A Note on Laws of Motion for Aggregate Distributions

12 Pages Posted: 8 Nov 2015 Last revised: 16 Sep 2020

See all articles by Damir Stijepic

Damir Stijepic

Johannes Gutenberg University Mainz

Date Written: August 10, 2018

Abstract

In the present paper, 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.

Keywords: aggregate distribution, law of motion, Kolmogorov forward equation, Fokker–Planck equation, wealth distribution, stochastic interest rates

JEL Classification: C02, C60, D30, D31, E21

Suggested Citation

Stijepic, Damir, A Note on Laws of Motion for Aggregate Distributions (August 10, 2018). Available at SSRN: https://ssrn.com/abstract=2644742 or http://dx.doi.org/10.2139/ssrn.2644742

Damir Stijepic (Contact Author)

Johannes Gutenberg University Mainz ( email )

Jakob-Welder-Weg 9
Mainz, 55128
Germany

HOME PAGE: http://www.damir.stijepic.com

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