Dealing with limited overlap in estimation of average treatment effects

Abstract

Moving the Goalposts: Addressing Limited Overlap in Estimation of Average Treatment Effects by Changing the Estimand *Estimation of average treatment effects under unconfoundedness or exogenous treatment assignment is often hampered by lack of overlap in the covariate distributions. This lack of overlap can lead to imprecise estimates and can make commonly used estimators sensitive to the choice of specification. In such cases researchers have often used informal methods for trimming the sample. In this paper we develop a systematic approach to addressing such lack of overlap. We characterize optimal subsamples for which the average treatment effect can be estimated most precisely, as well as optimally weighted average treatment effects. Under some conditions the optimal selection rules depend solely on the propensity score. For a wide range of distributions a good approximation to the optimal rule is provided by the simple selection rule to drop all units with estimated propensity scores outside the range [0.1, 0.9].

Causal Inference without Balance Checking: Coarsened Exact Matching

“…This procedure deletes treated units without good matches and so is a version of the third option of changing the estimand. This choice is reasonable so long as one is transparent about the choice and the consequences in terms of the new set of treated units over which the causal effect is defined (as, e.g., Crump et al 2009). The same change in the quantity of interest is common in other methods for observational data, such as local average treatment effects and regression discontinuity designs (Imbens and Angrist 1994).…”

Do spatially targeted redevelopment programs spillover?

“…(2) to create a predicted value, or propensity score, and define our treatment and control areas based on those values. This approach follows the use of the propensity score by Crump et al (2009) as a way to trim samples and estimate average treatment effects. We are searching for the sample that is most similar to the actual EZ/EC areas to check for spillover effects, so we define it by the propensity scores that are closest to the actual EZ/EC.…”

A simple and successful shrinkage method for weighting estimators of treatment effects

“…In other words, each unit in a defined population has a positive probability of being treated and of not being treated. Although this type of overlap assumption is standard in the literature (see, for example, Rosenbaum and Rubin, 1983;Heckman et al, 1997;Hahn, 1998;Wooldridge, 2002;Imbens, 2004), there is a stronger version of the overlap assumption called "strict 4 overlap" (see Robins et al, 1994;Abadie and Imbens, 2006;Crump et al, 2009). …”

“…In the second trimming rule, suggested by Crump et al (2009), all units with an estimated propensity score outside the interval [0.1; 0.9] are discarded.…”