0535228 - MÚ 2021 RIV FR eng J - Journal Article
Lamba, H. - Krejčí, Pavel - Rachinskii, D.
The global stability of a class of history-dependent macroeconomic models.
Mathematical Modelling of Natural Phenomena. Roč. 15, November (2020), č. článku 49. ISSN 0973-5348. E-ISSN 1760-6101
Institutional support: RVO:67985840
Keywords : dynamic stochastic general equilibrium model * global stability * multi-agent model * piecewise linear discrete time system
OECD category: Pure mathematics
Impact factor: 4.157, year: 2020
Method of publishing: Open access
https://doi.org/10.1051/mmnp/2019061

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.
Permanent Link: http://hdl.handle.net/11104/0313305