On the conditional likelihood ratio test for several parameters in IV regression
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 .
|Date of creation:||12 Dec 2006|
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- Hillier, Grant H., 1987. "Classes of Similar Regions and Their Power Properties for Some Econometric Testing Problems," Econometric Theory, Cambridge University Press, vol. 3(01), pages 1-44, February.
- Hillier, Grant H, 1990. "On the Normalization of Structural Equations: Properties of Direct Estimators," Econometrica, Econometric Society, vol. 58(5), pages 1181-94, September.
- Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, 07.
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