  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.
