عملکرد سیاست پولی با پیش بینی بانک مرکزی داخلی

Recent models of monetary policy have analyzed the desirability of different optimal and ad hoc interest rules under the restrictive assumption that forecasts of the private sector and the central bank are homogeneous. This paper studies the implications of heterogeneity in forecasting by the central bank and private agents for the performance of interest rules in a framework of econometric learning.

The question whether monetary policy should be forward-looking, i.e. based on forecasts of future inflation and other variables, has raised debates in the recent research into monetary policy making. On the one hand, empirical evidence on Germany, Japan and the US since 1979 provided by Clarida et al. (1998) suggests that central banks are forward looking in practice. More general discussions also pose the question whether central banks should focus attention to economic fundamentals or ‘follow the markets’, which ‘sometimes stray far from fundamentals’, see pp. 60–61 of Blinder (1998). Bank of England Inflation Reports (see Bank of England, 2003) discuss private sector forecasts, while the June and December issues of the monthly bulletin of the European Central Bank (see European Central Bank, 2003) present both internal macroeconomic projections and forecasts by other institutions. However, the precise role of these forecasts in the decision making of these central banks is not revealed. On the other hand, theoretical studies have shown that the conduct of optimal monetary policy on the part of the bank can lead to a choice of the instrument, the short-term nominal interest rate, which reacts to the next period forecast of inflation and/or output gap, see Clarida et al. (1999) for a survey of the recent literature. This conclusion can nevertheless be problematic as monetary policy rules, both some formulations of optimal setting of the instrument as well as Taylor rules based on forecasts of inflation and/or output gap, are subject to two potentially important difficulties. First, some interest rate rules lead to indeterminacy of equilibria, see. e.g. Clarida et al. (1999), Bernanke and Woodford (1997), Bullard and Mitra (2002) and Evans and Honkapohja (2003a). Under indeterminacy, the economy has multiple stationary rational expectations equilibria (REE), which can include undesirable outcomes. Second, the problem of instability under learning can also arise depending on the form of the interest rate rule, see Bullard and Mitra (2002) and Evans and Honkapohja (2003a). If the economy is not stable under learning, small displacements of expectations away from rational expectations (RE) will lead to volatility as the economy does not return to the REE when agents try to correct their forecast functions. Both of these problems can be avoided by careful design of monetary policy, i.e. the interest rate rule. In the literature just cited, the forecasts refer to those of the private sector, see e.g. Hall and Mankiw (1994) for a discussion of targeting of private forecasts. By considering both determinacy and stability under learning, Evans and Honkapohja (2003a) forcefully make a case for incorporating private forecasts of inflation and output gap into the interest rate rule as the reaction function of the optimal central bank behavior under discretion.1 Naturally, for such a proposal to make sense it is required that the private sector forecasts are observable. Evans and Honkapohja (2003a) show that small measurement errors would not lead to large deviations from optimality. However, Orphanides (2003) and others have argued that there are large errors in private forecasts. While private forecasts by different institutions are regularly published, it is not self-evident that these published numbers accurately represent the expectations of the private sector that are relevant for the key private economic decisions. Thus, the observability problems might in fact be more serious than they appear at first sight. Moreover, if it becomes known that the decisions of the monetary policy maker depend significantly on the forecasts by private institutions, these institutions might alter their forecasts in a strategic way so as to influence the decisions about the conducted monetary policy, so that the central bank may wish to use internal forecasts in its policy making. The preceding arguments make a case for the use of internal forecasts by the central bank as a proxy for private forecasts in monetary policy decisions. Moreover, it seems likely that internal forecasts, rather than those of other institutions, play the central role in actual monetary policy decisions. The recent literature by Bernanke and Woodford (1997), Svensson, 1997, Svensson, 1999 and Svensson, 2003, and Svensson and Woodford (2003) incorporates internal forecasts by the central bank in models of monetary policy. We will focus on the situation in which both the private sector and the central bank use their own forecasts in their decision-making and the forecasts are not available to the other agent. Consequently, the forecasts have no strategic role. This case can be seen as a natural benchmark. Taking the learning viewpoint, we will argue that heterogeneous forecasting by the private sector and the central bank poses a new stability concern that needs to be taken into account in policy design. The learning approach to modeling expectations formation has gained popularity in the recent literature.2 The economic agents are assumed to use forecast functions that depend on some parameters and, at any moment of time, the economic decisions are made on the basis of expectations/forecasts obtained from these functions. The values of the parameters in the forecast functions and the expectations of the agents are adjusted over time as new data become available. Following much of the literature, we will assume that parameter updating is done using standard econometric methods such as recursive least-squares (RLS) estimation. We see this approach as a natural first formulation, but it can be noted that other approaches to learning could also be considered in this context.3 A key issue of interest is whether this kind of adaptive learning behavior converges to REE over time. If this is the case, the forecast functions of the agents are eventually those associated with the REE. We will analyze the implications of heterogeneity in private sector and central bank forecasts for the performance of forward-looking interest rate rules.4 Our objective is to study how the conditions for learnability of equilibrium, i.e. stability of equilibrium under adaptive learning, are affected by heterogeneities in expectations and learning rules. The model we use is standard in the recent literature on monetary policy conducted with interest rates rules, see the surveys by Clarida et al. (1999) and Woodford (1999). The heterogeneity in expectations and learning can take some different forms even if attention is restricted to econometric learning. The first and simplest possibility is that both private sector and central bank forecast functions have the same parametric form and the updating of these forecast functions is done using the same learning algorithm. (We specifically assume the RLS algorithm that has been widely used in the literature.) Heterogeneity in expectations is then solely due to differences in initial beliefs. The second step we consider relaxes the assumption of identical estimation algorithms. One subcase here is that the updating algorithms are in the same class, but the strength of reaction to forecast errors in parameter updating differs between the private sector and the central bank. Another subcase arises when the algorithms used by the private agents and the policy maker are different. For example, the private sector might use the stochastic gradient (SG) algorithm that is simpler to implement than RLS.5 The analysis of learning dynamics in the context of monetary policies provides a very natural setting in which adaptive learning can take place under structural heterogeneity. We say that a model exhibits structural heterogeneity when different agents respond differently to expectations; compare p. 42 of Evans and Honkapohja (2001). In the model of monetary policy, the private sector expectations influence the economy directly through aggregate demand and the new Phillips curves, while the central bank forecasts enter through the interest rate rule. Our analysis make use of the general theoretical results for forward-looking multivariate linear models with structural heterogeneity derived in the companion paper ( Honkapohja and Mitra, 2003). We will show that the learnability restrictions for interest rate rules under the assumption of homogeneous expectations continue to be important. They are a necessary condition for convergence of adaptive learning with heterogeneous forecasts and learning rules. However, these conditions need not be sufficient for learnability. We look systematically at additional conditions that might lead to stability or instability. Interestingly, these results have natural interpretations as suggestions concerning the forecasting activity of the central bank.

