A DUPLICATION AND REPLICATION OF TWO ECONOMETRIC DEMAND
MODELS EXPLAINING THE EFFECTS OF PROMOTION ON MILLLEVEL
DEMAND OF U.S. UPLAND COTTON
Except where reference is made to the work of others, the work described in this thesis is
my own or was done in collaboration with my advisory committee. This thesis does not
include proprietary or classified information.
__________________________________________
Trent Alan Morton
Certificate of Approval:
_________________________ _________________________
Greg Traxler Henry W. Kinnucan, Chair
Professor Professor
Agricultural Economics Agricultural Economics
_________________________ _________________________
Patricia A. Duffy Stephen L. McFarland
Professor Acting Dean
Agricultural Economics Graduate School
A DUPLICATION AND REPLICATION OF TWO ECONOMETRIC DEMAND
MODELS EXPLAINING THE EFFECTS OF PROMOTION ON MILLLEVEL
DEMAND OF U.S. UPLAND COTTON
Trent Alan Morton
A Thesis
Submitted to
the Graduate Faculty of
Auburn University
in Partial Fulfillment of the
Requirements for the
Degree of
Master of Science
Auburn, Alabama
August 8, 2005
iii
A DUPLICATION AND REPLICATION OF TWO ECONOMETRIC DEMAND
MODELS EXPLAINING THE EFFECTS OF PROMOTION ON MILLLEVEL
DEMAND OF U.S. UPLAND COTTON
Trent Alan Morton
Permission is granted to Auburn University to make copies of this thesis at its discretion,
upon request of individuals or institutions and at their expense. The author reserves all
publication rights.
_________________________
Signature of Author
_________________________
Date
iv
VITA
Trent Alan Morton, son of Richard Morton and Denise Morton, was born in
Cullman, Alabama, February 27, 1979. He graduated from Cullman High School in May
1997. In September of 1997 he enrolled in Wallace State Community College. In
September of 1998, he transferred to Auburn University where he received the degree of
Bachelor?s of Science in Finance, May 2002. He entered Graduate School at Auburn
University in August 2003 and began work towards a Master?s of Science degree in
Agricultural Economics.
v
THESIS ABSTRACT
A DUPLICATION AND REPLICATION OF TWO ECONOMETRIC DEMAND
MODELS EXPLAINING THE EFFECTS OF PROMOTION ON MILLLEVEL
DEMAND OF U.S. UPLAND COTTON
Trent Alan Morton
Master of Science, August 8, 2005
(B.S., Auburn University, 2002)
101 Typed Pages
Directed by Henry W. Kinnucan
Many studies have been conducted to determine the effects of generic promotion
on the demand for a certain commodity. Two studies examining the effects that cotton
promotion expenditures by Cotton Incorporated has on the milllevel demand for U.S.
upland cotton are examined in this paper. Researchers at the Research Triangle Institute
conducted a study in collaboration with researchers from North Carolina State University
(hereafter Murray et al.). They found longrun elasticity estimates of 0.02 for promotion
and 0.35 for nonagricultural research. In addition, they found the longrun elasticity
estimate for the ownprice of cotton to be ?0.4. With these estimates, they suggested that
the U.S. Cotton Research and Promotion Program was effective in increasing the mill
level demand for U.S. Upland Cotton.
vi
Ding and Kinnucan conducted a study that found the longrun elasticity estimate
to be 0.06 for promotion. This estimate was somewhat larger than the Murray et al.
estimation. They, furthermore, found the longrun elasticity estimate for the ownprice of
cotton to be ?0.3. They, too, suggested that promotion expenditures expanded the mill
level demand for upland cotton.
Following William Tomek?s guidelines for duplication and replication of research
results, an attempt was made to duplicate the Murray et al. results and then, to replicate
Ding and Kinnucan?s results with Murray et al. data. Duplication is utilizing previous
research and trying to retrieve the exact results by implementing the same methods used
by the original researchers. Replication is defined as fitting the original specification of a
model to new data. If there are no major errors in the results, then the work of the
researcher is confirmed. Both duplication and replication are important to research
because with alternative models being presented by researchers, different economical
interpretations can be illustrated. Second, researchers learn from confirmation. Third,
confirmation brings about a more robust model. Finally, honesty in publications is
encouraged and careless work is deterred.
The Murray et al. OLS and GLS results were confirmed by duplication. The
duplicated results exhibited only slight differences in parameter estimates and tratios.
Problems did arise from the 2SLS results because of identification problems caused by
collinear variables. However, after deletion of two variables (justified by a variable
selection method utilized in SAS), regression analysis was continued (without correction
for firstorder autocorrelation because of unclear methods) and reasonable results were
attained although exact duplication of Murray et al. results could not be accomplished.
vii
One of the major problems that researchers run into in replication studies is
locating missing data. This was the main problem that was incurred during this study.
Replication was not perfect in that monthly, rather than quarterly, data were used and two
proxy variables had to be used due to some missing data. This coupled with the fact that
it was not known whether the researchers used unadjusted or seasonally adjusted
advertising data, may have caused different regression results.
It was first suggested, using unadjusted advertising data with Model D (the model
that compared directly with Ding and Kinnucan?s), that the inferences made by the
researchers were negated and their results were suggested to be very fragile. However, it
was later suggested, using seasonally adjusted advertising data with Model D, that Ding
and Kinnucan?s inferences (advertising expands the demand for cotton) were robust,
although many conclusions were altered and the model?s fit was not ideal. When an
interaction term was included in the model without the monthly dummy variables (Model
C with seasonally adjusted advertising data), it became significant. This implied that
advertising played the role of a ?taste shifter? by rotating the demand curve and therefore
changed Ding and Kinnucan?s findings of no curve rotation.
With the regression results being severely altered using seasonally adjusted
advertising data, it is suggested that the use of such data causes the inferences from these
studies to be conditional upon whether advertising data are seasonally adjusted and on the
particular model specification. Furthermore, questions about the robustness of the results
are brought up when such dramatic changes occur from the use of modified data.
viii
ACKNOWLEDGEMENTS
The author would like to thank Dr. Henry Kinnucan for assistance with statistical
analyses, economic theory, and data collection. Thanks are also due to family members
Denise, Butch, Tanya, Allene, and U. L. Morton and Ruth Morgan for their support
during the course of this research.
ix
STYLE MANUAL AND COMPUTER SOFTWARE
Style Manual or Journal Used: The journal used for formatting the thesis was the
American Journal of Agricultural Economics.
Computer Software Used: Microsoft Word was used for word processing,
Microsoft Excel was used for data storage during research and SAS, Version 9.1, was
used for all statistical regression analyses.
x
TABLE OF CONTENTS
LIST OF TABLES?????????????????????????.. xi
I. INTRODUCTION??????????????????????... 1
History of the U.S. Cotton Research and Promotion Program
Murray et al. Evaluation of the Cotton Program
for the William Crawford of the Cotton Board
Ding and Kinnucan Study of U.S. Cotton Promotion
Objective of Study
II. LITERATURE REVIEW???????????????????... 6
Tomek Guidelines for Duplication / Replication Studies
JMCB Project
Coulibaly and Brorsen Replication Study: Effectiveness of
U.S. Generic Meat Advertising on Consumer Demand
III. MURRAY et al. ESTIMATION PROCEDURES??????.???.. 23
IV. DING AND KINNUCAN ESTIMATION PROCEDURES?????? 31
V. DUPLICATION OF MURRAY et al. REGRESSION
RESULTS?????????????????????????. 38
VI. ADDITIONAL TESTS AND REGRESSIONS PERFORMED ON
MURRAY et al. MODEL???????????????????. 43
VII. REPLICATION OF DING AND KINNUCAN REGRESSION
RESULTS?????????????????????????. 54
VIII. SUMMARY AND CONCLUSIONS??????????????... 73
REFERENCES??????????????????????????. 78
APPENDIX..?????????????????????????.?? 82
xi
LIST OF TABLES
1. Variables Used in the Duplication of the Murray et al. Study of Cotton
Promotion, January 1986December 2000???????????????? 49
2. Duplication of Regression Results for the Domestic Mill Demand
Equation from the Murray et al. Study of Cotton Promotion,
January 1986December 2000????????????????????... 50
3. Additional
Tests and Regressions Performed on the Domestic Mill Demand
Equation from the Murray et al. Study of Cotton Promotion,
January 1986 ? December 2000????????????????????. 52
4. Variables Used for the Replication of the Ding and Kinnucan Study of U.S.
Cotton promotion, January 1986December 2000?????????????. 67
5. Ding and Kinnucan GLS Esimates (Corrected for ForthOrder
Autocorrelation) of Domestic Mill Demand for Cotton,
19761993 Quarterly Data??????????????????????.. 68
6. Replication of Ding and Kinnucan?s Cotton Demand Model
Using Seasonally Unadjusted Advertising Data,
January 1986December 2000????????????????????... 69
7. Replication of Ding and Kinnucan?s Cotton Demand Model
Using Seasonally Adjusted Advertising Data,
January 1986December 2000????????????????????... 71
1
I. INTRODUCTION
Since the 1800?s and before, cotton was considered the dominant fiber for
clothing in the U.S. It was also the country?s number one agricultural export for 150
years thereafter. But, in the 1950?s and 1960?s, cotton began to lose its stronghold in the
marketplace to manmade fibers such as polyester. Cotton?s weakening in the market
stimulated Congress to step in and take action. In 1966, the U.S. Cotton Research and
Promotion Act was established to offset synthetic fiber?s growth in the market and to
restore cotton as the number one fiber.
The U.S. Cotton Research and Promotion Program is designated to aid in
research for more cost efficient methods for cotton production therefore increasing the
producer?s profits. It also provides the necessary funding for promoting cotton and
cotton products. The program is carried out by way of funds collected from both
producers and importers of upland cotton via a mandatory checkoff program established
in 1990. The Cotton Program currently requires producers and importers to pay $1 per
bale, plus an additional assessment of onehalf of 1 percent of the value (Murray et al.,
p.2.3). The funds collected are sent directly to the Cotton Board after the USDA retains
enough to manage its expenses for the program. The Cotton Board then pays any in
house expenses and reimburses any governmental agencies, primarily the Customs
Agency whom assists in the import program. The balance is then sent to Cotton
Incorporated where the assessments are used to fund agricultural research, fiber research,
2
textile research, global product marketing, and consumer marketing. The Program
engages in promotion designed to increase retail demand, research into fiber and textile
quality that is aimed at increasing milllevel demand directly (because of reductions in
the costs of processing cotton), and agricultural research into methods of reducing
production costs or increasing yields (Murray et al., p.4.9). The spending patterns of
Cotton Inc. have been particularly stable over the years. From 1996 to 2000, agricultural
research took a consistent 11 percent of the budget, fiber and textile research 16 percent,
consumer marketing (primarily advertising) about 50 percent, and global product
marketing about 16 percent (Murray et al., p.2.6). Every five years, the Secretary of
Agriculture has the Cotton Program evaluated. The chief focus of the evaluation is to
determine how well the Cotton Research and Promotion Program, primarily through
promotion efforts, is expanding the demand for upland cotton and increasing the
profitability of cotton growers and of cotton product importers.
The Research Triangle Institute (RTI), in collaboration with researchers from
North Carolina State University (NCSU), conducted an evaluation of the Cotton Program
for William Crawford of the Cotton Board in 2001. RTI consisted of Brian C. Murray,
Robert H. Beach, William J. White, and Catherine Viator. NCSU consisted of Nick
Piggott and Michael Wohlgenant. Their study objectives were to assess the effects of the
program on the domestic demand for upland cotton, the return on investment (ROI) to
domestic cotton producers, and the value to importers of cotton products. They
furthermore estimated the overall ROI of the program and assessed the nonquantitative
program benefits. Ultimately, Murray et al. were to determine if the benefits to
producers outweighed the assessments collected from them.
3
By implementing an econometric demand model, Murray et al. concluded that the
benefits from the Cotton Program outweighed the perbale assessments collected from
producers. They found the ownprice elasticity of cotton to be approximately ?0.4. In
addition, they found the promotion elasticity to be approximately 0.02 and the longrun
elasticity estimate for the sum of the current and lagged effects of nonagricultural
research to be approximately 0.35. The promotion elasticity estimate presumes that a 10
percent increase in promotion expenditures would directly lead to a 0.2 percent increase
in the domestic milllevel demand for cotton. Furthermore, a 10 percent increase in
nonagricultural research expenditures would lead to a 3.5 percent increase in the
domestic milllevel demand for cotton.
By only using a distributed lag with the research variable and specifying the other
variables (cotton price and promotion) contemporaneously, the assumption of the
researchers was that the promotion effects were felt instantaneously, i.e., promotion
expenditures affect milllevel demand in the exact period that they are used. This
assumption contradicts many past studies that have shown that promotion expenditures
affect the domestic milllevel demand over a long time period. For example, a study by
Ding and Kinnucan concluded that advertising did not take hold until the second quarter
following the initial expenditure.
Ding and Kinnucan?s study focused on making optimal allocation decisions for
cotton promotion based on advertising elasticities in the domestic and export markets and
the export market share. In the course of their research, Ding and Kinnucan devised an
econometric model for the domestic mill use of upland cotton, with a different lag
specification than Murray et al., to estimate the domestic advertising elasticity. They
4
wanted to determine the effects that advertising expenditures had on the domestic mill
level demand for cotton. They furthermore wanted to determine if advertising
expenditures caused a structural shift in the demand curve (is advertising a taste shifter?).
They tested this with the inclusion of an interaction term.
Ding and Kinnucan obtained a larger estimate for the advertising elasticity than
did Murray et al. Their estimate for advertising elasticity was approximately 0.06. This
estimate implied that a 10 percent increase in cotton promotion would increase milllevel
demand by 0.6 percent. In addition, they found the ownprice elasticity of cotton to be
approximately ?0.30.
Ding and Kinnucan?s model differs significantly from the Murray et al. model.
First, Ding and Kinnucan used a different lag specification. Murray et al. used an Almon
distributed lag specification only lagging nonagricultural research instead of the fiber
prices or promotion. Ding and Kinnucan lagged advertising 6 months and the prices of
cotton, rayon, and polyester 12 months while excluding nonagricultural research
expenditures. Additionally, Ding and Kinnucan included a lagged dependent variable to
account for any advertising carryover effects. Also, Ding and Kinnucan?s use of
quarterly data differed from Murray et al.?s use of monthly data. Furthermore, Ding and
Kinnucan specified the model as a doublelog to allow advertising to display diminishing
marginal returns.
Following the guidelines of William Tomek and prior duplication and replication
studies, the first objective of my research is to duplicate Murray et al. regression results.
I will be focusing on their econometric demand model for the domestic mill use of upland
cotton. Duplication is utilizing previous research and trying to retrieve the exact results
5
by implementing the same methods used by the original researchers. If the exact results
are attained without any major errors, then the work of the researcher is confirmed. As
stated by William Tomek (p.7), one of the potential benefits of confirmation research is
an improved model. Duplicating and confirming the research of Murray et al. will
ultimately validate the adequacy of the econometric model that they developed to explain
the effects of promotion and research on the domestic milllevel demand for cotton.
The second objective of my research is to replicate Ding and Kinnucan?s
econometric results using Murray et al. updated data. Replication is defined as fitting the
original specification of a model to new data. Murray et al. used data ranging from 1986
2000 whereas Ding and Kinnucan used data ranging from 19761993.
In general, the purposes of my research are to compare and contrast two different
econometric demand models for the effects of promotion on the domestic mill use of
cotton and to test whether or not the Ding and Kinnucan model holds its validity when
estimated with updated data. Many researchers say that the strength of agricultural
economics comes from researchers combining theories, quantitative methods, and data to
do useful analyses of problems faced by society. Tomek (p.6) states that agricultural
economists are not accomplishing this very well and that one component of the problem
is that econometric results are often fragile. Many domestic cotton promotion studies
have proven Tomek to be correct. Hopefully, with the successful duplication of Murray
et al.?s results and the replication of Ding and Kinnucan?s results, the robustness of their
models explaining the relationship between promotion and the domestic milllevel
demand for cotton will improve.
6
II. LITERATURE REVIEW
?The strength of agricultural economics rests on its capacity to combine theory,
quantitative methods, and data to do useful analyses of problems faced by society?
(Tomek, p.6). A major problem faced by economic researchers is that econometric
results are often fragile. Large variation in results may be a major consequence of a
small change in a model or data, which, in turn, reduces the robustness, or explanatory
power, of the model. Nonetheless, there is no easy solution to improving upon unstable
results because econometric models are just approximations.
One possible way to reduce the variation in the results and contradictory
conclusions between researchers is to build upon prior research. The aim of the
researcher should be to expand or improve upon the previous research, not to disprove
others work. ?Replication and confirmation, I shall argue, are often essential components
in demonstrating such improvements? (Tomek, p.6). Confirmation may help in the
explanation of how researchers arrive at different results given the same model or data.
Different results may be a consequence of differences in models or data, but uses of
alternative estimators or dissimilarities in how the results are analyzed or applied by the
researcher can be other causes. For example, Murray et al. and previous researchers
(Capps et al., 1997; Ding and Kinnucan, 1996) used different lag specifications for the
econometric demand models. This led to different elasticity calculations. Murray et al.
concluded that the ownprice elasticity of demand for cotton was ?0.4, which was
7
significantly larger than Capps et al. estimate of ?0.16 and Ding and Kinnucan?s estimate
of ?0.3. The Murray et al. model implemented the Almon distributed lag on the
nonagricultural research expenditure variable without any other lagged variables. Capps
et al. lagged the price of cotton by 13 months. ?When we included the 13month lagged
price variable in our model (in addition to current price), we found no statistically
significant impact of lagged price. We take these results to strongly suggest that mill
consumption and the raw fiber price are contemporaneously determined? (Murray et al.,
p.5.12). Ding and Kinnucan did not include nonagricultural research expenditures, but
lagged the prices of cotton, rayon, and polyester by 12 months, as well as advertising by
6 months.
The scientific community is not a large supporter of confirmation and replication
research. ?Scientific and professional laurels are not awarded for replicating another
scientist?s findings. Further, a researcher undertaking a replication may be viewed as
lacking imagination and creativity, or of being unable to allocate his time wisely among
competing research projects. In addition, replications may be interpreted as reflecting a
lack of trust in another scientist?s integrity and ability, as a critique of the scientist?s
findings, or as a personal dispute between researchers. Finally, ambiguities and/or errors
in the documentation of the original research may leave the researcher unable to
distinguish between errors in the replication and in the original study? (Dewald et al.,
1986). Dewald et al. (p.601) suggests that given these circumstances, replication may be
considered a form of ?professional headhunting? instead of an important part of
scientific research.
8
Although unpopular among a number of researchers, confirmation offers several
benefits to the field of research. First, with alternative models being presented by
researchers, different economical interpretations can be illustrated. Second, researchers
learn from confirmation. ?True scholarship arises from building indepth expertise;
confirmation provides greater understanding of the strengths and weaknesses of prior
work; and it helps build the intellectual capital from which innovation can spring?
(Tomek, p.8). Third, confirmation brings about a more robust model. If the model were
being used for an important policy, one would want the model to be as errorfree as
possible. Furthermore, honesty in publications would be encouraged and careless work
would be deterred.
Although many benefits arise from confirmation work, there exist some implicit
difficulties. The number one difficulty in confirmation studies is that original data from
previous studies may not be available or may be incomprehensive to researchers. Many
times, data are lost or discarded once a paper has been published. Furthermore, errors
may occur in data input, the sample period stated may be different from the vintage
sample period, and data transformations may be unclear to the duplicating researcher.
The second most occurring difficulty in confirmation research comes from the
duplicating researcher?s poor comprehension of the original model. The structural form
of the model, specification of variables, or definitions of variables may be unclear to the
duplicating researcher.
A third difficulty may arise from differing minimization algorithms of different
statistical computer programs that researchers prefer. One econometric program may
present quite different results because of the methods that it employs in minimizing
9
estimates of parameters. Tomek (p.10) gives an example of how Generalized Least
Squares (GLS) functions of different econometric packages differ. He notes that Dewald,
Thursby, and Anderson were unable to duplicate results from a previous study, though
the exact data was used, because of differing econometric software amongst the
researchers.
Tomek (p.10) illustrates two confirmation studies in which some problems arise
for researchers. He demonstrates the difficulty of duplicating published results, the
problems arising from using revised data, the sensitivity of results to data revisions, and
the potential insights from attempted confirmations. He focuses on the importance of
obtaining the original data set.
One confirmation study was from an unpublished MS thesis by Miller who
attempted to confirm a paper by Braschler that focused on the structural change in meat
demand. In the original research, Braschler used the sample period 1950?1982.
Braschler concluded that the structural demand for beef changed between 1970 and 1971
causing a need for a break in the data. Applying the break in his data set minimized the
total sum of squared errors resulting in an F statistic of 11.12 (the model was statistically
significant).
Miller was able to confirm the results after acquiring the original data used by
Braschler. Following the confirmation, Miller attempted replicating the study with
revised data. The problem presented here was that the government had revised most of
the data more than once and the revisions were inconsistent amongst all the variables
used in the model (some variables were revised at different times). A second problem
that Miller faced was that the Consumer Price Index (CPI) had shifted to a smaller scale.
10
Remedies for these problems were unclear; therefore, Miller estimated the model
twice. By joining the revised data with the original data without adjustment, the first
estimation was performed. The second estimation involved adjusting the original data by
the revised CPI to be consistent with the more recent data. This caused the dependent
variable (deflated price) to be larger, thus causing overestimation of the model
parameters (this problem did not pose major concern for Miller because the paper
focused on the structural change dates, not the scale of the estimates).
Miller found that using revised data shifted the structural change dates. After the
first estimation, the structure changed between 1972 and 1973. Likewise, in the course of
the second estimation, the structure changed between 1958 and 1959. Furthermore, both
models had a smaller R
2
and autocorrelated residuals.
In general, instead of building upon previous results, the revised data that Miller
used actually changed Braschler?s results. The original research was duplicated but could
not be replicated with the available revised data therefore; the model or the previous
conclusions were not robust.
A further confirmation study discussed by Tomek was based on a Ziemer and
White paper that suggested that the U.S. beef sector was best modeled in disequilibrium.
Two researchers, Shonkwiler and Spreen, were the first to attempt to duplicate the
research. They could not acquire the original data so they collected data independently.
They failed to duplicate the original results because of significant differences in
coefficients in the demand equation. Ferguson, on the other hand, accomplished
duplication of the exact results because Ziemer and White?s original data became
available. Nevertheless, Ferguson ran into problems in the process. The trouble
11
occurred with matching the per capita personal income data in Ziemer and White?s data
files with other published works. After further examination, two income observations
were found to be approximately 20% too large with respect to the others. After
correcting these errors, Ferguson?s results were similar to Shonkwiler and Spreen?s
earlier results. Ferguson found that the residuals remained autocorrelated after the
corrections, which would require further research as to why. It was also proven that the
fed beef market was not in disequilibrium, which contradicted Ziemer and White?s
conclusions simply because of the errors in their data set.
Tomek (p.13) stated, ?Published and anecdotal evidence on confirmation in
economics suggests the disheartening conclusion that many published empirical studies
contain errors and that some of these errors are serious in the sense that, if corrected, the
stated conclusions of the study would change.? Furthermore, confirmation helps in
building upon the true scholarship of research and should be encouraged in the field of
agricultural economics to supplement existing empirical research.
Perhaps the most noted replication study was from the Journal of Money, Credit
and Banking (JMCB) Data Storage and Evaluation Project by Dewald, Thursby, and
Anderson in 1986. They examined the importance of replication in empirical economic
research by conducting a twoyear study that focused on the collection of data and
computer programs from various authors and attempting replications of their published
results. They found that published errors are rather common in economic articles and,
only if the replicating researcher makes the exact same errors while conducting research,
the replication of published results becomes impossible. They wanted to find out the
different causes for failures in replication research.
12
Dewald et al. suggest that the role of professional journals in attempting to deter
published errors should be to require authors to make available the data and computer
programs used for different economic analyses. They believed that there were two
significant advantages to having data and programs being made available to article
referees. First, it would greatly reduce the costs incurred by the researcher attempting to
replicate original results. Second, readers of journals benefit from being assured that the
probability of published errors is greatly diminished because referees have access to data
and programs.
Referees primarily focus on methodology, theoretical specification, statistical
estimators, and importance of results. The referee usually assumes that the authors?
calculations, data, and computer programs are correct. It would take an extraordinary
amount of time for referees of articles to be required to check the authors? data and
computer programs. Dewald et al. argue that by simply requiring the compilation of data
and computer programs for submission to the referee, ambiguities, oversights, and errors
that were otherwise undetected to the researcher will be brought forth. These oversights
can then be corrected before publication. Nevertheless, at the time Dewald et al. were
published, the only economic journal that had editorial policies that requested data and
programs from the author was the JMCB. Today, such requests are more common.
The first part of the project was to request data and computer programs from all
authors of empirical articles during or after 1980. The authors were divided into two
groups: authors of articles that were published before the start of the JMCB Project in
1982; and authors of articles after 1982 (either articles being accepted, but not yet sent for
publication or articles under review by referees). In group one (published before JMCB
13
Project), 42 out of 62 authors responded and 22 of them sent data and programs.
Approximately onethird never responded and onethird replied by saying that they could
not supply the data and programs. In the first half of group two (accepted, but not yet
published), 26 out of 27 responded. Only 5 authors failed to send data and programs and
one author never responded. In the second half of the group two (authors under review),
