Insurance within the firm



being matched with at least one of the workers in the INPS sample. Other characteristics
(such as location, industry, and workers’ demographic characteristics), are fairly similar in
the two samples.

We apply the identification strategy outlined in Section 4 to recover the parameters of
interest,
bu (the sensitivity of earnings shocks to permanent shocks to value added) and bυ
(the sensitivity to transitory shocks). In both cases, our estimating equation is:

(27)

As explained in Section 4, parameter bυ is identified using ∆εjt-1 and ∆εj(∣ɪ as instruments,
while parameter
bu is identified using ∑j⅛=_q ∆ε-j +⅛ (with q — 1,2,3) as instruments.
The overidentifying restrictions are tested with a standard
J-statistic (generalized Sargan
test). Under the null hypothesis that the model is correctly specified, J is asymptotically
distributed y2 with as many degrees of freedom as overidentifying restrictions and is robust
to heteroskedasticity of unknown form. Low values of J (high р-values of the test) will signal
that the model is correctly specified. The power of the instruments in the reduced-form
regressions is checked by looking at the р-value of the
F-test on the instruments excluded.
Finally, an exogeneity test for
∆εjt (Davidson and MacKinnon, 1993) is an implicit test for
bU   bV   b.

We also comment on the estimates of the variances of transitory and permanent shocks
to value added
(υjt and Ujt, respectively) and of idiosyncratic transitory and permanent
shocks to earnings
ijt and ξ,j-t, respectively). In both cases, we use minimum distance
estimation and for simplicity impose covariance stationarity. The resulting estimates can be
viewed as unconditional averages of the underlying (changing) variances. But it is possible
to allow for non-stationarity and still identify the parameters of interest (for brevity, these
are not reported here; they are available on request). Finally, we construct an estimate of
/

the ratio v ,     =⅞τ, which informs us on how much wage variability is due to workers

[(∆k¾t) ]

sharing the firm’s fortunes. This turns out to be a useful way to summarize the evidence.

23



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