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Characterizing the Instrumental Variable Identifying Assumption as Sample Selection Conditions

  • Belzil, Christian


    (Ecole Polytechnique, Paris)

  • Hansen, Jörgen


    (Concordia University)

We build on Rosenzweig and Wolpin (2000) and Keane (2010) and show that in order to fulfill 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 specific instrument, and they illustrate the link between identification and the statistical strength of an instrument. Finally, our characterization may also help designing a policy generating a valid instrument.

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Paper provided by Institute for the Study of Labor (IZA) in its series IZA Discussion Papers with number 6339.

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Length: 23 pages
Date of creation: Feb 2012
Date of revision:
Handle: RePEc:iza:izadps:dp6339
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  1. Christian Belzil, 2006. "The Return to Schooling in Structural Dynamic Models: A Survey," Post-Print halshs-00142538, HAL.
  2. Heckman, James J, 1979. "Sample Selection Bias as a Specification Error," Econometrica, Econometric Society, vol. 47(1), pages 153-61, January.
  3. Keane, Michael P., 2010. "Structural vs. atheoretic approaches to econometrics," Journal of Econometrics, Elsevier, vol. 156(1), pages 3-20, May.
  4. Christian Belzil & J. Hansen, 2010. "The distinction between dictatorial and incentive policy interventions and its implication for IV estimation," Working Papers hal-00463877, HAL.
  5. 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.
  6. 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.
  7. Edward Vytlacil, 2002. "Independence, Monotonicity, and Latent Index Models: An Equivalence Result," Econometrica, Econometric Society, vol. 70(1), pages 331-341, January.
  8. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-75, March.
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