Estimating the ECB Policy Reaction Function

Transcription

1 German Economic Review 7(1): 1 34 Estimating the ECB Policy Reaction Function Kai Carstensen Kiel Institute for World Economics Abstract. This paper estimates the policy reaction function of the European Central Bank in the first four years of EMU using an ordered probit model which accounts for the fact that central bank rates are set at multiples of 25 basis points. Starting from a baseline model which mimics the Taylor rule, the impacts of different economic variables on interest rate decisions are analysed. It is concluded that the monetary growth measure which was announced by the ECB as the first pillar of their monetary strategy does not play an outstanding role for the actual interest rate decisions. More sophisticated measures like the money overhang which uses information from both pillars are better suited. Overall, it is concluded that the revision of the monetary policy strategy in May 2003 which implied a downgrading of the first pillar will not induce any observable changes in monetary policy decisions. JEL classification: C24, E52, E58. Keywords: Taylor rule; monetary policy; EMU. 1. INTRODUCTION When the European Central Bank (ECB, 2003b) announced its revised monetary policy strategy on 8 May 2003, two remarkable changes over the initial strategy could be observed. First, money is no longer explicitly assigned a prominent role in the conduct of monetary policy but is rather used to cross-check the results from an economic analysis of inflationary risks. This is why the revision is generally interpreted as a weakening of the first pillar. 1 Second, the ECB clarified that it intends to maintain inflation rates close to 2% p.a. This implies that it takes deflationary risks seriously by preventing the inflation rate from moving too close to zero. 1. However, contrary to the press release (ECB, 2003b), Issing, in the press conference following the announcement of the strategy revision (ECB, 2003c) and in a speech at the ECB Watchers Conference (Issing, 2003), continues to speak of a prominent role of monetary analysis. r Verein für Socialpolitik and Blackwell Publishing Ltd. 2006, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main Street, Malden, MA 02148, USA.

2 K. Carstensen It is unclear, however, whether the strategy revision in fact marks a change of the monetary policy actions or is only a step towards reconciling words with deeds. The initial two-pillar strategy assigned a prominent role to monetary growth in the analysis of inflationary threats (ECB, 1998a, 1999a). In particular, the ECB (1998b) announced a reference value of 4.5% p.a. for monetary (M3) growth which has not been changed since then. While this suggested that any deviation of M3 growth rates from 4.5% would trigger a counteraction by monetary policy, the ECB (1999a) rejected the notion that it exercised a strict money-growth targeting rule by pointing out that it would act only if a threat for price stability was identified. This sounds more like using M3 growth as an important indicator variable and casts doubts on the sense of the twin-pillar architecture. Empirically, it is even unclear whether M3 growth plays any role at all in the practice of the ECB (Begg et al., 2002; Favero et al., 2000; Gali, 2001; Svensson, 2000; von Hagen, 1999). From a theoretical perspective, Svensson (1999a, 1999c) argues that monetary targeting is inferior to inflation targeting in terms of inflation and output variability. This holds not only for the New Keynesian model type but also for the P* model of Hallman et al. (1991) which is generally thought to provide a rationale for monetary targeting (Svensson, 1999b). Using US data, Rudebusch and Svensson (2002) empirically support this view. Moreover, even the German Bundesbank which officially exercised a monetary targeting is best described as an inflation targeter, as shown by Bernanke and Mihov (1997). Furthermore, Clarida et al. (1998) estimate a Bundesbank reaction function and do not find a significant influence of money supply. 2 On the other hand, there are several papers which indicate the usefulness of an appropriately defined monetary measure for predicting future inflation in the area of the European Monetary Union (EMU). Gerlach and Svensson (2000) and Trecroci and Vega (2000) find that the real money gap derived from the P* model is a good leading indicator for future inflation in the euro area. In an extensive out-of-sample forecasting exercise, Altimari (2001) also obtains evidence that several monetary variables contain information regarding future inflation, especially at horizons beyond one year. Moreover, Coenen et al. (2001) demonstrate that monetary variables may help estimating current output which is generally subject to substantial revisions and, thus, problematic as a basis for monetary policy decisions. Finally, it is argued that model uncertainty (Gerdesmeier et al., 2002) and potential stability problems of the New Keynesian model type (Masuch et al., 2003), which is often used to deny any role for money in monetary policy, are good reasons to keep money as an important indicator variable. With respect to the ECB reaction function before the May 2003 revision, the preceding discussion raises several questions: How did the ECB react to 2. Note, however, that this finding alone is not sufficient to conclude that the Bundesbank did not target money growth (Svensson, 1999c). 2 r Verein für Socialpolitik and Blackwell Publishing Ltd. 2006

