Claudiu Tiberiu Albulescu
email: claudiu.albulescu@upt.ro.

Daniel Goyeau

The interaction between trade and FDI: the CEE countries experience

Keywords: FDI, trade, complementarity, substitution, panel models, CEE countries JEL Classification: F15, F21, C23

Inside the EU, the commercial integration of the CEE countries has gained remarkable momentum before the crisis appearance, but it has slightly slowed down afterwards.

Consequently, the interest in identifying the factors supporting the commercial integration process is high. Recent findings in the new trade theory suggest that FDI influence the trade intensity but the studies approaching this relationship for the CEE countries present mixed evidence, and investigate the commercial integration of CEE countries with the old EU members. Against this background, the purpose of this paper is to assess the CEE countries' intra-integration, focusing on the Czech Republic, Hungary, Poland and the Slovak Republic.

For each country we employ a panel gravitational model for the bilateral trade and FDI, considering its interactions with the other three countries in the sample on the one hand, and with the three EU main commercial partners on the other hand. We investigate different facets of the trade -FDI nexus, resorting to a fixed effects model, a random effects model, as well as to an instrumental variable estimator, over the period 2000-2013. Our results suggest that outward FDI sustains the CEE countries' commercial integration, while inward FDI has no significant effect. In all the cases a complementarity effect between trade and FDI is documented, which is stronger for the CEE countries' historical trade partners. Consequently, these findings show that CEE countries' policymakers are interested in encouraging the outward FDI toward their neighbour countries in order to increase the commercial integration.

Introduction

Before the crisis appearance, the economy of the Central and Eastern European (CEE) countries has been immersed in an accelerated process of commercial integration. At the same time, the removal of barriers to capital flows has encouraged the regional outward and inward foreign direct investment (FDI). However, the crisis has slightly slowed down the CEE countries' real converge process, especially the bilateral investment. In this context, several simple questions arise: What is the influence of the trade -FDI interaction on the CEE countries' commercial integration? Do we notice a stabilisation of the CEE countries' commercial integration at long-run levels? Does the commercial integration with the new and old EU members present similar features for the CEE countries?

The relationship between trade and FDI is analysed from the point of view of the substitution or the complementarity effect which may appear between them. Historically, based on the theory of multinational firms, the horizontal FDI is considered as an alternative way for firms to internationalise. Therefore, the substitution effect between trade and FDI prevails over complementarity when countries are similar in size, technologies and factor endowments [START_REF] Markusen | Multinationals, multi-plant economies and the gains from trade[END_REF]Markusen and Venables, 1999;[START_REF] Türkcan | Outward foreign direct investment and intermediate goods exports: Evidence from the USA[END_REF]. When focusing on vertical FDI linkages, the literature documents in general a complementarity effect between trade and FDI [START_REF] Helpman | A simple theory of international trade with multinational corporations[END_REF][START_REF] Clausing | Does multinational activity displace trade?[END_REF]. Recent developments in the new trade theory also emphasise that trade and FDI can be positively correlated [START_REF] Lipsey | Foreign production and exports in manufacturing industries[END_REF][START_REF] Fontagné | Foreign Direct Investment and International Trade: Complements or Substitutes?[END_REF][START_REF] Fontagné | Foreign Trade and FDI Stocks in British, US and French Industries: Complements or Substitutes?[END_REF].

At the European Union (EU) level, most of the papers focus on the commercial integration between the old EU members [START_REF] Chiappini | FDI and trade: A Granger causality analysis in a heterogeneous panel[END_REF][START_REF] Chiappini | Investissement direct à l'étranger et performance à l'exportation[END_REF], or between the new EU members [START_REF] Herrmann | Trade balances of the central and east European EU member states and the role of foreign direct investment[END_REF][START_REF] Kutan | Foreign Direct Investment and Export Performance: Empirical Evidence[END_REF], and provide different results, depending on the empirical methodology and data employed. None of these studies investigates the particular case of the CEE countries' bilateral commercial integration. Thus, our paper brings several contributions to the existing literature.

First, our focus falls on testing the relationship between the bilateral trade and FDI considering the CEE countries, which recorded an increased regional commercial integration before the crisis outburst. As far as we know, this is the first paper addressing the linkages between the bilateral trade and FDI in the CEE countries. Data availability for this group of countries, especially in the case of the bilateral FDI, makes the task difficult. We need to deal with a trade-off between focusing on specific countries for which data are in general available for a longer period, or including in the sample more CEE countries, but reducing thus the number of observations. We therefore chose the first option and we test the trade -FDI nexus for the Czech Republic, Hungary, Poland and the Slovak Republic (CEE-4), using Organisation for Economic Co-operation and Development (OECD) statistics for the period 2000-2013. The OECD statistics contain information about the bilateral investments between the OECD members. Six CEE countries are OECD members, namely the Czech Republic, Estonia, Hungary, Poland, the Slovak Republic and Slovenia. However, Slovenia and Estonia are excluded from our sample because of insufficient number of observations. Moreover, we are forced to start with the year 2000 as no previous data are available for the Slovak Republic's inward FDI before this year 1 .

The selected countries (to a smaller extent Poland), represent the countries with the highest level of trade openness in the CEE group of countries. According to the World Bank statistics (World Development Indicators), over the period 2000-2013, the trade openness in CEE-4 is above the average level of the entire group of CEE countries (118% compared to 103%), and considerably above the EU level (72%). At the same time, CEE-4 is historically considered as representing the advanced group of CEE countries (together with Slovenia), where the commercial and capital flows are more developed as compared to other CEE countries.

The second contribution of the paper consists in drawing a comparison between the role of the bilateral FDI in explaining the trade for CEE-4 having as partners the CEE countries on the one hand (CEE-3) 2 , and the three main EU commercial partners (Austria, Germany and Netherlands -EU-3) 3 on the other hand. Assuming a complementary effect between trade and FDI, authorities must pay special attention to the bilateral investment between the CEE countries only if it determines a stronger commercial integration as compared to the main EU partners. The same applies in the case of a substitution effect. Third, we test the trade -FDI interactions in a panel gravitational framework, constructing a panel data for each CEE-4 country. Different from previous works which include in a single panel all the CEE countries and which consider a group of countries (usually the old EU members) as partners, we focus on each CEE country for two reasons. On the one hand, there are important discrepancies between the data reported by different 1 Indeed, alternative databases such as United Nations Conference on Trade and Development (UNCTAD) are richer in bilateral FDI statistics. Nevertheless, there is a large heterogeneity between the CEE countries regarding the data availability, and for a large number of countries data are provided only after 2007. 2 CEE-3 denotes the other three CEE countries acting as partners. For example, the CEE-3 in the case of the Czech Republic, are Hungary, Poland and the Slovak Republic. 3 The three main commercial partners of the CEE-4, based on the trade volume (UNCTAD data). countries4 . So, in order to obtain reliable results, we refer to the statistics reported by each country. On the other hand, building a panel for each CEE-4, allows us to make comparisons between these countries. Consequently, for each panel (corresponding to each CEE-4 country), we have as partners the other three CEE countries (CEE-3) and the three main EU commercial partners (EU-3). In order to make a comparison between the effect of FDI on trade in the case of CEE-3 and EU-3, we use a dummy variable. The empirical approach consists in drawing a comparison between a panel fixed effects model and a random effects model (classical approaches for dealing with macro panels). We also treat the endogeneity problems which may appear between trade and FDI, relying on an instrumental variable (IV) approach.

Finally, we contribute to the literature exploring different facets of the trade -FDI relationship. Most of the existing works pay attention to the role of inward FDI for the commercial integration. Following the Fontagné (1999) approach, we test for the role of both inward and outward FDI on trade, considering the volume of exports and imports. This way we are able to identify different transmission channels from FDI to trade, and to better understand the nature of this relation.

Our results show a complementary effect between trade and FDI in the case of CEE-4.

We document an important role of the outward FDI in favouring trade, while the role of the inward FDI is inconclusive. In addition, we find that this relation is stronger for the CEE-3 partners as compared to the EU-3 partners.

The remainder of the paper is organised as follows. Section 2 presents a short review of the literature. Section 3 describes the CEECs' commercial features, the data and the methodology. Section 4 presents the empirical results. Section 5 brings forward the conclusions and the policy implications of our findings.

Literature review

During the last decades, the world economy, and especially the EU economy, has become more integrated. The relationship between trade and FDI is considered as being at the core of this integration process. Consequently, the impact of FDI on trade has been intensely debated in the literature at macro level, since it provides information about the international specialisation of countries and about the general welfare effects. At the same time, at micro level, the firms' decisions to expand their markets encompass a combination of both trade and foreign direct investment, simultaneously determined by factors such as economies of scale, trade costs, market access and differences in factors endowments.

The trade -FDI nexus is examined both by the theories of international trade and by those of multinational companies. These theories, with an independent evolution, have emerged during the last years. Therefore, the common question nowadays is whether trade and FDI act as complements or substitutes in delivering goods across borders, whereas the answers to this question are quite divers. Overall, the new trade theory reveals that, depending on the circumstances, the FDI can have both a substitution5 , as well as a complementarity6 effect on trade. For example, relying on the trade theory, [START_REF] Markusen | Trade versus Investment Liberalization[END_REF] and [START_REF] Carr | Estimating the Knowledge-capital Model of the Multinational Enterprise[END_REF] admit the complementarity, as well as the substitution, between FDI and trade. Based on the theory of firms' location, [START_REF] Pontes | A theory of the relationship between foreign direct investment and trade[END_REF] and [START_REF] Africano | FDI and Trade in Portugal: a gravity analysis[END_REF] show that the complementarity between trade and FDI is normally found when foreign investments are vertical, meaning that the multinational companies split the production process across countries in order to reduce costs. At the same time, FDI substitutes trade when investments are horizontal.

