Integrated modified OLS estimation for cointegrating polynomial regressions - with an application to the environmental Kuznets curve for CO2 emissions

Abstract

This paper considers the integrated modified OLS (IM-OLS) estimator for cointegrating polynomial regressions recently developed in Vogelsang and Wagner (2014a; 2014b). Cointegrating polynomial regressions include deterministic variables, integrated processes and integer powers of integrated processes as explanatory variables. The stochastic regressors are allowed to be endogenous and the stationary errors are allowed to be serially correlated. The IM-OLS estimator allows for asymptotically standard inference in this framework when using consistent estimators of the long run variance. Additionally, we also provide fixed-b asymptotic theory for the case of full design to capture the impact of kernel and bandwidth choice on the sampling distributions of estimators and test statistics. We investigate the properties of the IM-OLS estimator and hypothesis tests based upon it by means of a simulation study to compare its performance with fully modified OLS (FM-OLS) and dynamic OLS (D-OLS). Finally, we apply the method to estimate the environmental Kuznets curve for CO2 emissions over the period 1870-2009.