WORKING PAPER SERIES

INFLATION EXPECTATIONS IN PHILLIPS CURVE MODELSFOR THE EURO AREADmitry Kulikov, Nicolas Reigl

82019

The Working Paper is available on the Eesti Pank web site DOI: 10.23656/25045520/082019/0171ISBN 978-9949-606-65-8 (pdf) Eesti Pank Working Paper Series, ISSN 2504-5520; 8/2019 (pdf)

Inflation Expectations in Phillips Curve Modelsfor the Euro Area

Dmitry Kulikov and Nicolas Reigl∗

Abstract

This paper takes a fresh look at the use of the Phillips curve and various inflationexpectation proxies for tracking euro area inflation dynamics in the aftermath ofthe global financial crisis of 2008. Because inflation expectations can be measuredin a multitude of alternative ways and the Phillips curve model itself is subject tomany potential specification choices, we employ a novel thick modelling perspectivethat is data and model-agnostic and estimate a large number of different Phillipscurve models using different data series for different components of our models. Wefind that Phillips curve models without any forward-looking expectational termsare uniformly the worst predictors of euro area inflation rates after 2013, whenmeasured for the RMSE criterion across all models and specifications. This resultunderlines the importance of inflation expectations in tracking the recent dynamicsof euro area inflation and shows that inflation persistence alone or in combinationwith different slack and cost push terms cannot satisfactorily explain the euroarea inflation story during the period of missing inflation after 2012. We alsoillustrate the usefulness of the thick modelling approach for practical modellingand forecasting of the euro area inflation series.

JEL Codes: E31, E37, E58, C13, C15, C52

Keywords: data-rich models, thick modelling, data and model uncertainty, Phillips curve,inflation expectations, inflation dynamics, euro area

The views expressed are those of the authors and do not necessarily represent the officialviews of the Eesti Pank or the Eurosystem.

∗Dmitry Kulikov (corresponding author): Eesti Pank. E-mail: dmitry.kulikov@eestipank.ee. NicolasReigl: Eesti Pank. E-mail: nicolas.reigl@eestipank.ee.We wish to thank Robin Hazlehurst for his excellent language editing of this working paper.

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Non-technical summary

In this paper, we look at how the Phillips curve model can be used in combinationwith various inflation expectations from professional forecasters and financial marketparticipants to track the dynamics of inflation in the euro area in the aftermath of theglobal financial crisis of 2008.

One key observation that came out of the global financial crisis of 2008 and the fol-lowing periods of low economic growth was that the Phillips curve relationship appearedto break down and a phenomenon known as the ”twin inflation puzzle” emerged. Thefirst part of the twin puzzle was a period of missing disinflation that started after theglobal financial crisis and lasted until late 2011, during which inflation was higher thanexpected given the length and the severity of the crisis. The second part of the twinpuzzle arose after 2012 and later after the start of the European Central Bank’s (ECB)Asset Purchase Programme in 2015, when inflation dynamics moved in the oppositedirection at the start of an economic recovery, as expectations that inflation would behigher as the recovery went on proved incorrect. With the ECB’s prime objective of pricestability commonly defined as inflation rates of below, but close to, 2% over the mediumterm, persistently low inflation rates pose multiple problems, one of which is the riskof long-term inflation expectations becoming de-anchored. The effect of de-anchoring isthat short-term price shocks can change long-term inflation expectations, which can notonly hurt central bank credibility, but also increase the risk of actual deflation.

Even before the global financial crisis of 2008, a new kind of Phillips curve model,known as a hybrid Phillips curve model, emerged, incorporating survey-based forward-looking terms as proxies of inflation expectations. We estimate over 2300 empiricalPhillips curves to address two empirical questions: (i) how useful is the Phillips curvemodel in its various forms as a tool of forecasting and policy analysis for understandingthe recent dynamics of inflation in the euro area? (ii) how important are inflationexpectations in their various forms for explaining the dynamics of euro area inflation?

Our Phillips curve models span a large number of traditional backward-looking andforward-looking specifications, and also include a few naive models that depend only onthe driving forces of alternative economic measures of slack such as the unemploymentrate and various cost-push shocks like oil prices. Our forward-looking models use severalalternative proxies for inflation expectations, among which are several variations of mea-sures of expectations based on surveys and financial markets that have been collectedfrom a number of different data sources. Given there are a large number of variables thatcould be predictive, we use a thick modelling approach by estimating a large number oflinear regression models based on backward and forward-looking specifications and alsonaive specifications, which are then used to produce an equally large number of inflationforecasts. In the final step we assess the predictive power of the main model terms bycomparing their forecast accuracy.

We find that among the set of models we estimate, those without forward-lookingterms almost always produce poorer conditional inflation projections than those of almostany Phillips curve model with forward-looking terms. This finding indicates that inflationexpectations continue to play an important role in explaining the recent dynamics ofinflation in the euro area and that the persistence of inflation is not in itself sufficient toexplain fully the story of euro area inflation after 2012. Furthermore, we find that amongthe set of proxies of inflation expectations, the indicators based on financial markets tendto deliver a somewhat more accurate outlook for the future path of inflation, especially

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after the start of the ECB’s Asset Purchase Programme in 2015, although the differencewith other expectational measures is not very large.

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Contents

1 Introduction 5

2 Lessons from the Low Inflation Task Force 7

3 Data on euro area inflation expectations 9

4 Data and model uncertainty in econometrics 14

5 The role of expectations in euro area inflation dynamics 18

6 Conclusion 25

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1 Introduction

One of the key observations that emerged from the global financial crisis of 2008 andthe following protracted period of depressed economic activity around the world is theapparent breakdown in the relationship between prices and wages on one side and eco-nomic slack on the other. This relationship, known as the Phillips curve after it wasfirst described in Phillips (1958), plays a pivotal role in modern theoretical and empir-ical macroeconomics. What has been observed since the global financial crisis of 2008,however, is that inflation rates at first stayed persistently high despite the severity andduration of the recession in most advanced and developing economies, but then remainedstubbornly low during the subsequent gradual economic recovery, and this is now knownas the twin inflation puzzle.

In this paper we concentrate on the second part of this twin puzzle, which is theperiod of missing inflation in advanced economies after 2012, when real output growthwas improving and unemployment rates falling; refer to IMF (2016).1 We focus on theeuro area, where one of the issues linked to persistently low inflation rates since 2012 hasbeen the prominent risk of long-term inflation expectations becoming de-anchored fromthe ECB policy target (see Ciccarelli and Osbat (2017)). Justified concerns have beenraised about how reliable the Phillips curve is as a tool for keeping track of inflationmovements in the wake of the global financial crisis given how the relationship betweeninflation rates and economic slack has flattened out. Both of these concerns speak to theuncertainty of policymakers about the models and data they use for understanding andpredicting the dynamics of inflation in a rapidly changing economic environment.

Even before the global financial crisis of 2008, academic researchers had done sub-stantial work on testing the empirical validity of the New Keynesian Phillips curve andother inflation models; see Mavroeidis, Plagborg-Møller and Stock (2014) for a recentoverview of the literature. The hybrid Phillips curve model with survey-based forward-looking terms, which used survey estimates as proxies of inflation expectations, wasan early attempt to test the theoretical implications of rational expectations in theframework of the New Keynesian Phillips curve; see Roberts (1997) and Roberts (2005).Paloviita (2006) and Paloviita (2008) compared several alternative forms of the hybridNew Keynesian Phillips curves, all estimated with survey-based inflation expectations,and found that models featuring both forward-looking and backward-looking inflationterms fit the pre-crisis European inflation data best. Brissimis and Magginas (2008) usedinflation forecasts from the Federal Reserve’s Greenbook and the survey of professionalforecasters to analyse the ability of the New Keynesian Phillips curve to track the dy-namics inflation before the crisis; a similar and more recent study for the US is Adamand Padula (2011). Estimates of the hybrid models reported in these papers are broadlyin line with the earlier benchmark studies by Galı and Gertler (1999), Galı, Gertler andLopez-Salido (2001), and Galı, Gertler and Lopez-Salido (2005). All these cases repeat-edly confirmed the important role of inflation expectations, in their various proxy formsand guises, through empirical observations.

