Oil price pass-through into core inflation

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Oil price pass-through into core inflation Cristina Conflitti and Matteo Luciani 2017-085 Please cite this paper as: Conflitti, Cristina and Matteo Luciani (2017). “Oil price pass-through into core inflation,” FinanceandEconomicsDiscussionSeries2017-085. Washington: BoardofGovernorsofthe Federal Reserve System, https://doi.org/10.17016/FEDS.2017.085. NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

Oil price pass-through into core inflation∗ Cristina Conflitti Matteo Luciani Banca d’Italia Federal Reserve Board cristina.conflitti@bancaditalia.it matteo.luciani@frb.gov August 2, 2017 Abstract Weestimatetheoilpricepass-throughintoconsumerpricesbothintheUSandinthe euro area. In particular, we disentangle the specific effect that an oil price change might haveoneachdisaggregateprice,fromtheeffectonallpricesthatanoilpricechangemight have since it affects the whole economy. To do so, we first estimate a Dynamic Factor Modelonapanelofdisaggregatepriceindicators, andthenweuseVARtechniquestoestimatethepass-through. Ourresultsshowthattheoilpricepassesthroughcoreinflation only via its effect on the whole economy. This pass-through is estimated to be small, but statistically different from zero and long lasting. JEL classification: C32, E31, E32, Q43. Keywords: Core inflation, oil price, dynamic factor model, pass-through, disaggregate consumer prices. ∗We would like to thank Stephanie Aaronson, Riccardo Cristadoro, Kirstin Hubirch, Stefano Neri, Jeremy Rudd, Stefano Siviero, Fabrizio Venditti, and Giovanni Veronese for useful comments on earlier drafts of the paper. Any errors are our responsibility. Disclaimer: theviewsexpressedinthispaperarethoseoftheauthorsanddonotnecessarilyreflecttheviews and policies of the Banca d’Italia or the Eurosystem, and of the Board of Governors or the Federal Reserve System.

1 Introduction Quantifyingthemagnitudeandestablishingthetimingofthepass-throughofoilpricechanges to consumer prices is crucial for forecasting inflation. Characterizing this pass-through is particularly important because oil prices tend to undergo wide fluctuations. Consider the recent plunge of oil prices from July 2014 to February 2016, from about $100 per barrel to $30. What is the effect of such a large swing in oil prices on core inflation? And how long will this effect last? In this paper, by using a novel econometric approach, we answer these questions and we conclude that oil price fluctuations have a limited but long lasting effect on core inflation. According to our estimates the recent plunge in oil prices shaved-off just a couple of tenths of a percentage point to core inflation in both the US and the euro area, but this effect is far from being fully absorbed as it will vanish by 2020. Oilpricefluctuationsaffectconsumerinflationthroughbothitsenergycomponentandthe non-energy components. However, while there is clear evidence that the pass-through from oil prices to energy prices is relatively fast and complete (Burdette and Zyren, 2003; Meyler, 2009), though it is still to be determined whether it is symmetric or not (Venditti, 2013; Atil et al., 2014; Chesnes, 2016), it is unclear to what degree changes in oil prices pass-through into non-energy prices (Kilian and Lewis, 2011; Kilian, 2014). In theory, an increase in oil prices might have an inflationary effect in at least four ways. First, because energy prices represent a portion (sometimes considerable) of production costs. Second, because it might lead to higher inflation expectations. Third, because it might lead workers to demand a higher wage to compensate for the increase in energy prices (Blanchard and Gali, 2007). And fourth, because it might mimic an adverse supply shock if real wages do not decrease sufficiently thus triggering an adjustment in employment (Bruno and Sachs, 1985). Bycontrast,anincreaseinoilpricesmighthaveadeflationaryeffectinthesamefashion asanadversedemandshockbecausehigherenergypricestendtoreducenet-disposableincome, and thus consumption (Edelstein and Kilian, 2009) and investments (Edelstein and Kilian, 2007). Empirically, despiteextensiveevidencethatchangesintheoilpricescontributetomacroeconomicfluctuations(seeHamilton,1983,2003;Hooker,1996;BarskyandKilian,2002;Kilian, 2008, among others), various authors have shown that the pass-through of oil price changes to core prices has declined since the mid-eighties (see Hooker, 2002; Chen, 2009; Clark and Terry, 2010, among others) up to the point that it is very limited if not zero (for example Cavallo, 2008; Clark and Terry, 2010). Inthispaperweuseanovelmethodologicalapproachtoestimatetheoilpricepass-through into core consumer prices. We first estimate a dynamic factor model on a panel of disaggregate prices, which allows us to disentangle common changes in disaggregate prices due to macroeconomic fluctuations from idiosyncratic changes due to sector specific characteristics. We next use VAR techniques to estimate the oil price pass-through via the common component, as well as via the idiosyncratic component. Both these pass-through are likely to be important. Indeed, given that they contribute to macroeconomic fluctuations, changes in the oil price might pass-through into core inflation via the common/macroeconomic component. At the same time, given that sectors differ in their use of energy as an input in production or 2

in their competitive structure, changes in the oil price might pass-through into core inflation via some idiosyncratic component. Our empirical analysis is carried out on a panel of US personal consumption expenditure (PCE) disaggregate price indexes from 1984 to 2016. We show that common and idiosyncratic dynamics in disaggregate prices have different statistical properties: common dynamics are slow moving, idiosyncratic dynamics fast moving and volatile. Disentangling these two components proved crucial when estimating the oil price pass-through into core inflation, as the estimated pass-through into the idiosyncratic component is not statistically different from zero, whereas the pass-through via the common component is small, but statistically different from zero, and long lasting. The subsample analysis confirms the result in the literature whereby the oil price pass– through into core inflation has decreased over time. However, in contrast with part of this literature(forexampleClarkandTerry,2010)wealwaysfindapositiveandstatisticallysignificant pass-through—the reason being that we disentangle between common and idiosyncratic components, thus not letting the noisy idiosyncratic component affect our estimation results. Finally, we estimate the oil price pass-through on a panel of euro area harmonized index of consumer prices (HICP) at a disaggregate level. This estimate yields a euro area pass-through similar to that of the US. Other papers have used dynamic factor models to study the effects of oil price fluctuations ontheeconomy,butnonehavefocusedonthepass-throughintoconsumerprices. Forexample, Aastveit (2014), Aastveit et al. (2015), Juvenal and Petrella (2015), and Stock and Watson (2016) study the effects of different structural oil price shocks on the economy, while An et al. (2014) study whether oil price shocks have asymmetric effects on the economy. Moreover, other papers have used dynamic factor models to analyze disaggregate prices (Cristadoro et al., 2005; Altissimo et al., 2009; Boivin et al., 2009; Reis and Watson, 2010, among others), butnonehaveusedthesemodelstostudytheoilpricepass-through. Finally, Gaoetal.(2014) studytheeffectofoilpriceshocksonanumberofdisaggregateUSconsumerpricesusingVAR techniques; they find a significant effect only on the price of energy-intensive goods but do not distinguish between macroeconomic and idiosyncratic effects. The rest of the paper proceeds as follows. Section 2 presents the methodology. Section 3 presents the empirical analysis on the US, namely: Section 3.1 describes the data used, and Section 3.2 discusses common and idiosyncratic dynamics in US PCE prices. Then, Section 3.3 presents estimates of the oil price pass-through, Section 3.4 presents subsample analysis, and Section 3.5 presents estimates obtained with a more structural model. Finally, Section 4 presents the empirical analysis on the euro area, and Section 5 briefly summarizes the results. 2 The econometric framework The goal of this paper is to quantify the effect of oil price changes on core, energy, and food price inflation. More precisely, we aim to disentangle the specific (idiosyncratic) effect that an oil price change might have on each disaggregate price, from its overall (common) effect that an oil price change has on all prices. To do so, we first estimate a dynamic factor model 3