3 Estimating the ECB Policy Reaction Function inflation rates deviating from the reference value of 2%? In this context it is of interest whether the empirical target rate is really 2% and whether deviations from the target rate entail symmetric reactions. Since the ECB initially did not specify any lower bound for inflation, it might well be that rising inflation induces stronger reactions than falling inflation. How seriously did the ECB take the first pillar? In particular, it shall be analysed whether the official money growth indicator, namely the threemonth moving average of the monthly M3 growth rates, was in fact a relevant monetary indicator as announced by the ECB (1998b). Even those authors who concede that monetary developments are important generally conclude that measures like the real money gap are much better suited to assess inflationary risks (e.g. Gerlach and Svensson, 2000; Svensson, 1999b). Which role does the second pillar play? Variables like the output gap, the exchange rate or interest rate spreads are often thought to affect monetary policy decisions. Both theoretical and empirical results suggest that at least the output gap is of importance for monetary policy decisions. Concerning the May 2003 revision of the ECB monetary strategy, answers to the preceding questions can help assessing whether any changes in the actual conduct of monetary policy should be expected. If the official money growth indicator was in fact of predominant importance in the past, one would conjecture that other variables now receive additional attention by the ECB. Otherwise, if the official indicator was only of minor importance or even not significantly related to policy decisions, one would not expect any observable changes. The questions shall be answered by means of an estimated ECB reaction function. While a Taylor rule for the average interest rate in the EMU countries is estimated by Gerlach and Schnabel (2000) with pre-emu data, a first attempt to analyse the ECB monetary policy rule is made by Faust et al. (2001) who estimate a forward-looking Bundesbank reaction function in the spirit of Clarida et al. (1998) and use it as a benchmark to assess the ECB policy. They conclude that the ECB attaches greater importance to the output gap than the Bundesbank and less to inflation. Neumann (2001) estimates a simple ECB reaction function where the overnight rate depends on its own lag, contemporaneous inflation and the output gap and reaches a similar conclusion. Based on more informal arguments, Gali (2001) finds that the ECB is not as concerned with inflation as one would expect from a simple Taylor rule. Gerdesmeier and Roffia (2003) estimate a forward-looking ECB reaction function with data since At least for their baseline specification they cannot reject the Taylor hypothesis that the weights on inflation and output are 1.5 and 0.5, respectively. However, combining pre-emu and EMU data implies the assumption that the transition from 11 independent central banks to the ECB did not induce any structural break which seems at least questionable. In fact, they perform stability tests which indicate that their estimated relationships are subject to structural change over time. Their results should thus be taken with care. Surico (2003) estimates non-linear r Verein für Socialpolitik and Blackwell Publishing Ltd

4 K. Carstensen reaction functions for the euro area, again combining pre-emu and EMU data. Therefore, the same caveat applies. At the moment, data limitations preclude the estimation of a forwardlooking policy rule for the euro area since this would amount to use, e.g., the one-year-ahead inflation rate as an explanatory variable. 3 The corresponding reduction of the small sample size would make inference even more problematic. We therefore analyse a backward-looking or, in the terminology of Svensson (1999c), explicit policy reaction function which allows us to use the whole sample since the beginning of the European Monetary Union in January This may be justified by the fact that of course only variables already known at the time of the policy decision can be used by the ECB to forecast inflation. 4 It should therefore be sufficient to specify a reaction function which includes the typical driving variables inflation and the output gap along with the most important leading indicators for future inflation. In order to model the interest rate decisions as closely as possible, we refrain from studying the overnight rate which is typically done in applied work. For large samples, it might be a good approximation for the policy instrument because the ECB clearly controls the overall path of the overnight rate. However, there are temporary deviations from the primary policy instrument, the rate of the main refinancing operations (MROs), which are difficult to explain (Bindseil and Seitz, 2001). Therefore, taking the overnight rate as the relevant policy instrument would introduce additional noise which we want to avoid in this small sample. Consequently, we directly use the MRO rate as the policy instrument of the ECB. This is justified by the following reasons (ECB, 1999b). First, the MRO rate is explicitly designated by the ECB as the instrument which signals the monetary policy stance to the public. Second, it explains most of the variations of the overnight rate and, thus, directly translates into the term structure. Finally, the main refinancing operations provide the bulk of liquidity to the banking system. Due to the fact that the MRO rate is always set at multiples of 25 basis points, it may not be appropriate to use a simple regression approach like Breuss (2002). Instead, we employ an ordered probit model which captures the censored character of the data. 5 This approach has the additional advantage that an underlying or desired non-censored MRO rate can be estimated. The paper proceeds as follows. In Section 2 the policy reaction function is outlined, while in Section 3 the estimation method is described. Estimation results are presented in Section 4. Section 5 concludes. 3. Due to sluggish propagation mechanisms, Clarida et al. (1998) and Faust et al. (2001) assume that monetary policy is concerned with expected inflation one year ahead. 4. However, we use revised rather than real-time data as advocated by Orphanides (2001). 5. Similar approaches have been put forward by Choi (1999) who studies the Federal Reserve s discount rate changes, Davutyan and Parke (1995) who analyse the operations of the Bank of England, and Dueker (2000) who asks whether US prime rate changes are asymmetric. 4 r Verein für Socialpolitik and Blackwell Publishing Ltd. 2006

