Approximate Aggregation in Dynamic Economies

We provide a characterization of aggregation in the neoclassical growth model with aggregate shocks and uninsurable employment risk. The extent to which an economy aggregates can be determined by examining the (lack of) linearity with respect to wealth in the household’s savings function. We take advantage of this fact and separate the consumption-savings problem of the individual household from the Walrasian auctioneer’s problem of clearing the aggregate capital market. This allows us to sidestep the curse of dimensionality associated with models of this type while rigorously analyzing household behavior. Our main theorem isolates the nonlinear elements of the savings function, which contain higher-order moments of the wage distribution. As wage dispersion increases, markets become less complete, precautionary savings motives become stronger and aggregation breaks down. Standard calibrations do not contain sufficient wage dispersion to generate substantial disaggregation. Our insights have broader implications for models with heterogeneous agents and can be used to shed light on existing computational techniques.