Econometric Theory

MISCELLANEA

THE ASYMPTOTIC DISTRIBUTION OF THE LIML ESTIMATOR IN A PARTIALLY IDENTIFIED STRUCTURAL EQUATION

Giovanni Forchinia1 c1

a1 Monash University

Abstract

We derive a closed-form expression for the asymptotic distribution of the LIML estimator for the coefficients of both endogenous and exogenous variables in a partially identified linear structural equation. We extend previous results of Phillips (1989) and Choi and Phillips (1992), where the focus was on IV estimators. We show that partial failure of identification affects the LIML in that its moments do not exist even asymptotically.

Correspondence

c1 Address correspondence to Giovanni Forchini, Department of Econometrics and Business Statistics, Monash University, Clayton, Victoria 3800, Australia; e-mail: giovanni.forchini@buseco.monash.edu.au.

Footnotes

I thank Richard Smith and two referees for useful comments. This research was partially supported by Australian Research Council grant DP0771445.

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