Surreal family tree representing intergenerational mobility.

Decoding Generational Mobility: Are Rank-Based Regressions Really Telling Us What We Think?

Beau Callahan in Business & Economy August 2025 • 4 min read.

"New research reveals the hidden complexities of using rank-rank regressions to measure intergenerational mobility, challenging common inference methods and urging caution in interpreting results."

In economics, understanding how socioeconomic status persists across generations is a key area of study. Rank-rank regressions, which measure the correlation between a child's and their parent's position in the income distribution, have become a popular tool for assessing intergenerational mobility. These regressions are used to understand how much a child's future success is tied to their family's background. Studies using these methods influence discussions about inequality, the impact of family and neighborhood environments, and strategies for helping children escape poverty.

However, recent research casts doubt on the reliability of standard rank-rank regressions. A groundbreaking article by Chetverikov and Wilhelm (July 3, 2024) reveals that common inference methods used in these regressions are often invalid. The study highlights a significant problem: when the income distribution isn't continuous (meaning there are income "clumps" or "ties"), the results of the regression can be highly sensitive to how these ties are handled. This sensitivity challenges the conclusions drawn from many existing studies on intergenerational mobility.

This article dives into the critical findings of Chetverikov and Wilhelm's work, explaining why conventional methods may mislead and what alternative approaches can provide more accurate and robust insights. We'll explore the implications of their research, offering a clearer understanding of how to interpret rank-rank regressions and assess intergenerational mobility.

The Flaws in Traditional Methods: Why Rank-Rank Regressions Can Mislead

Surreal family tree representing intergenerational mobility.

The core issue identified by Chetverikov and Wilhelm lies in the common statistical methods used to analyze rank-rank regressions. These methods often rely on variance estimators like homoskedastic and Eicker-White, which assume a certain level of smoothness in the data. However, income distributions are rarely smooth in the real world. Factors like income caps, minimum wages, and other economic realities create "ties," where many individuals have the same rank.

When these ties exist, the way they are handled in the regression can dramatically affect the results. For example, if several individuals have the same income, should they all be assigned the lowest rank, the highest rank, or an average rank? The choice can significantly alter the slope coefficient, which is the key measure of intergenerational mobility.

Invalid Inference Methods: Commonly used methods to draw conclusions about the slope parameter in rank-rank regressions are not reliable.
Sensitivity to Ties: When the income distribution isn't continuous, the OLS estimator (a common statistical tool) and its distribution become highly sensitive to how ties in the ranks are dealt with.
Variance Estimation Issues: Homoskedastic and Eicker-White variance estimators don't consistently estimate the true variance, leading to potentially incorrect conclusions.

To illustrate this point, consider a scenario where several individuals have zero income. Depending on whether these individuals are assigned the lowest possible rank or some other rank, the regression results will vary significantly. This sensitivity undermines the validity of conclusions drawn from studies that don't account for the impact of ties.

Moving Forward: Robust Methods for Understanding Generational Mobility

Chetverikov and Wilhelm's research provides a crucial correction to the field of intergenerational mobility studies. Their findings underscore the need for caution when interpreting results from rank-rank regressions that rely on traditional methods. By developing a new asymptotic theory that accounts for discontinuities in income distributions, they offer a more robust framework for future research. This new approach allows economists to draw more reliable conclusions about the factors influencing intergenerational mobility and to develop more effective policies for promoting economic opportunity.

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This article is based on research published under:

DOI-LINK: https://doi.org/10.48550/arXiv.2310.15512,

Title: Inference For Rank-Rank Regressions

Subject: econ.em math.st stat.th

Authors: Denis Chetverikov, Daniel Wilhelm

Published: 24-10-2023

Everything You Need To Know

What are rank-rank regressions and why are they used in economics?

Rank-rank regressions are statistical tools used in economics to measure intergenerational mobility. They assess the correlation between a child's position in the income distribution and their parent's position. These regressions help economists understand the extent to which a child's future success is linked to their family's socioeconomic background, influencing discussions on inequality and the impact of family environments on economic opportunity.

What are the limitations of traditional rank-rank regressions according to Chetverikov and Wilhelm's research?

Chetverikov and Wilhelm's research highlights that common inference methods used in traditional rank-rank regressions are often invalid. A key issue is the sensitivity to 'ties' in the income distribution, where many individuals have the same income rank. The way these ties are handled can significantly affect the regression results, leading to potentially misleading conclusions about intergenerational mobility. Traditional methods often rely on variance estimators like homoskedastic and Eicker-White, which don't account for these discontinuities.

What does it mean when the income distribution isn't continuous, and how does this affect rank-rank regressions?

An income distribution that isn't continuous means there are 'clumps' or 'ties' in income, where many individuals have the same income. This can occur due to factors like minimum wages or income caps. In rank-rank regressions, these ties create problems because the way they are handled (e.g., assigning the lowest, highest, or average rank to individuals with the same income) can dramatically alter the slope coefficient, which is a key measure of intergenerational mobility. This sensitivity undermines the validity of conclusions drawn from studies that don't account for the impact of ties.

How do homoskedastic and Eicker-White variance estimators relate to the problems identified in rank-rank regressions?

Homoskedastic and Eicker-White variance estimators are statistical methods commonly used to estimate the variance in regression models. However, they assume a certain level of smoothness in the data, which is often not the case with income distributions that contain 'ties.' Chetverikov and Wilhelm found that these estimators don't consistently estimate the true variance in the presence of ties, leading to potentially incorrect conclusions about the significance of the relationship between parent and child income ranks. This is because the presence of ties violates the assumptions these variance estimators rely on.

What alternative approaches do Chetverikov and Wilhelm suggest for more robust insights into generational mobility?

Chetverikov and Wilhelm's research provides a new asymptotic theory that accounts for discontinuities in income distributions. This new approach allows economists to draw more reliable conclusions about the factors influencing intergenerational mobility. By addressing the issue of ties and developing methods that are less sensitive to how these ties are handled, the new approach allows development of more effective policies for promoting economic opportunity and reduces reliance on OLS estimator and traditional variance estimation.