On Parameter Estimation in Cointegrating Polynomial Regressions: Single Equation, Seemingly Unrelated and Panel Estimators

Abstract

This thesis studies parameter estimation and inference in systems of seemingly unrelated cointegrating polynomial regressions as introduced in Hong and Wagner (2011). These are equation systems with deterministic regressors and integrated processes and their integer powers as stochastic regressors. The stochastic regressors are allowed to be endogenous and the errors are allowed to be dynamically correlated, both over time and across equations. In particular we consider a setting relevant for the analysis of the environmental Kuznets curve (EKC) hypothesis, including only one integrated regressor and its second and third power. In this setting we compare three estimation approaches by means of a simulaton study. These are the FM-OLS type estimator for (single equation) cointegrating polynomial regressions of Wagner and Hong (2015), the SUR estimators of Hong and Wagner (2011) and panel type estimators advocated by de Jong and Wagner (2016). This thesis investigates under which conditions on sample sizes (N and T), level of endogeneity and extent of serial and cross-sectional correlation, one of the three above mentioned estimators, as well as hypothesis tests, based upon it, performs relatively best. Not forgetting the fact that the results are based on a simulation study only, they provide some guidance with respect to estimator choice in cointegrating polynomial regression settings with panel-type data.