David De La Croix

Frédéric Docquier

Alice Fabre

Robert Stelter

Thomas Baudin

Simone Bertoli

Matteo Cervellati

Gregory Clark

Zvi Eckstein

Sven Feldman

James Fenske

Martin Fernandez- Sanchez

Mattia Fochesato

Oded Galor

Paola Giuliano

Paula Gobbi

Simone Meraglia

Omer Moav

Simone Moriconi

Luca Pensieroso

Giovanni Peri

Itay Saporta

Yannay Spitzer

Gonzague Vannoorenberghe

Nico Voigtlaender

Romain Wacziarg

Marlous Van Waijenburg

The Academic Market and the Rise of Universities in Medieval and Early Modern Europe ( -) *

Keywords: Upper-Tail Human Capital, Universities, Discrete choice model, Scholars, Publications, Agglomeration. JEL codes: N, O, I

We argue that market forces shaped the geographic distribution of upper-tail human capital across Europe during the Middle Ages, and contributed to bolstering universities at the dawn of the Humanistic and Scienti c Revolutions. We build a unique database of thousands of scholars from university sources covering all of Europe, construct an index of their ability, and map the academic market in the medieval and early modern periods. We show that scholars tended to concentrate in the best universities (agglomeration), that better scholars were more sensitive to the quality of the university (positive sorting) and migrated over greater distances (positive selection). Agglomeration, selection and sorting patterns testify to an integrated academic market, made possible by the use of a common language (Latin).

Introduction

Both scholars and universities are thought to have played a role in the Rise of the West (Mokyr , Cantoni and Yuchtman ). We argue and establish empirically that an integrated academic market in the preindustrial period was a powerful institution allowing them to operate together. This functioning market helped universities harness the potential of upper tail human capital at the dawn of the Humanistic and Scienti c Revolutions as well as, to a lesser extent, during the subsequent European primacy. Our results shed light on the importance of medieval roots in fostering scienti c output, confronting qualitative studies on the subject with unique data sources and sound estimates.

Universities are one of the most original creations of the Western Latin civilization during the Middle Ages, from the th century onwards. They came into existence when society recognized that masters and students as a collective (universitas means community) had legal rights. Universities are voluntary, interest-based, and self-governed permanent associations (Greif ). As highlighted in Rashdall ( ), "such Guilds sprang into existence, like other Guilds, without any express authorisation of King, Pope, Prince, or Prelate. They were spontaneous products of the instinct of association that swept over the towns of Europe in the course of the eleventh and twelfth centuries." A university was thus originally a guild of either students or masters. Near the end of the th century, foreign law students at Bologna formed a union for the purpose of protection from discrimination by the town against foreign residents. At about the same time, teachers in Paris formed a corporation. Universities then began to spread across Europe, either through secession from existing ones (Cambridge from Oxford, Padua from Bologna, Orléans from Paris, etc.), or through creation ex nihilo. Some universities were founded from scratch by a higher authority (the University of Naples was arguably the rst of this kind), but all followed the guild-like organizational principles of Bologna and Paris. Even at the Imperial Moscow University (established in , charter of ), the rector was elected by his peers, not nominated by the emperor.

The European academic world in the medieval and early modern era provides a rich background for identifying location patterns within the upper tail of the skill distribution. The use of Latin facilitated mobility and, despite the political fragmentation of Europe, medieval universities were recognized for their independence and intellectual unity. The integration of the academic market was even formalized via the licentia ubique docendi (licence to teach everywhere), granted by the Church to the universities at the end of the th century, and conferring the right to teach at every university in Europe once a doctoral degree had been awarded (Hermans and Nelissen ). Understanding the mobility of academic scholars in that period matters because it potentially in uenced the creation of knowledge in pre-industrial times, as well as technological and institutional progress. Focusing on a period from CE to CE, our paper investigates whether location decisions were associated with distance and with measures of individual and institutional quality. We distinguish three notions of quality. The human capital of an academic scholar is built from her/his achievements as seen today in the catalog of world libraries (Worldcat). The notability of a university in a given year is built from the human capital of its ve best scholars active just before that year. The simulated output of a university is the aggregation of the human capital of all scholars who were predicted to work there in a given year.

Although the economic literature has looked at the characteristics of migrant workers at di erent periods in history, little is known about the mobility of upper-tail human capital in general, and about the internationalization of medieval and early modern European universities in particular. To tackle this question, we develop a unique database that provides geolocalized information on the origin of thousands of academic scholars, on the location of universities, and on measures of individual human capital and institutional notability. We use it to estimate the e ects of distance, the human capital of scholars, the notability of universities, and the attractiveness of European cities on location decisions. More speci cally, we test (i) whether academic scholars tended to concentrate in the best universities in medieval Europe (agglomeration), (ii) whether those with more human capital were more likely to settle in more prestigious universities and/or in more attractive cities (positive sorting), and (iii) whether they were more mobile than others (positive selection). We nally use our estimated location choice model to compute the potential gains in the output of universities resulting from the agglomeration, positive sorting, and positive selection of academic scholars.

Our database builds on secondary sources (i.e. books and catalogues recovering information from institutional archives) and biographical dictionaries. It documents the mobility and the human capital of about , academic scholars over the whole period -. Their location choice set varies across years, as new universities were created or disappeared over time. On average, each scholar selected his/her optimal place of work out of about possible locations. After excluding scholars with an unknown birthplace and universities with partial coverage, the database used in our regression models includes about . million possible dyads (i.e. scholar-university pairs). By studying the mobility patterns of academic scholars at universities in the medieval and early modern periods, we capture a substantial part of upper-tail human capital. The two other -less numerous -groups were the members of scienti c academies that developed in Europe in the th century (preceded by the Renaissance academies in Italy in the th century), and the scholars making a living at the courts of princes, kings, or bishops.

We estimate the mobility patterns using a multinomial logit model, and several variants accounting for sample biases, heterogeneous e ects, and endogeneity issues. We show that agglomeration forces are at work: the destination choice of academic scholars depended on distance, on the notability of the university, on the size of the city (used as a proxy for its economic development), and on the communal freedom enjoyed by the city (used as a proxy for local democracy). We also nd robust evidence that better scholars were less sensitive to distance (positive selection) and more sensitive to the attractiveness of the university (positive sorting). Agglomeration and sorting patterns testify to the existence of a functioning academic market in We do not observe a clear separation between local and international markets in academia, contrary to most other kinds of markets before the industrial revolution (Polanyi ). In its common meaning, sorting is any process of arranging items systematically, and has two common, yet distinct meanings: ordering (arranging items in a sequence ordered according to a criterion) and categorizing (grouping items with similar properties). In the migration literature, it means that individuals with better attributes tend to concentrate in regions where returns are higher.

In biology, positive natural selection is the force that drives the increase in the prevalence of advantageous traits. In our location choice model, we test whether better scholars are less sensitive to the distance from their birthplace.

Europe.

Among the forces we consider, agglomeration and positive sorting are the most emblematic forces witnessing the competition among universities to attract talent. By attracting the best scholars at the same place, the academic market is a powerful engine to exploit the complementarities between scholars in the production function of universities, and to foster knowledge growth. They played an important role when there were few universities. Agglomeration and sorting substantially helped universities to create knowledge at the dawn of the Scienti c Revolution and during the subsequent European primacy. These e ects became negligible later when the number of universities increased. By contrast, selection patterns tended to scatter talent across universities, and hardly in uenced the aggregate production of knowledge.

Our paper speaks to three strands of literature. Firstly, we contribute to the literature on stagnation to growth and on the role of upper-tail human capital. Many authors have searched for the profound causes of the "Rise of the West" (e.g. Landes ; Maddison ; Galor and Moav ; Galor ; Mokyr ; Mokyr ). For most of them, the self-reinforcing dynamics of technological and institutional progress played a key role. In particular, De la Croix, Doepke, and Mokyr (

) argue that superior institutions for the creation and dissemination of productive knowledge help explain the European advantage in the medieval and early modern periods. The outstanding debate concerns the key forces that made these virtuous circles possible. There are currently no global quantitative analyses of the historical e ect of upper-tail human capital on the dynamics leading to the Industrial Revolution. Recent country-level studies include Dowey (

) for England, Squicciarini and Voigtländer ( ) for France, and Dittmar and Meisenzahl ( ) and Cinnirella and Streb ( ) for Germany. Squicciarini and Voigtländer ( ) show that the number of people who subscribed to Diderot's and d'Alembert's Grande Encyclopédie in th-century France predicts economic development later on, both at the city and county levels. Dittmar and Meisenzahl ( ) show that German cities that adopted better institutions following the Reformation grew faster and had more people recorded as famous in the German biography database.

There is a debate about whether or not universities facilitated the Scienti c Revolution. It is true that the new science developed in the th century came into con ict with the traditional Aristotelian approach taught at universities. Still, following Applebaum ( ), percent of the scientists listed in the Dictionary of Scientific Biography born between and were university educated, and percent of them were employed by universities. Beyond science, medieval universities may have contributed to the rise of the West through (i) the revival of Roman law, which was better suited to regulating complex economic transactions For Italy, historians, such as Cobban ( ) or Denley ( a), have documented the existence of a competitive academic market. Denley ( a), for instance, notes that the challenge for medieval Italian universities was "to attract su ciently highpro le faculty (...) to remain open". The transition to salaried teaching sta was a direct and early consequence of a competitive system with, what he calls, its own "transfer season". In addition to the salary, several other mechanisms added to this competition, such as the privileges granted to scholars, copied from one institution to another, the organization of intellectual competitions, bene ts in kind, etc.

As in the O-Ring theory of development (Kremer ) but not necessarily that strong. Galor and Moav ( ) explicitly refer to the universities: "Further, unlike the existing literature, investment in human capital increased gradually in the Pre-Industrial Revolution era due to a gradual increase in the representation of individuals who have higher valuation for o spring's quality. (...) In particular, in the Pre-Industrial Revolution era, the increase in the number and size of universities in Europe since the establishment of the rst university in Bologna in the eleventh century had signi cantly outpaced the growth rate of population." than the prevailing customary law, (ii) the translation of philosophical and scienti c works from Classical Arabic and Greek, (iii) the di usion of scienti c thinking in Europe (e.g. Ockham's parsimony principle, Duns Scotus's logic, or Roger Bacon's empiricism), and a certain universality of curricula (iv) the promotion by theologians of cultural norms such as the nuclear family, strict monogamy (De la Croix and Mariani ), and the education of children (Thomas Aquinas), and (v) the interest in the natural sciences, re ected in the establishment of botanical gardens next to medical faculties. A recent work by Dittmar ( ) lends credence to the idea of higher productivity of university scholars during the Renaissance. Dittmar computes the real wage of Italian professors during the Renaissance from archived payrolls, and shows that the premium of those involved in the new sciences increased after the adoption of the movable-type printing press. To our knowledge, this is the only paper other than ours focusing on university professors and using individual-level data. Closely related to our work, Schich et al. ( ) use birth and death locations of more then , notable individuals to investigate the cultural determinants of intellectual mobility and the dynamics of cultural centers over a period of , years.

Beyond the existence of universities (Cantoni and Yuchtman ) and the role of elites (Dittmar and Meisenzahl ), we stress what makes them operate better together, namely the integrated academic market. Higher education institutions and elites are present as soon as a civilization reaches a certain level of sophistication, but European universities were unique as they were bottom-up institutions operating in a continental market without many barriers (common language, political fragmentation of Europe, universality of curricula). This allowed top scholars to sort and concentrate, boosting thereby complementarities between them as well as the output of the whole academic system. Secondly, our paper relates to the migration literature in general, and to historical migration in particular. Migration is a selective process, with some individuals choosing to leave their region of birth and others choosing to stay. Who moves and who stays depends on the costs and bene ts of migration, which can vary across individuals for both systematic and idiosyncratic reasons. Two salient features of contemporary labor mobility are that well-educated people exhibit a much greater propensity to emigrate than the less educated, and they tend to agglomerate in countries/regions with high rewards to skill (Grogger and Hanson ; Beine, Docquier, and Ozden ; Kerr et al. ; Kerr et al. ). The geographic concentration of talent is stronger within the upper tail of the skill distribution and does not necessarily lead to a decline in returns to skills due to agglomeration spillovers. Skill-intensive clusters allow better technology exchanges, deeper labor market specialization, or strong complementarities (Stephan and Levin ; Kerr, Kerr, and Lincoln a; Kerr, Kerr, and Lincoln b; Franzoni, Scellato, and Stephan ). As far as positive selection is concerned, college-educated individuals are migrating three times more than the less-educated in the contemporary world. This ratio drastically varies with economic development at origin. It is slightly greater than one in high-income countries, while it reaches in low-income countries (Deuster and Docquier ). Such positive selection results from both heterogeneity in incentives and capacity to migrate (Borjas ; Chiquiar and Hanson ; McKenzie and Rapoport ), and immigration policies that favor education and skills.

