Measures of Underlying Inflation in the Euro Area
Assessment and Role for Informing Monetary Policy
Author: Mr. Emil Stavrev

Contributor Notes

Author(s) E-Mail Address: estavrev@imf.org
Publication Date:
01 Aug 2006
eISBN:
9781451864571
ISBN:
9781451864571
Language:
English
Keywords:
WP; headline inflation; Phillips curve; inflation risk; inflation forecasting performance; inflation process; inflation pickup; Phillips curve equation
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The paper evaluates the 24-month ahead inflation forecasting performance of various indicators of underlying inflation and structural models. The inflation forecast errors resulting from model misspecification are larger than the errors resulting from forecasting of exogenous variables. Also, measures derived using the generalized dynamic factor model (GDFM) overperform other measures over the monetary policy horizon and are leading indicators of headline inflation. Trimmed means, although weaker than GDFM indicators, have good forecasting performance, while indicators by permanent exclusion underperform but provide useful information about short-term dynamics. The forecasting performance of theoretically-founded models that relate monetary aggregates, the output gap, and inflation improves with the time horizon but generally falls short of that of the GDFM. A composite measure of underlying inflation, derived by averaging the statistical indicators and the model-based estimates, improves forecast accuracy by eliminating bias and offers valuable insight about the distribution of risks.

Abstract

The paper evaluates the 24-month ahead inflation forecasting performance of various indicators of underlying inflation and structural models. The inflation forecast errors resulting from model misspecification are larger than the errors resulting from forecasting of exogenous variables. Also, measures derived using the generalized dynamic factor model (GDFM) overperform other measures over the monetary policy horizon and are leading indicators of headline inflation. Trimmed means, although weaker than GDFM indicators, have good forecasting performance, while indicators by permanent exclusion underperform but provide useful information about short-term dynamics. The forecasting performance of theoretically-founded models that relate monetary aggregates, the output gap, and inflation improves with the time horizon but generally falls short of that of the GDFM. A composite measure of underlying inflation, derived by averaging the statistical indicators and the model-based estimates, improves forecast accuracy by eliminating bias and offers valuable insight about the distribution of risks.

I. Introduction

Headline and core inflation in the euro area have been sending divergent signals about underlying inflation over the past couple of years. On an annual basis, headline inflation has remained above the European Central Bank’s (ECB) “close to but below” 2 percent target since 2000 and is forecast to continue to do so through 2007 (Figure 1). Over the past several years various shocks such as increases in energy and administrative prices as well as hikes in indirect taxes have pushed headline inflation above the target. However, various core inflation measures (excluding energy and unprocessed food) have declined since 2004—to around 1½ percent in the spring of 2006—suggesting subdued inflationary pressures. Other indicators such as mild wage and unit labor cost growth also indicate little inflationary pressure in the near future, and, notably, no second-round effects from rising oil prices.

Figure 1.
Figure 1.

Euro Area: Headline and Core Inflation

(In percent)

Citation: IMF Working Papers 2006, 197; 10.5089/9781451864571.001.A001

For monetary policy, one key issues is what different indicators suggest about current underlying and future headline inflation.1 Specifically, how useful are indicators of underlying inflation in forecasting future inflation? Are there gains to be made in forecasting future inflation by utilizing information from a large set of underlying inflation indicators and using different modeling approaches? Finally, where is inflation headed over the medium-term—that is, the ECB’s monetary policy horizon?

Answering these questions requires an evaluation of the predictive performance and leading indicator properties of a broad range of underlying inflation measures using various methods. Based on the results, the indicators’ relative usefulness in informing monetary policy can be assessed. Furthermore, a composite indicator can be constructed that exploits the information content embedded in the large number of different measures of underlying inflation and modeling approaches. This indicator is used to produce a baseline forecast for headline inflation, using information available as of spring 2006. The paper is organized follows: Section II discusses theoretical foundations and the purpose of various indicators of underlying inflation. Section III discusses the properties of these indicators. Section IV describes the forecasting methodology and discusses forecasting performance of the indicators of underlying inflation; and Section V concludes.

The main findings are:

  • Inflation forecast errors over a 24-month horizon resulting from model misspecification are larger than errors resulting from forecasting of exogenous variables.

  • Measures derived using the generalized dynamic factor model (GDFM) overperform other measures over the monetary policy horizon and are leading indicators of headline inflation. Although weaker than GDFM indicators, trimmed means have good forecasting performance over a 24-month horizon. Indicators by permanent exclusion (notably core inflation) underperform but provide useful information about short-term dynamics. The forecasting performance of theoretically-founded models that relate monetary aggregates, the output gap, and inflation improves with the time horizon but generally falls short of that of the GDFM.

