⚡ TL;DR

The post-2020 DiD revolution produced several heterogeneity-robust estimators — Sun-Abraham, Callaway-Sant'Anna, Borusyak-Jaravel-Spiess, de Chaisemartin-D'Haultfœuille, Wooldridge ETWFE — each with different efficiency and identification properties. This paper shows how to combine the strengths of multiple estimators into a single "harvested" estimator with improved efficiency relative to any individual estimator.

🧩 Setup & motivation

Each of the modern DiD estimators uses a slightly different identification strategy: BJS imputes counterfactuals from pre-period unit fits; CS uses group-time ATT building blocks with flexible control-group choice; SA reweights TWFE coefficients to remove cohort contamination. They all converge in large samples under parallel trends, but each is more efficient in particular settings.

Borusyak-Hull-Roth ask: can we combine them? The answer is yes — under linear-combination conditions, the optimal weighted combination of multiple estimators achieves lower asymptotic variance than any single estimator. The paper provides theory and practical implementation.

📐 Main results

The harvesting framework

Let \(\hat\tau_1, \hat\tau_2, \dots, \hat\tau_K\) be \(K\) alternative DiD estimators of the same target parameter \(\tau\), with covariance matrix \(\Omega\) estimated jointly. The optimal linear combination is \(\hat\tau_{\text{combine}} = \sum_k w_k \hat\tau_k\) where the weights solve the minimum-variance problem. Closed-form: \(w^* = (\mathbf{1}'\Omega^{-1}\mathbf{1})^{-1} \Omega^{-1} \mathbf{1}\).

When does harvesting help?

Harvesting helps when individual estimators have imperfectly correlated sampling errors — i.e., they use different pieces of information from the same data. For well-known DiD estimators, the correlations are typically 0.7–0.9 but not 1.0, so combinations achieve 5–20% variance reduction. Bigger gains when the estimators use very different identifying variation (e.g., never-treated vs not-yet-treated controls).

Inference

Joint covariance is estimated via bootstrap or asymptotic theory. The paper provides a practitioner-friendly procedure that practitioners can run on top of existing estimator implementations.

🛠️ Implications for practice

• For headline efficiency, report the harvested estimate alongside the individual estimates.
• If the harvested estimate diverges substantially from individual estimates, that's a diagnostic for non-shared identifying variation.
• R implementation forthcoming; the paper provides pseudo-code.

🧭 Where this sits in the broader DiD literature

Builds directly on Borusyak-Jaravel-Spiess (2024, REStud), Callaway-Sant'Anna (2021, J Econometrics), and Sun-Abraham (2021, J Econometrics). Extends the BJS efficiency-bound result to combinations of estimators. Companion to Chen-Sant'Anna-Xie (2025) on the semiparametric efficient influence function — both papers chase the same efficiency frontier from different directions.

📥 Read the paper

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