The global stability of a class of history-dependent macroeconomic models

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F20%3A00535228" target="_blank" >RIV/67985840:_____/20:00535228 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/68407700:21110/20:00346071

Výsledek na webu

<a href="https://doi.org/10.1051/mmnp/2019061" target="_blank" >https://doi.org/10.1051/mmnp/2019061</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1051/mmnp/2019061" target="_blank" >10.1051/mmnp/2019061</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The global stability of a class of history-dependent macroeconomic models

Popis výsledku v původním jazyce

We consider piecewise-linear, discrete-time, macroeconomic models that have a continuum of feasible equilibrium states. The non-trivial equilibrium set and resulting path-dependence are induced by stickiness in either expectations or the response of the Central Bank. For a low-dimensional variant of the model with one representative agent, and also for a multi-agent model, we show that when exogenous noise is absent from the system the continuum of equilibrium states is the global attractor and each solution trajectory converges exponentially to one of the equilibria. Further, when a uniformly bounded noise is present, or the equilibrium states are destabilized by an imperfect Central Bank policy (or both), we estimate the size of the domain that attracts all the trajectories. The proofs are based on introducing a family of Lyapunov functions and, for the multi-agent model, deriving a formula for the inverse of the Prandtl-Ishlinskii operator acting in the space of discrete-time inputs and outputs.

Název v anglickém jazyce

The global stability of a class of history-dependent macroeconomic models

Popis výsledku anglicky

We consider piecewise-linear, discrete-time, macroeconomic models that have a continuum of feasible equilibrium states. The non-trivial equilibrium set and resulting path-dependence are induced by stickiness in either expectations or the response of the Central Bank. For a low-dimensional variant of the model with one representative agent, and also for a multi-agent model, we show that when exogenous noise is absent from the system the continuum of equilibrium states is the global attractor and each solution trajectory converges exponentially to one of the equilibria. Further, when a uniformly bounded noise is present, or the equilibrium states are destabilized by an imperfect Central Bank policy (or both), we estimate the size of the domain that attracts all the trajectories. The proofs are based on introducing a family of Lyapunov functions and, for the multi-agent model, deriving a formula for the inverse of the Prandtl-Ishlinskii operator acting in the space of discrete-time inputs and outputs.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/EF16_019%2F0000778" target="_blank" >EF16_019/0000778: Centrum pokročilých aplikovaných přírodních věd</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Mathematical Modelling of Natural Phenomena

ISSN

0973-5348

e-ISSN

—

Svazek periodika

15

Číslo periodika v rámci svazku

November

Stát vydavatele periodika

FR - Francouzská republika

Počet stran výsledku

24

Strana od-do

49

Kód UT WoS článku

000593874600001

EID výsledku v databázi Scopus

2-s2.0-85096243750