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 proce-dure seeks to minimize the resulting average treatment effect estimator’s mean squared error or the corresponding t-test’s power, subject to the researcher’s budget constraint. We rely on a modification 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.