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WORKING PAPER SERIES

No 56 / 2018

Slicing up inflation: analysis and forecasting of Lithuanian inflation components

By Julius Stakėnas

ISSN 2029-0446 (ONLINE) WORKING PAPER SERIES No 56 / 2018

SLICING UP INFLATION: ANALYSIS AND FORECASTING OF LITHUANIAN INFLATION COMPONENTS*

Julius Stakėnas†

* We are grateful for the participants of the internal Bank of Lithuania seminars for their helpful comments.The views expressed and the conclusions reached in this publication are those of the author and do not necessarily represent the official views of the Bank of Lithuania or the Eurosystem.† Bank of Lithuania, e.a.: [email protected].

© Lietuvos bankas, 2018Reproduction for educational and non-commercial purposes is permitted provided that the source is acknowledged.

Address Totorių g. 4 LT-01121 Vilnius Lithuania Telephone (8 5) 268 0103

Internet http://www.lb.lt

Working Papers describe research in progress by the author(s) and are published to stimulate discussion and critical comments.

The Series is managed by Applied Macroeconomic Research Division of Economics Department

and Center for Excellence in Finance and Economic Research.

All Working Papers of the Series are refereed by internal and external experts.

The views expressed are those of the author(s) and do not necessarily represent those of the Bank of Lithuania.

ISSN 2029-0446 (ONLINE)

Abstract

In this paper we model five Lithuanian HICP subcomponents in a medium scale BayesianVAR framework. We deal with the parameter proliferation problem by setting the appropri-ate amount of shrinkage determined in the out-of-sample forecasting exercise. The main bodyof the paper consists of displaying the model’s performance in two applications: forecasting andanalysis of inflation determinants. We find the model’s forecasts to be competitive against theunivariate statistical models, particularly in the cases of predicting processed food and energygoods inflation. What is more, exercises based on conditional forecasting show that these twoindices make the best use of accurate conditional information in terms of improving predictingaccuracy. In the decomposition of the drivers of HICP components, we demonstrate that both,domestic and foreign factors can be prevalent inflation determinants in certain time periods.We also find some evidence on employees’ bargaining power playing a role in determining theLithuanian consumer price inflation.

Keywords: HICP subindices, Bayesian VAR, Bayesian shrinkage, inflation forecasting,structural decomposition

JEL classification: C32, C53, E37

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1 Introduction

Monitoring and forecasting inflation is one of the primary interests of any inflation-targetingcentral bank, government concerned about its citizens’ income/wealth (re)distribution (as wellas tax collection), or any economic agent basing his/her consumption and investment decisionson inflation outcomes. As inflation determinants vary over time, it is instructive to go pastmonitoring just one measure of inflation and study its constituent parts in order to betterunderstand its causes and persistence. In this paper we use a Bayesian VAR (BVAR) modelto study inflation of 5 main HICP components: unprocessed food (UF), processed food (PF),services (SERV), non-energy industrial goods (NEIG) and energy goods (ENERG).

The choice of modelling the specific 5 HICP components was primarily motivated by theECB’s requirement for the Bank of Lithuania to provide forecasts of these price indices. On theother hand, the model is not reliant on the particular disaggregation scheme of consumer pricesand can be straightforwardly adjusted to incorporate a different number of HICP subindices ofvarious definitions. The benefit of modelling the HICP prices on a rather disaggregated level lies,firstly, in the ability to study prices that have quite different determinants separately (modellingstandpoint), and secondly, in the ability to address concerns of policy makers and consumergroups regarding the price dynamics in a more detailed way (consumer standpoint). We believe,that our chosen set of 5 HICP indices serves well in achieving these goals, while at the same timekeeping the level of aggregation high enough to justify the macroeconomic viewpoint. Note aswell, that the HICP subindices used in the study are provided by the Eurostat for all EuropeanUnion countries, making potential cross-country comparative analysis much easier.

The direct application of our research results is closely linked (but not limited) to the NarrowInflation Projection Exercise (NIPE) performed by the central banks in the Eurosystem. In thisexercise, central banks provide the ECB with short-term forecasts of 5 HICP components, whichthen are aggregated at the euro area level. Our paper is motivated by the work of Giannoneet al. (2010), who used a BVAR model to perform this exercise for the euro area data. In theirstudy, they list the apparent advantages of modelling HICP components in a single framework:availability of all possible interactions between the HICP components, ability to capture second-round effects (i.e. impact of assumptions on the future values of variables these assumptions areset for), easy scenario analysis (availability of incomplete conditioning, consistent inclusion ofexpert judgement), model-based risk assessment around the projections, etc. All these potentialuses and applications motivated our choice of a VAR model (over a framework of a set ofunivariate equations) for analysis and forecasting of HICP subindices.

The Lithuanian HICP component forecasts were already studied in Stakenas (2015), wherethe forecasts were generated on a rather disaggregate level with 44 univariate equations. Thepaper concluded that forecasting HICP components on a disaggregate level and later aggregatingthe forecasts, produces predictions that are hard to beat regarding their accuracy, however, italso implies that the there are no spillovers between the HICP components and any scenarioanalysis becomes quite restrictive. In this paper, our objective is twofold – we aim not onlyfor forecasting accuracy of the 5 HICP components, but also for their structural interpretation.We are interested in identifying the drivers of Lithuanian HICP components, their origin (globalvs. local), potential dependence on labour market conditions, differences in components’ factors,etc. Finally, multivariate modelling should also allow us to study interactions/spillovers betweenthe components before making any restrictions.

The flexibility of the model, allowing for interactions between the HICP subindices and de-pendence on a number of different determinants, comes at a cost of parameter proliferationand Bayesian shrinkage presents itself as a natural candidate to counter its adverse effects. As

5

demonstrated by De Mol et al. (2008), Bayesian regression can be a valid alternative to principalcomponents – the authors find that using a normal prior distribution, Bayesian regression gen-erates forecasts that are highly correlated with principal component forecasts. The authors alsoshow that in case of growing number of parameters, coefficients have to be increasingly shrunktowards zero in order to obtain consistent forecasts. Banbura et al. (2010) used this result toestimate high-dimensional VAR models (up to 131 variables) and found that, when the degreeof shrinkage is set in relation to cross-sectional dimension of the data, forecasts can be improvedby adding more variables.

The results of our paper link to the literature in three directions. First, we contribute to theBayesian hyperparameter selection literature, studying it in the small open economy setting witha focus on inflation dynamics. We find that in this setting, the parameter shrinkage schemessuggested by Litterman (1985) are applicable, i.e. more distant lags and cross-variable lagsought to be shrunk more. We also reiterate the results by De Mol et al. (2008), observing howhigh forecast RMSE (root mean squared error), that was induced by parameter proliferation,can be lowered by applying appropriate amount of shrinkage. The out-of-sample forecastingpart of the paper relates to the studies on the forecasting performance of BVAR models, suchas the already-mentioned Giannone et al. (2010) and Banbura et al. (2010), who find BVARmodels to produce competitive forecasts (see also Karlsson (2013) for the extensive review onthis strand of literature). While our benchmark model specifications are rather standard, wealso test some more recently suggested specifications using stochastic search variable selectionto allow for more heterogeneity across the equations. Lastly, our paper relates to the studieson business cycle drivers in a small open economy, attempting to find the balance betweenthe findings that inflation is largely (and increasingly) a global phenomenon (see e.g. studiesby Ciccarelli and Mojon (2010), Mumtaz and Surico (2012)) and the research that finds littlesupport for the globalisation hypothesis (see e.g. the works by Calza (2009), Ihrig et al. (2010)).

