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Monetary policy regime shifts: new evidence from time-varying interest rate rules.

I. INTRODUCTION

Interest rate policies are complex decisions. They rely on a multitude of indicators and models and are by nature associated to events not always captured by relatively simple econometric tools. Nonetheless, there is now a widespread consensus that the class of simple policy rules examined by recent microfounded models of the economy generates stabilization properties that are very close to those of optimal feedback rules (Woodford 2003). Feedback rules nowadays are customary tools for monetary policy analysis. Furthermore, rule-based policymaking is generally accepted as the reference framework of monetary policy strategies (Bank of England 1999; European Central Bank 2004).

Monetary policy reaction functions summarize the importance that policymakers attach to policy objectives as well as their views on the structure of the economy. Traditionally, those functions are estimated as constant parameters policy rules. This is a plausible simplification, but a number of reasons suggest that rules should allow for instability and parameter variation over time. Constant parameter reaction functions might blur the role played by various real-world factors: (1) model uncertainty, (2) conflicting objectives, (3) shifting preferences on policymakers' choices, and (4) nonlinearities. In particular, reduced-form policy models that do not allow for shifts and asymmetries in behavioral relationships could produce misleading results. Dynamic stochastic general equilibrium (DSGE) models represent one potentially promising way of overcoming these problems. This increasingly popular approach is based on microfounded descriptions of the economy. Recent studies also provide novel techniques to estimate and evaluate linearized DSGE models using Bayesian methods (Del Negro et al. 2007). The Bayesian framework represents a natural setup to account for model and parameter uncertainty. However, the DSGE approach imposes a large number of restrictions on the data. In the specific context of interest rate rules, its ability to generate qualitative and robust assessments on monetary policy conduct appears problematic.

This article provides some new evidence on interest rate policies in five large economies (United States, United Kingdom, Germany, France, and Italy) through the implementation of a time-varying parameters approach (TVP henceforth). We estimate policy rules as summarized by simple reaction functions defined in terms of expected inflation and output gaps. In contrast with most existing analyses, we employ a TVP methodology based on the Kalman filter algorithm to estimate our instrument rules. In practice, we allow the policy rules' coefficients to vary over time. What we obtain are estimates of the state vector for each observation in our sample. These estimates can then describe the evolution of monetary policy over time. Moreover, we evaluate the conditional variance of interest rates implied by our TVP methodology.

A host of factors may cause shifts in the estimated parameters of monetary policy reaction functions. Some of them may be due to institutional reforms like the introduction of inflation targets or the move to an exchange rate peg or a fixed exchange rate. In estimating reaction functions defined in terms of final policy objectives, one aims at capturing the relative emphasis placed by policymakers on the attainment of output and inflation targets. Over time, such emphasis might evolve. Therefore, one needs to model the observer's view on the likelihood that these shifts are smooth transitions or abrupt regime changes. By allowing the weights of the policy rule to vary only gradually, we are able to identify relevant shifts in policy conduct, regardless of their exact configuration. As argued at length in the next section, our approach is better suited than conventional fixed-parameter techniques to deal with Lucas critique and, more in general, with the issue of structural change. Last, our methodology addresses the well-known endogeneity of the regressors in the policy rules that severely constrains the use of ex post as opposed to real-time data.

We find that monetary policies followed in the countries we study, often described in terms of standard Taylor rules (Taylor 1999), are best summarized by feedback rules that allow for time variation in the policy responses to macroeconomic conditions. Overall, the evolution of parameters portraits a richer picture of central banks' conduct and it is consistent with accounts of historical macroeconomic events. Moreover, our estimated policy rules describe policies according to different coefficient estimates and, in some cases, different functional forms. Our parameters do shift over time in most cases in a smooth and gradual fashion. These findings corroborate the use of country-specific interest rate rules and the validity of the TVP approach. Finally, our rules outperform conventional specifications of the policy rules in tracking actual interest rate developments.

The article proceeds as follows. Next section discusses recent developments in the empirical literature on monetary policy and structural change and motivates our approach. Section III describes our interest rate rules and methodology, while Section IV presents estimation results. Section V concludes.

II. OPTIMAL AND ESTIMATED INTEREST RATE RULES

Most contemporary macroeconomic models posit that monetary policy decisions minimize the expected value of an intertemporal loss criterion (Woodford 2003). As a consequence, the nominal policy rate could evolve according to, for instance, the following implicit instrument rule: (1)

[i.sub.t] = (1 - [[phi].sub.1])[i.sup.*] + [[phi].sub.1][i.sub.t-1] + [[phi].sub.2] [DELTA][i.sub.t-1] + [[phi].sub.3][[pi].sub.t] + [[phi].sub.4] ([y.sub.t] - [y.sup.*.sub.t]) (1)

where ([y.sub.t] - [y.sup.*.sub.t]) is the output gap, [i.sub.t] is the nominal short-term (policy) interest rate, [[pi].sub.t] is inflation, and [i.sup.*] is the target level of the policy rate. The coefficients are convolutions of the structural parameters of the model. According to this rule, the policy instrument displays persistence, follows developments in inflation and the output gap, and responds to past interest rate changes.

Inflation (-forecast) targeting rules describe the behavior of policy rates as following the projections of inflation and some additional variables in the future. Simple policy rules like the above one are usually derived from models that often posit forward-looking pricing behavior and sticky prices (2) and usually comprise an intertemporal IS relation and a structural Phillips curve. The former is an approximation of the log linearized version of a consumption Euler equation, while the latter links current inflation and output (or the output gap) in a way that depends on the prevailing price-setting mechanism (in Calvo-type models on staggered pricing). These relations constrain stabilization policy.

Of course, there exists a wide range of differentiated models. For instance, assuming partial indexation to an aggregate price index or staggered wage and price contracts generates persistence in inflation (Christiano, Eichenbaum, and Evans 2005). The form of the optimal rule itself changes somewhat when both prices and wages are sticky (Amato and Laubach 2003; Erceg, Henderson, and Levin 2000) or if private expenditure displays habit persistence (as in Smets and Wouters 2003 or Muscatelli, Tirelli, and Trecroci 2004). Finally, one observes well-documented lags in the reaction of output and inflation to unexpected changes in interest rates due to predetermined pricing and spending decisions. This motivates the minimization of interest rate volatility as an additional goal of stabilization policies (the so-called interest rate smoothing effect).

Since Taylor's (1993) proposal of a simple interest rate rule defined in terms of current inflation and output gap, (3) the behavior of central banks has been analyzed via the estimation of equations like Equation (1) on quarterly or monthly data. (4) Examples include Batini and Haldane (1999), Clarida, Gali, and Gertler (2000), and Muscatelli, Tirelli, and Trecroci (2002b). An important issue has received only minor attention: how does the Lucas critique affect the evaluation of monetary policy models?

