Coordinate Space Versus Index Space Representations as Estimation Methods: An Application to How Macro Activity Affects the U.S. Income Distribution

Abstract

This article examines the impact of macroeconomic variables on the level of income inequality in the United States. The innovation is that we introduce what is known as an index space representation to do so. In an index space representation, income shares are considered as a linear combination of what are known as index functions. An index function is a polynomial function whose order is specified by the given index. The macroeconomic variables affect the function parameters corresponding to each index function. In early years, we have only quintile data, but we can still derive a well-behaved Lorenz curve, Gini coefficient, Theil's entropy measure, standard deviation of the logarithm of the share function, and Atkinson's inequality measure.

KEY WORDS:

• Global approximation
• Histogram
• Index function
• Lorenz curve
• Orthonormal basis
• Share function