A New Measure of Horizontal Equity

Abstract

In this paper, we propose a new measure of horizontal equity that overcomes many of the shortcomings of previous proposed measures. Our starting point is the observation that a well-behaved social welfare function need not evaluate global' (vertical equity) differences in after-tax income using the same weights it applies to local' (horizontal equity) differences, even though this constraint has been applied in the past. Following work on the structure of individual preferences, we show that a social welfare function can imply different preferences toward horizontal and vertical equity. Adopting the general approach to the measurement of inequality developed by Atkinson (1970), we use such a social welfare function to derive measures of inequality that are decomposable into components naturally interpreted as indices of horizontal and vertical equity. In particular, the former index measures deviations from the fundamental principle that equals be treated equally. Finally, we apply our new measure to two tax-return data sets, evaluating the degree to which the horizontal equity of the US personal income tax has changed over time, and how horizontal equity would be altered by one version of recent proposals to do away with the so-called marriage penalty.'