Portada del sitio > Asignaturas / Teaching > Trabajo de Fin de Grado (TFG). Grado en Economía > Materiales útiles para realizar el TFG > Modelos Diff-in-diff (DID) > Difference-in-Differences with Multiple Time Periods and an Application on (...)
Difference-in-Differences with Multiple Time Periods and an Application on the Minimum Wage and Employment
Authors: Brantly Callaway and Pedro H. C. Sant’Anna. March 28, 2018
Miércoles 14 de junio de 2023, por Carlos San Juan
Difference-in-Differences (DID) is one of the most important and popular designs for eval-uating 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 param-eters 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 proce-dure 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.
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Difference-in-Differences (DID) is one of the most important and popular designs for eval-uating 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 param-eters 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 proce-dure 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.
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