Financial interdependencies and causality in the European Union

95 FINANCIAL INTERDEPENDENCIES AND CAUSALITY IN THE EUROPEAN UNION José Ramos Pires Manso RESUMEN/ABSTRACT The main objectives of this paper are the study of foreign direct investment (FDI) among several UE countries, the appreciation of the interdependencies among them, the integration and co-integration of the FDI export series, in order to try to discover whose economies are the financial engines of the EU, the appreciation of the way of absorption of the FDI in the destiny countries of this money, the way that the economies found to regain the equilibrium after a foreign investment stimulus. In methodological terms the paper uses the VAR modelling theory, it optimizes the lag length, it uses the SURE method to estimate the parameters, it appreciates the IRF (functions), it uses the Granger causality and the Cholesky Variance Decomposition to study the degree of dependence or of independence of one economy against the others. Before this, it studies the stationarity, the integration and the co-integration of the series. KEY WORDS: foreign direct investment, VAR modelling, causality, co-integration, international financing 1. INTRODUCTION AND MAIN OBJECTIVES Before we enter more in the aim of this work dedicated to the study of the Foreign Direct Investment (FDI) it’s convenient to define what this kind of investment is. The FDI is defined as an investment that involves a long term relationship that reflects an interest and long term duration of an entity from one economy into another different from that of the capital owner – the foreign direct investor. This investment requires that the foreign investor controls or at least has a significant influence in the enterprise of the other economy. Such an investment involves an initial transaction between the two entities and all the subsequent transactions between them and between the foreign filials, either incorporated or not. Taking in account the definition of the OCDE a foreign direct investment enterprise is the one that through the foreign direct investment controls at least 10% of the shares or of the vote’s privilege and in which the foreign enterprise has the management decision power. With this work we try to study the relationships and inter-relationships among several countries of the western and central European Union (EU) – more precisely Portugal (P), Spain (S), France (F), United Kingdom (UK), Germany (G), and Italy (I) – departing from the capital exports of these countries – under the foreign direct investment (FDI) manner. In order to reach these objectives we use the Autoregressive Vector (VAR) and the Granger causality methodologies. More deeply we can say that the main objectives of this work are: (1) to study the international capital movements, namely those that can be called Foreign Direct Investment (FDI); (2) to appreciate the inter- CITIES IN COMPETITION 96 relationships that can be detected in this way among the 6 economies of Europe; (3) to verify if we can detect causality links among some of the economies; (4) to see which are the more opened and the more closed economies at this level; (5) to see how acts the autoregressive vector methodology (VAR) and the causality theory in this kind of approaches. In terms of structure the work begins to define his own objectives; the second part is relative to the methodologies used: the autoregressive vector and the Granger causality ones; the third part is dedicated to the presentation of the empirical data, its sources, and to the study of the stationarity and co-integration of the series; the fourth part shows the results obtained concerning either the autoregressive vector and causality methodologies or the interpretation of the results (the IRF functions and the Cholesky variance decomposition). It ends with a brief conclusion and a presentation of the main references consulted. 