In this paper we establish a link between the volatility of oil price shocks and a positive expected value of inflation in equilibrium (inflation premium). In doing so, we implement the perturbation method to solve up to second order a benchmark New Keynesian model with oil price shocks. In contrast with log linear approximations, the second order solution relaxes certainty equivalence providing a link between the volatility of shocks and inflation premium. First, we obtain analytical results for the determinants of the level of inflation premium. Thus, we find that the degree of convexity of both the marginal cost and the phillips curve is a key element in accounting for the existence of a positive inflation premium. We further show that the level of inflation premium might be potentially large even when a central bank implements an active monetary policy. Second, we evaluate numerically the second order solution of the model to explain the episode of high and persistent inflation observed in the US during the 70's. We find, in contrast with Clarida, Gali and Gertler (QJE, 2000), that even when there is no difference in the monetary policy rules between the pre-Volcker and post-Volcker periods, oil price shocks can generate high inflation levels during the 70's through a positive high level of inflation premium. As by product, our analysis shows that oil price shocks along with a distorted steady state can generate a time-varying endogenous trade-off between inflation and deviations of output from its efficient level. The previous trade-off, once uncertainty is taking into account, implies that a positive level of inflation premium is an optimal response to oil price shocks
