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1. This paper addresses several issues relating to the choice between different types of inflation targeting frameworks, with particular interest in evaluating key features of the Bank of England’s framework and experience. A question arising from the experience is whether or not interest rates in the United Kingdom have been “too variable” in recent years. A central issue relating to specific features of the United Kingdom concerns the merits of basing policy decisions on a constant-interest-rate forecast of inflation, as opposed to either a Taylor rule or a model-consistent forecast. A third issue is whether macroeconomic performance would be significantly improved if central banks published their policy models to enhance the transparency of the policy framework. Efforts to develop a better understanding of these issues are becoming increasingly relevant to the Fund’s policy advice as more countries begin to rely on inflation targets to provide a nominal anchor.

Abstract

1. This paper addresses several issues relating to the choice between different types of inflation targeting frameworks, with particular interest in evaluating key features of the Bank of England’s framework and experience. A question arising from the experience is whether or not interest rates in the United Kingdom have been “too variable” in recent years. A central issue relating to specific features of the United Kingdom concerns the merits of basing policy decisions on a constant-interest-rate forecast of inflation, as opposed to either a Taylor rule or a model-consistent forecast. A third issue is whether macroeconomic performance would be significantly improved if central banks published their policy models to enhance the transparency of the policy framework. Efforts to develop a better understanding of these issues are becoming increasingly relevant to the Fund’s policy advice as more countries begin to rely on inflation targets to provide a nominal anchor.

I. Issues Relating to Inflation Targeting and the Bank of England’s Framework1

A. Introduction

1. This paper addresses several issues relating to the choice between different types of inflation targeting frameworks, with particular interest in evaluating key features of the Bank of England’s framework and experience. A question arising from the experience is whether or not interest rates in the United Kingdom have been “too variable” in recent years. A central issue relating to specific features of the United Kingdom concerns the merits of basing policy decisions on a constant-interest-rate forecast of inflation, as opposed to either a Taylor rule or a model-consistent forecast. A third issue is whether macroeconomic performance would be significantly improved if central banks published their policy models to enhance the transparency of the policy framework. Efforts to develop a better understanding of these issues are becoming increasingly relevant to the Fund’s policy advice as more countries begin to rely on inflation targets to provide a nominal anchor.

2. Proponents of inflation targeting strategies perceive the advantages to include “more transparent and coherent policymaking, increased accountability, and greater attention to long-run considerations in day-to-day policy debates and decisions.”2 Several of the countries that are pursuing such strategies have taken the approach of targeting an inflation forecast, motivated by the fact that changes in monetary policy are only capable of influencing inflation with a lag. The Bank of England’s approach is widely regarded as a successful example of inflation-forecast targeting and a role model in transparency.

3. Yet several aspects of the recent U.K. experience and the prevailing policy framework have raised questions. Comparison of the U.K. experience with that in the United States during recent years has provoked the question of whether interest rates in the United Kingdom have been “too variable.” And comparison of the policy framework with that of New Zealand, also regarded as having designed a successful approach to inflation-forecast targeting, points to major differences between the two policy frameworks that warrant evaluation.

4. Analysis of these issues requires a formal model of macroeconomic behavior along with a formal description of monetary policy reactions to macroeconomic variables. This paper attempts to present the analysis in a non-technical way, discussing the main features of the model and the sensitivity of the analysis to key assumptions about macroeconomic behavior, and relegating the technical description of the model and simulation analysis to an Appendix. Section B provides perspectives on alternative forms and calibrations of monetary policy reaction functions. Section C briefly describes and contrasts the monetary policy frameworks of the Bank of England (BoE) and the Reserve Bank of New Zealand (RBNZ). Sections D-F then address the three main issues: Have U.K. interest rates been too variable? How does macroeconomic performance under a “Constant-Interest-Rate” (CIR) rule compare with performance under a Generalized Taylor (GT) rule or an Inflation-Forecast-Based (IFB) rule? Can significant benefits potentially be achieved from greater transparency about monetary policy?

5. The analysis in Sections D-F is developed with several variants of a small linear model of macroeconomic behavior and abstracts, inter alia, from uncertainty about the level of potential output or the non-accelerating-inflation rate of unemployment (NAIRU). Section G adds additional important perspectives on the dangers of particular types of policy rules in a nonlinear world with a NAIRU that is difficult to estimate precisely and appears to shift over time. Section H provides an example of how uncertainty about exchange rate models can be studied to provide some guidance about what model may be more appropriate for minimizing potential policy errors. Section I provides some concluding remarks.

B. Perspectives on Monetary Policy Rules

6. Countries have defined formal inflation targets in a number of different ways, most of which leave monetary policymakers with scope to react to output or unemployment gaps as well as to deviations from target of either the current rate of inflation or an inflation forecast. The analysis of how countries should implement inflation targeting strategies and explain their policy decisions to the public has focused on different forms of monetary policy rules or reaction functions. Central bankers and academic economists are well aware that it would be dangerous to adhere rigidly to any mechanical policy rule, and many describe the practice of inflation targeting as essentially involving “constrained discretion.”3 At the same time, policymakers have found that quantitative frameworks can be very important in helping them structure their thinking,4 and monetary policy rules play a central role as benchmarks or guidelines that make those quantitative frameworks internally consistent. Moreover, insofar as macroeconomic behavior depends importantly on the expectations of market participants, monetary policy that is consistent over time and guided by a well-chosen policy rule can have a significant influence on expectations that helps to stabilize the economy.

7. One widely discussed form of reaction function is the Taylor rule, under which the central bank would adjust its official short-term interest rate in response to the most-recently reported data on inflation and output (or unemployment).5 Simulation studies have demonstrated that within the confines of linear macroeconomic models, generalized Taylor rules that reflect an appropriate degree of “interest rate smoothing”—i.e., that adjust interest rates only gradually to changes in economic conditions—are remarkably successful in delivering a relatively low variance of inflation around the target rate. As elaborated below, however, because Taylor rules are essentially backward looking, they have been found to perform quite poorly in nonlinear models with forward-looking expectations.6

8. The class of rules used by the BoE and RBNZ has been referred to as inflation-forecast-based (IFB) rules.7 Under these rules, the policy interest rate setting depends on how much an inflation forecast deviates from target, and often depends on the output gap as well. Widely-cited empirical studies suggest that such rules provide reasonably accurate descriptions of monetary policy behavior in the United States, Japan, and Germany in the period since 1979.8 In macroeconomic models with relatively simple specification forms, such reaction functions for the policy instrument can be formally derived as (approximations to) conditions that are necessary for minimizing the variance of the inflation forecast around the inflation target.9

9. Although the policy frameworks employed by the BoE and RBNZ can each be described as analogous to relying on an IFB rule as a guideline, the two central banks have used substantially different types of IFB rules in elaborating and presenting their forecasts. The BoE Inflation Reports have featured inflation forecasts that assume an unchanged policy rate over a two-year horizon, with the forecasts showing 8-quarter-ahead inflation to be at or very near the target rate. By contrast, the approach followed by the RBNZ calculates and announces to the public an unconstrained time path for the policy interest rate that is projected to gradually equilibrate the inflation forecast with the target inflation rate. The particular time path announced by the RBNZ is chosen to be model-consistent in the sense that the model includes a well-calibrated unconstrained IMF rule for the policy interest rate and generates the interest rate forecast endogenously.

10. It should be noted that what is here referred to as a “rule” is referred to by the BoE as an “assumption.” It clearly functions as such in the elaboration of the forecast. Moreover, it is viewed as an assumption that has the added virtue of precluding the need to either agree on a rule or to “reveal one’s hand” about the likely future course of interest rates. Irrespective of whether it is viewed as an assumption or as a rule, however, the convention has implications for the elaboration of the forecasts that are at odds with the objectives of a forward-looking inflation targeting approach. This is the main focus of this paper, where the issue is cast in terms of the vocabulary of the literature on this subject, namely as a “rule”-the Constant-Interest-Rate (or CIR) rule. For the purpose of studying the consequences of following a CIR rule it is assumed that the CIR rule implies that the monetary authorities would adjust the level of the policy rate sufficiently each quarter to completely eliminate the gap between inflation and the target in the eigth quarter of the inflation forecast.

11. While several of the issues addressed below relate to the form of the monetary policy reaction function, the question of whether U.K. interest rates have been too variable primarily relates to the strength of monetary policy reactions, including in particular the degree of interest rate smoothing. As will be elaborated in Section D, under either a Generalized Taylor (GT) rule or an IFB rule, the optimal calibration of the reaction coefficients—including the optimal degree of interest rate smoothing—can depend importantly on both the nature of the relationship that links aggregate demand to interest rates and the degree of openness of the economy. Thus, the fact that interest rates have been much less variable in the United States than in the United Kingdom does not necessarily imply that U.K. interest rates have been “too variable.”