2. METHODOLOGICAL FRAMEWORK 2.1 AUTOREGRESSIVE VECTOR MODEL (VAR) The autoregressive vector model is used frequently either to foresee the interrelated time series systems or to analyse the dynamic impact of the random errors on the variables’ system. This model treats each endogenous variable of the system as a function of the past or lagged values of the endogenous variables in the system. The mathematical expression of the autoregressive vector model can be the following ttptpttt BxyAyAyAy ε ++ + ++= −−− ... 2211 (1-1), where yt is a vector of k endogenous variables, xt is a vector of d exogenous variables, A1, A2, ..., Ap and B are matrices of the parameters to be estimated and εt is a vector of innovations that can be contemporaneously correlated but that can not be correlated with their own past values and with all the variables of the second member of the equation. It is frequent to consider the autoregressive vector (VAR) model without exogenous variables, xt, or with these ones reduced to the c constants (the independent terms) reason why we can write the model as tptpttt cyAyAyAy ε ++ + ++= −−− ... 2211 (1-2) where c is a vector of constant terms c1, c2,... ck, Ai are squared matrices of the kxk type and εt is a vector of terms generated by a white noise process with the following proprieties: [] [] ⎩ ⎨ ⎧ ≠ =Ω = ∀= ts ts E tE tt t 0 ' 0 εε ε (1-3) where we assume that the covariance matrix Ω is positively definite. These properties indicate that the ε’s are not serially correlated (but can be contemporaneously correlated). Adopting a first difference reformulation of a second order autoregressive vector this model is equivalent to ttptpttt yyByByBcy ε π + − ∆++∆+∆+=∆ −+−−−− 1112211 ... (1-4) where the B’s are functions of the A’s, π=I-A1-A2-...Ap and ∆ is the first difference operator. The model doesn’t pose great problems or difficulties of estimation of the model’s parameters as the second member of each equation of the system has only lagged or pre-determined endogenous variables, reason why the NOTES ON STRATEGY, PLANNING AND INTERNATIONALIZATION 97 ordinary least squares (OLS) method gives consistent estimates of the model’s parameters. Besides this, even in the eventual case that the innovations εt are contemporaneously correlated, the OLS method gives consistent and equivalent estimates to those obtained with the GLS once all the equations have similar regressors. Following Johnston and Dinardo (p.325) we may say that there are two approaches to estimate the autoregressive vector model: (a) one, the direct estimation of the system (1-2) or of the alternative model (1-4); nevertheless, this way is only appropriated if all the eigenvalues of π are inferior to 1; and (b) another that is recommended when the variables y are not stationary; in this case we determine the number r of possible co-integrated vectors and then we estimate the system (1-4) restricting the π matrix to the r co-integrated variables. An important element in the estimating process of an autoregressive vector model is the determination of the lag length p. To achieve this aim usually we compute some indicators that help in this task. Among these there is the determinant of the residual covariance that can be defined as ∑ − =Ω tt pT ' ˆˆ 1 ˆ εε (1-5) where p is the number of parameters of each equation of the autoregressive vector model. Another important indicator is the logarithm of the likelihood function l whose value, assuming a normal multivariate function, is given by the expression { } Ω++−= ˆ log))2log(1( 2 π k T l (1-6). Other useful indicators are the Akaike Information Criterion (AIC) and the Schwarz Criterion (SC) whose mathematical expressions are: nTTlAIC 2/2 +−= (1-6) for the first one (AIC) and TTnTlSC /)log(/2 + −= (1-7), for the second one (SC), where n=k(d+pk) is the total estimated number of parameters of the autoregressive vector model. These two criterions are used for model selection namely for the selection of the lag length to consider in the model. They recommend the choice of the lag length for which the values of the AIC and SC are the least. To end this section let’s refer one more criterion to select the lag length – the LR test (initials of Likelihood Ratio) that tests the hypothesis that the coefficients on the lag l are jointly nulls using the statistic {} 2 12 ~loglog)( k ll mTLR χ Ω−Ω−= − (1-8) where m is the number of equation parameters under the alternative hypotheses. The test can be done like this: we begin by comparing the value of the modified LR statistic with the critical values at the level of significance of 5% beginning with the maximum possible lag and descending the lag length one unit each time until we obtain a rejection. When we adjust an autoregressive vector model of order p1 and we pretend to test the hypotheses that this order is p0<p1 we begin to write the logarithm of the likelihood function to maximize l, 1 ˆ ln 2 − Ω+= n cl (1-9) where n is the number of observations, and Ω^ is the estimated matrix of the residuals of the autoregressive vector equations, and the likelihood functions when we use p0 and p1 lags, respectively, as 1 11 1 00 ˆ ln 2 , ˆ ln 2 −− Ω+=Ω+= n cl n cl (1-10). On these circumstances the LR test statistics can be written as () [ ] 211 010 ~ ˆ ln ˆ ln2 q nllLR χ & −− Ω−Ω=−−= (1-11), where q is the number of restrictions imposed by the null hypotheses determination. In general q=k2(p1-p0) with k the number of variables of the autoregressive vector model. CITIES IN COMPETITION 98 2.2 THE GRANGER CAUSALITY It is worth to refer that correlation doesn’t imply necessarily causality. There are many examples of very high correlations that are either spurious or that have no sense. The Granger (1969) approach to the question of knowing if “x (Granger) causes y” permits to investigate how much of the current value y can be explained by the past values of y and if when adding lagged values of x we can improve the explanation of the model. We can say that “y is Granger caused by x” if x helps in the prevision of y, or if the coefficients of the x lagged variables are statistically significant. It’s important to refer that the conclusion that “x is Granger cause of y” doesn’t imply that y is the effect or the result of x, even when the Granger causality measures, in some aspects, the precedence. The Granger causality implies the estimation of 2 regressions, or, in other words, implies the estimation of a bivariate regression like the following: tltltltltt tltltltltt uyyxxx xxyyy +++++++= ++ + + + + + = −−−− −−−− ββααα ε β β α α α ...... ...... 11110 11110 (1-12), for all the possible pairs of values of the series (x,y) of the group. Sometimes we consider models like these ones but without independent terms (α0=0). The Granger causality test is not but the F. Wald test for the joint hypotheses 0... 21 === = l β β β for each equation. The null hypotheses can be expressed as: H01: ‘x is not Granger cause of y’, in the first equation, and H02: ‘y is not Granger cause of x’, in the second. The test statistic is given by ( ) () knSQEnr mSQEnrSQEr F− − =/ / (1-13) a statistic that follows the F distribution with m and n-k degrees of freedom, where m is the number of lagged terms of Y and k is the number of parameters estimated in the regression without restrictions, SQEr is the sum of squared errors in the restraint regression (when the hypotheses H0 is true) and SQEnr is a similar sum obtained with the unrestricted regression. Some econometric software computes routinely the values of the F statistic in each one of the hypotheses and the minimum levels of significance that are needed to reject H0 (usually identified by Prob.). If in such a test we reject both null hypotheses then we say that between the two x and y variables there is a bilateral relationship, if only one of them is rejected we say that there is a unilateral relationship and if we don’t reject none of them we say that there is an independent relationship. In more deeply terms there are four situations or cases in such an analysis: (1) Unidirectional causality of the foreign direct investments from the x economy to the y economy: when the estimated coefficients of the lagged Variables of the second economy (y), taken toghether, are statistically