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A time-varying “natural” rate of interest for the euro area
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European Economic Review 51 (2007) 1768–1784 www.elsevier.com/locate/eer
A time-varying ‘‘natural’’ rate of interest for the euro area Jean-Ste´phane Me´sonniera,, Jean-Paul Renneb a Monetary Policy Research Division, Banque de France, 41-1422, 75049 Paris cedex 01, France Growth Policy Division, Ministe`re de l’Economie, des Finances et de l’Industrie, 139 rue de Bercy, 75572 Paris cedex 12, France
b
Received 14 September 2004; accepted 15 November 2006 Available online 12 January 2007
Abstract We estimate a time-varying ‘‘natural’’ rate of interest (TVNRI) for a synthetic euro area over the period 1979Q1–2004Q4 using a small macroeconomic model, broadly following a methodology developed by Laubach and Williams [2003. Measuring the natural rate of interest. The Review of Economics and Statistics 85(4), 1063–1070] for the United States. The Kalman filter simultaneously estimates the output gap and the natural rate of interest. Our identifying assumptions include a close relationship between the TVNRI and the low-frequency fluctuations of potential output growth. The difference between the real rate of interest and its estimated natural level offers valuable insights into the monetary policy stance over the last two decades and a half. r 2006 Elsevier B.V. All rights reserved. JEL classification: C32; E32; E43; E52 Keywords: Natural rate of interest; Interest rate gap; Monetary policy; Kalman filter; Output gap; Euro area
1. Introduction In this paper, we apply the Kalman filter to a simple restricted VAR model of the euro area economy in order to estimate a time-varying ‘‘natural’’ rate of interest (NRI) for the euro area. The ‘‘natural’’ real rate of interest—also sometimes termed a neutral or real equilibrium rate of interest—is commonly defined as the real short-term rate of interest Corresponding author. Tel.: +33 1 4292 9163; fax: +33 1 4292 6292.
E-mail address: [email protected] (J.-S. Me´sonnier). 0014-2921/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.euroecorev.2006.11.006
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which is consistent with output at its potential level and a stable rate of inflation (see e.g. ECB, 2004).1 The real interest rate gap (IRG), the difference between the real short-term interest rate and its ‘‘natural’’ counterpart, seems to be an interesting candidate for assessing the current monetary policy stance, notably as an alternative to measures that employ monetary aggregates or exchange rates. Hence, it is not surprising that central banks and central bank economists have recently devoted much attention to these theoretical developments and the resulting empirical estimation strategies.2 A more careful reading of this burgeoning ‘‘natural’’ rate literature, however, reveals two main approaches, depending on whether the focus is on short-term or medium to long run implications of a nonzero gap and, simultaneously, on the degree of structure put into the models that yield the estimates (see Giammarioli and Valla, 2004, for a survey). The first strand broadly follows the lines of Woodford (2003) or Neiss and Nelson (2003) and derives the NRI within the framework of standard microfounded ‘‘new Keynesian’’ models (see, e.g. Giammarioli and Valla, 2003; Smets and Wouters, 2003, for applications to the euro area). From this perspective, the NRI equals the equilibrium real rate of return in an economy where prices are fully flexible, or in other words, it is the real short-term rate of interest that equates aggregate demand with potential output at all times. The emphasis is thus put on short-term developments, what Laubach and Williams (2003) term the ‘‘higher frequency component’’ of the NRI. The second strand of the literature follows Laubach and Williams (2003) and mixes the reference to simple macroeconomic models usually found in the monetary policy literature with the use of the Kalman filter in order to estimate the NRI, the potential level of output and/or the natural rate of unemployment as unobserved variables.3 In this view, the NRI is the real short-term rate of interest consistent with output at its potential and inflation stable in the medium run, i.e. once the effects of demand shocks on the output gap and supply shocks on inflation have completely vanished. Along with Larsen and McKeown (2004), we argue that such a semi-structural approach strikes a convenient compromise between the (more costly) DSGE approach and purely statistical trend estimates like the commonly used HP filter. Moreover, by allowing for large changes in unobservable variables like the growth rate of potential output and the NRI, they can deal with and reasonably account for the large shocks and many structural changes that have affected European economies over the last two to three decades. In contrast, large low-frequency movements of the NRI should remain a priori out of reach of more structural approaches using DSGE models, where aggregate relationships are expressed as log-linear approximations around a deterministic steady state.4
1 The concept of a ‘‘natural’’ real rate of interest and its prescriptive use for monetary policy is generally associated with Wicksell (1898, 1907). The recent revival of the concept owes much to the ‘‘neo-wicksellian’’ framework for monetary policy analysis advocated by Woodford (2003), where the neutral rate embedded in the Taylor rule varies continuously in response to various real disturbances. 2 See, e.g. Archibald and Hunter (2001), Christensen (2002), Williams (2003), Neiss and Nelson (2003), ECB (2004), Crespo-Cuaresma et al. (2004), Larsen and McKeown (2004) and Basdevant et al. (2004). 3 Recent examples include Orphanides and Williams (2002), Crespo-Cuaresma et al. (2004), Basdevant et al. (2004), Larsen and McKeown (2004) and Garnier and Wilhelmsen (2005). 4 It is most often the case that this steady-state level of an unobservable variable like the NRI is then conveniently proxied by some historical mean of the corresponding observed variable, then the ex post real rate of interest.
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However, the available empirical evidence about the existence of structural breaks in the real interest rates of European economies over the last few decades5 points to the plausibility of significant time variation in the NRI of these economies. This suggests the use of estimation methods that allow for large persistent fluctuations of this unobservable variable. We thus apply the methodology first developed by Laubach and Williams (2003) to a synthetic euro area over the period 1979–2004. Our model specification departs from theirs in at least two significant ways. First, we assume that the unobservable process that, as in Laubach and Williams (2003), drives the low-frequency common fluctuations of both the NRI and potential output growth remains stationary autoregressive instead of nonstationary, although we expect it to be quite persistent. This allows us to avoid the difficult reconciliation of a nonstationary output growth and a nonstationary equilibrium real interest rate with both economic theory and intuition. Second, we compute the real interest rate as a model-consistent ex ante real rate of interest, using the inflation expectations provided by the model instead of deriving them from univariate autoregressive models of inflation as Laubach and Williams and others do. The rest of the paper is organized as follows. Section 2 presents the data. Section 3 introduces the model. Section 4 develops estimation issues, discusses the results and checks their robustness to alternative calibrations of some parameters that cannot be estimated properly. Section 5 then conducts a retrospective evaluation of the euro area monetary policy stance on the basis of our baseline estimate. Section 6 concludes. 2. Data The euro area time series for real GDP, inflation and the short nominal rate of interest cover the period 1979Q1–2004Q4 with quarterly frequency. The first year marks the start of the EMS. Historical series for the euro area are taken from the ECB’s AWM database (see Fagan et al., 2000) and have been updated up to the end of 2004 with the official data published by Eurostat and the ECB.6 Whereas the real GDP figures provided by the AWM database are already seasonally adjusted, the HICP series is not and we hence adjust it using the Tramo/Seats procedure. In the following, the log real GDP is denoted by yt . Inflation is defined as the annualized quarterly growth rate of the HICP series (in logs) and is denoted by pt . The ex ante real short-term rate of interest rt is obtained by deducting from the current level of the 3month nominal rate of interest it the one-quarter-ahead expectation of (quarterly annualized) inflation as derived from the entire model estimation (denoted with ptþ1jt below). Finally, two variables are unobservable and constitute the state variables in the state-space model described in the following section, namely the output gap zt and the NRI rt .
5
See for instance Rapach and Wohar (2005), who find evidence of multiple structural breaks in the mean of real interest rates over the last four decades in 13 industrialized countries. Among them figure Belgium, France, Ireland, Italy and the Netherlands, which account for a rough half of the current euro area GDP. 6 Concretely, Eurostat official data were used over their whole period of availability (i.e. from 1991Q1, 1992Q1 and 1999Q1 onward, respectively) to allow for consistency with common knowledge of the recent economic juncture. These official series were then backdated with the corresponding AWM series.
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3. Model specification We base our analysis on a simple macroeconomic model for the euro area economy. Our specification is close to Laubach and Williams (2003), who partly follow the lines of Rudebusch and Svensson (1998). The model relies on six backward-looking linear equations and, as such, is obviously subject to the Lucas critique. However, empirical backward-looking models without explicit expectations are still widely used for monetary policy analysis and they appear to be fairly robust empirically.7 Regarding the dynamics of the NRI, which are central to our estimation framework, the economic intuition is given by the basic optimal growth model (the textbook Ramsey model). Intertemporal utility maximization by the representative household yields the following log-linear relationship between the real interest rate r and the (usually constant) rate of labor-augmenting technological change a, which is also the rate of growth of per capita output along a balanced-growth path r ¼ ya þ r
(1)
with constant relative risk aversion y (which corresponds to the inverse of the intertemporal elasticity of substitution) and where r stands for the household’s rate of time preference. Assuming that this trend growth rate a is in fact subject to low-frequency fluctuations, we get the intuition underlying our specification choice, which postulates a link between long run fluctuations in the growth rate of potential output and the NRI. In this respect, our approach lies between those of Laubach and Williams (2003) and Orphanides and Williams (2002). In the former, the NRI is the sum of the trend growth rate, which also drives the low-frequency fluctuations of potential output growth, and a second, specific (possibly nonstationary) component. In the latter study, the NRI and potential output growth are completely unrelated, which stands at odds with the theoretical intuition and may potentially result in a nonoptimal exploitation of the data. Laubach and Williams’ approach features a higher level of complexity than ours. It may therefore appear more attractive. However, this added complexity raises some cumbersome estimation problems, notably because it requires extracting two unobservable components out of an already unobservable variable (the NRI) which in turn is identified through the dynamics of another unobservable variable (i.e. the output gap, as in Eq. (3) below).8 Since we aim primarily at estimating a time-varying NRI in a way as transparent and robust as possible, we prefer our simpler specification. The model consists of the following six equations: pt ¼ a1 pt1 þ a2 pt2 þ a3 pt3 þ bzt1 þ pt , zt ¼ Fzt1 þ lðit2 pt1jt2 rt2 Þ þ zt ,
ð2Þ ð3Þ
7 See e.g. Rudebusch and Svensson (1998, 2002), Onatski and Stock (2002), Smets (2002), Dennis (2001), Laubach and Williams (2003), Fagan et al. (2001) and Fabiani and Mestre (2004). Regarding robustness issues, see also Rudebusch (2005), Bernanke and Mihov (1998), Estrella and Fuhrer (1999) and Leeper and Zha (2002), among others. 8 In particular, some estimates of key-parameters when several components enter the dynamics of the NRI are very sensitive to the initial state values and variances. More precisely, if the NRI is assumed to follow a twocomponent process (rt ¼ yat þ Zt ) and if the variance reflecting the confidence on the initial value Z0 is not large enough, the parameter y might be bounded to estimate the initial level of the NRI instead of assessing the extent to which the NRI and potential output growth fluctuate together.
