modeled system, react over time. Do the responses
for egg prices quickly fade out, or do they endure for
a long period of time? Do retail prices take longer to
respond than do farmgate prices of eggs? If so, how
much longer is the delay?
A second aspect of VAR econometrics that is of
interest is the relative strength of influence that one
variable has on another over alternative time
horizons. This is summarized through decomposi-
tions of forecast error variance (FEV). For example,
consider the retail egg price. Of the uncertainty in
retail egg prices at different horizons, what propor-
tion can be attributed to com price uncertainty?
What proportion is attributed to farmgate egg price
uncertainty? VAR econometrics can provide helpful
information for these questions concerning inter-
relationships among all of the modeled prices.
The PCN, PF, and PR equations may have contem-
poraneously correlated innovations. To avoid distor-
tion of impulse responses from contemporaneously
correlated current errors, a Choleski decomposition
was imposed in order to orthogonalize the current
innovation matrix, such that the variance∕covariance
matrix of the transformed current innovations is
identity. The ordering of farm com price, to farm-
level egg price, to retail egg price was chosen. The
ordering provides a line of causality (in contem-
poraneous time) consistent with theory, because
com price is an input price for farm-level egg output
priced by the farm egg price (PF), and because PF is
an input price for retail egg products priced by the
retail egg price (PR) (See Tomek and Robinson).
Further, the PCN-PF-PR ordering is an observed
chronology of egg-related pricing points in the food
chain. The chosen ordering also facilitates the
analytical purpose at hand: to model the dynamic
effects on egg-related prices from a crop sector
shock to com price (See Sims 1989).5
EGG PRICE IMPULSE RESPONSES TO A
RISE IN CORN PRICE
The impulse response function simulates, over
time, the effect of a one-time shock in one of a VAR ,s
series on itself and on other series in the system. The
VAR was shocked by a 5.6 percent (one standard
deviation) rise in the historical innovation in
farmgate com price. The impulse responses are
changes in the logged index and are hence ap-
proximate percent changes in the non-logged in-
dices.
Figure 1 provides impulse responses in farm- and
retail-level egg prices from the increase in com
price. Kloek and Van Dijk’s Monte Carlo method
was employed and provided t-values for each im-
pulse response. This paper focuses on the first 17
impulses in each egg price because most of these
were statistically nonzero at the 1 percent sig-
nificance level. Thirty-six impulses are provided to
demonstrate that the impulse responses implode,
rather than explode, at longer term horizons.
Farm egg price or PF increases have an immediate
reaction time because the first response to a com
price increase is significant. PF-impulses fluctuate
between magnitudes of 1.3 and 2.4 percent for 17
months.
Retail egg price increases also have an immediate
reaction time to the PCN-shock. These retail price
impulses fluctuate between magnitudes of 1.2 and
1.9 percent and are also statistically nonzero for 17
months.
Patterns of farm and retail responses have imme-
diate reaction times, have the same durations (17
months), and take on similar response patterns. Yet
the com price shock was followed by farm price
increases that ranged between 1.3 and 2.4 percent;
these were generally higher than the retail price
increases which ranged from 1.2 to 1.9 percent.
Previous research demonstrates that a com price
increase is expected to influence retail egg prices to
a lesser extent than farm egg prices (Babula and
Bessler 1989a). Retail price includes more transpor-
tation, packaging, and marketing costs than farm
prices, and poultry feed costs are a smaller com-
ponent of the retail egg price (Babula and Bessler
1989a, p.20).
A price sensitivity parameter (PSP) may be calcu-
lated from the impulse responses and may be used
to compare the relative degrees of response of the
egg prices to com price change. Recall that by a VAR
model’s definition, each of the three equations con-
tains lags of all three modeled indices, such that the
exogenously placed com price increase sets all three
VAR equations into motion. To calculate an egg
price’s PSP, the egg price’s impulses are summed
over the 17-month range of general significance, and
are then divided by the corresponding com price
change. Since each impulse approximates a percent-
age change in the nonlogged index, the summation
of impulses of a price index represents an accumu-
lated percent change in the index over the chosen
summation period. Such summations of egg price
5Pursuant to an anonymous reviewer’s suggestion, an alternative ordering, PC∕PR∕PF, was run. Results from analyses of this
additional run’s impulse responses and FEV decompositions were substantially similar to results which emerged from our chosen
ordering. Runs of the alternative ordering are available on request.
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