5 Estimating the ECB Policy Reaction Function 2. THE POLICY REACTION FUNCTION Since Taylor (1993) it is typically assumed that central bank behaviour can be characterized by a policy reaction function in which the interest rate is the policy instrument and depends on both inflation and the output gap. In particular, Clarida et al. (1998) estimate the reaction function r* t ¼ r* þ b 1 E t p tþn p* þ b2 E t y gap t ; ð1þ where r* t is the desired and, in our case, non-censored target rate, r* is its longrun equilibrium value, p tþn is the n-step-ahead inflation rate, p* is the desired inflation rate, y gap t ¼ y t y* t is the output gap, y t is output and y* t is potential output. Here and henceforth, all lowercase variables except for the interest rates are given in logs. Due to the fact that neither the future inflation rate nor the current output gap can be observed by the central bank at the time of the decision, expected rather than realized values enter the policy rule. Assuming rational expectations Clarida et al. (1998) estimate this equation with the general method of moments (GMM). This is essentially an instrumental variables estimation of (1) with observed instead of expected variables. If the ECB is concerned with the one- or even two-year-ahead inflation rate, the implied loss of observations renders this procedure problematic for the small sample at hand. In the terminology of Svensson (1999c), the reaction function (1) is of an implicit type because the interest rate depends on unknown future variables. In contrast, an explicit reaction function includes only variables which can be observed at the time of a policy decision with the obvious advantage at the estimation stage that the whole sample of observations can be used. 6 Theoretically, assuming a known linear structure of the economy, it is, at least in principle, straightforward to solve an implicit reaction function for an explicit one. In practice, however, the structure of the economy is unknown and a central bank will most probably operationalize the implicit reaction function (1) by relying on observed variables which have leading indicator properties for inflation. This is exactly the way the ECB (1999a) motivated the second pillar but it clearly also applies to the first pillar. It is therefore sensible to assume that the ECB bases its interest rate decisions on those variables or combination of variables which can help forecasting inflation. In order to put up an explicit ECB reaction function, we thus have to choose explanatory variables which are thought to possess this forecasting property. According to the first pillar, M3 growth plays a prominent role and should therefore be one of the indicator variables. Following the ECB definition, the official money growth gap is defined as 6. To some extent, the distinction between implicit and explicit reaction function corresponds to the well-known distinction between structural and reduced forms of econometric models. However, an implicit reaction function should only be labelled structural if it is derived from underlying economic reasoning, which is not always the case in the literature. r Verein für Socialpolitik and Blackwell Publishing Ltd

6 K. Carstensen Dm gap t 1 3 ðd 12m t þ D 12 m t 1 þ D 12 m t 2 Þ 0:045; ð2þ with D 12 m t ¼ m t m t 12. In addition, the real money gap and P* measures derived from a P* model as well as money overhang derived from a money demand function will be considered. These variables have predictive power for future inflation both from a theoretical and empirical perspective (Altimari, 2001; Gerlach and Svensson, 2000; Masuch et al., 2001; von Hagen, 2001) and are constructed as follows. The P* model defines the long-run equilibrium price level p* t with the help of the quantity equation p* t m t þ v* t y* t ; ð3þ where m t is the M3 money stock, v* t y* t m t þ p* t is long-run equilibrium velocity and y* t is potential output. The unobservable variable v* t can be inferred from the money demand function m t p t ¼ g 0 þ g 1 y t g 2 i t ; ð4þ where i t is an interest rate representing the opportunity costs of holding money. The long-run equilibrium money demand is then given by m t p* t ¼ g 0 þ g 1 y* t g 2 i* t : ð5þ Typically, i* t is assumed to be the sample average of i t and, thus, constant. 7 Given an estimate of (4), long-run equilibrium velocity can be calculated as Substituting this into (3) yields v* t ¼ g 0 þð1 g 1 Þy* t þ g 2 i* t : ð6þ p* t ¼ m t g 0 g 1 y* t þ g 2 i* t : ð7þ Altimari (2001) finds that equilibrium inflation Dp* t can help forecasting future inflation p tþn ¼ Dp tþn at horizons up to three years. Note, however, that there is no necessity that p t will change in the same direction as p* t. For example, consider the case where p t is below p* t. In order to close the gap one would expect p t to rise in the future even if the actual change Dp* t is negative. The reason for the wrong signal is that only growth rates are taken into account but no levels relationships. Interestingly, the official money growth gap and equilibrium inflation are similar measures under the assumptions on which the derivation of the 4.5% target M3 growth rate is based. Given average GDP and velocity growth rates of 2.25% and 0.75% (ECB, 1999a) and assuming a constant equilibrium interest rate i* t, the income part g 1 y* t must account for both trends and, thus, 7. Gerlach and Svensson (2000) discuss this point. 6 r Verein für Socialpolitik and Blackwell Publishing Ltd. 2006

7 Estimating the ECB Policy Reaction Function grow at an average rate of 3%. If these assumptions really hold, equilibrium inflation can be expressed as Dp* t ¼ Dm t g 1 Dy* t ¼ Dm t 0:03; ð8þ which differs, in principle, only by a constant from the somewhat smoother official money growth gap (2). As a consequence, both measures share the same disadvantages as outlined above. Therefore, more appealing from a theoretical point of view is to directly use the gap p t p* t as a predictor. Since a price gap should lead to an adjustment of prices, the future inflation rate should be a negative function of this variable. Instead of the price gap, many authors use the real money gap mp gap t ðm t p t Þ ðm t p* t Þ¼ ðp t p* t Þ; ð9þ which is simply defined as minus the price gap, and we will follow this practice of notation. Future inflation should be positively correlated to the real money gap. Altimari (2001) also considers a variable called money overhang which is defined as the difference between the real money stock and its equilibrium evaluated at current output and interest rate: m ov t ¼ m t p t g 0 g 1 y t þ g 2 i t : ð10þ From (4) it is obvious that m ov t is simply the equilibrium error of the money demand function. Differences and similarities between the real money gap and money overhang are easily seen when p* t is substituted out from (9) yielding mp gap t ¼ m t p t g 0 g 1 y* t þ g 2 i* t : ð11þ Both measures give the same information if actual GDP and interest rate equal their equilibrium values. Otherwise, there is an important difference. A positive money overhang indicates a future price increase only ceteris paribus, i.e. neglecting the possibility that, e.g., GDP is below trend. As a result, money overhang can give a wrong signal. This is circumvented when using the real money gap which measures a potential money overhang at equilibrium (or expected) values for GDP and the interest rate. It is therefore a strictly long-run concept. From the preceding discussion it may be fair to say that the real money gap is the most promising variable to predict future inflation and, thus, to enter the ECB reaction function, at least if the underlying assumptions concerning equilibrium GDP growth and equilibrium interest rate are satisfied. Nevertheless, P* inflation and money overhang are found to possess predictive power so the decision is left to the empirical analysis. In order to measure real activity, the output gap y gap t is used. As additional arguments for the ECB reaction function we consider nominal and real r Verein für Socialpolitik and Blackwell Publishing Ltd

