# «Christina Gerberding (Deutsche Bundesbank) Franz Seitz (University of Applied Sciences Amberg-Weiden) Discussion Paper Series 1: Economic Studies No ...»

One important reason for this largely negative verdict is the fact that in the canonical New Keynesian model which underlies much of the more recent literature on optimal monetary policy, money is irrelevant for the determination of real output, inflation and the interest rate. This property of the model has led the academic literature to focus on direct links between interest rate setting and objectives such as desired paths for inflation and real activity. Still, a number of authors have developed arguments for assigning a role to money even within the setup of the standard New Keynesian model.

For instance, Söderström (2005) has shown that stabilising money growth around a target can be a sensible strategy for a central bank acting under discretion because it introduces inertia and history-dependence into monetary policy. Coenen et al. (2005) have demonstrated that monetary aggregates may have information content about the “true” level of aggregate output if the environment is characterised by (a) measurement errors in GDP data, (b) a contemporaneous linkage between money demand and real output and (c) a sufficiently low variability of money demand shocks. Beck and Wieland (2007) have shown that ECB-style monetary cross-checking can generate *

**Corresponding author: Michael Scharnagl, Deutsche Bundesbank, e-mail:**

michael.scharnagl@bundesbank.de. Christina Gerberding, Deutsche Bundesbank. Franz Seitz, University of Applied Sciences Amberg-Weiden. The views expressed in this paper are those of the authors and should not be interpreted as those of the Deutsche Bundesbank. We thank Heinz Herrmann, Petra Gerlach-Kirsten and participants of workshops at the Bundesbank, the Oesterreichische Nationalbank and the Schweizer Nationalbank for helpful comments.

substantial stabilisation benefits in the event of persistent policy misperceptions regarding potential output.

The present paper contributes to this literature by exploring the potential role of money in simple interest rate rules when policymakers face measurement problems with respect to both the level and the change in the output gap. Orphanides (2001, 2003a) was the first to point out that the good performance of the popular Taylor rule across a wide array of macroeconomic models (see Taylor, 1999) crucially depends upon the assumption that policymakers have reasonably accurate information about the “true” level of the output gap. In practice, however, this variable is unobservable and its estimation is complicated by controversies surrounding the appropriate definition and estimation method. Moreover, estimates of the output gap suffer from real-time data problems and have been shown to undergo major revisions over time. In order to avoid the policy errors which may result from reliance upon inaccurate estimates of this variable, Orphanides (2003b, c) has recommended the use of first difference rules which prescribe a change in the interest rate when inflation and/or output growth deviate from target. He has also pointed out that with a standard money demand relationship, money growth targeting can be reformulated as an interest rate rule of this type (Orphanides, 2003b, p. 990). Gerberding et al. (2007) have shown that this type of rule characterises the Bundesbank’s monetary policy from 1979 to 1998 quite well.1 In the present paper, we take up this issue and look at it from a slightly different perspective. In particular, we ask whether adding a money growth term to an interest rate rule that already includes a response to both inflation and the output gap yields any extra benefits. On the one hand, augmenting a standard Taylor rule with a money growth target may be advantageous because it introduces inertia and history-dependence into the policy rule. On the other hand, this can also be achieved by including the lagged interest rate and output growth directly among the feedback variables (as in Stracca, 2007). However, even in this case, an additional response to money growth may be beneficial because money growth may have information content about the “true” rate of output growth which can only be measured imperfectly.

** This result is robust to the use of real-time or ex post data.**

To gauge the relevance of these arguments for the euro area, we extend the set of simple rules analysed by Stracca (2007) to include variants of the Taylor rule and the speed limit rule which feature an additional response to money growth. We then go on to calculate the optimal feedback coefficients and to compare the performance of the optimised simple rules in a small estimated model of the euro-area economy. The model that we use is a version of the canonical New Keynesian model which has been proposed by Rudebusch (2002) and estimated on euro-area data by Stracca (2007). To capture the implications of output gap uncertainty, we assume that policymakers observe only noisy measures of the output gap and of the change in the output gap.

Moreover, we assume that the observed uncertain variables enter the policy rule directly. In this respect, we follow the approach taken by Orphanides (2003c), Rudebusch (2001, 2002), or more recently, by Leitemo and Lonning (2006) as well as Beck and Wieland (2007). Alternatively, one could use the Kalman filter to derive optimal estimates of the variables in question. However, the optimal Kalman-filter estimates are complicated functions of past values of the observable variables and of the model parameters, which is at odds with the simple rules framework underlying our analysis.2 In order to assess the magnitude and the exact nature of the measurement errors, we draw on the Bundesbank’s real-time data set for Germany which includes real-time data on actual output as well as on the Bundesbank’s estimates of potential output (see Gerberding et al., 2004). The lessons to be learnt from the historical measurement errors in these data are described in Section 2 of the paper. In Section 3, we describe the aggregate demand, aggregate supply and money demand equations of the model, the set of policy rules that we consider and the details of the central bank objective function which we need to pin down the optimal values of the feedback coefficients. In Section 4.1, we present our results on the relative performance of the rules under different degrees of output gap uncertainty. The main finding is that, even at low levels of output gap uncertainty, an additional response to money growth significantly improves the performance of both the Taylor rule and the speed limit rule. In Section 4.2 and 4.3, we carry out a robustness analysis. Section 5 concludes.