49 out of 65 authors responded. Only 2 authors did not send data and programs and no
more than 16 failed to reply.
Dewald et al. examined the first 54 submitted data sets to determine if the data
was comprehensible enough for a replication. Only 8 or 15 percent of the data was
determined to be usable in a replication and 14 or 26 percent was incomplete. They
determined that the most prevalent problems with the data sets were that the author failed
to identify the sources of the data exactly and incomplete data sets. More problems
occurred from the authors? failures in identifying variable data sources and
incomprehensible variable transformations.
Dewald et al. illustrated three examples of what they found from the first half of
the project. First, they found a large number of transcription errors in the data set
submitted by Canarella and Neil Garston. After correction of the errors, regression
estimates and likelihoodratio test statistics changed significantly, but conclusions
remained the same. Second, in a data set submitted by Edward Gramlich, the sample
period cited in the manuscript and the actual sample period of the data set were in
contradiction. Before publication, the author found that one of the forecasts of the model
had been coded incorrectly by six months. The correction of this error caused the
conclusions to change considerably. The final example was from a coding error
14
discovered in the tenyear governmentbondrate series in data submitted by Thomas
Mayer and Harold Nathan. The conclusions were unchanged after the correction, but
their equations came to be substantially different.
The next element of the Dewald et al. study consisted of an attempted replication
of nine articles from the submitted data sets. Their goal was to obtain the same numerical
results as the original authors without having to examine the data sets for errors.
They found that they could only replicate, completely, the results of two articles
(James Johannes and Robert Rasche; and Robert Engle). They were almost able to
reproduce the results from Roley and attained approximately the same results as Merrick.
They replicated all of Roley?s results from a threeequation model for the impact of
weekly money stock announcements on Treasury bill yields except for the estimates of
the third equation. Dewald et al. were able to obtain the same sign and statistical
significance of the coefficients for Merrick?s equation for the determinants of money
growth, but failed in reproducing the exact regression estimates. They were unable to
uncover the reasons for the differences in estimates.
Dewald et al. found that a number of computer program errors hindered their
replications. Brian Maris cited in an article that 1952: III ? 1977: III was the estimation
period (101 observations) used while the original period used by the computer program
started with 1950: III (110 observations). This caused the computer program that was
used, FORTRAN, to compute errors. Dewald et al. found, after correction, that the
specific timeseries filters accepted by Maris were rejected by the data.
Dewald et al. discovered that they could not replicate two articles. The first
article, submitted by Bala Batavia and Nicholas Lash, stated that generalized least
15
squares (GLS) was used for estimation of both a singleequation and a simultaneous
equation model, but failed to report the estimator that they used. This coupled with the
fact that the authors failed to provide the computer programs, caused Dewald et al. to fail
to replicate the results of the article.
The second article, submitted by Woglom dealt with the role of stock prices as a
determinant of consumption in the MITPennSSRC (MPS) macroeconometric model.
The research contained in the original article had been completed several years before
Dewald et al. had requested it and had also been updated since the article?s publication.
The vintage data set that corresponded to the original article could not be recovered, so
Dewald et al. used revised data supplied by Woglom. Neither Dewald et al. or Woglom
could replicate the results from the original article. ?These results emphasize the
importance of maintaining intact the vintage data sets used in published articles,
especially when continuing research requires that active data sets be updated with revised
observations? (Dewald et al., 1986).
Dewald et al. attempted replication of a submitted article by Goldberg and
Saunders where the author claimed that the data had been lost but could easily be
obtained from other published sources. They provided the general sources for the data,
but failed to provide specific months, pages, or table numbers. Dewald et al. collected
the mostrecent published values for all missing variables and time periods. Their
regression coefficients and standard errors were significantly different from the
coefficients calculated by Goldberg and Saunders. Several of the insignificant
coefficients became significant and vice versa.
16
The last replication attempt was from a largescale macroeconometric model
submitted by Benjamin Freidman. His model was based on a version of the MITPenn
SSRC (MPS) macroeconometric model that contained a large model for the market for
U.S. government bonds. When Dewald et al. requested the programs and data used in the
article, they were sent an 87page manual describing the installation and usage of the
MPS model on Harvard University?s IBM VM/370 computer system and two tapes
containing over 2,500 files of programs and data. Needless to say, Dewald et al. gave up
any replication efforts because of limited time and resources.
Dewald et al. results suggest that published errors are a more common occurrence
than not. Because of these findings, several authors suggested that replication of
empirical research become an imperative preliminary step for new research. They
strongly reiterated that to deter many of the published errors in economic research,
authors should be required to submit all data and computer programs at the time the
papers are submitted to referees of journal articles.
In the U.S., different organizations spend millions of dollars per year on
promotion programs designed to increase consumer demand for a certain commodity.
Since they are the ones funding such programs, producers of commodity goods often
want to see empirical results on the effectiveness of these programs for increasing
consumer demand and producers? profits. Two such studies were conducted focusing on
the effectiveness of U.S. generic meat advertising but obtained contradictory results.
Coulibaly and Brorsen conducted a study as to why the two previous studies of
Brester and Schroeder and Ward and Lambert reached conflicting conclusions about the
effectiveness of U.S. generic meat advertising on consumer demand. One reason was
17
thought to be because Brester and Schroeder used generic advertising expenditure data
obtained from a media tracking service while Ward and Lambert used beef checkoff
expenditure data obtained from the promotion organization. Another possible reason was
the differences in the econometric models used by the researchers. Brester and Schroeder
used a Rotterdam demand system while Ward and Lambert used a singleequation price
dependent model. Coulibaly and Brorsen used both of the data sets with both previous
models for reestimation of parameters and misspecification testing.
Coulibaly and Brorsen learned from previous studies that increasing advertising
for established products like beef would only show effects approximately onethird of the
time, the demand elasticities for beef and pork with respect to advertising are small, and
the money spent on beef advertising is relatively small compared to the total value of
beef. They assumed that these facts combined might have led to statistical insignificance
in the models.
Ward and Lambert illustrated the effects of U.S. beef checkoff expenditures on
meat demand with three different models. The live weight level, boxed beef market
level, and retail market levels were used for the three models, respectively. Coulibaly
and Brorsen only examined the retail market model because it was comparable to Brester
and Schroeder?s retail demand system. Ward and Lambert?s model was specified as
(1) lnP
bt
= ?
0
+ ?
1
lnQ
bt
+
?
2
lnQ
kt
+ ?
3
lnQ
pt
+ ?
4
lnI
t
+ ?
5
T
1t
+ ?
6
T
2t
+ ?
7
S
1t
+ ?
8
S
2t
+ ?
9
S
3t
+ ?
10
FR
t
+ ?
1
ln[1 + exp(?/E
t
)] + ?
2
ln[1 + exp(?/E
t1
)] + ?
t?
Where P
bt
is the real price of beef at the retail level, Q
bt
,
Q
kt
, and Q
pt
are the per capita
disappearances of beef, pork, and poultry, respectively, I
t
is the real per capita income, S
it
are quarterly dummy variables, E
t
and E
t1
are the current and lagged beef checkoff
18
expenditures (also used as proxies for current and lagged generic beef advertising
expenditures), T
1t
and T
2t
are time trends, FR
t
is the feeder steer ratio, and ?
t?
is the error
term. T
1
increases one unit each quarter starting with T
1
= 58 in 1979:2. T
2
equals one
before 1990:1 and increases in units of one thereafter.
Because Brester and Schroeder also determined the effectiveness of pork
advertising with their model, Ward and Lambert?s model had to be converted to a pork
response function for comparison. The pork response model is specified as
(2) lnP
kt
= ?
0
+ ?
1
lnQ
bt
+
?
2
lnQ
kt
+ ?
3
lnQ
pt
+ ?
4
lnI
t
+ ?
5
T
1t
+ ?
6
S
1t
+ ?
7
S
2t
+ ?
8
S
3t
+ ?
1
ln[1 + exp(?/A
t
)] + ?
2
ln[1 + exp(?/A
t1
)] + ?
t?
where P
kt
is the real price of pork, A
t
and A
t1
are the current and oneperiod lagged per
capita generic pork expenditures, and all other variables are the same as the beef model.
T
1
starts at 1 in 1970:1 and increases in units of one until 1993:4. T
2
was not used in the
pork model.
Brester and Schroeder studied the effects of generic and branded advertising on
the consumer demand for beef, pork, and poultry. A different model, the Rotterdam
demand system with scaling, was used to estimate advertising effects. The advertising
variables were in the form of stock of investments and were obtained with a procedure
proposed by Cox, which was supposed to account for advertising spillover effects better.
The Rotterdam system, with scaling, that Brester and Schroeder used was
nonlinear in parameters. This would have made Coulibaly and Brorsen?s
misspecification tests rather challenging, thus the model was specified in linear form
without scaling for the tests. The linear model yielded similar results to the nonlinear
19
model, so the change did not affect the results a great deal. The Rotterdam model that
Coulibaly and Brorsen used for the misspecification tests was specified as
(3) w
i
d lnq
i
= ?
i
d lnQ + ?
j
?
ij
d lnp
j
+ ?
j
?
ij
d lnA
j
+ ?
j
?
3
m=1
?
ijm
d lnA
jm
+ ?
3
k=1
?
ik
D
k
+ e
i
where w
i
is the budget share of the i
th
good, q
i
is per capita consumption of good i, p
j
is
the nominal price of good j, A
j
is the real advertising expenditures on good j, d lnQ =
?
i
w
i
d lnq
i
is the Divisia volume index, A
jm
is the mperiod lagged advertising
expenditures, the D
k
?s are quarterly dummy variables, and e
i
is the error term.
Coulibaly and Brorsen used both generic and branded advertising variables in the
model for misspecification tests. Because Brester and Schroeder only included lagged
generic advertising expenditures with both generic and branded advertising expenditures
in the equation, Coulibaly and Brorsen did the same.
Coulibaly and Brorsen attempted estimating, confirming, and performing
misspecification testing on both the Ward and Lambert and the Rotterdam models. They
wanted to determine whether it was different data, different variables, or different
functional forms that caused the contradictory conclusions between the two studies.
To estimate Ward and Lambert?s model, Coulibaly and Brorsen used price,
quantity, and income data from Brester and Schroeder?s data set because they only
obtained the checkoff expenditures and feeder steer ratio from Ward and Lambert. They
estimated the model by OLS holding the checkoff coefficient (?) constant (the value
being the one for which the sum of squared errors was minimized). Next, Coulibaly and
Brorsen estimated the model using data from 19701993 to detect how different sample
periods affected the results. They obtained extra feeder steer ratio data from the USDA?s
20
1990 cattle slaughter data because the sample period for Ward and Lambert?s model only
went through 1992. Finally, the misspecification test proposed by McGuirk et al. was
used to find any problems with the model.
Coulibaly and Brorsen were able to confirm Ward and Lambert?s results. The
only differences in estimates came from income and the feeder steer ratio. Coulibaly and
Brorsen also found the responses from the checkoff program to be approximately the
same, only differing slightly. The joint misspecification test for the beef model exhibited
no problems, although the individual tests showed that the functional form of the model
was misspecified. Furthermore, the tests for the pork model showed the major problem
to be autocorrelation, which generally suggests a problem with the functional form of the
model.
Coulibaly and Brorsen then estimated the linear Rotterdam model, the alternative
for the Brester and Schroeder nonlinear model. They were able to use the exact sample
period from 1970:1 to 1993:4 for the estimation. They added 100 to all observations of
advertising (zero and nonzero expenditures) because a zero advertising expenditure
would create problems in the model due to the logarithms of the parameters.
Misspecification tests proposed by McGuirk et al. were used to test for problems.
After misspecification tests, the Rotterdam model was found to be severely
misspecified. The only assumptions that held up in the model were the homoskedastic
and independent error assumptions. Coulibaly and Brorsen then included women labor
force participation and cholesterol information index as extra variables for respecification
of the model. From previous studies, it was found that increases of women in the U.S.
21
labor force (McGuirk et al., 1995) and health information in the U.S. (McGuirk et al.,
1995; Kinnucan et al., 1997) has caused significant structural changes to meat demand.
The inclusion of the extra variables to the original model did not cure the
misspecification problem, so an alternate Rotterdam model was developed and tested for
misspecification. Initially, the extra variables were not included in the alternate model.
The joint test indicated that conditional mean and variances were misspecified (possibly
caused by nonnormality, heteroskedasticity, parameter stability, or functional form).
When they included the extra variables, women in the U.S. labor force and health
information in the U.S., and tested for misspecification, more of the underlying
assumptions held. The only problems found from the tests were unstable variances and
covariances. The instability was possibly due to the fact that the advertising varied
erratically over time.
In the alternate Roterdam model with the extra variables, most of Coulibaly and
Brorsen?s parameter estimates were statistically significant from zero, although some of
the advertising coefficients in the beef and pork models were negative. They found that
the advertising elasticities were insignificant, but were, at least, positive.
Coulibaly and Brorsen found that the major cause of the contradictory
conclusions between the two studies was due to the fact that Ward and Lambert
transformed the advertising variable. Because of the transformation, Ward and
Lambert?s model yielded very high advertising elasticities. When Coulibaly and Brorsen
used more recent data with Ward and Lambert?s model, the advertising coefficients for
beef turned negative. Also, when they used Brester and Schroeder?s data with Ward and
Lambert?s model, the results for advertising became insignificant.
22
The overall conclusion that Ward and Lambert?s model was fragile was not
changed. Both Ward and Lambert?s and Brester and Schroeder?s models were
misspecified. Furthermore, after correctly respecifying Brester and Schroeder?s
Rotterdam model, Coulibaly and Brorsen found no differences in the results.
23
III. MURRAY et al. ESTIMATION PROCEDURES
To measure the net benefits to producers of upland cotton from the Cotton
Program, Murray et al. carried out several tasks. First, a conceptual model of the cotton
market was specified. Next, parameters for the model were estimated. Then, demand
response (elasicities) to promotion and research were calculated. Finally, a simulation of
the cotton market, minus the Program expenditures, and a cost/ benefit analysis were
completed.
After careful consideration, Murray et al. adopted the following conceptual model
for the milllevel demand for domestic cotton:
(4) Q
d
fd
= D
fd
(P
cd
, P
cf
, A
g
, A
b
, A
f
, R
t
, W
r
, W
t
, Z
r
)
where Q
d
fd
is the quantity demanded (d) for U.S. upland cotton at the farm level (f), P
cd
is
the domestic mill price of cotton, P
cf
is foreign cotton fiber price, A
g
is the generic
promotion expenditures, A
b
is branded advertising for cotton, A
f
is advertising for man
made fibers, R
t
is nonagricultural research expenditures, W
r
is supply factors in the retail
market, W
t
is supply factors in the textile market, and Z
r
is demand factors in the retail
market.
With the conceptual model completed, Murray et al. began considering the
appropriate variables to include in the model for estimation of parameters. They
collected monthly data (ranging from January 1986 to December 2000) from the USDA,
the National Cotton Council, Cotton Inc., the U.S. Census Bureau, the St. Louis Federal
24
Reserve Bank, and the U.S. Bureau of Labor Statistics. A total of 180 observations were
gathered. They gathered data for the quantity of raw cotton consumed by domestic mills
from various issues of the USDA?s Cotton and Wool Outlook. The raw fiber equivalent
prices of cotton, polyester, and rayon and the foreign cotton price (A Index) were
obtained from the National Cotton Council (2001) website. Because the model was
estimated using per capita information, U.S. population data was obtained from the U.S.
Census Bureau (2001). The real wage rate in a U.S. textile manufacturing industry and
the U.S. energy cost index were obtained from the U.S. Bureau of Labor Statistics (BLS,
2001). Data for income were obtained from monthly data on total personal income for
the U.S. taken from the St. Louis Federal Reserve Bank?s FRED database on their
website (FRED, 2001). Foreign gross domestic product (GDP) was proxied by GDP for
Organization for Economic Cooperation and Development (OECD) countries after
subtracting the U.S. GDP from the total. These data were obtained from various issues of
Quarterly National Accounts of OECD Countries. The data was quarterly and had to be
converted to monthly data by using the EXPAND procedure by SAS statistical software.
The seasonally adjusted promotional and nonagricultural research expenditures were
obtained from Cotton Incorporated. All of the variables were deflated by the Consumer
Price Index (CPI) where 19821984=100. CPI data was obtained from U.S. Bureau of
Labor Statistics (2001).
One major concern for the researchers was the timing in which promotion and
research affected the domestic milllevel demand of cotton. They explored the possibility
that the impact of promotion and research did not affect the consumption of cotton
contemporaneously, i.e., research and promotion would have longterm rather than
25
shortterm effects on cotton consumption. For that reason, a distributed lag model, where
the effects of promotion and research were distributed over a certain period of months,
had to be developed. If the model did not allow for the proper amount of lag time, the
estimates would be biased because of omitted variables. Conversely, if the model
allowed for too much lag time, the estimates would be inefficient due to over
specification of the model. They required a lagged model that was finite in nature
because an infinite lagged model would allow the coefficient of the dependent variable to
be unstable. Thus, they decided on an Almon distributed lag model because of its
flexibility and finite nature. After deciding on the Almon model, they performed a grid
search to study the elasticities, Akaike Information Criteria (AIC), SchwartzBayesian
Criteria (SBC), and the adjusted R
2
of several different distributed lag models to decide
on the best one. They found that a threemonth lag on research, no lags on promotion,
and no lags on cotton price would be sufficient for their estimation purposes. In addition
to the research lags, monthly dummy variables were included to account for the
seasonality of the cotton data.
Murray et al.?s econometric demand model for the domestic mill use of upland
cotton was specified as
(5) Milluse
t
= ?
0
+ ?
1
pcotton
t
+ ?
2
ppoly
t
+ ?
3
prayon
t
+ ?
4
dtexw
t
+ ?
5
wpcot
t
+ ?
6
deci
t
+ ?
7
dpi
t
+ ?
8
fgdp
t
+ ?
9
sagprom
t
+ ?
10
sagnares
t
+ ?
11
sagnares
t1
+
?
12
sagnares
t2
+ ?
13
sagnares
t3
+ ?
14
M
1
+ ?
15
M
2
+ ?
16
M
3
+ ?
17
M
4
+
?
18
M
5
+ ?
19
M
6
+ ?
20
M
7
+ ?
21
M
8
+ ?
22
M
9
+ ?
23
M
10
+ ?
24
M
11
+ ?
t
where Milluse
t
is the U.S. per capita raw cotton used by mills (pounds per person),
pcotton
t
is the real U.S. raw fiber equivalent price of cotton (cents per pound), ppoly
t
26
is the real U.S. raw fiber equivalent price of polyester (cents per pound), prayon
t
is the
real U.S. raw fiber equivalent price of rayon (cents per pound), dtexw
t
is the real domestic
wage rate in the U.S. textile manufacturing industry (dollars per hour), wpcot
t
is the real
A Index of the world cotton price (cents per pound), deci
t
is the U.S. real energy cost
index (19821984=100), dpi
t
is the U.S. per capita real disposable income ($1,000?s per
person), fgdp
t
is the real GDP of OECD countries, excluding the U.S. (billions of dollars),
sagprom
t
is the seasonally adjusted Cotton Inc. real promotional expenditures (dollar
amounts), sagnares
t
, sagnares
t1
, sagnares
t2
, and sagnares
t3
are the current and lagged
seasonally adjusted Cotton Inc. real nonagricultural research expenditures (dollar
amounts), M
it
are monthly dummy variables (M
i
=1 for the i
th
month, 0 otherwise) for
i=1,?,11 where December is the reference month with its effect represented by the
intercept, and ?
t
is the error term.
With the formulation of the variables into an econometric demand model, linear
regression analysis was the next step taken by Murray et al. The exact statistical software
used by the researchers was unknown.
Murray et al. estimated the model with Ordinary Least Squares (OLS), OLS with
correction for firstorder autocorrelation, and TwoStage Least Squares (2SLS) with
correction for firstorder autocorrelation. The three models showed exceptional
similarities. All three models displayed a stable relationship between research and
promotion and mill consumption. All models showed the promotion elasticity to be
approximately 0.02 implying that a 10 percent increase in promotion expenditures would
lead to a 0.2 percent increase in cotton demand at the mill level, ceteris paribus. The long
run elasticity estimates of mill consumption with respect to research (the summation of
27
the current and lagged effects) were 0.33 (model 1), 0.31 (model 2), and 0.35 (model 3).
The 2SLS model (model 3) indicated that a 10 percent increase in nonagricultural
research expenditures would directly lead to a 3.5 percent increase in cotton demand,
ceteris paribus.
Because of the endogenous effects of the price of cotton, twostage least squares
(2SLS) was the preferred method for estimation by all researchers. A procedure
developed by Hatanaka was implemented with the 2SLS method because firstorder
autocorrelation was detected in the OLS model. The Hatanaka procedure involves two
steps. The method requires that one must; first, regress all endogenous variables on all
predetermined and lagged predetermined models of the system to get a consistent
estimate of rho. Then, use a quasidifferencing operator (1rho*L, where L is a lagged
operator) to transform the model into a form where the error term is uncorrelated. Next,
regress each of the quasidifferenced endogenous variables (w
it
=z
it
rho*z
it1
) on all of the
predetermined and lagged predetermined variables of the model and use those values as
instruments for the quasidifferenced endogenous variables. Finally, use the predicted
values and quasidifferencing predetermined variables as instruments in instrumental
variable estimation of the parameters.
?Overall, the results seem quite reasonable and suggest a strong and significant
impact of promotion and research on mill consumption of cotton? (Murray et al., p.511).
Mill consumption of cotton exhibited high seasonality supported by the extremely
significant monthly dummy variables. The ownprice elasticity of demand for cotton was
0.4, closely resembling estimates obtained from previous research [Wohlgenant (1986),
Lowenstein (1952), Ding and Kinnucan (1996), and Waugh (1964) estimated elasticities
28
of approximately ?0.3]. The estimate was smaller than Shui, Behgin, and Wholgenant?s
estimate of ?0.6. Nevertheless, as discussed earlier, the elasticity estimate differed from
Capps et al. Capps et al. determined that the ownprice elasticity for cotton was 0.16.
The most significant difference between the Murray et al. study and the Capps et al.
study was that Capps et al. stated that prices affect consumption after a 13month lag.
When Murray et al. included the 13month lag of cotton price along with current price,
they discovered that the lagged price had no statistical significance in the model. On the
other hand, Murray et al. and Capps et al. corroborated in that polyester and cotton were
complements and that rayon and cotton were substitutes. Capps et al. crossprice
elasticity calculations were much larger than those calculated by Murray et al. Murray et
al. calculated crossprice elasticities for polyester and rayon to be ?0.13 and 0.14,
respectively, while Capps et al. crossprice elasticities were ?0.55 and 0.27 for polyester
and rayon. The Murray et al. results verified that the mill consumption of cotton was less
responsive to a price change in polyester or rayon than it was to a change in cotton price.
Murray et al. found that their crossprice elasticity calculations were much more in
accordance with traditional economic theory than was Capps et al.
The textile manufacturing industry wage rate and the U.S. energy costs proved to
have a negative effect on the mill consumption of cotton, as expected. The foreign GDP
had a positive effect on the mill consumption of cotton. The per capita disposable
income had a negative effect, but was also statistically insignificant to the model. They
thought that disposable income could be highly correlated with the textile wage rate
therefore causing the insignificance. The world price of cotton had a highly significant
effect on mill consumption. The higher the world price, the more expensive that it
29
becomes to produce cotton in foreign markets. This causes the prices of cotton imported
into the U.S. to rise and as a result domestic mill consumption is increased.
Murray et al. had originally included some extra variables in their model but had
decided to exclude them on the grounds that they caused a substantial increase in
multicollinearity, which, in turn, led to inconsistent estimates. Two of the variables
omitted were foreign textile wages and the real exchange rate. Foreign textile wages and
the real exchange rate were highly collinear with foreign GDP, causing the increase in
multicollinearity.
In addition, monthly promotion expenditures made by Levi Strauss were initially
included in estimations to represent the effects of branded advertising on mill
consumption. By incorporating this variable into the equation, estimated returns from the
Cotton Program promotion expenditures became larger, but the variable did not improve
the fit of the model, so it was eliminated. Murray et al. found that branded advertising
did not influence the Cotton Program noticeably.
Subsequent to evaluating the model, Murray et al. estimated the model with only
the last five years of data (19962000), which was one of the periods when the checkoff
program was being evaluated for its effectiveness by the Secretary of Agriculture. They
wanted to confirm that the structure of the model did not change in the last five years.
Some coefficients of the model parameters changed slightly, but after implementing the
Chow Test, they failed to reject the null hypothesis that the structure of the model had
changed, therefore the model held its validity.
30
Murray et al. then reestimated the model using the square roots of promotion and
research to check if the linear model that was used sufficiently represented the effects of
promotion and research on mill consumption. After estimation of the square roots of
promotion and research, Murray et al. found that the linear model was sufficient for
determining the effects of promotion and research on the domestic mill demand for
cotton.
Overall, Murray et al. (p.524) concluded that the models ?provide fairly good
fits to the data and generate theoretically reasonable parameter estimates.? Most of the
coefficients had the correct signs and were highly significant. Only a few coefficients
generated the wrong signs, but they proved to be statistically insignificant to the model.
In general, they verified that the U.S. Cotton Research and Promotion Program did
increase the domestic mill demand for cotton, which increased producers? profits
31
IV. DING AND KINNUCAN ESTIMATION PROCEDURES
The major objective of the Ding and Kinnucan study was to determine optimal
allocation rules for a commodity that is traded in international markets but is protected in
the domestic model by deficiency payments. In the process of their research, Ding and
Kinnucan developed an econometric model to estimate advertising elasticities, which was
expected to explain the effects of advertising on the domestic milllevel demand for
cotton.
In order to determine how advertising affects the milllevel demand for cotton,
longrun elasticity estimates for the advertising variable had to be calculated. Before
calculating an advertising elasticity estimate, Ding and Kinnucan first established some
basic guidelines to follow. Their assumptions for the domestic side of the market were as
follows: there is competitive market clearing and a single price, quantity demanded is a
decreasing function of price and an increasing function of promotion, production is an
increasing function of the supplyinducing price, and the promoting country (in this case,
the U.S.) has sufficient market presence to affect price.
Ding and Kinnucan?s initial equilibrium model was
(6) Q
d
= f(P, A
d
) (domestic demand),
(7) Q
x
= g(P, A
x
) (export demand),
(8) Q
s
= h(P
s
) (domestic supply),
(9) Q
s
= Q
d
+ Q
x
(equilibrium quantity), and
(10) P
s
= ? P
T
+ (1  ?)P (supplyinducing price),
32
where Q
d
is the quantity demanded in the domestic market; Q
x
is the quantity demanded
in the export market; Q
s
is the promoting country?s total supply; P is the market price of
the promoted commodity; P
T
is the target price; P
s
is the supplyinducing price; A
d
is
advertising in the domestic market; and A
x
is advertising in the export market.