However, the influence of FDI on trade is complex and it can be analysed from the perspective of the home or of the host country, but also from the point of view of the inward and outward FDI 7 . From the point of view of the home country, FDI is seen as substitute for trade, as exports are replaced by local sales on foreign markets, particularly in the form of final goods. For the host countries, the relationship between FDI and trade can be considered symmetrical to that of the investing country. The difference in factor endowment also explains the linkages between trade and FDI (see [START_REF] Helpman | A simple theory of international trade with multinational corporations[END_REF]. At the same time, we can distinguish between the influence of the inward and outward FDI on trade, which needs not to be symmetrical. Therefore, [START_REF] Fontagné | Foreign Direct Investment and International Trade: Complements or Substitutes?[END_REF] underlines four situations:

-Inward FDI influences exports if foreign firms locate in the host economy to export back home, or provide products/services in a regional market.

-Outward FDI influences exports owing to enhanced competitiveness on foreign markets or reduces exports if the opposite applies.

-Inward FDI influences imports owing to enhanced competitiveness of foreign firms on the domestic market, but they may give rise to exports when the host country gains competitiveness.

-Outward FDI influences imports in the case of backward vertical integration and/or relocation of labour-intensive activities abroad, from a capital-intensive country.

The diversity of empirical works on the topic is really important. Most of the papers focus on FDI stocks [START_REF] Kutan | Foreign Direct Investment and Export Performance: Empirical Evidence[END_REF][START_REF] Fillat-Castejón | Trade through FDI: investing in services[END_REF][START_REF] Fontagné | Foreign Trade and FDI Stocks in British, US and French Industries: Complements or Substitutes?[END_REF][START_REF] Chiappini | Investissement direct à l'étranger et performance à l'exportation[END_REF], but there are also empirical works which take into account FDI flows [START_REF] Zarotiadis | FDI and Trade in the UK: Substitutes or Complements?[END_REF][START_REF] Aydin | On the Interaction between Foreign Direct Investment Inflows and International Trade: Complementary or Substitution? A Case Study of Turkey[END_REF]. The use of FDI stocks is in general preferred due to smaller variations in data (FDI flows are extremely volatiles, especially in crisis periods) and especially due to the fact that the influence of FDI on trade is not instantaneous. Therefore, the cumulative role of the investments' flow, namely the stocks, must be considered (for more arguments see [START_REF] Bayoumi | Japanese Foreign Direct Investment and Regional Trade[END_REF]. If the majority of authors analyse the case of a single country [START_REF] Pfaffermayr | Foreign direct investment and exports: A time series approach[END_REF][START_REF] Clausing | Does multinational activity displace trade?[END_REF][START_REF] Alguacil | Foreign direct investment, exports and domestic performance in Mexico: A causality analysis[END_REF], several recent papers use a panel data analysis [START_REF] Kutan | Foreign Direct Investment and Export Performance: Empirical Evidence[END_REF][START_REF] Chiappini | FDI and trade: A Granger causality analysis in a heterogeneous panel[END_REF][START_REF] Chiappini | Investissement direct à l'étranger et performance à l'exportation[END_REF].

The fact that the theoretical and empirical literature exploits different issues and provides such different results does not stand for a surprise [START_REF] Zarotiadis | FDI and Trade in the UK: Substitutes or Complements?[END_REF].

For example, in the case of the United States and Japan, [START_REF] Bayoumi | Japanese Foreign Direct Investment and Regional Trade[END_REF] find a substitutability relationship between trade and FDI, while [START_REF] Brainard | An Empirical Assessment of the Proximity Concentration Trade-off between Multinationals Sales and Trade[END_REF], [START_REF] Clausing | Does multinational activity displace trade?[END_REF] and [START_REF] Co | Japanese FDI into the US Automobile Industry: An Empirical Investigation[END_REF] argue in favour of the complementarity between trade and FDI.

In the EU case, the link between trade and FDI is studied both from the single country perspective [START_REF] Barry | FDI and Trade: the Irish host-country experience[END_REF][START_REF] Africano | FDI and Trade in Portugal: a gravity analysis[END_REF][START_REF] Zarotiadis | FDI and Trade in the UK: Substitutes or Complements?[END_REF] and from that of a group of countries [START_REF] Egger | European Exports and Outward Foreign Direct Investment: A Dynamic Panel Data Approach[END_REF][START_REF] Chiappini | FDI and trade: A Granger causality analysis in a heterogeneous panel[END_REF][START_REF] Chiappini | Investissement direct à l'étranger et performance à l'exportation[END_REF].

If for example [START_REF] Zarotiadis | FDI and Trade in the UK: Substitutes or Complements?[END_REF] find for the United Kingdom, a complementarity effect of FDI on trade, [START_REF] Chiappini | Investissement direct à l'étranger et performance à l'exportation[END_REF] documents a strong complementarity relationship in the case of Germany, but not for France and Italy. [START_REF] Martínez | Foreign Direct Investment and Trade: Complements or Substitutes? Empirical Evidence for the European Union[END_REF] show in their turn that the EU commercial integration and the FDI level reinforce each other. Conversely, [START_REF] Egger | European Exports and Outward Foreign Direct Investment: A Dynamic Panel Data Approach[END_REF] documents a substitution effect between exports and stocks of outward FDI in the EU member states.

However, only a small number of papers investigate the case of the CEE countries, and only in relation with the old EU members. For example, [START_REF] Herrmann | Trade balances of the central and east European EU member states and the role of foreign direct investment[END_REF] use aggregate industry data, and find that FDI and trade are complements. In the same line, [START_REF] Sapienza | The interaction between Export and FDI: Central-Eastern Europe and EU15[END_REF] tests the relationship between the bilateral flows of FDI and exports from the EU-15 towards the CEE countries, using an extended gravity approach that includes labour costs, and discovers a complementarity situation. [START_REF] Kutan | Foreign Direct Investment and Export Performance: Empirical Evidence[END_REF] analyse in their turn the potential effects of FDI inflows on exports in the case of twelve CEE countries, making the distinction between supply capacity-increasing effects and FDI-specific effects.

Nevertheless, none of the previous works analyses the effect of FDI on the CEE countries' intra-integration. In order to contribute to the empirical literature on this subject, we test the relationship between FDI and the bilateral trade in the case of four OECD countries, namely the Czech Republic, Hungary, Poland and the Slovak Republic, for the period 2000-2013.

Trade and FDI in the CEECs

Stylised facts

Until 1989, the CEE countries were planned economies with a trade organization based on the state's monopoly. The trade was characterised by a strong concentration inside the Council for Mutual Economic Assistance (CMEA). After 1989, during the structural reform period, the CEE countries' trade pattern has experienced significant changes [START_REF] Guerrieri | Trade Patterns, and Industrial Restructuring of Central and Eastern Europe[END_REF][START_REF] Rault | Modeling international trade flows between Eastern European countries and OECD countries[END_REF]. We have noticed a strong expansion of the trade, in particular with the EU countries, whereas the CMEA intra-regional trade collapsed.

Three countries are to be noticed in that period, namely the Czech Republic, Hungary and Poland. They represent almost two-thirds of the trade volume with the old EU members (EU-15) in the 1990s. The Slovak Republic can also be added to this group (CEE-4) due to its strong historical relationship with the Czech Republic and to the high level of trade openness.

The new policy configuration favoured the commercial integration between the CEE-4 and the EU-15. The commercial relationships with the old EU members became more and more important, with a growing trend situated well above the commercial trade between the CEE countries and the rest of the world, or between the CEE countries and the traditional Eastern European partners.

However, even if the CMEA disappeared, we remark a revival of the commercial trade between the CEE countries during the years preceding the crisis. Nevertheless, Fig 1 shows that, with the onset of the crisis, the commercial integration between the CEE-4 regressed in 2009, recovered immediately after and slowed down during the last years. intensification. If we compare the situation of each country, we notice that the Czech and the Slovak Republic are the destination countries of FDI from the CEE-3 partners. An opposite situation appears in the case of Poland and Hungary, where the inward FDI from the other three partners retained into the analysis is much more reduced as compared to the outward FDI toward these countries. Further, in all the countries, the bilateral outward FDI decreased after 2005, as compared to the total FDI stock (world as partner). We also notice that the outward FDI toward CEE-3, as compared to the total outward FDI in CEE countries is several times more important that the inward FDI, proving that CEE countries are FDI destination countries, while their investment abroad are mainly performed in the neighbouring countries.

Data description and methodology

The annual data for the bilateral trade are extracted form UNCATD database while the bilateral FDI statistics are extracted from the OECD database, covering the period 2000-20138 (data are expressed in US dollars and natural logarithm). Having in mind the historical background of the commercial relationships between the CEECs-4, we are interested in exploring several aspects of the trade -FDI nexus. First, we want to see if FDI enhances the competitiveness of the host country. Consequently, we test the relation between outward FDI and exports. Second, we want to see if FDI is accompanied by an increasing volume of factors from the investor countries, factors supporting the production process. These factors are meant to increase the competitiveness of foreign firms on the domestic market. Therefore, we test the relation between inward FDI and imports. Third, we analyse the backward vertical integration and the relocation abroad of labour-intensive activities. We thus analyse the impact of outward FDI on imports. Finally, we look for "export-back effect" and we test the relationship between inward FDI and exports.

To validate our results we use a large battery of control variables (all variables are expressed in natural logarithm). The general equation we propose is largely employed in the bilateral trade models with factor endowments [START_REF] Herrmann | Trade balances of the central and east European EU member states and the role of foreign direct investment[END_REF][START_REF] Fontagné | Foreign Trade and FDI Stocks in British, US and French Industries: Complements or Substitutes?[END_REF][START_REF] Egger | An econometric view on the estimation of gravity models and the calculation of trade potentials[END_REF][START_REF] Chiappini | Investissement direct à l'étranger et performance à l'exportation[END_REF]. The bilateral trade is influenced by the bilateral income, the country relative size, the difference in factor endowments and trade costs (associated with the geographical distance between countries). A description of the explanatory variables is presented in Table 1

(Appendix B) 9 .
The empirical methodology refers to a macro panel data analysis and a gravity approach. Two reasons underlie the choice of the panel data approach. First, the trade and FDI levels have both risen over time, due to generally better economic conditions. It thus makes little sense to investigate the impact of FDI on trade over time in isolation [START_REF] Pain | Export performance and the role of foreign direct investment[END_REF] 10 . Second, the lack of historical statistical data and their low frequency in the case of the CEE countries recommends the use of a panel analysis. We also employ a gravity equation which is widely and successfully used to explain bilateral trade flows. The trade patterns enable the analysis of the bilateral trade flow by taking in a simple manner into consideration few selected statistical data as the GDP, the geographical distance and a group of variables designed to capture specific aspects of the commercial integration of the considered countries [START_REF] Sapienza | The interaction between Export and FDI: Central-Eastern Europe and EU15[END_REF] 11 .