1The missing deflation part of the puzzle has also attracted considerable interest. The vast majority ofmainstream DSGE models used by central banks around the world are based around the New KeynesianPhillips curve, which struggles to explain stable inflation rates in the presence of large and persistentamounts of slack in economic activity; see Hall (2011) and Christiano, Eichenbaum and Trabandt (2015).This shortcoming can be seen in the notable deterioration in the predictive ability of the baseline DSGEmodel of inflation rates in the wake of the global financial crisis, as documented in King and Watson(2012) among others.

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In this paper we focus on the missing inflation in the euro area after 2012 and askhow useful the Phillips curve model is in its various forms as a forecasting and policyanalysis tool, and how important inflation expectations in their various forms are forexplaining those dynamics. Both questions must address specification uncertainty in themodels and data, as was recently highlighted by Mavroeidis et al. (2014) and others. Incontrast to all the other studies cited previously, we address these challenges head on byemploying a novel econometric approach that is data and model-agnostic.

We estimate more than 2300 empirical Phillips curves spanning a large number ofthe traditional backward and forward-looking specifications found in the literature, anda few naive models that depend only on the driving forces of alternative measures ofeconomic slack and various cost-push shocks. Our forward-looking models use variousalternative proxies for inflation expectations, including several variations of measuresbased on surveys or financial markets that use a number of different data sources. Wecompare and contrast the conditional forecasting performance of these models duringthe period of missing inflation in the euro area after 2012, and we look primarily at twoseparate groups of empirical Phillips curve models with and without the forward-lookinginflation terms.

We find that those of our estimated models that do not contain forward-looking termsalmost always produce poorer conditional inflation projections than almost any Phillipscurve model that includes forward-looking terms. This finding indicates that inflationexpectations continue to play an important role in explaining the recent dynamics of euroarea inflation and that the persistence of inflation alone is not sufficient to explain fullyinflation in the euro area after 2012, even in combination with different measures for theunderutilisation of economic resources and for cost-push shocks. Furthermore, we findthat the financial market-based indicators in the set of inflation expectations proxies tendto deliver a somewhat more accurate outlook for the future path of inflation, especiallyafter the ECB Asset Purchase Programme started in 2015, although the difference withother expectational measures is not very big.

Our work is closely related methodologically to Bundesbank (2016), where the thickmodelling approach of Granger and Jeon (2004) is used to analyse recent developments inGerman inflation. They use a data sample from 1995 to 2015, and estimate 72 differentPhillips curve specifications, combining nine alternative variables for capacity utilisa-tion and eight different measures of expectations. They find that inflation dynamicsin Germany were primarily driven by global factors from 2008 to 2015, while inflationexpectations also played a modest but non-negligible role during this period.

Our approach in this paper differs from Bundesbank (2016) in that we use a muchwider menu of alternative data proxies for inflation expectations, measures of economicslack and cost-push shocks in our thick modelling exercise in order to address the datauncertainty in the Phillips curve. In total we estimate more than 2300 Phillips curvemodels using our euro area dataset, and this makes our model space much wider than thatin the Bundesbank’s study. Apart from the full expectations-augmented Phillips curvemodels, we allow for purely backward-looking and naive models as explained previously,and in our thick modelling exercises we do not impose any a priori restrictions on thesigns of coefficient estimates nor on their levels of statistical significance, thus allowing allmodels to produce coefficient estimates regardless of their signs or statistical significance.This modelling strategy means we do not rely on the arbitrary red lines and decisionrules when we select models for the final analyses, thereby addressing the long-standingcritique of Leamer (1978). Another reason is that the best forecasting models are not

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necessarily the most consistent with theory, and in this paper we mainly judge models ontheir forecasting performance. This makes our approach more agnostic and data driven,and so it is closer to the thick modelling perspective of Granger and Jeon (2004).

The paper is organised as follows. In Section 2 we highlight the most importantfindings from the recent ECB Low Inflation Task Force report, concentrating on therole of inflation expectations. Section 3 details the various different sources of datafor inflation expectations in the euro area and describes the dynamics of some of theseseries during the global financial crisis of 2008. In Section 4 we focus on the statisticalmethodologies related to data and model uncertainty in econometrics, and we use theseapproaches in our empirical analyses in Section 5. Finally, we summarise our findingsand propose future research avenues in our concluding remarks.

2 Lessons from the Low Inflation Task Force

Recent research conducted by the ECB the has taken another look at the nature anddriving forces of inflation rates in the euro area. It has been well understood that euroarea inflation is driven mainly by wage and price setting behaviour on the domesticmarkets, which is linked to the euro area business cycle. External factors from supplyand demand shocks in the global economy affect domestic prices in the euro area mainlythrough their direct impact on prices for global commodities such as energy, and forimported final goods. Global factors also affect euro area prices indirectly by feedinginto producer prices through fluctuations in input costs (see ECB (2017)).

The Low Inflation Task Force (LIFT) was organised by the ECB in early 2014 withthe active involvement of many national central banks from the countries of the euro areaand delivered its report in early 2017, having been tasked with providing a compellingand coherent explanation of the dynamics of inflation in the euro area before the crisesand after 2012 (see Ciccarelli and Osbat (2017)). The final report focuses primarily ontwo interrelated episodes. The first was the missing disinflation after the global financialcrisis of 2008 that lasted until late 2011, when inflation was higher than expected giventhe length and severity of the crisis. The second was the missing inflation after 2012and again after the asset purchase programme started in 2015, when inflation dynamicsmoved in the opposite direction, as the expectation that inflation would be higher duringthe recovery was confounded. During the global financial crisis and the subsequent periodof economic instability, global factors were predominately responsible for inflation beinghigher than expected in 2008 to 2011, whereas it was mostly domestic factors thatcontributed to the deflationary pressures between 2012 and 2015. A recent ECB reportshows that global factors re-emerged after 2015 ahead of domestic factors as drivers ofinflation expectations in the euro area (ECB (2017)).2

In a follow-up to the report, Bobeica and Jarocinski (2019) conclude in their analysisthat the twin inflation3 puzzle in the aftermath of the global financial crisis arises be-

2Though the role of global factors seems to be time-varying, many research papers have found thatincluding them improves the predictive power of traditional models. Ciccarelli and Mojon (2010) showthat models that include a measure of global inflation have better predictive abilities than benchmarkmodels that only include domestic factors. Similarly, Borio and Filardo (2007) find that proxies of globalslack add explanatory power to traditional benchmark models and that the influence of global factorshas grown over time.

3The missing disinflation component of the twin puzzle was not a uniquely European phenomenon.Many advanced economies experienced only a small decline in inflation after the financial crisis of 2008–

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cause inflation forecasting models are too small or too simplified. Indeed neither simpleunivariate Phillips curve type regressions nor tightly restricted versions of New Keyne-sian DSGE models provide good conditional forecasts that are in line with the actualdynamics of inflation during that period. In contrast, Bobeica and Jarocinski (2019)find that data-rich and flexible medium-scale vector autoregressions that incorporatedomestic and external factors account well for the inflation dynamics in the period.

The periods of missing disinflation in 2008–2011 and missing inflation in 2012–2015in the euro area are very different from each other. The LIFT report shows that globalfactors like real activity in the rest of the world, commodity prices and nominal effectiveexchange rates were behind the positive inflation between 2008 and 2011. Oil pricescontributed to inflation but to a lesser extent than in the US. Bobeica and Jarocinski(2019) also show strong spillovers from US to euro area inflation in the Great Recessionthat cannot be explained by world commodity prices or real activity.4

During the episode of missing inflation in contrast, the dominant factor was weakdomestic real activity and deflationary domestic shocks, which affected inflation 2011–2014. The resurgence of external factors as important drivers of the dynamics of euro areainflation after the fourth quarter of 2014 can be explained by two major developments.First, the Chinese economy slowed down during that period, affecting export drivengrowth in the euro area, and second, oil prices fell substantially, affecting input costs.

