The Changing Nature of Inflation Persistence in Switzerland Peter Tillmann1 Swiss National Bank February 9, 2009

Abstract: This note analyzes the persistence of inflation in Switzerland. In particular, we assess the impact of the new monetary framework adopted by the SNB in 2000 on inflation persistence. A set of rolling-window estimates shows that inflation persistence has fallen significantly since the end of the 1990s. Keywords: Inflation persistence, structural change, sum of autoregressive coefficients, autoregressive root, monetary regimes JEL classification: E31, E52

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I am grateful to Barbara Rudolf and Mathias Zurlinden for stimulating discussions of an earlier draft. The views expressed in this paper do not necessarily reflect those of the Swiss National Bank. Contact: Swiss National Bank, Börsenstr. 15, CH-8022 Zurich, [email protected].

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Introduction

This note investigates whether the persistence of Swiss inflation has changed over time. In particular, we assess the impact of the new monetary framework adopted by the Swiss National Bank (SNB) in 2000 on inflation persistence. By persistence we mean the degree of serial correlation in the inflation process. Hence, persistence measures the speed at which shocks to inflation die out and the inflation rate returns to its mean. As such, the nature of inflation persistence is likely to reflect the underlying monetary regime. Strong anti-inflation credibility and well-anchored expectations are generally thought of as reducing inflation persistence. The SNB’s new policy framework explicitly defines the overall aim of price stability in terms of a CPI inflation rate below 2%. Furthermore, the inflation forecast plays a crucial role in formulating and communicating policy decisions. Hence, the importance of lagged inflation as explanatory variables for current inflation should decline. The persistence of inflation in Switzerland is analyzed in Benati (2008). He computes a pre- and post-2000 measure of the serial correlation of inflation and finds a substantial decline in inflation persistence.2 The present note extends Benati’s study in three respects. First, he obtains estimates surrounded by a very large degree of uncertainty. For example, in the post-2000 sample serial correlation lies in a confidence band ranging from −0.55 to 1.02. Due the width of this band we cannot say whether the fall in persistence has been statistically significant. Therefore, we use rolling—window regressions and a slightly larger data set to reduce the degree of estimation uncertainty. Second, it is well known that structural breaks in the mean and the variance of inflation affect the estimated degree of inflation persistence. 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. In fact, Savioz and Maag (2005) find structural breaks in Swiss inflation around 1993. Hence, this is likely to bias Benati’s pre-2000 results upwards. Using rolling-windows minimizes the impact of structural breaks and gives a more reliable picture of the changing nature of inflation persistence. In addition, we explicitly take account of a structural break in the inflation process. Third, the approach taken here allows for a gradual structural change in the inflation process while Benati (2008) focuses on one particular break date. The main finding of this note is that inflation exhibits significantly less persistence after the adoption of the new monetary regime in January 2000. In the benchmark 2

He also uses Bayesian methods to estimate a small DSGE model in order to assess the structural determinants of inflation persistence, i.e. the degree of forward- versus backward-looking price setting within a hybrid New Keynesian Phillips curve. His analysis, however, suffers from short sampleproblems as he has only seven years of quarterly data at hand to estimate 12 parameters and their entire posterior distributions.

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specification, the sum of the autoregressive coefficients in the inflation process drops from around unity at the end of the 1990s to 0.3 towards the end of the sample period in 2008. Once we take account of a structural break in inflation, persistence begins to drop already in the mid 1990s. Hence, the results support the notion that inflation expectations are well-anchored under the prevailing monetary policy regime.3 This note is structured as follows. Section two introduces the measurement of inflation persistence and the data set. Section three discusses the results from rolling-window regressions while section four draws some conclusions.

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Measuring inflation persistence

Following O’Reilly and Whelan (2005) and Levin and Piger (2006), among others, 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. Let π t be the inflation measure, α an intercept term, and εt be a serially uncorrelated error term. The AR(q) process is q X β k π t−k + εt (1) πt = α + k=1

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 . Rewrite expression (1) as π t = α + ρπ t−1 +

q−1 X

γ k ∆π t−k + εt

(2)

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 ≤ qmax 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 3

Gerlach-Kristen (2005) shows the impact of the new regime on inflation expectations. She concludes that under the post-2000 framework inflation expectations are less affected by actual inflation.

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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 as a second measure of persistence. This is used to cross check the findings based on the sum of the autoregressive coefficients ρ. Stock (1991) provides the standard method to obtain unbiased median estimates and 90% asymptotic localto-unity confidence bands. As mentioned in the introduction, the presence of structural breaks in the inflation process can bias the estimates of persistence upwards. To account for this bias we include an appropriate dummy variable dt in the regression equation, which is unity in t ≥ s, where s is the break date, and zero elsewhere π t = α + δdt + ρπ t−1 +

q−1 X

γ k ∆π t−k + εt

(3)

k=1

To locate the break date, we utilize the test provided by Andrews and Ploberger (1994). The policy framework of the SNB explicitly defines price stability in terms of the rate of change of the consumer price index. Therefore, we measure inflation as the annualized quarterly percentage change of the aggregate consumer price index. The series is obtained from the SNB’s database and covers the sample period 1980:1 to 2008:3. The X12 procedure is used to seasonally adjust the CPI series. A first visual inspection of the data series, which is plotted in figure (1), suggests that inflation fluctuations in the last third of the sample period are indeed more short-lived than before.

