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Risk matters: Breaking certainty equivalence in linear approximations

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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.

TidsskriftJournal of Economic Dynamics and Control
Antal sider25
StatusUdgivet - dec. 2021

Bibliografisk note

Funding Information:
We thank Serguei Mailiar, Johannes Pfeiffer, Alexander Meyer-Gohde, Martin M. Andreasen, Oskar Arnt Juul, participants of the 23rd International Conference in Computing in Economics and Finance (New York, 2017), the 13th Dynare Conference (Tokyo, 2017), the 11th International Conference on Computational and Financial Econometrics (London, 2017), the 26th Annual SNDE Symposium (Tokyo, 2018), the 23rd Annual LACEA Meeting (Guayaquil, 2018), the 6th International Conference on Economics of the Turkish Economic Association (Antalya, 2018), the 2020 EEA Annual Congress; and seminar participants for their valuable comments and discussions. We are also grateful to the anonymous reviewers for helpful comments.

Funding Information:
We appreciate financial support from the German Research Foundation (DFG, Project No. 268475812).

Publisher Copyright:
© 2021 Elsevier B.V.

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