Panel cointegrating polynomial regression analysis and an illustration with the environmental kuznets curve

The analysis of cointegrating polynomial regressions, i.e, regressions that include an integrated process and its powers as explanatory variables is extended from the time series to the panel case by developing two estimators, a modified and a fully modified OLS estimator. As usual in the cointegration literature, the stationary errors are allowed to be serially correlated and the regressors are allowed to be endogenous. Both individual and time fixed effects are accommodated and the analysis uses an 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. A brief application to the environmental Kuznets curve illustrates the developed methods.