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)| false Isard, Peter, and Douglas Laxton, 1999, “ Monetary Policy with NAIRU Uncertainty and Endogenous Policy Credibility: Perspectives on Policy Rules and the Gains from Experimentation and Transparency,” forthcoming in Reserve Bank of New Zealand conference volume on Monetary Policy Under Uncertainty.
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)| false Isard, Peter, Douglas Laxton, and Ann-Charlotte Eliasson, 1999, “ Simple Monetary Policy Rules Under Model Uncertainty,” forthcoming 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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)| false Tetlow, Robert J., Peter von zur Muehlen, and Frederico Finan, 1999, “ Simplicity Versus Optimality: The Choice of Monetary Policy Rules When Agents Must Learn,” forthcoming in Reserve Bank of New Zealand conference volume on Monetary Policy Under Uncertainty.
The first two authors are with the Research Department of the International Monetary Fund. The third author was at the Stockholm School of Economics when this paper was written. We are grateful for comments received from Lars Svensson, from participants at the Computational Economics Symposium at Cambridge University (June 29-July 1, 1998) and the Reserve Bank of New Zealand Conference on Monetary Policy Under Uncertainty (June 29-July 3, 1998), and from an anonymous referee. A slightly shorter version of this paper is forthcoming in the Journal of Economic Dynamics and Control. The views expressed in this paper are those of the authors and do not necessarily reflect those of the International Monetary Fund.
Finland and Spain also operated with quantitative inflation targets for several years prior to relinquishing monetary policymaking to the European Central Bank.
A number of recent examples of such papers were included in the programs of the NBER Conference on Monetary Policy Rules (January 15–17, 1998), the Federal Reserve Bank of San Francisco Conference on Central Bank Inflation Targeting (March 6–7,1998), the Bank of Sweden Conference on Monetary Policy Rules (June 12–13, 1998), the 1998 Symposium on Computational Economics at Cambridge University (June 29–Julyl, 1998), and the Reserve Bank of New Zealand Conference on Monetary Policy Under Uncertainty (June 29–July 3, 1998). Earlier contributions to the inflation targeting literature include the conference volumes Leiderman and Svensson (1995), Haldane (1995), Federal Reserve Bank of Kansas City (1996), and Lowe (1997).
Rudebush and Svensson (1999) and Svensson (1999) distinguish between reaction functions that are essentially derived as first-order conditions for minimizing policy loss functions and reaction functions that are simply postulated, suggest that the term “targeting rule” should only be applied to the former class of reaction functions.
Related to this point, the issue of rules versus discretion for monetary policy has become less actively debated during the 1990s. This may reflect, first, a general acceptance of the premise that a fully-state-contingent rule for monetary policy is not a relevant possibility in a world in which knowledge about the macroeconomic structure and the nature of disturbances is incomplete, and second, a general awareness of the fact that simple (or partially-state-contingent) rules and discretion cannot be unambiguously ranked. In this context, Flood and Isard (1989, 1990) suggested that monetary authorities should be given incentives to follow simple rules with “escape clauses,” in recognition of the tradeoff between the various benefits of the rules and the social costs of failing to modify reaction functions in certain unforeseeable circumstances. Amano, Coletti, and Macklem (1999), among others, emphasize that credibility is a two-edge sword, and that the credibility benefits of monetary policy rules cannot be effectively reaped unless the monetary authorities are prepared to change their reaction function over time in response to new information about macroeconomic structure.
Inflation expectations are often modeled as a weighted sum of backward- and forward-looking components, and in this context a number of studies have followed Freedman (1996) in defining the forward-looking component as the announced inflation target and in interpreting the weight on this component as a measure of policy credibility. Within this framework, Amano, Coletti, and Macklem (1999) have analyzed the implications for monetary policy of “exogenous” changes in credibility. In addition, Tetlow, von zur Muehlen, and Finan (1999) have analyzed the optimal form of simple rules when private agents have to learn about the rule. To our knowledge, however, few if any evaluations of policy reaction functions have modeled credibility as a variable that responds endogenously to the monetary authority’s performance in delivering macroeconomic stability.
See, for example, Isard and Laxton (1996), Clark and Laxton (1997), and Laxton, Rose, and Tambakis (1999). See also Summers (1988), who questioned the value of basing policy analysis on models in which monetary policy is incapable of influencing the average rates of inflation and unemployment.
