Measuring inequality change in an economy with income growth

This paper analyzes how to measure changes in inequality in an economy with income growth. The discussion distinguishes three stylized kinds of economic growth:

• 1.(1) high income sector enrichment,
• 2.(2) low income sector enrichment,
• 3.(3) high income sector enlargement, in which the high income sector expands and absorbs persons from the low income sector.

Th e two enrichment types pose no problem for assessing inequality change in the course of economic growth: for high income sector enrichment growth, inequality might reasonably be said to increase, whereas for low income sector enrichment, inequality might be said to decrease. These adjustments are non-controversial and non-problematical. Where problems arise is in the case of high income sector enlargement growth. In that case, the two alternative approaches have been shown in this paper to yield markedly results:

• 1.(1) The traditional inequality indices generate an inverted-U pattern of inequality. That is, inequality rises in the early stages of high income sector enlargement growth and falls thereafter.
• 2.(2) The new approach suggested here, based on axioms of gap inequality and numerical inequality, generates a U pattern of inequality. That is, inequality falls in the early stages of high income sector enlargement growth and rises thereafter.

The discrepancy between the familiar indices and the alternative approach based on axioms of gap inequality and numerical inequality bears further scrutiny. Two courses of action are possible. One might try to axiomatize inequality in ways that generate an inverted-U pattern in high income sector enlargement growth, thereby rationalizing the continued use of the usual inequality indices with the inverted-U property. Alternatively, one might retain the axioms proposed here, embed them into a more formal structure, and construct a family of inequality indices consistent with them. Others might wish to pursue the first course; I am at work on the second.