differents from zero and the estimated coefficients of the first lagged variable, x, in the second equation are not statistically different from zero. (2) Unidirectional causality of the foreign direct investments of the x economy to the y economy: when the set of coefficients of the lagged variable, y, in the first equation is not statístically different from zero and the set of coefficients of the lagged economy, x, in the second equation is not statistically different from zero. (3) Feedback or bilateral causality: when the sets of coefficients of the FDI of the two economies, x and y, are statistically different from zero in the two regressions. (4) Independence of the FDI originated on the x and y economies: when the sets of estimated coefficients of the y variable and of the x variable are not statistically different from zero in the two regressions. NOTES ON STRATEGY, PLANNING AND INTERNATIONALIZATION 99 3. CAPITAL EXPORTS AS FOREIGN DIRECT INVESTMENT 3.1 DATA BANK As we said before the data that we are going to use is referred to the capital exports as foreign direct investment (FDI, outflows) of 6 countries of the European Union – Portugal, Spain, France, United Kingdom, Italy and Germany – of the years 1970 till 2001. The values used in the empirical application were extracted from a data bank of the United Nations Conference on Trade And Development (UNCTAD) and published in the site www.unctad.org/FDI; they are referred to the capital flows and include the equity capital (capital that is bought by the investor), the reinvested results (the part of the foreign direct investor on the profit or gain that are not distributed to the filials or results that are not sent to the foreign direct investor) and the loans borrowing among the enterprises (short or long term loans and the fund’s loans among the mother and filials’ enterprises. The outflows that we consider here are the net way outs of capitals from a country to another to lasting control of a firm. The monetary unity in which are expressed the values is the USA million dollar. The following figure shows the evolution of the FDI outflows over the 32 years of the period. Graphic n. 2.1 – Capital Exports’ Evolution (in 106 USA dollars) -50000 0 50000 100000 150000 2 00000 2 50000 3 00000 70 75 80 85 90 95 00 POR2 SPA2 FRA2 ITA2 UKD2 GER2 Note: POR2-Portugal, SPA2-Spain, FRA2-France, ITA2-Italy, UKD2-United Kingdom, GER2-Germany. The Portuguese data from 2000 to 2001 are estimates done by UNCTAD. CITIES IN COMPETITION 100 3.2 NON STATIONARITY OF THE TIME SERIES – CORRELOGRAMS AND THE Q BOX-PIERCE, ADF AND PP TESTS Either the correlograms of the total and partial autocorrelation functions, ACF and PACF, respectively, of the natural logarithms of the time series that are being studied or the Q Box-Pierce test clearly show the non stationarity of the original series when taken in levels. In the same sense point the Augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) tests – when testing the null hypotheses of the integration or non-stationarity of the respective series, in levels, we could not reject them. Once certified that the series are not stationary we apply the same tests to the first differences of the same series to confirm that all of them are already stationary, fact that is equivalent to say that the original series in levels are I(1). 3.3 COINTEGRATION OF THE SERIES – THE JOHANSEN TEST The application of the Johansen test to appreciate the co-integration of the 6 series gave the following results: Table n. 3.31 – Results of the Johansen test to appreciate cointegration Likelihood 5 Percent 1 Percent Hypothesized Eigenvalue Ratio Critical Value Critical Value No. of CE(s) 0.975996 154.7625 94.15 103.18 None ** 0.759988 76.44243 68.52 76.07 At most 1 ** 0.691838 46.47401 47.21 54.46 At most 2 0.595345 21.75430 29.68 35.65 At most 3 0.122771 2.755153 15.41 20.04 At most 4 0.000211 0.004432 3.76 6.65 At most 5 *(**) denotes rejection of the hypothesis at 5%(1%) significance level L.R. test indicates 2 cointegrating equation(s) at 5% significance level The LR test denotes the existence of 2 cointegrating equations at the 5% level of significance. It also permits to reject, in 2 cases, the hypotheses of the existence of a linear trend at the s. levels of 5% and 1%. This fact means that among these series there are a long term equilibrium relationship. 