We report simulations for two calibrations of each class of rules. The first corresponds to the calibration suggested in Taylor (1993); the second is based on a calibration suggested by our analysis in Isard and Laxton (1999).
For most of the equations the sample period runs from the early 1980s through the mid-1990s.
Orphanides (1999) constructs a data base of the information available to U.S. policymakers in real time from 1965 to 1993 and suggests that misperception of the economy’s productive capacity was the primary underlying cause of the inflation of the 1970s.
In the linear variants of our model, the degree to which IFB rules outperform Taylor rules appears to be slightly greater under forward-looking expectations than under backward-looking expectations. This contrasts with results from other models, in which the optimal degree of forward-lookingness in expectations, which is often associated with the length of contract lags in wage and price setting; see, for example, Batini and Haldane (1999).
In Isard and Laxton (1999) we focus on a variant of IFB rules in which the authorities react to a weighted average of the deviation from target to their own inflation forecast and the deviation from target to the public’s inflation forecast (as reflected in survey measures of inflation expectations). Monetary rules that give weight to the latter deviation—that is, to the bias in the public’s inflation expectations—would appear to establish a channel for policy to respond directly to changes in credibility.
For most equations the sample period runs from the early 1980s through the mid-1990s.
The variables were detrended using the HP filter with a smoothing parameter of 1600; see Hodrick and Prescott (1981).
The specification explicitly treats
The appropriate interest factor corresponds to one plus the per-annum interest rate differential expressed as a quarterly rate.
Adjustment for the expected inflation differential is a necessary condition for ensuring that the behavior of the real exchange rate is independent of the target rate of inflation.
See Isard (1995). Although we do not investigate the issue in this paper, we have the impression that the choice between full model consistency and a backward- and forward-looking components specification of the expected future spot rate can make a considerable difference in using stochastic simulations to evaluate policy rules when the shocks that drive the simulations are drawn from distribution that reflect the variance of estimated residuals for the historical period over which the model is estimated.
As described in Appendix I, the Phillips curve is combined with an equation that describes a time-varying DNAIRU to provide a nonlinear estimation problem that can be solved using the Kalman filter technique. Kuttner (1991, 1992, 1994) has applied this idea to measuring potential output.
Econometric tests generally do not have sufficient power to reject with the hypothesis that the Phillips curve is linear or the hypothesis that the Phillips curve is convex. For discussions of potential pitfalls associated with conventional tests for asymmetries in the Phillips curve, see Clark, Laxton, and Rose (1996) and Laxton, Rose, and Tambakis (1999).
In equation (6) the estimated value of γ is 2.14. The estimation and stochastic simulations are based on the assumption that
The data are based on monthly surveys of 1200 randomly selected adults. Our time series was constructed by averaging the median responses over the three months of each quarter.
The methodology employed to develop the historical date for u* and
The model for the high-inflation state is based on work by Tarditi (1996); see the discussion in Callen and Laxton (1998). Note also that the 8.4 percent steady-state inflation rate used in the high inflation forecasting rule corresponds roughly to the average rate of inflation in Australia during the 1980s (recall Figure 2).
The measures of εH and εL are constructed by substituting the realized inflation outcomes into the left-hand-sides of equations (10) and (11), respectively. Such measures correspond to the ex-post errors associated with interpreting the realized inflation outcomes as ex ante forecasts of inflation under each scenario.
Flood and Garber (1983) presented an early model of stochastic switching in policy regimes, and Hamilton (1988, 1989) also contributed importantly to catalyzing the use of regime-switching models. See Laxton, Ricketts, and Rose (1994) for an application to the analysis of learning and endogenous monetary policy credibility in Canada; see Kaminsky and Leiderman (1998) for an application to developing countries.
In a more sophisticated model of learning, the measure of εH and εL would be adjusted for the public’s estimates of the authorities’ control errors. However, the development of such a learning model is beyond the scope of this paper, which simply aims to illustrate that endogenous policy credibility is a relevant consideration in the design of monetary policy rules.
The assumption of boundedness seems conceptually appropriate. However, the results we report in this paper are based on simulations that are all initialized with the DNAIRU at 7.0, and in which the DNAIRU rarely, if ever, hits its floor or ceiling.
Callen and Laxton (1998) describe the methodology employed to develop the historical estimate of the DNAIRU and NAIRU.
