NYC region using a time series model. Monthly data

from January 1980 through July 1989 were used. They found that the effect of the Alar

7
incident dated back to the time when EPA first announced in July 1984 that Alar was a
potential carcinogen. The study reported that over July 1984-July 1989 period, 70% of
the estimated total sales losses to NYC region’s retailers was attributable to the initial
and sustained demand shift in July of 1984. The sales loss estimate was calculated by
subtracting estimated actual apple sales from a projection of what sales would have been
had the Alar incident never occurred. The sales loss estimate for the period of June
1984 through July 1989 was $194.8 million (in 1983 dollars). The authors estimated
consumer’s willingness to pay to avoid Alar treated apples and use this estimate to
calculate willingness to pay to avoid cancer risks. They found that the willingness to pay
for reduced cancer risks were consistent with the existing estimates of willingness to pay
for reduced risk in the literature.

The findings of the above studies provide empirical evidence that the Alar
incident caused a reduction in apple purchases. It should be noted, however, that the
three studies differ from each other in several important aspects. For example, van
Ravenswaay and Hoehn (1991) showed that the change in apple sales associated with the
Alar incident started in 1984 and much of the sales losses are attributable to that event
while Buxton (1989) and O’Rourke (1991) examined the Alar incident only for the 1988-
1989 marketing season. Another notable difference is associated with the methods used
in the three studies in calculating the revenue losses due to the Alar scare. Buxton
(1989) and O’Rourke (1991) subtract the pm apple prices from the W
Mild apple prices and multiply the difference with the actual quantity sold. van
Ravenswaay and Hoehn (1991) subtract the M apple sales from the estimated
W apple sales. The reason why van Ravenswaay and Hoehn use this

method is to minimize estimation errors.l Still another difference between these three

 

1See, Mark E. Smith, Eileen 0. van Ravenswaay, and Stanley R. Thompson, "Sales
Loss Determination in Food Contamination Incidents: An Application to Milk Bans in

Hawaii.” We 70 (August 1988). pp. 513-520-

8
studies is that Buxton (1989) and O’Rourke (1991) examine the impact of the Alar scare
on the wholesale apple market while the study by van Ravenswaay and Hoehn covers the
retail apple market. For these reasons, it is not possible to compare the quantitative
findings from these three studies.

All three studies, however, indicate that there is a downward demand shift at the
apple market. O’Rourke’s findings indicate that the national wholesale prices dropped in
1988-1989 marketing season as a result of a downward demand shift at the wholesale
market, given that the supply of apples at the wholesale market is perfectly elastic.
Buxton also concludes that the Washington State red delicious apple FOB prices fell as a
result of a downward shift in wholesale apple demand. van Ravenswaay and Hoehn
model the retail apple market at the NYC region and found that the demand at the
retail level also shifts down.

This research examined the long term effects of the Alar scare by extending the
observation period of the study by van Ravenswaay and Hoehn (1991). This was the
major objective of the research. Several other objectives were also sought as listed

below.

1.5 Emmhghisctixcs

1. The long-term effects of the Alar incident are estimated by extending the
observation period used in the van Ravenswaay and Hoehn (1991) study to the period
after the withdrawal of Alar from the market.

2. The possibility that the Alar incident may have affected the retail price of
fresh apples at the retail market is examined. If the retail price of apples at the national
market is affected, then the retail price of apples in the NYC region should also be
affected under the assumption of perfectly elastic supply to the regional markets. If

information about risk at the national level affected the national demand and thus

 

9
national apple price, representing the NYC apple demand with a single equation would
cause the equation estimates to be inconsistent and biased. The estimated demand
model should therefore be tested for sirnultaneity bias.

This objective involves specifying an econometric model for apples that involves
the national retail market and the regional retail markets for apples. This enables us to
form testable hypotheses about the effect of health-risk information on apple purchases
at the regional level when the event actually covers the whole nation.

3. Alternative measures of the health-risk information variable are explored.

4. Improved methods to account for seasonality in apple purchases are
developed. Seasonality means there is a high degree of correlation between the values
observed during the same season across the years.

5. The findings of this model, which explicitly accounts for the seasonal error
structure, are compared to the findings obtained with a first order autoregressive error
structure reported in van Ravenswaay and Hoehn (1991). The comparison will be made
for the January 1980-July 1989 period to maintain consistency with the observation
period covered in the van Ravenswaay and Hoehn (1991) study.

This study will then extend the observation period through July 1991 and
compare the models with the seasonal error structure for the two observation periods
(i.e. January 1980-July 1989 period and January 1980-July 1991 period). This
comparison allows us to observe how extending the observation period changes the
equation estimates.

6. The change in revenues associated with the Alar event to the NYC apple
retailers are estimated.

7. The impact of the Alar event on consumer welfare is estimated. This
objective involves calculating the change in consumer surplus associated with the health-
risk information and deriving the consumer’s willingness to pay to avoid Alar residues in

apples.

10

8. From the estimate of the consumer’s willingness to pay to avoid Alar residues
in apples, the consumer’s willingness to pay for health-risk reduction is derived.

As the objectives stated above show, this research differs from the study by van
Ravenswaay and Hoehn (1991) in at least three aspects. One is the extension of the
observation period to include the period after Alar was removed from the market. The
second is the correction for seasonality in the demand model. This allows us to detect
the impact of the exogenous variables on quantity demanded in isolation of the
variations in apple sales associated with seasonality. The third difference is that this
research models the effect on regional apple prices of potential price adjustments in

national markets caused by the Alar controversy.

1.6 W

The research methods consist of the procedures listed below.

1. An econometric model of national retail demand and supply for fresh apples,
retail apple demand for all the regions in the nation except the NYC region, and retail
apple demand for the NYC region is developed.

2. The reduced-form equations for per capita apple consumption and the retail
price of apples in the NYC region is derived.

3. The reduced-form equations and the demand equation for apples in the NYC
region is used to derive testable hypotheses about the impact of health-risk information
on per capita apple purchases and the retail price of apples in that region. These
hypotheses test whether risk information affects purchases at the regional level through a
regional demand shift, or through a change in the national price induced by information
at the national level, or through both effects.

11

4. Alternative measures of the presence or absence of the reported risk over
time are developed. Testable hypotheses to specify the information effect on apple
demand are developed.

5. A seasonal time-series model of per capita apple consumption and apple
prices variables is specified.

6. Simultaneity bias in the demand equation is examined. This procedure
involves derivation of the asymptotic covariance matrix for the demand equation where
the price variable is replaced by the fitted values for the price variable and the error
structure of the demand equation is seasonal.1

7. The demand equation and the reduced-form equations are estimated using a
seasonal error structure.

8. The significance of the coefficients of the information variables in the demand
equation for the January 1980 through July 1989 observation period are compared with
W These are the first order
autoregressive error structure and the seasonal error structure.

9. The significance of the coefficients for the information variables are compared
with the seasonal error structure for the WM. These are
the periods of January 1980 through July 1989, and January 1980 through July 1991.

10. Hypotheses on different specifications of the information effect in the
demand equation are tested for the extended observation period, that is the January
1980 through July 1991 period.

1 1. Changes in apple sales associated with changes in health-risk information are

estimated in the NYC region.

 

1The reason that the estimate of the covariance matrix for the demand equation with
instrument for the price variable is separately calculated is because we are not able to do
the two-stage least squares estimation and get the coefficient estimates as well as the
asymptotic covariance matrix with the "BOXJENK" command in the Regression Analysis
Time Series (RATS) econometric package (version 3.1) for personal computers which is
used in this study to compute multiplicative seasonal ARIMA model.

12
12. Changes in consumer welfare associated with changes in health-risk
information are estimated by computing the change in consumer surplus.
13. The consumer’s implicit willingness to pay to avoid a one in one million risk

of cancer death is computed using the estimate of the change in consumer surplus.

1.7 Description of the Data

Since this research is an extension of the study by van Ravenswaay and Hoehn,
the data for the period between January 1980 through July 1989 is largely identical with
the data used in that study.1 There are two major differences, however. One difference
is that the monthly population estimates that are used in this research covers a smaller
area. The other difference is the inclusion of an income variable and a variable that
measures the national holdings of fresh apples. Appendix A presents the description of

the data used in this study. Appendix B reports the extended data set.

1.8 W

Chapter II develops a conceptual framework to analyze consumer response to
information on health-risk from food. This chapter defines the information variables and
states the hypotheses related to the information effect on the quantity of food
demanded. Methods to quantify the welfare effects associated with the changes in
health-risk information is presented later in the chapter. Chapter III presents the
econometric model for apples. This chapter discusses the estimation procedures for the

regression equations. Chapter IV presents the econometric findings of the research and

 

1F or a detailed description of the data used in Eileen van Ravenswaay and John
Hoehn, 1991, see William Preston Guyton, "Consumer Response to Risk Information: A
Case Study of the Impact of Alar Scare on New York City Fresh Apple Demand" (MS.
Thesis, Michigan State University, 1990).

 

 

13
discussion of the results. Chapter V presents the research conclusions, policy issues and

research needs.

 

CHAPTER II
CONCEPTUAL FRAMEWORK

This chapter develops a conceptual framework for the analysis of consumer
response to information on health risk from food. Section One presents a model of
consumption choice that establishes a relationship between health-risk information and
the demand for risky food. Section Two explains how the information variable in the
demand equation is defined. Section Three states the hypotheses concerning the effect
of health-risk information on food purchases. Section Four describes the methods used
to measure the welfare changes associated with the changes in information on health

risk.

2.1 Wills:

This section first defines the terms used in the conceptual framework. The

section then presents the consumer’s optimization problem and derives the demand

functions for risky and non-risky foods.

 

There are two concepts closely related to a consumer’s W
[is]; from any source in his/her lifetime. The first one is the Wills

that the consumer expects to experience during his/her lifetime. The second one is the

14

15
probability that a health problem will occur during the consumer’s lifetime. This second
concept is the W of the consumer.

There is a range of health problems that the consumer can face. Each is
characterized by the type of health problem, the severity of the health problem, the
duration of the symptoms, and the timing of their occurrence in the lifetime of the
consumer.1 Some examples of the type of health problem that the consumer might
expect to face during a lifetime are cancer, allergies, ulcer, heart diseases, etc. The
severity refers to the seriousness of the health problem. Curable cancer, for example, is
less severe than incurable cancer. The duration is the amount of time that the health
problem persists. The timing in a lifetime relates to the age the consumer expects
he/ she will be when the health problem is realized.

For the purpose of this study, we assume that there is only one health problem in
the lifetime of the consumer. The type of health problem, its severity, duration, and
timing in the lifetime of the consumer are well defined. The lifetime health risk of the
consumer is the probability that the health problem will occur during the consumer’s
lifetime. This is the actual health risk that is unknown to the consumer before he/ she
receives health-risk information. We assume lifetime health risk is a random variable
since we assume there is a range of heath-risk levels for the consumer at a given point in
his/her lifetime. The probabilities associated with the likelihood of the occurrences of a
range of lifetime health-risk levels are unknown until the consumer receives exogenous
information on the riskiness of practicing a specific activity or consuming a particular
food. The acquisition of the information can be considered a random experiment and
the probabilities associated with the likelihood of the occurrences of a range of lifetime

health-risk levels cannot be predicted with certainty prior to the experiment. These

 

lNicholas Reseller. WWWLM
W (New York: University Press of America, 1983).

16
probabilities constitute a probability distribution. This probability distribution is the
consumer’s lifetime health-risk perception function.

The concept of the lifetime health-risk perception function suggests that each
level of health risk is associated with the consumer’s perception of the likelihood of its
occurrence during a lifetime. Since the perceived lifetime health risk is defined as a
distribution function, it can be characterized by measures of center, such as mean,
median or mode. In this study, for convenience, the consumer’s health risk perception
function will be characterized by the health-risk level that has the highest perceived
probability of occurrence for the consumer (i.e., mode of the lifetime health-risk
perception function). Therefore, the consumer’s perceived lifetime health risk is the
health risk level that the consumer considers most likely to happen.

In summary, the consumer’s perceived lifetime health risk can be defined with
the help of two concepts. One is the set of health problems that may result from all
causes. Each health problem is characterized by the type, severity, duration, and timing
in the consumer’s lifetime. Note that the set is assumed to have only one element. The
characteristics of the health problem are well defined. The second concept is the
probability of the occurrence of the health problem in a lifetime. This is the lifetime
health risk. With the aid of exogenous information, the consumer forms a probability
distribution where each probability is the likelihood of the occurrence of the lifetime
health risk. This is the consumer’s health risk perception function. The conSumer’s
perceived lifetime health risk is the health risk level that the consumer believes to have
the highest probability of occurrence in the health risk perception function.

There are two types of health risks that the consumer faces in his/ her lifetime.
One is the baseline health risk associated with all the activities in the consumer’s lifetime
except the lifetime consumption of Alar-treated apples. These include dietary habits,

smoking, alcohol consumption and nonconsumption activities such as driving a car, being

17
exposed to radioactive substances, etc. The other one is the additional health risk
associated only with the lifetime consumption of Alar-treated apples.

We assume that the lifetime health risk is additive. That is, it consists of the
baseline health risk pig the additional health risk from consuming Alar-treated apples.
Perceived lifetime health risk is also assumed to be additive. The consumer has a
perceived baseline health risk and a perceived additional health risk that add up to the
perceived lifetime health risk.

Assume that the consumer lives for three periods. The first period is all the time
that has elapsed until the present time; it is denoted by the subscript 0. Since the
consumption decisions from this period have already been made, the health
consequences due to consumption in the past are taken as given. The second period is
the present period; it is denoted by the subscript t. The third period is the future; it is
denoted by the subscript f.

The perception of the chances that the consumer will experience the health
problem in the future period is xf= dove-t b,v,+ poqo-t- Pr‘lv where v0 and vt are the
quantities of the activities other than the consumption of Alar-treated apples in the past
and present periods, respectively. qo and q, are apple consumption in the past and
present periods, respectively. 60 and b, are the consumer’s past and present perception
of the marginal probability of the occurrence of the future health problem associated
with an addjmmal unit of all other activities except the consumption of Alar-treated
apples, respectively. 60 and 6, are the consumer’s perceived baseline marginal health
risk. p0 and p, are the consumer’s past and present perception of the marginal
probability of the occurrence of the health problem associated with consumption of an
m unit of Alar-treated apples, respectively. po and p, constitute the consumer’s
perceived additional marginal health risk. We also assume that v consists of two types of
activities, v1 and v2, both at time o and time t. Here, v1 includes consumer’s preventive

actions (i.e., investment in health care, exercise) and v2 includes all other activities. The

18
consumer reduces his/her chances that he/she will experience the health problem in the
future, rrf, by making changes in the consumption of v and q at times 0 and t. For
simplicity, we assume that the consumer finds it less costly to reduce marginal risk from
consuming Alar treated apples by reducing his/her consumption of q rather than
increasing his/ her consumption of v2.

60 and p0 are functions of the consumer’s knowledge about the marginal risk
associated with the consumer’s choice of v and q in the past period. Since this period is
already past, the risk consequences (bovo-I- poqo) associated with the past choice of these
goods and activities are taken as given.

5, and pt are functions of the consumer’s knowledge about the marginal risk
associated with the consumer’s choice of v and q in the present period. We assume that
the consumer receives information in the present period on the WW
associated with an mm of Alar-treated apples. The consumer
receives information through signals from a given information source. The signals differ
by their informational contents. The informational content of a signal indicates the
presence or absence of risk in apples.

The presence or absence of risk can be determined by the information on residue
and toxicity. The toxicity of a substance and how much residue there is in the food
supply are essential aspects of the food safety question.1 Toxicity information is
information about how toxic or hazardous a particular substance is. It is the information
about the dose-response relationship for a given exposure level. The dose-response
information defines the health risk concerning the consumer’s exposure to the risky food.
For example the lifetime health risk given the lifetime exposure to the risky food may be

1 in 10,000 cancer deaths. Residue information is information on the amount of

 

1Eileen van Ravenswaay, "Consumer Perceptions of Health Risks In Food, in

W (Oakbrookt Farm
Foundation, 1990).

19
substance in the food supply. A consumer’s exposure to the substance over a lifetime is
a function of the per-unit amount of residue as well as the total consumption of the risky
food. The lifetime health risk is a function of both the toxicity and the lifetime exposure.

Note that the reported risk in the present period is the MM
associated with an mm of Alar treated apples. With the aid of
this information, the consumer forms pt, his/ her perception of the WM
that is the marginal probability of the occurrence of the health problem associated with
the consumption of an W of Alar treated apple at time t. The reason why
the consumer can make this inference is because the reported lifetime health risk is
assumed to be proportional to the marginal health risk as explained in the paragraph
below.

Let the reported risk be E, where i is the lifetime health risk associated with
lifetime consumption of Alar treated apples. The lifetime health risk is assumed to
increase linearly with the consumption of the risky food. This is a result of the
assumption of the linear dose-response model.l Therefore, the lifetime health risk can
be annualized if we divide it by the consumer’s life expectancy (i.e., 70 years):

5' = (RHO), where 5 is the annual health risk associated with an average annual
consumption of Alar treated apples. This implies that E = F at 71', where E is the
average annual consumption of Alar treated apples and 7 is the marginal health risk
associated with the consumption of one unit of Alar treated apple. Therefore, F = 5'15 .

In summary, the reported risk (i.e., E) is the lifetime health risk associated with
the lifetime consumption of Alar treated apples. By the assumption of the linear dose-
response model, the annual health risk associated with an average annual consumption of

apples (i.e., S") is proportional to i. Since the marginal health risk associated with the

 

lEileen van Ravenswaay and John Hoehn, 1991.

20
consumption of one unit of Alar treated apple (i.e., F) is proportional to E, we can say
that the reported risk R is proportional to F as well.

The perception of the marginal probability of the occurrence of the health
problem associated with consumption of an additional unit of Alar-treated apple in the
present period (p,) is a function of the currently available information on the presence or
absence of risk. Note that the po, 60 and 6, are taken as given. The currently available
information can be measured in several ways. The following two ways are used. One is
by the timing of government announcements about new lifetime risks. The other is by
counting repetitions of these announcements by the media per time period. The
repetitions of the government’s announcements about risk are important because the
consumer’s assessment of the magnitude of the health problem may be subject to
learning. That is, the magnitude of a consumer’s perception of risk may increase as
he/ she hears more often about the presence of risk. Therefore, pt is characterized as a
function of two variables. One variable measures the presence or absence of the risk by
the timing of its initial announcement (d,). The other variable measures the presence or
absence of the risk by the number of times the same message is repeated at a given

point of time (g,).

(2.1) o, = 9.81.3)

To summarize, the consumer is assumed to live for three periods: the past, the
present and the, future. The consumer’s perceived risk of experiencing the health
problem in the future period is the sum of the perceived health risk associated with all
activities except the consumption of Alar-treated apples and the perceived health risk
associated with the consumption of Alar-treated apples in the past and in the present
periods. In the present period, the consumer receives new information on the presence

or the absence of health risk associated with the consumption of apples treated with

21
Alar. With the aid of this information, the consumer updates the perception of the
probability of experiencing the health problem in the future period.
The next section discusses the consumer’s optimization problem and derives the

demand function for apples.

2.1.2 The Model of Consumption Choice

The model of consumption choice in this study is based on the expected utility
model. This framework is useful in the food-safety context since consumption decisions
are made in the presence of uncertainty.1

Assume that the consumer’s preferences are separable. That is, preferences can
be partitioned into groups such that the preferences within each group can be described
independently of the quantities in other groups.2 Following this assumption, food will
be defined as a separate group.

Assume that the representative consumer consumes q (apples) and y (all other
foods) during a lifetime. Among all food items, assume that only apples contain residues
of a particular toxic substance (Alar).

The lifetime expected utility of the consumer is,

(2.2) EU a U,(q,y) +191: Ufi(q,y) +(1 -t)*vfi(qu)

where, 1!, = 9oVo*5r"t*Poqc*Pflr and p‘ = p'(d',g’). Here, U,(q,,y,) is the utility of the
consumer in the current period and Uh(qf,y,) is the utility associated with poor health

 

lean E. Choi and Helen H. Jensen, "Modelling the Effect of Risk on Food
Demand,” in Economig of Fggd Safety, ed. Julie A.Caswell (New York: Elseiver Science
Publishing Company, 1991), pp. 28-44; Young Sook Eom, ”Pesticide Residues and
Averting Behavior" (Raleigh: North Carolina State University, Division of Economics
and Business, February, 1991), photocopy.

2Angus Deaton and John Muellbauer, ' e
(Cambridge: Cambridge University Press, 1980), pp. 122- 125.

22

and Ufl,(qf,yf) is the utility associated with good health in the future. qt and y, are
consumption of apples and all other foods in the present period, respectively. q: and y,
are consumption of apples and all other foods in the future period, respectively. 1:, is the
consumer’s perceived probability of the occurrence of the future health problem, after
consuming qo and v0 in the past period and qt and vt in the present period. Note that we
assume that the past and present consumption is irrelevant to the current period’s utility,
i.e., the health effects are always delayed to the future period. We also assume that
there are no marginal health risks associated with the future consumption.

The optimization problem of the consumer is to maximize (2.2) subject to the

lifetime budget constraint. The lifetime budget constraint is,

(2.3) m = 154 + 19,?

where m is the consumer’s lifetime disposable real income, pq is the deflated retail price
of apples, p" is the deflated retail price of all other foods, q is the quantity of apple
consumption in a lifetime and y is the quantity of all other foods in a lifetime. Note that
m, pq and py are assumed to be constant over a lifetime. Therefore the per-period
budget constraint (i.e., the budget constraint at time t) is proportional to the lifetime
budget constraint.

The lagrangian expression for the utility maximization is,

(2.4) L . ”‘(q’y)+n"u"(q’y)
+0 4') * Up(4ry)”'("'t’Pflr'Pfl)

where, 2. is the Lagrange multiplier. Here, m,, pqt and p,, be the consumer’s disposable
real income, the deflated retail price of apples and the deflated retail price of all other
foods at time t, respectively .The first order conditions for this problem are shown in
equation (2.5). If the consumer maximizes utility, equation (2.6) will express his/her
demand for q and y in the present period.

U
9-1: - —1+p,vfi-p,ufi 1P, - o
8 8
an
(2.5) 21; . _‘._),p" e o
8 3
6L

qr = qro’qnpyt’mr’pr)
y. = rips-PM»)

(2.6)

Since pt is defined as a function of d, and g,, the demand functions for q and y in the

current period are as shown in equation (2.7).

q. = qfls-Pymrdrs)
y. = marshes)

(2.7)

To summarize, the demand for q (apples) is a function of its own price, the price
of its substitutes, income and health-risk information available at time t. The health-risk
information is measured by two variables. One represents government announcements
about risk and the other represents the repetitions of the announcements.

The following section discusses alternative ways in which the information variable

can be measured and incorporated in the demand function.
2-2 Spraifidnsihslnfcunaucnlar'ahlcs

Following van Ravenswaay and Hoehn (1991), the information variables (d, and
g,) in this study are measured by news media reports about Alar’s health risks. The
announcements of new risks are identified by dummy variables. The variables S1, and 82,
represent the two occasions when different estimates of health risk were announced. S1,

represents the July 1984 to June 1989 period. It begins with EPA’s initial announcement

24
in July 1984 that Alar was a potential carcinogen which EPA subsequently estimated as
posing a lifetime cancer risk to food consumers of 1.0* 10".1 The period ends in June
1989 with the removal of Alar from the market. Consequently, S1t takes the value of 1
between July 1984 through June 1989 and zero in all other months. 32, marks the
beginning of the period during which the N RDC announced a greater lifetime risk
estimate of 2.4"‘10‘4 and the EPA simultaneously released a revised risk estimate of
3.5*10'5. This is the period after February 1989 that lasted until Alar was removed from
the market. Consequently, 82, has the value of 1 between February 1989 through June
1989 and zero elsewhere.

The underlying hypothesis for this type of measurement of information is that the
initial announcements of the health risk matters for the consumer. SI, is hypothesized to
cause a sustained downward shift in demand associated with the initial announcement by
the EPA as found by van Ravenswaay and Hoehn (1991). However, the effect of this
announcement is assumed to disappear upon the withdrawal of Alar from the market.

Following van Ravenswaay and Hoehn (1991), 82, is hypothesized to cause an
additional downward shift in demand associated with the simultaneously reported revised
risk estimates of the EPA and the NRDC. This shift was also sustained through June
1989. The announcements of the revised risk estimates suggest the existence of a new
event that increased the consumer’s perceived risk level, thus causing apple purchases to
decline even further.

There is a third variable that is measured with the nominal scale. This variable
(83,) measures the effect of the withdrawal of Alar from the market. If the sales
returned to the pro-announcement levels, S1, and 82, should be sufficient to represent the
variations in sales during the Alar controversy given the way that these variables are

defined. S3t should then not bring any additional explanatory power to the model and

 

1F or the reported lifetime cancer risk estimates associated with consumption of Alar
from all food sources, see, Eileen van Ravenswaay and John Hoehn (1991).

25
should not be statistically different than zero, while S1, and SZt should be negative and
significant.

It is possible that the intensity of news reporting on risk announcements is
important in explaining the variations in apple purchases. This may be true if the risk
perceptions involve learning such that the magnitude of the consumer’s perceived risk
increases with subsequent repetitions of announcements. Therefore, a measure of the
intensity of the reporting over time should be considered.

An information variable can be constructed such that the risk information is
identified by the number of media reports per time period (NYTt). Using the intensity
variable, we can test the hypothesis that the intensity of the coverage of the health risk is
important for the consumers in making their consumption decisions. Lagged values of
the NYTt variable can also be incorporated in the model to test whether the intensity of
coverage affects future consumption or only current consumption.

The intensity of information can also be measured by the cumulative amount of
reporting at a given point in time. The information variable that is measured by the
cumulative number of articles over time can be incorporated in the demand model to
test the hypothesis that consumers update their risk perceptions with the receipt of new
information. This variable is not stationary, however, since it involves a time trend. In
econometric models that use time-series data, the dependent variable and the
independent variables should both be stationary. To eliminate the nonstationarity
problem, one can difference the variable. For example in a time-series model that
involves a highly seasonal dependent variable, such as apple purchases, both the
dependent variable and the independent variables may be seasonally differenced to
eliminate nonstationarity in the variables. After seasonally differencing, however, the
cumulative variable will no longer measure the cumulative number of articles, but will
measure the total number of articles in a given year. This makes it difficult to interpret

the coefficient estimate. For these reasons, the information variable that measures the

26
presence or absence of risk with the cumulative number of articles will not be
incorporated into the econometric model.

In summary, the information variables in this study are measured using both a
nominal scale and an interval scale. The nominal scale uses the beginning of the two
events during which the different risk estimates were announced to account for the one
time demand shift associated with each event. Another information variable using the
nominal scale is the variable that measures the presence or absence of the suspected
chemical in the market. The interval scale measures the intensity of the reported risk by

the amount of media reporting on risk each time period.

