Julie Bu Daher

Armelle Brun

Anne Boyer

Multi-Source

Multi-source Relations for Contextual Data Mining in Learning Analytics

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

LSAC 2018

Multi-source Relations for Contextual Data Mining in Learning Analytics

Julie Bu Daher, Armelle Brun, Anne Boyer KIWI team, LORIA laboratory University of Lorraine {julie.bu-daher, armelle.brun, anne.boyer}@loria.fr Track Academic research: comprehensive evaluations of recent innovations in learning and student analytics approaches.

Context and Purpose

The goals of Learning Analytics (LA) are manifold, among which helping students to understand their academic progress and improving their learning process, which are at the core of our work.

To reach this goal, LA relies on educational data: students' traces of activities on VLE, or academic, socio-demographic information, information about teachers, pedagogical resources, curricula, etc. The data sources that contain such information are multiple and diverse. Data mining, specifically pattern mining, aims at extracting valuable and understandable information from large datasets [START_REF] Han | Data mining: concepts and techniques[END_REF]. In our work, we assume that multiple educational data sources form a rich dataset that can result in valuable patterns. Mining such data is thus a promising way to reach the goal of helping students. However, heterogeneity and interdependency within data lead to a high computational complexity.

We thus aim at designing low complex pattern mining algorithms that mine multi-source data, taking into consideration the dependency and heterogeneity among sources. The patterns formed LSAC 2018 are meaningful and interpretable, they can thus be directly used for students.

Data and expected output

As previously mentioned, data comes from various sources. As an example, the Activity source is the log file of activities of students on their VLE and contains sequences of quadruplets <student_id, resource_id, timestamp, action>. The Resource source contains descriptions of pedagogical resources, whether descriptions are structured or not, if not unknown. For example, a resource can have the following attribute values <Mathematics, Exercise, Difficult, Linear Algebra>. Curriculum describes the different curricula offered by a school and Students contains demographic information of students.

Given these 4 sources, a mined pattern could be the following:

{14-years, Male, Mathematics-grade-9} R-15 R-42 R-Mathematics

This pattern is made up of two parts. The first one contains information about the student: age (14-years) and gender (Male) from Student and an element about a school program (Mathematics-grade-9) from Curriculum. The second part is a frequent sequential pattern from Activity and Resource sources: (R-15 R-42) represents a sequence of resources id (from Activity) frequently accessed by students; followed by (R-Mathematics), which is an attribute from Resource. None of the resources accessed following (R-15 R-42) are frequent, so they cannot be part of this pattern, but they all share the (R-Mathematics) attribute, which is frequent in this context, this attribute is a generalization. The resulting pattern is thus at the same time a specific pattern (as it is valid for {14-years, Male, Mathematics-grade-9} students only), and a general pattern.

LSAC 2018

Scientific Approach and Challenges

Pattern mining has mainly focused on mining one data source, but mining multi-source data is becoming an emerging challenge [START_REF] Han | Data mining: concepts and techniques[END_REF]. The literature proposes either to combine data sources together (through the use of the relations between them) and use a single mining process or to mine them independently and then merge the outputs [START_REF] Wang | Review on mining data from multiple data sources[END_REF], considering the sources of the same importance. In our work, we stress that these relations can be of different types, so they have to be managed differently, resulting in more valuable patterns. For example, a relation can be between two sources (a student Activity and a Curriculum), or between one source and one element of another source (a resource id from an Activity and the description of a Resource).

Contextual data mining [START_REF] Rabatel | Mining sequential patterns: a context-aware approach[END_REF] considers two types of data sources: core sources and contextual sources, where a contextual source provides additional information to a core source. A "starschema" representation was proposed to manage data such that there is one core source and other sources, related/linked to it, are considered as contextual data [START_REF] Dong | A general framework to encode heterogeneous information sources for contextual pattern mining[END_REF].

The approach we plan to adopt inspires from both previous approaches: a contextual data mining approach that exploits the types of relations/links between sources to guide the mining and obtain valuable patterns, while limiting the complexity.

We propose to consider Activity as the core source as it is the one representing the learning process; and other sources as contextual data. Of course, based on the types of links between core and context sources, some of them will be considered as real context (to refine the patterns) and others as additional information (to mine general patterns).

The first challenge is characterizing the data sources and possible relations/links between them.

Based on them, the second challenge is defining pattern mining algorithms to automatically manage data sources and their links, and upon needs (specific or general patterns). The numerous

Acknowledgments

This work has been funded by the PIA2 e-FRAN METAL Project.

LSAC 2018 possibilities of patterns that can be mined are a major advantage not only to capture the specificities of each student but also to provide personalized help.


Jérôme Hericourt
email: jerome.hericourt@univ-paris1.fr

Mathilde Maurel
email: maurelm@univ-paris1.fr

Anne-Célia Disdier

A New Look at the Feldstein-Horioka Puzzle: An European-Regional Perspective *

Keywords: JEL classication: E22, F21, G15 Feldstein-Horioka puzzle, regional savings, investment, capital market, capital ows. Résumé E22, F21, G15 Mots-clés : énigme de Feldstein-Horioka, épargne et investissement régionaux, marchés de capitaux, ux nanciers

The purpose of this paper consists in assessing the extent of nancial integration in the European Union using the Feldstein-Horioka criterion. More precisely, we test the cross-correlation of savings and investment rates across the regions of the European Union, using regional data from Regio and national statistical oces, over the period 1995-2000. Several important outcomes are reported by our article. First, we nd that the nancial integration seems to be realized inside each country, and we are able to rationalize the few puzzles we face. Second, we nd that overall nancial integration between EU regions is almost complete. After performing additional investigations on consistent sub-groups of regions, however, our analysis discards the illusion that the sole suppression of institutional barriers to capital mobility would be sucient to achieve a perfect nancial integration. In that spirit, our main nding is that History, language, borders and distance as a proxy for transaction and information costs, still matter.

Introduction

Conventional wisdom holds that international capital markets are now highly integrated. Almost non-existent at the beginning of the seventies, cross-border transactions in equity and bonds, were more than 150% of United States GDP in the mid-nineties. In France, this ratio turns from 3% in 1975 to 106 % in 1996, and exceeds 400% in Italy at the same era. In United Kingdom, international transactions on bonds and equities amount to more than ten times GDP at the end of the nineties (gures from [START_REF] Van Wincoop | Intranational versus International Saving-Investment Comovements[END_REF].

