ent influences, and a series of 11 indicator variables
to account for seasonal effects.
It is typical to first perform Stationarity tests on
each of the individual series before the series are
analyzed in a vector autoregression (Granger 1981).
Nerlove et al. (1979), however, suggest that
stationarity-inducing transformations be avoided
such that the nonstationarity of one series is used to
explain the nonstationarity in the others, whereby
one may avoid the sacrifice of valuable long-run
information through differencing. Individually non-
stationarity series may have combinations that are
stationary in that they generate stationary residuals
(Engle and Granger; Hendry). In such cases, station-
ary linear combinations of individually nonstation-
ary series may be modeled without differencing, and
hence without sacrificing the long-run dynamic in-
formation.
Accordingly, it is only the Stationarity of the es-
timated equations that is ultimately required (Sims
1980; Hendry). Thus, focus was placed on testing
the stationarity of the innovations from the above-
specified 21-order VAR model. Three tests were
performed on the residuals of each VAR model
equation: a Durbin-Watson (DW) test (Engle and
Granger); the Dickey-Fuller (DF) test (Fuller; Dick-
ey and Fuller 1979,1981); and the augmented Dick-
ey-FulIer (ADF) test (Engle and Granger; Hall). All
nine stationarity tests were conducted at the 5 per-
cent significance level.
The DW test for a VAR equation’s residuals invol-
ves the Durbin-Watson value. The null hypothesis of
nonstationary residuals is rejected when the DW
value exceeds 0,367 (Hall). Dickey and Fuller
(1979, 1981) developed a Stationarity test by
regressing a variable’s (here an equation’s residuals)
first differences against a one-period lag of the
variable’s non-differenced levels and a constant.
Engle and Granger, and Hall have employed an ADF
test. In addition to the DF test’s regressors, the ADF
test regressors include a number of lagged depend-
ent variables (i.e., lags of the differenced residuals).
Hsiao’s method of ch∞sing lag structure based on
the Akaike final prediction error criterion deter-
mined the number of lagged dependent variables in
each ADF test. With the DF and ADF tests, the null
hypothesis of a nonstationary series is rejected when
the t-like value on the non-differenced lagged vari-
able is negative and exceeds the 2.89 to 3.1 range in
absolute value (Fuller, Dickey and Fuller 1979,
1981; Hall).
Evidence from all nine tests was adequate to reject
the null hypotheses of nonstationarity for PCN, PF,
and PR residuals. The three DW values were ap-
proximately 2.0. The three t-like values ranged from
18.9 to 19.1 for the DF tests, and from 13.0 to 13.8
for the ADF tests.
The sample period (1957-1989) was large enough
to warrant checking whether there was structural
(market and institutional) change as manifested by
nonconstant coefficients. As recommended by Sims
(1980, p. 17), a Chow test on egg prices for the
periods before 1974 and after 1973 was conducted
to see whether evidence was sufficient at the 1
percent significance level to suggest that egg price
coefficients were nonconstant. Shrader et al. fully
describe this test’s application within an egg price
context. Evidence was not sufficient to reject the null
hypothesis of coefficient constancy. Accordingly,
the VAR model analyses in this paper utilized the
entire 1957:1 through 1989:12 period.
The model was validated beyond the sample by
estimating a version over the 1957:1 through
1986:12 period, by saving the 36 observations of the
1987:1 through 1989:12 period as an out-of-sample
validation period, and by predicting the VAR model
version estimated through 1986:12 over the latter
validation period. Validation results suggest that the
estimated VAR model predicts beyond the sample
more accurately than the naive model. This suggests
that gains in forecast accuracy have accrued to this
study’s VAR modeling efforts. 4 Then the model
used for analysis in the remainder of this paper was
estimated for the entire 1957:1 through 1989:12
period, which included the three-year validation
period.
Two aspects of the 21-order VAR model are of
interest. First is the response of variables in the
system to a large shock in com price (for example,
one standard error of com price’s historical innova-
tion). In particular, it is of interest to know how farm
and retail egg prices, constituting the rest of the
4Each equation (initially estimated with 1957:1 through 1986:12 data) generated as many “step-ahead” forecasts as the
validation period would allow. The forecasts were run through a Kalman filter. Thus, the 36-month validation period permitted 36
one-step-ahead forecasts; 35 two-step-ahead forecasts; 34 three-step-ahead forecasts, etc. Theil U-Statistics were provided for each
forecast horizon, that is, 36 Theil U-values for each equation. A Theil U-value of less than unity suggests a superior and more
accurate performance that does the naive model. A naive forecast equals last period’s observation. Further, a Theil U of less than
unity suggests that there were gains in forecast accuracy from modeling the VAR equations as a multivariable system as opposed to
expending no model efforts through naive forecasting. Gains to modeling were apparent. Of the farm egg price’s 36 Theil U-values,
35 were about unity or less and 31 were about 0.80 or less. Of the 36 retail egg price U-values, all but two were approximately unity
or less, and 31 were about 0.80 or less. More than three-fourths of both equations' 36 Theil U-values were 0.75 or less.
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