Risk matters: Breaking certainty equivalence in linear approximations

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

*Corresponding author for this work

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review


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 languageEnglish
Article number104248
JournalJournal of Economic Dynamics and Control
Number of pages25
Publication statusPublished - Dec 2021


  • Certainty equivalence
  • Perturbation methods
  • Pricing errors


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