This paper presents an incentive-based theory of the dynamics of the distribution of consumption in the presence of aggregate shocks. The paper builds on the models concerning the distribution of income or consumption and incentive problems of Green (1987), Thomas and Worrall (1991), Phelan and Townsend (1991), and Atkeson and Lucas (1992). By incorporating aggregate production shocks, the model allows an examination of the interactions between individual and aggregate consumption series given incomplete insurance. Further, the methodology outlined allows the incorporation of incentive considerations to macroeconomic environments similar to Rogerson (1988) and Hansen (1985).

This paper develops new recursive, set based methods for studying repeated games with private monitoring. For any finite-state strategy profile, we find necessary and sufficient conditions for whether there exists a distribution over initial states such that the strategy, together with this distribution, form a correlated sequential equilibrium (CSE). Also, for any given correlation device for determining initial states (including degenerate cases where players' initial states are common knowledge), we provide necessary and sufficient conditions for the correlation device and strategy to be a CSE, or in the case of a degenerate correlation device, for the strategy to be a sequential equilibrium. We also consider several applications. In these, we show that the methods are computationally feasible, and how to construct and verify equilibria in a secret price-setting game.