8 K. Carstensen effective exchange rates, eer t and reer t, respectively. 8 Since the yield spread s t and the real interest rate R t are sometimes employed to predict future inflation (Mishkin, 1990; Tzavalis and Wickens, 1996) they are also included. The target rate r* t may thus be a function of current or lagged realizations of the explanatory variables x t ¼ðp t ; Dm gap t ; Dp* t ; mp gap t ; m ov t ; y gap t ; eer t ; reer t ; s t ; R t Þ 0 : The individual lags will be chosen according to their observability as described below. Since central banks are generally found to smooth interest rate changes, we follow Clarida et al. (1998) who assume a partial adjustment of the actual to the desired interest rate. In our context, this can be modelled as follows: r t ¼ rr t 1 þð1 rþ r* t ; ð12þ where r t is the latent (non-censored) MRO rate, r t is the realized (censored) MRO rate and r is the smoothing parameter. Since interest rate smoothing has the aim not to disturb markets, we find it sensible to assume that the ECB takes account of the lagged realized MRO rate r t 1 instead of the lagged latent MRO rate r t 1 as proposed by Dueker (2000) because the latent MRO rate is not observed by the public. Now, the reaction function can be written in a compact form as r t ¼ rr t 1 þð1 rþðb 0 þ b 0 x t Þþe t ; ð13þ where b is a parameter vector with elements b 1 ;...; b n. 3. THE ESTIMATION PROCEDURE The policy rule (13) cannot be estimated directly because the ECB does not set the MRO rate as r t but rather as r t which is a multiple of 25 basis points and, thus, censored. Let us therefore assume that r t ¼ 0:25i if a i < r t < a iþ1 ; i ¼ 1; 2; 3;...; ð14þ where a i are threshold parameters with a i < a iþ1 for all i. In our baseline model we set their values to a i ¼ 0:25i 0:125 ð15þ so that the thresholds lie exactly in the middle of two adjacent MRO rates. In principle, we could also estimate the thresholds as individual parameters but this is clearly infeasible for the small sample at hand. However, a possible deviation from the simple threshold rule (15) is discussed in Section See, e.g., Taylor (2001) for a review of the role of the exchange rate in monetary policy rules. 8 r Verein für Socialpolitik and Blackwell Publishing Ltd. 2006

9 Estimating the ECB Policy Reaction Function We assume that e t, which subsumes implementation errors of the ECB and specification errors of the policy reaction function, is normally distributed: e t Nð0; s 2 Þ: Note that the variance s 2 is identified because the thresholds and, thus, the latent MRO rate have a well-defined scale in our formulation. 9 For this ordered probit model, the probability that r t ¼ 0:25i is observed can be expressed as Prðr t ¼ i=4þ ¼F a iþ1 rr t 1 ð1 rþðb 0 þ b 0 x t Þ s F a i rr t 1 ð1 rþðb 0 þ b 0 x t Þ ; ð16þ s where FðÞ denotes the standard normal cumulative distribution function. As shown by Maddala (1983) the likelihood function is given by L ¼ Y Y F a iþ1 rr t 1 ð1 rþðb 0 þ b 0 x t Þ s i t F a i rr t 1 ð1 rþðb 0 þ b 0 Zit x t Þ ; ð17þ s where Z it ¼ 1 if r t ¼ 0:25i and 0 else. The log-likelihood function can be maximized numerically with respect to the unknown parameters. When interpreting the parameters r and b i, one should bear in mind that the reaction function is formulated in terms of the latent MRO rate r t which does not translate one-to-one to the observable (censored) MRO rate r t. Consequently, the short-run marginal effect of, say, x 1;t on r t is given by ð1 rþb 1 while the marginal effect of x 1;t on r t is somewhat more difficult to obtain. It is, of course, straightforward to calculate marginal effects of the Prðr t ¼ i=4þ=@x 1;t but they depend both on i and x t (Greene, 2000) which makes them unattractive to report. Moreover, the model discussed here is at least approximately linear in the sense that there is not only a natural ordering but also, in contrast to typical ordered probit models, a well-defined scale. This implies that, starting from a situation in which r t 1 ¼ r t 1 ¼ 0:25i, the ceteris paribus effect of a change in x 1;t is simply Dr t ¼ 0:25j for 0:25j 0:125 < D r t ¼ð1 rþbdx 1;t < 0:25j þ 0:125: If changes in r t were symmetrically distributed across each cell ½0:25j 0:125; 0:25j þ 0:125Š, it would even be true that E½Dr t Š¼E½D r t Š¼ð1 rþbe½dx 1;t Š so that the usual interpretation of ð1 rþb is, at least on average, correct. Since 9. Maddala (1983) assumes that all thresholds can be freely estimated. Then the scale is not identified and it is necessary to restrict the variance. r Verein für Socialpolitik and Blackwell Publishing Ltd

