Title: Linear fully modified OLS estimation of cointegrating polynomial regressions
Authors: Oliver Stypka - TU Dortmund (Germany) [presenting]
Martin Wagner - University of Klagenfurt (Austria)
Abstract: In the empirical environmental Kuznets curve (EKC) literature, which investigates a potentially inverted U-shaped relationship between measures of economic development and pollution respectively emissions, it is common practice to use cointegration methods developed for the linear setting in nonlinear contexts. This means that integrated processes and its powers are both considered to be $I(1)$ and estimators designed for asymptotically valid inference in standard cointegration settings like the FM-OLS estimator are commonly applied as if there were multiple integrated regressors included in the regression. We show that this ``linear'' estimator has, surprisingly, the same limiting distribution as the FM-CPR estimator developed specifically for cointegrating polynomial regressions, which takes into account that nonlinear functions of integrated processes are not I(1). We also show, by means of simulations, that inference based on the FM-CPR estimator outperforms inference based on the ``linear'' FM-OLS estimator in terms of both lower size distortions and higher (size-corrected) power.