to the other, we report parameter estimates using two alternative combinations of indices, denoted
by mode 1 and 2, to proxy the bs, ps, and cs variables in (7).
In mode 1, bst (or pst or cst) is the square root of the beef (or pork or poultry) NIDX at t
net of the square root of the beef (pork/poultry) PIDX at t. Following Flake and Patterson, the
media indices were introduced in square root form to account for the diminishing marginal effect
of information. Mode 1 imposes the restriction that positive media has a quantitative identical
but opposite effect on consumption than negative media. The construction of mode 2 is similar to
mode 1 except that the PIDXs were not used. It follows from the hypothesis that “good” news has
no effect on consumer demand.
An empirical issue in conducting GMM estimation is to choose the lag order of the error term
when estimating the variance-covariance matrix of the moment conditions. According to the ra-
tional expectation hypothesis, the forecast error eit is serially uncorrelated. Thus, strict adherence
to economic theory suggests that the lag order should be zero. However, depending on model
specification and data, this theoretical restriction may not be upheld in empirical applications. An
alternative is to let data decide the appropriate lag length using, for instance, the heteroscedasticity
and autocorrelation consistent (HAC) covariance estimator of Newey and West (1987). We follow
the latter solution method and investigate the correlation structure of the estimated error term.
The coefficient estimates and standard errors reported in table (1) are the optimal two-step
GMM estimates obtained by exploiting the Newey and West covariance estimator in the second
step. Hansen’s J is a test for overidentifying restrictions. It is asymptotically χ2(q - k) distributed,
where q is the number of moment conditions and k is the number of model parameters. It is a
test of the extent to which the error term ∆4eit is orthogonal to the instruments. There are 24
instruments in each zit (i = 2, 3) resulting in a total of 48 moment conditions. The test statistics
are 13.97 for mode 1 and 14.85 for mode 2, which should be compared to a χ2 with 13 degrees of
freedom. The 10% critical value is 19.81. Thus, neither mode is statistically rejected.
The likelihood ratio test statistics of the null that food safety information at t - 1 does not
directly influence consumption decision at t are 22.3 for mode 1 and 32.6 for mode 2. These
statistics are χ2(9) distributed under the null, which is rejected at 1% level for both modes. It
is not feasible to test further lags in food safety information, because this will result in too many
moment conditions relative to the sample size.
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