The Limited Information Maximum Likelihood Estimator as an Angle

T. W. Anderson, Naoto Kunitomo and Yukitoshi Matsushita
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T. W. Anderson: Department of Statistics and Department of Economics, Stanford University
Naoto Kunitomo: Faculty of Economics, University of Tokyo

No CIRJE-F-619, CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo

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.

Pages: 34 pages
Date: 2009-05
New Economics Papers: this item is included in nep-ecm
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