A continuum of path-dependent equilibrium solutions induced by sticky expectations

Pavel Krejčí; Eyram Kwame; Harbir Lamba; Dmitrii Rachinskii; Andrei Zagvozdkin

Applications of Mathematics (2023)

  • Volume: 68, Issue: 6, page 751-793
  • ISSN: 0862-7940

Abstract

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We analyze a simple macroeconomic model where rational inflation expectations are replaced by a boundedly rational, and genuinely sticky, response to changes in the actual inflation rate. The stickiness is introduced in a novel way using a mathematical operator that is amenable to rigorous analysis. We prove that, when exogenous noise is absent from the system, the unique equilibrium of the rational expectations model is replaced by an entire line segment of possible equilibria with the one chosen depending, in a deterministic way, upon the previous states of the system. The agents are sufficiently far-removed from the rational expectations paradigm that problems of indeterminacy do not arise.The response to exogenous noise is far more subtle than in a unique equilibrium model. After sufficiently small shocks the system will indeed revert to the same equilibrium but larger ones will move the system to a different one (at the same model parameters). The path to this new equilibrium may be very long with a highly unpredictable endpoint. At certain model parameters exogenously-triggered runaway inflation can occur. Finally, we analyze a variant model in which the same form of sticky response is introduced into the interest rate rule instead.

How to cite

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Krejčí, Pavel, et al. "A continuum of path-dependent equilibrium solutions induced by sticky expectations." Applications of Mathematics 68.6 (2023): 751-793. <http://eudml.org/doc/299588>.

@article{Krejčí2023,
abstract = {We analyze a simple macroeconomic model where rational inflation expectations are replaced by a boundedly rational, and genuinely sticky, response to changes in the actual inflation rate. The stickiness is introduced in a novel way using a mathematical operator that is amenable to rigorous analysis. We prove that, when exogenous noise is absent from the system, the unique equilibrium of the rational expectations model is replaced by an entire line segment of possible equilibria with the one chosen depending, in a deterministic way, upon the previous states of the system. The agents are sufficiently far-removed from the rational expectations paradigm that problems of indeterminacy do not arise.The response to exogenous noise is far more subtle than in a unique equilibrium model. After sufficiently small shocks the system will indeed revert to the same equilibrium but larger ones will move the system to a different one (at the same model parameters). The path to this new equilibrium may be very long with a highly unpredictable endpoint. At certain model parameters exogenously-triggered runaway inflation can occur. Finally, we analyze a variant model in which the same form of sticky response is introduced into the interest rate rule instead.},
author = {Krejčí, Pavel, Kwame, Eyram, Lamba, Harbir, Rachinskii, Dmitrii, Zagvozdkin, Andrei},
journal = {Applications of Mathematics},
keywords = {macroeconomic model; rational expectation; hysteresis play operator; equilibrium point; path-dependence; sticky inflation},
language = {eng},
number = {6},
pages = {751-793},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A continuum of path-dependent equilibrium solutions induced by sticky expectations},
url = {http://eudml.org/doc/299588},
volume = {68},
year = {2023},
}

TY - JOUR
AU - Krejčí, Pavel
AU - Kwame, Eyram
AU - Lamba, Harbir
AU - Rachinskii, Dmitrii
AU - Zagvozdkin, Andrei
TI - A continuum of path-dependent equilibrium solutions induced by sticky expectations
JO - Applications of Mathematics
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 6
SP - 751
EP - 793
AB - We analyze a simple macroeconomic model where rational inflation expectations are replaced by a boundedly rational, and genuinely sticky, response to changes in the actual inflation rate. The stickiness is introduced in a novel way using a mathematical operator that is amenable to rigorous analysis. We prove that, when exogenous noise is absent from the system, the unique equilibrium of the rational expectations model is replaced by an entire line segment of possible equilibria with the one chosen depending, in a deterministic way, upon the previous states of the system. The agents are sufficiently far-removed from the rational expectations paradigm that problems of indeterminacy do not arise.The response to exogenous noise is far more subtle than in a unique equilibrium model. After sufficiently small shocks the system will indeed revert to the same equilibrium but larger ones will move the system to a different one (at the same model parameters). The path to this new equilibrium may be very long with a highly unpredictable endpoint. At certain model parameters exogenously-triggered runaway inflation can occur. Finally, we analyze a variant model in which the same form of sticky response is introduced into the interest rate rule instead.
LA - eng
KW - macroeconomic model; rational expectation; hysteresis play operator; equilibrium point; path-dependence; sticky inflation
UR - http://eudml.org/doc/299588
ER -

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