C. Inflation Forecast Targeting at the Bank of England and the Reserve Bank of New Zealand

General Background

12. The United Kingdom adopted a strategy of inflation targeting in October 1992, shortly after the summer exchange market crisis led to its withdrawal from the Exchange Rate Mechanism of the European Monetary System. The present framework for inflation-forecast targeting was established in May 1997, when responsibility for making interest rate decisions was transferred from the Chancellor of the Exchequer to the Monetary Policy Committee (MPC) of the Bank of England.10 The goals of monetary policy are now spelled out by statute; the primary objective that the MPC must pursue is price stability, as defined by the 2½ percent target for inflation. In practice, the MPC defines its objective as aiming to keep its two-year-ahead forecast for inflation on target. The target is symmetric; the MPC is expected to respond just as vigorously to prospective undershoots of the target as to prospective overshoots. Transparency and accountability are regarded as central to the system. Minutes of the monthly MPC meetings are now published within two weeks of each meeting and the BoE also publishes a quarterly Inflation Report that describes the MPC’s analysis of the U.K. economy and explains the factors underlying its policy decisions. If inflation deviates from target by more than 1 percentage point, the Governor of the Bank, as Chairman of the MPC, is required to write an open letter to the Chancellor explaining why and indicating what is being done to rectify the situation.

13. As indicated by Figure 1, long-term inflation expectations in the United Kingdom, based on comparisons of the yields on indexed and non-indexed bonds, dropped markedly following the introduction of the new framework in May 1997. Subsequently, long-term inflation expectations have fluctuated fairly closely around the 2½ percent target, suggesting that market participants have a high degree of confidence that the MPC will remain committed to its basic policy objective.

Figure 1:
Figure 1:

Inflation Expectations 10 Years Ahead

Citation: IMF Staff Country Reports 2000, 106; 10.5089/9781451814149.002.A001

14. New Zealand was the first country to set an official inflation target and to establish institutional arrangements under which the target could be credible.11 The Reserve Bank Act of 1989 provided the legislative support for inflation targeting and gave the RBNZ a high degree of independence; and in March 1990, a public Policy Target Agreement between the Governor of the RBNZ and the Minister of Finance created clear and transparent policy targets and well-defined accountability for achieving the targets. Following a decade during which inflation rates in New Zealand had averaged about 10 percent, the policy objective set initially was to bring inflation down to the range of 0 to 2 percent over a period of two or three years, and subsequently to keep inflation within that range. In implementing policy, the RBNZ initially established a horizon of about four quarters for purposes of calibrating the strength of monetary policy actions to offset the effects of shocks. Over time, and after success in reducing inflation sharply, the RBNZ has moved to a more flexible framework, widening its target band to 0 to 3 percent, and now aiming to hit the mid-point of this range at a policy horizon from 1½ to 2 years with willingness to accommodate greater near-term variability of inflation.12

The Decision-Making Process and the Inflation Forecast

15. In the United Kingdom, the MPC consists of nine members, including the Governor, two Deputy Governors, and two other members appointed by the BoE after consultation with the Chancellor, along with four external members appointed by the Chancellor. Each member of the MPC has one vote in the decision-making process, but in the event of a tie the Governor, as chair of the Committee, has a second casting vote. The members of the MPC are held accountable through the reporting of their individual votes in the published minutes of the monthly meetings. In New Zealand, the Governor selects his own monetary policy committee to help formulate decisions, but retains full authority to make decisions himself and formally is held solely accountable for achieving the inflation target agreed ex ante with the Minister of Finance.

16. At both monetary policy institutions, the inflation forecast plays a central role in informing policymakers and shaping policy decisions. However, the procedures through which the two institutions prepare their inflation forecasts differ significantly. Although in both cases policymakers “own” the published forecasts, at the RBNZ the professional staff is given a relatively large role in generating the forecast that serves as the starting point for the deliberations of the monetary policy committee, whereas in the United Kingdom the members of the MPC are more extensively involved in the nuts and bolts of putting together the forecast. To the extent that different members of the MPC have different views on how to model certain aspects of macroeconomic behavior, such as exchange rate determination, the U.K. inflation forecast—which is conveyed in terms of subjective confidence ranges—is produced by examining the implications of a number of different model variants in arriving at the central inflation projection and subjective confidence bands.

17. As mentioned earlier, the approaches used to generate inflation forecasts at the two central banks also reflect fundamentally different types of assumptions about the policy interest rate. The BoE sets its policy interest rate on the basis of a forecast for inflation that is conditioned on the assumption that the policy interest rate will be held constant over the first eight quarters of the forecast horizon. The RBNZ also used a constant policy rate assumption prior to June 1997, when it completed the development of a new macroeconomic model designed for policy analysis. Subsequently, the RBNZ has generated its inflation forecast and a model-consistent interest rate path simultaneously after including in its macro model an appealing specification of an inflation-forecast-based monetary policy rule.13 The RBNZ’s interest rate forecast is described to the public in the form of projected half-year averages for a 90-day interest rate.

18. At both central banks, the process of generating the inflation forecast relies on macroeconomic models that reflect specific views about the monetary policy transmission mechanism; and at both institutions—as at central banks in most other industrialized countries—the macro models are in a constant state of evolution. The BoE has recently published a book that documents the equations and some of the properties of their core forecasting model. The RBNZ has also recently published a series of papers that document their forecasting and policy analysis system and we have been told that they have plans to construct a website to provide the public with access to future versions of the model.

D. Have U.K. Interest Rates Been Too Variable?

Sketch of the Model

19. The appropriate choice between different types and calibrations of monetary policy rules depends critically on the responsiveness of aggregate demand to the policy interest rate and on the extent to which market participants are forward-looking in forming their expectations.14 Accordingly, most of the analysis in this paper is based on variants of a small linear macroeconomic model with essentially four behavioral equations. The key features of the model (see the Appendix for a detailed description) are as follows.

  • The output gap—defined as the difference between actual output (aggregate demand) and potential output—exhibits a high degree of persistence while also declining in response to an increase in the real interest rate or an appreciation of the real exchange rate. Different model variants are analyzed to explore the implications of different views about which concept of the interest rate is most relevant for explaining the behavior of aggregate demand, and of different assumptions about the sensitivity of aggregate demand to the real exchange rate.

  • The Phillips curve is a linear specification in which the observed rate of inflation depends positively on both the output gap and market expectations of future inflation,15 where the level of potential output is assumed to be measured with no uncertainty. (The implications of uncertainty about the output gap are discussed in Section G below.)

  • Drawing on estimates of a fairly standard specification, the rate of inflation expected by market participants is assumed to reflect a weighted average of an observed (backward-looking) inflation rate and the model-consistent (forward-looking) outcome for future inflation, with the latter component receiving a relatively-low weight (10 percent in the base-case specification). This specification provides a way of reconciling the notion that market participants are rational and forward-looking with the fact that many wages and prices are adjusted infrequently, in part reflecting the influence of contractual arrangements.

  • The exchange rate satisfies a generalized interest rate parity condition, with the expected future spot rate assumed to behave as a weighted average of an observed (backward-looking) spot rate and the model-consistent future spot rate. This specification is motivated in part by substantial econometric evidence that the short-run behavior of exchange rates cannot be explained very well by macroeconomic fundamentals alone. It is also consistent with survey evidence that participants in foreign exchange markets rely heavily on “technical analysis,” which essentially establishes a strong link between their short-run forecasts of (or expectations about) future exchange rates and the recent past behavior of exchange rates.

20. The model can be used to explore how well different monetary policy rules would succeed over time in keeping inflation close to target and the output gap close to zero when the economy is subject to different types of shocks. For any general type of policy rule, the “optimal” calibration of the reaction parameters can be approximated by searching over a range of possible parameter values and identifying those values for which the rule performs best. Moreover, by varying certain properties of the macroeconomic model—such as the degree of openness and the nature of the linkage between aggregate demand and interest rates—the analysis can shed light on why the “optimally” calibrated rule for the United Kingdom is likely to involve a different degree of interest rate variability than the optimally calibrated rule for the United States.

Optimal Calibration of Generalized Taylor Rules

21. Table 1 reports the “optimal values” of the parameters of a generalized Taylor rule under sixteen different combinations of assumptions about the behavior of aggregate demand and the nature of the “shocks” to which policy must react. The formulation of the generalized Taylor rule is shown by the equation at the top of the table; in each period, the setting of the short-term nominal interest rate (the policy instrument) is determined by the previous period’s interest rate—the interest rate smoothing component of the rule—as well as by the inflation rate (implicitly as a deviation from target) and the output gap. The parameter λ represents the degree of interest rate smoothing, while the parameters α and β characterize the strength of the reactions to inflation and the output gap.16

Table 1.

Optimal Strength of Policy Reactions Under Different Assumptions

(Based on a Generalized Taylor Rule)
article image

This formulation can be derived from the more general specification:

rst=λrst1 + (1λ)rst*rst*=(rreq + π4t)+[(α/(1λ))1](π4t π*)+[β/(1λ)]yt

where rst* is the level at which interest rate would be set in the absence of smoothing, rreq is the equilibrium level of the real interest rate, and π* is the inflation target. Since the model is linear, the parameter estimates are independent of the levels of rreq and π*, which for purposes of the simulations are set at zero.