  • A composite measure of underlying inflation, derived by averaging the statistical indicators and the model-based estimates, improves forecast accuracy by eliminating bias, and offers valuable insight about the distribution of risks.

II. Taxonomy of Underlying Inflation Indicators

The rationale behind indicators of underlying inflation is to facilitate disentangling the effects of idiosyncratic/temporary and policy-related/persistent forces that drive the inflation process. Some factors have a more permanent effect, while others have a more temporary one. The permanent component is related to the fundamental driving forces of inflation such as excess demand for goods and services and ultimately the macroeconomic policy mix. The transitory component can be a result of temporary shocks such as one-off indirect tax changes, changes in relative prices, unusual seasonal patterns, or measurement errors. Transitory shocks, however, can have more lasting effects on inflation, if they trigger second-round effects.

Monetary policy is known to affect inflation with long and variable lags, and cannot offset short-term, temporary shocks to inflation. However, it can affect the persistent component of inflation, notably through anchoring inflation expectations, and thus needs to be focused on stabilizing inflation over the medium term. Therefore, separating inflation in a persistent “common” component, driven by fundamental forces, and transient “noise,” due to mostly idiosyncratic shocks, is a useful exercise from a monetary policy standpoint. This is what indicators of underlying inflation are trying to achieve with a view to providing reliable information on current and future inflation dynamics.

Measures of underlying inflation can be separated into two main groups—statistical indicators and theoretical/structural measures (Table 1).

  • Statistical indicators are derived using pure econometric methods. They can be further divided into three subcategories—employing time series, cross-section distribution of prices, and panel data. Examples include various univariate filters (time series), indicators by permanent exclusion such as core inflation or variable exclusion such as trimmed means (cross-section), and the generalized dynamic factor model, GDFM, (panel data).

  • Theoretical measures are based on economic theory. The two most common theoretical frameworks used to estimate underlying inflation build on the long-run Phillips curve and the quantity theory of money. Vector autoregressive models (SVAR), as in Quah and Vahey (1995) and Blix (1995), and reduced form Phillips curve equations are the most common examples of the first group; money demand equations and P* models, as in Nicoletti Altimari (2001), are the most widespread examples of the second group.

Table 1.

Taxonomy of Underlying Inflation Indicators

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Table 2.

Euro Area: Descriptive Statistics of HICP Components

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Sources: EUROSTAT; and IMF staff estimates.

Annualized.

III. Features of the Indicators

All measures of underlying inflation have pros and cons.

  • A common advantage of the statistical indicators is that they are less volatile than headline inflation and thus, presumably, capture better fundamental price changes. To achieve this, core inflation excludes presumed idiosyncratic shocks from headline inflation (e.g., energy prices, unprocessed food); trimmed means apply objective statistical criteria to achieve the same (Bryan and Cecchetti, 1994, 1996); while GDFM measures do so by filtering idiosyncratic shocks with the help of both the cross-section and time series dimension of the data.2 A general disadvantage of the statistical indicators is that they are not backed by economic theory.3

  • The main advantage of the theoretical measures is that they have macroeconomic foundations. Consequently, they allow for an economic interpretation of the results by linking inflation developments to the macroeconomic variables relevant from a policy perspective. The main disadvantage of the theoretical measures is that it is difficult to identify structural shocks and estimate the parameters. Also, they suffer from behavioral invariance in that structural parameters remain constant, despite possible structural changes in the future (Lucas critique).

To gauge uncertainty and provide a comparative perspective, a wide set of statistical indicators and economic models are used to estimate underlying inflation. Representatives of all standard statistical indicators are included here—specifically, a univariate spectral density filter, permanent and variable exclusion indicators, and panel methods. Theoretically-founded models are represented by a bivariate SVAR model, a reduced form Phillips curve model that controls for oil prices and the exchange rate, and a P* model. The use of a large number of measures is intended to deal with single forecast uncertainty and provide the basis for risk assessment. At the same time, it allows an evaluation of the relative usefulness of each measure in forecasting future inflation over the medium term.

