Stable near-rational sunspot equilibria

George W. Evans; Bruce McGough

doi:10.1016/j.jet.2019.104987

Stable near-rational sunspot equilibria

Research output: Contribution to journal › Article › peer-review

Abstract

We introduce a new class of solutions to nonlinear forward-looking models called near-rational sunspot equilibria (NRSE). NRSE are natural nonlinear extensions of the usual sunspot equilibria associated with the linearized version of the economy, and are near-rational in that agents use the optimal linear forecasting model when forming expectations. Generic results for existence and stability under learning are established. NRSE in indeterminate nonlinear models are found to be stable under learning provided that the corresponding linearized model's minimal state variable solution is E-stable. NRSE are readily computable, and our results make it possible to use the standard linear tools to search for stable NRSE. We illustrate our results using a canonical nonlinear New Keynesian model.

Original language	English
Article number	104987
Number of pages	33
Journal	Journal of Economic Theory
Volume	186
Early online date	10 Jan 2020
DOIs	https://doi.org/10.1016/j.jet.2019.104987
Publication status	Published - Mar 2020

Keywords

E-stability
Sunspot equilibria
Nonlinear dynamics
Indeterminacy
MSV principle

Access to Document

10.1016/j.jet.2019.104987

Evans_2019_JET_Stable_AAM
Copyright © 2019 Published by Elsevier Inc. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1016/j.jet.2019.104987
Accepted author manuscript, 0.98 MBLicence: CC BY-NC-ND

George W Evans
- ge21st-andrews.acuk
- Economics (Business School) - Professor
Person: Academic

Cite this

@article{22ba765750d342fd96cc713ba6449895,

title = "Stable near-rational sunspot equilibria",

abstract = "We introduce a new class of solutions to nonlinear forward-looking models called near-rational sunspot equilibria (NRSE). NRSE are natural nonlinear extensions of the usual sunspot equilibria associated with the linearized version of the economy, and are near-rational in that agents use the optimal linear forecasting model when forming expectations. Generic results for existence and stability under learning are established. NRSE in indeterminate nonlinear models are found to be stable under learning provided that the corresponding linearized model's minimal state variable solution is E-stable. NRSE are readily computable, and our results make it possible to use the standard linear tools to search for stable NRSE. We illustrate our results using a canonical nonlinear New Keynesian model.",

keywords = "E-stability, Sunspot equilibria, Nonlinear dynamics, Indeterminacy, MSV principle",

author = "Evans, {George W.} and Bruce McGough",

note = "Financial support from National Science Foundation Grant No. SES-1559209 is gratefully acknowledged.",

year = "2020",

month = mar,

doi = "10.1016/j.jet.2019.104987",

language = "English",

volume = "186",

journal = "Journal of Economic Theory",

issn = "0022-0531",

publisher = "Academic Press/Elsevier ",

}

TY - JOUR

T1 - Stable near-rational sunspot equilibria

AU - Evans, George W.

AU - McGough, Bruce

N1 - Financial support from National Science Foundation Grant No. SES-1559209 is gratefully acknowledged.

PY - 2020/3

Y1 - 2020/3

N2 - We introduce a new class of solutions to nonlinear forward-looking models called near-rational sunspot equilibria (NRSE). NRSE are natural nonlinear extensions of the usual sunspot equilibria associated with the linearized version of the economy, and are near-rational in that agents use the optimal linear forecasting model when forming expectations. Generic results for existence and stability under learning are established. NRSE in indeterminate nonlinear models are found to be stable under learning provided that the corresponding linearized model's minimal state variable solution is E-stable. NRSE are readily computable, and our results make it possible to use the standard linear tools to search for stable NRSE. We illustrate our results using a canonical nonlinear New Keynesian model.

AB - We introduce a new class of solutions to nonlinear forward-looking models called near-rational sunspot equilibria (NRSE). NRSE are natural nonlinear extensions of the usual sunspot equilibria associated with the linearized version of the economy, and are near-rational in that agents use the optimal linear forecasting model when forming expectations. Generic results for existence and stability under learning are established. NRSE in indeterminate nonlinear models are found to be stable under learning provided that the corresponding linearized model's minimal state variable solution is E-stable. NRSE are readily computable, and our results make it possible to use the standard linear tools to search for stable NRSE. We illustrate our results using a canonical nonlinear New Keynesian model.

KW - E-stability

KW - Sunspot equilibria

KW - Nonlinear dynamics

KW - Indeterminacy

KW - MSV principle

U2 - 10.1016/j.jet.2019.104987

DO - 10.1016/j.jet.2019.104987

M3 - Article

SN - 0022-0531

VL - 186

JO - Journal of Economic Theory

JF - Journal of Economic Theory

M1 - 104987

ER -

Stable near-rational sunspot equilibria

Abstract

Keywords

Access to Document

Fingerprint

Profiles

George W Evans

Cite this