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

By Richard K. Crump, V. Hotz, Guido W. Imbens, Oscar A. Mitnik. 2006

971 citations recorded by the source corpus.

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].

Subfields: Statistics and Probability

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Citations in the corpus

Estimation Considerations in Contextual Bandits (2017, background): “Consequently, since eventually assignment probabilities should approach zero or one for all arms and contexts clipping the propensity scores [25, 39] with some threshold γ, e.”
Approximate residual balancing: debiased inference of average treatment effects in high dimensions (2016, background): “…extrapolation beyond the support of the features and thus makes estimation inherently sensitive to functional form assumptions; and, for this reason, overlap has become a common assumption in the literature on causal inference from observational studies (Crump et al., 2009; Imbens and Rubin, 2015).”
Automated versus Do-It-Yourself Methods for Causal Inference: Lessons Learned from a Data Analysis Competition (2017, background): “…group, many researchers would opt to reduce or reweight the inferential group (i.e., the set of treated observations about which we will make inferences) to those for whom overlap is satisfied (Hirano and Imbens, 2001; Hirano, Imbens and Ridder, 2003; Crump et al., 2009; Hill and Su, 2013).”
Assessing the Long-Term Effects of Conditional Cash Transfers on Human Capital: Evidence from Colombia (2011, background): “9 to make estimates more precise and less sensitive to changes in specification (Crump et al. 2009).”
Overlap in observational studies with high-dimensional covariates (2017, background): “All regular semiparametric estimators are subject to the following asymptotic variance lower bound, known as the semiparametric efficiency bound (Hahn, 1998; Crump et al., 2009),”
Start-Up Subsidies for the Unemployed: Long-Term Evidence and Effect Heterogeneity (2011, background): “Crump et al. (2009) suggest to base the common support decision rather on an objective measure.”
Matching for Balance, Pairing for Heterogeneity in an Observational Study of the Effectiveness of For-Profit and Not-For-Profit High Schools in Chile (2014, methodology): “For other methods of subset matching, see Crump et al. (2009), Traskin and Small (2011), Rosenbaum (2012b) and Hill and Su (2013).”
Shock-Based Causal Inference in Corporate Finance and Accounting Research (2015, background): “For trimming to common support, see Crump et al. (2009); for matching, see Rosenbaum (2010); for inverse propensity weighting, see Busso et al. (2014).”
Contamination Bias in Linear Regressions (2021, neutral): “But this approach may be infeasible or yield imprecise estimates under limited overlap—a common scenario in practice (Crump et al., 2009).”
Inference on a New Class of Sample Average Treatment Effects (2017, methodology): “We are not the first ones to discuss inference on a causal estimand that is a random variable (Robins 1988; Bowers and Hansen 2009; Crump et al. 2009; Li, Morgan, and Zaslavsky 2018).”