Has inflation persistence changed under EMU?

Peter Tillmann1 Swiss National Bank September 2, 2008

Abstract: This paper analyzes the persistence of inflation in the Euro area and, in particular, whether the persistence properties have changed since the start of European Monetary Union. For that purpose, we compare pre- and post-EMU inflation persistence, use rolling-window estimates of persistence, and apply tests specifically designed to detect break dates near the end of the sample period. In contrast to previous research, we find that inflation persistence has fallen significantly since the start of EMU. Persistence of consumer price inflation, which is central to the ECB’s policy mandate, has fallen more than the persistence of deflator inflation. The drop in inflation persistence is consistent with the results from a simulated small New-Keynesian model with a shift towards a more aggressive monetary policy stance. Keywords: Inflation persistence, structural change, sum of autoregressive coefficients, autoregressive root, end-of-sample break point tests, European Monetary Union JEL classification: E31, E52

1

Swiss National Bank, Economic Analysis, Börsenstrasse 15, CH-8022 Zurich, E-mail: [email protected] I thank Michael Massmann for stimulating conversations and, in particular, Todd E. Clark and Efrem Castelnuovo for detailed comments on an earlier draft. I am grateful to Todd E. Clark and Simon van Norden for sharing their RATS codes. The views expressed in this paper do not necessarily reflect those of the Swiss National Bank.

1

Introduction

The persistence of the inflation process has received considerable attention of academics and policymakers alike. The speed with which shocks to inflation die out and the inflation rate returns to its mean is crucial for the success of monetary policy. Well-anchored inflation expectations as well as a clear and credible policy mandate to achieve price stability are generally thought of as reducing inflation persistence.2 The importance of lagged dependent variable terms should decline as the credibility of a central bank’s anti-inflation commitment increases. Hence, the creation of the European Monetary Union (EMU) in 1999 is a natural laboratory to study the impact of a new and credible monetary policy framework on inflation persistence. In this light it is surprising that previous research finds no change in European inflation persistence over the last two decades. The paper closest to this work is the contribution of O’Reilly and Whelan (2005). These authors use Hansen’s (1999) unbiased mean estimate of the sum of autoregressive coefficients for a rolling window. They use data up to 2002:4 and find no change in inflation persistence over the sample period. The apparent stability of the autoregressive specification is interpreted as indirect evidence against forward-looking monetary policy models since the alleged instability of the backward-looking model cannot be supported by the data. It follows that the empirical weakness of backward-looking models appears to be less virulent.3 This paper revisits the estimation of Euro area inflation persistence and differs in several key aspects from O’Reilly and Whelan’s work. First, we have more data at hand. This paper provides rolling window estimates of inflation persistence to check whether four years of additional data affect their findings. Second, we formally test for structural stability of the autoregressive model for inflation using Andrew’s (2003) end-of-sample test that is able to detect structural instability in inflation dynamics even at the very end of the sample. O’Reilly and Whelan test for changes in persistence within a sample up to 2002:2. Their test procedure is Andrews and Ploberger’s (1994) test for a break at an unknown date. The drawback of this approach is that it requires to skip 15% of the observations on either side of the sample. Hence, their effective sample ends before EMU actually starts. In addition, they provide Monte Carlo results showing that the Andrews and Ploberger (1994) test suffers from power problems when used to detect small changes in inflation persistence. Third, we formally compare pre-EMU and post-EMU inflation persistence since the available eight years of post-EMU data are believed to be enough to reliably estimate inflation persistence. Fourth, we complement the analysis by using the largest autoregressive root as an alternative measure of persistence. In contrast to previous research, we find that inflation persistence has fallen significantly since the start of European Monetary Union. 2

See, among others, Erceg and Levin (2003). In fact, this evidence complements recent findings of Estrella and Fuhrer (2003) and Rudebusch (2005). These authors find only a most empirical relevance of the Lucas critique. 3

2

Although small, the drop of inflation persistence is consistent with the implications of a standard New-Keynesian model in which the policy regime shifts towards a more aggressive stabilization of inflation. Following the logic of O’Reilly and Whelan (2005) mentioned before, we therefore provide indirect evidence in favor of forward-looking monetary models. This paper is structured as follows: section two briefly surveys the literature on inflation persistence in the Euro area. In section three a standard New-Keynesian monetary model is simulated in order to analyze the impact of a monetary regime change on the autocorrelation of inflation. Section four introduces the measures of persistence and presents the data set while section five discusses the role of structural breaks for the measurement of inflation persistence. The main results are presented in section six. Section seven concludes with some remarks about the wider interpretation of the results.

