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SUBSET HYPOTHESES TESTING AND INSTRUMENT EXCLUSION IN THE LINEAR IV REGRESSION

Published online by Cambridge University Press:  17 November 2014

Firmin Doko Tchatoka
Firmin Doko Tchatoka*
Affiliation:
University of Tasmania
*
*Address correspondence to Firmin Doko Tchatoka, School of Economics, The University of Adelaide, Australia; e-mail: firmin.dokotchatoka@adelaide.edu.au.
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Abstract

This paper explores the sensitivity of plug-in subset tests to instrument exclusion in structural models. Identification-robust statistics based on the plug-in principle have been developed for testing hypotheses specified on subsets of the structural parameters. However, their robustness to instrument exclusion has not been investigated. This paper proposes an analysis of the asymptotic distributions of the limited information maximum likelihood (LIML) estimator and plug-in statistics when potential instruments are omitted. Our results provide several new insights and extensions of earlier studies. We show that the exclusion of instruments can eliminate the first-stage, thus weakening identification and invalidating the plug-in subset inference. However, when instrument omission does not affect LIML consistency, it preserves the plug-in subset test validity, although LIML is no longer asymptotically efficient. Unlike the instrumental variable (IV) estimator, the LIML estimator of the identified linear combination of the nuisance parameter is not asymptotically a Gaussian mixture, even without instrument exclusion.

Type
ARTICLES
Information
Econometric Theory , Volume 31 , Issue 6 , December 2015 , pp. 1192 - 1228
Copyright
Copyright © Cambridge University Press 2014 

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