Reduced Rank Regression Using Generalized Method of Moments Estimators, with Extensions to Structural Breaks in Cointegration Models.

Generalized Method of Moments (GMM) Estimators are derived for Reduced Rank Regression Models, the Error Corrections Cointegration Model (ECCM) and the Incomplete Simultaneous Equations Model (INSEM). The GMM (2SLS) estimators of the cointegrating vector in the ECCM are shown to have normal limiting distributions. Tests for the number of unit roots can be constructed straightforwardly and have Dickey-Fuller type limiting distributions. Two extensions of the ECCM, which are important in practice, are analyzed. First, cointegration estimators and tests allowing for structural shifts in the variance (heteroscedasticity) of the series are derived and analyzed using a Generalized Least Squares Estimator. Second, cointegrating vector estimators and tests are derived which allow for structural breaks in the cointegrating vector and/or multiplicator. The resulting cointegrating vectors estimators have again normal limiting distributions while the cointegration tests have limiting distributions which differ from the standard Dickey-Fuller type.