2

Inflation persistence in the Euro area

The fall in inflation persistence over the last two decades in major industrial countries, most notably in the U.S., is now well documented. The influential study of Cogley and Sargent (2007) shows reduced persistence in the gap between inflation and the pure random walk component of the inflation rate in the Volcker-Greenspan era. Taylor’s (2000) early study finds a break in U.S. inflation persistence that coincides with the Volcker disinflation. Levin and Piger (2006) assess inflation persistence for major industrial economies and find that conditional on a break in the intercept inflation is much less persistent than previously thought. Less supportive evidence for a reduction in inflation persistence is provided by Cecchetti and Debelle (2006). They stress that the principal change in the inflation processes of the past two decades has been the decline in the mean, not a significant change in persistence. Pivetta and Reis (2007) use Bayesian methods to find, provokingly, no change in U.S. inflation persistence. The adoption an inflation targeting regime is shown to have an effect on inflation persistence. Levin, Natalucci, and Piger (2004) argue that the adoption of inflation targeting lowers the degree of inflation persistence in major industrial countries. Furthermore, Caggione and Castelnuvo (2007) analyze persistence in the autocorrelation function domain. They support the notion that inflation targeting reduces (long-run) inflation persistence. For the aggregate Euro area, however, the results are ambiguous.4 The prominent study of O’Reilly and Whelan (2005) analyzes both deflator and HICP (Harmonized Index of Consumer Prices) inflation rates and uses Hansen’s (1999) unbiased mean 4

Benigno and López-Salido (2006) provide evidence on cross-country heterogeneity in the weights attached to forward- and backward-looking elements of a hybrid New Keynesian Phillips curve estimated for individual EMU member countries. Gadzinski and Orlandi (2004) find moderate persistence across EMU countries and point to the importance of shifting intercept terms.

3

estimate of the sum of autoregressive coefficients for a rolling window. They use data up to 2002:4 and, finding no change in inflation persistence over the sample period, conclude that (p. 709) "our results are consistent with a stable reduced-form representation for inflation and a high level of inflation persistence". Interestingly, Angeloni et al. (2006) also find no change in inflation persistence after the start of EMU. On a country level, Batini (2002) uses various measures of persistence, including the lag between monetary policy action and the reaction of inflation. She is able to show a drop in inflation persistence for Germany in the mid 1980s but not for other large EMU countries. The empirical impact of regime changes on inflation persistence is studied in Benati (2008). He estimates a small-scale New-Keynesian model for major industrial countries over various subperiods using Bayesian methods. His main result is that the degree of intrinsic inflation persistence, i.e. the coefficient of lagged inflation within a hybrid Phillips curve, drops significantly towards zero once a credible new monetary regime is in place. With the focus on intrinsic persistence, however, the paper focuses on too narrow an issue. Moreover, take the post-EMU period. His method requires the researcher to estimate 12 parameters reliably with just seven years of data at hand. Although his point estimates of the coefficient of past inflation support his interpretation, various other estimates are highly implausible. This paper contributes to this debate and analyzes the change in the persistence properties of various inflation series in the EMU period. The additional data we have at hand are likely to give a more reliable picture of the changing nature of inflation dynamics. Moreover, as mentioned in the introduction, we extend the analysis of O’Reilly and Whelan (2005) in several important aspects. In particular, we formally test for structural stability of the inflation process using Andrew’s (2003) test that is able to detect structural instability in inflation dynamics towards the end of the available sample.

3

A small New-Keynesian model as a laboratory

This section investigates how an unexpected shift in the monetary policy regime towards a systematically more aggressive stabilization of inflation and output fluctuations, which we take as a framework to study the shifts towards EMU, affects the persistence properties of inflation. We adopt a standard forward-looking monetary model of the business cycle as a laboratory.5 The IS curve (1) and the forward-looking Phillips curve (2) represent log-linearised equilibrium conditions of a simple sticky-price 5

See, among others, Clarida, Galí, and Gertler (1999) and Woodford (2003) for a deeper analysis and the complete derivation of the model.

4

general equilibrium model yt = α1 Et yt+1 + α2 yt−1 − σ −1 (it − Et π t+1 ) + ut

(1)

π t = β 1 Et π t+1 + β 2 π t−1 + γyt + et

(2)

where π t is the inflation rate, yt the output gap, it the risk-free nominal interest rate controlled by the central bank, and Et is the expectations operator. All variables are expressed in percentage deviations from their respective steady state values. The parameters α1 , α2 , β 1 , and β 2 are positive and are convolutes of the deep parameters of the underlying microeconomic structure. The inverse of the elasticity of intertemporal substitution is denoted by σ, and γ, the slope coefficient of the Phillips curve, depends negatively on the degree of price stickiness. The presence of backward-looking elements in this otherwise completely forward-looking model can be motivated by habit persistence in consumption and rule-of-thumb behavior of price-setters. The model is closed by assuming that the central bank sets the nominal interest rate according to a standard instrument rule with interest rate smoothing, i.e. ¡ ¢ it = ρi φπ π t + φy yt + (1 − ρi ) it−1 + vt

