THE WICKSELLIAN APPROACH

In his 1898 treatise, Knut Wicksell outlined a theory of price-level determination in which a key role was played by the relationship between the money rate of interest and the natural rate of interest.¹

Woodford correctly shows that there is no inconsistency in developing a theory of the general price level in which monetary policy is characterized by control of a nominal interest rate rather than control of the money supply. Beginning with a cashless endowment economy in which money serves only as a unit of account and prices are perfectly flexible, Woodford discusses how a central bank is able to determine the price level through its control over short-term nominal interest rates. Controlling the nominal rate does not require, as Woodford shows, that the central bank control a nominal aggregate whose demand is well defined. The current operating procedures of the Reserve Bank of New Zealand provide a functioning example of a central bank implementing monetary policy through interest rates while maintaining settlement balances constant. With flexible prices, the Fisher equation linking the nominal interest rate to expected inflation together with the central bank's policy rule determine the equilibrium behavior of the price level. When prices are sticky, as in most of Woodford's analysis, equilibrium also requires a specification of the factors that determine the real rate of interest outside the flexible-price equilibrium. In economies in which monetary frictions make money essential, there will be equilibrium paths for the money stock associated with interest rate policies, but Woodford argues that “it does not seem at all natural or useful to try to explain the predicted paths of inflation and output as consequences of the implied path of the money supply” (p. 48).

What is critical, as Woodford emphasizes in virtually every chapter, is the form of the interest rate rule. Rules that specify the setting of the nominal interest rate as a function purely of predetermined and exogenous variables do not ensure a unique, determinate equilibrium, even though, in equilibrium, the nominal rate is a function of such predetermined and exogenous variables. That is, the equilibrium solution for the nominal rate under the optimal policy cannot be used as the central bank's reaction function to implement the optimal policy. Attempting to do so leads to multiple rational expectations equilibria. What is required is a rule that responds to endogenous variables (and in a manner that generally obeys the Taylor principle) in a way that rules out all but the unique, optimal equilibrium.

Although Woodford emphasizes the gap between the nominal rate (the policy instrument) and the natural real rate, a natural question arises. If the purpose is to provide a theory to guide monetary policy, is this interest rate gap a useful quantity for policy makers? The answer depends, and for reasons Woodford himself clearly spells out. For example, in the simple versions of the basic model, the gap between the natural rate and the nominal interest rate is zero under an optimal monetary policy, but this does not mean that central banks should implement policy by moving the nominal rate to track movements in the natural rate. The natural rate of interest depends on all the various shocks that can affect the economy's flexible-price equilibrium level of output, and a policy that simply aims to keep the gap equal to zero leads to indeterminacy. Ensuring a unique, rational expectations equilibrium with zero inflation, for example, requires that the central bank move interest rates sufficiently if inflation should deviate from zero. However, because, in equilibrium, inflation does not deviate from zero, the public's beliefs about policy actions that are off the equilibrium path become critical for supporting the unique equilibrium. So just instructing a central bank to keep the gap equal to zero is not a sufficient description of policy. Still, an historical series on the gap could provide a useful ex-post indicator for evaluating policy, limited, however, by the fact that the flexible-price equilibrium real rate of interest is unobservable.

When the output gap relevant for welfare analysis (and so, an objective of monetary policy) is also the sole driving force for inflation, the interest rate gap provides a sufficient statistic for the impact of monetary policy. The standard new Keynesian model satisfies this requirement: inflation is a function of expected future inflation and real marginal cost, real marginal cost is proportional to the gap between output and the flexible-price equilibrium output, and this output gap is also the correct measure that appears in the second-order approximation to the welfare of the representative agent. However, this is a special case. It fails to hold when the flexible-price equilibrium output is not the welfare-optimal output level, although this case may be less relevant if central bankers view the output dimension of their task, as many actual central banks do, as one of stabilizing output around potential rather than around an optimal level that adjusts for the microeconomic distortions in the economy. More importantly, however, it fails to hold when Woodford adds a cost shock to the inflation equation or when wages (as well as prices) are sticky, cases of considerable relevance for policy design. In these more general cases, there is no presumption that optimal policy would result in a zero interest rate gap. Thus, the focus on the Wicksellian interest rate gap seems somewhat overdone.