The analysis of the indicators’ statistical properties provides insights into two main features—volatility and bias. Regarding volatility (Table 3), all indicators but core inflation excluding energy perform well in filtering noise—they have smaller variances than harmonized index for consumer prices (HICP) inflation. However, indicators differ substantially in the degree of noise reduction. GDFM measures outperform other measures according to this criterion, with their standard deviation ranging from 32 to 77 percent of HICP standard deviation for indicators with 1 and 2 dynamic factors, respectively. Theoretically-based (Quah and Vahey and Phillips curve) measures follow, with standard deviations of 38 percent and 54 percent, respectively. Trimmed mean indicators rank third, with their variability declining as the share of excluded goods increases. Core inflation indicators rank last. Regarding bias, GDFM and model-based indicators are unbiased, trimmed means have a small (0.1 percentage points) but statistically significant downward bias, while core measures again underperform, displaying the highest downward bias (0.2 percentage points in the sample).

Table 3.

Euro Area: Headline and Underlying Inflation Indicators: Descriptive Statistics /1

(Year-on-year, in percent)

article image
Sources: Eurostat; and IMF staff calculations.

Sample: January, 1997-December, 2005.

Relative to headline inflation.

A visual inspection of headline inflation and the indicators gives a sense about the indicators’ performance in signaling inflationary pressure over the sample (Figures 2-5). Qualitatively, GDFM measures seem to have good leading indicator properties, as they signaled the inflation pickup that started in 1999. They suggest that underlying inflation has remained stable since 2002. Both core and trimmed mean indicators performed well over 1997–99, lagged headline inflation during 1999–2001, and have implied declining (core indicators) or stable underlying inflation (trimmed means) since 2004. Model-based estimates (Quah and Vahey and Phillips curve) anticipated the 1999 pickup in inflation and indicate roughly stable underlying inflation over the past few years; only the Phillips curve indicator points to a slight increase of inflation since mid-2004, driven by high energy prices. Quantitatively, the indicators suggest that underlying inflation has been moving broadly sideways over the past year and is currently in a range of 1½ to 2¼ percent, with most indicators pointing to a figure under 2 percent.

Figure 2.
Figure 2.

Euro Area: Headline and GDFM Estimates of Underlying Inflation

(In percent)

Citation: IMF Working Papers 2006, 197; 10.5089/9781451864571.001.A001

Source: IMF staff estimates.
Figure 3.
Figure 3.

Euro Area: Headline and Permanent Exclusion Core Inflation

(Year-on-year, in percent)

Citation: IMF Working Papers 2006, 197; 10.5089/9781451864571.001.A001

Source: Eurostat.
Figure 4.
Figure 4.

Euro Area: Headline and Variable Exclusion Core Inflation

(Year-on-year, in percent)

Citation: IMF Working Papers 2006, 197; 10.5089/9781451864571.001.A001

Source: IMF staff estimates.
Figure 5.
Figure 5.

Euro Area: Headline and Model-based Underlying Inflation

(Year-on-year, in percent)

Citation: IMF Working Papers 2006, 197; 10.5089/9781451864571.001.A001

IV. Forecasting Methodology and Assessment of Forecasting Performance

A. Forecasting Methodology

Forecasting performance of the statistical indicators is assessed using several methods based on simulated out-of-sample forecasts.4,5 Specifically, for the statistical indicators (core, trimmed means, and GDFM) univariate, bivariate, and multivariate specifications are used to forecast headline inflation. In addition, inflation forecasts are produced with non-price variables (industrial production, monetary aggregates, wages, unit labor cost, unemployment, and interest rates). Simulated out-of-sample 24-month ahead forecasts start in November 2000. The equations are re-estimated each time a new month is added.

The 24-month ahead forecasts are made using two approaches—first, with 1-month lag equations and, second, with 24-month lag equations. Each of the two methods has pros and cons. An advantage of the first is that the estimated equations have better goodness of fit statistics and smaller standard errors compared to the second approach. A disadvantage, however, is that the indicators have to be forecast 24 months ahead in order to forecast inflation over that horizon, thereby adding exogenous variable forecast error to the model forecast error. For the forecast performance of the two approaches it is, therefore, important which forecast error is smaller—the one from model misspecification or the one from exogenous variable forecast. The semi-structural, distributed lag, and gap equations were estimated both with the indicator lagged one month (based on lag selection tests) and 24 months. At the time of the forecast, all right-hand side variables, (including the indicator for the models where the indicator is lagged one month) are assumed to be unknown and are projected using a nonparametric spectral density filter. A brief description of the equations used in the paper follows.

  • Static equation

    The static equation is used to forecast headline inflation with both the statistical and theoretically-founded indicators. The equation is defined as πt = xt −h +εt, where πt is headline inflation, xt−h is the indicator of underlying inflation, and εt is an error term. Headline inflation at time t is simply equal to the value of the indicator of underlying inflation x at time t-h.