Migrant selection has also been examined in historical studies, most of them focused on the Age of Mass Migration to the United States, a period of unrestricted entry starting in and ending around . Abramitzky, Boustan, and Eriksson ( and ) and Spitzer and Zimran ( ) show that selection patterns are consistent with income-maximization models. In the th and early th centuries, migration to the U.S. was positively selected from some European countries and negatively selected from others. The di erences in selection lined up with those in the relative returns to skill across sending countries, or with the easing or tightening of the liquidity constraints (Covarrubias, Lafortune, and Tessada ). Using data on servitude contracts from the th and th centuries, Abramitzky and Braggion ( ) found similar self-selection patterns (on health, physical strength, and literacy) of servants to the American colonies.

Thirdly, we shed light on the mobility patterns at the upper tail of the human capital distribution. Despite the potentially far-reaching implications for international knowledge creation and di usion (Breschi and Lissoni ; Trippl ; Miguelez and Moreno ; Pierson and Cotgreave ), empirical evidence about the drivers and selection of scientists' mobility remains scarce. Existing studies show that, compared to college-educated migrants, scientists and inventors are less sensitive to distance and more sensitive to linguistic proximity, economic conditions, resources dedicated to R&D, and visa-related restrictions (Laudel ; Agrawal et al. ; Kerr ; Fink, Miguelez, and Ra o ; Moed, Aisati, and Plume ; Grogger and Hanson ; Zhao et al. ). They also show the importance of circular ows which are mostly governed by the existence of scienti c collaborations. To the best of our knowledge, none of these studies have focused on the self-selection of scientists. One of the very few studies identifying selection e ects among scientists is that of Gibson and McKenzie ( ). Using a survey on the mobility of researchers from the Paci c Islands, they show that current migrants produce substantially more research than similarly skilled return migrants and non-migrants. Hoisl (

) also shows that mobility is generally found to be positively associated with inventor productivity as proxied, for example, by the education level of the inventor and the use of external sources of knowledge such as university research or scienti c literature. Finally, Akcigit, Baslandze, and Stantcheva ( ) nd that the international mobility of superstar inventors is in uenced by tax policies. A change in one country's top tax rate a ects the retention rate of domestic inventors, and has much greater e ects on the country's capacity to attract foreign inventors in general and those at the top of the ability distribution in particular.

The remainder of this paper is organized as follows. In Section , we present the data sources and de ne the key concepts used in our analysis. In Section , we describe the micro-foundations of our empirical model, present our main ndings, and discuss their robustness. In Section , we simulate the model to draw its implications for the humanistic and scienti c revolutions. The conclusion is in Section .

The structure of migration costs can give rise to many di erent migration patterns characterized by positive, negative, or intermediate selection. Chiquiar and Hanson ( ), however, observe that Mexican migrants to the United States are drawn from the middle rather than the low end of the Mexican skill distribution, although income inequality is higher in Mexico than in the United States. McKenzie and Rapoport ( ) con rm that Mexican migrants from rural areas mainly come from the middle class of the wealth distribution (those who have both the means and incentives to migrate), and that the intensity of selection decreases with the size of social networks abroad (in line with Beine, Docquier, and Ozden ( )). A few studies on intra-European migration support the positive selection hypothesis. Beltrán Tapia and de Miguel Salanova (

) show that, in the late th and early th centuries, the literacy level was higher among internal migrants moving to the Spanish capital city than among those who remained in their provinces of origin.

Data and Concepts

We collect a large sample of academic scholars (denoted by i = , ..., I) employed by the universities of Latin Europe over a time span that started around the year CE and lasted until CE. The year CE is a convenient date to stop for several reasons. At a broad level, it spelled the end of the Malthusian pre-industrial era. At the university level, it corresponded to profound changes: all French universities were abolished by the Revolution in , and would reappear in a di erent form later on. In Prussia, the Humboldt reform of was also a game changer.

In this section, we rst describe the institutional data sources used to identify academic scholars and their place of work. Secondly, we present the bibliographical data sources used to characterize the lifetime and place of birth of each academic scholar. In the third and fourth parts, we de ne an index of individual ability or human capital for each scholar, and go into a little more detail with regard to scholars with multiple a liations. We nally explain how we construct our proxies for institutional notability and quality.

Institutional secondary sources & quality of sampling. -The identi cation of academic scholars builds mostly on institutions' secondary sources of di erent types (see Appendix D). Ideally, we aim to cover the universe of scholars involved in university teaching and research before in Latin Europe. Although this universe is more precisely de ned than in other studies of European scholars (e.g. the universe of "famous people" in De la Croix and Licandro ( ), of "creative people" in Sera nelli and Tabellini ( ), or of "notable people" in Gergaud, Laouenan, and Wasmer (

)), its boundaries remain somewhat exible. For example, according to biographies of Nicolaus Copernicus, he delivered lectures as a professor of astronomy to numerous students while in Rome. It is unclear whether this teaching took place within the walls of the university of Rome (Sapienza), and how long it lasted. This appears however to be the only time Copernicus taught students. Should we count Copernicus when measuring the notability of the Sapienza? Probably not, as it would overestimate the attractiveness of Rome during this period. Should we include the decision of Copernicus to go to Rome in our study? We did, but it does not matter much as he is only one among thousands of scholars.

Another dimension of exibility concerns how we de ne a university. This seems simple a priori. We can rely on Frijho (

) who provides a list of institutions granting doctorate degrees, together with their o cial foundation date. It is however meaningful to extend this list in two directions. One extension is to include important learning institutions which were not formally universities. One example is the Herborn Academy (Academia Nassauensis) which was a Calvinist institution of higher learning in Herborn (Germany) from to . In addition, another relevant extension is to consider that universities were active before their o cial creation. For example, the University of Amsterdam was o cially founded in , but its roots go back to , when the Athenaeum Illustre was founded. For this reason, our period of analysis starts before the o cial creation date of the rst university.

For each university, we rst checked whether there is an online historical database of professors. For example, the list of professors at the University of Groningen has already been established. The Catalogus Pro-fessorum Academiae Groninganae includes all full professors from onwards (see the website at http: //hoogleraren.ub.rug.nl/). The website is still under development, but it shows the recent interest of universities themselves in looking at their past in a more systematic way. For those universities without such a database but with books of biographies of their professors, we encoded the contents of these books. For the remaining universities, we checked whether matricula (people registered at a given university) and chartularia (containing transcriptions of original documents related to the historical events of a university) exist. In some cases, the matriculum itself is of little use as the status of these people is not recorded (students, professors, etc.), but it follows the chronological succession of rectors, whose names are provided. As rectors were sometimes nominated every six months, their names provide good coverage of the universe of professors there (with some selection bias). We have built up a representative sample of professors from this information, and we are continually looking for other national biographies and other databases to complete the information needed. For example, for Jesuit universities, there is a biographical dictionary by Sommervogel (

) listing all Jesuits having published material; as they are classi ed by place of activity, we can match the professors to the relevant universities. Moreover, for the late Middle Ages and the Renaissance, information can be retrieved from two recent projects, both aimed at collecting biographical and social data on those who graduated from medieval universities: the project "Repertorium Academicum Germanicum -The Graduated Scholars of the Holy Roman Empire between and " and the project "Studium" for the University of Paris from the th century to the Renaissance. Both projects are currently under development.

We grouped universities into three categories, depending on the coverage of the sources (see Appendix D). We say the coverage is "comprehensive" when data collection was based on an existing website or book whose aim is to list all professors of a given institution. Coverage is "broad" when it is based on the combination of several sources, including books on the history of the university. The coverage is "partial" when the sample of scholars was informed by sources from other universities and general thematic biographies. Our benchmark analysis is based on universities with comprehensive and broad coverage. Notice that the quality of the coverage is not related to the prestige of the university. We have an excellent coverage of the University of Macerata -a small university in Italy, while there is no comprehensive list of professors for the University of Paris. A key requirement of our analysis is to cover almost all scholars with high human capital, and to include a large sample of unknown scholars as well. This requirement is met by encoding the academic scholars included in thematic biographies, such as Taisand ( ) for law, Eloy ( ) for medicine, Junius Institute (

) for Protestant theology, Herbermann ( ) for important Catholic gures, and Applebaum (

) for the key actors of the scienti c revolution.

Over the whole time span -, we identify universities and teaching institutions. The heterogeneity in the quality and coverage of the institutional data implies that the number of scholars identi ed varies drastically across universities. In the econometric analysis, we eliminate institutions with fewer than scholars or a coverage (total number of professors per year of existence) below . , and thus obtain a working sample of institutions (denoted by k = , ..., K). Each university k is linked to a geo-referenced location. Accounting for the date of creation of each university, we estimate that these institutions represent a total of , years of existence. A very comprehensive list of scholars can be obtained for the University of Heidelberg which includes , scholars over years of existence. Note that Heidelberg is not the largest university in our working sample; the data related to the University Bologna allow us to identify , scholars over the whole time span. However, Heidelberg is more representative of an average university than Bologna. Assuming Heidelberg is representative of all institutions, a back-of-the envelope calculation suggests that the order of magnitude of the universe of academic scholars for the medieval and early modern periods is around , (i.e. , / scholars per year × , years of existence). Observing that scholars taught in . universities on average, the universe has about , unique persons.

So far, our bibliographical searches have allowed us to identify , academic scholars. These include very well-known professors as well as obscure scholars. We thus estimate that our current sample covers around . % of the universe (i.e. , ÷ , ). This coverage is very likely to be higher for renowned scholars, as they are more likely to appear in the sources consulted, than for obscure scholars. Having obscure scholars in the sample is important to identify the characteristics of the famous ones -those who are more likely to play the academic market game. Including many obscure scholars in the analysis is thus a strength of our analysis.

Biographical individual data. -We match each scholar's name with bio-and bibliographical dictionaries to identify their place of birth and, later, their quality. We exclude the small number of persons born outside a rectangle encompassing Europe, North Africa, and the Middle East (de ned by latitudes ∈ [ , ] and longitudes ∈ [-, ]) because those would be outliers when computing distances. We also search online for Wikipedia and Worldcat pages to generate the ex-post indicators of human capital, as explained below.

One word about the quality of the bibliographical data. In many cases it is quite high, as the secondary sources used -biographical dictionaries and university sources -were often compiled from archive materials. We should however warn the reader that for the earlier periods, we have chosen to adopt some approximations. A good example is the oculist Benevenutus Hierosolymitanus, also called Benevenutus of Jerusalem. His life is totally unknown to historians, but his book, Ars probatissima oculorum, was immensely popular and in uential -having been translated into four languages already in medieval times. From other writings citing his work, historians infer he lived between and . Assigning Jerusalem as his place of birth is disputed, but seems the likeliest option, given the knowledge of Middle Eastern cultures displayed in his writings (remember that Jerusalem was for some time a Latin kingdom ( -)). He was also obviously acquainted with the medical school of Salerno, and he likely taught there (being called the physician from Salerno in one manuscript, namely the Besançon Manuscript). The most intriguing part concerns his relation with Montpellier, another famous medical school. In , the Faculty of Medicine in Montpellier placed a marble slab in its entrance hall listing him among its early faculty members. There are some arguments to link Benevenutus of Jerusalem to Montpellier, but there remains a "considerable disparity between the fragility of the documentary basis for the Montpellier inscription and the robustness of the stone on which it was engraved" (Kedar ).

Each individual at university k is characterized by at most ve dates: year of birth, year of death, rst year of observation at university k, last year of observation at university k, and approximate date of activity at university k (this corresponds to a date that is sometimes denoted by " .", from the Latin verb floruit "s/he ourished"). From these dates, we de ne two dates, t b i and t f i , which hypothetically bound the active life of each scholar. These dates are computed as follows: should be seen as a time when the individual can make location choices. The nal date t f i will be used to map the human capital achieved by a scholar to her universities. In the stylized facts, the period in which this end date falls determines the period for which we impute the quality of the scholar to their university.

t b i =
Universities' scholars were almost always male, but we found a few females: Trotula de Ruggiero ( th century) and a few others in Salerno, Maddalena Bonsignori, Clotilde Tambroni, Clotilde Zamboni, Bettina and Novella Calderini, and a few others in Bologna, Beatriz Galindo in Salamanca, Ekaterina Romanovna in Moscow, and Dorothea Christiane Erxleben in Halle. Female scholars were a rare exception though. Novellà Calderini, for example, allegedly replaced her father repeatedly, teaching at Bologna veiled so that her beauty would not distract the students, according to the Italian Encyclopedia Treccani.

