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Robust confidence sets in the presence of weak instruments

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  • Mikusheva, Anna

Abstract

This paper considers instrumental variable regression with a single endogenous variable and the potential presence of weak instruments. I construct confidence sets for the coefficient on the single endogenous regressor by inverting tests robust to weak instruments. I suggest a numerically simple algorithm for finding the Conditional Likelihood Ratio (CLR) confidence sets. Full descriptions of possible forms of the CLR, Anderson-Rubin (AR) and Lagrange Multiplier (LM) confidence sets are given. I show that the CLR confidence sets have nearly the shortest expected arc length among similar symmetric invariant confidence sets in a circular model. I also prove that the CLR confidence set is asymptotically valid in a model with non-normal errors.

Suggested Citation

  • Mikusheva, Anna, 2010. "Robust confidence sets in the presence of weak instruments," Journal of Econometrics, Elsevier, vol. 157(2), pages 236-247, August.
    • Handle: RePEc:eee:econom:v:157:y:2010:i:2:p:236-247
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    References listed on IDEAS

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    1. Jean-Marie Dufour & Mohamed Taamouti, 2005. "Projection-Based Statistical Inference in Linear Structural Models with Possibly Weak Instruments," Econometrica, Econometric Society, vol. 73(4), pages 1351-1365, July.
    2. Dufour, Jean-Marie & Khalaf, Lynda & Kichian, Maral, 2006. "Inflation dynamics and the New Keynesian Phillips Curve: An identification robust econometric analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 30(9-10), pages 1707-1727.
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    4. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, July.
    5. 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.
    6. 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 518-529, October.
    7. 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, May.
    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.
    9. 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.
    10. Kleibergen, Frank & Mavroeidis, Sophocles, 2009. "Weak Instrument Robust Tests in GMM and the New Keynesian Phillips Curve," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(3), pages 293-311.
    11. Frank Kleibergen, 2002. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Econometrica, Econometric Society, vol. 70(5), pages 1781-1803, September.
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