Improved Inference for CSDID Using the Cluster Jackknife

2026-02-12

AI Summary

This study addresses the issue of over-rejection in traditional difference-in-differences (DiD) and Callaway–Sant’Anna DiD (CSDID) estimators under settings with few clusters, sparse treated clusters, or serial correlation, which can severely distort inference. To mitigate this problem, the paper introduces the cluster jackknife method into the CSDID framework—the first such application—to correct bias arising from cluster structure and substantially improve inference reliability in small samples. By combining CSDID point estimates with jackknife-based standard errors, the proposed approach markedly enhances the accuracy of hypothesis testing in scenarios with a limited number of clusters. Extensive simulations demonstrate its superior finite-sample performance, and the authors provide publicly available software implementations in both Stata (csdidjack) and R (didjack) to facilitate adoption.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Calibration & Uncertainty Quantification
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

Obtaining reliable inferences with traditional difference-in-differences (DiD) methods can be difficult. Problems can arise when both outcomes and errors are serially correlated, when there are few clusters or few treated clusters, when cluster sizes vary greatly, and in various other cases. In recent years, recognition of the ``staggered adoption''problem has shifted the focus away from inference towards consistent estimation of treatment effects. One of the most popular new estimators is the CSDID procedure of Callaway and Sant'Anna (2021). We find that the issues of over-rejection with few clusters and/or few treated clusters are at least as severe for CSDID as for traditional DiD methods. We also propose using a cluster jackknife for inference with CSDID, which simulations suggest greatly improves inference. We provide software packages in Stata csdidjack and R didjack to calculate cluster-jackknife standard errors easily.

Problem

• difference-in-differences
• CSDID
• cluster inference
• staggered adoption
• over-rejection

Innovation

• CSDID
• cluster jackknife
• staggered adoption
• difference-in-differences
• inference