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Optimal Invariant Similar Tests for Instrumental Variables Regression

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  • Donald W.K. Andrews
  • Marcelo Moreira
  • James H. Stock

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 certain 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

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0299.

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Date of creation: Aug 2004
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Publication status: published as Andrews, Donald W. K., Marcelo J. Moreira and James H. Stock. "Optimal Two-Sided Invariant Similar Tests For Instrumental Variables Regression," Econometrica, 2006, v74(3,May), 715-752.
Handle: RePEc:nbr:nberte:0299

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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. 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.
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Cited by:
  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.
  2. James G. MacKinnon, 2006. "Applications of the Fast Double Bootstrap," Working Papers 1023, Queen's University, Department of Economics.
  3. Badinger, Harald, 2008. "Trade policy and productivity," European Economic Review, Elsevier, vol. 52(5), pages 867-891, July.
  4. Donald W.K. Andrews & James H. Stock, 2005. "Inference with Weak Instruments," Cowles Foundation Discussion Papers 1530, Cowles Foundation for Research in Economics, Yale University.
  5. Adrian Pagan, 2007. "Weak Instruments: A Guide to the Literature," NCER Working Paper Series 13, National Centre for Econometric Research.
  6. Russell Davidson & James G. MacKinnon, 2014. "Bootstrap tests for overidentification in linear regression models," Working Papers 1318, Queen's University, Department of Economics.
  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.
  8. 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.
  9. 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.
  10. 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.
  11. Russell Davidson & James G. MacKinnon, 2008. "Bootstrap inference in a linear equation estimated by instrumental variables," Econometrics Journal, Royal Economic Society, vol. 11(3), pages 443-477, November.
  12. 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.
  13. Badinger, Harald, 2009. "Globalization, the output-inflation tradeoff and inflation," European Economic Review, Elsevier, vol. 53(8), pages 888-907, November.
  14. 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.
  15. 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.
  16. 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.

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