Conceptualizing Inequality and Risk

Economists and finance researchers have long recognized the “close relation between the measurement of inequality and the measurement of risk” (Breitmeyer et al., 2004). Economists today agree that a measure of income inequality must respect the Pigou-Dalton transfer principle, that is, inequality cannot increase with a transfer from a richer person to a poorer person. Finance researchers today agree that a measure of risk must respect the diversification principle, that is, risk cannot increase when portfolios are combined. Where did these convictions originate? While both principles were advocated early in their respective fields, they were not viewed as definitive until relatively recently. In both fields major empirical and theoretical efforts were mounted in support of various conceptualizations at odds with these two principles. For example, Robert Gibrat advocated the use of the variance of log income despite the fact it is inconsistent with the Pigou-Dalton principle. In finance, value at risk (VaR), although it can violate the diversification principle, was widely advocated. People supporting research programs at odds with Pigou-Dalton or the diversification principle, based those programs on ambitious empirical and theoretical claims about distributions. Such claims could have been right and are not a priori or logically false. The purpose of this paper is to review these “at odds” conceptualizations, the types of arguments advanced for their legitimacy, and the reasons they have been given up.