Interpolating Population Distributions using Public-Use Data: An Application to Income Segregation using American Community Survey Data

Abstract

The presence of income inequality is an important problem to demographers, policy makers, economists, and social scientists. A causal link has been hypothesized between income inequality and income segregation, which measures how much households with similar incomes cluster. The information theory index is used to measure income segregation, however, critics have suggested the divergence index instead. Motivated by this, we construct both indices using American Community Survey (ACS) estimates of features of the income distribution. Since the elimination of the decennial census long form, methods of computing these indices must be updated to interpolate ACS estimates and account for survey error. We propose a novel model-based method to do this which improves on previous approaches by using more types of estimates, and by providing uncertainty quantification. We apply this method to estimate U.S. census tract-level income distributions, and in turn use these to construct both income segregation indices. We find major differences between the two indices and find evidence that the information index underestimates the relationship between income inequality and income segregation. The literature suggests interventions designed to reduce income inequality by reducing income segregation, or vice versa, so using the information index implicitly understates the value of these interventions. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

KEYWORD:

• Bayesian methods
• Density estimation
• Functional data
• Income distribution
• Pareto-linear procedure

Supplementary Materials

Online Appendix:

Includes several appendices adding relevant detail to the article.

Acknowledgments

The authors thank Prof. Noel Cressie for helpful discussion on earlier versions of this manuscript.

Additional information

Funding

This research was partially supported by the U.S. National Science Foundation (NSF) and the U.S. Census Bureau under NSF grant SES-1132031, funded through the NSF-Census Research Network (NCRN) program, and under NSF grants SES-1853096 and SES-1853099. This article is released to inform interested parties of research and to encourage discussion. The views expressed on statistical issues are those of the authors and not those of the NSF or the U.S. Census Bureau. The computation for this work was performed on the high performance computing infrastructure provided by Research Computing Support Services and in part by the National Science Foundation under grant number CNS-1429294 at the University of Missouri, Columbia MO.