(3)

with φπ , φy > 0 and 0 ≤ ρi < 1. The processes driving the demand shock ut , the supply shock et , and the monetary policy shock vt are given by ut = ρu ut−1 + εut et = ρe et−1 + εet vt = ρv vt−1 + εvt

with 0 ≤ ρu < 1, εut ∼ i.i.d. N (0, σ u ) with 0 ≤ ρe < 1, εet ∼ i.i.d. N (0, σ e )

with 0 ≤ ρv < 1, εvt ∼ i.i.d. N (0, σ v )

We solve this model using standard methods for linear Rational Expectations models and simulate the endogenous variables for a sample of 1000 observations.6 The resulting autocorrelation contains information about the persistence properties of inflation. To simulate the model, we resort to standard parameter values used in the literature. This implies α1 = 0.75, α2 = 0.25, β 1 = 0.75, β 2 = 0.25, γ = 0.05, and σ = 1.80. The serial correlations of the three shocks are given by ρu = ρe = 0.35, and ρv = 0.20, while the standard deviations are set to σ u = σ e = σ v = 0.02. In accordance to the large literature on estimated policy rules, we assume a fairly large degree of interest rate smoothing and calibrate ρi = 0.90. Let us assume that the move to a new monetary regime under the responsibility of the ECB can be interpreted as an increase in φπ . We should observe that the average φπ across countries is lower before the creation of EMU when compared with the ECB’s φπ . Hence, the anti-inflation response of the monetary authority increases under EMU. This is consistent with the clear mandate of the ECB that explicitly formulates the 6

Altissimo, Ehrmann, and Smets (2006) and Fuhrer (2006) simulate a similar New-Keynesian model to study inflation persistence.

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aim of price-stability. This shift to the ECB is interpreted as a move from φπ = 1.20 to φπ = 2.00 and from φy = 0.50 to φy = 0.80. We restrict the impact of the monetary regime change to the coefficients of the policy reaction function. This appears to be the most straightforward and immediate impact of EMU within this simple model structure.7 A recent paper by Boivin, Giannoni, and Mojon (2008) supports this notion. These authors argue that a shift towards a more aggressive monetary policy can best explain the observed changes in the transmission mechanism since the creation of EMU. This shift, the argument goes, can be represented by a switch to larger inflation and output response coefficients within the Taylor rule. For both monetary regimes the resulting autocorrelation of inflation and the output gap over eight lags is displayed in figure (1). Both regimes exhibit a large degree of inflation persistence. With a more vigorous anti-inflation stance in the EMU regime, however, inflation persistence falls at all lags. Hence, when analyzing empirical data we should expect a decline of inflation persistence after the start of EMU. This decline, however, is likely to be small. With a smaller degree of interest rate smoothing, the resulting fall in persistence would be more pronounced. Output gap persistence, on the contrary, drops only marginally under the new regime.

4

Measuring inflation persistence

Following O’Reilly and Whelan (2005), Levin and Piger (2006), and Clark (2006), our preferred measure of persistence, i.e. a measure of serial correlation of inflation, is the sum of the autoregressive coefficients in a univariate process of inflation.8 Hence, we do not take a stand on the sources of persistence, i.e. on the debate about intrinsic versus inherited persistence, see Fuhrer (2006) and Benati (2008) for this discussion. These papers focus on the coefficient β 2 from (2) as a measure of intrinsic inflation persistence, while we use a broader statistical measure that reflects various underlying sources of persistence. Let π t be the inflation measure, α an intercept term, and εt be a serially uncorrelated error term. The AR(q) process is πt = α +

q X

β k π t−k + εt

(4)

k=1

7

An alternative would be to let the relative weights of backward-looking versus forward-looking elements in the Phillips curve change, see Benati (2008) for a discussion. One way to motivate that backward-looking elements enter the Phillips curve is the existence of rule-of-thumb price setters. It is less clear, however, that a new monetary regime leads to immediate changes in the fraction of ruleof-thumb price setters. Therefore, we interpret the new monetary regime foremost as a change in the systematic component of policy. 8 Kumar and Okimoto (2007) discuss other measures of inflation persistence, in particular the degree of fractional integration of the inflation process.

