Partial Homogeneity in Staggered Difference-in-Differences

In staggered difference-in-differences designs the treatment effect is a vector of cohort-time effects rather than a single number. Estimating each separately is unbiased but imprecise when some are equal, while pooling them all is precise but biased under genuine heterogeneity. This package treats the choice as a partition-selection problem on the cohort-time cells and provides two estimators for it: a Dirichlet process mixture fitted by a collapsed Gibbs sampler, whose posterior marginalises over the unknown partition and reports co-clustering probabilities, and an 'L0'-penalised estimator that returns a single partition and arises as the fixed-variance maximum a posteriori solution of the same model. Also provides tests for whether the cohort-time effects carry recoverable heterogeneity at all, sampler diagnostics including exact enumeration of the partition posterior for small designs, regularisation paths for both estimators, and a calibrated data-generating process. All estimators accept a vector of first-stage cohort-time effects with their joint covariance, so any heterogeneity-robust first-stage estimator may be used. Methods are described in Arora and Wagle (2026) .

phdid

Partial homogeneity in staggered difference-in-differences.

In a staggered DiD design the treatment effect is not a single number but a vector of cohort-time effects (CATTs), one per cohort-time cell. Estimating every one separately is unbiased but inefficient when some are in fact equal; pooling them all into a single TWFE coefficient is efficient but biased whenever the heterogeneity is genuine.

phdid treats the choice between these extremes as a partition-selection problem on the cells, and implements the two estimators of Arora and Wagle (2026) that solve it, along with the specification tests and diagnostics needed to know whether either should be used at all.

Installation

# install.packages("remotes")
remotes::install_github("ronwag2005/phdid")

The idea in sixty seconds

With G treated cohorts and T periods there are K cohort-time cells. The true effect vector exhibits partial homogeneity if there is a partition of those cells into m < K groups within which the effects are equal. Under the true partition, the grouped estimator is both unbiased and strictly more efficient than the flexible one -- in a balanced design, exactly |C_p| times more efficient for every cell in a group of size |C_p|.

The partition is unknown, so the package recovers it two ways:

The two are not rivals: l0_ph() is the fixed-variance MAP of the same Bayesian model, differing only in the partition prior. Use l0_ph() when you want one interpretable grouping to report and bayes_ph() for inference.

Quick start

library(phdid)
library(did)
data(mpdta, package = "did")

# Any heterogeneity-robust first stage will do.
first <- att_gt(yname = "lemp", tname = "year", idname = "countyreal",
                gname = "first.treat", control_group = "notyettreated",
                data = mpdta, bstrap = FALSE)

d <- ph_data(first)   # keeps post-treatment cells + the exact joint covariance

# 1. Is there heterogeneity to recover at all?
homogeneity_test(d)
#> chi-squared = 25.29 on 6 df, p = 0.000302
#> heterogeneity share: 80%
#> Reading: recoverable heterogeneity.

# 2. One partition to report.
l0_ph(d)
#> Groups (m) : 4  (selected by BIC)
#> Mean variance ratio among pooled cells: 0.50

# 3. Inference that accounts for not knowing the partition.
fit <- bayes_ph(d, alpha = 1, iters = 20000, burn = 2000)
aggregate(fit, "overall")
#>     term  estimate  conf.low  conf.high
#>  overall   -0.0239   -0.0476    -0.0004

coclustering(fit)      # which groupings are firm
plot(fit)              # the co-clustering heatmap

Two things the package will keep telling you

The covariance is not diagonal. Cohort-time cells share units and share the unit and time fixed effects, so their estimates are correlated. Using the exact joint covariance is what makes the reported intervals honest: treating the cells as independent understates the posterior variance of aggregates by about 3.5x in the paper's design and can misstate individual co-clustering probabilities by up to 0.39. ph_data() warns when handed a diagonal covariance, and covariance_check() quantifies the difference on your design.

A partition is only worth reporting when the effects are separated enough to be recovered. Below that threshold both estimators return groupings that are quantiles of noise. In the paper's second application the l0 estimator splits 138 event effects into five neat "bands" while a randomization test cannot reject a single common effect. Run homogeneity_test() first; it says so plainly rather than letting the output speak for itself.

What's included

Estimation -- ph_data() (three entry points: a did::att_gt() fit, a micro panel, or any (tau, Sigma) pair), l0_ph(), bayes_ph(), ph_fit(), flex_twfe(), pooled_twfe().

Inference -- aggregate() for overall ATT, event-study, by-cohort and by-calendar estimands computed per posterior draw; coclustering(); point_partition() (Wade-Ghahramani VI and Binder losses); confint().

Specification testing -- homogeneity_test(), bundling a model-implied common-effect chi^2 test, an excess-dispersion heterogeneity share, and the placebo gauge and within-cell randomization test.

Diagnostics -- enumerate_partitions() for the exact posterior on small designs, ph_rhat() for multi-chain convergence, alpha_sensitivity() for the prior path, covariance_check() for exact vs. diagonal.

Simulation -- ph_design(), ph_truth(), ph_sample(), sim_study(), reproducing the paper's Monte Carlo tables.

Authorship and citation

The methods implemented here are joint work by Parush Arora and Rohan Wagle (Department of Economics, Ashoka University). The simulation and application code that this package generalizes was written by Parush Arora; the package itself is written and maintained by Rohan Wagle. Both are copyright holders under the MIT license.

If you use phdid, please cite both the Ashoka University discussion paper and the SSRN working paper:

Arora, Parush and Rohan Wagle (2026). "A Bayesian Approach to Partial Homogeneity in Staggered Difference-in-Difference." Ashoka University Economics Discussion Paper 166. Link

Arora, Parush and Rohan Wagle (2026). "A Bayesian Approach to Partial Homogeneity in Staggered Difference-in-Difference" (March 01, 2026). SSRN Working Paper 7207083. SSRN | doi:10.2139/ssrn.7207083

citation("phdid")

References

Arora, P. and Wagle, R. (2026). A Bayesian Approach to Partial Homogeneity in Staggered Difference-in-Difference. Ashoka University Economics Discussion Paper 166. https://www.ashoka.edu.in/research/a-bayesian-approach-to-partial-homogeneity-in-staggered-difference-in-difference/

Arora, P. and Wagle, R. (2026). A Bayesian Approach to Partial Homogeneity in Staggered Difference-in-Difference (March 01, 2026). SSRN Working Paper 7207083. https://doi.org/10.2139/ssrn.7207083

Callaway, B. and Sant'Anna, P. H. C. (2021). Difference-in-Differences with Multiple Time Periods. Journal of Econometrics 225(2), 200-230.

Neal, R. M. (2000). Markov Chain Sampling Methods for Dirichlet Process Mixture Models. JCGS 9(2), 249-265.

Wade, S. and Ghahramani, Z. (2018). Bayesian Cluster Analysis: Point Estimation and Credible Balls. Bayesian Analysis 13(2), 559-626.

Wooldridge, J. M. (2025). Two-Way Fixed Effects, the Two-Way Mundlak Regression, and Difference-in-Differences Estimators. Empirical Economics 69, 2545-2587.

License

MIT (c) 2026 Rohan Wagle and Parush Arora. See LICENSE.md.