Non-self-averaging in macroeconomic models: a criticism of modern micro-founded macroeconomics

When the coefficient of variation, namely the ratio of the standard deviation over the mean approaches zero as the number of economic agents becomes large, a system is called self-averaging. Otherwise, it is non-self-averaging. Most economic models take it for granted that the economic system is self-averaging. However, they are based on the extremely unrealistic assumption that all the economic agents face the same probability distribution, and that micro shocks are independent. Once these unrealistic assumptions are dropped, non-self-averaging behavior naturally emerges. Using a simple stochastic growth model, this paper demonstrates that the coefficient of variation of aggregate output or GDP does not go to zero even if the number of sectors or economic agents goes to infinity. Non-self-averaging phenomena imply that even if the number of economic agents is large, dispersion could remain significant, and we cannot legitimately focus solely on the means of aggregate variables. This, in turn, means that the standard microeconomic foundations based on representative agents have little value for they are meant to provide us with accurate dynamics of the means of aggregate variables. Contrary to the main stream view, micro-founded macroeconomics such as a dynamic general equilibrium model does not provide solid micro foundations.