10 K. Carstensen symmetry is certainly not fulfilled in practice, the latter equality holds only approximately but the approximation error should not be too large if typical changes ð1 rþbdx 1;t are not too small compared to the cell length of 25 basis points. Therefore, while the interpretation of the parameter values should be undertaken with some care, the similarity of the specific censored model applied here with continuous models usually analysed should be sufficient to permit, e.g., comparisons with results presented elsewhere in the literature. 4. THE ESTIMATION RESULTS In this section, we first describe how the explanatory variables are constructed from the data. Subsequently, estimated policy reaction functions with different explanatory variables are presented and compared The data We use monthly data from the ECB statistics website. The main refinancing operations of the eurosystem were conducted as fixed rate tenders from 01/ 01/99 to 21/06/00. Since then the ECB has practised a variable rate tender system with minimum bid rate. The MRO rate in this paper consists of the fixed rate for the first period and the minimum bid rate for the second period. It is constructed by using end-of-month values from January 1999 to January This can be justified by the fact that, with few exceptions, MRO rate changes were announced and took place at the beginning of a month so that end-of-month values reflect the MRO rate level which prevailed during the respective month. 10 All other data are at least available from September 1997 onwards so that even long lags of the explanatory variables can be used. The variables are defined as follows: m t is M3 money stock, p t is the Harmonized Index of Consumer Prices (HICP) from which p t ¼ p t p t 1 is calculated, y t is industrial production, i t is the yield on ten-year government bonds, eer t and reer t are the nominal and real effective exchange rates, respectively, of the euro against a group of the 38 most important trading partners of the EU, s t is the spread between the three-month money market rate and the overnight rate (EONIA). Finally, the one-month real interest rate R t ¼ i ð1þ t ðp tþ1 p t Þ is calculated from the one-month money market rate and the one-month-ahead inflation rate. All variables except for the interest rates are in logarithms. Potential output y* t is estimated from industrial production by means of a Hodrick Prescott filter with smoothing parameter 129,600 as advocated by 10. MRO rate changes were announced (first took place) at the following dates: 08/04/99 (14/04/ 99), 04/11/99 (10/11/99), 03/02/00 (09/02/00), 16/03/00 (22/03/00), 27/04/00 (04/05/00), 08/06/00 (15/06/00), 31/08/00 (06/09/00), 05/10/00 (11/10/00), 10/05/01 (15/05/01), 30/08/ 01 (05/09/01), 17/09/01 (19/09/01), 08/11/01 (14/11/01), 05/12/02 (11/12/02); see ECB (2003a). 10 r Verein für Socialpolitik and Blackwell Publishing Ltd. 2006

11 Estimating the ECB Policy Reaction Function Ravn and Uhlig (2002). The sample starts in January 1993 in order to obtain a more reliable trend estimate than simply using EMU data. 11 The money demand function is estimated with the available data from September 1997 onwards. The sample size is certainly not sufficiently long to use a full-system cointegration approach which is generally employed to analyse money demand. However, Brand and Cassola (2000) and Coenen and Vega (2001) find stable (cointegrated) money demand functions for the euro area. Presupposing that this long-run stability carries over to our sample, we simply re-estimate the long-run money demand function by least squares making use of the superconsistency of this estimate given that cointegration still holds. In order to account for the jump in M3 due to the euro area enlargement in January 2001, a dummy variable d t is included which takes the value 0 before the break and 1 afterwards. Except for the dummy, we make the same choice of variables as Brand and Cassola (2000) because Altimari (2001) finds their money demand specification to possess better predictive power for inflation than the one of Coenen and Vega (2001). We obtain m t p t ¼ 0:012 ð0:457þ þ 0:073 ð0:007þ d t þ 0:814 ð0:099þ y t 1:158 ð0:619þ i t þ ^m ov t : ð18þ The residual ^m ov t is the estimate of money overhang. Using potential output y* t and the average interest rate which is 6.09% in our sample, P* inflation Dp* t and the real money gap mp gap t are constructed as outlined in Section The baseline policy reaction function As our baseline specification we consider a standard policy reaction function with inflation and the output gap as explanatory variables. Assuming policy decisions are made at the beginning of a month, the information lag for officially published data is around two months for inflation and four months for output if one considers published data as a benchmark. For example, the latest information in the ECB Monthly Bulletin from January 2003 is HICP for November 2002 and industrial production for October Of course, the exact lag chosen for inflation and output gap can only be an approximation because the dating of policy decisions varies and the ECB perhaps obtains information earlier than the public. On the other hand, due to data revisions decision-makers might be cautious to fully rely on the latest data available. Therefore, alternative lags are considered: lags 2 to 4 for inflation and 3 to 5 for the output gap. Using lags 2 and 4 for inflation and the output gap, respectively, yields the reaction function in structural form: r t ¼ð1 rþb 0 þ rr t 1 þð1 rþb 1 p t 2 þð1 rþb 2 y gap t 4 þ e t: ð19þ 11. We also employed a linear trend estimate which yielded comparable output gaps and a similar reaction function. r Verein für Socialpolitik and Blackwell Publishing Ltd

