Repeated cross-sections (`panel=False`)¶

Classic Callaway–Sant'Anna requires a balanced panel: every unit observed in every period. Many causal-inference datasets are repeated cross-sections (RCS) — pooled surveys (CPS, ACS), rolling polls, independent samples per period — where no within-unit first difference is available. StatsPAI's RCS path solves this with the unconditional 2×2 cell-mean DID.

Estimator¶

For each (g, t, base) triple with never-treated control c = 0:

\[ \widehat{\text{ATT}}(g, t) = (\bar{Y}_{g, t} - \bar{Y}_{g, b}) - (\bar{Y}_{c, t} - \bar{Y}_{c, b}) \]

and observation-level influence functions

\[ \psi_i = \frac{\mathbf{1}\{G_i=g,\,T_i=t\}(Y_i - \bar{Y}_{g,t})}{p_{g,t}} - \frac{\mathbf{1}\{G_i=g,\,T_i=b\}(Y_i - \bar{Y}_{g,b})}{p_{g,b}} - \frac{\mathbf{1}\{G_i=c,\,T_i=t\}(Y_i - \bar{Y}_{c,t})}{p_{c,t}} + \frac{\mathbf{1}\{G_i=c,\,T_i=b\}(Y_i - \bar{Y}_{c,b})}{p_{c,b}} \]

where \(p_{\cdot,\cdot}\) is the empirical cell share. The influence functions are stacked into the same inf_matrix contract used by the panel estimator, so aggte, cs_report, ggdid, and honest_did work downstream without modification.

Usage¶

sp.callaway_santanna(
    df, y='y', g='first_treat', t='year', i='obs_id',
    estimator='reg',          # required for panel=False
    panel=False,
)

Covariate adjustment¶

Add x=[...] for regression-adjusted RCS. Y is residualised on X using OLS fit on the never-treated pool (with period fixed effects); the cell-mean DID then runs on the residualised outcome:

sp.callaway_santanna(
    survey_df, y='wage', g='g', t='year', i='obs',
    estimator='reg', panel=False,
    x=['age', 'education', 'female'],
)

Influence functions treat β̂ as known (plug-in IF), which is asymptotically valid at √n. A fully-coupled Sant'Anna–Zhao (2020) IF augmentation is planned.

Scope of the current implementation¶

estimator must be 'reg'
control_group must be 'nevertreated'
IPW / DR for RCS: planned for a future release

All other paths raise NotImplementedError with an actionable message.

Inference and weighting options (parity with R did / csdid)

Since 1.23.0 the repeated-cross-section route takes the same options as the panel route, so a panel = FALSE script from R ports across without dropping anything:

sp.callaway_santanna(
    df, y="y", g="g", t="t", i="i",
    panel=False,
    x="~ lpop + I(lpop**2)",     # R xformla; I(x^2) is rejected, use **
    weights="pop",               # part of the estimand, not a precision knob
    clustervars=["i", "state"],  # requires bstrap=True
    bstrap=True, cband=True, biters=1000, random_state=0,
)

Two rules carry over from the panel path and are enforced, not assumed:

Clustering beyond the unit requires bstrap=True. The analytic per-cell standard errors cannot express within-cluster dependence, so reporting them under clustervars would understate uncertainty.
Under allow_unbalanced_panel=True, weights and cluster labels must be time-invariant within unit. That route folds a unit's influence contributions together, so a within-unit-varying weight would silently reweight that unit's own periods against each other.

For Agents¶

Pre-conditions - data is panel or repeated cross-section with a time column - treat column is binary (0/1) for 2x2, or first-treatment-period (int) for staggered - at least one pre-treatment period (≥ 2 periods for 2x2; ≥ 3 recommended for event study) - for staggered designs: id column identifying units across time

Identifying assumptions - Parallel trends: treated and control groups would have followed the same trajectory absent treatment - No anticipation: outcomes in pre-treatment periods are unaffected by future treatment - SUTVA: no spillovers between units - For staggered / heterogeneous effects: use CS or SA — TWFE can produce negative weights (Goodman-Bacon)

Failure modes → recovery

Symptom	Exception	Remedy	Try next
Pre-trend joint test p < 0.05 (or underpowered at 0.10)	`AssumptionViolation`	Use sp.sensitivity_rr (Rambachan & Roth honest CI) or switch to sp.callaway_santanna.	`sp.sensitivity_rr`
Staggered treatment timing with TWFE method	`AssumptionWarning`	TWFE can give negative weights; use Callaway-Sant'Anna, Sun-Abraham, or BJS imputation.	`sp.callaway_santanna`
Pre-trend test underpowered (Roth 2022)	`AssumptionWarning`	Check sp.pretrends_power — if low, report honest CI via sp.sensitivity_rr.	`sp.sensitivity_rr`
Few clusters at unit level	`AssumptionWarning`	Use wild cluster bootstrap (sp.wild_cluster_bootstrap).	`sp.wild_cluster_bootstrap`

Alternatives (ranked) - sp.callaway_santanna - sp.sun_abraham - sp.did_imputation - sp.sdid - sp.synth

Typical minimum N: 50

Repeated cross-sections (panel=False)¶