22. The results in the table are organized into four panels, corresponding to the various combinations of two different assumptions about the responsiveness of the output gap to the real exchange rate and two different representations of the “shocks” that the economy is assumed to experience. Within each of these four panels, the four sets of results correspond to different specifications of the interest rate measure in the output gap (aggregate demand) equation. The top row in each panel corresponds to the case in which the output gap is perceived to depend on the short-term (90-day) nominal interest rate, mimicking a key property of the BoE’s core forecasting model, in which aggregate demand is assumed to depend on the short-term nominal interest rate.17 The fourth row assumes that aggregate demand depends on the two-year real market interest rate, based on estimation results summarized in the Appendix.18 The middle two rows consider intermediate cases in which aggregate demand depends on the short-term real interest rate and the two-year nominal interest rate. The first case of the output gap equation assumes that the ratio between the interest rate and exchange rate coefficients is 2.5 to 1, as in a model calibrated to U.K. data by BoE staff.19 For comparison, the second case assumes that a change in the real exchange rate has a stronger effect on aggregate demand. For each of these two cases, the results in the left panel are based on simulations in which the economy experiences three kinds of shocks or prediction errors: shocks to the output gap, (supply) shocks to inflation, and shocks to the exchange rate. The results in the right panels are based on simulations that suppress the effects of the shocks to the exchange rate.

23. The first interesting result is that the optimal degree of smoothing (persistence) in the policy interest rate is higher when the output gap depends on a medium-term (eight-quarter) interest rate than when it depends on the short-term interest rate. This can be seen by comparing the values of λ in the top two rows of each panel with those in the bottom two rows. Intuition for this result comes from recognizing that a greater degree of persistence implies that a given change in the policy interest rate will have a greater effect on medium-term and long-term interest rates. Thus, the greater is the extent to which monetary policy is transmitted to aggregate demand through medium-term or long-term interest rates rather than through the short-term policy interest rate directly, the smaller are the adjustments in the policy rate that are required, other things equal, to stabilize the economy in response to a given distribution of shocks, and hence the greater is the optimal degree of inertia in the level of the policy interest rate.

24. The table also provides two perspectives suggesting that the optimal degree of interest rate smoothing is probably inversely related to the degree of openness of the economy. One perspective is visible from comparing the results for the case 1 output gap equation with the results for case 2. Case 2, which is characterized by a stronger effect of the exchange rate on the output gap, can be taken to represent a more open economy than case 1; and the table indicates that the optimal degree of interest rate smoothing is lower in case 2. The second perspective comes from comparing the results in the left panels with those for analogous cases in which the economy is insulated from shocks that are transmitted through the exchange rate (right panels). These comparisons show that the optimal degree of interest rate smoothing is generally lower and policy is more aggressive in responding to inflation and output when exchange rate shocks represent a significant source of macroeconomic disturbances. This is because exchange rate shocks, as characterized in the model, have a large persistent component, implying that monetary policy should respond more promptly when exchange rate shocks are prominent.

25. The degree of policy credibility is another factor that is likely to influence the optimal degree of interest rate smoothing, with greater credibility implying less need to adjust interest rates quickly in reaction to changes in economic conditions. The implications of credibility are difficult to capture in the simple model employed here,20 but one way of addressing the issue is to interpret the degree of credibility as synonymous with the extent to which inflation expectations are based on the model-consistent inflation forecast.21 In this connection, simulation results (not shown in the table) with different specifications of the inflation expectations equation confirm that the optimal degree of interest rate smoothing is positively related to the weight on the forward-looking model-consistent component of those expectations.

26. These simulation results provide several relevant perspectives on the issue of whether interest rates in the United Kingdom have been “too variable.” In general, they emphasize that the optimal degree of interest rate variability depends importantly on factors that can differ across countries, such as the channels through which monetary policy is transmitted to aggregate demand, the degree of openness of the economy, and the degree of policy credibility. Moreover, each of these three factors appears to support the view that, other things equal, sound monetary policy in the United Kingdom is likely to be characterized by greater interest rate variability than sound monetary policy in the United States. In particular: empirical work on aggregate demand functions has found that aggregate demand appears to depend on longer-term interest rates in the United States than in the United Kingdom; the United Kingdom is a more open economy than the United States; and the performance of U.S. monetary policy in recent years appears to have earned the Federal Reserve a remarkably high degree of credibility.

Inflation-Forecast-Based Rules Versus Backward-Looking Taylor Rules

27. The previous section examined the implications of different assumptions about the structure of the U.K. economy for the optimal calibration of Generalized-Taylor (GT) rules. In this section we extend that analysis to consider rules that are, in principle, much more forward-looking because they assume that the monetary authority chooses the policy rate on the basis its own model-consistent forecast of future inflation. These types of IFB rules have been studied extensively at the Fund, the Bank of Canada, the Reserve Bank of New Zealand, and more recently at the Bank of England and other central banks that have adopted inflation-forecast targeting frameworks.22

28. There are several advantages that IFB rules have over GT rules. First, they contain much more information about nonlinear macroeconomic dynamics. This advantage will obviously be important in the presence of significant nonlinearities that result from zero nominal interest rate floors or nonlinearities inherent in the output-inflation process.23However, even in some linear models it has been shown that IFB rules deliver significantly better macroeconomic performance when these models are subjected to a large enough array of shocks because the entire information set of the monetary authorities cannot be summarized completely by the observed values for inflation, the output gap and the past level of the policy rate.24 Indeed, as we will show below this may be the case in open economy models that are subjected to large portfolio preference shocks that affect the value of a country’s exchange rate.

29. It is sometimes argued that one disadvantage of IFB rules is that unless the monetary authority makes its policy model, rule and assumptions available to the public, it will obviously be more difficult for market participants to infer the future path of the policy rate relative to a situation where it follows a simple rule like the Taylor rule. We do not find this argument very convincing because we doubt that any central bank would ever attempt to follow a Taylor rule in practice.

30. Table 2 reports the staff’s preferred IFB rule for the staff’s model of the U.K. economy. Under this rule the monetary authority is assumed to adjust the policy rate in response to the output gap, the lagged policy rate and its own forecast of future inflation four-quarters into the future. As can be seen in the table there are considerably larger weights on the inflation-forecast term than on the inflation term in a backward-looking Taylor rule and smaller weights on the output gap (compare results in Table 1 and Table 2). This is because information about the output gap is already summarized in the inflation forecast, and indeed for the staff’s preferred model where the output gap is a function of the real two-year market rate, the optimal weight on the output gap is zero.

Table 2.

Optimal Strength of Policy Reactions Under Different Assumptions

(Based on a inflation-forecast-based rule)
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31. Table 3 measures the improvement in the loss function from following the optimally calibrated IFB rule relative to the optimally calibrated Generalized Taylor rules reported in Table 1. As can be seen in the table, the IFB rule has a significant advantage over the GT rule in the presence of shocks that directly affect the value of the exchange rate but this advantage becomes smaller when exchange rate shocks are eliminated from the analysis. This is consistent with some findings that suggest that there are only small benefits (or no advantages) of IFB rules over GT rules in linear closed economy models.25

Table 3.

Comparison of the Values of Loss Functions for the Optimal Calibration of a Generalized Taylor (GT) Rule and an Inflation-Forecast-Based (IFB) Rule

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E. How does the “Constant-Interest-Rate (OR) Rule Compared with Alternatives?

32. This section illustrates some of the implications of the CIR rule. In contrast with the stochastic simulation results reported in the previous section, the focus here is on the implications of the assumption for getting inflation back to the target level following a shock to aggregate demand. For comparison, the analysis also considers the outcomes under a generalized Taylor rule and under the type of unconstrained IFB rule that guides the policy reactions of the Reserve Bank of New Zealand.

33. In most models of the monetary policy transmission mechanism for open economies, including the model that underlies the analysis in this paper, an increase in interest rates has a direct negative effect on aggregate demand and output and leads to exchange rate appreciation that also affects output negatively, with the output effects tending to be persistent. In addition, through the decline in output, the increase in the interest rate reduces inflation and thereby also reduces expected future inflation, which contributes to continuing reductions in observed inflation. These ongoing effects of interest rate changes on aggregate demand and inflation have implications for the stabilizing properties of the CIR rule.

34. Figures 2 and 3 reveal some interesting perspectives under the base-case output gap equation specified in terms of the two-year real interest rate. The figures show the quarter-to-quarter behavior of the policy interest rate, the rate of inflation, and the output gap following an unanticipated increase in aggregate demand.26 Figure 2 shows the amount by which the policy interest rate would be raised initially under the CIR’s rule, along with the path that inflation would follow, given the policy objective of bringing inflation back down to target over an eight-quarter horizon and subject to the intent of holding the interest rate constant at its new level over that horizon. Beyond the eight-quarter horizon, and consistent with the practice used by the BoE staff in its own simulations, another interest rate rule is imposed in order to gradually stabilize the economy.27

(Deviation from baseline)
Figure 2.

Responses to Aggregate Demand Shocks Based on the OR Rule : Forecast In Period One

Citation: IMF Staff Country Reports 2000, 106; 10.5089/9781451814149.002.A001

(Deviation from baseline)
Figure 3.

