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Treatment Effects: Theory and Implementation
Friday, Jan. 5, 2024
8:00 AM - 10:00 AM (CST)
American Economic Association
Recentered IV Identifies Convex Averages of Heterogeneous Effects
We study the causal interpretation of instrumental variable estimands in settings where the instrument combines a set of exogenous shocks with predetermined exposure variables by a known formula. Provided the expected instrument has been adjusted for (as in the recentering procedure of Borusyak and Hull, 2023), a convex weighted average of heterogeneous effects is identified under an appropriate monotonicity condition. In contrast to classic results (e.g. Imbens and Angrist, 1994), this result holds even when the first stage relationship is non-causal: for example, because shock exposure is misspecified. In some cases, the weights can be computed and – under an appropriate overlap condition – a feasible reweighting procedure yields the average causal effect.
Event Studies with Continuous Treatment
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
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
Panel Bartik regressions have been shown to be non-robust to heterogeneous treatment effects. Alternative correlated-random-coefficient estimators have been proposed, but they still rely on a linear treatment effect assumption, and assume that all locations experience the same evolution of their treatment effect. We propose an instrumental-variable difference-in-differences estimator for panel Bartik designs that does not rely on those assumptions. Our estimator accommodates the continuous nature of the Bartik instrument, and it can be used even when there are no stayers, namely locations that do not experience a Bartik shock. This estimator converges at a non-parametric rate.
When to Aggregate Data across Time for the Synthetic Control Method
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.
C1 - Econometric and Statistical Methods and Methodology: General
C4 - Econometric and Statistical Methods: Special Topics