Title of the Paper (Times New Roman 14, bold, center)

The Relationship between stock markets and gross domestic product in the Central and Eastern Europe Lumír Kulhánek College of Social and Administrative Affairs, Havířov and VŠB-Technical University of Ostrava Department of Economics and European Integration Vítězslava Nezvala 801/1 Havířov – Město, 736 01 Czech Republic e-mail: [email protected] Abstract Paper is concerned with causal linkages among stock prices, output and money supply development in the Central and Eastern European countries. The main objective is to investigate and evaluate long-run equilibrium relationships between stock prices and macroeconomic variables as well as short-run dynamics using both the Vector Autoregressive (VAR) and Vector Error Correction (VEC) models in Austria, the Czech Republic, Hungary, Poland, and Slovak Republic. National stock market indices, gross domestic product and money supply are used in this study. In the analysis quarterly data from 1995:Q1 to 2012:Q2 has been applied. We have applied tests for co-integration, it has been discovered that there is a long-run co-integration relationship between variables and we have estimated both the VAR and VEC models, along with comparing the usefulness of VAR and VEC models for the gross domestic product growth modeling. The evidence obtained from the analysis of time series suggests that in all cases we can discover the long-run relationships among variables applied. JEL classification: E44, G10 Keywords: Stock prices, GDP, money supply, VEC model 1. Introduction The relationship between macroeconomic variables and asset prices, in general, has recently renewed interest among academics, researchers and policy-makers. One of interesting discussion is whether real output responds to developments in money supply and financial markets. Under the standard prevailing approach, changes in money supply affect real economic activities through various channels. These include the liquidity channel, stock price channel, wealth effects, and household liquidity effects. Basis on these explanatory models, we can discern that interactions among real economic activities, money, and stock market prices are bound in a dynamic way. Macroeconomic variables influence and are influenced by stock prices and monetary variables. In addition, economic variables interact with each other. Unfortunately, the direction of the interactions and which variable is leader (dominant, contemporaneous, or lagged) in the interactions remains unclear. Thus, the nature, direction, strength or weakness of the interactions among them in short-run and long-run is of high interest and needs to be investigated and evaluated empirically. 2. Relationships between stock prices, money and gross domestic product Economic theory suggests that there should be a strong link between economic activity and security prices, given that the stock price is the present value of the future payout. Channels through which stock prices impact output are referred to as Tobin´s Q, the wealth effect, and the financial accelerator. Several empirical studies modeled relationships between real economic activity and stock prices in developed economies. Fama (1981), Huang and

Kracaw (1984), and Chen, Roll and Ross (1986), among others, are concerned with the USA, Poon and Taylor (1991) and Cheng (1995) with the United Kingdom. There are also a growing number of studies analyzing the relationships between economic factors and stock prices in developing and emerging countries. Examples for the Central European countries are Hanousek and Filler (2000) or Kulhánek and Matuszek (2007), among others. Following these authors we hypothesize a positive relation between gross domestic product and stock prices and we update research presented in Kulhánek (2011). Causality between money and stock prices traditionally has been assumed to run from money to stock prices. It is usually argued that a rise in the money demand facilitates an increase in output, profits and stock prices. As noted Friedman (1988) and number of other studies causality between money and stock prices have assumed to run from stock prices to money. A rise in stock prices could imply a rise in financial transactions both in the transaction money demand. A rise in stock prices caused through wealth effect higher wealth to income ratio and therefore higher money to income ratio. A rise in stock prices reflects a rise in expected return from risky assets relative to safe assets. To offset the subsequent rise in risk of an investor’s portfolio, relatively safe assets would be substituted for long-term bonds. All three factors should have produced a positive relationship between stock prices and money. To date there has been little attempt to determine in which direction causality actually runs in countries other than the USA. 3. Methodology and data The main aim of our research is an investigation if real outputs are cointegrated with monetary aggregates and stock prices in analyzed countries. Our empirical analysis includes five parts: 1. unit-root tests, 2. Granger causality tests, 3. vector autoregression (VAR models, Impulse-Response analysis, Variance Decomposition), 4. Johansen cointegration tests to find out that a set of variables are cointegrated or not, 5. Vector Error Correction models for cointegrated variables. Three variables are considered in this study, namely the real GDP, broad money and national stock market indices. The data used are tested for stationarity, which is a basic requirement for this type of analysis.1 Granger causality or non causality is concerned with whether lagged value of one variable (e.g. ”X”) do or not do improve on explanation of another variable (“Y”) obtainable from only lagged values of “Y”. We must note that the statement “X” Granger cause “Y” does not imply that “Y” is the effect or the result of “X”. Granger causality measures precedence and information content but does not indicate causality in the more common use of the term. In common tests, the null hypothesis is that “X” does not Granger-cause “Y” and that “Y” does not Granger-cause “X. A lag length in Granger causality tests corresponds to relevancy, to reasonable beliefs about the longest time over which one of the variables could help predict the other. In general, it is better to use more rather than fewer lags. Vector autoregression (VAR models) is an econometric model used to capture the evolution and the interdependencies between multiple time series, generalizing the univariate AR models. All the variables in a VAR are treated symmetrically by including for each variable an equation explaining its evolution based on its own lags and the lags of all the other variables in the model. The VAR approach treats every endogenous variable as a function of the lagged

