Adaptive Experimental Design Using the Propensity Score

• Published in: Journal of business & economic statistics Vol. 29; no. 1; pp. 96 - 108
• Main Authors: Hahn, Jinyong, Hirano, Keisuke, Karlan, Dean
• Format: Journal Article
• Language: English
• Published: Alexandria Taylor & Francis 01.01.2011; American Statistical Association; Taylor & Francis Ltd
• Subjects: Asymptotic methods; Conditional probabilities; Design efficiency; Design of experiments; Economic statistics; Efficiency bound; Estimating techniques; Estimators; Experiment design; Experimental design; Fundraising; Hunger; Probability; Propensity score; Sample size; Software; Statistical discrepancies; Statistical variance; Studies
• ISSN: 0735-0015; 1537-2707
• DOI: 10.1198/jbes.2009.08161

Many social experiments are run in multiple waves or replicate earlier social experiments. In principle, the sampling design can be modified in later stages or replications to allow for more efficient estimation of causal effects. We consider the design of a two-stage experiment for estimating an average treatment effect when covariate information is available for experimental subjects. We use data from the first stage to choose a conditional treatment assignment rule for units in the second stage of the experiment. This amounts to choosing the propensity score, the conditional probability of treatment given covariates. We propose to select the propensity score to minimize the asymptotic variance bound for estimating the average treatment effect. Our procedure can be implemented simply using standard statistical software and has attractive large-sample properties.