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The Validity of Instruments Revisited

Author

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  • Daniel Berkowitz
  • Mehmet Caner
  • Ying Fang

Abstract

Valid instrumental variables must be relevant and exogenous. However, in practice it is difficult to find instruments that are exogenous in that they satisfy the knife-edged orthogonality condition and at the same time are strongly correlated with the endogenous regressors. In this paper we show how a mild violation of the exogeneity assumption affects the limit of the Anderson-Rubin test (1949). This test statistic is frequently used in economics due to the fact that it is robust to identification problems. However, when there is mild violation of exogeneity the test is oversized and with larger samples the problem gets worse. In order to correct this problem, we introduce the fractionally resampled Anderson-Rubin test (FAR) that is derived by modifying the resampling technique introduced by Wu(1990). We show the FAR test does not overreject the null hypothesis when we use half of the sample without replacement as the block size from the original sample. As a novel scheme, we treat the block size as a random variable and prove that this choice recovers the limit of the Anderson-Rubin (1949) test. We also prove that this optimal choice of block size converges in probability to 1/2. Simulations show that in finite samples the FAR is conservative; thus, we propose a range of block size choices that has very good size and power when there are possible violations of the exogeneity assumption.

Suggested Citation

  • Daniel Berkowitz & Mehmet Caner & Ying Fang, 2013. "The Validity of Instruments Revisited," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
  • Handle: RePEc:wyi:wpaper:001990
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    References listed on IDEAS

    as
    1. Andrews, Donald W.K. & Guggenberger, Patrik, 2009. "Validity Of Subsampling And “Plug-In Asymptotic” Inference For Parameters Defined By Moment Inequalities," Econometric Theory, Cambridge University Press, vol. 25(03), pages 669-709, June.
    2. Guggenberger, Patrik & Smith, Richard J., 2005. "Generalized Empirical Likelihood Estimators And Tests Under Partial, Weak, And Strong Identification," Econometric Theory, Cambridge University Press, vol. 21(04), pages 667-709, August.
    3. Daron Acemoglu & Simon Johnson & James A. Robinson & Pierre Yared, 2008. "Income and Democracy," American Economic Review, American Economic Association, vol. 98(3), pages 808-842, June.
    4. Hall, Alastair R. & Inoue, Atsushi, 2003. "The large sample behaviour of the generalized method of moments estimator in misspecified models," Journal of Econometrics, Elsevier, vol. 114(2), pages 361-394, June.
    5. Berkowitz, Daniel & Caner, Mehmet & Fang, Ying, 2008. "Are "Nearly Exogenous Instruments" reliable?," Economics Letters, Elsevier, vol. 101(1), pages 20-23, October.
    6. K. Newey, Whitney, 1985. "Generalized method of moments specification testing," Journal of Econometrics, Elsevier, vol. 29(3), pages 229-256, September.
    7. James H. Stock & Jonathan Wright, 2000. "GMM with Weak Identification," Econometrica, Econometric Society, vol. 68(5), pages 1055-1096, September.
    8. repec:pit:wpaper:207 is not listed on IDEAS
    9. Andrews, Donald W.K. & Guggenberger, Patrik, 2010. "ASYMPTOTIC SIZE AND A PROBLEM WITH SUBSAMPLING AND WITH THE m OUT OF n BOOTSTRAP," Econometric Theory, Cambridge University Press, vol. 26(02), pages 426-468, April.
    10. 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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    More about this item

    Keywords

    Berry-Esseen Bound; Finite Sample of Random Variables; Near-Exogeneity;

    JEL classification:

    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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