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The Validity of Instruments Revisited

Listed author(s):
  • Daniel Berkowitz
  • Mehmet Caner
  • Ying Fang

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.

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Paper provided by Wang Yanan Institute for Studies in Economics (WISE), Xiamen University in its series WISE Working Papers with number 2013-10-14.

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Date of creation: 14 Oct 2013
Publication status: published
Handle: RePEc:wyi:wpaper:001990
Contact details of provider: Web page: http://www.wise.xmu.edu.cn/english/

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  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. Berkowitz, Daniel & Caner, Mehmet & Fang, Ying, 2008. "Are "Nearly Exogenous Instruments" reliable?," Economics Letters, Elsevier, vol. 101(1), pages 20-23, October.
  3. 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.
  4. 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.
  5. repec:pit:wpaper:207 is not listed on IDEAS
  6. 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.
  7. 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.
  8. K. Newey, Whitney, 1985. "Generalized method of moments specification testing," Journal of Econometrics, Elsevier, vol. 29(3), pages 229-256, September.
  9. Frank Kleibergen, 2002. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Econometrica, Econometric Society, vol. 70(5), pages 1781-1803, September.
  10. James H. Stock & Jonathan Wright, 2000. "GMM with Weak Identification," Econometrica, Econometric Society, vol. 68(5), pages 1055-1096, September.
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