COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1066 A Limit Theorem for a Smooth Class of Semiparametric Estimators Ariel Pakes and Steven Olley January 1994 We consider an econometric model based on a set of moment conditions which are indexed
by both a finite dimensional parameter vector of interest, , and an infinite dimensional
parameter, h, which in turn depends upon both and another infinite dimensional
parameter, tau. The model assumes that the moment conditions equal zero at the true value
of all unknown parameters. Estimators of are obtained by forming nonparametric estimates
of h and tau, substituting them into the sample analog of the moment conditions,
and choosing that value of that makes the sample moments as "close as possible"
to zero. Using independence and smoothness assumptions the paper provides consistency,
/n consistency, and asymptotic normality proofs for the resultant estimator. As an
example, we consider Olley and Pakes' (1991) use of semiparametric techniques to control
for both simultaneity and selection biases in estimating production functions. This
example illustrates how semiparametric techniques can be used to overcome both
computational problems, and the need for strong functional form restrictions, in obtaining
estimates from structural models. We also provide two additional sets of empirical results
for this example. First we compare the estimators of theta obtained using different
estimators for the nonparametric components of the problem, and then we compare
alternative estimators for the estimated standard errors of those estimators. |
