# Five years of single European monetary policy in practice: is the ECB rule-based?

I. INTRODUCTIONThe European Central Bank (ECB) was established in June 1998 and began its operations in January 1999, when European Monetary Union (EMU) was established and the euro was launched. Since then, the ECB has been responsible for monetary policy in the euro area. Because this marked a historical step in the process of political and economic integration in Europe, it seems to be worthwhile to take stock of the ECB's monetary policy after its first five years and to ask what lessons can be learned from this experience for the future. This is essentially the purpose of this article.

Due to the relatively short sample period, direct econometric estimates of the empirical reaction function of the ECB have been very limited so far. An exception is Hayo and Hofmann (2005) who compare the ECB reaction function to the Bundesbank reaction function over the period 1979:04 to 1998:12. However, they present only a single estimation specification for both central banks. They do not examine alternative specifications, nor do they test for different data representations within their given regression specification (e.g., different detrending methods). Fourcans and Vranceanu (2004) also estimate reaction functions for the ECB but use different specifications and data compared to this study. Most other existing studies do not investigate "real ECB" policy reaction function but rather focus on a "fictitious euro area central bank" by using aggregated and synthetic euro zone data extended backward to include time periods prior to the start of the common monetary policy. Among those studies are Gerdesmeier and Roffia (2003), Gerlach-Kirsten (2003), and Gerlach and Schnabel (1999). Although the method applied in these studies eliminates the otherwise occurring small-sample problem, it appears to be a relatively unreliable approach to generate conclusions for the ECB policy after 1999.

The article has the following structure. Section II describes the adaptation that took place during the first five years and asks for the appropriateness of the modification in the ECB's monetary policy strategy and its instrument setting. Section III examines whether a specific monetary policy rule can be identified for the ECB. It also compares the findings on such a rule with the strategy that the ECB defined for its policy. Finally, section IV concludes.

II. THE PROCESS OF ADAPTATION

The treaty and the statutes of the ECB define price stability as the primary objective of the single monetary policy and, thus, of the ECB. The objective was specified more precisely by the ECB (1998) "as a year-on-year increase in the Harmonized Index of Consumer Prices (HICP) for the euro area of below 2%." At the same time, the Governing Council also stated that price stability shall be maintained over the medium term because monetary policy is unable to fine-tune price developments over short horizons of a few weeks or months.

In addition to the formulation of price stability, the strategy consists of two pillars within which the forward-looking assessment of the economic situation takes place. The first pillar is a prominent role of the quantity of money in circulation. This role is also signaled by the regular announcement of a quantitative reference value for the growth of the broad monetary aggregate M3. The ECB refers to this pillar as the monetary analysis. The second pillar--the so-called economic analysis--consists of an analysis of a wide range of other economic and financial variables that normally affect price developments. From the very beginning, the ECB was criticized for the formulation of the two pillars, because this kind of strategy may lead to inconsistencies and contradictions and may also be difficult to be communicated to the markets. Figure 1 shows the development of the monetary aggregate M3 during the first five years. It shows that, since the fall of 2001, the growth rate of M3 was significantly above its target. Nevertheless, the ECB lowered interest rates several times during this period (see Figure 2) and explained the strong increase in M3 by several special circumstances, that is, portfolio shifts and an increase in precautionary money demand. However, it is difficult to base the strategy on monetary aggregates if these special effects occur over longer periods. If so, this pillar seems ineffective, as it has been the case for several economies in the past, which led them to formulate direct inflation-targeting strategies.

[FIGURE 1 OMITTED]

Although the ECB has not significantly changed its strategy, it did react to the problems and the criticism and modified the strategy after an internal revision in 2003 (ECB 2003b, 2003c). More specifically, the ECB clarified the relationship between the two pillars and, in particular, the communication on the cross-checking of information. To this end, the economic analysis serves to identify the short- to medium-term risks to price stability. As before, it includes an analysis of shocks hitting the euro area and the projections of key macroeconomic variables. In addition, the monetary analysis assesses the medium- to long-term trends in inflation in view of the relationship between the quantity of money and prices over extended horizons. To underscore the longer-term nature of the reference value for monetary growth as a benchmark for the assessment of monetary developments, the ECB Governing Council will no longer conduct a review of the reference value on an annual basis. However, it will continue to assess the underlying conditions and assumptions.