In their seminal paper of 1980, however, Feldstein and Horioka initiated a well-known quarrel by supporting the idea that international nancial markets were actually poorly integrated. They were driven to that conclusion by examining the cross-sectional correlation between savings and investment across OECD countries during the 1960s and 1970s. The intuition is straightforward: if capital is perfectly mobile, domestic saving and capital should not be correlated, and capital should move freely where the rate of return is the highest. The result pointed to a quite low degree of nancial integration, however: despite a large volume of international capital movements, domestic savings and investment across OECD countries were found to be highly correlated, with estimated coecients close to one. The resulting Feldstein-Horioka puzzle paved the way to an impressive number of subsequent analyses of the relationships between national savings and domestic investment, which focused either on the econometric and statistical caveats, responsible for a bias towards a signicant, positive and close to one coecient, or on the economic and historical circumstances akin to explain the discrepancy between an expected coecient close to zero and its eective value. This paper belongs to the latter category of empirical approaches, by correlating regional savings and investment to be compared with similar results but using international data. Indeed, regional investigation has recently retained a growing attention, essentially because it allows to study the Feldstein-Horioka relationship in a monetary integrated area, free from a number of barriers and transaction costs. In that spirit, this paper wants to examine if a study of the savings-investment relationship on a regional basis, combined with a historical/geographical perspective, can bring results which would support theinterpretation of the Feldstein-Horioka criterion as a relevant indicator of the degree of nancial integration 1 . This 1 The distinction has been rst introduced by [START_REF] Coakley | Current account Solvency and the Feldstein-Horioka Puzzle[END_REF], and recently reminded by Caporale et 1 is done in a panel data context, relying on recent estimations methods accounting for problems of xed eects, endogeneity and serial correlation altogether.

Until now, research dealt mainly with countries able to provide the necessary regional dataset, such as the big federations of North America or Japan. Regarding European Union (EU) however, the United Kingdom was the only one to be the subject of an intranational study by [START_REF] Bayoumi | Domestic Savings and Intra-national Capital Flows[END_REF]. For all other EU countries, the lack of required regional data made any intranational study impossible. Nevertheless, the recent development of harmonized regional data, both by Eurostat and some national statistical oces, allows now to ll this gap. Therefore, this article is the rst to provide an extensive regional analysis of the Feldstein-Horioka criterion for EU countries wherever it is possible and over a time span for which harmonized regional data are available -that is, the period 1995-2000. Consequently, our rst point is to study the correlation between investment and savings at the national level (i.e. between the regions forming a nation or a State). Furthermore, we will also try to emphasize some specic links between some specic cross-border regional groups, which could lead to a weaker correlation. Here, we want to explore the potential inuence of historical or geographical particularities, such as the presence of a common border or language. Last but not least, we want of course to assess the impact of the economic integration in Western Europe, on its way for several decades by now.

The paper is structured as follows: section 2 provides an overview of theoretical underpinning and related literature. Afterwards, section 3 describes the methodology and the dataset.

In section 4, we present and discuss two sets of results. The rst group of estimations details the correlations of saving and investment rates across the regions inside each country, while the second one tests the Feldstein-Horioka criterion on consistent transnational or intranational groups of regions. Here, we assess the possible inuence of geographical, historical or economic links on regions nancial integration. Section 5 provides concluding remarks.

2 Pieces in the Feldstein-Horioka puzzle

In their pioneering study, [START_REF] Feldstein | Domestic Saving and International Capital Flows[END_REF] 2

I Y it = α + β S Y it + ε it (1)
where I Y represents the ratio of investment over Gross Domestic Product (GDP), that is the investment rate. Similarly, the ratio of savings over GDP, S Y , can be interpreted as the savings rate of the economy. Indexes i and t respectively stand for the considered country and year. Consequently, it is the value of the β parameter which focused until today the interest of a substantial literature. Indeed, the apparent Feldstein-Horioka mystery has been constantly fuelled by new studies, a lot of them emphasizing the signicance and robustness of this β parameter, whatever the time span considered.

Explaining this so-called Feldstein Horioka puzzle is a matter of either econometrics or of economic analysis. Let us start with a brief review of the former (statistical drawbacks responsible for the bias of the correlation between savings and investment). [START_REF] Feldstein | Domestic Saving and International Capital Flows[END_REF], [START_REF] Bayoumi | Saving-Investment Correlations, Immobile Capital, Government Policy, or Endogenous Behavior[END_REF][START_REF] Tesar | Savings, Investment and International Capital Flows[END_REF] consider that net instead of gross savings and investment should be used. Others emphasize that savings and investment are procyclical, and that a common economic cycle determines simultaneously the former and the latter. Therefore, savings is endogenous and correlated with the residual. For addressing the resulting bias, one has to nd an instrument. [START_REF] Feldstein | Domestic Saving and International Capital Flows[END_REF] computed averages over a long enough period of time, and they used demographic variables to handle sources of endogeneity. One of them may occur if there is a policy reaction to incipient current account imbalances to reduce it. The policy reaction argument has been made by [START_REF] Fieleke | National Saving and International Investment[END_REF], [START_REF] Tobin | Discussion on Domestic saving and international capital movements in the long run and the short run by M. Feldstein[END_REF], [START_REF] Summers | Tax-policy and International Competitiveness[END_REF], or [START_REF] Bayoumi | Saving-Investment Correlations, Immobile Capital, Government Policy, or Endogenous Behavior[END_REF]. It is also made in a recent paper [START_REF] Coakley | Current account Solvency and the Feldstein-Horioka Puzzle[END_REF] which emphasizes a cointegration relationship between savings and investment, due to the fact that in the long run, policy must react to imbalance by equalling saving and investment. The resulting constraint explains both why the correlation between savings and investment is biased towards one, and why it is lower for developing countries. Not because their degree of nancial integration is higher than for developed countries, but because they are less capable of respecting the long run capital constraint equilibrium. In a time-series context, [START_REF] Obstfeld | Capital Mobility in the World Economy: Theory and Measurement[END_REF] argues that the world interest rate is not exogenous and determines both domestic savings and investment. A shortfall in domestic savings will drive up the world interest rate and thus crowed out investment in the country. This problem can be corrected by expressing saving and investment rates as deviations from their averages. But even with this adjustment, [START_REF] Frankel | International Capital Mobility and Crowding-Out in the US Economy: Imperfect Integration of Financial Markets or of Goods Markets[END_REF] nds that the correlation does persist. Much more recently, [START_REF] Caporale | The Feldstein-Horioka Puzzle Revisited: A Monte-Carlo-Study[END_REF] performed a Monte-Carlo study supporting the high correlation case, while emphasizing a signicant heterogeneity across the 23 considered OECD countries, however. Relying on a very similar set of countries (19 from OECD), [START_REF] Kim | The Saving-Investment Correlation Puzzle is still a Puzzle[END_REF] uses cointegrated panel techniques to control the potential inuence of various factors on the savings/investment relationship, such as aggregate shocks (productivity, scal and terms of trade), global shocks and country specicities, for example in size. On the whole, his analysis conrms the persistence of a high, positive correlation between savings and investment.

