Joint Distribution Theory for Some Statistics Based on LIML and TSLS

Grant Hillier

No 840, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: In the context of a single linear structural equation under classical assumptions, we derive the joint conditional density of the LIML endogenous coefficient estimator, and the usual characteristic root arising from the LIML procedure, given the OLS estimates of the reduced form coefficients for the excluded exogenous variables. This provides the joint distributions for various combinations of the statistics commonly used for inference in this model, and is hence an important stepping stone in the analysis of these procedures. The main result also leads to a new derivation of the density of the LIML estimator itself, and provides a result which is directly comparable to earlier results for IV estimators, including OLS and TSLS. We also consider briefly the density of the LIML structural variance estimator, and the joint density of the LIML and TSLS estimators for the endogenous coefficients.

Keywords: LIML; Two state least squares; density function (search for similar items in EconPapers)
Pages: 31 pages
Date: 1987-06
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