[FIGURE 2 OMITTED]

The revision of the monetary policy strategy also led to a reformulation of the definition of price stability. In the pursuit of price stability, the ECB changed the wording regarding the inflation objective from "below 2%" to "below but close to 2%" over the medium term. In sum, the modifications in the strategy were only of minor nature.

The monetary policy strategy of the ECB is based on a set of instruments, of which the most important one is the main refinancing operation (MRO), which is a short-term open market operation in form of reverse transactions. Together with the so-called standing facilities (i.e., the marginal lending facility and the deposit facility), the MRO enables the ECB to "tame" fluctuations in the short-term interest rate within a floor and a ceiling of a corridor as well as to control the degree of liquidity in the interbank market. Figure 2 shows the development of the short-term interest rate (European Overnight Index Average, EONIA) as well as the main refinancing rate (minimum bid rate), the deposit rate, and the marginal lending rate. It reveals that the ECB has indeed been able the control the short-term interest rate. It was very close to the main refinancing rate during the whole period under consideration. (1)

On the basis of its experience, the ECB did change some of the operational procedures during the first five years. In June 2000, the ECB switched from fixed-rate tenders to variable-rate tenders with a minimum bid rate in the MRO (ECB 2000) and, in a press conference on November 8, 2001, it announced that interest rate decisions will generally only take place on the first of the two monthly meetings of the Governing Council. The ECB also changed the maturity of the main refinancing operation from two weeks to only one week with the beginning of the first quarter 2004 and changed the timing of the reserve maintenance period to let its starting date coincide with the first monthly monetary policy meeting of the Governing Council of the ECB (ECB 2003a).

The changeover from fixed-rate tenders to variable-rate tenders was the most important modification in the monetary policy instruments during the ECB's first five years. Although the main advantage of the fixed rate tenders was that they enabled the ECB to set clear signals of the monetary policy stance, they also meant that the monetary financial institutions (MFIs) could offer large amounts with relatively little risk. As a consequence of the systematic overbidding behavior, the allotment ratio fell to below 1%. The changeover to variable-rate tenders effectively eliminated the appeal of speculative overbidding.

The decision to decide on monetary policy changes only on the first meeting of each month was a consequence of the phenomenon of underbidding behavior in the MRO starting in February 2001. At that time, market participants had strong expectations of an interest rate cut during the ongoing reserve maintenance period. As a consequence, the bidding by the MFIs in the main refinancing operation was so restrained that the total bid volume was insufficient to allot the amount that seemed appropriate from a liquidity policy perspective. This resulted in a significantly higher volatility in the market for overnight liquidity. Deciding on changes in monetary policy only once a month reduced the speculative underbidding behavior considerably.

The change in the reserve maintenance period and in the maturity of the main refinancing operations was also related to overbidding and underbidding incentives of the MFIs. The first measure that led to the reserve maintenance period coinciding with the period between the monthly monetary policy meetings ensures that as a rule the ECB would not change its policies during a reserve maintenance period. The second measure of shortening the maturity of the main refinancing operation to one week was taken to avoid that the latter hangs over into the subsequent reserve maintenance period.

In sum, the changes in the monetary policy instruments and in the monetary policy strategy during the first five years of European Monetary Union were relatively modest. The measures only aimed at removing existing frictions and enhancing the efficiency of the set of monetary policy instruments without changing their fundamental nature. In particular, many observers interpret the modification of the two pillar approach as half-hearted (e.g., Hefeker, 2003). (2) However, the ECB can counteract their arguments by pointing to the relative success of its strategy with respect to the objective of price stability. Figure 3 shows the development of the HICP over the last five years and clearly displays the ECB was able to satisfy the final goal.

