LWDiD: use covariance-aware inference for staggered overall ATT

[shawcharles]

Summary

For staggered LWDiD paths outside the composite-regression gate, _aggregate_cohort_effects() computes the overall standard error as a weighted sum of marginal cohort variances under an independence assumption. Cohorts can share control units, so their estimates need not be independent.

This is distinct from #733. That issue ensures aggregate(\"overall\") no longer replaces the inference produced by fit(). This issue concerns the statistical validity and provenance of the inference that fit() itself produces on the non-composite paths.

Evidence

On a fixed, staggered, never-treated synthetic panel with rolling=\"demean\", estimator=\"ra\", and vce=\"hc1\":

analytical delta SE:       0.0604633
unit-cluster bootstrap SE: 0.0740364
ratio:                     1.22448

The design uses three treated cohorts that share never-treated controls. A unit-cluster bootstrap is materially wider, consistent with positive cross-cohort covariance omitted by the current delta calculation.

Relevant implementation:

diff-diff/diff_diff/lwdid.py

Lines 1619 to 1625 in c2694ff

	# SE via delta method (assuming independence across cohorts)
	# Var(weighted_avg) = sum(w_g^2 * se_g^2)
	valid_ses = np.isfinite(ses) & (ses > 0)
	if valid_ses.all():
	var_att = float(np.sum(weights**2 * ses**2))
	se = float(np.sqrt(var_att))
	else:

Proposed direction

• Retain a joint covariance or influence-function representation for cohort effects and use it for overall aggregation.
• Surface an explicit inference provenance field, for example composite_joint or cohort_independence_delta, in result serialisation and summaries.
• Add a deterministic unit-cluster-bootstrap concordance test for the non-composite staggered path. Until covariance-aware inference is implemented, the test is expected to fail and documents the required target.

Acceptance criteria

• Overall staggered inference accounts for covariance among cohort effects that share controls.
• Result metadata identifies the inference basis.
• The bootstrap-concordance test passes without an xfail marker.
• The solution integrates with the shared result-object/event-study contract tracked in LWDiD event-study output needs the shared results contract #732.

[shawcharles]

A deterministic, slow, strict-xfail unit-cluster-bootstrap concordance test is now in gorgeousfish#1. It isolates the non-composite never_treated/HC1 path and becomes an ordinary passing test once the overall ATT uses covariance-aware inference.