WORKING PAPER SERIES No 56 / 2018

Slicing up inflation: analysis and forecasting of Lithuanian inflation components EXERCISE EVALUATION FORECAST REAL-TIME PSEUDO A DATASETS: MONTHLY LARGE USING GDP OF FORECASTING SHORT-TERM

No 1 / 2008

By Julius Stakėnas

BANK OF LITHUANIA. WORKING PAPER SERIES PAPER WORKING LITHUANIA. OF BANK 1 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, 2018 Reproduction for educational and non-commercial purposes is permitted provided that the source is acknowledged.

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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 Bayesian VAR framework. We deal with the parameter proliferation problem by setting the appropriate amount of shrinkage determined in the out-of-sample forecasting exercise. The main body of the paper consists of displaying the model’s performance in two applications: forecasting and analysis of inflation determinants. We find the model’s forecasts to be competitive against the univariate statistical models, particularly in the cases of predicting processed food and energy goods inflation. What is more, exercises based on conditional forecasting show that these two indices make the best use of accurate conditional information in terms of improving predicting accuracy. 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 the Lithuanian consumer price inflation.

Keywords: HICP subindices, Bayesian VAR, Bayesian shrinkage, inﬂation forecasting, structural decomposition JEL classiﬁcation: C32, C53, E37

4 1 Introduction

Monitoring and forecasting inflation is one of the primary interests of any inflation-targeting central bank, government concerned about its citizens’ income/wealth (re)distribution (as well as tax collection), or any economic agent basing his/her consumption and investment decisions on inflation outcomes. As inflation determinants vary over time, it is instructive to go past monitoring just one measure of inflation and study its constituent parts in order to better understand its causes and persistence. In this paper we use a Bayesian VAR (BVAR) model to 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 the ECB’s requirement for the Bank of Lithuania to provide forecasts of these price indices. On the other hand, the model is not reliant on the particular disaggregation scheme of consumer prices and can be straightforwardly adjusted to incorporate a different number of HICP subindices of various 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 (modelling standpoint), and secondly, in the ability to address concerns of policy makers and consumer groups 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 time keeping the level of aggregation high enough to justify the macroeconomic viewpoint. Note as well, that the HICP subindices used in the study are provided by the Eurostat for all European Union countries, making potential cross-country comparative analysis much easier. The direct application of our research results is closely linked (but not limited) to the Narrow Inflation Projection Exercise (NIPE) performed by the central banks in the Eurosystem. In this exercise, central banks provide the ECB with short-term forecasts of 5 HICP components, which then are aggregated at the euro area level. Our paper is motivated by the work of Giannone et al. (2010), who used a BVAR model to perform this exercise for the euro area data. In their study, 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 are set for), easy scenario analysis (availability of incomplete conditioning, consistent inclusion of expert judgement), model-based risk assessment around the projections, etc. All these potential uses and applications motivated our choice of a VAR model (over a framework of a set of univariate equations) for analysis and forecasting of HICP subindices. The Lithuanian HICP component forecasts were already studied in Stak˙enas(2015), where the forecasts were generated on a rather disaggregate level with 44 univariate equations. The paper concluded that forecasting HICP components on a disaggregate level and later aggregating the forecasts, produces predictions that are hard to beat regarding their accuracy, however, it also implies that the there are no spillovers between the HICP components and any scenario analysis becomes quite restrictive. In this paper, our objective is twofold – we aim not only for 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 (global vs. local), potential dependence on labour market conditions, differences in components’ factors, etc. Finally, multivariate modelling should also allow us to study interactions/spillovers between the components before making any restrictions. The flexibility of the model, allowing for interactions between the HICP subindices and dependence on a number of different determinants, comes at a cost of parameter proliferation and 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 principal components – the authors find that using a normal prior distribution, Bayesian regression gen- erates forecasts that are highly correlated with principal component forecasts. The authors also show that in case of growing number of parameters, coefficients have to be increasingly shrunk towards zero in order to obtain consistent forecasts. Banbura et al. (2010) used this result to estimate high-dimensional VAR models (up to 131 variables) and found that, when the degree of shrinkage is set in relation to cross-sectional dimension of the data, forecasts can be improved by adding more variables. The results of our paper link to the literature in three directions. First, we contribute to the Bayesian hyperparameter selection literature, studying it in the small open economy setting with a focus on inflation dynamics. We find that in this setting, the parameter shrinkage schemes suggested by Litterman (1985) are applicable, i.e. more distant lags and cross-variable lags ought to be shrunk more. We also reiterate the results by De Mol et al. (2008), observing how high 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 forecasting part of the paper relates to the studies on the forecasting performance of BVAR models, such as the already-mentioned Giannone et al. (2010) and Banbura et al. (2010), who find BVAR models to produce competitive forecasts (see also Karlsson (2013) for the extensive review on this strand of literature). While our benchmark model specifications are rather standard, we also test some more recently suggested specifications using stochastic search variable selection to allow for more heterogeneity across the equations. Lastly, our paper relates to the studies on business cycle drivers in a small open economy, attempting to find the balance between the findings that inflation is largely (and increasingly) a global phenomenon (see e.g. studies by Ciccarelli and Mojon (2010), Mumtaz and Surico (2012)) and the research that finds little support 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 inflation dynamics in a small open economy, while at the same time retaining consistent and transparent treatment of the data. This allows us to raise a number of questions which would not be possible in an aggregate inflation analysis. To the best of our knowledge, there are only few studies in the literature having similar disaggregate inflation approach. The closest to ours are the papers by Giannone et al. (2010) and Roma et al. (2004), focusing mostly on forecasting performance, and Szafranek and Halka (2017), who estimated separate BVAR models for each individual HICP component. 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 forecasting exercise to evaluate the forecasting accuracy of the model described in Section 2. Section 4 is devoted 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 contemplating potential determinants of the HICP components. As an initial step, we present some basic descriptive statistics of the Lithuanian HICP components in Table 1. For the full description of the 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 period in 2008 and during the global financial crisis in 2009, when there was a considerable degree of comovement across most of the HICP subcomponents, and consequently, across the 5 main components. 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 have a strong common trend. On the other hand, some subcomponents exhibit their own distinctive trends (recognised by the red horizontal lines in Figure 1) – these prices are mostly related to 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 in other HICP groups remain still rather mixed. The existence of interaction between the HICP components would validate our choice to model the components jointly. Assuming that spillovers between the HICP components are the result of one HICP product group being an intermediate input in the other’s production process, 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 of spillovers from the heatmap in Figure 1 as we do not take into account the effect of common environment.