on a panel of price indicators to separate common from idiosyncratic price changes, and then use VAR techniques to estimate the pass-through. Factor models are based on the idea that fluctuations in disaggregate prices are due to a few common (macroeconomic) shocks (u ) that affect all prices, and to several idiosyncratic t shocks(e ),resultingfromsector-specificdynamicsorfromsamplingerror,whichinfluenceone t or a few of them. Accordingly, each price component in the dataset can be decomposed into a common part χ , which is a linear combination of a small number r of common factors f that it t are driven by the common shocks, and an idiosyncratic part ξ that is driven by idiosyncratic it shocks. Let π = 1200×log( Pit ) be the annualized month-on-month log-change in the i-th it Pit−1 price component at time t, where i = 1,....,n and t = 1,....,T, we then have π = λ(cid:48)f +ξ (1) it i t it where λ is a r×1 vector containing the factor loadings of the i-th variable, and χ = λ(cid:48)f . i it i t Model (1) is the approximate dynamic factor model proposed by Stock and Watson (2002a,b), which is a particular case of the generalized dynamic factor model studied by Forni et al. (2000) and Forni and Lippi (2001). Itiswelldocumentedthatchangesintheoilpricecontributetomacroeconomicfluctuations (seeHamilton,1983,2003;Hooker,1996;BarskyandKilian,2002;Kilian,2008,amongothers), thus they are likely to have a macroeconomic effect on all prices. To incorporate this feature in our model, we assume that the common factors and the oil price evolve over time according to a VAR model. Let y = ∆log( oilt ) be the monthly real oil price growth rate, then we t pricet have (cid:32) (cid:33) (cid:32) (cid:33) f u t t A(L) = (2) y v t t where v is “the oil price shock”.1 t At the same time, given that sectors are more or less energy intensive so that energy costs represent a larger or smaller share of total costs, a change in the oil price might have a very different effect on disaggregate prices depending on how energy intensive is the production of each single item. This points at the possibility of idiosyncratic effects of oil price changes on each price component, and therefore we assume that the oil price and each idiosyncratic component evolve over time according to a bivariate VAR: (cid:32) (cid:33) (cid:32) (cid:33) ξ e it it B (L) = (3) i y v t t Bycomparing (2)and(3)wecanseethatthereisaconflictbetweenthesetwoequationsin 1Our model is very similar to a standard FAVAR model (Bernanke et al., 2005), which in its turn is a restrictedversionofthestructuraldynamicfactormodelfirstintroducedbyGiannoneetal.(2005),Stockand Watson(2005),andFornietal.(2009). InaFAVARmodeltheoilpriceistreatedasanobservedfactor,which means that the oil price is part of the common space only, while not having any effects on the idiosyncratic component. In formulas, equation (1) is replaced by π = λ(cid:48)f +γ y +ξ , while (2) stays the same and it i t i t it the idiosyncratic component is not modelled. As a robustness check, in Appendix B we show the estimated pass-through when a FAVAR model is used. 4

thatthechangesintheoilpricesarespecifiedintwodifferentways,namely:2 y = a (L)y + t 22 t−1 a (L)f +v from (2), and y = b (L)y +b (L)ξ +v , for i = 1,...,n, from (3). 21 t−1 t t i22 t−1 i21 it−1 t It is therefore clear that, in order for (2) and (3) to simultaneously hold, restrictions on A(L) and B (L) must be imposed. It turns out that the only possible restriction is to impose that i a (L) = 0 and b (L) = 0,3 so that: 21 i21 (cid:32) (cid:33) (cid:32) (cid:33) I−a (L) −a (L) 1−b (L) −b (L) 11 12 i11 i12 A(L) = and B (L) = i 0 1−a (L) 0 1−b (L) 22 i22 with a (L) = b (L), which yields 22 i22 y = a (L)y +v . (4) t 22 t−1 t Equation(4)clarifiestwothings: firstinourframeworktheoilpriceisexogenouslydetermined, that is it is not caused by US or euro area economy. In the literature, oil price shocks are often identified by assuming that energy prices are predetermined with respect to the US/EA economy at monthly frequency (for a thorough discussion of this identification strategy see Kilian and Vega, 2011), which in practice means using a Choleski decomposition with the oil price ordered first (for example Gao et al., 2014; Stock and Watson, 2016). The restriction in (4) is in the same spirit, though stronger, as we are imposing that the oil price is exogenous, rather than predetermined, to US/EA prices. Second, “the oil price shock” v is nothing else than a residual from an AR model, and as t such it has no structural interpretation, that is we do not disentangle between oil supply and oil demand shocks (a non exhaustive list of papers that do so is: Barsky and Kilian, 2002, 2012; Kilian, 2009; Lippi and Nobili, 2012; Baumeister and Peersman, 2013). Undertheassumptionthatallthecomponentsofπ arestationary,thecommonfactors,the t factor loadings, and the idiosyncratic components can be estimated by principal components (Stock and Watson, 2002a; Bai, 2003).4 Once the factors and the idiosyncratic components are estimated, the VAR in (2) and the n VARs in (3) can be estimated by OLS simply by replacing f and ξ with their principal components estimates, with the estimated parameters t it √ √ converging at the standard rate min( N, T) (Forni et al., 2009). Once A(L) and B (L) are estimated, by defining C(L) = A(L)−1 and D (L) = B (L)−1, i i i 2In what follows we use the notation according to which A(L)=I−A L−A L2−...A Lp =I−A(L), 1 2 p where A(L) is conveniently partitioned in four polynomials a (L), a (L), a (L), and a (L) of dimensions 11 12 21 22 r×r,r×1,1×r,and1×1,respectively. ThesamenotationisusedforB(L). Furthermore,letC(L)=A(L)−1 be the MA representation of (2), then we use the notation C(L) = I+C L−C L2+...=I+C(L), where 1 2 C(L)isconvenientlypartitionedinfourpolynomialsc (L),c (L),c (L),andc (L). Thesamenotationis 11 12 21 22 used for D(L)=B(L)−1. 3While from a theoretical point of view imposing this restriction is necessary, from an empirical point of view it is nearly irrelevant. Indeed, the estimated pass-through obtained without imposing this restriction is essentially the same as that reported in Section 3 and 4. 4Estimation of the factors when the data are I(1) is examined by Bai (2004), Bai and Ng (2004), and Barigozzi et al. (2016). Estimation of impulse response functions for non stationary dynamic factor models is considered in Barigozzi et al. (2016). 5

where (cid:32) (cid:33) (cid:32) (cid:33) I+c (L) c (L) 1+d (L) d (L) 11 12 i11 i12 C(L) = , and D (L) = , i 0 1+c (L) 0 1+d (L) 22 i22 and by substituting (2) and (3) in (1) we get π = (λ c (L)+d (L))v +λ c (L)u +(1+d (L))e it i 12 i12 t i 11 t i11 it = ψχ(L)v +ψξ(L)v +φ (L)u +θ (L)e (5) i t i t i t i it whereψχ(L)andψξ(L)measure,respectively,thecommon andtheidiosyncratic pass-through i i of an unexpected and unpredictable change in the real oil price to the inflation rate of price i. Having computed the oil price pass-through into each disaggregate price, we can construct the pass-through into core price inflation as: ψ (L) = (cid:88) w ψχ(L)+ (cid:88) w ψξ(L) = ψχ(L)+ψξ(L) c i i i i c c i∈core i∈core and likewise for energy price inflation and food price inflation simply by selecting the appropriate prices and weights. 3 Oil price pass-through into inflation in the US 3.1 Data The price data for the US are monthly price indexes for personal consumption expenditures (PCE) by type of product. The data are taken from the NIPA Table 2.4.4U from the Bureau of Economic Analysis and downloaded from Haver. Price data are available at different levels of disaggregation, the finest of which includes more than 200 price indexes (see Dolmas, 2005, for further details). However, for the purpose of our analysis 200+ series correspond to an unnecessary high level of detail, and, therefore, we chose a lower level of aggregation comprising 88 price indexes (the complete list of series is available in Appendix A). In this dataset 65% of the price indexes have a weight smaller than 1 , and just 16% of them have a weight larger than 2 . 100 100 To estimate the pass-through into the aggregates for core, energy, and food inflation we compute PCE weights as (see Dolmas, 2005, for details): Q P Q P it it i,t+1 it w = 0.5 +0.5 , (6) i,t+1 (cid:80) (cid:80) Q P Q P it it i,t+1 it in which data for Q are taken from the NIPA Table 2.4.6U. In other words, the weights for it the i-th item in, say, June 2016 is equal to an average of the expenditure share of that item in May 2016 and its expenditure share had it been bought in June 2016 at May 2016 prices. However, although PCE weights change every month, for the purpose of estimation of the oil 6