Quarterly data ranging from the first quarter of 1976 to the last quarter of 1993
(72 observations) were collected for the model from various sources. The rawfiber
equivalent prices and quantities demanded for cotton, rayon, and polyester were collected
from tables 15, 26, 7, 23, and 27 of the USDA?s Cotton and Wool: Situation and Outlook
Report. They adjusted the quantity data for polyester by its share in the noncellulosic
category (Ding). This data was obtained from Table 5 of World Textile Trade and
Production Trend in Textile Outlook International, January 1995. Prices for imported
textiles were obtained from table 3 of the U.S. Department of Commerce?s Survey of
Current Business. Domestic advertising data, which pertained to the expenditures made
by Cotton Inc., were collected from Leading National Advertisers (AD $ Summary). For
per capita information, population data were collected from tables b59 and b22 from
various issues of the Economic Report of the President (Council of Economic Advisors).
The Consumer Price Index data were also obtained from tables b59 and b22 of issues of
the Economic Report to the President.
Ding and Kinnucan then specified an econometric demand model to estimate the
advertising elasticity. They specified the basic model as
(11) ln Q
dt
= a
0
+ a
1
lnP
t4
+ a
2
lnP
R
t4
+ a
3
lnP
P
t4
+ a
4
lnP
I
t
+ a
5
ln(E
t
/P*
t
) + a
6
lnA
dt2
+ a
7
lnQ
dt1
+ ?
3
j=1
b
j
D
jt
+ u
t
33
where t=5,6,?,72 (the first four observations were dropped due to the lag specification);
Q
dt
is per capita mill consumption of cotton in period t, P
t4
is the domestic farm price of
cotton in period t4, P
R
t4
is the wholesale price of rayon in period t4, P
P
t4
is the
wholesale price of polyester in period t4, P
I
t
is the wholesale price of imported textiles in
period t, E
t
is the per capita total expenditures on cotton, rayon, polyester, and imported
textiles in period t, P*
t
is the Stone?s Price Index (lnP*
t
= w
1
lnP
t
+ w
2
lnP
R
t
+ w
3
lnP
P
t
+
w
4
lnP
I
t
, where w
j
are expenditure weights such that ?
4
j=1
w
j
= 1), A
dt2
is the total
expenditures on cotton promotion in the domestic market in period t2, Q
dt1
is the lagged
dependent variable, D
jt
are quarterly dummy variables where D = 1 in the specified
quarter and zero otherwise, and u
t
is the error term. All the variables were specified in
real terms through deflation by the Consumer Price Index where19821984=100.
Ding and Kinnucan specified the equation with fourquarter lags on the prices of
cotton, rayon, and polyester to account for forward contracts between mills and fiber
suppliers. Imported textile price and total expenditures were specified
contemporaneously. The advertising variable was lagged two quarters because of
preliminary testing that indicated a delayed advertising response. In addition, Ding and
Kinnucan specified the equation as a doublelog to allow advertising to display
diminishing marginal returns.
Ding and Kinnucan performed a preliminary test to determine if there was any
correlation in the advertising variable (A
d
) and equation (11)?s error term. They used the
Hausman test for this procedure because the sample size was larger than 50 (72
observations). The procedure is completed by way of instrumental variable estimation
34
where a one and two period lag is placed on the advertising variable and regressed with
the dummy variables (to account for the seasonality of advertising). The first stage in the
regression is specified as
(12) ln A
t
= a
0
+ a
1
lnA
t1
+ a
2
lnA
t2
+a
3
D
1
+ a
4
D
2
+ a
5
D
3
+ w
t
where w
t
is the error term. The estimated values for w
t
are kept for the second stage of
regression. The second stage of the regression is the original regression including the
variable w
t
. The second equation is specified as
(13) ln Q
dt
= a
0
+ a
1
lnP
t4
+a
2
lnP
R
t4
+ a
3
P
P
t4
+ a
4
lnP
I
t
+ a
5
ln(E
t
/P*
t
) + a
6
lnA
dt
+ a
7
lnQ
dt1
+ cw
t
where the null hypothesis for the test is
c=0. Ding and Kinnucan found that the
coefficient for w
t
was insignificant (tvalue 0.452) so they failed to reject the null
hypothesis and established that there was no evidence of measurement error in the
advertising variable.
Furthermore, Ding and Kinnucan tested whether or not advertising played the role
of a taste shifter that affected the marginal utility. They tested whether advertising
rotated the demand curve by including an interaction term and specifying the ownprice
coefficient in (11) as a linear function of advertising. The ownprice coefficient was
specified as:
(14) a
1
= c
1
+ c
2
lnA
dt2
They substituted this interaction term into the original equation developing the equation
35
(15) ln Q
dt
= c
0
+ c
1
lnP
t4
+ c
2
(
lnA
dt2
* lnP
t4
) + c
3
lnP
R
t4
+ c
4
lnP
P
t4
+ c
5
lnP
I
t
+ c
6
ln(E
t
/P*
t
) + c
7
lnA
dt2
+ c
8
lnQ
dt1
+ ?
3
j=1
d
j
D
jt
+ v
t
where c
2
was the interaction term between the ownprice of cotton and advertising.
They formed the following hypothesis to test the validity of the structural change
in the model:
(16a) H
N
: c
2
= 0
(16b) H
A
: c
2
? 0
where a ttest could be implemented for the test.
Ding and Kinnucan found from the ttest that the model without the interaction
term was appropriate for estimation because the values from regression containing the
interaction term were insignificant and close to zero. The tvalue for the structural
change was 1.367, not large enough to reject (16a) at the 5% level. They concluded that
advertising did not cause a structural change to the price elasticity of demand because of
changes in advertising expenditures so they used equation (11) for the regression.
Ding and Kinnucan then tested the model for first and fourthorder
autocorrelation with the Durbin mtest (one of the preferred tests suitable for models with
lagged dependent variables). From the test statistic, they found no firstorder
autocorrelation but fourthorder autocorrelation was present. Corrections for fourthorder
autocorrelation were made using the CochraneOrcutt algorithm in Generalized Least
Squares. This was accomplished by obtaining the residuals from the OLS regression
first. Next, the residuals were regressed on themselves lagged four periods and a
36
constant. Finally, the regression is transformed and adjusted by the estimate for the
autocorrelation coefficient.
Ding and Kinnucan estimated equation (11) with (Model A) and without (Model
B) the quarterly dummy variables to test whether or not the milllevel demand of cotton
was seasonal. They obtained reasonable results from GLS estimation. Both of their
models exhibited good explanatory power with an R
2
of approximately 0.95. Most of the
parameter coefficients were significant and exhibited the correctly hypothesized signs
(based on prior economic theory). They found that stability conditions were satisfied
with the lagged dependent variable showing high significance to the model (tratio of
8.7). They estimated longrun ownprice elasticities of 0.30 for Model A and 0.29 for
Model B. These elasticities were calculated by dividing the estimate of the cotton price
coefficient by one minus the estimate for the lagged dependent variable coefficient. With
their longrun ownprice elasticities corresponding to the results of previous studies, Ding
and Kinnucan suggested that the derived demand for cotton was inelastic and stable over
time.
The estimated elasticities for the textile price and total expenditures were positive
suggesting that increases in prices of imported textiles or consumer income may increase
the derived demand for U.S. cotton fiber. Furthermore, they concluded that polyester and
cotton are complements because of the negative estimated coefficient of polyester. This
was consistent with previous findings, which made sense because the two fabrics are
often used together in mills for manufacturing. Rayon was found to be a substitute for
cotton because of the positive estimated coefficient.
37
The major issue to Ding and Kinnucan?s study was the longrun advertising
elasticity. They found elasticities of 0.062 (Model A) and 0.066 (Model B). They
conducted a onetailed ttest and found that the advertising elasticity was significant at
the 10% level in Model A and at the 0.005% level in Model B.
Because multicollinearity was thought to be present between cotton price and the
quarterly dummy variables in Model A, Ding and Kinnucan performed an Ftest between
the full model (with dummy variables) and the reduced model (without dummy
variables). They obtained an Fvalue of 2.08, which was not large enough to reject the
null hypothesis of the dummy variables together equaling zero. Because of the Ftest
value and the higher tratios, Model B was the preferred model of Ding and Kinnucan.
They concluded from their preferred model (Model B) that the advertising
elasticity of 0.066 meant that a 10 percent increase in advertising expenditures would
lead to a 0.7 percent increase in the milllevel demand for cotton, ceteris paribus.
Furthermore, advertising was found to be a simple shifter and not a structural shifter of
the demand for cotton. Their results were consistent because they were comparable with
the results of previous researchers. Results for Ding and Kinnucan?s Models A and B
are reported in Table 5.
38
V. DUPLICATION OF MURRAY et al. REGRESSION RESULTS
Before any duplication procedures could be started, the raw data supplied in the
Murray et al. report to the Cotton Board had to be transformed to exactly match the
transformations used on the variables for earlier regression analyses. Variable
transformations for the duplication are documented in Table 1.
Transformations were completed fairly easily due to the indepth explanations
given by Murray et al. in their report. Most variables merely needed to be deflated by
CPI to adjust for inflation. The only transformation that presented any sort of problem
was disposable income (dpi
t
). Murray et al. regression estimates for the disposable
income variable were much larger than any estimates that the attempted transformed
variables yielded after regression analyses. Murray et al. did not clearly explain how
they devised their numbers and, as a result, transformation was practically impossible.
However, the variable did not create much of a dilemma for the duplication because
disposable income was found to be insignificant in all three models of both studies. After
transformation of all variables, SAS was utilized for regression analyses.
The first regression results duplicated from the report by Murray et al. was from
their Ordinary Least Squares (OLS) model. The first three observations were dropped
because of the lag specification of nonagricultural research expenditures; therefore 177
observations were used instead of 180.
39
After regression, all parameter estimates, tvalues, and standard errors matched
the Murray et al. results nicely except for the parameter estimate for disposable income
(dpi
t
). This estimate proved to be quite different from the Murray et al. estimate
(probably due to a different transformation of the variable). Three different variations of
the variable were used in the regressions but none of them yielded a parameter estimate
that even came close to the Murray et al. parameter estimate. Their estimate for
disposable income was ?15,866.9, which severely contradicted the duplicated estimate of
?0.0000256. This problem brought up questions about possible errors made by the
authors of the original report. Once more, this did not create a major threat to the
duplication because the variable was insignificant with a tvalue of ?0.37 (pvalue
0.7090) in the duplicated model and ?0.23 in the Murray et al. model.
All the signs of the coefficients yielded the correct positive or negative signs (in
accordance with economic theory). The ownprice elasticity for cotton, the seasonally
adjusted promotion elasticity, and the seasonally adjusted nonagricultural research
elasticity (the sum of the current and lagged elasticities) were all calculated to be
approximately the same as the Murray et al. estimated elasticitites. Furthermore, the
duplicated OLS regression results showed signs of firstorder autocorrelation just as did
the Murray et al. results with Durbin Watson statistics of 1.4790 (duplicated) and 1.5199
(Murray et al.).
With only slight differences between the Murray et al. regression results and the
duplicated regression results, the Murray et al. results were confirmed by the duplication.
The differences were probably due to different statistical software packages used and the
unknown steps taken to transform the disposable income variable.
40
The next regression results duplicated from the Murray et al. report were from
their GLS model (correction for firstorder autocorrelation). Again, SAS was utilized to
carry out regression analysis. The first three observations were dropped because of the
lag specification of the seasonally adjusted nonagricultural research expenditures (177
observations). Correction for firstorder autocorrelation was done in SAS by
implementing the AUTOREG procedure with the YuleWalker algorithm. The Yule
Walker estimates coincide with Prais and Winsten estimates for rho.
Parameter estimates, tvalues, the estimate for rho, and standard errors were
approximately the same as the Murray et al. regression estimates. Again, the duplicated
disposable income (dpi
t
) parameter estimate exhibited significant differentiation from the
Murray et al. estimate. Murray et al. came up with an estimate of 27,662.2 and the
duplication yielded an estimate of ?0.000032. Due to the insignificance of the variable
(tvalue of ?0.44), there was no major reason for concern.
All signs of parameter estimates were the same as before, in accordance with
economic theory. Furthermore, the ownprice elasticity for cotton, the seasonally
adjusted promotion elasticity, and the nonagricultural research elasticity (the sum of the
current and lagged elasticities) were all calculated to be approximately the same as the
Murray et al. estimated elasticitites. The firstorder autocorrelation problem seemed to
be corrected with the AUTOREG procedure in SAS (Durbin Watson statistics were
2.0671 for the duplication and 2.1243 for Murray et al.).
As a result of only yielding slight differentiation between the two studies, the
GLS results of Murray et al. were confirmed by duplication. Yet again, the slight
41
differentiation between the two studies was probably due to the different transformations
used on the disposable income variable and differing statistical packages.
For the attempted duplication of the preferred model of Murray et al., TwoStage
Least Squares (2SLS), SAS was used for regression analysis. The first three observations
were dropped due to the lag specification of the seasonally adjusted nonagricultural
research expenditures (177 observations were used). The endogenous variable in the
equation was the price of cotton, thus predicted values of the variable had to be estimated
to continue the 2SLS technique. First, the price of cotton variable was regressed on all
independent variables in the equation and the predicted values were saved for the second
regression. In the second regression, the mill use of cotton variable (dependent) was
regressed on all independent variables and the predicted values of the price of cotton.
The regression was completed without correction for firstorder autocorrelation because
the procedure that Murray et al. (Hatanaka estimator) used was unclear. Unclear
regression techniques were major problems that previous duplication researchers
encountered. The results were not duplicated because of the differences but, the equation
was reestimated and compared with the Murray et al. results.
After the first regression was finished, the model encountered a major problem.
Identification problems of the model became evident due to highly collinear variables,
which caused the parameter estimates to be imprecise. In order to solve the problem and
continue regression analysis, the disposable income and foreign GDP variables were
deleted from the equation and the equation was reestimated. Justification for eliminating
the two collinear variables came from the fact that they were insignificant in all three
Murray et al. models and from the outcome of the variable selection technique (backward
42
elimination) used in SAS. The technique eliminated both disposable income and foreign
GDP from the equation.
After the equation was reestimated without disposable income or foreign GDP,
the results appeared reasonable. The model exhibited good explanatory power with an R
2
of 0.8363. All the signs of the parameters were in accordance with economic theory and
the Murray et al. results. Most all variables exhibited significant tvalues. All of the
monthly dummy variables were found to be highly significant to the regression. The
equation still exhibited problems with autocorrelation with a Durbin Watson statistic of
1.377. Elasticity estimates for seasonally adjusted promotion and nonagricultural
research and the ownprice of cotton were similar to the Murray et al. estimates.
Seasonally adjusted promotion exhibited an elasticity of 0.026. The sum of the current
and lagged elasticity estimates for seasonally adjusted nonagricultural research was
0.346. Lastly, the elasticity estimate for the ownprice of cotton was 0.309. In general,
the 2SLS reestimation exhibited highly similar results when compared with the Murray
et al. results, despite the differences in the specification of the two equations.
Overall, despite the differences in the 2SLS equation, the main argument of the
researchers that promotion expands the demand for upland cotton was confirmed by the
duplications of the three models. All duplicated regression results are documented in
Table 2.
43
VI. ADDITIONAL TESTS AND REGRESSIONS PERFORMED ON THE MURRAY
et al. MODEL
A series of tests were performed on Murray et al.?s Ordinary Least Squares
model. Model adequacy tests, a test for any influencing observations or outliers, and a
correlation test for multicollinearity were performed with SAS.
The following model adequacy tests for checking whether or not the underlying
assumptions of the linear regression model held were performed with SAS by
constructing residual plots: normality, linearity, independent errors (autocorrelation), and
constant variance (heteroschedasticity). The residual plot for testing normality was
constructed by plotting the normal quartile against the residuals. The plots for testing the
constant variance and linearity assumption were both constructed by plotting the
residuals against the predicted values. Finally, the plot for testing the independent errors
assumption was constructed by plotting the residuals against time (observations).
The residual plots for testing normality, constant variance, and the linearity
assumptions showed that the assumptions were not violated. However, after the test for
the independent errors assumption, a pattern was detected in the residuals. The pattern
showed signs of positive autocorrelation supporting Murray et al.?s previous findings.
Several residual plots testing for influencing observations or outliers were
constructed. A leverage plot, the Cook?s Distance Measure Plot, and the DFFITS plot
were all constructed by plotting each one by the observations. After observing the plots,
44
there were a small number of outliers but, with 180 observations, none were considered
to have any influence on the regression.
Because of the fact that mulitcollinearity was thought to be present in the Murray
et al. OLS model, a Pearson?s correlation test was performed in SAS with the CORR
procedure. The disposable income variable (dpi
t
) was highly collinear with the foreign
GDP (fgdp
t
) with a correlation coefficient of 0.97. This may have led to the
insignificance of the disposable income variable in all three original models. In addition,
the A Index of the world cotton price was collinear with the domestic price of cotton, as
expected, with a correlation coefficient of 0.92.
After performing a sequence of different model tests, a few variations to the
original Murray et al. econometric demand model were completed with SAS. All
variations were regressed as OLS without corrections for firstorder autocorrelation and
compared to the original Murray et al. OLS regression results.
For the first variation of the Murray et al. model, unadjusted promotion and
nonagricultural research expenditure data were used instead of seasonally adjusted data.
Because of the inclusion of the monthly dummy variables into the original model, the use
of unadjusted promotion and research data were presumed to make the model less biased.
The reason for using the seasonally adjusted data by the original researchers was unclear.
After regressing model (5) with unadjusted promotion and nonagricultural
research data, the R
2
Adj
decreased in value, the Fvalue decreased, and the sum of squared
errors increased. Furthermore, the estimated coefficient for promotion became negative
and insignificant thus suggesting that promotion is immaterial to increasing milllevel
45
consumption. All other signs were the same as in the original OLS model. The longrun
elasticity estimates for promotion, the ownprice of cotton, and the sum of the current and
lagged effects of research were ?0.007, 0.133, and 0.217, respectively. In addition,
autocorrelation was still present (DurbinWatson 1.510). This variation certainly did
nothing to improve the fit of the model when compared to the original. This suggested
that the use of seasonally adjusted data was fitting for improvement of the model and that
the inferences made by the researchers are conditional on whether or not the promotion
data is seasonally adjusted.
Next, the square roots of promotion and nonagricultural research expenditures
were used with the original model (5) to try and observe diminishing marginal returns.
The linear model specification of the original model violates the law of diminishing
returns.
The R
2
Adj
and the Fvalue of the model
decreased slightly and the sum of squared
errors increased slightly. Most of the signs of the coefficient were the same except for
the first nonagricultural research lag becoming negative. The significance of promotion
and nonagricultural research expenditures increased slightly. Longrun elasticity
estimates for both advertising and research were calculated from the equation: q = a +
bA
1/2
+ cR
1/2
, where E
q,A
=? bA
1/2
/q and E
q,R
= ? cR
1/2
/q. These elasticities were evaluated
at data means. In the equation, the values used for q and A are sample means for both
promotion and research. The longrun elasticity estimate for promotion was 0.027. The
longrun elasticity estimate for the sum of the current and lagged effects of
nonagricultural research was 0.303. In addition, the longrun elasticity estimate for the
46
ownprice of cotton was ?0.170. Furthermore, autocorrelation was still present (Durbin
Watson 1.440).
The third variation consisted of implementing a lagged dependent variable, to
account for any advertising carryover effects, while eliminating the nonagricultural
research lags. The nonagricultural research expenditure variable was expressed
contemporaneously. Only the first observation was dropped allowing the regression to
contain 179 observations.
All parameter estimates exhibited correctly hypothesized signs after OLS was
completed. The R
2
Adj
of the model improved and the sum of squared errors decreased
compared to the original specification of the model. The lagged dependent variable
coefficient exhibited high significance to the model with a tvalue of 4.60 (pvalue
<.0001). The longrun elasticity estimates for promotion and the ownprice of cotton
were 0.026 and ?0.136, respectively. The longrun elasticity estimate for nonagricultural
research was 0.245. The elasticity estimates were calculated by, first, calculating the
shortrun estimates and then, dividing the shortrun estimate by one minus the coefficient
for the lagged dependent variable.
A different tactic was implemented to test for firstorder autocorrelation in the
lagged dependent variable model. The Durbin h test statistic was used instead of the
Durbin Watson because it is the preferred test for models with lagged dependent
variables. The following hypothesis was formed to determine if autocorrelation was
present:
47
(17a) H
N
: No autocorrelation
(17b) H
A
: Autocorrelation
The Durbin h statistic was ?3.3253 (pvalue 0.0004) so, hypothesis (17a) was rejected
and autocorrelation was thought to be present in the model.
The lagged dependent variable model exhibited good properties of fit; however
the lag structure of the model was still not specified correctly with respect to promotion.
Because of the collinear variables in the model, a variable selection method was
performed with SAS. After applying the variable selection method, backward
elimination, both the dpi and the fgdp variables were eliminated from the model.
Backward elimination is particularly popular because it provides information for the
analysts about the effect of including all the candidate predictors therefore no obvious
predictor will be missed. The procedure consists of starting with the full equation and
successively dropping one variable at a time. The first step is to start with the full
equation with k predictors. Next, drop the predictor that has the smallest partial F
statistic. The smallest F statistic is compared with the preselected F
out
and if the F
statistic is smaller than the F
out
, the predictor is removed from the equation. Next, the
model is fitted for k1 predictors. Then the partial F statistics for the new model are
found and the procedure is repeated. The final step is to stop when the smallest partial F
value is not less than the F
out
value.
Accordingly, after the backward elimination procedure results, the model was
regressed without the two variables (dpi and fgdp). After regression, the R
2
Adj
increased,
supporting the fact that the deletion of the two variables actually improved the model.
48
Furthermore, the Fvalue of the model and the significance of all variables in the model
increased although the elasticity estimates remained approximately the same as the
original Murray et al. estimates. An F test was executed to examine if, together, the two
variables equaled zero. The following hypothesis was developed:
(18a) H
N
: ?
7
=?
8
=0
(18b) H
A
: Full Model
The F value was 0.66708, which was not large enough to reject the null hypothesis
(compared to the critical value of 3.00 at the .05% level).
After all variations to the original model were completed, it was discovered that
the model without dpi and fgdp was the model that provided the best fit for estimation
purposes. However, with the deletion of variables, biasness is sometimes introduced into
an econometric model. In addition, with the unsuccessful attempts at transforming the
disposable income variable exactly as did Murray et al., the model without the two
variables may not be the most appropriate. Furthermore, autocorrelation presents
problems for every model, as expected because of the timeseries data. All additional
regression results are documented in Table 3.
49
Table 1. Variables Used in the Duplication of the Murray et al. Study of Cotton
Promotion, January 1986December 2000
Variable Definition
Per Capita Mill Use
(U.S. domestic mill
use*1,000)(480lbs.)/(U.S.
population*1,000)
Cotton Price Fiber equivalent effective mill price of
cotton/(CPI/100)
Polyester Price Fiber equivalent polyester price/(CPI/100)
Rayon Price Fiber equivalent rayon price/(CPI/100)
Domestic Textile Wages Domestic textile wages/(CPI/100)
A Index of the World Cotton Price Fiber equivalent A Index/(CPI/100)
Energy Cost Index Energy Price Index/(CPI/100)
U.S. Disposable Income [(Disposable income annual
rate*1,000,000,000)/(CPI/100)]/(U.S.
population*1,000)
Foreign Gross Domestic Product OECD GDP annual rate/(CPI/100)
Seasonally Adjusted Promotion CI seasonally adjusted promotional
expenditures/(CPI/100)
Seasonally Adjusted Nonagricultural
Research
CI seasonally adjusted nonagricultural
research expenditures/(CPI/100)
50
Table 2. Duplication
1
of Regression Results for the Domestic Mill Demand
Equation from the Murray et al. Study of Cotton Promotion, January 1986
December 2000
OLS GLS 2SLS Independent
Variable
Murray
et al.
Duplicated
Murray
et al.
Duplicated
2
Murray
et al.
Re
estimation
3
SAGPROM
t
2.04E08
(1.93)
[0.022]
2.06E08
(1.94)
[0.022]
1.57E08
(1.58)
[0.017]
1.60E08
(1.62)
[0.017]
2.12E08
(2.00)
[0.023]
2.36E08
(2.22)
[0.026]
SAGNARES
t
4.90E07
(4.55)
[0.145]
4.50E07
(4.24)
[0.134]
4.68E07
(4.61)
[0.139]
4.41E07
(4.46)
[0.131]
5.12E07
(4.72)
[0.152]
4.77E07
(4.37)
[0.143]
SAGNARES
t1
4.29E08
(0.42)
[0.013]
2.20E08
(0.21)
[0.007]
2.91E08
(0.28)
[0.009]
1.70E08
(0.17)
[0.005]
7.30E08
(0.68)
[0.022]
6.66E08
(0.66)
[0.020]
SAGNARES
t2
2.64E07
(2.67)
[0.078]
2.39E07
(2.44)
[0.071]
2.52E07
(2.62)
[0.075]
2.36E07
(2.52)
[0.070]
2.79E07
(2.75)
[0.083]
2.70E07
(2.79)
[0.080]
SAGNARES
t3
3.21E07
(3.10)
[0.095]
3.20E07
(3.05)
[0.095]
2.97E07
(3.06)
[0.088]
3.01E07
(3.06)
[0.089]
3.16E07
(3.06)
[0.094]
3.47E07
(3.32)
[0.103]
PCOTTON
t
0.00434
(2.52)
[0.165]
0.00430
(2.48)
[0.164]
0.00265
(1.35)
[0.101]
0.00274
(1.42)
[0.104]
0.01089
(3.21)
[0.413]
0.00812
(2.07)
[0.309]
PPOLY
t
0.00434
(2.43)
0.00364
(2.13)
0.00371
(1.64)
0.00325
(1.57)
0.00361
(1.65)
0.00393
(2.28)
PRAYON
t
0.00284
(1.99)
0.00172
(1.48)
0.00205
(1.15)
0.00134
(1.07)
0.00261
(1.50)
0.00215
(1.95)
DTEXWAGE
t
0.19959
(1.67)
0.25961
(2.31)
0.24807
(1.70)
0.28480
(2.15)
0.13169
(0.87)
0.18608
(1.60)
WPCOTTON
t
0.00710
(4.17)
0.00617
(4.03)
0.00548
(2.71)
0.00487
(2.74)
0.01264
(4.08)
0.00912
(3.02)
DECI
t
0.00683
(2.43)
0.00725
(2.58)
0.00713
(2.16)
0.00737
(2.26)
0.00723
(2.14)
0.00548
(2.20)
DPI
t
15866.9
(0.23)
2.56E05
(0.37)
27662.2
(0.37)
3.20E05
(0.44)
67879.7
(0.87)
**
FGDP
t
3.20E05
(0.47)
4.85E05
(0.71)
5.80E05
(0.76)
6.61E05
(0.90)
0.000061
(0.79)
**
CONSTANT
t
1.97714
(2.27)
2.41392
(2.98)
2.26220
(2.17)
2.52440
(2.68)
1.75181
(2.07)
1.93146
(2.49)
M1
t
0.24005
(7.19)
0.24087
(7.17)
0.23910
(8.23)
0.23990
(8.22)
0.23720
(7.57)
0.24205
(7.12)
M2
t
0.15837
(4.74)
0.15783
(4.69)
0.15725
(4.83)
0.15700
(4.82)
0.15811
(4.64)
0.16058
(4.71)
M3
t
0.32105
(9.60)
0.32192
(9.56)
0.32054
(9.59)
0.32130
(9.61)
0.32788
(9.43)
0.32759
(9.49)
51
Table 2. (Continued) Duplication
1
of Regression Results for the Domestic Mill
Demand Equation from the Murray et al. Study of Cotton Promotion, January
1986December 2000
OLS GLS 2SLS Independent
Variable
Murray
et al.
Duplicated
Murray
et al.
Duplicated
2
Murray
et al.
Re
estimation
3
M4
t
0.22697
(6.86)
0.22962
(6.90)
0.22504
(6.72)
0.22680
(6.79)
0.22650
(6.49)
0.23547
(6.83)
M5
t
0.30343
(9.06)
0.29799
(8.76)
0.29989
(8.81)
0.29570
(8.61)
0.32037
(8.99)
0.30318
(8.50)
M6
t
0.25450
(7.54)
0.25667
(7.56)
0.25163
(7.32)
0.25330
(7.39)
0.27420
(7.59)
0.26339
(7.42)
M7
t
0.10311
(3.10)
0.10225
(3.05)
0.09812
(2.91)
0.09790
(2.91)
0.11965
(3.38)
0.11161
(3.18)
M8
t
0.36200
(11.05)
0.36095
(10.95)
0.35981
(10.89)
0.35940
(10.90)
0.36604
(10.74)
0.36321
(10.83)
M9
t
0.28302
(8.54)
0.28392
(8.50)
0.28263
(8.47)
0.28330
(8.49)
0.28398
(8.23)
0.28232
(8.34)
M10
t
0.34242
(10.41)
0.34158
(10.32)
0.34239
(10.69)
0.34190
(10.66)
0.33890
(10.10)
0.33932
(10.09)
M11
t
0.19263
(5.88)
0.19100
(5.80)
0.19252
(6.78)
0.19150
(6.72)
0.18853
(6.15)
0.18969
(5.67)
rho
  0.26845
(3.32)
0.25753
(3.28)
0.19303
(2.62)