[FIGURE 3 OMITTED]

III. SEARCHING FOR A MONETARY POLICY RULE

Since the seminal paper of Taylor (1993), it has become very popular to describe the behavior of central banks by empirical reaction functions. (3) The vast literature on so-called monetary policy rules has generated a wide array of empirical formulations, all of which have one thing in common: They include at least the inflation rate and a variable of economic activity as the main explanatory variables for the determination of the short-term interest rate. The latter is considered the main policy instrument of the central bank. However, following a monetary policy rule mechanically is not a very realistic description of practical monetary policy because it is too simplistic. A simple rule is incapable of processing the entire information set that a central bank has and that can describe macroeconomic developments. Moreover, the practical implementation of such rules is difficult because some of the variables entering the rule are not directly observable (e.g., the output gap and the equilibrium interest rate) or are likely to be prone to real-time measurement errors. (4)

Despite the described considerations, monetary policy rules have received a great deal of attention in recent macroeconomic research. Furthermore, the ECB itself does not seem to totally reject the usefulness of monetary policy rules. In its Monthly Bulletin of October 2001 (ECB 2001, p. 38), the ECB states: "The emphasis [...] on rule-guided monetary policy [...] is generally welcome [because] it provides a salutary antidote to the perennial risks of a discretionary, ad hoc approach to monetary policy." This statement by itself provides enough motivation for the search of the monetary policy rule of the ECB. Although not quite satisfying from an econometric point of view, five years might represent a quite reasonable period to test for the presence of a stable policy rule.

A first but superficial analysis is the comparison of the short-term interest rate with the path that the Taylor rule would imply. Figure 4 shows the development of the EONIA and the Taylor rate that is generated by a Taylor rule of the form: (5)

[i.sup.Taylor] = (expected) inflation rate + 1.5 + 0.5 * inflation gap + 0.5 * output gap.

Figure 4 shows the overnight interest rate (EONIA) for the euro area and the Taylor rate generated according to the above equation where the inflation target is set to 1.5% during the whole sample range and the output gap is derived on the basis of a linear trend. It can be seen that, especially after the end of 1999, the Taylor rate has been nearly constantly above the short-term rate, indicating that the ECB was not too restrictive, although this was sometimes the impression of major critics from politics, markets, and academia. However, the fit is not very good. This changes when the authors consider some interest-smoothing behavior in addition. The smoothed Taylor rate, which is also depicted in Figure 4, is generated on the basis of a smoothing parameter of 0.8, a number that is quite common in the literature. The smoothed Taylor rate and the EONIA seemed to move very close to each other.

[FIGURE 4 OMITTED]

Among the empirical reaction functions, the forward-looking monetary policy rules are more popular. Following Clarida et al. (1998, 2000), the baseline policy rule takes the form:

(1) i* = [bar.i] + [[alpha].sub.1][E.sub.t]([[pi].sub.t+k] - [pi]*) + [[alpha].sub.2][E.sub.t]([y.sub.t+q] - [y*.sub.t+q]),

where i* is the desired level of the nominal short-term interest rate, and [bar.i] is its equilibrium level. The second term on the right-hand side is the expected deviation of the k-period ahead inflation rate ([pi]) from the target rate ([pi]*) which is assumed to be constant over time, and the third term is the expected deviation of output (y) from its natural level (y*) q periods ahead (i.e., the output gap). The coefficients [[alpha].sub.1] and [[alpha].sub.2] represent the intensity with which the desired interest rate of the central bank reacts to the inflation and the output gap.

