Estimation with Binned Data

TL;DR

This paper introduces a SAS macro for estimating mean and variance from binned data using multiple distributions, demonstrating high accuracy and comparing favorably with existing methods.

Contribution

It presents a novel macro that fits multiple distributions to binned data and selects the best estimate, improving accuracy over previous approaches.

Findings

Negligible bias in income estimates (0-2%)

Root mean squared error of 3-6%

Favorable comparison with existing distribution fitting methods

Abstract

Variables such as household income are sometimes binned, so that we only know how many households fall in each of several bins such as $0-10,000, $10,000-15,000, or $200,000+. We provide a SAS macro that estimates the mean and variance of binned data by fitting the extended generalized gamma (EGG) distribution, the power normal (PN) distribution, and a new distribution that we call the power logistic (PL). The macro also implements a "best-of-breed" estimator that chooses from among the EGG, PN, and PL estimates on the basis of likelihood and finite variance. We test the macro by estimating the mean family and household incomes of approximately 13,000 US school districts between 1970 and 2009. The estimates have negligible bias (0-2%) and a root mean squared error of just 3-6%. The estimates compare favorably with estimates obtained by fitting the Dagum, generalized beta (GB2), or logspline distributions.