12 K. Carstensen It is estimated in reduced form r t ¼ d 0 þ rr t 1 þ d 1 p t 2 þ d 2 y gap t 4 þ e t; ð20þ from which the structural parameters b 0, b 1 and b 2 are calculated. Standard errors are obtained by means of the delta method. Note that from (1) it holds that b 0 ¼ r* b 1 p* ¼ rr* þð1 b 1 Þp* ; ð21þ where rr* ¼ r* p* is the (non-censored) long-run equilibrium real interest rate. Clarida et al. (1998) suggest to solve (21) for the target inflation rate p* ¼ b 0 rr* ð22þ 1 b 1 and use estimates of b 0 and b 1 and the sample average of the real interest rate to obtain an estimate of p:* In Table 1 estimation results are displayed together with several model evaluation criteria. The most general model, 1, contains all lags simultaneously which leads to many insignificant and even implausible parameter estimates. In particular, the sum of the structural output gap coefficients has value 0.45 which implies a negative overall impact of the output gap on the MRO rate. Moreover, the target inflation rate is estimated as As a consequence, insignificant parameters have to be eliminated from this model before it can be interpreted. It is therefore only used as a starting point against which restricted versions can be tested. The restricted models 2 to 10 each contain one lag of inflation and one lag of the output gap. 12 Of those, models 3, 4, 7, 8, 9 and 10 are rejected against the most general model 1 at the 10% level. The remaining three models, 2, 5 and 6, all show similar structural form parameter estimates. Using generalized residuals as proposed by Gourieroux et al. (1985) the null hypothesis of no autocorrelation cannot be rejected. 13 The target inflation rate is estimated as roughly 2% which is the maximum inflation rate the ECB declared to tolerate. Note that this result is very robust over all model specifications. Consequently, the ECB failed to hit the target inflation rate of 1.5% which is implicit in the derivation of the ECB money growth target (ECB, 1999a, pp ). On the other hand, the results are well in line with a target rate of close to 2% as announced in the revised monetary strategy. The information lags implicit in models 2, 5 and 6 are two or three months for inflation and three or four months for the output gap. For what follows, 12. Less restrictive models with more than one lag of inflation and/or the output gap still yield insignificant parameter estimates. 13. This result holds for all models considered in the following and is, thus, left out of this discussion. Obviously, using r t 1 as explanatory variable is sufficient to guarantee uncorrelated residuals. Including additional lags leads to insignificant parameter estimates. 12 r Verein für Socialpolitik and Blackwell Publishing Ltd. 2006

13 r Verein für Socialpolitik and Blackwell Publishing Ltd Table 1 Explanatory variable The baseline specification Model Intercept (0.33) (0.24) (0.27) (0.09) (0.25) (0.26) (0.26) (0.26) (0.28) (0.29) r t (0.15) (0.11) (0.12) (0.01) (0.11) (0.11) (0.11) (0.11) (0.11) (0.12) p t (0.12) (0.08) (0.08) (0.08) p t (0.04) (0.09) (0.08) (0.08) p t (0.16) (0.04) (0.08) (0.08) y gap t (0.05) (0.03) (0.03) (0.02) y gap t (0.12) (0.03) (0.03) (0.03) y gap t (0.04) (0.03) (0.03) (0.04) s (0.02) (0.02) (0.02) (0.02) (0.02) (0.02) (0.02) (0.02) (0.02) (0.02) b (0.10) (0.27) (0.31) (0.54) (0.25) (0.26) (0.51) (0.39) (0.48) (1.82) b (0.16) (0.13) (0.16) (0.27) (0.12) (0.13) (0.27) (0.20) (0.25) (1.35) b (0.17) (0.05) (0.05) (0.10) (0.05) (0.05) (0.09) (0.08) (0.09) (0.30) p* (3.78) (0.18) (0.18) (0.20) (0.15) (0.15) (0.17) (0.22) (0.23) (0.27) (Continued) Estimating the ECB Policy Reaction Function

14 14 r Verein für Socialpolitik and Blackwell Publishing Ltd Table 1 Explanatory variable Continued Model Hits Above Below log(l) Pseudo-R LR (0.14) (0.07) (0.02) (0.45) (0.29) (0.08) (0.02) (0.01) (0.01) AK (0.23) (0.27) (0.27) (0.41) (0.18) (0.17) (0.26) (0.16) (0.18) (0.28) Notes: All parameters are displayed with standard errors in parentheses below. The parameters b 0, b 1 and b 2 are derived from the reduced form estimates. For model 1, b 1 and b 2 are the sum of the structural form parameters for inflation and output gap, respectively. The target inflation rate p* is calculated conditional on the average overnight real interest rate which has, in this sample, a value of 1.47%. The number of times a model correctly predicts the MRO rate is denoted by hits while overestimation (underestimation) is denoted by above ( below ). The pseudo-r 2 is calculated as 1 log(l)/ log(l 0 ) where log(l 0 ) is the log-likelihood of a model computed with only a constant term. The likelihood ratio statistic LR tests the restricted models against the most general model 1 and is w 2 (4) distributed. The corresponding p-values are given below the LR statistics. AK1 denotes the test for first-order autocorrelation of Gourieroux et al. (1985) which employs generalized residuals and is w 2 (1) distributed. The corresponding p-values are given below the AK1 statistics. K. Carstensen