price pass-through into core, energy, and food price inflation we need just one set of weights, and we choose to pick the last one available, which are the weights for June 2016. Finally, the oil price is measured by the West Texas Intermediate (WTI) spot crude oil price, which is deflated by the core PCE price index.5 The data for WTI are from the US Energy Information Administration and the Chicago Mercantile Exchange and they were downloaded from Haver (PZTEXP@USECON), while the core PCE price index is from the NIPA table (ID 368, Name DPCCRX). 3.2 Common and idiosyncratic dynamics in PCE prices InthisSectionwelookatcommonandidiosyncraticdynamicsinPCEpriceswiththeultimate goal of selecting the number of common factors, r, to be included in our model. The results are obtained on a sample starting in 1984:M1 and ending in 2016:M6 (see Section 3.3 for a discussion on the choice of the sample). Table 1 shows the percentage of overall variance explained by the first ten factors. The first factor explains a good chunk (8%) of the total variability in the dataset, while the other factors explain just a residual fraction of it. Thus, the numbers in Table 1 provide strong evidence pointing towards the existence of one common factor, but it is unclear if additional factors are needed. Table 1: Common dynamics in PCE prices r 1 2 3 4 5 6 7 8 9 10 µ 7.9 4.3 3.2 3.0 2.7 2.5 2.4 2.2 2.1 2.0 t Notes: µt isthepercentagesoftotalvarianceexplainedbythefirstr factors. Figure 1 shows the percentage of variance of each variable explained by the first four factors, where we have divided the disaggregate prices into four plots each of which represents a different category. If we look at food and energy, which we expect to be driven to a great extent by sectoral factors, such as weather in the case of food and various supply shocks in the case of energy, we see that the second and the fourth factor have good explanatory power thus suggesting that they capture mainly idiosyncratic food/energy related fluctuations. If we look at “Core Goods” prices“, Core Services I” prices, and “Core Services II” (market-based) prices, thesecond, thethird, andthefourthfactorhaveaverylowexplanatorypowersuggestingthat one factor suffices for these categories. The results in Table 1 and Figure 1 point out that, independently of the number of factors included in the model, idiosyncratic dynamics are the main driver of changes in disaggregate PCE prices (see also Boivin et al., 2009; Reis and Watson, 2010). However, although idiosyncratic dynamics dominate disaggregated prices’ fluctuation, they do not dominate the evolutionoftheaggregatecoreindex. Indeed,inamodelwithonecommonfactor,thecommon 5Blanchard and Gali (2007) argue that some of the oil price changes are extremely large and thus might bias the estimation of the oil price equation. We checked this issue by running on the real oil price growth rate the same procedure to remove outliers that we run on disaggregate prices (see Appendix A for details), and we found just one outlier in 1974:M1. Removing that outlier does not change any of the results shown in the paper. 7

Figure 1: Common dynamics in PCE prices Food (left) & Energy (right) Core Goods 80 80 r=1 r=2 70 r=3 70 r=4 60 60 50 50 40 40 30 30 20 20 10 10 0 0 Core Services I − Market Based Core Services II − Market based (left), non−market based (right) 80 80 70 70 60 60 50 50 40 40 30 30 20 20 10 10 0 0 Notes: This figure shows the percentage of variance (y-axis) of each variable (x-axis) explained by the first four factors. Each bar represent a different disaggregate price. Core Services I includes: “Housing and utilities”, “Healthcare”,“Transportationservices”,“Recreationservices”,“Foodservicesandaccommodations”. CoreServices IIincludes: “Financialservicesandinsurance”,“Otherservices”,and“FinalconsumptionexpendituresofNPISHs”. component accounts for 57% of core PCE fluctuation. Furthermore, the stochastic properties of the common and idiosyncratic components are different: the former are very persistent, whilethelattertendtohaveveryshortmemory(seeTable2). Notethattheselasttworesults are in line with the theoretical results in Zaffaroni (2004). Zaffaroni (2004) shows that, as the number of variables gets large, the aggregation of univariate heterogeneous ARMA processes driven by a common and an idiosyncratic shock yields a time series that (1) is more persistent than the disaggregate series, and (2) is mainly driven by the common shock; by contrast the disaggregated series are mainly driven by the idiosyncratic shocks (see also Granger, 1980). For empirical results similar to ours, see Clark (2006) and Maćkowiak et al. (2009) for the U.S., and Altissimo et al. (2009) and Beck et al. (2016) for the euro area. In summary, there is strong evidence indicating that PCE prices admit a factor representation, but there is high uncertainty on the number of factors to be included in the model. Furthermore, this uncertainty is not resolved even by resorting to more formal criteria, such as, for example, the Bai and Ng (2002) information criteria that support the choice of up to three common factors. 8

Table 2: Persistence of common and idiosyncratic dynamics ρ ρ ρ 1 6 12 ρξ(50) 0.12 0.07 0.06 j ρξ(75) 0.22 0.12 0.12 j ρξ(90) 0.38 0.21 0.21 j ρf 0.79 0.75 0.70 j Notes: Thistableshowsthepersistenceoftheidiosyncraticcomponentsandthecommon factor. In detail, ρξ(α) is the α percentile of the distribution of the estimated autocorj relation coefficient at lag j of the idiosyncratic component, while ρf is the estimated j autocorrelationcoefficientatlagj forthecommonfactor. 3.3 Oil price pass-through This Section presents estimates of the oil price pass-through into core PCE price inflation, food PCE price inflation, and energy PCE price inflation. Results for each of the 88 PCE price indexes in our dataset are available in an online appendix. Ourbenchmarkspecificationincludesonefactor(r = 1), andsixlagsfortheVARs(2)and (3). As discussed in Section 3.2 there is considerable uncertainty surrounding the appropriate number of factors. We took a conservative approach under the rationale that the existence of one factor is almost sure, while the presence of additional factors is not so sure (results with r = 3 are available in Appendix B). The choice of six lags, despite being larger than what selected by standard information criteria, is in line with the existing literature (see for example Edelstein and Kilian, 2009; Gao et al., 2014). The model is estimated on a sample starting in 1984:M1 and ending in 2016:M6, which contrasts with a large part of the literature on oil price shocks that uses samples starting in 1973/1974 (for example Kilian, 2009; Aastveit, 2014; Gao et al., 2014). There are at least two good reasons to consider a sample starting in 1984 rather than 1974. First, it is well known that during the 1970s and the early 1980s inflation was much more volatile than afterwards. Second, inflation in the 70s was heavily influenced by a number of food price shocks, and by the 1971-1974 wage and price controls (see Blinder and Rudd, 2013). These “structural breaks” are capable of distorting our estimates, and actually several authors (for example Hooker, 2002; Clark and Terry, 2010) found a structural break in the oil–inflation relation. For these reasons our sample starts in 1984, the year considered by the literature as the start of the “great moderation”. Figure 2 shows the impulse response function to an oil price shock of the percentage change of the real oil price, together with a bootstrapped 90% confidence interval. After an unexpected 10% increase, the real oil price increases further in the next two months by approximately 3% and 1%, respectively. 2 The upper plots in Figure 3 show the estimated oil price pass-through into the common component of energy, core, and food PCE price inflation, while the lower plots show the pass-through into the idiosyncratic component. As expected, the oil price passes through energy PCE price inflation almost entirely via the idiosyncratic component (left column). We estimate that an unexpected 10% increase in 9