7 Figure 1: Heatmap of m-o-m changes of 92 Lithuanian HICP components SERV ENERG UF PF NEIG

2000 2004 2008 2012 2016 Note: 92 components (seasonally adjusted) are grouped into 5 main product types. 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 using 1 − 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 variables – the “usual suspects” to explain their variation. As one might expect, global commodity prices seem to play an important role in determining food and energy prices in Lithuania: world food price index precedes UF and PF fluctuations, while the changes in ENERG index mostly coincide with changes in oil price. On the other hand, the economic activity variables appear to be the main drivers of core inflation subindices (NEIG and SERV). However, in this case it is hard to discern if the impact comes from domestic or foreign variables (especially considering that foreign variables can also have an indirect effect).

8 Figure 2: Lithuanian HICP components and their potential determinants

Unprocessed food Processed food Non−energy industrial goods y−o−y change y−o−y change y−o−y change

UF GDP PF GDP NEIG GDP

−40 −20 0World 20 40food 60 prices World demand −40 −20 0World 20 40food 60 prices World demand Unemployment Import deflator −20 −10 0 10 20

2005 2010 2015 2005 2010 2015 2005 2010 2015

Services Energy goods 50 0 y−o−y change y−o−y change

SERV GDP −50 ENERG Oil price Unemployment World demand Unemployment GDP −30 −20 −10 0 10 2005 2010 2015 2005 2010 2015 Note: For all variables yearly changes are in %, except for the unemployment rate, where yearly changes are in percentage points

