Difference-in-Differences Estimators of Intertemporal Treatment Effects (2007.04267v13)

Abstract: We study treatment-effect estimation using panel data. The treatment may be non-binary, non-absorbing, and the outcome may be affected by treatment lags. We make a parallel-trends assumption, and propose event-study estimators of the effect of being exposed to a weakly higher treatment dose for $\ell$ periods. We also propose normalized estimators, that estimate a weighted average of the effects of the current treatment and its lags. We also analyze commonly-used two-way-fixed-effects regressions. Unlike our estimators, they can be biased in the presence of heterogeneous treatment effects. A local-projection version of those regressions is biased even with homogeneous effects.

• The paper’s main contribution is the development of event-study and normalized difference-in-differences estimators to capture dynamic treatment effects.
• It employs robust panel data techniques under parallel trends to overcome biases present in traditional two-way fixed effects regressions.
• The approach enhances policy evaluation and long-term forecasting in economic, public health, and social program contexts.

Analysis of Difference-in-Differences Estimators for Intertemporal Treatment Effects

This paper addresses the estimation of intertemporal treatment effects using panel data, where the treatment is not restricted to being binary or non-absorbing, and allows the outcome to be influenced by treatment lags. The authors propose a robust methodological framework built on the parallel trends assumption, which offers flexibility and improved accuracy over the conventional two-way fixed effects (TWFE) regressions, particularly under heterogeneous treatment effects scenarios.

Methodological Innovations

The core contribution lies in the development of novel event-paper and normalized difference-in-differences (DID) estimators. These estimators target the effect of incrementally higher treatment doses over a defined period while accounting for potential biases in the presence of varying treatment effects.

1. Event-Study Estimators: The proposed estimators focus on evaluating the impact of exposure to increased treatment doses over ℓ periods. They make direct comparisons between groups whose treatment levels have changed and those with unchanged treatment levels during the assessed period. This feature is crucial in settings where past treatment decisions influence future outcomes.
2. Normalized Estimators: They offer a comprehensive metric by normalizing treatment effects against the cumulative treatment variations over time. This approach enables estimating weighted average effects by equally considering both current and preceding treatment influences, which is significant in understanding overall treatment impact.
3. Addressing TWFE Limitations: Unlike TWFE regressions that can incur biases when treatment effects are heterogeneous across time or groups, the proposed DID estimators maintain robustness against such variations. Moreover, they manage biases even within potentially homogeneous effect landscapes by incorporating local projections.

Empirical Implications

The paper's implications extend beyond theoretical refinements, offering practical applications where treatments are inherently dynamic and may undergo multiple changes:

• Effect Evaluation: Accurate identification of treatment effects is enabled in setups where treatment levels are neither binary nor constant, seen often within economic policies, public health interventions, and social programs.
• Policy Design and Analysis: The developed estimators provide more precise tools for policy evaluations by assessing the temporal dimension of treatments. This insight is crucial for long-term impact forecasting, allowing for better-informed policy adjustments and resource allocations.

Case Study: Banking Deregulations

The authors apply their methodology to analyze the US state banking deregulations of the 1990s and their effect on credit supply growth. Their results indicate significantly persistent effects of deregulations contrary to previously reported transient effects. This suggests that prior methodologies, like local-projection regressions, substantially underestimated the sustained impact due to mis-specification and weighting issues.

Conclusions and Future Directions

This paper introduces a robust framework for analyzing treatment dynamics in panel data, catering to the complexities introduced by non-binary and non-absorbing treatments. Future work could extend these methods to continuous treatment measures, further tuning them to capture nuanced treatment interaction effects or apply cross-sectional comparisons to complement panel-based insights. Moreover, expanding the inference frameworks to account for potential covariate interactions and more nuanced assumptions about unobserved heterogeneity could present clearer pathways for validating the methodology across diverse domains in economics and social sciences.