Title: Risk matters: Breaking certainty equivalence
Authors: Juan Carlos Parra-Alvarez - Aarhus University (Denmark) [presenting]
Olaf Posch - Hamburg University (Germany)
Hamza Polattimur - Hamburg University (Germany)
Abstract: The aim is to compare the effects of uncertainty in the solution to an otherwise standard neoclassical macroeconomic model subject to technology shocks for different degrees of approximation. Our results show that certainty equivalence breaks in a continuous time version of the model even to a first order approximation, in contrast to its discrete-time version. We compare both local and global numerical methods to compute the rational expectation equilibrium dynamics and impulse response functions. We show how perturbation and collocation methods based on the Hamilton Jacobi Bellman (HJB) equation can be used to compute the models equilibrium in the space of states, fully accounting for the effects of nonlinearities and uncertainty. We also show how a first order approximation is able to capture the effects of uncertainty if risk matters. We further illustrate our results in a model known to generate substantial risk premia: the capital adjustment cost and habit formation model.