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The Tail Behavior Of Maximum Likelihood Estimates Of Cointegrating Coefficients In Error Correction Models, Peter C.B. Phillips
The Tail Behavior Of Maximum Likelihood Estimates Of Cointegrating Coefficients In Error Correction Models, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper derives exact finite sample distributions of maximum likelihood estimators of the cointegrating coefficients in error correction models. The distributions are derived for the leading case where the variables in the system are independent random walks. But important aspects of the theory, in particular the tail behavior of the distributions, continue to apply when the system is cointegrated. The reduced rank regression estimator is shown to have a distribution with Cauchy-like tails and no finite moments of integer order. The maximum likelihood estimator of the coefficients in the triangular system representation has matrix t -distribution tails with finite integer …
Unidentified Components In Reduced Rank Regression Estimation Of Ecm's, Peter C.B. Phillips
Unidentified Components In Reduced Rank Regression Estimation Of Ecm's, Peter C.B. Phillips
Cowles Foundation Discussion Papers
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.