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Confidence Sets for Ranks with Applications to Intergenerational Mobility and Neighborhoods

Mogstad, M; Romano, J; Shaikh, A; Wilhelm, D; (2021) Confidence Sets for Ranks with Applications to Intergenerational Mobility and Neighborhoods. In: Proceedings of the Royal Economic Society Annual Conference 2020. Royal Economic Society Green open access

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Abstract

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 desired coverage properties under weak assumptions. 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.

Type: Proceedings paper
Title: Confidence Sets for Ranks with Applications to Intergenerational Mobility and Neighborhoods
Event: Royal Economic Society Annual Conference 2020
Location: Belfast, UK
Dates: 6th-8th April 2020
Open access status: An open access version is available from UCL Discovery
Publisher version: https://www.res.org.uk/resources-page/res-annual-c...
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher's terms and conditions.
Keywords: Confidence sets, Directional errors, Familywise error rate, Intergenerational mobility, Multiple testing, PISA, Ranks
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL SLASH
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of S&HS
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of S&HS > Dept of Economics
URI: https://discovery.ucl.ac.uk/id/eprint/10092545
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