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rt ¼ mr þ yat , Dyt ¼ my þ at þ yt ,
ð4Þ ð5Þ
at ¼ cat1 þ at ,
ð6Þ
yt ¼
yt
þ zt ,
ð7Þ
where the four shocks are independently and normally distributed, with variances s2p , s2z , s2y and s2a . The selection of lags on the RHS variables in Eqs. (2) and (3) is consistent with the data and is discussed in detail in Section 4 below, which deals with estimation issues. The first equation can be interpreted as an aggregate supply equation, or ‘‘Phillips curve’’. It relates consumer price inflation to its own lags and the lagged output gap. The second one is a reduced form of an aggregate demand equation, or ‘‘IS curve’’, relating the output gap to its own lags and the IRG—i.e. the difference between the short-term real rate and the NRI. Policy-makers control the inflation rate with a lag of three periods. The NRI is identified through the IRG. More precisely, the output gap is assumed to converge to zero in the absence of demand shocks and if the real rate gap closes. In this model, stable inflation is consistent with both zero output gap and IRG. Hence, our NRI could also be conveniently labelled as a ‘‘nonaccelerating-inflation rate of interest’’ (NAIRI). An important feature of the model is the fact that monetary policy affects the rate of inflation only indirectly via the output gap. Lastly, we take the nominal short-term rate of interest as exogenous, or, put differently, the reaction function of the central bank remains implicit. Departing from common specifications in the literature, we assume that the NRI rt follows an autoregressive process instead of a random walk, as specified by (4) and (6).9 Admittedly, the random walk assumption for the NRI has the technical advantage of combining persistent changes in the unobservable component with a smooth accommodation of plausible but unspecified structural breaks in the effective interest rate series, over a period of estimation that generally covers the last two to three decades. Nevertheless, postulating that the NRI follows a nonstationary process hinders the economic interpretation of the model, in particular if we assume, as we do here, that potential growth Dyt shares common fluctuations with rt .10 In practice, the complete estimation of our model confirms that this process is in fact highly persistent (see the estimator of c in Table 1 below), which fits our purpose of capturing large and low-frequency fluctuations in the level of the equilibrium real rate, as would the hypothesis of a nonstationary NRI also do. The autoregressive process denoted by at (see (6)) captures low-frequency variations in potential output growth assuming that these variations are common with those of the NRI. In addition, potential output growth (5) has another, stationary component, which may account for other sources of discrepancies with the NRI—e.g. due to shocks to preferences or changes in fiscal policies. Estimations show that a simple white noise is sufficient to model this second stationary component.11 Last but not least, these 9 Numerous studies specify a nonstationary process for the NRI and/or the rate of growth of potential output: See e.g. Laubach and Williams (2003), Orphanides and Williams (2002), Larsen and McKeown (2004) and Fabiani and Mestre (2001). Nevertheless, another exception to this widespread choice is Gerlach and Smets (1999), who assume in a framework analogous with ours that potential output is I(1). 10 A nonstationary specification for the NRI and then potential output growth—through the assumption of a random-walk for at —would indeed imply that potential output is integrated of order two. Besides, when translated into the set-up of a standard optimal growth model, this would mean a nonstationary path for the ratio of output to the stock of capital. 11 AR specifications systematically lead to nonsignificant autoregressive coefficients.
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Table 1 Parameter estimates (baseline: sy =sz ¼ 0:5 and y ¼ 16) sy sz
Unc. y Unc.
sy sz
Unc. y¼0
sy sz
Unc. y ¼ 16
sy sz
¼ 0:5 y ¼ 16
sy sz
¼ 0:5 y¼0
sy sz
¼ 0:5 y¼4
sy sz
¼ 0:5 No at
sy sz
Log-L LM test ðp-valueÞ LR test ðp-valueÞ a1
206.11
207.96 8%
206.44 43%
206.57 63%
207.97 89%
207.74 52%
215.76 27%
206.33 80%
5%
41%
63%
15%
20%
0:50
0:54
0:49
0:51
0:54
0:53
0:45
0:50
a2
0:17
0:18
0:18
0:17
0:18
0:17
0:21
0:17
ð1:8Þ
ð1:9Þ
ð1:9Þ
ð1:9Þ
ð1:9Þ
ð1:9Þ
ð2:2Þ
ð1:8Þ
a3
0:33
0:28
0:34
0:32
0:28
0:29
0:34
0:33
b
0:14
0:06
0:24
0:16
0:06
0:10
0:14
0:11
ð2:1Þ
ð1:0Þ
ð2:0Þ
ð2:2Þ
ð1:0Þ
ð1:3Þ
ð2:2Þ
ð2:3Þ
sp
0:91
0:94
0:90
0:91
0:94
0:93
0:91
0:91
F
0:76
0:74
0:67
0:73
0:74
0:73
0:96
0:77
ð5:9Þ
ð5:1Þ
ð4:1Þ
ð5:2Þ
ð5:0Þ
ð5:0Þ
ð22:5Þ
ð6:3Þ
l
0:17
0:23
0:17
0:19
0:23
0:21
0:01
0:16
ð2:8Þ
ð3:6Þ
ð2:7Þ
ð3:0Þ
ð3:6Þ
ð3:3Þ
ð0:4Þ
sz
0:36 ð4:7Þ
ð0:7Þ
ð0:0Þ
ð7:7Þ
ð8:2Þ
ð8:8Þ
ð14:3Þ
ð6:7Þ
c
0:94
0:87
0:93
0:93
0:87
0:91
–
0:94
sa
0:01
0:14
0:05
0:05
0:14
0:09
–
1:22
ð0:5Þ
ð1:2Þ
ð2:2Þ
ð2:2Þ
ð2:1Þ
ð2:2Þ
my
0:53
0:48
0:51
0:51
0:48
0:50
0:54
0:53
sy
0:00
0:00
0:41
0:17
0:17
0:17
0.23
0.16
ð0:0Þ
ð0:0Þ
ð2:3Þ
mr
2:41
2:60
3:02
2:86
2:60
2:73
0:41
2:26
y
81
0
16
16
0
4
–
ð5:7Þ
ð3:7Þ
ð14:2Þ
ð16:2Þ
ð15:7Þ
ð1:2Þ
ð6:5Þ
ð3:4Þ
ð14:4Þ
0:37 ð6:8Þ
ð4:4Þ
ð1:6Þ
ð5:5Þ
ð3:9Þ
ð14:1Þ
0:00 ð13:2Þ
ð6:9Þ
ð2:6Þ
ð5:9Þ
ð3:7Þ
ð14:3Þ
0:33 ð15:4Þ
ð7:7Þ
ð2:3Þ
ð6:5Þ
ð3:4Þ
ð14:4Þ
0:34 ð8:1Þ
ð4:4Þ
ð1:6Þ
ð6:3Þ
ð3:5Þ
ð14:4Þ
0:34 ð11:2Þ
ð5:3Þ
¼ 0:5 No at in Eq. (5)
51% ð4:8Þ
ð3:6Þ
ð14:2Þ
0:45
ð0:47Þ
ð3:7Þ
ð14:3Þ
ð2:7Þ
0:32 ð16:8Þ ð2:0Þ
ð19:1Þ
ð2:1Þ
ð0:0Þ
ð22:2Þ
ð1:0Þ
1
ð0:5Þ
Student-T in parenthesis—unc.: Unconstrained; Log-L: Log-likelihood value; LM test: Lagrange multiplier test; LR test: Likelihood ratio test.
