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The Limited Information Maximum Likelihood Estimator as an Angle

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Author Info
T. W. Anderson (Department of Statistics and Department of Economics, Stanford University)
Naoto Kunitomo (Faculty of Economics, University of Tokyo)
Yukitoshi Matsushita (JSPS and Graduate School 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.

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Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-619.

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Length: 34 pages
Date of creation: May 2009
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Handle: RePEc:tky:fseres:2009cf619

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Phillips, Peter C B, 1984. "The Exact Distribution of LIML: I," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 25(1), pages 249-61, February. [Downloadable!] (restricted)
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  2. Gary Chamberlain, 2007. "Decision Theory Applied to an Instrumental Variables Model," Econometrica, Econometric Society, vol. 75(3), pages 609-652, 05. [Downloadable!] (restricted)
  3. T. W. Anderson & Naoto Kunitomo & Yukitoshi Matsushita, 2008. "On Finite Sample Properties of Alternative Estimators of Coefficients in a Structural Equation with Many Instruments," CIRJE F-Series CIRJE-F-577, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
  4. Anderson, T W & Kunitomo, Naoto & Sawa, Takamitsu, 1982. "Evaluation of the Distribution Function of the Limited Information Maximum Likelihood Estimator," Econometrica, Econometric Society, vol. 50(4), pages 1009-27, July. [Downloadable!] (restricted)
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This page was last updated on 2009-11-27.

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