It is often argued that central banks do not adjust the interest rate toward its desired level given by equation (1) immediately, to avoid too large changes in the interest rate that might disrupt financial markets. However, the existing theory, by and large, does not readily account for why central banks should adjust their instrument in a sluggish fashion. Possible explanations are model uncertainties (Clarida et al., 1999), data uncertainties (Orphanides, 1998) or an optimal smoothing behavior of the central bank in the sense that lagged dependency of the short-term interest rate provides a leverage with respect to longer-term rates, which permits the central bank to better manipulate aggregate demand (Rotemberg and Woodford 1997; see also Woodford 1999). The assumption of interest rate smoothing behavior leads to

(2) [i.sub.t] = (1 - [rho])[i*.sub.t] + [rho][i.sub.t-1] + [[nu].sub.t],

where the parameter 0 [less than or equal to] [rho] < 1 describes the degree of interest rate smoothing behavior and [[nu].sub.t] is an i.i.d. exogenous random shock to the interest rate. Combining (1) and (2) leads to

(3) [i.sub.t] = (1 - [rho])([bar.i] + [[alpha].sub.1][E.sub.t]([[pi].sub.t+k] - [pi]*) + [[alpha].sub.2][E.sub.t]([y.sub.t+q] - [y*.sub.t+q])) + [rho][i.sub.t]-1 + [[nu].sub.t].

To arrive at a testable relationship, the unobservable terms in equation (3) have to be eliminated. Therefore, the authors rewrite equation (3) as

(4) [i.sub.t] = (1 - [rho])[[alpha].sub.0] + [[alpha].sub.1] (1 - [rho])[[pi].sub.t+k] + [[alpha].sub.2](1 - [rho]) ([y.sub.t+q] - [y*.sub.t+q]) + [rho][i.sub.t-1] + [[epsilon].sub.t],

where

[[alpha].sub.0] = [bar.i] - [[alpha].sub.1][pi]* and [[epsilon].sub.t] = [[nu].sub.t] - [[alpha].sub.1] (1 - p) ([[pi].sub.t+k] - [E.sub.t][[pi].sub.t+k]) - [[alpha].sub.2](1 - p)([y.sub.t+q] - [E.sub.t][y.sub.t+q]).

Furthermore, the authors assume that

(5) [E.sub.t][[[epsilon].sub.t] | [I.sub.t]] = 0.

Here [I.sub.t] is the central bank's information set available at time t. Equation (5) simply states that the central bank uses its best possible guess about future inflation and output in its interest rate decisions.

The authors estimate the reaction function (4) as suggested by Clarida et al. (1998, 2000). The authors use the popular general method of moments (GMM) estimator. Data are monthly. The inflation rate is the HICP, output is the industrial production in the euro area, and the short-term interest rate is the EONIA. The analysis uses three different trend-generating processes on the basis of the logarithm of industrial production: a quadratic trend (eurogap1), a linear trend (eurogap2), and a Hodrick-Prescott filter with the penalty parameter set to 14400 (eurogap3). Figure 5 displays their development. In addition to these three baseline trends, the authors also take monthly euro area-wide unemployment rates as an indicator of real activity in the ECB reaction function. In this case, they calculate the output gap (eurogap4) on the basis of a Hodrick-Prescott filter (again with penalty parameter of 14400). (6) The authors are aware of the fact that the unemployment rate has a high structural share. However, given the short time period under consideration, they assume that the structural share remained fairly constant during this period so that all variations can be interpreted as cyclical.

[FIGURE 5 OMITTED]

With the formulation off our different output gaps, this approach differs from Clarida and colleagues, who only use a quadratic trend. The present approach takes into account the critique of Orphanides (1999), who has extensively considered the problem of the output gap to show that different behavior by the Fed in the 1970s and 1980s can be explained by different measures of the output gap rather than by different parameters in the reaction function. (7)

The authors implement the GMM estimation using the correction for heteroscedasticity and autocorrelation of unknown form with a lag truncation parameter of 12. In addition, they chose Bartlett weights to ensure positive definiteness of the estimated variance-covariance matrix. They follow Clarida et al. and set k = 12 and q = 0. In the baseline regression, the authors use the following set of instruments: The constant as well as lagged values of the output gap and the inflation rate and the short-term interest rate. (8)

