Title: Cointegrating polynomial regression with an integrated regressor with drift: Fully modified OLS estimation and inference
Authors: Karsten Reichold - Technical University Dortmund (Germany) [presenting]
Martin Wagner - University of Klagenfurt (Austria)
Abstract: Fully modified OLS cointegrating polynomial regression analysis is reconsidered by focusing on the case where the integrated regressor has a drift, with in general unknown drift parameter. In case the deterministic component and the powers of the integrated regressor share at least one identical power of time, the ensuing asymptotic multi-collinearity needs to be addressed. This is done, as usual in the unit root and cointegration literature, by an appropriate linear transformation of the stochastic regressors. The corresponding inverse transformation then leads to the singular limiting distribution of the FM-OLS estimator corresponding to the untransformed variables. It is important to note that in case of unknown drift the FM-OLS limiting distribution of the intercept is contaminated by a second order bias term stemming from the fact that the drift parameter is also estimated at rate square root of sample size.