Analysis of cointegration vectors using the GMM approach

This paper generalizes Johansenʹs (1988) maximum likelihood approach of the analysis of cointegrating vectors to the generalized method of moments (GMM) approach. We derive the asymptotic distribution of the cointegration vectors estimated from the fully modified generalized method of moments (FM-GMM) estimation procedure. We also introduce the FM-GMM version of Johansenʹs (1988) likelihood ratio (LR) test for the rank of a cointegrating matrix. Unlike the LR test which has a nonstandard unit root distribution, the FM-GMM rank test has a standard χ2 distribution when the set of instruments differs from the set of regressors and when a particular form of the weight matrix is used in estimation. The form of this weight matrix corresponds to that of the optimal weight matrix of Hansen (1982) for efficient GMM estimation.