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Synthdid |
This package implements the Synthetic Difference-in-Differences method described by Arkhangelsky et al. (2021), who provide an implementation in R, with accompanying materials here: synthdid. We follow the implementation provided by Clarke et al. (2023) for Stata and adapt it for the Julia programming language.
The latest version can be downloaded and installed by running:
import Pkg; Pkg.add(url = "https://github.com/d2cml-ai/Synthdid.jl")The latest stable version can be downloaded from Registry by running:
import Pkg; Pkg.add("Synthdid")using Synthdid, DataFramesThe main function in Synthdid is the SynthDID constructor for the object type of the same name.
data:DataFramewith the necessary data for the estimation. It must contain panel data for an outcome column, a column with the names or IDs of the units in the sample, a time column, and a column with an indicator for the periods in which each unit has been treated.Y_col:StringorSymbolfor the outcome variableS_col:StringorSymbolfor the unit variableT_col:StringorSymbolfor the time variableD_col:StringorSymbolfor the treatment variablecovariates:Vectorwith column names for covariatescov_method: Either"projected"or "optimized". Choose how the residuals for estimation are calculated when adding covariates
This implementation is identical to the one presented by Arkhangelsky et al.
data = california_prop99();res = sdid(data, :PacksPerCapita, :State, :Year, :treated);
res["att"]-15.603827872733849
In the case of staggered treatments, the treated sample is separated by adoption year and several ATT are calculated with each partial sample and all the controls. The final ATT is the average of the partial ATTs weighted by the total amount of treatment years its subsample contains.
data = quota();res = sdid(data, :womparl, :country, :year, :quota);
res["att"]8.034101989321492
This method also stores each subsample's result, as well as relevant information and data for each iteration of the Synthetic Difference-in-Differences algorithm:
res["year_params"]7×7 DataFrame
Row │ treat_year tau weighted_tau N0 T0 N1 T1
│ Any Any Any Any Any Any Any
─────┼─────────────────────────────────────────────────────────────
1 │ 2000.0 8.38887 1.42789 110.0 10.0 1.0 16.0
2 │ 2002.0 6.96775 2.0755 110.0 12.0 2.0 14.0
3 │ 2003.0 13.9523 3.85913 110.0 13.0 2.0 13.0
4 │ 2005.0 -3.45054 -0.403787 110.0 15.0 1.0 11.0
5 │ 2010.0 2.74904 0.17547 110.0 20.0 1.0 6.0
6 │ 2012.0 21.7627 0.926073 110.0 22.0 1.0 4.0
7 │ 2013.0 -0.820324 -0.0261805 110.0 23.0 1.0 3.0
There are two methods for adjusting for covariates in the estimation. The first one is proposed by Arkhangelsky et al. (2021), and it adjusts the outcome by the covariates in each subsample. As a result, this method is fairly slow as the procedure repeats for every subsample. This method is the package's default and can be called using the cov_method = "optimized" option:
data = dropmissing(data, :lngdp);
res = sdid(data, :womparl, :country, :year, :quota, covariates = [:lngdp], cov_method = "optimized")
res["att"]8.047948491131669
The second method is proposed by Kranz (2022), for a faster adjustment of the outcome variable, as the procedure is only excecuted once for the whole sample. This method can be called using the cov_method = "projected" option:
res = sdid(data, :womparl, :country, :year, :quota, covariates = [:lngdp], cov_method = "projected")
res["att"]8.059034614789997
We implement three methods for standard error: jackknife_se, bootstrap_se y placebo_se. Details about the implementation can be found at Clarke et al. (2023)
placebo_se(data, :womparl, :country, :year, :quota, covariates = [:lngdp], cov_method = "projected")Placebo replications (50). This may take some time.
----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5
.................................................. 50
1.8918455360543351
For convenience, all the procedures described above can be executed and their results can be sumarized by using the SynthDID constructor and type.
res = SynthDID(data, :womparl, :country, :year, :quota, covariates = [:lngdp], cov_method = "projected");
resPlacebo replications (50). This may take some time.
----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5
.................................................. 50
1×6 DataFrame
Row │ ATT Std. Err. t P>|t| [95% Conf. Interval]
│ Float64 Float64 Float64 Float64 Float64 Float64
─────┼────────────────────────────────────────────────────────────────
1 │ 8.05903 1.65142 4.88005 1.06058e-6 4.82224 11.2958
This package uses the GR backend for Plotly, which allows to quickly generate plots and save them in png, pdf, ps, or svg format. All plots are stored in a dictionary by treatment year subsample.
We implement plotting outcome variable comparations:
plots = plot_outcomes(data, :PacksPerCapita, :State, :Year, :treated)
plots["1989"]
Plotting weights is also implemented:
plots = plot_weights(data, :PacksPerCapita, :State, :Year, :treated)
plots["1989"]
The dictionary design is specially useful for staggered treatment cases:
plots = plot_outcomes(data, :womparl, :country, :year, :quota)
plots["2000"]
plots["2002"]
plots["2003"]
plots["2005"]
plots["2010"]
plots["2012"]
plots["2013"]
plots = plot_weights(data, :womparl, :country, :year, :quota)
plots["2000"]
plots["2002"]
plots["2003"]
plots["2005"]
plots["2010"]
plots["2012"]
plots["2013"]
Dmitry Arkhangelsky, Susan Athey, David A. Hirshberg, Guido W. Imbens, and Stefan Wager. Synthetic Difference in Differences, American Economic Review, December 2021.
Damian Clarke, Daniel Pailañir, Susan Athey, and Guido Imbens. Synthetic Difference-in-Differences Estimation. Institute of Labor Economics Discussion Paper Series, January 2023.
Sebastian Kranz. Synthetic Difference-in-Differences with Time-Varying Covariates. January 2022.