The Exact Distribution of LIML: II
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 InfoArticle provided by Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association in its journal International Economic Review.
Volume (Year): 26 (1985)
Issue (Month): 1 (February)
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Other versions of this item:
- 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.
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
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- 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, vol. 47(1), pages 183-224, January.
- Naoto Kunitomo, 1981. "On A Third Order Optimum Property of The LIML Estimator When the Sample Size is Large," Discussion Papers 502, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Kelejian, Harry H, 1974. "Random Parameters in a Simultaneous Equation Framework: Identification and Estimation," Econometrica, Econometric Society, vol. 42(3), pages 517-27, May.
- Fuller, Wayne A, 1977. "Some Properties of a Modification of the Limited Information Estimator," Econometrica, Econometric Society, vol. 45(4), pages 939-53, May.
- Mariano, Roberto S, 1977. "Finite Sample Properties of Instrumental Variable Estimators of Structural Coefficients," Econometrica, Econometric Society, vol. 45(2), pages 487-96, March.
- Wegge, Leon L, 1971. "The Finite Sampling Distribution of Least Squares Estimators with Stochastic Regressors," Econometrica, Econometric Society, vol. 39(2), pages 241-51, March.
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