Figure 2: Impulse response function to an oil price shock Percentage change of the real oil price 10 8 6 4 2 0 -2 0 3 6 9 12 15 18 Notes: This figure shows the impulse response function to an oil price shockofthepercentagechangeofthereal(WTI)oilprice(straightline with markers) with 90% confidence bands (shaded area). The x-axis representsmonths,whilethey-axisrepresentspercentagepoints. therealoilpriceincreasesenergypricesofapproximately11%inthecurrentmonth, 19%after one month, 5% after two months, and 4% after three months. The pass-through is completed in three months. The middle column in Figure 3 shows the estimated oil-price pass-through into core PCE price inflation. The pass-through of an unexpected 10% increase in the real oil price into the idiosyncratic component of core prices is not significantly different from zero (lower plot), whilethepass-throughintothecommoncomponent,despitebeingsmall,isverypersistent: an unexpected 10% increase in the real oil price is estimated to increase core PCE price inflation for more than 4 years (not shown here). Although the pass-through into the idiosyncratic component is not statistically significant, for some of the components of core PCE—the more energy intensive ones—we estimate a positive and significant pass-through. However, these componentsaccountforaverysmallshareofcorePCEandthereforetheaggregateeffectturns out to be not statistically significant. This is the case, for example, of “Air transportation” that has a weight of 0.5 in core PCE, and for which we estimate an increase of roughly four 100 percent in the current month. The right column of Figure 3 shows the estimated oil price pass-through into food PCE price inflation. In line with at least one previous study, the estimated pass-through into the idiosyncratic component is not statistically different from zero (c.f. Baumeister and Kilian, 2014), while the pass-through via the common component is very similar to that for core PCE price inflation. Finally, having estimated the pass-through from oil prices to PCE price inflation, we can calculate what the oil price contribution to core PCE price inflation was. Figure 4 shows the average contribution per year of changes in the oil price to core inflation up to 2020. We estimate that the plunge in the WTI spot prices from roughly $100 per barrel to roughly $30 per barrel that occurred between July 2014 to February 2016 shaved-off a quarter of a 10

Figure 3: Oil price pass-through into US PCE price inflation: Energy price inflation Core price inflation Food price inflation nommoC 20.0 0.70 0.15 0.60 15.0 0.10 0.50 0.40 10.0 0.05 0.30 0.20 0.00 5.0 0.10 -0.05 -0.00 0.0 -0.10 -0.10 -0.20 0 3 6 9 12 15 18 21 24 0 3 6 9 12 15 18 21 24 0 3 6 9 12 15 18 21 24 citarcnysoidI 20.0 0.70 0.15 0.60 15.0 0.10 0.50 0.40 10.0 0.05 0.30 0.20 0.00 5.0 0.10 -0.05 -0.00 0.0 -0.10 -0.10 -0.20 0 3 6 9 12 15 18 21 24 0 3 6 9 12 15 18 21 24 0 3 6 9 12 15 18 21 24 Notes: Theupperplotsshowthepass-throughofanunexpected10%increaseintherealoilpriceintothecommon component,whilethelowerplotsshowthepass-throughintotheidiosyncraticcomponent. Oneachplottheblack lineisthepointestimate,whiletheshadedareaisthe90%confidenceband. Thex-axisrepresentsmonths,while they-axisrepresentspercentagepoints. percentage point from core PCE price inflation in 2015, and a third of a percentage point in 2016. We estimate that the drag from oil prices will persist in 2017 and 2018 (about two tenth each year), and that it will then disappear by 2020. Figure 4: Oil price contribution to US core PCE price inflation 0.5 0.4 0.3 0.2 0.1 0.0 -0.1 -0.2 -0.3 -0.4 -0.5 1985 1990 1995 2000 2005 2010 2015 2020 Notes: Thisplotshowstheaveragecontributionperyearofrealoilprice changes to US core PCE price inflation measured in percentage points (y-axis). The black line with markers is the point estimate while the shadedareaisthe90%confidenceband. 3.4 Has the oil price pass-through into core inflation changed over time? There is extensive evidence that the oil price pass-through to core inflation has decreased over time (see Hooker, 2002; Chen, 2009, among others), with some authors finding that the pass-through has become negligible (Clark and Terry, 2010). Figure 5 shows the estimated 11

pass-through into core PCE prices via the common component when the model is estimated on a longer sample starting in 1974 (left plot), and when the model is estimated on a shorter sample starting in 1996 (right plot). The choice of 1996 is for comparison with the euro area analysis performed in Section 4, while 1974 is the starting date of a large number of empirical analysis (for example Aastveit, 2014; Gao et al., 2014). The results in Figure 5 confirm that the oil price pass–through into core inflation has decreased over time. In contrast with part of the literature (for example Clark and Terry, 2010)westillfindastatisticallysignificantpass-throughevenonthesamplestartingin1996— the reason being that we disentangle between common and idiosyncratic movement in price fluctuations, thus not letting the noisy idiosyncratic component affect our estimation (see also the discussion in Section 3.5). The literature has also asked why the pass-through has declined over time pointing to several (non mutually exclusive) explanations. For example, a possible explanation is that part of the decline in the pass-through can be attributed to the adoption of energy-saving technologies (Hooker, 2002; Bachmeier and Cha, 2011), while another explanation (Nordhaus, 2007; Bachmeier and Cha, 2011) points towards a change in the monetary policy response to oil price shocks (see Blinder and Rudd, 2013, for a review). While investigating properly the economic reasons of the decline in the pass-through into core inflation would require a structural model, here we provide some reduced form evidence. Figure 5: Has the oil price pass-through changed over time? 1974–2016 1996–2016 0.30 0.30 0.25 0.25 0.20 0.20 0.15 0.15 0.10 0.10 0.05 0.05 0.00 0.00 -0.05 -0.05 -0.10 -0.10 -0.15 -0.15 0 3 6 9 12 15 18 21 24 0 3 6 9 12 15 18 21 24 Notes: In each plot the gray line is the estimated pass-through in the benchmark model (the shaded area is the 90% confidenceband), whilethethickblacklineisthepass-throughestimatedonthesamplestartingin1974(leftplot)or 1996(rightplot). Thethinblacklinesarethe90percentconfidencebandsforthesealternativetimeperiods. Thex-axis representsmonths,whilethey-axisrepresentspercentagepoints. Why does the oil price pass-through change when our model is estimated on different samples? To answer it is necessary first to notice that an alternative (and equivalent) way to estimate the oil price pass-through onto the common component of core inflation is to fit a bivariate VAR on the changes in the real oil price (y ) and the common component of core t inflation(χc).6 Second,itisimportanttokeepinmindthatwhenweestimatethemodelintwo t different samples, we re-estimate the common factor and the factor loadings, and therefore 6Let πc be the monthly core prices inflation rate, then by using (1) and the aggregation weights we can t write πc =χc+ξc, where χc = (cid:80) w λ f , and ξc = (cid:80) ξ . t t t t i∈core i i t t i∈core it 12