N 177 177 177 177 176 177
R
2
0.8453 0.8432 0.8550 0.8546 0.7990 0.8363
Dw 1.5199 1.4790 2.1243 2.0671 2.0318 1.3770
SSE 1.2064 1.2234 1.3020 1.1342 1.2413 1.2771
Notes: Figures in parentheses are absolute values of tratios. Figures in brackets are longrun elasticities.
1
All duplicated models were performed using the statistical software SAS.
2
Duplicated GLS regressions were performed with correction for firstorder autocorrelation using the
YuleWalker Method (Prais and Winsten) in SAS.
3
2SLS results were computed without correction for firstorder autocorrelation (Murray et al. used the
Hatanaka Procedure for the correction); therefore the results are not an exact duplication.
**
Disposable Income and Foreign GDP were eliminated from the regression because they were highly
collinear (correlation coefficient of 0.97) causing identification problems in the model.
52
Table 3. Additional
1
Tests and Regressions Performed on the Domestic Mill
Demand Equation from the Murray et al. Study of Cotton Promotion, January
1986 ? December 2000
Independent
Variable
Murray
et al.
Unadjusted
P&R
2
Square
Root P&R
3
Lagged
Response
4
Exempting
DPI
& FGDP
SAGPROM
t
2.04E08
(1.93)
[0.022]
4.13E09
(0.59)
[0.007]
6.55E05
(2.03)
[0.027]
1.66E08
(1.59)
[0.026]
2.26E08
(2.17)
[0.024]
SAGNARES
t
4.90E07
(4.55)
[0.145]
1.95E07
(3.90)
[0.085]
6.27E04
(4.29)
[0.142]
5.67E07
(6.05)
[0.245]
4.60E07
(4.35)
[0.137]
SAGNARES
t1
4.29E08
(0.42)
[0.013]
5.60E08
(1.14)
[0.024]
1.53E05
(0.11)
[0.003]