2-3 W

The hypotheses outlined in this section will be tested for the models that use
monthly observations from January 1980-July 1989 as well as for the models estimated
using the extended observation period through July 1991. This will allow us to compare
the models with seasonal error structure for two different observation periods. We will
then be able to understand if the extension of the observation period affects the model
estimates. We will also be able to explore the long-term effects of the Alar controversy.
We can also compare the models under two different error structures for the observation
period of January 1980 to July 1989. This allows us to see how a seasonal error
structure changes the model estimates when compared to a first-order autoregressive
error structure.

The first hypothesis is that information about Alar’s risk does not affect fresh
apple purchases. If we reject the first hypothesis, then the following four hypotheses
about the impact of risk information on apple purchases will follow.

Hypothesis two is that consumers do not forget the information that health risk is

present until they receive an announcement that it is no longer present. In other words,

27
consumers do not forget information that is still relevant to their well being. We use 81,,
the dummy variable that measures the presence or absence of the health risk to test this
hypothesis.

Hypothesis three is that the intensity of the reporting of risk intensifies consumer
risk perceptions and causes apple sales to drop. If this hypothesis is true, then the
coefficient on the NYTt variable and / or the lagged values of the NYTt variable should
be negative and significant. However, the period during which there was intense media
coverage involves the month in which the EPA announced a revised risk estimate and
the NRDC released its risk estimate (February 1989). Therefore, a different hypothesis
could be that announcements on the presence of risk is important to consumers in
determining their risk perceptions and thus their apple purchases. The presence or
absence of these levels of health risk is measured by 82,. It is not possible to test the two
hypotheses separately since either or both explanations may be true. Since 82, is likely to
be correlated with the current and lagged values of the intensity variable, including these
variables as separate regressors would cause a problem of multicollinearity. We can
estimate two separate models, i.e., one model with the current and lagged values of the
NYTt and another model with 82,. However, we would not be able to know which
specification represents hypothesis three. In other words, we cannot separate out the
effect of the variable that measures the intensity of the media coverage from the variable
that measures the presence or absence of the risk estimates made in February 1989.
There is not sufficient information to differentiate what the real cause of the drop in
apple sales between February 1989 through June 1989 was. It could have been the
announcement of the risk estimate made by the NRDC and a subsequent one made by
the EPA in February 1989, or it could have been the intense media coverage stirred by
the public controversy over what the correct risk assessment was which also was during

that period. We would only be able to distinguish the effect of the NYTt variable on per

28

capita apple purchases had the two events (i.e., the announcement of revised risk
estimates and the intense media coverage) occurred in separate time periods.

Hypothesis four is that consumers do not forget the initial risk information and
they continuously revise and update their risk perceptions as they receive new
information about risk. This hypothesis is likely to be true if there is a downward shift
in apple demand associated with the initial announcement of risk coupled with an
additional downward shift in demand when additional risks are reported. Similar to
hypothesis three, note that we are not able to distinguish what the real cause of this
additional drop in sales was since the period of the intense media coverage on the
presence of risk involves February 1989, the month in which the revised risk estimates
were released. W are used to test this
hypothesis. In one specification, the information variables would be S1‘ and the current
and / or the lagged values of the NYTt variable. This represents the added effect of the
intense media coverage. In another specification, the information variables would be S1,
and 82,. This represents the added effect of higher risks reported by the NRDC and
lower risks reported by the EPA. We do not reject hypothesis four if the coefficient on
the S1, variable and on the current and / or the lagged values of the NYTt variable is
significant. Similarly, we do not reject hypothesis four if the SI, and 53, are negative and
significant. Note that S1t represents the initial shift in demand associated with the initial
information on health risk. The current and lagged values of the NYTt variable and the
5,, variable represent the additional shift in demand. However, we do not know the real
reason for the additional drop in sales. One reason may be that the consumer may react
to the intense media coverage such that his/ her perception of health risk may increase.
The increased risk perception causes an additional downward shift in demand. Another
reason may be that the announcement of the revised risk estimate of the EPA and the
estimate made by the NRDC may intensify consumer’s risk perceptions and this may

cause an additional downward shift in demand. Similar to hypothesis three, both

29
specifications must be true and we cannot differentiate between the models. We would
be able to differentiate the reason why this additional downward shift in apple demand
occurs had the two events (different risk estimates and the intense media coverage)
happened in non-overlapping time periods.

The fifth hypothesis is that sales return to the pre-announcement levels once the
reported risk is declared to be eliminated from the market. This implies that consumers
regain confidence in the safety of the supply of apples once they receive a signal that
indicates the risk is no longer present. This hypothesis is likely to be correct if
consumers who switched to the apple substitutes during the Alar scare went back to their
old purchasing habits after the heath risk is eliminated. 83,, which measures the
presence or absence of the chemical in the market, is used to test this hypothesis. If the
fifth hypothesis is true, this variable should not provide any additional explanatory power
to the equation estimates when the variables that represent the presence or absence of

the risk are negative and significant, given the way S1, and 82, are defined.
2.4 u‘ Ion... .0 V1. 1’ I‘ WC: 8 it'll 0 I‘ trusty-i I 0 II; '1

After an appropriate specification of the information variable in the demand
function, the welfare effects of the Alar controversy can be estimated. By observing the
shifts in demand function associated with the changes in health-risk information, it is
possible to derive the marginal willingness to pay to avoid Alar residues in apples and to
use this estimate to derive an estimate of the willingness to pay for a unit change in risk.
This approach has been used in other studies that look at the welfare effects of the
health-risk information1

 

1Pauline M. Ippolitto and Richard A. Ippolitto, "Measuring the Value of Life Saving
From Consumer Reaction to New Information," WM 25 (1984),
pp. 53-81; Eileen van Ravenswaay and John P. Hoehn, 1991.

30

The Hicksian compensating and equivalent measures are considered to be the
correct theoretical measures of welfare. The compensating variation is the amount of
income, paid or received under the prospective policy change, that would leave an
individual at the initial level of utility. The equivalent variation is the amount of income,
paid or received, that would leave an individual at the post-change level of utility when
faced with the initial policy situation.1 Willig demonstrates that the consumer surplus is
a close approximation to the Hicksian measures of welfare when the budget share of a
commodity is Small?

The welfare measure used in this study is the change in consumer’s surplus due
to a shift in an individual’s apple demand associated with health-risk information. The
share of apple expenditures in an individual’s budget can be considered small. Following
Willig, the Marshallian demand should approximate the Hicksian welfare measures.
Therefore, observing the change in consumer surplus with and without the risk
information will give the individual’s willingness to pay to avoid Alar residues in apples.
This willingness to pay estimate reflects the individual’s total welfare change associated
with the Alar incident.

The underlying assumption in the econometric model in this study is that the
supply of apples to the NYC region is perfectly elastic at the national price plus a fixed
transportation cost. Therefore, the quantity demanded is hypothesized to vary with
changes in health-risk information at m. This implies that change in health-

risk information causes a shift in the individual demand curve

 

1John P. Hoehn and Douglas Kreiger, V '
Staff Paper no. 88-30 (East Lansing: Michigan Sate University, Department of
Agricultural Economics, 1988).

2Robert D. Willig, “Consumer Surplus Without Apology," Worms;
Rm 66(4) (September 1976), pp. 589-597. .

31
and thus reduces the quantity of apples the individual consumes. The change in
individual welfare comes from consuming less apples to avoid health risks associated with
the consumption of Alar-treated apples.
The individual willingness to pay for avoiding Alar residues in apples at a given

level of price at time t is,

W = 1;ng .MJJP

- Ltqupxnfip

where q(.) is the apple demand function, pqt is the retail price of apples, py, is the retail

(2.8)

price of apple substitutes, tilt is disposable income, to is the absence of the reported risk
and f1 is the presence of the reported risk at time t.1 p' denotes the given level of price
at time. The annual total willingness to pay can be obtained by summing the total
willingness to pay at each time t over a year.

Dividing the estimate of the individual’s annual total willingness to pay to avoid
health risks from consuming Alar-treated apples by the individual’s perception of the
annual health risks due to Alar residues in apples gives the individual’s annual marginal
willingness to pay to avoid health risks associated with Alar incident.2 However, the
consumer’s perceptions of health risks associated with the consumption of apples with
Alar residues are not known. Following van Ravenswaay and Hoehn, the next best
approach is to assume that the consumer’s perception of health risks are sirnilar to the

health risks reported in the media.

 

1Note that the presence or the absence of the reported risk is measured in various

ways as discussed in section 2.2. For convenience, the symbol ft will account for the risk
information in general.

inleen van Ravenswaay and John P. Hoehn, 1991.

CHAPTER III
THE ECONOMETRIC MODEL

Chapter 111 describes the econometric model used to estimate the retail demand
for apples and to examine the impact of health-risk information on apple purchases.
Section One presents the econometric model for apples. The econometric model
consists of the retail apple demand equation for the NYC region, the retail apple
demand equation for all other regions, and the retail apple demand and supply equations
for the nation. The model assumes that the national price and the quantity consumed of
apples are determined simultaneously by the national apple supply and demand. We
also assume that the supply of apples at the regional level is perfectly elastic at the
national price plus a fixed transportation cost to the region. Section Two specifies the
reduced-form equations for per capita quantity purchased and for the price of apples in
the NYC region. The section then explores the relationships between the coefficient
estimates for the information variables in the quantity and price reduced-form equations
and in the demand equation for the NYC region. The hypotheses on the effect of
information on price and quantity in the reduced-form equations and on quantity on the
demand equation are stated later in the section. Section Three discusses the methods
used to detect seasonality and to construct a stochastic model for the error structure
associated with the price and the quantity variables. It then explains the estimation

procedure for the demand equation.

32

33

3.1 n etic ode or es

In developing an econometric model for apples in a regional market such as the
NYC market, the supply and demand relationships at the national market and at the
regional markets should be jointly examined using a system of equations. This is
justified by the assumption that price and quantity are determined simultaneously in the

national market and that the supply of apples to the regional markets is perfectly elastic.

We assume that there are two regions in the national retail fresh apple market:
the NYC region and the aggregate of all other regions.

The national price of apples is determined by national supply and demand. The
supply of apples to the NYC region and all other regions is assumed to be perfectly
elastic at the national price plus a fixed transportation cost. For convenience, we assume
that the transportation cost to the NYC region is greater than zero and the
transportation cost to all other regions is equal to zero. This implies that the retail price
of apples in the NYC region is greater than the national retail price by a fixed
proportion and the retail price of apples in all other regions is equal to the national
retail price.

The econometric model for apples can be expressed in the following four
equations.

The retail apple demand equation for the NYC region is:

as' - Bin; + Bin: * 9;”: + Biff + 0t

(3.1)
p}. = (l + m; = up;

such that 0<gs1 and c=1+g; where,

f

q, : Per capita apple purchases in the NYC region at time t,

p; : Deflated retail price of apples in the NYC region at time t,

(3.2)

where,

where,

34
p): : Deflated retail price of the most common apple substitute (e.g.,

bananas) in the NYC region at time t,

p; : Deflated national retail price of apples at time t,

m,’ : Deflated per capita disposable income in the NYC region at time t,
f,’ : Health-risk information in the NYC region at time t,

et : Stochastic error term at time t, where e, ~ N(0,az) .

g : Proportionality factor between the national retail apple price and the

retail apple price in the NYC region,
B: B; : The regression parameters.

The retail apple demand equation for the other regions is:

9:0 ' PIP; + P3P; 4’ P; m: + 3:}: + “r

P; ' P5
q,” : Per capita apple purchases in all other regions at time t,
p; : Deflated retail price of apples in all other regions at time t,
p; : Deflated retail price of the most common apple substitute (e.g.,

bananas) in all other regions at time t,
m," : Deflated per capita disposable income in all other regions at time t,
f," : Health-risk information in all other regions at time t,
p; : Deflated national retail price of apples at time t,
u, : Stochastic error term at time t, where u, ~ N(0,o’) .
B‘,’ B: : The regression parameters.

The retail apple demand equation for the nation is:

wt : Stochastic error term at time t, where w, ~ N(0,o’).

35

q." = Bin; + 93?; + 93ml + W!
(3.3)

+ as: + nip; + aim: + air: + w.

and all other variables are identical to the ones in equations (3.1) and (3.2). Note that
the demand equation for the nation (equation (3.3)) is the sum of the demand equations
for the NYC region (equation (3.1)) and all other regions (equation (3.2)).

The retail apple supply equation for the nation is:

(3") p; = 9:4.“ + 92h.“ + B't'f.‘ + z.
where,
p; : Deflated national retail price of apples at time t,
q,“ : Per capita national apple purchases at time t,

h,‘ : National apple holdings at time t,

f,” : Health-risk information in the nation at time t,
zt : Stochastic error term at time t, where 2, ~ N(0,o’).
B; B; : The regression parameters.

Equations (3.1) and (3.2) indicate that the demand for apples at the NYC region
and all other regions could be affected by the health-risk information. We hypothesize
that there is a downward demand shift at the NYC region and/ or all other regions
associated with the health-risk information in these regions. Since the national demand
curve for apples is assumed to be the horizontal sum of the demand curves at the
regional level, the demand shift at the national level associated with the health-risk
information should be the result of the sum of the demand shifts at the NYC region
and/ or all other regions (equation (3.3)).

The downward shift in demand at the national level causes the national retail
price of apples to drop. If we assume that there is no shift in national retail apple

supply associated with the health-risk information at the national level such that estimate

36
of [3; is statistically equal to zero, and since the NYC region’s retail apple price is
assumed to be proportional to the national retail apple price, the price at the NYC
region should also drop.

It is possible, however, that the retail price at the NYC region does not change as
a result of the health-risk information at the national level. One possible explanation for
this may be that while the national wholesale apple prices decline as a result of a
downward shift in demand associated with the health-risk information at the national
level, the retailers at the NYC region and all other regions do not change the regional
retail apple prices. This implies that the national retail apple prices and thus the
regional prices are not affected by health-risk information. A possible reason that the
retailers do not change retail price of apples may be because that may not anticipate a
drop in demand such that they do not adjust prices. Still another reason may be that the
retailers may not want to signal lower quality by dropping apple prices in order to avoid
fueling consumers’ fears. Buxton (1989) reports that the wholesale price of the
Washington State red delicious apples dropped after February 1989 while the retail price
did not fully reflect the decline in the wholesale prices. This finding is one empirical
evidence that the price at the wholesale level drops as a result of a downward shift in
wholesale demand while the price at the retail market does not change.

Alternatively, the national wholesale price may drop as a result of the health risk
information at the national level and the retailers in all other regions change the retail
apple prices while the retailers in the NYC region do not change the retail apple prices.
In this research, however, we will only be able to explore the impact of the health risk
information on retail prices at the NYC region. We will not be able to know what the
effect of the health-risk information was on the national wholesale or retail price and to
the retail price in the aggregate of all other regions.

Another reason why the national retail price and thus the retail price at the NYC

region may not change as a result of the information on health risk is a possible

37
downward retail supply shift associated with the controversy on Alar. As seen from
equation (3.4), the health-risk information at the national retail level which is measured
by f;" could cause a downward shift in the national supply of apples at the retail market
commensurate with the downward shift ill retail apple demand. One reason for this may
be that the retailers may have removed apples from their shelves and they discontinued
marketing apples until the controversy on Alar comes to an end because of liability
concerns.1 Another explanation for a downward shift in the retail apple supply curve
may be the purchases of the unsold apples at the wholesale market made by the Federal
Government in order to stabilize apple prices. It is reported that the United States
Department of Agriculture purchased $15 million worth of apples in an effort to reduce
the surplus at the wholesale market.2 Therefore, the impact of the health-risk
information on the market clearing price for apples at the national retail market and
thus at the regional retail markets may be determined by both a supply and a demand
shift at the national retail market.

Note that we cannot form testable hypotheses on the reasons why the health-risk
information on the NYC retail apple price does or does not change with the health-risk
information. Several alternative interpretations outlined in this section might be true. In
this research, the only hypothesis regarding the retail price of apples at the NYC retail
market is related to the question of whether or not the price at the NYC retail market
was affected by the health-risk information. We do not know the reason why the NYC
retail apple price was or was not affected by information on risk. According to one of
the interpretations described above, the price change may be explained by a possible
demand and supply shift at the . national retail market associated with health-risk
information. The discussion in Section 3.2.3 adopts this interpretation. The hypotheses

 

1Richard Gibson, "Apples with Alar Frightened Grocers More than Buyers,” Ill:
W31. 7 August 1989. 9- B3-

2 "US to Bail Out Apple Growers,“ Wag, 9 July 1989, p. C22.

38
related to the effect of health risk information on price and quantity at the NYC region
outlined in Section 3.2.4 are also based on this interpretation.

In summary, the econometric model for apples at the retail market suggests that
the health-risk information can cause a downward shift in apple demand at the NYC
region and/ or all other regions. Since national apple demand is the sum of the regional
demands, the health-risk information should also cause a downward demand shift at the
national level. Since the national price and quantity are assumed to be determined
simultaneously, the national price, and thus the regional prices, will be affected by the
risk information at the national level. Regional prices will be affected by a change in
price at the national level since they are assumed to be proportional to the national
price. Estimating the consumer demand for apples in the NYC region by a single
equation may introduce Simultaneity bias if p; in the NYC region’s demand equation is
correlated with the error term in this equation. Simultaneity bias at the NYC region’s
demand equation will therefore be tested.

The next section derives the reduced-form equations for q" and p; at the
regional level. These reduced-form equations can then be used to construct hypotheses
on the effect of information on the equilibrium quantity of per capita apple purchases

and on apple prices at the NYC region.

 

As we see from the econometric model outlined in Section 3.1, we no longer can
assume that the price of apples at the NYC retail market is exogenous in equation (3.1).
Using the econometric model, we can derive the reduced-form equations for q,’ and p;
expressed as functions of all the exogenous variables in the system of equations. By
observing the coefficient estimates on the reduced-form equations, we can understand

whether a particular variable had a significant impact on the equilibrium price and

39

quantity. For example, we can form testable hypotheses on the impact of the health-risk
information on retail apple prices and per capita quantity purchases at the NYC retail
apple market. We will then be able to understand whether the information on health
risk has affected the equilibrium price and quantity through a shift in demand at the
NYC market or through a price change induced by the health-risk information at the
national market or through both effects. Section 3.2.4 summarizes the related
hypotheses.

The reduced-form equations for q" and p; are expressed as functions of all the
exogenous variables in the system of equations. ‘ The derivation of the reduced-form

equations is presented in Appendix D.

3.2.1 II‘ {‘0 atom 91.0! 0 " -o-.;H‘il_ “Jill“
Man

The reduced-form equation for q,’ is:

9:, " 71hr. + 7;: +130; + 74'”:
(3.5)

+vfl+vap;+m.'+v£+€.

where, 5, is the random error, '11-.“ are the regression parameters and the variables are
as defined in equations (3.1) through (3.4) in Section 3.1.1

Note that in equation (3.5) the observed variables are hf, p;, In: and f . We
do not have the data for the remaining four variables. Therefore equation (3.5) will be

estimated by using only the observed variables. This means that we are going to omit 1;“

P4,, In: and fl"

 

1Note that equation (D7) in Appendix D is identical to equation (3.5). Therefore,
the 71-73 coefficients consist of the parameters of the structural equations as explicitly
seen In equation (D7) in Appendix D.

40

The omission of some of the independent variables in the equation causes the
estimates of the coefficients in the remaining variables to be biased unless these
variables are orthogonal to the included variables. The estimate of the covariance matrix
is also biased upwards regardless of whether or not the omitted variables are orthogonal
to the included variables.1

If for example we estimate equation (3.5) using only the observed variables, the
coefficient on the information variable in the reduced-form equation is y’ and the

expected value of the estimator is:

(3'6) HY') = ‘9' = “*7: + b*75 + T.

where a is the slope of the least squares estimate from the regression of the information
variable at the NYC region on the information variable at the national level (f) and b
is the slope of the least squares estimate from the regression of the information variable
at the NYC region on the information variables for all other regions (f,o ).2 If a and b
are statistically different than zero, then the coefficient estimate of the information
variable in the reduced-form equation is biased.

For simplicity, assume that a and b are both equal to one. Following this

assumption, the expected value of the coefficient on If at the regional level is:3

(3-7) 9' = 1, + 7, + 1.
Note that the estimate of the covariance matrix of the reduced-form equation is

still biased upwards because of the omitted variables in the equation. This means that

the statistics that are used to test the significance of the coefficient estimates are likely

 

69 1Peter Kennedy. Wm 2d ed» (Cambridge1 MIT Press, 1985), P-

2William H. Greene, W (New York: Macmillan Publishing
Company, 1990), p. 259.

3See equations (D.16) and (D.17) in Appendix D.

41
to be lower than they actually are. This increases the likelihood that we do not reject
the null hypothesis that the coefficient estimates are equal to zero when the alternative
hypothesis is true. To overcome this problem we can increase the significance level of
the hypothesis test such that the percentage of the area in the rejection region increases.
For example, instead of using a 1% significance level we can use a 5% or a 10%

significance level.

3.2.2 II.‘ {‘1' d- 0m 9 1 0. 0 Dem- i‘ -_A_H_' in ‘ I tI‘ at

The reduced-form equation for price is:

p; - ash." + “it“ + “a”; + “4'":
(3.8)

+¢sfr’+¢s0;+¢smr'+atfs'+cr

where q, is the random error, ail-as are the regression parameters and the variables are
as defined in equations (3.1) through (3.4) in Section 3.11.

As in the case for the reduced-form equation for quantity equation note that in
(3.8) the observed variables are In", 12;, In: and f . Since we do not have the data for
the rest of the variables, we have to estimate (3.8) by using only the observed variables.
The coefficient estimates of the included variables may be biased because of their
possible correlation with the excluded variables.

If we estimate (3.8) using only the observed variables, the coefficient on the
information variable in the reduced-form equation is a‘ and the expected value of the

estimator is:

 

1Note that equation (D6) in Appendix D is identical to equation (3.8). Therefore,
the a «:8 coefi'icients consist of the parameters of the structural equations as explicitly
seen In equation (D6) in Appendix D.

42

(3.9) E(a") = 61' = are:2 + but, + a"

where a is the slope of the least squares estimate from the regression of the information
variable in the NYC region on the information variable at the national level (f) and b
is the slope of the least squares estimate from the regression of the information variable
at the NYC region on the information variables for all other regions (f;o ).

Following the assumption that a and b are both equal to one, the estimate of the

coefficient on f isl:

(3.10) a' = a, + a, + a,

Similar to the reduced-form equation for quantity, the estimate of the covariance
matrix of the reduced-form equation for price is biased upwards because of the omitted
variables in the equation. Therefore, the same caveat as in the reduced-form equation
for quantity applies here when making statistical inferences about the significance of the
coefficients for the reduced-form equation for price.

By examining the coefficient estimates of a, and 7', we can understand whether
the change in apple purchases in the NYC region is due to the price change at the
national level, the demand shift at the regional level, or both effects. This analysis is

outlined in the following section.

3.2.3 .1819 ‘ 1.! 0 I‘ t .11; 0 II“ 01".1 '1 I‘ Inns-I

V'll'lB! IE 2'

It is possible to form hypotheses to test whether health-risk information affects
per capita purchases at the regional level through a regional demand shift or through a

change in the national price induced by the information at the national level, or through

 

18cc equations (DH) and (D.12) in Appendix D.

43
both effects. The hypotheses can be tested by observing the estimates for the
coefficients on the information variables in the reduced-form equations for quantity and
price, and in the regional demand equation. The estimates for the information variables
in the reduced-form equations include the coefficients for the information variables in
the structural equations. The structural equations are the NYC region’s demand
equation, the other region’s demand equation, the national demand equation and the
national supply equation.

The estimate of the coefficient for the information variable in the reduced-form
for quantity has two components.1 One is the change in apple sales at the regional level
associated with the change in the national price induced by the risk information at the
national level (i.e, a; *a'). The other is the shift in the regional demand associated with
the information on per capita apple consumption at the regional level (i.e, pi). The net
effect of information at the regional level is determined by these two components that
are embodied in the coefficient estimate of the information variable in the reduced-form
equation for quantity.

The change in regional price associated with the risk information at the national
level is determined by the estimate of the coefficient on the information variable in the
reduced-form equation for price, a»: In this formulation, note that the denominator of
the a, is always positive because of the assumption that 3; >0, p‘,’ <0 and p; <0. The
sign of the numerator determines the sign of the coefficient estimate of the information
variable in the reduced-form equation for price. The information coefficients in the
numerator of the reduced-form equation for price are p; which corresponds to the
supply shift at the national level associated with the health-risk information and 3:45;,

which corresponds to the demand shift at the national level. The relative effects of the

 

1 See equation D.18 in Appendix D.
2 See equation D.12 in Appendix D.

44

demand and the supply shift at the national level determine the impact of information on
retail apple price at the national level and thus at the regional level. If the effect of the
supply shift at the national level is stronger (weaker) than the effect of the demand shift
at the national level, then the price should go up (down). If the two effects are equal,
there should be no change in the national price, and thus there should be no change
associated with the risk information in the regional price.

The following section describes the hypotheses concerning the effect of health-
risk information on quantity and price in the reduced-form equations and on quantity in

the demand equation.

 

The following four hypotheses represent the efiect of health-risk information on
equilibrium level of retail apple price and per capita apple consumption at the NYC
retail apple market. By observing the coefficient estimates on the information variables
in the reduced-form equations and in the NYC demand equation, we can understand
how the equilibrium price and quantity pair at the NYC region was affected by the Alar
incident.

Note that we are not able to observe the national retail market and all other
markets. Therefore, the following hypotheses are based on the estimates of the NYC
demand equation (equation (3.1)), the reduced-form equation for per capita apple
purchases in the NYC region (equation (3.5)) and the reduced-form equation for
deflated retail price in the NYC region (equation (3.8)). The testable hypotheses are on
the effect of information on the equilibrium price and quantity pairs at the NYC market
from the reduced-form equations. We are also able to estimate the demand curve for

apples in the NYC market such that we can observe shifts in the demand curve

45

associated with the Alar incident. Therefore, the hypotheses outlined below are going to
be tested by observing the significance of the coefficient estimates on the information
variables in the reduced-form equation for quantity (7'), the reduced-form equation for
price (a’) and the NYC demand equation (p: ). The algebraic derivation of the
estimates of the coefficients for the information variables in the reduced-form equations
is presented in Appendix D. As stated in Section 3.2.3 and explicitly derived in
Appendix D, the estimates of y, and orr include coefficients for the information variables
’ of the structural equations. The following hypotheses can be interpreted in terms of the
expected signs of the coefficients on the information variables in the structural equations
as outlined in Section 3.2.3.

