This package is intended to help R users estimate average effects on the treated (ATT) in panel data (under identifying assumptions) using synthetic difference-in-differences (SDiD). We built this package to implement key aspects of the related Stata package sdid by Clarke et al. (2024) in R. As in that package, our implementation accepts a long format panel dataset, detects whether a staggered treatment approach is needed, and estimates the effect with bootstrap, jackknife, or placebo inference.
We build on a prior R implementation of this method synthdid 0.0.9 by Arkhangelsky et al. (2021), adding staggered adoption, optimized and projected methods of covariate adjustment, and a redesigned interface. To substantially reduce computation time, we reimplement the estimation of the unit and time weights in compiled C++ code and parallelize the resampling procedures used for inference.
The development version can be installed from R-Universe.
install.packages("sdid", repos = c("https://alcocer-jj.r-universe.dev",
"https://cloud.r-project.org"))
Users who already have a C++ toolchain can also install sdid directly from GitHub, which compiles the package from source.[^1]
[^1]: This route requires Rtools on Windows, or the Xcode Command Line Tools and GNU Fortran on macOS.
# install.packages("remotes")
remotes::install_github("alcocer-jj/sdid")
A full call of the main function is shown below. For arguments that take one of several values, the first value listed is the default, except for vce, which has no default and must be given.
sdid(
data,
outcome,
unit,
time,
treatment,
vce = c("bootstrap", "jackknife", "placebo", "noinference"),
covariates = NULL,
method = c("sdid", "sc", "did"),
reps = 50,
seed = NULL,
level = 95,
alternative = c("two.sided", "greater", "less"),
covariate.method = c("optimized", "projected"),
standardize = TRUE,
projection.sample = c("controls", "untreated"),
num.threads = NULL,
graph = TRUE,
quietly = FALSE,
...
)
data: balanced panel in long format, one row per unit and period.outcome: name of the outcome variable.unit: name of the unit identifier.time: name of the time period variable.treatment: name of the binary treatment variable, equal to 1 for a treated unit in every period from its first treated period onward, and 0 otherwise.vce: inference method (required).covariates: names of time-varying covariate variables, if any.method: synthetic DiD, synthetic control, or difference-in-differences.reps: number of bootstrap or placebo replications.seed: random seed, applied to this call only.level: confidence level, in percent.alternative: alternative hypothesis of the test of the effect against zero.covariate.method: how covariates are adjusted for.standardize: standardize covariates under the optimized method.projection.sample: regression sample under the projected method.num.threads: threads for replications, all available when NULL.graph: produce the trends plot in this call.quietly: TRUE prints nothing, for use in loops.The example below estimates the effect of California's Proposition 99 on cigarette consumption, using placebo inference because California is the only treated state. An sdid() call describes the data and parameters in the console, shows the inference progress, and prints the results.
library(sdid)
data(california_prop99)
fit1 <- sdid(
california_prop99,
"PacksPerCapita", "State", "Year", "treated",
vce = "placebo", reps = 1000, seed = 444
)
#> Synthetic Difference-in-Differences Estimator
#>
#> Outcome PacksPerCapita
#> Treatment treated
#> Units 39 (38 never treated, 1 treated)
#> Periods 31 (1970 to 2000), treatment from 1989
#> Inference placebo, 1000 replications
#>
#> Placebo [========================] 1000/1000 100% 0.2s elapsed done 18 threads
#>
#> ATT Std. Err. z P>|z| [95% Conf. Interval]
#> treated -15.60383 8.71856 -1.79 0.073 -32.69189 1.48424
#>
#> 95% confidence intervals and p-values use the normal approximation.
It also draws the trends plot unless graph = FALSE.
