TITLE:
A Note on Laws of Motion for Aggregate Distributions
AUTHORS:
Damir Stijepic
KEYWORDS:
Aggregate Distribution, Law of Motion, Kolmogorov Forward Equation, Fok-ker-Planck Equation, Wealth Distribution
JOURNAL NAME:
Theoretical Economics Letters,
Vol.10 No.6,
December
25,
2020
ABSTRACT: I derive the law of motion for the aggregate
distribution directly from the laws of motion for the individuals’ states. By
relying on concepts from measure theory, the derivation is concise and intuitive.
I address random shocks both at the micro level and at the macro level.
Micro-level shocks completely cancel at the aggregate level provided that a law
of large numbers applies. Therefore, the law of motion for the aggregate
distribution is a deterministic process in the absence of macro-level
uncertainty. If there are macro-level risks, the law of motion for the
aggregate distribution exhibits a stochastic component additionally. I
illustrate the formalism in a model of wealth accumulation with stochastic
interest rates, deriving the law of motion for the aggregate wealth
distribution.