Mathieu Goudard

Michel Lubrano

Human capital, social capital and scientific research in Europe: an application of linear hierarchical models

Keywords: Economics of science, human capital, social capital, hierarchical models, European science. JEL codes: I21, D91, C49

 and Putnam (1995) as a necessary complement to explain the creation of scientific human capital. This paper connects these two concepts by means of a hierarchical econometric model which makes the distinction between the individual level (human capital) and the cluster level of departments (social capital). The paper shows how a collection of variables can be built from a bibliographic data base indicating both individual behaviour including mobility and collective characteristics of the department housing individual researchers. The two level hierarchical model is estimated on fourteen European countries using bibliometric data in the fields of economics.

Introduction

What are the motivations for academics to engage in scientific research and which outside factors influence their publication performance? These are two questions among others addressed in the field of economics of science. In their survey papers, [START_REF] Stephan | The economics of science[END_REF] and [START_REF] Diamond | The economics of science[END_REF] suggest a diversity of explanations for the individual production of scientific papers. Above the simple satisfaction of scientific curiosity, one of the main motivations of scientists is the recognition awarded by the scientific community for being the first to publish a main discovery. There is no prize for being second, remember the dispute around the discovery of the HIV. Because of this race, scientific activity becomes such a risky adventure that wages depends only for a fraction on scientific output. The American sociologist [START_REF] Merton | The Matthew effect in science[END_REF] pointed out the Matthew effect which shows that mature and recognised scientists are rewarded, both financially and by citations, above their real merit. The combination of these two characteristics (race for being the first and over recognition of already matured scientists) might explain the fact that we can observe scientists with an important and continuous production together with scientists who have a more cyclical production. This is illustrated for instance by [START_REF] Lotka | The frequency distribution of scientific productivity[END_REF] whose famous statistical law models the concentration of publications among very few scientists.

A major ingredient for individual scientific production is human capital which is a combination of basic intelligence and accumulation of efficient knowledge. The life-cycle theory predicts that, due to the finiteness of life, investment declines over time. Combined with a depreciation of human capital, this explains the inverted U shape of scientific output. Several models were developed around this idea, notably by [START_REF] Mcdowell | Obsolescence of knowledge and career publication profiles: Some evidence of differences among fields in costs of interrupted careers[END_REF], [START_REF] Diamond | An economic model of the life-cycle research productivity of scientists[END_REF][START_REF] Diamond | An optimal control model of the life-cycle research productivity of scientists[END_REF] and [START_REF] Levin | Research productivity over the life cycle: Evidence for academic scientists[END_REF]. These models recognise the importance of time in scientific discovery.

However, these models, mainly based on time trends and cohorts effects, even if they do find an age-publishing relationship, do lack an explanatory power for irregularities in the flow of output. Using panel data, [START_REF] Levin | Research productivity over the life cycle: Evidence for academic scientists[END_REF] introduce individual fixed effects to take into account the differences in productivity which are not explained by a life-cycle effect. But apart from displaying individual effects, no rational explanation for diversity is provided.

Life-cycle models are based strictly on individual behaviour, ignoring one fundamental aspect of human capital which is increased by sharing. Surroundings, contextual effects, networking are determinant. Following [START_REF] Coleman | Social capital in the creation of human capital[END_REF], the accumulation of human capital needs another ingredient that [START_REF] Bourdieu | Le capital social: Notes provisoires[END_REF] was the first to call social capital. If the notion of human capital comes from the economics literature and was the object of considerable modeling efforts, the notion of social capital comes mainly from the sociological literature which includes very little modeling. [START_REF] Coleman | Social capital in the creation of human capital[END_REF] provides justifications for showing how the two notions (human capital and social capital) can work together, taking the example of education to build his demonstration. But he provides no formal mathematical model.

The aim of this paper is to combine into a single econometric model the individual publishing behaviour explained by the life-cycle model together with individual effects and the social capital "model" represented by institutional characteristics variables. This combination will be operated by means of a two level hierarchical model. The paper is organised as follows. After reviewing the traditional human capital model of scientific production and proposing an estimable equation in section 2, we expose in section 3 how individual publishing strategies can be derived from a bibliometric data base and used to model individual fixed effects. In section 4, we show how the notion of social capital and its two accepted definitions can be transposed to the framework of economics of science. The next section is devoted to identifying institution variables which characterise scientific cooperation and social capital using bibliometric data bases. Section 6 reviews hierarchical linear models of [START_REF] Lindley | Bayes estimates for the linear model[END_REF] and [START_REF] Raudenbush | Hierarchical Linear Models: Applications and Data Analysis Methods[END_REF]. In section 7, we estimate our econometric model on a sample of European economists coming from fourteen different European countries and covering the period 1991-2007. In section 8, we show how these models can be used to rank economic departments. Section 9 concludes.

A model of life-cycle productivity for scientists

Most of the human capital models explaining the research productivity of scientists are based on the model in continuous time of [START_REF] Ben-Porath | The production of human capital and the life cycle of earnings[END_REF]. This model describes the accumulation of human capital and explains the life-cycle profile of earnings. Individuals invest in their human capital when they are young, anticipating future earnings. They continue to invest in their human capital after their initial formation, but at a lower rate which becomes zero at the end of their career. For instance the model used in [START_REF] Levin | Research productivity over the life cycle: Evidence for academic scientists[END_REF] is based on this theoretical framework. However, when it comes to estimation, we have to consider discrete time and calendar years. So instead of linearising a model initially devised in continuous time, we prefer to start directly from an economic model specified in discrete time and will follow, at least partly [START_REF] Diamond | An economic model of the life-cycle research productivity of scientists[END_REF] and adapt ideas taken in [START_REF] Diamond | An optimal control model of the life-cycle research productivity of scientists[END_REF], [START_REF] Mcdowell | Obsolescence of knowledge and career publication profiles: Some evidence of differences among fields in costs of interrupted careers[END_REF] and [START_REF] Heckman | Fifty years of Mincer earnings regressions[END_REF].

Intertemporal optimisation

In models for explaining scientific production, the main decision variable is s t ∈ [0, 1] which allocates time within a year between using human capital K t in a proportion (1 -s t ) for earning money and in a proportion s t for augmenting the existing stock of human capital. In academia, (1 -s t ) is the proportion of time devoted to routine academic occupation such as teaching, supervising PhD students, refereeing papers, participating to administrative tasks, while s t is the proportion of time devoted to the writing of articles or books that will increase the prestige of the scientist, her number of citations, the recognition she has from her peers. The production function for supplementary human capital Q t takes the simple form

Q t = β(s t K t ) α .
(1)

In [START_REF] Diamond | An optimal control model of the life-cycle research productivity of scientists[END_REF], human capital is seen as the prestige gained by a scientist and measured by the citations that other scientists make to her work. Due to the continuous progress of science, citations decrease over time and human capital experiences an obsolescence at rate δ so that the yearly variation of K t is given by

∆K t = -δK t-1 + Q t-1 . (2)
The objective function of the scientist is assumed to be the maximisation of her discounted future income. Current income Y t is provided by the exercise of her routine academic work, which consists globally in renting her human capital for a unit wage w

Y t = w(1 -s t )K t . (3)
This assumption is coherent with the observation that wages in academia do not depend directly on current scientific production, but mostly on routine academic work. Scientific output is primordial only for promotion or tenure acquisition. In the initial period of formation, Y t = 0 because s t = 1. In the second period of scientific activity, s t < 1, because this is the period when money is earned. With an actualisation rate of r, the objective function simply writes:

U = T t 1 (1 + r) t w(1 -s t )K t , (4)
T corresponding to the age of retirement. [START_REF] Diamond | An economic model of the life-cycle research productivity of scientists[END_REF] notices that with a general production function, the maximisation of U implies that s t will decrease as t → T . In order to formalise this life-cycle effect, we shall follow the procedure used in the derivation of a Mincer wage equation as detailed in [START_REF] Heckman | Fifty years of Mincer earnings regressions[END_REF]. We will thus propose for s t an had hoc expression which fulfils the time diminishing property. The derivation of a complete model in continuous time is proposed in the appendix.

An explicit solution

Let us first solve by successive substitutions the combination of (1) and (2) for α = 1 so as to obtain:

K t = t-1 j=0 (1 + βs j -δ)K 0 . (5)
Distinguishing between a first period of formation where s t = 1, devoted to the writing of the PhD dissertation and a second period where s t < 1 and using logs, we have

log K t = log K 0 + p-1 j=0 log(1 + β -δ) + t-1 j=p log(1 + βs j -δ). (6)
The first period lasts p years while the maximum length of the second period is Tp years. Using the approximation log(1 + x) ≃ x, we get

log K t ≃ log K 0 + p(β -δ) -(t -p -1)δ + β t-1 j=p s j , (7)
or expressed in term of academic experience e = tp:

log K t ≃ log K 0 + p(β -δ) -(e -1)δ + β e-1 j=0 s j+p , (8)
We now introduce the assumption that s t is time decreasing with the following linear expression

s e = κ(1 - e T -p ), (9)
so that s T -p = 0. The optimal capital stock is given by:

log K t = log K 0 + p(β -δ) + δ + e(βκ(1 + 1 2(T ) ) -δ) -e 2 1 2(T ) , (10)
as e-1 j=0 (1 -j/(Tp) = e(1 + 1/2(Tp)) -e 2 /2(Tp). Its variation in percentage being:

∆ log K t = -δ + βκ(1 - t -p -1 T -p ).
The stock of capital decreases linearly due to the effect of depreciation and of diminishing investment.