6

P The sum of autoregressive coefficients is ρ = qk=1 β k . According to Andrews and Chen (1994), ρ is the best scalar measure of persistence in π t , since a monotonic relationship exists between ρ and the cumulative impulse response function (CIRF) of π t+j to εt 1 CIRF = 1−ρ

Rewrite expression (4) as

π t = α + ρπ t−1 +

q−1 X

γ k ∆π t−k + εt

(5)

k=1

where ∆π t = π t − π t−1 . If ρ = 1, the inflation process contains a unit root. If |ρ| < 1, the process is stationary. In the empirical application below, the appropriate lag length q ≤ q max is chosen according to the Akaike information criterion (AIC) with a maximum lag length of q max = 6. Estimates of ρ obtained from least squares estimation suffer from a bias as ρ approaches unity. Furthermore, confidence bands based on a normally distributed ρ do not have the correct coverage. Therefore, we follow the literature and resort to Hansen’s (1999) median unbiased estimator of ρ. His grid bootstrap approach is used to construct confidence bands for ρ with correct coverage. The bootstrap calculations are based on 999 draws and 101 grid points over a range spanned by the sample persistence surrounded by four (OLS) standard errors. The CIRF is not well suited to distinguish between two impulse responses with different shapes. Suppose that one response exhibits a large initial increase followed by a quick decrease, whereas another response exhibits a small initial increase and a subsequent slow decrease. Both would result in a similar CIRF. We therefore use the largest autoregressive root μ as a second measure of persistence. This is used to cross check the findings based on the sum of the autoregressive coefficients ρ. The largest autoregressive root is defined as the largest root of the characteristic equation λq −

q X

β k λq−k = 0

(6)

k=1

Stock (1991) provides the standard method to obtain unbiased median estimates of μ and 90% asymptotic local-to-unity confidence bands.9 This measure also has intuitive ∂π when the horizon j appeal as μ determines the size of the impulse response ∂εt+j t becomes large. It is widely known that the presence of structural breaks in mean inflation obstructs the estimation of the persistence properties. Perron (1989) shows that the failure to account for such breaks could result in an upward bias of the persistence parameter. 9

Note that the sum of the autoregressive coefficients is a more reliable measure of persistence as the largest autoregressive root ignores the effect of the other roots

7

The literature forcefully demonstrates the role of shifts in mean inflation. Levin and Piger (2006) assess inflation persistence for major industrial economies and find that neglecting a break in the intercept term can lead to spurious overestimation of persistence. Clark (2006) stresses the importance of structural breaks in mean inflation to account for the persistence of U.S. inflation. Altissimo et al. (2006) document that inflation persistence in Europe falls drastically once we allow for structural breaks in mean inflation. We focus on structural breaks in the constant term of the autoregressive process. Suppose the break occurs at date t = s. We include an appropriate dummy variable dt which is unity in t ≥ s and zero elsewhere π t = α + δdt + ρπ t−1 +

q−1 X

γ k ∆π t−k + εt

(7)

k=1

To locate the break date, we utilize the test provided by Andrews and Ploberger (1994). This test computes a series of LM tests. The Andrews-Quandt test statistic uses the maximum of this test statistic (SupF ), while the Andrews-Ploberger test uses a weighted average (ExpF ). We measure inflation as the annualized quarterly percentage change of the underlying Euro area price index, which is either the GDP deflator or the Harmonized Index of Consumer Prices (HICP). Both series are obtained from the ECB’s Area Wide Model database and cover the sample period 1970:1 to 2006:4. The X12 procedure as implemented in EViews is used to seasonally adjust the HICP series. Both inflation series are depicted in figure (2). The inflation measure based on the change in the HICP is our preferred measure of inflation since the ECB explicitly defines its aim of price stability in terms of HICP inflation. Hence, it is the dynamics of HICP inflation that should reflect the new monetary policy regime most closely. We also report a set of baseline results for the inflation rate derived from the HICP series that excludes food and energy prices, which is available from 1988:1. To compare our results with the findings of O’Reilly and Whelan (2005), we will later also use the seasonally unadjusted series of HICP inflation. To test for a change in inflation persistence with the start of the monetary union, we analyze a pre-EMU sample covering 1970:1 to 1998:4, which is then contrasted to a post-EMU sample ranging from 1999:1 to 2006:4.