specifications are consistent with the hypothesis that potential GDP is an I(1) process, as is commonly found for the euro area.12 4. Estimation The previous equations can be written in the state-space form, and the parameters can be estimated by maximization of the likelihood function provided by the Kalman filter.13 This filter is a recursive algorithm for sequentially updating a linear projection for a dynamic system. Given a set of measurement and transition equations, the Kalman filter provides the best linear unbiased estimate of the state variables. A particularly attractive feature of this approach is its ability to quantify uncertainty around the estimated state variables. A filtered estimate of the state variables is one-sided—that is, it uses information 12
Besides, both the ADF and Phillips–Perron tests clearly reject the null hypothesis of an I(2) log real GDP. The state vector is ðzt ; zt1 ; at ; at1; Þ0 . The detailed state-space representation of the model is not reproduced here for the sake of brevity. It is available upon simple request from the authors. 13
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only up to time t, whereas a smoothed estimate is two-sided and uses information from the whole sample, i.e. up to time T.14 Two problems arise from direct estimation by maximum likelihood maximization. Firstly, the y parameter in Eq. (4) turns out to be difficult to estimate. Its unconstrained estimate appears to be particularly unstable with respect to the choice of the estimation period and, though very large, it is not statistically significant. This may stem from the fact that this coefficient links two unobservable variables, which makes its estimation ambitious when taking into account the modest size of the sample. Furthermore, the standard deviation sy of the innovation entering Eq. (5) is estimated to be zero. However, when varying the length of the sample used for estimation, either sy or sz is estimated to be zero. This suggests that it is difficult to disentangle idiosyncratic shocks to potential output from transitory shocks on output. Insofar as the output gap is persistent, this may not be too surprising. In order to deal with these problems, we resort to two calibrations.15 The first one is the calibration of the ratio sy =sz . Unfortunately, estimation results for similar models of the US and EU economies provide little basis for a consensus calibration.16 The second is the calibration of the y parameter. Due to the analogy between Eqs. (4) and (1), plausible values for this parameter ought to be consistent with the order of magnitude of empirical estimates of the inverse of the intertemporal elasticities of substitution (IES) found in the literature. According to Hall (1988), the IES is small and not statistically different from zero (corresponding then to an infinite risk aversion coefficient). However, Ogaki and Reinhart (1998a,b) obtain IES estimates ranging from 0.27 to 0.77 (which points to risk aversion coefficients ranging from 1.3 to 3.7). Using micro-data, Barsky et al. (1997) nevertheless obtain a sensibly lower estimate of 0.18 for the IES, implying a coefficient of risk aversion hovering at 5.5. Therefore, an interval of ½0; 20 could be considered as setting a reasonable range for plausible candidate values of our y parameter.17 Besides the calibration of these parameters, the full estimation of the model also requires the choice of an appropriate number of lags of the dependent variables on the RHS of the aggregate supply and demand curves. We proceed in the usual way, the choice of the order of the lag-polynomials being dictated by the significance of the last lag included. As regards
14 Running the Kalman filter requires the econometrician to choose initial values for the (unobservable) state vector. As regards at and its first lag, we used the unconditional mean and autocovariance that derive from Eq. (6). As for the output gap zt , whose unconditional mean and variance remain out of reach, we use the HP filter to get a prior estimate. The filtered series is then used to set the missing initial values as well as to derive the output gap block of the initial covariance matrix. 15 Larsen and McKeown (2004), who apply the Laubach and Williams (2003) approach to UK data, also mention difficulties in estimating their model by direct MLE with the Kalman filter without any calibration. They interpret part of the problem as resulting from a problem of dimensionality and try to solve it by ‘‘reducing the number of parameters’’. To do so, they calibrate a ratio similar to ours and the equivalent ratio of variances of shocks to the trend and cycle components of the rate of unemployment (since their model includes an Okun’s law equation). Contrarily to what is done in this paper, they, however, feel obliged by preliminary unsuccessful estimations to also calibrate the IRG-semi-elasticity of the output gap. 16 Fabiani and Mestre (2004) find a ratio of 0.94 for their baseline model of the euro area, while the same drops to 0.42 in Peersman and Smets’ (1999) model of EU 5. For the US, the estimates we are aware of vary within a range of 1.7–3.3. See notably Peersman and Smets (1999), Smets (2002) and Laubach and Williams (2003). 17 Since we use a quarterly growth rate of GDP but an annualised rate of interest, a relative risk aversion coefficient of 1 corresponds here to a value of 4 for y:
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the Phillips curve (Eq. (2)), the null hypothesis that the coefficients of the inflation lags sum to one was not rejected by the data, leading to an accelerationist form of the Phillips curve. In other words, inflation depends only on nominal factors in the long run. As regards the IS Eq. (3), only the first lag of the output gap was included. The tentative inclusion— following the example of Laubach and Williams—of two lags of the IRG in this equation revealed that only the second lag was significantly different from zero. We therefore kept only the second lag of the IRG. This suggests that it takes two quarters before a monetary policy move significantly affects the output gap in the euro area. The numerical BFGS algorithm provided by GAUSS is applied to get the ML estimator of the parameters.18 The computation of the information matrix is based on the expression given by Engle and Watson (1981), which has the advantage of only requiring the computation of first order derivatives.19 Table 1 summarizes the estimation results obtained for alternative assumptions regarding both the ratio sy =sz and y: (a) No calibration, (b) calibration of y (0 and 16) while sy =sz remains unconstrained and (c) calibration of both sy =sz (at 0.5) and y (at 0, 4 and 16, respectively). The log-likelihoods are reported, as well as the p-values of the Lagrange Multiplier test associated with the corresponding restrictions. Besides, for the sake of completeness, the last two columns of this table show the estimated parameters for two simpler models which would either feature a constant NRI (the no at case), or still allow for stationary NRI fluctuations, but ones that are not assumed to be associated with variations in potential growth anymore (concretely, the at process does not enter Eq. (5)). Note than in both cases, potential output would then follow a random walk with drift. Our preferred calibration for the complete model with co-varying NRI and potential growth—the baseline specification—are the following: sy ¼ 0:5 and sz
y ¼ 16.
Adopting this calibration, all estimated parameters have the expected sign and are significant (see the fourth column of Table 1). The ‘‘monetary policy transmission parameters’’—namely b, the slope of the Phillips curve and l, the IRG semi-elasticity of the output gap—are in line with estimates obtained in the closely related models for the European Union or the EMU of Peersman and Smets (1999) and Gerlach and Smets (1999). Interestingly, however, we get a semi-elasticity of the output gap to the real rate gap that is at least twice larger than their estimated slope of the standard IS curve, where the NRI is implicitly assumed to be constant. This suggests in turn that there is much point in taking the fluctuations in the ‘‘natural’’ level of the real interest rate into account in order to assess the strength of the interest rate channel of monetary policy. Finally, the significativity of both parameters compares broadly with the values obtained by Laubach and Williams.20 Recursive estimations were performed in order to detect potential parameter nonconstancy over the sample period and confirmed that the estimated parameters are fairly stable along time (Figs. 1 and 2). 18 As regards the initialization of the optimization algorithm, many starting values have been tested: Our estimates appear to be particularly robust to their choice. 19 Details of this computation are to be found in the appendices of Me´sonnier and Renne (2004). 20 The p-values associated with the Student T for our parameters b and l are 2% and 0%, respectively. In their baseline model for the United States, Laubach and Williams get p-values of 10% and 0% for the same parameters.
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Fig. 1. Natural rate of interest, output gap and potential output growth: Influence of the calibrations of sy =sz and y (solid line: y ¼ 16, dashed line: y ¼ 4, dotted line: y ¼ 0, squares: sy =sz ¼ 0, no symbol: sy =sz ¼ 0:5 and triangles: sy =sz ¼ 1).
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Fig. 2. Alternative specifications (thick line: Baseline specification, dashed line: No at variable, dotted line: y ¼ 0 and sy =sz ¼ 0:5, squares: Ex ante real rate of interest and triangles: Output growth). Note that there is no natural rate of interest in the no-at case since its estimate is not statistically different from zero.
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5. A retrospective assessment of the monetary policy stance in the euro area This section discusses the relevance of our baseline estimate for a retrospective assessment of the monetary policy stance in the euro area since the late 1970s. It also compares the NRI and IRG as computed here with the results of other studies, as well as with the outcome from simple univariate filters. Fig. 3 plots our estimated smoothed NRI, together with the actual real rate of interest and the 90% confidence interval around the estimates of state variables. The estimated real IRG offers a valuable insight into the monetary policy stance over the last decades. A positive IRG means that monetary policy aims at dampening the current rate of inflation, while a negative gap means that the central bank allows for a rise in inflation. We call the first scenario ‘‘tight’’ and the second ‘‘loose’’ monetary policy. According to our measure of the real IRG and taking into account filter-uncertainty, monetary policy in the euro area appears to have been significantly ‘‘tight’’ over three particular episodes: In the early 1980s in parallel with the ‘‘Volcker era’’ in the United States, in 1986 and from the EMS crisis of summer 1992 until 1996. It is noteworthy that these episodes of positive real IRG are effectively contemporaneous with periods of marked disinflation, as the lower panel of Fig. 3 illustrates. Conversely, two to three episodes of significantly ‘‘loose’’ monetary policy are identified, namely in the late 1970s during the ‘‘great inflation’’ and before the vigorous tightening of the early 1980s, possibly in 1988 while the output gap of the area was rapidly reverting, and finally in 1999, mainly as a consequence of the 50 bp cut in the ECB’s repo rate in April. Again, the significant negative sign of the gap entails a rise in inflation over the same periods, which validates our characterization of the monetary policy stance during these episodes. Finally, the actual real short-term rate of interest appears to be fairly in line with its estimated natural counterpart from 2000 on, which suggests that the monetary policy stance in the euro area has been broadly appropriate since then in terms of inflation stabilization. Turning to the output gap, Fig. 3 highlights periods of excess demand around 1980, 1990 and 2000 and periods of excess supply in the mid-1980s and mid-1990s. Resulting peaks and troughs are in line with available evidence about the business cycle in the main European countries over the last two decades. The at component satisfactorily tracks the low-frequency fluctuations of potential output growth (see the lower panel of Fig. 2) and can therefore be interpreted as the trend growth rate specified in Laubach and Williams (2003). According to our results, potential output growth would have reached a maximum of 3.2% in 1990 and a minimum of 1.5% in 2004. This low value of the trend growth rate partly accounts for the (slightly) positive output gap at the end of the sample. Indications of such a recent decrease in the trend growth rate for the euro area are in turn consistent with empirical evidence of a slowdown in trend productivity growth in European countries in the 1990s, together with the postulated end of the catching up process of American productivity levels in the mid-1990s (see, e.g. Maury and Pluyaud, 2004). How does our baseline estimate compare with other empirical measures for the euro area? Fig. 4 plots our NRI and real IRG against those obtained in two other recent papers by Giammarioli and Valla (GV, 2003) and Crespo-Cuaresma et al. (CGR, 2004).21 While the former replicate the Neiss and Nelson (2001) methodology for the euro area, basing 21
We are grateful to Natacha Valla and Ernest Gnan for kindly providing us with the final NRI and IRG series from their respective papers.
