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Optimal Invariant Similar Tests for Instrumental Variables Regression

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Author Info
Donald W.K. Andrews () (Cowles Foundation, Yale University)
Marcelo J. Moreira (Harvard University)
James H. Stock (Harvard University)

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Abstract

This paper considers tests of the parameter on endogenous variables 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 tests that maximize weighted average power (WAP) for arbitrary weight functions among invariant similar tests. Such tests include point optimal (PO) invariant similar tests. The results yield the power envelope for invariant similar tests. This allows one to assess and compare the power properties of existing tests, such as the Anderson-Rubin, Lagrange multiplier (LM), and conditional likelihood ratio (CLR) tests, and new optimal WAP and PO invariant similar tests. We find that the CLR test is quite close to being uniformly most powerful invariant among a class of two-sided tests. A new unconditional test, P*, also is found to have this property. For one-sided alternatives, no test achieves the invariant power envelope, but a new test -- the one-sided CLR test -- is found to be fairly close. The finite sample results of the paper are extended to the case of unknown error covariance matrix and possibly non-normal errors via weak instrument asymptotics. Strong instrument asymptotic results also are provided because we seek tests that perform well under both weak and strong instruments.

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Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 1476.

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Length: 83 pages
Date of creation: Aug 2004
Date of revision:
Publication status: Published in Econometrica (May 2006), 74(3): 715-752
Handle: RePEc:cwl:cwldpp:1476

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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Related research
Keywords: Instrumental variables regression; invariant tests; optimal tests; similar tests; weak instruments; weighted average power;

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Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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References listed on IDEAS
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. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May. [Downloadable!] (restricted)
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  2. Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 60(4), pages 953-66, July. [Downloadable!] (restricted)
    Other versions:
Full references

Cited by:
(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. Marcelo J. Moreira & Jack R. Porter & Gustavo A. Suarez, 2004. "Bootstrap and Higher-Order Expansion Validity When Instruments May Be Weak," NBER Technical Working Papers 0302, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  2. Justin McCrary & Heather Royer, 2006. "The Effect of Female Education on Fertility and Infant Health: Evidence from School Entry Policies Using Exact Date of Birth," NBER Working Papers 12329, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  3. Harald Badinger, . "Globalization,the Output-Inflation Tradeoff, and Inflation," FIW Working Paper series 010, FIW. [Downloadable!]
  4. Donald W.K. Andrews & Vadim Marmer, 2005. "Exactly Distribution-free Inference in Instrumental Variables Regression with Possibly Weak Instruments," Cowles Foundation Discussion Papers 1501, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  5. Donald W.K. Andrews & James H. Stock, 2005. "Inference with Weak Instruments," Cowles Foundation Discussion Papers 1530, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  6. Yukitoshi Matsushita, 2007. "t-Tests in a Structural Equation with Many Instruments," CIRJE F-Series CIRJE-F-467, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
  7. Richard Smith, 2005. "Weak instruments and empirical likelihood: a discussion of the papers by DWK Andrews and JH Stock and Y Kitamura," CeMMAP working papers CWP13/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
  8. Adrian Pagan, 2007. "Weak Instruments: A Guide to the Literature," NCER Working Paper Series 13, National Centre for Econometric Research. [Downloadable!]
  9. Russell Davidson & James G. MacKinnon, 2006. "Bootstrap Inference in a Linear Equation Estimated by Instrumental Variables," Working Papers 1024, Queen's University, Department of Economics. [Downloadable!]
    Other versions:
  10. James G. MacKinnon, 2006. "Applications of the Fast Double Bootstrap," Working Papers 1023, Queen's University, Department of Economics. [Downloadable!]
  11. David Albouy, 2006. "The Colonial Origins of Comparative Development: An Investigation of the Settler Mortality Data," Center for International and Development Economics Research, Working Paper Series 1055, Center for International and Development Economics Research, Institute for Business and Economic Research, UC Berkeley. [Downloadable!]
    Other versions:
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