On growing through cycles: Matsuyama’s M-map and Li–Yorke chaos

Deng, Liuchun; Khan, M. Ali

doi:10.1016/j.jmateco.2017.10.007

“…Finally, at the technical front, one may wonder whether our model harbors additional properties that are beyond the mathematical scope of the present paper. Contributions like Mukherji (2005), Gardini, Sushko, andNaimzada (2008), and Deng and Khan (2018) elicit such properties for the model of Matsuyama (1999). Studies of this kind applied to our model would certainly shed light on the role of the linear segment of our dynamical system for the global dynamics and on the link between the possibility of chaos and the instability of the cycles we identify.…”

Section: Discussionmentioning

confidence: 78%

The supply of hours worked and fluctuations between growth regimes

Iong

¹

,

Irmen

²

2021

Journal of Economic Theory

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Declining hours of work per worker in conjunction with a growing work force may give rise to fluctuations between growth regimes. This is shown in an overlapping generations model with two-period lived individuals endowed with Boppart-Krusell preferences (Boppart and Krusell (2020)). On the supply side, economic growth is due to the expansion of consumption-good varieties through endogenous research. A sufficiently negative equilibrium elasticity of the individual supply of hours worked to an expansion in the set of consumption-good varieties destabilizes the steady state so that equilibrium trajectories may fluctuate between two growth regimes, one with and the other without an active research sector. Fluctuations affect intergenerational welfare, the evolution of GDP, and the functional income distribution. A stabilization policy can shift the economy onto its steady-state path. Fluctuations arise for empirically reasonable parameter constellations. The economics of fluctuations between growth regimes is linked to the intergenerational trade of shares and their pricing in the asset market.

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“…Finally, at the technical front, one may wonder whether our model harbors additional properties that are beyond the mathematical scope of the present paper. Contributions like Mukherji (2005), Gardini, Sushko, and Naimzada (2008), and Deng and Khan (2018) elicit such properties for the model of Matsuyama (1999). Studies of this kind applied to our model would certainly shed light on the role of the linear segment of our dynamical system for the global dynamics and on the link between the possibility of chaos and the instability of the cycles we identify.…”

Section: Discussionmentioning

confidence: 85%

The Supply of Hours Worked and Fluctuations Between Growth Regimes

Iong

¹

,

Irmen

²

2021

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Declining hours of work per worker in conjunction with a growing work force may give rise to fluctuations between growth regimes. This is shown in an overlapping generations model with two-period lived individuals endowed with Boppart-Krusell preferences (Boppart and Krusell (2020)). On the supply side, economic growth is due to the expansion of consumption-good varieties through endogenous research. A sufficiently negative equilibrium elasticity of the individual supply of hours worked to an expansion in the set of consumption-good varieties destabilizes the steady state so that equilibrium trajectories may fluctuate between two growth regimes, one with and the other without an active research sector. Fluctuations affect intergenerational welfare, the evolution of GDP, and the functional income distribution. A stabilization policy can shift the economy onto its steady-state path. Fluctuations arise for empirically reasonable parameter constellations. The economics of fluctuations between growth regimes is linked to the intergenerational trade of shares and their pricing in the asset market.

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“…Recent studies examine conditions under which equilibrium dynamical systems generate paths with periodic fluctuations, as well as paths that converge to a steady state (see [27][28][29]). Several studies consider endogenous growth models with innovation and investigate the range of parameters in which complex periodic fluctuations can occur (see [30][31][32][33][34][35]). In these studies, endogenous cycles can occur by characteristics and constraints in the production sector.…”

Section: Introductionmentioning

confidence: 99%

Business Cycles in a Two-Sided Altruism Model

Fujiu

¹

2021

Mathematics

0

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This study demonstrates that business cycles with complex periodic fluctuations may arise in an overlapping generations model with two-sided altruism. The structure of an equilibrium dynamical system strongly depends on the degree of altruism in the model. If either altruism of a generation to the parent or the child disappears, the study also demonstrates that complex periodic fluctuations never occur. In this sense, two-sided altruism is essential for a complex business cycle.

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On growing through cycles: Matsuyama’s M-map and Li–Yorke chaos

Cited by 9 publications

References 18 publications

The supply of hours worked and fluctuations between growth regimes

The supply of hours worked and fluctuations between growth regimes

The Supply of Hours Worked and Fluctuations Between Growth Regimes

Business Cycles in a Two-Sided Altruism Model

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