synthdid-py

Synthetic Difference-in-Differences for Python — a complete port of the reference R package synthdid by Arkhangelsky, Athey, Hirshberg, Imbens and Wager.

Everything the R package does, this does: the estimator, the Frank-Wolfe solvers, covariate adjustment, all three variance estimators, the placebo diagnostic, and the full set of plots. Plus staggered adoption, which the R package does not support.

Point estimates agree with R to the fifth decimal on the canonical example.

日本語版の README は README.ja.md にあります。

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Install

pip install synthdid-py

Plots need matplotlib:

pip install "synthdid-py[plot]"

Quickstart

from synthdid import load_california_prop99, panel_matrices, synthdid_estimate

panel = panel_matrices(load_california_prop99())   # long panel -> Y, N0, T0, W
tau = synthdid_estimate(panel.Y, panel.N0, panel.T0,
                        unit_names=panel.units, time_labels=panel.time)

print(tau)
# synthdid_estimate: -15.6038. Effective N0/N0 = 16.4/38. Effective T0/T0 = 2.8/19. N1,T1 = 1,12.

print(tau.se(method="placebo"))    # ~9.8  (California is the only treated unit)
print(tau.ci(method="placebo"))    # ~(-34.8, 3.6)

tau is a float — compare it, add it, put it in a DataFrame — that also carries .weights, .setup and .opts.

tau.summary()          # estimate, se, effective sample sizes, leading weights
tau.controls()         # the control units that carry the weight, sorted
tau.effect_curve()     # the per-period effects that average to the estimate
tau.placebo()          # refit on pre-treatment data only
tau.plot()             # the trajectory + 2x2 diagram figure

Verified against the R implementation

Run on california_prop99 (39 states, 1970-2000, California treated from 1989):

estimator	this package	R synthdid 0.0.9
synthdid_estimate	−15.60383	−15.60383
sc_estimate	−19.61966	−19.61966
did_estimate	−27.34911	−27.34911

The test suite also checks, on synthetic panels, every invariance the R package tests for (unit and time fixed effects, rescaling, block shifts), and validates the Frank-Wolfe solver against an independent projected-gradient solver with a duality-gap optimality certificate.

pytest        # 108 tests

The three estimators

from synthdid import synthdid_estimate, sc_estimate, did_estimate

sdid = synthdid_estimate(Y, N0, T0)   # unit weights AND time weights
sc   = sc_estimate(Y, N0, T0)         # unit weights only  (synthetic control)
did  = did_estimate(Y, N0, T0)        # uniform weights    (difference-in-differences)

Y is an N x T array whose first N0 rows are the control units and whose first T0 columns are the pre-treatment periods. A DataFrame works too, and its index and columns become the unit and period labels.

Standard errors

method	algorithm in the paper	when to use
"bootstrap"	Algorithm 2	the default; resamples units
"jackknife"	Algorithm 3	fast; not recommended for synthetic control
"placebo"	Algorithm 4	the only option with a single treated unit

tau.se(method="bootstrap", replications=200, random_state=0)
tau.vcov(method="jackknife")            # 1x1 matrix, like R's vcov
tau.ci(level=0.95, method="placebo")

With one treated unit the bootstrap and jackknife are undefined and return nan — same as R. Pass random_state for reproducible resampling.

Covariates

Pass a time-varying N x T x C array. Weights and coefficients are solved jointly, as in Arkhangelsky et al.'s "optimized" adjustment:

panel = panel_matrices(df, unit="country", time="year",
                       outcome="log_gdp", treatment="dem",
                       covariates=["educ"])
tau = synthdid_estimate(panel.Y, panel.N0, panel.T0, X=panel.X)
tau.weights.beta        # the covariate coefficients

Staggered adoption

Units that start treatment at different times — the case the R package rejects. Cohorts are estimated separately and combined with weights proportional to treated unit-periods, following the Stata sdid package:

from synthdid import staggered_synthdid_estimate

est = staggered_synthdid_estimate(df, unit="state", time="year",
                                  outcome="y", treatment="d")
print(est.att)                                  # aggregate ATT
print(est.by_cohort)                            # one row per adoption date
print(est.se(method="jackknife"))
est.estimates[2005].plot()                      # drill into one cohort

control_pool="never_treated" (default) uses only never-treated units, matching Stata. control_pool="not_yet_treated" also admits units that adopt later, truncating each cohort's post-period at the next adoption date so those controls stay clean.

With a single adoption date this reduces exactly to synthdid_estimate.

Plots

tau.plot()                      # trajectories + parallelogram + effect arrow + lambda ribbon
tau.units_plot()                # each control's own diff-in-diff, sized by its weight
tau.placebo_plot()              # the estimate beside a pre-treatment placebo
tau.rmse_plot()                 # solver convergence diagnostic

synthdid_plot({"DiD": did, "SC": sc, "SDID": sdid})                 # one panel each
synthdid_plot({"DiD": did, "SC": sc, "SDID": sdid}, facet=["a"]*3)  # overlaid

Every plotting function returns (fig, ax), so styling is ordinary matplotlib. examples/quickstart.py reproduces Figure 1 of the paper.

API

Estimation	synthdid_estimate · sc_estimate · did_estimate · staggered_synthdid_estimate
Inference	vcov · synthdid_se · bootstrap_se · jackknife_se · placebo_se
Diagnostics	summary · synthdid_controls · synthdid_placebo · synthdid_effect_curve
Plots	synthdid_plot · synthdid_units_plot · synthdid_placebo_plot · synthdid_rmse_plot
Data	panel_matrices · PanelData · random_low_rank · load_california_prop99 · load_cps · load_penn
Solver	sc_weight_fw · sc_weight_fw_covariates · fw_step · sparsify_function · contract3

Notes for people coming from R

• synthdid_estimate(Y, N0, T0) returns a float subclass, not a scalar with attributes. attr(est, "weights") becomes est.weights; attr(est, "setup") becomes est.setup.
• weights$lambda is weights.lambda_ (lambda is a Python keyword). weights["lambda"] also works, as do the aliases weights.time and weights.unit.
• vcov() returns a 1×1 array so it stays a drop-in match; .se() gives the scalar directly.
• print(tau.hat) in R runs a jackknife. Here repr stays cheap and computes no standard error; use tau.format() for the R-style one-liner or tau.summary() for the full report.
• Column selectors in panel_matrices are 1-based integers or names, as in R.
• Resampling takes an explicit random_state rather than reading a global seed.

Citing

If you use this package, cite the method:

Arkhangelsky, D., Athey, S., Hirshberg, D. A., Imbens, G. W., & Wager, S. (2021). Synthetic Difference-in-Differences. American Economic Review, 111(12), 4088–4118.

License

BSD 3-Clause. This is a derivative work of the R package synthdid (© 2019 Stanford University), which is dual-licensed GPL (≥2) | BSD 3-Clause; this port takes the BSD option. See NOTICE for full attribution, including the Stata sdid package whose staggered-adoption design this follows, and the sources of the bundled datasets.