Identification, estimation and efficiency of nonparametric and semiparametric models in microeconometrics
The focal point of this thesis is on identification and estimation of nonparametric models, as well as the efficiency and higher order properties of a class of semiparametric estimators in Microeconometrics. We present a new identification result for a particular nonparametric model that nests many popular parametric/nonparametric Econometric models as special cases. Estimators are proposed and their asymptotic properties derived; in particular, they are shown to be consistent and asymptotically pointwise normally distributed. We implement these estimators for the nonparametric estimation and testing of production functions in 4 industries within the Chinese economy in the years 1995 and 2001. The statistical properties of an entire family of semiparametric estimators for Limited Dependent Variables models are also analyzed. The derived theoretical results have direct applicability to a wide range of estimation problems. In particular, we derive the semiparametric efficiency bounds and show that some of the already-proposed estimators achieve these bounds. A connection with the Programme Evaluation literature is established as well. Finally, we derive an asymptotic approximation to the Mean Square Error of this class of semiparametric estimators to aid the choice of smoothing parameter. It is demonstrated that this choice can be made on the basis of bias alone. Possible extensions in this framework are also discussed.