Welfare Consequences of Approximation Methods in a Nonlinear Model

Abstract

This paper investigates the welfare consequences of approximation methods conventionally used in business cycle analysis: the log-linear approximation of model dynamics and the second-order approximation of social welfare. In a canonical sticky-price business cycle model, the approximation around the deterministic steady state substantially understates the welfare losses associated with price rigidities as it fails to capture the misallocations in a steady state induced by precautionary behavior. Instead, the approximation around the risky steady state, which takes the precautionary behavior into account, delivers much smaller approximation errors. Implications to the optimal monetary policy and those in extended models are explored.