Measuring Income and Wealth Inequality: A Note on the Gini Coefficient for Samples with Negative Values

This study analyzes the measurement of income and wealth inequalities in samples with negative values. The Gini coefficient can exceed one when negative values represent a large share of the sample. A perfect concentration with non-negative values attains a Gini coefficient of one; thus, interpreting a Gini coefficient greater than one is difficult. Existing methods of deleting negative values or replacing them with zeros underestimate the inequality level. Alternative methods of normalizing the Gini coefficient to restrict it between zero and one cannot satisfy the basic requirements of an inequality index. Moreover, both methods distort inequality comparisons over time and across countries. This study analytically shows the theoretical drawbacks of extant methods and proposes measuring the standard Gini coefficient using an unadjusted sample, even when the sample contains negative values and the Gini coefficient exceeds one. This study also proposes generalizing the concentration such that it attains the same Gini coefficient value and is more severely concentrated than the perfect concentration with non-negative values. To facilitate the interpretation of a Gini coefficient greater than one, we can compare the generalized and perfect concentrations and infer the amount of transfer from one to the other. Finally, this study shows that the extant methods may cause a sizable distortion in inequality comparison over time for the U.S. net worth.