Unidentified Components in Reduced Rank Regression Estimation of ECM's

Reduced rank regression procedures in error correction models (ECM’s) permit consistent estimation of the cointegration space but do not provide consistent estimates of individual structural relations when the dimension of the cointegration space is greater than one. Indeed, individual structural cointegrating equations are unidentified without additional a priori restrictions, just as in the conventional simultaneous equations framework. The effect of this lack of identification is explored by considering the distributions and limit distributions of reduced rank regression estimates of unidentified components of the cointegrating matrix in a typical VAR formulation of the ECM. Some recommendations are made for empirical practice.