Available estimated policy rules acknowledge that central banks have displayed changing attitudes toward inflation and output stabilization. For instance, Taylor (1999) and Clarida, Gali, and Gertler (2000) find different parameter estimates over subsamples of the past three decades of U.S. data. (5) Muscatelli, Tirelli, and Trecroci (2002b) identify gradual changes (and some regime shifts) in the conduct of interest rate policies of major advanced countries.

According to Lucas critique, such changes could alter agents' expectations of the future policy course and affect the behavioral parameters of IS and Phillips curve relations. With models whose behavioral equations react to structural policy changes, forecasting and policy analysis could potentially be biased. On the other hand, Rudebusch (2005) points out that the observed stability of estimated reduced-form representations of the economy, like the vector autoregression (VAR) models so popular in the literature on the transmission mechanism, supports structural invariance. (6) Hence, Rudebusch (2005), but also Estrella and Fuhrer (2003), argue that the Lucas critique, while relevant at a theoretical level, might be less so on empirical grounds, especially in the context of Fed's reaction function and/or small shifts in the policy rule. However, some caution is in order, as this argument implies that some policy shifts might be detectable through econometric methods despite being irrelevant as to their effects on agents' expectations.

One obvious possibility is that changes in policymakers' preferences are in fact small and gradual, so that they are processed by private agents through a similarly gradual learning process. Overparameterized constant parameters representations of the economy, as VAR models typically are, make it difficult to evaluate these effects. Alternatively, there is a widespread conviction that Fed's inflation aversion was stronger in the 1980-1990s than in 1970s. Sims and Zha (2006) estimate various multivariate models with discrete breaks and allow for simultaneity and regime switches in coefficients and variances. Among various models with changes in coefficients, the best fit is found for a model that displays time variation only in the monetary policy rule. However, Sims and Zha argue that monetary policy changes are driven more by the time-varying variance of the shocks than by time variation in the coefficients of the policy rule. The estimates of Primiceri (2005) capture changes in private sector behavior. Primiceri models and estimates a structural VAR of the U.S. economy, allowing for time variation in both the coefficients and the covariance matrix of the model's innovations. His estimates support the view that important changes affected both the systematic and the nonsystematic components of U.S. monetary policy over the past 40 years. However, as the equations describing the private sector are convolutions of the underlying behavioral relationships, one cannot clearly disentangle policy and nonpolicy responses. Finally, Boivin (2006) computes time-varying estimates of policy responses using real-time data. The main drawback of his approach is that if the real-time forecasts used as regressors are not derived under the assumption that policy rates will remain constant within the forecasting horizon, the regressors will be correlated with the disturbance term of the reaction function.

Assenmacher-Wesche (2006) studies monetary policies in the largest European Union countries and in the United States via the estimation of a Markov-switching model that allows for independent switching processes in the parameters of policy rules and in their residual variance. The inflation and output coefficients of the policy rule appear to evolve according to two different regimes: a "hawkish" regime (low coefficient on output stabilization and a high one on inflation stabilization) and a "dovish" regime (where the opposite holds). Moreover, one-off shocks like supply-side disturbances or institutional reforms are accounted for by a switching in the residual variance. The focus of Assenmacher-Wesche (2006) was to investigate changes in central banks' attitude toward policy targets, and this makes it very close in spirit to our article.

The problem with discrete break (and conventional VAR) models is that they fail to account for gradual policy changes and lead to problematic interpretations when actual regime shifts do not fit exactly in one of the modeled regimes. Such approach considers the variation across averages of policy responses in each regime but ignores the variation of responses within each regime.

In this article, we treat policy responses as endogenous variables that vary over time and directly estimate them. An alternative, promising route to account for these and other problems is the DSGE-VAR approach employed, for instance, in Del Negro et al. (2007). However, DSGE models as tools for the evaluation of policy rules still pose several challenges, given their relative complexity.

Stability analysis on estimated forward-looking interest rate rules provides some indications about changes that take place in the actual conduct of monetary policies. Indeed, Muscatelli, Tirelli, and Trecroci (2002b) find evidence that changes in advanced countries' policies did occur, possibly echoing some preference shifts in the collective attitude toward the costs of inflation. Even in countries such as the United States and Japan, where monetary policies were not involved in major institutional innovations like the introduction of inflation targets, policy shifts were clearly visible. We believe that these findings motivate a focus on gradual policy change rather than on structural breaks.

The policies of countries now belonging to the European Monetary Union (EMU) have received large attention in the literature on interest rate rules. Most studies focus on single-country reaction functions (Clarida, Gali, and Gertler 1998; Muscatelli, Tirelli, and Trecroci 2002a), while others propose the estimation of area-wide policy rules. In the latter strand, Gerlach and Schnabel (2000) is one of the most influential contributions. The authors find that a modified version of the Taylor rule, specified in terms of area-wide inflation and output gaps, explains well the behavior of average interest rates in the EMU countries in 1990-1998, with the exception of the 1992-1993 years, when marked exchange rate turbulences hit those countries. However, those findings from aggregate data seem at odds with accounts of macroeconomic events of the 1990s.

The convergence that led to the EMU was a difficult and uncertain process. At least in its early years, some countries' domestic real interest rates commanded substantial risk premia, while inflation expectations remained stubbornly high. Throughout the 1990s, the process of macroeconomic convergence toward EMU took place in countries where initial monetary conditions and policy credibility were relatively similar (France) or relatively different (Italy) from those prevailing in Germany. During that period, the countries belonging to the exchange rate mechanism (ERM) went through a gradual hardening of the exchange rate constraint. The "hard ERM" phase followed an initial crawling-peg-like experience, and the "wide band" arrangements were enacted just after the 1992-1993 crisis. The rules in Gerlach and Schnabel (2000) attempt to capture the systematic component of monetary policy decisions. It is therefore puzzling that a euro area-wide rule turns out to fully track interest rate behavior in such a changing environment. We therefore estimate single-country instrument rules but adopt a procedure that allows for smooth changes in policymakers' reactions to the economy. This way we should be able to identify the effects of policy changes on the parameters of the rule. We adopt the class of simple reaction functions we illustrated above and measure the impact of policy change on interest rate rules by studying how their coefficients vary over time. We consider five advanced countries: the United States, the United Kingdom, Germany, France, and Italy (the so-called EMU3).

Our modeling approach has several advantages also when it comes to the issue of possible nonlinearities and asymmetries in policymakers' behavior (Cukierman and Gerlach 2003; Dolado, Pedrero, and Ruge-Murcia 2004). On the one hand, the central bank may react differently to inflation shocks in high and low inflation regimes. On the other hand, it could be more sensitive to output below than above potential. Finally, Smets (2002) shows that the extent of uncertainty about economic conditions crucially affects the coefficients of the Taylor rule. Since there is evidence of a worldwide decline in business cycle volatility over the 1980s and 1990s (McConnell and Perez-Quiros 2000; Stock and Watson 2003), this might have had an effect on interest rate rules that would be interesting to precisely evaluate. Next section describes our methodology.

