WORKING PAPER SERIES NO. 546 / NOVEMBER 2005 THE NATURAL REAL INTEREST RATE AND THE OUTPUT GAP IN THE EURO AREA A JOINT ESTIMATION by Julien Garnier and Bjørn-Roger Wilhelmsen In 2005 all ECB publications will feature a motif taken from the €50 banknote. WORKING PAPER SERIES NO. 546 / NOVEMBER 2005 This paper can be downloaded without charge from http://www.ecb.int or from the Social Science Research Network electronic library at http://ssrn.com/abstract_id=836428. 1 Work on the project began while Julien Garnier was doing an internship and Bjørn-Roger Wilhelmsen was on secondment at the European Central Bank. All views expressed in the paper are only those of the authors and are not necessarily those of the European Central Bank (ECB) or the institutions to which the authors are affiliated.We are grateful to Siem Jan Koopman for very helpful suggestions and comments.We also thank P. Cour-Thimann,V. Curdia, F. Drudi, S. McCaw, D. Rodriguez-Palenzuela, R. Pilegaard, H. Pill, L. Stracca,T. Laubach, J. C.Williams and the participants of the ECB workshop on natural interest rates on Februar 19th 2004. 2 European University Institute and University of Parix X-Nanterre.; e-mail: julien.garnier@iue.it 3 Central Bank of Norway, Economics Department; e-mai: bjorn-roger.wilhelmsen@norges-bank.no THE NATURAL REAL INTEREST RATE AND THE OUTPUT GAP IN THE EURO AREA A JOINT ESTIMATION 1 by Julien Garnier 2 and Bjørn-Roger Wilhelmsen 3 © European Central Bank, 2005 Address Kaiserstrasse 29 60311 Frankfurt am Main, Germany Postal address Postfach 16 03 19 60066 Frankfurt am Main, Germany Telephone +49 69 1344 0 Internet http://www.ecb.int Fax +49 69 1344 6000 Telex 411 144 ecb d All rights reserved. Any reproduction, publication and reprint in the form of a different publication, whether printed or produced electronically, in whole or in part, is permitted only with the explicit written authorisation of the ECB or the author(s). The views expressed in this paper do not necessarily reflect those of the European Central Bank. The statement of purpose for the ECB Working Paper Series is available from the ECB website, http://www.ecb.int. ISSN 1561-0810 (print) ISSN 1725-2806 (online) 3 ECB Working Paper Series No. 546 November 2005 CONTENTS Abstract 4 Non-technical summary 5 1 Introduction 6 2 The data 7 3 A review of the recent empirical literature: short vs long-run perspectives 8 4 Estimating the natural rate of interest 9 4.1 The model 9 4.2 Model estimation 11 4.3 Results 12 5 Statistical properties of the real interest gap in the euro area 18 6 Conclusion 19 References 20 Appendices 22 European Central Bank working paper series 28 4 ECB Working Paper Series No. 546 November 2005 Abstract The notion of a natural real rate of interest, due to Wicksell (1936), is widely used in current central bank research. The idea is that there exists a level at which the real interest rate would be compatible with output being at its potential and stationary inflation. This paper applies the method recently suggested by Laubach and Williams to jointly estimate the natural real interest rate and the output gap in the euro area over the past 40 years. Our results suggest that the natural rate of interest has declined gradually over the past 40 years. They also indicate that monetary policy in the euro area was on average stimulative during the 1960s and the 1970s, while it contributed to dampen the output gap and inflation in the 1980s and the 1990s. Key words: Real interest rate gap, output gap, Kalman filter, euro area JEL Classification Numbers: C32, E43, E52, O40 5 ECB Working Paper Series No. 546 November 2005 Non-technical summary The notion of a natural rate of interest knows a revival of interest in current monetary policy research. From a theoretical point of view, the natural real rate of interest is a central concept in the literature because it provides policymakers with a benchmark for monetary policy: Interest rates above the natural rate are expected to lower inflation, whereas rates below the natural rate are expected to raise inflation. In practice, however, the natural real rate is unobservable and has to be estimated. According to recent contributions to the literature, the concept of the natural real interest rate and the concept of potential output should be consistent, so that given the definition of potential output it will be clear how to define the natural real interest rate. The two equilibrium- variables are expected to change together over time with shocks and should therefore not be estimated independently. In line with this argument we estimate the natural real rate of interest and potential output simultaneously