In this paper we have considered the argument that the use of central bank internal forecasts in monetary policy making might be a source of instability of the economy. We studied the consequences of the use of internal forecasts for the stability of the economy by means of the learning approach to expectations formation, in which agents may at least temporarily have non-rational forecast functions that are corrected over time. For the analysis we employed a standard forward-looking model that is currently the workhorse for studies of monetary policy. For modeling adaptive learning we have focused attention of the benchmark case, where agents use standard econometric learning procedures and they perceive the environment as stationary. The limitations of our analysis suggest many possibilities for further research. The model of monetary policy could be enriched and the implications of other types of learning procedures could be studied. Moreover, our benchmark assumptions allowed us to leave out the strategic aspects of expectations formation, which can become important under different informational assumptions. While our results pertain to the specific model and specific ways of learning, they do suggest a general lesson. In these kinds of models the learning behavior of private agents can be a source of instability which needs to be offset by appropriate policy. We have shown that this task is more difficult when policy cannot react directly to private expectations and instead uses internal forecasts as a proxy and additional conditions have to be met to ensure stability of the economy under learning. The paper has looked at both some optimal policies and Taylor rules for some typical cases of heterogeneous learning. Looking at specific policies, the forecast based rule with internal central bank forecasts, recently suggested by Evans and Honkapohja (2003a), performed well more robustly than the other formulations of optimal discretionary policy. However, that policy – as well as learnable Taylor rules – may not be stable under heterogeneous learning for some parameter configurations. Based on our analysis, we can make the following general suggestions for the conduct of good monetary policy on the part of the central bank. First, the interest rate rule should satisfy the Taylor principle. Our analysis supports this suggestion since, with forward-looking rules, the Taylor principle is equivalent to E-stability of the equilibrium and it is always a necessary condition for convergence of the economy under heterogeneous learning. Second, the central bank should take incoming information about the economy seriously and put sufficient weight on these indicators while setting its interest rate rule. This suggestion is supported by our analysis of the differences in the degree of responsiveness when forecast functions are updated (Section 3.1). We emphasize that our focus has been on the use of incoming information in the updating of the internal forecasting. Naturally, there are further aspects of fine tuning in practice, e.g. getting good information on the exogenous shocks, which we have not covered. Observation errors need not affect stability under learning, see Evans and Honkapohja (2003a). The implications of observation errors in the data for learning could be analyzed but this must be left for another occasion. Third, the bank should spend sufficient resources in obtaining large amount of information about the exogenous shocks. This suggestion is supported by results in Section 3.2. It is also supported by our work in progress for cases of asymmetric information. Informal discussions of monetary policy do tend to support these suggestions. Our contribution has been to lend weight to these informal discussions in an analytical treatment of monetary policy. We conclude by re-emphasizing the importance of the learning approach for monetary policy design.