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Journal of the American Statistical Association Volume 74, 1979 - Issue 368
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Theory and Method

A Note on the Distribution Functions of LIML and 2SLS Structural Coefficient in the Exactly Identified Case

Roberto S. Mariano Department of Economics, University of Pennsylvania, Philadelphia, PA, 19174, USA
&
James B. McDonald Department of Economics, Brigham Young University, Provo, UT, 84601, USA
Pages 847-848 | Received 01 Dec 1977, Published online: 05 Apr 2012
 
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Abstract

Many alternative techniques of estimating coefficients appearing in the structural representation of econometric models have been developed. The techniques of two-stage least squares (2SLS) and limited information maximum likelihood (LIML) yield identical estimates in the exactly identified case. The derivations of the density functions of these estimators for overidentified structural equations do not formally include the exactly identified case. In this note we demonstrate that the previously obtained density functions include results consistent with exact identification as a special case. A correction to the expression for the LIML density function obtained by Mariano and Sawa is also reported.

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