using data for the euro area, Germany and the US. The modelling framework consists of a small macroeconomic model encompassing an IS curve and a Phillips curve that connects inflation, the output gap and the real interest rate gap, defined as the difference between the real short term interest rate and estimates of the natural real interest rate. In addition, the natural real interest rate is linked to the potential growth rate of the economy. This produces an estimate of the natural real interest rate that varies over time in harmony with lower-frequency evolutions in the real economy. We use relatively long datasets, starting in the early 1960s. Our results suggest that the natural real rate of interest in the euro area and Germany has declined gradually over the past 40 years, while the natural real interest rate in the US has been more stable around its long term average. The natural rate of interest in the euro area was, on average, higher than the actual rate in the 1960s and 1970s, while it was lower compared to the actual rate most of the time in the 1980s and 1990s. In other words, monetary policy was stimulative during the 1960s and 1970s, while it was on average tight in the 1980s and 1990s. Regarding the output gap, the length of the business cycle’s booms and busts are in line with the consensus view in the business cycle literature. However, the estimated output gap is influenced by the real interest rate gap, which implies that its average level is positive in periods of loose monetary policy (1960s and the 1970s) and negative in periods of tight monetary policy (1980s and 1990s). Indeed, the coefficient of correlation between the real interest rate gap and the output gap is strongly negative for the euro area. Moreover, we argue that the real interest rate gap may contain valuable information about future inflation in the euro area. However, it should be borne in mind that estimates of the natural real interest rate are imprecise. 1Introduction In the long run, economists assume that nominal in terest rates will tend to ward some equi- librium, or ”natural”, real rate of interest plus an adjustment for expected long-run inflation. The natural rate of in tere st is a cen tral concept in the mon eta ry policy literature since it provides policyma kers with a benchmark for monetary policy. In theory, it is important for evaluating the policy stance sin ce rates a bo ve (belo w ) the n atura l rate a re expected to lo wer (raise) inflation. From an empirica l point of view, the "natural" r eal rate of in ter est is unob servab le. The estimation of th e natural r eal interest rate is not str aightforward an d is associated with a very high degree of u n certainty. In practice, therefore, policymak ers cannot rely exclusively on the real interest rate gap, defined as the difference between the real short term in terest rate and estimates of the natural real in terest, as an indicator of the monetary policy stance. Rather, a c omprehensive approac h using a wi de set of information is re quired. This notwithstanding, central bank economists have increasingly devoted attention to developing estimation strategies for the natural real in terest rate. The methods used range from as simple as calculating the average actual real interest rate over a long period to building dynamic stochastic general equilibrium (DSG E) models with nominal rigidities. A recent contribution s to the literature on how to empirically a pp roa ch the c o ncep t of the natural rate is a paper by Laubach and W illiams (2003; henceforth LW) 1 with an application to data for the United States. They suggest to estimate the natural real interest rate and potential output gro w th simultaneously, using a small-scale macroeconom ic model and K alm an filtering tec h n iques. In this m odel, the natural real interest rate is rela ted t o the poten tial gro w th rate of the economy. Thus, the estimate of the natural real in terest rate is time-var ying and r elated to lon g-term d evelopments i n th e real c har acteristics of the economy, consisten t with econo m ic theory. This m eth od has become popular since it strikes a c ompromise bet ween th e theoretically coherent DS G E approac h and ad-hoc s tatistical approaches, as e mphasized by Larsen and M cKeo w n (2002). In this paper we employ the technique of LW for the e uro area. The present work differs from ot hers in that we use a relatively l ong ( synthetic) dataset starting in t he early 1960s. Besides, we estimate the natu ral real interest rate in G erman y and the U S for comparison. Such comparison is interesting because, prior to 1999, monetary policies in