χc. Indeed, had we not re-estimated χc, then the difference in the estimated pass-through t t would have been attributable to the mechanical fact that the coefficients of the VAR vary because they are estimated on two different samples. However, given that we re-estimate χc, t the estimated coefficients of the VAR vary also because the estimated common component changes depending on the estimation sample. To disentangle between the contribution of common component estimation and contribution of the different VAR estimation, in Figure 6 we show the pass-through obtained when the VAR is estimated on the 1996-2016 sample while the common component is estimated on different periods. Figure 6: Why has the oil price pass-through changed over time? 1974–2016 1984–2016 0.20 0.20 0.15 0.15 0.10 0.10 0.05 0.05 0.00 0.00 0 3 6 9 12 15 18 21 24 0 3 6 9 12 15 18 21 24 Notes: In each plot the black line is the estimated oil price pass-through into the common component of core inflationestimatedonthe1974-2016sample(leftplot),andinthe1984-2016benchmarksample(rightplot). The dotted black line in the left (right) plot is the pass-through estimated when χc is estimated over the 1974-2016 t (1984-2016) sample, but the VAR is estimated on the 1996-2016 sample. Finally, in both plots the gray line is the pass-through estimated on the 1996-2016 sample. The x-axis represents months, while the y-axis represents percentagepoints. By looking at Figure 6 we can see that the magnitude of the estimated pass-through varies between samples mainly because of the common component estimation, whereas the persistenceoftheestimatedpass-throughvariesbetweensamplesmainlybecauseoftheperiod used to estimate the VAR. The question then is why the common component estimated on different samples is different. The answer is straightforward: the estimation of the common component depends on the comovementinthedata,andthecomovementinUSdisaggregatepriceshaschangedovertime. Indeed, the average percentage of disaggregate prices fluctuation explained by the common component has decreased from 18% in the 1974-2016 sample, to 8% in the 1984-2016 sample, to 6% in the 1996-2016 sample—at the aggregate level, the common component accounts for 90%, 57%, and 11% of core PCE fluctuations in the three samples, respectively. In conclusion, our reduced form analysis points out that one of the reasons why the oil price pass-through onto core inflation has decreased over time is the fact that disaggregate prices have increasingly been driven by idiosyncratic dynamics. 3.5 Is our model miss-specified? Our model assumes that the common component is driven by two shocks: a common shock, which has no structural interpretation, and an oil price shock. This is clearly a simplifying 13

assumption as the common component might reflect the interplay of several different sources such as, for example, the Federal Reserve leaning against the inflationary pressure triggered by an oil price shock (Bernanke et al., 1997; Kilian and Lewis, 2011). Does this simplifying assumption bias our results? Are we making a mistake in not disentangling these different sources? This Section answers these questions. In order to account for the interplay of different macroeconomic forces, we estimate a larger VAR model. In detail, we first estimate equation (1), and then, rather than estimating the VAR (2), we estimate a four–variable VAR including the percentage change in the real oil price (y ), the unemployment rate, the Fed funds rate, and the common factor (f ).7 t t The left plot in Figure 7 compares the oil price pass-through into core inflation estimated with the larger VAR (black line) to that estimated with the benchmark model (gray line).8 Results are essentially unchanged: the estimated pass-through with the enlarged VAR is just a touch smaller than the one estimated with the benchmark model, which is reflected in a smaller estimated oil price contribution to core inflation (right plot). In other words, the main conclusion of the paper is confirmed—the oil price pass-through to core inflation is small but statistically significant and long lasting. The results in Figure 7 contrast with those in Clark and Terry (2010). Clark and Terry (2010), whoestimateatimevaryingparameterVARincludingcorepriceinflation(πc), energy t price inflation, the unemployment rate, and the Fed funds rate, conclude that starting from 1985 the pass-through from energy price inflation to core price inflation is essentially zero. It can be shown that our model is very similar to that of Clark and Terry (2010) as it can be rewritten as a four–variable VAR including the percentage change in the real oil price, the unemployment rate, the Fed funds rate, and the common component of core price inflation (χc). Therefore, our conclusions are different from Clark and Terry (2010) because we include t χc in lieu of πc in the VAR model, that is we back-out the more noisy idiosyncratic compot t nent thus not letting it affect our estimation. This result further confirms the importance of disentangling between common and idiosyncratic movement in price fluctuations. 4 Oil price pass-through into inflation in the euro area 4.1 Data The price data for the euro area are monthly Harmonized Indexes of Consumer Prices (HICP) (see Appendix A for details), while the weights are the official HICP item weights referred to 2016.9 Both the disaggregate prices and the weights are available from Eurostat starting in 1996, and therefore the results for the euro area are obtained on a sample starting in 1996:M1, 7Theunemploymentrateisthe“CivilianUnemploymentRate: 16yr+” fromtheBureauofLaborStatistics, while the Fed Funds Rate is from the Federal Reserve Board. Both series where downloaded from Haver (LR@USECON, and FFED@USECON). 8When we estimate the larger VAR we do not impose the restriction in (4). Furthermore, the oil price shock is identified using a standard Choleski decomposition with the oil price ordered first. 9Weights of the Classification of Individual Consumption by Purpose (COICOP) categories are revised yearly and released in February together with the data for the month of January. In other words, while PCE weights change every month, HICP weights are constant within a given year. 14

Figure 7: Is our model miss-specified? Oil price pass-through into core PCE Oil Price contribution to core PCE 0.15 0.5 0.4 0.10 0.3 0.2 0.1 0.05 0.0 -0.1 0.00 -0.2 -0.3 -0.05 -0.4 -0.5 0 3 6 9 12 15 18 21 24 1985 1990 1995 2000 2005 2010 2015 2020 Notes: The left plot shows the pass-through of an unexpected 10% increase of the real oil price into the common component of core PCE prices. The gray line is the estimated pass-through in the benchmark model (the shaded areaisthe90%confidenceband),whilethethickblacklineisthepass-throughestimatedusingtheenlargedVAR model(thethinblacklinesarethe90%confidencebands). Thex-axisrepresentsmonths,whilethey-axisrepresents percentage points. The right plot shows the average contribution per year of real oil price to US core PCE price inflation measured in percentage points (y-axis). The gray line is the estimated contribution in the benchmark model (the shaded is the 90% confidence band), while the black line is the point estimate estimated using the enlargedVARmodel(thethinblacklinesarethe90%confidencebands). and ending in 2016:M6. Furthermore, given that Eurostat publishes seasonal adjusted series only for the aggregate indexes, we seasonally adjusted the disaggregated price series ourselves using X12 ARIMA. HICP price indexes are available at 5-digit level Classification of Individual Consumption by Purpose (COICOP) for a total of 303 disaggregate prices, but for our analysis we consider disaggregated series at 3-digit level, which gives us a dataset of 95 series. From this 95 price dataset we remove the following components that are available only starting from January 2000: “Dental services”, “Hospital services”, “Social protection”, “Other insurance”, “Insurance connectedwithhealth”,and“Medicalandparamedicalservices”. Thefinaldatasetiscomposed of 87 price series covering 96.1% of the HICP index with 69% of the price indexes that have a weight smaller than 1 , and 14% of them that have a weight larger than 2 . 100 100 Finally, the oil price is measured by the Brent spot crude oil price, which is deflated by the HICP core price index. The data for the Brent price are taken from the US Energy Information Administration and the Wall Street Journal, and were downloaded from Haver (PEBRT@USECON), while the data for core HICP are taken from Eurostat (teicp200). 4.2 Common and idiosyncratic dynamics in HICP prices Table 3 shows the percentage of variance explained by the first r factors. Similar to US PCE prices, EA HICP prices clearly admit a factor structure, but again it is unclear if more than onefactorisneeded. Moreover, thefirstfactoraccountsonaverageforroughlythesameshare of variance of disaggregate prices as in the US (see second and the third row of Table 3).10 Figure 8 shows the percentage of variance of each variable explained by the first four 10Note also that in a model with one common factor, the common component accounts for 21% of core EA HICP inflation fluctuations. This is comparable to the shares estimated for US PCE prices on the 1996-2016 sample, which is 10%. 15