The main contribution of our paper, in our view, lies in the disaggregate analysis of inflationdynamics in a small open economy, while at the same time retaining consistent and transparenttreatment of the data. This allows us to raise a number of questions which would not be possiblein an aggregate inflation analysis. To the best of our knowledge, there are only few studies in theliterature having similar disaggregate inflation approach. The closest to ours are the papers byGiannone et al. (2010) and Roma et al. (2004), focusing mostly on forecasting performance, andSzafranek and Ha lka (2017), who estimated separate BVAR models for each individual HICPcomponent.

The paper is structured as follows. In Section 2 we describe the specification of the model:prior distributions, data and prior parameters. In Section 3 we use out-of-sample forecastingexercise to evaluate the forecasting accuracy of the model described in Section 2. Section 4 isdevoted to structural analysis and drivers of the HICP components. Lastly, Section 5 concludes.

2 Specification of the model

2.1 Data

In this subsection we familiarise with the data used in the analysis, while also contemplatingpotential determinants of the HICP components. As an initial step, we present some basicdescriptive statistics of the Lithuanian HICP components in Table 1. For the full description ofthe data used in the paper, refer to Appendix A.

The Lithuanian HICP (sub)components in Figure 1 exhibit both – common and their own

6

Table 1: Descriptive statistics of the Lithuanian HICP components

HICP % m-o-m mean m-o-m sd

Unprocessed food (UF) 8% 0.22 1.15

Processed food (PF) 21% 0.32 0.55

Non-energy ind. goods (NEIG) 32% -0.03 0.31

Services (SERV) 27% 0.29 0.55

Energy (ENERG) 12% 0.22 1.55

Note: Reported weights represent consumer spending in Lithuania in 2017, while the mean and

sd statistics of the seasonally adjusted monthly changes in inflation indices were computed for

the sample 2001M1-2017M7.

specific variation. The common variation is especially pronounced during the pre-crisis periodin 2008 and during the global financial crisis in 2009, when there was a considerable degreeof comovement across most of the HICP subcomponents, and consequently, across the 5 maincomponents. Also, over the long term, four of the five HICP subindex groups in Table 1 experi-enced quite similar growth rates, which leads us to conjecture that the HICP groups may havea strong common trend. On the other hand, some subcomponents exhibit their own distinctivetrends (recognised by the red horizontal lines in Figure 1) – these prices are mostly relatedto technology services/prices. Also, one can easily spot the recent pickup in prices of services(supposedly due to rising wages), reminiscent of the 2004-2005 behaviour, while the changes inother HICP groups remain still rather mixed.

The existence of interaction between the HICP components would validate our choice tomodel the components jointly. Assuming that spillovers between the HICP components arethe result of one HICP product group being an intermediate input in the other’s productionprocess, we expect the spillovers to be most visible in the cases of “4 HICP groups → services”and “energy → 4 other HICP groups”. However, it is hardly possible to infer the presence ofspillovers from the heatmap in Figure 1 as we do not take into account the effect of commonenvironment.

7

Figure 1: Heatmap of m-o-m changes of 92 Lithuanian HICP components

UF

PF

NE

IGS

ER

VE

NE

RG

2000 2004 2008 2012 2016

Note: 92 components (seasonally adjusted) are grouped into 5 main producttypes. Red colour denotes negative m-o-m change, while green – positive. In-tensity of colour defines magnitude of a change. To improve pattern visibility,the prices within the 5 types were ordered with single linkage clustering using1− corr(xi,t, xj,t) as a dissimilarity measure between time series xi,t and xj,t.

In order to get some intuition regarding the potential determinants of the HICP components,in Figure 2 we plotted the price indices against some domestic and foreign macroeconomic vari-ables – the “usual suspects” to explain their variation. As one might expect, global commodityprices seem to play an important role in determining food and energy prices in Lithuania: worldfood price index precedes UF and PF fluctuations, while the changes in ENERG index mostlycoincide with changes in oil price. On the other hand, the economic activity variables appearto be the main drivers of core inflation subindices (NEIG and SERV). However, in this case itis hard to discern if the impact comes from domestic or foreign variables (especially consideringthat foreign variables can also have an indirect effect).

8

Figure 2: Lithuanian HICP components and their potential determinants

Unprocessed food

2005 2010 2015

−40

−20

020

40

60

y−o−

y ch

an

ge

UFWorld food prices

GDPWorld demand

Processed food

2005 2010 2015

−40

−20

020

40

60

y−o−

y ch

an

ge

PFWorld food prices

GDPWorld demand

Non−energy industrial goods

2005 2010 2015

−20

−10

010

20

y−o−

y ch

an

ge

NEIGUnemployment

GDPImport deflator

Services

2005 2010 2015

−30

−20

−10

010

y−o−

y ch

an

ge

SERVUnemployment

GDPWorld demand

Energy goods

2005 2010 2015

−50

050

y−o−

y ch

an

ge

ENERGUnemployment

Oil priceGDP

Note: For all variables yearly changes are in %, except for the unemployment rate, where yearly changes are inpercentage points

Having presented some basic stylised facts regarding the HICP components’ dynamics, wenow turn to the model to explore the spillovers between the HICP components, identify theirdeterminants and study origin and forecasting ability of the determinants.

2.2 Model

Throughout the paper we use a basic Bayesian VAR model specification with p lags:

yt = µ+A1yt−1 +A2yt−2 + . . .+Apyt−p + εt. (1)

For hyperparameter selection and application to forecasting (Sections 2-3) we use the modelwith 14 variables: 5 Lithuanian HICP components (UF, PF, SERV, NEIG and ENERG), 5domestic variables (GDP, import deflator, unit labour cost index and unemployment rate) and5 foreign variables (oil price, food commodity price index, EUR/USD exchange rate, Eoniainterest rate and world demand index for Lithuanian exports). The model is specified for them-o-m differences of the variables.

Although technically, the model can handle any number of variables, our objective was (inaddition to 5 HICP indices) to include only the main price determinants, representing differentsources of inflation. We limited the model scale, as a large scale model may pose some issuesin the structural analysis part of the paper: results may be hard to interpret in the case ofCholesky decomposition scheme or it may be hard to define the structural shocks based on signrestrictions. On the other hand, we agree that for the forecasting application it may be beneficialnot to limit the number of variables included in the model.

We set the parameter prior distribution as in Litterman (1985), with parameter vector as-sumed to be jointly normal with means: E(µ) = 0n×n, E(Al) = 0n×n, l = 1...n. The parametervariances are parameterised as follows:

9

V ar(µi) = λ21λ

24σ

2i ,

V ar(ali,j) =σ2i

σ2j

(λ1λ2λ5(i, j)

lλ3

)2

, i 6= j,

V ar(ali,i) =

(λ1

lλ3

)2

,

(2)

where ali,j is an element of the matrix Al, l = 1...p, i, j = 1...n, σ2i are residual variances estimated

from univariate AR regressions for every variable, and λ1, λ2, λ3, λ4, λ5 are hyperparameters usedto control the shrinkage.

The model specification in (2) is controlled by 5 hyperparameters: λ1 sets the general shrink-age common to all coefficients in (1), λ2 additionally weights the cross-variable coefficients, λ3

controls for lag shrinkage and λ4 is used for intercept shrinkage. We employed λ5(i, j) to im-pose block exogeneity restriction between foreign and Lithuanian variables, i.e. we assume thatLithuanian variables do not influence foreign variables, while foreign variables can have influenceon Lithuanian variables. When i is a foreign variable and j is a Lithuanian variable, λ5(i, j) = λ5

is used to shrink the coefficient towards 0. In other cases λ5(i, j) = 1.We opted to use the Litterman prior as it is standard in the literature and allows to perform

computations in a reasonable amount of time. Other options were less suitable for our objective,as e.g. the normal-Wishart prior would not allow for the block-exogeneity feature, while otherpopular priors, such as normal-diffuse and independent normal-Wishart prior, would make therepeated estimations needed for the hyperparameter grid search too time consuming. We appliedthe independent normal-Wishart prior (based on the already found hyperparameter values) fora competing model in the forecasting application and as our only prior setting in the structuralanalysis part of the paper.

