Uncovering Gatsby Curves

Empirical findings suggest a positive correlation between inequality and social immobility, a phenomenon coined the Gatsby curve. This paper answers a simple question: When do Gatsby curves exist? We build a theoretical n-income environment in which parental investment and education improve the economic prospects of children. Gatsbian economies and Gatsby curves are formally defined, and we characterize the conditions under which they arise. A Gatsby curve arises when immobility (Trace of the transition matrix) and inequality (Gini coefficient) both change in the same direction following a change in an exogenous variable (an income level, the level of education).When an exogenous variable changes, the impact on inequality depends on a standard direct effect and on an indirect (composition) effect which accounts for the changes in the proportions of individuals with various incomes. We show that following an increase in some high income, immobility and inequality both increase if the indirect effect goes in the same direction as the direct effect. Thus, in such a case, the economy moves up a Gatsby curve. We also demonstrate that if the indirect effect goes in the same direction as the direct effect, and if education is a substitute to parental investment, then an increase in education leads to the economy moving down a Gatsby curve where it experiences both lower inequality and immobility. Finally, we show that an economy may go from being Gatsbian to non-Gatsbian, and vice versa.