1

To determine stationarity (or non-stationarity) of variables in original level and indicate which difference of time series is stationary we use unit root tests. We tested for stationarity using standard augmented Dickey-Fuller (ADF) tests and the Phillips-Perron (PP) tests. The results of unit root tests indicate that each variable is integrated of order 1, or I (1), and it is possible to test if the levels of these variables are cointegrated, The results of tests can be obtained from author.

values of all of the endogenous variables in the system. The principal mathematic representation of a VAR is: Yt = A1Yt-1 + A2Yt-2 + ... + ApYt-p + BXt + εt

(1),

where Yt is a k-vector of endogenous variables, Yt is an l-vector of exogenous variables, A1, ..., Ap and B are matrices of the coefficients to be estimated, εt is a vector of innovations that may be contemporaneously correlated but are uncorrelated with their own lagged values and uncorrelated with all of the right-hand side variables.2 Impulse–Response analysis traces out the responsiveness of the dependent variables in the VAR model to shocks for each of the variables. So, for each variable from each equation separately, a unit shock is applied to the error, and the effects upon the VAR system over time are noted. Provided that the system is stable, the shocks should gradually die away. Variance decomposition offers a slightly different method for examining VAR system dynamics. They give the proportion of the movements in the dependent variables that are due to their own shocks, versus shocks to the other variables. A shock to the i-th variable will directly affect that variable, but it will also be transmitted to all of the other variables in the system through the dynamic structure of the VAR. Thus, variance decomposition determines how much of s-step-ahead forecast error variance of a given variable is explained by innovations to each explanatory variable for s = 1, 2, … . In practice, it is usually observed that own series shocks explain most of the (forecast) error variance of the series in the VAR. Impulse-Responses and variance decomposition offers very similar information. The introduction of cointegration into econometric literature has become customary to investigate the existence of cointegrating relations among integrated (often called nonstationary) economic variables before conducting formal inference, like estimating parameters of model or testing hypotheses. If the data are cointegrated, vector error correction models (VECM) can be estimated. Otherwise, vector autoregressive models (VAR) are estimated in first differences.3 Cointegration of variables is at least a necessary condition for them to have a stable long-run relationship. However, if the no-cointegration hypothesis cannot be rejected, then the estimated regression is just a “spurious” one and has no economic meaning. The Johansen maximum likelihood estimator circumvents these problems and enables to test for the presence of multiple cointegrating vectors. Johansen shows how to test for linear restrictions on the parameters of the cointegrating vectors. It makes possible to test the symmetry and proportionality conditions exactly. The details of the Johansen procedure are very complex and we shall only focus on a few aspects. The main steps in the Johansen procedure and test hypotheses (the Trace statistic and the Maximum Eigenvalue statistic) are explained in Kulhánek and Matuszek (2004) in details. Our empirical analysis is based on quarterly data from 1995:Q1 to 2012:Q2. The gross domestic product (GDP) at market prices in national currency in constant prices (reference year 2005) is used as measure of the real economic activity. Not seasonally adjusted GDP data are obtained from Eurostat (GDP and main components - volumes [namq_gdp_k]); time series are seasonally adjusted using Census X12 multiplicative method. Data for stock prices are obtained from OECD (Monthly Monetary and Financial Statistics (MEI), Share price, 2

