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Optimal Two-Sided Invariant Similar Tests for Instrumental Variables Regression

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Author Info
Donald W. K. Andrews
Marcelo J. Moreira
James H. Stock

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Abstract

This paper considers tests of the parameter on an endogenous variable in an instrumental variables regression model. The focus is on determining tests that have some optimal power properties. We start by considering a model with normally distributed errors and known error covariance matrix. We consider tests that are similar and satisfy a natural rotational invariance condition. We determine a two-sided power envelope for invariant similar tests. This allows us to assess and compare the power properties of tests such as the conditional likelihood ratio (CLR), the Lagrange multiplier, and the Anderson-Rubin tests. We find that the CLR test is quite close to being uniformly most powerful invariant among a class of two-sided tests. Copyright The Econometric Society 2006.

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File URL: http://hdl.handle.net/10.1111/j.1468-0262.2006.00680.x
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Publisher Info
Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 74 (2006)
Issue (Month): 3 (05)
Pages: 715-752
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Handle: RePEc:ecm:emetrp:v:74:y:2006:i:3:p:715-752

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  8. Mathias D. Cattaneo & Richard K. Crump & Michael Jansson, 2007. "Optimal Inference for Instrumental Variables Regression with non-Gaussian Errors," CREATES Research Papers 2007-11, School of Economics and Management, University of Aarhus. [Downloadable!]
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  12. Yukitoshi Matsushita, 2007. "Approximate Distributions of the Likelihood Ratio Statistic in a Structural Equation with Many Instruments," CIRJE F-Series CIRJE-F-466, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
  13. 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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