Europe wer e con- siderably influenced b y the Bundesban k policy. At the same time, the US is often considered as a useful pro xy for global influences that affect monetary policy worldwide. T h ird, w e apply sim p le statistical tests to inv estig ate the leading indicator properties of the baseline estimate of the euro area real interest rate gap on inflation and ec onomic activity. Thepaperisstructuredasfollows.Insectiontwowetakealookatthedataforthereal in terest rate from 1960. Sections three reviews the recent empirical literature and discusses the n atu ral rate concept in t he context of differen t horizons. Section fou r presen ts the 1 Some papers have already used this framework on European data, including Sevillano and Simon (2004) for Germany, Larsen and McKeow n (2002) for the United Kingdom and Crespo-Cuaresma et al (2003) and Mésonnier and Renne (2004) for the euro area. 6 ECB Working Paper Series No. 546 November 2005 modeling approach and displa ys the estimation results. Section five briefly discusses the leading indicator properties of the estimated real rate gap. Section six concludes. 2 The data In this section we tak e a closer look at th e data used in this study. The data co vers a to tal of 161 q ua rterly observations from 1963q1 to 2004q1 for the eur o area an d Germa ny an d 162 quarterly observations from 1961q1 to 2002q4 for the U S . The dataset con sists of sho rt-ter m in terest rates, inflation and Gross Domestic Products for the three econom ies 2 . The compu- tation of real interest rates is subject to several pra ctical and c on cep tual difficulties . Ide a lly, an estimate of the real in terest rate should be obtained by substracting ex an te inflation expectations from nominal interest rates. Ho wev er, the lac k of good data for inflation ex- pectations forces us to take a more straightforward approach. In this paper, th e real interest rates are calculated fro m the th ree-m onth money m arket rates and annual consumer price inflation rates 3 . While we believe that the problem with using current inflation as a proxy for inflation expectations is less severe when assessing developments over longer horizons, the deviations may be stronger in periods with unanticipa ted inflation, notably in the 19 70s. It should be borne in mind th at monetary policy regim es differed significan t ly ov er time and a cross co untries. Moreov er, in m any euro a rea co untries, specifically in the 1960s and early 1970s, other instruments than in terest rates were important in the conduct of mon etary policy. In p ar ticular, capital controls prevailed in many e uro a rea countries. Furtherm ore, inflation, econom ic gr owth and interest rates were very volatile in some e uro area coun tries. Finally, the euro area real interest rate has been significantly influenced by other factors than monetary policy, suc h a s tensions within the Exchange Rate M ec hanism (ERM) at the turn of the 1990s (Cour-Thimann et al, 2004). The euro area real interest rate fell dramatically in the 1970s, when o verheated economies and rising oil prices pushed up inflation at a leve l that could not be offset by the nominal real interest ra tes (See Fig ur e 1 ). Fo llowing the trough in the mid-197 0s, a s European m on etar y authorities gradually put more emphasis on disinflationary policies, th e real in te rest rate increased slo wly over a period o f more than 15 years. After peaking in the early 1990s, the real rate declined gradually ag ain, influenced by the monetary authorities’ ac h ievemen t of more favourable inflation developemen ts. Similar to the euro area a gg regate, the real in terest ra te in the U nited Sta tes was also lo wer than average in the 1970s and higher thanitsaverageinthe1980s. However,the persistence in the data seems less pronounced, as in dica ted by the quick rise in the r eal r ate at the turn of the 1980s. In Germ any the real interest rate has been more stable around its long-term average, reflecting the achievment o f lower a n d more stable inflation ov er the whole sample. 2 We are grateful to the ECB for providing the data for Germany and the euro area, and Thomas Laubach and John C. Williams for providing the US data. 3 For the euro area, national levels for interest rates and consumer prices have been aggregated prior to 1999 using GDP and consumer spending weights respectively at PPP exchange rates, see ECB (2003). 