When treated units adopt treatment in different periods, sdid() estimates adoption-period effects. The overall effect is a weighted average of these effects with weights proportional to each cohort's number of treated units times its number of post-treatment periods, following Algorithm 1 of Clarke et al. (2024). Bootstrap, jackknife, and placebo inference then resample the whole panel jointly, as in Algorithms 2 to 4 of Clarke et al. (2024).
library(haven)
library(sdid)
data <- read_dta("https://github.com/Daniel-Pailanir/sdid/raw/refs/heads/main/simulations/cluster_data/quota_example_cluster.dta")
fit2 <- sdid(
data,
"womparl", "country", "year", "quota",
vce = "bootstrap", reps = 1000, seed = 444
)
#> Synthetic Difference-in-Differences Estimator
#>
#> Outcome womparl
#> Treatment quota
#> Units 119 (110 never treated, 9 treated)
#> Periods 26 (1990 to 2015), 7 adoption periods
#> Inference bootstrap, 1000 replications
#>
#> Bootstrap [========================] 1000/1000 100% 11.4s elapsed done 18 threads
#>
#> ATT Std. Err. z P>|z| [95% Conf. Interval]
#> quota 8.03410 3.18551 2.52 0.012 1.79062 14.27758
#>
#> Adoption-period estimates
#> Treated Post Weight ATT Std. Err. z P>|z| [95% Conf. Interval]
#> 2000 1 16 0.1702 8.38887 0.69893 12.00 0.000 7.01900 9.75874
#> 2002 2 14 0.2979 6.96775 0.57747 12.07 0.000 5.83592 8.09957
#> 2003 2 13 0.2766 13.95226 8.59993 1.62 0.105 -2.90329 30.80781
#> 2005 1 11 0.1170 -3.45054 0.67457 -5.12 0.000 -4.77268 -2.12841
#> 2010 1 6 0.0638 2.74904 0.43366 6.34 0.000 1.89908 3.59899
#> 2012 1 4 0.0426 21.76272 0.86701 25.10 0.000 20.06341 23.46203
#> 2013 1 3 0.0319 -0.82032 0.81086 -1.01 0.312 -2.40958 0.76893
#>
#> 95% confidence intervals and p-values use the normal approximation.
Time-varying covariates can be supplied with covariates, while covariate.method selects one of the two adjustments. The default, "optimized", estimates their coefficients jointly with the weights, following Arkhangelsky et al. (2021), after standardizing each covariate. The alternative, "projected", estimates them from a two-way fixed effects regression on the never-treated units, following Kranz (2022) and Clarke et al. (2024).
library(sdid)
data(CPS)
fit3 <- sdid(
CPS,
"log_wage", "state", "year", "abort_ban",
vce = "bootstrap", reps = 1000, seed = 444,
covariates = c("hours", "urate"),
covariate.method = "projected",
graph = FALSE
)
#> Synthetic Difference-in-Differences Estimator
#>
#> Outcome log_wage
#> Treatment abort_ban
#> Units 50 (32 never treated, 18 treated)
#> Periods 40 (1979 to 2018), treatment from 2018
#> Covariates hours, urate, projected
#> Inference bootstrap, 1000 replications
#>
#> Bootstrap [========================] 1000/1000 100% 1.0s elapsed done 18 threads
#>
#> ATT Std. Err. z P>|z| [95% Conf. Interval]
#> abort_ban 0.00261 0.01465 0.18 0.858 -0.02610 0.03132
#>
#> 95% confidence intervals and p-values use the normal approximation.
Results work with modelsummary and other packages that read results through tidy() and glance(). Each model's effect is named by its treatment column by default, so labels = "ATT" puts the effects of models with different treatment columns on one row. For a staggered design, cohorts = TRUE adds a row for each adoption period, and labels can then name every row.
