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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. The authors consider the design of a two-stage experiment for estimating an average treatment effect, when covariate information is available for experimental subjects. They 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.
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