5 5.1

Results Pre-EMU versus EMU inflation persistence

Table (1) reports results from estimating ρ over different sample periods. For each sample period, the lag order is chosen according to the AIC and confidence bands 8

for the persistence parameter ρ are obtained from Hansen’s (1999) grid bootstrap. It turns out that the persistence of both measures of inflation is significantly lower in the 1999-2006 period, i.e. the post EMU sample, than in the pre-EMU sample from 19701998. The fall in persistence of HICP inflation is particularly striking. We estimate ρ = 0.18 under EMU compared to ρ = 1.03 before EMU. The series of inflation that excludes food and energy prices, which are generally quite volatile, exhibits a larger degree of serial correlation than the other two inflation series. Nevertheless, serial correlation in the post-EMU subsample is significantly lower than pre-EMU inflation persistence. Estimates of the largest autoregressive root, see table (2), corroborate this finding. Again, both measures of persistence are significantly lower under EMU than in the pre-EMU period with the fall in HICP inflation persistence being particularly remarkable. As mentioned earlier, the presence of structural breaks within each subsample potentially biases the estimates of persistence. As a consequence, we use Andrews and Ploberger’s (1994) tests for breaks at unknown time and include appropriately specified dummy variables in the equation to estimate ρ. The test supports significant structural instability in the intercept term for deflator and headline inflation around 1982/83 and for core inflation in the early 1990s, see table (3). The table shows that taking account of these structural instabilities in the intercept term lowers estimated inflation persistence substantially during the pre-EMU period. Nevertheless, inflation exhibits a significantly lower degree of persistence since 1999 than before that start of EMU.

5.2

Rolling window estimates

To illustrate the behavior of the persistence measure over time, we estimate the model for a window of 40 observations and then move the window over the sample. In other words, we estimate the model and obtain measures of fit for a given sample-window and then add one observation to both the first and the last observation of the window. Note that if we take breaks seriously, we should also allow for varying lag lengths in each sample window. In contrast to O’Reilly and Whelan (2005), who fix the lag order to q = 4 in each window, we allow the lag order to be different in each window as determined by the AIC. Hence, we end with a series of measures of fit that indicate the empirical performance of the model over time. For each window, we also compute confidence intervals as explained above. The baseline results are depicted in figures (3) and (4). Both inflation series exhibit a fairly high degree of inflation persistence that falls around 1995 to return to its original level just before the start of EMU. After 1999, however, both series of ρ coefficients show a remarkable downward trend with the degree of persistence in 2005 lying below the persistence at the start of EMU. Note that the persistence in 2005 lies outside the confidence band surrounding the persistence estimate of 1998:4. Therefore, the change 9

in persistence is statistically significant. Figure (5) depicts the results from rollingwindow estimates based on an HICP inflation series that is not seasonally adjusted. This series corresponds to the (updated) data used by O’Reilly and Whelan (2005). We see that the empirical support for a break in the latter part of the sample becomes even more compelling. The persistence measure at the end of the sample lies significantly below its value at the start of EMU. Since the choice of a 10-year window is rather arbitrary, figures (7) and (6) present results base on an 12-year and an 8-year window for HICP inflation, respectively. All results are robust to the choice of the window size.

6

End-of-sample breaks in inflation persistence

In this section, we test for structural changes in the autoregressive model for inflation that coincide with the start of EMU in 1999. This task is complicated by the fact that the potential break date, i.e. 1999:1, is located close to the end of the available sample period leaving only 18% of the observations for the post-break period. This lack of data severely biases conventional testing procedures designed to detect unknown break dates. However, Andrews (2003) recently offers a break test that is specifically designed for the purpose of this paper. He formulates a generalization of the F test that is able to detect breaks at the end of the sample and could even find breaks with as little as one observation left for the post-break sample. The test is a generalization of the classic Chow test and tests the null hypothesis of structural stability over the last m observations of the sample. The test does not rely on asymptotic distributions which are likely to be biased at the fringe of the sample. Instead, it generates p-values and critical values using parametric subsampling. Figures (8) and (10) show the resulting p-values for the null hypothesis of structural stability of equation (5) over the last m observations for HICP inflation and deflator inflation. It turns out that the stability of the autoregressive specification of deflator inflation after the start of EMU cannot be rejected. For no potential post-break sample the p-value falls below the rejection threshold at a 10% significance level. For HICP inflation, on the contrary, the test shows clear signs of instability at the start of EMU or in the first two years of EMU. We can conclude that the transfer of monetary policy responsibility to the ECB changed the nature of the underlying inflation dynamics. In the following section we analyze whether this implies a smaller degree of inflation persistence. A shortcoming of the end-of-sample breakpoint test is its inability to identify which element of the AR(q) process is subject to structural change. Hence, we cannot say whether the breaks are due to changes in the intercept term or to changes in the autoregressive dynamics. To shed more light on the underlying causes of structural change, we try to isolate the effect of changes in persistence. For that purpose we

