Risk matters: Breaking certainty equivalence in linear approximations

Juan Carlos Parra-Alvarez; Hamza Polattimur; Olaf Posch

doi:10.1016/j.jedc.2021.104248

Risk matters: Breaking certainty equivalence in linear approximations

Juan Carlos Parra-Alvarez^*, Hamza Polattimur, Olaf Posch

^*Corresponding author for this work

Department of Economics and Business Economics - CREATES

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

Abstract

In this paper we use the property that certainty equivalence, as implied by a first-order approximation to the solution of stochastic discrete-time models, breaks in its equivalent continuous-time version. We derive a risk-sensitive first-order perturbation solution for a general class of rational expectations models. We show that risk matters economically in a real business cycle (RBC) model with habit formation and capital adjustment costs, and that neglecting risk leads to substantial pricing errors. A first-order perturbation provides a sensible approximation to the effects of risk in continuous-time models. It reduces pricing errors by around 90% relative to the certainty equivalent linear approximation.

Original language	English
Article number	104248
Journal	Journal of Economic Dynamics and Control
Volume	133
Number of pages	25
ISSN	0165-1889
DOIs	https://doi.org/10.1016/j.jedc.2021.104248
Publication status	Published - Dec 2021

Keywords

Certainty equivalence
Perturbation methods
Pricing errors

Access to Document

10.1016/j.jedc.2021.104248

Cite this

@article{89f45e86006145788e656bfd39c1c1b8,

title = "Risk matters: Breaking certainty equivalence in linear approximations",

abstract = "In this paper we use the property that certainty equivalence, as implied by a first-order approximation to the solution of stochastic discrete-time models, breaks in its equivalent continuous-time version. We derive a risk-sensitive first-order perturbation solution for a general class of rational expectations models. We show that risk matters economically in a real business cycle (RBC) model with habit formation and capital adjustment costs, and that neglecting risk leads to substantial pricing errors. A first-order perturbation provides a sensible approximation to the effects of risk in continuous-time models. It reduces pricing errors by around 90% relative to the certainty equivalent linear approximation.",

keywords = "Certainty equivalence, Perturbation methods, Pricing errors",

author = "Parra-Alvarez, {Juan Carlos} and Hamza Polattimur and Olaf Posch",

note = "Publisher Copyright: {\textcopyright} 2021 Elsevier B.V.",

year = "2021",

month = dec,

doi = "10.1016/j.jedc.2021.104248",

language = "English",

volume = "133",

journal = "Journal of Economic Dynamics and Control",

issn = "0165-1889",

publisher = "Elsevier BV",

}

TY - JOUR

T1 - Risk matters

T2 - Breaking certainty equivalence in linear approximations

AU - Parra-Alvarez, Juan Carlos

AU - Polattimur, Hamza

AU - Posch, Olaf

PY - 2021/12

Y1 - 2021/12

N2 - In this paper we use the property that certainty equivalence, as implied by a first-order approximation to the solution of stochastic discrete-time models, breaks in its equivalent continuous-time version. We derive a risk-sensitive first-order perturbation solution for a general class of rational expectations models. We show that risk matters economically in a real business cycle (RBC) model with habit formation and capital adjustment costs, and that neglecting risk leads to substantial pricing errors. A first-order perturbation provides a sensible approximation to the effects of risk in continuous-time models. It reduces pricing errors by around 90% relative to the certainty equivalent linear approximation.

AB - In this paper we use the property that certainty equivalence, as implied by a first-order approximation to the solution of stochastic discrete-time models, breaks in its equivalent continuous-time version. We derive a risk-sensitive first-order perturbation solution for a general class of rational expectations models. We show that risk matters economically in a real business cycle (RBC) model with habit formation and capital adjustment costs, and that neglecting risk leads to substantial pricing errors. A first-order perturbation provides a sensible approximation to the effects of risk in continuous-time models. It reduces pricing errors by around 90% relative to the certainty equivalent linear approximation.

KW - Certainty equivalence

KW - Perturbation methods

KW - Pricing errors

UR - http://www.scopus.com/inward/record.url?scp=85118864267&partnerID=8YFLogxK

U2 - 10.1016/j.jedc.2021.104248

DO - 10.1016/j.jedc.2021.104248

M3 - Journal article

AN - SCOPUS:85118864267

SN - 0165-1889

VL - 133

JO - Journal of Economic Dynamics and Control

JF - Journal of Economic Dynamics and Control

M1 - 104248

ER -

Risk matters: Breaking certainty equivalence in linear approximations

Abstract

Keywords

Access to Document

Other files and links

Cite this