Reduced Rank of Regression Using Generalized Method of Moments Estimators

Generalized Method of Moments (GMM) Estimators are derived for Reduced Rank Regression Models, the Error Correction 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 both a Generalized Least Squares Estimator and a White Covariance Matrix Estimator. The resulting cointegrating vectors estimators have again normal limiting distributions while the cointegration tests have identical limiting distributions which differ from the Dickey-Fuller type.Second, cointegrating vector estimators and tests are derived which allow for structural breaks in the cointegrating vector and/or multiplicator.The limiting distributions of the estimators are again shown to be normal and the limiting distributions.