understudy

understudy fits the synthetic difference-in-differences (SDID) estimator of Arkhangelsky et al. (2021) with the Frank-Wolfe weight solver written in Rust (via extendr) and an lm()-style interface. Beyond the core estimator it adds:

• staggered adoption with cohort aggregation, and event-study dynamic effects (event_study());
• conformal inference for the per-period counterfactual (augment(), conformal_test()), valid with a single treated unit;
• two covariate-adjustment methods (projected, and optimized).

Point estimates are validated to match the reference implementations exactly: the R packages synthdid and xsynthdid, and the Stata sdid library.

Installation

Installation compiles Rust, so a Rust toolchain (cargo, rustc) is required. Then, from GitHub:

# install.packages("pak")
pak::pak("belian-earth/understudy")

Example

Estimate the effect of California’s Proposition 99 on cigarette sales, and read off a check_model()-style diagnostic.

library(understudy)

fit <- sdid(california_prop99, outcome = PacksPerCapita, unit = State,
            time = Year, treatment = treated)
fit
#> ── Synthetic diff-in-diff ──────────────────────────────────────────────────────
#> Call `sdid(data = california_prop99, outcome = PacksPerCapita, unit = State,
#> time = Year, treatment = treated)`
#> Estimate: -15.6
#> Treated: 1 unit × 12 post-periods
#> Controls: 38 units (effective 16.4)
#> Pre-periods: 19 (effective 2.8)
#> Top units: Nevada 0.12, New Hampshire 0.11, Connecticut 0.08 (+25 more)
#> Top periods: 1988 0.43, 1986 0.37, 1987 0.21
#> Standard errors via `summary()` or `vcov()`

plot(fit, type = "diagnostic")

The panels show the treated-vs-synthetic trajectory, the per-period effect with a conformal band, each control’s weighted contribution, and the unit weights. See vignette("getting-started"), vignette("inference"), vignette("covariates"), and vignette("staggered") for more.

References and related work

• Arkhangelsky, Athey, Hirshberg, Imbens & Wager (2021), “Synthetic Difference-in-Differences,” American Economic Review. Reference R package: synthdid.
• Clarke, Pailanir, Athey & Imbens (2023), the Stata sdid command (staggered adoption).
• Kranz (2022), covariate projection, R package xsynthdid.
• Chernozhukov, Wuthrich & Zhu (2021), conformal inference for synthetic controls.
• Greathouse, mlsynth (Python): the reference implementation for the spatial estimator (spatial_sdid()), and the source of the power-analysis and balance diagnostics.