7 ECB Working Paper Series No. 546 November 2005 1965 1970 1975 1980 1985 1990 1995 2000 2005 0 5 Germany 1965 1970 1975 1980 1985 1990 1995 2000 2005 0 5 10 US 1965 1970 1975 1980 1985 1990 1995 2000 2005 0 5 10 Euro area Figure 1: Real interest rates 3 A review of the recen t em pirical literature: short vs long-run perspectives The c oncept of a natural rate of interest was first introduced by Knut Wicksell in the late 19 th century (1898, with 1936 translation ). Today the concept kno w s a revival of in terest following Wood ford’s seminal book, Interest a n d Prices. Accord ing to the recent literature, fluctua tions in the real interest rate may be decom posed in to t wo different components: a natural real r ate and a real r ate gap (Woodford, 2003; Neiss a nd Nelson, 2003; Cour-Th ima nn et al, 2004). The natural rea l rate is related to stru ctur al factors an d is the real in terest rate that in theory w ould prevail under perfectly flexible prices. This is comm o nly referred to as th e "Wicksellian" definition of the natura l ra te of in terest. The real in terest rate gap is related to the business cycle an d reflects the existence of nominal rigidities in the economy. The a vailab le estimates of historical dev elop m ents in the euro area natural real interest rate differ considerably from one author to the other. We briefly address these d ifferences belo w and classify estimates o f th e natural r eal rate, taking as cirterium the time horizon a t which they s hould be interpreted. Some papers find that most of the flu ctu ations in the real in t erest rate should be at- tributed to fluctua tions in the real interest rate gap rather than the natural real interest rate. This group of papers, which includes Giammarioli and Valla (2003), Mésonnier and Renne (200 4), Ne iss and Nelson (20 03 ), Sevilliano and Sim o n (200 4) and LW, a ssociate the fluctua tions in the natural real interest rate with the evolution of real fundamen ta ls such as determ inants of trend GDP growth and p r eferences. These va r iables are typically stable in the short to medium term, but ma y d isplay some variation in the longer run. Consequently, 8 ECB Working Paper Series No. 546 November 2005 the natural real interest rate is also relativ ely stable in the short run, and the natural rate in these papers sh ould be consider ed in a ”long-run” perspective . It refers i nd eed to the lev el expected to p reva il in, say, the next fiv e to ten y ears, after any business c ycle ”booms” and ”busts ” underw ay ha ve played out. Note ho wever that the estimated natural real rate of Méson nie r and R en ne (2004) i s mu ch m ore vo latile that tha t of LW or Sev illian o and S im on (2004). On the contrary, ot her p apers conclude that fluctuations in the natural real interest rate explain m ost of t he variatio n in t h e real interest rate (B asdeva nt et al, 2004; Cu aresma et al, 2004; Cour-Thimann et al, 2004; Larsen and McKeow n, 2002). The papers consistent with this view typ ically make use of the Kalman filter or other filtering t echniques to split the actual r eal r ate into a tren d ( the n atu ral real rate) and a cyclical com ponen t (the real rate gap ). How ever, the models they use d o not necessarily co ntain judgem ents about the determinants of the natural rate. Rather, the approac h they tak e is closer to a pure statistical measur e. C on sequently, variations in the natural rate are more pronou nced , because the natural rate tends to follow more closely the medium term fluctuation s in the actual real rate. The in terp retation of the natural real interest rate in this context is therefore likely to be m ore rel eva nt in a ”shorter” tim e perspective i n that it refers to a neutral moneta ry policy stance in a situation where the economy has not necessarily settled at its long-run levels. 4 Estim ating the natural rate o f in tere st This paper tak es a ”long-run ” time-perspectiv e and uses economic theory as a benc hm ar k for determ ining the d evelopments in the na tural real interest rate. As r eca lled b y LW, standard gro wth models im ply that the natural real in terest rate v aries over time in response to shifts in preferences a nd the trend gro wth rate of output, t hem selves unobservable variables. 4.1 The model The empirical frame work suggested by LW is to run the Kalman filter on a system of equ a- tions to j o intly estim ate the na tura l real interest rate, potentia l output g rowth and th e output gap. They propose a model of a neo-keynesian inspiration, that join tly c haracterises the behaviour of inflation and t he output gap t hrough m odified IS and P h illips c urves. Neo-keynesian models a re not so much i nterested in th e levels of variables co m posing these curves, but rath er the deviations fr om equilibrium values. The main equation s o f the m odel are given by: a y (L)˜y t = a r (L)˜r t + ε 1,t (1) b π (L)π t = b y (L)˜y t + ε 2,t (2) where ˜r t is the real in terest rate gap , ˜y t represents the output gap defined as the difference bet ween the (log) GD P y t and (log) poten tial outpu t y ∗ t suc h tha t ˜y t =100(y t − y ∗ t ) (3) 9 ECB Working Paper Series No. 546 November 2005 [...]