Non-Self-Averaging in Macroeconomic Models: A Criticism of Modern Micro-founded Macroeconomics

When the coefficient of variation, namely the standard deviation relative to mean approaches zero as the number of economic agents becomes large, the system is called self-averaging. Otherwise, it is non-self-averaging. Most economic models take it for granted that economic system is self-averaging. However, they are based on an extremely unrealistic assumption that all the economic agents face the same probability distribution. Once this unrealistic assumption is dropped, non-self averaging 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 implies that even if the number of economic agents is large, dispersion can remain significant, and, therefore, that we can not legitimately focus on the means of aggregate variables. It, in turn, means that the standard microeconomic foundations based on representative agents has 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.