Comment on "How Forward-Looking is Monetary Policy?"

I have learned a lot from this line of research. My concerns about the current paper stem from my view that some of the results—especially "super-inertia" and the precise form of forward-looking policy—may be too tightly linked to the specifics of the model, the loss function, and the RE solutions implied by them. I will focus my comments on three broad areas:

1. 1. Interest rate smoothing and where the super-inertia comes from.

2. 2. How much improvement can we obtain from super-inertial, forward-looking rules over simple rules?

3. 3. Some empirical results suggest that we should focus our attention on a subclass of the results in the paper. The estimates for this subclass suggest that private agents are very backward looking, with high discount rates.

1. Interest Rate Smoothing: The Interest Rate Term in the Loss Function is Critical

Interest rate smoothing in Giannoni and Woodford (2003, this issue of JMCB) is motivated from a money in the utility function (MIU) specification. As parameterized, rate smoothing has a very large weight—five times that of output—in the welfare function. The weight on the interest rate in the loss function is

(Q1)

where η_i is the interest elasticity of money demand, λ_x is the weight on output in the loss function, υ is the steady-state velocity of money, and ε_mc is the slope of the marginal cost function.

1.1 So How Realistic Is That?

Taken literally, the model implies that the Fed will act to limit the variability of the nominal interest rate—and perhaps act super-inertially—because it worries about consumers' desire to smooth "real currency balances." But how much do household currency holdings actually vary in response to nominal interest rates, particularly for fairly low nominal rates? Even if they respond, are currency balances large enough to matter? In my view, this specification does not provide a strong foundation for interest smoothing. And when the weight on the interest rate in the loss function goes to zero, the model no longer exhibits more super-inertia.

1.2. A Better Foundation for Smoothing?

The interest rate smoothing discussion arose after observing that empirical estimates of policy rules almost always required a lagged interest rate to adequately match the historical path of the funds rate. But of course, this lagged rate can also be interpreted as the outcome of a filtering problem (see Kozicki and Tinsley 2002), in which the central bank does not observe perfect measurements of the state of the economy and must filter the persistent signal from noisy data. A simple filter that could solve such a problem would look like

with geometrically declining weights on lagged inflation and output. (Svensson and Woodford, 2002, work out the filtering case in more detail.) Such a justification for the presence of the lagged interest rate in empirical policy rules would likely have very different implications for optimal policy (how likely would it be that the filtering coefficients would be consistent with ρ > 1, i.e., super-inertial filters?).

2. How Much Better Do Forward-Looking Super-Inertial Rules Perform?

To examine this question, I begin by taking Giannoni and Woodford's partial indexation model of inflation with the parameters calibrated as in Table 1 and use the implicit form of the optimal rule,

Table 1.

Comparison of Discounted Losses, Optimal and Simple Rules

Now it is straightforward to calculate the value of the loss function for different values of γ, ρ(rⁿ), ρ(u), λ_i, and λ_x. I then compare the losses so obtained to the losses for the optimal "simple" policy rules:

where the optimal coefficients are determined from a numerical minimization of Giannoni and Woodford's discounted loss function, and the rest of the model is parameterized as in table 1 of Giannoni and Woodford (2003). Now I compare the discounted losses from the optimal simple rules to the optimal rules (see Table 1).

As the table suggests, the losses under the simple rule differ little from those in the optimal rules. Of course, the...