Shilnikov chaos, low interest rates, and New Keynesian macroeconomics

Barnet, William; Bella, Giovanni; Ghosh, Taniya; Mattana, Paolo; Venturi, Beatrice

doi:10.1016/j.jedc.2021.104291

Cited by 17 publications

(28 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recent results obtained in the field of nonlinear methods of dynamic systems theory allow one to successfully analyze global and local dynamics using analytical procedures. These studies have extensive applications including the analysis of global dynamics in a number of economic models [4,47]. One efficient method for analysis of these models is discovering global attractors by constructing their absorbing sets, and subsequently implementing effective analytical and numerical procedures for investigation bounded sets of initial conditions.…”

Section: Discussionmentioning

confidence: 99%

Dynamics of the Shapovalov mid-size firm model

Alexeeva,

Barnett,

Kuznetsov

et al. 2020

Preprint

Self Cite

View full text Add to dashboard Cite

One of the main tasks in the study of financial and economic processes is forecasting and analysis of the dynamics of these processes. Within this task lie important research questions including how to determine the qualitative properties of the dynamics (stable, unstable, deterministic chaotic, and stochastic process) and how best to estimate quantitative indicators: dimension, entropy, and correlation characteristics.These questions can be studied both empirically and theoretically. In the empirical approach, one considers the real data represented by time series, identifies patterns of their dynamics, and then forecasts short-and long-term behavior of the process. The second approach is based on postulating the laws of dynamics for the process, deriving mathematical dynamic models based on these laws, and conducting subsequent analytical investigation of the dynamics generated by the models.To implement these approaches, both numerical and analytical methods can be used. It should be noted that while numerical methods make it possible to study complex models, the possibility of obtaining reliable results using them is significantly limited due to calculations being performed only over finite-time intervals, numerical integration errors, and the unbounded space of possible initial data sets. In turn, analytical methods allow researchers to overcome these problems and to obtain exact qualitative and quantitative characteristics of the process dynamics. However, their effective applications are often limited to low-dimensional models (in the modern scientific literature on this subject, two-dimensional dynamic systems are the most often studied).In this paper, we develop analytical methods for the study of deterministic dynamic systems based on the Lyapunov stability theory and on chaos theory. These methods make it possible not only to obtain analytical stability criteria and to estimate limiting behavior (localization of self-excited and hidden attractors, study of multistability), but also to overcome the difficulties related to implementing reliable numerical analysis of quantitative indicators (such as Lyapunov exponents and Lyapunov dimension). We demonstrate the effectiveness of the proposed methods using the "mid-size firm" model suggested recently by V.I. Shapovalov as an example.

show abstract

Section: Discussionmentioning

confidence: 99%

Dynamics of the Shapovalov mid-size firm model

Alexeeva,

Barnett,

Kuznetsov

et al. 2020

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…This paper shows that extending (Barnett et al (2020)) policy recommendation valid for continuous time model to discrete-time model, with the number (three) of eigenvalues of the discrete dynamic system inside the unit circle equal to the order of the dynamics of policy maker's state variables, is compatible with discrete-time (Blanchard and Kahn (1980)) determinacy condition when using Ramsey optimal policy instead of simple rules. Ramsey optimal policy determines optimal initial conditions for nonpredetermined inflation and output gap, as soon as the policy maker has a nonzero probability of not reneging his policy commitment.…”

Section: Introductionmentioning

confidence: 87%

“…These discrete-time results differ in several respects to the continuous-time results of Barnett et al (2020). First, the proposed methodology in Barnett et al (2020) to control chaos involves announcing a higher steady-state nominal interest rate and not just the nominal interest rate.…”

Section: Introductionmentioning

confidence: 92%

“…(2) With nonzero public debt, Ramsey optimal policy has the great virtue to eliminate the three simple-rules equilibria and the indeterminacy across them. After the policy advice of Barnett et al (2020) leaning against chaotic dynamics, this is a second argument for negative feedback policies leading to a number of eigenvalues inside the unit circle equal to the order of the dynamics of the policy maker's target variables. A third argument is that these negative feedback policies are also robust to misspecification due to policy maker's imperfect knowledge.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Ramsey Optimal Policy in the New-Keynesian Model With Public Debt

Chatelain

Ralf

2021

Macroecon. Dynam.

View full text Add to dashboard Cite

In the discrete-time new-Keynesian model with public debt, Ramsey optimal policy eliminates the indeterminacy of simple-rules multiple equilibria between the fiscal theory of the price level versus new-Keynesian versus an unpleasant equilibrium. If public debt volatility is taken into account into the loss function, the interest rate responds to public debt besides inflation and output gap. Else, the Taylor rule is identical to Ramsey optimal policy when there is zero public debt. The optimal fiscal-rule parameter implies the local stability of public-debt dynamics (“passive” fiscal policy).

show abstract

“…During the last few years, highly influential authors published a number of significant papers (see, e.g. [41][42][43][44][45][46][47][48][49]). The studies of models with irregular dynamics have received a new impetus and spread into many subfields of economic theory.…”

Section: Introductionmentioning

confidence: 99%

Study of irregular dynamics in an economic model: attractor localization and Lyapunov exponents

Alexeeva,

Kuznetsov,

Mokaev

2021

Preprint

View full text Add to dashboard Cite

Cyclicity and instability inherent in the economy can manifest themselves in irregular fluctuations, including chaotic ones, which significantly reduces the accuracy of forecasting the dynamics of the economic system in the long run. We focus on an approach, associated with the identification of a deterministic endogenous mechanism of irregular fluctuations in the economy. Using of a mid-size firm model as an example, we demonstrate the use of effective analytical and numerical procedures for calculating the quantitative characteristics of its irregular limiting dynamics based on Lyapunov exponents, such as dimension and entropy. We use an analytical approach for localization of a global attractor and study limiting dynamics of the model. We estimate the Lyapunov exponents and get the exact formula for the Lyapunov dimension of the global attractor of this model analytically. With the help of delayed feedback control (DFC), the possibility of transition from irregular limiting dynamics to regular periodic dynamics is shown to solve the problem of reliable forecasting. At the same time, we demonstrate the complexity and ambiguity of applying numerical procedures to calculate the Lyapunov dimension along different trajectories of the global attractor, including unstable periodic orbits (UPOs).

show abstract

Shilnikov chaos, low interest rates, and New Keynesian macroeconomics

Cited by 17 publications

References 26 publications

Dynamics of the Shapovalov mid-size firm model

Dynamics of the Shapovalov mid-size firm model

Ramsey Optimal Policy in the New-Keynesian Model With Public Debt

Study of irregular dynamics in an economic model: attractor localization and Lyapunov exponents

Contact Info

Product

Resources

About