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Global Representation of LATE Model: A Separability Result

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  • Yu-Chang Chen
  • Haitian Xie

Abstract

This paper studies the latent index representation of the conditional LATE model, making explicit the role of covariates in treatment selection. We find that if the directions of the monotonicity condition are the same across all values of the conditioning covariate, which is often assumed in the literature, then the treatment choice equation has to satisfy a separability condition between the instrument and the covariate. This global representation result establishes testable restrictions imposed on the way covariates enter the treatment choice equation. We later extend the representation theorem to incorporate multiple ordered levels of treatment.

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  • Yu-Chang Chen & Haitian Xie, 2020. "Global Representation of LATE Model: A Separability Result," Papers 2007.08106, arXiv.org.
  • Handle: RePEc:arx:papers:2007.08106
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    References listed on IDEAS

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    1. James J. Heckman, 1976. "Introduction to "Annals of Economic and Social Measurement, Volume 5, number 4"," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 5, number 4, National Bureau of Economic Research, Inc.
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    5. 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.
    6. Abadie, Alberto, 2003. "Semiparametric instrumental variable estimation of treatment response models," Journal of Econometrics, Elsevier, vol. 113(2), pages 231-263, April.
    7. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects, and Econometric Policy Evaluation," Econometrica, Econometric Society, vol. 73(3), pages 669-738, May.
    8. Edward Vytlacil, 2006. "Ordered Discrete-Choice Selection Models and Local Average Treatment Effect Assumptions: Equivalence, Nonequivalence, and Representation Results," The Review of Economics and Statistics, MIT Press, vol. 88(3), pages 578-581, August.
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    11. Edward Vytlacil, 2006. "A Note on Additive Separability and Latent Index Models of Binary Choice: Representation Results," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(4), pages 515-518, August.
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