Table 3: Common dynamics in EA HICP prices r 1 2 3 4 5 6 7 8 9 10 µEA 9.8 4.2 3.9 3.6 3.0 2.9 2.6 2.5 2.3 2.3 t µUS 5.7 4.9 4.0 3.1 3.0 2.8 2.6 2.4 2.3 2.2 t Notes: µEA is the percentages of total variance explained by the first r factors in the r EA, while µUS is the percentages of total variance explained by the first r factors in the r US. Both µEA and µUS were computed on a sample starting in 1996:M1 and ending in r r 2016:M6. factors,wherewehavedividedthedisaggregatepricesintothreeplotseachofwhichrepresents a different category. Although Figure 8 does not help in understanding how many factors to include in the model, it clearly shows that EA core services prices are more idiosyncratic than coregoods. TheuncertaintyonthenumberoffactorsisnotresolvedbytheBaiandNg(2002) criteria that supports up to eight factors. Figure 8: Common dynamics in EA HICP prices Food (left) & Energy (right) Core Goods Core Services 80 80 80 r=1 70 r r = = 2 3 70 70 r=4 60 60 60 50 50 50 40 40 40 30 30 30 20 20 20 10 10 10 0 0 0 Notes: This figure shows the percentage of variance (y-axis) of each variable (x-axis) explained by the first four factors. Eachbarrepresentadifferentdisaggregateprice. 4.3 Oil price pass-through In this Section we present estimates of the oil price pass-through into core EA HICP inflation, food EA HICP inflation, and energy EA HICP inflation. The benchmark specification is identical to the one used for US PCE prices, that is one factor (r = 1) and six lags in the VARs (2) and (3). Figure 9 reports the estimated oil price pass-through into energy HICP inflation (left column), core HICP inflation (middle column), and food HICP inflation (right column), together with 90% bootstrap confidence bands. An unexpected 10% increase in the real oil price increases energy prices of roughly 9% in the current month, of 8% after one month, of 11⁄ percent after two months, and of 21⁄ percent 2 2 after three months. The pass-through is completed after three months. These numbers are considerably lower than those estimated for the US, most likely due to higher fuel taxes in the euro area. More precisely, in the euro area taxes on average account for roughly 60% of total gasoline prices, with crude oil prices accounting for roughly 20% (see European Central Bank, 2011, page 87), while in the US the same shares are, respectively, 21% and 49% (source: EIA website http://www.eia.gov/petroleum/gasdiesel/). Theestimatedpass-throughintocoreHICPinflationintheEAissimilartothatestimated 16

for the US (middle column of Figure 9). The pass-through via the idiosyncratic component is not statistically different from zero, while the pass-through via the common component is null in the current month, but then small and persistent. Figure 9: Oil price pass-through into EA HICP inflation energy core food nommoC 25.0 0.25 0.80 0.20 20.0 0.15 0.60 15.0 0.10 0.40 10.0 0.05 0.20 5.0 0.00 0.00 -0.05 -0.20 0.0 -0.10 -0.40 -5.0 -0.15 -0.60 0 3 6 9 12 15 18 21 24 0 3 6 9 12 15 18 21 24 0 3 6 9 12 15 18 21 24 citarcnysoidI 25.0 0.25 0.80 0.20 20.0 0.15 0.60 15.0 0.10 0.40 10.0 0.05 0.20 5.0 0.00 0.00 -0.05 -0.20 0.0 -0.10 -0.40 -5.0 -0.15 -0.60 0 3 6 9 12 15 18 21 24 0 3 6 9 12 15 18 21 24 0 3 6 9 12 15 18 21 24 Notes: The upper plots show the pass-through of an unexpected 10% increase in the real oil price into the common component,whilethelowerplotsshowthepass-throughintotheidiosyncraticcomponent. Oneachplotthethickblack lineisthepointestimatefortheEA,whilethethinblacklinesarethe90%confidencebands. Likewise,thesolidgray lineandtheshadedareaarethepointestimateandtheconfidencebandsfortheUS,respectively. Thex-axisrepresents monthsaftertheoilpriceincrease,whilethey-axisrepresentspercentagepoints. Figure 10 shows the oil price contribution to core EA HICP inflation up to 2020. We estimate that the plunge in the oil price shaved-off approximately 17 basis points to core inflation in the euro area in 2015, and 19 basis points in 2016. The drag from oil prices will persistin2017and2018(8and5basispoints),butitwillfadeawayby2019.11 Thesenumbers are very similar to those estimated for the US, with the effect being just slightly delayed. 5 Conclusions In this paper we estimate the oil price pass-through into consumer prices both in the US and in the Euro area. To do so, we use a novel econometric approach based on dynamic factor modelsandVARs,whichallowustodistinguishbetweenthespecific(idiosyncratic)effectthat oil price changes might have on each disaggregate price, from the macroeconomic (common) effect that oil price changes might have since they contribute to macroeconomic fluctuations. Our results show that common and idiosyncratic dynamics in disaggregate prices have different statistical properties: common dynamics are slow moving, idiosyncratic dynamics fast moving and volatile. Disentangling these two components proved crucial when estimating the oil price pass-through into core inflation, as we estimate that there is essentially no oil price pass-through into core inflation via the idiosyncratic component, while the pass-through via the common component is small, but statistically different from zero and long lasting. 11In a recent paper Conti et al. (2017) estimate that oil prices shaved off an average of (roughly) 13 basis points to EA core inflation. Such an estimate is lower but not statistically different than ours. 17

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Appendix A Data Appendix A.1 The US dataset The price data for the US are monthly price indexes for personal consumption expenditures (PCE) by type of product. The data are taken from the NIPA Table 2.4.4U from the Bureau of Economic Analysis and downloaded from Haver. The data were seasonally adjusted by the Bureau of Economic Analysis, and large outliers—π is considered an outlier if its absolute it value is larger than 10 times the interquantile range—were replaced by centered 9-month medians. In the table below the column “ID” reports the position in the NIPA Table 2.4.4U, the column “share” reports the share of variance explained by the common component, while the column “weight” reports the weight of each component in the Total PCE index. The weights are those as of June 2016. ID Name Label share weight 5 New motor vehicles DNMVRX 4.4 2.1 10 Net purchases of used motor vehicles DNPVRX 0.0 1.0 18 Motor vehicle parts and accessories DMVPRX 0.3 0.5 22 Furniture and furnishings DFFFRX 8.3 1.5 27 Household appliances DAPPRX 2.3 0.4 30 Glassware, tableware, and household utensils DUTERX 4.6 0.4 33 Tools and equipment for house and garden DTOORX 0.0 0.2 37 Video, audio, photographic, and information processing equipment DVAPRX 13.9 1.8 and media 50 Sporting equipment, supplies, guns, and ammunition DSPGRX 6.2 0.6 51 Sports and recreational vehicles DWHLRX 1.7 0.4 58 Recreational books DRBKRX 5.3 0.3 59 Musical instruments DMSCRX 2.5 0.1 61 Jewelry and watches DJRYRX 2.0 0.6 64 Therapeutic appliances and equipment DTAERX 12.2 0.6 67 Educational books DEBKRX 2.8 0.1 68 Luggage and similar personal items DLUGRX 2.8 0.3 69 Telephone and facsimile equipment DTCERX 20.1 0.1 74 Cereals and bakery products DCBPRX 12.8 1.1 77 Meats and poultry DMAPRX 0.8 1.2 82 Fish and seafood DFISRX 0.9 0.1 83 Milk, dairy products, and eggs DMDERX 1.2 0.6 87 Fats and oils DFATRX 1.9 0.1 88 Fresh fruits and vegetables DFAVRX 0.5 0.7 91 Processed fruits and vegetables DPFVRX 2.7 0.2 92 Sugar and sweets DSWERX 2.4 0.4 93 Food products, not elsewhere classified DOFDRX 6.7 1.1 94 Nonalcoholic beverages purchased for off-premises consumption DNBVRX 1.0 0.7 97 Alcoholic beverages purchased for off-premises consumption DAOPRX 6.9 1.1 101 Food produced and consumed on farms DFFDRX 0.1 0.0 103 Garments DGARRX 3.2 2.4 107 Other clothing materials and footwear DOCCRX 2.3 0.7 112 Motor vehicle fuels, lubricants, and fluids DMFLRX 0.3 2.0 115 Fuel oil and other fuels DFULRX 0.6 0.2 119 Pharmaceutical and other medical products DPHMRX 15.2 3.8 124 Recreational items DREIRX 11.6 1.3 129 Household supplies DHOURX 6.9 1.0 135 Personal care products DOPCRX 2.9 1.0 139 Tobacco DTOBRX 3.0 0.8 140 Magazines, newspapers, and stationery DNEWRX 3.8 0.8 22

