Skip to content

statspai.bridge

bridge

Bridging theorems for causal inference (StatsPAI v0.10).

Each "bridging theorem" pairs two seemingly different estimators on the same target parameter and proves that — under appropriate conditions — they identify the same quantity. Reporting both estimates side-by-side gives doubly-robust identification: if either path's assumption holds, the estimate is consistent.

Six bridges shipped (per arXiv 2503.11375 / 2510.26723 / 2310.18563 v6 / 2404.09117 / 2411.02771 / 2202.07234, 2022-2025):

  • did_sc — DiD ≡ Synthetic Control (Sun-Xie-Zhang 2025)
  • ewm_cate — EWM ≡ CATE → policy (Kato 2025)
  • cb_ipw — Covariate Balancing ≡ IPW × DR (Słoczyński-Uysal-Wooldridge 2023)
  • kink_rdd — Kink-Bunching ≡ RDD (Lu-Wang-Xie 2025)
  • dr_calib — Doubly Robust via Calibration (van der Laan-Luedtke-Carone 2024)
  • surrogate_pci — Long-term Surrogate ≡ PCI (Imbens-Kallus-Mao-Wang 2025, JRSS-B)

The unified entry point is sp.bridge(data, kind=..., **kwargs), returning a :class:BridgeResult reporting the two path estimates, their agreement test, and the recommended doubly-robust point estimate.

BridgeResult dataclass

Result of a bridging-theorem comparison.

Attributes:

Name Type Description
kind str

Which bridge was applied (did_sc / ewm_cate / ...).
path_a_name, path_b_name str

Human-readable names of the two estimation paths.
estimate_a, estimate_b float

Point estimates from each path.
se_a, se_b float

Standard errors from each path.
diff, diff_se, diff_p float

Difference, its SE (assuming independence; conservative when the two paths share data), and the two-sided p-value for H0: paths agree.
estimate_dr float

Doubly-robust combined estimate (precision-weighted average when agreement_p > 0.05; falls back to estimate_a with a warning otherwise).
se_dr float

SE of estimate_dr.
n_obs int
detail dict

Extra path-specific metadata.
reference str

agreement property 

agreement: bool

True iff paths fail to reject equality at 5%.

bridge 

bridge(kind: str, **kwargs) -> BridgeResult

Run a bridging-theorem comparison.

Parameters:

Name Type Description Default
kind {'did_sc', 'ewm_cate', 'cb_ipw', 'kink_rdd', 
'dr_calib', 'surrogate_pci'}

Which bridge to run.

 required
**kwargs

Bridge-specific keyword arguments. See the per-bridge implementations in :mod:statspai.bridge for details.

 {}

Returns:

Type Description
BridgeResult

Two path estimates + agreement test + DR combined estimate.

Examples:

DID ≡ Synthetic Control (Shi-Athey 2025) on a panel where one unit gets treated at time T:

>>> result = sp.bridge(
...     kind="did_sc", data=df,
...     y='gdp', unit='state', time='year',
...     treated_unit='CA', treatment_time=1989,
... )
>>> print(result.summary())