100
test. The cross correlations are utilized in constructing the impulse
response functions or distributed lag expressions which are the neces
sary next step in operationalizing the causality results. These distri
buted lag expressions are utilized in the final specification of the
econometric model of prices. For the sake of simplicity and expediency,
the following discussion will center on only two price series for the
31-40 size class.
The Haugh-Pierce causality tests produced a set of residual cross
correlations between ex-vessel and wholesale 31-40 price series (Test I
in Table 1). The significance patterns in the estimated residual cross
correlations and the indicated causal direction suggested a dynamic
shock model written in backshift notation as
wt (Ag l1B)et + (1 ()1B)at
where Ag and Aj are impulse response weights at zero and one lags, et
and wt are the white noise residuals for the prewhitened ex-vessel and
wholesale price series, respectively, and at is some white noise process
written in first-order polynomial form in terms of $. The parameter
estimates of Aq and A^ are given as
A
\> =
a
c
^ a
.129
.149
(.752) .651
e
A
X1 "
a
(
a
)r2,l^
.129
.149
(.291) .252
The dynamic shock model can then be rewritten as
wt (.651 ,252B)et + (1