Fields’ Index of Economic Inequality

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Fields’ Index of Economic Inequality

The task of devising proper measures of income inequality is inherently controversial. Individuals have different notions about inequality and cannot always agree on an equity-based ranking of income distributions. Despite theoretical disagreement on proper measurement, applied work frequently adopts measures such as the Gini coefficient. In a series of papers, Gary Fields questioned the use of conventional inequality measures and proposed an alternative measure.

Fields was specifically interested in measuring how inequality responds to income growth in a two-sector (dual) economy where each individual earns either a “low” or “high” income. Economic growth in this context consists in individuals transitioning from the low-income sector to the high-income sector.

Fields (1993) introduced the concepts of “elitism of the rich” and “isolation of the poor.” “Elitism of the rich” captures the idea that when there are few rich people in an economy, these individuals enjoy an elite position that contributes to a high level of inequality in the economy. Conversely, when there are only a few poor individuals, then “isolation of the poor” contributes significantly to disparity.

Fields contended that for most individuals some combination of these two concepts is necessary to properly measure inequality. Consider a six-person dual economy starting at a point where five people are poor and one is rich and moving to a point where four are poor and two are rich. Fields would say that in this example, elitism of the rich has declined dramatically owing to the presence of a second rich individual. Isolation of the poor has increased in this case because the remaining poor are fewer in number. In this case Fields would argue that the drop in elitism overpowers the increase in isolation, thus reducing inequality. Continuing with this progression, one finds that economic growth generates a U-shaped inequality path on Fields’ measure, in sharp contrast to the Gini coefficient, which produces an inverted-U for the same scenario.

Fields’ controversial analysis has prompted a number of academic responses. Paolo Figini (1998) noted that Fields’s measure fails the test for Lorenz consistency (i.e., it violates commonly accepted axioms) when one allows for intrasector income inequality. Fields restricted his analysis to the special case where income is identical for each member of the high-income and low-income sectors.

John Burger (2001) provided a response to Fields’ (1987) contention that there is no intuition behind the traditional inverted-U shape generated by the Gini coefficient. Using Fields’ example, Burger demonstrated that as a six-person dual economy moves from incomes of (1, 1, 1, 1, 1, 4) to (1, 1, 1, 1, 4, 4), the individual income shares change from (1/9, 1/9, 1/9, 1/9, 1/9, 4/9) to (1/12, 1/12, 1/12, 1/12, 1/3, 1/3). The result is a transfer of income share from the four poor and one rich person to the newly wealthy second rich individual. Burger argued that the reduction in income share of several poor individuals impacts inequality more than the reduction in income share of the one wealthy individual, thus resulting in increased income inequality. Continuing with this logic, one finds that growth of the high-income sector generates an inequality path with an inverted-U shape. Burger concludes that the Gini coefficient and the resulting inverted-U shape are consistent with intuition based on income shares.

SEE ALSO Gini Coefficient; Lewis, W. Arthur; Lorenz Curve