... correlations of selected variables used in this analysis, namely log output yt , log potential output yt , the output gap yt , the actual and the natural real rate and the real rate gap (rt , rt and rt ) and ination t A notable feature of the reported statistics is that the correlation between the actual real interest rate and the real interest rate gap are high and their standard deviations are... was increasing For this reason, the Kalman lter generally provides more reasonable results of the real interest rate gap and the output gap than univariate time -series methods Figure 7 compares the baseline estimates of the natural real interest rates for the euro area, Germany and the US Evidently, while the estimated natural real interest rate in the euro area and Germany has declined over the sample,... sample, the natural real interest rate in the US has been more stable around its long term average The estimates also indicate that the level of the natural real interest rate is lower in the euro area, and in particular in Germany, than in the US It is important to stress that all estimates of the natural real interest rate are very imprecise and that caveats are associated with all estimation methods... interest rate gap is negatively ECB Working Paper Series No 546 November 2005 19 correlated with the output gap and ination Furthermore, the tests show that the real rate gap may contain valuable information about future ination in the euro area The general caveats associated with interpreting estimates of the natural real interest rate, which are highly uncertain, also applies for this paper References... 7: Baseline estimates of rt for the euro area, Germany and the US ECB Working Paper Series No 546 November 2005 17 5 Statistical properties of the real interest gap in the euro area We now examine some statistical properties of the euro area model, focusing on simple statistics that describe the relationship between the real interest rate gap and ination Table 2 and 3 report standard deviations and. .. roughly identical In other words, the variation in the real interest rate is not primarily related to variation in the natural real interest rate This is consistent with the results in Giammarioli and Valla (2003) for the euro area, Neiss and Nelson (2003) for the UK and LW for the US, but stands against the results of Cour-Thimann (2004) for the euro area Table 2: Standard deviations, euro area yt 0.35... natural real interest rate, potential output and trend growth rate of the three economies simultaneously Overall, the results are quite comparable with the original results of Laubach and Williams (2003) using US data According to our baseline estimate for the euro area, the uctuations in the natural real interest rate have been relatively low since 1963 The natural rate has declined gradually over the past... Stracca (2004): "The output gap and the real interest rate gap in the euro area, 1960-2003", paper presented at the Bank of Canada workshop on Neutral Interest Rates, 9-10 September 2004 (available on Bank of Canadas website) [5] Cuaresma, J.C., Gnan, E and D Ritzberger-Grunenwald (2004): "Searching for a natural rate of interest: a euro area perspective", Empirica, vol 31, p 185 - 204 [6] De Long and. .. degree at which the central bank policy inuences the real economy In the 1970s when ination become high the real interest rate gap was negative and the output gap was positive, on average Likewise, in the 1980s and 1990s, when ination fell to lower levels, the real interest rate was positive and the output gap was on negative, on average Simple empirical tests also suggest that the estimated real interest. .. impose a constraint on the possible range of values this coecient can take, the range of estimates of the level of the natural real interest rate diminishes For almost all signal-to-noise ratios in the model (having xed the c coecient to its baseline estimate), the estimated natural real interest rate seems to have been higher in the 1960s and early 1970s than in the 1990s and 2000s Moreover, the natural . WORKING PAPER SERIES NO. 546 / NOVEMBER 2005 THE NATURAL REAL INTEREST RATE AND THE OUTPUT GAP IN THE EURO AREA A JOINT ESTIMATION by Julien Garnier and. that the natural real rate of interest in the euro area and Germany has declined gradually over the past 40 years, while the natural real interest rate