Insurance within the firm

valid regardless of the covariance stationarity hypothesis, which provides a convenient level
of generality.¹¹

In our view, the identification strategy proposed in this paper can be usefully applied
to analogous problems confronted in other areas of research. For instance, in intertemporal
consumption choice models of the type considered by Blundell and Preston (1998), innova-
tions in consumption (the equivalent of Δ^₇∙t above) are directly related to the stochastic
process of income (if this is the only source of uncertainty in the model). The popular
income process involving permanent random walk plus transitory serially independent com-
ponent implies that the consumption innovation adjusts fully to permanent income shocks
(uj_t), but only to the annuity value of transitory shocks (vj_t). With longitudinal data on
consumption and income it is possible to identify the different response of consumption to
permanent and transitory income shocks using a slightly modified version of our strategy.

The foregoing is a discussion of the identification of the two insurance parameters b_u
and b_υ. To close the circle on identification, we need to identify the variances of the shock
to value added growth and the variances of the idiosyncratic component of earnings growth.

As far as the former are concerned, we will use the fact that (in the more general case
of covariance non-stationarity) the period t variances are identified by the expressions:

and use minimum distance estimation similar to that suggested by Chamberlain (1984) to
obtain the estimates of the parameters of interest. We do this by choosing the parameters

that minimize the distance between the actual moments and the moments predicted by the

¹¹Our identifying assumption is that measurement error is negligible given the administrative nature of our
data. What if we relax this assumption? The reader can verify that the presence of a classical measurement
error in the unexplained growth of value added (i.e. the fact that the true value obeys the standard relation:
∆εj_t = ∆ε;t + ∆rjt) implies that the estimate of b_υ is biased toward zero while that of b_u is unaffected. If
the true b_v is zero, however, there is no bias. The problem is one of invalid instruments; to some extent, it
is possible to check measurement error bias by checking whether overidentifying restrictions are rejected in
our model.

¹²In the empirical analysis for brevity we report estimates obtained under the assumption of covariance

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