Having presented some basic stylised facts regarding the HICP components’ dynamics, we now turn to the model to explore the spillovers between the HICP components, identify their determinants 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 model with 14 variables: 5 Lithuanian HICP components (UF, PF, SERV, NEIG and ENERG), 5 domestic variables (GDP, import deflator, unit labour cost index and unemployment rate) and 5 foreign variables (oil price, food commodity price index, EUR/USD exchange rate, Eonia interest rate and world demand index for Lithuanian exports). The model is specified for the m-o-m differences of the variables. Although technically, the model can handle any number of variables, our objective was (in addition to 5 HICP indices) to include only the main price determinants, representing different sources of inflation. We limited the model scale, as a large scale model may pose some issues in the structural analysis part of the paper: results may be hard to interpret in the case of Cholesky decomposition scheme or it may be hard to define the structural shocks based on sign restrictions. On the other hand, we agree that for the forecasting application it may be beneficial not to limit the number of variables included in the model. We set the parameter prior distribution as in Litterman (1985), with parameter vector assumed to be jointly normal with means: E(µ) = 0n×n, E(Al) = 0n×n, l = 1...n. The parameter variances are parameterised as follows:

9 2 2 2 V ar(µi) = λ1λ4σi , σ2 λ λ λ (i, j)2 V ar(al ) = i 1 2 5 , i 6= j, i,j 2 λ3 σj l (2) 2 l λ1 V ar(ai,i) = , lλ3

l 2 where ai,j is an element of the matrix Al, l = 1...p, i, j = 1...n, σi are residual variances estimated from univariate AR regressions for every variable, and λ1, λ2, λ3, λ4, λ5 are hyperparameters used to control the shrinkage. The model specification in (2) is controlled by 5 hyperparameters: λ1 sets the general shrinkage 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 that Lithuanian variables do not influence foreign variables, while foreign variables can have influence on 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 other popular priors, such as normal-diffuse and independent normal-Wishart prior, would make the repeated estimations needed for the hyperparameter grid search too time consuming. We applied the independent normal-Wishart prior (based on the already found hyperparameter values) for a competing model in the forecasting application and as our only prior setting in the structural analysis part of the paper.

2.3 Selection of hyperparameters The literature usually adopts one of few methods to set the hyperparameter values in (2) and thus control for informativeness of prior distribution: e.g. Banbura et al. (2010) proposed to select shrinkage which would yield a desired in-sample fit, whereas Giannone et al. (2012) argued that the most natural way to set the hyperparameters in a Bayesian framework is to let them maximise marginal likelihood of the data. Since one of the main applications of our model is forecasting, we opted for the intuitive approach used by Doan et al. (1983), i.e. to select the hyperparameters which minimise out-of-sample forecasting error in the “training” period. We performed a recursive out-of-sample forecasting exercise for various combinations of the hyperparameters in the period of 2006M12-2010M11. The first forecast was generated for the model estimated in 2000M1-2006M12, the second forecast was based on the 2000M1-2007M1 sample and so on, expanding the sample with every consecutive period. In the forecasting exercise we also retained the ragged-edge properties of the data, simulating the data publication lag at the end of the sample, and later using conditional forecasting methods developed by Waggoner and Zha (1999) with implementation of Jarocinski (2010) to fill in the missing values and generate the forecasts. In the grid search, we treated the lag number p as another unknown parameter jointly with the shrinkage parameters. To be specific, we were interested in the performance of different values of (λ1, λ2, λ3, p) parameter set. We fix λ4 = 100, which in essence states that we do not possess any additional information regarding the mean value of 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, cannot significantly 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 RMSE results of the exercise as a function of (λ1, λ2, λ3, p), cutting along two dimensions while holding other 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 model parameters)

RMSE(p,λ1|λ2=0.5,λ3=0.5) RMSE(λ2,λ1|p=6,λ3=0.5) RMSE(p,λ2|λ1=0.1,λ3=0.5)

1.5 1.5 ) ) 2 2 ) 0.5 1 RMSE RMSE RMSE 5 0.1 2.5 2.5 4 1 2.0 1 3 2.0 0.05 2 1.5 1.5

1 1.0 1.0

Overall shrinkage ( λ 0.01 Cross var. shrinkage ( λ Cross var. Cross var. shrinkage ( λ Cross var. 0.5 0.5

