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Global Representation of the Conditional 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 the Conditional LATE Model: A Separability Result," Papers 2007.08106, arXiv.org, revised Mar 2022.
    • Handle: RePEc:arx:papers:2007.08106
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    References listed on IDEAS

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    1. James J. Heckman, 1976. "The Common Structure of Statistical Models of Truncation, Sample Selection and Limited Dependent Variables and a Simple Estimator for Such Models," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 5, number 4, pages 475-492, National Bureau of Economic Research, Inc.
    2. Thomas Cornelissen & Christian Dustmann & Anna Raute & Uta Schönberg, 2018. "Who Benefits from Universal Child Care? Estimating Marginal Returns to Early Child Care Attendance," Journal of Political Economy, University of Chicago Press, vol. 126(6), pages 2356-2409.
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