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Efficient two-sided nonsimilar invariant tests in IV regression with weak instruments

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

As Nelson and Startz [Nelson, C.R., Startz, R., 1990a. The distribution of the instrumental variable estimator and its t ratio when the instrument is a poor one. Journal of Business 63, S125-S140; Nelson, C.R., Startz, R., 1990b. Some further results on the exact small sample properties of the instrumental variables estimator. Econometrica 58, 967-976] dramatically demonstrated, standard hypothesis tests and confidence intervals in instrumental variables regression are invalid when instruments are weak. Recent work on hypothesis tests for the coefficient on a single included endogenous regressor when instruments may be weak has focused on similar tests. This paper extends that work to nonsimilar tests, of which similar tests are a subset. The power envelope for two-sided invariant (to rotations of the instruments) nonsimilar tests is characterized theoretically, then evaluated numerically for five IVs. The power envelopes for similar and nonsimilar tests differ theoretically, but are found to be very close numerically. The nonsimilar test power envelope is effectively achieved by the Moreira [Moreira, M.J., 2003. A conditional likelihood ratio test for structural models. Econometrica 71, 1027-1048] conditional likelihood ratio test, so that test is effectively uniformly most powerful invariant (UMPI). We also provide a new nonsimilar test, P*, which has critical values, is asymptotically efficient under strong instruments, involves only elementary functions, and is very nearly UMPI.

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Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 146 (2008)
Issue (Month): 2 (October)
Pages: 241-254

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Handle: RePEc:eee:econom:v:146:y:2008:i:2:p:241-254
Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

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  1. Moreira, Marcelo J., 2009. "Tests with correct size when instruments can be arbitrarily weak," Journal of Econometrics, Elsevier, vol. 152(2), pages 131-140, October.
  2. Nelson, C. & Startz, R., 1988. "Some Furthere Results On The Exact Small Sample Properties Of The Instrumental Variable Estimator," Discussion Papers in Economics at the University of Washington 88-06, Department of Economics at the University of Washington.
  3. Charles R. Nelson & Richard Startz, 1988. "The Distribution of the Instrumental Variables Estimator and Its t-RatioWhen the Instrument is a Poor One," NBER Technical Working Papers 0069, National Bureau of Economic Research, Inc.
  4. Gary Chamberlain, 2007. "Decision Theory Applied to an Instrumental Variables Model," Econometrica, Econometric Society, vol. 75(3), pages 609-652, 05.
  5. Jiahui Wang & Eric Zivot, 1998. "Inference on Structural Parameters in Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 66(6), pages 1389-1404, November.
  6. Douglas Staiger & James H. Stock, 1994. "Instrumental Variables Regression with Weak Instruments," NBER Technical Working Papers 0151, National Bureau of Economic Research, Inc.
  7. Andrews, Donald W.K. & Moreira, Marcelo J. & Stock, James H., 2007. "Performance of conditional Wald tests in IV regression with weak instruments," Journal of Econometrics, Elsevier, vol. 139(1), pages 116-132, July.
  8. Hillier, Grant H, 1990. "On the Normalization of Structural Equations: Properties of Direct Estimators," Econometrica, Econometric Society, vol. 58(5), pages 1181-94, September.
  9. Donald W. K. Andrews & Marcelo J. Moreira & James H. Stock, 2006. "Optimal Two-Sided Invariant Similar Tests for Instrumental Variables Regression," Econometrica, Econometric Society, vol. 74(3), pages 715-752, 05.
  10. Frank Kleibergen, 2002. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Econometrica, Econometric Society, vol. 70(5), pages 1781-1803, September.
  11. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, 07.
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