Insurance within the firm

assumes that wage variability can only be explained by the combination of strength of in-
centives and output variability. With full insurance or no variability in performance, wages
should evolve deterministically. However, there may be additional sources of unexplained
wage variability that have nothing to do with the pay-performance relation.⁴ We augment
our wage specification to account for this. Fourth, in accordance with previous empirical
studies (Blanchflower, Oswald, and Sanfey, 1996; Aggarwal and Samwick, 1999), we use
total compensation as the empirical counterpart of the wage in equation (2). Finally, de-
parting from the theoretical model of the previous section, we consider a compensation
scheme that is linear in logarithms, rather than levels. This has the advantage of fitting
earnings and output data better. We now turn to the statistical characterization of the
model.

3.1 Firm performance

Consider the case where the unanticipated component of (log) firm performance contains a
permanent component ζj_t which follows a random walk process, and a transitory compo-
nent, Vjt_t which is serially uncorrelated. Permanent shocks may capture non-mean-reverting
unanticipated technological changes, changes in management or changes in the organiza-
tional structure of the firm, while mean-reverting transitory shocks are more likely to be
associated with fluctuations in demand. The firm can distinguish between transitory and
permanent shocks but cannot determine whether they are due to pure chance or to workers’
effort. In accordance with the basic model, the likelihood of both shocks may depend on
workers’ effort. For example, effort may influence performance permanently when the firm
is trying to secure a new contract or develop a new product, and in a transient way when it
is an input of a static production function. While partly neglected in the theoretical liter-
ature, the distinction between persistent and transitory shocks is important from the point
of view of the optimal wage contract. On the one hand, it may be optimal for a risk-neutral
firm to insulate workers from transitory fluctuations in output; on the other hand, it is less

⁴ For example, part of vector a in (2) could be unobservable to the econometrician even though perfectly
observable to the firm (unobservable human capital components, measurement error, etc.). In this case one
would record unexplained wage variability even in the absence of a contractual relationship between earnings
and firm performance.

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