The Limited Information Maximum Likelihood Estimator as an Angle
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.
|Date of creation:||May 2009|
|Date of revision:|
|Contact details of provider:|| Postal: Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033|
Web page: http://www.cirje.e.u-tokyo.ac.jp/index.html
More information through EDIRC
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.:
- Gary Chamberlain, 2007. "Decision Theory Applied to an Instrumental Variables Model," Econometrica, Econometric Society, vol. 75(3), pages 609-652, 05.
- Hillier, Grant H, 1990. "On the Normalization of Structural Equations: Properties of Direct Estimators," Econometrica, Econometric Society, vol. 58(5), pages 1181-94, September.
- 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.
- Peter C.B. Phillips, 1982. "The Exact Distribution of LIML: I," Cowles Foundation Discussion Papers 658, Cowles Foundation for Research in Economics, Yale University.
- Peter C.B. Phillips, 1983. "The Exact Distribution of LIML: II," Cowles Foundation Discussion Papers 663, Cowles Foundation for Research in Economics, Yale University.
- 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.
When requesting a correction, please mention this item's handle: RePEc:tky:fseres:2009cf619. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CIRJE administrative office)
If references are entirely missing, you can add them using this form.