The gravity equations are usually estimated in panel with fixed effects in order to eliminate the problem of unobserved variables and to overcome the lack of control for the heterogeneous trading relationships. We start then our empirical investigation resorting to a fixed effects model.

it i it ijt ijt X fdi trade           2 1 0 (1)
where: trade ijt is the bilateral trade between country i and country j at date t (exports and imports); fdi ijt is the bilateral FDI stock between country i and country j at date t; X it represents the set of control variables; β 0 is the intercept; α i represents all the stable characteristics of countries; ε it are the errors of the model. However, this method does not control for all stable covariates (Allison and Waterman, 2002). Therefore, we also test a random model and we compare the fixed and random effects models based on the Hausman test.

it it i it ijt ijt X fdi trade             2 1 0 (2)
where: μ ijt represents between-entity errors; ε it are the within-entity errors of the model. [START_REF] Fontagné | Foreign Direct Investment and International Trade: Complements or Substitutes?[END_REF] shows that trade may also cause FDI. Therefore, the endogeneity issue which arises between trade and FDI is not addressed by the previous models.

Consequently, we continue our analysis with an instrumental variable regression. We use a Two Stages Least Square estimator (2SLS) and we perform two endogeneity tests, namely the Wu-Hausman and the Durbin-Wu-Hausman tests. If the endogeneity is present, then the Ordinary Least Square (OLS) estimator is inconsistent and an IV approach is recommended [START_REF] Baum | Instrumental variables and GMM: Estimation and testing[END_REF]. We also check for the presence of heteroskedasticity using the Pagan-Hall general test. According to [START_REF] Baum | Enhanced routines for instrumental variables/generalized method of moments estimation and testing[END_REF], if the heteroskedasticity problem exists, it can be corrected using robust standard errors. Given the small number of observations, in the case of the 2SLS approach, usually the proliferation of instruments constitutes a problem.

Therefore we use the Sargan over-identification test for all instruments (the Hansen J test is recommended if robust standard errors are used).

Before performing the estimations, we check for the stationarity of our panel data. The common tests employed in the literature as the MW test [START_REF] Maddala | A Comparative Study of Unit Root Tests with Panel Data and a New Simple Test[END_REF], the Choi test [START_REF] Choi | Unit Root Tests for Panel Data[END_REF], the LLC test [START_REF] Levin | Unit Root Tests in Panel Data: Asymptotic and Finite-Sample Properties[END_REF] and the IPS test [START_REF] Im | Testing for Unit Roots in Heterogeneous Panels[END_REF], are based on the assumption of independent cross-section units. Moreover, their asymptotical properties require large data samples (N, T →∞). However, in the case of macro panels, the crosssectional independence hypothesis is strong and must be checked. We start thus with a series of cross-sectional dependence tests in order to verify this hypothesis [START_REF] Friedman | The use of ranks to avoid the assumption of normality implicit in the analysis of variance[END_REF][START_REF] Frees | Assessing cross-sectional correlation in panel data[END_REF][START_REF] Pesaran | General Diagnostic Tests for Cross Section Dependence in Panels[END_REF]. The results of the cross-sectional dependence tests for each panel (and each tested relationship between trade and FDI) are presented in Table 3. [START_REF] Pesaran | General Diagnostic Tests for Cross Section Dependence in Panels[END_REF] 5.060 (0.000) 1.065 (0.286) 3.674 (0.000) 2.769 (0.005) Friedman Chi-square [START_REF] Friedman | The use of ranks to avoid the assumption of normality implicit in the analysis of variance[END_REF] 32.70 (0.000) 17.25 (0.004) 30.43 (0.000) 23.88 (0.000) Frees Normal [START_REF] Frees | Assessing cross-sectional correlation in panel data[END_REF] 0.709 -0.050 0.587 0.186 Exportsinward FDI Pearson CD Normal [START_REF] Pesaran | General Diagnostic Tests for Cross Section Dependence in Panels[END_REF] 4.278 (0.000) 1.521 (0.128) 6.283 (0.000) 1.815 (0.069) Friedman Chi-square (Friedman, 1937) 32.11 (0.000) 17.60 (0.003) 42.13 (0.000) 20.76 (0.000) Frees Normal [START_REF] Frees | Assessing cross-sectional correlation in panel data[END_REF] 0.564 -0.033 1.154 0.442 Importsoutward FDI Pearson CD Normal [START_REF] Pesaran | General Diagnostic Tests for Cross Section Dependence in Panels[END_REF] 1.374 (0.169) 1.935 (0.053) 3.398 (0.000) 5.486 (0.000) Friedman Chi-square [START_REF] Friedman | The use of ranks to avoid the assumption of normality implicit in the analysis of variance[END_REF] 21.73 (0.000) 17.08 (0.004) 30.24 (0.000) 32.81 (0.000) Frees Normal [START_REF] Frees | Assessing cross-sectional correlation in panel data[END_REF] 0.271 1.075 0.485 0.698 Importsinward FDI Pearson CD Normal [START_REF] Pesaran | General Diagnostic Tests for Cross Section Dependence in Panels[END_REF] 1.972 (0.048) 2.053 (0.040) 5.775 (0.000) 3.571 (0.000) Friedman Chi-square [START_REF] Friedman | The use of ranks to avoid the assumption of normality implicit in the analysis of variance[END_REF] We notice that in almost all the cases the null of cross-sectional independence is rejected, which makes the use of the first generation of panel unit root tests inappropriate.

However, in several cases, the hypothesis cannot be rejected: in the case of Hungary, the Frees Normal test and the Pearson CD Normal test admit the cross-sectional independence for the exports -FDI relationship, while in the case of the Slovak Republic the independence is accepted at 10% confidence level by the same tests.

We then use the Pesaran cross-sectional Augmented Dickey-Fuller (CADF) test, to check for the presence of panel unit roots. [START_REF] Pesaran | A Simple Panel Unit Root Test in the Presence of Cross-Section Dependence[END_REF] advances a modified statistics based on the IPS test [START_REF] Im | Testing for Unit Roots in Heterogeneous Panels[END_REF], considering the average of the individual CADF. However, besides this new test from the second generation which does not assume the cross-sectional independence and can be performed for a limited number of observations, we also resort to the IPS test for comparison reasons and because the cross-sectional dependence tests (Table 3) do not reject the independence hypothesis in all the cases. The results of the panel unit root tests for all considered variables are presented in Table 4 below. The tests provide mixed evidence regarding the stationarity of our variables, underlining the differences between the results of the first and the second generation of panel unit root tests. [START_REF] Pesaran | A Simple Panel Unit Root Test in the Presence of Cross-Section Dependence[END_REF] assuming cross-sectional dependence, while the IPS test is proposed by [START_REF] Im | Testing for Unit Roots in Heterogeneous Panels[END_REF], assuming cross-sectional independence; (iii) t-bar is reported and the p-values are in brackets; (iv) 2 lags are used fort the CADF test; (v) t represents test performed with trend for achieving the stationarity (otherwise the constant is used).

Empirical findings

The trade -FDI nexus is estimated using three different methods (Tables 5678). Table 5 shows that the outward FDI has a positive effect on the level of exports, proving a complementarity effect between trade and FDI (similar findings are reported by [START_REF] Herrmann | Trade balances of the central and east European EU member states and the role of foreign direct investment[END_REF]. These results can be noticed for all CEE-4 countries but to a smaller extent for Poland, as the 2SLS approach indicates a non-significant, negative sign for the outward FDI. The results are robust regarding the empirical approaches used. In general, the Hausman test recommends the fixed effect model, except for Poland. The endogeneity tests show no endogeneity problems for the 2SLS estimation. However, the Pagan-Hall test underlines some concerns regarding heteroskedasticity issues for Poland and the Slovak Republic. Therefore, for these two countries we use robust standard errors in order to address these issues. The Hansen J test shows that the over-identification of instruments persists for these panels. If we look to the control variable, we notice that the GDP growth rate of the partner country does not explain the trade level (it is expected that the trade intensity grows in normal periods, while having an opposite trend in crisis times). The average GDP per capita positively influences the bilateral trade. At the same time, the distance between countries negatively affects their commercial integration. Furthermore, the coefficient of the dummy variable is positive and significant in general, showing that the link between trade and FDI is stronger in the case of the CEE countries as partners.

We further on test the "export-back effect" (Table 6). If the inward FDI favours exports, both a regional market and a complementarity effect appear. This phenomenon manifests in two cases: when the host country presents competitive advantages in terms of labour costs (it is not the case here), or when the host country disposes of necessary skills in some industries (more plausible in respect of the composition of our sample).

However, according to our results, this effect manifests only in the case of the Slovak Republic (the fixed and random effects models), but it is not sustained by the 2SLS estimation. It seems that the CEE countries which receive investments from the considered partners do not necessarily export the final goods toward these countries.

We continue our analysis exploring the role of FDI in stimulating the level of imports.