0.001

1 3 6 9 12 13 0.001 0.01 0.05 0.1 0.5 1 1 3 6 9 12 13 λ Number of lags(p) Overall shrinkage ( 1) Number of lags(p)

RMSE(λ3,λ1|p=6,λ2=0.5) RMSE(λ3,p|λ1=0.1,λ2=0.5)

1.5 1.5

RMSE

) RMSE ) 3 1 3 1 1.3 1.8 1.2 1.5 1.1 0.5 1.2 0.5

Lag decay ( λ 1.0 Lag decay ( λ

0 0

0.001 0.01 0.05 0.1 0.5 1 1 3 6 9 12 13 λ Overall shrinkage ( 1) Number of lags(p) Note: We computed the relative RMSE as follows. First, we forecasted 5 HICP components separately and obtained m-o-m inﬂation forecasts for 12 months ahead. Then we calculated an aggregate RMSE for total HICP 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 (the benchmark is an ARIMA model selected according to the Akaike criterion) and reported the average value over the 12 month horizon.

Figure 3 reveals several important results about the optimality of the parameters. First, as documented in other studies (e.g. De Mol et al. (2008)), it conﬁrms that inclusion of additional parameters (in this case in the form of lags) demands for an increase in shrinkage. This result can be seen in all three graphs in Figure 3 that include lag number p: for high lag numbers it is 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: after applying 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 less important 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 actually matter more than the recent ones (refer to Stak˙enas(2015) for some evidence on transmission

1In order to keep the computational time reasonable (which can rapidly inﬂate due to the high dimensionality of the grid), we restricted the grid search only to the values depicted in Figure 3. 2 Although λ1 is the main shrinkage parameter, up to some point λ1, λ2, λ3 substitute each other’s eﬀect, and we 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 should be cautious in selecting the shrinking parameters in an arbitrary manner as the forecasting performance of a model can change quite significantly. The posterior means of BVAR regression coefficients for the optimal hyperparameters are depicted in Appendix F, Figure F1. What we notice first, is that most of the parameters in Figure F1 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 all of the variables are informative for the common factors, growing number of variables requires using a prior which increasingly shrinks regression coefficients towards zero. Hence, a competing hypothesis 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 – the coefficients of variables with higher lag orders tend to get smaller in absolute values. Low coefficient values for high lag orders in Figure F1 may also explain why the improvement in RMSE values for models with lag orders higher than 3 is not very noticeable. In general, a practitioner may favour a more parsimonious (and therefore more transparent) model with 3 lags 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 the forecasting accuracy of its various specifications. We evaluated model’s prediction accuracy in the period 2010M12-2015M12 using a recursive forecasting design, i.e. the first forecast was generated based on the sample 2000M1-2010M12 and the last one – on the model estimated in 2000M1-2015M12. In the forecasting exercise, we try to mimic real-time conditions available to a forecaster, deleting data values that should not be available at the time of forecasting due to data publication lag.3 In the case of unconditional forecasting, these “ragged-edges” of the data are dealt with using the Gibbs sampling algorithm developed by Waggoner and Zha (1999) with implementation of Jarocinski (2010). In the case of actual conditional forecasting, we filled the “ragged-edges” with conditional assumptions and proceeded using the aforementioned methods. Note also that in the forecasting exercise we employed the model parameters found in Section 2. We tested the forecasting performance of several competing models. In addition to our main BVAR model specification based on the Minnesota prior (with residual covariance matrix assumed 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) is one of the most widely used methods of a practitioner, our objective in this case was to test how much modelling of the unknown residual covariance matrix can influence results, especially in the conditional forecasting setting. Also, motivated by the idea that the HICP component determinants can be quite different and potentially not all variables are helpful in forecasting all HICP 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 the coefficient. Lastly, as a benchmark model we used a univariate AR(p) model with a lag selected according 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-time seasonal adjustment. 4Refer to e.g. Dieppe et al. (2016) for model deﬁnition with the independent normal-Wishart prior.

