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The Exact Distribution of LIML: II

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  • Phillips, Peter C B

Abstract

This paper derives the exact probability density function of the limited information maximum likelihood (LIML) estimator of the coefficient vector of the endogenous variables in a structural equation containing n+1 endogenous variables and L >= 1 degrees of overidentification. This generalizes the presently known results for the two endogenous variable case (n+1 = 2) and the leading case analyses in the author's earlier paper (1982). Upon appropriate symbolic translation the results may be applied directly to the maximum likelihood estimator in the multivariate linear functional relationship.

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Bibliographic Info

Article 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)
Pages: 21-36

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Handle: RePEc:ier:iecrev:v:26:y:1985:i:1:p:21-36

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  1. 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.
  2. Fuller, Wayne A, 1977. "Some Properties of a Modification of the Limited Information Estimator," Econometrica, Econometric Society, vol. 45(4), pages 939-53, May.
  3. 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.
  4. Kelejian, Harry H, 1974. "Random Parameters in a Simultaneous Equation Framework: Identification and Estimation," Econometrica, Econometric Society, vol. 42(3), pages 517-27, May.
  5. Mariano, Roberto S, 1977. "Finite Sample Properties of Instrumental Variable Estimators of Structural Coefficients," Econometrica, Econometric Society, vol. 45(2), pages 487-96, March.
  6. 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.
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