As in the case of firms, we use the residual of the IV regression to construct a consistent
estimate of ∆ωγj∙t. We calculate the autocovariances of the latter pooling over all years and
report the results in Table 5.
A thorough examination of the estimated autocovariances of the unanticipated compo-
nent of the rate of growth of earnings reveals that there is no large or statistically significant
covariance at lags greater than one. This evidence is not entirely consistent with ∆ωijt being
an MA(2) process of the form:
∆ωjt = buuj t + bυ ∆vj t + A{L,p)ξij t + A{L,p)∆μijt (26)
as in the modified version of equation (11) with p = I.25 On average, the autocovariance
of order zero is 0.016, while the autocovariance of order one is -0.006.26 Autocovariances of
order higher than two are economically very small (between -0.0005 and 0.0004) and mostly
insignificant.
Armed with these results we can now recover the implied values of parameters bυ and
bu following the procedure described in Section 3.2 and focusing on the matched employer-
employee data set.
7 Shocks and insurance: the estimates
The matched data set includes 39,930 individual∕year observations for 8,228 workers and
4,194 firms. It is an unbalanced matched panel of firms and workers. The mean number of
matches (i.e., the number of workers) per firm is 1.96, with a minimum of 1 and a maximum
of 397 per year. Table 6 reports characteristics for the firms and the workers in the set. As
expected, the major difference with respect to the full sample is average firm size, which
is significantly greater. The median number of employees is 103 in the matched sample,
compared with 60 in the full sample. Naturally, larger firms have a greater likelihood of
2aThere are two possible explanations for this. First, σ2 = 0 (absence of a transitory component once the
AR component is removed from 24). Second, a low value of the AR coefficient may make an MA(2) hard to
detect in the data.
20These are much lower than the estimates for the US using the PSID (Meghir and Pistaferri, 2000),
perhaps reflecting the fact that measurement error is less of a problem in this data set.
22