Another way of understanding the Feldstein-Horioka result is to put it in historical perspective. According to the latter, capital controls would have been the rule rather than the exception up to a very recent period. Only the latest period from 1989 up to now can be compared to the Gold Standard in terms of nancial liberalization and break-up of nancial controls. In that process, international institutions have played a crucial role. One can distinguish several of them: OECD which issues regularly Code of Liberalization of Capital Movements, WTO, which negotiates the liberalization of banking and nancial services, attempts unsuccessfully to extend the liberalization of capital ows to Foreign Direct Investment. For developing countries, exposed to crisis of balance of payments and vulnerable to speculative attacks, IMF has recently been the proponent of dismantling regulations and capital controls, although in a less unambiguous manner than in the case of industrialized countries. Regionalism is also the locus of nancial liberalization, as emphasized in [START_REF] Flandreau | La Grande Retransformation ? Contrôle de Capitaux et Intégration Financière Internationale (1880-1996)[END_REF]: as soon as 1990, the Maastricht Treaty included explicitly the dismantling of all capital controls across European countries. Alongside with the monetary integration and the introduction of the euro, the very last obstacles to a complete nancial integration have been progressively eliminated. As a result, the prediction of a coecient close to nil should be validated either for the period prior to the First World War or to the period from the beginning of the nineties up to now. [START_REF] Frankel | Measuring International Capital Mobility: a Review[END_REF] argues that if the saving-investment regressions were a good test for barriers to nancial-market integration, one would expect to see the coecient falling over time. Until recently, this prediction has not been supported by the evidence, whether from cross section studies, which typically report pre-and post-1973 results (...) or from pure time series studies (...) (p.198-199). The contrary is emphasized in [START_REF] Flandreau | La Grande Retransformation ? Contrôle de Capitaux et Intégration Financière Internationale (1880-1996)[END_REF], who report that the coecient is generally lower after 1973, with two exceptions (see table 1): [START_REF] Murphy | Capital Mobility and the Relationship between Saving and Investment Rates in OECD Countries[END_REF], and [START_REF] Penati | Current Account Imbalances and Capital Formation in Industrial Countries[END_REF]. More importantly, the coecient is signicantly lower during the only period which is known to correspond to a period of deeper nancial integration, that is the Gold Standard2 .

Insert table 1 here

From Feldstein and Bacchetta (1991) one can already notices that the degree of capital mobility is higher across European countries. The coecient falls from respectively 0.73 to 0.46 when the equation is run before and after 1973 on a sample of nine EEC countries, and from 0.91 to 0.67 when it is run on a sample of 23 OECD countries. The latter remark points to the last possible explanation for the lack of international nancial integration over more recent periods of time. Following [START_REF] Frankel | Measuring International Capital Mobility: a Review[END_REF], the real interest dierential is made of three components. One can think rst of the covered interest dierential, which captures all barriers to integration of nancial markets across national boundaries, namely transactions costs, information costs, capital controls, tax laws (discriminating by country of residence). A similar argument is made in [START_REF] Obstfeld | The Six Major Puzzles in International Macroeconomics: Is There a Common Cause?[END_REF] who argue that the Feldstein Horioka puzzle can be solved by introducing costs of international trade in the form of iceberg costs.

The exchange risk premium and expected real depreciation are the two other components.

These two ones together constitute the currency premium, because they pertain to dierences in assets according to the currency in which they are denominated, rather than in terms of the jurisdiction in which they are issued (Frankel, 1992, p. 200). The currency premium is driven by a substantial exchange rate variability vis-à-vis the dollar since 1973 for European countries, which can explain in the above-mentioned Feldstein and Bacchetta (1991), the higher saving-investment coecient when estimated using a sample of OECD countries than that found with a sample restricted to European countries.

A more radical way of eliminating the currency premium problem is to rely on intranational data, that is to correlate regional savings and regional investment across regions of a single country, as originally suggested by McCloskey andZecher (1976, 1984). This has been done more recently in a few papers investigating the Feldstein-Horioka relationship on a regional basis and the results are summarized in the table 2 next page which reproduces and completes the survey table of van [START_REF] Van Wincoop | Intranational versus International Saving-Investment Comovements[END_REF]. Before presenting the main studies, it is worth noting that two methods are mainly used in the literature. On the one hand, the panel regression induces β from the estimation of :

( I Y ) it = α i + β( S Y ) it + ε it .
On the other hand, the cross-sectional regression estimates β from:

( I Y ) i = α + β( S Y ) i + ε i .
Here, it is important to understand that the index i stands for regions of the considered country or currency area.

Insert table 2 here

The very rst study is due to [START_REF] Sinn | Saving-Investment Correlations and Capital Mobility: On the Evidence from Annual Data[END_REF], which nds a comovement coecient not signicantly dierent from zero for the United States. Even if these results seem natural in the context of an old integrated monetary union, they are to be taken cautiously, since they have been computed on only two years, more than a half-century ago. Using UK intranational data, [START_REF] Bayoumi | Domestic Savings and Intra-national Capital Flows[END_REF] nd that investment and saving rates are poorly correlated for the eleven administrative regions of the UK, a diagnosis more or less conrmed by [START_REF] Thomas | Saving, Investment and the Regional Current Account: an Analysis of Canadian, British and German regions[END_REF]. The study he provides involves also Canada, and the main result he nds is almost the same that the one achieved by [START_REF] Bayoumi | Financial Integration and Real Activity[END_REF], that is a coecient really close to zero. For Japan, while [START_REF] Dekle | Savings-Investment Associations and Capital Mobility: on the Evidence from regional Data[END_REF] nds signicant negative coecients whatever the period considered, [START_REF] Iwamoto | Do Borders Matter? Evidence from Japanese Intranational Capital Flows[END_REF] and van Wincoop (2001) exhibit systematically signicant and positive coecients between 0.3 and 0.4, no matter the period studied or the econometric methodology used. Those coecients are higher than for the U.S. or the U.K., but more importantly lower than the coecients obtained using international variables (cf. supra).

