Business cycle uncertainty and economic welfare revisited

Cho, Cooley, and Kim (RED, 2015) (CCK) consider the welfare effects of removing multiplicative productivity shocks from real business cycle models. In a model that admits an analytical solution they argue convincingly that the positive welfare effect of removing uncertainty can be dominated by a negative mean effect arising from the optimal response of household labor supply. While the presentation of this model is quite elaborate, the details of their subsequent quantitative analysis of several versions of the standard real business cycle model remain vague. We lay out the general procedure of computing second-order accurate approximations of welfare gains or losses in the canonical dynamic stochastic general equilibrium model. In order to be able to consider mean preserving increases in the size of shocks we extend the computation of second-order approximations of the policy functions pioneered by Schmitt-Grohé and Uribe (JEDC, 2004). Our computations show that different from the results reported in CCK the mean effect never dominates the fluctuations effect. Welfare measures computed from weighted residuals methods confirm the logic behind our perturbation approach and verify the accuracy of our estimates.