Title: Cointegrating multivariate polynomial regressions: Fully modified OLS estimation and inference
Authors: Oliver Stypka - TU Dortmund (Germany)
Martin Wagner - University of Klagenfurt (Austria) [presenting]
Abstract: A fully modified OLS (FM-OLS) estimator is developed for cointegrating multivariate polynomial regressions, i.e. regressions that include as explanatory variables deterministic variables, integrated processes and products of non-negative integer powers of the integrated processes. The stationary errors are allowed to be serially correlated and the regressors are allowed to be endogenous. We extend existing variants of the FM-OLS estimator to cointegrating multivariate polynomial regressions, which overcomes the additive separability restriction typically used in nonlinear cointegration analysis for the polynomial case. The FM-OLS estimator has a zero-mean Gaussian mixture limiting distribution that allows for standard asymptotic inference. In addition to hypothesis testing on the parameters also Wald and LM specification tests are derived, as well as a KPSS-type test for cointegration. The theoretical analysis is complemented by a simulation study. Since the developed estimator immediately leads to a RESET-type specification test, we also compare in the simulation section the performance of our FM-OLS RESET with other (partly more restrictive) cointegration specification tests.