Estimation of nonlinear error correction models

Asymptotic inference in nonlinear vector error correction models (VECM) that exhibit regime-specific short-run dynamics is nonstandard and complicated. This paper contributes the literature in several important ways. First, we establish the consistency of the least squares estimator of the cointegrating vector allowing for both smooth and discontinuous transition between regimes. This is a nonregular problem due to the presence of cointegration and nonlinearity. Second, we obtain the convergence rates of the cointegrating vector estimates. They differ depending on whether the transition is smooth or discontinuous. In particular, we find that the rate 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 on short-run parameters. Third, we provide an alternative inference method for the threshold VECM based on the smoothed least squares (SLS). The SLS estimator of the cointegrating vector and threshold parameter converges to a functional of a vector Brownian motion and it is asymptotically independent of that of the slope parameters, which is asymptotically normal.