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We present an outline of relative distribution methods, with an
application to recent changes in the U.S. wage distribution. Relative
distribution methods are a nonparametric statistical framework
for analyzing data in a fully distributional context. The
framework combines the graphical tools of exploratory data analysis
with statistical summaries, decomposition, and inference. The
relative distribution is similar to a density ratio. It is technically
defined as the random variable obtained by transforming a variable
from a comparison group by the cumulative distribution
function (CDF) of that variable for a reference group. This transformation
produces a set of observations, the relative data, that
represent the rank of the original comparison value in terms of
the reference group’s CDF. The density and CDF of the relative
data can therefore be used to fully represent and analyze distributional
differences. Analysis can move beyond comparisons of
means and variances to tap the detailed information inherent in
distributions. The analytic framework is general and flexible, as
the relative density is decomposable into the effect of location
and shape differences, and into effects that represent both compositional
changes in covariates, and changes in the covariateoutcome
variable relationship.
The authors wish to thank Annette D. Bernhardt, Marc Scott, Paul Janssen, the
editor, and the anonymous reviewers for the many helpful comments that have much
improved this paper.
* Pennsylvania State University
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