The report highlights four major findings for inflation expectations in the euro area.First, not only has inflation been low but all measures of inflation expectations in theeuro area tended to over-predict inflation systemically after 2012. The one-year-aheadprojections from the European Commission (EC), the IMF, the OECD, the survey ofprofessional forecasters, the ECB/Eurosystem forecasts and others predicted for examplethat the average headline inflation rate for 2014 would fall between around 1.1 and 1.8per cent, but actual average HICP inflation turned out to be only 0.5 per cent. Themisalignment of the forecasts with actual inflation was especially worrying given thatHICP inflation excluding energy and food had already been low since early 2012.5 Thisalso raised the concern that agents observing how HICP inflation deviated persistentlyfrom its target would at some point become fixed in their expectations.

Second, the LIFT report documents how both survey-based and market-based mea-sures declined from early 2013 to early 2015, showing that inflation expectations werebelow the ECB target inflation rate. Market-based inflation expectations have beenfalling at various forecasting horizons, although less so than the survey-based forecasts.The LIFT report also analyses whether negative external factors such as falling commod-ity prices, the high euro exchange rate until 2014, or the unexpectedly long lags in thetransmission of new policy instruments contributed to the sluggish recovery of inflationexpectations. However, there is no strong evidence in favour of either theory.

Third, the results of the LIFT report for how far inflation expectations became de-anchored during the first two years of low inflation are inconclusive. The first signs of

2009. Economists have suggested a number of possible reasons for the missing disinflation. Coibion andGorodnichenko (2015) point out that for the US, the surge in oil and commodity prices between 2009and 2011, which was driven largely by continued growth in developing economies, had a sizeable impacton actual inflation and also boosted inflation expectations of households.

4Henriksen, Kydland and Sustek (2013) construct a model of cross-country spillovers based on aninteraction of total factor productivity spillovers and similar monetary policy rules. Whether this modelreflects the mechanism at play during the Great Recession is open to debate.

5HICP inflation excluding energy and food is a better predictor of the trend in headline inflationthan headline inflation itself is over the medium-term.

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de-anchoring started to appear after the oil price shock of mid 2014, which contributedto expectations of a prolonged slump in oil prices. Following the launch of the ECB’sasset purchase programme (APP) early in 2015, survey-based expectations started tostabilise, while market-based expectations continued to react strongly to developmentsin commodity prices. The report concludes that the announcement and subsequentimplementation of the APP supported the anchoring process, and that the credibility ofthe ECB inflation target was not impaired.

Finally, the LIFT report finds that the expectation-augmented Phillips curve stillprovides a reliable tool for tracking and forecasting developments in inflation in the euroarea. In euro area countries where there has been a lot of labour market slack, the slopeof the Phillips curve became steeper. This might indicate that the slope of the Phillipscurve is state-dependent, as the coefficient of real activity may depend on how longthe slack remains in the economy, how volatile inflation is, and how anchored inflationexpectations are. However, there is no conclusive evidence for whether the deep andlong-lasting slack in the economy or the effect of structural reforms drove the change inthe slope of the Phillips curve.

3 Data on euro area inflation expectations

In this paper we mainly use survey-based and market-based measures of inflationexpectations in the euro area for our quantitative assessment of the role of expectationsin the empirical Phillips curve models of Section 5. Below we describe these data sourcesand present a model-free description of the dynamics of inflation expectations in the euroarea over the last two decades, with a special focus on the global financial crisis of 2008and later developments.6

The following data sources are used to calculate euro area inflation expectations,which are subsequently used in the empirical Phillips curve models in Section 5 of thispaper:

• The ECB Survey of Professional Forecasters (SPF) is a quarterly dataset of expec-tations for the consumer price inflation rate, real GDP growth, and unemploymentin the euro area. In addition to these expectational data, the SPF also collectspoint forecasts for the annual growth in compensation per employee, the USD de-nominated oil price, the USD to EUR exchange rate, and the rates of the ECB mainrefinancing operations at different time horizons. The survey has been conductedregularly since 1999 and includes results from a panel of around 75 professionalforecasters. The SPF sample comprises a broad array of opinions, with around60% of the panel consisting of financial institutions and some 80% of the forecast-ers being based in the euro area. Additionally, the survey not only reports themean point expectations of the panel members, but it also includes the forecastdistributions as reported by the individual forecasters and across the entire panel,greatly enriching the information content of the survey;

• Consensus Economics publishes regular monthly surveys of worldwide economicactivity by broad geographical regions. On average about 30 forecasters regularly

6A brief description of the various sources of euro area expectational data can also be found in theLIFT report by Ciccarelli and Osbat (2017).

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contribute to the survey for the euro area, among them institutional forecasterssuch as Oxford Economics and the European Forecasting Network, and also privatecompanies such as Societe General, Goldman Sachs and Deutsche Bank. Quarterlyexpectations data are collected for the euro area on the real GDP growth, realpersonal consumption growth and consumer prices. These data are available from2003Q1 with a forecast horizon of up to eight quarters;

• MJEconomics is another source of regular monthly global economic surveys andforecasts. The survey results for the euro area are published in a monthly Euro-barometer report. The forecasters taking part in the survey include major finan-cial firms and independent institutions specialising in the euro area such as BBVA,BNP Paribas, and Commerzbank. Quarterly data on euro area expectations forreal GDP growth, real personal consumption growth, industrial production growth,consumer prices, and some key interest rates are available from 2003Q1 with a fore-cast horizon of up to eight quarters;

• In addition to these previously outlined sources of survey-based expectations, inthis paper we also employ Bloomberg market-based data on euro area inflationexpectations in this paper. It is well known that the pricing of many financial con-tracts is affected by the expectations of financial markets for forthcoming economicdevelopments, including future inflation rates. Sophisticated financial contracts likeinflation-linked derivatives offer a hedging instrument against future variations inthe inflation rate for parties that require stable and predictable money flows.7 Aside effect of observing the market prices of these inflation-linked derivatives, whichinclude inflation-linked swaps and bonds, is the potential to infer inflation expecta-tions directly from financial market data.This offers an alternative high-frequencyview of the inflation outlook in addition to the traditional survey-based measureswith quarterly frequency. In this paper we use market-based measures of inflationexpectations derived from daily inflation-linked swap prices with time horizons oneand two years ahead, and 1y1y-ahead, which is the anticipated one-year aheadinflation rate after one year.

Figure 1 plots the actual euro area inflation rate, calculated using year-on-year HICPgrowth rates excluding energy against the four measures of inflation expectations de-scribed previously, three of which are quarterly survey-based measures (SPF, Consensusand Eurobarometer), while the other is a daily market-based one (Bloomberg inflation-linked swaps).8

7An inflation-linked swap is a derivative contract between two parties in which they agree to swapa fixed payments stream for a variable payments stream tied to the contractual inflation rate, for agiven notional amount and for a specified period of time. In the euro area, the contractual inflationrate to which such contracts are tied is calculated using the HICP excluding tobacco which is publishedby Eurostat. The inflation-linked swap contracts are therefore indicative of the inflation rates expectedby financial markets over the contractual period. In contrast to expectations derived from break-eveninflation rates of the inflation-linked bonds, which are calculated as the spread between nominal andinflation-linked bond yields, inflation-linked swaps are less affected by time-varying liquidity effects andcountry-specific risk premiums. However, inflation-linked swaps are not fully immune to the influenceof time-varying risks, as one component of the risk premium in inflation-linked swaps reflects the uncer-tainties of the mean estimates of inflation rates by investors over the forecast horizon, while another isrelated to the information about inflation, which is what investors care about the most. For a detailedtechnical account of inflation-linked derivatives, see Kerkhof (2005).

