## Oil Shocks and Optimal Monetary PolicyBank for International Settlements, Monetary and Economic Department, 2010 - Monetary policy - 39 pages In practice, central banks have been confronted with a trade-off between stabilising inflation and output when dealing with rising oil prices. This contrasts with the result in the standard New Keynesian model that ensuring complete price stability is the optimal thing to do, even when an oil shock leads to large output drops. To reconcile this apparent contradiction, this paper investigates how monetary policy should react to oil shocks in a microfounded model with staggered price-setting and with oil as an input in a CES production function. In particular, we extend Benigno and Woodford (2005) to obtain a second order approximation to the expected utility of the representative household when the steady state is distorted and the economy is hit by oil price shocks. The main result is that oil price shocks generate an endogenous trade-off between inflation and output stabilisation when oil has low substitutability in production. Therefore, it becomes optimal for the monetary authority to stabilise partially the effects of oil shocks on inflation and some inflation is desirable. We also find, in contrast to Benigno and Woodford (2005), that this trade-off is reduced, but not eliminated, when we get rid of the effects of monopolistic distortions in the steady state. Moreover, the size of the endogenous "cost-push" shock generated by fluctuations in the oil price increases when oil is more difficult to substitute by other factors. |

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aggregate auxiliary variables Benigno and Woodford Cobb-Douglas coefficients cost-push shock costs in steady deﬁned deﬁnition distortions in steady economy effects of oil elasticity of substitution eliminating the distortions equation equilibrium ﬁgure ﬁnd ﬁrm ﬁrst order conditions ﬁt ﬂexible implies impulse response increases inﬂation and output inﬂation stabilisation input Keynesian model labour market Lagrange multiplier level of output linear linear-quadratic loss function lower marginal productivity marginal rate maximise monopolistic competition natural level nominal interest rate oil on total oil price shock oil shocks optimal monetary policy optimal non-inertial plan optimal unconstrained plan output ﬂuctuations Phillips curve policy problem price dispersion measure price level production function productivity of labour proposition quadratic rate of substitution real marginal costs real oil price real wage Replace second order approximation second order Taylor share of oil stabilising inﬂation standard New Keynesian target level Taylor expansion trade-off between stabilising utility function welfare losses welfare-relevant output gap zero