ESTIMATION OF NONLINEAR ERROR CORRECTION MODELS

Abstract

Asymptotic theory for the estimation of nonlinear vector error correction models that exhibit regime-specific short-run dynamics is developed. In particular, regimes are determined by the error correction term, and the transition between regimes is allowed to be discontinuous, as in, e.g., threshold cointegration. Several nonregular problems are resolved. First of all, consistency-square root n consistency for the cointegrating vector beta-is established for the least squares estimation of this general class of models. Second, the convergence rates are obtained for the least squares of threshold cointegration, which are n(3/2) and n for beta and gamma, respectively, where gamma denotes the threshold parameter. This fast rate for beta in itself is of practical relevance because, unlike in smooth transition models, the estimation error in beta does not affect the estimation of short-run parameters. We also derive asymptotic distributions for the smoothed least squares estimation of threshold cointegration.