Panel cointegrating polynomial regression analysis and the environmental Kuznets curve

Abstract

This paper develops a modified and a fully modified OLS estimator for a panel of cointegrating polynomial regressions, i.e. regressions that include an integrated process and its powers as explanatory variables. The stationary errors are allowed to be serially correlated and the regressors are allowed to be endogenous and we allow for individual and time fixed effects. Inspired by Phillips and Moon (1999) we consider a cross-sectional i.i.d. random linear process framework. The modified OLS estimator utilizes the large cross-sectional dimension that allows to consistently estimate and subtract an additive bias term without the need to also transform the dependent variable as required in fully modified OLS estimation. Both developed estimators have zero mean Gaussian limiting distributions and thus allow for standard asymptotic inference. Our illustrative application indicates that the developed methods are a potentially useful addition to not least the environmental Kuznets curve literature's toolkit.