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In a stylized DSGE model with an energy sector, the optimal policy response to an adverse energy supply shock implies a rise in core inflation, a larger rise in headline inflation, and a decline in wage inflation. The optimal policy is well approximated by policies that stabilize the output gap, but also by a wide array of “dual mandate” policies that are not overly aggressive in stabilizing core inflation. Finally, policies that react to a forecast of headline inflation following a temporary energy shock imply markedly different effects than policies that react to a forecast of core, with the former inducing greater volatility in core inflation and the output gap.

The pronounced divergence between headline and core inflation rates in response to the substantial energy price hikes of the past few years has intensified debate over which inflation measure is the more appropriate focus of policy. Some central banks, such as the Bank of England and European Central Bank, focus on headline inflation both in framing objectives, and as an operational guide to policy; while others appear relatively more concerned with the behavior of core inflation, at least in describing the basis for policy decisions.1 This paper uses a stylized optimization-based DSGE model to assess the implications of alternative monetary policies in response to energy shocks, as well as to compare such policies to the “optimal” policy that maximizes the utility of households. The model economy is formulated to allow a distinction between core and headline inflation, as in recent work by Blanchard and Galí (2007).2 In particular, goods comprising the core basket are produced by monopolistically competitive retailers that set prices in staggered Calvo-style contracts, so that core prices are sticky. By contrast, energy prices are flexible, and determined to equate the sum of household and firm demand to the available supply (a stochastic endowment process). Because wages are sticky, shocks that depress energy supply raise marginal cost even for a policy that keeps output at potential, pushing up both core and headline price inflation; thus, monetary policy faces a stabilization tradeoff. We derive a quadratic approximation to welfare following the seminal analysis of Rotemberg and Woodford (1997). As in the model of Erceg et al. (2000), the deviation of welfare from its Pareto-optimal level depends on the variance of price inflation, wage inflation, and the employment (or output) gap. But corroborating the insight of Goodfriend and King (1997), King and Wolman (1998), and Aoki (2001), it is core price inflation that matters for welfare, since the price of energy is assumed to be completely flexible.3 Welfare also turns out to depend on the price markup, which affects the intratemporal allocation of energy across households and firms. Given that the supply block of our model also parallels Erceg et al. (2000) quite closely, some key prescriptions about optimal policy derived in that setting for technology shocks carry over to energy supply shocks. In particular, in the case of a contractionary supply shock that pushes up the energy price, it is optimal for the required fall in the real wage to occur through a combination of a temporary rise in core inflation, and fall in wage inflation (with headline inflation increasing by more than core). Policies that keep output close to potential turn out to be nearly optimal even though the output gap receives a small weight in the welfare function, reflecting that such policies perform well in achieving the wage and price adjustment that occurs under the optimal policy. Perhaps surprisingly, “dual mandate” objective functions that simply penalize volatility in core inflation and the employment gap also perform remarkably well compared to the welfare-maximizing policy for a wide range of relative weights on these objectives, unless the policymaker only cares about stabilizing inflation. Following the seminal approach of Taylor (1979), this reflects that the variance tradeoff frontier (or “Taylor Curve”) implies that the cost of reducing inflation volatility in terms of employment gap volatility is very high. As a result, even a policymaker with a strong aversion to inflation variation does not find it worthwhile to bear the high cost of reducing inflation volatility, and chooses a policy that keeps employment close to potential. Finally, the performance of simple policy rules that respond to a forecast of either headline or core inflation is examined. This analysis is useful because many central banks describe their policy as aimed at adjusting policy rates so that a forecast of inflation reverts to target over a “medium-term” horizon of roughly two or three years, with most focusing on a forecast of headline inflation. Our model implies that forecasts of headline and core inflation can diverge markedly following a temporary shock to energy supply: as documented in Section 2, Federal Reserve Greenbook forecasts suggest numerous episodes in which such divergence occurred following large but temporary shocks to energy prices. Under such conditions, the particular inflation forecast measure (headline or core) to which the central bank chooses to react can have sizeable macroeconomic implications for the implied response to an energy price shock. Model simulations illustrate how a temporary rise in the energy price induces a much more accommodative policy response under the rule that responds to a headline inflation forecast, as expected headline inflation falls well below core due to predicted mean reversion in the energy price. As a result, a policy of responding to a forecast of headline inflation fuels a much larger rise in core inflation and the output gap than a policy of stabilizing a forecast of core (which more closely resembles the optimal policy). In the presence of uncertainty about the persistence of the shock, focusing on headline inflation may even contribute to greater volatility in realized headline inflation than the alternative of focusing on core. This paper is organized as follows. Section 2 provides some empirical motivation. Section 3 describes the workhorse model, Section 4 the model's log-linearized behavioral equations, and Section 5 the calibration. Section 6 describes the derivation of the welfare function, while Section 7 analyzes optimal policy and various simple rules. Section 8 concludes.

This paper has investigated the performance of alternative monetary rules in response to an energy supply shock, using the optimal rule that maximizes household welfare as the benchmark of comparison. A key finding is that the optimal response to an adverse energy supply shock involves a persistent rise in core and headline inflation. Moreover, under plausible conditions, policies responding to a forecast of headline inflation can induce very different macroeconomic effects than policies responding to a forecast of core inflation. The related finding that the latter type of policies exhibit better stabilization properties seems relevant for both the operational conduct of central banks and their communication strategies. There are some aspects that merit further investigation in subsequent work. In particular, the model assumes that monetary policy can commit to a time invariant rule, and that the central bank's inflation target is both known to private agents and fully credible. While the model implies that core inflation rises in response to higher energy prices under the optimal policy, many central banks perceive that their credibility depends on forestalling “second round” spillovers into core inflation. Accordingly, it would be interesting to examine the robustness of these conclusions to a setting in which monetary policy might not be fully credible, or in which the public may be uncertain about policymaker's objectives.