5.28E08
(0.53)
[0.016]
SAGNARES
t2
2.64E07
(2.67)
[0.078]
1.30E07
(2.71)
[0.056]
3.05E04
(2.28)
[0.071]

2.65E07
(2.79)
[0.078]
SAGNARES
t3
3.21E07
(3.10)
[0.095]
1.25E07
(2.57)
[0.052]
4.24E04
(2.95)
[0.093]

3.43E07
(3.35)
[0.101]
PCOTTON
t
0.00434
(2.52)
[0.165]
0.00350
(1.86)
[0.133]
0.00446
(2.55)
[0.170]
0.00247
(1.49)
[0.136]
0.00495
(3.13)
[0.188]
PPOLY
t
0.00434
(2.43)
0.00384
(2.08)
0.00317
(1.84)
0.00244
(1.44)
0.00481
(3.51)
PRAYON
t
0.00284
(1.99)
0.00104
(0.84)
0.00146
(1.26)
0.00089
(0.83)
0.00223
(2.06)
DTEXWAGE
t
0.19959
(1.67)
0.43715
(4.06)
0.25732
(2.24)
0.21840
(2.13)
0.22979
(2.22)
WPCOTTON
t
0.00710
(4.17)
0.00561
(3.38)
0.00643
(4.16)
0.00386
(2.53)
0.00677
(4.75)
DECI
t
0.00683
(2.43)
0.00945
(3.15)
0.00742
(2.63)
0.00642
(2.72)
0.00625
(2.72)
DPI
t
15866.9
(0.23)
2.35E05
(0.31)
2.52E05
(0.37)
5.60E05
(0.87)