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Fig. 3. State vector estimates, baseline specification (thick line: Smoothed estimates, dotted line: 90% confidence interval, dashed line: Filtered estimates, squares: Ex ante real rate of interest and circles: Inflation).
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Fig. 4. Comparison with other estimations of the natural rate of interest for the euro area (thick dashed line: Giammarioli and Valla, 2003, thick dotted line: Crespo-Cuaresma et al., 2004 and thick solid line: Our baseline smoothed NRI) and with real rate trend estimates yielded by various filters (squares: Ex ante real rate of interest, thin dashed line: Baxter and King band-pass filter and thin dotted line: HP filter).
their natural rate estimate on the calibration of a small structural model and the reconstruction of time series of real disturbances (a technology and a preference shock), the latter also use the Kalman filter and specify a small multivariate unobservable components model to extract the trend component of the real interest rate. Contrarily to ours, however, the CGR model does not take the form of a simplified aggregate demandaggregate supply relationship but focuses instead on a joint statistical trend-cycle decomposition of the fluctuations in the short-term real interest rate, industrial production and headline inflation. Taking into account the conceptual and methodological differences, it is not surprising that the three approaches deliver sensibly differing views on the level and fluctuations of both the NRI and the real IRG. As shown in the upper panel of Fig. 4, our NRI estimate exhibits much larger fluctuations than the rather flat GV estimate, but of similar amplitude as the CGR Kalman filter estimate. Admittedly, as illustrated by the sensitivity analysis presented in GV, the
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amplitude of the deviations of their NRI around its steady-state level is highly dependent on the calibrated persistence and variances of the two shocks that drive these fluctuations. Indeed, given the size of these parameters, the level of the reconstructed NRI appears to be roughly dictated by the historical average which is supposed to approximate this steadystate. This nevertheless echoes the point made in the introduction about the relatively better ability of semi-structural approaches to account for possible regime changes in the economy.22 Second and interestingly enough, our NRI estimate stands at a higher level than the CGR estimate over the first half of the 1990s, when there was some concern about the sustainability of the European exchange rate mechanism, although the latter estimate is corrected for the presence of exchange rate risk premia in the national short-term interest rates of the countries due to the participation of the EMU after 1999. However, the relevance of this apparent gap would probably be mitigated should the respective confidence intervals be taken into account. The lower panel of Fig. 4 shows that the fluctuations in our real IRG are sometimes driven by movements in the actual real interest rate and sometimes by movements in the NRI. In contrast, the GV IRG is roughly dictated by the larger fluctuations in the observed ex post real rate, since their NRI estimate is closely tied to the historical mean of the latter. For opposite reasons, the IRG estimated by CGR keeps confined within a relatively narrow band around zero. Finally, the outcome of different filtering techniques is also shown in Fig. 4. The comparison highlights the superiority of a multivariate filter like the Kalman filter over simpler univariate techniques. Two univariate filters have been used here: The basic Hodrick–Prescott (HP) filter with a standard smoothing coefficient of 1600 for quarterly data and a Band-Pass (BP) filter (see Baxter and King, 1999). Following Staiger et al. (1997), as well as Laubach and Williams (2003), the BP filter is used to discard the cyclical component from the real rate of interest, i.e. the frequencies corresponding to periods of up to 15 years. Consistently with their two-sided moving average representations (finite in the case of the Baxter and King approximate BP filter, infinite in the case of the HP filter), it is obvious that the two univariate filters simply track the trend of the real rate of interest, while our Kalman filter estimate also takes into account the actual fluctuations in the level of output and inflation. 6. Conclusion In this paper, we estimate a time-varying natural rate of interest (NRI) for the euro area considered as a single entity over the period 1979–2004. Our approach broadly follows the methodology recently developed by Laubach and Williams (2003) for the United States. Indeed, the Kalman filter is used to estimate a backward-looking state-space model which encompasses a Phillips-curve and an aggregate demand equation. The NRI belongs to the vector of unobserved variables, along with the output gap. However, two innovations of our approach are that (a) we assume a stationary process for the rate of growth of potential output instead of an I(1) process as frequently postulated by other authors and (b) we use model-consistent inflation expectations to compute the ex ante real rate of interest, instead of a proxy for inflation expectations as generated from a univariate model of inflation. 22
Of course, since we assume that the NRI follows a stationary process, this means that our estimate is also bound to mean revert.
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The empirical analysis shows that our estimates are robust to changes in the few calibrated parameters. The postulated strong relationship between the TVNRI and the low-frequency fluctuations of potential output growth appears to be well supported by the data. We obtain estimates of the real interest rate gap that offer valuable insights into the monetary policy stance over the last two decades and a half. According to our results and focusing on the last few years only, the monetary policy stance of the ECB appears to have been significantly loose in 1999, but broadly appropriate in terms of stabilizing inflation since then. This being said, the confidence intervals, which measure the uncertainty associated with Kalman filtering, remain relatively broad. Furthermore, real-time misperception of the natural rate of interest may also be substantial. We agree with Orphanides and Williams (2002), who warn against the adverse and often undervalued consequences of misperceptions in the NRI in terms of the stabilization properties of monetary policy rules that include such unobserved variables, as well as with Laubach and Williams, who also point out the high uncertainty surrounding estimates of ‘‘natural’’ rates in general. We thus would not advocate so far any prescriptive use of NRI estimates of the kind developed here as a guide or a firm anchor for monetary policy in real time. As a complement to our study, optimal policy issues could be raised within this framework. In particular, an advantage of the method used lies in the possibility to evaluate the uncertainty surrounding the unobserved variables, which allows one to conduct a study of the robustness of monetary policy rules to such estimation uncertainty. However, this is left for further research. Acknowledgements We are grateful to Gilbert Cette, Laurent Clerc, Patrick Fe`ve, Nicola Giammarioli, Enisse Kharroubi, Herve´ Le Bihan, Julien Matheron, Adrien Verdelhan, the Editor and two anonymous Referees for useful comments and suggestions. We also thank participants in the Banque de France workshop on Small Monetary Macromodels (Paris, September 2004) and the MMF Annual Conference 2004 (London, September 2004). Much of this research has been conducted while Jean-Paul Renne was working at the Banque de France. The views expressed herein are those of the authors and do not necessarily reflect those of the Banque de France or the French Ministry of Economy and Finance. References Archibald, J., Hunter, L., 2001. What is the neutral real interest rate, and how can we use it? Reserve Bank of New Zealand Bulletin 64 (3), September 2001. Barsky, R.B., Juster, F.T., Kimball, M.S., Shapiro, M.D., 1997. Preference parameters and behavioral heterogeneity: An experimental approach in the health and retirement study. The Quarterly Journal of Economics. Basdevant, O., Bjo¨rksten, N., Karagedikli, O¨., 2004. Estimating a time-varying neutral real interest rate for New Zealand. Reserve Bank of New Zealand, DP2004/01. Baxter, M., King, R.G., 1999. Measuring business cycles: Approximate band-pass filters for economic time series. The Review of Economic and Statistics 81 (4), 575–593. Bernanke, B., Mihov, I., 1998. Measuring monetary policy. Quarterly Journal of Economics 113, 869–902. Christensen, A.M., 2002. The real interest rate gap: Measurement and application. Working Paper No. 2002-6, Danmarks National Bank.
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Crespo-Cuaresma, J., Gnan, E., Ritzberger-Gru¨newald, D., 2004. Searching for the natural rate of interest: A Euro-area perspective. Empirica 31 (2–3), 185–204. Dennis, R., 2001. The policy preferences of the U.S. federal reserve. Working Paper Series, No. 01-08, Federal Reserve Bank of Chicago. ECB, 2004. The Natural real interest rate in the euro area. ECB Monthly Bulletin, May 2004. Engle, R.F., Watson, M., 1981. A one-factor multivariate time series model of metropolitan wage rates. Journal of the American Statistical Association 76 (376), 774–781. Estrella, A., Fuhrer, J.C., 1999. Are ‘deep’ parameter stable? The Lucas critique as an empirical hypothesis. Society for Computational Economics 621. Fabiani, S., Mestre, R., 2004. A system approach for measuring the Euro area NAIRU. Empirical Economics 29 (2), 311–342. Fagan, G., Henry, J., Mestre, R., 2001. An area-wide model (AWM) for the Euro area. Working Paper No. 42, European Central Bank. Garnier, J., Wilhelmsen, B.-R., 2005. The natural real interest rate and the output gap in the euro area: A joint estimation. Working Paper No. 546, European Central Bank. Gerlach, S., Smets, F., 1999. Output gaps and monetary policy in the EMU area. European Economic Review 43, 801–812. Giammarioli, N., Valla, N., 2003. The natural real rate of interest in the euro area. Working Paper No. 233, European Central Bank. Giammarioli, N., Valla, N., 2004. The natural rate of interest and monetary policy: A review. Journal of Policy Modelling 26, 641–660. Hall, R.E., 1988. Intertemporal substitution in consumption. Journal of Political Economy 96 (2). Larsen, J.D.J., McKeown, J., 2004. The informational content of empirical measures of real interest rate and output gaps for the United Kingdom. Working Paper No. 224, Bank of England. Laubach, T., Williams, J.C., 2003. Measuring the natural rate of interest. The Review of Economics and Statistics 85 (4), 1063–1070. Leeper, E., Zha, T., 2002. Empirical analysis of policy interventions. National Bureau of Economic Research, No. 9063. Maury, T.P., Pluyaud, B., 2004. The breaks in per capita productivity trends in a number of industrial countries. Banque de France Note d’Etudes et de Recherche No. 111. Me´sonnier, J.-S., Renne, J.-P., 2004. A time-varying ‘‘natural’’ rate of interest for the euro area. Banque de France. Note d’Etudes et de Recherche No. 115. Neiss, K.S., Nelson, E., 2003. The real interest rate gap as an inflation indicator. Macroeconomic Dynamics 7, 239–262. Ogaki, M., Reinhart, C.M., 1998a. Intertemporal substitution and durable goods: Long-run data. Economics Letters 61, 85–90. Ogaki, M., Reinhart, C.M., 1998b. Measuring intertemporal substitution: The role of durable goods. Journal of Political Economy 106 (5). Onatski, A., Stock, J., 2002. Robust monetary policy under model uncertainty in a small model of the U.S. economy. Macroeconomic Dynamics 66, 85–110. Orphanides, A., Williams, J.C., 2002. Robust monetary policy rules with unknown natural rates. Brookings Papers on Economic Activity 2 (2002), 63–145. Peersman, G., Smets, F., 1999. The Taylor rule, a useful monetary policy benchmark for the Euro area? International Finance 1, 85–116. Rapach, D.E., Wohar, M.E., 2005. Regime changes in international real interest rates: Are they a monetary phenomenon? Journal of Money, Credit and Banking 37 (5), 887–906. Rudebusch, G.D., 2005. Assessing the Lucas critique in monetary policy models. Journal of Money, Credit and Banking 37 (2), 245–272. Rudebusch, G.D., Svensson, L.E.O., 1998. Policy rules for inflation targeting. Working Paper Series, No. 6512, National Bureau of Economic Research. Rudebusch, G.D., Svensson, L.E.O., 2002. Eurosystem monetary targeting: Lessons from US data. European Economic Review 46, 417–442. Smets, F., 2002. Output gap uncertainty: Does it matter for the Taylor rule? Empirical Economics 27, 113–129. Smets, F., Wouters, R., 2003. An estimated stochastic dynamic general equilibrium model of the euro area. Journal of the European Economic Association 1 (5), 1123–1175.
