Essays on stability, functional form and poolability of nonlinear cointegrating regressions

This cumulative dissertation develops and examines cointegration regression techniques and their application to nonlinear cointegrating relationships between integrated time series, with a particular focus on the Environmental Kuznets Curve (EKC). The EKC hypothesis postulates an inverted U-shaped relationship between economic development and pollution. Chapter 1 introduces residual-based monitoring procedures for cointegrating polynomial regressions (CPRs) to detect and date structural changes, i.e. whether a relationship may turn into a spurious relationship or whether the parameters of the relationship change. CPRs capture nonlinear dynamics by incorporating integer powers of integrated regressors. Chapter 2 evaluates estimators for nonparametric cointegrating regressions and specification tests for nonlinear cointegrating relationships, comparing their performance through a large scale simulation study. Chapter 3 extends estimators for seemingly unrelated cointegrating polynomial regressions to accommodate common integrated regressors across equations. It provides limiting distributions for these estimators, along with Wald-type hypothesis tests, RESET-type specification tests, and methods for group-wise pooled estimation, enhancing flexibility and precision in modeling complex systems.