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Tests and confidence sets with correct size when instruments are potentially weak

  • Anna Mikusheva

    (Harvard University)

  • Brian P. Poi

    ()

    (StataCorp)

Registered author(s):

    We consider inference in the linear regression model with one endoge- nous variable and potentially weak instruments. We construct confidence sets for the coefficient on the endogenous variable by inverting the Anderson-Rubin, Lagrange multiplier, and conditional likelihood-ratio tests. Our confidence sets have correct coverage probabilities even when the instruments are weak. We propose a numerically simple algorithm for finding these confidence sets, and we present a Stata command that supersedes the one presented in Moreira and Poi (Stata Journal 3: 57–70). Copyright 2006 by StataCorp LP.

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    Article provided by StataCorp LP in its journal Stata Journal.

    Volume (Year): 6 (2006)
    Issue (Month): 3 (September)
    Pages: 335-347

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    Handle: RePEc:tsj:stataj:v:6:y:2006:i:3:p:335-347
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    1. Stock, James H & Wright, Jonathan H & Yogo, Motohiro, 2002. "A Survey of Weak Instruments and Weak Identification in Generalized Method of Moments," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 518-29, October.
    2. Marcelo J. Moreira & Brian P. Poi, 2003. "Implementing Tests with Correct Size in the Simultaneous Equation Model," Harvard Institute of Economic Research Working Papers 1993, Harvard - Institute of Economic Research.
    3. Frank Kleibergen, 2002. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Econometrica, Econometric Society, vol. 70(5), pages 1781-1803, September.
    4. 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.
    5. Nelson, C. & Startz, R., 1988. "Some Furthere Results On The Exact Small Sample Properties Of The Instrumental Variable Estimator," Working Papers 88-06, University of Washington, Department of Economics.
    6. 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.
    7. Donald W.K. Andrews & Marcelo Moreira & James H. Stock, 2004. "Optimal Invariant Similar Tests for Instrumental Variables Regression," NBER Technical Working Papers 0299, National Bureau of Economic Research, Inc.
    8. Jean-Marie Dufour, 1997. "Some Impossibility Theorems in Econometrics with Applications to Structural and Dynamic Models," Econometrica, Econometric Society, vol. 65(6), pages 1365-1388, November.
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