2.3 Selection of hyperparameters

The literature usually adopts one of few methods to set the hyperparameter values in (2) andthus control for informativeness of prior distribution: e.g. Banbura et al. (2010) proposed toselect shrinkage which would yield a desired in-sample fit, whereas Giannone et al. (2012) arguedthat the most natural way to set the hyperparameters in a Bayesian framework is to let themmaximise marginal likelihood of the data. Since one of the main applications of our model isforecasting, we opted for the intuitive approach used by Doan et al. (1983), i.e. to select thehyperparameters which minimise out-of-sample forecasting error in the “training” period.

We performed a recursive out-of-sample forecasting exercise for various combinations of thehyperparameters in the period of 2006M12-2010M11. The first forecast was generated for themodel estimated in 2000M1-2006M12, the second forecast was based on the 2000M1-2007M1sample and so on, expanding the sample with every consecutive period. In the forecastingexercise we also retained the ragged-edge properties of the data, simulating the data publicationlag at the end of the sample, and later using conditional forecasting methods developed byWaggoner and Zha (1999) with implementation of Jarocinski (2010) to fill in the missing valuesand generate the forecasts. In the grid search, we treated the lag number p as another unknownparameter jointly with the shrinkage parameters. To be specific, we were interested in theperformance of different values of (λ1, λ2, λ3, p) parameter set. We fix λ4 = 100, which inessence states that we do not possess any additional information regarding the mean valueof the intercept and we allow the data to speak. On the other hand, we set λ5 to be very

10

small (λ5 = 0.00001), which reflects our view that Lithuania, being a small economy, cannotsignificantly influence the global variables.

We find the parameter set generating the lowest RMSE to be: λ1 = 0.1, λ2 = 0.5, λ3 = 0.5,p = 6. In order to get more insight regarding the optimal parameters, we plotted the RMSEresults of the exercise as a function of (λ1, λ2, λ3, p), cutting along two dimensions while holdingother parameters fixed at their optimal values – see Figure 3.1

Figure 3: Parameter grid search results (relative RMSE of total HICP as a function of modelparameters)

0.001

0.01

0.05

0.1

0.5

1

1 3 6 9 12 13Number of lags(p)

Ove

rall s

hri

nkage

(λ 1

)

1

2

3

4

5

RMSE

RMSE(p,λ1|λ2=0.5,λ3=0.5)

0.5

1

1.5

0.001 0.01 0.05 0.1 0.5 1

Overall shrinkage (λ1)

Cro

ss v

ar.

sh

rin

kage

(λ 2

)

1.0

1.5

2.0

2.5

RMSE

RMSE(λ2,λ1|p=6,λ3=0.5)

0.5

1

1.5


Cro

ss v

ar.

sh

rin

kage

(λ 2

)

1.0

1.5

2.0

2.5

RMSE

RMSE(p,λ2|λ1=0.1,λ3=0.5)

0

0.5

1

1.5

0.001 0.01 0.05 0.1 0.5 1

Overall shrinkage (λ1)

Lag

dec

ay

(λ3)

1.2

1.5

1.8

RMSE

RMSE(λ3,λ1|p=6,λ2=0.5)

0

0.5

1

1.5


Lag

dec

ay

(λ3)

1.0

1.1

1.2

1.3

RMSE

RMSE(λ3,p|λ1=0.1,λ2=0.5)

Note: We computed the relative RMSE as follows. First, we forecasted 5 HICP components separately andobtained m-o-m inflation forecasts for 12 months ahead. Then we calculated an aggregate RMSE for totalHICP as a weighted average of components’ RMSE using components’ weights in the HICP as weights. Lastly,we computed the relative RMSE measure as a ratio to the RMSE produced by the benchmark model (thebenchmark is an ARIMA model selected according to the Akaike criterion) and reported the average value overthe 12 month horizon.

Figure 3 reveals several important results about the optimality of the parameters. First, asdocumented in other studies (e.g. De Mol et al. (2008)), it confirms that inclusion of additionalparameters (in this case in the form of lags) demands for an increase in shrinkage. This resultcan be seen in all three graphs in Figure 3 that include lag number p: for high lag numbers itis preferable to increase the shrinkage (but not too much!).2 Also, we observe that the cross-variable shrinkage, one of the features of Minnesota prior, actually works for our data: afterapplying cross-variable weighting, RMSE values decrease and it holds for all λ1 and p values.Results in Figure 3 also seem to favour lag weighting – more distant data is treated as lessimportant for forecasting. We consider this feature to be a property of average behaviour as,in some cases, due to commodity price/cost transmission lag, more distant lags may actuallymatter more than the recent ones (refer to Stakenas (2015) for some evidence on transmission

1In order to keep the computational time reasonable (which can rapidly inflate due to the high dimensionalityof the grid), we restricted the grid search only to the values depicted in Figure 3.

2Although λ1 is the main shrinkage parameter, up to some point λ1, λ2, λ3 substitute each other’s effect, andwe can think of all three parameters as representing general shrinkage for making this point.

11

lags for the Lithuanian data). Lastly, Figure 3 serves as a reminder that a researcher shouldbe cautious in selecting the shrinking parameters in an arbitrary manner as the forecastingperformance of a model can change quite significantly.

The posterior means of BVAR regression coefficients for the optimal hyperparameters aredepicted in Appendix F, Figure F1. What we notice first, is that most of the parameters in FigureF1 tend to be close to zero. This signals that the coefficient matrices may have a sparse structure.On the other hand, according to De Mol et al. (2008), if the data has a factor structure and allof the variables are informative for the common factors, growing number of variables requiresusing a prior which increasingly shrinks regression coefficients towards zero. Hence, a competinghypothesis could be that the variables with near-zero coefficients approximate common factors.Note as well that Figure F1 also illustrates (presumably) the result of the lag shrinkage – thecoefficients of variables with higher lag orders tend to get smaller in absolute values. Lowcoefficient values for high lag orders in Figure F1 may also explain why the improvement inRMSE values for models with lag orders higher than 3 is not very noticeable. In general, apractitioner may favour a more parsimonious (and therefore more transparent) model with 3lags rather than the one generating the lowest RMSE values.

3 Forecast evaluation

In this section we examine the out-of-sample forecasting properties of the model, comparing theforecasting accuracy of its various specifications.

We evaluated model’s prediction accuracy in the period 2010M12-2015M12 using a recursiveforecasting design, i.e. the first forecast was generated based on the sample 2000M1-2010M12and the last one – on the model estimated in 2000M1-2015M12. In the forecasting exercise, wetry to mimic real-time conditions available to a forecaster, deleting data values that should notbe available at the time of forecasting due to data publication lag.3 In the case of unconditionalforecasting, these “ragged-edges” of the data are dealt with using the Gibbs sampling algorithmdeveloped by Waggoner and Zha (1999) with implementation of Jarocinski (2010). In the caseof actual conditional forecasting, we filled the “ragged-edges” with conditional assumptions andproceeded using the aforementioned methods. Note also that in the forecasting exercise weemployed the model parameters found in Section 2.

