We generalize equation (2) as:
wij t = a'ijtδ + byj t + ψijt
(7)
where the subscript i stands for the i-th individual and w⅛t is the logarithm of worker
compensation.5 The term ⅛z∙t denotes a vector of systematic factors that affect individual
i's compensation, which can vary across workers, firms and time, while ψijt is the stochastic
component of earnings, which is unrelated to the firm’s fortunes. These idiosyncratic shocks
are meant to capture unanticipated fluctuations in individual ability, shocks to productivity
(such as illness), idiosyncratic changes in labor supply (child-raising, family labor supply
effects, etc.).
Let us assume that idiosyncratic earnings shocks are in turn the sum of a permanent
random walk component ηijt = ηijt-1 + ξijt and a serially uncorrelated transitory shock
μijt.6 Again to save on notation, it is maintained that covariance stationarity holds, i.e.
e (⅛t) = σ∣, and E ^lijt)
= σ⅛ for all t.
P,
The two shocks are serially uncorrelated and
uncorrelated with each other at all leads and lags.
Taking first differences of (5) and (7), and using the stochastic structure outlined above,
we get the following system of two equations:
A(L,p)Δy∙t = ∆^θ + uj t + ∆υjt (8)
A(L,p)Δwijt = ∆alijtλ + ∆z'jtbθ + buj t + b∆vjt
+A(L,p)ξij t + A(L,p)Δμijt (9)
where λ = A (L,p) δ. For the purpose of this paper it is more convenient to define firm per-
formance and earnings growth after adjusting for observable firm and worker characteristics,
aWe let earnings to depend on contemporary firm performance, i.e. assume that wages adjust immediately
to changes in performance. In practice, wages might adjust with a lag (think of overtime or bonus decisions,
which are usually taken at the end of the calendar year). Nevertheless, if adjustments are made at a frequency
higher than a year (say, a quarter), annual data of the type used here will not detect deviations from the
contemporaneous adjustment assumption.
0In this context, an idiosyncratic shock to earnings is a purely individual innovation, i.e. it is not shared
by co-workers within the firm.