This paper studies a penalized statistical decision rule for the treatment assignment problem. Consider the setting of a utilitarian policy maker who must use sample data to allocate a binary treatment to members of a population, based on their observable characteristics. We model this problem as a statistical decision problem where the policy maker must choose a subset of the covariate space to assign to treatment, out of a class of potential subsets. We focus on settings in which the policy maker may want to select amongst a collection of constrained subset classes: examples include choosing the number of covariates over which to perform best‐subset selection, and model selection when approximating a complicated class via a sieve. We adapt and extend results from statistical learning to develop the Penalized Welfare Maximization (PWM) rule. We establish an oracle inequality for the regret of the PWM rule which shows that it is able to perform model selection over the collection of available classes. We then use this oracle inequality to derive relevant bounds on maximum regret for PWM. An important consequence of our results is that we are able to formalize model‐selection using a “holdout” procedure, where the policy maker would first estimate various policies using half of the data, and then select the policy which performs the best when evaluated on the other half of the data.

This paper is concerned with inference in the linear model with dyadic data. Dyadic data is data that is indexed by pairs of "units", for example trade data between pairs of countries.Because of the potential for observations with a unit in common to be correlated, standard inference procedures may not perform as expected. We establish a range of conditions under which a t-statistic with the dyadic-robust variance estimator of Fafchamps and Gubert (2007) is asymptotically normal. Using our theoretical results as a guide, we perform a simulation exercise to study the validity of the normal approximation, as well as the performance of a novel finite-sample correction. We conclude with guidelines for applied researchers wishing to use the dyadic-robust estimator for inference.

This paper studies a new statistical decision rule for the treatment assignment problem.Consider a utilitarian policy maker who must use sample data to allocate one of two treatments to members of a population, based on their observable characteristics. In practice, it is often the case that policy makers do not have full discretion on how these covariates can be used, for legal, ethical or political reasons. We treat this constrained problem as a statistical decision problem, where we evaluate the performance of decision rules by their maximum regret. We focus on settings in which the policy maker may want to select amongst a collection of such constrained classes: examples we consider include choosing the number of covariates over which to perform best-subset selection, and model selection when approximating a complicated class via a sieve. We adapt and extend results from statistical learning to develop a decision rule which we call the Penalized Welfare Maximization (PWM) rule. We establish an oracle inequality for the regret of the PWM rule which shows that it is able to perform model selection over the collection of available classes. We then use this oracle inequality to derive relevant bounds on maximum regret for PWM. We illustrate the model-selection capabilities of our method with a small simulation exercise, and conclude by applying our rule to data from the Job Training Partnership Act (JTPA) study.

This paper proposes an adaptive randomization procedure for two-stage randomized controlled trials. The method uses data from a first-wave experiment in order to determine how to stratify in a second wave of the experiment, where the objective is to minimize the variance of an estimator for the average treatment effect (ATE). We consider selection from a class of stratified randomization procedures which we call stratification trees: these are procedures whose strata can be represented as decision trees, with differing treatment assignment probabilities across strata. By using the first wave to estimate a stratification tree, we simultaneously select which covariates to use for stratification, how to stratify over these covariates, as well as the assignment probabilities within these strata. Our main result shows that using this randomization procedure with an appropriate estimator results in an asymptotic variance which minimizes the variance bound for estimating the ATE, over an optimal stratification of the covariate space. Moreover, by extending techniques developed in Bugni et al. (2018), the results we present are able to accommodate a large class of assignment mechanisms within strata, including stratified block randomization. We also present extensions of the procedure to the setting of multiple treatments, and to the targeting of subgroup-specific effects. In a simulation study, we find that our method is most effective when the response model exhibits some amount of "sparsity" with respect to the covariates, but can be effective in other contexts as well, as long as the first-wave sample size used to estimate the stratification tree is not prohibitively small. We conclude by applying our method to the study in Karlan and Wood (2017), where we estimate stratification trees using the first wave of their experiment.

In this article, we present the wald_mse command, which computes the maximum mean squared error of a user-specified point estimator of the mean for a population of interest in the presence of missing data. As pointed out by Manski (1989, Journal of Human Resources 24: 343–360; 2007, Journal of Econometrics 139: 105–115), the presence of missing data results in the loss of point identification of the mean unless one is willing to make strong assumptions about the nature of the missing data. Despite this, decision makers may be interested in reporting a single number as their estimate of the mean as opposed to an estimate of the identified set. It is not obvious which estimator of the mean is best suited to this task, and there may not exist a universally best choice in all settings. To evaluate the performance of a given point estimator of the mean, wald_mse allows the decision maker to compute the maximum mean squared error of an arbitrary estimator under a flexible specification of the missing-data process.