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construct a dummy variable that has a value of one in those periods in which the Andrews (2003) test indicates a structural break. We then regress the inflation rate on a constant and this dummy to account for potential breaks in the constant. The residual of this regression is subsequently used for a new set of end-of-sample break point tests. If the test still indicates significant structural breaks, we can be certain that these breaks are not due to changes in the intercept term. Figure (9) shows the resulting series of p-values for HICP inflation conditional on a dummy for the intercept break. Apparently, the test still suggests structural breaks in the EMU period, although the breaks occur somewhat later than in the initial test documented in figure (8). This procedure leaves changes in the autoregressive dynamics, i.e. changes in persistence, as the only candidate explanation for these structural breaks. An alternative to the use of a dummy variable is simply to use a constant as the only regressor in the test equation, i.e. to apply the Andrews (2003) test to π t = α + εt . If the breaks were due to a break in the intercept term, we are likely to find a break also in this primitive regression. As figure (11) shows, however, the test is unable to detect a break in this simple inflation process. We can conclude that the breaks only occur once we allow for lagged inflation dynamics to enter the regression equation.

7

Conclusions

This paper provides evidence of a fall in the persistence of European inflation dynamics since the start of EMU in 1999. For both inflation series, i.e. for changes in the GDP deflator and the HICP, persistence as measured by the sum of the autoregressive coefficients or the largest autoregressive root, has fallen significantly. The findings are consistent with a shift towards a monetary policy strategy that stabilizes inflation and output more vigorously such as the policy stance of the ECB. A simulated standard New Keynesian model suggested that we should observe a drop, although small, in inflation persistence following the creation of EMU. credibly stabilizes inflation and inflation expectations around a long-run inflation target, but stand in sharp contrast to previous research that finds no evidence of an effect of the new monetary regime on European inflation persistence. To fully understand the underlying sources of inflation persistence, we require an analysis of structural models of inflation inertia. This is beyond the scope of this paper. Nevertheless, the reduced-form results presented in this paper add to the debate about the policy relevance of backward- versus forward-looking monetary models. The observed fall in inflation persistence corroborates the notion that backward-looking autoregressive models exhibit instability as the underlying policy regime changes. This paper therefore underlines this regime-sensitivity of backward-looking models and provides indirect evidence in favor of forward looking monetary models. To the extent that previous research such as O’Reilly and Whelan (2005) find no evidence of a change

11

in inflation persistence, their results have been interpreted as indirect evidence against forward-looking models. This paper instead clearly supports the need to formulate forward-looking and arguably more stable monetary models.

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References [1] Altissimo, F., M. Ehrmann, and F. Smets (2006): "Inflation persistence and price setting in the Euro area - A summary of the IPN evidence", ECB Occasional Paper No. 46. [2] Altissimo, F., L. Bilke, A. Levin, T. Mathä, and B. Mojon (2006): "Sectoral and aggregate inflation dynamics in the Euro area", Journal of the European Economic Association 4, 585-593. [3] Andrews, D. W. K. (2003): "End-of-sample instability tests", Econometrica 71, 1661-1694. [4] Andrews, D. W. K. and H.-Y. Chen (1994): "Approximately median-unbiased estimation of autoregressive models", Journal of Business and Economics Statistics 12, 187-204. [5] Andrews, D. W. K. and W. Ploberger (1994): "Optimal tests when a nuisance parameter is present only under the alternative", Econometrica 61, 1383-1414. [6] Angeloni, I., L. Aucremanne, and M. Ciccarelli (2006): "Price setting and inflation persistence: did EMU matter?", Economic Policy 46, 353-387. [7] Batini, N. (2002): "Euro area inflation persistence", ECB Working Paper No. 201. [8] Benati, L. (2008): "Investigating inflation persistence across monetary regimes", Quarterly Journal of Economics 123, 1005-1060. [9] Benigno, P. and J. D. López-Salido (2006): "Inflation persistence and optimal monetary policy in the Euro area", Journal of Money, Credit, and Banking 38, 589-614. [10] Boivin, J. , M. P. Giannoni, and B. Mojon (2008): "How has the Euro changed the monetary transmission?", forthcoming, NBER Macroeconomic Annual 2008. [11] Caggione, G. and E. Castelnuovo (2007): "Investigating inflation persistence in the ACF domain", unpublished, University of Padua. [12] Cecchetti, S. G. and G. Debelle (2006): "Has the inflation process changed?", Economic Policy April 2006, 311-352. [13] Clarida, R., J. Galí, and M. Gertler (1999): "The Science of Monetary Policy: A New Keynesian Perspective", Journal of Economic Literature 37, 1661-1707. [14] Clark, T. E. (2006): "Disaggregate evidence on the persistence of consumer price inflation", Journal of Applied Econometrics 21, 563-587. 13

