Showing papers by "T. W. Anderson published in 2009"

Likelihood Ratio Tests in Reduced Rank Regression with Applications to Econometric Structural Equations

Abstract: Likelihood ratio criteria are developed for hypotheses concerning multivariate regression matrices when reduced rank is assumed or equivalently hypotheses concerning linear restrictions on regression matrices. In an econometric simultaneous equation model a single restriction may be called a ”structural equation.” A model of reduced rank in statistics is often termed a ”linear functional relationship.” In this paper the likelihood ratio test that the regression matrix satisfies some specified restriction is developed under the assumption of normality. The test for the corresponding hypothesis that the regression matrix of given rank is a specified matrix is also developed. The asymptotic distribution of the test criterion is found under several alternative assumptions on the sequence of models. The ”cointegration model” is included in this study. The test for one structural equation is an advancement on the test statistic proposed by Anderson and Rubin (1949 and 1950).

The Limited Information Maximum Likelihood Estimator as an Angle

Abstract: When an econometric structural equation includes two endogenous variables and their coefficients are normalized so that their sum of squares is 1, it is natural to express them as the sine and cosine of an angle. The Limited Information Maximum Likelihood (LIML) estimator of this angle when the error covariance matrix is known has constant variance. Of all estimators with constant variance the LIML estimator minimizes the variance. Competing estimators, such as the Two-Stage Least Squares estimator, has much larger variance for some values of the parameter. The effect of weak instruments is studied.