Estimating equation (6) with OLS would give inconsistent estimates. In both the perfect
and imperfect information case, the comparative advantage hypothesis implies that rank as-
signment is endogenous, so θiet is correlated with the rank dummies. In addition, this term
cannot be eliminated by first-differencing (6) because it is interacted with the Dijt terms.
Holtz-Eakin, Newey and Rosen (1988) analyze models in which a fixed effect is interacted
with year dummies and show that consistent estimates can be obtained by quasi-differencing
the equation of interest and using appropriate instrumental-variable techniques. This method
will be applied here to estimate the wage equation (6). 8
2.3 Estimation and Interpretation of the Model Specification
This section describes the quasi-difference technique, the estimation method and the choice
of instruments in the perfect information case with comparative advantage and the imperfect
information case with both comparative advantage and learning. The estimation of the wage
equation also requires to specify a functional form for the human capital accumulation function
f which will be presented in the last part of this section.
The first step in estimating (6) is to eliminate θiet by quasi-differencing in the following
manner:
e
it =
wijt - ΣJ Dijtdj - Σj DijtXitβj - μit
∑J DijtCj f (Xit)
(7)
The martingale property of beliefs in innate ability which states that θiet = θiet-1 + uit, implies
that we can substitute a lagged version of equation (7) into (6). The final equation is therefore
given by: 9
wijt
JJ
∑ Dijtdj + ∑ DijtXitβj +
j=1 j=1
ΣjJ DijtCj f (Xit )
∑j' Dijt-Icj f (xit-1)
wijt-1
8This technique has been used previously by Lemieux (1998) in the case where the return to a time-invariant
unobserved characteristic is different in the union and non-union sector. Gibbons, Katz and Lemieux (1997)
formalize the estimation method in the presence of comparative advantage and learning with an application
to the estimation of the wage differentials by industry. Gibbons, Katz, Lemieux and Parent (2002) enrich the
preceding results by applying the method to the case of inter-occupation wage differentials.
9In the case with comparative advantage only, innate ability is time-invariant so θiet = θiet-1 and the lagged
version of (7) can be substituted into (6) in the same way. The difference is in the random term uit which drops
from (9).
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