The first hypothesis is that there is no effect of health-risk information on apple
purchases in the NYC region. One explanation of this hypothesis is that the Alar
incident had no impact on apple purchases across the nation at all. Another explanation
of this hypothesis is represented in Figure 3.1. In Figure 3.1, the Alar incident shifts
down the national retail apple demand curve from J: to d; . There is a commensurate
supply shift at the national retail market such that the retail supply shifts down from s,“
to s,“ which causes the national retail apple price and thus the price at the regional level
remain unchanged, ie, p,“ = pz', p," = p; and p,’ =- p; .1 Since there was no change in
demand at the NYC region, the equilibrium per capita apple consumption also remains
unchanged, i.e., q,’ =- q; in Figure 3.1. If the retail apple price at the NYC region
remains unchanged, then 8' a 0 which implies the effect of the national supply shift on
the equilibrium national retail apple price is equal to the effect of the national demand
shift as outlined in Section 3.2.3. Since the NYC retail apple demand curve remains
unchanged, then 91:0. As seen in equation D.18 in Appendix D, the net effect of

 

1Note that aside from the possibility of a supply shift at the retail level, there are
other explanations of why the national retail apple price and thus the NYC retail apple
price was not affected by the Alar incident (see, Section 3.1).

46

information at the NYC level is determined by two components. Therefore, 7' should

 

 

 

 

 

 

 

 

 

 

 

 

 

 

also be equal to 0.
pr“ p°ll pnl ‘2 sn
as»; e»: at;
= 6; \é ° / \Q
:3’ t 0 in
oi ' q; q oi oi q of q": q
NYC Region Other Regions Nation

Figure 3.1 Hypothesis I

If the coefficient on the information variable in the reduced-form equation for
price (a’) is statistically different than zero, then hypotheses two and three follow.

Hypothesis two is that the change in apple sales in the NYC region is due may to
a change in the national price induced by health-risk information at the national level.
As represented in Figure 3.2, this hypothesis implies that apple demand at the national
retail market shifts down from d,“ to d; which causes the national retail apple price to
drop from p,” to p; . Subsequently, the equilibrium price at the NYC region drops from p,’
to p; and the equilibrium per capita apple consumption increases from q" to q; as seen
in Figure 3.2. According to this hypothesis, there was no downward shift in the demand
curve at the NYC region such that d,’ = d; . If the retail apple price at the NYC region
drops, then d' < 0 which implies that the effect of the national supply shift on the
equilibrium price is less than the effect of the national demand shift as outlined in
Section 3.2.3. If the NYC retail apple demand curve remains unchanged, then B: - 0.
As seen in equation D.18 in Appendix D, the net effect of information at the NYC level
is determined by two components. Therefore, 9' should be less than 0. Note that this

47
hypothesis assumes that there is no supply shift at the national level associated with

health-risk information.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

f O n
p ll p I) p II - 2
3,; s"
f
’: p: \ v? \
P2 dr P; ‘— o P; x n
’ \a \i
2
t i O n n :qfl
q: cl; q R; Qt q2 q1
NYC Region Other Regions Nation

Figure 3.2 Hypothesis H

Hypothesis three is that the change in apple sales in the NYC region is due to
129111 a change in the national price induced by information and a regional demand shift.
This hypothesis is represented under three cases. These cases are represented by
Figures 3.3, 3.4 and 3.5. This hypothesis implies that the Alar incident causes a
downward demand shift at the NYC region, i.e., the NYC retail apple demand shifts
down from d,’ to d; . This hypothesis also implies that the national retail apple demand
curve shifts down from d,” to a; such that the price changes from p,” to p; at the
national level and thus changes from p,’ to p; at the NYC region as seen in Figures 3.3,
3.4 and 3.5. Since this hypothesis implies that there is a downward demand shift at the
NYC region, then 8; <0. The sign on a' and on 7' depends on the following three
cases:

The first case is that the impact on equilibrium quantity purchased in the NYC
region due to a regional demand shift is offset by the change in price at the national
level induced by information. Note that in Figure 3.3, the national retail apple demand
curve shifts down from d,“ to d; . This means that the national price drops from p,“ to

p; and thus the NYC region’s price drops from p,’ to p; as a result of the downward

48
demand shift at the national retail market. The demand curve at the NYC region also
shifts down from d,’ to d; such that the equilibrium quantity consumed remains
unaffected (q1' = q; ). If the retail apple price at the NYC region drOps, then a' <0
which implies that the effect of the national supply shift on the equilibrium price is less
than the effect of the national demand shift as outlined in Section 3.2.3. As seen in
equation D.18 in Appendix D, the net effect of information at the NYC level is
determined by two components. Therefore the effect of the drop in price on the
equilibrium per capita apple consumption at the NYC retail market is even with the

effect of the downward demand shift at the NYC retail market such that 7‘ =0.

pr II p?) p II 2
n

pl \ ,p°\ p:\

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

i, o 3 =
q? = q; q 9°, at q 4'; a? q

NYC Region Other Regions Nation

Figure 3.3 Hypothesis 111, Case 1

The second case is that the equilibrium per capita apple consumption at the NYC
region increased after the Alar incident. The reason is that the impact on qr of the
change in price at the national level induced by information is greater than the impact
on qr of the demand shift at the regional level. As seen in Figure 3.4, the national retail
apple demand shifts down from d" to d: . The downward shift in national retail apple
demand shift causes national retail apple price to drop from p: to pz'. Therefore the
retail price at the NYC region drops from p,’ to p; . The demand curve at the NYC
region also shifts down from d,’ to d; . The equih'brium per capita apple consumption at
the NYC region increases from 41' to q; . If the retail apple price at the NYC region

49
drops, then a' <0 which implies that the effect of the national supply shift on the
equilibrium price is less than the effect of the national demand shift as outlined in
Section 3.2.3. As seen in equation D.18 in Appendix D, the net effect of information at
the NYC level is determined by two components. According to this case, the effect of
the drop in price on the equilibrium per capita apple consumption at the NYC retail
market is greater than the effect of the downward demand shift at the NYC retail

market such that 9‘ >0.

n

Pit Po“ p ll 2

P: \ P: \ P: \
P2 \ o P; h

s; 61 \Q’ 40 \Q n

P2
«M Q' a; tit q q; q? q

NYC Region Other Regions Nation

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 3.4 Hypothesis 111, Case 2

Note that in both of the above cases, it is assumed that there is no shift in supply
at the national level associated with the health-risk information.

As seen in Figure 3.5, the third case is that the supply shift at the national level is
greater than the national demand shift such that the national apple prices increase from
p: to p; due to health-risk information. The equilibrium price at the NYC region
therefore increases from p,’ to 1);. The decrease on the equilibrium quantity purchased
at the NYC region is associated both with the downward demand shift at the regional
level an also with a price increase at the national level. Therefore the equilibrium per
capita apple consumption decreases from q,’ to q; . Since the retail apple price at the
NYC region increases, then a' > 0 which implies that the effect of the national supply

shift on the equilibrium price is greater than the effect of the national demand shift as

50
outlined in Section 3.2.3. As seen in equation D.18 in Appendix D, the net effect of
information at the NYC level is determined by two components. Therefore the effect on
the equilibrium per capita apple consumption a the NYC region is the sum of the price

increase and the downward demand shift at the NYC region such that 7' >0.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

pl) pll pll 3"
fi;\ , n:\ pg.
P‘ \ p: \ p1
\,\.; ., : .; ':
of <1? :q' :13 of 'q° q; d: 'qn
NYC Region Other Regions Nation

Figure 3.5 Hypothesis III, Case 3

Hypothesis four is that the change on quantity purchased in the NYC region is
due only to a demand shift at the regional level. This hypothesis is represented by
Figure 3.6. The national retail apple demand shifts down from d" to d; . There is a
commensurate supply shift at the national retail level such that the retail apple supply
shifts down from s,” to s,“ such that the national retail apple price remains unaffected
after the Alar incident, i.e., p: = p; . If the national price remains unaffected, then the
regional prices should also remain unaffected, such that p,“ s p; and p,’ = p; . This
hypothesis also implies that there was a downward demand shift at the NYC region such
that demand dropped from d,’ to a; such that the equilibrium per capita apple
consumption dropped from q,’ to q; as seen in Figure 3.6. Since the retail apple price
at the NYC region remains unchanged, then a' = 0 which implies that the effect of the
national supply shift on the equilibrium price is equal to the effect of the national
demand shift as outlined in Section 3.2.3. As seen in equation D.18 in Appendix D, the

net effect of information at the NYC level is determined by thwo components. Since the

51
NYC retail apple demand curve shifts down, then 5; <0. Since there was no effect of
information on price, the effect of information on the equilibrium per capita apple

consumption at the NYC region should be less than zero (i.e., 9' =0).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

pr p0 l pn I) g 7
a , ea\ ea‘
\' dr \ ° G d‘
as I \
45 a? Eq' 4% a? GI° «'2‘ 4: TI“
NYC Region Other Regions Nation
Figure 3.6 Hypothesis IV
3.3 U‘ 10L 0 t 11: l’t!‘ i" tk‘n- 0m .19.; II 2-1! I‘ "II-.I!

The first step in estimating the reduced-form equations and the demand equation
was to determine the error structure associated with their dependent variables: q" and
pé. This allows us to account for the time-series component in these variables. It is
then possible to explore the effects of the explanatory variables on q,’ and p; in the
reduced-form equations and in the demand equation in isolation from the time-series
component of the model.

Following van Ravenswaay and Hoehn (1991), the functional form used to
estimate the reduced-form equations and the demand equation in this study is log-linear.

Therefore, the time series model was specified for the logarithms of q,’ and pg.

52
3.3.1 S ec' ' ' e- e ies Mod 1n ' t e ' Va 'ables

When the errors are serially correlated and have a seasonal pattern, they can be
modelled by a seasonal integrated autoregressive moving average (Seasonal ARIMA or
SARIMA) modelsl. The methods to estimate a time-series model for the error terms
associated with the lnq: and lnp: are described in section 4.1.1.

After an appropriate specification of the error structures for the dependent
variables, the reduced-form equations and the demand equations can be estimated by
incorporating the relevant exogenous variables.

The econometric model outlined in Section 3.1 suggests that there may be a
simultaneity bias in the demand equation due to the impact of the health-risk
information at the national level on national, and thus on the regional prices. The
following section discusses how the demand equation will be estimated and how a

possible Simultaneity bias in the demand equation may be detected.

 

When a regressor is contemporaneously correlated with the disturbance term,
estimates are biased and inconsistent. For example, in the NYC region apple demand
equation, the apple price variable may be correlated with the disturbance term. One way
to deal with this problem is to find an instrument for the regressor. That is, a variable
that is correlated with the regressor but not with the disturbance term. Good

instrumental variables are hard to find, however. One method is to use the two-stage

 

1 George. 6 Judge and others, WWW 2d ed.
(New York: John Wiley and Sons, 1985), pp. 224-271.

53

least squares technique. The two-stage least squares technique is a special case of the
instrumental variable method.1

The two-stage least squares method is based on the idea that the exogenous
variables in the system of equation are good candidates for being instruments for the
variable that is suspected to be correlated with the error term. In this study, this
variable is the price variable. The problem is to find out which exogenous variable is the
best instrument for the price variable. One suggestion is to regress the price variable on
all the exogenous variables in the system and obtain the fitted values for the reduced
form. These fitted values can then be used as an instrument for the price variable 9;
they can be used in place of the price variables in the demand equation.2

Most econometric software packages can do the instrumental variable estimation
and provide the coefficient estimates as well as the estimates of the asymptotic
covariance matrix. This procedure can be done both in the linear and the nonlinear least
squares context. However, in the presence of a multiplicative error component in the
estimation procedure, it is currently not possible to find an econometric package that can
do the instrumental variable estimation. An alternative method is to estimate the
coefficient estimates for the demand model by applying the two-stage least squares
procedure 3 and then calculate the asymptotic covariance matrix for the demand
equation. The formula to calculate the asymptotic covariance matrix which is used to
calculate the asymptotic covariance matrix for the demand equation with instrument for

the price variable is derived in Appendix E.

 

1Peter Kennedy, p. 134.
2 William H. Greene, pp. 622-624.

3Applying the two stage least squares procedure means that the price variable is first
regressed on all the exogenous variables in the system. From this first regression the
fitted values of the price variable is obtained. These fitted values are then used as the
price variable in a W regression.

54

The presence of sirnultaneity bias in the demand equation may be detected with
the specification test developed by Hausman.l Under the null hypothesis of no
misspecification, there exists a consistent, asymptotically normal and efficient estimator.
The alternative hypothesis is that the estimator will be biased and inconsistent.2

An alternative to the Hausman test for Simultaneity bias in the regression
estimate is to perform the regression based specification test.3 This test is based on
testing whether the estimated residuals from the equation with no instrumental variables
are correlated with a particular linear combination of the exogenous variables in the

system.4

 

1J.A. Hausman, ”Specification Tests in Econometrics,” W 6 (46)
(November 1978), pp. 1251-1271.

2Hausman test statistic: (Bu-Bflxcovh-cov‘fkfib- 8d,) , where, 6,, is the vector of

coefficient estimates with instrumental variable, 8‘, is the vector of coefficient estimates

with no instrumental variable, covh, is the estimate of the covariance matrix with
instrumental variable and covniv is the estimate of the covariance matrix with no

instrumental variable. Under the null hypothesis, the Hausman test statistic is x’(k)
distributed, where k denotes the number of unknown parameters.

3Jeffrey M. Wooldridge, "Score Diognasties for linear Models Estimated by Two
Stage Least Squares” (East Lansing: Michigan State University, Department of
Economics, October 1992), pp. 20-21, photocopy.

‘The regression based specification test: Let X1, be the set of exogenous variables
and be the variable that is suspected to be correlated with the error term (for
examp e the price variable in the demand equation in this study). Let 12, be the residuals
from the regression with no instruments for the X”. Let X” be the fitted values of the
X” when it is regressed on the exogenous variables in the system. The regression based
specification test is based on regressing a, on X", X”, and X, and test whether the
coefficient estimate on X, is statistically different than zero. If it is zero, this implies
that the estimator without the instrumental variable is not biased.

CHAPTER IV
THE ECONOMETRIC RESULTS

This chapter summarizes the econometric findings of the study. Section One
starts with describing the methods to determine a stochastic model for the error term.
This section then specifies a time-series model for the dependent variables in the
demand equation and the reduced-form equations. These variables are per capita apple
consumption and apple prices in the NYC region. After the time-series model of the
dependent variable is specified, one must determine whether the apple price variable and
the error term are correlated in the NYC apple demand equation. This step involves
detecting the sirnultaneity bias in the demand equation. It is summarized in Section
Two. Section Three and Section Four estimate the demand equation for the different
specifications of the information variable and determine the information effect. Section
Three outlines the econometric findings for the period of January 1980 through July
1989. This section starts with specification of a time-series model for the dependent
variable in the demand equation for the January 1980-July 1989 period. The information
variables are then incorporated into the demand equation. The truncated observation
period allows us to compare the results with the ones from a nonseasonal specification
for the error term that van Ravenswaay and Hoehn (1991) report. The observation
period was then extended through July 1991. The results for this observation period are
reported in Section Four. Section Five summarizes the findings for the information
effect on quantity and price in the reduced-form equations. Section Six reports the
estimates of the change in total apple sales associated with the risk information that are

computed from the estimated demand models. Section Seven summarizes the estimates

55

56
of the change in consumer surplus associated with the risk information ad derives

consumer’s willingness to pay to avoid health risks.

4.1 Spggiflihg g m e-Series Moggl for thg Oughtigz and the Price Vagiables

The time-series components for Inc]: and lnpq', were specified using the Box-Jenkins
approach. This approach involves three steps: identification, estimation and diagnostic

checking. The following section describes the Box-Jenkins approach.

4.1.1 et od te ' ' ast'c t

The time-series models offer a framework for predicting the values of a particular
variable by observing its past values. This method does not depend on economic
knowledge about the process through which the data is generated. The underlying
assumption is that the data are generated by a stochastic process. The model that
represents this process is defined and estimated by using statistical tools.

The Box-Jenkins approach is a method to construct a time-series model for a
stochastic process that may have generated the observed data.1 This method consists of
three stages: identification, estimation, and diagnostic checking.

In the identification stage, a tentative time-series model is specified on the basis
of autocorrelations and partial autocorrelations. The autocorrelations are the
correlation coefi‘icients between the value of the variable at time t and the value of the
same variable lagged a number of periods. The partial autocorrelations show the
correlation between the value of the variable at time t and the value of the same variable

lagged a number of periods, when the previous lags are already accounted for in the

 

1For a discussion of the time series models see, for example, George, G. Judge and
others. WW PP 224-271

57
model. If a seasonal model is adequate, it is also possible to make a tentative
specification for a seasonal time-series model by observing the autocorrelations and the
partial autocorrelations.
The nonseasonal component of the time series model is illustrated by the

following model:

(4.1) (1-olL‘-...-¢,Lr)(l-L)‘x,=(1+e,L‘+...+e,Lt):,

where,

than», = Parameters of the autoregressive (AR) process of order p,

01,...,0' = Parameters of the moving average (MA) process of order q,

L = Lag operator,

d = Number of differencing,

xt = Value of the variable x at time t. In the context of the research, the variable x may
be lng,’ or hp}.

5, = Error term at time t.

The error term, 5, in equation (4.1) may be correlated with the error terms for
the same month across the years. The error term 5’ in April, for example, may be
correlated with the error terms in April in the previous years. Seasonality in the data
series indicates a high degree of correlation between the values during the same season

across years. In the presence of seasonality, multiplicative seasonal models can be

used.l Suppose that this relationship can be explained by the following model:

(4.2) (1 -Q 11.1 -... ‘0’]. ’Xl -L)D£'s(1 +8‘L ‘ «rm +601, 0k:
where,

¢,,...,0, = Parameters of the seasonal autoregressive (AR(Seas)) process of order P,

 

1(330%? HR BOX and GWilYm M- Jenkins, WW
{421111321 (San Francisco: Holden Day, 1976), p. 303.

58
61,...,60 = Parameters of the seasonal moving average (MA(Seas)) process of order Q,
L = Lag operator,
D = Number of seasonal differencing,

6 Stochastic error term at time t, where 5, ~ N(0,02).

8

Substituting equation (4.2) into equation (4.1) , the following multiplicative model
is obtained.
(1 -¢,L ‘-... -¢,I. ’)(1 ~01L ‘-...-¢,L ')(1-L)D(l -L)" x,=

(4.3)
(1+0,L‘+... +6}. ')(1 +91L1 +... +801. °)e,

The model represented in equation (4.3) is a multiplicative seasonal integrated
autoregressive moving average (ARIMA) model of order (p,d,q)x(P,D,Q)‘, where s is the
number of periods that the series show periodic behavior. For example for a monthly
data the basic time interval is one month and the period is s= 12.

After a tentative ARIMA or multiplicative seasonal ARIMA model is specified
and estimated, the model is tested for specification. A common method to test for
specification in time-series models is to do a residual analysis. In the residual analysis,
the estimated residual autocorrelations are examined. If the residuals of the estimated
model are white noise, the residual autocorrelations should be within twice the
approximate standard error bounds of the estimated autocorrelations, rah/7‘, where T is
the sample size. The overall acceptability of the residual autocorrelations is tested by
the portmanteau test statistic (Q-statistic).1

The following section presents the results from each stage of specification for the

lag: and the hip; series.

 

1 Q= 11T+2)2‘T i_r,. Here, the rt are the autocorrelations of the estimated

residuals and K ls some prespecified number (for example 1/5 of the total number of

observations). The Q statistic is approximately X2-distributed with K-p-q degrees of
freedom (see, George E. Judge and others, 0
mm 2d ed., (New York: John Wiley and Sons, 1988), p. 705).

59
4.1.2 Identificatign

The autocorrelations and the partial autocorrelations of the series are the
primary sources in identifying a tirne- series model. The autocorrelation function for
both the lnq: and the ln p", variables imply that there is seasonality in the series. The
inspection of the autocorrelation functions for these two series suggests nonstationarity
in the seasonal component of the series since the autocorrelations for the observations
twelve months away do not die out. Both of the series were thus seasonally differenced.

After seasonally differencing, we observe the autocorrelation and the partial
autocorrelation functions to identify the time-series model. As noted in 4.1.1, time-series
models in the presence of seasonality can be modelled as multiplicative ARIMA models.
This model involves a seasonal and a nonseasonal component for the error structure.
The autocorrelation and the partial autocorrelation functions for the seasonally
differenced lnq: and hip; suggest that the seasonal component of the series can be
represented by a first-order seasonal moving average model. For the nonseasonal
component, the autocorrelation and the partial autocorrelation functions for the
seasonally differenced lnq: series recommend a first-order moving average model. The
same analysis for the seasonally differenced 111p; variable suggests a first-order
autoregression in the series.

In summary, after the identification stage the lug: variable is represented by a
seasonal multiplicative ARMA model of order (0,0,1)x(0,1,1)12. The 1n 1;; variable is
represented by a seasonal multiplicative ARMA model of order (1,0,0)x(0,1,1)12.

4.1.3 Em 3119' n and 123' gngsng' Chfikfll' g

After the time-series model is identified, one can estimate the coefficients of the

model. The coefficients were estimated using the RATS econometric package (version

Table 4.1. Estimate of Seasonal ARMA models for Per Capita Apple Consumption and

60

Retail Price of Apples in the NYC Region (January 1980-July 1989)

 

 

 

 

 

 

 

 

 

 

 

DEPENDENT Alzln (per capita apple Alzln (retail apple
VARIABLE consumption) price)
(T = 127) (T: 126)‘
Constant -0.035 . -0.013
(-3201) (-1-044)
MA 0.577 .
(7.834)
AR 0.856 .
(17.73)
MA(Seas) -0.771 . -0.782 .
(-11.618) (-13.461)
Q-Stat 23.402 15.043
(lag=24)
Ad'. R2 0.590 0.713

(Figures in Parentheses are t-statistics.)

‘ Significant at the as0.01 level

‘Notctmtmc-Bomx-mmmoadmRATScmnomcuicpocnge(mam3.l)rmpcmmmputm
drops one observation when estimating a time-series model with an AR(1) error structure. Therefore the number of
observations here is 126 instead of 127.

A12 : Seasonal difference operator

T : Number of observations

(The variables are defined in Table 4.12.)

3.1) for personal computers. The "BOXJENK' command in this econometric package
uses the nonlinear least squares method to derive the coefficient estimates for the
seasonal ARIMA model.1 Table 4.1 reports the estimated time-series models for the
lnq: and the hip; variables.

To check the overall acceptability of the models, the Q-statisties were examined.
The Q-statistic for both models suggest that these specifications correctly represent the

 

1Note that the nonlinear least squares estimate is not the maximum likelihood since
it involves the Jacobian term (Peter Kennedy, p. 344). In deriving the full maximum
likelihood estimate it is necessary to take into account the stochastic nature of the vector
of starting values. For this reason, ARIMA models that are estimated by the nonlinear
least squares method are not the full maximum likelihood estimators but they are
approximate maximum likelihood estimators.

61
time-series model for the lnq: and the ln p; variables. The critical value for the fan
is equal to 29.62 at the «$0.10 level, where 21 is the degrees of freedom. This number is
obtained by subtracting 3 from 24, where 24 is one fifth of the total number of
observations and 3 is the number of the estimated seasonal ARMA coefficients
(including the constant term). The Q-statistics for both models are lower than the
critical value at the 10% significance level. Therefore, we must fail to reject the null
hypothesis that there is no serial correlation between the error terms for these two
specifications at the 1%, 5% and 10% significance levels.

Another check for the specification of the time-series model is to examine the
autocorrelations of the residuals. The significance of the residual autocorrelations is
compared with twice the approximate standard error of the estimated autocorrelations
(HA/7‘), where T is the number of observations. If the estimated residual
autocorrelations exceed filfi‘, the model should be reestirnated using a different
specification for the error structure. The residual autocorrelations for both of the series

suggested that the specifications are acceptable.

4.2Ell'ifi'l'E'lD lE'

After the specification of the time-series model of the dependent variable in the
demand equation, one must check for Simultaneity bias in the demand equation from
the correlation between the apple price variable and the disturbance term in the NYC
retail apple demand equation.1 The two methods that are discussed in Section 3 of

Chapter III are used to test for simultaneity bias.

 

1For the source of the possible sirnultaneity bias in the demand equation and
methods to detect the Simultaneity bias, see the discussion in Chapter III.

62

To test for sirnultaneity bias, the Hausman test was used to compare the demand
equation with the instrument for the price variable with the one without the instrument
for the price variable. The first step was to find an instrument for the price variable.

An instrument for the price variable was created by regressing the price variable
on all the exogenous variables in the system of equations. These exogenous variables are
the regional price of bananas, the regional disposable income, the national apple storage
holdings and the regional health-risk information.1 The predicted values from this
equation were then used as the price variable to estimate the demand equation in a
separate regression.

Two demand equations were estimated. These are, the demand equation without
an instrument for the price variable and the demand equation with an instrument for the
price variable. Initially, the other exogenous variables in the demand equations were
price of bananas, disposable income and risk information. The price of bananas and the
income variables did not provide significant coefficient estimates. Therefore, these
variables were excluded from the demand equation. The estimated demand equations
are reported in Table 4.2. Note that the covariance matrix for the demand equation with
an instrument for the price variable was calculated using the method outlined in
Appendix E. The covariance matrix for the demand equation with no instrument for the
price variable is the one reported in the regression output of the RATS econometric
package (version 3.1).

The Hausman test statistic was found to be 0.310. The critical value from the x2
distribution with 5 degrees of freedom at the a $0.10 level is equal to 9.24. Since the
Hausman statistic is lower than this critical value, we must fail to reject the null
hypothesis that there is no Simultaneity bias in the demand equation when the equation

is estimated without an instrument for the price variable at the 1%, 5% and 10%

 

1The information variables that are used in the demand models when testing for
simultaneity bias are the ones that are measured in the nominal scale (Sn, 52,, S3,).

63

Table 4.2. Estimate of the Demand Equation With Seasonal ARMA Errors With and
Without an Instrument for the Price Variable (January 1980-July 1991)‘

 

_

 

 

 

 

 

 

 

 

 

 

 

 

 

aonetailtestandtheothervariablesarefromatwotailtest.

variable are calculated by using the method outlined in Appendix E.