An estimable equation

The log of the human capital stock of a scientist with experience e at time t is a function of her initial conditions (log K 0 ), a term related to the initial period of formation (p(βδ)), a trend and a squared trend in experience.

In usual Mincer equations, p represents the number of years of schooling.

In science, the period of formation is entirely devoted to writing a PhD dissertation and we can suppose that this period is identical for everybody. However, because of the secular progress of science, the date of the PhD can be of importance. It is usually supposed that younger cohorts are more productive than older ones. At least, this has to be tested. [START_REF] Levin | Research productivity over the life cycle: Evidence for academic scientists[END_REF] introduce individual fixed effects in one of their equation, which is possible in their case because of the panel structure of their model. We have not this possibility here as our equation explains a stock of capital measured at the end of a period. So we have to introduce individual characteristics by mean of exogenous variables x i to be determined later on. We have finally an estimable equation of the following form where i denotes an individual:

log K i = β 0 + ρp i + β 1 e i -β 2 e 2 i + x ′ i β + v i . ( 11
)
β 0 is a constant term measuring a global mean score, p i the date of PhD for individual i, e i is her academic experience and x i a set of personal characteristics. The dependant variable is a stock of weighted publications. In order to give flesh to these variables, we have now to discuss the content of our data base.

3 The data base and its informational content

Formally, the information we need to estimate this first model would be contained in three different data bases: a list of PhD recipients, a list of department members and a bibliographical data base, such as that provided for instance by the Web of Science. [START_REF] Levin | Research productivity over the life cycle: Evidence for academic scientists[END_REF] underlined that for matching those three files, they had to ask the help of the National Research Council, because of the confidential nature of some of the lists. In this paper, we claim that most of the information we need is contained in bibliographical data bases, provided the latter includes affiliations. We shall use the ECONLIT data base, because it is the only one to contain detailed affiliations (the SSCI and SCI do not). We have thus to restrain ourselves to the economic profession. Our data cover the period 1991-2007 which represents a maximum span of 17 years. 1 We have selected in the data base fourteen European countries, Austria, Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy, the Netherlands, Spain, Sweden, Switzerland and the UK. They represent the major EEC countries having an important higher education sector.

Measuring individual scores and experience

The stock of human capital is difficult to define and to measure. Both [START_REF] Mcdowell | Obsolescence of knowledge and career publication profiles: Some evidence of differences among fields in costs of interrupted careers[END_REF] and [START_REF] Levin | Research productivity over the life cycle: Evidence for academic scientists[END_REF] have chosen to estimate a production equation where the dependent variable is the number of publications in a given year. For measuring the stock of human capital, (2) favours a measure based on the discounted sum of weighted publications. We want to take into account the obsolescence of knowledge. A paper written 20 years ago for an active researcher has less value than an article written last year. [START_REF] Mcdowell | Obsolescence of knowledge and career publication profiles: Some evidence of differences among fields in costs of interrupted careers[END_REF] has estimated the yearly obsolescence of a paper in different fields using the data of the Journal Citation Reports. He found δ = 13% for economics. With this assumption, we have

K i = lpy i t=f py i n it j=1 v j (1 -δ) lpy i -t+1 . ( 12
)
In this formula, n it is the number of articles published by author i in year t; v j an index measuring the quality of the journal: 1 for low quality till 10 for the narrow list of top journals. f py i and lpy i are respectively the first and last publishing years of author i.

We have used different values of δ according to the journal in which a paper is published. Papers in top journals have on average a longer citation life than papers published in lower ranked journals. The JCR publishes for each journal a half life citation indicator. We used it to compute a variable discount rate which covers the range [6.67, 50%], δ = 1 -exp(log(0.50)/half-life). For journals not in the JCR, we took the mean of their category. [START_REF] Levin | Research productivity over the life cycle: Evidence for academic scientists[END_REF] have a complete view of the experience of each author by having access: first to a list of PhD recipients with the date of their PhD, second to a member list for five top US universities and third to publication lists of the Web of Science. But they have introduced a selection bias because they selected only a very small portion of the PhD receivers; they had to introduce a correction for this selection bias. We have no selection bias because we consider all authors that have declared an academic affiliation in the ECONLIT data base. However, we do not know when a person started her academic career or the date of her PhD. We know only her first date of publication F P Y i and her last date of publication LP Y i . We assume that F P Y i is the starting year of scientific career. For the observed ending year of career, we have two possibilities. Either we take the date of the end of the sample or we take LP Y i , the date of the last publication. For the while, we have decided to measure total experience e i as:

e i = LP Y i -F P Y i + 1.
As we are considering a specific period of time (1991)(1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)), e i measures the time needed to accumulate a given stock of publications. It does not measure exactly academic experience, because the data base does not include for instance book chapters and so does not measure the complete output.

The need to trim the data base

When appearing in the ECONLIT data base, an author can be a regular academic member, a PhD student, a visitor or even an author with no academic affiliation. This make a much greater number of individuals than the one given by academic affiliation lists. Even if we eliminate the authors that have no academic affiliation, the data base still contains too many persons. Table 1 shows that there is a huge difference between the content of ECONLIT and for instance the number of economists that have registered in REPEC. That difference would be even larger when compared to the number of persons holding an academic tenure. For instance, in their study [START_REF] Henrekson | How should research performance be measured? The Manchester School[END_REF] report a mere total of 90 Swedish economic professors, to be compared to the 1 601 initial records of our data base. We have decided to eliminate authors with a too low activity. The chosen criterion is K i /e i < 1.5. This corresponds to eliminating authors who publish less than three lowest graded papers in two years when δ = 0. With this rule, we get figures that are not too far from those of REPEC. And we have eliminated more than half of the initial sample.

Cohorts

We identified a vintage to the first year of publication. The empirical distribution of F P Y , graphed in Figure 1, illustrates the general slightly increasing number of entries in the profession at the European level. A vintage effect is usually difficult to identify because we have the linear relation calendar time = experience + Vintage.

We can introduce the first year of publication as an explanatory variable together with experience as suggested in (11). The usual practice (see e.g. [START_REF] Levin | Research productivity over the life cycle: Evidence for academic scientists[END_REF] or Rauber and Ursprung 2008) is to build dummy variables corresponding intervals of several years, for instance four years for each vintage. The dummy will be one if the first year of publication falls into the corresponding interval, zero otherwise. We have a sample of 17 years, which means three cohorts of four years (the average time for preparing a PhD) and one cohort of five years. We have taken 1991-1994, 1995-1999, 2000-2003 and 2004-2007.

Individual characteristics

Bibliometric data bases can provide much information on the individuals characteristics x ij introduced in (11), in particular concerning their publishing strategies. We can distinguish between the choice of support of publication (national journal, top journal) and their type of collaboration (publishing alone, having international coauthors, choosing coauthors only in the same institution). Among the more than 1200 journals available for publication in economics, we have pointed out two categories. The first category corresponds to top journals in the field. The six top journals in economics are supposed to be American Economic Review, Econometrica, Journal of Economic Theory, Journal of Political Economy, Quarterly Journal of Economics, Review of Economic Studies. They are graded 10 on the scale used in [START_REF] Lubrano | Ranking European economics departments: a statistical approach[END_REF].2 An author having achieved to get such publications is supposed to be a potential leader in her institution. We constructed a first variable called P 10 i which is 1 if an author has managed to publish at least one article in that short list over the whole period and 0 otherwise.

The second category of journals that we pointed out are national journals.3 Authors publishing mostly in national journals favour national networks and thus avoid international competition. What is the consequence of this practice on their total output? We have computed P nj i as the proportion of articles that an author has published in national journals.

As research is a risky activity, there is an increasing tendency to publish papers with a greater number of coauthors. But this choice is not uniform among the disciplines. The number and the characteristics of coauthors is a decision variable reflecting a particular type of collaboration or absence of collaboration.

-We have defined P al i as the proportion of papers that an author has written alone, reflecting thus the absence of collaboration.

-Conversely, P si i measures the proportion of papers that an author has written with all coauthors belonging to the same institution. It is an indication of the absence of collaboration with the outside world.

-On the contrary, P int i measures the proportion of papers that an author has published with at least one foreign coauthor. This last variable measures international cooperation, but also the belonging to outside social networks.4

An empirical question is then to know if these publishing habit variables explain and replace the cohort effects. Before examining this question, we have to introduce a new concept, that of social capital and see its operation in the field of economics of science.

Social capital and scientific organisation

The life-cycle model gives a rational principle for individual action. But it does not say anything about the institutional framework that facilitates, shapes or limit individual actions. Contrary to physical capital, human capital is expandable and self generating with use. It is transportable and shareable. For instance, [START_REF] Coleman | Social capital in the creation of human capital[END_REF] shows how the initial accumulation of human capital relies on social context with the example of education. In our case, we could ask the question what is a good place for writing a PhD? We have to characterise the influence of the context on the production of scientific knowledge. A department is not a mere collection of individuals, there is something more that can be called the social capital of the department. Following a branch of the sociological literature initiated by [START_REF] Bourdieu | Le capital social: Notes provisoires[END_REF], [START_REF] Coleman | Social capital in the creation of human capital[END_REF] and [START_REF] Putnam | Bowling alone: America's declining social capital[END_REF], we would like to characterise what could be the notion of social capital applied in the domain of the economics of science. We shall propose in a next section how to measure it.

