Estimating heterogeneous causal effects in time series settings with staggered adoption: An application to neighborhood policing
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Communities often self select into implementing a regulatory policy, and adopt the policy at different time points. Researchers are interested in (1) evaluating the impact of the policy, and (2) understanding what types of communities are most impacted by the policy, raising questions of heterogeneous treatment effects. We develop novel statistical approaches to study the causal effect of policies implemented at the community level. Using techniques from high-dimensional Bayesian time-series modeling, we estimate treatment effects by predicting counterfactual values of what would have happened in the absence of the policy. We couple the posterior predictive distribution of the treatment effect with flexible modeling to identify how the impact of the policy varies across time and community characteristics. This allows us to identify effect modifying variables and capture nonlinear heterogeneous treatment effects. Importantly, our approach is robust to unmeasured confounding bias. Our methodology is motivated by studying the effect of neighborhood policing on arrest rates in New York City. Using realistic simulations based on the policing data in New York City, we show our approach produces unbiased estimates of treatment effects with valid measures of uncertainty. Lastly, we find that neighborhood policing slightly decreases arrest rates immediately after treatment adoption, but has little to no effect in other time periods or on other outcomes of interest.
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