PW 1200 Data-driven incidence difference-in-differences estimators for causal inference with aggregate counts and rates

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Abstract

The difference-in-differences (DD) method is a popular approach to dealing with unobserved confounding in controlled before-after quasi-experiments. In this paper, I consider a framework for control selection, estimation and inference in such analyses, focusing specifically on aggregate rate data. The main identifying assumption of the DD estimator is that the treatment and control group follow common trends in absence of treatment. To deal with this, the proposed method uses a nearest-neighbor algorithm to identify controls that share a common trend parameter with the treated unit(s) using data from the pre-period. Usually, a linear regression model is then fitted to obtain the DD estimate, which may result in biased inferences in aggregate rate data. Assuming a Poisson distribution on the underlying counts, I consider a new set of DD estimators for aggregate rates with small sample cluster-robust inference using a simple correction method based on the intra-cluster correlation coefficient. In addition to this, I propose a non-parametric test with corresponding confidence intervals based on subsampling and placebo studies. Monte Carlo simulations indicate that the matching method reduces bias if diverging trends are present. They also suggest that the confidence intervals have nominal coverage rates under certain conditions, and that the placebo-based strategy allows for robust inference when these conditions are violated. I illustrate the methods using a case study involving a community-based residential fires intervention. Strengths, limitations and potential extensions are discussed.

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