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Optimal Invariant Similar Tests for Instrumental Variables Regression

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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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File URL: http://cowles.econ.yale.edu/P/cd/d14b/d1476.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, 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

Note: CFP 1168.
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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

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References

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  1. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  2. Donald W.K. Andrews & Christopher J. Monahan, 1990. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Cowles Foundation Discussion Papers 942, Cowles Foundation for Research in Economics, Yale University.
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Cited by:
  1. Badinger, Harald, 2008. "Trade policy and productivity," European Economic Review, Elsevier, vol. 52(5), pages 867-891, July.
  2. Badinger, Harald, 2009. "Globalization, the output-inflation tradeoff and inflation," European Economic Review, Elsevier, vol. 53(8), pages 888-907, November.
  3. Andrews, Donald W.K. & Marmer, Vadim, 2008. "Exactly distribution-free inference in instrumental variables regression with possibly weak instruments," Journal of Econometrics, Elsevier, vol. 142(1), pages 183-200, January.
  4. 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.
  5. Dufour, Jean-Marie & Taamouti, Mohamed, 2007. "Further results on projection-based inference in IV regressions with weak, collinear or missing instruments," Journal of Econometrics, Elsevier, vol. 139(1), pages 133-153, July.
  6. 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.
  7. Andreea Balan-Cohen, 2008. "Healthy, Wealthy, and Wise? The Impact of the Old Age Assistance Program on Elderly Mortality in the United States," Discussion Papers Series, Department of Economics, Tufts University 0719, Department of Economics, Tufts University.
  8. 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.
  9. Michael P. Murray, 2006. "Avoiding Invalid Instruments and Coping with Weak Instruments," Journal of Economic Perspectives, American Economic Association, vol. 20(4), pages 111-132, Fall.
  10. Donald W.K. Andrews & James H. Stock, 2005. "Inference with Weak Instruments," NBER Technical Working Papers 0313, National Bureau of Economic Research, Inc.
  11. Justin McCrary & Heather Royer, 2011. "The Effect of Female Education on Fertility and Infant Health: Evidence from School Entry Policies Using Exact Date of Birth," American Economic Review, American Economic Association, vol. 101(1), pages 158-95, February.
  12. Russell Davidson & James G. MacKinnon, 2014. "Bootstrap tests for overidentification in linear regression models," Working Papers 1318, Queen's University, Department of Economics.
  13. Anna Mikusheva & Brian P. Poi, 2006. "Tests and confidence sets with correct size when instruments are potentially weak," Stata Journal, StataCorp LP, vol. 6(3), pages 335-347, September.
  14. Donald W.K. Andrews & Xu Cheng & Patrik Guggenberger, 2011. "Generic Results for Establishing the Asymptotic Size of Confidence Sets and Tests," Cowles Foundation Discussion Papers 1813, Cowles Foundation for Research in Economics, Yale University.
  15. Adrian Pagan, 2007. "Weak Instruments: A Guide to the Literature," NCER Working Paper Series 13, National Centre for Econometric Research.
  16. James G. MacKinnon, 2006. "Applications of the Fast Double Bootstrap," Working Papers 1023, Queen's University, Department of Economics.

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