Two definitions of social capital

Following [START_REF] Coleman | Social capital in the creation of human capital[END_REF], social capital is defined by its functions which are to facilitate individual actions that otherwise would be either more difficult or even impossible to achieve. When we try to go beyond this generality, we discover that social capital can receive two types of contradictory definitions as discussed in [START_REF] Siisiäinen | Two concepts of social capital: Bourdieu vs[END_REF]. For [START_REF] Bourdieu | Le capital social: Notes provisoires[END_REF][START_REF] Bourdieu | The forms of social capital[END_REF], the social capital is simply the value of an individual social network. This network is used as a resource in social competition and social reproduction. It explains unequal achievements of otherwise equal individuals. On the contrary, for the American tradition represented among others by [START_REF] Coleman | Social capital in the creation of human capital[END_REF] and [START_REF] Putnam | Bowling alone: America's declining social capital[END_REF], social capital is a collective good made of moral obligations and norms, social values and social networks. A society with a high level of social capital is an integrated society, functioning on trust and collaboration. [START_REF] Coleman | Social capital in the creation of human capital[END_REF] demonstrated the importance of social capital in the process of human capital accumulation using the example of education. He pointed out the influence of a collaborative attitude of parents helping children for their homework to illustrate the influence of social capital at the family level. At the public level, he noted the very small dropout rate of students in catholic schools compared to public schools, explaining this by a common ideology of solidarity. Bourdieu on the contrary is very skeptical with respect to altruistic actions. They cannot be free of any specific interest of the actor. Individuals are engaged in social competition and do not value altruism. His position is thus totaly opposed to Putnam's and Coleman's romantic ideas of generalised trust.

If the theory of human capital has been widely used (and criticised) for explaining scientific production, the theory of social capital has rarely been applied in the field of economics of science as underlined by [START_REF] Bozeman | Scientific and technical human capital: an alternative model for research evaluation[END_REF]. This last paper proposes to use some measures of social capital when evaluating research projects.

Social capital and scientific collaboration

This dual conception of social capital matches perfectly the opposition that exists in science between collaboration and competition. As we recalled in the introduction, scientific research is motivated by peer recognition, collaboration, co-authorship, but at the same time by a race for being the first. In a way or in another, social capital is imbedded in departments and universities characteristics. Researchers have networks, invite visitors, attend seminars thanks to their university. The question is to know whether competition is between departments and collaboration inside departments or whether there is competition everywhere. In hard sciences, we can suppose that competition is limited to competition between departments as the exploitation of large equipments need collaboration. [START_REF] Kim | Are elite universities losing their competitive edge?[END_REF] found that the specific university effect on researcher productivity has declined over the last three decades even if top departments still manage to concentrate top researchers. However, [START_REF] Kim | Are elite universities losing their competitive edge?[END_REF] consider only the case of economics and finance faculties. This would lead to think that there is more competition than collaboration in these departments. We can have doubts on extending this interpretation to other departments. [START_REF] Coleman | Social capital in the creation of human capital[END_REF] details three forms of social capital: obligations and expectations, information channels, and social norms. [START_REF] Coleman | Foundation of Social Theory[END_REF] introduces a fourth one with authority relations. We have three quasi identical components in [START_REF] Putnam | Bowling alone: America's declining social capital[END_REF]'s concept of social capital: social values such as trust, social networks (especially voluntary associations) and moral obligations and norms (see [START_REF] Siisiäinen | Two concepts of social capital: Bourdieu vs[END_REF]. We shall now review these general characteristics and see how they can be transcribed in the field of economics of science, showing each time the possible bent induced by scientific competition.

1. obligations and expectations, trust and cooperation: you help somebody once and you expect that in the future she will help you in the same way if necessary. This is mutual reciprocity and trust. At a department level, the best example is given by the relations between a superviser and a PhD student where altruism plays a major role. The PhD student expect good guidance, the professor expect good work and outside recognition. Relations between colleagues of the same department can be an illustration too. You discuss with a colleague concerning a problem for which you need help. That colleague gives you help and ideas. She then might expect either the same kind of service in the future or being the co-author of your work if the discussion goes far enough. But competition between two academics working on the same topic can also exist.

Information channels:

A community facilitates communication and general information. Collecting information is costly while being strategic; the group can provide it. In scientific communities, it is impossible to read all journals in order to maintain up-to-date information: the knowledge of the most recent research. Institutions organise seminars and conferences in order to diffuse this information. This lead to meet researchers outside the department and possibly to start new networks.

3. Social networks: Science is a risky activity, so that co-authorship can be seen as an insurance against risk. A social network is built by gaining new co-authors, either inside the same department, or outside it as a result of conferences, seminars. So the institution, by facilitation inside and outside communication, helps academics to build their social networks. This raises the question of individual mobility and its benefit to the department which may loose members in the process.

4. Authority relations: a skillful leadership in a group that is fully accepted and enhance the performance of everybody. At a department level, this is illustrated by the role that a scientific leader can play. This is a top researcher who initiates new lines of research, write papers with other members of the group and has a decisive role in scientific animation and in attracting new people. But also, the presence of a leader can lead to sterile competition and prevent younger researcher to take their full dimension (Matthew's effect). The importance of books is for instance declining in economics at the advantage of articles. Finally, the social norm publish or perish plays a fundamental role in scientific development. This is an internal norm in a social group, an unwritten norm which became explicit recently in some top departments. This social norm can lead to positive behaviours. By forcing to a given level of publishing quality, it can favour the building of new networks. But it can also lead to competition between groups or between single authors leading to writing papers alone when one is convinced to have the right idea and does not want to share it with others.

We now detail how we can build indicators from bibliographical data bases that give an account of these notions.

Tracking social capital in bibliometric data bases

Bibliographic data bases can provide information that goes far beyond counting publications, provided we exploit them on a relatively long period. We have seen how they can provide information on individuals' characteristics. They can also provide information on the main characteristics of the institutions housing the individual researchers. But of course, we will not be able to measure all the five features of social capital described in section 4.

Allocating authors to an institution

We are interested in measuring the common characteristics of the human capital hosted by an institution at the end of the period of observation. If we had affiliations lists, we could know exactly the composition of a department at a given date. However, we have no such lists and lists available on the web are sometime hard to interpret because they include permanent members, visitors and associate members. We think that an author knows her affiliation when she declares it. We have chosen to affect an author according to a rule based on her last declared affiliation.

When an author arrives in a new institution, she comes in with all her stock of past publications, so that in our model K i represents the total stock of human capital of an author at the end of the period of observation, whatever his past affiliations. This stock will be explained by personal characteristics and by the characteristics (or social capital) of her present affiliation.

The rule of the last declared affiliation for affecting an author to a department has to be applied with caution. First, there are errors in the data base so that the last declared affiliation might not be the real affiliation, coherent with the past declared affiliations. Second, we are going to explain a stock of publications. If an author has just moved to a new affiliation, her stock might not be so related with the characteristics of her new affiliation. Considering these two reasons, we have designed the following procedure:

-An affiliation is a valid affiliation if the author declared that affiliation at least for two different years, not necessarily consecutive. This definition applies only to authors with at least four years of experience.

For those with three years of experience or less, we just consider all of their affiliations as valid. This protocol should eliminate some of the errors contained in the data base.

-An author is affected to a given valid affiliation if the last publication year in this affiliation is either the author's last publication year or the preceding year.

Measuring the social capital of an institution

As social capital is a collection of social relations inside a department that facilitates individual scientific production by means of collaboration and of social networks, we can imagine that there is a positive correlation between the production of the different members of the same department and that this correlation could measure the importance of collaborative social capital in a department. The difference of individual performance between departments can be explained by a series of factors characterising differences in social capital allocation.

-Interactions between authors can be favoured by the size of a department. Below a minimal size, the possibilities of cooperation are nearly zero. But cooperation can be also impeded by the anonymity created by a too large number of colleagues. We call N z j the total number of active authors affiliated to department j.5

-The presence of a leader can have a tremendous effect, both by attracting other top researchers and for supervising PhD students. We can identify a top researcher and perhaps a leader by noting if she belongs to the small circle of authors having published at least one paper in a top journal. The variable N 10 j indicates the total number of top researchers affiliated to a department.

-The history of a department can be tracked by the number of top researchers that it has managed to attract in the past and that have left it. We measure it with N m10 j . There is apparently a strong correlation between N 10 j and N m10 j , meaning that present performance of a department is a function of its past achievements.

-With N mul j , we measure the proportion of authors having a current multiple affiliation in a department. This might be a sign of a lack of personal investment to the social capital of the department.

-The degree of openness to international cooperation can be measured by the proportion of articles inside the institution which were written with at least one foreign coauthor. We call this variable N int j . -The mean seniority in the department is also an important characterisation. Is the department composed mainly of seniors or of juniors? N ea j measures the mean total publishing experience of active members of a department, while N ei j corresponds to the mean affiliation length in this institution.