We tested the forecasting performance of several competing models. In addition to our mainBVAR model specification based on the Minnesota prior (with residual covariance matrix as-sumed to be known), we also tested a BVAR model with an independent normal-Wishart prior.4

As conditional forecasting (forecasting based on variable paths derived from other sources) isone of the most widely used methods of a practitioner, our objective in this case was to testhow much modelling of the unknown residual covariance matrix can influence results, especiallyin the conditional forecasting setting. Also, motivated by the idea that the HICP componentdeterminants can be quite different and potentially not all variables are helpful in forecasting allHICP indices, we added a BVAR model employing stochastic search variable selection (SSVS),based on the algorithm by Korobilis (2013). In this specification all the coefficients can individ-ually be excluded from the model based on the likelihood ratio of the model with/without thecoefficient. Lastly, as a benchmark model we used a univariate AR(p) model with a lag selectedaccording to the Akaike criterion – we allow for up to 12 lags and select the optimal lag at each

3Due to lack of real-time data vintages, we used only the revised dataset and we did not simulate real-timeseasonal adjustment.

4Refer to e.g. Dieppe et al. (2016) for model definition with the independent normal-Wishart prior.

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forecasting step.

3.1 Unconditional forecasts

Unconditional forecasting corresponds to a case when a forecaster does not possess any additionalinformation that would be useful in the forecasting process; therefore, we expect it to representa setting, producing the lower limit of model forecasting accuracy. The results of the out-of-sample exercise for unconditional forecasting are presented in Table 2. The RMSE values inTable 2 are relative to benchmark RMSE, with values lower than 1 representing improvementover the benchmark. The values in bold show statistically significant differences in the forecastingaccuracy according to the test by Diebold and Mariano (1995).

Table 2: Relative RMSE of unconditional forecasts

3m 6m 9m 12m

Litterman

UF 1.05 1.06 1.04 0.98PF 0.86 0.88 0.92 0.95NEIG 1.06 1.1 1.11 1.11SERV 1.12 1.15 1.12 1.11ENERG 0.94 0.93 0.96 0.97

Normal-Wishart


SSVS


Note: The RMSE values are relative to the benchmark RMSE. Values in bolddenote statistically significant difference according to the Diebold-Marianotest (two-sided alternative hypothesis, 95% confidence level). The forecasts(median of 1000 forecast draws) were generated every month in the period of2010M12-2015M12.

The results in Table 2 and Figure 4 indicate that modelling residual covariance matrixslightly improves RMSE values, though it comes with a cost of increased computational difficulty.Interestingly, BVAR models with Litterman and normal-Wishart priors improve only the PFand ENERG forecasts, while forecasts of e.g. SERV component, presumably more suitable formultivariate modelling due to dependence on a broad set of factors, worsen. What is more,applying SSVS to BVAR model starkly improves RMSE values for all HICP components exceptfor SERV.

Observing the improvement of forecasts under the SSVS model, one might be tempted toconclude that it would be helpful to reduce the number of variables in the HICP equations(as they are actually dependent on fewer factors); however, we believe it might not necessarilybe the case. Judging from the actual out-of-sample forecasts’ graphs in Appendix B, FigureB1, it seems that the differences in SSVS forecasts were generated by better prediction of themean and not by prediction of fluctuations around the mean. This suggests that a model with

13

a time-varying intercept might be a good modelling alternative. Lastly, note that we observestatistically significant improvement of forecasts only for the Litterman and normal-Wishartprior based models and only for some forecasting horizons of PF and ENERG inflation outcomes.Hence, while the RMSE improvement for SSVS model is generally much larger, it is also muchmore volatile, which does not allow us to claim that the SSVS model produces statisticallysignificantly more accurate forecasts than the benchnark.

Figure 4 summarises the main messages from the unconditional forecasting exercise. Whilewe observe that BVAR models do not outperform the benchmark model when measured bythe aggregated RMSE results, individual component forecasts using BVAR with SSVS lookpromising. On the other hand, the graph on the left in Figure 4 perfectly illustrates the meritsof Bayesian shrinkage – a non Bayesian VAR model with the same number of lags and dimensionperforms much worse, practically making it unusable.

Figure 4: Unconditional forecasting results

2 4 6 8 10 12

1.0

1.2

1.4

1.6

VAR models vs. benchmark

Horizon (months)

RM

SE

rati

o

BVAR (Litterman)BVAR (N.Wishart)

BVAR (SSVS)VAR

2 4 6 8 10 12

0.4

0.6

0.8

1.0

1.2

1.4

1.6

BVAR (SSVS) unconditional forecasts

Horizon (months)

RM

SE

rati

o

UFPF

NEIGSERV

ENERG

Note: RMSE values are relative to the RMSE values produced by the benchmark model.The RMSE values for total HICP in the left-hand side graph were aggregated from the HICPcomponents’ RMSE using component weights in 2016. The non Bayesian VAR model in theleft-hand side graph was estimated using 6 lags.

3.2 Conditional forecasts

In the conditional out-of-sample forecasting exercise we aim to examine the usefulness of addi-tional information (provided in the form of variables’ future paths) in predicting changes in theHICP components. We are interested in two conditional forecasting cases: forecasting based onpseudo real-time information and forecasting based on actually realised data. In the first case(which represents a realistic scenario), future paths of variables were constructed using Bank ofLithuania forecasts (for GDP, import deflator, ULC, unemployment rate and world demand ofexports) and random walk assumption (for oil price, food commodity price index, exchange rateand interest rate). In the second case (which represents the upper limit of conditional forecast-ing capabilities), we use the “perfect” conditions for conditional forecasting, i.e. the actuallyrealised data values for all the variables except the 5 HICP components.

Conditional forecasting results in Tables 3-4 convey several somewhat conflicting messages.On one hand, we observe that the PF and ENERG forecasts statistically significantly improvedover the benchmark for all the model specifications. On the other hand, conditional forecastsstatistically significantly deteriorated the NEIG forecasts for the Litterman and normal-Wishartprior specifications. We see two potential culprits for the increase in conditional forecastingRMSE: either it signals that the underlying factors of the NEIG component have changed in

14

Table 3: RMSE of conditional forecasts based on pseudo real-time data

3m 6m 9m 12m

Litterman


Normal-Wishart

UF 1.09 1 1.03 0.9PF 0.81 0.81 0.8 0.8NEIG 1.13 1.15 1.2 1.21SERV 1.15 1.18 1.11 1.07ENERG 0.94 0.91 0.94 0.93

SSVS



the out-of-sample period, or the conditional forecasting algorithm failed to realistically attributeinnovations in forecasting process. Lastly, we note that similarly to the unconditional forecastingresults, the SSVS model produces the most accurate forecasts for all the components other thanSERV. Again, after examining the graphs of historical forecasts in Appendix B, Figures B2-B3,we interpret this result as signalling some potential for a time-varying coefficient model – weobserve the main forecast differences in their levels and not in variation.

The results in Figure 5 suggest that conditioning on additional information is most useful forforecasting PF and ENERG components. This may not come as a surprise as these componentsare considered to be heavily dependent on volatile global commodity price fluctuations andknowing these fluctuations beforehand would certainly help to increase the forecasting accuracy.On the other hand, for the Litterman and normal-Wishart models, the ENERG forecastingaccuracy improved only about 15% after conditioning on the actually realised oil price variations(see Table 4). This improvement seems a bit too low and a more specific model for the ENERGcomponent is likely to achieve better results.

15

Table 4: RMSE of conditional forecasts based on actually realised data

3m 6m 9m 12m

Litterman


Normal-Wishart


SSVS

UF 1.06 1.07 1 0.91PF 0.85 0.71 0.59 0.5NEIG 1.03 0.97 0.93 0.9SERV 1.3 1.37 1.41 1.46ENERG 0.8 0.74 0.72 0.69


Figure 5: RMSE of conditional forecasts relative to unconditional forecasts’ RMSE

2 4 6 8 10

0.7

0.8

0.9

1.0

1.1

Real−time conditions vs. no conditions

Horizon (months)

RM

SE

rati

o

UFPF

NEIGSERV

ENERG

2 4 6 8 10

0.7

0.8

0.9

1.0

1.1

Realised data conditions vs. no conditions

Horizon (months)

RM

SE

rati

o

UFPF

NEIGSERV

ENERG

Note: Forecasts were produced using the BVAR model with the Litterman prior.