 

(Figures in parentheses are t-statistics.)
’ Significant at the a50.01 level.
" Significant at the as 0.05 level.
“The dependent variable: A12 lnq,.

l"The signficance levels for the coefficients on the lap, and the information variables are from

 

DEMAND” EQUATION DEMAND EQUATION
WITH INSTRUMENT WTTH NO
MODEL FOR THE PRICE INSTRUMENT FOR
VARIABLE‘ THE PRICE VARIABLE‘
(T = 127)
(T = 127)
! Constant -0.021 -0.031
(-0.761) (4.419)
Ania p, 4.200 0.739
(4.820)" (-2.782)°
Assn 0227 0.199
I ('3o547). (“1.678) 0‘
I
Ans, -0.396 0314
(-3.883)° (4.107)“
Ans, -0.236 0.105
(4586) (-0.544)
MA 0563 0.548
(4541)' (7.103)’
MA(Seas) 0.765 0.780
(40.241)‘ (.11.042)'
Adj. Rz 0.628 0.664
SSE 7.027 6.681
Q-Stat 23.165 27.441
(lac-=24)

'The instrument for the price variable was created by regressing [up], on lnpwlnh,,lnm,,S,,,S, and
S, to obtain the predicted values for lnpqp
’The estimated standard errors for the demand equation with the instrument for the price

.The estimated standard errors for the demand equation with no instrument for the price
variable are the ones reported in the output from the RATS econometric package (version 3.1) for
personal computers.
Au : Seasonal difference operator.

T: Number of observations.

(The variables are defined in Table 4.12.)

significance levels.

The regression-based test for the simultaneity bias also supports this finding.1 When
the estimated error terms from the demand equation without an instrument for the price
variable is regressed on all of the exogenous variables in the demand equation including
the price variable M the predicted values for the price variable from regressing price on
all the exogenous variables in the system of equations, the t-statistic on the fitted values
for the price variable was equal to 1.558. This implies that the estimate of the
coefficient for the fitted values for the price variable is not statistically different than
zero. We therefore conclude that when the demand equation is estimated without an
instrument for the price variable, the residuals are not correlated with the price variable.
This implies that there is no problem of simultaneity bias in the estimated demand

equation when the observed values for the price variable are included.

4.3 e t' ' n’s d e

W2

The time-series component of the lnq: variable for the period of January 1980-July
1989 was specified using the Box-Jenkins approach as discussed in Section 4.1.1. The
autocorrelation and the partial autocorrelation functions of the truncated sample also
suggest seasonality; seasonal difierencing is thus necessary. After seasonal differencing,
the autocorrelations and the partial autocorrelations were reexamined. The time-series
component of this variable was specified as a multiplicative seasonal ARMA model of
order (0,0,1)x(0,1,1)12.

 

1For the description of the regression-based test for simultaneity bias, see Section
3.3 .2.

2To maintain consistency in comparing results with the ones reported in van
Ravenswaay and Hoehn (1991), the data used for the January 1980-July 1989 observation
period is identical to the ones reported in Guyton (1990)

65

After specifying the time-series model of the dependent variable in the demand
equation, the next step was to search for the impact of the explanatory variables on the
per capita apple purchases by incorporating these variables into the demand equation.
The information variables that are initially incorporated are identical to the ones that are
reported in van Ravenswaay and Hoehn (1991). The same set of information variables
from the previous study is used because we want to be able to compare the information
effect on per capita apple purchases under two specifications for the error structure in
the demand equation for the same observation period. One specification is the AR(1)
specification that is reported in van Ravenswaay and Hoehn (1991). The other
specification is the multiplicative seasonal ARMA specification. The only difference of
this model from the one reported in van Ravenswaay and Hoehn (1991) is that the
variable that measures the presence or the absence of the reported risk by the
cumulative number of articles was excluded since this variable is non-stationary. After
seasonally differencing the dependent and the independent variables to obtain
stationarity in the series, the cumulative variable no longer measures the cumulative
effect. Therefore, only the $1,, NYT,, NYTM, NYT,_2 and NYT,_3 were incorporated to
the model estimates. The results are reported in Table 4.3.

In Table 4.3, the unrestricted model represents the hypothesis that information
on risk does not affect apple purchases and it embodies all of the information variables.1
To test the hypothesis that the risk information did not have any effect on apple
purchases, the unrestricted model was compared to the model that restricts the

coefficients of the information variables to be zero. The likelihood ratio test was

 

1Note that to maintain consistency with the van Ravenswaay and Hoehn (1991)
study, the information variables are S1, and the current and three period lagged NYT3
variable. In this specification, 52, was not included ill the unrestricted model since this
variable was not reported among the regression results in the study by van Ravenswaay
and Hoehn (1991).

66

Table 4.3. Estimate‘ of the Demand Equation” with Seasonal ARMA Errors (January 1980-
July 1989)c

 

UNRESTRICTED RESTRICTED
MODEL MODEL

rr= 100)“ cr= 103)

 

Constant 0.045 0.071
(-1.750)”' (-5.179)‘

A,,ln p, 0.991 0.967
(0337)" (-3250)‘

A,,In p, 0.024 0 .088
(0.069) (0270)

Ans, 0.143
(.1059)

AM, 0.013
(4304)

Alamo: 0.018
(4.705)“

AuNYTn 0.0007
(0.064)

ADNYTN 0.010
(0843)

0.658
(8.143)‘

-0.836 .
(-11.365)'
0.661
2.134

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(Figures in Parentheses are t-statistics.)

‘ Significant at the “0.01 level.

“ Significant at the “0.05 level.

“‘ Significant at the a$0.10 last.

The demand equation was estimated without an instrument for the price variable.

”The dependent variable: Auln q.

“The significance levels for the coefficients of the ln pg, 1n p, and the information variables are from a
one tail test and the othervariablesare from a twotail test.

‘ Note that T reduces to 100 from 103 when we include a three-period lagged value of the NYT, variable.

Au : Seasonal difference operator.

T : Number of observations. (The variables are defined in Table 4.12)

67
employed to test this hypothesis.1
The likelihood ratio value was calculated by using the SSRR, the SSRU and the number

of observations that are reported in Table 4.3. The likelihood ratio value was 8.17. The
critical value in the X2 distribution table at the 5 degrees of freedom is 9.24 at the
«$0.10 level. This implies that we fail to reject the null hypothesis at the 1%, 5% and
10% significance levels such that the restricted model is not superior when compared
with the unrestricted model. This finding implies that the information variables do not
add any additional explanatory power to the demand model at these significance levels.

In the above specification of the information variables, when the current and
lagged values of the NYTt variable were included in the demand equation as the only
information variables, the estimates of the coefficients for the NYTt and the NYT,_1 were
significant while the estimates of the coefficients for the NYT,_2 and NYT .3 were not
significant. These two variables were therefore excluded from the unrestricted model.
The inclusion of the retail price of bananas also fail to provide additional explanatory
power to the equation estimates. This variable was thus also eliminated from the
equation estimates. The demand model was respecified by using only the apple prices
and the remaining information variables as the independent variables. The information
variables are the variables that represent the second, third and fourth hypotheses (Sm
NYTt, NYT,_1 and $2,) variable. The results are reported in table 4.4.

When the restricted model is compared to the unrestricted model, the likelihood

ratio value was 7.92. The critical value at the 4 degrees of freedom is 7.78 at the «$0.10

 

1The likelihood ratio value was obtained by using the following

a
formula: LR = Te “Mg—U) , where the SSRR is the sum of square residuals obtained

from the restricted model, SSRU is the sum of square residuals obtained from the
unrestricted model. T is the number of observations. The likelihood ratio value is

asymptotically distributed as 12(K) where K represents the number of restrictions. See,

Jan Kmenta, Wm 2d ed., (New York: Macmillan Publishing Co.,
1986), p. 492.

Table 4.4. Estimate‘ of the Demand Equation” With Seasonal ARMA Errors (January
1980-July 1989)c

68

 

 

 

UNREST‘RICTED RESTRICTED
MODEL MODEL
('r = 102)‘ (T = 103)
Constant 0.043 0.070
(4.779)” (-5.621)'
Auln p, 0.965 0.973
(-3301)' (-3.296)'

 

 

 

 

 

 

 

 

 

 

 

 

 

(Figures in Parentheses are t-statistics.)

‘ Significant at the «$0.01 level.

” Significant at the “0.05 level.

“‘ Significant at the «$0.10 level.

1114: demand equationwasestimatedwithout aninstrument forthepricevariable.

"The dependent variable: Au lnqr

'The significance levels for the coefficients of the lap, and the information variables are from a one tail
testanddresignificancelevelsofanothercoefficientsarefromatwotailtest.

‘Note thatT'reduwsto 102 from 103whenweinclude acne-period laggedvalueoftheNYT, variable.

Au : Seasonal difference operator. ‘

T : Number of observations.

(The variables are defined in Table 4.12.)

69
level, 9.49 at the «$0.05 level and 13.28 at the «$0.01 level. The result suggest that we
do not reject the null hypothesis that the information variables are all equal to zero at
the 1% and 5% significance levels while we reject it at the 10% significance level. This
implies that the unrestricted model in Table 4.4 is superior to the restricted model at the
10% significance level when the error structure is specified with the seasonal error
structure.

The same hypothesis was tested in van Ravenswaay and Hoehn (1991) where the
error structure was specified by an AR(1) process. The demand equations from the
study by van Ravenswaay and Hoehn (1991) were replicated and are reported in Table
4.5.1 When the restricted model is compared with the unrestricted model, the likelihood
ratio value was found to be 15.32. The critical value from the X2 distribution at the 6
degrees of freedom is 10.64 at the «$0.10 level, 12.59 at the « $0.05 level and 16.81 at the
« $0.01 level. The calculated likelihood ratio value is greater than the 1’ values at the
5% and 10% levels. Therefore we conclude that we must reject the null hypothesis that
the information variables are all equal to zero at the 5% and 10% significance levels
while we fail to reject at the 1% significance level. This implies that the unrestricted
model in Table 4.5 is superior to the restricted model at the 5% and 10% significance
levels when the error structure is specified with an AR(1) model.

To test which specification of the error structure for the demand equation is
correct, the Q-test was applied to the estimated demand equations under the two
specifications (the AR(1) specification and the multiplicative seasonal specification).
The null hypothesis is that there is no serial correlation between the error terms. When

Model 1 in van Ravenswaay and Hoehn (1991) is duplicated, the Q-statistic was 36.92.

 

1Note that the information variables in this model incorporates the information
variables of the unrestricted model in Table 4.3 plus the variable that measures the
cumulative number of articles on Alar. Also note that the data is identical to the data
reported in Guyton (1990), i.e., the population figures covers a larger metropolitan area
than the population figures used in this study.

70
Table 4.5. Estimate‘ of the Demand Equation" with AR( 1) Errors (January 1980-July 1989)c

UNRESTRICTED

 

 

 

 

 

 

 

 

 

 

 

 

 

 

l MODEL MODEL
(T=111)" Cr=114)
Constant -0.631 0.772 I
(-1.6l4)' (-1.967)' ‘
ln pg, .2052 -1957 ‘
(6.098)’ (-5-650)' I
In p, 0303 0328 '
(0.758) (0.852)
ln s,, -0.260
(-1813)‘
CNYT, 0.003
(0.459)
NYT, 0.0005
(0.040)
NYT... 0.016
(-1250)
mm, 0.009
(0.613)
NYT,,, 0.017
(.1264)
AR 0.587 0.717
(7.135)‘ (10.479)‘
Adj.Ra 0.619 0598
D“! 1.702 1.753
Q-Stat 36.915 36.003
(Ins-=20)
SSE 7.352 8.440

 

 

(Figuresinl’arenthesesaret-statistics.)

‘ Significant at the «$0.01 level.

“ Significant at the a$0.05 level.

'l‘hedemand equationwasestirnatedwithoutanimtrumultforthepricevariable.

’Ihedependentvariable:h1p,.

“Thedgnificancelevelsforthecocfficientsofthelnp‘mrp,andtheinforrnationvariablesarefromaone
tailtestandthesignificancelevelsofanotherooefficientsarefiomatwotailtest.

‘NotcthatTreduwsto 111fi0m114whcnweindudcathree-periodlaggedvahreoftheNYT,variable.
T:Number ofobservations. Clhevariablesaredefinedin'l‘able4JZ.)

7 1
This value is compared with the x209), where 19 is the degrees of freedom. This value
is obtained by subtracting 1 from 20. 20 is one fifth of the total observations and 1 is the
number of ARMA coefficients in the specification. The critical value from the 12 table
at the 19 degrees of freedom is 27.20 at the a $0.10 level, 30.14 at the a $0.05 level and
36.19 at the 0150.01 level. This implies that we reject the null hypothesis that there is no
serial correlation at the 1%, 5% and 10% significance levels and the error structure is
misspecified with the AR(1) specification.

The Q-statistics for the demand models with the seasonal error structure are
reported in Table 4.3 and 4.4. These values are compared with the x207), where 17 is
obtained by subtracting 3 from 20. 20 is one fifth of the total observations and 3 is the
number of the estimated seasonal ARMA coefficients (including the constant term).
The critical value from the 12 table at the 17 degrees of freedom is 24.77 at the «$0.10
level, 27.59 at the «$0.05 level and 33.41 as0.01 level. This means that we do not reject
the null hypothesis that there is no serial correlation at the 1%, 5% and 10% significance
levels. This result suggests that when compared to the AR(1) model, the multiplicative
seasonal model is the correct specification for the error structure at the 1%, 5% and
10% significance levels.

The results imply that when the seasonal error structure is employed to estimate the
demand function over the observation period of January 1980 to July 1989, the
information variawa do not add any explanatory power to the equation estimate at the
1% and 5% significance levels while they are all significant at the 10% significance level.
The Q-Statistics imply that the seasonal ARMA specification is the correct specification
for the demand equation when compared to the AR(1) specification. However, the
information variables are significant only at the 10% level with the seasonal ARMA
specification while they are significant at the 5% level with the AR(1) specification .
Since with the seasonal ARMA specification we are able to reject the null hypothesis

that the coefficient estimates of the information variables are all equal to zero only at a

72
higher significance level (10%), it is ambiguous that the Alar incident had any impact on
apple demand in the NYC region at all. i
In order to find out whether the information about Alar had any impact on apple
purchases, the next step is to extend the observation period to see if additional
observations would make any difference in the equation estimates. This means that we
add 24 more observations to the sample. The following subsection summarizes the

findings for the extended observation period.

 

The hypotheses about the effect of risk information on apple purchases were tested
by estimating the demand model for the extended time period. The results are reported
in Table 4.6. The numbers 1-6 in Table 4.6 indicates the models that embody the
hypotheses on modelling the risk information effect presented in 2.3.

To test whether the information on Alar had any impact on apple purchases, the
unrestricted model (model 1) was compared to the restricted model (model 6) with a
likelihood ratio test. The likelihood ratio was 13.98. The critical value at the 5 degrees
of freedom is 9.24 at the «$0.10 level, 11.07 at the «$0.05 level and 15.09 at the «$0.01
level. Therefore, the null hypothesis that the restricted model is superior to the
unrestricted model was rejected at the 5% and 10% significance levels but not rejected at
the 1% significance level. This result implies that there is evidence that all of the
information variables are different than zero for the extended observation period since

they all are different than zero at the 5% and 10% significance levels.

 

1The data used to estimate the models for the January 1980-July 1991 observation
period are the ones described in Appendix A and reported in Appendix B and C.

73

 

gamma

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

8a 3.: Sea 898 82" 8mm 500
82. 28.8 «8.8 33 8% 83 «mm
55 83 :85 «as 986 88.0 R?
.523 .3123 .523 .AfinoE .823 .3583 A869
83. 83 83 88. 33 83 <2
has has .996 has bag .38:
82 82 82 88 $2 82 <2
198.3 98.3 198.3
BS. 08°. no.0. :trznq
52¢ 38.3 88.3
5.9 .88.? ~85- E916
32¢ 28.3
88. 23 .84
192.3 93.3
:2. «86. £3
88.3 LEW: $33 68.3
:83 RS. .38. 83. =06
#83 .3283 x820 bani bani .383 .
89o. 88. 83 36.9 «8.? En- tn 5:4
.663 83.3 .933 .Gzi .933 :33
82.. H8? «28. 83. 3.9 5.9 2228
92:8 Sanbm 32...? 5798 57% .62.? doc:
.22:

b: 783 5:50 finger nous—~83 on“ .8.“ 8038583 “conga .5qu 955 52% Ransom 5m? ocean—Gm vSEoQ 05 .8 .Baflmum 6... mid.

74

3... as“... 3 Bacon an 8525, 25
.maocatumpo .8 838:2 H...
.8222? 3:208? Enogom ”:4
673.5, .E 05 we on?» Ecume— votoméao a ova—05 03 non? ha." Sea 8« 2 3032 H :2: Sol 6
.82 :2 oi n .
89c 98 3333, couscous “05° 05 v3 $8 :2 one a Bob 8a 33%? gauges 2: 38 an 5 05 we «gnome—boon. 05 “8 £96. 8588ch of. 6
.65 24 “053.5, Eovcoeuu 2E. n
diets, 81a 2: .8.“ 80:5me 5 :55? 33:53 33 82280 “858% BE. .
.93 Sewn 2: a 58%me :
.352 Sewn 2: a 28%me .
“66333.6... 2a 385."on 3 35mm:

95.88 64. 035.

75
Since we fail to reject the first hypothesis that there is no impact of risk information
on'purchases and since we do not know what the appropriate specification for the
information effect is, the hypotheses that are outlined in Section 2.3 for the alternative
specifications of the information effect were tested.

The second hypothesis that the consumers do not forget the risk information
available to them is embodied in model 2. The estimate for the coefficient on the
information variable in this model suggest that we fail to reject the hypothesis meaning
that the information about risk is not forgotten until the announcement is made that the
source of risk is eliminated from the market. The reason that this hypothesis is not
rejected is that the estimate of the coefficient on the Sn variable is significant which
implies that there is a one time and a sustained demand shift associated with the initial
announcement on the presence of the risk.

The third hypothesis is that the intensity of the reporting on the presence or
absence of risk intensifies consumer’s risk perception and thus causes a downward shift
in individual apple demand. Model 3 incorporates the information variables that
represent this hypothesis. Following the discussion in Section 2.3, note that we cannot
test this hypothesis with model 3 since the period during which there was intense media
coverage on the presence of risk involves February 1989, the month when the revised
risk estimates were released. We cannot distinguish the effect of the intensity of the
media coverage that is measured by the current and the lagged values of the NYT,
variable from the effect of the variable that measures the presence or absence of the
revised risk estimates (Sh) since these variables are highly correlated. The correlation
coefficient between $2, and NYT. is 0.76 and NYTM is 0.77.

Models 4 and 5 incorporate the variables that represent the fourth hypothesis.
The coefficients on S1‘ in both models 4 and 5 are significant indicating that there is a
one time and a sustained shift in demand with the initial health-risk information in July

1984. The lagged value of the NYTt variable is negative and significant in model 4. The

76
52: variable is negative and significant in model 5. The significance of the coefficients of
NYTt,1 and 82, suggests that the consumers continuously revise their risk perceptions
when they receive additional information on health-risk.

The fifth question is whether there is a long-run effect of the Alar controversy.
Model 5 incorporates the S3, variable that measures the presence or the absence of Alar
in the market. If the hypothesis that the sales return to the pre-announcement levels is
correct, then the coefficient on the 83' should be insignificant while the coefficient
estimates on 81, and 52: will be negative and significant. The results suggest that this

hypothesis is true.

4.5 atio ua ' d i ' educ -

mum

After the information effect in the demand equation is specified, the next step is
to examine the information effect in the reduced-form equations for quantity and price.
As noted in Sections 3.2 and 3.3, by looking at the coefficient estimates of the
information variables in the reduced-form equations for quantity and price, we can
understand the effect of the health-risk information on the equilibrium price and
quantity levels at the NYC region. This section reports the findings on the information
effect from the reduced-form equations for quantity and price.

As the Hausman test and the regression-based specification test suggest in
Section 2 of this Chapter, the simultaneity bias is rejected in the estimated demand
equation. This implies that the price variable in the demand equation is not correlated
with the error term in this equation. Therefore, if there is a change in per capita apple
purchases in the NYC region because of the health-risk information, it is associated only

with the demand shift in that region and not with the change in national price due to the

77
information at the national level. The results from the estimated reduced-form
equations are also consistent with this finding.

Table 4.7 and Table 4.8 report the results from the estimated reduced-form
equation for quantity and price, respectively. The numbers 1-6 in Tables 4.7 and 4.8
indicate the models that embody the hypotheses presented in Section 2.3. The results
are used to discuss the hypotheses on the information coefficients in the reduced-form
equations and in the demand equation. The hypotheses on the effect of information on
the reduced-form equations and on the demand equation are outlined in Section 3.2.4.

The first hypothesis is that there is no effect of health-er information on apple
purchases in the NYC region. If this hypothesis is true, then the coefficient estimates of
the information variables in the reduced-form equations for price and quantity and the
demand equation should all be zero, i.e, ‘9' =0, a' =0 and 0; =0. This hypothesis is
rejected since in the sections above, we already concluded that risk information is a
significant variable in the demand equation.

The second hypothesis is that the change in apple sales is associated only with the
change in apple prices in the national market induced by risk information. If this
hypothesis is true, then the coefficient estimate for the information variable in the
reduced-form equation for price should be greater than zero, i.e., a' > 0 and the
coefficient estimate for the information variable in the demand equation should be
insignifieant, i.e., B: = 0. 'lhis hypothesis is rejected since the estimated coefficients for
all of the information variables in the reduced-form equation for price are statistically
equal to zero since the likelihood ratio value that compares model 1 (unrestricted
model) to model 6 (restricted model) in Table 4.8 is 2.98. The critical value at the 5
degrees of freedom is 9.24 at the «$0.10 level, 11.07 at the «$0.05 level and 15.09 at the
a $0.01 level. Since 2.98 is smaller than these critical values, we conclude that the
information variables are statistically not different than zero. Furthermore, we already

concluded in Section 4.4 that the coefficient estimates for the information variables in

78

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5.3 ”9.3 :3” 888 :92 was .560
E: as.» was :2 on: «as «3
an. no.9 was «8.0 as 3.0 3.3
.8843 2333 .3863 .8253 .83.:3 .9303
SS. 83. 5.9 9.3 85.9 $3. 939.32
.988 .523 .383 .233 .825 .883
32 Ed :3 «So 82 22 <2
LE3 .983 L8...3
mod. «.86. «8.9 .52 "a
88.3 .1933 A53
28. «8.9 29? EE :4
883 83.3
$3. «8.9 .m :4
I333 98.3
9.8. 23. am .6
183.3 -383 .333 99.3
3.8. $8. and. 83. ._m =4
$8.5 98.8 523 £98.: £98 93.:
a8 38 Q3 53 :8 23 a .6
lead $8.8 :83 163.3 38.8 5.3
32. a8 83 RS. 32 and. .e 5.5.
$83 :83 63.3 88.3 L53 83.3
Kg 33. :3 £3 02.9 5.9 .a 2:4
.83.”.3 88.3 -683 -983 .323 A803
n86. 89o. ~80. ~86. mad. «8.? 2228
57.5... 57.6“ 62.9. SE: 92...? .82.? doc:

 

 

 

 

 

 

 

avg—ohm (32¢. Enemaom £5 moms—UH: 039‘ 235 “on .5.“ .32an Eoméoosvum 2: no 8.35am .5. as:

 

79

3... 2...... a. 382. 2.. 83...... 25

«8253.... .o .352 a.

.2223 8535—. flag . =< 653.9 .E 05 mo 02.5 comma— eotoaéuo a 3:3 oi «2.3 5 82a and 8 «82.0.. h. .25 202 o

.8. =8 25 a 69a

2.. 23.0508 22.... .1... 22.2 8:85.22 2.. .2... .8. .3 26 a as. a. 8......» 8:38.... 2.. .o 2288.8 2.. 2.. 226. 8.555.. 2.... .
é... 2.. "2.2.: .5293. 2.... .

.25. Same 2.. .. 3.23.2 :.

.26. 8...“: 2.. .. saga ..

.25. Same 2.. .. .555... .

..a.....§.. a. 8858.... a. 82.2....

£9.89 .56 03:...

80

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

canto

 

 

 

 

 

 

RS. 222 ~82 .82 «8.2 :2. .320
2...... 8.... 82.... 52.... .5... .83 2mm
:8 8:. 8:. 8.... 8:. 2.... 2.8...
.8833 .8823 .882.-. .533 .8853 .8223
E... 22.. E... E? 3.9 8...... 838...:
.8223 88.2. .8223 .892. .85.: .882.
$2. .2... 2...... 8.... 2.2. 82. a...
82.8 82.8 883
38... .8... .8... :trz 2..
83.8 88.3 82.8
as... .8... 38... HE 2..
82.3 883
5.... 82.... am ._<
88.3 88.3
8...... 88.... J. «.4
88.3 82.8 888 838
3.9 NS... 2.... 8v... .8 a...
88.3 82.3 82.3 88.3 88.3 8a....
.2... 88.... 82.9 8...... «8.... 2...... ._. =4
8.8.: 83.8 82.8 88.8 83.8 82.:
an... :2. 3a... «a... 83 :3 .6 2.3
82.8 82.8 88.3 88.3 82.8 88.8
NS... .8... 88.... 88.... .8... «8... 2.. 5....
82.3 82.3 823 533 8.8..-. 88.8
2...... n8? 2...? 2...... 2...... 88... .588
5.an 82 It. Erubn 8". IS 82...... fine:

 

.uuohm <2 m< 1.533 .23 3E 33¢. :83— 5u .335 Each—éogtod 0.: mo 82.55 .3 033—.

 

81

.8828923883282538

3080203.. .0 .3822 u...

£280.... 005.05.. 109.com . ad

2.2.9 6.2 2.. .o 2..2 .38.. 818-08 a 25.2.. 2. =2... R. as. .a. 2 .882 .. .2. 2oz .

.8. .8. 25 a

8.... 0... 880.0508 .05.. :0 .0 «.30. 005055... 0... 8.8 .8. a... 0.... a :8... 0.8 830.5. 58083.... 05 .0 880.0508 05 8.. 32.0. 0050558 2: a
.8... 2.. “2......2 2.2.8.2. 2... .

.92 8...“: 2.. a .588... .

A833... 0.0 00853.:— am 00.35.

3.300. dd 030,—.

82
the demand equation are all negative and significant.

We also reject the third hypothesis that the effect on sales is due to both to a
national price change and to a regional demand shift. This is justified by the finding
from the second hypothesis that price is not affected by the health-risk information.

Models 4 and 5 in Table 4.8 indicate that the retail price of apples in the NYC
region was not affected with the initial announcement of the health risk in July 1984.
The presence or absence of this risk is measured by Sn- The coefficient estimate of this
variable is statistically equal to zero. The retail price remained unaffected with the
series of events after February 1989. The added effect after this date is represented by
the S2t and/ or the current and the lagged values of the NYTt variable."Ihe estimated
coefficients in models 4 and 5 show that both the initial announcement and the
subsequent announcements on health risk did not cause any effect on the equilibrium,

. price level at the NYC region.

