YALE DEPARTMENT OF ECONOMICS
WORKING PAPER NO. 59

Adaptive Experimental Design Using the Propensity Score

Jinyong Hahn, Keisuke Hirano, Dean Karlan

January 2009

Many social experiments are run in multiple waves, or are replications of 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.

Keywords: experimental design, propensity score, efficiency bound

JEL Codes: C1, C9, C13, C14, C93