contingent if workers are to share part of the Hrm risk.22
We use the IV estimator suggested by Anderson and Hsiao (1982), which provides
consistent estimates of the parameters of interest in dynamic panel data models.23 The
results of the IV regression are reported in Table 2. We assume that p = 1 and q = O, and
check whether such restrictions are consistent in the data (see below). A look at the reduced
form shows that these instruments are powerful for identiHcation (a p-value on the excluded
instruments below 0.1 percent). We Hnd an AR parameter of 0.28 with a standard error
of 0.02. Time, area and sector effects are not statistically signiHcant; interactions between
time and area and between time and sector, however, are jointly signiHcant.
We use the residual of the IV regression above to construct a consistent estimate of ∆εjt.
A close examination of the estimated autocovariances (∆εj∙∆^Sjt-τ), reported in Table 3
pooling over all years, reveals the absence of any large or statistically signiHcant correlation
at lags greater than one, consistent with ∆εjt being an MA(1) process. This can be tested
more formally using the zero restriction test proposed by Abowd and Card (1989). We Hnd
that the null that ∆εjt is an MA(0) process is overwhelmingly rejected (p-value <0.0001),
while the null of MA(1) has a borderline p-value of 4.5 percent. The p-value of the test
increases slightly with the order of the MA process being tested. A difference test MA(0)
vs. MA(1) rejects the null (p-value<0.0001), while a difference test MA(1) vs. MA(2)
supports the null (p-value 28 percent) and the proposition above that ∆εjt ~ MA(1). This
makes us conHdent that in the estimation of bu and bυ below, one need not be concerned
about instrument validity, just about power. Thus one autoregressive lag is sufficient to
characterize the predictable dynamics in the growth rate of Hrm value added (alongside the
indicators for a given time∕sector∕location conHguration); there is thus evidence for value
added growth being an ARMA(1,1) process. Overall, these results suggest that the random
walk plus serially uncorrelated transitory shock speciHcation is a reasonable representation
“We run the value added regression on a sample of Hrms with non-missing values for the variables of
interest (i.e., value added, year, sector and location), irrespective of whether there are workers to match
them with. This ensures that the results for the value added speciHcation are not peculiar to large Hrms,
which are obviously over-represented in the subset of Hrms with matched workers.
23More efficient estimates can be obtained using the two-step procedure suggested by Arellano and Bond
(1991). This, however, may have severe Hnite sample bias, as noted by Blundell and Bond (1999) among
others. We thus resort to a simple one-step estimator.
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