15 Estimating the ECB Policy Reaction Function model 5, r t ¼ 0:63 ð0:11þ r t 1 þð1 0:63 ð0:11þ Þð2:45 ð0:25þ þ ð0:12þ 0:50 p t 2 þ 0:30 ð0:05þ y gap t 4 Þþ^e t; ð23þ will be used as the baseline model because it shows the highest likelihood value and closely corresponds to the data availability arguments discussed above. The parameter ^r ¼ 0:63 indicates that there is a considerable amount of interest rate smoothing. While this parameter is smaller than typical estimates which are around 0.9 (Clarida et al., 1998; Faust et al., 2001; Gerdesmeier and Roffia, 2003), there are, e.g., episodes in the Fed s history where comparable smoothing parameters are found (Clarida et al., 2000). Moreover, Gerlach and Schnabel (2000) do not even find any significant smoothing parameter for pre-emu data, Breuss (2002) obtains GMM estimates for the euro area in the range between 0.59 and 0.96 and Surico (2003) finds values between 0.65 and Note that all model specifications analysed in this paper, which are not rejected by the data, yield estimates similar to The weights of inflation and output with respect to the latent MRO rate are ^b 1 ¼ 0:50 and ^b 2 ¼ 0:30, respectively. This means that the ECB responds to a 1% rise of inflation by raising the latent MRO rate by 50 basis points while it responds to a 1% rise of the output gap by raising the latent MRO rate by 30 basis points. Compared to the forward-looking policy rules estimated by Clarida et al. (1998), these values indicate that the ECB is much less concerned with inflation and slightly more concerned with the output gap than its predecessor, the German Bundesbank. 14 However, Gerlach and Schnabel (2000) find that the inflation coefficient is smaller and the output gap coefficient is larger when current instead of future inflation enters the reaction function. This reflects the difficulty to compare parameters of implicit and explicit reaction functions. Since we even use lagged variables, the differences should be even larger. Actual and predicted MRO rates are displayed in Figure 1. In the upper panel, the actual MRO rate is compared to the latent MRO rate predicted by the baseline model. The latent rate closely matches the actual rate in most instances. In particular, both the rise and the decline of the MRO rate are accounted for. However, the dates of the interest rate changes are sometimes missed and the long period of a constant MRO rate from the end of 2001 to the end of 2002 seems difficult to explain. This can also be inferred from the lower panel where the actual MRO rate is compared to the predicted censored rate. It has been argued, inter alia, by Alesina et al. (2001) and Begg et al. (2002) that core inflation might explain the interest rate path better than overall 14. This point has been raised by many observers of the ECB s policy, e.g. by Artus et al. (2002a), Faust et al. (2001), Gali (2001) and Neumann (2001). r Verein für Socialpolitik and Blackwell Publishing Ltd

16 K. Carstensen Figure 1 Predicted MRO rates in the baseline model Notes: The upper panel shows the actual MRO rate (solid line) together with the latent MRO rate (dashed line); the lower panel shows the actual MRO rate (solid line) together with the predicted MRO rate (dashed line). HICP inflation because the former excludes food and energy prices and, consequently, does not exhibit the pronounced rise in HICP inflation induced by increasing oil prices. However, estimating a model with HICP inflation replaced by core inflation does not lead to favourable results. In particular, the weight of core inflation is insignificant and, for some specifications, even negative. We therefore proceed using the HICP inflation rate which constitutes the official inflation target The influence of the ECB money growth target In a next step it is analysed whether the money growth target announced by the ECB has any explanatory power in addition to the baseline model. To this end, the baseline model is augmented by the money growth gap variable Dm gap t. Due to the fact that money growth data are quickly available at least to the central bank a specification with money growth gap lagged by two periods seems sensible, giving rise to the reaction function 16 r Verein für Socialpolitik and Blackwell Publishing Ltd. 2006

17 Estimating the ECB Policy Reaction Function r t ¼ rr t 1 þð1 rþðb 0 þ b 1 p t 2 þ b 2 y gap t 4 þ b 3Dm gap t 2 Þþe t: ð24þ The sensitivity of this choice is evaluated by also reporting lag 3 for Dm gap t. 15 The estimation results are given in the left columns of Table 2. They show that the choice of the lag is not essential. Both in the reduced and structural form, the money growth gap parameters are highly significant. This is confirmed by likelihood ratio tests of the baseline model against each of the augmented models which yields the unanimous result that the exclusion of the money growth gap has to be rejected with p-values of 0.01 and 0.003, respectively. Moreover, the money growth gap seems to take some of the weight of the inflation rate with the effect that the sum of the parameters of both variables is the same as the weight of inflation alone in the baseline model. From this perspective, the money growth gap is in fact used by the ECB to gain additional information about future inflation. The strong rise of money growth rates over the target value of 4.5% starting in the second half of 2001 might call the stability of the preceding reaction function into question. Therefore, the model is re-estimated with an interaction variable included which is defined as dum 1t ¼ Dm gap t if Dm gap t > 1:0% or Dm gap t < 1:0% and zero else. A significant parameter value would imply a change in the weight of the money growth gap if the growth rates are outside the reference band of 3.5% to 5.5% advocated by Artus et al. (2002b). Given lags 2 and 3 of the money growth lags, the estimated parameters of the dummy variable are (standard error 0.08) and 0.06 (standard error 0.08), respectively. Testing for exclusion of the dummy variable leads to likelihood ratio statistics of (p-value ) and 0.60 (p-value ), respectively. Thus, there is no significant sign of structural instability at this point. As an even simpler rule, the ECB might be concerned with the money growth number most recently observable, i.e. the deviation of D 12 m t from the reference value of 4.5%. Although this variable is prone to erratic fluctuations and, thus, not used officially by the ECB, it is easily understandable by the public. Therefore, the ECB might feel a particular pressure to react if D 12 m t exceeds 4.5%. As for the official money growth gap, lags 2 and 3 are taken into consideration. The estimation results in Table 2 show a similar picture as before: the lags of D 12 m t 4:5% are significant at the 5% level and the likelihood ratio test rejects the baseline model. However, the likelihood criterion does not improve as much as for the preceding model which might indicate that the ECB prefers the official money gap over the money growth. Instead of a rather simple money growth number, the ECB perhaps uses more sophisticated measures which are even better suited to indicate monetary developments signalling a threat to price stability. Such measures can be derived from a P* model as outlined in Section 2. We therefore replicate the preceding analysis with the money growth gap replaced by P* inflation Dp* t, the real money gap mp gap t and, finally, money overhang m ov t 15. The results remain mainly unchanged when using lag 1 or even higher lags. r Verein für Socialpolitik and Blackwell Publishing Ltd

