Book Description

"This dissertation is a collection of two papers studying the identification, estimation and testing of Econometrics problems using nonparametric methods. In Chapter 1, we study the estimation and testing of structural changes in panel data models with cross-sectional dependence and local stationarity. Instead of focusing on detection of abrupt structural changes, we consider smooth structural changes for which model parameters are unknown deterministic smooth functions of time, except for a finite number of time points. Such smooth alternatives are expected to be more realistic than sudden structural changes. We use nonparametric local smoothing method to consistently estimate the smooth changing parameters and develop two consistent tests for smooth structural changes in panel data models. The first test is to check whether all model parameters are stable over time. The second test is to check potential time-varying interaction while allowing for a common trend. Both tests have an asymptotic N (0, 1) distribution under the null hypothesis of parameter constancy and are consistent against a vast class of smooth structural changes as well as abrupt structural breaks with possibly unknown break points alternatives. Simulation studies show that the tests provide reliable inference in finite samples. Applying our tests to the cross-country growth accounting model using 14 OECD (Organisation for Economic Co-operation and Development) countries, we find instability in the model parameters. In Chapter 2, we study an under-identified triangular system of equations model that has k endogenous variables, but only strictly less than k excluded instrumental variables (k = 1, 2, ...). We consider a partially linear model. The endogenous variables for which excluded instruments are available are allowed to have a non-parametric effect. The linear part contains the endogenous variables (and higher order moments and interactions of these) for which we have no excluded instruments. Without the availability of additional instrumental variables, we exploit the additive separability in the partially linear model to generate additional exogenous variation that allows us to identify the coefficients of the endogenous regressors for which no excluded instruments are available. An easy-to-implement consistent estimator for the parametric part is presented. By applying the empirical process methods, we show that the estimator retains ?n-convergence rate and asymptotic normality even with the presence of generated regressors (when k > 1). The nonparametric part of the model is identified, and can be estimated with the standard nonparametric convergence rate. Monte Carlo simulation demonstrates our estimator performs well in finite samples."--Pages v-vi.