-The degree of cooperation inside a department can be measured by two antinomic variables: the proportion of papers that are produced alone N al j and the proportion of papers that are written with co-authors belonging all to the same department N sia j .

Exploring the social characteristics of departments

Most of the previous variables are supposed to have a positive influence on the accumulation of human capital. It is useful to analyse the correlation matrix between these nine variables in order to statistically figure out positive associations and to check also for the coherency of these.

We have 502 departments. We reproduce the correlation matrix, keeping only the significant correlations. The inspection of Table 2 shows that negative correlation usually results from a mechanical effect and thus are not to be commented.

-N al, the proportion of papers written alone is correlated with no other variable. This seems to be a pure individual characteristics.

-N sia, representing inside collaboration depends positively on the size N z and on N ei the mean duration of affiliation in the institution, indicating that it takes time to create fruitful inside collaboration.

-N 10, the number of current top authors depends positively again on the size, the history of the department(represented by the number of leaders that have left), N int the degree of international collaboration, N ei the mean affiliation time in the institution and N ea the mean total experience.

-There is a large inertia in the history of institutions as N m10 and N 10 are strongly correlated (0.90), and they are correlated with the same variables. Top authors know the glorious past of an institution which has a virtuous signaling effect.

-N int represents international collaboration and depends positively again on the size N z, the number of leaders N 10, the history of the department N m10 and the proportion of multiple affiliations N mul.

Former researchers keep relations with their former institution and multiple affiliations can be a by-product of this collaboration.

-N ei, the mean affiliation time, may be interpreted as the ability of the institution to keep its members. It depends positively on the size N z, the number of leaders N 10, N m10 the history of the institution, N sia the ability of people to work together inside the institution, not on international collaboration, and on N ea the total mean experience.

-N mul, multiple affiliations seems to be an historical by product of N m10, of international collaboration N int and of total experience N ea.

As a summary, we have a bundle of positive association between size, international collaboration, the attraction of new top researchers, institution reputation. We expect these variables to have a positive impact on scientific production. But we have at the same time negative by-products as multiple affiliations, which are associated to the dispersion of social capital, are also positively correlated with past history, international collaboration and total experience.

Individual mobility

Individual mobility was identified by [START_REF] Putnam | Bowling alone: America's declining social capital[END_REF] as a factor explaining the decrease in US social capital. In his case, mobility endamages existing networks and volunteer associations. Can we conclude that mobility of researchers between different universities indicates a lack of collective investment of the researcher in her institution? Or does mobility correspond to the dissemination of new ideas and thus benefits to the hosting institution which welcomes a new researcher? We have here an example where the specificity of academic science can imply totally different consequences.

Mobility can easily be tracked by means of the declared affiliations. There is mobility whenever the last affiliation is different from the previous or initial affiliation. We can identify two types of individual mobility: P mi i indicates past mobility inside the same country; P mo i indicates mobility between two different countries. Finally, we have noted with P mul i the fact that an author has multiple affiliations. In Table 3, we have reported Column 2 gives the number of active authors in the country and column 3 the number of authors having published at least one paper in a top journal. Mobility is indicated as the percentage of these publishing authors that have moved at least once. P mi i and P mo i correspond to the columns marked All.

the percentage of authors that had a national or an international mobility. We made that computation for all researchers and for top researchers separately. We have obtained a contrasted sketch of individual mobility in Europe. Most authors never change, except eventually in countries like France, Italy and Switzerland. In France and in Italy, the centralised procedure for recruiting based on the Napoleonian model of organisation may be an explanation. When we turn to top authors, the picture becomes totally different. Most authors do change, except in Austria, Spain and Sweden.

In small countries that share a common language with an immediate neighbouring large country like Belgium, Finland, Ireland and Switzerland, top authors move most often for a foreign country. This also the case for Greece.

In other countries, top authors move in a comparable proportion inside their country and for a foreign country.

Hierarchical multilevel models

Hierarchical linear models were designed to model observations that are regrouped into clusters. The main domain of application in economics is school achievement where individuals are scholars endowed with a measure of schooling performance and clusters are schools (see the US High School and Beyond data set from The National Center for Education Statistics and the survey article of [START_REF] Goldstein | League tables and their limitations: Statistical issues in comparisons of institutional performance[END_REF]. Hierarchical linear models will be the device that we shall use to mix together the log linear individual life-cycle model with the theory of social capital that consider the individual in her environment. To quote [START_REF] Coleman | Social capital in the creation of human capital[END_REF] "The conception of social capital as a resource for action is one way of introducing social structure into the rational action paradigm". He illustrates his demonstration using an example concerning high school dropouts. He showed that Catholic schools had a lower rate of drop out than public schools, explaining this difference by a common background both at the school and the parent levels. The same data were analysed, with similar conclusions in Raudenbush and Bryk (2002) using linear hierarchical models. We shall follow the same route, showing how individual decision parameters of the life-cycle model are modified by contextual variables at the department level and can thus contribute to explain the variability of scientific production.

A simple model with random effects

Let us consider log of the total score K ij of an individual i belonging to institution j and measured at the end of the period. Our regression model is log

K ij = β 0 + β 1 e ij + β 2 e 2 ij + x ′ ij β + v ij v ij ∼ N (0, σ 2 ). ( 13
)
The log score is explained by a constant term and a set of predictors, all observed at the individual level. These variables are on one side the lifecycle variables (experience and cohort dummies), and on the other side variables representing the individual network characteristics and publishing habits. These variables indicate how the individual has made use of her social capital (collaborations and network).

Authors are regrouped into departments (or clusters) where they can share unobserved common individual features, due for instance to a particular recruiting policy but also a place where they share a common social capital. The first way of introducing the possibility of a department effect is to consider a specific constant term per institution called β 0j . In a random effect model, the β 0j are normally distributed with mean β 0 and variance ω 2 while being independent of the v ij . We have thus a hierarchical structure, here represented in a simplified manner as:

log K ij = β 0j + x ′ ij β + v ij v ij ∼ N (0, σ 2 ) β 0j = β 0 + u j u j ∼ N (0, ω 2 ), u j ⊥v ij , (14)
This model introduces a correlation between individuals inside the same department which is given by

ρ = ω 2 ω 2 + σ 2 . ( 15
)
The higher this correlation, the higher will be the unobserved sharing of a common social capital. We must note that this variance decomposition assumes that u j ⊥v ij and β 0j ⊥v ij . The interpretation of constant terms in this model depends heavily on the metric which is used for measuring the predictors. β 0 represents the average score of all the departments while β 0j represents the average score of department j. This interpretation is valid when all the predictors are set equal to zero. This particular value of zero might be meaningful for most variables, but certainly not for experience that has to be strictly positive. In order to recover a clear interpretation for the constant terms, the predictors are usually centered around a common value, usually their sample mean. We have the choice between centering around the grand mean (the mean of the whole sample) or around the local mean (the institution or cluster mean). When the predictors are centered around their local mean, β 0j = β 0 + u j represents the cluster mean of the log individual scores when the predictors are taken equal to their local mean. More precisely:

log K ij = β 0j + (x ′ ij -X′ .j )β + v ij (16)
where X.j is a vector of empirical means computed over i for a given j. The u j = β 0j -β 0 represent the deviation of the department means from the grand mean. The u j can be used to rank departments according to their mean score. This is the usual way to rank schools (see e.g. [START_REF] Goldstein | Using examination results as indicators of school and college performance[END_REF]. How to center the predictors constitutes a large debate in the applied literature, see for instance Raudenbush and Bryk (2002, page 31). Because it cannot be zero, the experience predictor e ij is centered around a given value L. We have chosen to center it around L = 1, so the obtained mean score will be that of authors having one year of experience, which is the modal value in many countries of our sample.

A more general model

Cooperative social capital variables are introduced at the department level. They modify the potentialities of the individuals, which means either their mean score or the yield of their experience. We regroup in z j these surrounding variables.6 Introducing a second random effect, for instance on experience, the enlarged model is log

K ij = β 0j + ẽij β 1j + ẽ2 ij β 2 + xij β + v ij β 0j = β 0 + z j γ 0 + u 0j β 1j = β 1 + z j γ 1 + u 1j . ( 17
)
where ẽij is experience centered around L and xij are the other predictors centered around their local mean. This model says that individual scores vary around a local mean β 0j , the mean department score, according to experience and individual characteristics xij . The local mean β 0j varies around the grand mean and this variation depends on department characteristics z j . The yield of individual experience β 1j varies around a global mean β 1 and this variation depends also on department characteristics.

Both u 0j and u 1j are independent of v ij . But u 0j and u 1j can be correlated. If u j is the vector formed by the concatenation of u 0j and u 1j , we have u j ∼ N(0, Ω). ( 18) u 0j indicates how much the mean log score of department j deviates from the grand mean β 0 , conditionally on z j . u 1j indicates how much the average yield of a supplementary year of experience deviates from its average β 1 , conditionally on z j . A positive correlation would mean that the higher the average score of the department is, the higher the return to one year of experience. Model ( 17) can be expressed in a reduced form which is convenient for estimation:

log K ij = β 0 + ẽij β 1 + ẽ2 ij β 2 + xij β +z j γ 0 + ẽij z j γ 1 + u 0j + ẽij u 1j + v ij .
Note the rather complex structure of the error term u 0j + ẽij u 1j +v ij and the fact that level-two variables appear in a product with the predictors. Due to the particular structure of the error term, this model has to be estimated using either iterated GLS, the EM algorithm or a Gibbs sampler (see Zeger and Karim 1991 for a Bayesian approach).

