Inference for Ranks with Applications to Mobility Across Neighborhoods and Academic Achievement Across Countries

101 Pages Posted: 16 May 2020 Last revised: 23 Jan 2022

See all articles by Magne Mogstad

Magne Mogstad

University of Chicago

Joseph P. Romano

Stanford University - Department of Statistics

Azeem Shaikh

University of Chicago

Daniel Wilhelm

University College London

Multiple version iconThere are 2 versions of this paper

Date Written: March 2020

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 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. The confidence sets for the ranking of the 50 most populous commuting zones by measures of mobility are also found to be small. These rankings, however, become much less informative if one includes all commuting zones, if one considers neighborhoods at a more granular level (counties, Census tracts), or if one uses movers across areas to address concerns about selection.

Suggested Citation

Mogstad, Magne and Romano, Joseph P. and Shaikh, Azeem and Wilhelm, Daniel, Inference for Ranks with Applications to Mobility Across Neighborhoods and Academic Achievement Across Countries (March 2020). NBER Working Paper No. w26883, Available at SSRN: https://ssrn.com/abstract=3599663

Magne Mogstad (Contact Author)

University of Chicago ( email )

1101 East 58th Street
Chicago, IL 60637
United States

Joseph P. Romano

Stanford University - Department of Statistics ( email )

Stanford, CA 94305
United States

Azeem Shaikh

University of Chicago ( email )

1101 East 58th Street
Chicago, IL 60637
United States

Daniel Wilhelm

University College London ( email )

UCL Economics
30 Gordon Street
London, WC1H 0AX
United Kingdom

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