III. GRADUAL POLICY CHANGE: ATVP APPROACH

The models we estimate drop the constant coefficients hypothesis on which existing estimates of interest rate rules are based. The coefficient vectors of our rules change over time according to the implementation of the Kalman filter algorithm. The intuitive appeal of this methodology is that changes in policy regimes and the structure of the economy can be modeled as a gradual evolution of the rules' coefficients.

Doan, Litterman, and Sims (1984) pioneered the estimation of models with TVPs, and this article follows their methodology by letting the parameters of the models evolve as more observations are added. (7) Let us represent the model in a general state-space form (Harvey 1989; Kim and Nelson 1999):

[i.sub.t] = [c.sub.t] + [x'.sub.t][b.sub.t] + [e.sub.t] (2)

[b.sub.t+1] = d + [T'.sub.t][b.sub.t] + [z.sub.t+1], (3)

where [e.sub.t] [approximately equal to] N (O, [[sigma].sup.2]), [z.sub.t] [approximately equal to] N(O, Q), and

[b.sub.o] [approximately equal to] N ([a.sub.0] , [[SIGMA].sub.0]), (4)

with [x.sup.t] containing the explanatory variables.

Equation (2) is the so-called measurement or observation equation. It is the classical linear regression model except that the parameter vector [b.sub.t] (representing the state variables) is allowed to change stochastically according to the transition Equation (3). We follow Doan, Litterman, and Sims (1984) in positing the so-called Minnesota prior distribution for the state vector. This prior distribution holds that changes in the endogenous variable modeled are so difficult to forecast that in the AR(1) process of the unobserved state vector, the coefficient on its lagged value is likely to be near unity, while all other coefficients are assumed to be near zero. The prior distribution is independent across coefficients, so that the mean squared error (MSE) of the state vector is a diagonal matrix. Measurement errors and the disturbances to transition equations are assumed to be serially and mutually independent. The initial conditions (i.e., the prior distribution) for the state vector [b.sub.t] are specified in Equation (4); the elements of Q are estimated through maximum likelihood (ML) methods along with the other parameters of the model.

Summing up, this time-varying formulation involves forecasting the optimal state vector in each period based on information available up to the previous period. Under the normality and independence assumptions about the disturbances, the computation of the state vector is obtained via application of the Kalman filter (Hamilton 1994). This way we compute filtered estimates of the parameters and the residuals for each observation in the sample, thus accounting for the potential variation over time of the underlying parameters. This allows us to capture structural regime shifts.

A further advantage of our Kalman filter-based approach is that it yields partial information estimates of the policy coefficients. One of the problems with the use of ex post data is that the forward-looking regressors included in the policy rule are correlated with the equation's disturbance term. This endogeneity problem can be dealt with by using an instrumental variables methodology or by allowing the time t estimated coefficients to be based only on information up to time t. The filtering algorithm we employ provides the time t expected value of the state vector conditional only on information available at time t. (8)

To fully take into account the effects of uncertainty about regression coefficients, we also compute the variance of the conditional forecast error in the Kalman filter. The ARCH approaches often employed in such context allow for randomness in the variability of shocks to the regression equation and in so doing they offer a reasonable way to model changing uncertainty about the future. It is worth noting that the estimates we obtain for the variance of the Kalman-based conditional forecast error go well beyond that, as they also account for both parameter and model uncertainty. This is because they provide a direct measure of the conditional variance of the policy rate, as a result of the changes in the time-varying components of the model.

We report estimates for the best-fitting reaction functions among the various specifications we tried. The sample period was early 1970s to 1998 for Germany, France, and Italy, (9) whereas for the United States and United Kingdom, we use data spanning, respectively, 1970-2006 and 1980-2006. We included the United Kingdom also because its monetary policy went through important reforms partly shared by other economies. Last, but not least, the United Kingdom adhered to the ERM between 1990 and 1992.

Our starting model was in each case Equation (1). That formulation stems from forward-looking specifications of the type (Woodford 2003):

[i.sub.t] = [alpha] + [beta][E.sub.t][[pi].sub.t+j] + [gamma][(y - [y.sup.*]).sub.t-s] + [k.summation over n=1] [[rho].sub.n] [i.sub.t-n] + [l.summation over p=1] [[delta].sub.p] [x.sub.t-p] + [[epsilon].sub.t], (5)

in which, for simplicity, we have not included time subscripts for the coefficients.

In line with the existing literature (Clarida, Gali, and Gertler 1998), we also estimated specifications with additional variables ([x.sub.t]), such as measures of the exchange rate and a relevant international interest rate. This permits to check whether monetary authorities targeted intermediate or final objectives over and beyond those included in the baseline specification. As to the output term, Woodford (2003) argues for including the difference between real gross domestic product (GDP) and its long-run level. This variable will change in response to real disturbances (preferences, technology, and fiscal policy). However, the evolution of all these real factors may not follow the smooth trends (Hodrick-Prescott [HP] derived) that the literature commonly employs.

To measure inflation expectations and the output gap various methods are available. It is common to extract trend inflation through the application of HP, linear, or band-pass filters. Alternatively, results from market surveys or measures extracted from inflation swaps or bond-based break-even inflation rates are available, but only for relatively short samples of data. For the measurement of output gap, the production function approach and various multivariate methods provide more sophisticated alternatives to available filtering methods. The use of the HP filter to proxy the output gap is popular in applied work, although it is often questioned. Estimates do not take into account potential measurement errors, or the two-sided nature of the filter, which may cause violations of weak and strong exogeneity assumptions.

In this article, we employ the structural time series approach proposed by Harvey (1989) to generate series for the output gap. The procedure amounts to decomposing the series into trends, recursive stochastic cycles, and irregular components that vary over time. This way we fit univariate models for real GDP for each country and extract time-varying measures of potential output that for each observation rely only on information available up to the point of estimation. This modeling approach too applies a Kalman filter estimation procedure in line with a plausible learning process for both the central bank and the private agents. As a robustness check, we also tried with a measure of output gap provided by the Organization for Economic Cooperation and Development (OECD), and with HP- and band-pass filters, but we found very little differences in the resulting estimates of the policy functions.

We measured inflation expectations by fitting a trend to the original inflation series using either the HP filter or the Kalman-based procedure we illustrated for the output gap term. This permits to compare our results with most existing studies. Other procedures, like alternative filtering methods or polynomial trends, did not yield significantly better fit for our models.

