Better estimates from binned income data: Interpolated CDFs and mean-matching

TL;DR

This paper introduces a fast, nonparametric method using interpolated CDFs to estimate income statistics from binned data, outperforming traditional midpoint approaches and fitting well with known means.

Contribution

It proposes a novel nonparametric interpolation method for income data, improving accuracy and speed over parametric models, and provides implementations in R and Stata.

Findings

Interpolated CDFs are faster and slightly more accurate than parametric fits.

Constraining methods to match known means significantly improve estimates.

The approach performs well across all US counties in estimating Gini coefficients.

Abstract

Researchers often estimate income statistics from summaries that report the number of incomes in bins such as \$0-10,000, \$10,001-20,000,...,\$200,000+. Some analysts assign incomes to bin midpoints, but this treats income as discrete. Other analysts fit a continuous parametric distribution, but the distribution may not fit well. We fit nonparametric continuous distributions that reproduce the bin counts perfectly by interpolating the cumulative distribution function (CDF). We also show how both midpoints and interpolated CDFs can be constrained to reproduce the mean of income when it is known. We compare the methods' accuracy in estimating the Gini coefficients of all 3,221 US counties. Fitting parametric distributions is very slow. Fitting interpolated CDFs is much faster and slightly more accurate. Both interpolated CDFs and midpoints give dramatically better estimates if constrained to match a known mean. We have implemented interpolated CDFs in the binsmooth package for R. We have implemented the midpoint method in the rpme command for Stata. Both implementations can be constrained to match a known mean.