8Note that the actual euro area inflation rate series in Figure 1 is time-shifted forward by one year

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EA inflation HICP excl. energy Y-o-Y annual rate (1Y LEAD)SPF HICP y-o-y inflation rate forecast 1 year ahead

Consensus y-o-y HICP inflation rate forecast 1 year ahead

Eurobarometer y-o-y HICP inflation rate forecast 1 year aheadBloomberg 1Y1Y expectation from inflation-linked swaps

Figure 1: Expectations for euro area inflation one year ahead from various data sources

During the two years before the global financial crisis from 2006 to 2007, none ofthe measures of inflation expectations anticipated the rapid pick-up in inflation that wasobserved before the crash in 2008Q3, and they only reacted to the elevated inflation ratesafter they had actually appeared. Likewise, none of the measures of inflation expectationsforesaw how steeply inflation would drop during the early episode of missing deflationstarting from 2008Q4 that coincided with the fall in real economic activity, and againthey only reacted ex post to events as the crisis unfolded.

The expected inflation rates in 2009 show that market-based sentiments initially ex-pected inflation to drop more steeply than it actually did, whereas survey-based measuresconsistently expected it to be higher than it actually proved. During the episode of miss-ing inflation from 2012 until the start of the APP in 2015, all expectational measuresconsistently missed how far prices would fall, as they continued to do so even duringan ongoing economic recovery. The comparison of the four different measures of infla-tion expectations in Figure 1 shows that the market-based expectations reacted morestrongly and much faster than the survey-based expectations did, often overshooting orundershooting them over extended time periods. This may reflect the timeliness of theday-to-day information available to financial markets from which these market-basedinflation expectations measures are derived, but it also may indicate the presence ofdistorting effects from time-varying market risks.

Figure 2 explores the relationship between the observed and expected inflation ratesusing distributional data available from the SPF. The top panel shows the one-yearahead point expectations for inflation in blue against the current headline inflation ratein red, while the bottom panel displays the probability distributions of forecasts of one-year ahead inflation rates running 2007Q1 to 2009Q4. Starting from 2008Q1, when the

relative to the measures of inflation expectations, which are plotted in the real time scale. Therefore,the actual inflation rates in this figure correspond to inflation rates that had come to pass a year laterthan the expected one-year ahead inflation rates in each moment of time.

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2007Q1 2007Q2 2007Q3 2007Q4 2008Q1 2008Q2 2008Q3 2008Q4 2009Q1 2009Q2 2009Q3 2009Q4

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Figure 2: Euro area one-year ahead SPF inflation expectations data in probability format

current inflation rate was running at close to 3.6%, forecasters were still expecting a meanyear-ahead inflation rate of 2% in 2009Q1, which was close to the official ECB policytarget. The bottom panel shows that forecasters were also quite certain about theirexpectations in 2008Q1 as they assigned the probability of 38% to the interval 2.0–2.4%inflation rate and another 36% to the interval 1.5–1.9% inflation rate in 2009Q1. Theremaining probability was allocated to the tails, with only a little more going to theupper part of the distribution.

One year later, in the early stages of the global financial crisis in 2009Q1, the headlineinflation rate stood at around 0.63%, far below the forecast from the previous yearof close to 2%. The mean one-year ahead inflation expectation in the top panel ofFigure 2 indicates that although the current inflation rate was approaching zero, the pointexpectation for inflation one-year ahead was still around 1.5%, reflecting the strength ofthe official ECB policy target in early 2009. However, there was also a pronounced changein the shape of the forecast probability distribution. The forecasters now only assigned27% probability to the middle part of the forecast probability distribution, where theinterval inflation rate is 1.5–1.9%, while much higher probabilities went to the tails,especially to the negative part of the forecast probability distribution. This indicatesthat the forecasters became more uncertain about the future path of inflation and thelikelihood of the ECB inflation target being achieved. This finding holds true duringsubsequent periods of low inflation as well. In general, we can say that when inflation ishigher or is close to the target, forecasters appear to be more certain about their futureexpectations and whether the mandate to meet the ECB target will be fulfilled. Whenactual inflation is far below the official target though, forecasters become more uncertainin their expectations of future price changes, which may potentially reflect doubts aboutthe ability of the ECB to hold inflation rates close to 2% in the medium term.

Our tentative conclusion from Figure 2 is that while the one-year ahead point expec-tations for inflation are relatively sluggish and show substantial inertia over time, evenduring the period of high stress from 2007Q1 to 2009Q4, the probability forecast distri-

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HICP y-o-y change: Inflation expectations: 1 year ahead 2 years ahead 5 years ahead

Figure 3: SPF Data on euro area inflation expectations at different time horizons Euroarea inflation expectations

butions exhibit a higher degree of flexibility and change significantly in response to theincreasing uncertainty about the future dynamics of prices and the ability of the ECBto stabilise inflation at the target rate over the medium-term horizon. This observationindicates the importance of taking distributional data into account in empirical modelsof inflation dynamics in the euro area.

Finally, Figure 3 displays the series of mean expectations for euro area inflation atdifferent forecasting horizons from the SPF dataset over the period 1999 to 2019.9 Thevariability of these data series follows a distinct pattern. At short forecasting horizonsbetween one and two years ahead, the forecasters observe the current state of the economyand adjust their expectations for short-term inflation rates accordingly, creating a volatilepattern that moves in sync with the business cycle.10 However, at the long horizon ofup to five years ahead, the mean inflation rate expected in the forecasts remains stablearound 2%, which is in line with the assumption that the ECB medium-term inflation

9The timing of this figure differs from that of Figure 1 in that the headline inflation rate is nowplotted on the real time scale, while the inflation expectations series correspond to the time points whenthe forecasts are supposed to play out, that is one, two and five years later than the real time scale.

10We do not formally assess whether forecasters just set their expectations in the short term to matchthe current inflation rates or whether they follow a Bayesian updating strategy by adjusting their beliefsabout future inflation every quarter when new information arrive There is some evidence that evenprofessional forecasters do not always update their short-run forecasts to reflect new or revised macroe-conomic data. Clements (2012) shows for the US Survey of Professional Forecasters that professionalforecasters do not always use updated or revised estimates of past data to form their new expectations.Andrade and Le Bihan (2013) arrive at a similar conclusion when testing the hypothesis for the ECBSurvey of Professional Forecasters. When new information is released, not all forecasters update theirforecasts and those who revise their estimates tend to disagree on their forecasts.

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rate would be anchored around the official ECB policy target. It is worth noting thatwhen inflation was lower than expected and there was a prolonged decline in inflationrates starting in 2012, the impact was felt by long-term inflation expectations. Firstas the upward trend was arrested in the inflation expectations for five years ahead thatlasted from early to 2000-s, and then long-term inflation projections moving below the2% target when the headline inflation dipped into negative territory at the end of 2014.This comes as a contrast to the short and sharp period of deflation in 2009, which didlittle to shift long-term inflation expectations for the euro area at the time.

The implication of Figure 3 for the empirical Phillips curve models of euro area in-flation dynamics that are built in Section 5 of this paper is that the series for inflationexpectations at different time horizons are likely to contain mutually complementaryindicators for the future path of inflation rates. We approach this issue from the sameperspective of data uncertainty that we do the alternative sources of expectational datadescribed earlier in this section, and we estimate multiple empirical Phillips curve re-lationships using inflation expectations series at different time horizons. Our empiricalresults are presented and interpreted across all the models estimated, not as a choice ofa single specification using a particular combination of the available data series.

4 Data and model uncertainty in econometrics

This section describes the econometric and statistical methodology behind the thickmodelling approach to the dynamics of euro area inflation used in Section 5 of this paper.We focus specifically on the econometric implications of data and model uncertainty, andthe range of available methodologies that have been designed for coping with these twointerrelated issues.