As to the coefficients' lags, we report only estimates for equations with significant coefficients. Typically, we found that a lag length of n = 1 was sufficient to capture the inertial behavior of the policy instrument induced by monetary authorities. As to the lead on inflation, we performed a search for it on the basis of conventional goodness-of-fit criteria. In most cases, the reaction lead was decided by statistical significance and in one or two cases by the ease of convergence of the optimization algorithm. For this reason, we found that when using filtered measures of expected inflation, the appropriate lead was between j = 2 and j = 4 quarters. This is in line with most dynamic simulations of calibrated theoretical models (Taylor 1999; Woodford 2003).

As is well known, the lack of statistical significance for the output term in a policy rule does not imply that interest rate policy is not geared at stabilizing output shocks. Indeed, monetary authorities can fine-tune the degree of inflation versus output stabilization by simply adjusting the responsiveness of policy rates to inflation shocks and their overall degree of inertia. However, in most of our estimates, one lag of the dependent variable and the output gap, either lagged or current, turned out to be significant.

IV. ESTIMATION RESULTS

For each country, we report estimates of the coefficients in the instrument rule (5). A t subscript indicates that we allow the coefficient to vary over time according to the stationary first-order autoregressive process with drift of Equation (3). In some cases, the specification with the best fit implied time invariance for specific coefficients; in those cases, a time subscript will not appear. The Data Appendix describes definitions and sources of our data.

Our main findings can be summarized as follows:

1. Interest rate rules diverge widely across our sample; for example, they identify policy conducts across countries according to different coefficient estimates and, in some cases, different functional forms.

2. Coefficient estimates seldom display statistically constant behavior.

These results corroborate our choice of single-country instrument rules and the validity of a TVP approach. Below we present detailed results for each country.

A. United States

For the United States (sample 1970:1 to 2006:2), the best-fitting model refers to the following specification:

[i.sub.t] = [[alpha].sub.t] + [[beta].sub.t][E.sub.t][[pi].sub.t+2] + [[gamma].sub.t] [(y - [y.sup.*]).sub.t-1] + [[rho].sub.t][i.sub.t-1] + [[epsilon].sub.t],

where it is the nominal Federal Funds Rate, [E.sub.t][[pi].sub.t+2] is four quarters expected change in the price level, two quarters ahead, computed by applying the standard HP filter to the inflation series, and (y - [y.sup.*]) is the output gap. (10)

Figure 1, top panel, plots the estimates of the state vector ([[beta].sub.t], [[gamma].sub.t], [[rho].sub.t]) along with two standard error bands. Table 1 reports, for each state variable, the minimum, maximum, and mean values of the coefficients in the sample and the date they occurred.

The response of policy rates to inflation rises significantly since around 1977-1978, reaching a very high level that lasts essentially for a decade, then gradually falls toward a low level. At the turn of the millennium, it displays insignificant point estimates. These estimates confirm that the Fed followed generally looser monetary policies since 1995, around the so-called productivity miracle and the spell of low interest rates between 2002 and 2004. The behavior of the interest rate smoothing term is pretty symmetrical. Its coefficient is statistically significant for most of the sample period, negative at times between 1980 and 1994, and positive elsewhere. This means that interest rate inertia seems to be a systematic feature of Fed's policies. The output gap enters significantly the policy rule, particularly during the long tenure of Alan Greenspan at the Fed. Finally, the conditional forecast error variance of the policy rate exhibits a general downward trend starting with Volcker's monetarist experiment during which uncertainty reached a maximum.

[FIGURE 1 OMITTED]

Overall, while these results largely coincide with narrative accounts of Fed's policy, they also raise some novel points. Volcker's chairmanship clearly stands out as the only significant break in American monetary policy. Once one accounts for the autoregressive behavior of policy rates and the relative size of macroeconomic shocks, the Fed's inflation stances of the 1970s and 1990s cannot easily be disentangled. (11) The coefficient estimates for the early 2000s confirm the adoption of a particularly inertial and accommodative policy stance.

The charts on the bottom panel of Figure 1 show the behavior of the coefficients on inflation ([[beta].sub.L]) and output gap ([[gamma].sub.L]) derived from the long-run solution of our estimated interest rate reaction function. The long-run static reaction function obtained by inserting the mean values of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], and [[gamma].sub.L] = [[??].sub.t]/(1 - [[??].sub.t]) is:

[i.sub.t] = 0.66 + 1.79[E.sub.t][[tau].sub.t+2] + 0.28[(y - [y.sup.*]).sub.t - 1] + [[epsilon].sub.t].

The long-run policy rule (12) points to a broadly stabilizing reaction of policy rates to inflation: the inflation coefficient is sizeable and largely exceeds unity. Coefficients' values are very much in line with standard Taylor rule figures. Interestingly, the 1980s were characterized by high values of the inflation response and low ones for the reaction to output shocks, while the 1990s and 2000s saw a growing emphasis on output stabilization. In the context of shallower business cycle fluctuations (Stock and Watson 2003), this led to a dramatic fall of the long-run inflation coefficient for the early 2000s, which apparently did not entail higher uncertainty of policy rates.

B. Germany

For Germany (sample 1971:3 to 1998:4), we show results for the following reaction function:

[i.sub.t] = [[alpha].sub.t] + [[beta].sub.t][E.sub.t][[tau].sub.t+2] + [[gamma].sub.t][(y - y.sup.*]).sub.t-1] + [[rho].sub.t][i.sub.t-1] + [[epsilon].sub.t].

Figure 2 and Table 2 show that the underlying policy objectives appear to have remained overall stable. Notwithstanding, even for Germany, it is possible to find interesting dynamics in the behavior of policy responses. The short-run coefficient on inflation is always sizeable but its magnitude rises significantly during the first half of 1980s and falls thereafter, hitting a trough later in the decade. Although falling toward negligible values at the end of the sample, the coefficient on the output gap is significant. By coupling this with a significant interest rate inertia post-1985, we cannot reject the hypothesis that Bundesbank's policies systematically followed cyclical conditions, despite being formulated in terms of explicit monetary targets. The reunification of Western Germany with Eastern Landers clearly affected the stability of the policy objectives and this shows up also in the behavior of the conditional forecast error variance of the policy rate, whose fall is dramatically reversed at the end of 1980s, before decreasing again toward the end of our sample.

The long-run static solution of the reaction function,

[i.sub.t] = - 0.14 + 1.91[E.sub.t][[tau].sub.t+2] + 0.2[(y - [y.sup.*]).sub.t-1] + [[epsilon].sub.t],

yields numerical values for the policy responses to macroeconomic developments that are consistent with a very strong antiinflationary commitment (the inflation coefficient is well above unity). Figure 2, bottom panel, also confirms that the Bundesbank's policy thrust turned gradually less sensitive to output gap developments.