Due to the use of the 12-months-ahead inflation rate in the regression analysis, the effective sample period is reduced to 1999:01 to 2002:12. The use of the lagged instrument variables does not shorten the sample because the authors are able to use the 1998 values as instruments for 1999 (the beginning of the period of interest) regardless of the ECB regime. (9)

The regression results are shown in Table 1. The statistical properties appear quite remarkable, although the authors are aware that the short sample period can cause difficulties in the estimation. The coefficient of inflation is always significant and higher than one, reflecting that the Taylor principle holds. The output gap also significantly enters the reaction function of the ECB. This is independent of the concept of type of concept that is employed for the output gap. However, the magnitude of the reaction is always less than to inflation. The interest-smoothing parameter is also significant and of a magnitude suggested by the recent literature. (10) An exception is specification (2) with the linear trend. The smoothing parameter is unusually low, but the Durbin Watson statistic suggests that there is some serious autocorrelation left in the residuals. Table 1 also presents the result of specification (4) based on the "unemployment gap." The coefficients have again the expected values, although response to the inflation gap seems very high and less significant in that specification. The reported J-statistics indicate that the authors have chosen a set of valid instruments.

Given that the equilibrium real interest rate is given by [bar.r] = [bar.i] - [pi]* and that [[alpha].sub.0] = [bar.i] - [[alpha].sub.1][pi]*, the implicit inflation target can be extracted from the regressions according to

(6) [pi]* = [[[bar.r] - [[alpha].sub.0]]/[[[alpha].sub.1] - 1]].

The results that are again based on the assumption that the equilibrium real interest rate for the euro area is 1.5% are also given in Table 1. The implicit inflation target ranges between 1.56 and 2.46. These values are also quite impressive because they lie exactly in the range of the (new) definition of price stability of near 2%.

Given the fact that industrial production (because of its volatility) and unemployment (because of its high structural share) may represent only incomplete measures of economic activity, the authors additionally constructed output measures based on gross domestic product (GDP) data to see whether the results stay robust. Therefore, they employed a method suggested by Gandolfo (1981, p. 118ff.) and performed a monthly interpolation from quarterly GDP data to obtain monthly GDP values. Based on this monthly GDP series, the authors constructed output gap measures based on a quadratic trend (gdp_gap1), a linear trend (gdp_gap2) and a Hodrick-Prescott filter (gdp_gap3). Table 2 shows the results of the baseline regressions with the GDP measures instead of industrial production. The results indicate that the reaction to the output gap is higher in this case. However, the Taylor principle still holds, and the implied inflation target is again in a reasonable range. The smoothing parameter also stays in a reasonable range. (11) The authors interpret this as an indication for the robustness of the estimations previous in Table 1.

Another question that seems to be worthwhile to examine in this framework is the role of money growth in the reaction function of the ECB. According to the strategy of the ECB, the growth rate of M3 relative to the reference value of 4.5% per annum should be of some significance. The GMM estimation provides a straightforward test of the importance of money growth rate in the form of a test of the validity of instruments. This test is based on the J-statistic. To perform the test, the authors reestimated the baseline regressions shown in Table 1 with additional instruments. The authors take the first six lags, the ninth, and the twelfth lag of the excess money growth. (12) The latter is defined as the difference between the seasonally adjusted three-month moving average growth rate of M3 in the euro area and its reference value of 4.5%. Table 3 presents the results based on industrial production for the output measures. Because of its inferior result, the authors excluded the regression based on the linear trend of industrial production (eurogap2). (13)

