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Bounds on functionals of the distribution treatment effects


  • Firpo, Sergio Pinheiro
  • Ridder, Geert


Bounds on the distribution function of the sum of two random variables with known marginal distributions obtained by Makarov (1981) can be used to bound the cumulative distribution function (c.d.f.) of individual treatment effects. Identification of the distribution of individual treatment effects is important for policy purposes if we are interested in functionals of that distribution, such as the proportion of individuals who gain from the treatment and the expected gain from the treatment for these individuals. Makarov bounds on the c.d.f. of the individual treatment effect distribution are pointwise sharp, i.e. they cannot be improved in any single point of the distribution. We show that the Makarov bounds are not uniformly sharp. Specifically, we show that the Makarov bounds on the region that contains the c.d.f. of the treatment effect distribution in two (or more) points can be improved, and we derive the smallest set for the c.d.f. of the treatment effect distribution in two (or more) points. An implication is that the Makarov bounds on a functional of the c.d.f. of the individual treatment effect distribution are not best possible.

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  • Firpo, Sergio Pinheiro & Ridder, Geert, 2010. "Bounds on functionals of the distribution treatment effects," Textos para discussão 201, FGV/EESP - Escola de Economia de São Paulo, Getulio Vargas Foundation (Brazil).
  • Handle: RePEc:fgv:eesptd:201

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    References listed on IDEAS

    1. Djebbari, Habiba & Smith, Jeffrey, 2008. "Heterogeneous impacts in PROGRESA," Journal of Econometrics, Elsevier, vol. 145(1-2), pages 64-80, July.
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    Cited by:

    1. Fan, Yanqin & Park, Sang Soo, 2009. "Partial identification of the distribution of treatment effects and its confidence sets," MPRA Paper 37148, University Library of Munich, Germany.
    2. Sergio Firpo & Cristine Pinto, 2016. "Identification and Estimation of Distributional Impacts of Interventions Using Changes in Inequality Measures," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(3), pages 457-486, April.
    3. Gautier, Eric & Hoderlein, Stefan, 2011. "A triangular treatment effect model with random coefficients in the selection equation," TSE Working Papers 15-598, Toulouse School of Economics (TSE), revised 25 Aug 2015.
    4. Erich Battistin & Mario Padula, 2016. "Survey instruments and the reports of consumption expenditures: evidence from the consumer expenditure surveys," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 179(2), pages 559-581, February.
    5. Jinhyun Lee, 2013. "Sharp Bounds on Heterogeneous Individual Treatment Responses," Discussion Paper Series, Department of Economics 201310, Department of Economics, University of St. Andrews.
    6. Toru Kitagawa, 2011. "Inference and decision for set identified parameters using posterior lower and upper probabilities," CeMMAP working papers CWP16/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    7. Juan Carlos Escanciano & Lin Zhu, 2013. "Set inferences and sensitivity analysis in semiparametric conditionally identified models," CeMMAP working papers CWP55/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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