Besides, the two latter studies are basically the only ones to nd a positive relationship, all the other ones supporting evidence of a negative comovement between savings and investment.

As emphasized by [START_REF] Van Wincoop | Intranational versus International Saving-Investment Comovements[END_REF], this negative comovement cannot be attributed only to a measurement bias, but also to possible disagreements regarding the denition of regional saving and investment rates.

Among this overview, the paper by [START_REF] Armstrong | Domestic Savings, Intra-national and Intra-European Capital Flows, 1971-1991[END_REF] oers an original perspective.

Following explicitly the path of [START_REF] Bayoumi | Domestic Savings and Intra-national Capital Flows[END_REF], they tested the correlation saving/investment for the mid-1990s twelve EU members. Relying on national data, their study considered EMU as an area on the way of integration, that is presumably in an intermediary situation between the United Kingdom (an already integrated capital market) and OECD countries (with a high correlation between savings and investment rates). Their empirical work supports the idea that the EU capital markets exhibited levels of integration on the whole close to the UK intra-national one. However, the puzzle of negative coecients remain, with a downward bias seemingly due to the inclusion of Portugal in the sample. Besides, the authors emphasized, without explaining it, a possible business cycle bias, according to which the correlation would be stronger (sometimes around 0.5-0.6) during period of recessions. Finally, their study do not perform any kind of intranational analysis inside European Union countries, considered explicitly as homogenous regions of a wider area.

Consequently, beyond the updating of [START_REF] Armstrong | Domestic Savings, Intra-national and Intra-European Capital Flows, 1971-1991[END_REF]'s results using regional more recent data, the present paper has two main purposes. First, it aims at generalizing Bayoumi and Rose (1993)'s results for the United Kingdom to all other European countries, by testing the Feldstein-Horioka criterion on a regional basis for each of them. Second, the use of a regional basis will help to investigate the possibility of transnational/cross-border strengthened nancial integration between some specic regions, which could arise from geographic or historical reasons. In that spirit, we are going to work on the following variant of equation 1:

I jt Y jt = α j + β S jt Y jt + ε jt (2)
where the letter j stands this time for regions, and not for countries, at a period of time t. This will allow for a double study, intranational on the one hand (how integrated can be all regions from the same country?), transnational on the other hand (how may be integrated some regions from dierent countries?).

3 Data and methodology: from regions to countries Before getting into the details of our methodological choices, it seems useful to highlight that the series required in such a regional investigation of the savings/investment relationship are much more dicult to get than their national counterparts. Indeed, the heterogeneity of savings and investment denitions used in the few aforementioned studies comes mainly from the lack of easily accessible regional data, which leads to choices for dierent proxies and partial denitions according to the considered country. For instance, [START_REF] Bayoumi | Domestic Savings and Intra-national Capital Flows[END_REF] do not have complete data on regional investment. They use data for specic industries, which exclude between 25 and 50% of private sector investment. Besides, they rely alternatively on an evaluation for households savings and on a more comprehensive other one, including government consumption, however. By contrast, [START_REF] Iwamoto | Do Borders Matter? Evidence from Japanese Intranational Capital Flows[END_REF] could access much more complete data for their study on the Japan. Therefore, regional saving is the sum of saving by all residents and institutions of a region. Similarly, regional investment is the sum of physical investment by rms, households and the local government in a region.

In the context of our research, an additional problem arises from the need for homogenous macroeconomic accountancy denitions across countries.

Turning to our dataset, we could therefore retrieve homogeneous annual series for investment (gross xed capital formation, GFCF) and gross domestic product coming from Eurostat harmonized regional accounts, available over the 1995-2000 period (Regio NUTS 2, European System of Accounts, ESA 95. For Germany, only NUTS 1 data of GFCF were available).

Unfortunately, Regio does not provide any harmonized savings data at the regional level.

Additional investigations in publicly available national databases showed that this absence could be explained for most countries by a lack of accessibility of such data, which are either non-existent, or too partial to be exploitable, and/or condential. However, a complete regional database of GFCF and savings is available for Germany, from the Statistic national oce of Baden-Württemberg (Statistisches Landesamt Baden-Württemberg). For Italy, we could rebuild series of savings, using the dierence between regional GDP data provided by Regio database and the total regional consumption, available from a regional database provided by the Italian research center CRENOS (Centro Ricerche Economiche Nord Sud, Center for North South Economic Research). For these two countries, a direct regional study of the Feldstein-Horioka criterion according to equation 2 could therefore be proceeded.

For the other EU countries, we decided to proxy regional savings using disposable income 3 data, the closer aggregate to savings we had. For this purpose, we postulate that disposable income and savings rates grow identically, and consequently, the Feldstein-Horioka model can be estimated using dierentiated variables instead of levels. Formally, denoting disposable income as INC, this leads to assume that ∆

S jt Y jt = ∆ IN C jt Y jt
, and to estimate:

3 This aggregate is accountably equal to the sum of households consumption and savings. It is therefore dierent from GDP Y , which is roughly equal to the sum of gross values added created in the economy ∆

I jt Y jt = γ + β × ∆ IN C jt Y jt + υ jt (3)
This method relies on two distinct hypothesis which can be immediately checked for Germany and Italy. The rst one postulates that households savings are suciently well correlated to total (that is households plus rms plus government) savings, so that the variations of the former mimic correctly the variations of the latter. The second one asks that the variations of the households savings rate and the ones of the ratio of disposable income over GDP ( IN C Y ) move proportionally.

In our case, the rst requirement is easily met for both Germany and Italy, since the correlations of households savings with total savings reach respectively 90.7% and 88.3%.

Regarding the second requirement, it is easily conrmed for Italy, with a 96.9% correlation between households savings rate and the ratio IN C Y ; for Germany, the picture is somewhat less clear, with a correlation reaching only 52%. But on the whole, our assumptions seem to be validated. Besides, we will be able to check directly the empirical virtues of our proxying method for Germany and Italy in the next section, where will be compared the estimations deduced from the real savings data and the ones coming from disposable income. Eventually, it is useful to highlight that our dataset stands halfway between the one of [START_REF] Bayoumi | Domestic Savings and Intra-national Capital Flows[END_REF], constrained to rely on partial and heterogenous denitions for variables, and [START_REF] Iwamoto | Do Borders Matter? Evidence from Japanese Intranational Capital Flows[END_REF], who could access a complete and homogenous database.

Consequently, we can consider that our estimations will be reasonably reliable in terms of national accountancy denitions.