library(modelsummary)
gm <- data.frame(
raw = c("nobs", "n.units", "n.periods"),
clean = c("Observations", "Units", "Periods"),
fmt = 0
)
modelsummary(
models = list("Prop 99" = fit1, "Quota" = fit2, "Abortion Ban" = fit3),
labels = "ATT",
gof_map = gm,
stars = TRUE,
output = "markdown"
)
#> +--------------+----------+---------+--------------+
#> | | Prop 99 | Quota | Abortion Ban |
#> +==============+==========+=========+==============+
#> | ATT | -15.604+ | 8.034* | 0.003 |
#> +--------------+----------+---------+--------------+
#> | | (8.719) | (3.186) | (0.015) |
#> +--------------+----------+---------+--------------+
#> | Observations | 1209 | 3094 | 2000 |
#> +--------------+----------+---------+--------------+
#> | Units | 39 | 119 | 50 |
#> +--------------+----------+---------+--------------+
#> | Periods | 31 | 26 | 40 |
#> +==============+==========+=========+==============+
#> | + p < 0.1, * p < 0.05, ** p < 0.01, *** p < |
#> | 0.001 |
#> +==============+==========+=========+==============+
modelsummary(
models = list("Quota" = fit2),
coef_rename = c("quota" = "Weighted ATT"),
cohorts = TRUE,
gof_map = gm,
stars = TRUE,
output = "markdown"
)
#> +--------------+-----------+
#> | | Quota |
#> +==============+===========+
#> | Weighted ATT | 8.034* |
#> +--------------+-----------+
#> | | (3.186) |
#> +--------------+-----------+
#> | 2000 | 8.389*** |
#> +--------------+-----------+
#> | | (0.699) |
#> +--------------+-----------+
#> | 2002 | 6.968*** |
#> +--------------+-----------+
#> | | (0.577) |
#> +--------------+-----------+
#> | 2003 | 13.952 |
#> +--------------+-----------+
#> | | (8.600) |
#> +--------------+-----------+
#> | 2005 | -3.451*** |
#> +--------------+-----------+
#> | | (0.675) |
#> +--------------+-----------+
#> | 2010 | 2.749*** |
#> +--------------+-----------+
#> | | (0.434) |
#> +--------------+-----------+
#> | 2012 | 21.763*** |
#> +--------------+-----------+
#> | | (0.867) |
#> +--------------+-----------+
#> | 2013 | -0.820 |
#> +--------------+-----------+
#> | | (0.811) |
#> +--------------+-----------+
#> | Observations | 3094 |
#> +--------------+-----------+
#> | Units | 119 |
#> +--------------+-----------+
#> | Periods | 26 |
#> +==============+===========+
#> | + p < 0.1, * p < 0.05, |
#> | ** p < 0.01, *** p < |
#> | 0.001 |
#> +==============+===========+
The plotting functions take the result of sdid() and draw one panel per adoption cohort for a staggered design.
sdid_plot(fit1) # trajectories and time weights
sdid_plot(fit1, style = "effects") # with a DiD effects diagram
sdid_plot(fit1, x.breaks = seq(1970, 2000, by = 5)) # custom ticks
sdid_units_plot(fit1) # unit weights
sdid_units_plot(fit1, type = "bars") # unit weights with bars instead
sdid_placebo_plot(fit1, placebo.time = 1981) # in-time placebo plot
Unit and time weights are estimated in C++, and bootstrap, jackknife, and placebo replications run in parallel across all available threads. The option sdid.num.threads, or the num.threads argument of sdid(), limits the number of threads.
This package builds heavily on the work of Dmitry Arkhangelsky, Susan Athey, David A. Hirshberg, Guido W. Imbens and Stefan Wager, the authors of the synthdid package for R, and Damian Clarke, Daniel Pailañir, Susan Athey, Guido Imbens, Diego Ciccia, and Tommy Morgan, the authors and contributors of the sdid package for Stata. We build on their methods and the code they made openly available.
Development of this package was assisted by Claude Code, an AI coding assistant by Anthropic, for code refactoring, documentation updates, and package restructuring.
Arkhangelsky, Dmitry, Susan Athey, David A. Hirshberg, Guido W. Imbens, and Stefan Wager. (2021). "Synthetic Difference-in-Differences." American Economic Review 111(12): 4088-4118.
Clarke, Damian, Daniel Pailañir, Susan Athey, and Guido Imbens. (2024). "On Synthetic Difference-in-Differences and Related Estimation Methods in Stata." The Stata Journal 24(4): 557-598.
Kranz, Sebastian. (2022). "Synthetic Difference-in-Differences with Time-Varying Covariates." Working paper. https://github.com/skranz/xsynthdid.
BSD 3-Clause. See LICENSE.md. The package derives from synthdid 0.0.9, Copyright 2019 Stanford University, used under its BSD 3-Clause option.