After rejecting the first three hypotheses we conclude that the we do not reject
the fourth hypothesis which states that the impact on quantity purchased in the NYC
region is due only to the demand shift at the regional level. This hypothesis also implies
that there is no change in the retail apple price at the NYC region associated with the
risk information. This hypothesis suggests that a' =0, 9' <0 and 3: <0. We do not
reject this hypothesis because the estimates of the coefficients of all the information
variables in the reduced-form equation for price are not significant while they are
significant in the reduced-form equation for quantity, i.e., a' = 0 and 7' < 0. The
likelihood ratio value that compares model 1 (unrestricted model) to model 6 (restricted
model) in Table 4.7 is equal to 13.19. The critical value at the 5 degrees of freedom is
9.24 at the «$0.10 level, 11.07 at the «$0.05 level and 15.09 at the «$0.01 leveLSince this

value is greater than the critical value at the 5% and 10% significance levels we conclude

 

1F or the definitions of the information variables, see Section 2.2 and Table 4.12.

83
that the coefficient estimates of all of the information variables in the reduced-form
equation for quantity are significant. In addition to this finding, we already noted in
Section 4.4 that the coefficient estimates for the information variables in the demand
equation are all negative and significant, i.e., B: <0.

In summary, the findings from the reduced-form equations imply that there is no
evidence of a price change at the NYC region associated with the risk information. The
findings from the reduced-form equations imply that there is a drop in the equilibrium
level of per capita purchases in the NYC region and this drop is due only to a demand
shift in the NYC region. As outlined in Section 3.1, there are several interpretations
which might explain why the price at the NYC region did not change. One reason may
be that wholesale prices dropped as a result of a downward shift in wholesale apple
demand, but retailers did not adjust apple prices at the retail level. Still another reason
may be that there was a commensurate supply shift at the retail apple market such that
the retail apple prices remained unaffected. Note that in this research we cannot test
which of the above interpretations is true. The findings from the reduced-form
equations only tell us that the retail price at the NYC region remained unaffected by the
Alar incident. Further research on the effect of the Alar incident at the national market
is needed to understand the reason why the regional retail price remained unchanged.
We also need additional research to examine the impact of the Alar incident in other
regions across the nation. When we examine the other regions, however, we should
consider the possibility that the change in the equilibrium quantity in those regions may
be associated with both a change in retail price and a downward demand shift at the
regional level. In other words, we cannot generalize the result obtained from the NYC

region that the retail price was unaffected in the other regions across the nation.

84

4.6 Est' at' theC a e' Revenu to the e' es

Emil—era

The estimates of the demand equation under alternative specifications of the
information variable reported in section 4.4 can be used to estimate the total change in
retail apple sales in the NYC region associated with the risk information during the
January 1980-July 1989 period. This gives an estimate of the revenue loss to the retailers
of fresh apples in the NYC region. The estimate of the revenue loss is the difference
between the estimated actual sales and the projected sales that would have occurred had
the Alar incident never occurredl. The mathematical derivation to calculate the
estimated actual sales, the estimate of sales without the risk effect and the estimate of
the lost revenue is presented in Appendix F.

The estimates for the actual sales and the projected sales without the Alar
controversy were calculated for models 4 and 5 reported in Table 4.5.2 These two
models represent the hypothesis that there is a one time, sustained demand shift
associated with the initial health-risk information. The consumer continuously updates
his/her health-risk perception as he/ she receives additional information on health risk.
Figures 4.1 and 4.2 show the projected sales without the Alar incident and the estimated
actual sales that are calculated using models 4 and 5.

The area under the curve that represents the projected sales without the risk
information is the total projected sales without the Alar incident. The area under the

curve that represents the estimated actual sales is the total estimated sales with the Alar

 

1In estimating the change in sales, estimated actual sales rather than the observed
values of the sales were used. The reason to use this approach is to minimize the errors

is sales loss estimates (see, Mark Smith and others, 1988; Eileen van Ravenswaay and
John Hoehn, 1991).

2Since the coefficient estimate of the S variable was not significant, model 5 was
reestimated without the 83, when making e sales projections.

85

 

30

N
(1'
1

N
o
1

 

 

 

Dollars
(Millions)
6?

 

10---"'

 

 

 

 

 

 

 

O {YTTIIIIITFIIIUUIUIIIIIIIIIIFIIUIIIIIIWUFUIIIIIIIIIIITITIIII

1985 1986 1987 1988 1989
Years

—- Proi.Soles w/o Alar °°°°° Est.Ac’tual Soles

Figure 4.1. Estimates of the Apple Sales in the New York Region With and Without the
Risk Information (Model 4)

incident. The area between these two curves gives an estimate of the lost revenue to the
retailers due to the Alar controversy between the period of July 1984 to June 1989.
These estimates are reported in Table 4.9.

The results indicate that the Alar incident caused a sales loss of approximately
15% during the July 1984 to June 1989 period. The majority of this sales loss is
attributable to the initial announcement on the presence of the risk that is represented
by the dummy variable, Sn. According to both of the models, the share of the events in
and after February 1989 was relatively small in total revenue loss. In other words, the
sales declined around %12 after the initial risk announcement by the EPA an the
revenue loss increased as much as to 15% following February 1989. Consistent with the

study by van Ravenswaay and Hoehn (1991), the results suggest that the events in and

86

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

30
25‘
20‘
2 2?
:2 £15-
8 :2,
10-..'."..:'..
s-.
0 I'I'I'I"1'..111lIIII'U"T""IUI'Ir'UIUIUITTIYVTIIUVIII—11"
1985 1986 1987 1988 1989
Years
-- Proj.$oles w/o Alar °°°°°° EstAcfuol Soles

Figure 4.2. Estimates of the Apple Sales in the New York Region With and Without the
Risk Information (Model 5)

after February 1989 accounts for a relatively small portion in the total sales loss. Note
that we do not know the real reason for the additional shift in demand in February 1989.
It can be the intense media coverage on the presence of the risk in and after February
1989 or it can be the release of the revised risk estimates made by the EPA and the
NRDC in February 1989.

4.7

 

The estimates of the change in consumer surplus associated with the risk information

can be calculated using the estimated demand curves. The mathematical derivation of

87

Table 4.9. Estimates of Total Apple Sales in the New York Region With and Without
the Effect of Alar for the July 1984-June 1989 Period (1983 Dollars)

 

REVENUE ESTIMATES

MODEL 4

MODEL 5

 

1. Projected sales without
the risk Information

$ 716,816,422

$ 715,139,655

 

2. Actual estimated sales

$ 610,549,321

5 606,971,036

 

3. Change in sales =

 

 

 

 

 

 

 

(1-2) $ 106,267,321 3 108,168,618
4. % Change in sales =
(3/1)‘100 % 14.8 % 15.1
5. Change in sales due to Sn

3 84228450 3 88,343,595
6. Share of S1t in total change
in sales =(5/3)*100 % 79.3 % 81.7
7. Change in sales in July 1984-
January 1989 period 3 87,713,103 $ 94,676,810
8. Share of July 1984-January
1989 period in total change in % 82.54 % 87.53
sales=(7/3)* 100
9. % Change in sales in July
1984-January 1989 %12.24 %13.24

eriod= 7 1 ’100

 

 

 

the expected value of the consumer surplus with and without the risk information is
presented in Appendix G. In order to calculate the expected value of the consumer
surplus from an estimated log-linear demand curve, the price elasticity of demand should
be greater than one. Otherwise, the value of the consumer surplus and thus its expected
value approaches infinity (see Appendix G). The previous research does not reach a
consensus as to the ”correct" estimate for the price elasticity of demand for fresh apples

at the retail level. It is reported, however, that the demand for apples at the retail level

88

is price elastic both for the studies using annual data and for intraseasonal demand
studies.1

The estimated demand curves in this study suggest that apple demand is inelastic at
the retail level. This result should be interpreted with caution because of the highly
seasonal apple demand and apple price. The observation period covers only 11 years.
When the price and quantity variations due to seasonality are taken into account during
this time period, there is very little variation left in the price and quantity variations. It
is then difficult to estimate a reliable price elasticity. This may explain why the price
elasticity estimates reported in this study are so low.

Since it is not possible to use the estimated price elasticities from this study to
estimate the consumer surplus, the next best alternative is to use the range of own-price
elasticity estimates from other studies. The studies that use monthly data have
estimated the retail level own-price apple demand elasticities to be between -1.3 and -
4.62. Several values from this range of elasticities were used to calculate the expected
value of the change in consumer surplus. The estimates from model 4 and model 5 are
virtually identicaL Therefore, the results from model 4 are reported in Table 4.9. The
annual change in consumer surplus associated with the information on the presence of
the risk due to Alar can be interpreted as the consumer’s annual willingness to pay to
avoid health risks due to consuming apples that are treated with Alar.3 Following van
Ravenswaay and Hoehn (1991), dividing annual willingness to pay to avoid health risks
due to Alar by the individual’s perceived risk of experiencing the health-problem gives an

 

1Harry S. Baumes. Jr. and Roger K. Conway. MW;
t ERS Staff Report No. AGES850110, 1985 (Washington, DC: Economic
Research Service, U.S. Department of Agriculture).

2See, for example, Henry S. Baumes and Roger K. Conway, 1985; Dana G. Dalymple,
"Economic Aspects of Apple Marketing in the United States” (Ph.D. diss., Michigan
State University, 1962).

3See the discussion on section 4 of Chapter II.

89

Table 4.10. The Expected Value of the Annual Change in Consumer Surplus Under
Alternative Elasticity Estimates (1983 Dollars)

 

 

 

 

 

 

 

 

 

 

 

 

 

a W a
Elas- -1.2 -14 -1.6 -1.8 -2.0 -2.2
ticity
19841 2.68 1.35 0.90 0.68 0.55 0.46
1985 6.17 3.11 2.09 1.58 1.27 1.07
1986 7.15 3.49 2.27 1.67 1.30 1.06 1
1987 6.84 3.41 2.26 1.69 1.35 1.12
1988 5.85 2.95 1.98 1.50 1.20 1.10
19892 9.40 4.75 3.21 2.43 1.97 1.66

fl _ l

 

 

 

 

1 The estimates for the change in consumer surplus represents only the last
six months of 1984. The implied change in consumer surplus for this year under the
alternative price elasticities are: $5.35 ,$2.69, $1.81, $1.37, $1.13 and $0.92 for own
price elasticities of -1.2, -1.4, -1.'6. -1.8, -2.0 and -2.2, respectively.

2 The estimates for the change in consumer surplus represents only the first
six months in 1989. The implied change in consumer surplus for this year under the
alternative price elasticities are: $18.81, $9.51, $6.41, $4.86, $3.94 and $3.32 for own
price elasticities of -1.2, -1.4, -1.6, -1.8, -2.0 and -2.2, respectively.

estimate of the marginal willingness to pay for risk reduction. Since the individual’s risk

perceptions associated with the consumption of apples that are treated with Alar are not

known, the next best alternative is to assume that the individuals believe that the risks

are similar to the ones reported in the media. Therefore, these risk levels will be used

to estimate the marginal willingness to pay for risk reduction. van Ravenswaay and

Hoehn (1991) use a similar approach and employ several alternative assumptions for the

90

risk perception of the consumer.1 Table 4.11 summarizes the individual’s implicit
willingness to pay to avoid annual cancer deaths that are calculated by using Model 4.
This table replicates the estimates of the implicit willingness to pay that are reported in
van Ravenswaay and Hoehn (1991). There are two major differences, however. The
first difference is that the demand functions in this study are estimated by using a
seasonal error structure, rather than an AR(1) specification. The second is that several
own price elasticities were used since a reliable elasticity estimate could not be obtained.

The implicit willingness to pay to avoid a one in one million risk of cancer death can
be compared with the willingness to pay to save a statistical life. The results in Table
4.11 suggest that for a higher range of own price elasticity estimates, the willingness to
pay to avoid cancer deaths are very close to the range that are reported in the value of
life studies.2 This result is consistent with the findings by van Ravenswaay and Hoehn
(1991). It implies that the consumers react to risks associated with the consumption of
Alar-treated apples consistent with their behavior toward other health-risks, assuming the
own price elasticity of apples at the retail level is high and / or that consumer’s risk
perceptions were similar to the EPA’s initial risk estimate and the risk estimate by the

N RDC.

 

1The derivation of the annual risk estimates from consuming Alar treated apples are
explained in van Ravenswaay and Hoehn (1991). The authors use a linear dose-response
model such that the lifetime risk mcrease linearly and can be annualized dividing by
individual’s life expectancy (e. g. ., 70 years). It 1s also reported 111 van Ravenswaay and
Hoehn (1991) that approximately 17% of the risk from Alar 1n all food sources is due to
the consumption of fresh apples. Therefore, the reported health risk 18 multiplied by
0.17 to obtain the health risk associated with the consumption of apples treated with
Alar. The authors note that the value of life studies are based on assumptions about
perceived mortality risks. The assumptions about perceived risk here are based on risks
of getting cancer. The NYT initially reported the risks as cancer death risks but it is not
known whether the subsequent cancer risk estimates are equated with mortality risks.
Therefore, the implicit willingness to pay estimates for reduced death 1n this study should
be treated as rough indicators.

2The willingness to pay to save a statistical life 1s approximately $1.44 to $7. 64 m
1983 Dollars. See van Ravenswaay and Hoehn, 1991; A. Fisher and others, "The Value

of Reducing Risks of Death. A Note on New Evidence” W
Management 8(1989) PP 83-100

91

Table 4.11. The Implicit Willingness to Pay for an Annual Reduction of One in One

Million (1 x 10") Risk of Cancer Death (1983 Dollars)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ESTIMATE OF LIFETIME CANCER RISK
FROM ALAR=
EPA (1985 : 1.7 x 10-5
OWN PRICE
ELASTICI- -12 -1.4 -1.6 -1.8 -2.0 -2.2
TIES
1984 22.03 11.08 7.45 5.64 4.65 3.79
1985 25.41 12.81 8.61 6.51 5.23 4.41
1986 29.44 14.37 9.35 6.88 5.35 4.36
1987 28.16 14.04 9.31 6.96 5.56 4.61
1988 24.09 12.15 8.15 6.18 4.94 4.53
1989 77.45 39.16 26.39 20.01 16.22 13.67
ESTIMATE OF LIFETIME CANCER RISK
FROM ALAR -
NRDC (1989) : 4.1 x 10'5
1984 9.13 4.59 3.09 2.34 1.93 1.57
1985 10.53 5.31 3.57 2.70 2.17 1.83
1986 12.21 5.96 3.88 2.85 2.22 1.81
1987 11.68 5.82 3.86 2.89 2.30 1.91
1988 9.99 5.04 3.38 2.56 2.05 1.88
1989 32.11 16.24 10.94 8.30 6.73 5.67
I ESTIMATE OF LIFETIME CANCER RISK
FROM ALAR= -
EPA (1989) : 6.0 x 1045
1984 62.42 31.38 21.12 15.98 13.18 10.73
1985 71.98 36.28 24.38 18.43 14.82 12.48
1986 83.42 40.72 26.48 19.48 15.17 12.37
26.37 19.72
23.10 17.50
74.78 56.70

 

92

Table 4.12. Definitions of the Variables Used in the Econometric Model

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

VARIABLES

pqt Peflated retail price of apples in the NYC market at time

py, Peflated retail price of bananas in the NYC market at time

m, Per capita deflated earnings in the NYC market at time t.

h, National apple storage holdings at time t.

S1t Dummy variable that takes the value of 1 between July
1984 throuthune 1989 and 0 otherwise.

521 Dummy variable that takes the value of 1 between
February 1989 through June 1989 and 0 otherwise.

S3t Dummy variable that takes the value of 1 after June 1989
through July 1991 and 0 otherwise.

CNYT, Cumulative number of articles in the New York Times on
the presence of health risk associated with Alar at time t.

NYTt Number of articles in the New York Times on the presence
of health risk associated with Alar at time t-1.

NYTm One period lagged value of NYT,.

NYTQ Two period lagged value of NYT”

NYTM Three period lagged value of NYT,.

MA Moving average term.

AR Autoregfissive term.

MA(Seas) Seasonal moving average term.

 

 

 

CHAPTER V
CONCLUSIONS, POLICY ISSUES, AND FURTHER RESEARCH

5.1 u a of Research oble C! et 0

This research investigated how food purchases are affected when consumers
receive information on the existence of a health-risk associated with the consumption of
a particular food. More specifically, it examined the effect of the Alar scare on retail
fresh apple purchases in the NYC region. The observation period was January 1980
through July 1991. Having data on apple purchases two years after the date Alar was
withdrawn from the market allowed us to examine whether the Alar controversy had a
long-term effect on apple demand in the NYC region.

In answering this research question, Chapter II developed a conceptual model of
consumption that incorporates the health-risk information in a demand function. The
information variables that would measure the risk were then identified and the
hypotheses specifying the impact of changes in health-risk information on food purchases
were developed. Chapter III defined the econometric model for apple . demand and
derived the reduced-form equations for quantity and price. The methods to empirically
estimate the demand equation and the reduced-form equations were presented. Chapter
IV reported the empirical findings of the research.

The following sections in this Chapter summarize the empirical results of the
study that are reported in Chapter IV and derive policy implications. Further research

needs stemming from this research are identified later in the Chapter.

93

94
5.2 Summagy of the Research Results

5.2.1 The Importance of Considering Seasonalig when gtimatm' g the
Regression Equation

This research demonstrates that seasonal variation in variables, such as the
variable that measures the per capita apple purchases in the NYC apple demand model,
must be taken into account in estimating a time-series econometric model. If we do not
correct for seasonality, we do not know whether the variation in the dependent variable
is due to the seasonal variation or to the variations in the nonseasonal factors. The
seasonal variation is specified by a seasonal ARMA model and the variations associated
with the nonseasonal factors are explained by the exogenous variables in the demand
model.

In order to determine how the seasonal error specification affects the demand-
equation estimates and thus the coefficient estimates for the information variables, the
demand model reported in van Ravenswaay and Hoehn was reestimated using a seasonal
error structure. It was found that with a seasonal error structure, the information
variables do not provide any additional explanatory power to the equation estimate at
the 1% and 5% significance levels in the January 1980-July 1989 observation period and
they are significant only at the 10% significance level. Without the seasonal component
in the equation for the same observation period, however, the information variables were
jointly significant at both the 5% and 10% significance levels.l The Q-statistic, which
tests the overall acceptability of the residual autocorrelations, suggests that for the AR( 1)
specification the serial correlation in the demand model was not yet eliminated. When

we specify a seasonal error structure, the O-statistic suggests that the serial correlation in

 

lEileen van Ravenswaay and John Hoehn, 1991.

95

the model was eliminated. This implies that the seasonal ARMA model is the correct
specification when compared to the AR(1) model. Since with the seasonal error
specification we are able to reject the null hypothesis that the coefficients for all of the
information variables are equal to zero only at the 10% significance level but not at the
5% and 1% significance levels, it is not certain whether the Alar incident caused a
downward shift in apple demand in the NYC region at all

When the observation period was extended two years beyond the removal of Alar
from the market, we found that the information effect on the quantity demanded was
significant with the seasonal model at the 5% and 10% significance levels. This implies
that there is a stronger evidence of the impact of Alar on apple demand in NYC region
with the extended observation period. This may mean that a longer observation period

added more precision to the demand equation estimate.

5.2.2 W190

The results from the tests for simultaneity bias in the NYC demand equation
confirm that the price variable and the error term are not correlated. This finding
implies that simultaneity bias is not an issue in analyzing the impact of health-risk
information in the regional market such as the NYC market when the incident actually
covers the whole nation.

The findings from the reduced-form equations for the NYC retail apple price
also support this finding In the reduced-form equation for price, we found that risk
information at the national level does not affect the NYC region’s retail apple prices.

One possible reason why the NYC retail price did not change may be that there
was an offsetting supply shift at the national retail market for apples such that the retail
price of apples in the national retail market and thus at the regional retail markets was

not affected by the risk information. Another reason may be that the national wholesale

96
price may drop as a result of a demand shift in the national wholesale market but the
regional retailers do not change their prices. We do not know which of the above
interpretations is true in explaining the reason why the NYC retail price did not change.
To find out which interpretation is true, further research is needed to examine what
happened to quantity and price of apples at the national wholesale and the retail apple

markets as a result of information on Alar.

52-3 Infcunati90§ff99t

Consumers Show a swift and systematic response when they are informed about
the presence or absence of the reported risk in the market. Consistent with the findings
by van Ravenswaay and Hoehn (1991), the effect of the Alar incident in the NYC region
started in July 1984, when the EPA first announced the potential health effects
associated with the lifetime consumption of Alar-treated apples. The findings show that
consumers update their risk perceptions as they receive additional information on health
risk In other words, the events in and after February 1989 caused an additional shift in
apple demand. Note that with the available data, we are not able to distinguish the real
cause of the additional shift in demand. It could have been the presence of the revised
risk estimates released by the EPA and the NRDC or it could have been the intense
media coverage. Both of these two incidents happened between February 1989 to June
1989. The variable that measures the presence or absence of the revised risk estimates
($2,) is closely correlated with the current and one period lagged value of the variable
that measures the intensity of the reporting (NYTt). There is not sufficient information
that will enable us to differentiate between the impact of these two variables on the per
capita apple purchases. If the period during which there was intense media coverage did

not overlap with the period during which the revise estimates were released, it would

97
have been possible to estimate the separate effects of the intense media coverage and

the release of new risk estimates on the per capita apple purchases.

5.2.4 Own-Brice Elastigities

The price elasticity of apple demand was estimated to be less than one. This
estimated own-price elasticity is smaller than that estimated by previous research.1 An
inelastic own-price elasticity estimate may be a result of the variations in apple price and
apple purchases being explained by the seasonality in the demand model. When we
account for seasonality in the demand model, there is little variation left to estimate a
reliable own-price elasticity figure. A longer time series would allow us to estimate a

more reliable own-price elasticity.

 

The apple sales at the retail market in the NYC market would have been 15%
higher had the Alar event never occurred. This implies that a drop in apple sales of
almost $100 million was realized in the NYC region during the June 1984-July 1989
period. About 80% of this drop in apples sales is attributable to a one-time and
persistent demand shift associated with the initial announcement made by the EPA that

Alar was a potential carcinogen.

 

1See, Henry S. Baumes and Roger K. Conway, 1985.

98

5.2.6 ha e ' ons er lus ss 'ated wit pormatio on

Since it was not possible to estimate a reliable price elasticity of demand, several
different assumptions on the price elasticity had to be made in order to calculate the
change in expected consumer surplus. Following previous research1 the assumed own-
price elasticity was between -1.3 to -4.6. It was found that as the assumption on the
magnitude of the price elasticity was increased, the change in the expected consumer
surplus became increasingly smaller. Following the discussion in Section 4 of Chapter H,
the change in expected consumer surplus can be approximated to represent the
consumer’s willingness to pay to avoid Alar residues. If we assume that the consumer’s
perceived risk is similar to the risks reported in the media, it is possible to infer the
implicit willingness to pay for an annual reduction of one in one million risk of cancer
death. For higher own-price elasticity estimates (-1.8 to -2.2), the implicit willingness to
pay to avoid cancer deaths was close to the range that was reported in value of life
studies. Following van Ravenswaay and Hoehn (1991), it should be noted that the
implicit willingness to pay estimates in this research are based on very restrictive

assumptions on the risk perceptions of consumers.2

5.3 1191mm

This research shows that consumers respond immediately once they are informed
on the presence or absence of the reported risk in the market. Sales of apples drop even
further as consumers receive additional information on health risk. This result has

important implications for policy makers making decisions in the presence of health-

 

1Henry S. Baumes and Roger K. Conway, 1985; Dana G. Dalymple, 1962.
2See Section 4.7.

99
scare events such as the Alar incident. Since many of the older pesticides currently used
have not yet been fully tested for toxicity, it is likely that as new toxicity estimates are
released, conflicts similar to the Alar controversy will arise. Consumers are likely to shift
away from foods that contain residues of toxic substances. In order to minimize the
revenue losses to the food industry, the government could recall the suspected chemical
as soon as the initial reporting of the toxicity of a substance is released. In the Alar
controversy, for example, the drop in apple demand that took place between July 1984 to
June 1989 could have been avoided had the Government recalled the existing quantities
and suspended the sale of Alar in July 1984 while it continued the toxicity studies. An
alternative policy option for the Government could have been not announcing the
preliminary findings of the toxicity studies until a consensus was reached regarding
health risks associated with Alar. Still another policy could be that the interest goups
releasing statements about risks prior to definitive government study be subject to
product disparagement suits.

We would not know which policy option is the most feasible to implement unless
we estimate the benefits and costs associated with each policy alternative. The estimate
of the risk reduction benefits from this study provides information on the benefits of a
policy that would eliminate health risks associated with Alar. The findings of this study
indicate that the consumers are willing to pay amounts of money that are consistent with
the previous literature on the value of life, i.e., between the range of $1.44 and $7.64 in
1983 dollars.l This result implies that in similar health scare incidents in the future, if
the costs of a policy such as product recalling that would eliminate health risks from the

chemical are smaller than this estimated range, the Government should implement that

policy option.

 

1We note in Section 4.7 that the estimate of the benefits from avoiding risks from
Alar is based on very restrictive assumptions about risk perceptions and we assume that
own price elasticity of apples are high.

100
The food industry might also learn from the findings of this study. In the future,
when conflicts similar to the Alar incident arise, in order to minimize the revenue losses
the food industry may announce that they voluntarily stop using the chemical right after
the chemical is announced to be harmful to human health. The food industry may
therefore minimize likely conflicts. Alternatively, the food industry may direct its
policies to ask Government to recall the chemical or not to announce the preliminary

findings until the toxicity studies are finalized.

5.4 fo u e r

The findings of this research suggest that the Alar controversy affected the apple
demand in the NYC market. The research should be duplieated to other markets to test
whether the Alar incident had the same effect across the nation. 'We also find in this
research that the problem of simultaneity bias is not an issue in analyzing the effect of
the information on Alar in apple demand in a regional retail market using a single
equation model. This means that there was no evidence of a price change associated
with the Alar incident at the NYC region. The reason why the retail apple price at the
NYC region did not change can be interpreted in several ways.1

The finding that the price at the NYC level did not change with the Alar incident
could not be generalized to the other markets at the nation unless we find that the price
at the other regions remained unaffected. Further research is needed to examine the
other regions across the nation. Another way to support the results obtained from this
research is to examine the effect of the Alar controversy in the national retail apple
market. Examining the effect of health-risk information at the national retail market

using a simultaneous supply and demand model may strengthen the finding of this study

 

1See the discussion in Section 3.1.

101

if we find that the retail price at the national market was not affected by the Alar
controversy. This would confirm that we need not worry about the simultaneity bias
when estimating apple demand in a regional market by a single equation, when the event
actually covers the whole nation.

The effect of the Alar incident on the processed apple market could also be
explored in further research. A downward shift in processed apple demand would also
be expected associated with the reports in the media on the toxicity of UDMH, a

derivative of Alar which is found in processed apple products.

