The Kaldor–Kalecki stochastic model of business cycle

Mircea, Gabriela; ̧u, Mihaela Neamt; Opris, Dumitru

doi:10.15388/na.16.2.14105

Cited by 16 publications

(8 citation statements)

References 11 publications

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“…where (u, pu q ) corresponds to a fixed point (Y,K), and r is an adjustment cost. In our simulation, we use (p,q,r,u) = (0.3,0.2,1.0,3.0) [22]. To evaluate the system behavior under an income bias, weak signal, and noise, we consider b as the bias term ofẎ , a weak sinusoidal signal I ext (t) = Asin2πf S t, and a Gaussian white noise Dξ(t) (< ξ(t) >= 0,< ξ(t),ξ(t ′ ) >= δ tt ′ , < • > indicates average in t) for Eq.…”

Section: The Kaldor Business Cycle Modelmentioning

confidence: 99%

“…(These phenomena, which include coherence resonance, stochastic resonance, and noise-induced transitions, are called noiseinduced phenomena in this study.) Recent studies have examined the effects of additive noise on business cycles based on non-linear economic dynamic theory [21,22]. Especially, Bashkirtseva et al have shown that noise-induced transitions [17] arise in nonlinear economic dynamic models, such as the Kaldor business cycle model and the Goodwin business cycle model, with multiple attractors around the subcritical Hopf bifurcation [23,24].…”

Section: Introductionmentioning

confidence: 99%

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Noise-Induced Phenomena in the Kaldor Business Cycle Model

Nobukawa¹,

Hashimoto

Nishimura

et al. 2017

Transactions of ISCIE

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The periodic behavior of macroeconomic indicators or business cycles is a common observation in the economic system. In the past, business cycle modeling often involved the use of non-linear economic dynamic theory, general equilibrium theory, and methods to analyze complex systems, such as agent-based modeling and complex network theory. Several studies have shown that crisis and synchronization in business cycles can be modeled using threshold characteristics in the economic systems. In a non-linear system, it is well known that additive noise leads to qualitative transformations in system behavior, such as coherence resonance, stochastic resonance, and noise-induced transitions (referred to as noise-induced phenomena in this study). Recent studies have shown that noise-induced transitions arise in the non-linear economic business cycle model with multiple attractors around the sub-critical Hopf bifurcation. However, the relationship between the threshold characteristics in the economic dynamics and noise-induced phenomena has not been studied. In this study, we focus on the threshold characteristic of the Kaldor business cycle model under the bias of income, and show that coherence resonance and stochastic resonance can be produced as an effect of this threshold characteristic.

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Section: The Kaldor Business Cycle Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Noise-Induced Phenomena in the Kaldor Business Cycle Model

Nobukawa¹,

Hashimoto

Nishimura

et al. 2017

Transactions of ISCIE

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“…In the studies [2,3,4,6,8], the mechanisms for generating chaos in systems with asymptotically stable equilibria are provided. In contrast, in [54,55,56,60] unpredictability in the solutions of differential equations was considered a result of random perturbations with small probability. P.A.…”

Section: Introductionmentioning

confidence: 99%

Exogenous Versus Endogenous for Chaotic Business Cycles

Akhmet

Akhmetova²,

Fen³

2016

DNC

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We propose a novel approach to generate chaotic business cycles in a deterministic setting. Rather than producing chaos endogenously, we consider aggregate economic models with limit cycles and equilibriums, subject them to chaotic exogenous shocks and obtain chaotic cyclical motions. Thus, we emphasize that chaotic cycles, which are inevitable in economics, are not only interior properties of economic models, but also can be considered as a result of interaction of several economical systems. This provides a comprehension of chaos (unpredictability, lack of forecasting) and control of chaos as a global economic phenomenon from the deterministic point of view.We suppose that the results of our paper are contribution to the mixed exogenous-endogenous theories of business cycles in classification by P.A. Samuelson [76]. Moreover, they demonstrate that the irregularity of the extended chaos can be structured, and this distinguishes them from the generalized synchronization. The advantage of the knowledge of the structure is that by applying instruments, which already have been developed for deterministic chaos one can control the chaos, emphasizing a parameter or a type of motion. For the globalization of cyclic chaos phenomenon we utilize new mechanisms such that entrainment by chaos, attraction of chaotic cycles by equilibriums and bifurcation of chaotic cycles developed in our earlier papers.

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“…Kaldor type macroeconomic models with shocks have been paid much attention by many authors as well. Mircea et al [18] studied the dynamics depicting the mean and variance of the system. The result suggests that the cyclic fluctuation is inherited by the mean and variance although perfect cyclic dynamics of the system has gone due to the shock.…”

mentioning

confidence: 99%