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

Brantly Callaway () and Pedro Sant'Anna ()

Papers from arXiv.org

Abstract: In this article, we consider identification and estimation of treatment effect parameters using Difference-in-Differences (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 properties of the proposed estimators, and prove the validity of a computationally convenient bootstrap procedure to conduct asymptotically valid simultaneous (instead of pointwise) inference. Our proposed inference procedure naturally adjusts for autocorrelation and other forms of clustering in the data. We also propose a semiparametric data-driven testing procedure to assess the credibility of the DID design in our context. Finally, we illustrate the relevance of our proposed tools by analyzing the effect of the minimum wage on teen employment from 2001-2007. Open-source software is available for implementing the proposed methods.

Date: 2018-03, Revised 2018-08
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http://arxiv.org/pdf/1803.09015 Latest version (application/pdf)

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Working Paper: Difference-in-Differences with Multiple Time Periods and an Application on the Minimum Wage and Employment (2018) Downloads
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