Risk Matters: Breaking Certainty Equivalence

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 study the extent to which a firstorder approximated solution built by perturbation methods accounts for risk. 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 approximation in continuous time reduces pricing errors by 90 percent relative to the certainty equivalent linear solution.

Resurrecting the New-Keynesian Model: (Un)Conventional Policy and the Taylor Rule

“…First, the effects of risk affect the long-term interest rates and are one potential explanation for changes at the long-end of the yield curve (term premia) similar to changes in the inflation target. This risk channel, however, is negligible in the standard NK model, but can be relevant in models where risk matters quantitatively for asset pricing (see Parra-Alvarez, Polattimur, and Posch, 2018). 29 Second, shifts in monetary policy, or its perception, are important to generate the inflation dynamics and the correlation with interest rates as in the data.…”