C. United Kingdom

For the United Kingdom (sample 1980:1 to 2005:3), we report estimates for the following interest rate reaction function:

[i.sub.t] = [[alpha].sub.t] + [[beta].sub.t][E.sub.t][[tau].sub.t+2] + [[gamma].sub.t][(y - [y.sup.*]).sub.t-1] + [[rho].sub.t][i.sub.t-1] + [[delta].sub.t][i.sup.f.sub.t] + [[epsilon].sub.t],

where, alongside regressors we have already used, we inserted the 3-month FIBOR German rate (13) ([i.sup.f.sub.t]). This inclusion seemed plausible since external constraints did seem to have some importance for the conduct of monetary policies in the United Kingdom. In particular, the linkage with Bundesbank's policies emerges very clearly from existing narrative and econometric accounts (see, for instance, Nelson 2002; Muscatelli, Tirelli, and Trecroci 2002b).

[FIGURE 2 OMITTED]

Results shown in Table 3 and Figure 3 portrait a very rich picture of UK's monetary policy. The short-run inflation coefficient turns out to be significant and substantially growing in magnitude over almost the entire sample period. We remind that the United Kingdom adopted an inflation-targeting framework in 1992, while the Bank of England obtained full independence over interest rate policy in May 1997. Overall, our results point to a policy stance becoming gradually more inflation-averse over time. Although the output gap does not enter significantly, the interest rate smoothing effect is significant and with the correct sign starting from 1996. Therefore, we cannot rule out a systematic attention of the Bank of England to output stabilization. Interestingly, the coefficient of the FIBOR-EURIBOR regressor becomes statistically significant shortly before UK's entry in the ERM. The early 1990s saw the abandonment of the loose monetary targeting regime implemented since the late 1970s and a renewed emphasis on exchange rate targeting (the "shadowing the D-Mark" phase). The significance and persistence of this effect suggest that external developments have maintained a role in the setting of domestic policy rates even in a system of floating exchange rates.

[FIGURE 3 OMITTED]

Our long-run static estimates suitably confirm this claim,

[i.sub.t] = 1.5 + 1.28[E.sub.t] [[tau].sub.t+2] - 0.09[(y - [y.sup.*]).sub.t-1] + [0.40i.sup.f.sub.t] + [[epsilon].sub.t],

where the most important feature to notice is the magnitude of the coefficient associated with the reference foreign interest rate.

D. France

For France (sample 1971:3 to 1998:4), the specification with the best fit was again14

[i.sub.t] = [[alpha].sub.t] + [[beta].sub.t][E.sub.t][[tau].sub.t+2] + [[gamma].sub.t][(y - [y.sup.*]).sub.t-1] + [[rho].sub.t][i.sub.t-1] + [[delta].sub.t][i.sup.f.sub.t] + [[epsilon].sub.t].

We also experimented with a rule that featured a measure of the real effective (trade-weighted) exchange rate, but we found it never significant. Since this also impaired the convergence of our algorithm, we dropped it altogether.

The charts in Figure 4 and Table 4 show that, while the late 1970s saw a marked rise in the response of policy rates to changes in inflation, after 1982-1983, a more decisive policy change materialized. The response to cyclical conditions, that is, the reaction to the output gap, basically faded. That to external conditions, as summarized by developments in the FIBOR rate, rose to unprecedented levels. This means that French monetary policy turned overall more hawkish, especially as it became better synchronized with Bundesbank's. French interest rates too displayed significant inertia.

In the latter part of the sample, output developments seem to become more relevant and coordination with German rates less tight likely because of the stabilization of inflation expectations. Finally, the long-run static solution to the reaction function,

[i.sub.t] = 0.096 + 0.58[E.sub.t][[tau].sub.t+2] + 0.005[(y - [y.sup.*]).sub.t-1] + [0.86i.sup.f.sub.t][[epsilon].sub.t].

shows a long-run response of rates to inflation falling short of 1 and a negligible response to output. The systematic tendency of French rates to follow German interest rates clearly affects the size of the inflation coefficient. Interestingly, the conditional variance of the forecast error of the policy rate does display a downward trend, but it stabilizes at low levels only after reaching a medium-term peak around ERM's crises in 1992-1993.

E. Italy

The model with the best fit for the Italian reaction function over the available sample 1971:1 to 1998:4 was the following:

[i.sub.t] = [[alpha].sub.t] + [[beta].sub.t] [E.sub.t][[tau].sub.t+2] + [[gamma].sub.t][(y - y.sup.*]).sub.t-1] + [[rho].sub.t][i.sub.t-1] + [[DELTA].sub.t][i.sup.f.sub.t] + [[epsilon].sub.t].

where [E.sub.t][[tau].sub.t+2] is as above two quarters ahead annualized expected inflation, computed by applying the standard HP filter to the inflation series. The estimates displayed in Table 5 and Figure 5 show a long-term increase for the inflation coefficient, which ends up with a value significantly above unity. In particular, the early 1980s, 1986-1987, and 1996-1997 appear as instances in which monetary policy turned markedly more aggressive toward inflation; those years also saw changes in the other coefficient estimates, consistently with those policy shifts. The growing importance of external constraints is easily summarized by the behavior of the DELTA coefficient, which becomes statistically significant in the 1990s, in correspondence of the hardening of the ERM. (15) This is also mirrored in the fall of the size and significance of the interest-smoothing term.

[FIGURE 4 OMITTED]

This dynamics is broadly confirmed by the values of the parameters in the long-run solution,

[i.sub.t] = 1.54 + 1.21 [E.sub.t][[tau].sub.t+2] + [[gamma].sub.t][(y - y.sup.*]).sub.t-1] + [0.26i.sup.f.sub.t] + [[epsilon].sub.t]

All in all, the observed evolution of coefficients is consistent with the historical analysis regarding Italian monetary policy. (16) Specifically, for the years 1981-1986, the rise in the inflation coefficient accords well with the view that, after the "divorce," (17) Italian monetary policy shifted to a more inflation-averse stance. The Bank of Italy gained further independence during 1992-1993. (18) Finally, commitment to ERM forced Italian monetary policy to pay growing attention to the external constraint. The TVP estimates show that the external constraint became particularly binding around the speculative attacks against the lira in 1976, 1985, and 1992. As in the French case, the policy rate's conditional variance settles down persistently only after reaching a medium-term peak around ERM's crises in 1992-1993.

[FIGURE 5 OMITTED]

Overall, while the average point estimates of short-term coefficients appear similar to the case of France, the evolution of Italian monetary policy responses depicts a different dynamics, consistently with a diverse macroeconomic context.

