...stabilization. consider

the case where the central bank lacks a commitment technology and the

case of full commitment. We show that for both cases, optimal policy rules

yield rational expectations equilibria that are E-stable for a wide range of

empirically plausible parameter values. These findings stand in contrast to

Evans and Honkapohja's findings for optimal monetary policy rules in environments

where interest rate stabilization is not a central bank objective.

JEL codes: D83, E43, E52

Keywords: learning, E-stability, monetary policy, New Keynesian model.

EVANS AND HONKAPOHJA (2003a, 2003b, 2006) examine the stability, under adaptive learning dynamics, of rational expectations equilibrium (REE) in the standard New Keynesian model of the monetary transmission mechanism (1) when the policy rule of the central bank is optimally derived. (2) Specifically, they suppose that the central bank minimizes a quadratic loss function that penalizes deviations of inflation and output from certain exogenous target values. The result of this minimization problem is an optimal interest rate rule which is used together with equations describing private sector behavior to characterize the equilibrium of the economy.

Evans and Honkapohja (2003a, 2003b, 2006) report that, regardless of whether the central bank operates under commitment or discretion, the REE of the system is always expectationally unstable when the policy rule is derived under the incorrect assumption that the private sector has rational expectations--they call the policy rule in this case the "fundamentals-based" policy rule. While the private sector is assumed to use a correctly specified model to form expectations, it does not initially possess knowledge of the REE parameterization of the model; instead it updates the parameters of its model in real time using all relevant data. However, the central bank's fundamentals-based interest rate policy causes this adaptive learning process to diverge away from the REE, and for this reason, the fundamentals-based policy rule is considered undesirable--it is expectationally unstable. (3) Evans and Honkapohja (2003) find this instability of optimal policy "deeply worrying" and suggest that the central bank might do well to assume that the private sector does not (initially) possess rational expectations. Indeed, Evans and Honkapohja show that if the central bank does not assume rational expectations on the part of the private sector, the resulting, optimally derived, "expectations-based" interest rate rule, which conditions on the private sector's expectations of inflation and output, results in a REE that is always expectationally stable.

In this paper, we consider an alternative approach to optimal monetary policy under learning using the same New Keynesian framework and maintaining the assumption that the private sector does not have rational expectations. We show that it is possible for the central bank to use an optimally derived policy rule that does not condition on private sector expectations and which results in a REE that is stable under adaptive learning dynamics in contrast to the findings of Evans and Honkapohja (2003a, 2003b, 2006). What is needed to obtain our result is for the central bank to expand its loss function to include interest rate stabilization as a third objective, in addition to the traditional twin objectives of inflation and output stabilization. Our result concerning the stability of REE under adaptive learning holds for a wide range of empirically plausible parameter values across all calibrations found in the literature and regardless of whether the central bank operates under discretion or commitment.

There are several advantages to studying optimal policy using a loss function that gives weight to interest rate stabilization. First, as Woodford (2003) shows, if there are transactions frictions of the type that would give rise to a demand for money then an appropriate welfare-theoretic loss function for the central bank is one that includes interest rate stabilization as a third objective in addition to the standard two objectives of inflation and output stabilization. Second, there is substantial empirical evidence that central banks adjust their interest rate targets only gradually over time--consistent with having interest rate stabilization as a goal (see, e.g., Goodhart 1997). Finally, as Giannoni and Woodford (2003) note, the optimal policy rules derived under the three-element loss function resemble the much-studied Taylor instrument rule, while rules derived under the more typical two-element (inflation and output stabilization) objective function do not.

Evans and Honkapohja's proposed resolution to the monetary policy instability problem--conditioning policy on private sector expectations--strikes us as problematic for several reasons. First, operationally speaking, the private sector's expectations may not be observable, or may be heterogeneous; figuring out which expectations to use is a complicated task. Second, as Honkapohja and Mitra (2005) point out, if the central bank is known to be conditioning policy on private sector expectations, the private sector might choose to be strategic about its expectations. Third, in certain environments, conditioning on private sector expectations may increase the likelihood...

NOTE: All illustrations and photos have been removed from this article.



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