آموزش و بانک مرکزی

It is well known that sunspot equilibria may arise under an interest rate operating procedure in which the central bank varies the nominal rate with movements in future inflation (a forward-looking Taylor rule). This paper demonstrates that these sunspot equilibria may be learnable in the sense of E-stability.

The celebrated Taylor rule (1993) posits that central bank behavior can be described by a fairly simple rule linking nominal rate movements to movements in inflation and output. This seminal paper has spawned a large literature concerned with issues of stability: under what situations can a Taylor-rule formulation of monetary policy create real indeterminacy and thus sunspot1 fluctuations in the model economy? (see for example, Benhabib et al., 2001; Bernanke and Woodford, 1997; Carlstrom and Fuerst 2000a, Carlstrom and Fuerst 2001a and Carlstrom and Fuerst 2001b; Clarida et al. (2000); Kerr and King, 1996). As forcefully argued by Evans and Honkapohja, 2001, sunspot equilibria are compelling only if they are not “fragile” to reasonable assumptions about “learning”. We follow Evans and Honkapohja (2001), and interpret “learning” as E-stability, so that an equilibrium is “fragile” if it is not E-stable. The issue raised in this paper is whether the sunspot equilibria induced by some Taylor rules are E-stable.2,3 A robust result of the papers on indeterminacy is that sunspots are most likely in cases in which the central bank responds to forecasted inflation. We will thus focus on Taylor rules in which the central bank responds to forecasted inflation. Honkapohja and Mitra (2001) analyze the basic monetary model considered here, and conclude that the sunspot equilibria arising from a forward-looking monetary policy are not E-stable.4 They show that the only equilibria that are E-stable are the minimum state vector (msv) solutions where inflation depends only on fundamental shocks. McCallum (2001) concludes from this that only the msv solution is empirically relevant. In this paper, we consider two variants of the analysis in Honkapohja and Mitra (2001) and demonstrate the existence of E-stable sunspot equilibria. Our first modeling variation is a different assumption on the nature of learning. Honkapohja and Mitra (2001) examine a model in which there is symmetric learning by both the public and the central bank. That is, both the central bank and private sector have common expectations. This can be interpreted as the private sector learning, and the central bank operating off of private sector forecasts. In contrast, this paper examines a case in which the forecasts of the central bank and private sector differ, and coincide only in the long run. There are many possible differential learning scenarios. Here we take one extreme: We assume that only the central bank is subject to a learning process, while private sector expectations are always rational. This assumption is analogous to the assumption in Sargent's (1999) analysis of The Conquest of American Inflation. The principle contribution of this paper is to demonstrate that in the case of central bank learning the sunspot equilibria are typically E-stable. If the monetary authority believes in a particular sunspot, rational expectations on the part of the public dictate that they too will believe in that sunspot. In essence, central bank policy can lead the public to believe in sunspots. Our second modeling variation on the Honkapohja and Mitra analysis is a different timing scenario. In Honkapohja and Mitra, money balances at the end of goods market trading are assumed to aid in transactions. Carlstrom and Fuerst (2001a) refer to this as “cash-when-I'm-done” (CWID) timing. But CWID is a peculiar timing convention. In contrast, suppose that cash balances held in advance of goods trading are the balances that aid in transactions, what Carlstrom and Fuerst (2001a) call “cash-in-advance” (CIA) timing. Surprisingly, this paper shows that whether or not sunspots are E-stable depends on this timing convention. Sunspot equilibria are more likely to be learnable with CIA timing. The outline of the paper is as follows. In the next section, we present the basic CWID and CIA monetary models and discuss under what conditions rational expectation sunspot equilibria arise. We also outline why sunspots are not likely to be learnable with symmetric learning on the part of the public and the central bank. In Section 3, we demonstrate that sunspots are typically learnable when there is asymmetric learning and it is the central bank doing the learning. We also briefly discuss the implications of different types of asymmetric learning. Section 4 concludes

There are several natural areas of further work. First, the Taylor rule examined depended only on expected inflation. Future work will consider the case of including a measure of future output in the policy rule. Second, the sunspot equilibria arise because of the endogeneity of the supporting money supply process. What features of this money supply behavior lead to E-stability? Finally, work by Carlstrom and Fuerst 2000a and Carlstrom and Fuerst 2001b suggests that sunspot equilibria are much more likely when investment spending is added to the model. Are any of these sunspot equilibria E-stable? We leave these issues for future work. This paper has shown that the developing consensus that policy-induced sunspots are not learnable may be premature. Sunspots are typically learnable if the central bank is the one doing the learning. Central bank learning is likely to arise under any forecast-based Taylor rule. A common criticism of sunspot equilibria is the coordination issue: how do agents choose which sunspot variables to coordinate upon? In the present context, there is a dominant actor and thus a natural choice: the central bank. If the monetary authority believes in a particular sunspot, rational expectations on the part of the public dictates that they too will believe in that sunspot. The central bank can lead us to real indeterminacy.