Parush Arora | Searcharxiv

arXiv2026

Trading Scope for Credibility in Difference-in-Differences

When parallel trends fails for some treated cohorts but not others, the average treatment effect on the treated (ATT), an average over all of them, is exactly the target that becomes hard to recover. We propose changing the estimand rather than defending it. The credible-subpopulation local ATT (LATT) is the effect for the subpopulation of cohorts whose parallel trends is credible, and it is point-identified under parallel trends for the selected cohorts alone, a weaker requirement that can hold when the ATT's fails. It is estimated by reweighting standard group-time effects toward those cohorts, and paired with honest sensitivity bounds on the residual violation that a pre-trend screen cannot rule out. The method's advantage grows with how informative pre-trends are about post-treatment violations, as simulations confirm. In an application, a significantly positive pooled estimate of the shale boom's effect on local house prices proves to rest on cohorts already trending before onset, and the credible subpopulation reveals no effect.

econ.EM↗

arXiv2026

Partial Homogeneity in Staggered Difference-in-Differences

In staggered difference-in-differences (DiD) designs, units enter treatment at different calendar times, so the treatment effect is not a single number but a set of Cohort-Average Treatment effects on the Treated (CATTs), one per cohort-time cell. Estimating every CATT as its own parameter, as the standard fully flexible estimator does, is unbiased but inefficient when some of these effects are in fact equal, whereas pooling them all into a single two-way fixed effects (TWFE) coefficient is efficient but, whenever the heterogeneity is genuine, biased for the individual effects. We frame the choice between these extremes as a partition-selection problem on the cohort-time cells and address it with a Dirichlet Process (DP) mixture prior on the CATTs. The model favors parsimonious groupings without fixing their number, and a collapsed Gibbs sampler delivers point estimates, credible intervals that marginalize the unknown partition, and co-clustering probabilities for every pair of CATTs. With the error variance held fixed and a pairwise penalty placed on the partition, a maximum a posteriori (MAP) partition reduces to an $\ell_0$-penalized regression, connecting the Bayesian formulation to the homogeneity-pursuit literature. In a calibrated simulation, the model cuts the sampling variance of the cohort-time effects by 26--52\% relative to the fully flexible estimator, without the pooled estimator's bias, provided the distinct effects are separated enough to be recovered, and the posterior delivers near-nominal confidence-interval coverage by averaging over the unknown partition. In two applications the method recovers a precision-improving partial-homogeneity structure in one, where the cohort-time effects are genuinely heterogeneous, and reports that full pooling is adequate in the other, where they are not.

econ.EM↗