The nature of economics as a subject and the scientific processes it involves in econo-metrics and statistics have placed it at the forefront of thinking about the issues andimplications of data and model uncertainty. One early widely cited example is Leamer(1978) and his quest to ”robustify” econometric analysis by insisting on the systematicexploration of the modelling space through the processes of ”specification searches” and”extreme bounds analyses”. These two methodological innovations essentially aim toexplore and report systematically the inherent fragility of many empirical econometricfindings, where the fragility flows from twin uncertainties about the measurements andthe models used in any applied statistical study involving non-experimental data.11 Oneinfamous example of the potential dangers of glossing over these issues that was used byLeamer (1978) and subsequently popularised by many statisticians in social sciences andbeyond comes from economics and is the study of the deterrent effects of law enforcementon crime rates in the US by Ehrlich (1973); for details see Raftery (1995).

There has been progressively increasing interest since the early 1980-s in the statisticalliterature in a systematic discussion of the twin issues of data and model uncertainty,though professional statisticians have always been aware of these complexities. Hodges(1987) and the adjoining discussions provide a systematic treatment of wider statisticaluncertainty, with many references to previous studies, and an example of the real-worldstatistical decision-making processes used by the US Air Force. In this study, Hodges(1987) highlights three types of uncertainty in any realistic statistical context, which are

11Leamer (2010) reinforces these points after reflecting on the intervening 30 years of progress ineconometrics since the publication of the original book.

14

structural uncertainty, risk uncertainty, and technical uncertainty. Structural uncertaintyin his terminology corresponds to the multiplicity of potentially good models that can beused in real-world decision-making, while risk and technical uncertainties correspond tothe data collection, estimation and procedural types of hazard involved in any realisticdecision-making process. All three types of uncertainty need to be accounted for to givean end-measure of the wider statistical uncertainty that goes into the final decision-making process.

Departing from the very broad perspective of statistical uncertainty adopted byHodges (1987), Draper (1995) takes a narrower view of the uncertainty that can prac-tically be addressed in a statistical context, dividing it into structural uncertainty andparametric uncertainty. Let M = (S,θ) represent a statistical model that is, one amongthe set M of many alternative models, were S represents the assumed structure of M ,and θ stands for the parameters of a particular structural form of M . Then the twotypes of statistical uncertainty in Draper (1995) correspond to the potential choices ofM among the set of possible modelsM, and the usual statistical estimation uncertaintyabout θ for a given choice of M ∈M.Draper (1995) advocates the Bayesian solution toboth types of uncertainties, starting from the Bayes formula for assessing the posteriorprobability of M in view of the observed data X:

π(M |X) ∝ π(X |M) · π(M) ,

where the model prior is denoted by π(M), the marginal data density is π(X |M), andthe model posterior distribution is π(M |X); and thereafter using the same Bayes formulafor quantifying the usual estimation uncertainty about θ conditional on a given modelM :

π(θ |X,M) ∝ LM(θ; X) · π(θ |M) ,

where LM(θ; X) denotes the likelihood function for the statistical model M ∈M.12 TheBayesian solution provides the most elegant and conceptually consistent approach to theissues of data and model uncertainty in statistics, and is now used extensively adoptedin the literature on applied econometrics under the banner of Bayesian model averaging;see Steel (2019).13 14

Since the early 1990-s, and coinciding with the increase in the power and availability ofdigital computers, another school of statistical thinking had emerged that tackled manyof the same issues of uncertainty and complexity under the banner of algorithmic models,or what is now more popularly known as machine learning; see Breiman (2001) andAthey and Imbens (2019). Although not universally Bayesian, the literature on machinelearning addresses issues of statistical data and model uncertainty in a wide variety ofsurprisingly fresh and efficient ways. Breiman (2001) and the subsequent discussion

12In practice, the order of evaluation for these two formulae is reversed, so π(X |M) in the first onecorresponds to the normalising constant in the second, which needs to be evaluated before the firstformula is applied.

13Although Draper (1995) does not explicitly address the issue of data uncertainty in this context,Bayesian model averaging can easily deal with models based on different subsets of one full observeddataset.

14The probabilistic modelling approach, which is synonymous with Bayesian statistics, can also dealwith non-enumerable sets of models by means of Bayesian non-parametrics; see Grahramani (2013) fora high-level overview.

15

provide a good introduction to the sharply contrasting ways in which machine learningand mainstream statistics address the same issues. Statistics is based on the pervasiveuse of ready-made data models, while machine learning views any statistical problemas a closed box and works around it using computer algorithms based on predictiveperformance. Data and model complexities are very much at the centre of the machinelearning approach, as data complexity appears in the form of big data, while modelcomplexity takes the shape of an unknown true data generator inside the closed box andis addressed by a multitude of competing algorithmic models.

Another agnostic approach to the twin issues of data uncertainty and model uncer-tainty can be found in a recent paper by Lavine (2019) in the context of an on-goingdiscussion of statistical significance in theoretical and applied statistical research. Theauthor strongly advocates using a multitude of good models in statistical analysis toarrive at robust and sensible descriptions of the available data. He pointedly rejects thenotion of one true model that the traditional statistical methodologies, both frequentistand Bayesian, assume, because in practice it simply cannot be known what the truemodel may be, as the target population is often ill-defined, fuzzy and changing over timeand space, while the available data are collected in wildly imperfect ways. This raisesthe question of how then to proceed with statistical analysis. Lavine (2019) suggestsestimating a lot of good models rather than focusing on the one best model, using anyavailable estimation techniques and metrics of goodness of fit, and then investigatingthe common features of all these good models, by looking for the common subsets ofregressors across the linear regressions that best fit the available data for example.

The thick modelling perspective advocated by Granger and Jeon (2004) is close tothe spirit and methods of these unorthodox statistical approaches. They support the useof a large number of alternative models that may run on different data with differentestimation techniques, and they argue in favour of producing combined forecasts fromthe predictions of all the individual models, all of which are ideas that can be foundin the literature on machine learning, Bayesian model averaging, and the multiple goodmodels approach of Lavine (2019). In addition, Granger and Jeon (2004) also bring aunique economist’s perspective to the idea of the multiplicity of models and data byshowing how to interpret a thick model from the economic point of view.

In this paper, we follow the thick modelling methodology of Granger and Jeon (2004)in our empirical investigations of the dynamics of inflation in the euro area after in Sec-tion 5. This approach is well suited for our goals because we face the twin issues ofdata uncertainty and model uncertainty in our empirical analysis of inflation expecta-tions. Data uncertainty arises because there are so many alternative proxies for inflationexpectations in the euro area, as detailed in Section 3 of this paper, all of which aretreated a priori on an equal footing in our models in Section 5. On top of the alternativeproxies for inflation expectations, all the other data series in our empirical Phillips curvemodels are also viewed as uncertain measurements of the underlying economic conceptslike economic slack and exogenous cost-push shocks. Model uncertainty considerationsmeanwhile have previously been stressed in the literature and clearly manifest themselvesin the form of the many alternative formulations of the basic Phillips curve model, asdetailed by Mavroeidis et al. (2014) and in the references therein.15

15In addition, there is a clear need to consider the distributional characteristics of inflation expec-tations because we are dealing with uncertainties expressed in terms of probability distributions; seeFigure 2 in Section 3 and the discussion therein. Historically, only point expectations in the form ofmeans or medians have been used in the empirical Phillips curve models. Although today we have data

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SPACE

CLASS

FAMILY

SPECIFICATION

⇐= Universe of inflation models

⇐= Linear inflation models

⇐= Phillips curve family

⇐= Alternative data choices

Figure 4: Hierarchy of thick models with examples

On the issue of model uncertainty, there is a wide range of possible links in everytime period between inflation rates and the corresponding set of economic fundamen-tals, including inflation expectations. It is conceivable that this range is far richer andwider than the traditional linear expectations-augmented Phillips curve model knownfrom macroeconomics. This point is illustrated in Figure 4, where the universe of allconceivable linkages between inflation and its predictors sits at the top of the hierarchy.In many respects, it would be more expedient to tackle this vast universe using the closedbox approach of machine learning, and focusing solely on the predictive performance ofvarious flexible non-linear specifications estimated using a large set of data. The draw-back of this methodology lies in how difficult it can be to interpret the best predictivemodels obtained in this way, although Breiman (2001) insists that not all algorithmicmodels suffer from this disadvantage. At the other end of the spectrum, where the spacefor allowable inflation linkages is restricted in some specific manner, for example by con-centrating only on the linear Phillips curve family as shown in Figure 4, our empiricalinflation models retain the comfort of theoretical familiarity and interpretability. Al-though the machine learning approach is gaining popularity in the literature on appliedeconometrics, especially in pure forecasting contexts such as Ng (2014), we have chosenin this paper to restrict the range of specifications in our empirical analysis in Section 5to the family of theory-based linear Phillips curve models.

