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A New Paradigm: A Joint Test of Structural and Correlation Parameters in Instrumental Variables Regression When Perfect Exogeneity is Violated

  • Caner, Mehmet
  • Sandler Morrill, Melinda

Currently, the commonly employed instrumental variables strategy relies on the knife-edge assumption of perfect exogeneity for valid inference. To make reliable inferences on the structural parameters under violations of exogeneity one must know the true correlation between the structural error and the instruments. The main innovation in this paper is to identify an appropriate test in this context: a joint null hypothesis of the structural parameters with the correlation between the instruments and the structural error term. We introduce a new endogeneity accounted test by combining the structural parameter inference while correcting the bias associated with non-exogeneity of the instrument. To address inference under violations of exogeneity, significant contributions have been made in the recent literature by assuming some degree of non-exogeneity. A key advantage of our approach over that of the previous literature is that we do not need to make any assumptions about the degree of violation of exogeneity either as possible values or prior distributions. In particular, our method is not a form of sensitivity analysis. Since our test statistic is continuous and monotonic in correlation, one can conduct inference for the structural parameters by a simple grid search over correlation values. We can make accurate inferences on the structural parameters because of a feature of the grid search over correlation values. One can also build joint confidence intervals for the structural parameters and the correlation parameter by inverting the test statistic. In the inversion, the null values of these parameters are used. We also propose a new way of testing exclusion restrictions, even in the just identified case.

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File URL: http://mpra.ub.uni-muenchen.de/17689/1/MPRA_paper_17689.pdf
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 17689.

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Date of creation: 06 Oct 2009
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Handle: RePEc:pra:mprapa:17689
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  1. Richard Ashley, 2009. "Assessing the credibility of instrumental variables inference with imperfect instruments via sensitivity analysis," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(2), pages 325-337, 03.
  2. Costas Meghir & Mårten Palme, 1999. "Assessing the effect of schooling on earnings using a social experiment," IFS Working Papers W99/10, Institute for Fiscal Studies.
  3. Daniel Berkowitz & Mehmet Caner & Ying Fang, 2013. "The Validity of Instruments Revisited," Papers 2013-10-14, Working Paper.
  4. Daniel Berkowitz & Mehmet Caner & Ying Fang, 2006. "Are "Nearly Exogenous" Instruments Reliable?," Working Papers 219, University of Pittsburgh, Department of Economics, revised Jan 2006.
  5. Mehmet Caner, 2005. "Near Exogeneity and Weak Identification in Generalized Empirical Likelihood Estimators: Fixed and Many Moment Asymptotics," Econometrics 0509018, EconWPA.
  6. Aviv Nevo & Adam M. Rosen, 2012. "Identification With Imperfect Instruments," The Review of Economics and Statistics, MIT Press, vol. 94(3), pages 659-671, August.
  7. Richard A. Ashley., 2006. "Assessing the Credibility of Instrumental Variables Inference With Imperfect Instruments Via Sensitivity Analysis," Working Papers e06-9, Virginia Polytechnic Institute and State University, Department of Economics.
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