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Estimating Functionals of the Joint Distribution of Potential Outcomes with Optimal Transport

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  • Daniel Ober-Reynolds

Abstract

Many causal parameters depend on a moment of the joint distribution of potential outcomes. Such parameters are especially relevant in policy evaluation settings, where noncompliance is common and accommodated through the model of Imbens & Angrist (1994). This paper shows that the sharp identified set for these parameters is an interval with endpoints characterized by the value of optimal transport problems. Sample analogue estimators are proposed based on the dual problem of optimal transport. These estimators are root-n consistent and converge in distribution under mild assumptions. Inference procedures based on the bootstrap are straightforward and computationally convenient. The ideas and estimators are demonstrated in an application revisiting the National Supported Work Demonstration job training program. I find suggestive evidence that workers who would see below average earnings without treatment tend to see above average benefits from treatment.

Suggested Citation

  • Daniel Ober-Reynolds, 2023. "Estimating Functionals of the Joint Distribution of Potential Outcomes with Optimal Transport," Papers 2311.09435, arXiv.org.
    • Handle: RePEc:arx:papers:2311.09435
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    References listed on IDEAS

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    1. Charles F. Manski, 1997. "Monotone Treatment Response," Econometrica, Econometric Society, vol. 65(6), pages 1311-1334, November.
    2. Sergio Firpo, 2007. "Efficient Semiparametric Estimation of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 75(1), pages 259-276, January.
    3. Werner Ehm & Tilmann Gneiting & Alexander Jordan & Fabian Krüger, 2016. "Of quantiles and expectiles: consistent scoring functions, Choquet representations and forecast rankings," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(3), pages 505-562, June.
    4. Brigham R. Frandsen & Lars J. Lefgren, 2021. "Partial identification of the distribution of treatment effects with an application to the Knowledge is Power Program (KIPP)," Quantitative Economics, Econometric Society, vol. 12(1), pages 143-171, January.
    5. James J. Heckman & Jeffrey Smith & Nancy Clements, 1997. "Making The Most Out Of Programme Evaluations and Social Experiments: Accounting For Heterogeneity in Programme Impacts," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(4), pages 487-535.
    6. 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.
    7. Abadie, Alberto, 2003. "Semiparametric instrumental variable estimation of treatment response models," Journal of Econometrics, Elsevier, vol. 113(2), pages 231-263, April.
    8. Alfred Galichon, 2017. "A Survey of Some Recent Applications of Optimal Transport Methods to Econometrics," SciencePo Working papers Main hal-03948107, HAL.
    9. Guido W. Imbens & Charles F. Manski, 2004. "Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 72(6), pages 1845-1857, November.
    10. Toru Kitagawa, 2015. "A Test for Instrument Validity," Econometrica, Econometric Society, vol. 83(5), pages 2043-2063, September.
    11. William Torous & Florian Gunsilius & Philippe Rigollet, 2021. "An Optimal Transport Approach to Estimating Causal Effects via Nonlinear Difference-in-Differences," Papers 2108.05858, arXiv.org, revised Mar 2024.
    12. Hunt Allcott & Luca Braghieri & Sarah Eichmeyer & Matthew Gentzkow, 2020. "The Welfare Effects of Social Media," American Economic Review, American Economic Association, vol. 110(3), pages 629-676, March.
    13. Alfred Galichon, 2017. "A survey of some recent applications of optimal transport methods to econometrics," Econometrics Journal, Royal Economic Society, vol. 20(2), pages 1-11.
    14. 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.
    15. Zheng Fang & Andres Santos, 2019. "Inference on Directionally Differentiable Functions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(1), pages 377-412.
    16. Alexis Diamond & Jasjeet S. Sekhon, 2013. "Genetic Matching for Estimating Causal Effects: A General Multivariate Matching Method for Achieving Balance in Observational Studies," The Review of Economics and Statistics, MIT Press, vol. 95(3), pages 932-945, July.
    17. Guido Friebel & Matthias Heinz & Mitchell Hoffman & Nick Zubanov, 2023. "What Do Employee Referral Programs Do? Measuring the Direct and Overall Effects of a Management Practice," Journal of Political Economy, University of Chicago Press, vol. 131(3), pages 633-686.
    18. Alfred Galichon, 2017. "A survey of some recent applications of optimal transport methods to econometrics," Econometrics Journal, Royal Economic Society, vol. 20(2), pages 1-11, June.
    19. Fan, Yanqin & Park, Sang Soo, 2012. "Confidence intervals for the quantile of treatment effects in randomized experiments," Journal of Econometrics, Elsevier, vol. 167(2), pages 330-344.
    20. Thomas M. Russell, 2021. "Sharp Bounds on Functionals of the Joint Distribution in the Analysis of Treatment Effects," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(2), pages 532-546, March.
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