relationships among the three price series. A final
section provides conclusions.
A DIGRESSION ON THE VAR MODEL’S
SPECinCATION
Certain aspects of VAR model specification have
generated criticism among some economists (see
Sims 1989). Some contend that the number of in-
cluded variables and lags are determined in too
mechanical a manner, without enough attention to
theory. Another criticism has been that modeling
efforts have not employed economic theory in an
intensive enough manner, as when formulating the
Choleski ordering of the VAR’s variables in contem-
poraneous time.
One cannot expect economics to differ from other
disciplines and be exempt from having an expanding
choice of different model types with varying levels
of detail for different purposes (Sims 1989). “It is
dismaying... that as economists begin to use an in-
creasingly differentiated array of modeling types,
we seem to be dissipating energy in argument over
what kind of modeling style is correct” (Sims 1989,
p. 489). Sims (1989) further contends that meaning-
ful modeling efforts in economics range along a
wide spectrum: from unrestricted and data-oriented
VAR models which loosely use theory to purely
theoretical models with Iitde or no connection to
observed data or events. One ch∞ses a modeling
effort along this spectrum by using, as does this
study, model choice Criteriapresentedby individuals
such as Sims (1989) and Friedman (1953).
An ideal, but seldom achieved, model would (a)
incorporate explicit behavioral theory, (b) connect
to the data, (c) permit acceptably high confidence
levels for tests of hypotheses and inferences, (d)
have a specification partially guided by the analyti-
cal purpose at hand, and (e) predict accurately
beyond the sample (Friedman 1953; Sims 1989).
Any particular model is a compromise and no model
can be expected to meet all five of these criteria
perfectly (Sims 1989, p. 489). VAR models typically
adhere to criteria (b), (d), and (e), while often
sacrificing much with regard to criteria (a) and (c).
Reasons may vary from study to study, but prime
among such reasons is the uncontrolled nature of the
data generating process. Most VAR applications are
with secondary data in which no control is made for
omitted variables. That is, there is usually not a
random assignment of independent variables, so that
one is never sure that the error terms are not corre-
lated with the independent variables. Thus, usual
hypothesis tests and inferences on structure will be
subject to question (Rubin 1978). Accordingly,
rather than seeking a close link with a priori theoreti-
cal structure with the data, some VAR modelers (see
Bessler 1990) choose to obtain a summary of
regularities present in the data which have good
forecasting characteristics. This study follows this
latter data-oriented and a theoretic approach. (For a
detailed discussion on the role of randomization and
control in obtaining structure, the reader is referred
to Rubin 1978, and Pratt and Schlaifer 1988).
DATA SOURCES AND THE ESTIMATED
Varmodel
The data used in this study are monthly time series
observations obtained from the U.S. Bureau of
Labor Statistics (BLS).2 The BLS ,s producer price
index (PPI), farm products, com no. 2, Chicago, was
chosen to represent the com price near the farmgate
(PCN). The PPI, farm products, eggs, serves as the
farm-level egg price (PF).3 Retail egg price (PR) is
represented by the consumer price index, all urban
consumers, eggs. The sample or estimation period
spans monthly observations over the years 1957-
1989. These data were transformed to natural
logarithms. The statistical package, Regression
Analysis for Time Series (RATS), generated all VAR
econometric results (Doan and Litterman).
Under rather general conditions, a set of theoreti-
cally-related time-ordered variables can be sum-
marized as a vector autoregression. Such a model
relates current levels of each variable to lags of itself
and of every other variable in the system. In the
application under study, monthly com, farm egg, and
retail egg prices were each posited as a function of
lags of all three variables. Tiao and Box’s lag selec-
tion method was used to determine lag Stmcture. The
Tiao-Box likelihood ratio tests, conducted at
LutkepohTs suggested 1 percent significance level,
suggested a 21-order lag on each variable in each of
the three VAR relations. Each equation also included
a constant, a time trend to account for time-depend-
2 Nominal prices were used for two reasons. This is an applied time series analysis, and the public and media focus primarily on
nominal movements. Further, a VAR was estimated with deflated prices, and provided results similar to those which emerged from
this nominal price model.
3 The BLS failed to re∞rd PF values for three months (October, November, and December) in 1983. Approximations for these
three observations were obtained through the application of observed percentage changes in the Umer-Bany quotes for the missing
months. These three BLS PF-Values in 1983 were the only missing values in an otherwise unbroken sample of 396 observations for
the 1957:1 throughl989:12period.
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