[15] Cogley, T. and T. J. Sargent (2007): "Inflation-gap persistence in the U.S.", unpublished, University of California, Davis. [16] Erceg, C. J. and A. T. Levin (2003): "Imperfect credibility and inflation persistence", Journal of Monetary Economics 50, 915-944. [17] Estrella, A. and J. C. Fuhrer (2003): "Monetary policy shifts and the stability of monetary policy models", The Review of Economics and Statistics 85, 94-104. [18] Fuhrer, J. C. (2006): "Intrinsic and Inherited Inflation Persistence", International Journal of Central Banking 2, 49-86. [19] Gadzinski, G. and F. Orlandi (2004): "Inflation persistence in the European Union, the Euro area, and the United States", ECB Working Paper No. 414. [20] Hansen, B. E. (1999): "The grid bootstrap and the autoregressive model", The Review of Economics and Statistics 81, 594-607. [21] Kumar, M. S. and T. Okimoto (2007): "Dynamics of persistence in international inflation rates", Journal of Money, Credit, and Banking 39, 1457-1479. [22] Levin, A. T. and J. M. Piger (2006): "Is inflation persistence intrinsic in industrial economies?", unpublished, Board of Governors of the Federal Reserve System. [23] Levin, A. T., F. M. Natalucci, and J. M. Piger (2004): "The macroeconomic effects of inflation targeting", Federal Reserve Bank of St. Louis Review 86(4), 51-80. [24] O’Reilly, G. and K. Whelan (2005): "Has Euro-area inflation persistence changed over time?", The Review of Economics and Statistics 87, 709-720. [25] Perron, P. (1989): "The great crash, the oil price shock, and the unit root hypothesis", Econometrica 57, 1361-1401. [26] Pivetta, F. and R. Reis (2007): "The persistence of inflation in the United States", Journal of Economic Dynamics and Control 31, 1326-1358. [27] Rudebusch, G. D. (2005): "Assessing the Lucas critique in monetary policy models", Journal of Money, Credit, and Banking 37, 245-272. [28] Stock, J. H. (1991): "Confidence intervals for the largest autoregressive root in U.S. macroeconomic time series", Journal of Monetary Economics 28, 435-459. [29] Taylor, J. B. (2000): "Low inflation, pass-though, and the pricing power of firms", European Economic Review 44, 1389-1408. [30] Woodford, M. (2003): Interest and Prices, Princeton University Press: Princeton.

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Table 1: The persistence of inflation as measured by the sum of autoregressive coefficients inflation series sample lag order ρ 90% confidence band deflator

HICP

HICP excl. energy

1970:1 - 2006:4

6

1.023

[0.957, 1.059]

1970:1 - 1998:4

4

1.034

[0.956, 1.077]

1999:1 - 2006:4

3

0.782

[0.382, 1.182]

1970:1 - 2006:4

6

1.016

[0.947, 1.046]

1970:1 - 1998:4

6

1.030

[0.968, 1.066]

1999:1 - 2006:4

3

0.179

[−0.173, 0.547]

1988:1 - 2005:4

4

0.937

[0.823, 1.051]

1988:1 - 1998:4

5

1.107

[0.997, 1.198]

1999:1 - 2006:4

5

0.596

[0.297, 1.018]

Notes: The table reports Hansen’s (1999) mean unbiased estimator of the sum of autoregressive coefficients ρ and the bootstrapped 90% confidence bands based on 101 grid points and 999 replications. The lag order is chosen according to the AIC.

15

Table 2: The persistence of inflation as measured by the largest autoregressive root inflation series

sample

lag order

μ

90% confidence band

deflator

1970:1 - 2006:4

6

1.022

[0.946, 1.063]

1970:1 - 1998:4

4

1.024

[0.958, 1.064]

1999:1 - 2006:4

3

0.977

[0.831, 1.050]

1970:1 - 2006:4

6

1.021

[0.935, 1.066]

1970:1 - 1998:4

6

1.026

[0.971, 1.066]

1999:1 - 2006:4

3

0.765

[0.588, 0.974]

1988:1 - 2006:4

4

0.928

[0.784, 1.043]

1988:1 - 1998:4

5

1.032

[1.005, 1.071]

1999:1 - 2006:4

5

0.755

[0.625, 1.009]

HICP

HICP excl. energy

Notes: The table reports Stock’s (1991) mean unbiased estimator of the largest autoregressive root μ and the asymptotic 90% confidence bands. The lag order is chosen according to the AIC.

