Lorenz Interpolation: A Method for Estimating Income Inequality from Grouped Income Data

Abstract

To understand how income inequality affects individuals and communities, researchers must have accurate measures of income inequality at lower geographic levels, such as counties, school districts, and census tracts. Studies of income inequality, however, are constrained by the tabular format in which censuses publish income data. In this article, the author proposes a new method, Lorenz interpolation, for estimating income inequality from binned income data. Using public microsample data from the American Community Survey (ACS), the author shows that Lorenz interpolation produces more accurate and reliable income inequality estimates than do alternative estimation methods. Then, using restricted ACS income data obtained through a Federal Statistical Research Data Center, the author evaluates the accuracy of Lorenz interpolation at the census tract and school district levels. Lorenz interpolation produces reliable school district–level estimates, but the method produces less reliable estimates for some income inequality measures at the tract level. These findings indicate that researchers should refrain from estimating tract-level income inequality measures from tabular data. They also show that aggregating tract income distributions to higher geographic levels can produce valid estimates of income inequality.