Table 7 presents the results for the influence of outward FDI. Three situations appear. First, in the case of the Czech Republic, a positive influence of outward FDI on imports is noticed, validated by all the tests, and showing its backward vertical integration, stronger for the CEE-3 as partners, as compared to EU-3. Second, the complementarity is also document for Hungary and Poland, but the results are not robust (while the 2SLS shows a significant and positive coefficient for Hungary, the results for Poland are sustained only by the fixed and random effects models). Third, no significant relationship is found for the Slovak Republic. The Pagan-Hall test signals heteroskedasticity concerns for all the panels. Therefore, we estimate the 2SLS model with robust standard errors. The Hansen J test shows in general that there are no over-identification concerns regarding the instruments, except for the Czech Republic.

After exploring the inward FDIexports relationship, we are particularly interested in the influence of inward FDI on imports. If the inward FDI stock stimulates imports, this could be a sign that fairly large volumes of the parent company's intermediate products flow into the subsidiary's output, or that the foreign firms draw on established business relationships with foreign partner firms for intermediate products. Another explanation could be that the aim of the direct investments of the parent company is to acquire better access to the markets of the host country [START_REF] Herrmann | Trade balances of the central and east European EU member states and the role of foreign direct investment[END_REF]. Table 8 presents the results. In general, a positive relationship is documented, except for Poland, where none of the retained models validates the inward FDIimports link. However, this complementarity effect documented inter-alia by [START_REF] Fillat-Castejón | Trade through FDI: investing in services[END_REF] is not supported by all the models and then, the results lack in robustness. There is a significant difference between the CEE-3 and EU-3 as partners, only in the case of the Czech Republic and Poland. In this case also, the average GDP per capita positively influences the imports, showing that more developed countries are more integrated.

To conclude, we can state that trade and FDI are complements rather that substitutes, in all the cases. We notice that investments in the partner countries enhance competitiveness on the foreign markets and conduct to a vertical integration and to a reallocation of labourintensive activities from a capital-intensive country. However, the impact of the inward FDI on trade is less obvious. For all the CEE-4 countries, in all the cases, the trade -FDI nexus is more intense when considering the CEE countries as partners. Consequently, the bilateral trade between the CEE countries is influenced to a larger extent by the bilateral FDI, as compared to the bilateral trade between the CEE countries and the main EU commercial partners.

We admit however several limits of our estimations, generated especially by the small data sample and by possible manifestations of muticollinearity problems, given the characteristics of our control variables. Even if our estimations look robust, we only consider linear models. However, the crisis appearance may have caused structural breaks in the analysed relationships, but the lack of sufficient data for the CEE countries makes such analysis difficult for the moment (i.e. the consideration of time-dummy variables might represent a solution, but it leads to the weak instruments problem in the case of 2SLS estimation). In addition, we did not consider the role of business cycles correlation between the CEE countries. Finally, we did not examine the trade and investment's structure. A general picture of this nexus does not bring sufficient information about the role of FDI in promoting trade in the CEE countries. A sectorial analysis at firm level could lead to more diversified results, depending on the characteristics of the firms or industry in question.

Conclusions and policy implications

This paper aims to study the relationship between the bilateral trade and FDI in the case of four CEE countries, namely the Czech Republic, Hungary, Poland and the Slovak Republic, drawing a comparison between the role of bilateral investment between the CEE historical commercial partners and the main EU partners, namely Austria, Germany and Netherlands .

The trade -FDI nexus has been a topic of serious interest during the last decades, both for the trade and FDI theories, though it has generated different empirical results. Lately, these two different views emerged, accepting a complementarity effect, as well as a substitution effect between trade and FDI. However, at macro level, the complementarity effect prevails according to previous studies. Even if the subject is of great interest for the EU, little empirical evidence appears for the CEE countries. The few papers approaching the case of CEE countries investigate the role of FDI in the bilateral trade between these countries and the old EU members. None of these studies pays attention to the bilateral trade between the CEE countries, which knew great expansion in the period before the crisis and slowed down afterwards. Our paper is meant to fill in this gap and to analyse the relationship between the bilateral trade and FDI, from the perspective of each reporting country retained in the analysis.

We build a panel for each analysed country and we test four different crossrelationships which emerge between the outward/inward FDI and exports/imports. For robustness purposes and also for dealing with reverse causality issues, we compare a panel fixed effect and a random effect model, and we resort to a 2SLS estimation. We find a complementarity effect between trade and FDI, for all the investigated countries, which manifests especially in the case of the outward FDI. Moreover, the complementarity effect is stronger when we consider the CEE countries as partners. Therefore, vertical FDI outflows toward the historical trade partners encourage the commercial integration of the considered CEE countries.

These findings have several policy implications. First, because the inward FDI has no considerable influence on trade, the efforts of the authorities to attract FDI in order to support an increased commercial integration will be in vain. Second, we notice that the outward FDI favours both exports and imports, supporting thus the commercial integration of the CEE countries. These phenomena are stronger in the case of the CEE countries' bilateral investment. Consequently, in order to foster the commercial integration, the CEE countries' outward FDI shall be oriented toward their historical partners.

Two reasonable questions arise in this moment: (i) Toward which sectors shall the outward FDI be oriented? and (ii) How can it be encouraged? The response to the first question is complex. On the one hand, the outward FDI influences exports, owing to enhanced competitiveness on foreign markets. These findings characterise in particular the Czech and the Slovak Republic which exploit to a larger extent the local labour force of the CEE partner countries, and their natural resources, in order to increase the export levels. On the other hand, the outward FDI influences imports. This proves a backward vertical integration and a relocation of labour-intensive activities abroad. Regarding the theoretical considerations, our results are not surprising for the Czech Republic, but are questionable in the case of Poland, a country which is more labour-intensive than its CEE partners. In order to answer to the second question, we may consider the implementation of trade agreements.

However, given the absence of trade barriers inside the EU and the cultural linkages of CEE-4, it is hard to consider new trade agreements as a viable solution. Nevertheless, increased transportation costs or euro adoption by the Czech Republic, Hungary and Poland, can favour the outward FDI.

All in all, the results indicate a complementarity effect between trade and FDI, which manifests in particular for the outward FDI and which is stronger between the CEE countries and their historical partners, as compared to the actual main EU partners. Nevertheless, more detailed information regarding the trade -FDI nexus can be obtained analysing the bilateral trade and FDI by industries, which can represent a subject for future developments of the present research. The average population of the two countries at moment t, associated with a big market favouring the trade. However, trade openness is much higher in small CEECs. Thus, either a positive or a negative sign is expected.

Appendix B. Explanatory variables

+/- [START_REF] Fontagné | Foreign Trade and FDI Stocks in British, US and French Industries: Complements or Substitutes?[END_REF], [START_REF] Kyrkilis | The European Union and the Central and Eastern European Countries on integration, foreign direct investment and international trade[END_REF] OECD UNCTAD

bexr ijt

The bilateral exchange rate of the declaring country i with its partner j at moment t. An appreciation of the domestic currency favours imports and has a negative impact upon exports.

-/ + Carter and Yilmaz (1999), [START_REF] Kutan | Foreign Direct Investment and Export Performance: Empirical Evidence[END_REF] Central banks statistics

dist ij
The geographical distance between the country i and country j (the distance between the capital cities of two countries). It represents a proxy for transportation costs. If the distance is high, the transportation costs negatively affect trade creation.

- [START_REF] Cheng | Controlling for heterogeneity in gravity models of trade and integration[END_REF], [START_REF] Africano | FDI and Trade in Portugal: a gravity analysis[END_REF] Via Michelin dummy Takes value 1 if the partner country is a CEEC, while taking value 0 for ole EU members.

+ --

Notes: The GDP related variables are expressed in constant prices (US $).

Fig

  Fig 1 Bilateral trade between each CEE-4 country and the CEE-3 partners (stocks, mil. US dollars)

Table 3 . Cross-sectional dependence tests

 3

	Tests	Czech	Hungary	Poland	Slovak
		Republic			Republic
		Exports -outward FDI
	Pearson CD Normal

Table 4 . Panel unit root tests

 4

		Czech Republic	Hungary	Poland	Slovak Republic
	Variables	CADF test	IPS test CADF test	IPS test CADF test	IPS test CADF test	IPS test
	ex	-1.382	-2.131	-1.958	-1.614	-2.134	-1.699	-3.223 t	-1.419
		(0.77)	(0.05)	(0.28)	(0.30)	(0.17)	(0.21)	(0.01)	(0.50)
	im	-2.842 t	-1.860	-1.920	-1.557	-1.553	-1.371	-3.092	-1.882
		(0.09)	(0.12)	(0.31)	(0.34)	(0.63)	(0.52)	(0.00)	(0.11)
	outfdi	-2.964	-2.650	-2.585	-2.071 t	-3.023	-2.093	-1.832	-2.235
		(0.00)	(0.09)	(0.02)	(0.10)	(0.00)	(0.18)	(0.39)	(0.04)
	infdi	-1.727	-1.977	-1.840	-2.196	-2.833	-1.739	-2.719	-2.119
		(0.48)	(0.10)	(0.38)	(0.04)	(0.00)	(0.19)	(0.01)	(0.05)
	gdpav	-2.241	-1.524	-2.063	-1.745	-1.412	-3.214 t	-2.484	-1.343
		(0.11)	(0.39)	(0.21)	(0.21)	(0.78)	(0.00)	(0.04)	(0.60)
	gdpdif	-0.988	-0.864	-1.088	-1.922 t	-0.389	-2.353 t	-1.866	-0.981
		(0.94)	(0.95)	(0.91)	(0.16)	(0.99)	(0.01)	(0.36)	(0.91)
	gdpcav	-1.626	-1.759	-1.341	-1.890	-2.395	-1.183	-2.093	-1.427
		(0.57)	(0.18)	(0.49)	(0.07)	(0.06)	(0.75)	(0.19)	(0.48)
	gdpcdif	-1.747	-0.724	-1.341	-1.290	-3.365 t	-1.042	-0.254	-0.519
		(0.46)	(0.97)	(0.77)	(0.64)	(0.00)	(0.91)	(0.99)	(0.99)
	gdpg	-2.083	-3.018	-1.901	-2.943	-1.498	-3.036	-1.686	-2.905
		(0.20)	(0.00)	(0.33)	(0.00)	(0.68)	(0.00)	(0.52)	(0.00)
	popav	-0.987	-1.435 t	-0.671	-1.273	-0.480	-1.087	-1.253	-0.491
		(0.94)	(0.68)	(0.99)	(0.70)	(0.99)	(0.82)	(0.84)	(0.99)
	bexr	-2.238	-2.291 t	-1.968	-2.547 t	0.072	-2.566 t	-1.680	-2.152 t
		(0.11)	(0.03)	(0.28)	(0.00)	(1.00)	(0.00)	(0.52)	(0.09)
	Notes: (i) The null hypothesis for both tests is the presence of panel unit root; (ii) The cross-sectional ADF
	(CADF) test is proposed by

