zit = (yijt - dj )/cj = ηit + εijt
Note that zit is independent of job assignment so that learning takes place identically across
jobs. Expectations of the innate ability of worker i with x years of prior labor-market expe-
rience at period t will therefore be conditioned on the history of signals extracted from the
observed outputs. Formally, this expectation is defined as:
Oft = E (θi∣Zit-χ,...,Zit-ι)
Because output is a linear function of effective ability, expected output at the beginning
of period t, and therefore wages, will be based on expected effective ability (conditional on
the information available at t - 1). Task assignment in each period is then based on the
maximization of current expected output.
In addition to the stylized facts previously discussed in the perfect information model, the
addition of imperfect information and learning allows the model to explain the possibility of
real wage decreases. The argument is based on the fact that wages depend on expected innate
ability, the evolution of which is now driven by the evolution of agents’ beliefs. Because agents
have rational expectations, expected innate ability follows a martingale process:
θiet = θiet-1 + uit (4)
This means that the best prediction of future expected innate ability is current expected
innate ability. In other words, any change in current beliefs is caused by the arrival of new
information contained in the observation of current output and could not be predicted from
previous realized outputs.
In the model with imperfect information a worker’s expected innate ability can fall from
one period to the next if uit is negative. If the decrease is sufficiently large, it will dominate
the increase in effective ability due to human capital accumulation and next period wage will
fall. For the same reason, there will be a positive frequency of demotions.
Average wage increases at promotion are larger than average wage increases before and after
promotion. The worker promoted at the end of the period had a larger increase in expected
effective ability than the worker not promoted. The wage increase will then be higher for
this reason and also because the increase in expected ability will be valued at a bigger rate
(cj+1 > cj). After the promotion, the expected change in expected innate ability is zero so the
wage increase is smaller on average than the wage increase at promotion.