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Fuzzy differences in differences

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  • Clément De Chaisemartin

    (EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris, PSE - Paris-Jourdan Sciences Economiques - CNRS : UMR8545 - École des Hautes Études en Sciences Sociales (EHESS) - École des Ponts ParisTech (ENPC) - École normale supérieure [ENS] - Paris - Institut national de la recherche agronomique (INRA))

Abstract

Difference in differences require that 0% of observations are treated in the control group and during period 0 (no "always takers") and 100% in the treatment group in period 1 (no "never takers"). Sometimes, the treatment rate increases more in the treatment than in the control group but there are never or always takers. This paper develops results to identify treatment effects in such settings. They only require one common trend assumption on the outcome of interest Y whereas the standard instrumental variable result also requires common trend on treatment D. I derive bounds for treatment effects which are tight when there are no or few always takers. This can be the case in applications considering the effect of an innovation, where by definition no observations are treated in period 0. I derive other bounds that are tight when the treatment rate does not change much between the two periods in the control group, which can be the case in applications considering the extension of a program to a group previously not eligible. I use my results to measure the efficacy of a new drug for smoking cessation.

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Paper provided by HAL in its series PSE Working Papers with number halshs-00671368.

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Date of creation: Feb 2012
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Handle: RePEc:hal:psewpa:halshs-00671368

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Keywords: Difference in Differences ; Heterogeneous Treatment Effect ; Imperfect Compliance ; Partial Identification ; Smoking Cessation;

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  10. William N. Evans & Jeanne S. Ringel, 1997. "Can Higher Cigarette Taxes Improve Birth Outcomes?," NBER Working Papers 5998, National Bureau of Economic Research, Inc.
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  13. Field, Erica Marie, 2005. "Property Rights and Investment in Urban Slums," Scholarly Articles 3634150, Harvard University Department of Economics.
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