Cumulative Responses to Aggregate Demand Shocks Given Repeated Application of the CIR Rule

Citation: IMF Staff Country Reports 2000, 106; 10.5089/9781451814149.002.A001

35. Note that this type of policy response reduces inflation back to its target level in eight-quarters, but pushes inflation below target thereafter. Accordingly, the intent of holding the interest rate constant for eight-quarters would not remain consistent with the policy objective, and when the MPC met in the second period to review its policy stance, its objective of hitting the 2½ percent inflation target under the constraint of a constant interest rate rule would call for a reduction in the level of the “constant interest rate.” For similar reasons, further gradual reductions in the policy interest rate would be called for in subsequent quarters. Thus, the intent of holding the interest rate constant for eight quarters is not time consistent.

36. Figure 3 shows the implications of such period-to-period revisions in the level of the “constant interest rate.” Note that as a result of these period-to-period interest rate adjustments, it would actually take much longer than eight quarters to get inflation back down to target.

37. The lack of credibility (time consistency) of the constant-interest-rate forecasts appears to be reflected in the recent history of two-year market interest rates (Figure 4). Indeed, market interest rates have provided a fairly accurate leading indicator of the policy rate over the past year and a half.

Figure 4.
Figure 4.

Official and Market Interest Rates

Citation: IMF Staff Country Reports 2000, 106; 10.5089/9781451814149.002.A001

38. For comparison, Figures 5 and 6 show the paths that inflation and the interest rate would follow under a generalized Taylor rule and under a model-consistent inflation-forecast-based rule that broadly resembles the RBNZ’s reaction function.28 Both of these alternative rules would call for higher real interest rates in the first year than the CIR rule, and would succeed in steering the inflation rate much closer to the target level within eight quarters. Another important difference is that the IFB rule results in a more preemptive tightening in real monetary conditions than the GT rule reflecting the fact that it is a more forward-looking rule.

(Deviation from baseline)
Figure 5.

Inflation-Forecast-Based Rule

Citation: IMF Staff Country Reports 2000, 106; 10.5089/9781451814149.002.A001

(Deviation from baseline)
Figure 6.

Generalized-Taylor Rule

Citation: IMF Staff Country Reports 2000, 106; 10.5089/9781451814149.002.A001

F. Potential Gains from a Transparent and Forward-looking Framework

Pros and Cons of Policy Transparency

39. This section uses stochastic simulation analysis to compare the degree of macroeconomic variability that is generated under different assumptions about the policy framework and the information or procedures on which market participants base their expectations.

40. Before discussing the simulation results, it is relevant to note that a number of considerations argue against being transparent.29 Transparency about policy decisions can be destabilizing when the analytic foundations for the decisions are weak; and by analogy, transparency about the central bank’s policy model might not help anchor expectations on the inflation target if the properties of the model were not sufficiently plausible. In the case of the BoE, moreover, significant differences of opinion among members of the Monetary Policy Committee make it difficult to reach a consensus on which, if any, of the BoE models could serve as an official policy model. It has also been argued that market participants can read too much into, and can react counterproductively to, the announcement of a non-constant path for the interest rate.30 Furthermore, when central banks become more transparent about their forecasts ex ante, they almost inevitably confront additional questioning about why their forecasts were not fully realized ex post, which can consume significant amounts of time.

41. On the other side of the coin, some key points in favor of increased transparency about the policy framework are that it can strengthen incentives for central banks to pursue their announced goals and can increase the effectiveness of monetary policy through enhancing its predictability by market participants. Indeed, this will be the case if the monetary authority’s main informational advantage over market participants is that it has a greater awareness about how it is likely to respond to new information. It has been argued, in addition, that subjecting policy models to public scrutiny and criticism is likely to catalyze significant improvements in the policy framework over time.31

42. In weighing these considerations, it may be noted that the RBNZ did not make their model transparent and begin announcing a model-consistent interest rate forecast until mid-1997, seven years after New Zealand adopted an inflation targeting strategy for monetary policy. Prior to that, the RBNZ invested significant resources in developing a policy model that better reflected policymakers’ views about the monetary policy transmission mechanism and the manner in which the economy responded to standard shocks. It may also be noted, in the New Zealand context, that it is difficult to separate the benefits of making the policy model transparent to the public from the benefits of simply having a macro model that policymakers accept as a basis for framing their analysis and that thus contributes to the coherence of internal policy discussions.

Illustrative Simulation Results

43. Given the various potential costs and benefits just described, any attempt to quantify the potential gains from policy transparency and an improved forecasting and decisionmaking framework requires strong qualification. It is instructive, nevertheless, to illustrate the potential benefits by simulating the performance of the basic model variant under different assumptions about the policy framework and the information, or procedures, on which market participants base their expectations. For this purpose we consider a benchmark case in which the policy interest rate is based on an optimally calibrated unconstrained inflation-forecast-based (IFB) rule (the rule reported in Table 2) and the policy framework is made fully transparent to informed market participants. The alternative policy frameworks include cases in which the policy interest rate is based on a constant-interest-rate (CIR) forecast of inflation, as well as cases in which the policy interest rate is based on the benchmark IFB rule, but the policy framework is not fully transparent to market participants. The simulations suggest that there are potential gains from shifting from a CIR rule to an IFB rule even in the absence of full transparency, and that there are further potential gains from making the IFB framework transparent.

44. The simulation analysis emphasizes that the degree of macroeconomic variability depends on market participants’ perceptions about how the policy interest rate will be adjusted over time. Under the CIR rule, the forecast may be published and “fully transparent” in that sense, but the prospect of a “constant” interest rate will generally not be regarded as credible. Thus, under either a “transparent” CIR rule or an IFB rule without full transparency, market participants must somehow form expectations based on limited information. To the extent that market participants draw inferences from the observed behavior of the policy interest rate and other macroeconomic variables and refine their inferences over time, efforts by the monetary authority to develop a coherent view of the monetary transmission mechanism and adopt a forward-looking policy reaction function may have significant benefits for the economy if it allows market participants to better predict the systematic component of monetary policy. Indeed, increasing the predictability of the systematic component of monetary policy by following a forward-looking IFB rule may be particularly important if the staff’s model of the UK economy is correct in presuming that aggregate demand depends not just on past movements in the policy rate, but also on movements in the expected future policy rate.32

45. These points are illustrated under alternative assumptions about the way that market participants form their expectations. In each case the basic model variant is simulated 100 times over 20 quarters, starting from an initial position with inflation at the target and the level of output at potential. Market expectations during the first 10 quarters are assumed to be based on one of three sets of initial beliefs about how monetary policy is likely to respond to new information about inflation and the output gap. Beginning in the 11th quarter, it is assumed that market participants start to base their expectations on an estimated Generalized Taylor (GT) rule that depends on the observed history of inflation, the output gap, and the policy rate. The estimated parameters of the GT rule are updated each quarter as the “historical” sample period gets larger.

46. The first set of experiments illustrate the potential benefits of basing monetary policy on an unconstrained IFB rule relative to a CIR rule. In this first set of experiments monetary policy is assumed to be completely transparent to informed bond market participants under the IFB rule; in particular it is assumed that the monetary authority publishes both its IFB rule and its model. However, because the CIR rule is not time consistent, market participants in this case have to infer how the “constant” interest rate is likely to be changed over time based on the observed historical data. The direct benefits of publishing an IFB rule and the model are estimated by comparing macroeconomic performance under situations where the monetary authority’s IFB rule and model are known to the public with situations where they are not known and informed market participants have to infer the parameters of the GT rule. An interesting result that emerges is that the gains from policy transparency are potentially greater when market participants are faced with a limited track record from which to infer how aggressively the monetary authority is likely to respond to inflationary pressures.

47. The left column of Table 4 reports standard deviations for the year-on-year RPIX inflation rate, the output gap, a 90-day interest rate, and a 2-year interest rate, for the benchmark case where the monetary authority follows an IFB rule and policy is fully transparent. The other columns represent cases in which market participants are assumed to infer how the policy interest rate will be adjusted over time under three alternative assumptions about their initial beliefs. As can be seen in the left column, an aggressive IFB rule delivers a fairly low level of variability in inflation, the output gap, and the 2-year market rate, but it produces significantly greater variability in the 90-day rate.33 The lower variability in the 2-year rate relative to the variability in the 90-day rate is a direct consequence of the assumption that policy is fully transparent. In this case informed bond market participants know that the policy rate will have a tendency to converge back to a more neutral stance over time in situations where the MPC is working against a potential inflationary shock by aggressively adjusting the policy rate. Figure 4 above, which plots the 90-day rate and the 2-year yield on gilts, provides some indications that bond market participants do not extrapolate very high policy rates (rates above 7 percent) into the future, but it is obviously too soon to tell if the “excess relative volatility” in 2-year rates that has been observed since the new regime was introduced is related to imperfect policy transparency.

Table 4.

Estimates of Short-Run Macroeconomic Variability Under Different Policy Frameworks and Different Initial Beliefs by Market Participants

(Standard deviations of selected variables in percentage points)
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The different cases are defined as:

Simple unaggresive rule (rst–1.10π4t);

Conventional Taylor Rule (rst = 1.50π4t + 50yt);

Approximately Optimal Generalized Taylor Rule (rst = 55 rst-1 + 1.40π4t + 55 yt);

where rs denotes the policy interest rate, π4 is the year on year inflation rate, and y is the output gap.

