Precision and Heterogeneity in Staggered Adoption Designs: An Empirical Bayes Approach

• In Event: Innovations in Causal Inference: Quantile Mixtures, Empirical Bayes Aggregation, and Synthetic Controls

Abstract

A staggered adoption design can be partitioned into a collection of sub-experiments, each of which identifies a group-time ATT parameter under common trend and no-anticipation assumptions. Recent work on the staggered adoption design proposes strategies for aggregating disparate group-time ATTs into summary averages that maintain a coherent causal interpretation. However, researchers may also want to average group-time ATTs as a way to improve statistical precision. A challenge is that estimated group-time ATTs may differ from one another because of both true treatment effect heterogeneity, and statistical uncertainty due to sampling error. The true treatment effect heterogeneity itself may occur across sub-experiments if the same policy has a different effect on some units than others, or over event time if the policy has a different effect in some time periods or event time periods than others.

 

This paper proposes Empirical Bayes strategies that are intended to improve precision by shrinking group-time ATTs towards a pooled average, while also allowing the construction of a summary aggregate causal effect  parameter that can be defined ex ante on conceptual grounds. We propose two versions of the same basic idea: the first version uses shrinkage across sub-experiments for a fixed event time, and the second version uses shrinkage over event time for each sub-experiment. Monte carlo simulations are used to assess the mean square error of the empirical bayes aggregators compared with conventional aggregation schemes. We also apply the method to real world cases with different data structures.

Author

• Coady Wing, Indiana University
  Presenting Author