Turning to estimations concerns, our overall panel consists of 108 European Union regions, i.e. a 557 observations sample in levels (436 in rst dierences) including Belgium, Denmark, Germany, Greece, France, Ireland, Italy, Luxembourg, Netherlands, Austria, Portugal, Finland and Sweden -unfortunately, required NUTS 2 data were not available for Spain.

Regarding the special cases of Germany and Italy, the national databases amount respectively to 96 and 114 observations. For all countries, the short time span prevents us de facto to use the recent cointegration panel methods [START_REF] Kim | The Saving-Investment Correlation Puzzle is still a Puzzle[END_REF][START_REF] Banerjee | A New Look at the Feldstein-Horioka Puzzle using an Integrated Panel[END_REF]. Besides, this period includes the ocial launch of scriptural (written) euro: it could therefore legitimately be argued that such an event is likely to have created a structural modication of the relationship between savings and investment. From a statistical point of view, however, the very short time span does not allow the implementation of standard structural breakdown tests (like the ones proposed by Chow, 1960, or Bai and[START_REF] Bai | Computation and analysis of multiple structural change models[END_REF] for checking this intuition 4 . At the economic level, one can highlight, nonetheless, that scriptural euro launch did not fundamentally modify the process of nancial integration, on its own track since the Single European Act of 1986 and the total liberalization in 1993.

Besides, the time dimension of our study asks to check for the possibility of serial correlation in the residuals. To do so, we implement a [START_REF] Wooldridge | Econometric Analysis of Cross Section and Panel Data[END_REF] test for temporal autocorrelation in panel data. On the whole5 , the test highlights the presence of highly serially correlated residuals for Germany, but not for Italy, when estimating equation 2. For equation 3, the presence of serial correlation is conrmed for most countries. Furthermore, the exogeneity of right-hand side variables, namely the savings rate or the rst dierence of the ratio IN C GDP must be tested, in order to check for an endogeneity bias. For that purpose, we use [START_REF] Hausman | Specication Tests in Econometrics[END_REF] and [START_REF] Nakamura | On the relationships among several specication error tests presented by Durbin, Wu, and Hausman[END_REF] tests. The table 3 presents the results of these tests for Germany and Italy, and for equations 2 et 3 respectively. Regarding the savings rate, two alternative sets of instruments have been selected6 : in a rst specication, the savings rate is instrumented using two of its own lags and in a second one, using the contemporaneous value of the ratio IN C GDP . Concerning regressions in rst dierences, the two rst lags of IN C GDP are used as instruments.

Insert table 3 here

Regarding equation 2, both tests fully agree to reject the hypothesis of exogeneity for Germany, whereas evidence is more mixed for Italy. Turning to equation 3, the exogeneity of The estimation strategy we set up accounts for the results of these tests for serial correlation and endogeneity. For Germany and Italy, next section will present two sets of estimation for equation 2, the rst one coming from a panel regression with xed eects, the second one produced by a two-stage least squares (2SLS) regression with xed eects7 . However, the panel regression for Germany will postulate rst-order autoregressive residuals, while the Italian one will use conventional identically and independently distributed errors. Concerning equation 3, the use of a panel regression is not relevant for a specication based on rst dierences. In the context of the widespread serial correlation of residuals and the exogeneity of right-hand side variable, all estimations based on equation 3 were processed using Ordinary Least Squares with Newey-West standard errors for coecients -that is, corrected for heteroskedasticity and rst-order autocorrelation.

IN C/Y rst dierence
More precisely, the subsequent analysis will divide in two parts, each of them relying on a dierent panel. The rst one follows explicitly the path opened by [START_REF] Bayoumi | Domestic Savings and Intra-national Capital Flows[END_REF] on the United Kingdom, and wants to check if each country of our European sample can be considered as a highly integrated capital market8 according to the Feldstein-Horioka equation. The second one comes from the testing of Feldstein-Horioka criterion on consistent transnational and/or intranational groups of regions. Here, we assess the possible inuence of historical, geographical or economic links on the nancial integration of regions. Accounting for the constraints arising from data availability, we are able to study seven consistent transnational groups, represented on the maps located at the end of the section.

For clarity, transnational groups are indexed from 1 to 7 on the maps presented at the end of the section. Scandinavian group involves Denmark, Finland and all the regions of Sweden (Group 1 on the map). A second association is made of East of France (Alsace, Lorraine) and regions from West of Germany, that is Baden-Württemberg and Rheinland-Pfalz (Group 2). Rhônes-Alpes, Provence-Alpes-Côtes d'Azur for France, and Piemonte, Lombar-dia, Valle d'Aosta, Liguria, Veneto, Friuli-Venezia Giulia, Emilia Romagna, Toscana, Umbria, Marche, Lazio for Italy, jointly form a consistent area covering Southeast of France and North of Italy (Group 3). Another pool includes Northern French regions (Nord-Pas de Calais, Champagne-Ardenne, Picardie, Lorraine), the bordering Belgian regions (Luxembourg, Namur, Hainaut, Vlaanderen, that is Flanders) and Luxembourg (Group 4). We examine also the relevance of an area involving all regions from the Benelux association and neighboring German regions, that is Nordrhein-Westfalen, Rheinland-Pfalz and Niedersachsen (Group 5).

Encompassing Veneto, Salzburg, Tirol and Oberösterreich, group 6 tests the likelihood of an Austrian-German-Italian mix. Finally, the capital group (7 on the map) comprises all the capital regions or main economic centers of the studied countries: Paris, Berlin, Bonn (as the former West Germany capital), Brussels, Wien, Roma, Milano, Copenhagen, Luxembourg, Dublin, Stockholm, Amsterdam, Athens, Lisboa9 . Regarding intranational specicities, we will focus our attention on North/South Italy, Flanders/Wallonia (Belgium), and West Germany/East Germany. Beyond the constraint of the number of observations, these cuttings seem relevant both from historical and economic point of views.

Insert Figure 1 here 4 Results: a double look at the EMU

The intranational look

The results for Germany and Italy are based upon a complete dataset including investment and savings, while for other European countries having the latter but not the former we will have to use a proxy for savings. The availability of the complete dataset for two countries allows testing the quality of the subsequent proxy, simply by comparing the estimates of the Feldstein Horioka model (equation 2) and those of equation 3. Tables 4 and5 The second result concerns the validity of proxying savings by disposable income that is of estimating equation 3 instead of equation 2. Comparing the estimates obtained for Italy and Germany, for which both datasets are available, conrms the intuition we had by simply correlating savings and disposable income. The signs are the same and the absolute values of the coecients are of the same order of magnitude. For Italy, -0.12 obtained for equation 2 is not far from -0.07 which corresponds to equation 3. The estimate obtained with lagged savings (2SLS(1)) is signicantly dierent, -0.42, but the Sargan test indicates that this estimate is not statistically valid. Besides, equations 2 and 3 deliver very close and not signicantly dierent from zero estimates for East Germany and the whole country. Estimations for West Germany are the only ones to diverge a bit since the 2SLS(2) estimate for equation 2 is signicantly negative on the one hand, while all other estimates support a non-signicantly dierent from zero β. Apart from this single exception, results in tables 4 and 5 conrm that disposable income can be used for proxying regional saving.

