Fully modified OLS estimation and inference for seemingly unrelated cointegrating polynomial regressions and the environmental Kuznets curve for carbon dioxide emissions

This paper develops two fully modified OLS (FM-OLS) estimators for systems of seemingly unrelated cointegrating polynomial regressions, i.e., systems of regressions that include deterministic variables, integrated processes, and integer powers of integrated processes as explanatory variables. The stationary errors are allowed to be serially correlated and the regressors to be endogenous. Furthermore, the errors and regressors are allowed to be dynamically cross-sectionally correlated. The developed estimators have zero mean Gaussian mixture limiting distributions that allow for asymptotic chi-squared inference. The Wald-type hypothesis test results are the basis for considering detailed tests for general forms of group-wise poolability. We provide the corresponding group-wise pooled variants of our estimators, in case the poolability restrictions are not rejected. Our simulations indicate that appropriate pooling leads, as expected, to improved performance of the estimators and tests. Data-driven group-wise pooling turns out to be crucial in our illustrative application that analyzes the environmental Kuznets curve for CO2 emissions for six early industrialized countries.