16

Table 3: The persistence of inflation conditional on structural breaks inflation series

sample

lag order

break date

ρ

90% confidence band

deflator

1970:1 - 2006:4

6

1982:2

0.818

[0.712, 0.929]

1970:1 - 1998:4

4

1982:1

0.851

[0.714, 1.021]

1999:1 - 2006:4

3

-

0.782

[0.382, 1.182]

1970:1 - 2006:4

6

1981:4

0.850

[0.763, 0.942]

1970:1 - 1998:4

6

1981:4

0.888

[0.784, 1.014]

1999:1 - 2006:4

3

-

0.179

[−0.173, 0.547]

1988:1 - 2006:4

4

1993:2

0.715

[0.591, 0.940]

1988:1 - 1998:4

5

1991:3

1.050

[0.906, 1.152]

1999:1 2006:4

5

-

0.596

[0.297, 1.018]

HICP

HICP excl. energy

Notes: The table reports Hansen’s (1999) mean unbiased estimator of the sum of autoregressive coefficients ρ and the bootstrapped 90% confidence bands based on 101 grid points and 999 replications conditional on a break as suggested by the break test of Andrews and Ploberger (1994). The lag order is chosen according to the AIC.

17

inflation autocorrelation

0.8 0.6 0.4 0.2 0 -0.2

1

2

3

4

5

6

7

8

6

7

8

lag output gap autocorrelation

0.8 0.6 0.4 0.2 0

1

2

3

4

5

lag

Figure 1: Autocorrelation of inflation and the output gap implied by the simulated standard New-Keynesian model for φπ = 1.20 and φx = 0.50 (red line, squares) and for φπ = 2.00 and φx = 0.80 (blue line, stars)

18

17.5 15.0 12.5 10.0 7.5 5.0 2.5 0.0 1970

1975

1980

1985

1990

1995

2000

2005

Figure 2: EMU inflation based on GDP deflator (solid line) and HICP (dotted line) in % p.a. The shaded area indicates the EMU period.

19

1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 1983 1985

1987 1989

1991 1993

1995 1997

1999 2001

2003 2005

Figure 3: Median unbiased estimate of the sum of autoregressive coefficients with a 90% confidence band based on a 10-year rolling window for HICP inflation. The shaded area indicates the EMU period.

1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005

Figure 4: Median unbiased estimate of the sum of autoregressive coefficients with a 90% confidence band based on a 10-year rolling window for deflator inflation. The shaded area indicates the EMU period.

20

1.4

1.2 1.0 0.8 0.6 0.4 0.2

0.0 1983

1985

1987

1989

1991 1993

1995

1997

1999

2001

2003

2005

Figure 5: Median unbiased estimate of the sum of autoregressive coefficients with a 90% confidence band based on a 10-year rolling window for non-seasonally adjusted HICP inflation. The shaded area indicates the EMU period.

1.25

1.00

0.75

0.50

0.25 1985

1987 1 989

1991

1993

1995

1997

1999

2001

2003

2005

Figure 6: Median unbiased estimate of the sum of autoregressive coefficients with a 90% confidence band based on a 12-year rolling window for HICP inflation. The shaded area indicates the EMU period.

21

1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005

Figure 7: Median unbiased estimate of the sum of autoregressive coefficients with a 90% confidence band based on an 8-year rolling window for HICP inflation. The shaded area indicates the EMU period.

0.8 q=1 q=2 q=3 q=4

0.7 0.6

p-value

0.5 0.4 0.3 0.2 0.1 0.0 5

10

15

20

25

30

35

40

m

Figure 8: p-values for Andrew’s (2003) test of structural stability of the last m observations of the sample period for HICP inflation with different lag lengths q. The shaded area marks the start of EMU.

22

0.8 q=1 q=2 q=3 q=4

0.7

0.6

p -valu e

0.5

0.4

0.3

0.2

0.1

0.0 5

10

15

20

25

30

35

40

m

Figure 9: p-values for Andrew’s (2003) test of structural stability of the last m observations of the sample period for HICP inflation with different lag lengths q. A dummy is included as explained in the text. The shaded area marks the start of EMU.

0.8

q=1 q=2 q=3 q=4

0.7 0.6

p-value

0.5 0.4 0.3 0.2 0.1 0.0 5

10

15

20

25

30

35

40

m

Figure 10: p-values for Andrew’s (2003) test of structural stability of the last m observations of the sample period for deflator inflation with different lag lengths q. The shaded area marks the start of EMU.

23

0 .8

0 .7

0 .6

p-value

0 .5

0 .4

0 .3

0 .2

0 .1

0 .0 5

10

15

20

25

30

35

40

m

Figure 11: p-values for Andrew’s (2003) test of structural stability of the last m observations of the sample period with a constant as the only regressor. The bold line pertains to deflator inflation, the dotted line to HICP inflation. The shaded area marks the start of EMU.

24