APPENDIX A

DESCRIPTION OF DATA

APPENDIX A

DESCRIPTION OF DATA

The data consist of monthly observations of apple purchases, population, retail
prices of fresh apples and bananas, consumer price index, disposable income, number of
articles on the presence of Alar reported in the New York Times (NYT) and the
national fresh apple holdings. As stated in Section 1.7 of Chapter I, the data used in this
study is largely identical to the one reported in Guyton (1990). The difference in the
two data sets is related with the definition of the population area in the NYC market
and we include variables on income and national fresh apple storage holdings to the
model. Data described below is reported in Appendix 3.1

TOTAL FRESH APPLE PURCHASES: Monthly data on fresh apple purchases
consist of the arrivals of fresh apples to the NYC market reported by the United States
Department of Agiculture (USDA).2

POPULATION: The population figures in this study cover a smaller area than
the ones reported in Guyton. This is because the monthly arrivals of apples for fresh
consumption to the New York-Newark metropolitan area covers five Primary
Metropolitan Statistical Areas (PMSA) in the New York-Northern New Jersey, Long
Island Consolidated Metropolitan Statistical Area (CMSA). These PMSAs are, Bergen-

 

1F or a detailed description of data on total fresh apple purchases, retail prices of

apples and bananas and articles on the presence of Alar reported in the NYT, see,
William P. Guyton, 1990.

2U.S. Department of Agiculture, Agicultural Marketing Service, '
We. Washington. DC. Jammy 1980 - July 1991-

102

103
Passaic, Jersey City, Nassau-Suffolk, New York and N ewark.1 The population figures
that are reported in Guyton cover the whole CMSA. Since only annual population
figures were available, the monthly figures were derived from the annual data by using
the following formula that demonstrates as an example of the calculation procedure for

the monthly gowth rate between 1981 and 1982:

1981 population estimate(1+r)‘2=l982 population estimate

where r is the monthly population gowth rate and 12 denotes the number of months
between two annual observations. Since we have the 1981 and 1982 population estimates
that are reported in July of 1981 and 1982, we can solve for r and then use this gowth
rate to calculate the monthly population rate. Similar procedure was used to calculate
the monthly population figures for each year.

The 1989 population estimate was not available since the population estimates
are usually not released for the years before the census year. Therefore, the population
figures for the months between July 1988 and April 1990 were calculated in the similar
way for the 21 months as described in the example above. Note that for the census years
(1980 and 1990) the p0pulation figures were released in April and for the remaining
years the population figures were released in July.

The population estimate for 1991 was not yet released. Therefore, the projection
for the months after the 1990 population figure was based on the gowth rate from April
1980 to April 1990 by using the following formula: ’

 

1The population estimates are not reported 10 the years before the census, i. e., 1979
and 1989. The population estimate for the years of census are reported' In April and for
all other years they are reported In July. Annual population data for 1978;1988 were
obtained fron U. S. Department of Commerce, Bureau of the Census,

Rm Series P25, 1978- 1988. The population for 1990 was obtained froem U. S.

Department of Commerce, Bureau of the Census, WW
911mm CPH-l 1990

104

1980 population estimatea +r)“°=1990 population estimate

The gowth rate is calculated by solving for r. This figure was multiplied by the
population estimate in 1990 and then added to the 1990 population estimate to get the
subsequent month’s figure. This procedure was repeated until July 1991’s population
estimate was obtained.

FRESH APPLE AND BANANA PRICES: Prices of fresh apples and bananas
were obtained from the monthly market basket reports published by the NYC
Department of Consumer Affairs.1 Both prices were deflated by the consumer price
index for all urban consumers (CPI-U) for the New York City-Newark Metropolitan
Area.

We chose bananas to be a substitute for fresh apples in the demand model
because bananas were the only fruit whose prices were reported in the NYC Market
Basket Reports. Guyton (1991) reports that oranges may be used as another substitute
for fresh apples. He incorporated a variable that measures the regional deflated retail
prices of oranges. However, the coefficient for the orange price variable yielded a
negative Sign. He therefore dropped the orange price variable. The possibility of
incorporating the prices of other fresh fruits was therefore restricted. For example, we
wanted to incorporate a variable that measures the availability of specialty fruits in the
market. The reason to have such a variable in the model is to be able to account for the
increasing availability of such fruits which may cause consumers to shift away from
consuming apples.2 However, since the retail price of such fruits were not reported, the

option of constructing such a variable was dropped.

 

1New York City of Consumer Affairs, MW New York, January
1980 July 1991.

”USDA, Agricultural Marketing Service W309
W Washington, D. C, January 1980- -July 1991.

105

INCOME: A proxy to represent the personal income variable was sought. The
closest variable that would measure the personal income with no seasonal adjustment
across the months were the earning data that are reported monthly by The State of
New York, Department of Labor.1 The Department of Labor reports the number of
employees and weekly earning in nonagicultural establishments by industry in New
York City. The industries for which both the number of employees and weekly earnings
are, manufacturing, construction, telephone and telegam, electric gas and sanitary
services, and wholesale trade. The total weekly earning were calculated by multiplying
the number of employees in that industry with the average weekly earning in each
industry. The average total weekly earning was obtained by dividing the total weekly
earnings by the total number of employees in the five industries. The average weekly
earnings was expressed in 1983 dollars through dividing by the NYC consumer price
index for all urban consumers (CPI-U). Deflated average monthly earnings was obtained
by multiplying the deflated weekly average earning with the number of weeks in each
month. The data that are used to calculate the monthly earnings is reported in
Appendix C.

APPLE HOLDINGS: Another variable that was not used in the study by van
Ravenswaay and Hoehn (1991) but was included in this research is the national fresh
apple holding. The variable that represents the monthly national fresh apple holdings
was obtained from the International Apple Institute.2 The data involves the total fresh
apple holdings of all varieties in cold storage and controlled atmosphere excluding the

processor’s holding.

 

1State of New York, Department of Labor, W New York, January
1980 - July 1991.

’International Apple Industry. WWW Mc Lean.
Virginia, January 1980 - July 1991.

106

National fresh apple holdings were used as one explanatory variable in the
national retail apple supply equation in the econometric model. The data represent
holding at the wholesale level. Apples are stored when they are at the wholesale
market. There are three types of storage facilities: common storage, cold storage and
controlled atmosphere storage.1 The supply of fresh apples from wholesale market to
retail market and thus from retail market to consumer is determined by the quantity of
fresh apple holding at the wholesale market. Therefore, a variable that measures the
quantity of fresh apple holding at the wholesale market was incorporated in the retail
apple supply equation.

Note that in July - October, the holding are reported to be zero. The reason for
this is that since the holding are very small at those months, the International Apple
Institute does not report apple holding these months. In the econometric model the
logarithms of the holding variable were used. Therefore we add 1 to the variable that
measures holding (HOLD) in order to gat a variable in logarithms (lnht =
ln(HOLD + 1)). ’

AR’ITCLES ON THE PRESENCE OF ALAR: Following Guyton (1990), since
the NYT had the largest circulation size, we chose this newspaper as a proxy for the
newspaper coverage on Alar. Using the "Alar” and 'Daminozide" keywords, a search of
the full text of the NYT article from the Nexis data base of the full text of the NYT
articles from January 1980-July 1991 was performed.

Figure A.1 shows the per capita apple consumption and retail price of apples in

the NYC region for the extended observation period.

 

1John Mark Halloran, " Price Forecasting Model for Michigan Fresh Apples." MS.
Thesis, Michigan State University, 1981, pp.22-23.

107

 

in

ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo

d
O"!
n

oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo

1:.
I

 

 

 

1’:

 

 

0.6 +---

 

Dollars or Pounds

 

 

 

 

 

   

 

 

 

ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo

 

F’
.1;
l

 

0.2 .. ..............................................................................................

 

 

 

O-
80 81 82 83 84 85 86 87 88 89 90 91
Years

-- PC Apple Cons. --...- Retail Apple Pr.

Figure A.l. Retail Fresh Apple Prices (1983 Dollars) and Per Capita Fresh Apple
Purchases in the NYC Region (Pounds)

APPENDIX B

THE DATA

1980

1981

1982

1983

MONTHS

Jan.
Feb.
Mar.
Apr.
May
June
July
Aug.
Sep.
Oct.
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.
May
June
July
Aug.
Sep.
Oct.
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.
May
June
July
Aug.
Sep.
Oct.
Nov.
Dec.
Jan.
Feb.

.APPENLHXIB

TTHEIMYDA

QNY‘
18,900,000
19,600,000
19,800,000
15,000,000
15,200,000
13,200,000

8,300,000

4,700,000
10,300,000
20,100,000
18,100,000
22,000,000
24,800,000
24,600,000
23,700,000
17,500,000
17,200,000
11,900,000

9,200,000
10,200,000
11,300,000
17,700,000
25,800,000
21,200,000
16,100,000
19,900,000
22,100,000
19,100,000
21,900,000
13,600,000

7,700,000

7,800,000

7,900,000
13,700,000
17,400,000
18,500,000
14,400,000
18,700,000

KB

POPNYZ
14,645,742
14,633,820
14,621,909
14,610,000
14,610,999
14,611,999
14,612,998
14,613,998
14,614,997
14,615,997
14,616,997
14,617,997
14,618,996
14,619,996
14,620,996
14,621,996
14,622,997
14,623,997
14,625,000
14,626,416
14,627,832
14,629,248
14,630,664
14,632,080
14,633,496
14,634,913
14,636,329
14,637,746
14,639,163
14,640,580
14,642,000
14,645,246
14,648,493
14,651,741
14,654,989
14,658,238
14,661,488
14,664,738

PCQNY3
1.290477
1.339363
1.354132
1.026694
1.040312
0.903367
0.567987
0.321609
0.704756
1.375206
1.238284
1.504994
1.696423
1.682627
1.620957
1.196827
1.176230
0.813731
0.629060
0.697368
0.772500
1.209905
1.763420
1.448871
1.100216
1.359762
1.509941
1.304846
1.495987
0.928925
0.525884
0.532596
0.539305
0.935042
1.187309
1.262089
0.982165
1.275168

1984

1985

1986

1987

Mar.
Apr.
May
June
July
Aug.
Sep.
Oct.
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.
May
June
July
Aug.
Sep.
Oct.
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.
May
June
July
Aug.
Sep.
Oct.
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.
May
June
July
Aug.
Sep.
Oct.
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.
May
June
July

109

21,300,000
19,600,000
18,000,000
13,500,000
9,400,000
7,300,000
10,300,000
15,700,000
23,700,000
16,000,000
18,600,000
18,200,000
19,300,000
15,400,000
15,500,000
8,500,000
6,600,000
6,900,000
7,200,000
11,000,000
14,800,000
11,800,000
12,900,000
12,700,000
14,300,000
16,000,000
15,000,000
8,300,000
7,100,000
5,900,000
7,000,000
11,800,000
13,700,000
14,900,000
13,200,000
13,400,000
13,400,000
13,500,000
10,700,000
6,500,000
4,100,000
2,100,000
9,500,000
18,700,000
14,700,000
20,100,000
10,700,000
8,500,000
14,900,000
11,200,000
9,600,000
17,500,000
15,000,000

14,667,989
14,671,241
14,674,494
14,677,747
14,681,000
14,687,981
14,694,965
14,701,952
14,708,943
14,715,937
14,722,935
14,729,935
14,736,940
14,743,947
14,750,958
14,757,972
14,765,000
14,772,230
14,779,464
14,786,702
14,793,943
14,801,188
14,808,436
14,815,687
14,822,943
14,830,201
14,837,464
14,844,730
14,852,000
14,851,667
14,851,333
14,851,000
14,850,667
14,850,333
14,850,000
14,849,667
14,849,333
14,849,000
14,848,667
14,848,333
14,848,000
14,851,662
14,855,324
14,858,987
14,862,651
14,866,317
14,869,983
14,873,650
14,877,317
14,880,986
14,884,656
14,888,326
14,892,000

1.452142
1.335947
1.226618
0.919760
0.640283
0.497005
0.700920
1.067885
1.611265
1.087257
1.263335
1.235579
1.309634
1.044496
1.050779
0.575960
0.447003
0.467093
0.487162
0.743912
1.000409
0.797233
0.871125
0.857200
0.964721
1.078879
1.010954
0.559121
0.478050
0.397262
0.471338
0.794559
0.922518
1.003344
0.888889
0.902377
0.902397
0.909152
0.720603
0.437760
0.276131
0.141398
0.639501
1.258498
0.989056
1.352050
0.719570
0.571480
1.001525
0.752638
0.644959
1.175418
1.007252

1988

1989

1990

1991

Aug.
Sep.
Oct.
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.
May

June
July
Aug.
Sep.
Oct.
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.
May

June
July
Aug.
Sep.
Oct.
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.
May

June
July
Aug.
Sep.
Oct.
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.
May

June
July

110

7,800,000
8,400,000
15,700,000
13,200,000
12,000,000
16,700,000
16,400,000
16,000,000
15,400,000
11,900,000
8,900,000
8,100,000
6,300,000
6,200,000
8,600,000
9,800,000
9,700,000
9,100,000
9,800,000
10,300,000
8,100,000
8,800,000
7,000,000
9,400,000
9,800,000
10,600,000
8,500,000
10,900,000
14,300,000
13,100,000
11,100,000
17,200,000
15,300,000
12,100,000
12,700,000
10,100,000
9,500,000
6,800,000
12,400,000
12,500,000
11,700,000
12,100,000
13,100,000
12,200,000
12,500,000
12,600,000
10,700,000
10,100,000

14,894,829
14,897,659
14,900,490
14,903,321
14,906,153
14,908,985
14,911,818
14,914,651
14,917,485
14,920,319
14,923,154
14,926,000
14,920,504
14,915,011
14,909,519
14,904,029
14,898,541
14,893,056
14,887,572
14,882,091
14,876,611
14,871,133
14,865,658
14,860,184
14,854,713
14,849,243
14,843,776
14,838,310
14,832,847
14,827,385
14,821,926
14,816,469
14,811,000
14,812,687
14,814,374
14,816,061
14,817,749
14,819,437
14,821,125
14,822,813
14,824,501
14,826,190
14,827,878
14,829,567
14,831,256
14,832,946
14,834,635
14,836,325

1. Fresh apple purchases in the NYC region (pounds).

0.523672
0.563847
1.053657
0.885709
0.805037
1.120130
1.099799
1.072771
1.032346
0.797570
0.596389
0.542677
0.422238
0.415689
0.576813
0.657540
0.651070
0.611023
0.658267
0.692107
0.544479
0.591750
0.470884
0.632563
0.659723
0.713841
0.572631
0.734585
0.964077
0.883500
0.748891
1.160870
1.033016
0.816867
0.857276
0.681693
0.641123
0.458857
0.836644
0.843295
0.789234
0.816123
0.883471
0.822681
0.842815
0.849460
0.721285
0.680762

1 11
2.NYC population.
3.Per capita apple purchases in the NYC region (QNY/POPNY).

1980

1981

1982

1983

1984

MONTHS

Jan.
Feb.
Mar.
Apr.
May
June
July
Aug.
Sep.
Oct.
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.
May
June
July
Aug.
Sep.
Oct.
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.
May
June
July
Aug.
Sep.
Oct.
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.
May
June
July
Aug.
Sep.
Oct.
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.

112

DRPANY‘

0.728900
0.760456
0.787500
0.818859
0.838471
0.852619
0.883777
0.996399
0.933014
0.713436
0.673759
0.678363
0.637312
0.640732
0.660592
0.656852
0.641892
0.681564
0.715859
0.796943
0.763441
0.679612
0.680346
0.679612
0.678149
0.676692
0.745946
0.700431
0.725720
0.721003
0.761210
0.737279
0.710608
0.660569
0.652396
0.656410
0.644172
0.622449
0.621814
0.615540
0.623742
0.661986
0.700000
0.729271
0.772277
0.651530
0.648968
0.648330
0.642023
0.628627
0.626808
0.691643

DRPBNY5
0.409207
0.456274
0.475000
0.459057
0.468557
0.426309
0.411622
0.432173
0.430622
0.404281
0.413712
0.421053
0.428737
0.423341
0.444191
0.430351
0.450450
0.413408
0.396476
0.393013
0.419355
0.399137
0.399568
0.399137
0.409042
0.397422
0.421622
0.431034
0.405550
0.397074
0.354536
0.353063
0.370752
0.335366
0.346585
0.338462
0.378323
0.377551
0.377166
0.454087
0.482897
0.471414
0.450000
0.439560
0.425743
0.394867
0.363815
0.353635
0.359922
0.377176
0.366442
0.384246

CPINY‘

0.782
0.789
0.800
0.806
0.811
0.821
0.826
0.833
0.836
0.841
0.846
0.855
0.863
0.874
0.878
0.883
0.888
0.895
0.908
0.916
0.930
0.927
0.926
0.927
0.929
0.931
0.925
0.928
0.937
0.957
0.959
0.963
0.971
0.984
0.981
0.975
0.978
0.980
0.981
0.991
0.994
0.997
1.000
1.001
1.010
1.013
1.017
1.018
1.028
1.034
1.037
1.041

1985

1986

1987

1988

May

June
July
Aug.
Sep.
Oct.
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.
May

June
July
Aug.
Sep.
Oct.
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.
May

June
July
Aug.
Sep.
Oct.
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.
May

June
July
Aug.
Sep.
Oct.
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.
May

June
July
Aug.
Sep.

NB

0.691643
0.699904
0.696565
0.710900
0.725047
0.725730
0.629108
0.657277
0.609185
0.643057
0.679070
0.658017
0.638298
0.683287
0.710332
0.677656
0.729927
0.673953
0.623306
0.639640
0.724508
0.735426
0.735426
0.746403
0.775473
0.823635
0.826667
1.029281
1.000000
0.749559
0.750221
0.711775
0.706190
0.711188
0.708117
0.720412
0.852515
0.780985
0.814249
0.782170
0.742905
0.623960
0.564315
0.563847
0.623330
0.660125
0.633745
0.611746
0.619397
0.641755
0.736246
0.909823
0.896825

0.374640
0.383509
0.381679
0.369668
0.329567
0.367578
0.309859
0.328638
0.365511
0.382106
0.390698
0.417053
0.388529
0.378578
0.359779
0.357143
0.374088
0.346084
0.316170
0.396396
0.357782
0.367713
0.376682
0.458633
0.477908
0.384960
0.355556
0.346051
0.362832
0.361552
0.370697
0.333919
0.348736
0.364267
0.371330
0.351630
0.383632
0.373514
0.347752
0.336417
0.358932
0.332779
0.340249
0.339967
0.356189
0.401427
0.370370
0.358891
0.374898
0.446791
0.380259
0.338164
0.341270

1.041
1.043
1.048
1.055
1.062
1.061
1.065
1.065
1.067
1.073
1.075
1.079
1.081
1.083
1.084
1.092
1.096
1.098
1.107
1.110
1.118
1.115
1.115
1.112
1.109
1.117
1.125
1.127
1.130
1.134
1.133
1.138
1.147
1.153
1.158
1.166
1.173
1.178

1.179

1.189
1.198
1.202
1.205
1.206
1.123
1.121
1.215
1.226
1.227
1.231
1.236
1.242
1.260

UM

Oct. 0.649762 0.340729 1.262
NOV. 0.611597 0.357427 1.259
Dec. 0.619048 0.365079 1.260
1989 Jan. 0.629921 0.346457 1.270
Feb. 0.650470 0.352665 1.276
Mar. 0.636152 0.403413 1.289
Apr. 0.594595 0.440154 1.295
May 0.591398 0.460829 1.302
June 0.605364 0.413793 1.305
July 0.604900 0.367534 1.306
Aug. 0.649351 0.366692 1.309
Sep. 0.605144 0.363086 1.322
Oct. 0.549699 0.384036 1.328
NOV. 0.525526 0.360360 1.332
Dec. 0.525131 0.360090 1.333
1990 Jan. 0.525537 0.399704 1.351
Feb. 0.569106 0.428677 1.353
Mar. 0.571010 0.409956 1.366
Apr. 0.568099 0.393299 1.373
May 0.575802 0.393586 1.372
June 0.598104 0.364697 1.371
July 0.628613 0.440751 1.384
Aug. 0.685714 0.385714 1.400
Sep. 0.681818 0.383523 1.408
Oct. 0.600282 0.360169 1.416
NOV. 0.579505 0.360424 1.415
Dec. 0.593220 0.360169 1.416
1991 Jan. 0.622378 0.370629 1.430
Feb. 0.640669 0.376045 1.436
Mar. 0.641562 0.446304 1.434
Apr. 0.661100 0.424495 1.437
May 0.694444 0.451389 1.440
June 0.726141 0.421853 1.446
July 0.750689 0.385675 1.452

4.Deflated retail apple price in the NYC region (1983 dollars).
5.Deflated retail banana price in the NYC region (1983 dollars).

6.Consumer price index in the NYC region for all items.

1980

1981

1982

1983

1984

MONTHS

Jan.
Feb.
Mar.
Apr.
May
June
July
Aug.
Sep.
Oct.
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.
May
June
July
Aug.
Sep.
Oct.
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.
May
June
July
Aug.
Sep.
Oct.
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.
May
June
July
Aug.
Sep.
Oct.
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.

U6

INCOME7

1578.634
1476.705
1551.665
1474.719
1526.071
1477.181
1532.385
1515.234
1474.841
1542.238
1522.024
1574.549
1570.320
1400.637
1561.691
1494.169
1539.756
1481.312
1515.616
1528.019
1463.309
1540.839
1516.792
1583.651
1581.489
1388.502
1604.991
1527.768
1583.073
1516.135
1563.020
1570.380
1518.425
1568.507
1568.832
1662.004
1643.152
1453.454
1626.420
1567.737
1615.443
1569.354
1617.066
1514.769
1567.353
1644.196
1631.270
1688.571
1641.401
1525.934
1605.585
1581.505

HOLD8
49,868,000
39,613,000
30,095,000
20,564,000
13,042,000

6,240,000
0

0

0

0
89,392,000
77,355,000
63,066,000
51,904,000
40,676,000
30,190,000
20,497,000
12,057,000
0

0

0

0
71,452,000
60,775,000
49,363,000
40,059,000
31,689,000
23,233,000
15,507,000
9,294,000
0

0

0

0
79,833,000
69,116,000
58,092,000
47,807,000
38,169,000
27,063,000
17,254,000
9,743,000
0

0

0

0
76,283,000
68,390,000
56,534,000
45,410,000
36,336,000
26,613,000

2

K1

0'3
0

OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

1985

1986

1987

1988

May
June
July
Aug.
Sep.
Oct.
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.
May
June
July
Aug.
Sep.
Oct.
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.
May
June
July
Aug.
Sep.
Oct.
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.
May
June
July
Aug.
Sep.
Oct.
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.
May
June
July
Aug.
Sep.

116

1631.301
1584.119
1635.834
1626.068
1592.595
1665.451
1636.418
1718.671
1672.560
1516.377
1667.883
1599.447
1669.996
1631.009
1696.756
1676.381
1647.302
1694.433
1682.624
1751.948
1715.945
1532.789
1719.671
1668.059
1742.229
1678.300
1724.353
1689.381
1691.428
1725.194
1727.925
1789.157
1762.128
1543.497
1730.284
1664.993
1740.462
1691.758
1763.116
1735.950
1692.276
1737.629
1715.832
1759.852
1846.423
1728.918
1741.795
1656.813
1721.739
1669.664
1729.196
1707.874
1643.642

17,884,000
10,349,000
0

0

0

0
76,680,000
68,295,000
56,450,000
45,997,000
35,751,000
26,865,000
17,832,000
10,839,000
0

0

0

0
69,153,000
59,239,000
47,907,000
37,639,000
28,523,000
19,800,000
11,642,000
5,889,000
0

0

0

0
77,452,000
65,529,000
52,849,000
42,499,000
32,524,000
23,049,000
14,484,000
8,274,000
0

0

0

0
96,453,000
81,291,000
67,832,000
55,176,000
42,897,000
29,700,000
19,180,000
10,614,000
0

0

0

HOOOOOHHOOOHI—‘OOHNOOOUOHOOONHNOl-‘ONOOOHNOOOOOOOOOOOOHOO

1989

1990

1991

Oct.
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.
May

June
July
Aug.
Sep.
Oct.
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.
May

June
July
Aug.
Sep.
Oct.
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.
May

June
July

117

1721.664
1698.880
1760.965
1711.916
1532.095
1707.559
1664.113
1684.681
1640.445
1692.289
1675.431
1633.923
1681.306
1654.425
1714.878
1655.626
1503.807
1551.338
1567.521
1660.109
1610.297
1650.857
1522.613
1586.543
1521.130
1482.130
1462.946
1610.991
1455.881
1612.496
1556.808
1606.141
1552.139
1583.827

0
87,027,000
73,754,000
61,161,000
50,372,000
39,433,000
29,730,000
21,397,000
13,673,000
0
0
0
0

102,000,000

86,341,000
71,382,000
57,629,000
46,366,000
33,852,000
23,137,000
14,027,000

0

0

0

0
87,827,000
74,361,000
62,877,000
50,479,000
39,553,000
29,361,000
20,278,000
13,378,000

0

7.The derivation of the income variable is explained in Appendix C.

8.National fresh apple holdings (bushels).

9.Number of articles in the New York Times on the presence of health risk associated

with Alar.

N

1.1
OOOOOOOOOOOOOOOOOOOOOOOOOONU‘O\ll-‘OOO

APPENDIX C

WEEKLY DATA ON EARNINGS

1980

1981

1982

1983

MONTHS

Jan.
Feb.
Mar.
Apr.
May
June
July
Aug.
Sep.
Oct.
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.
May
June
July
Aug.
Sep.
Oct.
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.
May
June
July
Aug.
Sep.
Oct.
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.

AXPPETH)EK(3

nasal

492,600
503,700
508,900
493,000
501,400
503,000
480,900
492,400
496,800
497,800
494,400
483,500
469,900
482,700
488,600
488,500
491,300
496,000
478,900
489,400
495,700
487,500
483,600
469,500
452,800
642,600
466,000
455,000
456,700
459,200
438,800
449,100
453,000
445,800
440,300
430,500
417,200
426,100
432,300
430,300

MAWERZ.

