The role of parallel trends in event study settings: An application to environmental economics

TL;DR

This paper examines how different parallel trends assumptions impact the identification and estimation of causal effects in staggered Difference-in-Differences designs, proposing new estimators and illustrating their practical relevance in environmental policy analysis.

Contribution

It clarifies the role of parallel trends assumptions in event-study DID, introduces estimators reflecting trade-offs between robustness and efficiency, and applies these to environmental policy data.

Findings

Identifies a robustness vs. efficiency trade-off in DID assumptions.

Proposes new DID estimators with known large sample properties.

Demonstrates the practical importance in environmental regulation analysis.

Abstract

Difference-in-Differences (DID) research designs usually rely on variation of treatment timing such that, after making an appropriate parallel trends assumption, one can identify, estimate, and make inference about causal effects. In practice, however, different DID procedures rely on different parallel trends assumptions (PTA), and recover different causal parameters. In this paper, we focus on staggered DID (also referred as event-studies) and discuss the role played by the PTA in terms of identification and estimation of causal parameters. We document a ``robustness'' vs. ``efficiency'' trade-off in terms of the strength of the underlying PTA, and argue that practitioners should be explicit about these trade-offs whenever using DID procedures. We propose new DID estimators that reflect these trade-offs and derived their large sample properties. We illustrate the practical relevance of these results by assessing whether the transition from federal to state management of the Clean Water Act affects compliance rates.