ID Name Label share weight 152 Rental of tenant-occupied nonfarm housing DTENRX 30.7 4.0 156 Imputed rental of owner-occupied nonfarm housing DOWNRX 26.1 11.5 159 Rental value of farm dwellings DFARRX 1.4 0.2 160 Group housing DGRHRX 28.8 0.0 163 Water supply and sewage maintenance DWSMRX 1.4 0.6 164 Garbage and trash collection DREFRX 37.2 0.1 166 Electricity DELCRX 1.7 1.4 167 Natural gas DGHERX 0.5 0.4 170 Physician services DPHYRX 30.9 4.0 171 Dental services DDENRX 29.2 1.0 172 Paramedical services DPMSRX 22.5 2.7 179 Hospitals DHSPRX 44.9 8.0 183 Nursing homes DNRSRX 5.5 1.4 187 Motor vehicle services DMVSRX 12.5 2.1 196 Ground transportation DGRDRX 1.5 0.4 203 Air transportation DAITRX 0.4 0.4 204 Water transportation DWATRX 1.2 0.0 206 Membership clubs, sports centers, parks, theaters, and museums DRLSRX 6.5 1.5 214 Audio-video,photographic,andinformationprocessingequipment DAVPRX 6.0 0.8 services 220 Gambling DGAMRX 12.9 1.0 224 Other recreational services DOTRRX 7.3 0.5 231 Meals and nonalcoholic beverages DMABRX 24.2 4.8 239 Alcohol in purchased meals DAPMRX 13.1 0.7 240 Food furnished to employees (including military) DFOORX 2.7 0.2 243 Accommodations DACCRX 1.6 1.0 248 Financial services furnished without payment DIMPRX 5.0 2.6 252 Financial service charges, fees, and commissions DOFIRX 0.5 2.0 265 Life insurance DLIFRX 13.3 0.7 266 Net household insurance DFINRX 0.1 0.1 269 Net health insurance DHINRX 3.9 1.5 273 Net motor vehicle and other transportation insurance DTINRX 0.0 0.5 275 Communication DCORMG 3.3 2.2 285 Higher education DHEDRX 18.8 1.5 288 Nursery, elementary, and secondary schools DNEHRX 23.1 0.3 291 Commercial and vocational schools DVEDRX 0.0 0.4 293 Legal services DGALRX 11.6 0.8 294 Accounting and other business services DPRORX 2.0 0.3 298 Labor organization dues DUNSRX 3.0 0.1 299 Professional association dues DAXSRX 11.6 0.1 300 Funeral and burial services DFUNRX 16.5 0.2 302 Personal care services DPCSRX 12.4 1.1 305 Clothing and footwear services DCFSRX 12.4 0.1 310 Child care DCHCRX 0.9 0.3 311 Social assistance DSCWRX 8.4 0.9 318 Social advocacy and civic and social organizations DSADRX 5.5 0.1 319 Religious organizations’ services to households DRELRX 0.5 0.1 320 Foundations and grantmaking and giving services to households DGIVRX 1.5 0.0 321 Household maintenance DHHMRX 3.1 0.6 339 Final consumption expenditures of NPISH DNPIRX 8.3 2.7 23

Appendix A.2 The euro area dataset ThepricedatafortheeuroareaaremonthlypriceindexesforHarmonizedIndexesofConsumer Prices(HICP)bytypeofproducttakenfromtheEurostatwebsitehttp://appsso.eurostat. ec.europa.eu/nui/show.do?dataset=prc_hicp_midx&lang=en. The data were seasonally adjusted by using the X-12-ARIMA seasonal adjustment method, and large outliers—π is it considered an outlier if its absolute value is larger than 10 times the interquantile range—were replaced by centered 9-month medians. In the table below the column “share” reports the share of variance explained by the common component, while the column “weight” reports the weight of each component in the Total HICP index. The weights are those as of 2016. Name Label share weight Bread and cereals CP0111 48.1 2.6 Meat CP0112 28.2 3.5 Fish and seafood CP0113 2.6 1.0 Milk, cheese and eggs CP0114 27.4 2.1 Oils and fats CP0115 0.7 0.4 Fruit CP0116 2.7 1.2 Vegetables CP0117 1.4 1.7 Sugar, jam, honey, chocolate and confectionery CP0118 31.5 1.0 Food products n.e.c. CP0119 36.9 0.5 Coffee, tea and cocoa CP0121 3.1 0.4 Mineral waters, soft drinks, fruit and vegetable juices CP0122 29.5 0.9 Spirits CP0211 5.6 0.4 Wine CP0212 9.9 0.8 Beer CP0213 4.5 0.6 Tobacco CP022 2.4 2.4 Clothing materials CP0311 0.2 0.0 Garments CP0312 2.4 4.4 Other articles of clothing and clothing accessories CP0313 0.6 0.3 Cleaning, repair and hire of clothing CP0314 17.6 0.2 Shoes and other footwear CP0321-322 1.9 1.2 Actual rentals paid by tenants CP0411-412 5.0 6.5 Materials for the maintenance and repair of the dwelling CP0431 21.2 0.4 Services for the maintenance and repair of the dwelling CP0432 31.1 0.9 Water supply CP0441 0.0 0.6 Refuse collection CP0442 0.9 0.6 Sewerage collection CP0443 1.1 0.6 Other services relating to the dwelling n.e.c. CP0444 1.4 0.9 Electricity CP0451 7.7 2.7 Gas CP0452 11.9 1.9 Liquid fuels CP0453 0.2 0.6 Solid fuels CP0454 10.2 0.2 Heat energy CP0455 15.0 0.2 Furniture and furnishings CP0511 30.4 1.9 Carpets and other floor coverings CP0512 2.8 0.2 Repair of furniture, furnishings and floor coverings CP0513 12.1 0.1 Household textiles CP0520 5.5 0.4 Major household appliances whether electric or not CP0531-532 5.8 0.9 Repair of household appliances CP0533 10.6 0.1 Glassware, tableware and household utensils CP0540 10.2 0.5 Major tools and equip. and small tools and misc. accessories CP0551-552 20.8 0.5 24

