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Characterizing the Instrumental Variable Identifying Assumption as Sample Selection Conditions

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  • Christian Belzil

    (Department of Economics, Ecole Polytechnique - CNRS : UMR7176 - Polytechnique - X, ENSAE - École Nationale de la Statistique et de l'Administration Économique - ENSAE ParisTech)

  • Jörgen Hansen

    (Department of Economics, Concordia University - Concordia University, CIRANO - Centre interuniversitaire de recherche en analyse des organisations - Université du Québec à Montréal)

Abstract

We build on Rosenzweig and Wolpin (2000) and Keane (2010) and show that in order to ful ll the Instrumental variable (IV) identifying moment condition, a policy must be designed so that compliers and non-compliers either have the same average error term, or have an error term ratio equal to their relative share of the population. The former condition (labeled Choice Orthogonality) is essentially a no-selection condition. The latter one, referred to as Weighted Opposite Choices, may be viewed as a distributional (functional form) assumption necessary to match the degree of selectivity between compliers and noncompliers to their relative population proportions. Those conditions form a core of implicit IV assumptions that are present in any empirical applications. They allow the econometrician to gain substantial insight about the validity of a speci c instrument, and they illustrate the link between identi cation and the statistical strength of an instrument. Finally, our characterization may also help designing a policy generating a valid instrument.

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Bibliographic Info

Paper provided by HAL in its series Working Papers with number hal-00753539.

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Date of creation: 19 Nov 2012
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Handle: RePEc:hal:wpaper:hal-00753539

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Keywords: Instrumental Variable methods; Implicit Assumptions; Treatment E ects.;

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  1. Heckman, James J, 1979. "Sample Selection Bias as a Specification Error," Econometrica, Econometric Society, vol. 47(1), pages 153-61, January.
  2. James Heckman, 1997. "Instrumental Variables: A Study of Implicit Behavioral Assumptions Used in Making Program Evaluations," Journal of Human Resources, University of Wisconsin Press, vol. 32(3), pages 441-462.
  3. Belzil, Christian, 2006. "The Return to Schooling in Structural Dynamic Models: A Survey," IZA Discussion Papers 2370, Institute for the Study of Labor (IZA).
  4. Edward Vytlacil, 2002. "Independence, Monotonicity, and Latent Index Models: An Equivalence Result," Econometrica, Econometric Society, vol. 70(1), pages 331-341, January.
  5. Joshua D. Angrist & Guido W. Imbens, 1995. "Identification and Estimation of Local Average Treatment Effects," NBER Technical Working Papers 0118, National Bureau of Economic Research, Inc.
  6. Christian Belzil & J. Hansen, 2010. "The distinction between dictatorial and incentive policy interventions and its implication for IV estimation," Working Papers hal-00463877, HAL.
  7. Abbring, Jaap H. & Heckman, James J., 2007. "Econometric Evaluation of Social Programs, Part III: Distributional Treatment Effects, Dynamic Treatment Effects, Dynamic Discrete Choice, and General Equilibrium Policy Evaluation," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 72 Elsevier.
  8. Keane, Michael P., 2010. "Structural vs. atheoretic approaches to econometrics," Journal of Econometrics, Elsevier, vol. 156(1), pages 3-20, May.
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