Empirical results for Europe

We have a pooled sample of 14 European countries covering 16 750 individuals indexed by i distributed over 512 departments indexed by j. For measuring their capital stock, we have used ( 12) with a δ taken as a function of journal quality. 7

The initial life-cycle model

We first estimate our model allowing for a random effect on the constant term, with the clusters being the departments. The first estimation is simply an analysis of variance:

log K ij = 2.09 [0.014] + v ij + u j -2 log lik = 43 276, BIC = 43 288.
There is definitively a clustering effect because of the large significance of 4. However, 93.9% of the variance is located within the departments and only 6.1% between the departments. So that of course the intra-class correlation is small (ρ = 0.061), which is not uncommon with education data.

Let us now introduce the life-cycle variables and see how this initial variance is reduced. This will be a test of the validity of the initial life-cycle model: 7 Note that in usual bibliometric studies and rankings, δ = 0.

log K ij = 1.46 [0.014] -0.016
The human capital variables (cohorts and experience) have a very high explanatory power. They manage to explain 71% of the variance at the individual level (1-0.220/0.755). The within correlation has increased slightly up to 0.073. Cohort effects are important, the last cohorts being more productive than the initial one by 8 and 10 percent. This surprisingly high explanatory power is due to the fact that we are explaining a stock of publications at the end of a period and not an annual flux. In Figure 2, we illustrate the experience curve and its inverted U shape. The period of estimation covers 17 years and we present these curves for 20 years. If we suppose that career begins at 30, decline in productivity begins around 43. 8 Kim et al. (2009) estimated a decline in productivity after only four years of career in the US, mainly explained by tenure acquisition.

Cohort effects have always been difficult to identify in the literature. For instance [START_REF] Levin | Research productivity over the life cycle: Evidence for academic scientists[END_REF] never found that more recent vintages are more productive than older ones in the US. [START_REF] Rauber | Life cycle and cohort productivity in economic research: The case of Germany[END_REF] quote other references for the US leading to the same conclusion. However, the same Rauber and Ursprung ( 2008) did find a vintage effect for German economists, which they explain by the enormous and recent changes in the organisation of the German academic system. The same type of changes seems to have also occurred in the rest of Europe.

The impact of individual characteristics

Are cohort effects solely a proxy for the change in publishing habits in term of outlet of publication and co-authorship? If in the previous model, we replace the cohort dummies by a set of four publishing habit variables, P nj, P al, P si and P int, we explain 73% of the variance instead of 71%. So publishing habits and co-authorship have a slightly better explanation power than the cohort effect.

Let us introduce the full set of individual variables x ij in the life-cycle model. They regroup the already detailed publication habits, the ability of publishing in top journals and the two mobility variables. They manage to reduce further the individual variance σ 2 by 18% (1-0.180/0.220) while the within correlation stays at 0.070. Estimation results for this model are displayed in Table 5. The cohort effects, which were very significant in the pure life-cycle model, are now reduced to a single dummy, suggesting again that cohort effects were a proxy for the change in publication habits.

Let us now analyse these results in detail:

-Publishing strategies play a very important role in explaining differences of output. In some European countries, the established social norm is or was to publish in national journals. This has a strong negative impact on performance. This should be put in parallel with the findings of [START_REF] Bauwens | The resistible decline of European science[END_REF] concerning the use of English as a scientific vehicle. At the other extreme, being able to publish at least once in a top journal has a very strong impact on the performance of an author and has a high signaling power.

-It is profitable to have individual networks as publishing alone has always a negative impact. But not every network is profitable. Being in the same institution as her co-authors has a small negative impact while choosing foreign co-authors is profitable. This can be interpreted in two ways. Foreign co-authors can be chosen just because they have a higher publishing score and thus illustrate one of the conclusions in [START_REF] Kim | Are elite universities losing their competitive edge?[END_REF]. Or the opposition inside-outside networks shows simply the importance of new ideas in scientific development.

-In the social capital literature (see [START_REF] Putnam | Bowling alone: America's declining social capital[END_REF], mobility has always be seen as a factor decreasing social capital because it breaks social links. Here the effect seems to be just the opposite. Productive researchers have a tendency to be mobile both inside their country and also outside their country. Mobility is a positive factor for bringing in new ideas and the effect is greater for foreign mobility.

The result on mobility should be taken with care. We have seen in Table 3 that mobility was concentrated mostly among top researchers, which creates the possibility of a bias of endogeneity.9 We shall check for this now.

Testing for exogeneity

We can suppose that mobility inside the same country is motivated by administrative reasons and so cannot be endogenous. International mobility on the contrary can be motivated by scientific reasons and authors with a top score have a tendency to be more mobile as shown in Table 3. This table also shows that there are large country differences. We are going to build a two level model explaining international mobility, using the same exogenous variables as in model ( 5) and add instrumental variables. As instruments, we have chosen country dummies (using UK as a reference) plus characteristics of the hosting institution which has managed to attract the new researcher: N m10, N al, N sia, N z, N 10, N ei, N ea, N int, N mul. A specification search produced the results displayed in Table 6 with a random coefficient on the grand mean. From this model, we infer that a department manages to attract foreigners when it has already strong international cooperations (N int), researchers with a strong experience (N ea), not necessarily Let us now introduce the predicted value of the endogenous variable in model ( 5). This is a test of exogeneity. This predicted variable appears with a t value of 0.14 which shows that there is no endogeneity bias for the mobility variable P mo.

Explaining department effects

Individuals do have a different mean score according to which department they belong. But differences in mean score are certainly not the sole random effect as departments can have a specific effect on productivity for instance. We have tried to introduce all random effects whenever they were significant. Starting from an initial model with a BIC = 19 408, we managed to add three extra random effects on the following variables: e, P 10, P mo to reach a BIC = 19 208. The yield of experience varies between departments as well as the efficiency of being able to publish in a top journal and the efficiency of international mobility. The importance and significance of these random effects are indicated in Table 7. At level-two, the total variance is 0.0531 so that differences in mean score still represents 22% of the variance. Differences in international mobility represents 20% of the variance while the capacity to publish in top journals represent the greatest part with 58% of the variance. Differences in experience (measured in years) are a negligible part of the variance even if they are very significant.10 With this simple analysis of variance, we can say that 78% of the differences between departments are due to specific department effects while 22% are due to their capacity in attracting researchers with an important score.

What are the characteristics that explain these differences between departments? We introduce now level-two variables for each of the four leveltwo equations. Section 5.2 has given us hints on the possible nature of these effects. They are indicators related to the nature of the department social capital.

The final list appearing in Table 8 was obtained as follows. We tried the whole list of variables provided in section 5.2 and reduced it sequentially, equation by equation. Among the nine variables proposed in section 5.2, we managed to introduce only six of them: N 10 the number of top authors in the department, N z the size of the department (in term of productive authors), N ei the mean experience within the department, N ea the mean total experience, N int the proportion of papers written with foreign co-authors, N mul the number of authors having multiple affiliations. Other variables were not significant (N al the proportion of papers written alone, N si the proportion of papers written only with members of the same department, N m10 the number of top authors that have left the department). Adding these six variables reduces the level-two variance by 30%.

The mean score of a department β 0j is influenced in a positive way by the number of top authors N 10 who thus play there a leading role. The mean score of a department is also influenced by the proportion of papers written with foreign coauthors N int (with a large coefficient) and by the mean duration in the affiliation N ei. Conversely, the mean number of explicitly declared affiliations has a negative influence on the mean total score. Multiple affiliations in a department corresponds to a scraping of social capital. We have here for science a correspondance with the diagnostic made by [START_REF] Putnam | Bowling alone: America's declining social capital[END_REF] for everyday society.

Variations in the yield of experience, in the yield of being able to publish in top journals and in the yield of mobility still represent 82% of the level-two residual variance. The size of a department positively influences the yield of experience, with however a very small coefficient. The yield of being able to publish in top journals is positively influenced by the number of top authors in the department. We have a collaboration enhancing effect, simply due to the presence of other top authors which does not necessarily goes through effective collaboration. As a matter of fact N sia does not enter the model.

The yield of international mobility P mo enters the model solely in interaction with the mean total experience of members of the department, N ea. Stated otherwise, mobility brings in new idea; when joining a new department, it is better to have stayed abroad. And this effect is larger when the mean seniority of your new department is higher.

Bourdieu or Putnam?

Collaboration or competition? We have a mixed view on the internal structure of a department. Social capital and the scientific collaboration it entails have a clear positive influence on the production of science. However, mobility has to be interpreted in a different way as that of [START_REF] Putnam | Bowling alone: America's declining social capital[END_REF]. Mobility brings in new ideas, while multiple affiliations is a waste for collaboration and personal investment in the functioning of the institution.

Formal inside-collaboration has a negative effect at the individual level while it does not appear at the institutional level. The yield of being able to publish in a top journal is enhanced by the presence of other top researchers in the department, but this does not result necessarily in formal collaboration (as N sia does not enter the model).

