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, the system is called self-averaging. Otherwise, it is non-selfaveraging.
Most economic models take it for granted that economic system
is self-averaging. However, they are based on extremely unrealistic assumptions
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 can not legitimately focus on the means of aggregate
variables. It, 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.
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