A step-by-step outline of our thick modelling estimation methodology used in Section5 of this paper is given below:

1. We select the set of N candidate specifications {M1, . . . ,MN} ⊂ M from the classM of linear regression models, using a priori restrictions to narrow down the fullspace of 2M potential linear models that could be attained using our full dataset.As discussed before, our first restriction on the modelling space encompasses therequirement of working with the theory-based linear Phillips curve family, whichmay include terms for lagged inflation, forward looking inflation expectations, eco-nomic slack, and exogenous cost-push shocks. More basic Phillips curve modelsthat may omit one or more of these four terms are also included in our analysis,starting from the most naive model containing only the constant term as its singleexplanatory variable. In addition, we impose a second restriction on the complex-ity of the upper modelling space by including at most one lag of any of the four

on the full probability distributions of the expected inflation rates over a range of time horizons into thefuture, there is a lack of suitable econometric approaches to make full use of these distributional datain empirical analysis of inflation.

17

terms for a given model in our analysis. Each of these four terms is representedin an individual specification Mn by a specific choice of data made from severalpossible alternatives available in our full dataset;

2. Each individual specification Mn in the set of N candidates is viewed as a linearregression model:

y[n] = X[n]β[n] + ε[n] for 1 ≤ n ≤ N ,

where both the dependent variable y[n] and the explanatory variables X[n] containthe specific data series to match the specification Mn, and where the column dimen-sion of X[n] varies from one (constant term) to five (constant plus one of each of thePhillips curve terms listed above) across the specifications in the set {M1, . . . ,MN}.The number of observations in y[n] and X[n] is restricted by the shortest availabledata series in the given Mn. For each of these individual linear regressions weobtain point coefficient estimates of β[n] using the usual least-squares algorithm.We do not impose any requirements on the signs of estimated coefficients nor ontheir p-values, and we retain all the estimated specifications for the evaluation ofthe conditional forecasting performance;

3. Finally, in order to analyse the role of inflation expectations in the dynamics of euroarea inflation, we rank all the estimated regressions in the set {M1, . . . ,MN} bytheir conditional pseudo out-of-sample forecasting performance as follows. For eachindividual Mn in the set {M1, . . . ,MN}, we obtain the least-squares estimate of β[n]

using a pre-set fraction of the full available sample period, and produce an inflationforecast for the remaining fraction of the sample period such that the values of allthe other conditioning variables apart from the inflation rate are assumed to beknown. We compare the root mean square errors (RMSEs) of these conditionalforecasts and rank the relative performance of different groups of models by thetype of expectational data they contain, including the group of models without anyforward-looking terms. Our conclusions are based on the relative improvements inforecasting performance obtained from using alternative types of expectational dataacross all the Phillips curves specifications estimated.

5 The role of expectations in euro area inflation dy-

namics

This section of the paper reports our main empirical findings on the role of expectationsfor developments in inflation in the euro area around the time of missing inflation in2012. Among the outcomes of the LIFT report summarised in Section 2 of this paperwas the continued insistence on the usefulness of the expectations-augmented Phillipscurve models for understanding the dynamics of euro area inflation. In this paper wecontinue to examine various aspects of these models to gain a better understanding ofeuro area inflation with a view to improving the policy advice.

As previously discussed in this paper and emphasised in the LIFT report, an area ofparticular policy concern is the role of inflation expectations and how they contributeto the overall dynamics of inflation in the euro area. Inflation expectations can bemeasured in a number of ways, often using very different methodologies. The strength of

18

the forward-looking terms in the empirical Phillips curve models can vary substantiallydepending on the particular expectational proxy used and other specification choices.This may matter for the dynamics of inflation in the euro area.

To provide a comprehensive answer to this important policy question, we use a novelmodelling strategy that allows us to explore quickly a very large set of empirical Phillipscurve models fitted to the data series for euro area inflation. This methodology wasalready used in Bundesbank (2016) and Ciccarelli and Osbat (2017), and in this analysiswe deploy it to examine the role of inflation expectations around the period of missinginflation 2012 and after the start of the APP in 2015.

As detailed in Section 4, we estimate a large number of empirical Phillips curvemodels, 2304 in total, that are specified in a thick model as follows:

{πt

}= c+ φ

{πt−1

}+ γ

{πet+1

}+ β

{xt−1

}+ θ

{δt−1

}+ εt , (1)

where πt denotes the rate of euro area consumer price inflation, πet+1 are various inflation

expectation proxies, xt represents a number of possible measures of economic slack forthe euro area economy, and δt denotes cost-push shocks selected from a menu of severalalternative exogenous price shock measures. All terms in the curly brackets on bothsides of equation (1) are allowed to vary across a number of alternative data choices,including the case where explanatory variables in the curly brackets on the right side ofthis regression may be fully omitted from a particular model specification.

Thus this thick modelling approach spans a large set of backward and forward-lookingPhillips curve models and includes a number of naive models that depend only on thedriving forces of different measures of slack and cost-push terms, including the mostprimitive Phillips curve model that has only the constant term c and the white noiseinnovations εt. Following the methodology of the LIFT report, we compute conditionalmultiple quarters ahead inflation rate forecasts for all these empirical Phillips curvemodels and compare these forecasts against the actual inflation rate paths in differentsub-samples as explained later in this section.16

For a detailed summary of our full dataset, including variable descriptions, sampleperiods and data sources, see Table A1 in the Appendix. An outline of all the alternativedata series used in this paper in our empirical Phillips curve models is given below:

• The inflation rate, πt,is measured using the annualised quarter-on-quarter changesof one of two alternative data series, either the harmonised index of consumer prices(HICP) excluding energy, or the HICP excluding energy food, alcohol and tobacco;

• The measure of inflation expectations, πet+1, is based on one of the following survey-

based proxies: 1-year and 2-year ahead, Consensus and Eurozone Barometer 1-quarter, 2-quarter, 3-quarter and 1-year ahead, EC measure of consumer infla-tion expectations, and a number of market-based measures derived from the zero-coupon inflation-linked swaps at the horizons of 1-year, 2-years and 1y1y ahead:

16Clearly all the Phillips curve models estimated in this paper are partial equilibrium models, wherethe measures of both economic slack and inflation expectations are taken as exogenous. However, ina fully structural general equilibrium modelling approach, measures of both inflation expectations andeconomic slack would be an integral part of the empirical model; see for example Chan, Clark and Koop(2018). One advantage of modelling expectations explicitly as part of a larger econometric model wouldbe reflected in more realistic policy advice based on alternative scenarios for how different policies affectinflation expectations and the actual path of the inflation rate.

19

• The measure of economic slack, xt, is selected from the real growth rate of out-put annualised quarter-on-quarter, two ECB measures of the real output gap, theunemployment rate, the unemployment gap, the unemployment recession gap, ameasure of labour underutilisation, the growth rate of unit labour costs annualisedquarter-on-quarter, two different measures of the EC output gap, and the IMFWorld Economic Outlook output gap17;

• The cost push term, δt, is represented by the annualised quarter-on-quarter growthrates of one oil prices in euros, the non-energy commodity price index, the agricul-tural price index, the nominal effective exchange rate based on the currencies ofmain 38 trading partners, and the index of import prices.

