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Characterizing the Instrumental Variable Identifying Assumption as Sample Selection Conditions

Author

Listed:
  • Belzil, Christian

    () (Ecole Polytechnique, Paris)

  • Hansen, Jörgen

    () (Concordia University)

Abstract

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.

Suggested Citation

  • Belzil, Christian & Hansen, Jörgen, 2012. "Characterizing the Instrumental Variable Identifying Assumption as Sample Selection Conditions," IZA Discussion Papers 6339, Institute for the Study of Labor (IZA).
  • Handle: RePEc:iza:izadps:dp6339
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    References listed on IDEAS

    as
    1. Keane, Michael P., 2010. "Structural vs. atheoretic approaches to econometrics," Journal of Econometrics, Elsevier, vol. 156(1), pages 3-20, May.
    2. Belzil, Christian, 2007. "The return to schooling in structural dynamic models: a survey," European Economic Review, Elsevier, vol. 51(5), pages 1059-1105, July.
    3. Belzil, Christian & Hansen, Jörgen, 2010. "The Distinction between Dictatorial and Incentive Policy Interventions and its Implication for IV Estimation," IZA Discussion Papers 4835, Institute for the Study of Labor (IZA).
    4. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-475, March.
    5. 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.
    6. Heckman, James, 2013. "Sample selection bias as a specification error," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 31(3), pages 129-137.
    7. 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.
    8. Edward Vytlacil, 2002. "Independence, Monotonicity, and Latent Index Models: An Equivalence Result," Econometrica, Econometric Society, vol. 70(1), pages 331-341, January.
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    More about this item

    Keywords

    instrumental variable methods; implicit assumptions; treatment effects;

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables

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