The lag length specification (“p”) can be determined by information criteria (e.g. the Akaike Information Criterion (AIC) or the Schwarz Information Criterion (SC), with smaller values of the information criterion being preferred). 3 Even though many economic series are routinely found to be cointegrated, it should be emphasized that cointegration is a very special phenomenon indeed. Cointegration occurs because economic data share common stochastic trends, which are eliminated by cointegrating linear combinations. Common stochastic trends are usually expressed as a linear combination of the shocks of a system. Putting it differently, economic data are cointegrated because they respond to shocks together.

Index 2005=100). For money supply broad monetary aggregates are used. Data for Hungary, Poland, the Czech Republic, and the United Kingdom are obtained from Monthly Monetary and Financial Statistics OECD, data for Austria, Germany, and Slovakia are obtained from International Financial Statistics (IFS) IMF and from national central banks databases. All time series are rescaled taking the year 2005 as 100. Figure 1 shows development both of GDP and stock market indices in analyzed countries in the sample period from 1995:Q1 to 2011:Q2. Figure 1 GDP and Stock Prices in analyzed counties (1995:Q1 to 2011:Q2) 140

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96:1 98:1 00:1 02:1 04:1 06:1 08:1 10:1 12:1 EXP(SP_DE) EXP(SP_EA)

EXP(SP_AT) EXP(SP_UK)

Source: author’s calculations based on OECD Monthly Monetary and Financial Statistics (http://stats.oecd.org/ Index.aspx?DatasetCode=MEI_FIN) and Eurostat (http://epp.eurostat.ec.europa.eu). Notes: Indices, year 2005=100.

4. Results of tests and evaluation of models Appendix 1 reports the results for the Granger causality tests between the stock market indices and GDP, between money supply and GDP, and between money supply and stock

market indices in the various countries under consideration, using first differences. The results can be taken into consideration in several of reasons. For example, the question of interest may be exogenity variables in a bivariate regression model. We must note that we should be careful when comparing the test results because number of available observations is low (1), and Granger causality tests are based on the first differenced (de-trended) variables (2). Thus, very important trend information is eliminated. Despite of these facts, the results show a rich, but non-stable structure of Granger causality relationships in examined countries. The main aim of our study is to investigate if money supply and stock market have an influence upon real economic output. In line with this aim, we can detect important relationships among growth of monetary aggregate, stock market returns, and growth of real GDP in analyzed countries, but at different significance levels. In euro area we can state only interaction between stock market returns and growth of real GDP. In some cases, Germany and the UK, growth of monetary aggregate and stock market returns can be seen as strong exogenous variables for parameters of models in which growth of real GDP is dependent variable. In the Czech Republic, we find out that growth of monetary aggregate is a strong exogenous variable for parameters of real GDP model. The VAR models are commonly used for analyzing and forecasting system of interrelated time series or for analyzing the dynamic impact of random disturbances on the system of variables. Summary statistic evaluation for the VAR (unrestricted) models for analyzed countries is in Table 1. Table 1 Evaluation of the VAR models for dependent variable the real GDP growth CZ SK HU PL DE EA R-squared 0,428 0,242 0,536 0,495 0,257 0,402 Adj. R-squared 0,296 0,079 0,391 0,230 0,098 0,157 Sum sq. resids 0,004 0,017 0,003 0,003 0,006 0,003 S.E. equation 0,009 0,018 0,008 0,009 0,010 0,008 F-statistic 3,242 1,488 3,692 1,868 1,613 1,640 Log likelih. 220,6 188,4 226,8 215,7 226,8 229,6 Mean depend. 0,006 0,010 0,005 0,011 0,003 0,004 S.D. depend. 0,011 0,018 0,010 0,011 0,011 0,008

