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Ergodic chaos and aggregate stability: A deterministic discrete‐choice model of wealth distribution dynamics
Author(s) -
Kamihigashi Takashi
Publication year - 2013
Publication title -
international journal of economic theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.351
H-Index - 11
eISSN - 1742-7363
pISSN - 1742-7355
DOI - 10.1111/j.1742-7363.2013.12007.x
Subject(s) - ergodic theory , distribution of wealth , mathematics , stability (learning theory) , aggregate (composite) , distribution (mathematics) , invariant (physics) , wealth distribution , statistical physics , economics , mathematical economics , instability , econometrics , mathematical analysis , physics , computer science , inequality , materials science , composite material , machine learning , mechanics , mathematical physics
This paper studies wealth distribution dynamics in a small open economy with a continuum of consumers indexed by initial wealth. Each of them solves a discrete‐choice problem whose optimal policy function exhibits ergodic chaos. We show that for any initial distribution of wealth given by a density, the wealth distribution converges to a unique invariant distribution, and aggregate wealth converges to the corresponding value. Thus ergodic chaos leads to aggregate stability rather than instability. These results are illustrated with various numerical examples.