4. CAPITAL EXPORTS TO FOREIGN DIRECT INVESTMENT – EMPIRICAL APPLICATION 4.1 ESTIMATES OF THE AUTOREGRESSIVE VECTOR MODEL (VAR) Following step by step everything that was said in the third section of this paper (when we spoke of the methodology framework) we obtained the estimates for each one of the components of the VAR model with 6 endogenous Variables– one for each exporting country (Portugal, Spain, France, United Kingdom, Italy and Germany) that are written in the table n. 4.1. Unhappily not all the series covered the period 1970-2001 reason why in the estimation process we only use the period 1974-2001 for the estimation process. For other reasons 7 other observations have to be excluded (the missing values, related especially to the fact that the negative flows could not be converted in logarithms as happen for 3 times in the Portuguese case). Due to these facts the optimisation process of the lag length indicated the value of 1. NOTES ON STRATEGY, PLANNING AND INTERNATIONALIZATION 101 The variables of the VAR model were expressed in the first differences of the natural logarithms. As can be seen by the table n. 4.1 the estimated VAR model has 42 parameters resulting from the fact of having 6 endogenous variables by the same number of pre-determined ones more 6 constant terms c in the pre-defined VAR model. The values found for these parameters translate thus the relations and interrelations’ network among the 6 capital exporting economies. Table n. 4.1 Estimation of the VAR(1) model with 6 endogenous Variables Sample(adjusted): 1974 2001 Included observations: 21 Excluded observations: 7 after adjusting endpoints Standard errors & t-statistics in parentheses DLP DLE DLF DLUK DLI DLG DLP(-1) -0.074502 -0.006705 -0.133861 -0.188842 0.131378 0.021746 (0.24144) (0.13419) (0.11496) (0.17754) (0.13455) (0.10811) (-0.30858) (-0.04996) (-1.16439) (-1.06368) (0.97643) (0.20115) DLE(-1) 0.705092 -0.055122 0.228890 0.015038 0.087416 0.076157 (0.47328) (0.26306) (0.22536) (0.34802) (0.26375) (0.21192) (1.48979) (-0.20955) (1.01568) (0.04321) (0.33143) (0.35937) DLF(-1) 0.053966 0.266972 -0.394063 -0.143895 -0.060200 -0.336927 (0.47758) (0.26545) (0.22741) (0.35118) (0.26615) (0.21384) (0.11300) (1.00575) (-1.73287) (-0.40974) (-0.22619) (-1.57559) DLUK(-1) -0.072430 0.148914 0.167828 0.034453 -0.287839 0.063492 (0.49560) (0.27546) (0.23598) (0.36443) (0.27619) (0.22191) (-0.14615) (0.54060) (0.71118) (0.09454) (-1.04218) (0.28612) DLI(-1) 0.271013 0.011272 0.076890 -0.059939 -0.810538 0.024155 (0.33276) (0.18495) (0.15845) (0.24469) (0.18544) (0.14900) (0.81444) (0.06094) (0.48527) (-0.24496) (-4.37082) (0.16212) DLG(-1) 0.179212 0.701871 0.842340 0.647878 -0.180234 0.044613 (0.57826) (0.32141) (0.27534) (0.42522) (0.32226) (0.25892) (0.30991) (2.18375) (3.05922) (1.52364) (-0.55929) (0.17230) C -0.061283 0.069310 -0.007167 0.022086 0.223237 0.100479 (0.23466) (0.13042) (0.11173) (0.17255) (0.13077) (0.10507) (-0.26116) (0.53142) (-0.06415) (0.12800) (1.70710) (0.95632) R-squared 0.215212 0.345618 0.506226 0.202413 0.596682 0.165508 Adj. Rsquared -0.121126 0.065169 0.294608 -0.139410 0.423831 -0.192131 Sum sq. Resids 10.59911 3.274359 2.403103 5.731155 3.291728 2.124986 S.E. equation 0.870103 0.483614 0.414307 0.639819 0.484895 0.389596 F-statistic 0.639869 1.232373 2.392173 0.592157 3.452008 0.462779 CITIES IN COMPETITION 102 Log likelihood -22.61831 -10.28450 -7.036211 -16.16235 -10.34005 -5.744756 Akaike AIC 2.820791 1.646143 1.336782 2.205938 1.651434 1.213786 Schwarz SC 3.168966 1.994317 1.684956 2.554112 1.999608 1.561960 Mean dependent 0.135095 0.168023 0.072634 0.028266 0.093872 0.091083 S.D. dependent 0.821757 0.500187 0.493295 0.599400 0.638812 0.356822 Determinant Residual CoVARiance Log Likelihood Akaike Information Criteria Schwarz Criteria 1.57E-05 -62.62051 9.963858 12.05290 4.2 INTERPRETATION OF THE RESULTS The direct interpretation of the VAR model is very complicated and most time conducts to poor conclusions. Instead of this in general this interpretation uses the impulse response function (IRF), or the error variance decomposition analysis. 