The results are quite comparable to their respective baseline regressions reported in Table 1. Although the parameter values for inflation and the output gap are somewhat lower, all main features (e.g., the Taylor principle) again hold significantly. In addition, the range of the implied inflation target is fairly close to the expected value indicating the relative robustness of the estimation. Given that the authors choose a valid set of instruments in the baseline regressions of Table 1, the results of the J-statistic for the test of overidentifying restrictions in Table 3 does not reject the null hypothesis of validity of the additional instruments. This indicates that excess money growth did not affect the ECB's behavior directly but instead served as a good instrument for the right-hand side variables. (14) The absence of a direct link between monetary aggregates and interest rate reactions might have two reasons. First, the ECB could well have reacted to monetary figures which were purged from the influence of portfolio shifts and precautionary money holdings that the ECB (2004) identified as special effects. Second, the ECB has emphasized on various occasions and has also clarified in the revision of its strategy that the monetary analysis is of medium- to longer-term nature. In these cases, it is not surprising that no mechanical link between interest rate setting and monetary developments can be detected econometrically. With this in mind, the result does not contradict the two-pillar strategy.

IV. CONCLUSIONS

During the first five years of EMU, only minor changes in the monetary policy strategy of the ECB were implemented. Using a regression analysis of forward-looking reactions function as popularized by Clarida et al. (1998, 2000), the authors find that the ECB followed the Taylor principle. Furthermore it also reacted to real activity. This result holds for a variety of different specifications of the output gap. The ECB also showed significant interest-smoothing behavior, a phenomenon also reported for other major central banks. The implied inflation target is very close to the level the ECB announced within its strategy.

From an econometric point of view, it is difficult to identify the role of monetary aggregates. Formal testing supports that monetary aggregates serve as a good instrument for the other explanatory variables and the ECB did not react directly to monetary developments. This does not contradict the announced two-pillar strategy, but the fact that it is difficult to observe the role of monetary aggregates could be seen as an indication for a lag of transparency in the sense that the monetary pillar is somewhat opaque. However, the lag of a mechanical answer to monetary developments and given the fact that the ECB nevertheless reached the goal of price stability in a difficult environment (i.e., the unknown transition mechanism in EMU) can also be seen as an indication that situational decisions are important for the "art of central banking," although monetary policy rules provide a convenient way the describe monetary policy.

REFERENCES

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Gerlach, S., and G. Schnabel. "The Taylor Rule and Interest Rates in the EMU Area: A Note." BIS Working Paper no. 73, Basle, 1999.

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Hefeker, C. "The ECB's 'New' Strategy." Intereconomics, 38(3), 2003, 114-15.

Henderson, D., and McKibbin, W. J. "A Comparison of Some Basic Monetary Policy Regimes for Open Economies: Implications of Different Degrees of Instrument Adjustment and Wage Persistence." Carnegie Rochester Conference Series on Public Policy, 39(December), 1993, 221-318.

Jaeger, A. "The ECB's Money Pillar: An Assessment." IMF Working Paper WP/03/82, Washington, DC, 2003.

Orphanides, A. "Monetary Policy Evaluation with Noisy Information." Finance and Economics Discussion Series Working Paper no. 1998-50, Board of Governors of the Federal Reserve System, New York, 1998.

______. "The Quest for Prosperity without Inflation." Mimeo, Board of Governors of the Federal Reserve System, New York, 1999.

______. "Monetary Policy Rules Based on Real-Time Data." American Economic Review, 91(4), 2001, 964-85.

Rotemberg, J., and M. Woodford. "An Optimization-Based Econometric Framework for the Evaluation of Monetary Policy." NBER Macroeconomics Annual 1997, 1997, 297-346.

Rudebusch, G. D. "Term Structure Evidence on Interest-Rate Smoothing and Monetary Policy Inertia." Journal of Monetary Economics, 49(6), 2002, 1161-87.

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RALF M. FENDEL and MICHAEL R. FRENKEL*

*The authors are grateful for comments and suggestions made by two anonymous referees.

