Synthetic Difference In Differences Estimation

Abstract

In this paper, we describe a computational implementation of the Synthetic difference-in-differences (SDID) estimator of Arkhangelsky et al. (2021) for Stata. Synthetic difference-in-differences can be used in a wide class of circumstances where treatment effects on some particular policy or event are desired, and repeated observations on treated and untreated units are available over time. We lay out the theory underlying SDID, both when there is a single treatment adoption date and when adoption is staggered over time, and discuss estimation and inference in each of these cases. We introduce the sdid command which implements these methods in Stata, and provide a number of examples of use, discussing estimation, inference, and visualization of results.

The effects of the decentralization of collective bargaining on wages and wage dispersion: Evidence from the Finnish forest and IT industries

“…Arkhangelsky et al (2021) simulation studies show good properties, with similar numbers of cross-sectional units and periods to those in my analysis. To estimate the model, I use the Stata command described by Clarke et al (2023).…”

Políticas activas de mercado laboral en Bolivia: impacto del Programa de Apoyo al Empleo II

“…El estimador del impacto promedio del tratamiento para los tratados es generado a partir de una regresión de efectos fijos individuales y temporales, con ponderadores ω i sdid y λ t sdid optimizados. Acorde a Clarke et al (2023), este procedimiento permite la presencia de factores agregados temporales compartidos, debido a la estimación de los efectos fijos temporales β t , y factores específicos de la unidad invariables en el tiempo, debido a la estimación de los efectos fijos unitarios α i . La presencia de efectos fijos unitarios implica que el estimador sintético de diferencias en diferencias buscará emparejar las unidades de tratamiento y control en las tendencias previas al tratamiento, y no necesariamente en tendencias y niveles previos al tratamiento.…”

“…Luego, se calcula un promedio ponderado de cada uno de los sub-grupos basado en el número de unidades tratadas y periodos que posee cada sub-grupo que adopta un tratamiento en algún momento del tiempo. Siguiendo lo indicado por Clarke et al (2023), el proceso de estimación del impacto promedio del tratamiento, en el caso de adopción escalonada, se basa en el siguiente algoritmo:…”

The Effects of the Dobbs Decision on Fertility

“…To estimate SDID event studies with confidence intervals, we follow Clarke et al (2023) and use the di↵erence between the treatment and control group in each period relative to their time-weighted pre-period and bootstrap inference for the calculation of 95 percent confidence intervals. In all our analyses, we estimate the averaged treatment e↵ect by treatment group in time compared to sets of never-treated control units.…”

“…Synthetic di↵erence in di↵erences estimate of the impact of the Dobbs decision on fertility using the first six months of every period,[2019][2020][2021][2022][2023] Notes: The reported coe cients are estimated e↵ects of Dobbs ban states relative to protected states where the e↵ects are estimated using Synthetic Di↵erence-in-Di↵erences fromArkhangelsky et al (2021) and implemented byClarke et al (2023) in Stata. Fertility is measured based on the first six months of every period in each state in each group and measured as 1,000 multiplied by the number of births in each group divided by the number of women in each group multiplied by two to annualize the estimates.…”