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Bounds on functionals of the distribution treatment effects

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  • Firpo, Sergio Pinheiro
  • Ridder, Geert

Abstract

Bounds on the distribution function of the sum of two random variableswith known marginal distributions obtained by Makarov (1981) canbe used to bound the cumulative distribution function (c.d.f.) of individualtreatment effects. Identification of the distribution of individualtreatment effects is important for policy purposes if we are interested infunctionals of that distribution, such as the proportion of individuals whogain from the treatment and the expected gain from the treatment forthese individuals. Makarov bounds on the c.d.f. of the individual treatmenteffect distribution are pointwise sharp, i.e. they cannot be improvedin any single point of the distribution. We show that the Makarov boundsare not uniformly sharp. Specifically, we show that the Makarov boundson the region that contains the c.d.f. of the treatment effect distributionin two (or more) points can be improved, and we derive the smallest setfor 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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Paper provided by Escola de Economia de São Paulo, Getulio Vargas Foundation (Brazil) in its series Textos para discussão with number 201.

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Date of creation: 01 Jun 2010
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Handle: RePEc:fgv:eesptd:201

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  1. Djebbari, Habiba & Smith, Jeffrey A., 2008. "Heterogeneous Impacts in PROGRESA," IZA Discussion Papers 3362, Institute for the Study of Labor (IZA).
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Cited by:
  1. Erich Battistin & Mario Padula, 2010. "Survey Instruments and the Reports of Consumption Expenditures: Evidence from the Consumer Expenditure Surveys," CSEF Working Papers 259, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
  2. 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.
  3. Firpo, Sergio, 2010. "Identification and Estimation of Distributional Impacts of Interventions Using Changes in Inequality Measures," IZA Discussion Papers 4841, Institute for the Study of Labor (IZA).

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