4 Structural analysis

In this section we present the structural BVAR model. First, we present the shock identificationschemes used to achieve a structural interpretation and then we turn to the analysis of HICPcomponents’ determinants.

16

4.1 Shock identification

To identify our model’s structural shocks we used two methods: sign restrictions and Choleskydecomposition. We treat identification by sign restrictions as our main method, as it usuallyprovides more economic interpretation. We applied identification by Cholesky decompositionmainly as a robustness check and also to obtain additional insights regarding the drivers ofthe Lithuanian HICP components. To ease shock identification and interpretation of results,we slightly reduced the number of variables included in the model (compared to the modelin Section 3). For structural analysis we used the model with the following variables (in theorder used for the Cholesky decomposition): oil price, global food commodity prices, worlddemand for Lithuanian exports, Lithuanian GDP, Lithuanian import deflator, Lithuanian ULC(unit labour costs), ENERG, UF, PF, NEIG and SERV. The identification by sign restrictionsrequired restrictions on real wages, therefore, for this case we replaced the Lithuanian ULC withreal wages. For modelling the residual covariance matrix we employed the normal-Wishart priorwith hyperparameters set to the values found in Section 2.

Table 5 summarises sign and zero restrictions used to identify 5 structural shocks. Since themodel is estimated at monthly frequency, the identification based on contemporaneous restric-tions may be hard to justify – economic agents, likely, are not able to react to shocks already inthe same month. Therefore, we implemented the restrictions presented in Table 5 for variablecumulative responses three months after the shock. Note also that the sign restrictions in Table5 are defined for headline HICP responses, but we do not have an explicitly defined the headlineinflation variable in the model. In order to test the “HICP(total)” restrictions, we obtainedthe headline inflation reactions by aggregating the reactions of HICP components using averageconsumer basket weights in the 2000-2017 period. Additionally, we filtered out extreme impulseresponses by imposing magnitude restrictions on contemporaneous variable responses. Specifi-cally, we bounded the contemporaneous responses in world demand, aggregate HICP, real wages,GDP and import deflator variables in absolute value not to exceed 10% variation in case of a1% change in a target variable (target variables are: GDP for domestic demand/supply, wagesfor wage bargaining shock, oil price for oil supply shock and world demand for world demandshock).5

The identification by Cholesky decomposition is based on the following ordering of variables:foreign variables, Lithuanian GDP and Lithuanian price variables. This ordering naturallyplaces the needed small-country restrictions on the Lithuanian variables – shocks to the Lithua-nian variables cannot affect foreign variables contemporaneously (and due to block exogeneityrestrictions in the subsequent periods as well). Among the foreign variables, we ordered globalcommodity prices first, as they are determined by global demand and supply and are less likelyto be affected contemporaneously by the demand for Lithuanian export. Similarly to the for-eign variables, we motivate the ordering of Lithuanian HICP components based on the assumedorigin of their determinants, placing components which are most affected by global commodityprices first (ENERG, UF and PF), followed by NEIG and SERV.

The sign restrictions in Table 5 are based on impulse responses in the New Keynesian macroe-conomic models (see e.g. Peersman and Straub (2004)) with the additional assumption that asmall open economy cannot affect global variables (this assumption is also used e.g. in Jovicic

5Kilian and Murphy (2012) showed that sign restrictions alone are insufficient to infer impulse responses inthe crude oil market, therefore placing additional magnitude restrictions. In our case, magnitude restrictionsserve mainly for tightening the confidence bounds around the impulse responses by eliminating economicallyunreasonable structural models. We consider the magnitude restrictions to be loose enough to avoid circularreasoning critique, while also noting that our main focus in the section is on historical decomposition of variables,which remains robust to the addition of magnitude restrictions.

17

Table 5: Sign and zero restrictions for shock identification

GDP HICP (total) ENERG Real wages Oil price World demand

Domestic demand + + 0 0

Domestic supply + - + 0 0

Wage barg. + - - 0 0

Oil supply - + + -

Foreign activity + + +

and Kunovac (2017)). The restrictions for somewhat less common shock “wage bargaining”are based on the paper by Foroni et al. (2015). The authors model wage bargaining shock us-ing dynamic stochastic general equilibrium framework: a decrease in an employee’s bargainingpower reduces real wages in the economy, lowering marginal costs and prices. This allows firmsto increase employment and output. Foroni et al. (2015) also used the responses of unemploy-ment and vacancies to separate labour supply and matching efficiency shocks from the wagebargaining shock. In our case, although the three labour market shocks are inseparable, wechose to name the shock “wage bargaining”, as it provides the most interpretable story and, inour view, was the most important of the three in the analysed period. As in Foroni et al. (2015),in order to differentiate from the wage bargaining shock, we also restricted domestic supply/technology shock to have a positive impact on real wages. As regards to the foreign shocks,foreign activity/demand shock acts as the main foreign shock affecting the Lithuanian economyand is distinguished from the domestic shocks through non zero reactions of the global variables.Lastly, following the reasoning in Kilian (2009), who states that oil supply and demand shockshave very different economic implications and should be treated separately, we identified the oilsupply shock having positive oil price and ENERG responses, while the reactions to the Lithua-nian GDP and world demand are negative. In our case, oil demand shock remains inseparablefrom the foreign demand shock: a surge in foreign demand also triggers demand in oil.

We implemented identification by sign and zero restrictions using the algorithm of Ariaset al. (2014), which provides us with 11 (the number of variables in the system) uncorrelatedshocks. Table 5, however, presents a partially identified model with only 5 identified structuralshocks. This raises a question how to treat the remaining 6 shocks. The question is particularlyrelevant for HICP components’ decomposition into their determinants (the subject of the nextsubsection). One of the solutions would be to leave the 6 shocks (and their contributions)unidentified. On the other hand, note that having found that there exist 5 structural shockssatisfying the restrictions in Table 5 (and, thus, accepting the system as representing the maindrivers in the economy), the rest of the shocks in most cases can also be identified as one ofthe structural shocks from Table 5.6 As a result, we may have several, e.g. domestic demandshocks, that are orthogonal to each other. In the subsequent forecast decomposition graphs wechose to add up the contributions of multiple structural shocks having the same identificationpattern.

6Given that the shocks satisfy the magnitude restrictions, only the following 3 response patterns are leftunidentified (the sign of a variable’s response in parenthesis): [GDP(-), ENERG(-), oil price(+), world demand(-)], [GDP(+), oil price (+), world demand (-)] and [GDP(-), oil price (+), world demand (+)].

18

4.2 Drivers of HICP components

In this subsection we analyse the drivers of HICP components, examining historical decomposi-tion of their year-on-year growth rates. The decomposition allows us to estimate how much eachof the shocks contributes to the components’ annual inflation at each time period, identifyingtheir origins and dynamics. We examine historical decompositions of the five HICP componentsone by one, emphasising the main drivers, their differences, contributions to the largest pricechanges and recent developments in the contributions.

Historical decomposition of the Lithuanian unprocessed food inflation based on sign restric-tions is presented in Figure 6. The black line in the figure (and in the subsequent historicaldecomposition graphs) represents the actual annual inflation. The “Other” part in the graphmainly accounts for inflation forecast by the constant in equation (1) (a small part of it alsoconsists of some unidentified shocks). We can interpret this part as representing the monetarypolicy targeted inflation rate, general price convergence to the EU level or any other long-termUF market-specific process.