229.40
232.63
233.25
227.76
231.25
234.47
234.33
234.15
234.21
239.85
245.23
250.21
249.75
250.43
254.25
253.27
253.57
254.76
253.46
252.50
255.76
259.78
263.75
267.81
265.36
268.28
271.57
265.72
267.91
269.37
270.03
267.89
270.05
275.15
282.96
287.36
283.75
278.17
284.34
287.73

118

WEEKLY DATA ON EARNINGS

coau3

71,400
70,500
72,100
73,300
76,000
78,000
79,100
79,400
80,200
80,800
80,800
80,400
75,500
76,700
78,900
80,800
82,200
84,100
84,400
85,400
86,000
86,200
85,200
85,100
79,900
79,300
82,400
84,100
86,600
88,500
85,300
86,000
87,900
87,900
88,500
87,900
81,900
81,100
83,600
86,800

cowaR‘
393.54
396.89
396.23
394.28
400.58
412.62
421.11
418.74
421.61
409.52
424.45
436.93
438.70
416.29
447.58
446.40
441.77
452.45
445.42
465.26
455.70
444.04
455.68
470.02
469.22
449.88
479.82
467.82
488.07
499.85
490.10
499.37
504.75
499.73
525.62
531.80
536.51
527.95
535.36
542.36

1984

1985

1986

1987

432,900
439,000
421,400
435,600
441,900
441,800
441,800
432,800
420,700
431,600
437,800
431,700
433,100
436,300
420,300
432,200
435,700
429,200
427,300
419,100
403,800
411,900
416,100
407,600
410,100
411,700
398,700
407,200
410,100
407,200
408,300
399,600
388,600
395,600
399,000
392,500
392,000
392,800
383,500
390,700
395,100
393,100
390,900
384,000
370,000
378,400
384,100
377,700
379,800
382,600
373,200
380,800
384,900

119

289.25
291.19
289.38
286.04
291.40
298.34
300.58
303.62
299.02
299.84
298.74
302.29
301.10
303.32
299.67
299.92
306.64
310.70
322.34
326.86
313.05
318.84
317.46
314.03
317.83
318.20
320.62
315.25
320.79
322.65
333.14
336.90
329.15
326.68
330.93
330.71
330.62
330.30
328.33
332.84
333.16
335.07
342.00
347.22
345.03
345.20
346.30
344.28
348.94
350.81
346.45
341.50
344.93

88,300
90,100
90,200
91,100
91,400
91,300
91,700
91,400
87,200
87,900
89,200
91,600
93,500
95,700
95,600
96,800
97,900
99,400
99,700
99,800
95,500
95,000
97,800
102,800
105,200
107,600
108,900
110,000
112,000
112,600
114,100
113,800
106,300
106,100
108,900
110,900
112,500
114,900
116,600
117,500
119,000
117,700
117,200
116,300
110,500
109,500
112,400
115,700
118,500
121,500
121,400
122,800
123,800

548.63
559.40
565.39
561.34
569.88
554.21
589.26
592.96
584.82
577.81
573.13
588.06
592.92
584.22
578.14
584.77
603.88
604.76
601.43
621.23
605.63
607.34
623.90
627.99
639.48
646.65
643.32
657.37
666.85
651.48
681.90
692.65
694.90
652.91
687.02
693.41
703.64
699.74
715.17
713.22
736.06
678.46
729.96
726.14
701.06
639.54
707.49
705.39
722.87
741.90
748.70
752.72
742.77

120

Oct. 382,800 350.34 123,000 714.99
Nov. 382,500 350.02 123,300 776.75
Dec. 377,800 351.87 123,200 763.75
1988 Jan. 362,100 339.84 112,800 736.99
Feb. 370,000 347.26 114,100 689.64
Mar. 375,000 350.62 117,800 752.84
Apr. 369,600 338.89 119,300 748.70
May 369,900 342.80 120,100 757.20
June 372,300 343.17 122,700 779.39
July 362,700 340.40 121,200 778.87
Aug. 370,400 345.38 121,300 776.14
Sep. 374,700 346.39 124,100 777.45
Oct. 372,900 356.38 123,000 786.37
Nov. 374,400 360.61 123,100 830.65
Dec. 367,100 362.33 121,800 823.25
1989 Jan. 353,300 359.41 113,100 797.16
Feb. 360,200 356.96 113,600 778.96
Mar. 363,700 360.98 116,700 821.38
Apr. 361,700 359.20 119,000 835.89
May 362,100 356.96 120,600 818.44
June 364,100 358.30 123,300 828.07
July 354,800 356.72 122,600 834.77
Aug. 362,600 360.51 124,100 828.37
Sop. 365,000 360.14 125,900 868.23
Oct. 360,000 361.72 124,100 857.38
Nov. 357,400 366.92 123,900 891.70
Dec. 349,200 372.25 123,300 862.07
1990 Jan. 332,900 366.83 112,600 823.37
Fob. 338,500 368.56 112,400 827.64
Mar. 342,900 376.29 115,100 596.54
Apr. 337,700 364.97 113,400 779.80
May 341,500 377.03 114,500 822.11
Juno 343,900 378.42 115,500 819.36
July 333,700 378.38 113,800 815.78
Aug. 339,700 377.68 113,700 606.70
Sop. 341,600 376.66 113,500 853.76
Oct. 338,200 378.96 112,300 619.28
Nov. 333,100 379.25 110,800 635.38
Doc. 326,400 338.13 106,800 609.61
1991 Jan. 316,100 379.34 100,300 835.67
Fob. 320,600 381.55 96,500 847.39
Mar. 323,200 383.63 98,500 844.88
Apr. 321,600 382.21 99,700 841.66
May 322,700 382.21 100,800 844.73
Juno 324,100 386.05 102,300 843.01
July 316,800 381.30 100,700 845.15

l.Number of employees in the manufacturing industry.
2.Average weekly earning in the manufacturing industry.

3.Number of employees in the construction industry.

121

4.Average weekly earning in the construction industry.

1980

1981

1982

1983

1984

MONTHS

Jan.
Feb.
Mar.
Apr.
May
June
July
Aug.
Sep.
Oct.
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.
May
June
July
Aug.
Sep.
Oct.
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.
May
June
July
Aug.
Sep.
Oct.
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.
“BY
June
July
Aug.
Sep.
Oct.
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.

reams

59,000
59,400
59,600
59,000
59,000
59,300
59,900
59,200
59,000
58,500
58,300
59,000
59,400
60,100
60,200
59,800
59,900
60,200
60,600
60,500
60,000
59,600
59,300
59,400
59,300
59,700
59,700
59,300
59,300
59,700
59,700
59,500
58,600
58,500
58,400
57,700
57,600
57,700
57,400
57,000
56,700
56,600
56,600
34,600
56,300
55,400
56,100
56,400
55,300
56,300
55,200
54,300

122

TEWER‘
402.79
421.26
401.60
389.65
390.85
393.22
391.02
392.00
408.00
455.20
463.61
452.09
449.63
465.19
435.51
417.76
427.60
423.87
428.79
464.09
487.81
491.78
501.90
497.90
473.98
495.81
472.42
469.64
466.88
476.39
465.68
499.28
503.79
521.11
525.71
513.20
512.00
518.46
506.09
517.69
499.50
505.60
519.79
304.80
530.32
560.05
620.49
581.30
529.99
543.35
514.56
524.40

ELEM7
24,800
24,900
24,900
24,800
24,800
24,900
25,200
25,300
25,100
24,800
24,900
24,900
24,800
24,800
24,800
24,700
24,700
25,000
25,600
25,500
25,400
24,800
24,800
24,800
24,700
24,600
24,600
24,600
24,400
24,600
25,000
25,000
24,700
24,700
24,700
24,800
24,500
24,500
24,500
24,500
24,400
24,700

9,600

9,700
24,400
24,300
24,300
24,200
24,200
24,000
23,900
23,800

aLwaR°

413.34
419.24
410.35
403.92
410.18
413.88
414.54
448.16
467.42
463.76
480.24
465.70
470.81
483.57
472.94
470.55
456.46
455.52
449.96
481.50
490.35
503.70
515.57
496.34
503.18
524.61
497.80
503.14
488.92
501.83
490.99
520.57
551.69
550.95
578.16
558.39
541.68
542.88
537.35
527.85
538.32
525.68
519.84
540.35
540.60
573.70
575.46
567.60
590.67
590.39
581.09
580.13

1985

1986

1987

1988

Apr.

June
July
Aug.
Sep.
Oct.
Nov.
Dec.
Jan.
Feb.

Apr.
May

June
July
Aug.
Sep.

54,100
54,000
53,400
53,000
53,000
52,500
52,100
52,200
51,400
51,300
50,900
50,600
50,200
49,900
49,400
49,100
48,500
47,500
47,700
47,600
44,900
45,200
45,300
43,300
43,100
40,000
42,800
26,600
42,300
41,600
41,500
41,000
40,500
40,400
40,400
39,700
39,800
40,000
39,800
39,800
39,900
39,900
40,000
40,200
40,600
40,500
40,500
40,600
40,300
40,500
40,300
40,400
40,200

123

518.90
529.20
557.69
559.47
565.65
575.74
589.36
574.73
561.56
599.63
553.42
545.27
552.42
554.21
551.60
583.78
584.99
592.59
624.70
596.96
588.63

‘605.05

587.73
591.34
600.07
615.68
590.24
477.59
595.50
641.45
685.97
671.23
678.26
640.90
654.91
638.15
631.31
633.23
686.99
688.42
716.72
743.15
745.07
698.21
694.59
736.79
706.48
687.52
687.52
673.32
664.26
669.06
664.47

23,900
24,000
24,200
24,200
23,700
23,700
23,700
23,700
23,700
23,600
23,500
23,400
23,400
23,700
23,800
23,800
23,400
23,300
23,400
23,300
23,200
23,200
23,100
23,100
23,100
23,100
23,500
23,500
20,800
20,600
22,800
22,900
22,800
22,800
22,700
22,700
22,800
22,800
23,200
23,200
22,700
22,600
22,600
22,600
22,600
22,500
22,400
22,600
22,600
22,900
23,300
23,300
22,800

576.15
585.90
599.71
616.28
641.78
629.58
652.74
633.14
625.10
632.91
621.65
619.06
627.27
610.61
623.17
604.78
667.93
703.95
696.78
663.34
650.60
669.11
654.99
649.30
647.79
644.54
642.64
576.67
744.11
737.38
677.30
681.33
676.82
700.13
690.99
682.08
678.51
677.04
686.45
686.71
699.08
733.04
687.04
727.72
679.90
670.23

7718.96

657.61
707.19
696.14
721.11
712.75
736.50

124

Oct. 40,800 654.46 22,800 740.15
Nov. 40,900 652.76 22,900 736.56
Dec. 41,200 699.34 22,900 743.04
1989 Jan. 40,300 642.80 22,900 745.04
Feb. 40,400 647.54 23,000 732.34
Mar. 40,600 622.05 23,000 739.47
Apr. 38,800 634.81 23,000 749.83
May 38,700 624.87 23,000 745.27
June 38,900 608.79 23,200 734.60
July 38,500 609.52 23,600 729.17
Aug. 21,300 637.78 23,500 704.16
Sep. 18,800 626.94 22,700 769.52
Oct. 19,700 652.69 22,500 784.80
Nov. 19,300 629.53 22,400 790.27
Dec. 37,800 628.62 22,400 817.78
1990 Jan. 36,600 633.29 22,300 795.22
Feb. 36,900 633.36 22,300 779.68
Mar. 35,000 634.92 22,300 779.64
Apr. 36,700 633.04 22,400 767.37
May 36,900 643.36 22,400 766.04
June 35,900 641.03 22,500 753.86
July 35,700 647.60 22,900 769.63
Aug. 35,600 659.15 22,900 752.80
Sop. 35,600 669.61 22,300 792.51
Oct. 35,900 701.78 22,200 796.72
Nov. 35,600 696.80 22,200 802.68
Dec. 35,600 664.97 22,100 786.92
1991 Jan. 34,900 675.68 22,200 789.70
Feb. 35,100 694.55 22,100 804.69
Mar. 35,200 668.68 22,100 803.73
Apr. 35,200 656.00 22,100 796.21
May 35,000 652.38 22,100 801.10
June 35,000 648.76 22,200 789.26
July 35,300 635.90 22,600 795.07

5 .Number of employees in the telephone and telegam industry.
6.Average weekly earning in the telephone and telegam industry.
7 .Number of employees in the electric, gas and sanitary services.

8.Average weekly earning in the electric, gas and sanitary services.

1980

1981

1982

1983

[1984

MONTHS

Jan.
Feb.
Mar.
Apr.
May
June
July
Aug.
Sep.
Oct.
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.
May
June
July
Aug.
Sep.
Oct.
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.
May
June
July
Aug.
Sep.
Oct.
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.
May
June
July
Aug.
Sep.
Oct.
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.

WHEM9
245,000
245,600
247,300
245,100
245,900
246,400
244,900
245,100
245,800
246,300
246,900
247,800
246,300
246,700
247,500
247,300
247,300
248,400
246,300
247,100
247,700
248,600
248,800
248,500
246,400
246,200
246,600
246,600
246,600
246,800
243,900
243,900
243,200
242,200
242,000
421,700
237,400
236,300
237,500
238,400
237,900
239,400
239,300
240,600
241,100
242,200
242,600
242,200
240,600
241,400
243,100
243,700

125

wawaa“’
301.18
299.83
301.13
302.44
300.58
301.38
304.37
301.32
305.04
306.16
313.96
314.42
321.58
323.95
328.10
327.75
330.75
327.62
332.63
337.19
334.43
344.96
348.23
348.30
357.93
363.65
357.96
353.81
358.52
360.02
361.95
364.62
364.34
366.49
374.40
380.16
387.54
378.62
383.53
378.13
376.50
377.88
380.46
359.07
381.58
389.06
395.64
399.19
395.37
395.20
391.23
402.34

TWERn'
249,000,000
254,000,000
256,000,000
248,000,000
254,000,000
258,000,000
254,000,000
257,000,000
261,000,000
266,000,000
272,000,000
272,000,000
268,000,000
273,000,000
279,000,000
277,000,000
280,000,000
283,000,000
278,000,000
287,000,000
291,000,000
292,000,000
296,000,000
294,000,000
286,000,000
340,000,000
295,000,000
288,000,000
293,000,000
298,000,000
289,000,000
295,000,000
298,000,000
299,000,000
307,000,000
374,000,000
297,000,000
294,000,000
301,000,000
303,000,000
305,000,000
310,000,000
298,000,000
278,000,000
316,000,000
322,000,000
332,000,000
329,000,000
316,000,000
320,000,000
319,000,000
325,000,000

S'I'Isznn12

892,800
904,100
912,800
895,200
907,100
911,600
890,000
901,400
906,900
908,200
905,300
895,600
875,900
891,000
900,000
901,100
905,400
913,700
895,800
907,900
914,800
906,700
901,700
887,300
863,100

1,052,400

879,300
869,600
873,600
878,800
852,700
863,500
867,400
859,100
853,900

1,022,600

818,600
825,700
835,300
837,000
840,200
849,800
817,100
811,600
855,100
855,000
856,500
847,000
828,000
841,200
849,200
845,100

1985

1986

1987

1988

244,800
246,700
246,600
248,200
247,900
248,600
249,000
248,600
245,700
245,800
247,000
246,100
245,600
245,700
242,400
242,500
241,100
242,000
243,000
242,200
237,500
237,600
238,300
238,500
238,200
238,600
237,900
237,700
238,400
238,600
239,300
240,100
235,400
235,200
236,000
236,100
236,200
237,200
234,000
234,100
234,000
234,300
234,000
233,200
230,800
231,800
232,700
230,200
230,700
231,800
231,200
231,800
232,900

126

400.60
403.10
404.46
403.77
406.73
410.08
411.92
420.92
417.58
414.63
414.32
405.75
407.96
419.14
420.66
414.32
421.47
415.45
426.72
436.24
435.86
436.54
436.97
430.14
433.96
437.76
431.67
429.79
435.85
440.63
450.07
453.66
457.25
456.32
446.31
450.30
460.31
458.89
462.22
458.89
477.88
470.78
479.42
473.69
477.92
484.38
480.95
493.01
487.30
485.01
494.92
480.53
490.81

326,000,000
330,000,000
325,000,000
331,000,000
339,000,000
341,000,000
346,000,000
349,000,000
331,000,000
337,000,000
338,000,000
334,000,000
340,000,000
346,000,000
342,000,000
344,000,000
352,000,000
350,000,000
364,000,000
363,000,000
347,000,000
345,000,000
353,000,000
350,000,000
353,000,000
354,000,000
352,000,000
342,000,000
364,000,000
359,000,000
371,000,000
370,000,000
356,000,000
350,000,000
360,000,000
359,000,000
368,000,000
374,000,000
372,000,000
373,000,000
381,000,000
379,000,000
387,000,000
382,000,000
360,000,000
364,000,000
377,000,000
371,000,000
374,000,000
379,000,000
376,000,000
377,000,000
384,000,000

849,400
856,700
840,100
854,400
858,200
853,400
851,800
843,400
820,100
827,600
835,300
830,500
834,500
838,600
823,200
832,600
835,100
832,600
836,500
826,500
800,500
807,700
814,600
808,300
808,900
809,400
804,300
796,000
815,600
811,600
811,700
804,300
779,200
786,300
795,600
791,900
797,100
804,100
791,600
800,700
805,300
802,600
802,400
797,000
768,900
778,900
788,400
782,300
783,600
790,200
778,700
787,200
794,700

127

Oct. 233,000 496.44 389,000,000 792,500
Nov. 234,400 496.37 397,000,000 795,700
Dec. 234,900 492.53 395,000,000 787,900
1989 Jan. 229,500 490.68 373,000,000 759,100
Feb. 229,700 499.53 375,000,000 766,900
Mar. 230,500 501.42 385,000,000 774,500
Apr. 229,000 509.76 388,000,000 771,500
May 228,900 497.07 383,000,000 773,300
June 230,000 505.02 389,000,000 779,500
July 227,300 497.79 383,000,000 766,800
Aug. 226,800 493.49 376,000,000 758,300
Sep. 226,400 496.87 383,000,000 . 758,800
Oct. 226,400 496.49 380,000,000 752,700
Nov. 227,000 503.26 386,000,000 750,000
Dec. 226,300 501.40 392,000,000 759,000
1990 Jan. 220,400 500.83 366,000,000 724,800
Feb. 220,800 512.86 372,000,000 730,900
Mar. 222,000 520.51 353,000,000 737,300
Apr. 220,100 521.14 367,000,000 730,300
May 221,300 520.13 379,000,000 736,600
Juno 222,000 524.37 381,000,000 739,800
July 219,800 521.88 375,000,000 725,900
Aug. 218,900 519.99 352,000,000 730,800
Sop. 217,400 522.96 381,000,000 730,400
Oct. 217,200 517.78 353,000,000 725,800
Nov. 215,600 518.16 351,000,000 717,300
Dec. 214,500 528.99 330,000,000 705,400
1991 Jan. 211,000 527.39 356,000,000 684,500
Fob. 210,000 530.46 358,000,000 684,300
Mar. 210,700 529.92 360,000,000 689,700
Apr. 210,100 533.27 360,000,000 688,700
May 210,400 531.84 361,000,000 691,000
June 211,400 531.88 364,000,000 695,000
July 209,300 522.15 356,000,000 684,700

9.Number of employees in the wholesale trade.

10.Average weekly earning in the wholesale trade.

11. Total employees:

(MAEM‘MAWER) + (COEM‘COWER) + (TEEM‘T'WER) + (ELEM‘ELWER) + (WI-IE
M *WHWER)

12.Total employees: MAEM+COEM+TEEM+ELEM

1980

1981

1982

1983

1984

MONTHS

Jan.
Feb.
Mar.
Apr.
May

June
July
Aug.
Sep.
Oct.
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.
May

June
July
Aug.
Sep.
Oct.
Nov.
Dec.
Jan.
Feb.

avawaan3

278.7923
281.2262
280.3370
277.3917
279.5040
283.0258
285.8515
285.0475
287.7404
292.9137
300.4976
304.0288
306.0494
306.0392
309.6578
307.9000
308.7859
309.3989
310.7902
316.0943
317.5910
322.5741
327.7829
331.5367
331.7984
323.1738
335.2793
330.8679
334.9909
338.6093
338.5131
341.5257
344.0817
348.5571
359.1656
365.9563
362.9184
356.0961
360.3248
362.5734
362.6355
365.1448
365.1910
342.4308
369.4343
376.1450
387.1650
388.2035
381.0661
380.8389
376.0143
384.2115

128

DAVEWERL‘

356.5119
356.4338
350.4213
344.1584
344.6412
344.7331
346.0672
342.1939
344.1870
348.2921
355.1981
355.5893
354.6343
350.1593
352.6854
348.6977
347.7318
345.6971
342.2800
345.0812
341.4957
347.9763
353.9772
357.6448
357.1565
347.1255
362.4641
356.5387
357.5143
353.8237
352.9855
354.6477
354.3581
354.2247
366.1219
375.3398
371.0822
363.3634
367.3036
365.8662
364.8245
366.2436
365.1910
342.0887
365.7766
371.3179
380.6932
381.3394
370.6868
368.3162
362.5982
369.0793

WEEK15
4.428
4.143
4.428
4.285
4.428
4.285
4.428
4.428
4.285
4.428
4.285
4.428
4.428
4.000
4.428
4.285
4.428
4.285
4.428
4.428
4.285
4.428
4.285
4.428
4.428
4.000
4.428
4.285
4.428
4.285
4.428
4.428
4.285
4.428
4.285
4.428
4.428
4.000
4.428
4.285
4.428
4.285
4.428
4.428
4.285
4.428
4.285
4.428
4.428
4.143
4.428
4.285

INC16

1578.634
1476.705
1551.665
1474.719
1526.071
1477.181
1532.385
1515.234
1474.841
1542.238
1522.024
1574.549
1570.320
1400.637
1561.691
1494.169
1539.756
1481.312
1515.616
1528.019
1463.309
1540.839
1516.792
1583.651
1581.489
1388.502
1604.991
1527.768
1583.073
1516.135
1563.020
1570.380
1518.425
1568.507
1568.832
1662.004
1643.152
1453.454
1626.420
1567.737
1615.443
1569.354
1617.066
1514.769
1567.353
1644.196
1631.270
1688.571
1641.401
1525.934
1605.585
1581.505

1985

1986

1987

1988

383.5105
385.5860
387.1622
387.4213
394.7109
399.0612
406.7177
413.3659
403.0310
406.7681
404.9173
402.7547
407.6932
412.2248
415.3756
413.4164
421.3402
420.1642
434.6941
439.1739
433.2489
427.2649
433.0247
432.8778
436.3441
437.4939
438.0977
429.9757
446.0476
441.8179
456.8819
459.8150
456.4501
444.9130
452.4996
453.0645
461.0575
465.0854
469.4475
466.1348
473.1263
471.6871
482.5151
479.3093
468.2775
467.8053
477.9316
474.0379
477.0943
479.6630
482.6752
479.0377
483.3112

129

368.4058
369.6894
369.4296
367.2240
371.6675
376.1180
381.8945
388.1370
377.7235
379.0942
376.6673
373.2666
377.1445
380.6323
383.1878
378.5864
384.4345
382.6632
392.6776
395.6522
387.5213
383.1972
388.3630
389.2786
393.4573
391.6687
389.4202
381.5224
394.7324
389.6102
403.2497
404.0554
397.9513
385.8742
390.7596
388.5630
393.0584
394.8093
398.1743
392.0394
394.9302
392.4186
400.4275
397.4372
416.9880
417.3107
393.3593
386.6541
388.8299
389.6532
390.5139
385.6986
383.5803

4.428
4.285
4.428
4.428
4.285
4.428
4.285
4.428
4.428
4.000
4.428
4.285
4.428
4.285
4.428
4.428
4.285
4.428
4.285
4.428
4.428
4.000
4.428
4.285
4.428
4.285
4.428
4.428
4.285
4.428
4.285
4.428
4.428
4.000
4.428
4.285
4.428
4.285
4.428
4.428
4.285
4.428
4.285
4.428
4.428
4.143
4.428
4.285
4.428
4.285
4.428
4.428
4.285

1631.301
1584.119
1635.834
1626.068
1592.595
1665.451
1636.418
1718.671
1672.560
1516.377
1667.883
1599.447
1669.996
1631.009
1696.756
1676.381
1647.302
1694.433
1682.624
1751.948
1715.945
1532.789
1719.671
1668.059
1742.229
1678.300
1724.353
1689.381
1691.428
1725.194
1727.925
1789.157
1762.128
1543.497
1730.284
1664.993
1740.462
1691.758
1763.116
1735.950
1692.276
1737.629
1715.832
1759.852
1846.423
1728.918
1741.795
1656.813
1721.739
1669.664
1729.196
1707.874
1643.642

130

Oct. 490.6820 388.8130 4.428 1721.664
Nov. 499.1575 396.4714 4.285 1698.880
Dec. 501.0876 397.6886 4.428 1760.965
1989 Jan. 490.9968 386.6116 4.428 1711.916
Feb. 488.7382 383.0237 4.000 1532.095
Mar. 497.0740 385.6276 4.428 1707.559
Apr. 502.9233 388.3577 4.285 1664.113
May 495.3603 380.4610 4.428 1684.681
June 499.5989 382.8344 4.285 1640.445
July 499.1258 382.1790 4.428 1692.289
Aug. 495.2890 378.3720 4.428 1675.431
Sep. 504.0949 381.3123 4.285 1633.923
Oct. 504.2399 379.6987 4.428 1681.306
Nov. 514.2811 386.0969 4.285 1654.425
Dec. 516.2449 387.2805 4.428 1714.878
1990 Jan. 505.1379 373.8992 4.428 1655.626
Feb. 508.6628 375.9518 4.000 1503.807
Mar. 478.5745 350.3474 4.428 1551.338
Apr. 502.2652 365.8159 4.285 1567.521
May 514.3788 374.9116 4.428 1660.109
June 515.2199 375.7986 4.285 1610.297
July 515.9860 372.8223 4.428 1650.857
Aug. 481.4044 343.8603 4.428 1522.613
Sep. 521.3190 370.2550 4.285 1586.543
Oct. 486.4320 343.5254 4.428 1521.130
Nov. 489.4314 345.8879 4.285 1482.130
Doc. 467.8256 330.3853 4.428 1462.946
1991 Jan. 520.2614 363.8192 4.428 1610.991
Fob. 522.6611 363.9702 4.000 1455.881
Mar. 522.2039 364.1589 4.428 1612.496
Apr. 522.0847 363.3157 4.285 1556.808
May 522.3223 362.7238 4.428 1606.141
June 523.7789 362.2261 4.285 1552.139
July 519.3578 357.6844 4.428 1583.827

13.Average weekly earning: TWER/ST'EM

14.Deflated average weekly earning: AVEWER/CPINY
15.Number of weeks in the month: number of days in the month /7
16.Deflated monthly income: DAVEWER‘WEEK

APPENDIX D

DERIVATION OF THE REDUCED—FORM EQUATIONS FOR q: and pf

APPENDIX D

DERIVATION OF THE REDUCED-FORM EQUATIONS
FOR q,' AND p;

Using equations (3.1),(3.2),(3.3) and (3.4) in Chapter III, we can derive the
reduced-form equations for q,' and p; For doing this, we first need to solve for the
reduced- form equations for q,' and p; as functions of all the exogenous variables in the
system. ‘

The reduced-form equation for q," is obtained by substituting p; in equation
(3.4) into p; in equation (3.3). Note that p; = p;, since the transportation costs to

region 0 is assumed to be equal to zero in equation (3.2).

q.” - 31(939.'+Plh.'+l3§f.‘)+flip;+l3§m’

 

 

 

(D.l)
+316” +P§P$+B;P;+B§m{+flif{ +1.
. 31$; . 9153 B; . B; B‘.’
9: " hrl ¢+ T "'1’... 1
14:9; 1410'.“ 14391-010; 14:9;
(D2)

 

 

Bi r 95 r B; . 65
p + p + ”3,4 '+(‘
1410;" 1410;" 14:0: 14:01,!

