The Asymptotic Validity of "Standard" Fully Modified OLS Estimation and Inference in Cointegrating Polynomial Regressions

The paper considers estimation and inference in cointegrating polynomial regressions, i. e., regressions that include deterministic variables, integrated processes and their powers as explanatory variables. The stationary errors are allowed to be serially correlated and the regressors are allowed to be endogenous. The main result shows that estimating such relationships using the Phillips and Hansen (1990) fully modified OLS approach developed for linear cointegrating relationships by incorrectly considering all integrated regressors and their powers as integrated regressors leads to the same limiting distribution as theWagner and Hong (2016) fully modified type estimator developed for cointegrating polynomial regressions. A key ingredient for the main result are novel limit results for kernel weighted sums of properly scaled nonstationary processes involving scaled powers of integrated processes. Even though the simulation results indicate performance advantages of the Wagner and Hong (2016) estimator that are partly present even in large samples, the results of the paper drastically enlarge the useability of the Phillips and Hansen (1990) estimator as implemented in many software packages.