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Risk matters: Breaking certainty equivalence in linear approximations

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  • Parra-Alvarez, Juan Carlos
  • Polattimur, Hamza
  • Posch, Olaf
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.

Suggested Citation

  • Parra-Alvarez, Juan Carlos & Polattimur, Hamza & Posch, Olaf, 2021. "Risk matters: Breaking certainty equivalence in linear approximations," Journal of Economic Dynamics and Control, Elsevier, vol. 133(C).
    • Handle: RePEc:eee:dyncon:v:133:y:2021:i:c:s0165188921001834
    DOI: 10.1016/j.jedc.2021.104248
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    More about this item

    Keywords

    Certainty equivalence; Perturbation methods; Pricing errors;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • E13 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Neoclassical
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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