Optimal data collection for randomized control trials

In a randomized control trial, the precision of an average treatment effect estimator and the power of the corresponding t-test can be improved either by collecting data on additional individuals, or by collecting additional covariates that predict the outcome variable. We propose the use of pre-experimental data such as other similar studies, a census, or a household survey, to inform the choice of both the sample size and the covariates to be collected. Our procedure seeks to minimize the resulting average treatment effect estimator's mean squared error and/or maximize the corresponding t-test's power, subject to the researcher's budget constraint. We rely on a modication of an orthogonal greedy algorithm that is conceptually simple and easy to implement in the presence of a large number of potential covariates, and does not require any tuning parameters. In two empirical applications, we show that our procedure can lead to reductions of up to 58% in the costs of data collection, or improvements of the same magnitude in the precision of the treatment effect estimator.