Table shows the number of scholars per period, with some of their characteristics. We also report the number of universities per period, which increases steadily except from periods to , especially when French Protestant "academies" had to close (Bourchenin ). On average, institutional data and bibliographical dictionaries allow us to identify the birthplace of . % of university professors. Hence, we can compute the cost distance d ik associated with each possible scholar-university dyad. Such a cost is de ned as

The scholars for which we have no dates cannot be incorporated into the analysis.

corresponds to the foundation of the University of Marburg, the oldest Protestant university in the world. This war was of major importance for Germanic universities and the life expectancy of their scholars, as shown in Stelter, de la Croix, and Myrskylä ( ). In , the University of Göttingen was founded to propagate the ideas of the European Enlightenment. See De la Croix and Vitale ( ) for details.

d ik = ln(cost min + cost ij ) where cost ij is computed using Özak ( , )'s human mobility index and cost min is the minimum cost incurred when having a position in one's own place of birth. The human mobility index is the cost-minimizing path between two locations. It depends on geographical, technological, topographic and terrain conditions, and performs better than standard great circle distance in gravity models. We assume cost min is equivalent to the cost of walking within the old city of Rome between the Vatican City and the Colosseum ( . km).

In addition, . % of our identi ed scholars have a Wikipedia page, and . % have at least one recorded publication in Worldcat. Overall, these shares increase from periods ---(the Middle Ages) to periods ---(early modern period). The least well documented period is -, when we nd many names of professors with no publications, either because they did not publish a lot, were never printed, or their publications did not survive. Figure shows the university-scholar maps for all periods. Red dots correspond to universities. The top universities are labelled in bold. Blue dots represent scholars' birthplaces and again we have labelled some prominent names. Small blue dots refer to obscure scholars whose normalized ability index is equal to zero (see below). The dashed lines link academic scholars to the university for which they taught. They represent the optimal (i.e. travel-time minimizing) route.

As the rst two maps ( -and -) show, universities emerged in the territory of the late Western Roman Empire. Paris clearly attracted scholars from all over Europe, from Portugal to Scotland and the south of Italy. The density of universities in Italy was already impressive. The period -saw a decline in the number of observations in France, probably due to the Hundred Years' War, combined with the Black Death. West German universities started to play a role, while Italy was very active. We can also see Greek scholars such as John Argyropoulos eeing the expected fall of the Byzantine Empire (from Harris (

)). The next period ( -) has the same characteristics, but with more observations in Spain, Scotland, and southern Germany. The number of observations over the period -is high, with good coverage from Portugal to Poland: the portfolio of universities is expanding. The period -saw the development of Nordic universities, and a decline in movement in the south of Europe. A similar trend is observed for the period -. The last period -is particularly rich in Germany, and universities expanded to the East. From Iceland comes Grímur Jónsson Thorkelin, who was professor of antiquities at Copenhagen University and is known for the rst full translation of the poem Beowulf. On the whole, what can be seen on these eight maps corresponds closely to changes in economic primacy over time in Europe (Kindleberger ). More descriptive statistics (including barycenters) can be found in Appendices A, B and C.

Using bibliographical data, we de ne two key concepts that characterize the notability of academic scholars and institutions, and can potentially in uence location choices.

Scholars' human capital. -Firstly, we construct an index of ability or human capital of scholar i, denoted by q i . A standard way to measure human capital is to consider wages paid. While the latter might be the more standard measure of markets, it su ers from strong limitations. First, existing data on salaries are scarce, incomplete, or completely missing for several universities. Secondly, faculty compensation took a variety of forms, like payments directly from students, bene ts in kind (rent, various expenses, allocations of wine and grain like in Heidelberg ( Drüll), among others), xed salaries subject to contingencies (recessionary times, will of the prince, etc.) or prestige. In addition, theology professors were often not paid for their teaching, and received prebends outside the university (Post ; Paquet ). All these challenges make it impossible to have su cient informative, individual wage data. We discuss these issues in more detail in Appendix F, where we have compiled available wage data.

As an alternative, we measure human capital by individual notability as seen today in contemporary sources, Worldcat and Wikipedia. Worldcat provides a comprehensive measure of scienti c output and citations, as books about the person are included in the measure. Wikipedia completes this measure by putting more weight on the mission of academics called, on today's terms, "service to society" (e.g. becoming an ambassador or a pope, or being canonized a saint). The distributions of Worldcat and Wikipedia indicators are heavily right skewed, with low levels featuring typically obscure scholars. Consequently, without loss of generality, we make two normalization assumptions for those who have no Wikipedia and/or Worldcat pages. We assume rst that having no Wikipedia page or a very short Wikipedia page of characters is the same in terms of human capital (the shortest Wikipedia page has characters). Second, we assume that having one publication in one language held by one library worldwide is the same as having no publication at all. To combine the information provided by Worlcat and Wikipedia into one measure, we compute the rst principal component of ve indicators: (i) the log of the number of characters of the longest Wikipedia page across all languages (ranging from a minimum of to , ), (ii) the log of the number of languages in which a Wikipedia page exists (ranging from a minimum of to ), (iii) the log of the number of works (by We include a breakdown of scholars by broad elds of knowledge. We were surprised to see "theology" decline from % to . % between period and period (The Renaissance) and surge again at the occasion of the Reformation, peaking at . % during period . It is interesting to contrast this result with the idea that the Reformation led to a secularization of the society. This secularization process is shown in Cantoni, Dittmar, and Yuchtman ( a) through the reallocation of students across elds in Germany (measured by degrees granted and rst jobs). Such a reallocation did not seem to be matched by a similar process at the level of the teachers, or might be compensated by more theology in Catholic lands, under the lead of the Jesuits.

A correction for di erent languages length was performed, using the translations of the Gospel according to Saint Mark. or about) in Worldcat (ranging from a minimum of to , ), (iv) the log of the number of publication languages in Worldcat (ranging from a minimum of to ), and (v) the log of the number of library holdings in Worldcat (ranging from a minimum of to , , ).

The results of this analysis are presented in col. ( ) of Table . Usual heuristics used to identify relevant principal components is to keep those having eigenvalues above one and explaining at least % of the total variance. In our case, the rst principal component alone satis es these two conditions. We use it as an index of scholar's human capital. We nally subtract its minimum value from the rst principal component in such a way that a person with no Wikipedia page and no Worldcat entry will have a human capital of zero (q i = ).

One could argue that a measure of human capital should be based on the works published while the author was still alive. What was published after the death of the person might re ect how the author gained popularity post-mortem, which might not be relevant to determining their market value when they were active. It is not possible to implement this because many rst editions have not survived. For example, there is no doubt that Pierre Abélard ( -) was a philosopher of great renown during his life. All his written output available in libraries today, from philosophical works to love letters, was published after , and, in many cases, in the last years (see https://www.worldcat.org/identities/lccn-n79142562/).

Pierre Abélard is also known to the general public for his love a air and correspondence with his pupil Héloïse.

Our measure of q i is very robust to changes in assumptions. Disregarding Wikipedia leads to col. ( ) of Table . The correlation between the ability indices computed with and without Wikipedia equals . . In col. ( ), we separate the publications by and the publications about the person, and replace the number of works aggregating both types by these two indicators. There is little gain in doing this, and the new measure is correlated with the benchmark with a coe cient of . . The most famous scholars according to our measure are presented in Table by period τ. The scholar with the all-time highest human capital is Martin Luther. He was not a scientist like Galileo Galilei, Isaac Newton, or Carl Linnaeus, but it is fair to recognize that he profoundly in uenced institutional changes in Europe (Becker et al. ), and a shift of resources from religious to secular purpose as education and public administration (Cantoni, Dittmar, and Yuchtman b). In the list of Table , there are some scholars who only have a weak link to a university, and are thus not used to compute the notability of the university. For example, Baruch Spinoza never taught at a university, but interacted with people at the University of Leiden; the same holds for Montaigne and his links with Bordeaux. There are also some who were actual teachers but are better known, at least nowadays, for non-scholarly reasons: François Rabelais, known for his novels, was also in fact a physician who taught at Montpellier; Enea SB Piccolomini (Pope Pius II) or Friedrich von Schiller (German poet) also fall in this category. Their celebrity, even if not strictly academic, was taken into account to compute the notability of the university.

In the same table, we also report the median value of q i from the set of positive q i (those with either a Wikipedia or Worldcat reference). It is surprising that there is no visible trend for this q i over time, which implies that more recent scholars did not produce more than older ones. It may be more likely that the writings of medieval scholars were lost compared to those of scholars active in the early modern period, yet this loss is compensated for by the accumulation of citations and new editions over time. Let us also note that the particularly high median q i for the rst period, which probably re ects a selection phenomenon, and the low median after the Black Death. Finally, it is reassuring that the correlation between wages paid and q i is positive -a nding that is in line with human capital theory and our understanding of early academic markets -but rather small, for the above reasons.

Scholars with multiple a liations (repeat movers).

Our database includes some scholars with multiple career spells or a liations. Over the whole time span, . % of our scholars are linked to more than one university, and the average number of a liations per scholar equals . . We denote by S i the number of universities where scholar i spent time during her career (i.e. the number of career spells). With a record number of recorded a liations, Jean de Coras and Francisco Suarez are extreme examples of this feature. Jean de Coras ( -) was a French jurist who taught at Padua, Toulouse, Ferrara, Valence, but also, according to Taisand ( ) at Orléans, Paris, and Angers (but we do not even know in which order). Francisco Suarez ( -) was a Spanish Jesuit philosopher and theologian who taught at Avila, Valladolid, Alcala, Salamanca, and Coimbra according to Herbermann ( ), but also at Paris and Rome according to Sommervogel (

).

If a scholar left a position and came back to the same institution after a while, we consider it as only one a liation. Jean the Coras might be known to the international audience as he instructed the famous trial of Martin Guerre. He wrote its best-known record, which was the basis for the movie The Return of Martin Guerre with Gérard Depardieu, which was nominated for Best Foreign Language Film by the U.S. National Board of Review of Motion Pictures in .

Table : Top scholars by period with their We refer to multi-a liation scholars as repeat movers, and to those who have been only employed by a single university, as one-time movers. It is di cult to make any statement on the reasons for multiple moves. However, there is clear evidence that repeat movers are more likely to belong to the top of the distribution of human capital. Repeat movers are performing better than others at both the extensive and intensive margins. On average, . % of repeat movers have at least one recorded publication, as opposed to . % for one time movers. Focusing on scholars with at least one publication, the average q of repeat movers ( . ) is % greater than that of one-time movers ( . ). Combining both margins and keeping in mind that the minimal ability level is normalized to zero, the average ability index in the total population of repeat movers ( . ) is . times greater than the average ability index in the total population of one-time movers ( . ). The shares of repeat movers in the population in periods to are equal to %, %, %, %, %, %, % and %, respectively. The greatest shares, observed in the rst two periods, are likely due to a lower coverage of the population of obscure scholars. As for the heterogeneity by place of birth, the share of repeat movers varies from % in Denmark to % in the Netherlands, and % in Great-Britain.

q i Period τ - - - - Med[q i | q i > ]
Institutional notability. -In theory, we can compute a measure of annual quality for each university using the observed location and ability levels of all scholars identi ed in our database. In particular, for each year t, we can de ne the set of scholars a liated with university k as Λ k,t = {i|p ikt = } where p ikt is a dummy equal to one if scholar i was a liated with university k at year t (implying that t b i ≤ t ≤ t f i ), and equal to zero otherwise. Nevertheless, given that sampling varies from one institution to the other, computations based on the total number of observed scholars are not directly comparable across places. Taking the means or medians of individual human capital would also be biased in favor of the least well covered universities. Hence, we introduce the concept of notability of university k in year t as a CES combination of the ability or human capital of the top academic scholars having spent time there in a years window preceding t. Figure shows an example. These top scholars are extracted from the sets Λ k,t-...Λ k,t-and should not belong to Λ k,t . The notability index is denoted by Q kt . To account for the partial presence of repeat movers, we weight the individual ability q i by ( /S i ) ω where S i is the number of universities where scholar i spent Those shares are computed on the sample of scholars for whom the birth place is known. time during their career, and we de ne the adjusted ability level as q i ≡ q i ( /S i ) ω . In our descriptive tables and benchmark regressions, we assume ω = (i.e. the ability of each multi-destination scholar is divided by their number of career spells). We then denote by q kt , q kt , q kt , q kt , q kt the ability of the top academic scholars of university k in year t, and we de ne the notability index as:

Q kt = q σ- σ kt + q σ- σ kt + q σ- σ kt + q σ- σ kt + q σ- σ kt σ σ- , ( )
where σ is the elasticity of substitution between scholars in producing notability.