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Staiger, D., Stock, J., Watson, M., 1997. The NAIRU, unemployment, and monetary policy. Journal of Economic Perspectives 11, 33–49. Wicksell, K., 1898. Interest and Prices. Macmillan, London, 1936, translation of the 1898 edition by R.-F. Kahn. Wicksell, K., 1907. The influence of the rate of interest on prices. The Economic Journal 17, 213–220. Williams, J.C., 2003. The Natural Rate of Interest. The Federal Reserve Bank of San Francisco Economic Letter No. 2003-32. Woodford, M., 2003. Interest and Prices. Princeton University Press, Princeton.
European Economic Review 51 (2007) 1768–1784 www.elsevier.com/locate/eer
A time-varying ‘‘natural’’ rate of interest for the euro area Jean-Ste´phane Me´sonniera,, Jean-Paul Renneb a Monetary Policy Research Division, Banque de France, 41-1422, 75049 Paris cedex 01, France Growth Policy Division, Ministe`re de l’Economie, des Finances et de l’Industrie, 139 rue de Bercy, 75572 Paris cedex 12, France
b
Received 14 September 2004; accepted 15 November 2006 Available online 12 January 2007
Abstract We estimate a time-varying ‘‘natural’’ rate of interest (TVNRI) for a synthetic euro area over the period 1979Q1–2004Q4 using a small macroeconomic model, broadly following a methodology developed by Laubach and Williams [2003. Measuring the natural rate of interest. The Review of Economics and Statistics 85(4), 1063–1070] for the United States. The Kalman filter simultaneously estimates the output gap and the natural rate of interest. Our identifying assumptions include a close relationship between the TVNRI and the low-frequency fluctuations of potential output growth. The difference between the real rate of interest and its estimated natural level offers valuable insights into the monetary policy stance over the last two decades and a half. r 2006 Elsevier B.V. All rights reserved. JEL classification: C32; E32; E43; E52 Keywords: Natural rate of interest; Interest rate gap; Monetary policy; Kalman filter; Output gap; Euro area
1. Introduction In this paper, we apply the Kalman filter to a simple restricted VAR model of the euro area economy in order to estimate a time-varying ‘‘natural’’ rate of interest (NRI) for the euro area. The ‘‘natural’’ real rate of interest—also sometimes termed a neutral or real equilibrium rate of interest—is commonly defined as the real short-term rate of interest Corresponding author. Tel.: +33 1 4292 9163; fax: +33 1 4292 6292.
E-mail address: [email protected] (J.-S. Me´sonnier). 0014-2921/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.euroecorev.2006.11.006
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which is consistent with output at its potential level and a stable rate of inflation (see e.g. ECB, 2004).1 The real interest rate gap (IRG), the difference between the real short-term interest rate and its ‘‘natural’’ counterpart, seems to be an interesting candidate for assessing the current monetary policy stance, notably as an alternative to measures that employ monetary aggregates or exchange rates. Hence, it is not surprising that central banks and central bank economists have recently devoted much attention to these theoretical developments and the resulting empirical estimation strategies.2 A more careful reading of this burgeoning ‘‘natural’’ rate literature, however, reveals two main approaches, depending on whether the focus is on short-term or medium to long run implications of a nonzero gap and, simultaneously, on the degree of structure put into the models that yield the estimates (see Giammarioli and Valla, 2004, for a survey). The first strand broadly follows the lines of Woodford (2003) or Neiss and Nelson (2003) and derives the NRI within the framework of standard microfounded ‘‘new Keynesian’’ models (see, e.g. Giammarioli and Valla, 2003; Smets and Wouters, 2003, for applications to the euro area). From this perspective, the NRI equals the equilibrium real rate of return in an economy where prices are fully flexible, or in other words, it is the real short-term rate of interest that equates aggregate demand with potential output at all times. The emphasis is thus put on short-term developments, what Laubach and Williams (2003) term the ‘‘higher frequency component’’ of the NRI. The second strand of the literature follows Laubach and Williams (2003) and mixes the reference to simple macroeconomic models usually found in the monetary policy literature with the use of the Kalman filter in order to estimate the NRI, the potential level of output and/or the natural rate of unemployment as unobserved variables.3 In this view, the NRI is the real short-term rate of interest consistent with output at its potential and inflation stable in the medium run, i.e. once the effects of demand shocks on the output gap and supply shocks on inflation have completely vanished. Along with Larsen and McKeown (2004), we argue that such a semi-structural approach strikes a convenient compromise between the (more costly) DSGE approach and purely statistical trend estimates like the commonly used HP filter. Moreover, by allowing for large changes in unobservable variables like the growth rate of potential output and the NRI, they can deal with and reasonably account for the large shocks and many structural changes that have affected European economies over the last two to three decades. In contrast, large low-frequency movements of the NRI should remain a priori out of reach of more structural approaches using DSGE models, where aggregate relationships are expressed as log-linear approximations around a deterministic steady state.4
1 The concept of a ‘‘natural’’ real rate of interest and its prescriptive use for monetary policy is generally associated with Wicksell (1898, 1907). The recent revival of the concept owes much to the ‘‘neo-wicksellian’’ framework for monetary policy analysis advocated by Woodford (2003), where the neutral rate embedded in the Taylor rule varies continuously in response to various real disturbances. 2 See, e.g. Archibald and Hunter (2001), Christensen (2002), Williams (2003), Neiss and Nelson (2003), ECB (2004), Crespo-Cuaresma et al. (2004), Larsen and McKeown (2004) and Basdevant et al. (2004). 3 Recent examples include Orphanides and Williams (2002), Crespo-Cuaresma et al. (2004), Basdevant et al. (2004), Larsen and McKeown (2004) and Garnier and Wilhelmsen (2005). 4 It is most often the case that this steady-state level of an unobservable variable like the NRI is then conveniently proxied by some historical mean of the corresponding observed variable, then the ex post real rate of interest.
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However, the available empirical evidence about the existence of structural breaks in the real interest rates of European economies over the last few decades5 points to the plausibility of significant time variation in the NRI of these economies. This suggests the use of estimation methods that allow for large persistent fluctuations of this unobservable variable. We thus apply the methodology first developed by Laubach and Williams (2003) to a synthetic euro area over the period 1979–2004. Our model specification departs from theirs in at least two significant ways. First, we assume that the unobservable process that, as in Laubach and Williams (2003), drives the low-frequency common fluctuations of both the NRI and potential output growth remains stationary autoregressive instead of nonstationary, although we expect it to be quite persistent. This allows us to avoid the difficult reconciliation of a nonstationary output growth and a nonstationary equilibrium real interest rate with both economic theory and intuition. Second, we compute the real interest rate as a model-consistent ex ante real rate of interest, using the inflation expectations provided by the model instead of deriving them from univariate autoregressive models of inflation as Laubach and Williams and others do. The rest of the paper is organized as follows. Section 2 presents the data. Section 3 introduces the model. Section 4 develops estimation issues, discusses the results and checks their robustness to alternative calibrations of some parameters that cannot be estimated properly. Section 5 then conducts a retrospective evaluation of the euro area monetary policy stance on the basis of our baseline estimate. Section 6 concludes. 2. Data The euro area time series for real GDP, inflation and the short nominal rate of interest cover the period 1979Q1–2004Q4 with quarterly frequency. The first year marks the start of the EMS. Historical series for the euro area are taken from the ECB’s AWM database (see Fagan et al., 2000) and have been updated up to the end of 2004 with the official data published by Eurostat and the ECB.6 Whereas the real GDP figures provided by the AWM database are already seasonally adjusted, the HICP series is not and we hence adjust it using the Tramo/Seats procedure. In the following, the log real GDP is denoted by yt . Inflation is defined as the annualized quarterly growth rate of the HICP series (in logs) and is denoted by pt . The ex ante real short-term rate of interest rt is obtained by deducting from the current level of the 3month nominal rate of interest it the one-quarter-ahead expectation of (quarterly annualized) inflation as derived from the entire model estimation (denoted with ptþ1jt below). Finally, two variables are unobservable and constitute the state variables in the state-space model described in the following section, namely the output gap zt and the NRI rt .