Name Label share weight Non-durable household goods CP0561 35.9 1.0 Domestic services and household services CP0562 8.6 0.9 Pharmaceutical products CP0611 0.0 1.3 Other medical products, therapeutic appliances and equipment CP0612-613 6.0 0.8 Motor cars CP0711 0.3 3.5 Motor cycles, bicycles and animal drawn vehicles CP0712-714 0.1 0.3 Spare parts and accessories for personal transport equipment CP0721 17.9 0.6 Fuels and lubricants for personal transport equipment CP0722 0.3 4.2 Maintenance and repair of personal transport equipment CP0723 42.2 2.5 Other services in respect of personal transport equipment CP0724 12.2 1.2 Passenger transport by railway CP0731 2.2 0.6 Passenger transport by road CP0732 4.0 0.6 Passenger transport by air CP0733 0.6 0.7 Passenger transport by sea and inland waterway CP0734 0.5 0.1 Combined passenger transport CP0735 1.8 0.6 Other purchased transport services CP0736 6.2 0.1 Postal services CP081 4.3 0.2 Telephone and telefax equipment CP0820-830 0.2 3.0 Equipment for the reception, recording and reproduction of sound and CP0911 5.8 0.4 picture Photographic and cinematographic equipment and optical instruments CP0912 14.8 0.1 Information processing equipment CP0913 19.4 0.5 Recording media CP0914 0.0 0.2 Repairofaudio-visual,photographicandinformationprocessingequip- CP0915 5.3 0.1 ment Major durables for outdoor recreation and indoor recreation CP0921-922 1.0 0.3 Maintenance and repair of other major durables for recreation and cul- CP0923 1.4 0.0 ture Games, toys and hobbies CP0931 1.6 0.6 Equipment for sport, camping and open-air recreation CP0932 2.8 0.3 Gardens, plants and flowers CP0933 0.6 0.6 Pets and related products; veterinary and other services for pets CP0934-935 37.7 0.7 Recreational and sporting services CP0941 6.6 0.9 Cultural services CP0942 6.7 1.4 Books CP0951 0.0 0.5 Newspapers and periodicals CP0952 0.2 0.7 Miscellaneous printed matter;stationery and drawing materials CP0953-954 11.0 0.3 Package holidays CP096 0.1 1.7 Pre-primary, primary, second., etc, and educ. not def. by level CP10X0 7.5 1.1 Restaurants, cafés and the like CP1111 48.2 7.1 Canteens CP1112 6.6 0.7 Accommodation services CP112 0.0 1.8 Hairdressing salons and personal grooming establishments CP1211 25.7 1.2 Electrical appliances for personal care; other appliances, articles and CP1212-1213 46.5 1.7 products for personal care Jewellery, clocks and watches CP1231 11.9 0.5 Other personal effects CP1232 5.7 0.5 Insurance connected with the dwelling CP1252 0.5 0.3 Insurance connected with transport CP1254 1.1 0.8 Other financial services n.e.c. CP12622 0.5 0.6 Other services n.e.c. CP127 14.8 1.1 25

Appendix B Robustness In this section we provide robustness checks for the US. AsexplainedinSection3.2thereisconsiderableuncertaintyonthenumberoffactorstobe included in the model, and in the first robustness check we show results with a larger number of factors included. Figure B1 reports results when r = 3 as in Reis and Watson (2010). In a nutshell: results do change in that, although the sum of the point estimates of common andidiosyncraticpass-throughdoesnotchange, thecompositionbetweenthetwocomponents slightly does. For example, in the model with one factor an unexpected 10% increase in the real oil price pass-through via the idiosyncratic component increases PCE energy by 11.1% in the current month, while the (point-estimate) pass-through via the common component is 0.2%. In the model with three factors an unexpected 10% real oil price increase pass-through via the idiosyncratic component increases PCE energy by 5%, while the pass-through via the common component is 7%. Figure B1: Robustness analysis with respect to number of factors Oil price pass-through into US PCE price inflation Energy price inflation Core price inflation Food price inflation nommoC 20.0 0.20 0.60 0.15 15.0 0.40 0.10 10.0 0.05 0.20 0.00 5.0 0.00 -0.20 -0.05 0.0 -0.40 -0.10 -0.60 0 3 6 9 12 15 18 21 24 0 3 6 9 12 15 18 21 24 0 3 6 9 12 15 18 21 24 citarcnysoidI 20.0 0.20 0.60 0.15 15.0 0.40 0.10 10.0 0.05 0.20 0.00 5.0 0.00 -0.20 -0.05 0.0 -0.40 -0.10 -0.60 0 3 6 9 12 15 18 21 24 0 3 6 9 12 15 18 21 24 0 3 6 9 12 15 18 21 24 Notes: The upper plots show the pass-through of an unexpected 10% increase in the real oil price into the common component,whilethelowerplotsshowthepass-throughintoidiosyncraticcomponent. Oneachplotthegraylineisthe estimated pass-through in the benchmark model (the shaded area is the 90% confidence band), while the black line is isthepass-throughestimatedwhenr=3(thedashedblacklinesarethe90%confidencebands). Thex-axisrepresents months,whilethey-axisrepresentspercentagepoints. The second check is done with respect to the structure of the model. As explained in Section 2 our model is very similar to a standard FAVAR model (Bernanke et al., 2005). In our model, the oil price is expected to have not only a common effect on all prices, but also to possibly have an idiosyncratic effect on energy intensive items. In a FAVAR model, instead, the oil price is treated as an observed factor, which means that the oil price is part of the common space only, and it has no effects on the idiosyncratic component. In formulas, equation (1) is replaced by π = λ(cid:48)f +γ y +ξ (B1) it i t i t it while (2) remains equal and the idiosyncratic component is not modeled. By substituting (2) into (B1) we can derive the oil price pass-through into the inflation rate of price i implied by 26

the FAVAR as: ψ˜(L) = λ(cid:48)c (L)+γ c (L). (B2) i i i12 i i22 Now, in principle ψ˜(L) should be equal to ψ˜χ(L), and ψ˜ξ(L) should be zero, as in a FAVAR i i i model the oil price is treated as an observed factor. However, with a clear and acknowledged abuse of notation, we are going to write ψ˜χ(L) = λ c (L) and ψ˜ξ(L) = γ c (L), and then i i i12 i i i22 by comparing (B2) with (5) we can see that ψ˜χ(L) = ψχ(L), and ψ˜ξ(L) (cid:54)= ψξ(L). i i i i FigureB2comparesourbenchmarkestimatedoilpricepass-throughwiththeoneestimated using a FAVAR.12 More precisely, the top row of Figure B2 shows the pass-through into the common component, while the bottom row shows the pass-through into the idiosyncratic component. Asexpected,theestimatedpass-throughintothecommoncomponentisidentical, while the estimated idiosyncratic pass-through is similar. All in all, the results in Figure B2 show that had we estimated a standard FAVAR rather than the model in Section 2 we would have reached the same conclusions. Figure B2: Robustness analysis with respect to model structure Oil price pass-through into US PCE price inflation Energy price inflation Core price inflation Food price inflation nommoC 20.0 0.70 0.15 0.60 15.0 0.10 0.50 0.40 10.0 0.05 0.30 0.20 5.0 0.00 0.10 -0.05 -0.00 0.0 -0.10 -0.10 -0.20 0 3 6 9 12 15 18 21 24 0 3 6 9 12 15 18 21 24 0 3 6 9 12 15 18 21 24 citarcnysoidI 20.0 0.70 0.15 0.60 15.0 0.10 0.50 0.40 10.0 0.05 0.30 0.20 5.0 0.00 0.10 -0.05 -0.00 0.0 -0.10 -0.10 -0.20 0 3 6 9 12 15 18 21 24 0 3 6 9 12 15 18 21 24 0 3 6 9 12 15 18 21 24 Notes: Theupperplotsshowthepass-throughofanunexpected10%increaseintherealoilpriceintothecommon component(λ(cid:48) i ci12(L)),whilethelowerplotsshowthepass-throughintoidiosyncraticcomponent(di12(L)forthe benchmarkmodel,andγici22(L)fortheFAVAR).Oneachplotthegraylineistheestimatedpass-throughinthe benchmarkmodel(theshadedareaisthe90%confidenceband),whiletheblacklineisthepass-throughestimated with the FAVAR (the dashed black lines are the 90% confidence bands). The x-axis represents months, while the y-axisrepresentspercentagepoints. 12The FAVAR is estimated using PCA and OLS. More specifically, we follow Boivin et al. (2009) and Aastveit (2014) and we first estimate f t by PCA, call it(cid:98)f t 0, and then we iterate between (1) estimate λ i and γ i by regressing x it into(cid:98)f t j−1 and y t , and (2) estimate(cid:98)f t j by PCA on x˜ t =x t −γ (cid:98) jy t . Alternatively a FAVAR couldbeestimatedinoneshoteitherbyestimatingarestrictedDFMwithMaximumLikelihoodasinJuvenal and Petrella (2015) and Luciani (2015), or with Bayesian method as in Bernanke et al. (2005). 27