Dynamic (S,s) Economies

In this paper we provide a framework to study the aggregate dynamic behavior of an economy where individual units follow (S,s) policies. We characterize structural and stochastic heterogeneities that ensure convergence of the economy's aggregate to that of its frictionless counterpart, determine the speed at which convergence takes place, and describe the transitional dynamics of this economy. In particular, we consider a dynamic economy where agents differ in their initial positions within their bands and face both stochastic and structural heterogeneity; where the former refers to the presence of (unit specific) idiosyncratic shocks, and the latter to differences in the widths of units' (S,s) bands and their response to aggregate shocks. We study the evolution of the economy's aggregate and the evolution of the difference between this aggregate and that of an economy without macroeconomic friction, where the latter pertains to a situation where individual units adjust with no delay to all shocks. We also examine the sensitivity of this difference to common shocks. For example, in the retail inventory problem the aggregate deviation and sensitivity to common shocks correspond to the aggregate inventory level and its sensitivity to aggregate demand shocks, respectively