2,482 research outputs found
Expected Inflation, Sunspots Equilibria and Persistent Unemployment Fluctuations
We propose and estimate a model where unemployment fluctuations result from self-fulfilling changes in expected inflation (sunspot shocks) affecting nominal wage bargaining. Since the estimated parameters fall near the locus of Hopf bifurcations, country-specific expected inflation shocks can replicate the strong persistence and heterogeneity observed in European unemployment rates. They also generate positive comovements in macroeconomic variables and a large relative volatility of consumption. All these features, hardly accounted for by standard sunspot-driven models, are explained here by the fact that liquidity constrained workers, facing earnings uncertainty in the context of imperfect unemployment insurance, choose to consume their current income.unemployment fluctuations, sunspots equilibria, expected inflation, wage bargaining
Bifurcation Dodge: Avoidance of a Thermoacoustic Instability under Transient Operation
Varying one of the governing parameters of a dynamical system may lead to a
critical transition, where the new stable state is undesirable. In some cases,
there is only a limited range of the bifurcation parameter that corresponds to
that unwanted attractor, while the system runs problem-less otherwise. In this
study, we present experimental results regarding a thermoacoustic system
subject to two consecutive and mirrored supercritical Hopf bifurcations: the
system exhibits high amplitude thermoacoustic limit cycles for intermediate
values of the bifurcation parameter. Changing quickly enough the bifurcation
parameter, it was possible to dodge the unwanted limit cycles. A low-order
model of the complex thermoacoustic system was developed, in order to describe
this interesting transient dynamics. It was afterward used to assess the risk
of exceeding an oscillation amplitude threshold as a function of the rate of
change of the bifurcation parameter
Bifurcation Routes to Volatility Clustering under Evolutionary Learning
A simple asset pricing model with two types of adaptively learning traders, fundamentalists and technical analysts, is studied. Fractions of these trader types, which are both boundedly rational, change over time according to evolutionary learning, with technical analysts conditioning their forecasting rule upon deviations from a benchmark fundamental. Volatility clustering arises endogenously in this model. Two mechanisms are proposed as an explanation. The first is coexistence of a stable steady state and a stable limit cycle, which arise as a consequence of a so-called Chenciner bifurcation of the system. The second is intermittency and associated bifurcation routes to strange attractors. Both phenomena are persistent and occur generically. Simple economic intuition why these phenomena arise in nonlinear multi-agent evolutionary systems is provided.
Fiscal policy, increasing returns, and endogenous fluctuations
We examine the quantitative implications of government fiscal policy in a discrete-time one-sector growth model with a productive externality that generates social increasing returns to scale. Starting from a laissez-faire economy that exhibits an indeterminate steady state (a sink), we show that the introduction of a constant capital tax or subsidy can lead to various forms of endogenous fluctuations, including stable 2-, 4-, 8-, and 10- cycles, quasi-periodic orbits, and chaos. In contrast, a constant labor tax or subsidy has no effect on the qualitative nature of the model's dynamics. We also show that the use of local steady-state analysis to detect the presence of multiple equilibria in this class of models can be misleading. For a plausible range of capital tax rates, the log-linearized dynamical system exhibits saddle-point stability (suggesting a unique equilibrium) while the true nonlinear model exhibits global indeterminancy. Finally, we explore the use of a state-contingent capital subsidy/tax scheme for stabilization purposes. We show that a local control policy designed using the log-linearized model can rule out sunspot equilibria near the steady state but may not prevent fluctuations arising from global indeterminacy. We proceed to use the nonlinear model to design a policy that can stabilize the economy against all forms of endogenous fluctuations and select a globally unique equilibrium.Fiscal policy ; Business cycles ; Chaotic behavior in systems
Sequential noise-induced escapes for oscillatory network dynamics
It is well known that the addition of noise in a multistable system can
induce random transitions between stable states. The rate of transition can be
characterised in terms of the noise-free system's dynamics and the added noise:
for potential systems in the presence of asymptotically low noise the
well-known Kramers' escape time gives an expression for the mean escape time.
This paper examines some general properties and examples of transitions between
local steady and oscillatory attractors within networks: the transition rates
at each node may be affected by the dynamics at other nodes. We use first
passage time theory to explain some properties of scalings noted in the
literature for an idealised model of initiation of epileptic seizures in small
systems of coupled bistable systems with both steady and oscillatory
attractors. We focus on the case of sequential escapes where a steady attractor
is only marginally stable but all nodes start in this state. As the nodes
escape to the oscillatory regime, we assume that the transitions back are very
infrequent in comparison. We quantify and characterise the resulting sequences
of noise-induced escapes. For weak enough coupling we show that a master
equation approach gives a good quantitative understanding of sequential
escapes, but for strong coupling this description breaks down
Trapping Phenomenon Attenuates the Consequences of Tipping Points for Limit Cycles
We would like to thank the partial support of this work by the Brazilian agencies FAPESP (processes: 2011/19296-1, 2013/26598-0, and 2015/20407-3), CNPq and CAPES. MSB acknowledges EPSRC Ref. EP/I032606/1.Peer reviewedPublisher PD
A logistic map approach to economic cycles I. The best adapted companies
A birth-death lattice gas model about the influence of an environment on the
fitness and concentration evolution of economic entities is analytically
examined. The model can be mapped onto a high order logistic map. The control
parameter is a (scalar) "business plan". Conditions are searched for growth and
decay processes, stable states, upper and lower bounds, bifurcations, periodic
and chaotic solutions. The evolution equation of the economic population for
the best fitted companies indicates "microscopic conditions" for cycling. The
evolution of a dynamic exponent is shown as a function of the business plan
parameters.Comment: 10 pages, 5 postscript figure
Dynamics of Moving Average Rules in a Continuous-time Financial Market Model
Within a continuous-time framework, this paper proposes a stochastic heterogeneous agent model (HAM) of financial markets with time delays to unify various moving average rules used indiscrete-time HAMs. The time delay represents a memory length of a moving average rule indiscrete-time HAMs.Intuitive conditions for the stability of the fundamental price of the deterministic model in terms of agents' behavior parameters and memory length are obtained. It is found that an increase in memory length not only can destabilize the market price, resulting in oscillatory market price characterized by a Hopf bifurcation, but also can stabilize another wise unstable market price, leading to stability switching as the memory length increases. Numerical simulations show that the stochastic model is able to characterize long deviations of the market price from its fundamental price and excess volatility and generate most of the stylized factso bserved in financial markets.asset price; financial market behavior; heterogeneous beliefs; stochastic delay differential equations; stability; bifurcations; stylized facts
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