Under the assumption of perfect information, the random shock uit drops from the error
term of equation (6). The elimination of θi resulting from the quasi-difference corrects the
problem of endogeneity in the assignment of workers to ranks. The equation still needs to be
instrumented due to the presence of lagged wage on the right-hand side, correlated with μit-1
given (5). With imperfect information about innate ability, mobility is driven by the learning
process so Dijt is correlated with the new information obtained from the observation of current
output, uit.
Equation (13) states that conditional on observed innate ability, individual characteristics
and rank assignments each period are uncorrelated with the error term in the wage equation
(6). Therefore, this condition provides a set of potentially valid instruments with the property
that they are not correlated with the μ terms in the e term from equation (8).
In the perfect information case, given the assumption of workers’ comparative advantage
in a given job rank and the fact that wages are linearly related to effective ability, the history
of previous period rank assignment should help predict wages. In particular, interaction terms
between Dijt-1 and Dijt help predict wijt-1. Consider a high and a low ability worker with the
same experience and the same rank in period t - 1. Because of different levels of innate ability,
the workers have different wages and so contemporaneous rank assignment is not informative
enough to identify differences in wages. On the other hand, the high ability worker may be at
the level of effective ability required to get promoted next period. Therefore, having additional
information on next period rank helps to make inferences on each worker’s ability level (for a
given level of experience) and therefore on their wage.
Under imperfect information, expected innate ability evolves over time as beliefs change. In
this case, changes in expected effective ability resulting from a positive (or negative) realization
of uit affect rank assignment and therefore Dijt . To find instruments for Dijt , one can rely on
the characteristics of the martingale process for beliefs. Agents have rational expectations so
changes in beliefs are serially uncorrelated. Therefore Dijt-1 and also Dijt-2 are not correlated
with uit as they result from the realizations of uit-1 and uit-2 respectively. Moreover as before,
condition (13) applies so they are not correlated with the μ,s error terms of the wage equation.
They then represent potentially valid instruments for Dijt. The interaction between Dijt-2
and Dijt-1 constitutes a good predictor of current rank affiliation because it helps identify
differences in expected ability in period t - 1 (using the same argument as in the perfect
information case) as well as in period t. 11
11Given the martingale hypothesis for the evolution of the beliefs, expected ability at the beginning of period
t (before the realization of output in t) is not expected to be different from expected ability at t - 1.
11