SEMINONPARAMETRIC MAXIMUM LIKELIHOOD ESTIMATION OF CONDITIONAL MOMENT RESTRICTION MODELS*

Abstract

This article studies estimation of a conditional moment restriction model with the seminonparametric maximum likelihood approach proposed by Gallant and Nychka ( Econometrica 55 (March 1987), 363–90). Under some sufficient conditions, we show that the estimator of the finite dimensional parameter θ is asymptotically normally distributed and attains the semiparametric efficiency bound and that the estimator of the density function is consistent under L 2 norm. Some results on the convergence rate of the estimated density function are derived. An easy to compute covariance matrix for the asymptotic covariance of the θ estimator is presented.