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Exact properties of the conditional likelihood ratio test in an IV regression model

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Author Info
Grant Hillier () (Institute for Fiscal Studies and University of Southampton)

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Abstract

This paper was revised in May 2007.

For a simplified structural equation/IV regression model with one right-side endogenous variable, we obtain the exact conditional distribution function for Moreira's (2003) conditional likelihood ratio (CLR) test. This is then used to obtain the critical value function needed to implement the CLR test, and reasonably comprehensive graphical versions of the function are provided for practical use. The analogous functions are also obtained for the case of testing more than one right-side endogenous coefficient, but only for an approximation to the true likelihood ratio test. We then go on to provide an exact analysis of the power functions of the CLR test, the Anderson-Rubin test, and the LM test suggested by Kleibergen (2002). The CLR test is shown to clearly conditionally dominate the other two tests for virtually all parameter configurations, but none of these test is either inadmissible or uniformly superior to the other two.

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Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP23/06.

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Length: 44 pp.
Date of creation: Oct 2006
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Handle: RePEc:ifs:cemmap:23/06

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Kleibergen, Frank, 2007. "Generalizing weak instrument robust IV statistics towards multiple parameters, unrestricted covariance matrices and identification statistics," Journal of Econometrics, Elsevier, vol. 139(1), pages 181-216, July. [Downloadable!] (restricted)
  2. Frank Kleibergen, 2002. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Econometrica, Econometric Society, vol. 70(5), pages 1781-1803, September. [Downloadable!] (restricted)
  3. Breusch, Trevor S, 1986. "Hypothesis Testing in Unidentified Models," Review of Economic Studies, Blackwell Publishing, vol. 53(4), pages 635-51, August. [Downloadable!] (restricted)
  4. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, 07. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Russell Davidson & James G. MacKinnon, 2008. "Bootstrap Inference in a Linear Equation Estimated by Instrumental Variables," Working Papers 1157, Queen's University, Department of Economics. [Downloadable!]
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