UK macroeconomic volatility and the welfare costs of inflation

This paper explores the implications of time varying volatility for optimal monetary policy and the measurement of welfare costs. We show how macro-economic models with linear and quadratic state dependence in their variance structure can be used for the analysis of optimal policy within the framework of an optimal linear regulator problem. We use this framework to study optimal monetary policy under inflation conditional volatility and find that the quadratic component of the variance makes policy more responsive to inflation shocks in the same way that an increase in the welfare weight attached to inflation does, while the linear component reduces the steady state rate of inflation. Empirical results for the period 1979-2010 underline the statistical significance of inflation-dependent UK macroeconomic volatility. Analysis of the welfare losses associated with inflation and macroeconomic volatility shows that the conventional homoskedastic model seriously underestimates both the welfare costs of inflation and the potential gains from policy optimization.