Fendel: Assistant Professor of Economics, Otto Beisheim School of Management, Burgplatz 2, 56179 Vallendar, Germany. Phone +49-261-6509-284. Fax +49-261-6509-279, E-mail ralf.fendel@whu.edu

Frenkel: Professor of Economics, Otto Beisheim School of Management, Burgplatz 2, 56179 Vallendar, Germany. Phone +49-261-6509-280, Fax +49-261-6509-279, E-mail michael.frenkel@whu.edu

ABBREVIATIONS

ECB: European Central Bank

EMU: European Monetary Union

EONIA: European Overnight Index Average

GDP: Gross Domestic Product

GMM: Generalized Method of Moments

HICP: Harmonized Index of Consumer Prices

MFI: Monetary Financial Institutions

MRO: Main Refinancing Operation

1. Because Figure 2 is constructed on the basis of monthly data, however, it understates the degree of volatility that can be found in daily data for some subperiods. As will be discussed, the ECB reacted to this unwanted high degree volatility by modifying its instrument set.

2. From the very beginning, the ECB's hybrid strategy has been controversial. In particular, the role of the monetary pillar has remained opaque. For the criticism and its discussion, see Jaeger (2003) and Begg et al. (2002).

3. Although these rules have become known as Taylor rules, it should be noted that Henderson and McKibbin (1993) were the first ones to estimate such reaction functions.

4. A more detailed description on the caveats of Taylor rules from the point of view of the ECB can be found in ECB (2001).

5. The equilibrium real interest rate has been set close to the mean of the ex post real interest rate over the sample period of about 1.4%.

6. The so-called end point problem renders the Hodrick-Prescott procedure a somewhat inadequate choice, especially when central banks face decision problems in real time. However, the authors consider the Hodrick-Prescott filter as a supplement for the other detrending methods to check for the robustness of the results.

7. Another issue that should be mentioned here is the estimation of monetary policy rules based on real-time data. Orphanides (2001) has shown that estimation results might change substantially when one considers the data on which a central bank historically had to decide, that is, data that had not gone through ex post revisions. For the relevance of that issue for the euro area reaction functions, see Gerdesmeier and Roffia (2004).

8. More specifically the authors use the first, sixth, ninth, and twelfth lag of the output gap and inflation rates as well as the first, sixth, ninth, and twelfth lag of the short-term interest rate. This is close to the instruments suggested by Clarida et al., except that here the authors reduced the number of lagged values of the short-term interest rate and left out the IMF commodity price index as lagged values.

9. The authors set initial values as follows: [rho] = 0.8, [[alpha].sub.0] = 1, [[alpha].sub.1] = 2, and [[alpha].sub.2] = 1.5. The initial coefficient values for inflation and the output gap are in a range that a Taylor rule would normally suggest and are also in line with the previous results based on other data sets and countries. However, because the estimation results might be somewhat sensitive to the initial values of the coefficients in the iteration process, the authors also experimented with variations of the initial values, which indicated that the results are indeed robust to changes up to [+ or -] 50% of the values. However, for the smoothing parameter, the authors only used values ranging from 0.6 to 0.95, because the condition for stability is that 0 < [rho] < 1. As a further alternative and an additional check of the robustness of the results, the authors also employed the coefficients obtained from ordinary least squares estimations as starting values, but the results remained unchanged.

10. The statistical significance of the lagged interest rate could have a very different interpretation than the interest smoothing behavior determinants mentioned before. Based on evidence from the term structure of interest rates, Rudebusch (2002) believes that the reason might be the serial correlation of shocks rather than interest rate smoothing behavior of central banks.

11. The authors also performed a stability analysis for the smoothing parameter. The general formulation of equation (2) is [i.sub.t] = (1 -[rho])[i.sub.t] + [GAMMA](L)[i.sub.t-1] + [[nu].sub.t] with [GAMMA](L) = [[rho].sub.1] + [[rho].sub.2]L + ... + [[rho].sub.n][L.sup.n-1] and dynamic stability imposes [rho] = [[summation].sub.j=1.sup.n] [[rho].sub.j] < 1. The authors therefore included higher-order lags of the interest rate. It turned out that these higher-order interest rate lags appear to be statistical not significant and, therefore, they are not reported here. However, the coefficient values satisfied the stability condition.

