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

Author

Listed:
  • Magne Mogstad

    (University of Chicago, Statistics Norway, and NBER)

  • Joseph P. Romano

    (Stanford University)

  • Azeem M. Shaikh

    (University of Chicago)

  • Daniel Wilhelm

    (University College London)

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. By comparison, several celebrated findings about intergenerational mobility in the United states are not robust to taking uncertainty into account.

Suggested Citation

  • Magne Mogstad & Joseph P. Romano & Azeem M. Shaikh & Daniel Wilhelm, 2020. "Inference for Ranks with Applications to Mobility across Neighborhoods and Academic Achievement across Countries," Working Papers 2020-16, Becker Friedman Institute for Research In Economics.
    • Handle: RePEc:bfi:wpaper:2020-16
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Condence sets; Directional errors; Familywise error rate; Intergenerational mobility; Multiple testing; PISA; Ranks;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • I20 - Health, Education, and Welfare - - Education - - - General
    • J62 - Labor and Demographic Economics - - Mobility, Unemployment, Vacancies, and Immigrant Workers - - - Job, Occupational and Intergenerational Mobility; Promotion

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