Turning back to economic concerns, our results for Germany and Italy corroborate the conclusions in [START_REF] Bayoumi | Domestic Savings and Intra-national Capital Flows[END_REF] regarding the United Kingdom. The estimates are never signicantly positive and Germany as a whole exhibits a β coecient not signicantly dierent from zero, while estimates for Italy lie between 0 and -0.1. This suggests that both countries exhibit an high degree of nancial integration according to the Feldstein-Horioka denition. If this result is totally conrmed for North and South Italy, and East Germany, there is a slight divergence for West Germany, 2SLS(2) estimates supporting a signicant negative coecient a bit below -0.2. However, all other estimates, from panel least squares with AR(1) disturbance, 2SLS(1) (statistically valid for West Germany) and from equation 3 agree to nd a nil β, which is more conform to economic intuition, since West Germany is an old integrated monetary area.

Until now, German and Italian examples conrm the idea of [START_REF] Frankel | Measuring International Capital Mobility: a Review[END_REF] that the exchange premium would explain the biggest part of the Feldstein-Horioka puzzle. Furthermore, another important lesson from the analysis is that equation 3 can be estimated instead of equation 2. The subsequent step is therefore to estimate it for all European countries, including those for whom real saving data are missing. This is done in the table 711 below:

Insert table 7 here Some striking features emerge from a rst reading of the table. First, the coecient for the whole Europe is positive and non-signicant. It stands just below 0.1, which according to the criteria proposed by Feldstein and Horioka validates the hypothesis of a high degree of capital market integration. This result is dierent from that reported in [START_REF] Armstrong | Domestic Savings, Intra-national and Intra-European Capital Flows, 1971-1991[END_REF], where β tended to be most of the time negative, with signicance depending upon the period of time under consideration.

Two patterns of countries emerge. The rst one includes the geographic, historical, and economic core of Europe. For this group of countries -Germany, France, Italy, Belgium, Netherlands -the Feldstein Horioka coecients are close to zero and not signicantly dierent from nil. Those countries are rich, the three largest are members of the G7, they are all provided with a large international nancial market. The second group of countries is constituted of smaller countries belonging to the European periphery, namely Portugal, Greece and Sweden. For them the correlation between savings and investment is signicantly dierent from zero, either positive or negative. As mentioned previously, negative β coecients are widespread in the Feldstein-Horioka literature studying intranational data. If they are hard to explain in most cases, the case of Portugal is pretty clear. Since 1975, the country benets from a high level of FDI, and from 1986 from a high level of Structural Funds. Over 1995-2000 the inows of FDI increased by 38.7%12 but real GDP by only 21.7%, while the saving rate proxied by the ratio of disposable income over GDP decreased. As a consequence the β coefcient turns out to be negative in emerging countries like Portugal where investment exceeds for structural reasons the country saving capacity. This nding echoes a recent conclusion of [START_REF] Bayoumi | Why Has there Been less Financial Integration in Asia than in Europe?[END_REF], namely that one key determinant of nancial integration is the level of economic development. The implication is that the ending process of Portuguese convergence should be accompanied by a decrease of the absolute value of the beta coecient towards zero13 . Although Greece is like Portugal a catching-up country, it has not been able

to attract the same amount of FDI. Between 1995 and 2000 instead, FDI decreased by 2%, while real GDP increased by 18.4%. As a result and not surprisingly the correlation between disposable income and investment turns out to be (not very) signicantly dierent from zero but unlike Portugal it is positive: no foreign inows has come to push the investment rate up, while the variation of the ratio IN C Y is close to zero on overage over the period. Lastly, the Swedish case is a priori more puzzling. Indeed, the Swedish GDP per head is amongst the highest in the world; hence the rational behind a β equal to 0.53 cannot be that the nancing of the economic development requires a high investment rate compared with a low saving rate.

The explanation is rather that the distribution of the population is concentrated in the south, with a density of 253 inhabitants per km 2 in the urban triangle (Malmö, Göteborg, Stockholm) but only 3 in the region of Norrbotten. As a consequence, most of the economic activity is likely to be concentrated in the three corresponding regions from NUTS 2 classicationthat is Stockholm, Sydsverige, Västsverige. Conversely, the savings and investment rate of the northern regions should be characterized by a huge inertia, due to the lack of investment opportunities and the underdevelopment of nancial intermediation. This intuition is tested by running two additional estimations of the Feldstein-Horioka equation on two separate subsamples. The rst one consists of the three regions forming the urban triangle, and leads to a

The positive coecient for G7 (capitals) or the relatively low degree of nancial integration between capitals, which by denition do not share a common border and do not speak the same language14 , strengthens a contrario the result about borders and languages. Our regions crossing borders are also characterized by short internal distances. [START_REF] Portes | The Determinants of Cross-border Equity Flows[END_REF] use distance as a proxy for information costs and for asymmetry of information between domestic and foreign investors. They use a gravity approach and show that distance exerts a negative inuence on international capital ows. Our regions crossing borders are characterized by short distances within them, which suggest the same link between geography (distance) and nance. Consequently, European nancial integration, while being strongly supported by the process of EMU, remains somewhat imperfect by phenomena related to distance and to a kind of home market bias and for close, or at least frontier, regions. This is illustrated by the positive and signicant coecient for the capitals and main economic centers.

Results for intranational sub-groups do not bring any big innovation relatively to our previous ndings: for Germany and Italy, estimates on Eurostat data are very close to the ones deduced from national statistical oces, and keeps emphasizing that these sub-national groups are well integrated according to Feldstein-Horioka criterion. A noticeable exception is Flanders however, which is featured by a positive and signicant coecient around 0.4, whether Brussels is included in the estimation or not. This relatively low capital mobility can be explained by a combination of a language barrier (French and English remain the main language spoken by Belgian businessmen, Flemish remaining fairly isolated), and the lack of a large nancial center. The case empirically illustrates a recent argument of [START_REF] Martin | Financial Super-Markets: Size Matters for Asset Trade[END_REF], who stress the importance of the market size in explaining the volume of nancial transactions. Indeed, the result for Flanders suggests that the narrowness of the capital market jointly with the existence of a linguistic and cultural fracture blocking the access to the great local market (Brussels), are likely to explain the low degree of nancial integration.

