Insurance within the firm

obvious that the firm will be prepared to supply insurance against permanent shocks.

We model firm performance according to the following stochastic process:

A(L,p)y_jt = z^,_jtθ + ε_jt

where j and t are subscripts for the j-th firm at time t, A(L,p) is a lag polynomial of
order p > 0 (i.e. A(L,p)xj_t = ∑%.=₀a_τXjt-_τ, with ɑo ≡ 1), yj_t is a measure of observed
firm performance, such as the logarithm of profits, value added or output, Zj_t a vector of
observable attributes, εp the stochastic component of firm performance, and θ and A are
parameters to be estimated. We assume that the stochastic component of firm performance
has the following structure:

^εj^{t =} ^j t ^{+ v}i^t                                         (⁵)

C?t = ^jt-1 ^{+ u}i^{t                                    (6)}

Equations (5) and (6) decompose the disturbance into a transitory component, v_j∙_t, and a

permanent one, ζ ∙_t. To simplify subsequent notation, assume covariance stationarity, so that

= σ² for all t. We assume that the two shocks Vj_t and Uj_t are

serially uncorrelated and uncorrelated with each other. This structure (and subsequent
identification strategy) can be generalized to the case where Vj_t is serially correlated (for
instance it follows an MA(q) process).

3.2 Workers’ earnings

Consider now workers’ compensation. The standard principal-agent model described above
assumes that the only source of unanticipated fluctuations in wages is variability in the firm’s
performance. In reality, fluctuations in individual compensation depend also on individual
idiosyncratic shocks (i.e., shocks that are unrelated to unanticipated changes in firm output,
such as a spell of illness affecting productivity on the job). From a purely statistical point
of view, another source of random variation in wages is measurement error.

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