F. TVP Rule versus Taylor Rule in the United States

The Taylor rule is widely employed as a tool for tracking actual policy rates, both for academic policy analysis and for forecasting purposes by market participants (see, for instance, Goldman Sachs 2007). In this subsection, we briefly look at how our TVP rule fares vis-a-vis the Taylor rule. To this end, we feed the values of expected inflation, output gap, and lagged policy instrument into our TVP reaction function and obtain a series for the policy rate "implied" by our rule. We perform a similar computation using the rule proposed by Taylor (1993):

[i.sub.t] = 4% + 1.5([[tau].sub.t] - 2.00%) + 0.5[(y - [y.sup.*]).sub.t],

where the constants conventionally account for an implicit inflation target of 2% per annum and an estimate of the long-run real policy rate of 2% (for the United States) as well. (19) As an additional check, we compare the policy rates implied by the TVP and by the conventional Taylor rule (CT) with what one obtains by estimating, via generalized method of moment (GMM), the forward-looking rule (CGG) proposed by Clarida, Gali, and Gertler (1998, 2000).

To give a visual idea of how the three rules track the behavior of historical policy rates, Figure 6 plots the deviations of implied rates from the actual Fed funds rate over the period 1972Q4-2005Q4. (20)

The most visible fact is that CT fares worst in tracking the developments of policy rates, as pointed out by the very large deviations in the late 1970s and early 1990s and 2000s. The CT rule also markedly undershoots the actual rate in the first half of the 1980s. The TVP and CGG rules follow much more closely the actual behavior of the short-term rate: their correlations with the Fed funds rate are 0.99 and 0.92, respectively.

Table 6 lists (1) the mean value of deviations (ME), (2) the mean value of absolute deviations (MAE), (3) the root mean squared error (RMSE) of each rule' s implied rate from actual data. The difference in the correlation index reverberates in the more accurate tracking performance of TVP against CGG, as measured by the simple statistics of Table 6. The TVP rule seems to fare better than the GMM-based alternative likely because of its ability to pick up shifts and nonlinearities in the response of monetary authorities to business cycle developments.

[FIGURE 6 OMITTED]

Finally, we examine the out-of-sample forecasting performance of TVP and CGG models. A full investigation of the forecasting performance of alternative monetary policy models is well beyond the aim of this article. However, the above in-sample measures clearly support the TVP model. We feel that a formal test of out-of-sample predictive accuracy could add further robustness to this result.

We employ the t-based test suggested by Diebold and Mariano (1995). (21) In our case, the test's null is that CGG and TVP models have the same predictive accuracy. The procedure amounts to regressing the difference of the absolute deviations of the models' forecast errors on a constant and checking the latter's statistical significance. The test statistics allows to reject the null hypothesis at the 99% confidence interval. This means that TVP and CGG models do not have the same forecasting ability. Although the test does not permit to infer which of the models fares best, its result and the computed values of our simple tracking statistics confirm that our TVP rule largely outperforms the popular forward-looking rule of Clarida, Gali, and Gertler (1998, 2000).

The absence in the Taylor rule of a smoothing term could partly account for the relative inability of CT in describing policy developments. However, our proposal appears richer than the CT rule on various grounds. First, it allows for forward-looking behavior of the policymaker in setting interest rates. Second, time-varying coefficients for expected inflation, output gap, and the lagged interest rate provide a fuller picture of monetary policy shifts than any constant coefficients approach--like the one on which the CGG rule is based--could support. The latter feature in particular does not impair the descriptive power of our rule given that it also performs well in tracking actual policy rates.

V. CONCLUSIONS

In this work, we evaluated forward-looking interest rate rules for five major economies. We estimated policy reaction functions allowing for time variation in their parameters and in the variance of the policy rate. Linear objective, constant coefficient instrument rules, a common paradigm for monetary policy reaction functions, likely blur the impact of a series of relevant features of modern policymaking, like model uncertainty, conflicting objectives, shifting preferences, and nonlinearities in policymakers' behavior. Our approach instead frames monetary policy conducts in a dynamic and evolving context. The aim was to capture monetary policy shifts otherwise missed by conventional, constant parameters approaches to interest rate policies. Besides the richer picture of monetary policies we are able to describe, our results highlight at least three general issues.

First, estimated policy rules summarize policy conducts according to different coefficient estimates and, in some cases, different functional forms. This implies that interest rate policies diverge widely across countries. Second, estimated parameters tend to shift over time and in most cases in a smooth and gradual fashion. We believe that approaches like DSGE and time-varying VAR models will be able to assess the extent to which changes in preferences or shifts in "deep" parameters account for this evolution.

Finally, given the widespread interest in the evaluation of European Central Bank policy conduct so far, our work sheds some light on the degree to which any average measure of policy rates in the euro area pre-1999 should be used in such exercises. Our results therefore question the conventional wisdom that a common historical Taylor rule for EMU3 countries could be used as a basis to make inference on euro area monetary policies.

DATA APPENDIX

The data we used were quarterly series, extracted from OECD Main Economic Indicators, Thomson Financial Datastream, and International Monetary Fund (IMF)'s International Financial Statistics (IFS). In all cases, we were able to employ seasonally adjusted data.

For each country, we measured output using GDP at constant price series. The output gap is defined as the quarter-on-quarter log difference between actual and potential levels of the series. The inflation series were defined as the four quarters log differences in the all items, seasonally adjusted consumer price index. The index of effective exchange rates (trade weighted) was our measure for the exchange rates.

The following is a short description of the variables' sources.

* United States: The output series is the real GDP, in billions of chained 2000 dollars (source: U.S. Congress, Congressional Budget Office). The output gap is obtained using the real potential GDP, defined in billions of chained 2000 dollars, same source as actual output. Inflation is the four quarters (log) difference in the GDP chain-type price index, 1996 = 100, seasonally adjusted (source: U.S. Department of Commerce, Bureau of Economic Analysis). The call money rate is the Federal Funds rate obtained from IMF's IFS.

* Germany, France, United Kingdom, and Italy: IMF's IFS for the call money rate, consumer price index, and GDP. OECD general economic indicators for output gaps.

The short-term interest rate employed as the monetary policy indicator for the European countries was the following:

* Germany, overnight money market rate.

* United Kingdom, overnight interbank rate series post-1983; pre-1983 we employ the rate on 90-d Treasury Bills, which displays a very close correlation with the interbank lending rate (source: IMF, IFS).

* France, overnight money market rate.

* Italy, 3-month interbank deposits (overnight).

ABBREVIATIONS

CT: Conventional Taylor

DSGE: Dynamic Stochastic General Equilibrium

EMU: European Monetary Union

GDP: Gross Domestic Product

GMM: Generalized Method of Moment

HP: Hodrick-Prescott

IFS: International Financial Statistics

IMF: International Monetary Fund

OECD: Organization for Economic Cooperation and Development

TVP: Time-Varying Parameter

VAR: Vector Autoregression

doi: 10.1111/j.1465-7295.2009.00222.x

REFERENCES

Amato, J. D., and T. Laubach. "Estimation and Control of an Optimization-Based Model with Sticky Prices and Wages." Journal of Economic Dynamics and Control, 27, 2003, 1181-215.

