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ON THE CONDITIONAL LIKELIHOOD RATIO TEST FOR SEVERAL PARAMETERS IN IV REGRESSION

Published online by Cambridge University Press:  01 April 2009

Grant Hillier
Grant Hillier*
Affiliation:
CeMMAP and University of Southampton
*
*Address correspondence to Grant Hillier, Department of Economics, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom; e-mail: ghh@soton.ac.uk.
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Abstract

For the problem of testing the hypothesis that all m coefficients of the right-hand-side endogenous variables in an instrumental variables (IV) regression are zero, the likelihood ratio (LR) test can, if the reduced form covariance matrix is known, be rendered similar by a conditioning argument. To exploit this fact requires knowledge of the relevant conditional cumulative distribution function (c.d.f.) of the LR statistic, but the statistic is a function of the smallest characteristic root of an (m + 1)-square matrix and is therefore analytically difficult to deal with when m > 1. We show in this paper that an iterative conditioning argument used by Hillier (2009) and Andrews, Moreira, and Stock (2007 Journal of Econometrics 139, 116–132) to evaluate the c.d.f. in the case m = 1 can be generalized to the case of arbitrary m. This means that we can completely bypass the difficulty of dealing with the smallest characteristic root. Analytic results are obtained for the case m = 2, and a simple and efficient simulation approach to evaluating the c.d.f. is suggested for larger values of m.

Type
ARTICLES
Information
Econometric Theory , Volume 25 , Issue 2 , April 2009 , pp. 305 - 335
Copyright
Copyright © Cambridge University Press 2009

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References

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