Semiparametric estimation of nonlinear simultaneous equations models

Semiparametric and nonparametric estimation methods have been employed in the estimation of many important econometrics models. Among many interesting econometrics models, we consider nonlinear simultaneous equations models that are known not to be adaptive, which implies that we cannot estimate the parameter vector as efficient asymptotically as if the true distribution of structural errors were known. The nonlinear full information maximum likelihood estimator is in general inconsistent unless the assumed density for the structural errors is the true one. The nonlinear three stage least squares estimator, while robust against misspecification of the error distribution, is not efficient.; In order to overcome these known limitations of existing parametric estimators, a semiparametric one-step estimator, the Pseudo Adaptive Maximum Likelihood (PAML) estimator, for nonlinear simultaneous equations models is proposed in this dissertation, which is N -consistent and asymptotically normal. The PAML estimator is obtained by approximating the log gradients for correctly specified maximum likelihood estimator as if the density estimated nonparametrically is the true density. The PAML estimator is different from the semiparametric maximum likelihood one-step estimator proposed by Ai (1997), which takes it into account the direct effect of parameters on the nonparametric density estimates. We also investigate the finite sample properties of the PAML estimator comparing with existing estimators. The results show that it overcomes the limitations of parametric estimators for some non-normal errors and it often shows equivalent or better performances than the semiparametric maximum likelihood one-step estimator for small or moderate sample size.