Insurance within the firm

From the autocovariance function of workers’ earnings, we can recover the variance of
the transitory and permanent idiosyncratic shocks to wages. In the simple case where p = 0,
with heterogeneous partial insurance and covariance stationarity, one obtains:

Conditioning on the estimated values for b_u, b_υ, σ²_a and σ², the remaining two variances
can be identified. A slightly more complicated expression can be derived for arbitrary values
of p. Again, minimum distance estimation is used to identify the variances.

Before turning to the description of the data, it is worth remarking that the identification
strategy outlined in this section is implemented in a series of steps. First, one needs to
filter predictable components from both firm performance and workers’ earnings. Since
these are perfectly observable, incentive contracts will not be made contingent on their
realizations. The observables include the autoregressive components (if any), and exogenous
characteristics Zj_t and a^∙_t. When the empirical exercise is implemented using standard IV
estimation techniques, the resulting residuals are consistent estimates of the unexplained
growth rates ∆ε_j∙_t and ∆ω_ljt.¹³

The next step is to use (16)-(18) to estimate b_u and b_υ and check whether these are
affected by observable firm and individual characteristics along the lines of what is predicted
by agency models.

We then calculate the sample analogs of the theoretical autocovariances E (∆εj∆^jt-τ)
and E {∆ωi_j∙∆^^ijt-τ)∙ For more technical details see Appendix B; for a more thorough
discussion of covariance estimation see Chamberlain (1984). Estimated autocovariances are
then used as inputs for the minimum distance estimation of the variances of shocks to value
added and earnings conditioning on insurance∕incentive arrangements.

stationarity. Those obtained under covariance non-stationarity are available on request.

¹³A technical requirement for inference to be valid when working with residuals rather than with true
disturbances is that fourth moments of both ∆εjt and ∆u⅛∙_t exist and are constant across individuals
(MaCurdy, 1982).

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