The usefulness of simple rules for monetary policy is discussed by Williams (2003) or Berg et al.

(2006).

2. Modelling data uncertainty – Lessons from German data Data uncertainty arises because the relevant statistics provide only incomplete or unreliable information about the actual state of the economy. A second, maybe even more important reason is that the interpretation of the available data often depends on the assessment of their development relative to their trend or long-run equilibrium levels which are unobservable and can only be estimated with large margins of error.

The problem is therefore especially acute for variables which are formulated in deviations from their equilibrium or “natural rate” levels. A well-known example are the measurement problems regarding the output gap, a variable which figures prominently in much of the academic literature on monetary policy rules. Differences

**between real-time and revised estimates of the output gap may arise from three sources:**

(a) revisions in GDP data, (b) the arrival of new data which changes the assessment of past developments and (c) changes in the method used for estimating potential output.

The problem is by no means new. However, in order to assess its implications for monetary policy, one needs to form a judgement on the magnitude and the exact nature of the measurement errors. Real-time data sets containing subsequent historical vintages of key macro variables constitute a valuable source for this kind of information.3 In this paper, we draw on real-time data sets for German GDP and for the Bundesbank’s estimates of potential output described in Gerberding et al. (2004) to assess the likely extent of real-time uncertainty about the level of the output gap, the change in the output gap and its components, actual and potential output growth, prevailing in the euro area. Figure 1 illustrates the extent of revisions between the Bundesbank’s real-time estimates of the output gap (that is, the initial estimates available at t+1) and a series of ex post revised estimates which is based on the last available vintage of Bundesbank estimates of the production potential dating from January 1999 and on the March 1999 vintage of GDP data. The pattern that emerges from Figure 1 is very similar to the one found for other countries, e.g. by Orphanides (2001) and Nelson and Nikolov (2001) for the US and the UK, respectively. With few exceptions, the ex post series is always above the real-time series, suggesting that from today’s perspective, the initial estimates of the output gap persistently overestimated the Such data sets are by now available for a number of countries, among them US, UK and Germany. See Croushore and Stark (2001), Orphanides (2001, 2003a) and Gerberding et al. (2004, 2005a).

amount of slack in the economy. When splitting up the overall measurement error in the output gap into its components (Figure 2), it becomes apparent that the errors were mainly due to a persistent overestimation of potential output. In fact, there is only one subsample – the early 1990s – when revisions in actual GDP data dominate the overall forecast error.

The magnitude and persistence of these measurement errors suggest that monetary policymakers would have been ill-advised to respond strongly to real-time estimates of the level of the output gap. Of course, other potential feedback variables like the change in the output gap, the rate of inflation or money growth may be subject to their own set of measurement errors. However, with a high degree of level persistence, the errors in the estimates of the change in the output gap should be less severe than the errors in the level of the gap.4 As shown in the first graph of Figure 3, this is indeed the case. When splitting up the change in the output gap into its components (second graph), we find that the measurement errors in output growth and in the change in the output gap follow very similar patterns while the measurement errors regarding potential output growth are smaller, but more persistent. Finally, as illustrated by the third graph in Figure 3, revisions in consumer prices and in money growth were even smaller in size throughout the sample period, with money growth figures being hardly ever revised at all. While this may not have been true for other countries over different sample periods (see Amato and Swanson, 2001), Coenen et al. (2005) reach very similar conclusions with respect to euro area data since 1999.5 Table 1 provides some statistics on the extent and nature of the revisions which will later be used to calibrate the parameters of the measurement error processes of the model. In order to allow some time for revisions between the initial and the ex post observations, we shorten the sample period to 1974Q1 to 1995Q1 (which has the additional advantage of leaving us with West German data only). We report results for this sample period as well as for the - arguably more “normal” – sample period 1980Q1 As shown by Walsh (2004), the variance of the error in the measured change of the output gap depends negatively on the degree of persistence in the measurement error of the corresponding level estimates.

Coenen et al. (2005, p. 982) show that the ECB’s preferred measure of the broad money stock, M3, is subject to only small revisions after the first quarter and to negligible revisions in subsequent quarters.

to 1995Q1. As the data frequency of the model underlying the analysis in the next section is quarterly, we focus on quarter-to-quarter rates of change.6 To capture the potential persistence in the measurement errors, we follow Orphanides et al. (2000) and assume that they follow an AR(1) process. Of course, such a first-order process represents a simplification of the true revision process in the data, but it offers a parsimonious way of capturing the size and persistence in the revisions.