Households, auctioneers, and aggregation

We examine aggregation in the neoclassical growth model with aggregate shocks and uninsurable employment risk, as well as related environments. We introduce a Walrasian auctioneer whose job is to report to households all possible state-contingent future prices. Households take these as given when forming expectations and making optimal consumption/savings decisions, and the auctioneer adjusts her forecasts until markets clear. This natural dichotomy between the households and the auctioneer allows us to study each problem in isolation as well as to discuss the intersection. On the household side, we separate an explicit expression for the linear permanent income component of savings from a well-behaved nonlinear adjustment arising from precautionary behavior and incomplete markets. Equipped with this decomposition, we then study how economies aggregate in the presence of various auctioneer types that are popular in the literature. The steady-state auctioneer of Huggett (1997) and Aiyagari (1994) offers a paper-and-pencil analysis of aggregation that provides a bound on more complex environments. We provide an economic interpretation of the regression coefficients and explain the lack of time variation in the auctioneer of Krusell and Smith (1998). We also introduce a new numerical method which uses the empirical distribution of auctioneer forecasts to substantially improve solution accuracy in cases where the standard coefficient of determination and other well-known statistics prove to be misleading.