Moving the Goalposts: Addressing Limited Overlap in the Estimation of Average Treatment Effects by Changing the Estimand

Abstract

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].

Dealing with limited overlap in estimation of average treatment effects

“…The following choice for ψ(y, w, x) is shown in the supplementary materials (Crump, Hotz, Imbens and Mitnik, 2006b) to satisfy the condition:…”

Does Gerrymandering Cause Polarization?

“…8 7 Hereafter we abbreviate DW-NOMINATE to NOMINATE. 8 Crump, Hotz, Imbens and Mitnick (2006) argue for the appropriateness of trimming the observations where the propensity of treatment is less than α or greater than 1 α − . They provide an algorithm for estimating the optimalα .…”

The negative impacts of starting middle school in sixth grade

“…First, we ran a logit regression analysis on the 342 schools that included sixth grade (both middle and elementary schools) in our district sample to predict the likelihood that the school was a middle school on the basis of its locale, per-pupil expenditure levels, and student socioeconomic characteristics. 6 We then excluded schools where the imputed probability was very high (higher than for any of the elementary schools in the sample) or low (Crump, Hotz, Imbens, & Mitnik, 2006;Dehejia and Wahba, 1999). In our subsequent analysis, we experimented with two standards for this sample-trimming procedure.…”