Biometrika Advance Access originally published online on January 24, 2009
Biometrika 2009 96(1):187-199; doi:10.1093/biomet/asn055
Articles |
Dealing with limited overlap in estimation of average treatment effects
Department of Economics, University of California, Berkeley, California 94720, U.S.A. crump{at}econ.berkeley.edu
Department of Economics, Duke University, Durham, North Carolina 27708, U.S.A. hotz{at}econ.duke.edu
Department of Economics, Harvard University, Cambridge, Massachusetts 02138, U.S.A. imbens{at}harvard.edu
Department of Economics, University of Miami, Coral Gables, Florida 33124, U.S.A. omitnik{at}miami.edu
Received for publication 1 June 2007. Revision received 1 June 2008.
Estimation of average treatment effects under unconfounded or ignorable treatment assignment is often hampered by lack of overlap in the covariate distributions between treatment groups. 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 ad hoc methods for trimming the sample. We develop a systematic approach to addressing lack of overlap. We characterize optimal subsamples for which the average treatment effect can be estimated most precisely. 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 rule of thumb to discard all units with estimated propensity scores outside the range [0.1,0.9].
Key Words: Average treatment effect • Causality • Ignorable treatment assignment • Overlap • Propensity score • Treatment effect heterogeneity • Unconfoundedness
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