UC Riverside

In the first chapter of this thesis, we propose a penalized splines (P-splines) estimator for random effects panel data model. While being a nonparametric technique, one of the most attractive properties of splines methods is their analogous setup to parametric regression model. Compared to kernel-based methods, however, splines methods are far less developed at least for econometric models. The asymptotic results of our P-splines estimator are established in this chapter. Monte Carlo simulation is conducted to compare the performance of our P-splines estimator with different kernel-based estimators proposed in recent literature. It turns out that the P-splines estimator consistently performs well and is computationally efficient.

In the second chapter, we develop a general procedure to derive the asymptotic variance-covariance matrices of two-stage estimators that can be used to estimate simultaneous equation systems with a mixture of any number of binary and continuous dependent variables. To demonstrate the usefulness of our procedure, we apply our formulas to empirical data with one continuous and two binary dependent variables in the simultaneous equations system. Our results are expected to be of tremendous help to numerous practitioners of econometrics using two-stage procedures to estimate their simultaneous equations models.