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In the standard new Keynesian framework, an optimizing policy maker does not face a trade-off between stabilizing the inflation rate and stabilizing the gap between actual output and output under flexible prices. An ad hoc, exogenous cost-push shock is typically added to the inflation equation to generate a meaningful policy problem. In this paper, we show that a cost-push shock arises endogenously when a cost channel for monetary policy is introduced into the new Keynesian model. A cost channel is present when firms’ marginal cost depends directly on the nominal rate of interest. Besides providing empirical evidence for a cost channel, we explore its implications for optimal monetary policy. We show that its presence alters the optimal policy problem in important ways. For example, both the output gap and inflation are allowed to fluctuate in response to productivity and demand shocks under optimal monetary policy.

In the standard new Keynesian framework, an optimizing policy maker does not face a trade-off between stabilizing the inflation rate and stabilizing the gap between actual output and output under flexible prices. The result that the optimal policy problem has a trivial solution is widely recognized as a shortcoming of this framework. Clarida et al. (1999) show that the introduction of an ad hoc, exogenous cost-push shock allows the new Keynesian model to generate a meaningful policy problem. In this paper, we show that a cost-push shock arises endogenously in the presence of a cost channel for monetary policy. A cost channel is present when firms’ marginal cost depends directly on the nominal rate of interest. Barth and Ramey (2001) provide evidence based on industry level data for the cost channel, and Christiano et al. (2005) have incorporated a cost channel into an aggregate model estimated using U.S. aggregate data. Besides providing additional empirical evidence for a cost channel of monetary policy, we explore its implications for monetary policy trade-offs, the objectives of monetary policy, and the effects of shocks on the economy under optimal discretionary and commitment policies. We derive the appropriate welfare-based loss function that should be the policy-maker's objective in a cost-channel economy and show it is possible to express the loss function in terms of the gap between output and a measure of potential output that is invariant to assumptions on monetary policy in the flexible-price equilibrium. As a consequence, the optimal policy implications can be directly compared with standard new Keynesian results. As we show, the presence of a cost channel alters these standard policy conclusions in important ways. If a cost channel exists, any shock to the economy—whether a productivity, government spending, or preference shock—generates a trade-off between stabilizing inflation and stabilizing the output gap. In the standard new Keynesian model of Clarida et al. (1999), the optimal response to such shocks guarantees that neither inflation nor the output gap deviate from their flexible-price equilibrium values. In contrast, these shocks lead to inflation and output gap fluctuations under optimal policy (either commitment or discretion) when a cost channel is present. An adverse productivity shock, for example, leads to a fall in the output gap and a rise in inflation under optimal policy. Hence, if we assume the central bank behaves optimally, observing a rise in the inflation rate does not imply that a cost push-shock has hit the economy; an adverse productivity shock would generate the same inflation behavior. Conversely, observing a positive productivity shock coupled with constant inflation would imply that the central bank is not following the optimal policy. We also show that the optimal policy does not fully insulate the output gap and inflation from fiscal shocks. This finding is independent of the presence of the cost channel, and it parallels the results of Khan et al. (2003) and Benigno and Woodford (2004). A common conclusion from many recent analyses of monetary policy is that shocks to the expectational ISIS curve should be neutralized so that they do not affect the output gap. We show that when the objective function is derived as a second order approximation to the representative agent's utility function, neutralizing ISIS shocks arising from fiscal policy is not optimal, because such shocks affect welfare even when the output gap and inflation remain equal to zero. The rest of the paper is organized as follows. In Section 2, the model is set out and the equilibrium under flexible prices and under sticky prices is derived. Section 3 estimates a new Keynesian inflation–adjustment equation and tests for the presence of a cost channel. We find that we cannot reject the hypothesis that a cost channel is present. Hence, in Section 4 we analyze the consequences of the cost channel for optimal policy. We derive a second order approximation to the utility of the representative agent and use this to define optimal policy objectives. Then, we analyze optimal policy under discretion and under commitment and show how previous results are modified when monetary policy operates through the cost channel. Finally, conclusions are contained in Section 5.

In the new Keynesian model that has become a standard framework for investigating monetary policy issues, policy operates on aggregate spending through an interest rate channel. For many purposes, the exact nature of the monetary policy transmission mechanism is unimportant—the critical factors for policy are the objective function of the central bank and the inflation–adjustment mechanism. The details of the channels through which interest rate changes affect spending are only relevant for determining the actual nominal interest rate behavior that is required to achieve the desired time paths of inflation and the output gap. In this paper, we have investigated the implications for optimal policy when monetary policy also affects the economy through a cost channel. If nominal interest rate movements directly affect real marginal cost, as the empirical evidence of Barth and Ramey (2001) and the evidence we reported in Section 3 suggest, then monetary policy directly affects the inflation–adjustment equation. We derived the appropriate welfare-based loss function for the cost channel economy. The flexible-price level of output is not independent of monetary policy as in the standard model—therefore a reference ‘potential output’ for the economy is not uniquely defined. But since welfare can be expressed as a function of the gap between output and the level of output conditional on a constant interest rate policy, the policy-maker's loss can still be written in terms of inflation and a well-defined measure of an output gap. Interest rate changes necessary to stabilize the output gap lead to inflation rate fluctuations when a cost channel is present. As a consequence, the output gap and inflation will fluctuate in response to productivity and demand disturbances even when the central bank is setting policy optimally. A positive productivity shock leads to a fall in inflation and a rise in the output gap under either optimal commitment or optimal discretionary. Thus, a period of above average productivity should also be associated with a rise in output above the flexible-price level (a rise in the output gap) and a decline in inflation. Finally, we also showed that an optimal policy, either under commitment or discretion, does not stabilize the output gap and inflation in the face of fiscal shocks. This result holds regardless of whether a cost channel is present. In earlier analyses, an ad hoc demand shock was often added to the expectational ISIS curve, and optimal policy would always move the interest rate to ensure these shocks did not affect the output gap or inflation. When fiscal shocks alter the share of output available for consumption, stabilizing their impact on the output gap is not an optimal policy. Instead, a positive shock to government spending increases the flexible-price level of output. Under an optimal monetary policy, the output gap and inflation both fall, implying that it is optimal to ensure actual output rises less than the flexible-price level of output.