5
See for instance Rapach and Wohar (2005), who find evidence of multiple structural breaks in the mean of real interest rates over the last four decades in 13 industrialized countries. Among them figure Belgium, France, Ireland, Italy and the Netherlands, which account for a rough half of the current euro area GDP. 6 Concretely, Eurostat official data were used over their whole period of availability (i.e. from 1991Q1, 1992Q1 and 1999Q1 onward, respectively) to allow for consistency with common knowledge of the recent economic juncture. These official series were then backdated with the corresponding AWM series.
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3. Model specification We base our analysis on a simple macroeconomic model for the euro area economy. Our specification is close to Laubach and Williams (2003), who partly follow the lines of Rudebusch and Svensson (1998). The model relies on six backward-looking linear equations and, as such, is obviously subject to the Lucas critique. However, empirical backward-looking models without explicit expectations are still widely used for monetary policy analysis and they appear to be fairly robust empirically.7 Regarding the dynamics of the NRI, which are central to our estimation framework, the economic intuition is given by the basic optimal growth model (the textbook Ramsey model). Intertemporal utility maximization by the representative household yields the following log-linear relationship between the real interest rate r and the (usually constant) rate of labor-augmenting technological change a, which is also the rate of growth of per capita output along a balanced-growth path r ¼ ya þ r
(1)
with constant relative risk aversion y (which corresponds to the inverse of the intertemporal elasticity of substitution) and where r stands for the household’s rate of time preference. Assuming that this trend growth rate a is in fact subject to low-frequency fluctuations, we get the intuition underlying our specification choice, which postulates a link between long run fluctuations in the growth rate of potential output and the NRI. In this respect, our approach lies between those of Laubach and Williams (2003) and Orphanides and Williams (2002). In the former, the NRI is the sum of the trend growth rate, which also drives the low-frequency fluctuations of potential output growth, and a second, specific (possibly nonstationary) component. In the latter study, the NRI and potential output growth are completely unrelated, which stands at odds with the theoretical intuition and may potentially result in a nonoptimal exploitation of the data. Laubach and Williams’ approach features a higher level of complexity than ours. It may therefore appear more attractive. However, this added complexity raises some cumbersome estimation problems, notably because it requires extracting two unobservable components out of an already unobservable variable (the NRI) which in turn is identified through the dynamics of another unobservable variable (i.e. the output gap, as in Eq. (3) below).8 Since we aim primarily at estimating a time-varying NRI in a way as transparent and robust as possible, we prefer our simpler specification. The model consists of the following six equations: pt ¼ a1 pt1 þ a2 pt2 þ a3 pt3 þ bzt1 þ pt , zt ¼ Fzt1 þ lðit2 pt1jt2 rt2 Þ þ zt ,
ð2Þ ð3Þ
7 See e.g. Rudebusch and Svensson (1998, 2002), Onatski and Stock (2002), Smets (2002), Dennis (2001), Laubach and Williams (2003), Fagan et al. (2001) and Fabiani and Mestre (2004). Regarding robustness issues, see also Rudebusch (2005), Bernanke and Mihov (1998), Estrella and Fuhrer (1999) and Leeper and Zha (2002), among others. 8 In particular, some estimates of key-parameters when several components enter the dynamics of the NRI are very sensitive to the initial state values and variances. More precisely, if the NRI is assumed to follow a twocomponent process (rt ¼ yat þ Zt ) and if the variance reflecting the confidence on the initial value Z0 is not large enough, the parameter y might be bounded to estimate the initial level of the NRI instead of assessing the extent to which the NRI and potential output growth fluctuate together.
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rt ¼ mr þ yat , Dyt ¼ my þ at þ yt ,
ð4Þ ð5Þ
at ¼ cat1 þ at ,
ð6Þ
yt ¼
yt
þ zt ,
ð7Þ
where the four shocks are independently and normally distributed, with variances s2p , s2z , s2y and s2a . The selection of lags on the RHS variables in Eqs. (2) and (3) is consistent with the data and is discussed in detail in Section 4 below, which deals with estimation issues. The first equation can be interpreted as an aggregate supply equation, or ‘‘Phillips curve’’. It relates consumer price inflation to its own lags and the lagged output gap. The second one is a reduced form of an aggregate demand equation, or ‘‘IS curve’’, relating the output gap to its own lags and the IRG—i.e. the difference between the short-term real rate and the NRI. Policy-makers control the inflation rate with a lag of three periods. The NRI is identified through the IRG. More precisely, the output gap is assumed to converge to zero in the absence of demand shocks and if the real rate gap closes. In this model, stable inflation is consistent with both zero output gap and IRG. Hence, our NRI could also be conveniently labelled as a ‘‘nonaccelerating-inflation rate of interest’’ (NAIRI). An important feature of the model is the fact that monetary policy affects the rate of inflation only indirectly via the output gap. Lastly, we take the nominal short-term rate of interest as exogenous, or, put differently, the reaction function of the central bank remains implicit. Departing from common specifications in the literature, we assume that the NRI rt follows an autoregressive process instead of a random walk, as specified by (4) and (6).9 Admittedly, the random walk assumption for the NRI has the technical advantage of combining persistent changes in the unobservable component with a smooth accommodation of plausible but unspecified structural breaks in the effective interest rate series, over a period of estimation that generally covers the last two to three decades. Nevertheless, postulating that the NRI follows a nonstationary process hinders the economic interpretation of the model, in particular if we assume, as we do here, that potential growth Dyt shares common fluctuations with rt .10 In practice, the complete estimation of our model confirms that this process is in fact highly persistent (see the estimator of c in Table 1 below), which fits our purpose of capturing large and low-frequency fluctuations in the level of the equilibrium real rate, as would the hypothesis of a nonstationary NRI also do. The autoregressive process denoted by at (see (6)) captures low-frequency variations in potential output growth assuming that these variations are common with those of the NRI. In addition, potential output growth (5) has another, stationary component, which may account for other sources of discrepancies with the NRI—e.g. due to shocks to preferences or changes in fiscal policies. Estimations show that a simple white noise is sufficient to model this second stationary component.11 Last but not least, these 9 Numerous studies specify a nonstationary process for the NRI and/or the rate of growth of potential output: See e.g. Laubach and Williams (2003), Orphanides and Williams (2002), Larsen and McKeown (2004) and Fabiani and Mestre (2001). Nevertheless, another exception to this widespread choice is Gerlach and Smets (1999), who assume in a framework analogous with ours that potential output is I(1). 10 A nonstationary specification for the NRI and then potential output growth—through the assumption of a random-walk for at —would indeed imply that potential output is integrated of order two. Besides, when translated into the set-up of a standard optimal growth model, this would mean a nonstationary path for the ratio of output to the stock of capital. 11 AR specifications systematically lead to nonsignificant autoregressive coefficients.
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Table 1 Parameter estimates (baseline: sy =sz ¼ 0:5 and y ¼ 16) sy sz
Unc. y Unc.
sy sz
Unc. y¼0
sy sz
Unc. y ¼ 16
sy sz
¼ 0:5 y ¼ 16
sy sz
¼ 0:5 y¼0
sy sz
¼ 0:5 y¼4
sy sz
¼ 0:5 No at
sy sz
Log-L LM test ðp-valueÞ LR test ðp-valueÞ a1
206.11
207.96 8%
206.44 43%
206.57 63%
207.97 89%
207.74 52%
215.76 27%
206.33 80%
5%
41%
63%
15%
20%
0:50
0:54
0:49
0:51
0:54
0:53
0:45
0:50
a2
0:17
0:18
0:18
0:17
0:18
0:17
0:21
0:17
ð1:8Þ
ð1:9Þ
ð1:9Þ
ð1:9Þ
ð1:9Þ
ð1:9Þ
ð2:2Þ
ð1:8Þ
a3
0:33
0:28
0:34
0:32
0:28
0:29
0:34
0:33
b
0:14
0:06
0:24
0:16
0:06
0:10
0:14
0:11
ð2:1Þ
ð1:0Þ
ð2:0Þ
ð2:2Þ
ð1:0Þ
ð1:3Þ
ð2:2Þ
ð2:3Þ
sp
0:91
0:94
0:90
0:91
0:94
0:93
0:91
0:91
F
0:76
0:74
0:67
0:73
0:74
0:73
0:96
0:77
ð5:9Þ
ð5:1Þ
ð4:1Þ
ð5:2Þ
ð5:0Þ
ð5:0Þ
ð22:5Þ
ð6:3Þ
l
0:17
0:23
0:17
0:19
0:23
0:21
0:01
0:16
ð2:8Þ
ð3:6Þ
ð2:7Þ
ð3:0Þ
ð3:6Þ
ð3:3Þ
ð0:4Þ
sz
0:36 ð4:7Þ
ð0:7Þ
ð0:0Þ
ð7:7Þ
ð8:2Þ
ð8:8Þ
ð14:3Þ
ð6:7Þ
c
0:94
0:87
0:93
0:93
0:87
0:91
–
0:94
sa
0:01
0:14
0:05
0:05
0:14
0:09
–
1:22
ð0:5Þ
ð1:2Þ
ð2:2Þ
ð2:2Þ
ð2:1Þ
ð2:2Þ
my
0:53
0:48
0:51
0:51
0:48
0:50
0:54
0:53
sy
0:00
0:00
0:41
0:17
0:17
0:17
0.23
0.16
ð0:0Þ
ð0:0Þ
ð2:3Þ
mr
2:41
2:60
3:02
2:86
2:60
2:73
0:41
2:26
y
81
0
16
16
0
4
–
ð5:7Þ
ð3:7Þ
ð14:2Þ
ð16:2Þ
ð15:7Þ
ð1:2Þ
ð6:5Þ
ð3:4Þ
ð14:4Þ
0:37 ð6:8Þ
ð4:4Þ
ð1:6Þ
ð5:5Þ
ð3:9Þ
ð14:1Þ
0:00 ð13:2Þ
ð6:9Þ
ð2:6Þ
ð5:9Þ
ð3:7Þ
ð14:3Þ
0:33 ð15:4Þ
ð7:7Þ
ð2:3Þ
ð6:5Þ
ð3:4Þ
ð14:4Þ
0:34 ð8:1Þ
ð4:4Þ
ð1:6Þ
ð6:3Þ
ð3:5Þ
ð14:4Þ
0:34 ð11:2Þ
ð5:3Þ
¼ 0:5 No at in Eq. (5)
51% ð4:8Þ
ð3:6Þ
ð14:2Þ
0:45
ð0:47Þ
ð3:7Þ
ð14:3Þ
ð2:7Þ
0:32 ð16:8Þ ð2:0Þ
ð19:1Þ
ð2:1Þ
ð0:0Þ
ð22:2Þ
ð1:0Þ
1
ð0:5Þ
Student-T in parenthesis—unc.: Unconstrained; Log-L: Log-likelihood value; LM test: Lagrange multiplier test; LR test: Likelihood ratio test.
