Treatment Effects: Theory and Implementation
Paper Session
Friday, Jan. 5, 2024 8:00 AM - 10:00 AM (CST)
- Chair: Serena Ng, Columbia University
Event Studies with Continuous Treatment
Abstract
This paper builds on the identification results and estimation tools for continuous DiD designs in Callaway, Goodman-Bacon, and Sant'Anna (2023) to discuss aggregation strategies for event studies with continuous treatments. Estimates from continuous designs are functions of the treatment dosage/intensity variable. Nonparametric plots of these functions show heterogeneity across doses, but not heterogeneity over time. Event-study-type plots of aggregated parameters achieve the opposite. We describe how partially aggregating across treatment doses and event time can lead to readable yet nuanced figures that reflect how causal effects evolve over time, potentially in different parts of the treatment dose distribution.Empirical Bayes Approaches to Parallel Trends
Abstract
Researchers are often concerned about the validity of the parallel trends assumption underlying difference-in-differences analyses. Recent work has proposed partial-identification approaches that bound the worst-case violation of parallel trends using pre-treatment differences in trends (“pre-trends”). Rather than focusing on worst-case bounds, this paper develops Bayes and empirical Bayes approaches to dealing with possible violations of parallel trends. In the Bayesian approach, the econometrician places a prior over the possible violations of parallel trends and then updates the prior using the observed pre-trends. In the empirical Bayes approach, the prior on post-treatment violations of parallel trends is calibrated using the pre-trends.Difference-in-Differences Estimators with Continuous Treatments and No Stayers
Abstract
Many treatments such as prices, taxes or temperatures are continuous in nature. Applied researchers usually rely on two-way fixed effect regressions to estimate treatment effects in such cases. However, such estimators are not robust to heterogeneous treatment effects in general, and rely on linearity of treatment effects. We develop a difference-in-difference strategy for continuous treatments without imposing such restrictions, when the treatment of all units changes between periods. We extend the nonparametric results of de Chaisemartin et al. (2023) to this setup and present a parametric approach that overcomes some limitations of the nonparametric approach.When to Aggregate Data across Time for the Synthetic Control Method
Abstract
The synthetic control method (SCM) is a popular approach for estimating the impact of a treatment on a single unit in panel data settings. The “synthetic control” is a weighted average of control units that balances the treated unit’s pre-treatment outcomes as closely as possible. Two challenges arise with higher frequency data, such as when the outcome is measured every month versus every year: (1) because the problem is higher dimensional, achieving excellent pre-treatment fit is typically more challenging; and (2) even when this is possible, higher-frequency observations raise the possibility of bias due to overfitting to noise. Casting high-frequency data in a linear factor model, we argue that under some conditions, aggregating the outcome into lower-frequency observations can help reduce the bias of SCM, both by achieving better pre-treatment fit in practice and by reducing the risk of overfitting to noise. We illustrate this with a simulation study and an applied example.JEL Classifications
- C1 - Econometric and Statistical Methods and Methodology: General
- C4 - Econometric and Statistical Methods: Special Topics