Table 5 . Exports and outward FDI relationship

 5

	exports	Czech Republic		Hungary			Poland		Slovak Republic
		FE	RE 2SLS	FE	RE 2SLS	FE	RE 2SLS r FE	RE 2SLS r
	c	-51.4 -46.2*** -48.0	35.5	-83.2***	-	90.4	-9.77 -176	-88.2** -56.4*** -40.4**
	outfdi	0.06*** 0.10*** 0.07* 0.02	0.08*** 0.17** 0.10*** 0.10*** -0.36	0.05*** 0.05*** 0.13***
	gdpav	-1.83* -0.25 -0.80 -4.26*** -1.00	4.79*** 3.43*** 2.96*** -0.27 -2.18** 0.70	1.66**
	gdpdif	-0.20	0.17	0.03	0.30** 0.33** -0.20 -0.02 -0.01 -0.17 -0.58** -1.16** -1.00***
	gdpcav	6.34*** 4.95*** 5.38** 9.91*** 7.09*** 0.78* 0.89	1.21* 11.6* 6.60*** 4.41*** 3.19***
	gdpcdif	0.12	0.16	0.04	-0.01	0.06** 0.14** 0.03	0.02	-0.08	0.00	-0.04 -0.01
	gdpg	-0.03 -0.02 -0.43	0.05	-0.04	0.81	0.09	0.10*	0.05	0.07	0.08	0.06
	popav	1.85	1.17*** 1.49	-4.36	2.54	-3.07*** -7.58 -1.48** 4.72	4.44* 2.25*** 1.10
	bexr	-0.94*** 0.08	0.05	0.99*** -0.08	0.44*** -0.06	0.02	0.18	-0.43** -0.39*** -0.24**
	dist	-	-1.57*** -1.56*	-	-1.12*** -1.24***	-	-0.34** 0.13	-	-0.50*** -0.54***
	dummy	-	2.00*** 1.93	-	1.43*** 2.83***	-	1.53*** 5.39**	-	0.52	0.95***
	Hausman test	P > χ 2 = 0.00		P > χ 2 = 0.00			P > χ 2 = 0.97		P > χ 2 = 0.06
	(recommended)	(Fixed)		(Fixed)			(Random)		(Fixed)
	Pagan-Hall test			5.83			1.10			0.17			0.17
				(0.82)			(0.99)			(1.00)			(1.00)
	Wu-Hausman test			1.38			1.67			-1.24			1.13
				(0.25)			(0.18)			(1.00)			(0.34)
	Durbin-Wu-			4.72			5.55			-4.76			3.89
	Hausman test			(0.19)			(0.13)			(1.00)			(0.27)
	Sargan test /			0.00			0.00			1.30			2.12
	Hansen J test										(0.51)			(0.34)
	Observations	84	84	83	84	84	83		84	84	83	84	84	83
	Notes: (i) *, **, *** means significance at 10 %, 5 % et 1 %; (ii) p-values are reported in brackets; (iii) The

instruments used for the endogenous variables

(outfdi, gdpg and bexr)

are the first lags of these variables; (iv) Sargan statistic represents the over-identification test for all instruments and equals 0.00 if the equation is exactly identified. However, if the Pagan-Hall test documents the presence of heteroskedasticity, the Hansen J is recommended for identifying over-identification issues; (v) 2SLS r means 2SLS with robust errors if the heteroskedasticity is present; (vi) for endogeneity issues we resort to the

Wu-Hausman and Durbin-Wu-Hausman tests; (vii)

the dummy variable takes value1 for CEE-3 as partners, and 0 otherwise.

Table 6 . Exports and inward FDI relationship

 6

	exports	Czech Republic		Hungary		Poland		Slovak Republic
		FE	RE 2SLS	FE	RE 2SLS r FE	RE 2SLS	FE	RE 2SLS r
	c	-127*** -54.6*** -56.8	61.0	-77.0*** -118*** 79.7	-38.2*** -38.5 -134*** -81.2*** -105***
	infdi	0.01	0.04	0.00	0.01	0.06** -0.03	0.08	0.08* 0.13	0.13*** 0.14*** 0.40
	gdpav	-3.56*** -1.09** -1.49 -4.28*** -1.02 -3.25	2.86*** 2.16*** 1.68	-2.61*** -2.01*** -5.65
	gdpdif	-0.06	0.43** 0.53	0.36*** 0.59*** 0.71*** -0.07 -0.06 -0.02 -0.80*** -0.92*** -0.32
	gdpcav	7.98*** 5.96*** 6.44* 9.95*** 7.08*** 9.99*** 2.42** 2.96*** 2.73	6.36*** 5.84*** 6.81***
	gdpcdif	0.07	-0.05 -0.12 -0.02	0.05** 0.03	0.02	0.01	0.08	-0.00 -0.03	0.02
	gdpg	-0.02 -0.06 -0.39	0.03	-0.06 -0.10	0.08	0.08	-0.46	0.08	0.08	0.08
	popav	6.75** 1.59*** 1.80	-6.00* 2.02	4.44* -7.36 -0.16 0.32	7.86*** 4.75*** 7.82**
	bexr	-1.16*** 0.08	0.04	0.95*** -0.20 -0.24 -0.05	0.03	0.02	-0.45** -0.48*** -0.49***
	dist	-	-1.42*** -1.47*	-	-1.09*** -1.06***	-	-0.45** -0.39	-	-0.45*** -0.42***
	dummy	-	2.16*** 2.04	-	1.51*** 1.06*	-	2.39*** 2.51***	-	0.13	-0.18
	Hausman test	P > χ 2 = 0.00		P > χ 2 = 0.00		P > χ 2 = 0.97		P > χ 2 = 0.95
	(recommended)	(Fixed)		(Fixed)		(Random)		(Random)
	Pagan-Hall test			8.78			0.62			1.61			0.44
				(0.55)			(1.00)			(0.99)			(1.00)
	Wu-Hausman test			0.65			2.14			0.98			0.73
				(0.58)			(0.10)			(0.40)			(0.53)
	Durbin-Wu-			2.28			6.97			3.42			2.58
	Hausman test			(0.51)			(0.07)			(0.33)			(0.46)
	Sargan test /			0.00			8.52			0.00			0.71
	Hansen J test						(0.01)						(0.70)
	Observations	84	84	83	84	84	83	84	84	83	84	84	83
	Notes: (i) *, **, *** means significance at 10 %, 5 % et 1 %; (ii) p-values are reported in brackets; (iii) The
	instruments used for the endogenous variables (infdi, gdpg and bexr) are the first lags of these variables; (iv)
	Sargan statistic represents the over-identification test for all instruments and equals 0.00 if the equation is
	exactly identified. However, if the Pagan-Hall test documents the presence of heteroskedasticity, the Hansen J is
	recommended for identifying over-identification issues; (v) 2SLS r means 2SLS with robust errors if the
	heteroskedasticity is present; (vi) for endogeneity issues we resort to the Wu-Hausman and Durbin-Wu-Hausman
	tests; (vii) the dummy variable takes value1 for CEE-3 as partners, and 0 otherwise.

Table 7 . Imports and outward FDI relationship

 7

	imports	Czech Republic			Hungary			Poland		Slovak Republic
		FE	RE 2SLS r FE	RE 2SLS r FE	RE 2SLS r FE	RE 2SLS r
	c	-38.8 -27.3*** -19.9 -582*** -130*** -123*** -15.4	4.57	-115* 63.6	-28.8*** -40.7***
	outfdi	0.05*** 0.09*** 0.13** 0.00	0.02	0.09** 0.08*** 0.08*** -0.26	0.02	-0.00 -0.09
	gdpav	-0.10	0.13	0.54	-4.16** -4.48** -3.78*** 2.07** 3.05*** 0.81	-1.95	2.88*** 2.10**
	gdpdif	0.08	0.41*** 0.30* -0.35* 0.51*** 0.25	-0.07* -0.06 -0.18** -0.92*** -1.32*** -1.38***
	gdpcav	3.96*** 3.96*** 3.29*** 11.3*** 10.5*** 9.65*** 1.54	0.23	7.81* 6.78*** 2.10*** 3.12***
	gdpcdif	0.03	0.08	0.08	-0.00	0.00	0.01	0.04	0.01	-0.06 -0.03 -0.04 -0.08***
	gdpg	0.05	0.06	0.10* -0.06 -0.13 -0.081 0.04	0.12** 0.08	0.03	0.11	0.13
	popav	1.06	0.26	0.00	32.9*** 5.96*** 5.65*** -0.70 -1.68** 2.67	-4.92	0.49	1.29
	bexr	-1.21*** -0.24* -0.28** -0.25 -0.33* -0.24** -0.59*** -0.06*** 0.06	0.31	-0.62*** -0.75***
	dist	-	-1.63*** -1.67***	-	-0.95*** -0.96***	-	-0.53*** -0.25	-	-0.61*** -0.56***
	dummy	-	1.64*** 1.46***		-	0.57	0.62*		-	0.71*** 3.57**	-	0.59	0.30
	Hausman test	P > χ 2 = 0.00		P > χ 2 = 0.00		P > χ 2 = 0.26		P > χ 2 = 0.00
	(recommended)	(Fixed)			(Fixed)		(Random)		(Fixed)
	Pagan-Hall test			0.36				25.4				0.06		0.21
				(1.00)				(0.00)				(1.00)		(1.00)
	Wu-Hausman test			2.87				1.56				-6.38		5.64
				(0.04)				(0.20)				(1.00)		(0.00)
	Durbin-Wu-			9.21				5.22				-31.8		16.3
	Hausman test			(0.02)				(0.15)				(1.00)		(0.00)
	Sargan test /			1.99				4.36				6.18		6.71
	Hansen J test			(0.36)				(0.11)				(0.04)		(0.03)
	Observations	84	84	83	84		84	83	84		84	83	84	84	83
	Notes: (i) *, **, *** means significance at 10 %, 5 % et 1 %; (ii) p-values are reported in brackets; (iii) The
	instruments used for the endogenous variables (outfdi, gdpg and bexr) are the first lags of these variables; (iv)
	Sargan statistic represents the over-identification test for all instruments and equals 0.00 if the equation is
	exactly identified. However, if the Pagan-Hall test documents the presence of heteroskedasticity, the Hansen J is
	recommended for identifying over-identification issues; (v) 2SLS r means 2SLS with robust errors if the
	heteroskedasticity is present; (vi) for endogeneity issues we resort to the Wu-Hausman and Durbin-Wu-Hausman
	tests; (vii) the dummy variable takes value1 for CEE-3 as partners, and 0 otherwise.