specifications are consistent with the hypothesis that potential GDP is an I(1) process, as is commonly found for the euro area.12 4. Estimation The previous equations can be written in the state-space form, and the parameters can be estimated by maximization of the likelihood function provided by the Kalman filter.13 This filter is a recursive algorithm for sequentially updating a linear projection for a dynamic system. Given a set of measurement and transition equations, the Kalman filter provides the best linear unbiased estimate of the state variables. A particularly attractive feature of this approach is its ability to quantify uncertainty around the estimated state variables. A filtered estimate of the state variables is one-sided—that is, it uses information 12
Besides, both the ADF and Phillips–Perron tests clearly reject the null hypothesis of an I(2) log real GDP. The state vector is ðzt ; zt1 ; at ; at1; Þ0 . The detailed state-space representation of the model is not reproduced here for the sake of brevity. It is available upon simple request from the authors. 13
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only up to time t, whereas a smoothed estimate is two-sided and uses information from the whole sample, i.e. up to time T.14 Two problems arise from direct estimation by maximum likelihood maximization. Firstly, the y parameter in Eq. (4) turns out to be difficult to estimate. Its unconstrained estimate appears to be particularly unstable with respect to the choice of the estimation period and, though very large, it is not statistically significant. This may stem from the fact that this coefficient links two unobservable variables, which makes its estimation ambitious when taking into account the modest size of the sample. Furthermore, the standard deviation sy of the innovation entering Eq. (5) is estimated to be zero. However, when varying the length of the sample used for estimation, either sy or sz is estimated to be zero. This suggests that it is difficult to disentangle idiosyncratic shocks to potential output from transitory shocks on output. Insofar as the output gap is persistent, this may not be too surprising. In order to deal with these problems, we resort to two calibrations.15 The first one is the calibration of the ratio sy =sz . Unfortunately, estimation results for similar models of the US and EU economies provide little basis for a consensus calibration.16 The second is the calibration of the y parameter. Due to the analogy between Eqs. (4) and (1), plausible values for this parameter ought to be consistent with the order of magnitude of empirical estimates of the inverse of the intertemporal elasticities of substitution (IES) found in the literature. According to Hall (1988), the IES is small and not statistically different from zero (corresponding then to an infinite risk aversion coefficient). However, Ogaki and Reinhart (1998a,b) obtain IES estimates ranging from 0.27 to 0.77 (which points to risk aversion coefficients ranging from 1.3 to 3.7). Using micro-data, Barsky et al. (1997) nevertheless obtain a sensibly lower estimate of 0.18 for the IES, implying a coefficient of risk aversion hovering at 5.5. Therefore, an interval of ½0; 20 could be considered as setting a reasonable range for plausible candidate values of our y parameter.17 Besides the calibration of these parameters, the full estimation of the model also requires the choice of an appropriate number of lags of the dependent variables on the RHS of the aggregate supply and demand curves. We proceed in the usual way, the choice of the order of the lag-polynomials being dictated by the significance of the last lag included. As regards
14 Running the Kalman filter requires the econometrician to choose initial values for the (unobservable) state vector. As regards at and its first lag, we used the unconditional mean and autocovariance that derive from Eq. (6). As for the output gap zt , whose unconditional mean and variance remain out of reach, we use the HP filter to get a prior estimate. The filtered series is then used to set the missing initial values as well as to derive the output gap block of the initial covariance matrix. 15 Larsen and McKeown (2004), who apply the Laubach and Williams (2003) approach to UK data, also mention difficulties in estimating their model by direct MLE with the Kalman filter without any calibration. They interpret part of the problem as resulting from a problem of dimensionality and try to solve it by ‘‘reducing the number of parameters’’. To do so, they calibrate a ratio similar to ours and the equivalent ratio of variances of shocks to the trend and cycle components of the rate of unemployment (since their model includes an Okun’s law equation). Contrarily to what is done in this paper, they, however, feel obliged by preliminary unsuccessful estimations to also calibrate the IRG-semi-elasticity of the output gap. 16 Fabiani and Mestre (2004) find a ratio of 0.94 for their baseline model of the euro area, while the same drops to 0.42 in Peersman and Smets’ (1999) model of EU 5. For the US, the estimates we are aware of vary within a range of 1.7–3.3. See notably Peersman and Smets (1999), Smets (2002) and Laubach and Williams (2003). 17 Since we use a quarterly growth rate of GDP but an annualised rate of interest, a relative risk aversion coefficient of 1 corresponds here to a value of 4 for y:
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the Phillips curve (Eq. (2)), the null hypothesis that the coefficients of the inflation lags sum to one was not rejected by the data, leading to an accelerationist form of the Phillips curve. In other words, inflation depends only on nominal factors in the long run. As regards the IS Eq. (3), only the first lag of the output gap was included. The tentative inclusion— following the example of Laubach and Williams—of two lags of the IRG in this equation revealed that only the second lag was significantly different from zero. We therefore kept only the second lag of the IRG. This suggests that it takes two quarters before a monetary policy move significantly affects the output gap in the euro area. The numerical BFGS algorithm provided by GAUSS is applied to get the ML estimator of the parameters.18 The computation of the information matrix is based on the expression given by Engle and Watson (1981), which has the advantage of only requiring the computation of first order derivatives.19 Table 1 summarizes the estimation results obtained for alternative assumptions regarding both the ratio sy =sz and y: (a) No calibration, (b) calibration of y (0 and 16) while sy =sz remains unconstrained and (c) calibration of both sy =sz (at 0.5) and y (at 0, 4 and 16, respectively). The log-likelihoods are reported, as well as the p-values of the Lagrange Multiplier test associated with the corresponding restrictions. Besides, for the sake of completeness, the last two columns of this table show the estimated parameters for two simpler models which would either feature a constant NRI (the no at case), or still allow for stationary NRI fluctuations, but ones that are not assumed to be associated with variations in potential growth anymore (concretely, the at process does not enter Eq. (5)). Note than in both cases, potential output would then follow a random walk with drift. Our preferred calibration for the complete model with co-varying NRI and potential growth—the baseline specification—are the following: sy ¼ 0:5 and sz
y ¼ 16.
Adopting this calibration, all estimated parameters have the expected sign and are significant (see the fourth column of Table 1). The ‘‘monetary policy transmission parameters’’—namely b, the slope of the Phillips curve and l, the IRG semi-elasticity of the output gap—are in line with estimates obtained in the closely related models for the European Union or the EMU of Peersman and Smets (1999) and Gerlach and Smets (1999). Interestingly, however, we get a semi-elasticity of the output gap to the real rate gap that is at least twice larger than their estimated slope of the standard IS curve, where the NRI is implicitly assumed to be constant. This suggests in turn that there is much point in taking the fluctuations in the ‘‘natural’’ level of the real interest rate into account in order to assess the strength of the interest rate channel of monetary policy. Finally, the significativity of both parameters compares broadly with the values obtained by Laubach and Williams.20 Recursive estimations were performed in order to detect potential parameter nonconstancy over the sample period and confirmed that the estimated parameters are fairly stable along time (Figs. 1 and 2). 18 As regards the initialization of the optimization algorithm, many starting values have been tested: Our estimates appear to be particularly robust to their choice. 19 Details of this computation are to be found in the appendices of Me´sonnier and Renne (2004). 20 The p-values associated with the Student T for our parameters b and l are 2% and 0%, respectively. In their baseline model for the United States, Laubach and Williams get p-values of 10% and 0% for the same parameters.
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Fig. 1. Natural rate of interest, output gap and potential output growth: Influence of the calibrations of sy =sz and y (solid line: y ¼ 16, dashed line: y ¼ 4, dotted line: y ¼ 0, squares: sy =sz ¼ 0, no symbol: sy =sz ¼ 0:5 and triangles: sy =sz ¼ 1).
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Fig. 2. Alternative specifications (thick line: Baseline specification, dashed line: No at variable, dotted line: y ¼ 0 and sy =sz ¼ 0:5, squares: Ex ante real rate of interest and triangles: Output growth). Note that there is no natural rate of interest in the no-at case since its estimate is not statistically different from zero.