12 forecasting step.

3.1 Unconditional forecasts Unconditional forecasting corresponds to a case when a forecaster does not possess any additional information that would be useful in the forecasting process; therefore, we expect it to represent a 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 in Table 2 are relative to benchmark RMSE, with values lower than 1 representing improvement over the benchmark. The values in bold show statistically signiﬁcant diﬀerences in the forecasting accuracy according to the test by Diebold and Mariano (1995).

Table 2: Relative RMSE of unconditional forecasts

3m 6m 9m 12m UF 1.05 1.06 1.04 0.98 PF 0.86 0.88 0.92 0.95 Litterman NEIG 1.06 1.1 1.11 1.11 SERV 1.12 1.15 1.12 1.11 ENERG 0.94 0.93 0.96 0.97 UF 1.05 1.08 1.06 0.95 PF 0.82 0.82 0.86 0.90 Normal-Wishart NEIG 1.03 1.05 1.08 1.08 SERV 1.05 1.12 1.13 1.09 ENERG 0.92 0.89 0.91 0.92 UF 0.99 0.97 0.92 0.90 PF 0.88 0.77 0.65 0.59 SSVS NEIG 0.91 0.85 0.82 0.79 SERV 1.39 1.53 1.63 1.73 ENERG 0.86 0.79 0.77 0.73

The results in Table 2 and Figure 4 indicate that modelling residual covariance matrix slightly 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 PF and ENERG forecasts, while forecasts of e.g. SERV component, presumably more suitable for multivariate 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 except for SERV. Observing the improvement of forecasts under the SSVS model, one might be tempted to conclude 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 necessarily be the case. Judging from the actual out-of-sample forecasts’ graphs in Appendix B, Figure B1, it seems that the differences in SSVS forecasts were generated by better prediction of the mean 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 observe statistically significant improvement of forecasts only for the Litterman and normal-Wishart prior 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 much more volatile, which does not allow us to claim that the SSVS model produces statistically significantly more accurate forecasts than the benchnark. Figure 4 summarises the main messages from the unconditional forecasting exercise. While we observe that BVAR models do not outperform the benchmark model when measured by the aggregated RMSE results, individual component forecasts using BVAR with SSVS look promising. On the other hand, the graph on the left in Figure 4 perfectly illustrates the merits of Bayesian shrinkage – a non Bayesian VAR model with the same number of lags and dimension performs much worse, practically making it unusable.

Figure 4: Unconditional forecasting results

VAR models vs. benchmark BVAR (SSVS) unconditional forecasts RMSE ratio RMSE ratio 1.0 1.2 1.4 1.6 BVAR (Litterman) BVAR (SSVS) UF NEIG ENERG BVAR (N.Wishart) VAR PF SERV 0.4 0.6 0.8 1.0 1.2 1.4 1.6

2 4 6 8 10 12 2 4 6 8 10 12 Horizon (months) Horizon (months) 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 HICP components’ RMSE using component weights in 2016. The non Bayesian VAR model in the left-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 additional information (provided in the form of variables’ future paths) in predicting changes in the HICP components. We are interested in two conditional forecasting cases: forecasting based on pseudo 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 of Lithuania forecasts (for GDP, import deflator, ULC, unemployment rate and world demand of exports) and random walk assumption (for oil price, food commodity price index, exchange rate and interest rate). In the second case (which represents the upper limit of conditional forecasting capabilities), we use the “perfect” conditions for conditional forecasting, i.e. the actually realised 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 improved over the benchmark for all the model specifications. On the other hand, conditional forecasts statistically significantly deteriorated the NEIG forecasts for the Litterman and normal-Wishart prior specifications. We see two potential culprits for the increase in conditional forecasting RMSE: 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 UF 1.02 0.94 0.92 0.85 PF 0.84 0.84 0.84 0.84 Litterman NEIG 1.1 1.14 1.17 1.18 SERV 1.16 1.23 1.2 1.16 ENERG 0.94 0.91 0.94 0.93 UF 1.09 1 1.03 0.9 PF 0.81 0.81 0.8 0.8 Normal-Wishart NEIG 1.13 1.15 1.2 1.21 SERV 1.15 1.18 1.11 1.07 ENERG 0.94 0.91 0.94 0.93 UF 1.01 0.95 0.98 0.89 PF 0.81 0.69 0.57 0.52 SSVS NEIG 0.98 0.98 1.01 1.01 SERV 1.31 1.4 1.46 1.49 ENERG 0.86 0.78 0.76 0.73