From technical and strategic perspectives, giving the authorities knowledge of the period-t inflation rate reduces the incidence of unstable stochastic simulations for the Taylor rule cases and appears to act in the direction of understating the extent to which IFB rules dominate Taylor rules in our simulation experiments.
The procedure that the authorities are assumed to use to update their estimates of the DNAIRU and NAIRU is described in Appendix I.
A value of 50 quarters is sufficiently long to insure that errors in the terminal conditions will not induce errors in the variables of interest. Under inflation targeting, the price level has a unit root, and the procedure for period-to-period updating of the authorities’ forecasts also involves period-to-period updating of the terminal conditions.
For the model variants with endogenous policy credibility, a few draws of the random shocks led to explosive simulations under rule calibrations that placed relatively high weights on the unemployment gap—specifically, the (α, γ) = (0.5, 1) calibrations; see below. We actually performed somewhat more than 100 sets of simulations and then discarded the results for the draws in which convergence failure was experienced under any one of the rule calibrations.
Faust and Svensson (1999) focus on a similar loss function with β > 0 in analyzing the pros and cons of central bank transparency.
The simulation set
Forward-looking IFB rules have been used for almost a decade at the Bank of Canada to solve nonlinear macroeconomic models designed for policy analysis. With the development of more robust and efficient solution methods, these rules are now starting to be used in other policymaking institutions. See Armstrong and others (1998) and Julliard and others (1998) for a discussion of the algorithms that can be used to solve these types of models.
Taylor’s (1993) version of the Taylor rule used a backward-looking measure of inflation expectations to measure the real interest rate.
We have not undertaken an extensive search for the optimal inflation forecast horizon. It may be noted that three quarters is roughly half the time that is generally believed to be required for interest rates to have their full effects on the economy.
See Isard, Laxton, and Eliasson (1999) for stability analysis of conventional Taylor rules in linear and nonlinear variants of a closed-economy model of the U.S. economy. In that study, simulations with conventional Taylor rules in the nonlinear model variants with forward-looking expectations generated explosive behavior under most drawings of the random shocks.
See Isard and Laxton (1999). We also experimented with a third calibration of the Taylor rule, namely (α, γ) = (.5, 2), corresponding to a suggestion in Taylor (1999). Our results suggested that moving from (.5, 1) to (.5, 2) tends to worsen macroeconomic performance under conditions of NAIRU uncertainty and endogenous policy credibility. Consistently, the results reported below suggest that performance under a Taylor rule can be improved by moving from (.5, 1) to (2, 1).
It may be noted that the sample means and standard deviations of the DNAIRU are identical for all combinations of model variants and policy rules, reflecting the fact that in each case the stochastic simulations are based on identical initial positions and sequences of random shocks.
Other papers that have employed stochastic simulations to evaluate the performances of monetary policy rules have focused almost exclusively on linear models and have often summarized the relative performances of different rules by plotting the associated standard deviations of unemployment and inflation on a two-dimensional graph.
Taylor’s (1999) suggestion was that a calibration of (.5, 1) would outperform (.5, .5) in a rule specification analogous to equation (15) but with the output gap in place of the unemployment gap. As noted earlier, based on a rough estimate that the unemployment gap tends to vary about half as widely as the output gap over the business cycle, we view a weight of unity on the unemployment gap as broadly comparable to a weight of 0.5 on the output gap.
This result does not necessarily imply that estimates of the unemployment gap are too imprecise to inform monetary policy in a useful way, even though the authorities’ estimates of the unemployment gap may often be incorrect as well as in magnitude. In particular, in simulations not reported in this paper, we have shown that IFB rules that place no weight on the unemployment gap are dominated by other calibrations.
See, for example, Amano, Coletti, and Macklem (1999) and Batini and Haldane (1999) for studies that have influenced thinking at the Bank of Canada and Bank of England, respectively. See Kohn (1999) for perspectives on how information about the implications of monetary rules helps structure thinking by some members of the U.S. Federal Open Market Committee.
As noted earlier, in simulation analysis of a closed-economy model of the United States, Isard, Laxton, and Eliasson (1999) found that in nonlinear model variants with forward-looking expectations, conventional Taylor rules led to explosive behavior for most drawings of random shocks.
This is especially the case for the conventional form of the Taylor rule, which embodies a backward-looking measure of the real interest rate and reacts to a backward-looking measure of inflation.
In the true model we assume that the DNAIRU process is a bounded random walk that ranges between 4 and 10. However, for the purpose of updating the u* and