We use Q kt as a proxy for the attractiveness of the university. When making location decisions, it is unlikely that scholars were able to accurately quantify the quality of each university. However, they were aware of complementarity forces and they observed the highest ability scholars of each university belonging to their choice set. From the Black Death to the rise of Protestantism, we see the universities of Florence, Prague, Rome, and Louvain. After the Reformation, Wittenberg appears as the most notorious, followed some time later by Padua, Leiden, Cambridge, and Oxford. In the last century, we nd the Royal College in Paris, the universities of Halle, Uppsala, Copenhagen, and St Petersburg (a university attached to the academy there). The Royal Gardens in Paris comes at the end of the parade. This ranking contains a few surprises. For example, the University of Cambridge does very well in the eighteenth century, contradicting the view that it was "an intellectual desert, in which a solitary man constructed a system of the world" (see Manuel ( ) about Isaac Newton in Cambridge).

One can evaluate the relevance of our ranking of universities by comparing it with rankings obtained using di erent methods. The Casati Law (Italy,

) sets rules for accrediting the pre-existing universities into the new Italian University system (Cottini, Ghinetti, and Moriconi ). It ranked universities into three categories, A-B-C depending on their quality. We can compare this ranking with our estimate of Q kt , averaged over the eighteenth century. The average for the universities ranked A is . . The average for the universities ranked B is . . And the two universities ranked C have a similar level of . (including the university of Macerata for which we harvested about professors). This suggests that our approach is very likely to allow for a proper identi cation of the top institutions.

Empirical analysis

We now turn our attention to the empirical analysis of the determinants of location choices. Economists have long recognized that spatial mobility decisions play a key role in the career choices of workers (e.g. Keane and Wolpin ; Neal ). Two types of models, spatial search and location choice, have been used to link mobility decisions to career choices. Spatial search and matching models formalize job search decisions across geographically segmented labor markets; they shed light on the e ect of distance on the e ciency of a job search, on spatial heterogeneity in search frictions, and on the persistence of labor market disparities between regions (e.g. Manning and Petrongolo ; Schmutz and Sidibe ). Ideally, the estimation of matching models requires observing a large number of repeat movers with match-speci c outcomes such as individual levels of earnings or employer's pro t (e.g. Abowd, Kramarz, and Margolis ). This approach is unworkable for us, given the absence of data on match speci c outcomes. Moreover, even if we had such outcomes, using only about % of the sample (the share of repeat movers) would be costly in terms of external validity of the analysis. Location choice models explain how di erent types of workers self-select into labor market areas by maximizing their current and expected future levels of income (e.g. Borjas ; Dahl ; Gallin ; Grogger and Hanson ). The latter framework is particularly relevant when focusing on the role of workers' attributes, and when match-speci c outcomes, demand-side factors and local matching frictions are unobservable. Hence, we opt for this type of framework.

In this section, we rst explain the microfoundations and speci cities of our location choice model (Section . ). We then estimate the determinants of location decisions with a standard multinomial logit model in (Abramitzky and Sin ).

Sections . , and conduct a heterogeneity analysis in . . The standard logit framework raises a number of econometric issues that might generate inconsistent estimates. Firstly and despite the fact that our database includes a large number of obscure scholars, renowned scholars are more likely to be recorded and information about place of birth is missing for a relatively large number of obscure scholars. In the benchmark regressions, these unknowns are eliminated from the sample. This raises sample selection issues that we address in Section . . A related problem is due to the presence of scholars with multiple a liations. Each (i, k) dyad appears as one observation in the database and is assimilated to a career spell. This means that scholars with seven a liations appear seven times, while those with a single a liation appear only once. This also induces possible sample biases and raises the question of the relevance to model scholar i's choice at stage s independently from her other career spells s . These issues are addressed in Section . . Finally, the benchmark speci cation disregards the potential endogeneity of q i , arising from the fact that the ability of scholar i is likely to be a ected by her academic environment. We address this issue in Section . .

. A microfounded gravity model

We formalize the discrete location-choice problem of academic scholars in medieval and early modern Europe using a Random Utility Model (RUM), which provides the state-of-the-art microfoundations for most recent gravity models of migration. Our RUM leads to an empirical multinomial logit model which is in line with Akcigit, Baslandze, and Stantcheva ( ), who study the international mobility of superstar inventors since . Standard location choice models assume that the demand-side of the market is perfectly elastic. In our context, this means that the demand for academic scholars (or equivalently, the supply of academic positions) adjusts perfectly to supply. Although most universities have a xed number of chairs, they also o er a set of other positions which are easily adjusted (e.g. the fellows in Oxbridge, the professores designati in Copenhagen (Slottved ) , the survivanciers (designated successor) in Montpellier (Dulieu )). We account for potential demand-side factors by including "competition costs" whose size depends on the attractiveness of universities and cities as well as on the ability and "market value" of academic scholars.

Compared with the standard literature on the determinants of migration, and beyond the fact that we use unique micro-data, our approach has three speci cities. Firstly, we use geo-referenced location data. Each scholar i is assigned to a geo-referenced place of birth, whereas each university k is linked to a geo-referenced position. Each scholar-university dyad is associated with a cost distance d ik , measured with the human mobility index (see supra). Since the place of residence of academic scholars before moving to university k cannot be observed, the distance between the place of birth and the university may capture the separation from family and friends (i.e. homesickness), the travel distance per se, or the costs of obtaining information about remote places. A striking example of the importance of distance is provided by Eloy ( ) and Michaud ( ) about Septalius (Lodivico Settala, -). Born and living in Milan, he taught medicine at the nearby University of Pavia and received o ers from: the King of Spain, the Duke of Bavaria, the Duke of Tuscany, the city of Bologna, and the Senate of Venice, all o ers above what any local citizen could have dreamed of receiving. He enjoyed receiving them as tokens of well-deserved honors, but accepted none. He preferred the company of his fourteen children to the luster of these foreign positions. Another clue to the preference for one's place of birth is the following. Among the , scholars with a known death place, , of them went back to their hometown before dying, although they held appointments in other places during their life. Another , were born, worked and died at the same place.

Secondly, we exploit the unbalanced panel dimension of our database as some scholars made multiple/repeated choices. We do not necessarily know the timing of choices, but our database links several universities to some scholars. We assume an academic career is made of a maximum of S spells indexed by s. At each stage of their career, each professor has to select their preferred location from the feasible university choice set. In practice, if scholar i taught at S i universities, we include S i dyadic matches in the database. Robustness checks will be conducted in Section . to assess the role of repeat movers.

Thirdly, our discrete choice model allows for varying choice sets. As new universities are created (or abandoned) over time, the choice sets are individual speci c depending on the universities that existed during the active life of the scholar. Each university has a founding date t k and an end date t k , which we mostly take from Frijho ( ). Sometimes universities -or some schools which would later become universities -existed before this o cial date. For example, the University of Paris was o cially founded in , but colleges and cathedral schools existed before that date. Gerard Pucelle ( -), an Anglo-French scholar in canon law, taught at Paris from to (Arabeyre, Halpérin, and Krynen ), before becoming the Bishop of Coventry. We should thus lower the initial date t k for the University of Paris to match the rst scholar who can be found there. More generally, the most ancient scholars in the database are Adelbold ( -), who taught, at the turn of the millennium, at the cathedral school in Liège, and Fulbert de Chartres ( -) who taught at the cathedral school in Chartres and at what would become the University of Angers (Rangeard and Lemarchand ). This explains why our time span starts in the year CE. As far as individuals are concerned, we use the time interval [t b i , t f i ] de ned in Eqs. ( ) and ( ). Each scholar i makes location choices at the start of the career, in year t(i) ≡ t b i . The portfolio available to individual i is denoted by K t(i) . We include a university k in the choice set of individual

K t(i) if t k ≤ t(i) ≤ t k .
The utility that a professor i obtains from locating at university k ∈ K t(i) at the stage s ∈ S of her career is given by:

U iskt(i) = V ikt(i) + ϵ isk = βx ikt(i) + ϵ isk , ( )
where V ikt(i) = βx ikt(i) represents the deterministic component of the indirect utility (net of moving costs), which depends on a vector of observable variables, and ϵ isk is a vector of person-speci c random taste shocks representing the unobservable determinants which enter the utility function and are orthogonal to the deterministic component.

Assuming the random term ϵ isk is independently and identically distributed as Extreme Value Type I (EVT-I), which implies that multiple career choices are independent, we can model the probability that university k represents the utility-maximizing choice for professor i at the stage s of her career as the outcome of a standard multinomial logit model (McFadden ):

p iskt(i) ≡ Prob U iskt(i) = Max k ∈K t (i) U isk t(i) = exp(βx ikt(i) ) k ∈K t (i) exp(βx ik t(i) )
.

( )

Both Liège and Chartres had cathedral schools which failed to morph into universities, see Jaeger ( ) on those early cathedral schools in Europe.

In this formula, the probability of going to a given place depends on the features of that place (the numerator) compared to the features of all the other places in the portfolio (the denominator). The property of the multinomial logit model is that the relative probability of choosing between two alternative options in K t(i) depends on the attractiveness of these two options only, i.e. ln p iskt(i)ln p isk t(i) = βx ikt(i)βx ik t(i) , and is independent of the presence of other alternatives (IIA: Independence of Irrelevant Alternatives). In addition, the choice probabilities are independent across career spells as long as ϵ isk and ϵ is k are assumed to be independently distributed. The latter assumption will be relaxed later.

As in the literature on migration, in which the location choice of migrants conditional on the decision to migrate (Bertoli and Ruyssen

) is studied, our estimations are conditional on the choice of having an academic career. As we cannot observe the universe of scholars, including those not choosing to teach at universities, we cannot model the ex-ante problem of choosing between universities and other activities. Notice that this choice is more complex than a binary choice, as many scholars combined positions at universities with other occupations (such as physician or astronomer to the monarch, bishop or judge). Our estimation thus rests on the independence of irrelevant alternatives property within the choice set K t(i) , which implies that the relative probability of choosing between two alternative options in K t(i) depends exclusively on the attractiveness of these two options. Even if selection into academia would not a ect the location choice of individuals having chosen to teach, it might a ect our simulations if, for example, the total number of professors depends on the notability of universities. Hence it is fair to acknowledge that our results remain partial equilibrium results.

Estimating the multinomial logit ( ) requires specifying the analytical form of the deterministic component of the utility function as a function of observable individual (q i ), institutional (Q kt(i) ), and dyadic characteristics (d ik ). In the benchmark model, we consider q i as independent of her location choice. We also consider Q kt(i) as exogenous as it depends on scholars who are no longer active at t (as illustrated in Figure ). The endogeneity of individual ability will be treated later.

The deterministic component of the utility function captures the average bene ts and the average cost for i of locating at k, and is independent of the career spell s:

V ikt(i) ≡ B ikt(i) (.) -C ikt(i) (.). ( )
We model the bene ts (B ikt(i) ) as an increasing function of the attractiveness of the city where the university is located (proxied by the population density, P kt(i) , and by the indicator of local democracy from Bosker, Buringh, and Van Zanden ( ), D kt(i) ), as well as of the adjusted notability of the university (Q kt(i) ), as suggested by anecdotal evidence. For example, Navarro-Brotons ( ) discusses the case of Jeronimo Munoz, who moved from Valencia to Salamanca in . Although Munoz was one of the best paid professors at the University of Valencia, his salary was considerably lower than those paid at universities in Castille. The prestige of the University of Salamanca, and its greater proximity to the seat of royal power, was probably also a factor in Munoz's decision to accept Salamanca's o er. Furthermore, the e ect of Q kt(i) can vary with the ability of the professor as, for example, high-ability professors bene t more (or less) from expected interactions with high-ability colleagues (e.g. Stephan ). We assume the following speci cation:

B ikt(i) = a + a Q kt(i) + a P kt(i) + a D kt(i) + a q i Q kt(i) ( )
where all coe cients are predicted to be non-negative.