4.

The reduced-form equation for p; is obtained by substituting q," in equation

(3.3) into q,' in equation (3.4).

131

132

p; - 9;<9'.p,'.+9’.v,2+9;m.'+01f.’ +921»;

 

 

 

 

(D3)
+620;+BZM.°+Bif.°)+BZh,'+B;f,’+v,
" a; 3 p7 9:9; 0
P = 15+ ‘74
" I-B‘IB; 1410;" 14:9; "
(0.4) + 3:63 "1’4 B233 ,1, 629? .

1-0‘.’9:' 1419:" 1419;"

 

, 133953;, 0:13;,“ 1:0: 192‘

714:9. 14:01' 14:15.

The reduced-form equation for p", is obtained by substituting the reduced-form

equation for p; into p; = up; in equation (3.1).

 

. ca: 4:». on; f, can; .

P = 1
" l-ata; 14:0. 14:13:"

 

 

+ can; ., 4:01., can: .

 

 

 

(D5) "'1 ‘ t T
143:9; 14:9. 14:11:10"
c9335 . will; . 6153131
+ + m‘ + ‘ +t,
14:9. " 14:9; 1470.],
Let K 1 €035; The ' '
= — . n we can sunphfy (D.5) as,

 

1-929’.‘

133

'3‘ u)/th, +[( ”jg/K16“

15 IBIS

p; = [(1-

 

 

69333 . 05553

 

 

 

 

+[( . _)/KIp,.+I(_,)/K1m°.
1" 135 1 5
(D.6)
9:9: )IKIr.‘+ +[( :B’B’p/np;
1 5 155

+11 ”DD/Kim {+I( ”BU/K1494,

1"915 n 5

 

 

The reduced-form equation for q,’ is obtained by substituting the reduced-form

equation for p; into the p", in the demand equation for NYC region (equation (3.1)).

9199; . BIC B7

 

 

 

 

 

 

 

 

q.’ =11 . ,I/KIh. +I< )IKV.‘
1’9195 1-5135
.[(pch:p:)lKlp;+ [(B‘f ”Bu/K94" m.
1' 135 n 5
(D.7)
11':l ’i’wxw «(:1 ”’B’IIKF 9+9»;
155 1 5
«up: ”pg/KP +9;)m. '+(I(”’ ”gnu/KP +921r.'+ :
1 5 1 5
Equations (D.6) and (D.7) are the reduced-form equations for price and quantity
in the NYC region.

The coefficients on the information variables in the reduced-form equation for

price are as follows:

134

Coefficient for the f,” variable:

 

(D.8) a2 = .—1_fl = CB7 r
_ 413:9; 1-9;<9‘.’+c9.)

1-9Y92

 

 

Coefficient for the f," variable:

1—919: g c929:
_ 49:9: 1-9;(9‘.’+c9:>
1-919';

(0.9) a, =

 

 

Coefficient for the f,’ variable:

ebgfli
(D.10) as = 1‘9195 a c0584
1- 013551 1'15;(Bi+cfii)

1-979:

 

 

 

We can express equation (3.11) in Chapter III as,

,, _ +9: + 4:9:

' 1-919‘.’ + c911 1-9;<9:+c91’)

 

 

(0.11)
c6293

l-PKBMBD

 

By collecting terms (D.11) can be expressed as,

_ «99939992»
1-9’;(9‘.’+c9:)

(D.12) 8'

 

135
The coefficients on the information variables in the reduced-form equation for
quantity are as follows:

Coefficient for the f,’I variable:

 

 

CBIB;
(D.13) Y2 = l-plfsr = 291097 '
l- C9591 l‘ps(91+cfln)
1-919;
Coefficient for the f," variable:
ebiflifli

1-919: . c919:9:

 

 

 

(1114) Y5 = n r u o r
1_ c9591 1795(91+091)
1-919;
Coefficient for the f,’ variable:
6316291
(0.15) v. = ___1-0,.9,' = 43,939, , +91
1- 99591 1’95(91+Cpn)
1—919:

We can express equation (3.7) in Chapter III as,

9,3: c919; ,_ c919:92
1439980 143911491)

 

(D.16)

 

1 0315;“ r
T l 0 ' +p‘
l‘psmn‘wpr)

By collecting terms (D.16) can be expressed as,

136

.. c9k93+92<92+92>> ,
v = +9

(D.17) n a r ‘
1755(BH’CBI)

 

Substitute (D.12) into (D.17),

am) 7, =19: + a') + 9:

APPENDIX B

THE ASYMPTOTIC COVARIANCE MATRIX FOR THE TWO-STAGE LEAST SQUARES
ESTIMATOR WITH SEASONAL ARIMA ERRORS

APPENDIX B

THE ASYMPTOTIC COVARIANCE MATRIX FOR THE
TWO-STAGE LEAST SQUARES ESTIMATOR
WITH SEASONAL ARIMA ERRORS

Demand equation for apples in the NYC region is,

(El) 4" a: fxpfiyet

where q,’ is the per capita quantity of apples at time t, f,(0,a) is the demand equation, 0
and a are vectors of regession parameters and et is the random error term at time t.
Here, a is the parameter vector of the price equation that we use to obtain the fitted
values for the price variable. These fitted values are then used in the demand equation
in place of the observed values of the price variable. 0 denotes the vector of the
parameters for all other variables in the demand equation.

The equation to estimate the fitted values for the price variable is,

(El) P}. = s,(¢)+V,

where p,’, is the retail price of apples at time t, g,(a) is the price equation, a is the vector
of regession parameters and v, is the random error term at time t.

The fitted values of the price is estimated by equation (E2) and is replaced in
the demand equation in place of the price variable.

Nonlinear least squares method is used irn estimating the equations in the

presence of a seasonal error structure. The demand equation and the price equation are

137

138
both defined to be nonlinear to obtain the general form of the asymptotic covariance
matrix.
The criterion function to obtain the estimate [3, B, in the demand equation by

nonlinear least squares is,
(93) 09) = 21,10,509»)?

The first order conditions for a minimum are,

E.4 - r _‘
( ) 2 “(69

.e,)|, =0

Equation (E.4) defines the standard problem in the nonlinear optimization, which
can be solved by number of methods. One most frequently used method is the Gauss-
Newton method. This method provides the correct estimate of the asymptotic

covariance matrix for the parameter estimates.1

Divide both sides of (E4) by -2,
(1:3) 3" =0
Err-1 ('35-‘90
The above equation can be rewritten in matrix form as:
I
(E.6) (6193):, . 0

where 828 is a (T‘xK) matrix and e is a (Txl) vector. T denotes the number of
observations and K denotes the number of estimated parameters in the demand

equation.

 

lWilliam H. Greene, p.336.

139
Following the central limit theorem that provides the asymptotic normality result

of the least squares estimator,1 we can write the following equality:

'm1, =
(E.7) T 33 .e 0

Using the mean-value theorem,2 we can write (E.7) as,

T431]: = T -1rz( afl-fllg

60 60
(E.8)
. .1. if . 1 1’9: -
I T(a9= .01, 1133 .apnnfiu 9)
where, %I‘ = -3—B—|a. The mean value of B, 8, is a value between 8 and the estimate

of 0, 6. Note that in equation (E.8), T-m‘810,°el’ = o.ThiS result comes from (E6). We

can then write equation (E.8) as,

I

'mi’ a -1 fl
T an .8 I 1‘63: .9)“

(5.9)

. .1. 1’1 -

1136.65107719 9)
Define,
.. -1 if . .1. 1’1
A 1(apz '7" 7(89 ‘89)“

and

a 'mi’

K T 33 .e

Then we can write (E.9) as,

 

1William H. Greene, p.315-l6.

2See, Alpha C. Chiang,

' 3rd ed.,
(New York: McGraw-Hill Book Company, 1984), p. 261.

140

(5.10) (718-0) = A".K

Note that the price variable in the demand equation (equation (E.l)) is the fitted
values of the price variable from equation (E.2). Following the mean-value theorem we

can write K in equation (E.10) as,

K = T'Vz( afie)“ +

59
(E.ll)
[%(gg‘m + %g—I-gmlfila-fi)
where, %I‘ = "%li’ The mean value of a, a, is a value between a and the estimate of
a, a .
Define,

I
B a —l(_yL _¢)|‘ + lbliin.

7' 8988 T 89 81!
We can write (E.ll) as,
(E.12) K = T'W(%I.e)|, + Nina-a)
Substitute (E. 12) into (E.10),
(5.13) «719-9) + A"[T"”(%’.¢)I, + Nina -a>1

The criterion function to estimate a by nonlinear least squares is,
02.14) so) - 23., 0,2114)?

The first order conditions for the minimum are,

141

(5.15) ~22); (%ygl, = 0

Divide both sides of the equation (E.15) by +2,

(E.l6) 2; (Sign, = 0

The above equation can be written in matrix form as,
I
(E.l7) (2i 3,)“ = 0
8a

where, 613- is a (T‘xZ) matrix and v is a (Txl) vector. T denotes the number of
a
observations and Z denotes the number of estimated parameters.

Following the central limit theorem,
(E.18) T'mi’y = 0
311
Following the mean-value theorem, we can write (E.18)

T “2 .v T "'( .v)|.

4713:5281. + 43 71.177144)

where g—Vh = ‘33? .The mean value of a, a, is a value between a and the estimate of
a, a .Note that In 6equation (E.19) T'mgiyh :- 0. This result comes from (E.l7). We
a
can write equation (E.19) as,
I'd/3%, v s [—_(.?I v”.
(E20)
1 (29125
_ a-
+T( ad .03 ”111/71 a)
Define,

142

. -12’3’ 195’ as
C T8012 .14, + T601 87."

Then we can write (E.20) as,
I
(13.21) fine-a) = c". (T‘mg- .v)
Substitute (E.21) into (E.13),

(719-9) = A“ [rm-9’5 01.

(13.22)
+ a. clam-3'»)
8a

In order to find the expected value of (E22), we need to have the expected
values for A, B and C.
The expected value for A is:

' g _ 9! _a_r_
9(4) El T 69 331,]
The expected value for B is:
-11
900+ agent—1.13
The expected value for C is:

910+ +04% %"J

Note that the expected values of the first terms in A, B and C equal to zero since

the expected values of the error terms are defined to be equal to zero (i.e., E(e) = 0 and
E( v ) = 0).

143

Define,
r=(-§-fétet)’|.+8.'lC .(::-—'* v,)’
where, * denotes element-by-element multiplication.
(E22) can be written as,
(E23) fitB—p) = A" 1"” 2:11}
(E24) anti-m - m“ T" 23mm]
Ema-BY] =
(E25)
l’af. 3f. -1 -1 1 95’ if,“
(%(53 a—BM) T 21,,E(r{,')(1.(—— as an up
tub-m --
“‘3’" «3" at. a: at.

-1
[(6—5 a—Bna 2,21% 1.6K an '63 )1.)

The above equation is the asymptotic covariance matrix. Since in practice, we cannot
evaluate the matrices defined in (E26) at B and a , we evaluate them at B and a. We

can write (E26) as:

FEB-5):] =

(E27) “’3‘ a.
t 3

[(8B 6B

ear.

—)I,)'1 ,,t£(r;.’)«-aT3 a—fl )w

where,

144

38.

r =(%*e,-"--5-)’l3+80( WM,

and,

E(B)= [fl-(a); Z:

I
E(C) = EI%,-:§a! %IJ

To estimate (E27), we need to define matrices %Ipaa 312' and %h. We also
a

need to define eh and VJ. in ’3' ch is the estimated residual: from the demand
equation with instrument for the price variable. v). is the estimated residuals from the

equation to estimate the fitted values for the price variable.

In defining %|’,a%|.and 81;", we should first write out the demand equation

with the instrument for the price variable and the equation to estimate the fitted values
for the price variable.

Demand equation with instrument for the price variable:

(E28) mm = Auq: -= Bo+B,A.,p.'.+Aur.'+a+¢L‘x1+u“)e,

We can rewrite (E28) as,

(E29) 1; = A124: ‘ BO+BlAIIpI'+A11fI' *¢%-1+Q‘:-n*¢¢et-u+‘

The equation to estimate the fitted values for the price variable in (E28) is,

(E30) p,’ -= g,(a) = ao+a,p;+a2h,'+a,m,'+aj;'+v,

Substitute the estimate of (E30) into (E29),

145

f: = A124: ‘ Bo+B,A12(&0+&,p;+&2h,'+&3m,'+&fl)

 

 

 

 

(E31)
+Anfi’ +¢‘:-1+¢‘c-12+¢¢‘r-13+‘:
Define,
1 A139; A125, é:-1*°es-u 5:42" :43
3f,
3‘" '
B .
_ 1 A094,; A121; ér-1*¢ér-13 ér-u*“r-t3 .
1 P; mt, hi. I:
38:. .
6a ‘ ‘.
L l pyT m; h; f;
0 61AM): 61AM: 61AM: “Ali:
93' ___ . .
6a ‘ . . . .
_0 61AM; 91AM; 91AM; btAufi'.

 

 

93., an .nd 21;:
6B 6a 6a
vectors e,..e,, 9,...9Tin (E.27).(E.27) is calculated by using GAUSS program version 2.1

To estimate (E27), we substitute matrices, |& and the

for personal computers. This calculation is applied to the demand equation with

instrument for the price variable that is reported in Table 42 in Chapter IV.

APPENDIX F

EXPECTED VALUE OF THE CHANGE IN APPLE SALES ASSOCIATED WITH
HEALTH RISK INFORMATION

APPENDIX F

EXPECTED VALUE OF THE CHANGE IN APPLE SALES ASSOCIATED
WITH HEALTH RISK INFORMATION

Let q(pJf) be the individual demand function for apples when health risk is not
present in the market and let q(pfi') be the demand function for apples when health risk
is present in the market. Here, pt is the apple price, If is the absence of the reported
risk, and f,1 is the presence of the reported risk at time t. These demand functions are

demonstrated in Figure 1.

 

 

 

 

: q(p.°f)
% q(p.i)
fl

Figure F.l. Change in Apple Sales Asociated With Health-Risk Information

 

Here, 4,0 denotes per capita quantity of apples demanded when risk is not

present, 4,1 denotes per capita quantity of apples demanded when risk is present. p,' is

the retail price of apples at time t.

146

147

The change in per capita apple purchases at time t is,

(El) A4, = a} - q?

The expected value of the change in per capita apple purchases at time t is

obtained by taking the expectation of (RI):

(F2) E(Aq.) = E(q?) - 15(4))

The expected value of the change in per capita apple sales at time t is obtained
by multplying (F2) by price of apples at time t, 1):. This gives an estimate of the value
of the shaded area in Figure RI. The total value of the change in apple sales is
obtained by multipliying the change in per capita apple sales with the population at time
t.

In this study, the demand function for apples is specified as log-linear. The
following equation is the individual demand function for apples that is specified in this
study when health risk is present in the market. Note that the variables are seasonally
differenced since the dependent variable in the demand equation is nonstationary.

139:1 —lnq,‘_n-B0+B1(lnp,-lnp 42)
(F3)

+ 320}. 15:12) +¢£bl + Qet-tz"'¢°ec-13 +6:

where B0, B1, B2, 4) and 4’ are the regression coefficients and e, is the random error
term. Here, 4) and ¢ are the seasonal ARIMA coefficients.
(R3) can be written as,

mq:-1nq,‘.,,+p,+p,anp,-mp m)
(F.4)

+ 520}! 751-12) +¢et-l +¢ebn+¢°et~13 +6,

where,

148

104:1”N (p902)

e,~N (0,02)
(F.4) can be written as,

(F5) 4:54.142 p," ”:2; camel-13...) ec ea.

where,
c = 436'_1+¢£‘_u+¢0£'_13
and
q} ~Iognoma1(e“°”*.e’"‘°’(e°’ -1»
e"~lognormal(e '3”; “(ea-1))
The expected value of individual demand for apples when risk is present in the
market is,
(F.6) 5(4)) 8:5,}.01/2

where, liq“ is the estimate of big" and o is the estimate of a which are obtained by
estimating equation (FA).

(F.6) can be written as,

(F07) E(q‘l) =e &;n.‘0"|(~g.h'p|1)’m ’ ”19“.?”

149
where, 60, B1, Bl are the estimates of the regression parameters from equation (R4)
and e is the estimate of c. The expected value of individual demand for apples when

risk is not present in the market is identical to (R7) with the exclusion of 520: 711,):
(F3) E(q?) =e H:u*ao*filwc’hP:-iz)‘e*°2/2
The expected value of the change in per capita purchases is obtained by
subtracting (F.7) from (F8), ((3.8):
E(Aq.) = e‘°"1"""“"-n’*‘*°’ ’2

(F3)
1“[e file—u -¢ fivn‘bz‘fi‘fc-uh

APPENDIX G

EXPECTED VALUE OF THE CHANGE IN THE CONSUMER SURPLUS ASSOCIATED
WITH HEALTH-RISK INFORMATION

APPENDIX G

EXPECTED VALUE OF THE CHANGE IN THE CONSUMER SURPLUS
ASSOCIATED WITH HEALTH-RISK INFORMATION

Let q(pgf) be the individual demand function for apples when health risk is not
present in the market and let q(pntf) be the individual demand function for apples when
health-risk is present in the market. Here, pt is the apple price, f,0 is the absence of the

reported risk and ff is the presence of the reported risk at time t. These demand

functions are demonstrated in Figure G. 1.

PA

1!

 

Mn”
(N)

 

 

b

q
Figure G.l. Change in Consumer Surplus Associated with Health-Risk Information

The consumer surplus is the area under the demand curve above the price that

the consumer pays for the good. The consumer surplus for the demand curve when

health-risk is present in the market is,

150

151
(6.1) CS,‘=L'I q(M'fip.

The consumer surplus for the demand curve when health-risk is not present in the

market is,

(62) CS.°=L'I qwbdp.

The change in consumer surplus is the difference between (6.1) and (G2).

(G3) ACS,=cs,°-cs,‘

The expected value of the change in consumer surplus is obtained by taking the
ewectation of (G3)

Demand function for apples when health risk is present in the market is identical
to the demand equation presented in Appendix F (Equation ES).

The consumer surplus when health risk is present in the market is,

1 " 1
CS: ' 1;. 92¢;

(GA)
In B -’ 4 ..
= L. (qtl-lz Pr ' Pt-t; 9" W4”) 6:“? d”;
-3 ”vhf PM“
(GS) cs: = mime” ""”“"’3’:i"
1
where,
c = $6,_1+0€‘_u+¢06,_13

and

(6.5) is infinity for Blz-l. Therefore, the consumer surplus should be calculated

conditional that the own price elasticity of apples is greater than unity.

152
(1,1 ~ lognormal(e'”°z’2,e2“‘°z(e°1—l))
ee‘ ~ lognormal(e°zfl, e°2-1))
If [31> -1, then the consumer surplus when the health risk is present in the market
is,

ofl‘+l
(G.6) CS,‘= -q,-,2 pi; e“ M: "1' ‘9 em‘ (%t— +1 —)
l

The expected value of the consumer surplus when risk information is present in

the market is obtained by taking the expected value of (G.6):

c"+ln

'3 P
EI-Qt-lz pt-l; ‘30 ‘30: £43) e“(—— B‘) +1]
1

ms)

"g’l

’1 “0‘32”: ‘et-n) £_ p‘ E(e")
B.+1

efl'el

’1 ‘0 “(41.1.9 £p_'
4.4192429
Bwl

(G.7)

'34-sz

a”:

G?

The expected value of the consumer surplus when risk information is not present

in the market is:

(G3) E(CSto) g ‘410-12 P332 the eL‘ 9"”
The expected value of the change in consumer suplus is thus:

E(CS°)- E(CS )= n-1, e"‘ e

((;49) OB‘OI

'L“ ew’l’fin + 43-12 em’hn’]
B,+1

BIBLIOGRAPHY

 

BIBLIOGRAPHY

”After Scare, Suit by Apple Farmers.“ flhe New 10:15 film cs, 29 November 1990, A22.

Baumes, Harry S. Jr. and Roger K. Conway. & mpometfic Mggel of the US Apple
Market. ERS Staff Report No: AGE8850110. Washington, DC: United States

Department of Agriculture, Economic Research Service, 1985.

Box, George ER and Gwilym M. Jenkins. Time Series allysis Eorecasting and
Control. San Francisco: Holden Day, 1976.

 

Buxton, Boyd. ”Economic Impact of Consumer Health Concerns About Alar on Apples.”

Eruit and flee Nuts Situation and Outlook Yearmok TFS-ZSO, United States
Department of Agriculture, Economic Research Service (August 1989): 85-88.

Caswell, Julie A. ed. Ecopomics of Food Safeg. New York: Elseiver Science
Publishing Co., 1991.

Chiang, Alpha C. Fundamental Methods of Mathematical Economics. 3rd ed., New
York: McGraw Hill Book Company, 1984.

Choi, Kwan E. and Helen H. Jensen. "Modelling the Effect of Risk on Food Demand."
In W edited by Julie Caswell, New York: Elseiver Science
Publishing Co., 1991.

City of New York, Department of Consumer Affairs. Market Basket Report. New
York, January 1980 - July.1991.

Dalymple, Dana. ”Economic Aspects of Apple Marketing in the United States.” Ph.D.
diss., Michigan State University, 1962.

Deaton, Angus and John Muellbauer. Economics and Consumer Behavior. Cambridge:
Cambridge University Press, 1980.

Born, Young Sook. ”Pesticide Residues and Averting Behavior.” Raleigh: North
Carolina State University, Division of Economics and Business, February 1991,

[photocopy].

Fisher, A., L.G. Chestnut, and D.M. Violette. "The Value of Reducing Risks of Death:

A Note on New Evidence.” Journal of Poligv Analysis and Management 8(1) (1989): 88-
100.

 

153

154

GAUSS System Version 2.1 for IBM PC-XT-AT-PS/2 & Compatibles. Aptech Systems
Inc., Kent, Washington.

Gibson, Richard. ”Apples With Alar Frightened Grocers More Than Buyers." M
Street ,lgurnfl, 7 August 1989, B3.

Gold, Allan. "Company Ends Use of Apple Chemical.“ flhe fig Yprk film es, 18
October 1989, A18.

Guyton, William Preston. “Consumer Response to Risk Information: A Case Study of
the Impact of Alar Scare on New York City Fresh Apple Demand.“ MS. Thesis,
Michigan State University, 1990.

Greene, William H. mnometric Analysis. New York: Macmillan Publishing Co., 1990.

Halloran, John Mark. "Price Forecasting Model for Michigan Fresh Apples." MS.
Thesis, Michigan State University, 1981.

Hausman, J .A. ”Specification Tests in Econometrics.” Econometrig, 6(46) (November
1978): 1251-1271.

Hoehn, John and Douglas Kreiger. Methods for Valuing Environmental Change. Staff
Paper no. 88-30. East Lansing: Michigan State University, Department of Agricultural
Economics, 1988.

International Apple Institute. National and International Apple News. Mc. Lean,
Virginia, January 1980 - July 1991.

Ippolitto, Pauline and Richard A. Ippolitto. ”Measuring the Value of Life Saving From

Consumer Reaction to New Information.” Journal of Public Egppmics, 25 (1984): 53-.

81.

Judge, George G., W.E. Griffiths, R. Carter Hill, Helmut Lutkepth Tsoung-Chao Lee.

Introduction to the 1th and fiactice of Econometrics. 2d ed. New York: John

Wiley and Sons, 1988.

Judge, George 6., WE. Griffiths, R. Carter Hill, Helmut Lutkepth Tsoung-Chao Lee.
co and act'ce o Econometrics. 2d ed. New York: John Wiley and Sons,

1985.

Kennedy, Peter. A Guide to Econometrics. 2d ed. Cambridge: MIT Press, 1985.

Kmenta, Jan. Elements of Econometrics. 2d ed. New York: Macmillan Publishing Co.,
1986.

New York City, Department of Consumer Affairs. Market Basket Report. New York.

O’Rourke, Desmond. ”Anatomy of a Disaster.” Agtibusiness, 6 (5) (1991): 417-424.

 

155

PC RATS (Regression Analysis Time Series) Version 3.1, VAR Econometrics Inc.,
Evanston, Il.

Rescher, Nicholas. RE k: A Rhilomphimotl Introduction to the Theogt of Risk Evaluation
and Mapagemept. New Yorszniversity Press of America, 1983.

Sewell, Bradford H. and Robin M. Whyatt. ”Intolerable Risk: Pesticides in Our
Children’s Food." Washington DC: Natural Resources Defense Council, 1989.

Smith, Mark, Eileen O. van Ravenswaay and Stanley R. Thompson. ”Sales Loss
Determination in Food Contamonation Incidents: An Application to Milk Bans in

Hawaii." American Journal 01 Agticultural Economics, 70(3) (August 1988): $13-$20.

State of New York, Department of Labor. Emploment Review. New York, January
1980 - July 1991.

”US to Bail Out Apple Growers." Chicago Tribune, 9 July 1989, C22.

United States Department of Agriculture, Agricultural Marketing Service. Fresh Fruit
and Vegetable Arrivals in Eastern Cities. Washington, DC, January 1980 - July 1991.

United States Department of Agriculture, Agricultural Marketing Service. Eresh Fruit

and Vegetable Shipments in the United States. Washington, DC, January 1980 — July
1991.

United States Departmant of Commerce, Bureau of the Census. Current Population
Reports. Series P25, Washington, DC, 1978 - 1988.

United States Department of Commerce, Bureau of the Census. Summag Population
and Housing Characteristics. CPH-l, 1990.

United States Department of Commerce, Bureau of Labor Statistics. CPI Detailed
Report. Washington, DC, January 1980 - July 1991.

van Ravenswaay, Eileen. "Consumer Perceptions of Health Risks in Food.” In

luggsm' g Updgmtapdm' g of flblic Emblems and Eoliglgs-l990. Oak Brook, 11: Farm
Foundation, 1990.

van Ravenswaay, Eileen and John P. Hoehn. "The Impact of Health Risk on Food
Demand: A Case Study of Alar and Apples." In Economics of Food Safeg, edited by
Julie A. Caswell, New York: Elseiver Science Publishing Co., 1991.

Willig, Robert D. ”Consumer Surplus Without Apology.” The American Economic
Review, (September 1976): 589-597.

Wooldridge, Jeffrey M. ”Regression-Based Inference in Linear Time Series Models with
Incomplete Dynamics." East Lansing: Michigan State University Department of
Economics, August 1989, [photocopy].