UK 0,548 0,480 0,002 0,005 8,091 276,2 0,005 0,007

AT 0,117 0,032 0,006 0,010 1,385 229,2 0,005 0,010

Source: author’s calculations. Notes: The lag length in the VAR models is 2 for Austria, 3 for the U.K., 4 for the Czech Republic, Slovak Republic, and Germany, 5 for Hungary, 6 for Euro area, and 7 for Poland.

From the results of the VAR models in the Table 1 we can note the good VAR models for the United Kingdom and Hungary, under the average VAR models for the Czech Republic, Poland, Euro area, and the weak VAR models for Germany and Slovak Republic. We must note that the VAR model is, as a matter of fact, the system of linear regression equations. Thus, entering variables must be stationary (weak or covariance stationary). In practice commonly they are in the first differences. So, the VAR models reflect (mainly) the short-run dynamics of the variables, but they are not able to capture the long-run equilibrium relationships among the variables. To examine further dynamic interactions among variables, we generate impulse-response functions from the estimated VAR models. This approach involves orthogonalizing innovations in each of the variables using Choleski decomposition of the residual covariance matrix, imposing a recursive structure on the contemporaneous relationship among variables. We present the plots of the impulse-response functions as interactions between the growth of real GDP and other variables in Figure 2. From Figure we may find out several notable points.

It can be noted a short-run and a long-run positive lagged response of the real GDP growth to the stock market returns and a negative response to the monetary aggregate growth shocks for the Czech Republic, Germany, and the United Kingdom. In short-run horizon, it can be shown a positive impact of the growth of monetary aggregate on the growth of real GDP in other analyzed countries, and a positive impact of the stock market returns on the real GDP growth in all countries (except euro area). Interestingly, the growth of monetary aggregate shocks and the stock market returns shocks have an alternating and a very weak impact on the growth of real GDP for the United Kingdom. Figure 2 Response of the GDP growth to money growth and stock returns Response of D(GDP_CZ) to Cholesky One S.D. Innovations

Response of D(GDP_SK) to Cholesky One S.D. Innovations

Response of D(GDP_HU) to Cholesky One S.D. Innovations

Response of D(GDP_PL) to Cholesky One S.D. Innovations

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Source: author’s calculations.

Figure 3 shows results for variance decompositions at time horizon of 12 quarters. The plots suggest the presence of interactions among the growth of real GDP, the growth of money supply, and stock market returns in analyzed countries. Focusing on the data in Figure, we may observe that variations in the growth of real GDP are predeterminantly attributed to its own variations in all analyzed countries. As we can see, very interesting situation is in the Czech Republic, Poland, and Hungary. Variation of money supply growth is accounted for about 17 % of the real GDP growth forecast error variance after 12 quarters. In addition, the innovations in the stock market returns also explain quite sizable fractions of the real GDP growth variation Looking at the other countries, we can note very low importance of the growth of monetary aggregate to variation of the real GDP growth in the Slovak Republic, Germany, and the United Kingdom. Next, we test the number of significant cointegrating vectors for each country. We used the Johansen approach to test for cointegration among real GDP (natural logarithm of real GDP), money supply (natural logarithm of broad monetary aggregate) and stock market indexes (natural logarithm of values). Table 2 displays the results of test. We can note that there are sufficient evidences for one non-zero cointegrating vector in unrestricted models. These tests indicate that a set of variables is cointegrated. Thus, for each set of variables we can form at most one cointegration equation. The Johansen approach to cointegration tests considers five test type cases: model 1. the level data have no deterministic trends and the cointegrating equation does not have intercepts, model 2. the level data have no deterministic trends and the cointegrating equation have intercept, model 3. the level data have linear trends

and the cointegrating equation have only intercepts, model 4. the level data and the cointegrating equation have linear trends, model 5. the level data have quadratic trends and the cointegrating equation have linear trends. Only model 3 is used in this paper for the VEC models. Figure 3 Variance Decomposition of real GDP growth in the VAR models Variance Decomposition of D(GDP_CZ)

Variance Decomposition of D(GDP_SK)

Variance Decomposition of D(GDP_HU)

Variance Decomposition of D(GDP_PL)

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Source: author’s calculations.

