The Exact Distribution of LIML: I

Peter Phillips

No 658, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

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.

Pages: 22 pages
Date: 1982-12
Note: Extended version of CFDP 626. CFP 589.
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Published in International Economic Review (February 1984), 25(1): 249-261

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Related works:
Journal Article: The Exact Distribution of LIML: II (1985)
Journal Article: The Exact Distribution of LIML: I (1984)
Working Paper: The Exact Distribution of LIML: II (1983)
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