18 18 r Verein für Socialpolitik and Blackwell Publishing Ltd Table 2 Explanatory variable The baseline model augmented by monetary measures Lag of Dm gap t Lag of D 12 m t Lag of Dp t Lag of mp gap t Lag of m ov t l 5 2 l 5 3 l 5 2 l 5 3 l 5 4 l 5 5 l 5 4 l 5 5 l 5 4 l 5 5 General model Intercept (0.22) (0.24) (0.21) (0.22) (0.25) (0.23) (0.20) (0.19) (0.19) (0.20) (0.20) r t (0.09) (0.10) (0.08) (0.09) (0.11) (0.10) (0.08) (0.08) (0.08) (0.08) (0.08) p t (0.08) (0.08) (0.08) (0.07) (0.08) (0.08) (0.07) (0.07) (0.07) (0.07) (0.07) y gap t (0.03) (0.03) (0.03) (0.03) (0.03) (0.03) (0.02) (0.02) (0.02) (0.02) (0.03) Dm gap t l (0.03) (0.03) (0.04) D 12 m t l (0.03) (0.03) Dp t l (0.04) (0.04) mp gap t l (0.02) (0.02) (0.03) m ov t l (0.01) (0.01) (0.03) s (0.02) (0.02) (0.02) (0.02) (0.02) (0.02) (0.02) (0.02) (0.02) (0.02) (0.02) K. Carstensen

19 r Verein für Socialpolitik and Blackwell Publishing Ltd b (0.25) (0.22) (0.28) (0.24) (0.26) (0.25) (0.22) (0.19) (0.20) (0.20) (0.21) b (0.16) (0.14) (0.18) (0.15) (0.13) (0.12) (0.11) (0.09) (0.10) (0.10) (0.14) b (0.06) (0.06) (0.07) (0.06) (0.05) (0.05) (0.04) (0.03) (0.05) (0.04) (0.08) b (0.10) (0.08) (0.11) (0.09) (0.13) (0.11) (0.06) (0.05) (0.05) (0.04) (0.09) b (0.08) b (0.09) p* (0.14) (0.12) (0.16) (0.15) (0.16) (0.15) (0.18) (0.16) (0.14) (0.14) (0.19) Hits Above Below log(l) Pseudo-R LR (0.01) (0.003) (0.02) (0.03) (0.62) (0.54) (0.0002) (0.0002) (0.0001) (0.0002) (0.0000) AK (0.51) (0.55) (0.19) (0.47) (0.18) (0.17) (0.98) (0.59) (0.38) (0.89) (0.53) Notes: Money growth D 12 m t is measured as the deviation of annual money growth from the target rate of 4.5%. The variables Dp t, mpgap t are demeaned in order to facilitate the estimation of the target inflation rate p*. The general model in the last column is estimated with lags 3, 5 and 4 of the variables Dm gap t, mp gap t and m ov t and is w 2 (1) distributed. The corresponding p-values are given below the LR statistics. See also Table 1. and m ov t, respectively. The likelihood ratio statistic LR tests the baseline model against the augmented model Estimating the ECB Policy Reaction Function

20 K. Carstensen which is directly derived from a money demand function. Since all three measures are calculated by using, inter alia, output data we suppose that they are observable to the ECB with a lag of four months which turned out to be the optimal lag of the output gap in the baseline reaction function. To assess the sensitivity of this assumption, lag 5 is also considered. Estimation results are presented in Table 2. Including DP* does not lead to a significant improvement over the baseline model. Both the estimated weights of DP* and the likelihood ratio statistic are not significant. As a consequence, DP* does not seem to be a relevant additional variable in the ECB information set. In contrast, adding the real money gap as explanatory variable to the baseline model makes a difference; see Table 2. The estimated parameters are highly significant and the likelihood ratio tests reject the baseline model at any common significance level. It is again not essential which lag is included. As argued above, lag 4 is the most natural choice so we concentrate on this case. The real money gap has an estimated weight of The weight of inflation now is 0.62 in contrast to 0.50 in the baseline model while the weight of the output gap remains roughly constant at So the model with mp gap t 4 as additional variable indicates a little bit more than the baseline model that the ECB is concerned with inflationary risks. As a final monetary measure money overhang is considered. The estimated parameters are again highly significant and the baseline model is rejected by means of a likelihood ratio test. In terms of the likelihood value, the model with lag 4 performs best of all models considered so far (lnðlþ ¼ 45:73Þ. It exhibits a weight of 0.53 for inflation which is similar to the baseline model, a weight of 0.41 for the output gap which is somewhat larger than in the baseline model, and a weight of 0.16 for money overhang. So far, we can conclude that monetary measures in fact enter the ECB reaction function in addition to the inflation rate. It is, however, not obvious which of the measures performs best because the models are not nested within each other. Simply ordering them according to the likelihood value gives the following ranking: the model augmented by money overhang has the highest likelihood value followed by the real money gap and the official money gap. To gain further insight, a model with all three measures included is also estimated; see Table 2, last column. Due to collinearity, the weights of Dm gap mp gap t and m ov t are all insignificant. This stresses the fact that they carry similar information. However, comparing the likelihood values of this general model with the values of the preceding models leads to some interesting results. Excluding mp gap t and m ov t from the general model leads to the model in column 2. The corresponding likelihood ratio statistic is 8.74 ( p-value ) which implies that the exclusion has to be rejected. In contrast, excluding Dm gap t and mp gap t or Dm gap t and m ov t cannot be rejected at likelihood ratio statistics of 0.58 (p-value ) and 3.18 (p-value ), respectively. From this we conclude that at least one of the measures mp gap t and m ov t is a necessary part of the reaction function while the official monetary measure Dm gap t can be excluded. 20 r Verein für Socialpolitik and Blackwell Publishing Ltd t,