48. The benefit of announcing a forward-looking IFB rule that is consistent with the monetary authority’s views about the structure of the economy and its underlying objectives, is that it may serve to anchor expectations about the future evolution of the policy rate and, on average, this may result in a better level for market-based real interest rates. This may be particularly important when the track record is rather limited because it will be more difficult in such circumstances for informed bond market participants to understand how aggressively the MPC is likely to respond to potential inflationary pressures.

49. The top panel of Table 4 also reports estimates of variability in the macroeconomic indicators when the policy rate is determined by a CIR rule and market participants attempt to infer the parameters of the GT rule. The bottom panel present the results for similar experiments except in this case the monetary authority is assumed to follow an IFB rule but not to make its rule and model available to the public. Because the results of these experiments will be sensitive to assumptions about “initial beliefs” of market participants, when insufficient data are available to estimate the parameters of the GT rule, three cases are considered. The first case assumes that for the first 10 quarters of the simulation horizon the market believes that the monetary authority will follow a simple unaggressive Taylor rule that has a small weight of 1.1 on observed inflation and zero weights both the lagged policy rate and the output gap. The parameters of this rule were chosen because they imply a policy response that returns the inflation forecast back to the target very slowly, a result that roughly mimics the slow convergence properties for both inflation and the policy rate that is consistent with the “logical updating process” of the CIR rule (see Figure 3). The other two cases provide assumptions for initial beliefs that assume that the monetary authority will respond much more aggressively to inflation and the output gap.

50. The estimates of short-run variability reported in Table 4 indicate that there may be significant benefits in terms of reduced variability in inflation from adopting an IFB rule and making the policy framework fully transparent. Indeed, relative to both a CIR rule and an imperfectly transparent IFB rule, there can be significantly lower variability in inflation under the IFB rule with full transparency. These results suggest that when a monetary policy regime is new, or there has been a significant revision in the monetary authority’s objectives or views about the monetary policy transmission mechanism, that there may be significant benefits from making these changes in views as transparent as possible in order to reduce uncertainty in the monetary transmission mechanism. This basic intuition is confirmed by an additional simulation experiment reported in Table 5, which extends the simulation horizon by a further 80 quarters in order to compute longer-term measures of variability in these macroeconomic indicators. Note, first, from the lower panel, that in this case there are smaller benefits from announcing the IFB rule and making policy fully transparent because simply following the rule over a long enough period of time provides sufficient guidance to market participants about the systematic component of monetary policy.

Table 5.

Estimates of Long-Run Macroeconomic Variability Under Different Policy Frameworks and Different Initial Beliefs by Market Participants

(Standard deviations of selected variables in percentage points)
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The different cases are defined as:

Simple unaggresive rule (rst = 1.10π4t);

Conventional Taylor Rule (rst = 1.50π4t + 50 yt);

Approximately Optimal Generalized Taylor Rule (rst = 55 rst-1 + 1.40π4t +55 yt);

where rs denotes the policy interest rate, π4 is the year on year inflation rate, and y is the output gap.

51. Comparison of the upper panels of Tables 4 and 5 provides additional perspectives on the credibility problems that would likely develop under the CIR rule. Indeed, when we repeat the same experiments reported in Table 4 but consider a case where the CIR rule is assumed to be followed for an additional 80 quarters (Table 5) it becomes apparent that the CIR rule would be abandoned at some point because the higher inflation persistence that would develop as market participants more accurately inferred the rule would result in enormously high levels of variability in inflation, output, and interest rates.

G. The Dangers of Interest Rate Smoothing and Taylor Rules

52. The analysis in the previous sections has been based on a very simple model of macroeconomic behavior. One major simplification is the implicit assumption that the monetary authorities do not make serially-correlated errors in estimating the output gap. Such an assumption is extremely unrealistic. Potential output is not an observable variable, so its level needs to be inferred from other observable information and assumptions about the economy, and experience suggests that policymakers and their staff’s periodically conclude that they have been making serially-correlated errors in estimating potential output and need to significantly revise their historical data series. This contributes to the phenomenon of policymakers occasionally coming to realize that their assessments of the strength or weakness of the economy have gone badly off track, and that they have allowed a state of significant excess demand or supply to develop.

53. A second major simplification of the previous analysis is the assumption that the world is linear. This abstracts, inter alia, from the possible relevance of convex Phillips curves, floors on nominal interest rates, and inflation expectations that respond endogenously and in an asymmetric manner to the track record (credibility) of the authorities in hitting their inflation target.

54. Analysis that avoids these two types of simplifications points to the dangers of the types of myopic policy reactions that are prescribed by backward-looking Taylor rules or rules with high degrees of interest rate smoothing.34 In a nonlinear world in which serially-correlated errors in estimating output gaps create a significant probability that states of significant excess demand will sometimes develop, monetary authorities who remained committed to a policy rule that called for myopic reactions would run the risk of inflation expectations skyrocketing, particularly if market participants were (partially) forward-looking in forming their inflation expectations.

55. These considerations imply that forward-looking inflation-forecast based (IFB) rules are inherently superior to backward-looking Taylor rules as guidelines for monetary policy.35

H. Some Implications of Uncertainty in the Monetary Transmission Mechanism

56. The success and credibility of an inflation-targeting framework ultimately depends on the abilities and systematic judgements of the policymakers. One of the potential advantages of an open and transparent inflation targeting framework is that it will foster debate about uncertainties in the forecast process and this over time will improve the decision making process.

The Exchange Rate-Interest Rate Nexus

57. One important issue on which policymakers can disagree on the basis of econometric evidence is the question of how exchange rates are likely to respond to policy actions. This is illustrated in the November 1999 Inflation Report, which indicates that there was considerable disagreement within the MPC about the choice of the exchange rate model. Some members believed that this uncertainty was so large that they favored replacing the exchange rate equation in the BoE’s core forecasting model, which was based on uncovered-interest-parity (UIP), with the assumption that the exchange rate will remain constant. The argument for doing this is reported succinctly in the Box on page 48 of the November Inflation Report: “Some statistical tests on past data indicate that the random walk hypothesis performed no worse than—indeed often better than—the uncovered interest parity theory…and for this reason and given the merit in a simple approach some Committee members were inclined toward this benchmark.”

58. As shown below, such differences in model specifications can have significantly different implications for how monetary policy should respond to inflation and output gaps. The UIP equation implies that an increase in the policy interest rate will lead to an exchange rate appreciation, other things being equal. By contrast, a random walk view is tantamount to saying that policymakers do not know the expected sign of the reaction of the exchange rate to a policy-induced change in short-term interest rates. In the end, the MPC decided to take an average of these two approaches—a wise decision from the standpoint of the staff’s model.

59. The staff’s exchange rate model is based on an extended risk-adjusted theory of UIP where market expectations are assumed to be generated by a linear combination of last period’s exchange rate and the model-consistent solution; see equation in Table 6.36 By varying the weights on the forward-looking and backward-looking components in the equation that determines the private sector’s forecast of next period’s exchange rate, it is possible to capture the range of views that members of the MPC had leading up to the November 1999 Inflation Report.37 In terms of the equation in the table, some members on the MPC preferred a model where Φ was 0 (an unchanged exchange rate assumption) and some other members preferred a model where Φ was 1 (pure UIP).

Table 6.

Optimal Generalized Taylor Rule Parameters under Different Assumptions of Exchange Rate Expectations

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60. To illustrate the implications for the behavior of monetary policy of these various approaches, the weights for the Generalized Taylor rule were optimally recalibrated for different specifications of the weight on the forward-looking component of expectations in the exchange rate equation; the weights for Φ that are considered vary between 0 and 1 in increments of 0.2. As can be seen from Table 6, the policy rate must be adjusted more aggressively in the short run in response to changes in inflation when interest rates have smaller short-run effects on the exchange rate (the values of α in Table 6 are generally larger when Φ is smaller). This is because the lags in the monetary transmission mechanism become longer for smaller values of Φ as the exchange rate adjusts more gradually in response to a change in the policy interest rate. Note, that in the special case where Φ is zero the exchange rate is assumed to be completely unresponsive to a change in the policy rate. By contrast, when there is a weight of one on the model-consistent solution in the exchange rate equation, monetary policy works much more through expectational effects in the foreign exchange market and as a consequence can react more gradually and less aggressively in the short run to changes in inflation.

What are the implications of basing the forecast and interest rate setting on an incorrect degree of forward lookingness in the foreign exchange market?

61. To illustrate the implications of basing monetary policy on an incorrect degree of forwardlookingness in the foreign exchange market we compute the additional losses that would be imposed on the economy if the MPC were to base its interest rate reactions on an incorrect value of Φ. The specific loss function that is chosen is explained in the Appendix and places a weight of one half on interest rate volatility and weights of one on both variability in inflation and the output gap.

62. Table 7 reports the percent increase in the value of the loss function when the MPC’s interest rate reaction is based on an incorrect assumption about the degree of forwardlookingness in foreign exchange markets. In the experiments the MPC is assumed to follow the generalized Taylor rule that is optimally calibrated given their views on Φ.

Table 7.

