synthdid: Synthetic Difference in Differences Estimation

This package implements the synthetic difference in difference estimator (SDID) for the average treatment effect in panel data, as proposed in Arkhangelsky et al (2019). We observe matrices of outcomes Y and binary treatment indicators W that we think of as satisfying Y_ij = L_ij + τ_ij W_ij + ε_ij. Here τ_ij is the effect of treatment on the unit i at time j, and we estimate the average effect of treatment when and where it happened: the average of τ_ij over the observations with W_ij=1. All treated units must begin treatment simultaneously, so W is a block matrix: W_ij = 1 for i > N₀ and j > T₀ and zero otherwise, with N₀ denoting the number of control units and T₀ the number of observation times before onset of treatment. This applies, in particular, to the case of a single treated unit or treated period.

This package is currently in beta and the functionality and interface is subject to change.

Some helpful links for getting started:

• The R package documentation contains usage examples and method reference.
• The online vignettes contains a gallery of plot examples.
• For community questions and answers around usage, see Github issues page.

Installation

devtools::install_github("susanathey/MCPanel")
devtools::install_github("apoorvalal/ebal")
devtools::install_github("apoorvalal/synthdid")

Example

Omnibus function

The panel_estimate function accepts a data frame, unit_id, time_id, treatment, outcome name, and optionally an inference method (jackknife/bootstrap/placebo) and internally performs the reshaping to $N \times T$ matrices and calls several estimators to produce a large table with multiple estimates and corresponding standard errors.

SDID call

library(synthdid)

# Estimate the effect of California Proposition 99 on cigarette consumption
data('california_prop99')
setup = panel.matrices(california_prop99)
tau.hat = synthdid_estimate(setup$Y, setup$N0, setup$T0)
se = sqrt(vcov(tau.hat, method='placebo'))
sprintf('point estimate: %1.2f', tau.hat)
sprintf('95%% CI (%1.2f, %1.2f)', tau.hat - 1.96 * se, tau.hat + 1.96 * se)
plot(tau.hat)

References

Dmitry Arkhangelsky, Susan Athey, David A. Hirshberg, Guido W. Imbens, and Stefan Wager. Synthetic Difference in Differences, 2019. [arxiv]