Welfare Consequences of Approximation: The Case of Monetary Policy Analysis

This paper investigates the welfare consequences of linear-quadratic approximation. In a canonical New Keynesian model, the approximation around the deterministic steady state understates the welfare loss associated with price rigidities by 30% compared to the full nonlinear solution. The discrepancy primarily arises from the failure to capture steady-state misallocations induced by agents’ precautionary behavior. Under the full nonlinear solution, the monetary policy response to inflation substantially alleviates welfare losses, implying the potential for a more aggressive monetary policy. The paper also finds that the approximation around the risky steady state, which incorporates precautionary behavior, reduces the approximation error to 3%.