Insurance within the firm

7.1 Main results

Table 7 shows the results of our exercise. The Hrst thing to emerge from the table is that
workers’ wages do reflect shocks to the firm’s value added: E(ωij_tεj_t) = 0.0019 with a
standard error of 0.0002 (Panel B). Moreover, there is a substantial difference in impact
between permanent and transitory shocks: wages do respond to permanent shocks but the
hypothesis of full insurance with respect to transitory shocks cannot be rejected (Panel A).
The estimated value of b_υ (which measures the sensitivity of workers’ earnings to transitory
shocks) is economically small (point estimate 0.007) and not statistically different from zero
(standard error 0.0051). The estimated value of b_u (responsiveness to permanent shocks)
is 0.06, an order of magnitude greater, with a small standard error of 0.0154.²⁷ Joint con-
sideration of the point estimates and of the standard errors of the two parameters suggests
that b_u = b_υ.²⁸ More precisely, while we cannot reject the hypothesis of “full transitory”
insurance, “full permanent” insurance can be ruled out. The J-test of overidentifying re-
striction has a p-value well above 10 percent in both cases, which signals that the models
are not misspecified (and that measurement error bias in the estimation of b_υ is negligible,
see note 11). Instruments’ power is not a concern, as is shown by the low p-value of the
F-test in the reduced form regressions.

Our findings imply that a 10 percent permanent change in firm performance induces
a 0.6 percent permanent variation in earnings for those employed at the same firm on a
continuing basis.²⁹ To get a sense of the economic significance of this effect consider the
median firm (value added of 3.49 million euro, 103 employees, paying an average salary
of 12,409 euro per year). Evaluated at the sample median, a permanent decrease in value
added of 349,500 euro (10 percent) - equivalent to a 3,413 euro drop in value added per

“'There may be some concern due to the fact that we regress wage shocks against firm shocks, which
are common to all individuals working in the same firm. Moulton (1986) shows that the effect of common
group errors is to produce artificially low standard errors in such regressions. We corrected standard errors
assuming that errors are not independent within firm and find that the correction has no dramatic effects:
b_u is estimated with a slightly higher standard error of 0.0252, but the associated p-value is still only 1.7
percent.

²⁸This is confirmed by the result of the exogeneity test conducted on ∆ε_j∙t. The test statistic displays a
p-value below 0.1 percent, which rejects the null b_u = b_υ = b.

²⁹Using gross rather than net earnings produces a slightly higher coefficient of 0.0692, implying less
insurance than when net earnings are used. This is consistent with the view that tax progressivity provides
implicit insurance.

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