“Linear” fully modified OLS estimation of cointegrating polynomial regressions

Abstract

A large part of the empirical environmental Kuznets curve literature uses cointegrating regressions involving a unit root process and its powers as regressors. In this literature the unit root process and its powers are, incorrectly, all treated as integrated processes and modified least squares estimation methods for linear cointegrating regressions are routinely employed. We show that this approach to estimation leads for the Fully Modified OLS estimator surprisingly to the same limiting distribution as obtained for the version of the Fully Modified OLS estimator adapted to the cointegrating polynomial regression setting of Wagner and Hong (2016).