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The Exact Distribution of LIML: I

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  • Phillips, Peter C B

Abstract

It 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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  • 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 249-261, February.
  • Handle: RePEc:ier:iecrev:v:25:y:1984:i:1:p:249-61
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    References listed on IDEAS

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    1. 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.
    2. Fuller, Wayne A, 1977. "Some Properties of a Modification of the Limited Information Estimator," Econometrica, Econometric Society, vol. 45(4), pages 939-953, May.
    3. Wegge, Leon L, 1971. "The Finite Sampling Distribution of Least Squares Estimators with Stochastic Regressors," Econometrica, Econometric Society, vol. 39(2), pages 241-251, March.
    4. P. C. B. Phillips, 1980. "Finite Sample Theory and the Distributions of Alternative Estimators of the Marginal Propensity to Consume," Review of Economic Studies, Oxford University Press, vol. 47(1), pages 183-224.
    5. Kelejian, Harry H, 1974. "Random Parameters in a Simultaneous Equation Framework: Identification and Estimation," Econometrica, Econometric Society, vol. 42(3), pages 517-527, May.
    6. Mariano, Roberto S, 1977. "Finite Sample Properties of Instrumental Variable Estimators of Structural Coefficients," Econometrica, Econometric Society, vol. 45(2), pages 487-496, March.
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    More about this item

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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