12. The authors also stepwise tested other lag structures that had no major influence on the results.

13. The results in Table 3 are again robust against a change in the output measure from industrial production to the monthly GDP measure. However, to save space, the authors do not report the results here.

14. From a purely econometric point of view. excess money growth could be highly correlated with inflation, the output gap, or the lagged interest rate. Further tests did not enable the authors to draw final conclusions as to which variable exactly is instrumented for by which particular lag. The authors also included excess money with various leads and lags as additional explanatory variable but could not detect a significant influence. This supports the result of the J-test.

TABLE 1 Baseline Estimation Results Coefficient Regression (1) Regression (2) Regression (3) [rho] 0.92 (0.01) 0.69 (0.05) 0.84 (0.01) [[alpha].sub.0] -0.91 (0.97) 0.44 (0.94) -0.68 (0.65) [[alpha].sub.1] 2.54 (0.49) 1.43 (0.44) 2.00 (0.30) [[alpha].sub.2] 1.69 (0.26) (eurogap1) [[alpha].sub.2] 0.29 (0.02) (eurogap2) [[alpha].sub.2] 0.53 (0.03) (eurogap3) [[alpha].sub.2] (eurogap4) Implied [pi]* 1.56 2.46 2.18 Adj. [R.sup.2] 0.94 0.90 0.96 DW 1.49 0.8 1.84 J-statistic 16 5.04 4.19 4.5 df Coefficient Regression (4) [rho] 0.95 (0.02) [[alpha].sub.0] -4.83 (4.92) [[alpha].sub.1] 4.32 (2.45) [[alpha].sub.2] (eurogap1) [[alpha].sub.2] (eurogap2) [[alpha].sub.2] (eurogap3) [[alpha].sub.2] 0.65 (0.14) (eurogap4) Implied [pi]* 1.96 Adj. [R.sup.2] 0.95 DW 1.52 J-statistic 16 5.09 df Note: SEs are in parentheses. TABLE 2 Estimation Results with Splined GDP data Regression Regression Regression Coefficient (5) (6) (7) [rho] 0.91 (0.007) 0.94 (0.009) 0.92 (0.007) [[alpha].sub.0] 0.79 (0.59) -1.41 (1.26) -0.28 (0.66) [[alpha].sub.1] 1.29 (0.262) 1.78 (0.54) 1.59 (0.29) [[alpha].sub.2] 2.84 (0.17) (gdp_gap1) [[alpha].sub.2] 2.55 (0.26) (gdp_gap2) [[alpha].sub.2] 3.03 (0.21) (gdp_gap3) Implied [pi]* 2.45 3.6 3.02 Adj. [R.sub.2] 0.97 0.96 0.97 DW 2.52 1.95 2.48 J-statistic 24 5.22 5.16 5.19 df Note: SEs are in parentheses. TABLE 3 Supplementary Regression Results with Excess Money Growth as Instrument Regression Regression Regression Coefficient (8) (9) (10) [rho] 0.85 (0.01) 0.75 (0.01) 0.91 (0.01) [[alpha].sub.0] 0.20 (0.30) 1.19 (0.16) 0.63 (0.56) [[alpha].sub.1] 1.84 (0.15) 1.24 (0.07) 1.60 (0.29) [[alpha].sub.2] 0.49 (0.03) (eurogap1) [[alpha].sub.2] 0.45 (0.02) (eurogap3) [[alpha].sub.2] 0.56 (0.04) (eurogap4) Implied [pi]* 1.54 1.29 1.45 Adj. [R.sub.2] 0.95 0.93 0.94 DW 1.43 1.10 1.40 J-statistic 24 4.43 4.47 5.33 df Note: SEs are in parentheses.

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Title Annotation: | European Central Bank |
---|---|

Author: | Fendel, Ralf M.; Frenkel, Michael R. |

Publication: | Contemporary Economic Policy |

Geographic Code: | 1USA |

Date: | Jan 1, 2006 |

Words: | 6163 |

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