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5. A retrospective assessment of the monetary policy stance in the euro area This section discusses the relevance of our baseline estimate for a retrospective assessment of the monetary policy stance in the euro area since the late 1970s. It also compares the NRI and IRG as computed here with the results of other studies, as well as with the outcome from simple univariate filters. Fig. 3 plots our estimated smoothed NRI, together with the actual real rate of interest and the 90% confidence interval around the estimates of state variables. The estimated real IRG offers a valuable insight into the monetary policy stance over the last decades. A positive IRG means that monetary policy aims at dampening the current rate of inflation, while a negative gap means that the central bank allows for a rise in inflation. We call the first scenario ‘‘tight’’ and the second ‘‘loose’’ monetary policy. According to our measure of the real IRG and taking into account filter-uncertainty, monetary policy in the euro area appears to have been significantly ‘‘tight’’ over three particular episodes: In the early 1980s in parallel with the ‘‘Volcker era’’ in the United States, in 1986 and from the EMS crisis of summer 1992 until 1996. It is noteworthy that these episodes of positive real IRG are effectively contemporaneous with periods of marked disinflation, as the lower panel of Fig. 3 illustrates. Conversely, two to three episodes of significantly ‘‘loose’’ monetary policy are identified, namely in the late 1970s during the ‘‘great inflation’’ and before the vigorous tightening of the early 1980s, possibly in 1988 while the output gap of the area was rapidly reverting, and finally in 1999, mainly as a consequence of the 50 bp cut in the ECB’s repo rate in April. Again, the significant negative sign of the gap entails a rise in inflation over the same periods, which validates our characterization of the monetary policy stance during these episodes. Finally, the actual real short-term rate of interest appears to be fairly in line with its estimated natural counterpart from 2000 on, which suggests that the monetary policy stance in the euro area has been broadly appropriate since then in terms of inflation stabilization. Turning to the output gap, Fig. 3 highlights periods of excess demand around 1980, 1990 and 2000 and periods of excess supply in the mid-1980s and mid-1990s. Resulting peaks and troughs are in line with available evidence about the business cycle in the main European countries over the last two decades. The at component satisfactorily tracks the low-frequency fluctuations of potential output growth (see the lower panel of Fig. 2) and can therefore be interpreted as the trend growth rate specified in Laubach and Williams (2003). According to our results, potential output growth would have reached a maximum of 3.2% in 1990 and a minimum of 1.5% in 2004. This low value of the trend growth rate partly accounts for the (slightly) positive output gap at the end of the sample. Indications of such a recent decrease in the trend growth rate for the euro area are in turn consistent with empirical evidence of a slowdown in trend productivity growth in European countries in the 1990s, together with the postulated end of the catching up process of American productivity levels in the mid-1990s (see, e.g. Maury and Pluyaud, 2004). How does our baseline estimate compare with other empirical measures for the euro area? Fig. 4 plots our NRI and real IRG against those obtained in two other recent papers by Giammarioli and Valla (GV, 2003) and Crespo-Cuaresma et al. (CGR, 2004).21 While the former replicate the Neiss and Nelson (2001) methodology for the euro area, basing 21
We are grateful to Natacha Valla and Ernest Gnan for kindly providing us with the final NRI and IRG series from their respective papers.
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Fig. 3. State vector estimates, baseline specification (thick line: Smoothed estimates, dotted line: 90% confidence interval, dashed line: Filtered estimates, squares: Ex ante real rate of interest and circles: Inflation).
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Fig. 4. Comparison with other estimations of the natural rate of interest for the euro area (thick dashed line: Giammarioli and Valla, 2003, thick dotted line: Crespo-Cuaresma et al., 2004 and thick solid line: Our baseline smoothed NRI) and with real rate trend estimates yielded by various filters (squares: Ex ante real rate of interest, thin dashed line: Baxter and King band-pass filter and thin dotted line: HP filter).
their natural rate estimate on the calibration of a small structural model and the reconstruction of time series of real disturbances (a technology and a preference shock), the latter also use the Kalman filter and specify a small multivariate unobservable components model to extract the trend component of the real interest rate. Contrarily to ours, however, the CGR model does not take the form of a simplified aggregate demandaggregate supply relationship but focuses instead on a joint statistical trend-cycle decomposition of the fluctuations in the short-term real interest rate, industrial production and headline inflation. Taking into account the conceptual and methodological differences, it is not surprising that the three approaches deliver sensibly differing views on the level and fluctuations of both the NRI and the real IRG. As shown in the upper panel of Fig. 4, our NRI estimate exhibits much larger fluctuations than the rather flat GV estimate, but of similar amplitude as the CGR Kalman filter estimate. Admittedly, as illustrated by the sensitivity analysis presented in GV, the
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amplitude of the deviations of their NRI around its steady-state level is highly dependent on the calibrated persistence and variances of the two shocks that drive these fluctuations. Indeed, given the size of these parameters, the level of the reconstructed NRI appears to be roughly dictated by the historical average which is supposed to approximate this steadystate. This nevertheless echoes the point made in the introduction about the relatively better ability of semi-structural approaches to account for possible regime changes in the economy.22 Second and interestingly enough, our NRI estimate stands at a higher level than the CGR estimate over the first half of the 1990s, when there was some concern about the sustainability of the European exchange rate mechanism, although the latter estimate is corrected for the presence of exchange rate risk premia in the national short-term interest rates of the countries due to the participation of the EMU after 1999. However, the relevance of this apparent gap would probably be mitigated should the respective confidence intervals be taken into account. The lower panel of Fig. 4 shows that the fluctuations in our real IRG are sometimes driven by movements in the actual real interest rate and sometimes by movements in the NRI. In contrast, the GV IRG is roughly dictated by the larger fluctuations in the observed ex post real rate, since their NRI estimate is closely tied to the historical mean of the latter. For opposite reasons, the IRG estimated by CGR keeps confined within a relatively narrow band around zero. Finally, the outcome of different filtering techniques is also shown in Fig. 4. The comparison highlights the superiority of a multivariate filter like the Kalman filter over simpler univariate techniques. Two univariate filters have been used here: The basic Hodrick–Prescott (HP) filter with a standard smoothing coefficient of 1600 for quarterly data and a Band-Pass (BP) filter (see Baxter and King, 1999). Following Staiger et al. (1997), as well as Laubach and Williams (2003), the BP filter is used to discard the cyclical component from the real rate of interest, i.e. the frequencies corresponding to periods of up to 15 years. Consistently with their two-sided moving average representations (finite in the case of the Baxter and King approximate BP filter, infinite in the case of the HP filter), it is obvious that the two univariate filters simply track the trend of the real rate of interest, while our Kalman filter estimate also takes into account the actual fluctuations in the level of output and inflation. 6. Conclusion In this paper, we estimate a time-varying natural rate of interest (NRI) for the euro area considered as a single entity over the period 1979–2004. Our approach broadly follows the methodology recently developed by Laubach and Williams (2003) for the United States. Indeed, the Kalman filter is used to estimate a backward-looking state-space model which encompasses a Phillips-curve and an aggregate demand equation. The NRI belongs to the vector of unobserved variables, along with the output gap. However, two innovations of our approach are that (a) we assume a stationary process for the rate of growth of potential output instead of an I(1) process as frequently postulated by other authors and (b) we use model-consistent inflation expectations to compute the ex ante real rate of interest, instead of a proxy for inflation expectations as generated from a univariate model of inflation. 22
Of course, since we assume that the NRI follows a stationary process, this means that our estimate is also bound to mean revert.
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The empirical analysis shows that our estimates are robust to changes in the few calibrated parameters. The postulated strong relationship between the TVNRI and the low-frequency fluctuations of potential output growth appears to be well supported by the data. We obtain estimates of the real interest rate gap that offer valuable insights into the monetary policy stance over the last two decades and a half. According to our results and focusing on the last few years only, the monetary policy stance of the ECB appears to have been significantly loose in 1999, but broadly appropriate in terms of stabilizing inflation since then. This being said, the confidence intervals, which measure the uncertainty associated with Kalman filtering, remain relatively broad. Furthermore, real-time misperception of the natural rate of interest may also be substantial. We agree with Orphanides and Williams (2002), who warn against the adverse and often undervalued consequences of misperceptions in the NRI in terms of the stabilization properties of monetary policy rules that include such unobserved variables, as well as with Laubach and Williams, who also point out the high uncertainty surrounding estimates of ‘‘natural’’ rates in general. We thus would not advocate so far any prescriptive use of NRI estimates of the kind developed here as a guide or a firm anchor for monetary policy in real time. As a complement to our study, optimal policy issues could be raised within this framework. In particular, an advantage of the method used lies in the possibility to evaluate the uncertainty surrounding the unobserved variables, which allows one to conduct a study of the robustness of monetary policy rules to such estimation uncertainty. However, this is left for further research. Acknowledgements We are grateful to Gilbert Cette, Laurent Clerc, Patrick Fe`ve, Nicola Giammarioli, Enisse Kharroubi, Herve´ Le Bihan, Julien Matheron, Adrien Verdelhan, the Editor and two anonymous Referees for useful comments and suggestions. We also thank participants in the Banque de France workshop on Small Monetary Macromodels (Paris, September 2004) and the MMF Annual Conference 2004 (London, September 2004). Much of this research has been conducted while Jean-Paul Renne was working at the Banque de France. The views expressed herein are those of the authors and do not necessarily reflect those of the Banque de France or the French Ministry of Economy and Finance. References Archibald, J., Hunter, L., 2001. What is the neutral real interest rate, and how can we use it? Reserve Bank of New Zealand Bulletin 64 (3), September 2001. Barsky, R.B., Juster, F.T., Kimball, M.S., Shapiro, M.D., 1997. Preference parameters and behavioral heterogeneity: An experimental approach in the health and retirement study. The Quarterly Journal of Economics. Basdevant, O., Bjo¨rksten, N., Karagedikli, O¨., 2004. Estimating a time-varying neutral real interest rate for New Zealand. Reserve Bank of New Zealand, DP2004/01. Baxter, M., King, R.G., 1999. Measuring business cycles: Approximate band-pass filters for economic time series. The Review of Economic and Statistics 81 (4), 575–593. Bernanke, B., Mihov, I., 1998. Measuring monetary policy. Quarterly Journal of Economics 113, 869–902. Christensen, A.M., 2002. The real interest rate gap: Measurement and application. Working Paper No. 2002-6, Danmarks National Bank.
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