I am currently working on problems in multiple testing - more projects in progress
Working Papers:
Inference After Ranking with Applications to Economic Mobility [slides] (with Azeem Shaikh)
submitted
Abstract: This paper considers the problem of inference after ranking. In our setting, we are interested in any population whose rank according to some random quantity, such as an estimated treatment effect, a measure of value-added, or benefit (net of cost), falls in a pre-specified range of values. As such, this framework generalizes the inference on winners setting previously considered in Andrews, Kitagawa, and McCloskey (2024), in which a winner is understood to be the single population whose rank according to some random quantity is highest. We show that this richer setting accommodates a broad variety of empirically-relevant applications. We develop a two-step method for inference, which we compare to existing methods or their natural generalizations to this setting. We first show the finite-sample validity of this method in a normal location model and then develop asymptotic counterparts to these results by proving uniform validity over a large class of distributions satisfying a weak uniform integrability condition. Importantly, our results permit degeneracy in the covariance matrix of the limiting distribution, which arises naturally in many applications. In an application to the literature on economic mobility, we find that it is difficult to distinguish between high and low-mobility census tracts when correcting for selection. Finally, we demonstrate the practical relevance of our theoretical results through an extensive set of simulations.
Uncertainty in Compound Decisions (draft and slides coming soon)
Abstract: Researchers and policymakers often make a large number of decisions, such as classifications or selections, simultaneously over multiple units according to some unit-level measure of value. For example, a policymaker may seek to distinguish low- from high-performing schools according to a value-added measure on test scores in order to optimally allocate funding. To make such decisions, researchers often adopt the compound decision framework of Robbins 1956, assuming that the true values of each unit are drawn from some prior common across units. Given estimates of these true values and knowledge of the prior, researchers form posterior beliefs about each unit's true value, leading to a notion of Bayes-optimal decision making. In practice, the prior is unknown and can only be estimated, leading to a source of sampling uncertainty. This paper develops methods to account for this uncertainty. Importantly, my methods build on the observation that Bayes-optimal decisions depend on the prior only through the posterior means of true value given realizations of the data, implying that it suffices to obtain uniform confidence bands for these posterior means. This observation allows for a tractable approach to inference that focuses power on these decision-relevant features of the prior. To illustrate my methods, I consider the problems of identifying high-opportunity neighborhoods and of selecting discriminatory employers. In both settings, I obtain informative confidence sets for the Bayes-optimal decisions and on the performance of feasible decision rules, suggesting that researchers can credibly claim that their feasible decisions are welfare-improving.