Assenmacher-Wesche, K. "Estimating Central Banks' Preferences from a Time-Varying Empirical Reaction Function." European Economic Review, 50, 2006, 1951-74.

Bank of England. The Transmission Mechanism of Monetary Policy. A Paper by the Monetary Policy Committee. 1999.

Batini, N., and A. G. Haldane. "Forward-Looking Rules for Monetary Policy, in Monetary Policy Rules, edited by J. B. Taylor. Chicago: University of Chicago Press, 1999.

Boivin, J. "Has U.S. Monetary Policy Changed? Evidence from Drifting Coefficients and Real-Time Data." Journal of Money, Credit and Banking, 38, 2006, 1149-73.

Christiano, L. J., M. Eichenbaum, and C. L. Evans. "Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy." Journal of Political Economy, 113, 2005, 1-45.

Clarida, R., J. Gali, and M. Gertler. "Monetary Policy Rules in Practice: Some International Evidence." European Economic Review, 42, 1998, 1033-67.

--. "Monetary Policy Rules and Macroeconomic Stability: Evidence and Some Theory." Quarterly Journal of Economics, 115, 2000, 147-80.

Cukierman, A., and S. Gerlach. "The Inflation Bias Revisited: Theory and Some International Evidence." Manchester School, 71, 2003, 541-65.

Del Negro, M., F. Schorfheide, F. Smets, and R. Wouters. "On the Fit and Forecasting Performance of New-Keynesian Models." Journal of Business and Economic Statistics, 25, 2007, 123-62.

Diebold, F. K., and B. G. Mariano. "Comparing Predictive Accuracy." Journal of Business and Economic Statistics, 13, 1995, 134-44.

Doan, T., R. Litterman, and C. Sims. "Forecasting and Conditional Projections Using Realist Priori Distributions." Econometric Review, 3, 1984, 1-100.

Dolado, J., R. M.-D. Pedrero, and F. J. Ruge-Murcia. "Nonlinear Monetary Policy Rules: Some New Evidence for the U.S.," in Nonlinear Dynamics and Econometrics, Vol. 8, No. 3. Berkeley, CA: Berkeley Electronic Press, 2004.

Erceg, C. J., D. W. Henderson, and A. Levin. "Optimal Monetary Policy with Staggered Wage and Price Contracts." Journal of Monetary Economics, 46, 2000, 281-313.

Estrella, A., and J. C. Fuhrer. "Monetary Policy Shifts and the Stability of Monetary Policy Models." Review of Economic and Statistics, 85, 2003, 94-104.

European Central Bank. The Monetary Policy of the ECB. Frankfurt, Germany: European Central Bank, 2004.

Fratianni, M., and F. Spinelli. Storia Monetaria d'Italia. Milan: ETAS.

Gerlach, S., and G. Schnabel. "The Taylor Rule and Interest Rates in the EMU Area." Economics Letters, 67, 2000, 165-71.

Goldman Sachs. "Taylor Rule Points to Upside Risk for ECB Rates." European Weekly Analyst, 07/40, November 15, 2007.

Gordon, R. J. "What Caused the Decline in U.S. Business Cycle Volatility?" NBER Working Paper No. 11777, 2005.

Hamilton, J. Time Series Analysis. Princeton, NJ: Princeton University Press, 1994.

Harvey, A. C. Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge: Cambridge University Press, 1989.

Kim, C.-J., and C. R. Nelson. State-Space Models with Regime Switching. Cambridge, MA: MIT Press, 1999.

--. "Estimation of a Forward-Looking Monetary Policy Rule: A Time-Varying Parameter Model Using Ex Post Data. Journal of Monetary Economics, 53, 2006, 1949-66.

McConnell, M. M., and G. Perez-Quiros. "Output Fluctuations in the United States: What Has Changed Since the Early 1980s?" American Economic Review, 90, 2000, 1464-76.

Muscatelli, A., P. Tirelli, and C. Trecroci. "Monetary Policy on the Road to EMU: The Dominance of External Constraints on Domestic Objectives." Annales d'Economie et de Statistique, Vol. 67-68, 2002a. (Paris: ADRES, INSEE.)

--. "Does Institutional Change Really Matter? Inflation Targets, Central Bank Reform and Interest Rate Policy in the OECD Countries." Manchester School, 70, 2002b, 487-527.

--. "Fiscal and Monetary Policy Interactions: Empirical Evidence and Optimal Policy Using a Structural New-Keynesian Model." Journal of Macroeconomics, 26, 2004, 257-80.

Muscatelli, A., and C. Trecroci. "Central Bank Goals, Institutional Change and Monetary Policy: Evidence from the United States and United Kingdom," in Monetary Transmission in Diverse Economies, edited by L. Mahadeva, P. Sinclaire, and G. Stern. Cambridge: Cambridge University Press for the Bank of England, 2002.

Nelson, E. "What Does the UK's Monetary Policy and Inflation Experience Tell Us About the Transmission Mechanism?" in Monetary Transmission in Diverse Economies, edited by L. Mahadeva, P. Sinclaire, and G. Stern. Cambridge: Cambridge University Press for the Bank of England, 2002.

Primiceri, G. E. "Time Varying Structural Vector Autoregressions and Monetary Policy." Review of Economic Studies, 72, 2005, 821-52.

Rudebusch, G. D. "Assessing the Lucas Critique in Monetary Policy Models." Journal of Money, Credit, and Banking, 37, 2005, 245-72.

Sims, C. A., and T. Zha. "Were There Regime Switches in U.S. Monetary Policy?" American Economic Review, 96, 2006, 54-81.

Smets, F. "Output Gap Uncertainty: Does It Matter for the Taylor Rule?" Empirical Economics, 27, 2002, 113-29.

Smets, F., and R. Wouters. "An Estimated Stochastic General Equilibrium Model of the Euro Area." Journal of the European Economic Association, 1, 2003 5.

Stock, J. H., and M. W. Watson. "Has the Business Cycle Changed? Evidence and Explanations," in Monetary Policy and Uncertainty. Federal Reserve Bank of Kansas City, 2003, 9-56.

Taylor, J. B. "Discretion versus Policy Rules in Practice." Carnegie-Rochester Conference Series in Public Policy, 39, 195-214.

--, ed. Monetary Policy Rules. Chicago: University of Chicago Press, 1999.

Woodford, M. Interest and Prices: Foundations of a Theory of Monetary Policy. Princeton, NJ: Princeton University Press, 2003.

(1.) The specification below is standard in applications based on quarterly data. See, for instance, the studies in Taylor (1999).

(2.) Woodford (2003) and Christiano, Eichenbaum, and Evans (2005) are some examples.

(3.) See Taylor (1999) for an estimated version of this proposal.

(4.) Many studies included additional variables to a baseline specification in terms of inflation and output to account for intermediate or alternative central bank targets.