Table 8 . Imports and inward FDI relationship

 8

	imports	Czech Republic			Hungary			Poland		Slovak Republic
		FE	RE 2SLS r FE	RE 2SLS	FE	RE 2SLS r FE	RE 2SLS r
	c	-103** -28.2** -39.3*** -543*** -96.9***	-	-12.1 -20.2 -0.55	51.8	-43.3*** -39.2
	infdi	0.04	0.09* 0.00	0.05	0.11*** 0.35	0.04	0.04	0.30	0.16*** 0.17*** 0.14
	gdpav	-1.93 -0.45 -0.72 -3.44** -2.84	2.82** 1.69	2.46*** 2.00*** -2.13** 0.56	0.84
	gdpdif	0.19	0.64*** 0.66*** -0.30	0.44*** 0.15	-0.10** -0.10** -0.11** -1.13*** -0.93*** -0.98*
	gdpcav	5.41*** 4.27*** 5.30*** 10.1*** 8.20*** 1.05	2.85*** 1.78*** 0.28	6.03*** 2.63*** 2.38**
	gdpcdif	-0.01 -0.12 -0.15 -0.01 -0.00	0.15	0.03	0.00	0.04	-0.04 -0.00 -0.02
	gdpg	0.06	0.02	0.03	-0.06 -0.14	1.42	0.04	0.11* 0.09* 0.04	0.11	0.13**
	popav	5.48* 0.48	0.75	30.6*** 4.10** -2.00 -1.32 -0.63 -0.51 -3.50	2.43*** 2.16
	bexr	-1.39*** -0.26* -0.23* -0.28 -0.40** -0.34 -0.57** -0.04 -0.13* 0.08	-0.62*** -0.63***
	dist	-	-1.49*** -1.48***	-	-0.93*** -0.95***	-	-0.56*** -1.03**	-	-0.60*** -0.59***
	dummy	-	1.75*** 1.77***		-	0.76	1.69		-	1.38*** 1.43***	-	0.40	0.29
	Hausman test	P > χ 2 = 0.00		P > χ 2 = 0.00		P > χ 2 = 0.40		P > χ 2 = 0.00
	(recommended)	(Fixed)			(Fixed)		(Random)		(Fixed)
	Pagan-Hall test			0.65				0.88				0.46		0.21
				(1.00)				(0.99)				(1.00)		(1.00)
	Wu-Hausman test			1.19				1.21				1.45		5.70
				(0.31)				(0.31)				(0.23)		(0.00)
	Durbin-Wu-			4.08				4.09				4.92		16.4
	Hausman test			(0.25)				(0.25)				(0.17)		(0.00)
	Sargan test /			1.28				0.00				3.78		5.98
	Hansen J test			(0.52)								(0.15)		(0.05)
	Observations	84	84	83	84		84	83	84		84	83	84	84	83
	Notes: (i) *, **, *** means significance at 10 %, 5 % et 1 %; (ii) p-values are reported in brackets; (iii) The
	instruments used for the endogenous variables (infdi, gdpg and bexr) are the first lags of these variables; (iv)
	Sargan statistic represents the over-identification test for all instruments and equals 0.00 if the equation is
	exactly identified. However, if the Pagan-Hall test documents the presence of heteroskedasticity, the Hansen J is
	recommended for identifying over-identification issues; (v) 2SLS r means 2SLS with robust errors if the
	heteroskedasticity is present; (vi) for endogeneity issues we resort to the Wu-Hausman and Durbin-Wu-Hausman
	tests; (vii) the dummy variable takes value1 for CEE-3 as partners, and 0 otherwise.

Table 1 . Explanatory variables description Variables Description Exp. sign Employed in the literature by Database outfdi

 1 ijtThe volume of outward FDI from country i to country j at moment t. If FDI creates trade, then a positive influence is expected. The substitution is associated with a negative sign. The volume of inward FDI from country j to country i at moment t. If FDI create trade, then positive influence is expected (complementarity relationship). The substitution relationship is associated with a negative sign. The average GDP volume of the countries i and j at moment t. It represents a proxy for the factors' income. The difference between the GDP volume of country i and j at moment t, in module. It represents a proxy for the difference of consumer preferences of the declaring country compared to its partner's. The average income per capita of the declaring country i and its partner j at moment t. It expresses the demand for variety. The differences between the GDP per capita in country i and country j at moment t. It represents the difference in factors endowments in the declaring country and in its partner country. It is measured in module. Depending on the structure of the relationship between trade and FDI, the expected sign can be either positive or negative. The GDP growth rate in the partner country j at moment t. The economic growth of the partner country favours the intensification of trade flows with this country. Because the values of the indicators are negative in 2009, and because all the variables were transformed in logarithm, we employ the formula: gdpg = 10% + real growth rate.

	+ / -Pain and	OECD
	Wakelin (1998),
	Fontagné (1999)

For example, there are noticeable differences between the bilateral inward FDI reported by one country and the bilateral outward FDI reported by the partner country. At the same time, the exports reported by one country differ from the imports reported by the partner country. These discrepancies can be explained by different methodologies used. The exports are registered as FOB (free on board), while the imports as CIF (cost, insurance, freight). Another explanation regarding the statistical discrepancies is related to the exchange rate differential between the domestic currencies and the international currency used for transactions.

The substitution effect is traditionally advanced by the international trade theory. As[START_REF] Pain | Export performance and the role of foreign direct investment[END_REF] show, in the conventional trade models based on the Heckscher-Ohlin-Samuelson (H-O-S) framework, the equalisation of factor prices across countries can be achieved either through the international trade, or through the international mobility of factors. In the latter case, factor mobility may be a substitute for trade if the production functions are identical[START_REF] Mundell | International trade and factor mobility[END_REF].

The theory of multinational companies shows that through direct investments, these companies exploit natural resources which are not available in the home country. These investments are then more likely to create trade, by raising exports of capital equipment and factor services from the home country and exports of resource-based products from the host economy. Therefore, the trade and FDI are considered alternative means for entering foreign markets, underlying their complementarity[START_REF] Caves | Multinational Enterprise and Economic Analysis[END_REF].

The trade -FDI nexus is also influenced by the effect of FDI on the economic activity and welfare in general. There are numerous benefits and costs associated with the FDI entrance(Markusen and Venables, 1999). While the benefits are associated with technological externalities, knowledge spillover and demonstration effects which may foster the trade, the costs are associated with the interaction between multinational companies and fixed distortions in the economy, and with additional competition. If for example the import tariff exceeds its optimal level because of the "tariff-hopping" FDI, the quantity of imports decreases.

For the Slovak Republic, the FDI data for 2013 were extracted from the Investment Climate Statements 2014 (Bureau of Budget and Planning, US Department of State), as they were not available in the OCDE statistics. For the Czech Republic, the FDI data for 2002 are not available (we use linear interpolation to avoid broken panel problems). In line with most of previous works we use stock data (see the related arguments in the Literature review section).

The correlation matrix, computed for each panel, can be provided by the authors, under request.

[START_REF] Rault | Modeling international trade flows between Eastern European countries and OECD countries[END_REF] state, the standard cross-section estimates tend to ignore the unobservable characteristics of bilateral trade relationships (historical, cultural and linguistic links).

In its simplest form, the gravity equation states that the volume of trade between any two countries is positively correlated with the economic size of these countries and negatively correlated with the geographic distance between them[START_REF] Martínez | Foreign Direct Investment and Trade: Complements or Substitutes? Empirical Evidence for the European Union[END_REF].

Appendixes


Wahid Nasri
email: wahid.nasri@ensi.rnu.tn

Angelo Luiz

Denis Steffenel

Trystram

Steffenel

Denis Trystram
email: denis.trystram@imag.fr

Adaptive Performance Modeling on Hierarchical Grid Computing Environments

Keywords: Cluster computing, Performance modeling, Adaptive techniques, Polymodels of communications, Collective communication operations

whether they are published or not. The documents may come

Introduction

Recent Challenges of Efficient Parallel Algorithms

In the last years, there was a huge development in the field of parallel and distributed processing, especially at the architectural level leading to a wide variety of execution supports. The major innovation was the phenomenal spread of architectures like clusters and grids. These platforms represent a reasonable alternative to traditional parallel machines and have become the most cost-effective computing supports for solving a large range of high performance computing applications due the good cost/performance ratio that they provide. However, the introduction of such computational systems has a major impact on the design of efficient parallel algorithms. Moreover, such parallel systems are often upgraded with new generation of processors and network technologies. This fact will change the balance between computations and communications.

