SyntheticDifferenceInDifferences

class causalpy.experiments.synthetic_difference_in_differences.SyntheticDifferenceInDifferences

Bayesian Synthetic Difference-in-Differences experiment.

Combines the synthetic control method’s unit weighting with difference-in-differences time weighting. The treatment effect (tau) is computed analytically from the posterior weight distributions via the double-difference formula, rather than being estimated inside the MCMC model (cut-posterior formulation).

Parameters:

• data (DataFrame) – A dataframe in wide format (columns = units, rows = time periods).

• treatment_time (int | float | Timestamp) – The time when treatment occurred, should be in reference to the data index.

• control_units (list[str]) – A list of control unit column names.

• treated_units (list[str]) – A list of treated unit column names.

• model (PyMCModel | RegressorMixin | None) – A SyntheticDifferenceInDifferencesWeightFitter instance. Defaults to SyntheticDifferenceInDifferencesWeightFitter.

• **kwargs (dict) – Additional keyword arguments (currently unused).

Examples

>>> import causalpy as cp
>>> df = cp.load_data("sc")
>>> treatment_time = 70
>>> result = cp.SyntheticDifferenceInDifferences(
...     df,
...     treatment_time,
...     control_units=["a", "b", "c", "d", "e", "f", "g"],
...     treated_units=["actual"],
...     model=cp.pymc_models.SyntheticDifferenceInDifferencesWeightFitter(
...         sample_kwargs={
...             "tune": 20,
...             "draws": 20,
...             "chains": 2,
...             "cores": 2,
...             "progressbar": False,
...         }
...     ),
... )

Notes

This implements Bayesian SDiD method. The model fits two weight modules via MCMC:

• Unit weights (omega): balance control units against treated units in the pre-treatment period, similar to synthetic control.

• Time weights (lambda): balance pre-treatment periods against post-treatment periods for control units.

The treatment effect is then computed analytically via the double-difference:

\[\tau = \bar{\Delta}_{\text{post}} - \boldsymbol{\lambda}^\top \boldsymbol{\Delta}_{\text{pre}}\]

where \(\Delta_t = y_{\text{tr},t} - (\omega_0 + \boldsymbol{\omega}^\top \mathbf{Y}_{\text{co},t})\) is the gap between the observed treated outcome and the synthetic control at time t.

References

[1]

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

Methods

SyntheticDifferenceInDifferences.algorithm()	Run the SDiD algorithm: fit weight modules, compute tau analytically.
SyntheticDifferenceInDifferences.effect_summary(*)	Generate a decision-ready summary of causal effects for SDiD.
SyntheticDifferenceInDifferences.fit(*args, ...)	Fit the underlying model.
SyntheticDifferenceInDifferences.generate_report(*)	Generate a self-contained HTML report for this experiment.
SyntheticDifferenceInDifferences.get_plot_data(...)	Recover the data of an experiment along with the prediction and causal impact information.
SyntheticDifferenceInDifferences.get_plot_data_bayesian(...)	Return plot data for Bayesian models.
SyntheticDifferenceInDifferences.get_plot_data_ols(...)	Return plot data for OLS models.
SyntheticDifferenceInDifferences.input_validation(...)	Validate the input data for correctness.
SyntheticDifferenceInDifferences.plot(*[, ...])	Plot SDiD results: counterfactual, period impact, and cumulative impact.
SyntheticDifferenceInDifferences.print_coefficients([...])	Ask the model to print its coefficients.
SyntheticDifferenceInDifferences.set_maketables_options(*)	Set optional maketables rendering options for this experiment.
SyntheticDifferenceInDifferences.summary([...])	Print summary of main results.

Attributes

datapost	Data from on or after the treatment time (inclusive).
datapre	Data from before the treatment time (exclusive).
expt_type
idata	Return the InferenceData object of the model.
post_design	Post-treatment design dataset with control and treated variables.
post_impact	Post-treatment impact (observed minus counterfactual).
post_impact_cumulative	Cumulative post-treatment impact.
post_pred	Post-treatment counterfactual predictions.
pre_design	Pre-treatment design dataset with control and treated variables.
pre_impact	Pre-treatment impact (observed minus counterfactual).
pre_pred	Pre-treatment counterfactual predictions.
supports_bayes
supports_ols
tau_posterior	Posterior samples of the ATT.
labels
data

__init__(data, treatment_time, control_units, treated_units, model=None, **kwargs)

Parameters:

• data (DataFrame)

• treatment_time (int | float | Timestamp)

• control_units (list[str])

• treated_units (list[str])

• model (PyMCModel | RegressorMixin | None)

• kwargs (dict)

Return type:

None

classmethod __new__(*args, **kwargs)