Conclusion

To conclude, our major original contribution in this paper consists in applying the Feldstein-Horioka criterion to European regional data for a large number of EU members. This dataset allowed us to estimate the comovement coecient between savings and investment not only inside each individual country but also, between transnational groups our inside intranational sub-groups. Several important outcomes are reported by our article.

First of all, nancial integration seems to be realized inside most of the considered countries, which corroborates a contrario Frankel (1992)'s hypothesis of a currency premium impeding the realization of a perfect nancial world. Moreover, we propose an explanation for some puzzles already highlighted in the literature, like the negative coecient in the Portuguese case, already stressed in [START_REF] Armstrong | Domestic Savings, Intra-national and Intra-European Capital Flows, 1971-1991[END_REF], and new ones like the Swedish positive coecient. As in [START_REF] Bayoumi | Why Has there Been less Financial Integration in Asia than in Europe?[END_REF], we especially argue that the process of economic development does inuence the extent of nancial integration. Furthermore, we found a coecient of 0.09 across all the regions forming European Union.

This gure indicates that overall nancial integration seems to be completed with the euro launch. In order to shed a new light on the latter result, we have tested the relationships between saving and investment in consistent sub-groups of regions (designed according to geographical, economic or historical criteria). Following a recent strand of research applying the analytical frameworks of international trade to nancial transactions, our nding is that History, language, borders and distance as a proxy for transaction and information costs, matter. Especially, we show that nancial integration is not impeded by the existence of borders, but by distance and by linguistic diversity, interpreted as proxies for transaction and information costs. Consequently, if monetary integration is a necessary step in the process of nancial integration, it is not sucient, in as much as other barriers, including information and transaction costs, are still important.

Finally, our analysis discards the illusion that the sole suppression of institutional barriers to capital mobility would be sucient to achieve a perfect nancial integration everywhere and at any moment. As in [START_REF] Flandreau | La Grande Retransformation ? Contrôle de Capitaux et Intégration Financière Internationale (1880-1996)[END_REF], [START_REF] Bayoumi | Saving-Investment Correlations, Immobile Capital, Government Policy, or Endogenous Behavior[END_REF][START_REF] Eichengreen | Trends and Cycles in Foreign Lendings[END_REF], [START_REF] Zevin | Are World Financial Markets More Open? If so, Why and With What Eects[END_REF], [START_REF] Taylor | Argentina and the World Capital Market: Saving, Investment, and International Capital Mobility in the Twentieth Century[END_REF], and others, we emphasize that history, geography, culture and policy altogether matter. All these factors keep contributing today to nancial markets incompleteness, preventing therefore a perfect capital mobility. [START_REF] Flandreau | La Grande Retransformation ? Contrôle de Capitaux et Intégration Financière Internationale (1880-1996)[END_REF]) 1880-19131918-19391945-19731974- [START_REF] Bayoumi | Saving-Investment Correlations, Immobile Capital, Government Policy, or Endogenous Behavior[END_REF]Bayoumi ( ) 1880Bayoumi ( -1913Bayoumi ( 1966Bayoumi ( -1970Bayoumi ( 1981-- 2) refer respectively to instruments sets 1 and 2 described in the previous section. a , b and c denote signicance, respectively at the 1, 5 and 10% levels.

Standard errors in parentheses.

  examined the cross-sectional correlation between savings and investment by testing this very simple equation: al. (2005).

Figure

  Figure 1: Transnational groups

  is widely accepted, even if a small uncertainty remains for Germany.

	exogenous.
	Concerning all other countries, for which are only available disposable income data, endogene-
	ity tests, available upon request to the authors, conrm that ∆	IN C jt Y jt	can be considered as

  From a statistical perspective, two main features arise. First of all, the Sargan test strongly rejects lagged savings rates as a valid instrument for contemporary savings rate. This rejection seems to be due to the inclusion of the poorest sub-regions, namely South Italy and East Germany. If we restrict the sample to West Germany and North Italy indeed, the null assumption is validated 10 . Unlike for the richest regions, saving rate in less advanced regions is likely to be determined by other variables than its lagged values, like disposable income. Whatever the exact reasons, the results are not robust and therefore they are excluded from subsequent analysis. Thereafter, we will focus instead on 2SLS(2), based upon disposable income.

	Insert table 5 here
	Finally, table 6 presents the results of Sargan (1958) overidentication test, necessary for
	validating estimations deduced by the 2SLS relying on the set of instruments 1:
	Insert table 6 here
	report also the
	results for the decomposition of Germany according to a West-East separation, and for Italy
	according to a North-South axis.
	Insert table 4 here

Table 1 :

 1 Correlation between savings and investment: the historical perspective

	Authors	Gold Standard	Interwar	Bretton Woods	Floating rates

  Notes: adapted from[START_REF] Flandreau | La Grande Retransformation ? Contrôle de Capitaux et Intégration Financière Internationale (1880-1996)[END_REF]. Standard errors in parentheses.

				1985
	Between	0.29 (0.46)	0.96 (0.10)	0.72(0.12)
	Number of countries	8	10	10
	Tesar (1991)		1960-1974	1975-1986
	Between		0.89 (0.10)	0.81 (0.18)
	Coakley et al. (1994)		1960-1974	1975-1992
	Between		0.88(0.06)	0.65 (0.10)
	Number of countries		23	23
	Bayoumi (1997)	1885-1913	1960-1971	1975-1993
	Between	0.53 (0.29)	0.84 (0.07)	0.65 (0.10)
	Number of countries	9	22	22
	Kim (2001)			1960-1992
	Cointegrated panel			0.69 (0.25)
	Number of countries			19 (OECD)
	Caporale et al. (2005)			1948-1998
	Various estimators/MC simulations			close to 1
				for 3/5 countries
	Number of countries			23 (OECD)

Table 2 :

 2 Correlation between savings and investment: the intranational look

Table 3 :

 3 Endogeneity tests of right-hand side variables : N.R.: Non Relevant. For equation 2, Instruments 1 = two lags of S/Y , Instrument 2: IN C/Y . For equation 3, Instruments 1 = two lags of ∆ IN C

	Germany	Italy
	Equation 2

Notes

Table 5

 5 -0.12 c (0.07) -0.42 b (0.17)1.43 (3.03) 95 -0.07 c (0.04) North 1995-2000 66 -0.08 (0.06) -0.21 (0.14) 1.03 (1.02) 55 -0.06 (0.06) South 1995-2000 48 -0.27 (0.18) -0.73 (0.47) 0.61 (1.15) 40 -0.09 c (0.05) Notes: (1) and (2) refer respectively to instruments sets 1 and 2 described in the previous section. a , b and c denoting respectively signicance at the 1, 5% and 10% levels.Standard errors in parentheses.