Percent Increase in Value of the Loss Function when MPC’s Model has the Wrong Φ Value

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63. As can be seen in the Table there can be significant benefits from knowing the true weight and large costs from assuming an unduly large weight of 1 for Φ if it is possible that the weight might be smaller. In this sense the assumption that was agreed upon by the MPC may be a useful step in the right direction because not only did it represent an “averaging” of the range of views in the MPC, it also may represent a more judicious choice from the strategic perspective of eliminating potentially large errors when there is uncertainty about the magnitude of the response of the exchange rate to a change in the policy rate. Indeed, an interesting aspect of the results in Table 7 is that the costs of overestimating and underestimating the value of Φ are not symmetric. For example, there can be greater costs from overestimating the degree of forwardlookingness (and not adjusting the policy rate sufficiently in response to a change in inflation) than underestimating the degree of forwardlookingness (and adjusting the policy rate too aggressively): the additional losses in the shaded area in the top right-side part of the table are considerably larger than the losses in the shaded area in the bottom left side of the table.

I. Concluding Remarks

64. This paper has addressed several issues that arise in designing a framework for inflation targeting, with particular attention to features of the Bank of England’s approach and experience. Because it takes time for monetary policy to affect inflation and economic activity, central banks generally strive to make forward-looking decisions. Most policymakers are well aware of the perils of adhering rigidly to any particular monetary policy rule, as opposed to exercising constrained discretion; but there is considerable interest in identifying the types and calibrations of policy rules that can provide the most effective guidelines or benchmarks. In part this interest reflects the usefulness of quantitative frameworks for helping policymakers structure their thinking in a forward-looking context; monetary policy rules or assumptions are required to make those frameworks complete and internally consistent. Moreover, to the extent that macroeconomic behavior depends importantly on the expectations of market participants, monetary policy that is guided by a well-chosen policy rule, and that therefore tends to be relatively consistent and transparent over time, can induce market expectations to evolve in a manner that helps stabilize the economy.

65. Comparison of the U.K. experience in recent years with that of the United States has provoked suggestions that the Bank of England’s policy framework gives rise to excessive interest rate variability. The analysis in this paper, however, does not support that assessment. Rather, it has emphasized that the optimal strength of monetary policy reactions—including the optimal degree of interest rate smoothing—depends importantly on, among other things, both the nature of the direct linkages between aggregate demand and interest rates and the sensitivity of aggregate demand to the real exchange rate. Both of these factors would appear to imply a need for greater interest rate variability in the United Kingdom than in the United States.

66. The Bank of England Inflation Report features an inflation forecast based on a constant interest rate assumption.38 While this approach may simplify internal policy discussions and external communication in certain ways, the constant-interest-rate assumption underlying the forecast in the Inflation Report has not been regarded as credible, as can be inferred from the term structure of market interest rates. Indeed, under many plausible models of how monetary policy is transmitted to aggregate demand and inflation, the “constant-interest-rate” framework is not time consistent since it tends to induce periodic changes in the policy interest rate. Moreover, the pattern of these changes operates to substantially lengthen the time required to return inflation to the target level following a shock.

67. The main alternatives to constant-interest-rate IFB rules are generalized Taylor rules and model-consistent IFB rules. The latter unconstrained form of IFB rule plays a central role in the monetary policy framework of the Reserve Bank of New Zealand.

68. Unlike IFB rules, Taylor rules have the undesirable feature of being backward-looking; they call for policy to respond to the deviation from target of the most recently observed rate of inflation rather than the deviation from target of an inflation forecast. Various simulation studies have found that Taylor rules have remarkably good stabilization properties in linear macroeconomic models, but most of these studies have abstracted from -the fact that economists tend to make serially correlated errors in estimating the level of potential output. In general, myopic policy reaction functions—such as Taylor rules or rules with a high degree of interest rate smoothing—do not provide desirable or credible guidelines for policy in a world in which monetary policy credibility can quickly be lost and only slowly regained, and in which policymakers are sometimes confronted with substantial revisions in macroeconomic indicators of the state of the economy. In such a world, it can be very costly to follow myopic policy rules that risk falling systematically behind shifts in the Phillips curve.

69. The New Zealand experience suggests that there are large potential gains from developing a macroeconomic model that succeeds in capturing policymakers’ views of the monetary policy transmission mechanism and embodies a well-chosen IFB rule. Quantitative models that are broadly consistent with policymakers’ views, and the model-consistent interest rate paths that are generated from those models, can add significantly to the coherence of the central bank’s internal discussions and policy decisions. Developing such a model takes time, but considerable payoffs can potentially be gained in a relatively short period by keeping the model small and concentrating initially on capturing policymakers’ views about a few key relationships, such as the aggregate demand function.

70. To succeed in developing a model on which policymakers will feel comfortable relying, it is important to draw them into the process of specifying the model and determining the values of its key parameters. Econometric studies have proposed and estimated different specifications of most macroeconomic relationships, and the choice among them can rarely be based on statistical tests alone. To make responsible policy decisions, policymakers need to be involved, for example, in making judgments about whether to view aggregate demand as responsive to the short-term nominal interest rate, a medium- to long-term real interest rate, or some combination or other alternative. In times of rising inflation expectations, such judgments about the aggregate demand function are critical for coming to a view on how much monetary policy is being tightened or allowed to ease.

71. The analysis in this paper suggests that once a central bank has developed a macroeconomic model that conforms with policymakers’ views, there can be significant potential gains from basing policy on unconstrained model-consistent forecasts, and from making both the model and the interest rate forecasts transparent. That conclusion abstracts from a number of arguments against model transparency and remains controversial. It would be difficult, however, to dispute the case for developing better policy models, and for continuing to strengthen those models over time.

APPENDIX I

The Staff’s Quarterly Model of the U.K. Economy

72. Table A1 presents the equations of the model and Table A2 defines notation; time periods correspond to calendar quarters. Four of the equations in Table A1 reflect behavioral assumptions; the others amount to definitions or arbitrage conditions.

Table A1:

A Small Model of the U.K. Economy

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73. Equation (1) is a linear Phillips curve that describes the behavior of the inflation rate, where inflation in period t is measured as the change in the price level over the year from period t-4 through period t. The specification allows for a significant influence of the contemporaneous change in import prices but otherwise corresponds to a linear specification of an expectations-augmented Phillips curve estimated on U.K. data by Fisher, MahadEva, and Whitley (1996). Note that the coefficients of the first two right-hand-side terms sum to unity, consistent with the long-run natural rate hypothesis. The coefficient on the output gap was derived (before rounding).

Table A2:

Notation; Time Periods Correspond to Calendar Quarters

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by first estimating a convex Phillips curve for the United Kingdom and then calculating the corresponding value of the coefficient in the associated linear approximation.

74. Equation (2) is a fairly standard forward- and backward-looking representation of the private sector’s inflation expectations. In line with other work on empirical Phillips curves, it features a small weight on the forward-looking model-consistent component.(Φ = in the base-case model). The large weight on the backward-looking component is consistent with the view that wages and prices are sticky, reflecting in part the influence of contractual arrangements, but in addition the presence of a large proportion of the population that is uninformed. This estimated weight is roughly consistent with reduced-form evidence on Phillips curves for other countries, which also suggests a very small weight on the forward-looking component.1

75. Equation (3) relates the output gap to its own lagged value, the eight-quarter real interest rate, and the real exchange rate. The basic form of the output gap specification in the staff’s model has some similarities with the one employed by Batini and Haldane (B-H 1999 b) to study optimal monetary policy rules in the United Kingdom. However, there are two important differences. One that concerns whether or not expected changes in the real policy rate also affect the output gap. In the B-H model changes in the output gap depend on lagged movements in the policy interest rate and are independent of what the market expects the policy rate to do in the future. By contrast, in the staff’s model the output gap depends on an eight-quarter real interest rate that in turn reflects market participants’ expectations of future levels of the policy rate. This is a substantive difference insofar as the staff’s model provides a channel where the systematic component of monetary policy can influence the market’s expectations of future changes in the policy rate.

76. The other main difference between the B-H output gap model and the staff’s model involves the absolute and relative sizes of the effects of real interest rates and the real exchange rate on the output gap. The specification in the B-H model has an output gap coefficient of 0.5 on the 90-day real short-term interest rate and a coefficient of 0.2 on the real exchange rate. Based on the staff’s empirical work with reduced-form output gap equations, we posit a much smaller coefficient on the real interest rate term; and given uncertainties about the estimated effects of real exchange rates, we consider the implications of two possible calibrations of the real exchange rate term. In the first case, we assume that the coefficient is the same as in the B-H model (0.2), while in the second case we assume the same relative importance that the B-H model attaches to the real interest rate and the real exchange rate. This implies a coefficient on the real exchange rate of slightly less than 0.1 (0.2 / 2.5) and is more consistent with our reduced-form empirical evidence on the relative and absolute importance of the real exchange rate. These estimates suggest that the effects of a 100 basis point increase in the real interest rate on the output gap is equivalent to a 2.5 percent appreciation in the real exchange rate.

77. Equations (4) and (5) define the two-year (eight-quarter) real interest rate in a manner consistent with the behavior of inflation expectations, as described in Equation (2). The first term on the right-hand-side of Equation (5) is the model-consistent component of the annualized inflation rate expected over the eight quarters ahead, which receives a weight of λ, while the backward looking component receives a weight of (1-λ). In our base case model we assume that λ is 0.1 but we consider alternatives where we increase it to 0.5. It has been quite common to interpret this parameter as an index of policy credibility because higher values imply that market participants are provided with more information about the monetary policy rule.

