Estimation of Nonlinear Error Correction Models. Forthcoming in Econometric Theory

Asymptotic theory for the estimation of nonlinear vector error correction mod-els (VECM) that exhibit regime-speci\u85c short-run dynamics is developed. In par-ticular, 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, consistencysquare root n consistency for the cointegrating vector is established for the least squares estimation of this general class of models. Second, the convergence rates are ob-tained for the least squares of threshold cointegration, which are n3=2 and n for and; respectively, where denotes the threshold parameter. This fast rate for in itself is practically relevant since the estimation error in does not a¤ect the estimation of short-run parameters unlike in smooth transition models. We also derive asymptotic distributions for the smoothed least squares estimation of threshold cointegration