THE NATURE OF OPTIMAL RULES

Woodford argues consistently for rule-based monetary policy, but rules of a specific sort. As is well known, in forward-looking models the standard solution to optimal policy under commitment, when the policy decision is taken at an initial time t₀, sets the Lagrangian multipliers associated with past commitments to zero while simultaneously committing never to do so again. That is, there is an inherent time inconsistency in the initial period of the optimal commitment policy. This problem is common; in models of optimal seigniorage, it is efficient to engage in rapid inflation in the first period to tax existing holdings of money, while promising not to do so again.

Woodford argues instead for policy that is optimal from a “timeless perspective,” a perspective that does not privilege period t₀ in any way. Under the timeless perspective, the Lagrangian multipliers associated with earlier commitments must be the same (time-invariant) function of the predetermined and exogenous variables as the current and future multipliers are in the optimal commitment equilibrium. Heuristically, this requires that at time t₀ the central bank implement the policy that it would have found optimal to commit to if it had solved the optimal commitment policy at some earlier date. In doing so, “the central bank is choosing to conform to a rule to which it should have wished to be expected to conform had the question been considered earlier without any restriction of this kind upon conduct at date t₀” (p. 539).

As McCallum and Nelson (2004) stress, economists have, since Lucas (1976), focused on the behavior of economies under alternative policy regimes. That is, the assumption lying behind the standard rational expectations solution is that all agents have been behaving in systematic ways that allow rational expectations to be well defined and a stationary stochastic equilibrium to be obtained. Thus, the notion that the policymaker has been behaving in a manner that remains constant (not that the actions taken each period are the same but rather the decision rules are) is the most natural way to think of a commitment policy.

Less clear is the extent to which Woodford's policy recommendations can provide actual guidance to central banks that find themselves, for one reason or another, in a situation of high inflation and low credibility. There is little analysis of how such a central bank can best move from its current policy to an optimal commitment policy. Policy evaluations are conducted assuming the private sector knows the central bank will honor its future commitments without fully discussing how this comes about. Ultimately, Woodford requires that central banks “just do it.”

The advantage of commitment in forward-looking models comes from the ability of the central bank to affect the public's expectations of future interest rates. However, the difficulty of doing so is illustrated by the Federal Reserve's recent attempts to signal its future intentions. By inserting the language “considerable period” into FOMC press releases during 2003, the Fed was attempting to let private agents know that interest rates would remain low for some time. However, as the Fed attempted in 2004 to modify its language about the future path of interest rates, it discovered that “fine-tuning” expectations is difficult. The central bank in Woodford's model is never faced with such problems. While he does examine the learnability of the rational expectations equilibrium, there is less discussion of the potential short-run costs of adopting the optimal commitment policy. In a sense, the focus is on situations in which a central bank has already achieved low and stable inflation and now is concerned with fine-tuning its optimal rule.

Woodford's analysis deals with situations in which the principle of certainty equivalence applies. Policy rules that are robust to misspecification of the exogenous error processes are considered, but more fundamental and important sources of uncertainty are not dealt with. As Levin and Williams (2003) demonstrate, the optimal policy rules Woodford proposes may produce very bad outcomes if the model on which they are based turns out to be wrong or if the central bank employs parameter estimates that are incorrect. This argues for viewing the approach to policy that Woodford develops as an important starting point for further research that will investigate the manner in which these rules must be modified to address the uncertainty about the economy's structure that policymakers confront in practice.

INTEGRATING THEORY AND POLICY

Perhaps the most important contribution of Woodford's work is his successful integration of monetary policy analysis with welfare economics. Although this has also been done by others [e.g., Friedman (1969)], the earlier literature focused on inflation as a tax, integrating it into the more general Ramsey approach to optimal taxation. This earlier work is important, but it appeared to have little to say about the types of macroeconomic stabilization issues that occupy the attention of most central bankers and many monetary economists.

What Woodford has shown is that maximizing the welfare of the representative agent can also provide a framework for evaluating and designing stabilization policies. And, as he emphasizes, his approach provides strong support for price stability as an outcome of optimal policy. Whether the distortions that are central to this approach (i.e., relative price dispersion generated by nominal rigidities) will ultimately turn out to be those most relevant for the design of stabilization policies remains an open question. Woodford closes his treatise by saying “It is hoped that the present study will help to stimulate further work in this sphere and, in so doing, reveal as a practical possibility the sort of rational management of national standards of value that could only be dreamed of by the monetary reforms of a century ago” (p. 623). His work has already stimulated a great deal of interesting research; whether it will live up to the promise contained in the final sentence remains to be seen. What is already clear, though, is that Interest and Prices is a major contribution to monetary economics.