FGDP
t
3.20E05
(0.47)
3.71E05
(0.48)
4.63E05
(0.68)
7.74E05
(1.24)

CONSTANT
t
1.97714
(2.27)
3.55993
(4.57)
1.93547
(2.20)
2.13910
(3.07)
2.21079
(3.17)
M1
t
0.24005
(7.19)
0.39625
(4.69)
0.24098
(7.14)
0.29860
(8.34)
0.24161
(7.24)
M2
t
0.15837
(4.74)
0.22703
(2.70)
0.15751
(4.66)
0.14550
(4.49)
0.15909
(4.75)
M3
t
0.32105
(9.60)
0.41786
(4.86)
0.32199
(9.52)
0.32640
(10.04)
0.32305
(9.62)
53
Table 3. (Continued) Additional
1
Tests and Regressions Performed on the Domestic
Mill Demand Equation from the Murray et al. Study of Cotton Promotion, January
1986 ? December 2000
Independent
Variable
RTI
Results
Unadjusted
P&R
2
Square
Root P&R
3
Lagged
Response
4
Exempting
DPI & FGDP
M4
t
0.22697
(6.86)
0.46505
(7.73)
0.22940
(6.87)
0.19170
(5.66)
0.22886
(6.91)
M5
t
0.30343
(9.06)
0.49672
(8.32)
0.29843
(8.75)
0.29530
(8.89)
0.29394
(8.76)
M6
t
0.25450
(7.54)
0.45722
(7.53)
0.25749
(7.57)
0.23260
(6.86)
0.25490
(7.58)
M7
t
0.10311
(3.10)
0.27413
(4.59)
0.10280
(3.06)
0.08660
(2.64)
0.10354
(3.11)
M8
t
0.36200
(11.05)
0.53156
(8.78)
0.36586
(11.06)
0.38550
(11.73)
0.36121
(10.98)
M9
t
0.28302
(8.54)
0.47105
(7.57)
0.28547
(8.53)
0.23590
(6.72)
0.28267
(8.49)
M10
t
0.34242
(10.41)
0.52281
(8.51)
0.34284
(10.34)
0.32600
(9.94)
0.34115
(10.33)
M11
t
0.19263
(5.88)
0.37024
(6.28)
0.19366
(5.86)
0.14620
(4.34)
0.19147
(5.83)
MILLLAG
t
   0.31090
(4.60)

N 177 177 177 179 177
R
2
0.8453 0.8172 0.8421 0.8515 0.8418
Dw/Dh 1.5199 1.5100 1.4400 3.3253
**
1.4980
SSE 1.2064 1.4258 1.2317 1.2010 1.2342
Notes: Figures in parentheses are absolute values of tratios. Figures in brackets are longrun elasticities.
1
All additional regressions were performed using the statistical software package SAS.
2
Unadjusted promotion and research data were used instead of seasonally adjusted data.
3
The seasonally adjusted promotion and research variables were the only variables transformed to square
roots; the other variables remained the same as in the original Murray et al. model.
4
Elasticities computed for the Lagged Response model are longrun, i.e., the shortrun elasticity divided by
one minus the coefficient of the lagged dependent variable.
**
The Durbin h Statistic was used with the lagged response model as an autocorrelation test.
54
VII. REPLICATION OF DING AND KINNUCAN REGRESSION RESULTS
The replication was not exact for two reasons: first, the replication was
completed with monthly, rather than quarterly, data and second, the textile price and
expenditure variables had to be proxied. Despite these differences, the overall issue of
whether the inferences (advertising shifts the demand curve for cotton) are robust to
sample updating could still be tested.
Before any attempts at replicating the regression results could be started, the data
for the variables had to be transformed to match Ding and Kinnucan?s specification of
their demand model for explaining the effects of advertising on the mill level demand of
upland cotton. All of the data used for the replication was acquired directly from the
Murray et al. study. The data for the domestic consumption of rayon, polyester, and
imported textiles could not be obtained. This data was needed to form the total
expenditure variable and the Stone?s Price Index from the Ding and Kinnucan model.
Furthermore, the prices of imported textiles could not be obtained. Sources of the data
tables reported in the study were unclear therefore proxies for these variables were used
to continue regression analyses. In place of the total expenditure variable, disposable
income was used. In addition, the A Index of the world cotton price (rawfiber
equivalent) was used in place of imported textile prices. Both variables were also
obtained from the Murray et al. study.
55
The mill use of cotton variable (ln Q
dt
), the raw fiber equivalent prices of cotton
(ln P
t12
), rayon (ln P
R
t12
), and polyester (ln P
P
t12
), the A index of the world cotton price
(ln P
wc
t
), U.S. disposable income (DPI
t
), and the advertising variable (ln A
dt6
) were
transformed by simply taking the natural log of the previous transformations used in the
duplication of the Murray et al. regression results. Transformations for the replication
are documented in Table 4.
The Ding and Kinnucan model was specified with quarterly data, but the
replication was performed using monthly data. The raw fiber equivalent prices of cotton,
rayon, and polyester were specified with 12month lags to compare with the 4quarter
lags used in the Ding and Kinnucan model. The U.S. disposable income and A Index of
the world cotton price variables were specified contemporaneously. The advertising
variable was specified with a 6month lag to compare with the 2quarter lag used in the
Ding and Kinnucan study. Furthermore, for consistency with the Ding and Kinnucan
model, 11 monthly dummy variables were used instead of 3 quarterly dummy variables.
The full model used for replication was specified as
(19) ln Q
dt
= a
0
+ a
1
lnP
t12
+ a
2
lnP
R
t12
+ a
3
P
P
t12
+ a
4
lnP
WC
t
+ a
5
lnDPI
t
+ a
6
lnA
dt6
+ a
7
lnQ
dt1
+ ?
11
j=1
b
j
D
jt
+ u
t
where P
WC
t
is the A index of the world cotton price and DPI
t
is the U.S. disposable
income. All other variables were the same as in the original Ding and Kinnucan model.
To test whether or not advertising rotated the demand curve in the replicated
model, i.e., advertising plays the role of a ?taste shifter?, an interaction term was included
with equation (19) and the model was specified as
56
(20) ln Q
dt
= c
0
+ c
1
lnP
t12
+ c
2
(
lnA
dt6
* lnP
t12
) + c
3
lnP
R
t12
+ c
4
lnP
P
t12
+ c
5
lnP
WC
t
+ c
6
lnDPI
t
+ c
7
lnA
dt6
+ c
8
lnQ
dt1
+ ?
11
j=1
d
j
D
jt
+ v
t
where c
2
was the interaction term between the ownprice of cotton and advertising.
The following hypothesis was formed to test the validity of the structural change
in the replicated model:
(21a) H
N
: c
2
= 0
(21b) H
A
: c
2
? 0
where a ttest was implemented for the test.
After correctly specifying the models for replication and forming hypotheses to
test the validity of the structural change, regression analyses were performed with SAS.
Regressions were run for two different sets with four different model variations (Models
A, B, C, and D) to each set. The first set of regressions was run with unadjusted
advertising data while the second set was run with seasonally adjusted advertising data.
Model A was the full model (with monthly dummy variables) including an interaction
term. Model B was the full model (with monthly dummy variables) without the
interaction term. Model C was the model with an interaction term and without the
monthly dummy variables. Finally, Model D was the model without an interaction term
or the monthly dummy variables. All models were regressed in GLS (the PROC
AUTOREG procedure in SAS utilized the YuleWalker algorithm for correction of
autocorrelation).
57
Initially, the regressions were performed using the unadjusted advertising data.
The first model replicated (Model A) with unadjusted advertising data was the full model
including the interaction term. The first 12 observations were dropped due to the lag
specification of the model (168 observations). The model showed fair explanatory power
with an R
2
of 0.7892. Most variables exhibited the correct positive or negative signs
according to economic theory, except the ownprice coefficient of cotton, which was
positive. The rayon price coefficient (positive) and the polyester price coefficient
(negative) were in accordance with economic theory being that rayon is a substitute and
polyester is a complement to cotton. The lagged dependent variable was highly
significant (tratio of 14.63) implying that advertising has carryover effects to domestic
mill demand of cotton. The monthly dummy variables were also highly significant which
implied that there is substantial seasonality in the data. The interaction term and all other
variables displayed insignificant tratios. The longrun elasticity estimate for advertising
was 0.098 and the longrun elasticity estimate for the ownprice of cotton was ?0.009.
Because of the inclusion of the lagged dependent variable, the longrun elasticity
estimates were calculated by dividing the shortrun estimate
1
by one minus the estimate
for the lagged dependent variable. Because of the insignificance of the advertising
variable from data updating, one could not be confident that advertising shifted the
demand curve, despite the positive demand elasticity.
The next model to be replicated (Model B) with unadjusted advertising data was
the full model without an interaction term (This model could be directly compared to
1
Shortrun elasticities for Models A and C (with an interaction term) in both sets of regressions were
calculated from the following example equation: ln q = a + b lnP + c lnA + d(lnA * lnP), where E
q,A
= c + d
* lnP; and E
q,P
= b + d * lnA, where lnP and lnA are evaluated at data means.
58
Ding and Kinnucan?s Model A). The interaction term was eliminated because of its
insignificant tratio in the previous regression. The first 12 observations were dropped
due to the lag specification of the model (168 observations). The model showed fair
explanatory power with an R
2
of 0.7890, but Ding and Kinnucan?s model had an R
2
of
0.9550. All variables exhibited the correct positive or negative signs. The lagged
dependent variable (tratio of 15.03) and all monthly dummy variables were, again,
highly significant. The high significance of the monthly dummy variables contradicted
Ding and Kinnucan?s results of insignificant dummy variables. The significance of the
other variables increased slightly with the deletion of the interaction term, but the
variables were still insignificant to the regression. The longrun elasticity estimate for
advertising was 0.096. This estimate was somewhat higher than Ding and Kinnucan?s
estimate of 0.062. The estimated longrun elasticity for the ownprice of cotton was ?
0.012. This estimate was extremely lower than Ding and Kinnucan?s estimate of ?0.30.
The longrun elasticity estimates were calculated by dividing the shortrun estimate for
the elasticity by one minus the estimate for the lagged dependent variable.
Because of the insignificance of the advertising variable in Model B, one could
not be certain that advertising shifts the demand for cotton, despite the positive demand
elasticity. Furthermore, the conclusions of Ding and Kinnucan?s model were found to be
conditional on the time period in which the data was tested or on the particular model that
they used which means that the inferences that they made are fragile.
The next model to be replicated (Model C) with unadjusted advertising data was
the model with an interaction term and without the monthly dummy variables. The
model showed very poor explanatory power with an R
2
of 0.3993. Most of the variables
59
exhibited the correct positive or negative signs. The advertising variable became
negative, implying that advertising would decrease mill level demand for cotton, but the
variable was insignificant (tratio of ?1.62). The lagged dependent variable was still
highly significant to the regression (tratio of 6.39). The rayon variable became
significant to the regression (tratio of 2.83). All other variables in the equation increased
in significance from the previous regression, but were still insignificant. The longrun
elasticity estimate for advertising was 0.012 and the estimated elasticity for the ownprice
of cotton was ?0.011 (longrun elasticity estimates were calculated the same as in Model
A). Because of the insignificance of the advertising variable, one could not make
confident inferences as to whether advertising shifts the demand for cotton.
The final model replicated (Model D) with unadjusted promotion data was the
model without the interaction term or the monthly dummy variables (This model could be
directly compared to Ding and Kinnucan?s Model B). The model exhibited very poor
explanatory power with an R
2
of 0.3896 compared to 0.95 in Ding and Kinnucan?s
model. All signs were in accordance with economic theory. The lagged dependent
variable was highly significant (tratio of 6.70). All other variables, except rayon, were
insignificant to the regression. The longrun elasticity estimate for advertising was
0.016. This estimate was much smaller than Ding and Kinnucan?s estimate of 0.066. In
addition, the estimated elasticity for the ownprice of cotton was ?0.011, which was also
much smaller than Ding and Kinnucan?s estimated elasticity of ?0.29.
Once more, because of the insignificance of the advertising variable in Model D,
one could not be certain that advertising shifts the demand for cotton. Furthermore, the
conclusions of Ding and Kinnucan?s model were found to be conditional on the time
60
period in which the data was tested or on the particular model that they used which means
that their inferences are fragile.
After regressions were complete, and Ftest was performed on Model B vs. D to
observe if together the dummy variables equaled zero. The following hypothesis was
constructed for the test:
(22a) H
N
: a
8
=a
9
=,...,a
18
=0
(22b) H
A
: Full model
The Fvalue was 25.41, which was larger than the critical value of 1.645 (at the .05%
level) so the null hypothesis was rejected and the monthly dummy variables were
definitely needed in the equation.
When compared to Ding and Kinnucan?s regression results, the results for Models
B and D with unadjusted data did not show good properties of fit. The major difference
may have been due to the use of the proxied variables in the replicated models and the
use of monthly, rather than quarterly, data. The models with monthly dummy variables
(A and B) contradicted Ding and Kinnucan?s earlier finding for the need to eliminate
these variables because of insignificance to the regression (the dummy variables were all
highly significant in the replication). In fact, it was shown that the model shows severe
seasonality because of the high significance of the monthly dummy variables (also
supported by the Ftest value of 25.41). Overall, with the use of unadjusted advertising
data, the conclusions made by Ding and Kinnucan were found to be conditional on the
time period in which they tested the data. Furthermore, their previous results were
61
negated and their inferences were found to be fragile. All replicated regression results for
unadjusted advertising data are documented in Table 6.
The next set of regressions was performed with seasonally adjusted advertising
data to observe any differences between seasonally adjusted and unadjusted advertising
data. In addition, regressions were compared with the Ding and Kinnucan results. All
models (A, B, C, and D) were specified the same as with the unadjusted advertising data
models.
The first model replicated (Model A) with seasonally adjusted advertising data
was the full model including the interaction term. The first 12 observations were dropped
due to the lag specification of the model (168 observations). The model showed fair
explanatory power with an R
2
of 0.7894. Most variables exhibited the correct positive or
negative signs according to economic theory, except advertising. The advertising
coefficient was negative but was also insignificant. The rayon price coefficient (positive)
and the polyester price coefficient (negative) were in accordance with economic theory
being that rayon is a substitute and polyester is a complement to cotton. The lagged
dependent variable was highly significant (tratio of 14.14) implying that advertising has
carryover effects to domestic mill demand of cotton. The monthly dummy variables
were also highly significant which implied that there is substantial seasonality. The
interaction term and all other variables displayed insignificant tratios. The longrun
elasticity estimate for advertising was 0.085 and the longrun elasticity estimate for the
ownprice of cotton was ?0.014. The longrun elasticity estimates were calculated by
62
dividing the shortrun estimate
2
by one minus the estimate for the lagged dependent
variable. Because of the insignificance of the advertising variable from data updating,
one could not be confident that advertising shifted the demand curve.
The next model to be replicated (Model B) with seasonally adjusted promotion
data was the full model without an interaction term (This model could be directly
compared to Ding and Kinnucan?s Model A). The interaction term was eliminated
because of its insignificant tratio in the previous regression. The first 12 observations
were dropped due to the lag specification of the model (168 observations). The model
showed fair explanatory power with an R
2
of 0.7890, but Ding and Kinnucan?s model had
an R
2
of 0.9550. All variables exhibited the correct positive or negative signs. The
lagged dependent variable (tratio of 15.03) and all monthly dummy variables were,
again, highly significant. The high significance of the monthly dummy variables
contradicted Ding and Kinnucan?s findings of insignificant dummy variables. The
significance of the other variables increased slightly with the deletion of the interaction
term, but the variables were still insignificant to the regression. The longrun elasticity
estimate for advertising was 0.096. This estimate was only slightly higher than Ding and
Kinnucan?s estimate of 0.062. The estimated longrun elasticity for the ownprice of
cotton was ?0.012. This estimate was extremely lower than Ding and Kinnucan?s
estimate of ?0.30. The estimates from adjusted Model B were almost exactly the same as
the unadjusted estimates for Model B (parameter estimates and tratios for dummy
variables differed slightly). The longrun elasticity estimates were calculated by dividing
2
Shortrun elasticities for Models A and C (with an interaction term) in both sets of regressions were
calculated from the following example equation: ln q = a + b lnP + c lnA + d(lnA * lnP), where E
q,A
= c + d
* lnP; and E
q,P
= b + d * lnA, where lnP and lnA are evaluated at data means.
63
the shortrun estimate for the elasticity by one minus the estimate for the lagged
dependent variable.
Because of the insignificance of the advertising variable in Model B, one could
not be certain that advertising shifts the demand for cotton. Furthermore, the conclusions
of Ding and Kinnucan?s model were found to be conditional on the time period in which
the data was tested or on the particular model that they used which means that the
inferences are fragile.
The next model to be replicated (Model C) with seasonally adjusted promotion
data was the model with an interaction term and without the monthly dummy variables.
The model showed very poor explanatory power with an R
2
of 0.4326. Most of the
variables exhibited the correct positive or negative signs. The parameter estimate for the
advertising variable became negative and was also significant (tratio of ?2.47). The
lagged dependent variable was still highly significant to the regression (tratio of 6.17).
Most variables gained significance. The interaction term was significant to the regression
(tvalue of 2.60), which says that advertising does rotate the demand curve for cotton, i.e.,
advertising is a ?taste shifter? in reference to the cotton market. This finding contradicted
Ding and Kinnucan?s earlier results of advertising not causing rotation in the demand
curve with insignificant interaction terms in their regressions. The longrun elasticity
estimate for advertising was 0.070, implying that a 10 percent increase in advertising
would lead to a 0.7 percent increase in mill level consumption of cotton, ceteris paribus.
The estimated elasticity for the ownprice of cotton was 0.015. This calculation
contradicts many past studies with its positive coefficient being that cotton price is
usually inelastic.
64
From the results of Model C, Ding and Kinnucan?s prior results were negated in
the fact that the interaction term in the replicated model was significant. This finding led
us to infer that, with the updated data, advertising may, in fact, play the role of a ?taste
shifter? by rotating the demand curve for cotton. The longrun elasticity estimate for
advertising (because of its significance to the regression) in the replication did support
Ding and Kinnucan?s conclusion that advertising shifted the demand for cotton which
made the inference more robust.
The final model replicated (Model D) with seasonally adjusted promotion data
was the model without the interaction term or the monthly dummy variables (This model
could be directly compared to Ding and Kinnucan?s Model B). The model exhibited very
poor explanatory power with an R
2
of 0.4081 compared to 0.95 in Ding and Kinnucan?s
model. Most signs were in accordance with economic theory, except for the ownprice of
cotton, which was positive (the tratio was 0.05, so the positive coefficient did not hold
validity). The lagged dependent variable was highly significant (tratio of 6.70). Most of
the variables were significant to the regression, except for the ownprice of cotton and
disposable income. The longrun elasticity estimate for advertising was 0.095, implying
that a 10 percent increase in advertising would lead to a 0.95 percent increase in mill
level consumption of cotton, ceteris paribus. This estimate was larger than Ding and
Kinnucan?s estimate of 0.066 and was significantly larger than the estimate that the
unadjusted regression (Model D) yielded. In addition, the estimated elasticity for the
ownprice of cotton was 0.005, which very much contradicted economic theory (with the
positive coefficient) and Ding and Kinnucan?s estimated elasticity of ?0.29. Again, the
65
price of cotton is usually inelastic. Despite the differences in certain results, Ding and
Kinnucan?s results were affirmed.
The significance of the advertising variable increased with the use of the
seasonally adjusted data. This proves that the use of seasonally adjusted data, compared
to using unadjusted data, greatly increases the model?s fit.
After regressions were complete, and Ftest was performed on Model B vs. D to
observe if together the dummy variables equaled zero. The following hypothesis was
constructed for the test:
(23a) H
N
: a
8
=a
9
=,...,a
18
=0
(23b) H
A
: Full model
The Fvalue was 24.28, which was larger than the critical value of 1.645 (at the
.05% level) so the null hypothesis was rejected and the monthly dummy variables were
definitely needed in the equation.
When compared to Ding and Kinnucan?s regression results, Models B and D with
seasonally adjusted advertising data did not show good properties of fit. Again, the major
difference may have been due to the use of the proxied variables in the replicated models
and the use of monthly, rather than quarterly, data. The models with monthly dummy
variables (A and B) negated Ding and Kinnucan?s earlier finding of the need to eliminate
these variables because of insignificance in their regressions (again, the dummy variables
were all highly significant). Furthermore, it was shown that the model shows severe
seasonality because of the high significance of the monthly dummy variables (also
supported by the Ftest value of 24.28). Model C, the model without the monthly dummy
66
variables but with the interaction term, suggested that advertising actually rotated the
demand curve for cotton. This negated Ding and Kinnucan?s earlier inferences of no
rotation of the demand curve caused by advertising expenditures.
Overall, it can be deduced that Ding and Kinnucan?s earlier inferences that
advertising shifts the demand curve for cotton are fragile and are conditional on the
sample period used and on the use of modified (seasonally adjusted) data. When using
unadjusted advertising data, none of the inferences made by Ding and Kinnucan held up.
However, after using seasonally adjusted advertising data, advertising showed a
significant effect to the mill level demand of cotton, thus suggesting that Ding and
Kinnucan?s results were robust. It can not be positively suggested, from the replicated
results, that advertising expands the demand for cotton. Replicated regression results for
the seasonally adjusted advertising data are documented in Table 7.
67
Table 4. Variables Used for the Replication of the Ding and Kinnucan Study of U.S.
Cotton Promotion, January 1986December 2000
Variable Definition
Per Capita Mill Use
ln [(U.S. Mill Use*1,000*480lbs.)/(U.S.
population*1,000)]
Cotton Price
ln [Fiber equivalent effective mill
price/(CPI/100)]
Rayon Price
ln [Fiber equivalent rayon price/(CPI/100)]
Polyester Price
ln [Fiber equivalent polyester
price/(CPI/100)]
A Index if the World Cotton Price
1
ln [Fiber equivalent A Index /(CPI/100)]
U.S. Disposable Income
2
ln[[(Disposable income annual
rate*1,000,000,000)/(CPI/100)]/(U.S.
population*1,000)]
Advertising
ln [CI Seasonally Adjusted Promotional
Expenditures/(CPI/100)] and
ln [CI Unadjusted Promotional
Expenditures/(CPI/100)]
1
The A Index of the world cotton price was used as a proxy for Ding and Kinnucan?s imported textile price
variable.
2
U.S. disposable income was used as a proxy for Ding and Kinnucan?s expenditure variable.
68
Table 5. Ding and Kinnucan GLS Esimates (Corrected for ForthOrder
Autocorrelation) of Domestic Mill Demand for Cotton, 19761993 Quarterly Data
Variable Model A Model B
Advertising 0.01967
(1.32)
[0.062]
0.02395
(3.16)
[0.066]
Cotton Price 0.0952
(2.51)
[0.30]
0.1055
(2.77)
[0.29]
Rayon Price 0.2236
(2.39)
0.2518
(2.66)
Polyester Price 0.2686
(2.78)
0.3053
(3.19)
Imported Textile Price 0.1372
(2.72)
0.1595
(3.15)
Expenditure 0.1124
(2.11)
0.1295
(2.41)
Lagged Dependent Variable 0.6843
(8.66)
0.6390
(8.70)
Constant 0.23683
(0.97)
0.28003
(1.14)
Spring 0.0311
(1.94)