Note: The RMSE values are relative to the benchmark RMSE. Values in bold denote statistically significant difference according to the Diebold-Mariano test (two-sided alternative hypothesis, 95% confidence level). The forecasts (median of 1000 forecast draws) were generated every month in the period of 2010M12-2015M12. the out-of-sample period, or the conditional forecasting algorithm failed to realistically attribute innovations in forecasting process. Lastly, we note that similarly to the unconditional forecasting results, the SSVS model produces the most accurate forecasts for all the components other than SERV. 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 – we observe 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 for forecasting PF and ENERG components. This may not come as a surprise as these components are considered to be heavily dependent on volatile global commodity price fluctuations and knowing these fluctuations beforehand would certainly help to increase the forecasting accuracy. On the other hand, for the Litterman and normal-Wishart models, the ENERG forecasting accuracy 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 ENERG component is likely to achieve better results.

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

3m 6m 9m 12m UF 1.08 1.07 1.01 0.95 PF 0.79 0.71 0.69 0.67 Litterman NEIG 1.09 1.11 1.13 1.12 SERV 1.07 1.15 1.11 1.11 ENERG 0.88 0.84 0.85 0.85 UF 1.17 1.25 1.13 1.03 PF 0.78 0.69 0.67 0.64 Normal-Wishart NEIG 1.17 1.12 1.12 1.1 SERV 1.11 1.15 1.09 1.07 ENERG 0.88 0.85 0.86 0.86 UF 1.06 1.07 1 0.91 PF 0.85 0.71 0.59 0.5 SSVS NEIG 1.03 0.97 0.93 0.9 SERV 1.3 1.37 1.41 1.46 ENERG 0.8 0.74 0.72 0.69

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

Real−time conditions vs. no conditions Realised data conditions vs. no conditions RMSE ratio RMSE ratio

0.7 0.8 0.9 1.0UF 1.1 NEIG ENERG 0.7 0.8 0.9 1.0UF 1.1 NEIG ENERG PF SERV PF SERV

2 4 6 8 10 2 4 6 8 10 Horizon (months) Horizon (months) 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 identiﬁcation schemes used to achieve a structural interpretation and then we turn to the analysis of HICP components’ determinants.

16 4.1 Shock identification To identify our model’s structural shocks we used two methods: sign restrictions and Cholesky decomposition. We treat identification by sign restrictions as our main method, as it usually provides more economic interpretation. We applied identification by Cholesky decomposition mainly as a robustness check and also to obtain additional insights regarding the drivers of the 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 model in Section 3). For structural analysis we used the model with the following variables (in the order used for the Cholesky decomposition): oil price, global food commodity prices, world demand for Lithuanian exports, Lithuanian GDP, Lithuanian import deflator, Lithuanian ULC (unit labour costs), ENERG, UF, PF, NEIG and SERV. The identification by sign restrictions required restrictions on real wages, therefore, for this case we replaced the Lithuanian ULC with real wages. For modelling the residual covariance matrix we employed the normal-Wishart prior with hyperparameters set to the values found in Section 2. Table 5 summarises sign and zero restrictions used to identify 5 structural shocks. Since the model is estimated at monthly frequency, the identification based on contemporaneous restrictions may be hard to justify – economic agents, likely, are not able to react to shocks already in the same month. Therefore, we implemented the restrictions presented in Table 5 for variable cumulative responses three months after the shock. Note also that the sign restrictions in Table 5 are defined for headline HICP responses, but we do not have an explicitly defined the headline inflation variable in the model. In order to test the “HICP(total)” restrictions, we obtained the headline inflation reactions by aggregating the reactions of HICP components using average consumer basket weights in the 2000-2017 period. Additionally, we filtered out extreme impulse responses 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 a 1% change in a target variable (target variables are: GDP for domestic demand/supply, wages for wage bargaining shock, oil price for oil supply shock and world demand for world demand shock).5 The identification by Cholesky decomposition is based on the following ordering of variables: foreign variables, Lithuanian GDP and Lithuanian price variables. This ordering naturally places the needed small-country restrictions on the Lithuanian variables – shocks to the Lithua- nian variables cannot affect foreign variables contemporaneously (and due to block exogeneity restrictions in the subsequent periods as well). Among the foreign variables, we ordered global commodity prices first, as they are determined by global demand and supply and are less likely to be affected contemporaneously by the demand for Lithuanian export. Similarly to the foreign variables, we motivate the ordering of Lithuanian HICP components based on the assumed origin of their determinants, placing components which are most affected by global commodity prices 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 macroeconomic models (see e.g. Peersman and Straub (2004)) with the additional assumption that a small open economy cannot affect global variables (this assumption is also used e.g. in Joviˇcić

