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Identification Based on Difference-in-Differences Approaches with Multiple Treatments

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  • Hans Fricke

Abstract

This paper discusses identification based on difference-in-differences (DiD) approaches with multiple treatments. It shows that an appropriate adaptation of the common trend assumption underlying the DiD strategy for the comparison of two treatments restricts the possibility of effect heterogeneity for at least one of the treatments. The required assumption of effect homogeneity is likely to be violated because of non-random assignment to treatment based on both observables and unobservables. However, this paper shows that, under certain conditions, the DiD estimate comparing two treatments identifies a lower bound in absolute values on the average treatment effect on the treated compared to the unobserved non-treatment state, even if effect homogeneity is violated. This is possible if, in expectation, the effects of both treatments compared to no treatment have the same sign, and one treatment has a stronger effect than the other treatment on the respective recipients. Such assumptions are plausible if treatments are ordered or vary in intensity.
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Suggested Citation

  • Hans Fricke, 2017. "Identification Based on Difference-in-Differences Approaches with Multiple Treatments," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 79(3), pages 426-433, June.
  • Handle: RePEc:bla:obuest:v:79:y:2017:i:3:p:426-433
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    File URL: http://hdl.handle.net/10.1111/obes.12178
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    References listed on IDEAS

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    1. Douglas Holtz-Eakin & David Joulfaian & Harvey S. Rosen, 1993. "The Carnegie Conjecture: Some Empirical Evidence," The Quarterly Journal of Economics, Oxford University Press, vol. 108(2), pages 413-435.
    2. Michael Lechner, 2002. "Program Heterogeneity And Propensity Score Matching: An Application To The Evaluation Of Active Labor Market Policies," The Review of Economics and Statistics, MIT Press, vol. 84(2), pages 205-220, May.
    3. Lars J. Kirkeboen & Edwin Leuven & Magne Mogstad, 2016. "Editor's Choice Field of Study, Earnings, and Self-Selection," The Quarterly Journal of Economics, Oxford University Press, vol. 131(3), pages 1057-1111.
    4. Esther Duflo, 2001. "Schooling and Labor Market Consequences of School Construction in Indonesia: Evidence from an Unusual Policy Experiment," American Economic Review, American Economic Association, vol. 91(4), pages 795-813, September.
    5. Lechner, Michael, 2011. "The Estimation of Causal Effects by Difference-in-Difference Methods," Foundations and Trends(R) in Econometrics, now publishers, vol. 4(3), pages 165-224, November.
    6. Alberto Abadie, 2005. "Semiparametric Difference-in-Differences Estimators," Review of Economic Studies, Oxford University Press, vol. 72(1), pages 1-19.
    7. Vivi Alatas & Lisa A. Cameron, 2008. "The Impact of Minimum Wages on Employment in a Low-Income Country: A Quasi-Natural Experiment in Indonesia," ILR Review, Cornell University, ILR School, vol. 61(2), pages 201-223, January.
    8. Hans Fricke, 2017. "Identification Based on Difference-in-Differences Approaches with Multiple Treatments," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 79(3), pages 426-433, June.
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    Cited by:

    1. Beestermöller, Matthias, 2017. "Striking Evidence? Demand Persistence for Inter-City Buses from German Railway Strikes," Discussion Papers in Economics 31768, University of Munich, Department of Economics.
    2. repec:bla:obuest:v:79:y:2017:i:3:p:426-433 is not listed on IDEAS
    3. Ni Huang & Yili Hong & Gordon Burtch, 2015. "Digital Social Visibility, Anonymity and User Content Generation: Evidence from Natural Experiments," Working Papers 15-04, NET Institute.
    4. repec:lrk:eeaart:35_3_13 is not listed on IDEAS
    5. Huber, Martin & Tyahlo, Svitlana, 2016. "How war affects political attitudes: evidence from eastern Ukraine," FSES Working Papers 472, Faculty of Economics and Social Sciences, University of Freiburg/Fribourg Switzerland.
    6. Hans Fricke, 2017. "Identification Based on Difference-in-Differences Approaches with Multiple Treatments," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 79(3), pages 426-433, June.
    7. repec:eee:eecrev:v:98:y:2017:i:c:p:240-263 is not listed on IDEAS

    More about this item

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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