between transitory and permanent shocks is not found in the theory, nor has been taken
into account in previous empirical work. This can perhaps explain why several studies
have found that wages are little responsive to measures of performance, i.e. that insurance
appears to dominate incentives. In fact, ignoring the distinction between transitory and
permanent shocks biases the estimate of the pay-per-performance coefficient towards full
insurance if transitory shocks are more likely to be insured than permanent shocks (a solid
conclusion of our empirical analysis).41 Third, the supply of insurance depends on firm
characteristics other than size (a well known fact of the labor market), such as location
within an industrial district, which presumably helps employers to disentangle random
common fluctuations from idiosyncratic fluctuations in output.
Overall, the firm proves to be an important provider of insurance for individuals. The
average standard deviation of wage growth shocks is about 10 percent while that of shocks to
value added growth is 30 percent; about one-tenth of the wage variability is due to workers
sharing the firm’s (permanent) risk. If temporary shocks were transferred to workers in the
same proportion as permanent shocks, the variability of earnings would increase by as much
as 15 percent.
41To show this notice that the unexplained component of earnings growth can be written as in equation
(26):
ʌ^ʊ t — buuj + + b1∙^>l'i- + + Ψijt
which explicitly takes into account the different nature of the shocks to output and the fact that they may
have a different impact on wages. The term φi-1 reflects residual unexplained variation not accounted for
by shocks. Our empirical analysis suggests that b,i > 0 and bυ — 0. Thus in this model ʌw^ — — buuj + + φijt
and transitory shocks to firm performance do not affect wages because they are smoothed away at the firm
level. Suppose that the distinction between transitory and permanent shocks is ignored and that a common
sensitivity factor bu is imposed. In this case:
ʌutj — — bu (uj + + ʌvjt) + $ij-t
The residual term ⅛j∙t includes residual unexplained variation not accounted for shocks, φijt, and -buʌvjt,
a term that reflects the failure to account for the different sensitivity of wages to shocks of different nature.
In this simple univariate case the OLS estimate of b„ has probability limit:
p Iim bu — bu
The OLS estimate of b„ is therefore downward-biased. The sign of the bias remains negative also when
bv > 0 but bu > b,,.
35