International collaboration, both at the personal level and at the institutional level, has a large positive role. But we have also seen in section 5.3 that it was correlated with multiple affiliations, which plays a negative role.

Social capital in the fields of economics of science is a complex phenomenon which mixes contradictory aspects. It is a balance between personal and collective strategies. Personal strategies clearly need collective goods in order to be efficient. But if they are pushed too far with multiple affiliations, they lead to a loss of collective efficiency. This fragile balance is illustrated by some of the findings of [START_REF] Kim | Are elite universities losing their competitive edge?[END_REF] who show that elite US universities (in economics and finance) are loosing their competitive edge as authors affiliated to second rank universities also manage to publish in top journals.

Ranking European economic departments

Mixed linear models are used for combining data collected at different levels and take advantage of particular correlation structures. In the above sections, we have detailed how fixed factors, at the individual level and at the department level, had a significant impact on individual research output. A random effect on the mean indicates how institutions deviate from an average European score. Random effects have been used in the literature to rank institutions. [START_REF] Goldstein | League tables and their limitations: Statistical issues in comparisons of institutional performance[END_REF], [START_REF] Goldstein | Using examination results as indicators of school and college performance[END_REF] are good examples of what can be done in this respect for secondary schools and other public institutions.

Rankings using multilevel models

The best way to understand how these models can be used for ranking is to start from the pure variance component model which includes only an overall constant term (the grand mean) and a random effect which considers random deviations from that grand mean at the institution level. When one wants to rank schools using student results at standardised tests such as those collected in PISA,11 the best school is the one for which the average rate of success or the average grade is the highest. In the pure variance component model of individual scores y ij ,

y ij = β 0j + v ij β 0j = β 0 + u j , (20)
u j represents the gap between the grand mean β 0 and the local mean of school j, so that β 0 + u j can thus be directly used for ranking. Standard deviations are of course necessary to appraise the uncertainty attached to the ranking. In this model, the u j are normally distributed with:

u j ∼ N i (y ij -ȳ.j ) n j + σ 2 /ω 2 , (n j + σ 2 /ω 2 ) -1 (21)
where n j is the number of scholars in school j.

In our case, the grand mean represents the author mean log score computed over the entire population and u j represents the the gap between the grand mean and the mean log score of department j. In order to get the total log score of department j, we must consider an expression like

sct j = (β 0 + u j ) × n j (22)
where n j represents a department size to be discussed later on. Departments are usually ranked according to their total score. Eventually according to the total number of authors. It was shown in [START_REF] Lubrano | Density inference for ranking European research systems in the field of economics[END_REF] that this corresponds to a notion related to stochastic dominance at the order one or two when a minimum level of activity is defined. Ranking departments according to the mean score of their members makes no sense.

The initial model was enriched by adding individual exogenous variables, leading to

y ij = β 0j + x ij β 1 + v ij β 0j = β 0 + u j . (23)
The ranking can be done here according to the same principle, except that this time, the u j are distributed according to:

u j ∼ N i (y ij -x ij β 1 ) n j + σ 2 /ω 2 , (n j + σ 2 /ω 2 ) -1 , (24)
leading to smaller standard deviations than in the pure ANOVA model.

Figure 3: European ranking using a random intercept In Figure 3, we give the ranking of the first thirty European departments, using these two methods. On the left panel, the ranking is obtained using the pure variance component model, while in the right panel we have added individual exogenous variables. There are some marginal variations between the two rankings, especially around the bottom. The ranking which makes use of exogenous variables provides smaller standard errors.

UK-UL-LSE UK-U OXFORD NLD-U ERASMUS UK-U CAMBRIDGE NLD-U TILBURG NLD-U AMSTERDAM UK-U MANCHESTER FRA-U PARIS 1-SORBONNE UK-U NOTTINGHAM NLD-U MAASTRICHT BEL-CATHOLIC U LOUVAIN UK-U YORK FRA-U TOULOUSE UK-U WARWICK UK-UL-UCL NLD-FREE U AMSTERDAM NLD-U GRONINGEN BEL-CATHOLIC U LEUVEN GER-U MANNHEIM DEN-U COPENHAGEN GER-U BONN UK-U READING UK-U BRISTOL UK-U NEWCASTLE SWE-U STOCKHOLM FRA-PSE UK-U SHEFFIELD SPA-U
-UL-LSE UK-U OXFORD NLD-U ERASMUS UK-U CAMBRIDGE NLD-U TILBURG UK-U MANCHESTER NLD-U AMSTERDAM FRA-U PARIS 1-SORBONNE UK-U NOTTINGHAM NLD-U MAASTRICHT BEL-CATHOLIC U LOUVAIN UK-U YORK NLD-FREE U AMSTERDAM UK-U WARWICK UK-UL-UCL FRA-U TOULOUSE NLD-U GRONINGEN BEL-CATHOLIC U LEUVEN GER-U MANNHEIM DEN-U COPENHAGEN GER-U BONN UK-U READING UK-U BRISTOL UK-U NEWCASTLE UK-U SHEFFIELD SWI-ETH-ZURICH SWE-U STOCKHOLM NLD-U WAGENINGEN UK-U LEEDS SWE-STOCKHOLM SC OF ECON
Confidence intervals show that the significant differences are at the top of the ranking, while most of the departments are equivalent when reaching the bottom. With the pure ANOVA model, UK has 14 departments in this ranking, the Netherlands 5, France 3, Belgium 2, Germany 2, Denmark 1, Sweden 1, Spain 1 and Switzerland 1. We have given countries in the rank of their first appearance. Note the performance of the Netherlands that manage to have 40% of its departments in the top 30.

Size effects

In the two rankings given in Figure 3, there is a huge size effect which explains incidently why smaller departments with a high reputation like the European Institute of Florence do not appear favourably, while larger departments like Leeds, Manchester, Nottingham, Groningen or Wageningen have a surprising good position. The size effect appears because we have chosen n j = N z j in ( 22). We could perfectly use another size indicator based on for instance:

n j = N z α j × N 10 1-α j . (25)
N z j represents the total number of productive authors in department j while N 10 j represents the number of top authors present in department j at the end of the period of observation. ( 25) entails a weight of zero if there is no top researcher in a department and then lowers the size effect as a function of α. With α = 1, we recover the previous ranking based solely on N z j . α monitors the trade-off between size N z and quality N 10. We present in Figure 4 two alternative rankings: one with α = 0.50 in the left panel, one with α = 0.10 in the right panel. Already with α = 0.50, the resulting ranking is totally modified. Most of the large departments like Leeds, Manchester, Reading and Sheffield in the UK or Groningen and Wageningen in the Netherlands have left the top thirty group. However, we need α = 0.1 for allowing the small and elitist European Institute to enter the list. With this last value for α, the UK looses some ground with 7, but keeps its first position, France comes next and has 5 ranked departments, Belgian 1, Spain climbs up in the ranking and has 3, the position of the Netherlands drops in the ranking and has 5, Germany 3, Sweden 2, Switzerland 1, Italy 2, Denmark 1 and Austria 1 enters the list.

Ranking and social capital

Ranking is a very crude ordinal operation that usually piles up weighted articles, independently of any type of explanations. We have tried in section 7 to find some of the determinants to scientific production and we have used one of our models to propose rankings with associated confidence intervals. We try now to answer the question concerning the link between rankings and social capital. We have measured the social capital of an institution with nine department variables. How are these variables related to our rankings filiations.12 All rankings are highly correlated with past reputation (N m10).

A greater weight put on quality (a smaller α) corresponds to a greater influence given to international collaboration, a greater weight given to the mean length of affiliation (the ability of an institution to keep its members) and to a smaller extend a greater weight given to total experience.

Conclusion

In this paper, we have shown how to derive a theoretical model of scientific production based on the human capital model. We empirically verified the life-cycle assumption which appears to be an important factor explaining scientific production. However, this simple individual decision model is not sufficient to explain the diversity of scientific productivity. We completed this model by introducing individual characteristics, and by situating the individual action in a social context, namely external networks and the hosting institution. Personal characteristics have a large impact to explain diversity: clearly belonging to the small class of authors being able to publish in top journals is a strong positive marker. Conversely, publishing alone is a negative personal marker.

Personal networks are associated with Bourdieu's view on social capital. We have a kind of selfish use of social networks. International collaboration is profitable for individuals while internal collaboration is not. Personal networks are the occasion of international mobility which brings in new ideas and are profitable for individuals.

At the institutional level, we observe the negative effect of some parts of individual networks. For instance, simultaneous multiple affiliations have no explanatory power at the individual level, but have a negative influence at the collective level. If at the individual level, internal collaboration is negative, at the collective level, there must exist some sort of invisible collaboration because total size, total number of top researchers and mean seniority in the institution have a positive influence. Finally, there exists some common features between individual and collective social capital: international collaboration is profitable at both levels.