Summer 0.0009
(0.051)

Fall 0.00149
(0.076)

R
2
0.955 0.950
Durbin mtest for serial correlation:
First order
Forth order
Ftest: Model A vs. B
0.778
2.232

0.218
2.027
2.0832
a
Notes: Figures in parentheses are absolute values of tratios. Figures in brackets are longrun elasticities.
a
The probability for 3 and 57 degrees of freedom is 0.1125, which means that Models A and B are
statistically equivalent.
69
Table 6. Replication of Ding and Kinnucan?s Cotton Demand Model Using
Seasonally Unadjusted Advertising Data
1
, January 1986December 2000
Variable Model A
2
Model B
3
Model C
4
Model D
5
Advertising
0.0799
(0.49)
[0.098]
0.0182
(1.18)
[0.096]
0.4160
(1.62)
[0.012]
0.007395
(0.44)
[0.016]
Cotton price
0.2137
(0.38)
[0.009]
0.002260
(0.07)
[0.012]
1.4759
(1.65)
[0.011]
0.003960
(0.07)
[0.008]
Interaction
0.0153
(0.38)
 0.1045
(1.65)

Rayon Price
0.1179
(1.75)
0.1183
(1.76)
0.3170
(2.83)
0.3191
(2.84)
Polyester Price
0.0504
(0.71)
0.0511
(0.72)
0.1798
(1.51)
0.1733
(1.45)
A Index Price
0.0334
(0.95)
0.0321
(0.92)
0.0918
(1.54)
0.1026
(1.73)
Disposable Income
0.1292
(0.65)
0.1284
(0.65)
0.5067
(1.47)
0.5256
(1.52)
Lagged Response
0.8168
(14.63)
0.8113
(15.03)
0.4932
(6.39)
0.5142
(6.70)
January
0.3251
(10.27)
0.3235
(10.34)
 
February
0.1228
(4.65)
0.1221
(4.65)
 
March
0.2735
(9.87)
0.2736
(9.90)
 
April
0.1095
(3.96)
0.1098
(3.99)
 
May
0.2028
(7.30)
0.2028
(7.32)
 
June
0.1284
(4.16)
0.1273
(4.16)
 
July
0.0773
(2.44)
0.0781
(2.48)
 
August
0.3337
(11.71)
0.3318
(11.86)
 
September
0.1133
(4.03)
0.1137
(4.06)
 
70
Table 6. (Continued) Replication of Ding and Kinnucan?s Cotton Demand
Model Using Seasonally Unadjusted Advertising Data
1
, January 1986December
2000
Variable Model A
2
Model B
3
Model C
4
Model D
5
October
0.2151
(8.28)
0.2147
(8.29)
 
November
0.0865
(2.74)
0.0862
(2.75)
 
Constant
2.8885
(0.95)
1.9997
(1.03)
0.2244
(0.04)
6.0076
(1.72)
R
2
0.7892 0.7890 0.3993 0.3896
Ftest: B vs. D    25.41
Notes: Figures in parentheses are absolute values of tratios. Figures in brackets are longrun elasticities.
1
GLS estimates were obtained in SAS using the YuleWalker algorithm for correction of firstorder
autocorrelation.
2
Model A is the full model with an interaction term.
3
Model B is the full model without an interaction term.
4
Model C is the model with an interaction term and without the monthly dummy variables.
5
Model D is the model without the interaction term or the monthly dummy variables.
71
Table 7. Replication of Ding and Kinnucan?s Cotton Demand Model Using
Seasonally Adjusted Advertising Data
1
, January 1986December 2000
Variable Model A
2
Model B
3
Model C
4
Model D
5
Advertising
0.1589
(0.59)
[0.085]
0.0182
(1.18)
[0.096]
1.0014
(2.47)
[0.070]
0.0487
(1.95)
[0.095]
Cotton price
0.6209
(0.67)
[0.014]
0.002259
(0.07)
[0.012]
3.6405
(2.60)
[0.015]
0.002785
(0.05)
[0.005]
Interaction
0.0436
(0.66)
 0.2574
(2.60)

Rayon Price
0.1200
(1.78)
0.1183
(1.76)
0.3161
(2.94)
0.3224
(2.95)
Polyester Price
0.0561
(0.78)
0.0511
(0.72)
0.2284
(1.99)
0.1955
(1.68)
A Index Price
0.0289
(0.82)
0.0321
(0.92)
0.0898
(1.57)
0.1111
(1.92)
Disposable Income
0.1214
(0.61)
0.1284
(0.65)
0.2105
(0.61)
0.2889
(0.82)
Lagged Response
0.7998
(14.14)
0.8113
(15.03)
0.4606
(6.17)
0.4855
(6.44)
January
0.3150
(9.82)
0.3190
(10.14)
 
February
0.1164
(4.45)
0.1184
(4.58)
 
March
0.2701
(9.82)
0.2698
(9.83)
 
April
0.1139
(4.11)
0.1128
(4.08)
 
May
0.2020
(7.28)
0.2019
(7.29)
 
June
0.1453
(5.25)
0.1448
(5.24)
 
July
0.0603
(2.20)
0.0600
(2.20)
 
August
0.3165
(11.38)
0.3208
(11.89)
 
September
0.1144
(4.07)
0.1136
(4.06)
 
72
Table 7. (Continued) Replication of Ding and Kinnucan?s Cotton Demand
Model Using Seasonally Adjusted Advertising Data
1
, January 1986December
2000
Variable Model A
2
Model B
3
Model C
4
Model D
5
October
0.2118
(8.18)
0.2130
(8.26)
 
November
0.0835
(2.67)
0.0843
(2.69)
 