We model the cost of locating at university k (C ikt(i) ) as an increasing function of the cost distance from the place of birth (d ik ) and of the competition for nding a job at university k in year t(i). The competition for nding a job re ects the demand side of the academic market. Again, anecdotal evidence suggests that the recruitment policy of the best universities included e orts to attract international talent. To give two examples, Eloy ( ) reports that Leonhart Fuchs (after whom the plant fuchsia was named), a professor at Ingolstadt in , was o ered six hundred gold coins by the Duke of Tuscany, Como, to teach at the University of Pisa. Nadal ( ) discusses the case of the University of Valence, which was searching for a renowned legal scholar in . They sent a messenger to convince a famous lawyer in Grenoble, Jean-Antoine de Lescure, to join the university. The latter reported that he would be willing to come for a salary of , pounds, provided his moving and house rental costs were covered by the university. They nally agreed on , pounds plus the house, partly paid by four merchants of the city. Later on, his colleague François Josserand became jealous of Lescure's treatment, threatened to go elsewhere, and obtained a pay rise.

We reasonably assume that the "competition cost" incurred by a professor increases with the attractiveness of the city (P kt(i) and D kt(i) ), as well as with the (adjusted) notability of the university (Q kt(i) ). However, we also allow the latter "competition cost" to be negatively a ected by the individual level of ability, as high-ability professors have a higher market value and receive more generous o ers from top universities. In line with the literature on self-selection in migration (e.g. Grogger and Hanson ; Beine, Docquier, and Ozden ; Kerr et al.

; Kerr et al. ), we allow the cost of distance to be negatively a ected by the individual level of ability. We assume the following speci cation:

C ikt(i) = b + b Q kt(i) + b P kt(i) + b D kt(i) + b q i Q kt(i) + b d ik + b d ik q i ( )
where b and b are predicted to be negative, whereas the other bs are expected to be non-negative.

Plugging ( ) and ( ) into ( ) gives the expression for the net bene t of an (i, k) employment match. However, in our empirical regressions, we extend the number of generic determinants of location choices (x ikt(i) ) to account for the imperfect coverage of our database and for unobserved heterogeneity. We add a university xed e ect, γ k , which captures both the unobserved pull factors associated with university/city k that do not vary across years and the quality and extent of the sources used for each university. This yields:

V ikt(i) ≡ βx ikt(i) = β + β Q kt(i) + β P kt(i) + β D kt(i) Agglomeration + β q i Q kt(i) Sorting + β d ik Distance + β d ik q i Selection + γ k ( )
where β is a set of parameters that are common to all individuals and that can be estimated. Unlike standard (linear) regression models, the speci cation of the multinomial logit model depicted in Equation ( ) implies that the individual probability to take a position in a university k depends on the characteristics of all universities and cities. Any change in one of these characteristics impacts the whole system.

Identi cation. In line with ( ) and ( ), the constant is given by β ≡ ab . Coe cients β ≡ ab , β ≡ ab and β ≡ ab can be positive or negative and re ect the agglomeration (or dispersion) e ects resulting from the attractiveness and competition e ects. As the university xed e ect captures the mean level of agglomeration/dispersion forces throughout the entire time span covered by our sample, our estimation of these coe cients exploits the within (or demeaned) variations over time in the notability of universities and in the attractiveness of cities. Coe cients β , β and β are identi ed by the fact that the number of scholars who decide to take a position in university k decreases when this university becomes worse in terms of quality (e.g., Spanish universities in periods and ) and when a city loses its communal freedom (e.g., Northern Italian cities after the Renaissance); by contrast, it increases when a city becomes relatively bigger (e.g., Amsterdam in periods and ).

Just as V ikt(i) , the other determinants of location choices are dyadic by construction (sorting and selection terms) or in nature (distance), which makes their identi cation and estimation possible. Coe cient β ≡ a -b is positive if high-ability scholars tend to agglomerate at better universities (what we refer to as positive sorting) due to higher bene ts or smaller costs; it is identi ed by the fact that the best scholars are more likely to take a position in university k when its quality increases. Coe cient β ≡ -b is the standard Distance term capturing the expected negative e ect of remoteness; it is identi ed by the fact that a given university attracts more scholars born in its vicinity than born far away. As for β ≡ -b , it is positive if high-ability individuals are more mobile than lower-ability ones (what we refer to as positive selection); it is identi ed by the fact that renowned scholars are less sensitive to distance and are more likely to take a position in a remote university than obscure scholars.

Finally, the multinomial logit expression ( ) implies that variables that are not speci c to a destination k, directly or through their interaction with individual characteristics, cannot be identi ed, as they would a ect the net bene t of all (i, k) employment matches symmetrically. This explains why our set of regressors in ( ) includes neither purely personal characteristics (such as the ability of scholar i per se) nor purely temporal phenomena (such as time xed e ects).

. Results from the multinomial logit model

Table contains the results of a standard multinomial logit regressions for the whole time span -. The sample includes scholars who have been members of universities with comprehensive and broad coverage (see Appendix D). The estimations are obtained by using the mlogit package of Croissant (

), which allows for varying choice sets. These regressions characterize the location choices of , scholars with a mean number of career spells equal to . , which gives a total of , individual observations. Denoting the number of elements in set S, by S, the mean number of institutions is equal to E i K i = (the total number ∪ i K i = ). Our database includes . million possible dyadic matches. We focus here on the sign and signi cance of the agglomeration, distance, selection, and sorting terms. In all regressions, we control Positive selection and sorting can also arise if the utility function ( ) is not additively separable.

for institution xed e ects. The sizes of cities, P kt = log( + thousands of inhabitants) are obtained from Bairoch, Batou, and Chevre (

). The level of local democracy, D kt , is obtained from Bosker, Buringh, and Van Zanden ( ) who created a binary variable equal to one when cities could organize themselves and claim a kind of self-rule that was often acknowledged by the sovereign in return for taxes or loyalty. The rst occurrences of communal self-government were identi ed in the th and th centuries in Spain and Italy. They spread across the rest of Europe in the following centuries. For all dates t at which P kt and D kt are not available, we impute the closest available data (for example, for population in , we impute population in ). The regression in col. ( ) can be seen as a textbook gravity equation, including distance d ik and mass (in the xed e ect γ k ). This standard gravity regression shows that the probability of observing a scholar-university match decreases with the cost distance between the birthplace and the university location. This e ect remains strong in all speci cations. The coe cient of distance is above unity, b = -β > , which is unsurprisingly greater than in the contemporary era. Focusing on the stock of international migrants in , Beine, Docquier, and Ozden ( ) nd a coe cient of . for all migrants and of . for college-educated migrants. Focusing on current academic researchers, Fink, Miguelez, and Ra o ( ) nd a smaller coe cient around . . Agglomeration forces are added in col. ( ). Scholars are attracted by the notability of the university, the size of the city, and the level of local democracy. Notice that due to the presence of university xed e ects, the agglomeration e ects are identi ed through the variations in institutional notability, city size, and democracy over time, while the e ect of distance is identi ed through the spatial variation in d ik . In col. ( ), we add the interaction between distance and individual human capital d ik q i . This term is positive, which suggests that the most notable professors were more mobile than others (positive selection). In col. ( ), we interact the individual human capital index with the notability of the university. We nd evidence of positive sorting: the most notable professors were more likely to settle in more prestigious universities. Putting all regressors together in col. ( ) shows that agglomeration, selection, and sorting are all signi cant. Using the values of the log likelihoods, we can compute some simple LR tests: comparing ( ) to ( ), we can reject the null hypothesis that there is no agglomeration e ect. Similarly, comparing ( ) to ( ), we reject the absence of selection and sorting. To illustrate, university xed e ects are excluded in col. ( ); all results are similar with the exception of the local population e ect, which becomes insigni cant.

To determine whether the coe cient of distance is stable over time, we also ran a speci cation with distance interacted with a period (τ) dummy. This allows us to test whether the speed of travel improved before . The eight estimated coe cients are: -. , -. , -. , -. , -. , -. , -. , and -. . The coe cient is thus quite stable over the last periods, but lower during the Middle Ages, and especially during the periods before the Black Death. The other coe cients are una ected, except the e ect of communal freedom, which is reinforced. The unexpected non-decreasing pattern in this coe cient re ects that there was little progress in the quality of roads until the th century (Bogart ), and little innovation in traveling by boat before the invention of steamboats in the th century. The lower cost of moving during the Middle Ages may re ect weaker national states, and also the lower density of universities in this period.

The coe cient of the interaction term Q kt(i) q i captures the fact that high-quality scholars are more sensitive to the reputation of the university when solving the location-decision problem that they face, and/or that higher-quality universities reward scholars' quality more (i.e. higher wages per unit of quality). Remember that the few wages we observe are generally positively correlated with q i at di erent points in history (see Appendix F). This is in line with our assumption that a higher level of q i usually translates into a higher level of remuneration.

In a non-linear model, the coe cients cannot be interpreted in terms of predicted probability as the e ect of a change in a variable depends on the values of all variables in the model. To put it di erently, the e ect depends on where we evaluate it: the derivatives of the choice probabilities are given by 𝜕p isk

x ik = βp isk ( -p isk ), which is largest when p isk = . . For this reason, our coe cients β can only be interpreted as the e ect of x ik on indirect utility. This will be very clear at the beginning of the next section, where we will simulate the model with and without selection and sorting for a person with a high q i , and compare with another

We may further want to include q i among the determinants of location-speci c utility, allowing its coe cient to vary across alternatives. This is standard in the estimation of a multinomial logit model with variables that are individual but not alternative speci c. Still under the assumption that wages are proportional to q i , it would purge the estimated coe cient of Q kt (i) q i from the confounding e ect of di erences in wages across universities. Including these choice-speci c terms, we obtain ∪ i K i = more parameters to estimate. The estimated coe cients of these q i s vary from one university to the other, as does the university xed factor. They also sometimes have a negative value, which is hard to interpret in the context where scholars would be remunerated in proportion to their q i . In this new speci cation, the interaction term Q kt (i) q i is weakened but remains highly signi cant ( . ( . ) instead of . ( . )) despite the inclusion of many terms correlated with q i . The three agglomeration e ects are barely a ected. one with a low q i . The results in Table also indicate that the e ect of positive selection is relatively small, albeit non negligible: when q i is around (scholars at the top of the ability distribution), the utility loss due to distance is reduced by just %. By contrast, the e ect of positive sorting is large: when q i is around , sorting increases the gains from settling in a more prestigious university or in a more attractive city by a factor of . as compared with obscure scholars (i.e. q i = ). Besides the standard distance term, agglomeration and positive sorting are important forces governing the mobility decisions of academic scholars. Table E. in Appendix E shows that our estimation results are highly robust to the choice of σ and ω.

.

Heterogeneous e ects

The benchmark assumption of a constant university xed e ect across elds of knowledge and across years (γ k ) is made for simplicity. In practice, the attractiveness of a university varied over time and across elds of study. To solve this problem, we separately re-estimate the multinomial logit ( ) after excluding some periods (τ), some elds of study, and some regions of birth. As for the elds, we distinguish between Theology, Law, Medicine, and Science. The eld(s) of a scholar are mostly identi ed through the courses taught. Law includes both canon and civil law. Medicine includes Anatomy, Surgery, and Pharmacy. Sciences include Mathematics, Logic, Physics, Chemistry, Biology, Astronomy, Earth Science, Geography, and Botany. One should be aware that the distinction between these elds is a bit arbitrary, in particular when going back in time. For example, the theologians Thomas Aquinas and Albertus of Saxonia spent time reconciling the Aristotelian view of a nite world with the Christian view of an in nite God. In doing so, they contributed to the development of the mathematical notion of limit ( Sergescu). Pierre Gassendi ( -) is known as an astronomer (a crater on the moon was named after him), but was a professor of theology at Aix-en-Provence.

In Table , we separately estimate the multinomial logit (a) for ve periods (i.e. to , to , to , to , and to ), (b) after excluding one eld at a time (i.e. Theology, Law, Medicine, and Science), and (c) after excluding one region of origin at a time. We successively exclude the Low Countries (Benelux), Germany (as of today), France (as of today), Italy, and the British Isles (currently the United Kingdom and Ireland). Our sub-samples include smaller numbers of observations. In each of these sub-samples, the portfolio of possible universities di ers. For example, when we exclude scholars born in Germany, some German universities cannot be included in the estimation as only German scholars worked there during their existence.