The drivers of the UF inflation vary quite a bit over time. During the pre-crisis period in 2007-2008 the UF inflation was driven mainly by domestic components – domestic demand/supplyand wage bargaining shock. This period coincided with the overheating of the economy, hence,unsurprisingly we see domestic demand shocks producing the biggest contributions to the UFinflation. On the other hand, the inflation dip in 2009-2010 tells quite a different story, as itcan be mainly attributed to the foreign shocks: foreign demand and oil supply. The negativeforeign factors were also present in the recent period of 2015-2016 when the shale oil boom ledto the decline in oil prices, while the euro area economic activity remained weak. Given thatthese factors have disappeared, we might expect higher UF inflation in the near future. For theUF decomposition graph based on Cholesky identification scheme refer to Appendix C, FigureC1.

Figure 6: Decomposition of UF y-o-y growth (identification by sign restrictions)

−20

−10

010

OtherForeign act.Wage barg.Oil supplyDom. demandDom. supply

2002 2006 2010 2014

−20

−10

010

y−o−

y ch

an

ge (%

)

Note: The graph depicts the average of decompositions based on 1000 Gibbs sampler draws.

PF inflation decomposition in Figures 7-8 has several common features with the UF graph– namely, the dominance of domestic shock contributions in the pre-crisis period and foreignshock contributions in 2015-2016. Interestingly, unlike UF, SERV and NEIG components, the

19

PF annual inflation remained positive in the wake of the 2008-2009 economic crisis. Indeed,the decline in m-o-m PF prices in 2009 was short-lived (see Figure 1 for m-o-m changes in thesubcomponents). The result resonates with the so-called missing disinflation phenomenon, wheninflation in advanced countries in the post-crisis period remained higher than expected, given theunfavourable economic conditions (see e.g. Friedrich (2016)). This PF price behaviour can beexplained by several factors: tax increases in 2009 (excise and value added taxes were increasedin order to improve fiscal deficit), global food commodity price growth in 2010-2011 and PFtradability. The effect of tax changes can be seen in both PF decompositions: in Figure 7 it wasinterpreted as a domestic supply shock (a drop in GDP, increase in prices), while in Figure 8shocks were attributed to the PF variable itself.7 Note as well that the Cholesky-scheme-baseddecomposition helps to identify global food commodity prices as one of the main factors drivingPF prices – we could not identify commodity supply shock in the sign restriction framework andit seems it was often attributed to the domestic supply shock. Lastly, partly due to tradabilityand dependence on global commodity prices, the annual PF inflation is highly correlated to theEuropean Union PF prices (refer to Appendix D, Table A1 and Figure D1) which, we believe,contributed to producing the aforementioned “missing disinflation” period in 2009-2011 also forthe Lithuanian PF prices.

Figure 7: Decomposition of PF y-o-y growth (identification by sign restrictions)

−5

05

10

15


2002 2006 2010 2014

−5

05

10

15

y−o−

y ch

an

ge (%

)


7This example demonstrates that the Cholesky decomposition sometimes can produce more interpretableresults, complementing analysis based on sign restrictions. On the other hand, we can broaden the “domesticsupply” labelling to incorporate tax shocks as they also fall under the same sign restrictions (positive valueadded tax shock suppresses consumption and increases prices). The downside of that is, of course, obscuredinterpretation. In a similar example, the increase of PF annual inflation at the very end of the sample of PFdecomposition (2017M3), caused by the excise tax increase for alcohol, in Figure 7 is explained by domesticdemand and supply shocks, while Figure 8 more naturally attributes it to shocks to the PF variable itself.

20

Figure 8: Decomposition of PF y-o-y growth (identification by Cholesky scheme)

−5

05

10

15 Other

SERVNEIGPFUFENERGULCIM_deflGDPWDRFPIOil

2002 2006 2010 2014

−5

05

10

15

y−o−

y ch

an

ge (%

)


The annual SERV inflation in Figure 9, as expected, is mainly driven by domestic factors(domestic demand/supply) and the long-term inflation trend. Also, note that although thewage bargaining shock contribution was already visible in the decomposition of UF and PFinflation, it becomes much more apparent in the SERV decomposition. During the periodsof high unemployment, lower opportunity to bargain for wages affects the prices of servicesnegatively, while during the periods of tight labour market, employees have more bargainingpower and it contributes to the SERV prices positively. Decomposition based on the Choleskyscheme in Figure 10 confirms the importance of wage dynamics in determining the SERV prices,as the ULC contribution to SERV prices is the most visible, compared to the decompositions ofother price components.

Figure 9: Decomposition of SERV y-o-y growth (identification by sign restrictions)

−5

05

10


2002 2006 2010 2014

−5

05

10

y−o−

y ch

an

ge (%

)


21

Figure 10: Decomposition of SERV y-o-y growth (identification by Cholesky scheme)

−5

05

10 Other

SERVNEIGPFUFENERGULCIM_deflGDPWDRFPIOil

2002 2006 2010 2014

−5

05

10

y−o−

y ch

an

ge (%

)


The decomposition of NEIG prices in Figures 11-12 tells two quite different stories: accordingto Figure 11, NEIG prices are mostly determined by domestic demand and supply shocks,while the decomposition based on Cholesky scheme emphasises mostly “foreign” shocks (foreigndemand and oil price shocks) and shocks to the NEIG variable itself. At first, the story inFigure 11 may not look very convincing – Lithuania is a small open economy with a very highopenness ratio (average trade to GDP ratio was 125% in the period of 2000-2016), therefore,we expect prices of tradable goods to be set in the global market. However, the dynamics ofNEIG prices in the European Union and Lithuania appear to be quite different: the correlationbetween annual inflation values is negative in the whole sample and only recently the indiceshave been becoming more aligned (see Appendix D, Figures D1-D2 and Table A1).8 This makesus believe that domestic demand and supply played an important role in determining LithuanianNEIG prices in the past (especially during the boom and bust periods in 2007-2008 and 2009-2010). The importance of local factors in the NEIG decomposition can be explained by lack ofcompetition, pricing-to-market effects and changes in non-production related costs. However,judging from the Figure D2 in Appendix D, Lithuanian and EU NEIG prices are becoming moresynchronised in the recent period and we should expect foreign factors to become more prevalentin determining the NEIG dynamics in the future.

8EU28 is Lithuania’s largest import partner for non-energy industrial goods – in the sample of 2002-2016,NEIG imports from the EU28 on average comprised 79% of all the NEIG imports (data from Eurostat).

22

Figure 11: Decomposition of NEIG y-o-y growth (identification by sign restrictions)

−4

−2

01

23


2002 2006 2010 2014

−4

−2

01

23

y−o−

y ch

an

ge (%

)


Figure 12: Decomposition of NEIG y-o-y growth (identification by Cholesky scheme)

−4

−2

02

OtherSERVNEIGPFUFENERGULCIM_deflGDPWDRFPIOil

2002 2006 2010 2014

−4

−2

02

y−o−

y ch

an

ge (%

)


The decomposition of ENERG prices (see Appendix C, Figure 13 and Figure C2), as ex-pected, reveals the importance of foreign activity and oil prices for the component dynamics.Interestingly, domestic supply shocks also produced sizeable contributions in Figure 13. Weinterpret the positive domestic supply contributions in 2010-2012 as caused partly by the clo-sure of Ignalina nuclear power plant (and the subsequent increase in electricity prices), whilethe negative contributions in 2014-2015 are likely related to the increase in competition in thenatural gas and heat energy markets.