5Kilian and Murphy (2012) showed that sign restrictions alone are insuﬃcient to infer impulse responses in the crude oil market, therefore placing additional magnitude restrictions. In our case, magnitude restrictions serve mainly for tightening the conﬁdence bounds around the impulse responses by eliminating economically unreasonable structural models. We consider the magnitude restrictions to be loose enough to avoid circular reasoning 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 using dynamic stochastic general equilibrium framework: a decrease in an employee’s bargaining power reduces real wages in the economy, lowering marginal costs and prices. This allows firms to increase employment and output. Foroni et al. (2015) also used the responses of unemployment and vacancies to separate labour supply and matching efficiency shocks from the wage bargaining shock. In our case, although the three labour market shocks are inseparable, we chose to name the shock “wage bargaining”, as it provides the most interpretable story and, in our 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 economy and 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 shocks have very different economic implications and should be treated separately, we identified the oil supply 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 inseparable from 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 Arias et al. (2014), which provides us with 11 (the number of variables in the system) uncorrelated shocks. Table 5, however, presents a partially identified model with only 5 identified structural shocks. This raises a question how to treat the remaining 6 shocks. The question is particularly relevant for HICP components’ decomposition into their determinants (the subject of the next subsection). 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 shocks satisfying the restrictions in Table 5 (and, thus, accepting the system as representing the main drivers in the economy), the rest of the shocks in most cases can also be identified as one of the structural shocks from Table 5.6 As a result, we may have several, e.g. domestic demand shocks, that are orthogonal to each other. In the subsequent forecast decomposition graphs we chose to add up the contributions of multiple structural shocks having the same identification pattern.

6Given that the shocks satisfy the magnitude restrictions, only the following 3 response patterns are left unidentiﬁed (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 decomposition of their year-on-year growth rates. The decomposition allows us to estimate how much each of the shocks contributes to the components’ annual inflation at each time period, identifying their origins and dynamics. We examine historical decompositions of the five HICP components one by one, emphasising the main drivers, their differences, contributions to the largest price changes and recent developments in the contributions. Historical decomposition of the Lithuanian unprocessed food inflation based on sign restrictions is presented in Figure 6. The black line in the figure (and in the subsequent historical decomposition graphs) represents the actual annual inflation. The “Other” part in the graph mainly accounts for inflation forecast by the constant in equation (1) (a small part of it also consists of some unidentified shocks). We can interpret this part as representing the monetary policy targeted inflation rate, general price convergence to the EU level or any other long-term UF 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/supply and 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 UF inflation. On the other hand, the inflation dip in 2009-2010 tells quite a different story, as it can be mainly attributed to the foreign shocks: foreign demand and oil supply. The negative foreign factors were also present in the recent period of 2015-2016 when the shale oil boom led to the decline in oil prices, while the euro area economic activity remained weak. Given that these factors have disappeared, we might expect higher UF inflation in the near future. For the UF decomposition graph based on Cholesky identification scheme refer to Appendix C, Figure C1.

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

Other Foreign act. Wage barg. Oil supply Dom. demand Dom. supply y−o−y change (%) −20 −10 0 10