  • Spectral density filter

    The spectral density filter is similar in nature to the Box-Jenkins autoregressive moving average model (ARMA). However, there are some key differences. First, this is a nonparametric technique, which does not depend on the lag selection procedure, and, second, the model is estimated in the frequency domain instead of the time domain (see Hamilton, 1994).

  • Semi-structural equation controlling for oil and exchange rate

    This equation is an unrestricted version (the coefficient on xt−1 (xt−24) is estimated instead of being restricted to 1) of the static equation extended with oil prices and the exchange rate to control for these shocks. From a practical perspective, the semi-structural equation is attractive because forecasts are typically made conditional on certain exchange rate and oil price assumptions. Formally: πt = α + β xt−1 + γ oilt−1 + δ zt−1 + εt (πt = α + β xt−24 + γ oilt−1 + δ zt−1 + εt), where oilt−1 is oil prices in euros, and zt−1 is the exchange rate. As noted above, the 24-month ahead simulated out-of-sample forecast with this equation (and all equations described below) is done in two steps: first, the right-hand side variables (xt−1, oilt−1, and zt-1) are forecast with the spectral density filter, and, second, the equation is solved for the headline inflation πt.

  • Distributed lag equation

    The distributed lag equation has the following form: πt = α + A(L)πt−1 + B(L)xt−1 + εt, (πt = α + A(L)πt−24 + B(L)xt−24 + εt) where A(L) and B(L) are lag polynomials (the lag selection is determined by the Akaike and Schwartz information criteria), and xt−1(xt−24) stands for the indicator of underlying inflation or the non-price variables (this model is also estimated with the non price variables).

  • Gap equation

    Depending on the indicators, two forms of the gap equation are estimated. For the statistical indicators, it has the following form: πt − πt−1 = α + β (xt−1 − πt−1) + εt (πt − πt−24 = α + β (xt−24 − πt−24) + εt), where πt is headline inflation and xt−1(xt−24) is one of the statistical indicators (GDFM, core, or trimmed means). The equation allows to assess whether there is a tendency for headline inflation to converge to the estimate of underlying inflation over the medium term. If underlying inflation is leading the headline number, the coefficient β should be positive. For the non-price variables ct, (wages, monetary aggregates, etc.) the above equation is estimated in deviation from the means, namely: πt−π¯=α+β(ct−1−c¯)+εt(πt−π¯=α+β(ct−24−c¯)+εt), where π¯ is headline inflation mean and c¯ stands for the mean of the non-price variables.

The forecast with the theoretically-founded models is done with the estimated equations for each model. A short description of each model follows below.

  • Reduced form Phillips curve model

    This model is a version of the traditional Phillips curve, with inflation depending on the deviation of output from its potential instead of unemployment from its non-accelerating inflation rate (NAIRU). Similar models have been used to describe inflation dynamics in the forecasting and policy analysis models in several central banks—see, for example, Coletti and others (1996) and Coats (2000). Inflation dynamics are specified as: πt = α + β πt−1 + γgapt−1 + δzt−1 + ηoilt−1 + εt, where gapt−1 is output gap, zt is the change in the exchange rate, and oilt−1 is the change in oil prices.6

  • P* model

    Following Nicoletti Altimari (2001), the quantity equation of money gives the P* indicator as: pt*=mt+vt*−yt*, where yt* denotes potential output, mt is the current money stock and vt* is equilibrium velocity; all variables are in natural logarithms. Inflation dynamics are given by the following equation: πt=(1−λ)πt−1+λΔpt−1*−α(pt−1−pt−1*)+εt, which implies that after the shocks disappear the price level returns to its long-run equilibrium P*.

  • Bivariate SVAR

    In this model, it is assumed that two types of exogenous shocks affect headline inflation—one that has no impact on output beyond the short term,7 and, the other that might have significant medium- to long-run effects on output (a supply shock that shifts potential output for instance). Underlying inflation is, therefore, defined as the unobserved component of headline inflation that is driven by the first type of shocks. Given the above assumptions, the bivariate SVAR can be written as:
    (Δytπt)=D(L)(εt1εt2),
    where Δyt is the change in industrial production, πt is headline inflation, and εt1,εt2 are the two disturbances. This presentation implies that inflation can be decomposed as: with underlying inflation defined as:
    πt=∑j=0∞d21(j)εt−j1+∑j=0∞d22(j)εt−j2,
    with underlying inflation defined as:
    xt=∑j=0∞d21(j)εt−j1.

