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A Vector Monotonicity Assumption for Multiple Instruments

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  • Leonard Goff

Abstract

When a researcher combines multiple instrumental variables for a single binary treatment, the monotonicity assumption of the local average treatment effects (LATE) framework can become restrictive: it requires that all units share a common direction of response even when separate instruments are shifted in opposing directions. What I call vector monotonicity, by contrast, simply assumes treatment uptake to be monotonic in all instruments. I characterize the class of causal parameters that are point identified under vector monotonicity, when the instruments are binary. This class includes, for example, the average treatment effect among units that are in any way responsive to the collection of instruments, or those that are responsive to a given subset of them. The identification results are constructive and yield a simple estimator for the identified treatment effect parameters. An empirical application revisits the labor market returns to college.

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  • Leonard Goff, 2020. "A Vector Monotonicity Assumption for Multiple Instruments," Papers 2009.00553, arXiv.org, revised Mar 2024.
    • Handle: RePEc:arx:papers:2009.00553
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    References listed on IDEAS

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    1. James J. Heckman & Sergio Urzua & Edward Vytlacil, 2006. "Understanding Instrumental Variables in Models with Essential Heterogeneity," The Review of Economics and Statistics, MIT Press, vol. 88(3), pages 389-432, August.
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    7. Magne Mogstad & Andres Santos & Alexander Torgovitsky, 2018. "Using Instrumental Variables for Inference About Policy Relevant Treatment Parameters," Econometrica, Econometric Society, vol. 86(5), pages 1589-1619, September.
    8. Fan, Yanqin & Park, Sang Soo, 2010. "Sharp Bounds On The Distribution Of Treatment Effects And Their Statistical Inference," Econometric Theory, Cambridge University Press, vol. 26(3), pages 931-951, June.
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    10. Junlong Feng, 2019. "Matching Points: Supplementing Instruments with Covariates in Triangular Models," Papers 1904.01159, arXiv.org, revised Jul 2020.
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    Cited by:

    1. Sokbae Lee & Bernard Salani'e, 2020. "Treatment Effects with Targeting Instruments," Papers 2007.10432, arXiv.org, revised Nov 2023.
    2. Manudeep Bhuller & Henrik Sigstad, 2022. "2SLS with Multiple Treatments," Papers 2205.07836, arXiv.org, revised Mar 2024.

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