Table 2 Number of cointegrating equations by test models of Johansen approach Data trend None None Linear Linear Test type Model 1 Model 2 Model 3 Model 4 CZ Trace 1 2 2 1 Max-Eig 1 2 1 1 SK Trace 0 1 1 1 Max-Eig 0 0 0 0 PL Trace 1 1 1 2 Max-Eig 1 1 1 0 HU Trace 0 0 1 0 Max-Eig 0 0 1 0 DE Trace 2 2 1 1 Max-Eig 2 1 1 1 EA Trace 2 2 1 2 Max-Eig 2 2 0 0 UK Trace 1 1 1 0 Max-Eig 1 1 1 0 AT Trace 1 1 0 1 Max-Eig 1 1 1 1

Quadratic Model 5 1 1 1 1 3 0 1 0 1 1 1 0 0 0 1 1

Source: please provide a source website, paper, author’s calculations, etc. Notes: Selected on 0,05 level of significance, except Slovakia (on 0,1 level of significance). Critical values based on MacKinnon-Haug-Michelis (1999). The lag order of the underlying test VAR is 2 for Austria, 3 for the U.K., 4 for the Czech Republic, Slovak Republic, and Germany, 5 for Hungary, 6 for Euro area, and 7 for Poland.

The Granger representation theorem states that if a set of variables are cointegrated, then there exists a valid Vector Error-Correction (or equilibrium-correction) representation of the data. In this paper, the vector error-correction model is used to the real GDP growth. In this model, the real GDP growth is dependent variable. Money supply growths (∆m) and stock market returns (∆smi) are explanatory variables. In error correction models, four additional lagged first differences of variables are used in regression equations for the Czech Republic, Slovak Republic and Germany, five for Hungary, six for euro area, seven for Poland, three for the United Kingdom, and two for Austria. The number of lags is based on the lag order of the underlying VAR tests. Table 3 shows theoretical structure and estimated parameters of the VEC models for analyzed countries. We can evaluate estimated parameters of models by tstatistics or probability, it is possible to verify statistic significance of cointegrating vectors in error correction models using the Wald tests as well. Table 3 Error (Equilibrium) Correction Models for the real GDP Growth Δrgdpt= α1+γ1(rgdpt-1–φmt-1–λsmit-1+c) + Σδ1,i Δrgdpt-i + Σθ1,i Δmt-i + Σπ1,i Δsmit-i + ε1,t Cointegration rgdp m

smi

C Adj. Coeff. γ CointEq1

R-squared Adj. R-sq. F-statistic Log likelih. Akaike AIC D-W stat

CZ SK vector β 1 1 -0,361 -0,500

HU

PL

DE

EA

UK

AT

1 -0,315

1 -0,520

1 -0,308

1 -0,233

1 -0,372

1 -0,610

(0.014) [-25,91]

(0.029) [-17,43]

(0.033) [-9,45]

(0.058) [-8,98]

(0.043) [-7,23]

(0.102) [-2,28]

(0.030) [-12,48]

(0.079) [-7,71]

-0,103

-0,043

-0,011

0,127

0,136

-0,353

-0,026

0,248

(0.009) [-11,63]

(0.021) [-2,06]

(0.023) [-0,47]

(0.053) [ 2,39]

(0.039) [ 3,45]

(0.087) [-4,04]

(0.056) [-0,45]

(0.061) [ 4,09]

-2,486

-2,136

-3,076

-2,788

-3,818

-1,890

-2,732

-2,818

-0,352

-0,107

-0,065

0,164

0,027

-0,045

0,032

-0,004

(0.094) [-3.75]