B. Assessment of Forecasting Performance

Forecasting performance is evaluated by two statistics—root mean square error (RMSE) and bias. These two statistics are estimated for forecast horizons of 6, 12, 18, and 24 months. Given that the simulated out-of-sample forecasts start in November 2000 and the sample ends in November 2005, there are 61 forecast rounds. The number of observations available to estimate the RMSE and the bias are equal to the number of forecast rounds minus the length of the forecast horizon (i.e., there are 37, 43, 49, and 55 observations for the 24-, 18-, 12-, and 6-month horizons, respectively). The RMSE and the bias are calculated as follows:

RMSEh=∑(πt+h−π^t+h)2/T, andBiash=∑(πt+h−π^t+h)/T,

where T is the number of observations.

The forecasts with a 1-month lag overperform those with a 24-month lag, suggesting that errors due to model specification are larger than exogenous variables forecast errors (Tables 4, 5, and 6). Exceptions are trimmed means and M2, which perform better with the 24-month lag distributed lag equation, and 5 and 10 percent trimmed means and M3, which perform better with the 24-month lag gap equation. However, the RMSE of the best performing indicators with the 24-month lag equations are larger than the best performing indicators with the 1-month lag equations. This implies that the errors resulting from model misspecification are larger than the forecast errors of exogenous variables with the spectral density filter. Therefore, in what follows, the forecast performance across models and indicators is assessed based on the forecasts with the 1-month lag equations.

Table 4.

Euro Area: Forecast Performance of Indicators of Underlying Inflation 1/

(Root mean square error/RMSE/and bias in percentage points)

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Source: IMF staff estimates.

Forecast evaluation for estimates with year-on-year inflation. Gap and semi-structural equations are estimated with one month lag; lag length of the distributed lag equation is based on Akaike and Schwarz criteria; right-hand side variables in the bivariate and multivariate models are forecast with a spectral density filter.

Table 5.

Euro Area: Forecast Performance of Indicators of Underlying Inflation 1/

(Root mean square error/RMSE/and bias in percentage points)

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Source: IMF staff estimates.

Forecast evaluation for estimates with year-on-year inflation. Bivariate and multivariate models are estimated using 24-month lag.

Table 6.

Euro Area: 1-month Lag versus 24-month Lag Model Forecast Performance 1/

(Root mean square error/RMSE/and bias in percentage points)

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Source: IMF staff estimates.

Forecast evaluation for estimates with year-on-year inflation; 1-month lag minus 24-month lag.

The measures can be compared across two dimensions—forecast horizons and models. The benchmark for comparison is the random walk forecast of headline inflation, in which future inflation is simply equal to current inflation. In addition to the random walk forecast, two spectral density forecasts (in levels and first differences) are produced with headline inflation. The GDFM, core, and trimmed mean indicators are used for two types of forecasts—a static one, in which headline inflation is forecast as the current value of the indicator; and a model-based one, in which distributed lag, gap, and semi-structural equations are used (bivariate model-based forecasts are done also with the non-price variables). Finally, structural forecasts are done the SVAR, Phillips curve, and P* models.

GDFM measures outperform other statistical measures, including the random walk forecast, across time and models (Table 4).8 GDFM performance is superior according to both assessment statistics—the RMSE and the bias.9 Trimmed means come second, although they are performing slightly worse than the random walk by the RMSE statistic. The trimmed means, however, are the best indicators for the short run—6 to 12 months. Core indicators have the worst performance. Labor market variables (wages, unit labor cost, and unemployment) perform on average better than the three monetary aggregates (M1-M3) by the RMSE statistics; however, they are somewhat worse than the monetary aggregates by the bias criterion.

The static equation overperforms all other specifications at the 24-month horizon. The gap equation comes second—it has a good performance with labor market variables (and monetary aggregates less M3) over the long run. The RMSE of the gap equation with these variables improves significantly with the forecast horizon. This result is in line with theoretical findings that the forecast performance of labor market variables and monetary aggregates should improve with the length of the forecast horizon. The semi-structural equation controlling for oil and exchange rate has a good performance with GDFM and trimmed means. The distributed lag model has acceptable performance over the short run (6 to 12 months); however, its performance deteriorates significantly towards the medium term across all indicators.

The measures derived from the theoretical models, particularly the Phillips curve, provide valuable insights into the driving forces of inflation. The Phillips curve-based models outperform the P* model at the 24-month horizon, ranked by the RMSE criterion.10 The Phillips curve models have