The Exact Distribution of LIML: I
AbstractIt is shown that the exact finite sample distribution of the limited information maximum likelihood (LIML) estimator in a general and leading single equation case is multivariate Cauchy. When the LIML estimator utilizes a known error covariance matrix (LIMLK) it is proved that the same Cauchy distribution still applies. The corresponding result for the instrumental variable (IV) estimator is a form of multivariate t density where the degrees of freedom depend on the number of instruments.
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Bibliographic InfoPaper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 658.
Length: 22 pages
Date of creation: Dec 1982
Date of revision:
Publication status: Published in International Economic Review (February 1984), 25(1): 249-261
Note: Extended version of CFDP 626. CFP 589.
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Phone: (203) 432-3702
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Web page: http://cowles.econ.yale.edu/
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA
Other versions of this item:
- Phillips, Peter C B, 1985. "The Exact Distribution of LIML: II," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(1), pages 21-36, February.
- 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.
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
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.:
- Kelejian, Harry H, 1974. "Random Parameters in a Simultaneous Equation Framework: Identification and Estimation," Econometrica, Econometric Society, Econometric Society, vol. 42(3), pages 517-27, May.
- Wegge, Leon L, 1971. "The Finite Sampling Distribution of Least Squares Estimators with Stochastic Regressors," Econometrica, Econometric Society, Econometric Society, vol. 39(2), pages 241-51, March.
- Phillips, P C B, 1980. "Finite Sample Theory and the Distributions of Alternative Estimators of the Marginal Propensity to Consume," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 47(1), pages 183-224, January.
- Fuller, Wayne A, 1977. "Some Properties of a Modification of the Limited Information Estimator," Econometrica, Econometric Society, Econometric Society, vol. 45(4), pages 939-53, May.
- Naoto Kunitomo, 1981. "On A Third Order Optimum Property of The LIML Estimator When the Sample Size is Large," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 502, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Mariano, Roberto S, 1977. "Finite Sample Properties of Instrumental Variable Estimators of Structural Coefficients," Econometrica, Econometric Society, Econometric Society, vol. 45(2), pages 487-96, March.
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