78. Equation (6) defines the real exchange rate; an increase represents a real appreciation of the domestic currency. Equation (7), which includes an error term, can be regarded as a generalized form of the interest rate-parity arbitrage condition. Equation (8) assumes that the future spot rate expected by the private sector is a weighted average of the forward-looking model-consistent expectation and a component that is essentially backward-looking. The latter component is simply the lagged spot rate adjusted for the expected inflation differential.2 This specification provides a way of reconciling the notion that market participants are rational and forward looking with econometric evidence that exchange rates cannot be explained very well by macroeconomic fundamentals alone. It is also motivated by survey evidence that participants in foreign exchange markets rely heavily on “technical analysis,” which essentially links their exchange rate forecasts (expectations) to the level of exchange rates in the recent past.3

79. Equation (9) is the expectations theory of the term-structure, which relates the yield on eight-period maturities to the cumulative yield on a sequence of one-period contracts. Equation (10) simply defines the inflation rate as the change in the price level over four quarters, and Equation (11) is an analogous definition of the rate of inflation of import prices (i.e., of foreign prices converted into domestic currency units).

The Stochastic Simulation Framework Without Learning

80. The assumptions underlying the stochastic simulation experiments are as follows. The model of macroeconomic behavior is assumed to consist of the equations in Table A1 (with other vari ants of the output gap equation in some cases), along with an equation for the policy interest rate. In some of the simulations the interest rate is determined by a generalized Taylor rule, as described in Table 1. In other simulations the interest rate follows an IFB rule, as described in Table 2, As discussed later, the set up is somewhat more complicated for cases in which the MPC relies on a constant-interest-rate forecast that market participants deem to not be credible.

81. Unless otherwise indicated the simulations extend over a horizon of 100 periods (calendar quarters). In each period the economy experiences three types of exogenous shocks: a shock to the output gap, a supply shock to the inflation rate, and a shock to the exchange rate. These exogenous shocks are drawn randomly from independent normal distributions with zero means and standard deviations of 0.8, 0.4 and 1.9 percentage points respectively.

82. The initial state of the economy is characterized by a steady state where all variables are zero. Following the realizations of the shocks in the first period, the authorities use their prespecified policy rule—along with the assumption that the realizations of random shocks in future periods will coincide with their expected values of zero—to determine the interest rate setting for that period and to generate forecasts, over a horizon of 50 periods, of the future time-paths of all of the endogenous macroeconomic variables in the model, including interest rates.4 The shocks for the second period are then realized, after which the authorities update their forecasts and adjust their policy settings. And so forth until the end of period 100.

83. Unless otherwise indicated the 100-period simulation is repeated 10 times, each time drawing a different sequence of the random shocks, but saving the shocks and subjecting each different form and calibration of policy rule to the same sequences of shocks. For each specified policy rule, the process of generating 10 simulations over 100 quarters results in 1000 observations on the outcomes for inflation, output, and the policy interest rate. The performances of the different rules are characterized by a set of five summary statistics: the standard deviations of the inflation rate, the output gap, the 90-day interest rate, and the two-year interest rate, as well as the value of a policy loss function.

The Policy Loss Function

84. The literature on optimal policy rules has traditionally relied on quadratic loss functions that are separably additive in the deviation of inflation from target, the output gap, and sometimes also the change in the nominal interest rate; see, for example, Rudebusch and Svensson (1998) and Wieland (1998). To remain consistent with this literature, we adopt an objective function in which the period-t loss has the following general form

Lt = (π4t  πTAR)2 +  θ[yt]2 + v(rs1t  rs1t1)2

where π4 is year-on-year RPIX inflation, y is the output gap, rsl is the one-quarter interest rate, and [θ, υ] are the relative weights of output gap variability and interest rate volatility. These relative weights have been set at 1 and 0.5 to be consistent with other studies on monetary policy rules. The optimal parameters for the reaction functions reported in Table 1 and Table 2 have been derived numerically by searching over a grid of policy-rule parameter values for the calibration that minimizes the value of the loss function averaged over the 1000 observations generated by the stochastic simulations.

The Stochastic Simulation Framework with Learning

85. For cases where the MPC projects a path for the policy interest rate that is either unobserable or deemed to be noncredible—such as the “constant” interest rate forecast—market participants are forced to use some other behavioral rule to forecast the future path of the policy rate. In such cases market participants are assumed to efficiently use historical information about past movements in inflation, output, and the policy rate to infer the parameters of a Generalized Taylor rule. Note, that one of the conditions for stability in this class of linear models is that the asymptotic response to inflation under the Generalized Taylor rule must exceed one. Otherwise the real interest rate would not rise sufficiently in response to an inflationary shock to ensure that there is an anchor for inflation expectations. This necessary restriction for stability is imposed whenever the estimated parameters from the historical data would suggest that this asymptotic response is less than one. This biases the results in the sense that it rules out either explosiveness or indeterminacy and the associated policy errors that John Taylor and others have attributed to falling systematically behind shifts in the Phillips curve. In order to initialize the start of the stochastic simulations when the data set is too short to estimate the parameters of the reaction function, it is assumed during the first 10 periods that market participants base their expectations of future changes in the policy rate on an optimally calibrated GT rule. We have experimented with different assumptions about “initial beliefs” in order to evaluate how sensitive the results are to different assumptions. In one case a simple Taylor rule is specified that has a zero weight on the output gap and a small weight of 1.1 on inflation. These parameters were chosen to illustrate the implications of a perceived policy rule that does not respond aggressively to inflationary shocks. In addition, an intermediate case is considered that imposes weights of 1.5 on inflation and 0.5 on the output gap.

References

  • Amano, Robert, Coletti, Don Macklem, Tiff 1999, “Monetary Rules When Economic Behavior Changes,” in Benjamin Hunt and Adrian Orr (eds.), Monetary Policy Under Uncertainty, (Wellington: Reserve Bank of New Zealand) pp. 157 -200.

    • Search Google Scholar
    • Export Citation
  • Barro, Robert J., B. Gordon, David 1983, “Positive Theory of Monetary Policy in a Natural Rate Model,” Journal of Political Economy, Vol. 91 (August), pp. 589-610.

    • Search Google Scholar
    • Export Citation
  • Batini, Nicoletta Haldane, Andrew 1999a, “Forward-Looking Rules for Monetary Policy,” in John Taylor, ed., Monetary Policy Rules (Chicago: University of Chicago Press).

    • Search Google Scholar
    • Export Citation
  • Batini, Nicoletta Haldane, Andrew 1999b, “Monetary Policy Rules and Inflation Forecasts,” Bank of England Quarterly Bulletin (February), pp. 60 -67.

    • Search Google Scholar
    • Export Citation
  • Bernanke, Ben S., S. Mishkin, Frederic 1997, “Inflation Targeting: A New Framework for Monetary Policy?” Journal of Economic Perspectives, Vol. 11, pp. 97 -116.

    • Search Google Scholar
    • Export Citation
  • Clark, Peter, Laxton, Douglas Rose, David “An Evaluation of Alternative Monetary Policy Rules in a Model with Capacity Constraints,” paper submitted for publication at the Journal of Money Credit and Banking.

    • Search Google Scholar
    • Export Citation
  • Clark, Peter, Laxton, Douglas Rose, David 1995, “Capacity Constraints, Inflation, and the Transmission Mechanism: Forward-Looking Versus Myopic Policy Rules,” IMF Working Paper 95/75 (Washington: International Monetary Fund).

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    • Export Citation
  • Clarida, Richard, Gali, Jordi Gertler, Mark 1998, “Monetary Policy Rules in Practice: Some International Evidence,” European Economic Review, Vol. 42, pp. 1033 -67.

    • Search Google Scholar
    • Export Citation
  • Drew, A. Orr, A. 1999, “The Reserve Bank’s role in the recent business cycle: actions and evolution,” Reserve Bank Bulletin.

  • Faust, Jon E.O. Svensson, Lars, 1999, “The Equilibrium Degree of Transparency and Control in Monetary Policy,” NBER Working Paper 7276.

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  • Fisher, P. G., Mahadeva, L. Whitley, J. D. 1996, “The Output Gap and Inflation-Experience at the Bank of England,” paper prepared for B.I.S. Model-builders’ Meeting, Basle.

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    • Export Citation
  • Isard, Peter, 1995, Exchange Rate Economics (Cambridge: Cambridge University Press).

  • Isard, Peter, Laxton, Douglas Eliasson, Ann-Charlotte 1999, “Simple Monetary Policy Rules Under Model Uncertainty,” in Peter Isard, Assaf Razin, and Andrew Rose, eds., International Finance and Financial Crises: Essays in Honor of Robert P. Flood Jr. (Washington: International Monetary Fund and Boston: Kluwer).

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  • Isard, Peter, Laxton, Douglas Eliasson, Ann-Charlotte 2000, “Inflation Targeting with NAIRU Uncertainty and Endogenous Policy, Credibility,” Journal of Economic Dynamics and Control, forthcoming.