23

Figure 13: Decomposition of ENERG y-o-y growth (identification by sign restrictions)

−20

−10

010

20


2002 2006 2010 2014

−20

−10

010

20

y−o−

y ch

an

ge (%

)


Apart from the general drivers of HICP components, we are also interested in the size ofspillovers between the HICP components: e.g. what if ENERG administered prices are raised,how is it going to influence other prices? What if taxes are hiked for PF products, is it going tospill over to other price components?

The annual inflation decomposition graphs based on the Cholesky scheme suggest that amongthe 5 HICP components, SERV is the most dependent on shocks in other components.9 Notethat in Figure 10, we observe spillovers to SERV prices from all the other HICP components– this feature is not so distinct in the decompositions of other HICP components. To separatethe magnitude of contributions from the transmission of shocks, we also computed the impulseresponses of HICP components for shocks in one of the components (see Appendix E, FiguresE1-E5). Impulse responses highlight that the contributions from other HICP components, visiblein Figure 10, are not only due to the magnitude of shocks in the components, but also due tostrong transmission links. SERV component reacts statistically significantly to shocks in allHICP constituents, while the reactions of other HICP components are statistically significantonly in several cases. Furthermore, the SERV reactions are largest for NEIG and PF shocks,which suggests that the spillovers can be interpreted as a cost structure story.

5 Conclusions

We have analysed 5 Lithuanian HICP components employing the medium scale Bayesian VARmodel. To avoid the curse of dimensionality we applied Bayesian shrinkage with parametersset in the out-of-sample forecasting exercise. We demonstrated the use of the model for twoarguably the most important applications from a practitioner’s point of view: forecasting andstructural decomposition.

We find that an increase in the number of model parameters demands a higher degree ofshrinkage, confirming earlier findings in the literature. We also find that cross-variable and lag

9Although we agree that part of the effect may be attributed to SERV being ordered last in the Choleskydecomposition, we do not present results for alternative orderings, as we believe this ordering provides the mostreasonable set of identifying assumptions among the orderings.

24

shrinkage improve the forecasts of Lithuanian HICP data. Although we believe these featuresto work on average, one can find specific cases when applying structure to the data can be alsodetrimental to the forecasts.

The model’s application to forecasting brings out several important results. First and fore-most, it shows that the model’s forecasts can be competitive against the benchmark model.Although the model can be used unconditionally – without assuming future paths of certainvariables, its main advantage (and user case) lies in conditional forecasting, which provides away to incorporate additional information into the forecasting process in a consistent manner.Second, although the SSVS model’s often low RMSE values can be interpreted in several ways,we believe they signal that the Lithuanian data may have experienced some structural changesand a model with time-varying coefficients (or at least time-varying mean) is a perspectivemodelling choice. Lastly, we note, that while our BVAR model provides a consistent modellingframework to analyse and forecast the five Lithuanian HICP components, from a perspectiveof pure prediction accuracy, for some components, a more promising alternative may be to useunivariate component-specific models, thus allowing for individual structure and reducing thenumber of estimated coefficients.

Using the decomposition of Lithuanian HICP components we find that the drivers of infla-tion components change quite a bit over time with both, domestic and foreign factors playingdominant roles at certain time periods. These influences are especially emphasised during theperiods of large inflation fluctuations: the pre-crisis period with prevalent domestic drivers, the2009-2010 crisis period with large foreign contributions and again – the 2015-2016 period withlarge negative shocks coming from abroad, resulting in low inflation in Lithuania and the euroarea. Moreover, we find the employee bargaining power to play an important role in determin-ing inflation outcomes: during the periods of low unemployment we find positive contributionsfrom the wage bargaining shock, while during periods of high unemployment the contributionsare negative. This result highlights that wages (and consequently inflation) in Lithuania aredetermined through interaction of economic growth and labour market tightness.

25

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27

Appendix

A Data description

Table A1: Data description.

Variable Source Transformations Description

UF Eurostat Log, data in differences, seasonally ad-justed using X-12-ARIMA

HICP unprocessed food index,2015=100

PF Eurostat Log, data in differences, seasonally ad-justed using X-12-ARIMA

HICP processed food index, 2015=100

SERV Eurostat Log, data in differences, seasonally ad-justed using X-12-ARIMA

HICP service price index, 2015=100

NEIG Eurostat Log, data in differences, seasonally ad-justed using X-12-ARIMA

HICP non-energy industrial goodsprice index, 2015=100

ENERG Eurostat Log, data in differences, seasonally ad-justed using X-12-ARIMA

HICP energy goods price index,2015=100

GDP Eurostat Log, data in differences, seasonally andcalendar adjusted data, quarterly datainterpolated to monthly using Denton-Cholette method

Gross domestic product at marketprices, chain linked volumes (2010)

Pimport Eurostat Log, data in differences, seasonally andcalendar adjusted data, quarterly datainterpolated to monthly using Denton-Cholette method

Deflator, imports of goods

ULC Eurostat Log, data in differences, seasonally ad-justed using X-12-ARIMA, quarterlydata interpolated to monthly usingDenton-Cholette method

Nominal unit labour cost based onhours worked

U Eurostat Log, data in differences, seasonally ad-justed

Unemployment rate, percentage of ac-tive population

Poil Bloomberg, own computa-tions

Log, data in differences Oil price for a barrel (in litas, mean ofthe period)

FPI Food and Agriculture Or-ganization of the UnitedNations

Log, data in differences Consists of the average of 5 commod-ity group indices (meat, dairy, cere-als, vegetable oils and sugar) weightedby their average export shares during2000-2004

Eonia Eurostat Log(1+x), data in differences Eonia rate (euro area, changing com-position), 3-month rate

EUR/USD Eurostat Log, data in differences Euro/dollar exchange rate, average inthe month

WDR Own computations Log, data in differences World demand indicator – weightedaverage of import volumes of tradingpartners. The weighting is by thethree-year moving average of the shareof LT export going to trading partnerk of total LT export).

Note: Seasonal adjustment was performed using default X-12-ARIMA parameters. The applied Denton-Cholette method min-imises the sum of high frequency series first difference (proportional) deviations. The method ensures that the average of highfrequency series in a low frequency period is equal to the low frequency series value in the same period.

28

B Out-of-sample forecasting graphs

Figure B1: Unconditional 12 month ahead out-of-sample forecasts of HICP components forvarious BVAR specifications

UF change over 12 months

2012 2013 2014 2015 2016 2017

−4

−2

02

46

%

Actual dataLitterman

N.WishartSSVS

PF change over 12 months

2012 2013 2014 2015 2016 2017−2

02

46

%


N.WishartSSVS

NEIG change over 12 months

2012 2013 2014 2015 2016 2017

−1

01

2%


N.WishartSSVS

SERV change over 12 months

2012 2013 2014 2015 2016 2017

−1

01

23

45

%


N.WishartSSVS

ENERG change over 12 months

2012 2013 2014 2015 2016 2017

−20

−15

−10

−5

05

10

%


N.WishartSSVS

Note: The forecasts were computed as a median of 1000 forecast draws.

