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Counting Defiers

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  • Amanda Kowalski

Abstract

The LATE monotonicity assumption of Imbens and Angrist (1994) precludes "defiers," individuals whose treatment always runs counter to the instrument, in the terminology of Balke and Pearl (1993) and Angrist et al. (1996). I allow for defiers in a model with a binary instrument and a binary treatment. The model is explicit about the randomization process that gives rise to the instrument. I use the model to develop estimators of the counts of defiers, always takers, compliers, and never takers. I propose separate versions of the estimators for contexts in which the parameter of the randomization process is unspecified, which I intend for use with natural experiments with virtual random assignment. I present an empirical application that revisits Angrist and Evans (1998), which examines the impact of virtual random assignment of the sex of the first two children on subsequent fertility. I find that subsequent fertility is much more responsive to the sex mix of the first two children when defiers are allowed.

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  • Amanda Kowalski, 2019. "Counting Defiers," Papers 1908.05811, arXiv.org, revised Jul 2020.
    • Handle: RePEc:arx:papers:1908.05811
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    References listed on IDEAS

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    1. Donald B. Rubin, 1977. "Assignment to Treatment Group on the Basis of a Covariate," Journal of Educational and Behavioral Statistics, , vol. 2(1), pages 1-26, March.
    2. Angrist, Joshua D & Evans, William N, 1998. "Children and Their Parents' Labor Supply: Evidence from Exogenous Variation in Family Size," American Economic Review, American Economic Association, vol. 88(3), pages 450-477, June.
    3. Amanda E. Kowalski, 2019. "A Model of a Randomized Experiment with an Application to the PROWESS Clinical Trial," NBER Working Papers 25670, National Bureau of Economic Research, Inc.
    4. Joshua D. Angrist & Jörn-Steffen Pischke, 2009. "Mostly Harmless Econometrics: An Empiricist's Companion," Economics Books, Princeton University Press, edition 1, number 8769.
    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. Guido W. Imbens & Donald B. Rubin, 1997. "Estimating Outcome Distributions for Compliers in Instrumental Variables Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(4), pages 555-574.
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    More about this item

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C9 - Mathematical and Quantitative Methods - - Design of Experiments
    • H10 - Public Economics - - Structure and Scope of Government - - - General
    • J01 - Labor and Demographic Economics - - General - - - Labor Economics: General

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