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  • King, Mervyn, 1999, “Challenges for Monetary Policy: New and Old,” paper prepared for the Jackson Hole Symposium on New Challenges in Monetary Policy.

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  • Kohn, Donald, 1993, “Comment, o in John Taylor, ed., Monetary Policy Rules (Chicago: University of Chicago Press).

  • Laxton, Douglas, Rose, David Tambakis, Demosthenes 1999, “the U.S. Phillips Curve: The Case for Asymmetry,” Journal of Economic Dynamics and Control, Vol. 23.

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  • Sarel, Michael, 1999, “New Zealand’s Evolving Approach to Inflation Targeting,” in SM/99/209, New Zealand-Selected Issues.

  • Svensson, Lars E.O., 1999, “Inflation Targeting as a Monetary Policy Rule,” Journal of Monetary Economics, 43, pp. 607 -54.

  • Taylor, John, 1993, “Discretion Versus Policy Rules in Practice,” Carnegie-Rochester Conference Series on Public Policy, Vol. 39 (December), pp. 195 -214.

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    • Export Citation
  • Taylor, John, 1999, “An Historical Analysis of Monetary Policy Rules,” in John Taylor, ed., Monetary Policy Rules (Chicago: University of Chicago Press).

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  • Vickers, John, 1999, “Economic Models and Monetary Policy,” Bank of England Quarterly Bulletin (May), pp. 210 -16.

1/

Prepared by Peter Isard and Douglas Laxton.

3/

Bernanke and Mishkin (1997), King (1999), Svensson (1999), Taylor (1999).

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Kohn (1999).

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Taylor (1933, 1999), has emphasized the importance of calibrating the rule to insure that nominal interest rates are adjusted by more than any change in the inflation rate in order to prevent monetary policy from falling behind “shifts in the Phillips curve.”

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Isard, Laxton, and Eliasson (1999) show that because these rules are myopic, making a firm commitment to them would not be effective in stabilizing inflation expectations in such models, but would rather result in interest rate adjustments that fell behind “shifts in the Phillips curve” and would risk repeating the types of policy errors that were made in several industrial countries in the 1970s.

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Svensson (1999) refers to such (approximate) first-order conditions as “targeting rules” to emphasize their distinction from instrument rules that are simply postulated.

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Prior to May 1997, the Chancellor made interest rate decisions, taking into account the views of the Governor of the BoE. Vickers (1999) provides a concise description of the monetary policy framework now in place.

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For background, see M. Sarel, 1999, “New Zealand’s Evolving Approach to Inflation Targeting,” in SM/99/209, New Zealand—Selected Issues.

12/

See A. Drew and A. Orr, “The Reserve Bank’s role in the recent business cycle: actions and evolutions,” Reserve Bank Bulletin, March 1999.

13/

RBNZ insiders report that the quality of the policy discussions has improved considerably since that time, but that it would be difficult to disentangle how much this is associated with having the new macro model available to structure the policy discussions and how much it reflects the shift away from conditioning the policy discussions on a constant interest rate assumption.

14/

As explained in Section G below, the effectiveness of a policy rule can also depend critically on the nature of the uncertainties about important model parameters, such as the NAIRU, and on whether the model includes nonlinearities—such as a convex Phillips curve, an explicitly-recognized floor on the nominal interest rate, or inflation expectations that respond endogenously and in a nonlinear manner to the track record (credibility) of the authorities in hitting their inflation target. See Isard, Laxton, and Eliasson (1999, 2000).

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The observed rate of inflation also depends positively on the rate of import-price inflation, and the coefficients of the Phillips curve are constrained to be consistent with the long-run natural rate hypothesis.

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For each set of assumptions, the optimal values of the parameters in the rule are determined by searching for the calibration that leads to the best summary measure of macroeconomic performance when the model is simulated ten times over a horizon of a hundred quarterly time periods. The simulations are stochastic in the sense that in each time period the levels of the output gap, the inflation rate, and the exchange rate are subject to random shocks or prediction errors. The summary measure of macroeconomic performance—the minimum value of which determines the optimal calibration of (λ, α, β)—is the average (over the ten simulations and a hundred quarters per simulation) of a “conventional” quadratic policy loss measure that corresponds to a weighted sum of the squared deviation of the inflation rate from its target, the squared value of the output gap, and the squared value of the change in the policy interest rate. Additional details are provided in the Appendix.

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In the BoE core forecasting model the main direct effects of interest rates on aggregate demand is based on an assumption that the short-term nominal interest rate affects aggregate real consumption expenditures.

18/

The basic form of the aggregate demand specification is taken from Batini and Haldane, as publised in BoE Quarterly Bulletin, Feb 99. We estimated variants of this specification exploring the relationship between aggregate demand and the real interest rate (based on indexed-bond yields) at different horizons, and found that the specification based on the two-year real rate fit better than specifications with longer-horizon real rates. We also found significantly smaller point estimates of the effects of real exchange rates on the output gap although there was considerable uncertainty in these estimates.

20/

See Isard, Laxton, and Eliasson (2000) for a more ambitious effort to model the credibility component of inflation expectations as an endogenous variable that responds asymmetrically to the track record of policymakers in keeping inflation on target.

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For example, see Amano, Coletti, and Macklem (1999).

22/

The exact form of the IFB rule used in this paper is a simplification of a more complicated rule that also includes information on the private sector’s forecast of future inflation. The basic argument for including information on the private sector’s forecast of future inflation in IFB rules is that the private sector’s expectation of inflation and real short-term interest rates are critical in many models for determining the appropriate level and time path for real monetary conditions. The IFB rule used at the Reserve Bank of New Zealand and the Bank of Canada includes long-term interest rates because aggregate demand in their models depends on the slope of term structure rather than market-based real interest rates.

23/

For examples see Clark, Laxton and Rose (1995, 2000), Isard, Laxton and Eliasson (1999, 2000), Laxton, Rose and Tambakis (1999) and the discussion in section G.

24/

See Batini and Haldane (1999b).

25/

See Levin, Wieland and Williams (1999).

26/

The residual of the output gap equation is set equal to 0.5 in period 1, 1.0 in period 2 and 0.5 in period 3.

27/

In constructing the inflation forecast, the BoE staff assume that the CIR rule reverts to a Taylor rule after the eighth quarter of the forecast horizon while the staff assume that it reverts back to an IFB rule.

28/

The specific calibrations of the two rules are the optimal base-case calibrations shown in Tables 1 and Table 2.

29/

This paper abstracts from the possibility that the policy objective function may motivate the authorities to pursue time-inconsistent policies, as suggested by Barro and Gordon (1983). See Faust and Svensson (1999) for perspectives on the tradeoffs between transparency and control in such a framework.

30/

Market reactions to the “biases” announced by the Federal Reserve’s Open Market Committee during 1999 illustrate this possibility.

31/

This may be particularly the case in countries where there is significant interest and expertise outside the central bank in developing macro models to support inflation targeting. In this case, making an up-to-date version of the model available on the central bank’s web site may result in more constructive suggestions by outsiders if they have a more precise understanding about how the policymakers view the economy and the nature of the monetary transmission mechanism.

32/

The main advantage of complete openness, where the central bank releases its model as well as all of the judgmental add-factors that are used to construct the forecast, is that it would allow outsiders to more effectively analyze their performance and the relative contributions of the model and the judgement. This presumably would make it easier to distinguish between policy errors that arise from bad luck (large shocks that do not offset each other) and policy errors that arise because of weaknesses in the framework.

33/

In the model there is no distinction between the 90-day market rate and the MPC’s policy rate and the former is assumed to move one-for-one with the latter.

34/

Isard, Laxton, and Eliasson (1999).

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The same considerations pose a serious challenge to the common practice of basing the analysis of monetary policy issues on linear models of macroeconomic behavior.

36/

This model of expectations is sometimes referred to as a backward-and-forward-looking components model. It is regarded in several central banks as a useful way to specify expectations in models that are designed to do both forecasting and policy analysis. The development of macro models that have these features has proceeded considerably faster at central banks that have had access to more efficient and robust and solution algorithms.

37/

In the staff’s model the lagged exchange rate term is combined with an additional term that reflects a possible inflation differential with other countries, so setting the weight on the model-consistent forecast to zero does not exactly deliver a random walk exchange rate—see the Appendix for a description of the staff’s model. The inflation differential term is necessary in the staff’s model to prevent a super non-neutrality from creeping into the model’s structure. The experiments reported in this section, however, were generated by excluding the inflation differential term in order to produce something closer to the random walk assumption when the weight on the model-consistent forecast is imposed to be zero.

38/

The Bank of England also publishes inflation forecasts based on the market’s expectations of future policy rates. The path of policy rates is imposed exogenously rather than being derived endogenously within the forecast to change real monetary conditions as needed for inflation to converge on the target.

1/

For example, see J. Fuhrer, 1997, “The (Un)Importance of Forward-Looking Behavior in Price Specifications,” Journal of Money Credit and Banking, Vol. 29, No. [ ] (August), pp. 338–50.

2/

Adjustment for the expected inflation differential is necessary for ensuring that the behavior of the real exchange rate is independent of the target rate of inflation.

4/

The only exogenous variables in the model are the foreign price level and the foreign interest rate. These variables are held constant in the simulation experiments.

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International Monetary Fund