Before we present our main thick modelling analysis, we start from the traditionalempirical Phillips Curve model with forward-looking expectational terms that is widelyused by central banks around the globe for tracking and forecasting the dynamics of infla-tion. This familiar econometric workhorse model, estimated at the quarterly frequency,is given below:

πt = c+ φπt−1 + γ πet+1 + β xt−1 + θ δt−1 + εt ,

where the absence of curly brackets in this equation emphasises the specific choices ofdata series in this thin model in contrast to the thick model in equation (1). In thisexample we use the HICP inflation rates excluding energy πt, a one year ahead measureof inflation expectations from the SPF as πe

t+1, the unemployment rate as a measure ofeconomic slack xt, and the annualised quarter-on-quarter changes in the oil price as thecost-push shock δt. The coefficient estimates and other statistics of the two thin modelsestimated, one with the lagged inflation term and the other without it, are shown inTable 1.

Table 1: Two estimated thin Phillips curve modelsModel 1 Model 2

Estimate Std. Error p-value Estimate Std. Error p-value

Intercept (c) 0.7192 0.8486 0.3997 0.9196 0.8807 0.3000Lagged inflation term (φ) 0.3045 0.1151 0.0101 — — —Forward-looking term (γ) 0.8120 0.2819 0.0053 1.2019 0.2503 0.0000Slack measure (β) -0.0986 0.0585 0.0962 -0.1359 0.0591 0.0246Cost-push shock (θ) -0.0015 0.0010 0.1427 -0.0022 0.0010 0.0347

Adjusted R2: 0.5208 0.4797Log-likelihood: -50.8372 -53.8786No. of observations: 74 74

Notes: Least-squares point estimates, standard errors and p-values are shown. Dependent variable andthe lagged inflation term: HICP inflation rates excluding energy; forward-looking term: SPF one yearahead inflation expectations; economic slack measure: unemployment rate; cost-push shock: oil pricechanges. Sample period is from 1999Q2 to 2017Q4.

17One of the ECB’s measures of the real output gap and the unemployment gap are taken from theECB Spring 2018 projections dataset; the other ECB real output gap is based on the large-dimensionalfactor model of Lenza and Jarocinski (2018). The unemployment recession gap is based on Stockand Watson (2010). The measure of labour underutilisation takes in discouraged workers, marginallyattached labour market participants and underemployed part-time workers.

20

Figure 5: Conditional inflation projections based on Phillips curve models with differentexpectational data groups over the sample from 2013Q1 to 2017Q4

While our results in Table 1 offer a moderate degree of surprise in terms of theirestimates of the point coefficient estimates because of the counterintuitive sign of θ,they also illustrate the inherent fragility of thin models since the statistical uncertaintiesassociated with the strength of the estimated effects depend on the model specificationselected and the specific choices of data series. For example, the effects of economicslack and the cost push-shocks across two models in Table 1 remain unclear despite thesame data series being used in two both models for both of these explanatory variables.Furthermore, in the absence of a larger reference frame of competing models, we mayask how good these two models are in a relative sense and whether we can do better interms of the in-sample fit or some other relevant statistical criteria?

These and other issues are addressed by our main thick modelling results presentedin Table 2 for the full sample period available. The distributions of the point coefficientestimates across the Phillips curve models estimated in our thick modelling exercisereveal no surprises in the directions of the effects estimated, and their strength can beassessed from the upper and lower quantiles of the corresponding distributions. Theeffects of the cost push shocks on the inflation dynamics in the euro area appear to beweakly positive across all the model specifications estimated, which stands in contrastto the counterintuitive result in our thin model in Table 1. However, the size of theestimated φ and γ coefficients appears to be sensitive to the choice of the inflation rateseries, with considerably less persistence in the HICP inflation rates that exclude energy,food, alcohol and tobacco.

In addition, the distribution of in-sample fit criterion in the upper half of Table 2indicates that two of our thin models in Table 1 are relatively mediocre at describing

21

Table 2: Two estimated thick Phillips curve models25% quantile Mean Median 75% quantile

Model 1Intercept (c) 0.0989 0.4462 0.4725 0.7844Lagged inflation term (φ) 0.2385 0.3021 0.3056 0.3640Forward-looking term (γ) 0.4371 0.6684 0.5799 0.7866Slack measure (β) -0.1069 -0.0655 -0.0802 -0.0350Cost-push shock (θ) -0.0023 0.0017 0.0012 0.0077

Adjusted R2: 0.5284 0.5756 0.5954 0.6453Log-likelihood: -41.658 -32.988 -27.241 -23.821No. of observations: 56.000 60.007 58.000 66.500

Model 2Intercept (c) 0.4178 0.7718 0.7366 1.0149Lagged inflation term (φ) 0.0922 0.1704 0.1578 0.2452Forward-looking term (γ) 0.2527 0.4451 0.3524 0.5177Slack measure (β) -0.1041 -0.0678 -0.0834 -0.0211Cost-push shock (θ) -0.0006 0.0026 0.0007 0.0063

Adjusted R2: 0.3604 0.3919 0.3979 0.4334Log-likelihood: -36.218 -30.267 -25.632 -23.055No. of observations: 56.000 60.007 58.000 66.500

Notes: Means and quantiles of the least-squares point estimates and other statisticsare computed across 2304 specifications for each model shown in the table. Dependentvariable and lagged inflation term in Model 1 are given by HICP inflation rates ex-cluding energy, and in Model 2 by HICP inflation rates excluding energy, food, alcoholand tobacco. Other explanatory variables are described in Table A1. Sample period isfrom 1999Q2 to 2017Q4.

22

Figure 6: Conditional inflation projections based on Phillips curve models with differentexpectational data groups over the sample from 2015Q1 to 2017Q4

the dynamics of euro area inflation over the full sample period that is available from to1999Q2 to 2017Q4.

Our main results, however, are for the forecasting performance of our thick models,and particularly for how these forecasts depend on the type of expectational data used inthe models. Figures 5 and 6 illustrate how this type of conditional inflation forecastingtakes in the role of expectations for the euro area inflation dynamics after 2012. Inthese figures the actual yearly inflation rates for consumer prices in the euro area areplotted against the conditional forecasts from the models for all the 2304 Phillips curvespecifications estimated over two alternative pseudo out-of-sample forecasting periods,one from 2013Q1 to 2017Q4, and one from 2015Q1 to 2017Q4. The forecasts frommodels with four alternative groups of expectational data are shown in four differentcolours, with yellow for models without any forward-looking expectational terms, greyfor models based on SPF inflation expectations, green for models that use Consensusand Eurozone Barometer survey-based measures, and blue for models based on inflationexpectations found from financial markets.

In all cases the models without any forward-looking expectational terms produceconditional inflation forecasts that are uniformly inferior to those of the expectations-augmented empirical Phillips curve models, for both the sample prior to the start ofAPP in Figure 5 and the sample which includes the start of the APP in Figure 6. Thisfinding testifies to the importance of expectations in explaining the recent dynamics ofinflation rates in the euro area and shows that the persistence of inflation alone cannotsatisfactorily explain recent developments in inflation, even when it is combined with theslack and cost push terms.

23

Table 3: Median RMSEs of two thick Phillips curve models by expectational data groupsModel 1 Model 2

2012Q1 2013Q1 2015Q1 2012Q1 2013Q1 2015Q1

Group A: 0.4460 0.5178 0.3694 0.4140 0.4864 0.3532Group B: 0.2831 0.2868 0.2564 0.2647 0.2593 0.1782Group C: 0.2350 0.2376 0.1819 0.3076 0.3393 0.1862Group D: 0.3353 0.2447 0.2527 0.2403 0.2682 0.1345

Notes: Median RMSEs of conditional forecasts by four expectational datagroups:

A: without expectational termsB: SPF expectationsC: Consensus and Eurozone Barometer expectationsD: market-based expectations

Models 1 and 2 are described in Table 2. Conditional pseudo out-of-sampleforecasting periods start from the dates indicated and end in 2017Q4.