Today, due to the increasing diversity of existing parallel systems consisting on collections of heterogeneous machines, it is very difficult for a user to choose an adequate algorithm because the execution supports are continuously evolving. One version will be well-suited for a parallel configuration and not for another one. This portability issue becomes crucial because of the frequent changes of the components of the systems. Moreover, the inherent heterogeneity and the diversity of networks of such environments represent a great challenge to model and optimize communications for high performance computing applications. These different elements require to revise the classical parallel algorithms which consider only regular architectures with static configurations and to develop more powerful approaches to benefit well from the capacities of these new execution supports.

Contribution of this Work

Our objective within this work is to propose a generic framework based on communication models and adaptive techniques for dealing with prediction and modeling communications, and integrating scalability and portability issues. More precisely, the contribution of this paper is to propose a methodology with two level adaptation. Indeed, at the first level we proceed, given a target architecture, by determining the more appropriate model from a set of selected ones to better predicting performances. We will finally obtain a Poly-model of communication, as described later in section 3.2. Next, we will have to determine the best algorithm among multiple algorithmic options for resolving a given problem.

Related Works

Our framework differs from the other works in a significant aspect. Indeed, all existing adaptive approaches presented in the literature like those of [START_REF] Bhat | Adaptive communication algorithms for distributed heterogeneous systems[END_REF][START_REF] Whaley | Automated empirical optimization of software and the ATLAS project[END_REF][START_REF] Steffenel | LaPIe: communications collectives adaptées aux grilles de calcul[END_REF][START_REF] Hartmann | Adaptive selection of communication methods to optimize collective mpi operations[END_REF] proceed by selecting, using different techniques, one algorithm or eventually combining from a library containing multiple algorithmic choices. In [START_REF] Pjesivac-Grbovic | Performance analysis of MPI collective operations[END_REF], the authors conduct an extensive experiment to determine the model that better represents the execution time of collective communication operations. Indeed, that work provides meaningful insights on the accuracy levels obtained with different performance models, and the importance to avoid relying on a single model. Therefore, to the best of our knowledge, our framework provides the first general methodology for automatically associate the more appropriate communication model to the best algorithm among multiple model and algorithmic options. It determines the best combination model-algorithm and computes an efficient execution scheme that minimizes the overall execution time of a parallel application.

Organization of the Paper

The remainder of the paper is organized as follows. We begin, in section 2, by presenting the architectural model of the target parallel and distributed system and the performance evaluation models of a parallel algorithm. In section 3, we first define the concept of poly-model, present our adaptive framework for poly-models of communication, and detail its components. Section 4 is devoted to a case study where we apply our adaptive framework on collective communication operations. We present indeed numerical simulations and practical experiments performed on a heterogeneous hierarchical grid proving the interest of this work. Finally, section 5 concludes the paper and discusses some perspectives to extend this work.

Preliminaries

Description of the Architectural Model

We assume in this work a generic model of a platform composed by heterogeneous hierarchical clusters as described in [START_REF] Capello | An algorithmic model for heterogeneous hyper-clusters: Ratio-nale and experience[END_REF]. The platform studied enjoys heterogeneity along three orthogonal axes:

1. The processors that populate the clusters may differ in computational powers, even within the same cluster.

2. The clusters comprising the platform are organized hierarchically and are interconnected via a hierarchy of networks of possibly different latencies, bandwidths and speeds. At the level of physical clusters, the interconnection networks are assumed to be heterogeneous.

3. The clusters at each level of the hierarchy may differ in sizes.

Adaptive Approaches

The adaptive approaches are a promising answer to the challenges presented previously in section 1.1. The idea is to adapt algorithms together with their execution to the target architecture. They propose adaptive algorithms for solving the same problem which have different behavior and performances and to derive the best one for a target parallel system. These algorithms may be automatically adapted to the execution context (data and support). In a parallel context, the adaptive algorithm should be scalable. Indeed, it should maintain a given efficiency when the size of the problem and the number of processors grow. Other approaches are possible for adapting the algorithms to new supports. For instance, adequate software can be developed in the middleware. We are interested in this work in the adaptability at the algorithmic level.

Communication Models

Choosing the right algorithm for solving a parallel application requires being able to predict the performances. There are many parallel communication models in the literature that analyze performances based on system parameters [START_REF] Hockney | The communication challenge for MPP: Intel paragon and meiko cs-2[END_REF][START_REF] Alexandrov | LogGP: Incorporating long messages into the LogP model -one step closer towards a realistic model for parallel computation[END_REF][START_REF] Culler | LogP -a practical model of parallel computing[END_REF][START_REF] Clement | Network performance modelling for PM clusters[END_REF][START_REF] Frank | LoPC: Modeling contention in parallel algorithms[END_REF][START_REF] Kielmann | Network performance-aware collective communication for clustered wide area systems[END_REF][START_REF] Moritz | LoGPC: Modeling network contention in message-passing programs[END_REF][START_REF] Teresco | Resource-aware scientific computation on a heterogeneous cluster[END_REF]. More sophisticated models have been proposed for complex architectures [START_REF] Capello | An algorithmic model for heterogeneous hyper-clusters: Ratio-nale and experience[END_REF][START_REF] Steffenel | LaPIe: communications collectives adaptées aux grilles de calcul[END_REF]. All these models differ on the assumptions about the computational support parameters, such as latency, heterogeneity, network contention, etc., and therefore are able to cover a great variety of architectures and modeling aspects. For instance, the selection between these models will depend on the data size to communicate, the models accuracy and their relative cost (parameters acquisition and models complexity). We present and summarize in Table 1 a comparison between some of these models.

Description of the Adaptive Framework for

Performance Modeling

Overview of the Methodology

In this section, we describe our framework for adaptively modeling communications in an execution environment characterized by its heterogeneity and its hierarchical organization. An overview of the methodology is sketched in Figure 1. The processing is separated in two successive phases. During the first one, we aim to partition the target execution platform to form subnets of similar characteristics by automatically discover the network topology. Then, when executing the second phase, we have to determine for each subnet (i.e. cluster) the more appropriate communication model to better predicting performances. We will finally obtain a Poly-model of communication. In the sequel, we more detail the major components of the framework.

Concept of Poly-Model

1. Better model the communications in terms of the characteristics of the hardware resources of the target parallel system. 2. Reduces the cost of modeling parallel applications on complex architectures.

Provides precise prediction results.

We finish this description by mentioning that the complexity of the overall process of the scheme adaptation does not affect the global cost of the application to be modeled.

Platform Partitioning

Since the target parallel system may be heterogeneous at many levels (computing powers, interconnection network performances, etc), it is very difficult to manage such platform towards a high performance computing. One way to answer this problem and to minimize the inherent heterogeneity is to subdivide the network in homogeneous subnets (or logical clusters), as described below. At the end of this phase, we will get a set of logical clusters of homogeneous nodes and accurate interconnection network, which will be used to adaptively modeling communications inside each cluster during the second phase of the framework.

Network Performance Measurements

The framework starts by collecting available information from the target execution environment to be used in the step of clustering (see next section). There exist many tools for network monitoring, such as NWS (Network Weather Service) [START_REF] Wolski | Implementing a performance forecasting system for metacomputing: The network weather service[END_REF]. These tools permit to determine many useful parameters of the target parallel system like the current network status, the communication latency, the speeds of the processors, the CPU load, the available memory, etc. For instance, the communication latency and throughput permit to identify groups of machines with similar communication parameters.

Clustering

One reason to construct logical clusters is that machines may behave differently, and the easiest way to optimize communications is to group machines with similar performances [START_REF] Barchet-Steffenel | Identifying logical homogeneous clusters for efficient wide-area communication[END_REF][START_REF] Steffenel | LaPIe: communications collectives adaptées aux grilles de calcul[END_REF]. In order to classify nodes in logical clusters, we can use a clustering algorithm similar to the one presented in [START_REF] Lowekamp | ECO: Efficient collective operations for communication on heterogeneous networks[END_REF]. This algorithm analyzes each interconnection on the distance matrix containing the latencies between links in order to group nodes for which their incident edges respect a latency bound (by default 20%) inside that subnet. Note that the distance matrix was obtained when applying NWS on the clusters to determine the network information.

Adaptive Modeling

Once the platform is partitioned in separated homogeneous hierarchical clusters, we determine, using an adaptive approach, an adequate model from the set of selected models for each cluster. Indeed, we modeled and implemented several algorithms from the literature, which perform differently according to the network environment. By selecting the best adapted algorithm to each different cluster in our grid, we contribute to a poly-algorithmic modeling of communications in a grid environment. Any necessary characteristics are measured during the first phase corresponding to the network partitioning. We recall that the algorithm selection is made in terms of information which is interesting to the problem, such as the size of data to communicate, the type of interconnection network, the number of nodes, etc.

It is also important to take into account the cost involved on the acquisition of models parameters. For instance, both LogP and LogGP models rely on a reduced number of measurements (they extrapolate the cost per byte from a few measurements), while pLogP requires several measurements to cover a large range of message sizes. Hence, while the later model is most expensive, it can be more precise when the communication cost does not varies linearly with the message size (a typical case with MPI, whose transmission policies depend on the message size).

For instance, we are able to define a communication schedule that minimizes the overall execution time through the analysis of the inter-cluster communication performance and the intra-cluster performance prediction. Once again we implement different schedule policies, which are selected according to their estimated termination time. The framework allows, indeed, implementing scheduling heuristics that perform on different communication levels according to the target communication pattern.

Application on Collective Communications

We apply our adaptive framework on collective communication operations by determining the best combination model-algorithm depending on the problem and architecture parameters. We refer here by algorithm a possible method to resolve the operation, as for example Pipeline, Binomial, Binary and Linear for Broadcast. At this level, our framework automatically associates the more appropriate model to the best algorithm among multiple model and algorithmic options.

