On the conditional likelihood ratio test for several parameters in IV regression

Grant Hillier

No CWP26/06, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

Abstract: For the problem of testing the hypothesis that all m coefficients of the RHS endogenous variables in an 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 cdf 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 (2006) and Andrews, Moreira, and Stock (2007) to evaluate the cdf 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 cdf is suggested for larger values of m .

Pages: 24 pp.
Date: 2006-12-12
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http://cemmap.ifs.org.uk/wps/cwp2606.pdf (application/pdf)

Related works:
Journal Article: ON THE CONDITIONAL LIKELIHOOD RATIO TEST FOR SEVERAL PARAMETERS IN IV REGRESSION (2009)
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