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Difference-in-Differences with Multiple Time Periods and an Application on the Minimum Wage and Employment

Author

Listed:
  • Brantly Callaway

    () (Department of Economics, Temple University)

  • Pedro H. C. Sant'Anna

    () (Department of Economics, Vanderbilt University)

Abstract

Difference-in-Differences (DID) is one of the most important and popular designs for evaluating causal effects of policy changes. In its standard format, there are two time periods and two groups: in the first period no one is treated, and in the second period a "treatment group" becomes treated, whereas a "control group" remains untreated. However, many em- pirical applications of the DID design have more than two periods and variation in treatment timing. In this article, we consider identification and estimation of treatment effect parameters using DID with (i) multiple time periods, (ii) variation in treatment timing, and (iii) when the "parallel trends assumption" holds potentially only after conditioning on observed covariates. We propose a simple two-step estimation strategy, establish the asymptotic prop- erties of the proposed estimators, and prove the validity of a computationally convenient bootstrap procedure. Furthermore we propose a semiparametric data-driven testing procedure to assess the credibility of the DID design in our context. Finally, we analyze the effect of the minimum wage on teen employment from 2001-2007. By using our proposed methods we confront the challenges related to variation in the timing of the state-level minimum wage policy changes. Open-source software is available for implementing the proposed methods.

Suggested Citation

  • Brantly Callaway & Pedro H. C. Sant'Anna, 2018. "Difference-in-Differences with Multiple Time Periods and an Application on the Minimum Wage and Employment," DETU Working Papers 1804, Department of Economics, Temple University.
  • Handle: RePEc:tem:wpaper:1804
    as

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    File URL: http://www.cla.temple.edu/RePEc/documents/DETU_18_04.pdf
    File Function: First version, 2018
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    References listed on IDEAS

    as
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    8. Jonathan Meer & Jeremy West, 2016. "Effects of the Minimum Wage on Employment Dynamics," Journal of Human Resources, University of Wisconsin Press, vol. 51(2), pages 500-522.
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    More about this item

    Keywords

    Difference-in-Differences; Multiple Periods; Variation in Treatment Timing; Pre- Testing; Minimum Wage;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • 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
    • J23 - Labor and Demographic Economics - - Demand and Supply of Labor - - - Labor Demand
    • J38 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs - - - Public Policy

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