4.2.1 IMPULSE RESPONSE FUNCTIONS – GRAPHICAL ANALYSIS Let us see the shape of the IRF – the response of the different FDI or economies to impulses of size 1 standard deviation (s. d.). The following illustration give us the evolution of the Foreign Direct Investment of the 6 economies – in IRF terms – to variations, shocks or unitary innovations (of one standard deviation) introduced in the error terms of the VAR model. From these graphics we can retain the quickly convergence of these functions, fact that, in some sense, translates the rapidity of absorption of the innovations by the six economies. It is worth to refer that the innovation absorption takes 5/6 years for all the economies; the only exception is the Italian one that is slower taking more then 10 years. NOTES ON STRATEGY, PLANNING AND INTERNATIONALIZATION 103 Illustration n. 4-1: Economical Response to Impulses of 1 s. d. -0.2 0.0 0.2 0.4 0.6 0.8 1 2 3 4 5 6 7 8 9 10 D(L OG(POR2 )) D(LOG(SPA2)) D(L OG(FRA2 )) D(L OG(UKD2 )) D(L OG(ITA2 )) D(L OG(GER2 )) Response of D(LOG(POR2)) to One S .D. Innovations -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 1 2 3 4 5 6 7 8 9 10 D(L OG(POR2 )) D(LOG(SPA2)) D(L OG(FRA2 )) D(L OG(UKD2 )) D(L OG(IT A2 )) D(L OG(GER2 )) Response of D(LOG(SP A 2)) to One S .D. Innovations -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 1 2 3 4 5 6 7 8 9 10 D(L OG(POR2 )) D(LOG(SPA2)) D(L OG(FRA2 )) D(L OG(UKD2 )) D(L OG(ITA2 )) D(L OG(GER2 )) Response of D(LOG(FRA2)) to One S .D. Innovations -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 1 2 3 4 5 6 7 8 9 10 D(L OG(POR2 )) D(LOG(SPA2)) D(L OG(FRA2 )) D(L OG(UKD2 )) D(L OG(IT A2 )) D(L OG(GER2 )) Response of D(LOG(UKD2)) to One S.D. Innovations -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 1 2 3 4 5 6 7 8 9 10 D(L OG(POR2 )) D(LOG(SPA2)) D(L OG(FRA2 )) D(L OG(UKD2 )) D(L OG(ITA2 )) D(L OG(GER2 )) Response of D(LOG(ITA2)) to One S.D. Innovations -0.2 -0.1 0.0 0.1 0.2 0.3 1 2 3 4 5 6 7 8 9 10 D(L OG(POR2 )) D(LOG(SPA2)) D(L OG(FRA2 )) D(L OG(UKD2 )) D(L OG(IT A2 )) D(L OG(GER2 )) Response of D(LOG(GE R2)) to One S .D. Innovations 4.2.2 IMPULSE RESPONSE FUNCTIONS – NUMERICAL ANALYSIS In order to short the size of this paper we don’t put here the numerical values that support the graphics of the impulse response functions (IRF) to innovations introduced in the VAR model structure. Following a methodology that other authors use – like, for instance, Goux (1996) – if we sum the values of the IRF obtained by each variable along the 10 years in analysis, we may say that the Portuguese FDI exports answer positively to innovations in the Spanish, British, Italian, and German economies and negatively to innovations or impulses in the French economy (FDI exports). Doing the same thing for Spain we may say that the Spanish FDI exports answer positively to innovations in the French, British, Italian, German and Spanish and negatively to impulses in the Portuguese economy. The same analysis for France says that the French FDI exports answer positively to innovations in the economies of Spain, France, UK, Italy and Germany and answer negatively to innovations in the Portuguese economy. The British FDI exports answer positively to innovations in the economies of Portugal, France, UK and Germany, and negatively in the economies of Spain and Italy. The Italian FDI exports answer positively to innovations in the economies of Portugal, Spain and itself (Italy) and negatively in the economies of France, UK and Germany. And the German FDI exports answer positively to innovations in the economies of Portugal, Spain and Italy and negatively in the economies of France, Italy and itself (Germany).