The grasp we had about social capital is not perfect. Bibliographical data bases reveal a lot of information concerning authors habits, choices and networks. They are however mute on a tiny part of papers, we mean acknowledgments. Acknowledgements refer to conversations, discussions, information release, comments and improvements made on the paper. They relate to a participation to social capital, not necessarily the social capital of the authors' institution, but sometime yes. This fact was pointed out to us by Tony Atkinson who alluded to some department members who were not productive in the usual meaning of this word, i.e. they did not write many papers, but who contributed very much to the work of others by their remarks and implications. These people are outside any type of statistical evaluation, but clearly belong to the social capital of the institution.

Appendix: A life-cycle model in continuous time

The proposed model in continuous time draws extensively on the papers by [START_REF] Diamond | An optimal control model of the life-cycle research productivity of scientists[END_REF][START_REF] Mcdowell | Obsolescence of knowledge and career publication profiles: Some evidence of differences among fields in costs of interrupted careers[END_REF]. The production function for supplementary human capital Q t has the form of a Cobb-Douglas

Q t = β(s t K t ) α . ( 26
)
The stock of human capital has a rate of obsolescence δ so that

. K t = Q t -δK t . (27)
The objective function of the scientist is to maximise his discounted future income. Current income Y t is given by

Y t = w(1 -s t )K t , (28)
and the present value at age t of disposable future income:

U = T t
e -r(τ -t) Y (τ ) dτ = T t e -r(τ -t) w(1 -s(τ ))K(τ ) dτ,

A solution to this problem is found by writing the Hamiltonian

H = e -rt Y t + λ(Q t -δK t ). ( 30
)
Its solution expresses Q t as a function of the parameters of the model and of the remaining time to retirement, Tt. Production or investment in human capital Q t is a non-linear decreasing function of time with: -t) ). ( 31)

log Q t = 1 1 -α log β + α 1 -α log α δ + r + α 1 -α log(1 -e -(δ+r)(T
The solution in Q t is zero when t = T (the age of retirement). The existence of the solution requires that α < 1 (contrary to our discrete time model where α = 1). When combining this equation with the capital variation equation, K t has an inverted U shape life-cycle profile.

Figure

  Figure 1: First year of publication

  v ij + u j σ 2 = 0.220 ω 2 = 0.0174 -2 log lik = 22 745, BIC = 22 758,(19)

Figure 2 :

 2 Figure 2: Estimated life-cycle and cohorts for all countries

Figure

  Figure 4: European ranking using a composite size

Table 1

 1

		: Sample characteristics
	Country Academic Registered Productive
		authors in REPEC	authors
	Austria	832	243	282
	Belgium	1 729	536	575
	Denmark	904	230	376
	Finland	915	134	243
	France	5 570	1 794	1 767
	Germany	4 897	2 275	1 898
	Greece	1 296	272	375
	Ireland	438	157	181
	Italy	4 132	1 920	1 092
	Netherds	3 480	903	1 682
	Spain	4 704	1 259	1 282
	Sweden	1 601	400	703
	Swiss	1 529	435	508
	UK	12 729	2 324	5 786
	Total	44 756	12 882	16 750

Table 2 :

 2 Correlation matrix for department characteristics

		N z N 10 N m10 N al N sia N int N ei N ea N mul
	N z	1.0 0.78	0.72	-	0.17 0.13 0.31 0.22	-
	N 10	0.78 1.0	0.90	-	-	0.20 0.30 0.24	-
	N m10 0.72 0.90	1.0	-	-	0.19 0.29 0.24 0.11
	N al	-	-	-	1.0	-	-0.25	-	-	-
	N sia 0.17	-	-	-	1.0 -0.19 0.21	-	-0.14
	N int 0.13 0.19	0.18 -0.25 -0.19 1.0	-	-	0.15
	N ei	0.31 0.30	0.29	-	0.21	-	1.0 0.86	-
	N ea	0.22 0.24	0.24	-	-	-	0.86 1.0	0.15
	N mul	-	-	0.11	-	-0.14 0.15	-	0.15	1.0
	Calculations are based on 512 departments. Significance is determined assuming that r √ n -2/ √ 1 -r

2 ∼ t(n -2), using a 5% level of significance.

Table 3 :

 3 Individual mobility within Europe of productive authors

	Country	Authors No change National	Foreign
			mobility	mobility
		All Top All Top All Top All Top
	Austria	270	28 74% 57% 10% 11% 17% 32%
	Belgium	551	52 70% 23% 06% 12% 23% 65%
	Denmark 365	17 78% 41% 13% 35% 10% 24%
	Finland	236	8 78% 25% 11% 25% 11% 50%
	France	1538 162 59% 25% 28% 44% 13% 30%
	Germany 1835 109 77% 43% 13% 25% 10% 32%
	Greece	366	18 68% 33% 11% 11% 21% 56%
	Ireland	154	12 77% 42% 01% 08% 22% 50%
	Italy	1030	94 62% 33% 17% 30% 20% 37%
	Netherds 1628	94 76% 40% 11% 31% 12% 29%
	Spain	1245 126 78% 52% 13% 18% 10% 29%
	Sweden	683	40 85% 65% 09% 18% 06% 18%
	Swiss	486	42 63% 33% 07% 07% 30% 60%
	UK	5573 290 76% 44% 17% 32% 08% 23%

Table 4

 4

			: ANOVA
	Parameter Estimate Std Error Z Value
	σ 2 v ω 2 u	0.755 0.0493	0.0084 0.0055	90.4 8.92
	ρ	0.061
	ω 2 u , given in Table

Table 5 :

 5 life-cycle and social norms in EuropeThe first cohort is taken as the reference. All variables are taken in deviation to their local mean, except for experience which is in deviation to 1. Cohort dummies are treated as the constant term. The constant term (grand mean) measures the average European score (geometric mean). -2 * log lik = 19 395, BIC = 19 407.

	Effect	Estimate Std. Error t or Z Value
	Intercept 1.5196	0.00785	193.57
	Co95-99	-0.0625	0.00808	-7.74
	e	0.2412	0.00262	91.89
	e 2 /10	-0.0855	0.00183	-46.59
	P nj	-0.0042	0.00015	-27.09
	P al	-0.0011	0.00012	-8.63
	P si	-0.0005	0.00012	-4.71
	P int	0.0003	0.00013	2.55
	P 10	0.6623	0.01419	46.68
	P mi	0.1120	0.01012	11.07
	P mo	0.1840	0.01165	15.80
	σ 2 v ω 2 u	0.1808 0.0136	0.001992 0.001510	90.29 9.02
	ρ	0.070

Table 6 :

 6 Decision to join a new department when leaving a foreign country

	Effect Estimate Std. Error t or Z Value
	Cste	-0.09054	0.01958	-4.62
	e	0.02855	0.00168	16.96
	e 2 /10 -0.00902	0.00121	-7.41
	P 10	0.06791	0.00981	6.92
	P al	0.00097	0.00008	11.07
	P sia	0.00055	0.00008	6.39
	P int	0.00210	0.00008	23.72
	Aus	0.05613	0.02355	2.38
	Bel	0.09170	0.02237	4.10
	Fra	0.03875	0.01130	3.43
	Gre	0.07976	0.02012	3.96
	Ita	0.1015	0.01276	7.96
	Nld	0.03836	0.01540	2.49
	Spa	0.05444	0.01373	3.96
	Swi	0.1215	0.02045	5.94
	N al	0.1108	0.03722	2.98
	N int	0.3987	0.03170	12.58
	N ei	-0.04105	0.00676	-6.07
	N ea	0.02766	0.00568	4.87
	σ 2 v ω 2 u	0.08730 0.00176	0.000965 0.000331	90.47 5.32
	ρ	0.020
	gained in the hosting institution (N ei) which suggest the influence of a past
	mobility of the members of the hosting institution.

Table 7 :

 7 Random effects without Z variables

	Parameter Estimate Std Error Z Value
	σ 2 v ω 2 cste ω 2 e ω 2 P 10 ω 2 P mo	0.1738 0.01148 0.00016 0.03082 0.01060 -2 log lik = 19 176, BIC = 19 207 0.00196 88.46 0.00143 8.02 0.00002 5.73 0.00895 3.44 0.00402 2.64

Table 8 :

 8 Random effect and departments characteristicsThe first cohort is taken as the reference. All variables are taken in deviation to their local mean, except for experience which is in deviation to 1. The constant term (grand mean) measures the average European score (geometric mean because of the logs). -2 log lik = 19153, BIC = 19122.

	Effect	Estimate Std. Error t or Z Values
	Intercept	1.5318	0.06450	23.75
	Co00 -07	0.0483	0.00800	6.05
	e	0.2330	0.00283	82.17
	e 2 /10	-0.0830	0.00179	-46.28
	P 10	0.5473	0.02759	19.84
	P nj	-0.0042	0.00015	-26.84
	P al	-0.0011	0.00012	-8.28
	P si	-0.0006	0.00012	-4.87
	P int	0.00033	0.00012	2.54
	P mi	0.1221	0.01016	12.01
	F in	-0.0989	0.03885	-2.55
	F ra	-0.0830	0.02100	-3.96
	Gre	-0.1184	0.03290	-3.60
	Irl	-0.1655	0.05266	-3.14
	N 10	0.0033	0.00087	3.80
	N int	0.2875	0.05826	4.93
	N ei	0.0152	0.00573	2.66
	N mul	-0.1418	0.06078	-2.33
	P 10 * N 10	0.00633	0.00183	3.45
	e * N z	0.000063 0.000015	4.10
	P mo * N ea 0.03724	0.00278	13.38
	σ 2 v 2 cste σ 2 e σ 2 P 10 σ 2 P mo	0.1742 0.00665 0.00013 0.02249 0.00772	0.00196 0.00105 0.00002 0.00761 0.00367	88.47 6.34 5.58 2.95 2.10

We could not consider a longer period, because affiliations are not reported before 1991 in ECONLIT. Note also that ECONLIT was much more difficult to access for bibliometric studies after

For more details on this data base, see[START_REF] Lubrano | Ranking European economics departments: a statistical approach[END_REF].