Collective communication operations encompass a wide range of possible algorithms. The optimal implementation of such operations for a given parallel system depends on many factors, including for example, physical topology of the system, number of processes involved, message sizes, and the location of the root node [START_REF] Pjesivac-Grbovic | Performance analysis of MPI collective operations[END_REF][START_REF] Steffenel | LaPIe: communications collectives adaptées aux grilles de calcul[END_REF]. Figure 2 shows how to implement a collective communication operation using our framework. Indeed, the adaptive algorithm selection is based on two types of models: the analytical and experimental ones. Experimental techniques use information derived from previous operation executions to optimize processing for future problem instances, a service similar to an optimization cache. The analytical models will be useful to validate actual versus predicted performances.

Description of the Execution Platform

We have considered a Grid platform from to the project Grid'50001 to achieve our experiments. The architecture is initially composed of four clusters, distributed over sites in France: GRENOBLE, ORSAY, SOPHIA-ANTIPOLIS and TOULOUSE. This platform will first be partitioned into logical homogeneous clusters. The latencies intra and inter-clusters are presented in Table 2.

Network Partitioning

We applied our approach on a target parallel system composed of four clusters -C1 (20 machines ORSAY), C2 (19 machines GRENOBLE), C3 (19 machines SOPHIA-ANTIPOLIS) and C4 (20 machines TOULOUSE) with two levels of hierarchy distributed over four sites in France. Figure 3 shows the organization of the clusters.

The first phase of the framework leads to a new organization of the machines (see Figure 4). The cluster C2 will be partitioned into three sub-clusters, C21 (11 machines), C22 (1 machine) and C23 (7 machines), according to the latencies of the links between machines. Once the clustering phase is done, we have six logical clusters with homogeneous resources.

Model Selection

We have considered the Broadcast operation. With Broadcast, a single process, called root, sends the same message of size m to all other (P -1) processes. Classical implementations of the Broadcast operation rely on fixed shapes such as Linear (Flat Tree) for small number of nodes and Binomial Trees for P > 3.

In our work we developed the communication models for some current techniques and their "flavors", which are presented on Table 3 in terms of pLogP parameters (which can be easily adapted to other models such as LogP and LogGP). Hence, we chose to compare in this paper four of the most known techniques, namely the Linear, the Binary, the Binomial and the Pipeline Broadcasts. Indeed, we perform the MPI_Bcast optimization in two hierarchical levels, as described below:

Table 3. Communication models for the Broadcast operation

Strategy Communication Model

Linear (Flat Tree)

L + (P -1) × g(m)
Segmented Chain (Pipeline)

(P -1) × (g(s) + L) + (g(s) × (k -1)) Binary Tree ≤ log 2 P × (2 × g(m) + L) Binomial Tree log 2 P × L + log 2 P × g(m)
First hierarchical level: First, we deal with local-area communications, where a cluster "coordinator" will be charged to broadcast locally the message to all processes composing the cluster. Later, we integrate these clusters through the generation of efficient inter-cluster communication schedules. Therefore, at the first hierarchical level, we proceed by selecting the most appropriate performance model and broadcast algorithm for each cluster according to two steps:

Poly-adapt-1: For a given problem (message size and number of processes) and for each implementation algorithm, we select the most accurate performance model such that its predictions correspond to our base of experimentations;

Poly-adapt-2: From the performance models selected in the previous step we select the most efficient implementation algorithm (i.e., the algorithm that terminates earlier).

For instance, we select the algorithm that minimizes the completion time of the operation, as summarized in Table 4, using the most accurate performance model for each problem instance (as we can observe in Figure 5).

Second hierarchical level:

Once Poly-adapt-2 selected the best algorithm for each cluster, we must determine an efficient inter-cluster communication scheduling. Using inter-cluster communication parameters, we can construct an optimized broadcast tree between clusters using scheduling heuristics, an approach that provides better performances on grid environments than traditional grid-unaware algorithms found on most MPI distributions [START_REF] Barchet-Steffenel | Scheduling heuristics for efficient broadcast operations on grid environments[END_REF]. Indeed, in this example we rely on the Early Completion Edge First -ECEF heuristic, proposed by [START_REF] Bhat | Adaptive communication algorithms for distributed heterogeneous systems[END_REF]. This heuristic proceeds by selecting a pair sender-receiver where the sender is available and the choice of the sender-receiver pair depends on the earliest possible moment when this transmission may effectively be finished. Therefore, we use a Ready Time (RT i ) parameter, evaluated conjointly with the transmission time between the processes, such that the pair i, j minimizes the following expression:

t = RT i + g i,j (m) + L i,j
We can eventually integrate the communication time inside each cluster, as stated by the ECEF-LAt heuristic [START_REF] Barchet-Steffenel | Scheduling heuristics for efficient broadcast operations on grid environments[END_REF], where the communication schedule minimizes the overall broadcast time by taking into account both inter and intracluster communication times

Performance Analysis

As stated above, our politic of performance evaluation consists in implementing the broadcast when applying a one level of adaptation on the poly-model, i.e. choosing the more appropriate model with a fixed algorithm (Poly-adapt-1), and then a second level of adaptation, i.e. both model and algorithm are adaptive (Poly-adapt-2). Therefore, Figure 5 represents the completion time of a broadcast executed with different algorithms on the ORSAY clusters with different message sizes. We denote by Poly1 the first adaptation and Poly2 our full adaptation. The curves show that Poly1 adapts to the performance model that closely predicts the performance of real experiences kept in our experiments base. Similarly, Poly2 represents the expected performance of the best algorithm, proving the interest of the two-level adaptation. Indeed, this two-level adaptation mechanism is applied at each cluster, giving therefore the fastest implementation strategy for each environment.

As a result, Figure 6 depicts the completion time of a broadcast executed on two layers with Poly2 and the ECEF heuristic on the global platform composed by many clusters of different characteristics and network hierarchies. We observe that the optimized broadcast operation easily outperforms the traditional "grid-unaware" binomial broadcast implemented on most MPI distributions, and giving this example, we proceed at least twice as fast as the binomial tree. Summing up, the obtained results confirm the remarks mentioned previously, concerning the power and the benefits of a multi-level adaptive approach.

Concluding Remarks and Future Works

We have presented in this paper a new adaptive framework for dealing with performance modeling on grid computing platforms. The proposed methodology, based on communication models and adaptive approaches, proceeds in two level adaptation to automatically associate the more appropriate model to the best algorithm among multiple model and algorithmic options for each part of a large parallel execution support being used. The best identified combination model-algorithm and the determined execution scheme permit to minimize the overall execution time of a target problem. This approach was applied on an important collective communication pattern, the broadcast operation, proving the interest of a multilevel adaptive approach and the worthy of this work.

As future prospects, we intend to perform experiments on other collective communication operations, and apply the framework on other types of target problems. We also plan to integrate other existing adaptive approaches to our framework to benefit well from the powerful of these techniques. Further, we intend to evaluate the impact of our framework on the performance of real scientific applications which perform intensive communication among the nodes.

Figure 1 .

 1 Figure 1. Adaptive framework.

Figure 2 .

 2 Figure 2. Execution of a collective communication operation using the framework.

Figure 3 .

 3 Figure 3. Grid'5000 sites.

Figure 4 .

 4 Figure 4. Platform after partitioning.

Figure 5 .Figure 6 .

 56 Figure 5. Completion time of Broadcast in the cluster ORSAY: (a) Linear, (B) Pipeline, (c) Binary and (d) Binomial

Table 1 . Communication models for performance prediction

 1

	Hockney pLogP Hierarchical LogP LogGP LoPC LoGPC No No No No No Yes	Yes	Yes
	Latency	α	L	L	L	L	L	λ	L
	Gap	1/β	g	g+G	g	g+G	g	included	g
	Sender overhead		o	o	o	o	os	π	os
	Receiver overhead		o	o	o	o	or	π	or
	Contention modeling	No	No	No	Yes	Yes	No	No	Yes*
			* depending on the communication pattern

Table 2 . Latency (microseconds) intra and inter-clusters.

 2

		C1	C21	C22	C23	C3	C4
		20 x Orsay	11 x Grenoble	7 x Grenoble	1 x Grenoble	20 x Toulouse	19 x Sophia
	C1	48.39	6577.49	6586.49	6592.51	5211.94	8602.73
	C21	6577.49	35.52	59.96	59.96	5387.48	2736.56
	C22	6586.49	59.96	60.08	79.51	5393.98	2740.26
	C23	6592.51	59.96	79.51	0 *	5405.78	2745.98
	C3	5211.94	5387.48	5393.98	5405.78	26.94	3630.51
	C4	8602.73	2736.56	2740.26	2745.98	3630.51	35.04

* this "logical cluster" has only one machine.

Table 4 . Summarize of the adaptive execution scheme for m=8kB and m=512kB.

 4

		Cluster	C1	C21	C22	C23	C3	C4	inter-clusters
	m=8k	Selected model Selected algorithm binomial binomial linear binomial binomial binomial LogP LogP -LogP LogP LogP	Hierarchical [3] ECEF
	m=512k	Selected model Selected algorithm	LogGP pipeline	pLogP pipeline	-linear	pLogP pipeline	pLogP pipeline	pLogP pipeline	Hierarchical [3] ECEF

Generally, in order to predict and model the overhead due to communications in a parallel application, we use a single communication model, like, for instance, Hockney[START_REF] Hockney | The communication challenge for MPP: Intel paragon and meiko cs-2[END_REF], LogP[START_REF] Culler | LogP -a practical model of parallel computing[END_REF], pLogP[START_REF] Kielmann | Network performance-aware collective communication for clustered wide area systems[END_REF], etc. Due to the wide variety of existing parallel machines, which requires determining multiple parameters to get more precise results, a sophisticated model is necessary. On the other hand, using such a model on "simple" architectures is not useful due to the cost of determining their parameters. For that reasons, we introduce the concept of Poly-model which determines adaptively the more appropriate model for a target platform according to the problem and architecture parameters. In fact, the poly-model that we propose is equivalent to a combination of multiple models, to be used on different clusters. It chooses an adequate model in terms of several information, including the size of data to communicate, the type of interconnection network (with contention or not), the number of nodes, etc. Let us remark that the generated poly-model which uses adaptive techniques will:

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