(with Jean-Yves Duclos and Joan Esteban), Econometrica 72, 1737–1772, 2004.
Summary. We develop the measurement theory of polarization for the case in which income distributions can be described using density functions. The main theorem uniquely characterizes a class of polarization measures that fits into what we call the “identity-alienation” framework, and simultaneously satisfies a set of axioms. Here is a link to a somewhat expanded version, which was published in C. Barrett (ed), The Social Economics of Poverty: Identities, Groups, Communities and Networks, London: Routledge (2005).
(with Joan Esteban), American Economic Review101, 1345–1374, 2011.
Summary. In this paper we study a behavioral model of conflict that provides a basis for choosing certain indices of dispersion as indicators for conflict. We show that a suitable monotone transform of the equilibrium level of conflict can be proxied by a linear function of the Gini coefficient, the Herfindahl-Hirschman fractionalization index, and a specific measure of polarization due to Esteban and Ray.
International Journal of Economic Theory6 11–28, 2010.
Summary. The Phelps–Koopmans theorem states that if every limit point of a path of capital stocks exceeds the “golden rule,” then that path is inefficient: there is another feasible path from the same initial stock that provides at least as much consumption at every date and strictly more consumption at some date. I show that in a model with nonconvex technologies and preferences, the theorem is false in a strong sense. Not only can there be efficient paths with capital stocks forever above and bounded away from a unique golden rule, such paths can also be optimal under the infinite discounted sum of a one-period utility function.