Title: Cointegrating polynomial regressions with integrated regressors with drift: Fully modified OLS estimation and inference
Authors: Karsten Reichold - University of Klagenfurt (Austria) [presenting]
Martin Wagner - University of Klagenfurt (Austria)
Abstract: Although many macroeconomic variables are well described as integrated processes with drift, the cointegrating polynomial regression (CPR) literature lacks a complete analysis of the implications of the presence of integrated regressors with drift on estimation and inference. We address this issue by developing a fully modified (FM-)OLS estimator for CPRs with integrated regressors with potentially (unknown) non-zero drift. In case the deterministic regressors and the powers of the stochastic regressor share at least one identical power of time, the ensuing asymptotic multi-collinearity needs to be addressed to develop asymptotic theory. Although the limiting distribution of the FM-OLS estimator is not invariant to the presence of an unknown and non-zero drift, it allows for standard asymptotic inference for Wald-type hypotheses and common specification tests. However, the limiting distributions of widely used (non-)cointegration test statistics depend on the presence of a non-zero drift. Corresponding critical values are provided. Simulation results show that the developed estimator and tests based upon it perform well in finite samples and also highlight that not taking a non-zero drift into account has substantial detrimental effects on estimator and test performance. In particular, the test for the null hypothesis of cointegration exhibits serious over-rejections.