Five alternative methods of estimating long-run equilibrium relationships

Abstract

This paper compares several methods (ordinary least squares, nonlinear least squares, maximum likelihood in an error correction model, principal components, and canonical correlations) of estimating cointegrating vectors. Although all of them are superconsistent, an empirical example shows that the estimates can vary significantly. The paper examines the asymptotic distribution of the estimators resulting from these methods, and shows that maximum likelihood in a fully specified error correction model (Johansen's approach) has clearly better properties than the other estimators. A Monte Carlo study indicates that finite sample properties are consistent with the asymptotic results. This is so even when the errors are non-Gaussian or when the dynamics are unknown.