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Treatment effect identification using alternative parallel assumptions

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  • Ricardo Mora
  • Iliana Reggio

Abstract

The core assumption to identify the treatment effect in difference-in-differences estimators is the so-called Parallel Paths assumption, namely that the average change in outcome for the treated in the absence of treatment equals the average change in outcome for the non-treated. We define a family of alternative Parallel assumptions and show for a number of frequently used empirical specifications which parameters of the model identify the treatment effect under the alternative Parallel assumptions. We further propose a fully flexible model which has two desirable features not present in the usual econometric specifications implemented in applied research. First, it allows for flexible dynamics and for testing restrictions on these dynamics. Second, it does not impose equivalence between alternative Parallel assumptions. We illustrate the usefulness of our approach by revising the results of several recent papers in which the difference-in-differences technique has been applied.The core assumption to identify the treatment effect in difference-in-differences estimators is the so-called Parallel Paths assumption, namely that the average change in outcome for the treated in the absence of treatment equals the average change in outcome for the non-treated. We define a family of alternative Parallel assumptions and show for a number of frequently used empirical specifications which parameters of the model identify the treatment effect under the alternative Parallel assumptions. We further propose a fully flexible model which has two desirable features not present in the usual econometric specifications implemented in applied research. First, it allows for flexible dynamics and for testing restrictions on these dynamics. Second, it does not impose equivalence between alternative Parallel assumptions. We illustrate the usefulness of our approach by revising the results of several recent papers in which the difference-in-differences technique has been applied

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Bibliographic Info

Paper provided by Universidad Carlos III, Departamento de Economía in its series Economics Working Papers with number we1233.

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Date of creation: Dec 2012
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Handle: RePEc:cte:werepe:we1233

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Keywords: Difference-in-differences; Parallel paths; Treatment effect;

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  1. Redding, Stephen J & Sturm, Daniel M & Wolf, Nikolaus, 2007. "History and Industry Location: Evidence from German Airports," CEPR Discussion Papers, C.E.P.R. Discussion Papers 6345, C.E.P.R. Discussion Papers.
  2. Ran Abramitzky & Adeline Delavande & Luis Vasconcelos, 2010. "Marrying Up: The Role of Sex Ratio in Assortative Matching," Discussion Papers, Stanford Institute for Economic Policy Research 09-030, Stanford Institute for Economic Policy Research.
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  7. Seema Jayachandran & Adriana Lleras-Muney & Kimberly V. Smith, 2010. "Modern Medicine and the Twentieth Century Decline in Mortality: Evidence on the Impact of Sulfa Drugs," American Economic Journal: Applied Economics, American Economic Association, American Economic Association, vol. 2(2), pages 118-46, April.
  8. Janet Currie & W. Reed Walker, 2009. "Traffic Congestion and Infant Health: Evidence from E-ZPass," NBER Working Papers 15413, National Bureau of Economic Research, Inc.
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  10. Leora Friedberg, 1998. "Did Unilateral Divorce Raise Divorce Rates? Evidence from Panel Data," NBER Working Papers 6398, National Bureau of Economic Research, Inc.
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