The e ect of distance is always negative and highly signi cant. As far as agglomeration forces are concerned, the notability of the university is always positive and signi cant. The attracting e ect of city size is always positive, with the exception of the rst period. The e ect of communal freedom, which is found to be important in general by Sera nelli and Tabellini (

) in their study of the migration patterns (from birth to death) of creative people, is found to be signi cant in most sub-samples. The estimates by region show that Italy is key to identifying this e ect, as communal freedom stops being signi cant when one removes Italian scholars from the sample. Italian cities are unique in that many lost their freedom during the Renaissance. This echoes the study of Buonanno et al. ( ) who show that territories with communal freedom in the Middle Ages display more positive features and attitudes today than territories without such freedom. As

d ik Q kt(i) P ikt(i) D ikt(i) d ik q i Q kt(i) q i of obs.
of average scholars. This is con rmed by the increase in the coe cient associated with the cost of distance.

.

Sample selection

Our database does not include the universe of professors. This implies two sources of sample selection issues: (i) many obscure scholars are not included in the sample, and (ii) there is a considerable heterogeneity in the coverage of institutions. We assess whether our results are robust to sample selection. Results are reported in col. ( ) and col. ( ) of Table . We report our benchmark results in col. ( ).

As far as scholars are concerned, some are included in the sample but data on their place of birth are missing. This is usually the case for less well known professors. Indeed, among the scholars with a known birthplace, % have a positive q i . This proportion drops to % for those with an unknown birthplace. Hence, our sample is likely to overweight top-quality professors (high q i ) and underweight the less well known (low q i ). This is a limitation because the co-existence of professors who are famous and those who are not is key to identifying selection and sorting patterns. To measure the importance of sample selection, we re-estimate the multinomial logit ( ) by making the sample less selective. To do so, we use the identi ed scholars of unknown origin, and assume that they were born in the city of their university, implying d ik = ln(cost min ) for them.

Col. ( ) shows the results obtained when assuming that all identi ed scholars from unknown origin are locals. This increases the sample size by one third, reinforces substantially the positive selection e ect (almost doubling the corresponding coe cient), and increases the agglomeration terms; positive sorting is not much a ected. These results suggest that if we had observed the whole universe of scholars, which contains many more unknown people born locally, positive selection would appear stronger while leaving sorting una ected. Hence, our benchmark estimates might give a lower bound on selection.

As far as institutions are concerned, our benchmark regression sample excludes universities with fewer than scholars in total and those with partial coverage. We relax the latter constraint in col. ( ) of Table , which increases the sample by about , observations. Our empirical results are highly robust to these changes. In col. ( ), we restrict our working sample to universities with at least scholars (instead of in the benchmark). This amounts to reduce the sample size (by %) as well as the choice set of every scholar by removing some small universities. We loose the signi cance of the population and communal freedom variables, probably because some important cities for identifying this e ect were removed, but selection and sorting mechanisms are reinforced.

. Treatment of repeat movers

Remember that . % of our scholars are linked to more than one university and we count each dyadic match as one observation. This raises two potential issues. Firstly, the weight of repeat movers exceeds that of one-time movers. As the number of career spells increases with human capital, this reinforces the overrepresentation of renowned scholars in our database. Secondly, by assuming that career-spell-speci c choices are independent, we ignore the possibility that movers may have had correlated preferences. The rst problem can be easily addressed by removing repeat movers from the regression sample, which eliminates many famous scholars, or by linking them to a single university. We do both and, when following the second option, randomly select one of their a liations. Solving the problem of correlated career spells is more complicated. To account for it, we generalize the standard logit model by relaxing the hypothesis of independence of individual choices. The independence property can be unrealistic in many settings, especially in situations with repeated choices over time. We can expect unobserved factors that a ect a decision maker to persist over time. In a multinomial logit, we cannot include individual xed e ects since they would not a ect the probability that a university k dominates another university k . A more general deterministic component of utility can be written V ikt(i) = β i x ikt(i) , where β i is a vector of coe cients that is unobserved for each i and varies randomly across professors, representing their tastes. This speci cation is the same as for the logit except that now the coe cients β i vary in the population rather than being xed. In particular, the coe cient β i can be expressed as the sum of a population mean, β, and an individual deviation, η i , such that their utility of moving to destination k is written

U iskt(i) = βx ikt(i) + η i x ikt(i) + ϵ isk .
The last two terms of such a Random-Parameter Logit capture the unobserved portion of utility. In other words, the marginal e ect on the latent dependent variable is individual speci c. The same tastes are used by the decision maker for each career spell and the variance in β i induces correlation in utility across destinations and career spells.

How these parameters vary across individuals is unknown. The mixed logit model assumes that these parameters vary according to the population PDF g β i |θ , where θ represents the moments of the distribution such as the mean and the variance, which must be estimated. A fully parametric mixed logit model arises once g β i |θ is speci ed. We assume that the coe cient vector is independent and normally distributed, β i N β, σ . The unobserved portion of utility is correlated across destinations and career stages due to the common in uence of η i , which violates the IIA property of the standard logit (Revelt and Train ). The full parametric model can be estimated using the simulated maximum-likelihood procedure (Sarrias et al. ).

In col. ( ) of Table , we show that most of our results are highly robust to the exclusion of repeat movers. Compared to the benchmark speci cation of col. ( ), removing repeat movers increases the magnitude of the agglomeration and gravity terms. As for sorting and selection, their identi cation relies on the di erence between famous and obscure scholars in the sensitivity of location choices to institutional quality and distance. Remember repeat movers exhibit an average ability index that is . times greater than the mean; they account for % of our scholars and are linked to . universities, on average. Removing them from the sample decreases the number of observed dyads by . % (from , to , ) and eliminates many famous scholars at the upper end of the ability distribution. The sorting term resists this change and its magnitude is drastically strengthened compared to the benchmark. This is important because we will see it is the e ect that is driving our simulation results in Section . By contrast, the selection term is reduces by two thirds compared with the benchmark. Instead of removing entirely the repeat movers, we keep them but associate them with only one of their a liations (randomly chosen) in col. ( ). Compared with col. ( ), the drop in selection term is less pronounced; the coe cient is equal to half of the level obtained in the benchmark regression. This demonstrates once again that including famous and obscure scholars is key to identifying sorting and selection patterns. In particular, the magnitude of the selection term are strongly governed by the fact that the location choices of (high-ability) repeat movers are less sensitive to distance than those of lower-ability scholars.

In col. ( ) of Table , we relax the assumption of independent career choices for multi-destination scholars, and estimate a mixed logit model with individual-speci c vectors of coe cients drawn from a normal distribution. The agglomeration, selection, and sorting mechanisms are preserved. Although the mixed logit entails six additional parameters (the s.e. of the six coe cients -not reported), a likelihood ratio test would reject the benchmark formulation in favor of the mixed logit formulation. The mixed logit has a disadvantage though: the estimates are obtained by simulation, while in the multinomial logit, a likelihood function is maximized. In addition, the results depend on the assumption regarding the distribution of the random parameters.

.

Endogeneity of q i

The most problematic endogeneity issue arises because the ability of each professor i is measured by an index of human capital observed a long time after the end of her career (q i ), which is likely to be in uenced by the quality of the university that was chosen. This means that we should distinguish between q i , the innate/exogenous level of ability, and q i , the ex-post level of notability. Let us denote by k * the university chosen by a scholar. Ideally, we should use q i to estimate the multinomial logit ( ). However, we only observe q i , and this ex post level might be a ected by Q k * t(i) , the notability of the chosen university. This implies that we do not observe the potential level of human capital if the individual had been working at a di erent university k. Assume for example that q i = q i + θQ k * t(i) and denote by V ikt(i) the indirect utility level obtained after replacing q i by q i in Eq. ( ).

In theory, the multinomial logit implies that university k dominates university k if V ikt(i) + ϵ isk > V ik t(i) + ϵ isk , which only depends on the characteristics of individual i and universities k and k . In practice, we are unable to model V ikt(i) and V ik t(i) properly because our measure of individual human capital is k * -speci c (i.e. in uenced by Q k * t(i) ). The endogeneity of q i implies that the di erence in utility is measured with additional noise: university k dominates university k if

V ikt(i) + ϵ isk > V ik t(i) + ϵ isk + θQ k * t(i) Δ ikk t(i) , ( )
where

Δ ikk t(i) ≡ β Q kt(i) -Q k t(i) + β (d ik -d ik )
results from the two interaction terms that are affected by our noisy measure of individual human capital in Eq. ( ). The term +θQ k * t(i) Δ ikk t(i) in Eq. ( ) is correlated across destinations, due to the presence of Q k * t(i) . Hence, the inability to observe q i leads to the violation of the IIA property.

To mitigate this problem, we estimate a nested logit model (McFadden ) where nests are de ned as groups of universities sharing similar levels of notability (Q kt(i) ≈ Q k t(i) ) during the years of activity of individual i. We partition the choice set K t(i) into four groups of alternatives, K mt(i) with m = ( , , , ) for the top, mid-high, mid-low, and bottom universities. Our partition is based on the notability index observed in the th and th periods. Each university belongs to exactly one nest. Building on Ortega and Peri (

) and Bertoli and Moraga ( ), we assume that the individual random taste shock is a mixture of a location-speci c and a nest-speci c term:

ϵ isk = ψ m υ isk + ( -ψ m )υ im ,
where ψ m ∈ [ , ] is the weight associated with the location-speci c term, υ isk , which is assumed to be independently and identically distributed as EVT-I; and υ im is an error term that is speci c to the m th nest (k ∈ K mt(i) ), whose distribution depends on ψ such that the marginal distribution of ϵ isk is also EVT-I (Cardell ). Parameter ψ m also determines the mutual correlation in the realizations of the nest-speci c error term. We have ψ m = √ ρ m , where ρ m represents the correlation coe cient within nest m. Hence, ψ m is a dissimilarity parameter. The higher ψ m , the smaller the weight of the nest-speci c component and the smaller the within-nest correlation of error term. When ψ m = for all m, the nested logit boils down to the standard multinomial logit (ϵ isk = υ isk ).

The nested logit model assumes a generalized version of the EVT-I distribution, such that (i) the mean error varies across nests, and (ii) alternatives within a nest exhibit mutually correlated error terms (but the same mean). On the contrary, the error terms of two alternatives belonging to di erent nests are uncorrelated but have di erent means. In our context, this di erence in the means captures the component of the error term θQ k * t(i) Δ ikk t(i) and hence corrects for the endogeneity bias. It re ects the in uence of the chosen university on individual quality. Within a nest, this component is close to zero because Δ ikk t(i) ≈ . Notice that this technique to correct for the endogeneity bias is possible only because the q i always appears interacted with a variable for which we can build nests, and never appears alone (it cannot explain location choice alone as it is not destination speci c).

The probability of individual i choosing university k ∈ K mt(i) is equal to the product of the probability of choosing alternatives in nest K mt(i) and the probability of choosing exactly k in K mt(i) (Heiss et al.

). It is given by

p iskt(i) = exp(βx ikt(i) /ψ m ) exp(IV mt(i) ) × exp(IV mt(i) ψ m ) m exp(IV m t(i) ψ m ) ∀t, ( )
where

IV mt(i) = ln k ∈K mt (i) exp(βx ikt(i) /ψ m )
is the inclusive value of each nest K mt(i) , representing the rescaled measure of attractiveness of the nest for individual i (i.e. the expected value of the utility individual i obtains from the alternatives in nest K mt(i) ).

Results are provided in col. ( ) of Table . Compared to the benchmark, the e ects of agglomeration are weakened but still positive and highly signi cant; part of the agglomeration force is likely to be captured by the nest-speci c error term. The selection coe cient is slightly greater. Sorting is weakened but remains highly signi cant and important compared to the agglomeration e ect: when q i is around , positive sorting increases the gains from settling in a more prestigious university by a factor of . Note that we reject the assumption of no nests, either through a likelihood ratio test (lr= . ), or by testing whether the correlations within nests are zero, or equivalently ψ m = ∀n (Wald= . , p-val= .

). We also reject that the degree of correlation inside each nest is the same, ψ m = ψ t(i) ∀m (Wald= . , p-val= .

).