We could also have chosen the ten top journals in term of total citations in 2008, i.e. American Economic Review, Econometrica, Journal of Political Economy, Quarterly Journal of Economics, Journal of Financial Economics, Journal of Econometrics, Review of Economics and Statistics, Review of Economic Studies, Economic Journal, Journal of Economic Theory.

A national journal can be easy to define, just by looking at the language it uses. But sometimes a national journal turned for English as Economic Notes in Italy or Journal of Economics in Germany or Spanish Economic Review in Spain. For the UK, the matter is more complex. We have to look deeper into the journal. A journal has a national coverage if it serves as a major means of diffusion for national authors. It is considered as mainly national if in addition it does not serve as a major means of diffusion for other countries. A more precise definition is given in[START_REF] Lubrano | Ranking European economics departments: a statistical approach[END_REF].

We also created the variable P mul which indicates multiple affiliations, but it was never significant in the subsequent regressions.

In fact, N zj indicates the total number of active members of a department and whose last affiliation is department j, and not the total number of members of a department because there can be inactive members who are not reported in the data base or who have published in different outlets than journals.

The level-two variables are usually not centered because we are not interested in the interpretation of the grand mean β0 or of β1.

Due to the small span of the data (17 years), we cannot reasonably introduce higher powers to have a more precise shape for the life-cycle productivity as was done for instance in[START_REF] Rauber | Life cycle and cohort productivity in economic research: The case of Germany[END_REF].

This question was raised by Russell Davidson.

There is a scaling effect because our model is formulated in terms of number of years of experience. If we scale it differently, the value of ω 2 e will be different.

OECD Programme for International Student Assessment.

However with a simple linear correlation coefficient, multiple affiliations seems to be inversely related to a better rank.

 9reports the significant correlations between our different rankings and the nine social capital variables.

All rankings seems to be independent of internal collaboration or multiple af- A negative correlation is associated to a better ranking. Correlations were computed for the 212 departments that had at least one top author, as the other departments could not be ranked whenever α < 1. The non-parametric Spearman correlation is used to cope with any type of non-linearity.


Through the use of statistical distribution Data of experience feedback, probability distributions, etc.

Highlighting issues of the problem of uncertainty

Data of experience feedback, probability distributions, etc. Modeling of physico-chemical variables (temperatures, flows, etc.)

Human and Organisational assessment

Through the use of expert judgments Degradation or non degradation of items Presence or absence of POFs Collection of expert judgments in IRA via elicitation grids Collection of expert judgments in IRA via elicitation grids Constrain the expert to choose only one pre-defined single value Objectives How to collect and model the expert's knowledge in a less biased way? How to implements tools to collect and handle expert judgments? Component in « Failure1 » or « Failure 2 » Total ignorance : the expert totally ignores the repartition on the modalities Component state is unknown 9/21 H 1 : no failure H 2 : failure 1 H 3 : failure 2 2 -DCDS'11 -16/06/2011 11/21

Belief (Bel) : degree of credibility on a hypothesis H i Plausibility (Pls) : quantity of belief that would not contradict the hypothesis H i Bel(H i )≤ P(H i ) ≤Pls(H i )

Principle of IRA methodology

Highlighting issues of the problem of uncertainty

Possibility theory [Zadeh, 1977] Intervals theory [Moore,1966] Evidence theory [Dempster,1967]

Uncertainty modeling -Basics

Mutually exclusive and exhaustive

Possible events space

Ω Ω={H 1, …,H q } Probability assignment function p : Ω [0;1] such as p(H i ) = 1
Interval theory [Moore,1966] Deals only with the problems of imprecision

  Poor handling of organisational complexity Production pressures …2 -DCDS'11 -16/06/2011 Bow-tie (Faults Tree + Events Tree) of statistical distribution Data of experience feedback, probability distributions, etc.

  Data of experience feedback, probability distributions, etc. Modeling of physico-chemical variables (temperatures, flows, etc.) Human and Organisational assessment Through the use of expert judgments Degradation or non degradation of items Presence or absence of POFs Collection of expert judgments in IRA via elicitation grids Collection of expert judgments in IRA via elicitation grids Constraint the expert to choose only one pre-defined single value Objectives How to collect and model the expert's knowledge in a less biased way? How to implements tools to collect and handle expert judgments? to natural variability of a physical phenomenon (e.g. failure rates, physico-chimical variables …) Epistemic uncertainty Due to the imprecise or incomplete character of the information or a lack of knowledge 2 -DCDS'11 -16/06/2011 Due to the imprecise or incomplete character of the information or a lack of knowledge (imprecision, ignorance (partial or total), incompleteness) Uncertainty modeling Probabilistic vs. Non-probabilistic theories Probability theory is the usual framework for uncertainty representation Introduction of new uncertainty modeling frameworks in the last decades

  … Aims at better handling the different types of uncertainties 2 -DCDS'11 -16/06/2011 Aims at better handling the different types of uncertainties Can be used to manipulate data from expert judgments

  only with the problems of imprecision Extension of conventional arithmetic operators Consider tree intervals [a], [b] and [c] with bounds [a 1 ;a 2 ], [b 1 ;b 2 ] and [c 1 ;c 2 ] [c] = [a] + [b] then c 1 = a 1 + b 1 and c 2 = a 2 + b 2 [c] = [a] -[b] then c 1 = a 1 -b 1 and c 2 = a 2 -b 2 [c] = [a] * [b] then c 1 = min(a 1 * b 1 ; a 1 * b 2 ; a 2 * b 1 ; a 2 * b 2 ) c 2 = max(a 1 * b 1 ; a 1 * b 2 ; a 2 * b 1 ; a 2 * b 2 ) Focusing on an elementary pattern of IRA Relationship between human and technical components Focus on the assessment of item De by expert judgment (consider item Ai and influencing factors perfectly known) Efficiency of the preparation phase P ? Focusing on an elementary pattern of IRA Relationship between human and technical components Focus on the assessment of item De by expert judgment (consider item Ai and influencing factors perfectly known) Efficiency of the preparation phase P ? Focusing to an elementary pattern of IRA Relationship between human and technical components Focus on the assessment of item De by expert judgment (consider item Ai and influencing factors perfectly known) Efficiency of the preparation phase P ? able to choose with certainty one modality of De Soft evidence The expert encodes his knowledge by attributing a prior distribution on De Imprecision The expert cannot express a precise value 2 -DCDS'11 -16/06/2011 Partial ignorance The expert partially ignores the distribution on the modalities of De Total ignorance The expert totally ignores the repartition on the two modalities of De particular modeling framework or expression form of expert judgment, the risk is to force the expression of expert's of expert judgment, the risk is to force the expression of expert's knowledge Risk of loosing a part of the imperfect expert knowledge by forcing him too strictly Working on unique values when there are intervals may present a possibility of error/bias guided with only one possible choice among predefined values in elicitation grids Not the most suitable for a consistent representation of knowledge owned by the expert Let him express his " real " knowledge helping the expression of expert's judgment To collect at best the knowledge of the experts Including guides, questionnaire, charts, etc. … implement them on a full study on a real industrial application (> hundred nodes) To validate industrially works presented here … provide tools to help the decision-making Most useable not to force the expression of the expert knowledge but to be able to handle various imperfections of his knowledge A with epistemic uncertainty in Bayesian Networks Implementation of Evidence Theory in Baeysian Networks [Simon & Weber] Development of uncertain pattern to take into account both uncertainties Help the knowledge collection and modelisation without biased the expert knowledge Contribute to limiting the uncertain nature of the information collected Contribute to a better assessment of different issues and help decision-making

-DCDS'11 -16/06/2011 6/21

-DCDS'11 -16/06/2011 11/21

-DCDS'11 -16/06/2011

-DCDS'11 -16/06/2011 15/21

-DCDS'11 -16/06/2011 18/21

-DCDS'11 -16/06/2011 20/21

Uncertainty modeling

Five types of knowledge expression

Hard evidence : the expert is able to choose with certainty one hypothesis Component in « Failure 1 » Soft evidence : the expert encodes his knowledge by attributing a prior distribution P(Failure1) = 0.8 / P(Failure2) = 0.2 Imprecision : the expert cannot express a precise value

Uncertainty modeling -Basics

Evidence theory [Dempster,1967] [Shafer,1976] Possible events H i

Mutually exclusive and exhaustive Mutually exclusive and exhaustive

Possible events space Probability theory

Difference depending on the modeling framework …

Knowledge Expression

Interval theory The expert knows that " the occurrence of modality {Present} of the item De is between 0.7 and 0.8 " (imprecision)

Case study -Simulation Collection if imprecision

Modelisation Bias if imprecision

Collection Bias