(0.067) [-1.59]

(0.053) [-1.21]

(0.053) [ 3.11]

(0.034) [ 0.80]

(0.017) [-2.62]

(0.014) [ 2.34]

(0.021) [-0.21]

0,552 0,437 4,828 228,49 -6,60 2,01

0,275 0,104 1,606 189,93 -5,10 1,82

0,550 0,396 3,587 227,79 -6,59 2,18

0,595 0,367 2,607 222,56 -6,44 1,57

0,265 0,092 1,528 227,18 -6,18 2,07

0,511 0,295 2,367 235,97 -6,86 1,99

0,587 0,516 8,371 279,30 -7,67 2,06

0,117 0,017 1,175 229,27 -6,32 1,98

Source: author’s calculations. Notes: Data in (...) – standard deviation, [...] – t-stat. Variables: ∆rgdp (lnrgdp - lnrgdp(-1)) = real GDP growth, α and c – intercepts, β – cointegration vector, γ – adjustment coefficient, φ and λ – coefficients (parameters) of cointegrating equations (cointegrating vector), δ, θ, and π – coefficients (parameters) of models (short-run coefficients), ε – errors.

Outputs of the VEC models for analyzed countries are presented in Figures 4 (for the Czech Republic, Slovak Republic, Poland, and Hungary) and 5 (for Germany, Austria, the United Kingdom, and euro area).

Figure 4 VEC models for GDP growth in the Czech Republic, Slovak Republic, Hungary and Poland .04

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Figure 5 VEC models for GDP growth in the Germany, Austria, the United Kingdom, and euro area .04

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10

Fitted

5. Conclusions In this study we have addressed the relationship and interaction among the measure of real economic activity (represented by the real GDP), money supply (broad monetary aggregate), and stock market development (stock market indices) in the Czech Republic, Slovak Republic, Poland, Hungary, and Austria, in comparison with Germany, the United Kingdom, and euro area. The empirical part of our study exploits appropriate econometric techniques to test stationarity (unit root tests), Granger causality (bivariate regression models), short-run dynamics (the VAR models, Impulse-Response analysis, Variance Decomposition), and longrun relationship (Johansen cointegration tests, the VEC models). The evidence obtained from analysis of time-series quarterly data from 1995:Q1 to 2012:Q2 suggest that in all cases we can find out the long-run equilibrium relationships (cointegration) among the real GDP, broad money supply, and stock market indices. This is the most important result of our study. Thus, we may conclude that the broad monetary aggregate and the stock market development have a certain predictive content for the real economic activity in the long-run horizon. We can also claim positive influences of money supply and the stock prices development on the real economic output for all analyzed countries and euro area in the long-run. Looking at the results of the short-run analyses, we have to accept the great difference among countries, especially for the Czech Republic and the other analyzed countries. This conclusion is confirmed by Impulse-Response analysis both Variance Decomposition for example. If long-run cointegration relationship is present, then the VEC models are much more useful then the VAR models. Based on results of comparisons of the VEC models and the VAR models, we may state that the VEC models are the better when the cointegrating relationships are enforce References Chen, N.F., Roll, R., Ross, S.A. (1986). Economic forces and the stock market. Journal of Business, Vol. 59 (3), pp. 383-403. Cheng, A.C. (1995). The U.K. stock market and economic factors: a new approach. Journal of Business, Finance and Accounting, Vol. 22 (1), pp. 129-142. Fama, E. (1981). Stock returns, real activity, inflation and money. American Economic Review, 71, 1981, pp. 545-565. Friedman, M. (1988). Money and the Stock Market. Journal of Political Economy, 96, pp. 221–245. Hanousek, J., Filer, R.K. (2000). The Relationship between Economic Factors and Equity Markets in Central Europe. Economics in Transition, 8, pp. 623-638. Huang, R.D., Kracaw, W.A. (1984). Stock market returns and real activity: a note. Journal of Finance, Vol. 39, pp.267-273. Kulhánek, L., Matuszek, S. (2004). Macroeconomic Factors and the Stock Market. In Lis, S., Miklaszewski, S. (eds.) Transformacja, Integracja, Globalizacja. Krakow: Akademia Ekonomiczna, pp. 467-488. Kulhánek, L., Matuszek, S. (2007). Development of Relationship between Stock Market Indices and Money Supply in Poland, Czech Republic and Euro Area. In Owsiak, S. (ed.) Finasowe warunki rozwoju regionalnego po wejściu Polski do Unii Europejskiej. BielskoBiala: WSBiF, pp. 401-412. Kulhánek, L. (2011). Money, Stock Prices and Economic Activity in Selected European Countries. Journal of Advanced Studies in Finance, Vol. 2, Iss. 2 (4), pp. 101-115. Poon, S., Taylor, S. J. (1991). Macroeconomic factors and the U.K. stock market. Journal of Business, Finance and Accounting, Vol. 18 (5), pp. 619-636.