			: Italy
			Equation 2	Equation 3
	N	LS	2SLS (1)	2SLS (2) N OLS Newey-West
				All Italy
	1995-2000 114

Table 6 :

 6 Overidentication test Notes: a , b and c denoting respectively signicance at the 1, 5 and 15% levels. Standard errors in parentheses.

		χ 2 (1) Signicance
			level
	Germany	43.02	0.00
	West Germany 1.34	0.25
	East Germany 20.71	0.00
	Italy	3.42	0.08
	North Italy	0.39	0.53
	South Italy	3.94	0.05

Table 8 :

 8 Comovement between savings and investment in transnational/intranational groups , b , and c respectively denoting signicance at the 1%, 5% and 10% levels. Standard errors in parentheses.

	Regional Group	number of	estimate
		observations of coecient β
	G1: Scandinavia	55	0.32 (0.59)
	G2: East France/West Ger.	16	-0.53 (0.47)
	G3: North Italy/South France	59	0.04 (0.15)
	G4: North France/Belg./Lux.	32	-0.23 (0.27)
	G5: Germany/Benelux	44	-0.52 (0.37)
	G6: Austria/Germany/Italy	27	-0.04 (0.21)
	G7: Capitals	58	0.25 b (0.13)
	North Italy	55	0.07 (0.16)
	South Italy	40	-0.11 (0.16)
	Flanders(Bruss. incl.)	30	0.39 b (0.17)
	Flanders (Bruss. excl.)	25	0.41 b (0.18)
	Wallonia (Bruss. incl.)	30	-0.25 (0.29)
	Wallonia (Bruss. excl.)	25	-0.28 (0.34)
	West Germany	55	0.15 (0.26)
	East Germany	25	0.45 (0.46)
	Notes: a

Close arguments can be found in[START_REF] Lothian | The Internationalization of Money and Finance and the Globalization of Financial Markets[END_REF], who focuses on real stock returns and real interest rates convergence. Using a database covering several centuries, the paper concludes that periods such as interwar appear as temporary disruptions in the historical process of nancial markets globalization.

The obstacle could be partly overcome using time dummies, however. Subsequent additional investigation emphasized that dummies for 1998 and 1999 were not signicant most of the time, comforting our intuition of no signicant breakdown.

The full set of results is available upon request to the authors.

The choice for instruments is often a complex matter, especially when estimations are performed over a short time period, like in our case. The ones used in this article have been selected after a preliminary analysis which have tested several possibilities the number of lags for the savings rate and the ratioIN C GDP . All results from this preliminary investigation are available upon request to the authors.

Actually, all regressions, whether they were performed with instrumental variables or not, have been performed twice, rst in a model with xed eects, then in a model with random eects. A Hausman test has subsequently been run in order to discriminate which estimation is ecient, giving then a clear preference for xed eects.

Anintranational study cannot be provided for Denmark, Luxembourg, Ireland and Finland: the two rsts are two small countries which are considered as single regions at the NUTS 2 level, while third and fourth do not have more than two regions with observations.

No data at the NUTS 2 level was available for the region of Lisboa, so we substituted data from the wider cutting NUTS 1.

It is worth noting that the conclusions of the test remains identical when increasing the number of lags, either for savings rate or disposable income.

For the sake of consistency, estimates for Germany and Italy presented in this table and in table 8 are estimated using Eurostat data, in order to avoid confusion of data from dierent sources.

See the World Bank (2004), by the World Bank.

According to OECD, FDI decreased by 27.1% in 2002, and by 56% in 2003, because of the strong competition between EU members to attract FDI. In 2003, public investments have also been cut by 26%, reaching their lowest level since 1999.

English language is of course often used, but still remain the problems of commercial habits and negotiation cultures, which can constitute real barriers to trade. On that ground,[START_REF] Mélitz | Language and Foreign Trade[END_REF] emphasizes that the practice of English does not foster the trade of goods more than French or Spanish.

β coecient equal to 0.29, but really far from being signicantly dierent from zero -not even at the 25% level. Consequently, capital seems to move freely across the three main economic centers of the country, which seems quite natural. The second one is made of all Sweden excluding these specic three regions; unsurprisingly, the regression gives an estimate of 0.77 (signicant at the 5% level) for the coecient β, conrming the aforementioned argument.

Regions crossing borders

Table 8 contains the estimates of equation 3 for the subsets of regions previously described.

Most of them are not signicantly dierent from zero, with three exceptions: G7 and the two Flanders estimates are positive, and the order of magnitude is similar to that found in [START_REF] Iwamoto | Do Borders Matter? Evidence from Japanese Intranational Capital Flows[END_REF] for Japan.

Insert table 8 here

The Swedish puzzle vanishes when one considers a larger group of Scandinavian countries.

The coecient characterizing the degree of nancial integration for this group is close to zero. Furthermore, they are related by close commercial links, echoing another result by [START_REF] Bayoumi | Why Has there Been less Financial Integration in Asia than in Europe?[END_REF] who highlight that nance follows trade (p.3 and p.19), i.e. that nancial integration is superior in areas where the intra-regional trade is highly developed. It is also worth noticing that G1 group is mainly made of regions (those of Sweden more Denmark) which are excluded from the European process of monetary integration. In the same spirit, the groups based upon historical links, like G3 and G6, are nancially integrated, with coecients not signicantly dierent from zero. Groups 2, 4 and 5 exhibit negative coecients, none of them being statistically signicant. Nevertheless, the extent of theses negative coecients remains puzzling. The composition of the group excludes of course to rely on the same kind of explanation than the one used for Portugal. It seems therefore plausible that we face an accountancy problem similar to the one analyzed by van [START_REF] Van Wincoop | Intranational versus International Saving-Investment Comovements[END_REF], for whom the negative β are related to a problem of regional public savings denitions. Anyhow, all these six groups are characterized by a high degree of nancial integration, which emphasizes the importance of sharing a common border and/or a common language in promoting capital mobility, as emphasized in [START_REF] Bayoumi | Why Has there Been less Financial Integration in Asia than in Europe?[END_REF].