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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. We allow the lag order to be different in each window as determined by the AIC. Hence, we end with a series of persistence measures that summarize the dynamics of inflation persistence over time. The baseline results are depicted in figure (2). Apparently, inflation persistence has fallen significantly since 2000. Moreover, in the pre-2000 period the confidence bands also include the unit root case, i.e. ρ = 1. After 2000, however, the unit root can be ruled out at high levels of significance. A set of results based on a six-year window is presented in figure (3). The fall in persistence is even more pronounced. To control for the possibility of a change in the seasonal pattern around 2000, we seasonally adjust the pre-2000 and post-2000 CPI series separately and then link the adjusted series again. Inflation based on this series is slightly less volatile in the post-2000 period than the conventional inflation rate. All findings about the changing nature of the persistence properties (not reported in the appendix for brevity), however, remain unchanged. Likewise, in figure (4) the largest autoregressive root 4

exhibits a similar decline, although not as clear-cut as the sum of the autoregressive coefficients. We search for a structural break in the inflation process in the pre-2000 sample. Based on a sequential F -test, the Andrews-Quandt test statistic uses the maximum of this test statistic (SupF ), while the Andrews-Ploberger test uses a weighted average (ExpF ). The SupF test statistic is 8.59, the ExpF test statistic is 2.23. Both lead to a rejection of the null hypothesis of no structural break in α in 1993:2 at a 5% level of significance. The break date corresponds to the findings of Savioz and Maag (2005). Hence, we include an appropriate dummy variable in all sample windows covering this break date. The results of this specification are presented in figure (5). Two findings stand out. First, throughout the sample period the degree of persistence is lower than in the baseline specification reported in figure (2). The confidence bands no longer include the unit root case. Second, the fall in inflation persistence appears more gradual and to a lesser extent associated with the shift in the policy regime in 2000. In fact, persistence starts to decline as early as 1997.

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Conclusions

This note showed that Swiss inflation became less persistent under the new monetary policy regime. It appears that the adoption of the new policy framework in early 2000 contributed to the anchoring of inflation expectations, thus reducing the role of past inflation for expected future inflation. While the fall in inflation persistence is ultimately due to monetary policy, it appears only loosely connected the official adoption of a policy regime such as in 2000:1. In fact, the evidence presented here supports the notion of a gradual decline starting in the mid-1990s. A central pillar of the SNB’s strategy is to communicate an inflation forecast. In fact, a policy framework that sets the policy instrument to meet the target rate of inflation h periods ahead implies that information at time t should contain less information about future inflation deviations from target. If policy faces no trade-off and sets the instrument so as to exactly meet the target rate, time t information should be orthogonal to realized inflation at time t + h. Therefore, current inflation becomes less important in forecasting future inflation. The results also corroborate earlier evidence presented by Levin et al. (2004). These authors suggest that the adoption of an inflation targeting framework leads to a reduction of inflation persistence in major industrial and emerging market economies.

References [1] Andrews, D. W. K. and H.-Y. Chen (1994): "Approximately median-unbiased estimation of autoregressive models", Journal of Business and Economics Statistics

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12, 187-204. [2] Andrews, D. W. K. and W. Ploberger (1994): "Optimal tests when a nuisance parameter is present only under the alternative", Econometrica 61, 1383-1414. [3] Benati, L. (2008): "Investigating inflation persistence across monetary regimes", Quarterly Journal of Economics 123, 1005-1060. [4] Clark, T. E. (2006): "Disaggregate evidence on the persistence of consumer price inflation", Journal of Applied Econometrics 21, 563-587. [5] Gerlach-Kristen, P. (2005): "The impact of the new Swiss monetary policy framework on inflation expectations", unpublished, Swiss National Bank. [6] Hansen, B. E. (1999): "The grid bootstrap and the autoregressive model", The Review of Economics and Statistics 81, 594-607. [7] Levin, A. T. and J. M. Piger (2006): "Is inflation persistence intrinsic in industrial economies?", unpublished, Board of Governors of the Federal Reserve System. [8] 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. [9] O’Reilly, G. and K. Whelan (2005): "Has Euro-area inflation persistence changed over time?", The Review of Economics and Statistics 87, 709-720. [10] Savioz, M. and T. Maag (2005): "Changes in the Swiss Inflation Process - Stylized Facts, Determinants, and Policy Implications", unpublished, Swiss National Bank. [11] Stock, J. H. (1991): "Confidence intervals for the largest autoregressive root in U.S. macroeconomic time series", Journal of Monetary Economics 28, 435-459.

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