Another important finding from these conditional forecasting exercises is the differentinformational content of the alternative proxies for inflation expectations in our thickmodels. The inflation expectations based on financial markets that are used in theestimation sample prior to the APP, and to a lesser extent after the start APP in thesecond quarter of 2015, appear to provide a somewhat more accurate outlook for thefuture paths of inflation than the survey-based expectations do. The formal criteriaused to assess the goodness of the conditional forecasts show the expectations basedon financial markets and the consensus and Eurobarometer measures to be closely tiedfor the best forecasting performance, as shown in Table 3, with expectations laggingbehind.18 Note that in addition to the two forecasting periods described previously,Table 3 also includes a longer conditional pseudo out-of-sample forecasting period from2012Q1 to 2017Q4, which corresponds to the start of missing inflation episode in theeuro area.

One plausible explanation for this finding might lie in the up-to-date nature of fi-nancial markets, which absorb and process new information on a daily basis, whereasthe survey-based measures typically represent a static inflation outlook from variousinstitutions in a particular week at the start of each quarter.

After the start of APP in the second quarter of 2015, all proxies for inflation ex-pectations foresaw the inflation rate in the euro area gradually taking off after that,as shown in Figure 6. This attests to how effective the ECB communication strategywas over this period. However, the measures of inflation expectations based on financialmarkets appear to be more conservative in their outlooks for future inflation than thesurvey-based measures are. Because the nature of these systematic differences across theclasses of proxies of inflation expectations is not yet fully understood, and given theirperformance across three different forecasting periods in Table 3, careful surveillance ofthe outlooks for euro area inflation found from financial markets should be advised. Aswas also underlined in the LIFT report, the financial market-based measures of inflationexpectations may contain time-varying inflation risk premiums, which have most prob-ably turned negative over the past few years, resulting in a possible downward bias inthe RMSE results. This suggests a degree of caution is needed when these market-based

18The average RMSE of the financial market-based group of inflation expectations across the twomodels and six forecasting periods in Table 3 is 0.2460, while for the Consensus and Eurobarometermeasures it is 0.2479 and for SPF expectations it is 0.2548.

24

measures are used for monetary policy decisions.

6 Conclusion

In this paper, we take a fresh look at the use of the Phillips curve model in combinationwith various proxies for inflation expectations for tracking the dynamics of inflation inthe euro area in the aftermath of the global financial crisis of 2008. Because inflationexpectations can be measured in multiple alternative ways and there are many possiblespecifications to choose for the Phillips curve model, this paper employs the relativelynovel thick modelling perspective of Granger and Jeon (2004) that allows a certain degreeof data and model agnosticism in our empirical estimations. Specifically, we estimate alarge number of Phillips curve models, including a set of naive ones that are based onlyon the driving forces of the various available measures of slack and cost-push shocks, andwe use different data series for the different components of our models.

We find that euro area inflation expectations do appear to have a role as a keypredictor of future inflation rates in our empirical Phillips curve models during the periodof missing inflation after 2012. However, different expectation measures vary in theirpredicting ability, with those based on financial markets usually coming out on topof the other proxies of inflation expectations. This result probably arises because theexpectations of financial markets are by their nature much more up to date than thetraditional survey-based measures, which are usually only collected once per quarter.Since the start of the APP the programme in 2015, the role of inflation expectationmeasures appears to have strengthened even more.

The policy implications of our findings support the central role of the ECB in steeringinflation expectations in the economic environment after the global financial crisis. Thisrole will be even more important in a forward monetary policy guidance regime giventhe exit from non-standard monetary policy in the euro area in the coming years. Howthe end of the non-standard policy will affect various measures of expectations, includingmeasures of inflation expectations, has to be monitored closely and carefully assessed.Our findings imply that measures based on financial markets need to receive especiallycareful attention in this regime.

A few research issues still remain open and they could be addressed more carefully inthe future. The distributional aspects of inflation expectations have not yet been takeninto account; a new econometric methodology has to be invented to make this possible;model uncertainty is currently addressed only to a limited degree, using thick modellingover the limited space of Phillips curve models that are founded in theory; and finally,we need to think how high-frequency financial data can be used directly in our quarterlyinflation models.

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Table A1: Data AppendixVariable Sample period Obs. Data source

InflationHICP excluding energy (ann. Q-o-Q rate) 1999Q1–2017Q4 76 EurostatHICP excluding energy, food, alcoholand tobacco (ann. Q-o-Q rate)

1999Q1–2017Q4 76 Eurostat

Inflation expectationsSPF inflation expectations one year ahead 1999Q1–2017Q4 76 SDWSPF inflation expectations two years ahead 1999Q1–2017Q4 76 SDWConsensus Economics inflation expectationsone quarter ahead

2003Q1–2017Q4 60 Concensus

Consensus Economics inflation expectationstwo quarters ahead

2003Q1–2017Q4 60 Concensus

Consensus Economics inflation expectationsthree quarters ahead

2003Q1–2017Q4 60 Concensus

Consensus Economics inflation expectationsone year ahead

2003Q1–2017Q4 60 Concensus

Eurozone Barometer inflation expectationsone quarter ahead

2003Q1–2017Q4 60 Eurobarometer

Eurozone Barometer inflation expectationstwo quarters ahead

2003Q1–2017Q4 60 Eurobarometer

Eurozone Barometer inflation expectationsthree quarters ahead

2003Q1–2017Q4 60 Eurobarometer

Eurozone Barometer inflation expectationsone year ahead

2003Q1–2017Q4 60 Eurobarometer

Bloomberg 1y1y ILS inflation expectations 2004Q2–2017Q4 55 BloombergECB 1y1y ILS inflation expectations 2005Q2–2017Q4 51 ECBECB 1y ILS inflation expectations 2005Q2–2017Q4 51 ECBECB 2y ILS inflation expectations 2005Q2–2017Q4 51 ECBEuro area consumer inflation expectations 1999Q1–2017Q4 76 AMECO

29

Table A1: Data Appendix (cont.)Variable Sample period Obs. Data source

Economic slack measuresEuro area real grossdomestic product (ann. Q-o-Q rate)

1999Q1–2017Q4 76 Eurostat

ECB euro area output gap 1999Q1–2017Q4 76 ECBEC euro area gap between actual and potential 1999Q1–2017Q4 76 AMECOEC euro area gap between actual and trend 1999Q1–2017Q4 76 AMECOIMF euro area output gap 1999Q1–2017Q4 76 IMFLenza and Jarocinski (2018) euro area output gap 1999Q1–2017Q4 76 ECBEuro area unit labour costsindex (ann. Q-o-Q rate)

1999Q1–2017Q4 76 SDW

Euro area unemployment rate 1999Q1–2017Q4 76 SDWEuro area labour underutilisation measure 1999Q1–2017Q4 76 ECBGap between euro area unemployment rateand NAIRU

1999Q1–2017Q4 76 ECB

Stock and Watson (2010) euro areaunemployment recession gap

1999Q1–2017Q4 76 Authors

Cost push shocksOil price in euros (ann. Q-o-Q rate) 1999Q1–2017Q4 76 SDWEuro area nominal effectiveexchange rate (ann. Q-o-Q rate)

1999Q1–2017Q4 76 SDW

Non–energy commoditiesprice index (ann. Q-o-Q rate)

1999Q1–2017Q4 76 SDW

Agricultural commoditiesprice index (ann. Q-o-Q rate)

1999Q1–2017Q4 76 AMECO

Euro area imports of goods and servicesprice index (ann. Q-o-Q rate)

1999Q1–2017Q4 76 SDW

Notes: The data series described in the table originate from the following data sources:

• Eurostat: Statistical Office of the European Union• SDW: ECB Statistical Data Warehouse• Consensus: Consensus Economics consultancy company• Eurobarometer: MJEconomics consultancy company• Bloomberg: Bloomberg financial data• AMECO: European Commission macroeconomic database• IMF: IMF World Economic Outlook data• ECB: ECB internal projections dataset and other ECB confidential data• authors’ own calculations

30

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