We consider the problem of extrapolating treatment effects across heterogeneous populations (“sites”/“contexts”). We consider an idealized scenario in which the researcher observes cross-sectional data for a large number of units across several “experimental” sites in which an intervention has already been implemented to a new “target” site for which a baseline survey of unit-specific, pre-treatment outcomes and relevant attributes is available. We propose a transfer estimator that exploits cross-sectional variation between individuals and sites to predict treatment outcomes using baseline outcome data for the target location. We consider the problem of obtaining a predictor of conditional average treatment effects at the target site that is MSE optimal within a certain class and
subject to data constraints. Our approach is design-based in the sense that the performance of the predictor is evaluated given the specific, finite selection of experimental and target sites. Our approach is nonparametric, and our formal results concern the construction of an optimal basis of predictors as well as convergence rates for the estimated conditional average treatment effect relative to the constrained-optimal population predictor for the target site. We illustrate our approach using a combined data set of five multi-site randomized controlled trials (RCTs) to evaluate the effect of conditional cash transfers on school attendance.