29

Figure B2: Conditional 12 month ahead out-of-sample forecasts of HICP components for variousBVAR specifications based on pseudo real-time assumptions


2012 2013 2014 2015 2016 2017

−4

−2

02

46

%


N.WishartSSVS


2012 2013 2014 2015 2016 2017

−2

02

46

%


N.WishartSSVS


2012 2013 2014 2015 2016 2017

−2

−1

01

2%


N.WishartSSVS


2012 2013 2014 2015 2016 2017

01

23

45

%


N.WishartSSVS


2012 2013 2014 2015 2016 2017

−20

−15

−10

−5

05

10

%


N.WishartSSVS


Figure B3: Conditional 12 month ahead out-of-sample forecasts of HICP components for variousBVAR specifications based on actual data assumptions


2012 2013 2014 2015 2016 2017

−4

−2

02

46

8%


N.WishartSSVS


2012 2013 2014 2015 2016 2017

−2

02

46

%


N.WishartSSVS


2012 2013 2014 2015 2016 2017

−2

−1

01

2%


N.WishartSSVS


2012 2013 2014 2015 2016 2017

01

23

45

%


N.WishartSSVS


2012 2013 2014 2015 2016 2017

−20

−15

−10

−5

05

10

%


N.WishartSSVS


30

C Historical decomposition of annual growth rates

Figure C1: Decomposition of UF y-o-y growth (identification by Cholesky scheme)

−20

−10

010


2002 2006 2010 2014

−20

−10

010

y−o−

y ch

an

ge (%

)


Figure C2: Decomposition of ENERG y-o-y growth (identification by Cholesky scheme)

−20

−10

010

20


2002 2006 2010 2014

−20

−10

010

20

y−o−

y ch

an

ge (%

)


31

D Correlation between LT and EU HICP components

Table A1: Correlation between LT and EU HICP component counterparts

HICP total UF PF SERV NEIG ENERG

monthly changes 0.49 0.50 0.49 0.16 0.15 0.58

annual changes 0.65 0.53 0.75 0.36 -0.11 0.77

Note: Correlations were computed for seasonally adjusted (using X-12-ARIMA) monthlydata in the period of 2000M1-2017M11. EU data is of changing country composition.

Figure D1: Correlation between LT and EU HICP component counterparts’ annual changes ina 5-year moving window

2006 2008 2010 2012 2014 2016 2018

−0.5

0.0

0.5

1.0

Cor

rela

tion

UFPF

SERVNEIG

ENERG

Note: The graph depicts rolling correlations between LT and

EU inflation components in a 5-year (60 observations) moving

window. The dates denote last observations in the samples.

Figure D2: LT and EU NEIG annual changes

2005 2010 2015

−4

−2

02

An

nu

al ch

an

ge (%

)

LT EU

32

E Spillovers between HICP components: impulse responses basedon Cholesky scheme

Figure E1: Responses to 1% UF shock

0 5 10 15 20

0.0

0.5

1.0

1.5

2.0

2.5

UF

Months

%

0 5 10 15 20

−0.2

−0.1

0.0

0.1

0.2

PF

Months

%

0 5 10 15 20

0.0

0.1

0.2

0.3

SERV

Months

%

0 5 10 15 20

−0.0

50.0

00.0

50.1

0

NEIG

Months

%

0 5 10 15 20

0.0

0.2

0.4

0.6

ENERG

Months

%

Note: IRFs show median of 1000 bootstrap draws with 68% confidence interval.

Figure E2: Responses to 1% PF shock

0 5 10 15 20

0.0

0.5

1.0

UF

Months

%

0 5 10 15 20

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

PF

Months

%

0 5 10 15 20

0.0

0.2

0.4

0.6

0.8

1.0

SERV

Months

%

0 5 10 15 20

0.0

0.1

0.2

0.3

0.4

NEIG

Months

%

0 5 10 15 20

0.0

0.5

1.0

1.5

ENERG

Months

%


33

Figure E3: Responses to 1% SERV shock

0 5 10 15 20

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

UF

Months

%

0 5 10 15 20

0.0

0.2

0.4

0.6

PF

Months

%

0 5 10 15 20

0.0

0.5

1.0

1.5

2.0

2.5

SERV

Months

%

0 5 10 15 20

−0.1

5−0.0

50.0

50.1

5

NEIG

Months

%

0 5 10 15 20

−0.4

0.0

0.2

0.4

0.6

0.8

ENERG

Months

%Note: IRFs show median of 1000 bootstrap draws with 68% confidence interval.

Figure E4: Responses to 1% NEIG shock

0 5 10 15 20

−1.0

−0.5

0.0

0.5

1.0

1.5

UF

Months

%

0 5 10 15 20

−0.2

0.0

0.2

0.4

0.6

0.8

PF

Months

%

0 5 10 15 20

0.0

0.5

1.0

1.5

SERV

Months

%

0 5 10 15 20

0.0

0.5

1.0

1.5

2.0

2.5

NEIG

Months

%

0 5 10 15 20

−1.0

−0.5

0.0

0.5

1.0

ENERG

Months

%


Figure E5: Responses to 1% ENERG shock

0 5 10 15 20

−0.4

−0.3

−0.2

−0.1

0.0

0.1

UF

Months

%

0 5 10 15 20

0.0

00.0

50.1

00.1

50.2

00.2

5

PF

Months

%

0 5 10 15 20

0.0

00.0

50.1

00.1

50.2

0

SERV

Months

%

0 5 10 15 20

−0.0

20.0

20.0

60.1

0

NEIG

Months

%

0 5 10 15 20

0.0

0.5

1.0

1.5

2.0

ENERG

Months

%


34

F Posterior mean of regression coefficients

Figure F1: Posterior means of Ai elements (see equation (1)) for i = 1, 2, ..., 6

●

●●●●●●●●●●●●●

●

●

●●●●●●●●●●●●●●

●

●●●●●●●●●●●

●●

●

●

●●●

●

●

●●●●●

●

●●

●

●

●

●●●

●

●

●●

●●●●●●

●

●●

●●●●●●●●●●●●

●

●●●●●●●●●●●●●

●

●

●

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●

●●●●●●●●●●●●●●

●

●●●●●●●●●●●●●●

●

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●

●●

●

●●●●●●●●●●●●

●●

●

●●●●●●●●●●

●

●●●

●

0 50 100 150 200

−2.0

−1.0

0.0

0.5

1.0

Coefficients for lag=1

Coeff. index

Coe

ff. va

lue

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●●

●●

●

●

●●●●●●●●●●

●

●

●

●●

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●

●

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●

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●

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●

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●●

●

●●●●●●●●●●●●●

●

●●●●●

0 50 100 150 200

−2.0

−1.0

0.0

0.5

1.0


Coeff. index

Coe

ff. va

lue

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●

●●

●

●●●●●●●●●●

●

●

●●●●●●●●

●●●●●●●●●

●

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●

●●●●●●●●●●●●●●

●●

●●●●●●●●●●●●●

●●●●●●●●●●●●●●●

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●●●

●●●●●●●

0 50 100 150 200

−2.0

−1.0

0.0

0.5

1.0


Coeff. index

Coe

ff. va

lue

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●

●●

●●●●●●●●●●●

●

●●

●●●●●●

●●●●●●●●●●

●●●●●●●●●●●●●●●

●

●●●●●●●●●●●●●●

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●●●●●●

0 50 100 150 200

−2.0

−1.0

0.0

0.5

1.0


Coeff. index

Coe

ff. va

lue

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●●●

●

●

●●●●●●

●●●●●●●●●●●●●●

●●●●●●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

0 50 100 150 200

−2.0

−1.0

0.0

0.5

1.0


Coeff. index

Coe

ff. va

lue

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●●●●●●

●

●

●●●●

●●●

●

●●●●●●●●●●●●

●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

0 50 100 150 200

−2.0

−1.0

0.0

0.5

1.0


Coeff. index

Coe

ff. va

lue

Note: The graphs depict posterior means of BVAR regression coefficients at

different lags. The model includes 14 variables (as defined in subsection 2.2)

and uses Litterman prior with λ1 = 0.1, λ2 = 0.5, λ3 = 0.5, p = 6.

35

Slicing up inflation: analysis and forecasting of ...€¦ · ISSN 2029-0446 (ONLINE) WORKING PAPER...

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