Constant
0.6142
(0.14)
1.9996
(1.03)
11.5544
(1.66)
4.3187
(1.25)
R
2
0.7894 0.7890 0.4326 0.4081
Ftest: B vs. D    24.28
Notes: Figures in parentheses are absolute values of tratios. Figures in brackets are longrun elasticities.
1
GLS estimates were obtained in SAS using the YuleWalker algorithm for correction of firstorder
autocorrelation.
2
Model A is the full model with an interaction term.
3
Model B is the full model without an interaction term.
4
Model C is the model with an interaction term and without the monthly dummy variables.
5
Model D is the model without the interaction term or the monthly dummy variables.
73
VIII. SUMMARY AND CONCLUSIONS
Murray et al. suggested in the course of their research that the U.S. Cotton
Research and Promotion Program was successful in expanding the U.S. mill level
demand for upland cotton. To test whether advertising affects demand, the researchers
implemented the use of regression analyses to estimate elasticities of demand with
respect to nonagricultural research and promotion. Based on the regression analyses,
Murray et al. suggested that the promotion and research expenditures made by Cotton
Incorporated positively affected the mill level demand for upland cotton in the U.S., i.e.
the demand curve was positively shifted by the expenditures. They concluded that for a
10 percent increase in promotional expenditures, the mill level demand for cotton
increased by 0.2 percent, ceteris paribus. In addition, they found that for a 10 percent
increase in nonagricultural research expenditures, the mill level demand for cotton would
increase by 3.5 percent.
Ding and Kinnucan also found in their study that advertising expenditures made
by Cotton Incorporated increased the mill level demand for upland cotton in the U.S.
They concluded this from regression analyses that suggested the longrun elasticity
estimates were posotive. They specified their econometric demand model a good deal
differently than did Murray et al. Ding and Kinnucan found from preliminary tests that
advertising effects did not set in until two quarters after the initial expenditures; therefore
they specified the model with a 2quarter lag on advertising. Murray et al. specified the
74
promotion variable contemporaneously. In addition, Ding and Kinnucan specified the
model with 4quarter lags on the cotton, rayon, and polyester prices. Ding and Kinnucan
calculated a longrun demand elasticity of 0.066 with respect to advertising. This implied
that for a 10 percent increase in generic advertising expenditures, the mill level demand
would increase by approximately 0.7 percent, ceteris paribus. Ding and Kinnucan also
found that the seasonal dummy variables were insignificant to the regression whereas
Murray et al. found the dummy variables to be highly significant.
William Tomek (p.6) stated, ?The strength of agricultural economics rests on its
capacity to combine theory, quantitative methods, and data to do useful analyses of
problems faced by society.? A major problem faced by economic researchers is that
econometric results are often fragile. Large variations in results may be a major
consequence of a small change in a model or data, which, in turn, reduces the robustness,
or explanatory power, of the model. There is no easy solution to improving upon
unstable results because econometric models are simply approximations. Tomek
suggested that a possible way to reduce the variation in the results and contradictory
conclusions between researchers is to build upon prior research with further caution.
By following closely the guidelines for duplication and replication of research
results by William Tomek, the models of Murray et al. and Ding and Kinnucan were re
estimated and judged for consistency. The duplication of the Murray et al. results was
considered a success with only slight differences in OLS, GLS and 2SLS parameter
estimates. The research was confirmed by duplication.
By means of replication of Ding and Kinnucan?s research results, it was suggested
that their inferences (advertising expands the demand for cotton) were fragile.
75
The models (Models A, B, C, and D) were regressed with unadjusted advertising
data and seasonally adjusted advertising data to observe any changes. Models B and D
could be directly compared with Ding and Kinnucan?s Models A and B. With the use of
the unadjusted data, most all variables exhibited insignificant tvalues, poor R
2
?s, and in
some cases, the wrong signs. The results of the replication negated Ding and Kinnucan?s
earlier results because advertising was insignificant in all models. One could not be
confident in saying that advertising expenditures expand the demand for cotton given the
replication results. Furthermore, all dummy variables were significant to the replicated
regressions whereas, Ding and Kinnucan found them to be insignificant (this suggests
that there is high seasonality in the data). However, from the unadjusted advertising
replication results, it was suggested that Ding and Kinnucan were correct in suggesting
that there are carryover effects from advertising with the highly significant lagged
dependent variables. Overall, differing conclusions led us to believe that the original
conclusions were conditional upon a specific time period or the model specification when
using the unadjusted advertising data.
By using the seasonally adjusted data, regressions yielded somewhat improved
results although they were not as ideal as the Ding and Kinnucan results. All monthly
dummy variables and lagged dependent variables were highly significant in every model
(AD). All models, except for Models C and D, exhibited mostly insignificant tvalues,
poor R
2
?s, and some wrong signs. Model C did yield fair results, although it negated
Ding and Kinnucan?s inferences about curve rotation. From the results, it was suggested
that advertising actually is a ?taste shifter? by rotating the demand curve because of the
significant interaction term.
76
When compared to Ding and Kinnucan?s regression results, Models B and D with
seasonally adjusted advertising data did not show good properties of fit. Again, the major
difference may have been due to the use of the proxied variables in the replicated models
and the use of monthly, rather than quarterly, data. Furthermore, it was shown that the
model shows severe seasonality because of the high significance of the monthly dummy
variables (also supported by the Ftest value of 24.28).
Overall, despite the ?less ideal? properties of fit exhibited by the model, from the
results of Model D with seasonally adjusted advertising data, it can be deduced that Ding
and Kinnucan?s earlier inferences that advertising shifts the demand curve for cotton
were robust. Furthermore, after observing the results of Model D, sample updating
(using seasonally adjusted data) did not change the inferences of Ding and Kinnucan
according to the elasticity estimates for the advertising variable.
By observing both sets of regressions, it could easily be demonstrated that the use
of seasonally adjusted data will have a significant impact on the final results. By using
the seasonally adjusted data, the advertising variable?s tratio changed from 0.44 in the
unadjusted advertising regression (Model D) to 1.95 in the seasonally adjusted
advertising regression (Model D). This increases skepticism about how robust the models
are when regressed with different data.
Cotton producers need to have hard evidence to support the U.S. Cotton Research
and Promotion Program?s importance. Because of the sensitivity of the results obtained
from this study, cotton producers in the U.S. may not be willing to invest in the Program
to any further extent. Further research is needed in finding an appropriate model for
77
demonstrating the effects of generic advertising on the milllevel demand for upland
cotton in the U.S. because of the sensitivity of the results from different time periods.
Tomek (p.13) stated, ?Published and anecdotal evidence on confirmation in
economics suggests the disheartening conclusion that many published empirical studies
contain errors and that some of these errors are serious in the sense that, if corrected, the
stated conclusions of the study would change.? Furthermore, confirmation helps in
building upon the true scholarship of research and should be encouraged in the field of
agricultural economics to supplement existing empirical research.
78
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82
APPENDIX A: DATA
A1. Variable Definitions and Source
1. qc  (1,000 480lb. bales). U.S. Domestic mill consumption of cotton.
Obtained from Murray et al. report to the Cotton Board who gathered data from
various issues of the USDA?s Cotton and Wool Outlook.
2. pc  (cents / lb.). Fiber equivalent effective mill price of cotton.
Obtained from Murray et al. report to the Cotton Board who gathered data from
the National Cotton Council (2001) web site.
3. pp  (cents / lb.). Fiber equivalent polyester price.
Obtained from Murray et al. report to the Cotton Board who gathered data from
the National Cotton Council (2001) web site.
4. pr  (cents / lb.). Fiber equivalent rayon price.
Obtained from Murray et al. report to the Cotton Board who gathered data from
the National Cotton Council (2001) web site.
5. w  ($ / hour). Domestic textile wages.
Obtained from Murray et al. report to the Cotton Board who gathered data from
the U.S. Bureau of Labor Statistics (BLS, 2001).
83
6. wpc  (cents / lb.). A Index of the world cotton price.
Obtained from Murray et al. report to the Cotton Board who gathered data from
the National Cotton Council (2001) web site.
7. epi  (19821984=100). U.S. Energy Price Index.
Obtained from Murray et al. report to the Cotton Board who gathered data from
the U.S. Bureau of Labor Statistics (BLS, 2001).
8. dpi  (billions). U.S. disposable income annual rate.
Obtained from Murray et al. report to the Cotton Board who gathered data from
the St. Louis Federal Reserve Bank?s FRED database on their web site
(FRED, 2001).
9. fgdp  (billions of $). OECD GDP annual rate excluding the U.S.
Obtained from Murray et al. report to the Cotton Board who gathered data from
various issues of Quarterly National Accounts and National Accounts of OECD
Countries. The data was obtained in quarterly frequencies; therefore, by applying
PROC EXPAND in the SAS statistical software package to quarterly data, they
generated monthly estimates.
10. adjpro  ($). Cotton Incorporated seasonally adjusted promotional expenditures.
Obtained from Murray et al. report to the Cotton Board who gathered data from
Cotton Inc.
11. unpro  ($). Cotton Inc. unadjusted promotional expenditures.
Obtained from Murray et al. report to the Cotton Board who gathered data from
Cotton Inc.
84
12. adjres  ($). Cotton Inc. seasonally adjusted nonagricultural research expenditures.
Obtained from Murray et al. report to the Cotton Board who gathered data from
Cotton Inc.
13. unres  ($). Cotton Inc. unadjusted nonagricultural research expenditures.
Obtained from Murray et al. report to the Cotton Board who gathered data from
Cotton Inc.
14. cpi  (19821984=100). Consumer Price Index.
Obtained from Murray et al. report to the Cotton Board who gathered data from
the U.S. Bureau of Labor Statistics (2001) web site.
15. pop  (thousands). U.S. population.
Obtained from Murray et al. report to the Cotton Board who gathered data from
the U.S. Census Bureau (2001).
85
A
2
.
Raw Dat
a
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:
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1986
.
01
583
72.
1
65.
6
81.
3 5.
83
57.
8
85.
2 3193.
2 6734.
44
1348345
502663
359254
225486
109.
9
239638
1986.
02
523
73.
4
65.
6
81.
3 5.
8
60.
7
76.
5 3209.
7 6769.
32
686137
379914
315667
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109.
7
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1986.
03
542
75.
6
65.
6
81.
3 5.
82
58.
5
67.
3 3236.
1 6766.
88
505453
508991
308087
263356
109.
1
239928
1986.
04
572
76.
4
65.
6
78.
1 5.
83
53.
8
62.
9 3236.
3 6766.
62
1031919
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108.
7
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1986.
05
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1
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6
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1 5.
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50.
4
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9 3246.
5 6801.
1
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109
240271
1986.
06
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2
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6
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1 5.
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45.
9
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2 3257.
7 6835.
08
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109.
4
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1986.
07
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81.
8
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6
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1 5.
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41.
7
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1 3273.
7 6845.
36
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417824
407938
109.
5
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1986.
08
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39.
2
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6
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1 5.
83
41.
2
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4 3282.
4 6852.
62
1108461
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109.
6
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1986.
09
603
49
64.
6
78.
1 5.
9
48.
5
57.
3 3296.
7 6877.
51
930516
766094
311133
264444
110
241068
1986.
10
660
58.
5
64.
6
78.
1 5.
86
57
54.
9 3295.
6 6890.
73
554040
659474
319221
284260
110.
2
241274
1986.
11
554
61.
1
64.
6
78.
1 5.
87
58.
5
55.
1 3303.
1 6906.
72
694184
670512
306841
294601
110.
4
241467
1986.
12
556
68.
7
64.
6
78.
1 5.
9
66.
5
55.
2 3319.
1 6940
1191169
3140041
328880
822643
110.
8
241620
1987.
01
621
72.
7
64.
6
83.
3
5.
94
73
58 3360.
4
6999.
18
1020351
380387 347082
217846 111.
5
241784
1987.
02
587
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3
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6
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3 5.
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3
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5 3393.
8 7047.
18
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418279
371331
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111.
9
241930
1987.
03
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69.
7
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6
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3 5.
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3
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2 3411.
4 7103.
94
994920
1001884
358118
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112.
3
242079
1987.
04
661
73.
7
64.
6
83.
3 5.
93
73.
2
61.
7 3290.
2 7172.
62
1204838
1111102
394432
325840
112.
8
242252
1987.
05
642
83
64.
6
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3 5.
87
84.
5
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6 3434.
5 7226.
92
1077736
977722
313676
296734
113.
1
242423
1987.
06
655
89.
5
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7
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3 5.
89
89
62.
5 3446.
7 7288.
09
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891763
297650
268397
113.
6
242608
1987.
07
655
90.
1
71.
9
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92.
6
63.
4 3465.
6 7332.
72
1521490
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113.
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242804
1987.
08
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93.
6
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9
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96.
1
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9 3495.
1 7391.
41
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114.
4
243012
1987.
09
694
88.
9
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9
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5 6
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7
63.
4 3508.
3 7447.
09
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629462
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114.
8
243223
1987.
10
713
80.
7
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9
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2
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4 3544.
7 7498.
09
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115.
1
243446
1987.
11
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6
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9
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84.
4
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5 3564.
1 7557.
19
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115.
5
243639
1987.
12
582
78.
6
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9
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5 6.
01
83.
5
61.
4 3598.
9 7599.
82
1070561
2822106
337259
843602
115.
7
243809
1988.
01
621
76.
7
71.
9
86.
5
6.
02
80.
6
59.
2
3617 7651.
39
1066306
397519 315756
198184 116.
1
243981
1988.
02
649
73.
5
71.
9
86.
5
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03
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1
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5
3641 7675.
87
1547174
856670 446600
333150 116.
2
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1988.
03
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74.
8
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90.
6 6.
05
73.
8
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2 3668.
9 7714.
1
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1097775
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116.
6
244279
1988.
04
610
75.
1
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90.
6 6.
06
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1
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9 3688.
6 7765.
53
1808112
1667441
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117.
2
244445
1988.
05
630
77.
1
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1
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7 6.
07
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9
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6 3707.
3 7811.
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117.
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1988.
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118.
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1988.
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118.
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1988.
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1 3787.
4 8009.
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1988.
09
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9
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7 8077.
02
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119.
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1988.
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1
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3
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7 3841.
9 8126.
77
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1988.
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1988.
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1989.
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1989.
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1989.
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3 3979.
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122.
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1989.
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4 3987.
5 8478.
49
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123.
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1989.
05
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9
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9
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8 3987.
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1989.
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1989.
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9
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1989.
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8
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6
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1
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6 4029.
1 8677.
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1989.
09
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92.
7 114.
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4
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7
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9 4036.
7 8721.
49
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124.
9
247816
1989.
10
792
86.
2
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7 124
6.
39
91.
3
65.
8 4060.
4 8784.
36
1112524
1324237
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125.
5
248067
1989.
11
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84.
9
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7 124
6.
42
91.
3
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6 4095.
2 8837.
2
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125.
9
248281
1989.
12
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80.
1
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7 124
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44
86.
2
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8 4112.
6 8905.
26
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2789058
320966
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126.
4
248479
1990.
01
754
77.
7
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7 124
6.
39
83.
1
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7 4176.
2 9028.
98
1118216
416871
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127.
6
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1990.
02
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80
92.
7 124
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44
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6
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2 4210.
5 9102.
6
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128.
1
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1990.
03
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7 124
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2
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8 9172.
35
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128.
6
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1990.
04
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2
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7
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55
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3
68 4261.
6
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1990.
05
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4
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1
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5 4263.
1 9263.
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129.
2
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1990.
06
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7
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4 124
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2
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6 4290.
5 9332.
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130
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1990.
07
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3
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1
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1 4318.
9 9379.
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130.
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1990.
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1
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2 4328.
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131.
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1990.
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132.
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1990.
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7
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1 9591.
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133.
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1990.
11
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87.
2
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3 127.
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7
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5 4360.
4 9623.
14
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133.
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1990.
12
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3
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7 4378.
9 9678.
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1991.
01
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9 82.
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1
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1991.
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134.
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1991.
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9 251772
1991.
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7
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135.
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1991.
05
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7
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135.
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1991.
06
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2
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1 78.
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136.
1
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1991.
07
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5
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136.
3 252665
1991.
08
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129.
2
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82 81.
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pc
pp
pr
w
wpc
e
p
i
dpi
f
g
dp
a
d
j
p
r
o
u
n
pr
o
a
j
dr
e
s
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r
e
s
c
p
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po
p
1998.
10
957
72.
1 55.
2
105.
2
8.
65 67.
6
74.
6
6410
13309.
32
6654223
7920522
793853
706910
163.
9
271240
1998.
11
806
65.
3 55.
2
105.
2
8.
64 63
72.
8
6466.
7
13372.
21
4711629
4550962
694047
666361
164.
2
271459
1998.
12
722 66.
1
55.
2
105.
2
8.
71
62.
3
70.
8
6446.
7
13562.
11
3463125
9129145 695269
1739110 164.
5
271644
1999.
01
882
71.
6 53.
1
105.
2
8.
68 62
71.
3
6488.
4
13816.
43
4756293
1773146
820913
515246
164.
8
271841
1999.
02
824
70.
4 53.
1
105.
2
8.
64 62.
4
70.
1
6515.
6
13996.
74
3824136
2117424
803662
599508
164.
8
271987
1999.
03
940
73.
7 53.
1
105.
2
8.
78 63
71.
2
6540.
8
14091.
15
3217180
3239700
826122
706177
165
272142
1999.
04
888
71.
9 52.
1
105.
2
8.
83 64.
3
75.
9
6569
14184.
11
3163253
2917152
658400
543904
166
272317
1999.
05
864
70.
2 52.
1
104.
2
8.
81 66.
5
77.
5
6583.
1
14183.
64
2868781
2602558
636664
601966
166
272508
1999.
06
885
67.
6 53.
1
105.
2
8.
89 65.
1
78.
6
6636.
9
14231.
69
3228069
3262287
666921
601376
166.
1
272718
1999.
07
785
62.
5 54.
2
99
8.
83 60.
5
80.
7
6638.
3
14349.
49
3514762
2782637
976554
953449
166.
7
272945
1999.
08
883
63.
5 54.
2
102.
1
8.
88 56.
6
83.
5
6686.
8
14443.
68
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2321296
709541
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167.
1
273197
1999.
09
878
62.
2 55.
2
101
9.
01 54.
8
85.
8
6668.
3
14532.
76
3055541
2515627
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658578
167.
8
273439
1999.
10
872
55.
6 55.
2
101
8.
99 52.
7
83.
5
6760
14578.
48
3200839
3809959
719103
640347
168.
2
273672
1999.
11
873
53.
9 55.
2
101
8.
98 51.
3
83.
6
6781.
6
14622.
24
3231144
3120962
540278
518726
168.
5
273891
1999.
12
762 52.
3
55.
2
101
9.
04
49.
1
83.
6
6783.
4
14698.
05
3297063
8691388 825078
2063808 168.
9
274076
2000.
01
810
55
55.
2
101
9.
03
52.
9 83.
8 6830.
6
14799.
41
3001376
1118913
748261
469646
169.
4
274271
2000.
02
849
61
57.
3
101
9.
03
59.
7 87.
5 6858.
5
14925.
01
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937089
938624
700185
170.
2
274423
2000.
03
935
64.
8 57.
3
101
9.
05 63.
8
90.
9
6910.
4
15058.
49
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5125882
967787
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171.
2
274583
2000.
04
811
63.
3 57.
3
101
9.
05 65.
3
89.
2
6939.
7
15088.
79
2257552
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726345
171.
1
274765
2000.
05
931
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6 60.
4
101
9.
05 67.
2
90.
9
6963.
5
15143.
76
3382576
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171.
3
274952
2000.
06
907
63.
1 60.
4
102.
1
9.
07 66.
1
97.
7
6991.
5
15264.
07
4380625
4427060
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172.
2
275155
2000.
07
730
63.
9 60.
4
102.
1
9.
06 64.
9
97.
3
7006.
4
15351.
89
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172.
7
275372
2000.
08
920
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4
102.
1
9.
09 67.
6
95.
9
7017.
8
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1
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172.
8
275619
2000.
09
804
68.
1
60.
4
102.
1 9.
16
68.
5
100.
6 7098.
6
15517.
8
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2864756
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173.
6 275857
2000.
10
846
68.
8 61.
5
102.
1
9.
16 67.
7
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7
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8
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04
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173.
9
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2000.
11
749
71.
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5
102.
1
9.
16 71.
1
99.
3
7079.
2
15645.
89
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174.
3
276298
2000.
12
640 74.
6
61.
5
102.
1
9.
21
73.
2
97.
9
7109.
8
15691.
72
3367223
8876336 602415
1506851 174.
6
276513
1
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