scholarly journals Business Cycles in a Two-Sided Altruism Model

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2054
Author(s):  
Hiroshi Fujiu
Keyword(s):  
Dynamical System ◽  
Business Cycles ◽  
Business Cycle ◽  
Overlapping Generations ◽  
Overlapping Generations Model ◽  
Periodic Fluctuations

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.

Li-Yorke chaos in models with backward dynamics

2016 ◽  
Vol 20 (5) ◽  
Author(s):  
David R. Stockman
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Overlapping Generations ◽  
Sufficient Conditions ◽  
Economic Models ◽  
Limited Commitment ◽  
Inverse Limits ◽  
Overlapping Generations Model ◽  
Definition Of ◽  
Cash In Advance

AbstractSome economic models like the cash-in-advance model of money, the overlapping generations model and a model of credit with limited commitment may have the property that the dynamical system characterizing equilibria in the model are multi-valued going forward in time, but single-valued going backward in time. Such models or dynamical systems are said to have backward dynamics. In such instances, what does it mean for a dynamical system (set-valued) to be chaotic? Furthermore, under what conditions are such dynamical systems chaotic? In this paper, I provide a definition of chaos that is in the spirit of Li and Yorke for a dynamical system with backward dynamics. I utilize the theory of inverse limits to provide sufficient conditions for such a dynamical system to be Li-Yorke chaotic.

scholarly journals SELF-FULFILLING PROPHECIES AND THE BUSINESS CYCLE

1997 ◽  
Vol 1 (4) ◽  
pp. 740-769 ◽  
Author(s):  
ROGER E.A. FARMER ◽  
MICHAEL WOODFORD
Keyword(s):  
Business Cycle ◽  
Wide Class ◽  
Rational Expectations ◽  
Overlapping Generations ◽  
Phillips Curve ◽  
Signal Extraction ◽  
Overlapping Generations Model ◽  
Sunspot Equilibria ◽  
The Business Cycle ◽  
States Of Nature

We demonstrate that multiple stationary rational-expectations equilibria exist in a version of Lucas's island economy. The existence of these equilibria follows from the fact that there is an indeterminate set of monetary equilibria in the two-period overlapping-generations model. We show how to construct stationary rational-expectations equilibria by randomizing over the set of nonstationary monetary equilibria. In some of our equilibria, a positively sloped Phillips curve exists even though our economy contains no signal-extraction problem as in the original Lucas paper. Our equilibria are indexed by beliefs and are examples of the existence of sunspot equilibria in which allocations may differ across states of nature for which preferences, technology, and endowments are identical. Our technique for constructing stationary sunspot equilibria should prove useful in a wide class of models in which an indeterminate stationary equilibrium exists.

EXPANSIONS AND RECESSIONS IN THE MEXICAN STATES: A CLASSICAL BUSINESS CYCLES APPROACH

2017 ◽  
Vol 3 (5) ◽  
pp. 32
Author(s):  
Pablo Mejía-Reyes
Keyword(s):  
Business Cycles ◽  
Business Cycle ◽  
Monthly Basis ◽  
Production Index ◽  
Clear Cut ◽  
Output Measure ◽  
Central Regions ◽  
The Business Cycle ◽  
National Business ◽  
Cycle Indicator

This paper aims to document expansions and recessions characteristics for 17 states of Mexico over the period 1993-2006 by using a classical business cycle approach. We use the manufacturing production index for each state as the business cycle indicator since it is the only output measure available on a monthly basis. According to this approach, we analyse asymmetries in mean, volatility and duration as well as synchronisation over the business cycle regimes (expansions and recessions) for each case. Our results indicate that recessions are less persistent and more volatile (in general) than expansions in most Mexican states; yet, there is no clear cut evidence on mean asymmetries. In turn, there seems to be strong links between the business cycle regimes within the Northern and Central regions of the country and between states with similar industrialisation patterns, although it is difficult to claim that a national business cycle exists.

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