"Inference for Ranks with Application to Intergenerational Mobility and Neighborhoods." (coauthored with Joe Romano, Azeem Shaikh, and Daniel Wilhelm.) It is often desired to rank different populations according to the value of
“Inference for Ranks with Application to Intergenerational Mobility and Neighborhoods.”
(coauthored with Joe Romano, Azeem Shaikh, and Daniel Wilhelm.)
It is often desired to rank different populations according to the value of some feature of each population. For example, it may be desired to rank neighborhoods according to some measure of intergenerational mobility or countries according to some measure of academic achievement. These rankings are invariably computed using estimates rather than the true values of these features. As a result, there may be considerable uncertainty concerning the rank of each population. In this paper, we consider the problem of accounting for such uncertainty by constructing confidence sets for the rank of each population. We consider both the problem of constructing marginal confidence sets for the rank of a particular population as well as simultaneous confidence sets for the ranks of all populations. We show how to construct such confidence sets satisfying the desired coverage properties under weak assumptions. Our first construction exploits simultaneous confidence sets for differences in the values of the features for certain pairs of populations. We then show how to improve upon this construction by connecting it to an appropriate multiple hypothesis testing problem. An important feature of all of our constructions is that they remain computationally feasible even when the number of populations is very large. We apply our theoretical results to re-examine the rankings of both neighborhoods in the United States in terms of intergenerational mobility and developed countries in terms of academic achievement. The conclusions about which countries do best and worst at reading, math, and science are fairly robust to accounting for uncertainty. By comparison, several celebrated findings about intergenerational mobility in the United states are not robust to taking uncertainty into account.
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