The name is absent

- ^R.D^ijtc^jf (x^it) , ∣∑ Dijt-Idj + Σ, Dijt-ιX<t-ιβjl + e<t        (8)

j^JDijt-1cjf(xit-1) j=1             j=1

,                  IJn           RJ D^ijt^{cj f} (x^it)                                /ɑʌ

where e_it = μt + У DijtUt — J_j '------μ----r μit-i                   (9)

j=1              j^JDijt-1cjf(xit-1)

This equation cannot be estimated using non-linear least square because wijt-1 is correlated
with μ_it-1. Moreover, because of the presence of learning, the new information on innate
ability at time t, ui_t , is correlated with Dij_t since beliefs on ability influence the current rank
assignment. These problems can be solved by choosing appropriate instruments for wijt-1 and
Dijt , in which case consistent estimates will be obtained. The set of instruments, Zi , has to
satisfy the following condition:

E(eitZi) = 0                                        (10)

The objective is then to minimize the following quadratic form:

min e(γ)^,Z (Z ^,ΩZ )^-1Z ^,e(γ)                              (11)

^γ

where Z^,ΩZ is the covariance matrix of the vector of moments Z^,e(γ), Ω is the covariance
matrix of the error term ei_t and γ is the vector of parameters. An efficient estimator can be
obtained by estimating equation (6) in a first step with Ω = I.

Finally, the unmeasured ability term θ_i^e_t in the error term of equation (6) is normalized to
zero for the parameters to be identified. ¹⁰ This is done by adding the following equation as a
constraint on the optimization of (11):

(1/TN) ΣΣθit = 0                         (12)

where N is the number of individuals, T is the number of periods for each individual and θi_t
satisfies equation (7).

Instruments are chosen using the identification assumption for estimation of panel data
equations that imposes strict exogeneity of right-hand side variables. More formally:

E (μit∕Xii...XiT, Diji ...Dj, θi) = 0                           (13)

The estimation is done in two parts. First the role of comparative advantage under the
assumption of perfect information is examined. Then the combined impact of comparative
advantage and learning is estimated under the assumption of imperfect information.

¹⁰A proof of the necessity of this constraint is given in Lemieux (1998).

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