App. 1: Results of pairwise Granger causality tests Lags SP_CZ dnot GC GDP_CZ GDP_CZ dnot GC SP_CZ M3_CZ dnot GC GDP_CZ GDP_CZ dnot GC M3_CZ M3_CZ dnot GC SP_CZ SP_CZ dnot GC M3_CZ SP_SK dnot GC GDP_SK GDP_SK dnot GC SP_SK M2_SK dnot GC GDP_SK GDP_SK dnot GC M2_SK M2_SK dnot GC SP_SK SP_SK dnot GC M2_SK SP_PL dnot GC GDP_PL GDP_PL dnot GC SP_PL M3_PL dnot GC GDP_PL GDP_PL dnot GC M3_PL M3_PL dnot GC SP_PL SP_PL dnot GC M3_PL SP_HU dnot GC GDP_HU GDP_HU dnot GC SP_HU M3_HU dnot GC GDP_HU GDP_HU dnot GC M3_HU M3_HU dnot GC SP_HU SP_HU dnot GC M3_HU SP_AT dnot GC GDP_AT GDP_AT dnot GC SP_AT M3_AT dnot GC GDP_AT GDP_AT dnot GC M3_AT M3_AT dnot GC SP_AT SP_AT dnot GC M3_AT SP_DE dnot GC GDP_DE GDP_DE dnot GC SP_DE M3_DE dnot GC GDP_DE GDP_DE dnot GC M3_DE M3_DE dnot GC SP_DE SP_DE dnot GC M3_DE SP_UK dnot GC GDP_UK GDP_UK dnot GC SP_UK M3_UK dnot GC GDP_UK GDP_UK dnot GC M3_UK M3_UK dnot GC SP_UK SP_UK dnot GC M3_UK SP_EA dnot GC GDP_EA GDP_EA dnot GC SP_EA M3_EA dnot GC GDP_EA GDP_EA dnot GC M3_EA M3_EA dnot GC SP_EA SP_EA dnot GC M3_EA

1 0,002 0,919 0,454 0,724 0,762 0,238 0,028 0,599 0,752 0,019 0,114 0,145 0,005 0,637 0,065 0,762 0,382 0,841 0,060 0,783 0,071 0,813 0,081 0,451 0,019 0,749 0,823 0,986 0,980 0,796 0,001 0,574 0,138 0,421 0,762 0,825 0,083 0,063 0,640 0,732 0,917 0,634 0,000 0,746 0,017 0,735 0,509 0,706

2 0,001 0,501 0,185 0,423 0,783 0,493 0,042 0,801 0,557 0,014 0,254 0,109 0,013 0,535 0,382 0,068 0,398 0,574 0,150 0,013 0,162 0,192 0,146 0,219 0,043 0,634 0,975 0,963 0,751 0,090 0,005 0,069 0,325 0,152 0,187 0,655 0,233 0,020 0,896 0,222 0,971 0,019 0,002 0,222 0,014 0,086 0,774 0,308