Secondly, we go beyond individual cases by using our estimated model to simulate the contribution of agglomeration, positive selection, and positive sorting to total university output by year. We construct a proxy for the total output of university k in year t, denoted by Y kt , which is an aggregation of the human capital of all scholars predicted to work there. Denoting the number of active scholars in year t by

Λ t = {i|t b i ≤ t ≤ t f i }
, we de ne Y kt as a CES (constant elasticity of substitution) combination of the ability levels of its predicted members:

Y kt = ∑ i∈Λ t pikt q σ- σ i σ σ- , ( )
where pikt is the weight given to professor i at university k in year t. We set it equal to the simulated probability that i goes to k from the multinomial logit model -like the probabilities shown in Table for two cases. It to Smith, it would have been better to have professors paid by students and not by the university. He was convinced that the governance and incentives o ered by Scottish universities (a small xed wage, plus fees paid by students) better guaranteed a high quality. This opinion did not prevent him from leaving in his chair at Glasgow university to become the tutor of the young Duke of Buccleugh during his trip to France (notably to Toulouse). This way, he more than doubled his salary in addition to a lifetime pension once his tutoring was over (Rae ); see also Appendix F.

di ers from the actual probability p ikt , which is equal to one if scholar i was a liated with university k at year t. Parameter σ represents the elasticity of substitution between academic scholars' human capital in producing scienti c knowledge, assumed to be equal to the elasticity of substitution between the topscholars in producing notability in Eq. ( ).

The simulated output Y kt should be interpreted as including advancement to knowledge, quality of teaching, and service to society (such as supplying cautious physicians, rigorous lawyers to the local courts, or well-educated priests and pastors to parishes). Then, we compare the total simulated output,

Y t = ∑ k Y kt , ( )
in the benchmark -we use the term "benchmark" for the simulation and for the regression model -with the counterfactual output levels obtained after neutralizing the agglomeration, positive selection, and sorting terms (separately or jointly). Hence, the important point here is not the level of Y t in itself, but the gap between Y t with and without academic market forces. We de ne the university output gain due to market forces as the di erence between the predicted academic output and the counterfactual level, expressed as percentage of deviation from the counterfactual level.

When the elasticity of substitution tends to in nity (σ = ∞), we have perfect substitutability between scholars. The total output is the sum of individual human capital, independent of location (represented by the pikt(i) ):

lim σ→∞ Y t = ∑ k ∑ i∈Λ t pikt(i) q i = ∑ i∈Λ t q i .
Hence, there is no gain to expect from market forces. By contrast, when σ is nite, there is a complementarity relationship between academic scholars. The smaller σ, the greater the knowledge gain from agglomerating high-ability scholars at the same university, and the agglomeration of the highest ability scholars leads to output gains. In our benchmark regressions and simulations, we use a CES production function with σ = , in line with the de nition of the notability of the university in Eq. ( ). ). Focusing on the benchmark model in Panel (a), the black curve shows the output gains from academic market forces (i.e., agglomeration, selection and sorting jointly). These gains are obtained after neutralizing the e ect of agglomeration, positive selection, and positive sorting on pikt(i) in the multinomial logit model, while keeping the distance term and the university xed e ects (i.e. basic gravity). The other curves in gray show the gain from agglomeration, sorting and selection forces in isolation. We nd that market forces increase the total output of Europe by about % before the Black Death ( universities), by about % before the invention of the printing press ( universities), and by % after the rise of Protestantism ( universities), at the beginning of the Scienti c Revolution.

It is worth noticing that academic market forces do not necessarily increase total simulated output, as ap- pearing in the rst century. Their joint e ect on output depends on the correlation between the notability of universities and the level of city/university amenities (captured, in our regressions, by the university xed e ect and the attractiveness of the city). When the correlation is high, the e ects of notability and amenities point in the same direction; the best scholars agglomerate in the best universities. When the correlation is lower, agglomeration and sorting can result in the concentration of talent in second-best universities, which reduces total academic output. This is at least the case if the intensity of agglomeration and sorting forces is limited.

The e ects of academic market forces become weaker after . They increase total output by about -% over this period. Overall, we nd that agglomeration and sorting induce smaller output gains when the individual choice set is large. For this reason, their e ect on academic output diminished in the th centuries, when the number of universities almost doubled. What is speci c to this period is the presence of many universities with a large number of scholars having published something (q i > ) which was not highly in uential. Shutting down agglomeration redistributes superstars to the advantage of these less prestigious universities, thus increasing the output of the many average people there.

When decomposing the total output gains in its three components, we nd that agglomeration and positive sorting play an important role, especially in earlier times, when there are few universities. By contrast and in line with our empirical ndings, positive selection hardly in uences the total simulated output. We have seen in Table that positive selection tends to scatter talents across universities by increasing the menu of options for the highest-ability scholars, but the total e ect of this increased dispersion is small. It is worth noting that the sum of the three components taken in isolation signi cantly exceeds the total output gains in most years. This is because our model is non linear; the e ect of positive sorting is greater when agglomeration forces are not accounted for, and vice versa.

The bottom panel of Figure shows that very similar ndings are obtained when using estimates from the nested logit model with σ = . By contrast, our results are quantitatively sensitive to the value of σ. As stated above, the gains from market forces would disappear if we had taken σ = ∞, as the allocation of scholars (represented by the pikτ(i) ) across places would not matter. Although the bene ts of sorting however only slightly exceed those obtained in the benchmark, the positive e ects of agglomeration are magni ed under the high-complementarity variant with σ = . . In addition, with this variant, we nd smaller variations in output gains across years. This means that the huge gains from agglomeration in the top universities are not compensated for by losses in average-and low-quality universities in the more recent periods. Overall, when combining all mechanisms, the simulated output increases by % in the th and th centuries, and by % in the rst half of the th century.

To further understand the role of market forces, Figure maps the winners (in green) and losers (in red) due to market forces in the period -. The surface of each circle represents the di erence in simulated output between the benchmark case and the basic gravity case. An easily understandable case is Lund vs Copenhagen. With market forces, scholars born in Sweden are more likely to locate in Copenhagen which has a high notability rather than in Lund, which is just average, while without agglomeration and sorting forces, they are content with Lund. We also note that Rinteln is a big loser in Germany, being surrounded by many good universities such as Leipzig and Jena. It is also noteworthy that the South of Europe is not doing so poorly, although the bigger gains are in the North. Renowned Southern universities still attract talents (Salamanca, Padua, Bologna, and Rome). In a sense, without market forces, the fate of the South would have been worse.

When looking at universities which were permanently closed down over the period -, many of them were losers from the market in the last periods. Altdorf Overall, our results show that agglomeration and sorting e ects in the academic market contribute to fostering university output. The sizes of the agglomeration and sorting e ects before the middle of the th century are quantitatively signi cant. Thanks to these e ects, university output increases by % when considering conservative complementarity forces, and almost doubles when considering greater complementarity forces. In addition, we do not model any cumulative e ect of knowledge creation. Hence, our % should be understood as a lower bound.

Several economic historians claim that labor markets were relatively complete and competitive in Medieval Europe: "Given the low reproductive success of the urban population there had to be a constant ow of labor from the country to the city (Clark ). The records of a tax levied by Philip the Fair on the commoner households of Paris show that percent were foreigners: . percent English, . percent Italian, . percent German, . percent Flemish, . percent Jewish, and . percent Scottish" (Clark , Sussman ). We can compare these numbers with the origin of the scholars of Paris University in the rst two periods of our sample ( -). Based on the persons with known origin, we obtain that % of the scholars were born in France (in its limits), % are British, % are from Germany, % are from Italy, and % are from the Low Countries -the data for this period are mostly based on Courtenay (

), Gorochov ( ), and Genet (

). Although the mobility of ordinary people seems quite high already, the mobility of university scholars is higher by an order of magnitude.

The importance of market forces seem particularly relevant in the years preceding and coinciding with the dawn of the Scienti c Revolution, a period commonly de ned as spanning Copernicus's and Newton's times, i.e.

- (Applebaum ). In the last two centuries before the Industrial Revolution, these e ects decrease signi cantly or even become non-existent. Hence, although we provide no causal evidence of such a link, our simulations lend credence to the hypothesis that universities might have been key to triggering the rise of this new science. This view is corroborated by the analysis of the gains from the market at the local level. In our simulations, the universities gaining the most from agglomeration and sorting forces in the period -are Rome, Bologna, Padua, Paris, and Louvain. In the period -, one can add Cambridge and Leiden to the list. Those were indeed leading universities for the Scienti c Revolution.

Conclusions

In European universities, students were educated by a plurality of masters, and schools were open to students and scholars from all parts of Europe. In this paper, we map the European academic market in the medieval and early modern times. We build an original database of thousands of scholars from university sources to study the location pattern of scholars over the time span -. The quality of scholars is measured using information provided by Worldcat and Wikipedia. Using a multinomial logit, we show that scholars tend to agglomerate in the best universities, and that this phenomenon is more pronounced within the upper tail of the talent distribution: better scholars are more sensitive to the quality of the university (positive sorting), and migrate over greater distances (positive selection). Agglomeration and sorting patterns in uenced the distribution of upper-tail human capital across Europe, and contributed to fostering university output at the dawn of the Scienti c Revolution.

Agglomeration, sorting, and selection testify to market forces at work. They appear when there is a competition between universities to attract scholars, or among scholars to land the best positions available. This contrasts with a common but mistaken view that markets are a modern phenomenon, but our ndings are in line with the qualitative evidence put forward by historians such as Denley ( b) who describes the emergence in Italy of "an e cient and sometimes cut-throat academic market, with its own 'transfer season,' clearly de ned hierarchies, rocketing salaries for the top players, and a mentality of academic celebrity that fed o it." At the European level, two features may have helped the academic market to develop. First, political fragmentation, together with competition between church and state, prevented a centralized control by the political sphere of universities. Second, the use of Latin as a lingua franca, which persisted late into the early modern period and allowed scholars to teach anywhere at low cost.

Our simulations suggest that the presence of a functioning academic market in Europe helped universities to produce more at the dawn of European primacy. This might have paved the way for the Enlightenment, humanistic, and scienti c revolutions. We thus provide some quantitative support to the views developed by historians, such as Hu (

)'s approach to the Scienti c Revolution, comparing the West to China and the Islamic World. Hu suggests that the origins of the stronger support given to scienti c inquiry in the West during the early modern period can be traced back to medieval times when European institutions were reconstructed. In this context, he sees the rise of European universities in the Middle Ages and their long-run contribution to the Scienti c Revolution as highly signi cant.

0km 300km 600km N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N 30°N 35°N 40°N 45°N 50°N 55°N 60°N 65°N 20°W 10°W 0°10°E 20°E 30°E

B Barycenters

The top panel of Figure B. shows the barycenter, with coordinates R. If each scholar i is born in a space with coordinates r i , the barycenter is such that:

i (r i -R) = .
It gives equal mass to each scholar. The bottom panel of Figure B. shows the quality-adjusted barycenter, with coordinates R q . Is solves:

∑ i q i (r i -R) = .
where q i is the human capital of each scholar i. Adjusting for quality does not change the qualitative changes seen in the previous gure, but ampli es the movement towards the North. We provide here some statistics for each university, classifying them according to the coverage o ered by the sources: comprehensive, broad, partial. We also provide references to the sources used. We also indicate when the institution was not in the list provided by Frijho ( ).

C Allocation of Academic Scholars by Field of Knowledge

D. Universities with Comprehensive Coverage

The coverage is de ned as "comprehensive" when data collection is based on an existing website or book whose aim is to list all professors of a given institution.

-

D. Universities with Broad Coverage

Coverage is de ned as "broad" when it is based on the combination of several sources, including books on the history of the university.

-Cathedral school of Chartres ( ): Herbermann ( ). One of the most famous cathedral school, already active before our sample starts. Did not transform into a university (not in Frijho (

)).

D. Universities with Partial Coverage

The coverage is de ned as "partial" when the sample of scholars was informed by sources from other universities and general thematic biographies.

- D.

E Additional Robustness Tests

In Table E. , we assess the robustness of our results to two identifying assumptions. The benchmark results are repeated in col. ( ). Then, in col. ( ), we decrease σ from to . (i.e. a stronger complementarity between top-scholars in the notability equation). This does not change the estimation results much (but this might be important for the simulations). In col. ( ), we set ω = , counting each repeat mover as contributing in full to the notability of their universities of destination.

Benchmark

F Scholars' Human Capital and Salaries

There is considerable anecdotal evidence that compensations for academic contracts go well beyond paid salaries. They include payments from students, prebends, and many forms of in-kind bene ts. Yet, it is interesting to examine the relationship between scholar's human capital (as measured by q i ) and existing data on monetary remunerations. In the two sub-sections below, we rst review the available data on salaries, and argue that such data are poor proxies for the overall remuneration for academic services (i.e. the market value of a scholar). Keeping in mind such limitations, we then document a positive correlation between monetary income and scholar's human capital.