(5.) The start of tenures of Paul Volcker (April 1979) and Alan Greenspan (July 1987) as Chairman of the Fed, as well as the end of the "monetarist experiment" engineered during Volcker's chairmanship (1982Q3), are often held as break dates for U.S. monetary policy. Kim and Nelson (2006) identify alternative regime dates.

(6.) For an exception, see Muscatelli and Trecroci (2002).

(7.) Our description closely follows Hamilton (1994).

(8.) Boivin (2006) instead opts for the use of real-time forecasts, while Kim and Nelson (2006) obtain TVP estimates via a more complex two-step procedure.

(9.) We stopped the sample to the establishment of the European System of Central Banks, as this marked the end of national monetary policies for those countries.

(10.) We experimented with a four quarters lead for expected inflation; our results were unchanged. We also employed the measures computed by the Congressional Budget Office and the OECD for output gap and our own Kalman filter-based one. Results differed very little from those shown here.

(11.) This interpretation is in line, for instance, with Gordon (2005).

(12.) It would be helpful to have an idea of the statistical significance of the long-run static coefficients. However, we are not aware of simple procedures to obtain such "long-run standard errors" in the context of our approach. We could obviously resort to Monte Carlo methods or similar techniques, but they would surely make our simple exercise much more cumbersome.

(13.) We employed the EURIBOR rate after 1998Q4. We do not present the estimates we obtained when the exchange rate was included, as the relative coefficients were never significant.

(14.) [i.sup.f.sub.t] is the 3-month FIBOR rate.

(15.) Clarida, Gali, and Gertler (1998) conclude that monetary policy in Italy (but the same held true for France and the United Kingdom) boiled down to fighting inflation by following the Bundesbank.

(16.) See, for instance, Fratianni and Spinelli (2001).

(17.) So was defined the relationship between the Italian government and the Bank of Italy following the law (June 1981) that lifted the obligation to buy unsold Italian Treasury Bonds by the Bank.

(18.) The most important innovations were the fixing of the official discount rate by Bank of Italy (BI) alone, without any ratification by the Treasury (January 30, 1992) and the abolition, dating November 12, 1993, of the use of the Treasury's account at BI to finance public deficit (it was possible up to the 14% of its amount). Also, new rules regarding the compulsory reserves of the banking system at BI were of great importance. In fact, even after divorce, the BI would use that liquidity to buy Treasury bonds at nonmarket conditions.

(19.) Obviously, this implies that keeping the long-run average inflation rate at the target requires a long-run average policy rate of 4%. We also remind that the original specification of Taylor (1993) was derived for the 1987-1992 sample.

(20.) We do not report here results for the remaining countries for sake of brevity. However, our findings for those cases broadly reflect what we show for the United States and are available from the authors upon request.

(21.) We thank an anonymous referee for kindly suggesting the use of this test.

CARMINE TRECROCI and MATILDE VASSALLI *

* We thank Franco Spinelli, Raffaele Miniaci, Roberto Casarin, Katrin Assenmacher-Wesche, and an anonymous referee for helpful comments on an earlier draft of this article.

Trecroci: Associate Professor, Department of Economics, University of Brescia, Via San Faustino 74/B, I-25122 Brescia, Europe. Phone +39 030 2988812, Fax +39 030 2988837, E-mail trecroci@eco.unibs.it

Vassalli: Assistant Professor, University of Brescia, Via San Faustino 74/B, I-25122 Brescia, Europe. Phone +39 030 298818, Fax +39 030 2988837, E-mail vassalli@ eco.unibs.it
TABLE 1
USA, 1970:1-2006:2; State Variables:
Minimum, Maximum, and Mean Values.
Standard Deviations of Estimated Parameters
Are in Parentheses

State Minimum Maximum Mean

[[beta].sub.t] 2001:4 1989:1 1.53 (0.21)
 -0.48 2.87
[[gamma].sub.t] 1982:3 1973:4 0.24 (0.07)
 0.12 0.31
[[rho].sub.t] 1980:1 1987:2 0.14 (0.07)
 0.65 -0.35

TABLE 2
Germany, 1971:3-1998:4; State Variables:
Minimum, Maximum, and Mean Values.
Standard Deviations of Estimated Parameters
Are in Parentheses

State Minimum Maximum Mean

[[beta].sub.t] 1988:2 1983:2 1.51 (0.16)
 0.05 3.11
[[gamma].sub.t] 1991:1 1975:3 0.17 (0.01)
 0.02 0.68
[[rho].sub.t] 1975:3 1998:2 0.21 (0.1)
 0.00 0.28

TABLE 3
United Kingdom, 1980:1-2005:3; State
Variables: Minimum, Maximum, and Mean
Values. Standard Deviations of Estimated
Parameters Are in Parentheses

State Minimum Maximum Mean

[[beta].sub.t] 1980:4 2003:1 1.30 (0.15)
 0.93 2.1
[[gamma].sub.t] 1986:3 1993:4 -0.12 (-0.25)
 -1.95 1.25
[[rho].sub.t] 1985:2 1998:4 -0.05 (-0.04)
 -0.38 0.17
[[delta].sub.t] 1980:1 1984:3 0.41 (0.18)
 0.99 0.1

TABLE 4
France, 1971:3-1998:4; State Variables:
Minimum, Maximum, and Mean Values.
Standard Deviations of Estimated Parameters
Are in Parentheses

State Minimum Maximum Mean

[[beta].sub.t] 1982:1 1977:1 0.35 (0.06)
 0.12 0.63
[[gamma].sub.t] 1993:2 1976:3 0.00 (0.04)
 -0.32 0.46
[[rho].sub.t] 1993:3 1975:3 0.39 (0.1)
 0.32 0.53
[[delta].sub.t] 1976:2 1982:3 0.52 (0.05)
 0.30 0.78

TABLE 5
Italy, 1971:3-1998:4; State Variables:
Minimum, Maximum, and Mean Values.
Standard Deviations of Estimated Parameters
Are in Parentheses

State Minimum Maximum Mean

[[beta].sub.t] 1975:3 1998:1 0.84 (0.1)
 0.31 1.31
[[gamma].sub.t] 1992:4 1976:3 0.22 (0.09)
 -0.56 1.37
[[rho].sub.t] 1993:1 1976:3 0.29 (0.11)
 0.12 0.84
[[delta].sub.t] 1976:3 1995:2 0.22 (0.12)
 -0.26 0.65

TABLE 6
United States, 1972:4-2005:4; Deviations of
TVP, CGG, and CT-Implied Policy Rates from
Actual Fed Funds Rate; Mean Value of
Deviations (ME), Mean Value of Absolute
Deviations (MAE), and Root Mean Squared
Error (RMSE)

Rule ME MAE RMSE

TVP 0.003 0.305 0.475
CGG -0.063 0.786 1.403
CT 2.102 2.848 3.610
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Date:Oct 1, 2010
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