Abstract
We develop a simple piecewise linear overlapping generations model exhibiting endogenous business cycles, which is based on Matsuyama's (2007) model of credit cycles. Some sort of “noise” representing information imperfection is shown to transform the Matsuyama model into a continuous, eventually expanding, piecewise linear map on the interval, which is tractable enough to investigate the dynamics in depth by using the techniques of the Frobenius–Perron operators to find observable chaos. While, according to the analysis of Asano et al. (2012), the Matsuyama model exhibits periodic cycles of arbitrarily large period, it is essentially not capable of chaotic dynamics. However, our model exhibits ergodic chaos with some robustness.
| Original language | English |
|---|---|
| Pages (from-to) | 9-21 |
| Number of pages | 13 |
| Journal | Journal of Mathematical Economics |
| Volume | 80 |
| DOIs | |
| Publication status | Published - Jan 1 2019 |
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Keywords
- Chaotic dynamics
- Credit cycle
- Ergodic chaos
- Matsuyama model
- Piecewise linearity
ASJC Scopus subject areas
- Economics and Econometrics
- Applied Mathematics
Cite this
Chaotic dynamics of a piecewise linear model of credit cycles. / Asano, Takao; Yokoo, Masanori.
In: Journal of Mathematical Economics, Vol. 80, 01.01.2019, p. 9-21.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Chaotic dynamics of a piecewise linear model of credit cycles
AU - Asano, Takao
AU - Yokoo, Masanori
PY - 2019/1/1
Y1 - 2019/1/1
N2 - We develop a simple piecewise linear overlapping generations model exhibiting endogenous business cycles, which is based on Matsuyama's (2007) model of credit cycles. Some sort of “noise” representing information imperfection is shown to transform the Matsuyama model into a continuous, eventually expanding, piecewise linear map on the interval, which is tractable enough to investigate the dynamics in depth by using the techniques of the Frobenius–Perron operators to find observable chaos. While, according to the analysis of Asano et al. (2012), the Matsuyama model exhibits periodic cycles of arbitrarily large period, it is essentially not capable of chaotic dynamics. However, our model exhibits ergodic chaos with some robustness.
AB - We develop a simple piecewise linear overlapping generations model exhibiting endogenous business cycles, which is based on Matsuyama's (2007) model of credit cycles. Some sort of “noise” representing information imperfection is shown to transform the Matsuyama model into a continuous, eventually expanding, piecewise linear map on the interval, which is tractable enough to investigate the dynamics in depth by using the techniques of the Frobenius–Perron operators to find observable chaos. While, according to the analysis of Asano et al. (2012), the Matsuyama model exhibits periodic cycles of arbitrarily large period, it is essentially not capable of chaotic dynamics. However, our model exhibits ergodic chaos with some robustness.
KW - Chaotic dynamics
KW - Credit cycle
KW - Ergodic chaos
KW - Matsuyama model
KW - Piecewise linearity
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UR - http://www.scopus.com/inward/citedby.url?scp=85057262484&partnerID=8YFLogxK
U2 - 10.1016/j.jmateco.2018.11.001
DO - 10.1016/j.jmateco.2018.11.001
M3 - Article
AN - SCOPUS:85057262484
VL - 80
SP - 9
EP - 21
JO - Journal of Mathematical Economics
JF - Journal of Mathematical Economics
SN - 0304-4068
ER -