On the Conditional Likelihood Ratio Test for Several Parameters in IV Regression
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.
Institute for Fiscal Studies
Hillier, Grant
3423bd61-c35f-497e-87a3-6a5fca73a2a1
2006
Hillier, Grant
3423bd61-c35f-497e-87a3-6a5fca73a2a1
Hillier, Grant
(2006)
On the Conditional Likelihood Ratio Test for Several Parameters in IV Regression
(CeMMAP Working Paper, CWP26/06)
London, UK.
Institute for Fiscal Studies
Record type:
Monograph
(Working Paper)
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.
Text
cwp2606.pdf
- Author's Original
Restricted to Registered users only
Request a copy
More information
Published date: 2006
Identifiers
Local EPrints ID: 43576
URI: http://eprints.soton.ac.uk/id/eprint/43576
PURE UUID: f8a3b6a0-5390-419f-846e-39e5fafd71c4
Catalogue record
Date deposited: 14 Feb 2007
Last modified: 16 Mar 2024 02:42
Export record
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.
View more statistics
