Marco Ranaldi
Silvia Vannutelli
Raymond Fisman
John Voorheis
Reed Walker
Janet Currie
Roel Dom
Marcos Vera-Hernández
Emla Fitzsimons
José V. Rodríguez Mora
Tomasa Rodrigo
Álvaro Ortiz
Stephen Hansen
Vasco Carvalho
Gergely Buda
Gabriel Zucman
Anders Jensen
Matthew Fisher-Post
José-Alberto Guerra
Myra Mohnen
Christopher Timmins
Ignacio Sarmiento-Barbieri
Peter Christensen
Linda Wu
Gaurav Khatri
Julián Costas-Fernández
Eleonora Patacchini
Jorgen Harris
Marco Battaglini
Ricardo Fernholz
Alberto Bisin
Jess Benhabib
Cian Ruane
Pete Klenow
Mark Bils
Peter Hull
Will Dobbie
David Arnold
Eric Zwick
Owen Zidar
Matt Smith
Ansgar Walther
Tarun Ramadorai
Paul Goldsmith-Pinkham
Andreas Fuster
Ellora Derenoncourt
Golvine de Rochambeau
Vinayak Iyer
Jonas Hjort
Elena Simintzi
Paige Ouimet
Holger Mueller
Pablo Garriga
Gabriel Ulyssea
Costas Meghir
Pinelopi Koujianou Goldberg
Rafael Dix-Carneiro
Alessandro Toppeta
Áureo de Paula
Orazio Attanasio
Seth Zimmerman
Joseph Price
Valerie Michelman
Camille Semelet
Anne Brockmeyer
Pierre Bachas
Santiago Pérez
Elisa Jácome
Leah Boustan
Ran Abramitzky
Jesse Rothstein
Jeffrey T. Denning
Sandra Black
Wei Cui
Mathieu Leduc
Philippe Jehiel
Shivam Gujral
Suraj Sridhar
Attila Lindner
Arindrajit Dube
Pascual Restrepo
Łukasz Rachel
Benjamin Moll
Kirill Borusyak
Michael McMahon
Frederic Malherbe
Gabor Pinter
Angus Foulis
Saleem Bahaj
Stone Centre
Phil Thornton
James Baggaley
Xavier Jaravel
Richard Blundell
Parama Chaudhury
Dani Rodrik
Alan Olivi
Vincent Sterk
Davide Melcangi
Enrico Miglino

Inference for ranks with applications to mobility across neighborhoods and academic achievement across countries

What is this research about and why did you do it?

Rankings (e.g., of hospitals, political parties, schools) are ubiquitous. These are often based on estimated features of the objects to be ranked (e.g., hospital or school performance, a party’s vote share). As a result, there may be considerable uncertainty concerning the true ranking. An important example of contemporary interest is the ranking of neighbourhoods by measures of intergenerational mobility to study which neighbourhoods provide relatively more opportunities for children to rise out of poverty. 

How did you answer this question?

In this paper, we develop confidence sets for ranks which, for each neighbourhood, indicate the range in which its true rank lies with high probability. We also provide confidence sets containing the neighbourhoods that truly are among the best/worst with high probability. 

We apply our theoretical results to re-examine the rankings of neighbourhoods in the United States by intergenerational mobility.

What did you find?

Rankings of neighbourhoods by measures of intergenerational mobility differ substantially in the degree to which they are informative. Specifically, the confidence intervals for the ranks are fairly narrow, and thus informative, when using so-called correlational measures of mobility, but they can be very wide, and thus uninformative, when using so-called movers measures of mobility.

Ranking of the 50 most populous commuting zones in the U.S. by two different measures of intergenerational mobility (“correlational” and “movers”) together with 95% simultaneous confidence intervals for the ranks. The left panel shows a relatively informative ranking with narrow confidence intervals; the right panel shows an uninformative ranking with very wide confidence intervals. “Correlational” estimates measure the correlation between children’s and parents’ rank in their respective income distributions. “Movers” estimates measure the causal impact of a child spending an additional year in a given commuting zone on their adult income.

What implications does this have for the research on wealth concentration or economic inequality?

Rankings of neighbourhoods by intergenerational mobility have been used to study how “bad” neighbourhoods can be improved by changing some of their attributes to become more like those of the “good” neighbourhoods. Our research cautions that such findings may not be reliable when the rankings are too uninformative to distinguish “good” from “bad” neighbourhoods.

What are the next steps in your agenda?

The next step is to develop statistical methods that reliably identify characteristics that separate “good” from “bad” neighbourhood. 

Citation and related resources

This paper can be cited as: Mogstad, M., Romano, J., Shaikh, A. and Wilhelm, D. (2022) 'Inference for Ranks with Applications to Mobility across Neighborhoods and Academic Achievement across Countries'. Review of Economic Studies (forthcoming). A pre-publication version is available from the NBER website.

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About the authors