Chaotic sets and Euler equation branching

Raines, Brian E.; Stockman, David R.

doi:10.1016/j.jmateco.2010.09.004

Cited by 9 publications

(19 citation statements)

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“…As a consequence, local determinacy of the steady state may co‐exist with various forms of global indeterminacy and chaotic equilibrium paths . Raines and Stockman () and Stockman () illustrate how the existence of Euler equation branching under such circumstances gives rise to topological chaos. In this paper's setting where productive externalities are not strong enough to generate sustained economic growth (see the social production technology ), the model displays a unique steady state.…”

Section: Resultsmentioning

confidence: 99%

“…In this paper's setting where productive externalities are not strong enough to generate sustained economic growth (see the social production technology ), the model displays a unique steady state. Because Euler equation branching does not exist, regime switching sunspot fluctuations like those in Christiano & Harrison (), Raines & Stockman (), and Stockman () will not occur . However, Figures and a of this paper imply that the model economy undergoes a flip/Hopf bifurcation (the steady state turns from a saddle into a sink/source) under a high/low debt‐to‐capital ratio coefficient.…”

Section: Resultsmentioning

confidence: 99%

“…As a consequence, local determinacy of the steady state may co-exist with various forms of global indeterminacy and chaotic equilibrium paths. 20 Raines and Stockman (2010) and Stockman (2010) This paper can be extended in several directions. For example, it would be worthwhile to incorporate multiple production sectors (Meng, 2003;Meng & Velasco, 2004;Weder, 2001), and to consider government expenditure, public debt, and taxes (Huang et al, 2017;Koyunc & Turnovsky, 2016;Morimoto, Hori, Maebayashi & Futagami, 2017; Le Van et al, forthcoming).…”

Section: Discussionmentioning

confidence: 97%

“…Note that Christiano & Harrison () and Raines & Stockman () analyze the endogenous growth model of Benhabib and Farmer (, section ) where a strong productive externality from aggregate capital gives rise to the the emergence of two steady states and Euler equation branching.…”

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confidence: 99%

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International bond risk premia, currency of denomination, and macroeconomic (in)stability

Chen

2018

J Public Economic Theory

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I show that, in real small‐open as well as large‐open economies, international borrowing produces a destabilizing effect that significantly lowers the minimum level of increasing returns to scale needed for indeterminacy. In this case, a sufficiently high debt‐to‐capital ratio coefficient in the borrowing rate schedule operates like an automatic stabilizer that mitigates belief‐driven cyclical fluctuations. The analysis conducted within the monetary setting shows that both the benchmark nominal interest rate and the inflation rate of the country of the denominated currency may lessen the destabilizing effect of international borrowing. When domestic sunspot shocks exert sufficiently strong effects on these two variables, international borrowing may instead stabilize the domestic economy. I also find that inflation indexed bonds remove the stabilizing effect of the inflation rate of the country of the denominated currency and make different types of international bonds under different monetary regimes exhibit qualitatively the same destabilizing effect as real bonds in real economies. In addition, flexible inflation targeting performs no worse than rigid inflation targeting in all cases. Finally, the quantitative analysis undertaken shows that in the past few decades the considerable increase in foreign indebtedness may have destabilized the U.S. economy by giving rise to belief‐driven fluctuations.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 97%

mentioning

confidence: 99%

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International bond risk premia, currency of denomination, and macroeconomic (in)stability

Chen

2018

J Public Economic Theory

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“…In a one-sector growth model with a production externality, Christiano and Harrison (1999) illustrate the possibility of deterministic and stochastic regime switching equilibria along with equilibria that appear chaotic. Raines and Stockman (2007) provide necessary and sufficient conditions for the existence of Euler equation branching in a one-sector model with a production externality. They also provide sufficient conditions for the existence of chaos in models with Euler equation branching and prove that these conditions are almost always satisfied near a steady state equilibrium.…”

Section: Introductionmentioning

confidence: 99%

Chaos and sector-specific externalities

Stockman

2009

Journal of Economic Dynamics and Control

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a b s t r a c t Benhabib and Farmer [1996. Indeterminacy and sector specific externalities. Journal of Monetary Economics 37, 397-419] explore the possibility of local indeterminacy in a two-sector model with sector-specific externalities. They find that very small sectorspecific externalities are sufficient for local indeterminacy. In this case, it is possible to construct sunspot equilibria where extrinsic uncertainty matters. In this paper, I provide a global analysis of their model revealing the existence of Euler equation branching. This branching allows for regime switching equilibria with cycles and chaotic behavior. These equilibria occur whether the ''local dynamics'' are determinate or indeterminate.

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Comparing recursive equilibrium in economies with dynamic complementarities and indeterminacy

Reffett

Woźny

2017

Econ Theory

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Chaotic sets and Euler equation branching

Cited by 9 publications

References 15 publications

International bond risk premia, currency of denomination, and macroeconomic (in)stability

International bond risk premia, currency of denomination, and macroeconomic (in)stability

Chaos and sector-specific externalities

Comparing recursive equilibrium in economies with dynamic complementarities and indeterminacy

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