3 0,005 0,503 0,074 0,663 0,803 0,619 0,085 0,729 0,405 0,034 0,209 0,215 0,029 0,683 0,843 0,050 0,501 0,179 0,214 0,015 0,213 0,051 0,306 0,140 0,097 0,090 0,865 0,015 0,748 0,060 0,012 0,083 0,537 0,248 0,335 0,798 0,362 0,037 0,981 0,322 0,855 0,042 0,004 0,126 0,028 0,050 0,889 0,469

4 0,003 0,585 0,118 0,379 0,490 0,532 0,108 0,829 0,586 0,043 0,241 0,287 0,031 0,483 0,993 0,122 0,673 0,059 0,179 0,022 0,464 0,101 0,309 0,339 0,083 0,021 0,156 0,005 0,556 0,047 0,017 0,157 0,396 0,331 0,510 0,360 0,412 0,056 0,989 0,109 0,792 0,007 0,002 0,213 0,054 0,049 0,831 0,026

5 0,024 0,707 0,212 0,212 0,736 0,661 0,101 0,647 0,437 0,038 0,390 0,531 0,106 0,565 0,934 0,033 0,255 0,115 0,029 0,073 0,178 0,228 0,172 0,526 0,005 0,019 0,032 0,009 0,709 0,043 0,030 0,210 0,473 0,361 0,207 0,380 0,589 0,008 0,993 0,130 0,456 0,018 0,006 0,345 0,066 0,013 0,832 0,047

6 0,038 0,321 0,295 0,335 0,711 0,701 0,099 0,768 0,537 0,061 0,597 0,678 0,152 0,727 0,866 0,006 0,051 0,065 0,043 0,025 0,294 0,193 0,102 0,581 0,000 0,010 0,046 0,006 0,757 0,044 0,046 0,126 0,529 0,232 0,194 0,397 0,790 0,009 0,962 0,025 0,600 0,011 0,009 0,161 0,092 0,018 0,870 0,047

7 0,022 0,263 0,367 0,294 0,825 0,295 0,071 0,822 0,492 0,101 0,681 0,806 0,006 0,795 0,672 0,017 0,021 0,014 0,118 0,060 0,475 0,232 0,138 0,550 0,001 0,034 0,093 0,022 0,612 0,110 0,109 0,121 0,722 0,299 0,280 0,267 0,758 0,026 0,593 0,055 0,749 0,021 0,022 0,323 0,189 0,022 0,649 0,031

Source: author’s calculations. Notes: Probability (p-value) of the null hypothesis. dnot GC = does not Granger Cause.

8 0,025 0,267 0,215 0,435 0,784 0,094 0,077 0,830 0,614 0,151 0,732 0,865 0,053 0,583 0,345 0,004 0,091 0,034 0,209 0,251 0,599 0,265 0,179 0,757 0,004 0,071 0,343 0,090 0,774 0,011 0,083 0,072 0,899 0,420 0,383 0,157 0,560 0,029 0,741 0,047 0,746 0,043 0,034 0,167 0,263 0,090 0,759 0,091

9 0,026 0,048 0,270 0,267 0,845 0,123 0,027 0,448 0,544 0,192 0,824 0,906 0,086 0,491 0,500 0,003 0,083 0,043 0,225 0,330 0,644 0,277 0,055 0,833 0,009 0,123 0,068 0,100 0,828 0,027 0,155 0,140 0,927 0,537 0,362 0,277 0,194 0,034 0,613 0,105 0,848 0,057 0,061 0,151 0,291 0,113 0,777 0,008

10 0,024 0,136 0,236 0,286 0,926 0,265 0,022 0,577 0,577 0,204 0,891 0,919 0,087 0,643 0,588 0,003 0,106 0,148 0,214 0,398 0,613 0,237 0,004 0,813 0,019 0,135 0,060 0,175 0,788 0,051 0,074 0,250 0,962 0,658 0,224 0,351 0,168 0,054 0,747 0,047 0,631 0,109 0,028 0,208 0,280 0,099 0,909 0,022