Inference for Ranks with Applications to Mobility across Neighbourhoods and Academic Achievement across Countries
Review of Economic Studies · 2023 · Magne Mogstad、Joseph P. Romano、Azeem M. Shaikh、Daniel Wilhelm
中文摘要
人们常常希望根据各总体某一特征的值对不同总体进行排序。例如，可能希望根据某种代际流动性指标对邻里进行排序，或根据某种学业成就指标对各国进行排序。这些排序无一例外是使用这些特征的估计值而非真实值计算得出的。因此，各总体的秩可能存在相当大的不确定性。本文考虑通过为各总体的秩构建置信集合来处理这种不确定性的问题。我们既考虑了为某一特定总体的秩构建边际置信集合的问题，也考虑了为所有总体的秩构建同时置信集合的问题。我们展示了如何在弱假设下构建此类置信集合。我们所有构建方法的一个重要特征是，即使总体数量非常庞大，它们在计算上仍然可行。我们应用理论结果重新审视了美国邻里在代际流动性方面的排序以及发达国家在学业成就方面的排序。关于哪些国家在阅读、数学和科学方面表现最好和最差的结论，在考虑不确定性后是相当稳健的。按流动性指标对人口最多的五十个通勤区进行排序所得的置信集合也被发现较小。然而，如果纳入所有通勤区，如果在更细粒度的层级（县、普查区）考察邻里，或者如果使用跨地区迁移者来应对选择性问题，这些置信集合所包含的信息就会大幅减少。
Abstract
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 neighbourhoods 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 neighbourhoods in the U.S. 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 fifty most populous commuting zones by measures of mobility are also found to be small. These confidence sets, however, become much less informative if one includes all commuting zones, if one considers neighbourhoods at a more granular level (counties, census tracts), or if one uses movers across areas to address concerns about selection.