Estimation of Nonlinear Error CorrectionModels

Asymptotic inference in nonlinear vector error correction models (VECM) thatexhibit regime-specific short-run dynamics is nonstandard and complicated. Thispaper contributes the literature in several important ways. First, we establish theconsistency of the least squares estimator of the cointegrating vector allowing forboth smooth and discontinuous transition between regimes. This is a nonregularproblem due to the presence of cointegration and nonlinearity. Second, we obtainthe convergence rates of the cointegrating vector estimates. They differ dependingon whether the transition is smooth or discontinuous. In particular, we find that therate in the discontinuous threshold VECM is extremely fast, which is n^{3/2},compared to the standard rate of n: This finding is very useful for inference onshort-run parameters. Third, we provide an alternative inference method for thethreshold VECM based on the smoothed least squares (SLS). The SLS estimatorof the cointegrating vector and threshold parameter converges to a functional of avector Brownian motion and it is asymptotically independent of that of the slopeparameters, which is asymptotically normal.