F. Data on Salaries: Availability and Relevance

Data availability. -Few data are available on academic scholars' earnings during the Middle Ages and the Early Modern period, Italy being an exception. As early as in the th century, the competition between Italian cities to attract students fostered the demand for renowned academic scholars. This competition A prebends is a stipend paid by a cathedral or collegiate church to a clergyman in its chapter.

encouraged medieval Italian universities to pay high salaries to their sta in law and medicine (Verger ;

Grendler

). Furthermore, the need to increase sta visibility encouraged Italian universities to publish rather comprehensive lists of professors. These records (rotuli) are still relatively well preserved today, and often document -even if not systematically -the salary received by ordinary professors. No such data are available for the myriad of extraordinary professors (Zanetti ). In the early northern European universities (e.g. Oxford, Paris, Louvain), teaching of theology was predominant. Monetary payments came directly from fees paid by students, of which little information has been recorded, or from prebends (Verger ; Grendler

). Furthermore, clergymen were paid little or nothing for their teaching (Post ; Paquet ).

For the Early Modern period, data on scholars' remuneration remain scarce, even though wage payments by the community or the Prince became the norm in most universities. For the majority of universities, nancial records are incomplete or inexistent. Information on wages appears occasionally in deliberations or in dispute settlements (through notarial record or trial records, as in the case of French universities for example). In addition to Italian institutions, the universities of Ingolstadt and Basel -where there exists detailed annual accounts for the periods -and -, respectively -provide wage data (Rosen ; von Schrottenberg

). In the national accounts documenting revenues and expenditures of the university of Basel, we have a comprehensive list of salaries as well as data on the share of expenditures for the university in total expenditures of the city over this period (Rosen ).

Relevance. -In addition to the loss/destruction of archives or the absence of systematic recording, the hybrid mode of remuneration of professors challenges a systematic use and analysis of salaries. This concerns the de nition of the "salary", as well as the direct comparisons between individuals and institutions. Professors are remunerated in a variety of ways:

A) In monetary form as a xed wage (like in Pavia for instance, see Zanetti ); B) Supplemented with fees from their students for attending classes and/or taking the exam (for Edinburgh, see Rae ); C) In kind (rent, various expenses, crop, wine) (see Drüll for Heidelberg); D) In the form of privileges or bene ts (see Nadal for Valence, Evans for Oxford); E) Reputation and prestige, which are di cult to quantify.

Friedrich Spanheim, a well-known theologian, for instance, was paid in Guilder, corn and wine by the University of Heidelberg (Drüll ). In the Scottish system, the salary frequently constituted only a small part of the professor's emoluments, as reported by Adam Smith (Smith ). The greater part was received from the fees/dues of students, an incentive mechanism that seemed desirable to him. His regular income at Glasgow University ( -) was estimated by John Rae to have been no more than £ (£ maximum for a xed salary, £ maximum in fees), plus the free use of a large manse on campus (Rae ). Adam Smith left his chair in Glasgow in to become the itinerant tutor of the young Duke of Buccleugh, with a wage of £ per year, travel expenses abroad and a pension of £ per year for life thereafter. It was not uncommon for an academic career to be a stepping stone to a better paid career, or to be conducted with another parallel activity (lawyers, doctors) or public o ce. Reputation and prestige were then the best forms of remuneration. As Zanetti (

) notes, for the University of Pavia, the university gave prestige, not fortune.

Another di culty is the lack of continuity of payments. Wage payments were subject to the hazards of history (black death, wars, etc.). It was not uncommon for payments to be interrupted. The university of Greifswald serves as an example for the unpleasant situation of scholars and universities during the Thirty Years' war. It was mainly due to the commitment of the (remaining) scholars that academic life could be sustained. Already at the beginning of the war, when academic life was unaltered, salaries were not continuously paid. In the second part of the war, the situation deteriorated further (Langer ).

F. Salaries and notability

The available wage data are too fragmented to be included in our econometric analysis. More importantly, wage data are very likely not representative for our universe and have limited relevance, as explained above.

Another issue related to the use of wage date arises due to the timing of information. While our notability index is an ex-post indicator, salaries would be linked to scholars' historical notability and seniority. Thus, earning capacities of the same person changed over the life-cycle.

Nevertheless, we collected data on wages paid to professors from some Italian universities (Florence, Padua, Pavia, Perugia, Pisa), northern Alps universities (Basel, Ingolstadt, Louvain) and, with much more fragmented and scarce data, southern French universities (Aix, Bordeaux, Montpellier, Valence). Data are expressed in local currency and obtained from secondary sources compiled from archives materials. We focus on the highest monetary salary of each professor i, and compute the correlation with our index of notability or human capital (q i ) within each institution. We spilt data in short periods of years to mitigate the role of changing prices.

Figure F. shows the correlation between q i and salaries by periods of years between -and -. For each period, we select one university with a su cient number of observations. Data for other universities with at least some wage data are summarized in Tables F. by period, which lists our main data sources.

All panels in Figure F. show a positive correlation between the recorded monetary salary and our notability index. This nding is consistent with human capital theory. We identify one exception (the university of Ingolstadt in -) for which the correlation is slightly negative. In some cases, the sample is too small to be conclusive, as documented in Tab. F. . Another challenge arises from the high share of scholars who did not leave any footprint on Wikipedia or Worldcat. The university of Perugia (faculty of law and medicine), before printing, exempli es such a situation. Despite these limitations, the correlation remains positive, even if not highly signi cant.

  . ( ) de nes the period. Cols. ( ) and ( ) report the period-speci c numbers of scholars and universities covered by the database. Col. ( ) gives the fraction of scholars whose birthplace is known. Cols. ( ) and ( ) give the fraction of scholars who have a Wikipedia page and at least one recorded publication in Worldcat.

Figure

  Figure : Maps of scholar-university dyads by period ( / )

  Notes: Col. ( ) gives the results of the PCA analysis conducted with two Wikipedia and three Worldcat indicators. The two Wikipedia indicators are removed in Col. ( ). Col. ( ) decomposes the number of works into two categories, namely works by and works about each scholar. The top panel gives the estimated weight of each component. The middle panel gives the number of eigenvalues greater than unity as well as the share of the variance explained by the rst component. The bottom panel reports the correlation between the three indices of human capital.

  on ( . ) Theophrastus von Hohenheim ( . ) Jakob I. Bernoulli ( . ) Daniel Bernoulli ( . ) Jeremy Bentham ( . ) Notes: Scholars' ranking by period based on the index of human capital computed in Col. ( ) of Table .

Figure :

 : Figure : Computing the notability of the University of Louvain in

  Figure shows the evolution of institutional notability of universities which topped the ranking of institutions during at least one year over the whole time span -. The median notability indices of each university are provided in Appendix D. Compared with the full sample shown in Figure ,we have removed universities with fewer than scholars in total (as we need enough observations to identify university-speci c xed e ects in our econometric analysis), and also those with extremely low coverage, i.e. fewer than scholar per time window of years on average.

Figure :

 : Figure : Institutional notability of top universities over the whole time span -

Figure

  Figure shows the university output gains obtained with the benchmark model (i.e. standard multinomial logit (ML) model with σ = ) in the top Panel (a), and with alternative estimates in the bottom Panel (b).In Panel (b), we compare the total output gain obtained with the benchmark model, with that obtained under the nested logit (NL) variant, and under the high-complementarity variant (i.e. multinomial logit model with σ = . ). Focusing on the benchmark model in Panel (a), the black curve shows the output gains from academic market forces (i.e., agglomeration, selection and sorting jointly). These gains are obtained after neutralizing the e ect of agglomeration, positive selection, and positive sorting on pikt(i) in the multinomial logit model, while keeping the distance term and the university xed e ects (i.e. basic gravity). The other curves in gray show the gain from agglomeration, sorting and selection forces in isolation. We nd that market forces increase the total output of Europe by about % before the Black Death ( universities), by about % before the invention of the printing press ( universities), and by % after the rise of Protestantism ( universities), at the beginning of the Scienti c Revolution.

Figure :

 : Figure : University output gain from market forces by year (

  Valence (closed in ) are in this category. A few winners were closed too: Erfurt (closed in ) and Frankfurt (Oder) (closed in ).

Figure

  Figure : Winners (green) and Losers (red) from Market Forces in -

Figure

  Figure A. : Coverage of the database: places of birth of scholars

  Figure B. shows that the barycenter moves East then North as time passes.

Figure

  Figure C. : Fields of knowledge, periods to

  min max Year of Birth + , min

						k	[ rst year of obs. at univ. k],
				min k	[approximate date at univ. k] , min k	[last year of obs. at univ. k], Year of Death . ( )
	t	f i = max min {Year of Birth + , Year of Death} , max k	[ rst year of obs. at univ. k],
						max k	[last year of obs. at univ. k], max k	[approximate date at univ. k] . ( )
	For simplicity of exposition of the stylized facts, we divide the whole observation window into eight periods,
	denoted by τ ∈ { , , , , , , , }, corresponding to major historical events: from the urban revolution
	to the rst universities (	-	), from the o cial foundation of Paris and Oxford in	to the Black
	Death (	-	), from the Black Death to the invention of the movable-type printing press (	-	),
	from the printing press to the rise of Protestantism (	-	), from Protestantism to the beginning of
	the Thirty Years' War (	-	), from the Thirty Years' War to the revocation of the Edict of Nantes
	(	-	), from this revocation to the rise of Enlightened universities (	-), and from Enlightened
	universities to	(	-	). We assign each scholar to a period τ based on t b i . The beginning date t b i

Table :

 :

					Summary statistics for scholars by period
	Periods τ		Nb. obs. Nb. univ. Birthplace (%) Wikipedia (%)	Worldcat(%)
	(	-	)		.	.	.
	(	-	)	,	.	.	.

Table :

 : First principal component of scholars' human capital

		( )	( )	( )
		Benchmark No Wikipedia	Works by or about
	Nb. characters of Wikipedia page	.	-	.
	Nb. languages Wikipedia	.	-	.
	Nb. works in Worldcat	.	.	-
	Nb. languages in Worldcat	.	.	.
	Nb. library holdings in Worldcat	.	.	.
	Nb. publications by in Worldcat	-	-	.
	Nb. publications about in Worldcat	-	-	.
	Nb. Eigenvalues >
	% variance explained by st PC	. %	. %	. %
	S.E.	.	.	.
	Corr. with ( )	.	.	.
	Corr. with ( )	-	.	.
	Corr. with ( )	-	-	.

Table :

 :

	Multinomial logit regressions: results from a standard logit model
		( )	( )		( )	( )		( )		( )
	Distance:
	d ik	-. ( .	) ( .	)	( . )	( .	)	( . )	( . )
	Agglomeration:
	Q kt(i) (notability of k)		. ★★★	. ★★★	. ★★★	. ★★★	. ★★★
			( . )	( . )	( .	)	( .	)	( . )
	P kt(i) (pop. in city k)		. ★★★	. ★★★	. ★★★	. ★★★	. ★★★
			( . )	( . )	( . )	( . )	( .	)
	D kt(i) (democracy in k)		. ★★★	. ★★★	. ★★★	. ★★★	. ★★★
			( . )	( . )	( . )	( . )	( . )
	Selection:
	d ik q i				. ★★★			. ★★★	. ★★★
					( . )			( . )	( . )
	Sorting:
	Q kt(i) q i					. ★★★	. ★★★	. ★★★
						( . )	( . )	( . )
	k FE	yes	yes		yes	yes		yes		no
	N. Obs.	,	,		,	,		,		,
	Log Likelihood	-,	-,		-,	-,		-,		-,

★★★ -. ★★★ -. ★★★ -. ★★★ -. ★★★ -. ★★★ Notes: Estimation of the multinomial logit model involving Eqs. ( ) and ( ) using the package mlogit in R (tstat in parentheses). Cols. ( ) to ( ) include university xed e ects. * p < . , * p < . , * * * p < . .

Table :

 : Multinomial logit regressions: heterogeneous e ects

	Distance	Agglomeration	Selec	Sorting	Nb

Table :

 : Multinomial logit regressions: robustness to selection and coverage Estimation of the multinomial logit model (Equation ( )) using the package mlogit in R (tstat in parentheses). Col. ( ) recalls the benchmark results. In Col. ( ), scholars with unknown birthplace are assigned the minimal distance ( . kms) from their university. In Col. ( ), we include all universities with at least. In Col. ( ), we exclude universities with less than recorded scholars. All columns include university xed e ects. Robustness to Repeat Movers, Mixed and Nested logit Estimation of the multinomial logit model (Equation ( )) using the package mlogit in R (tstat in parentheses). Col. ( ) recalls the benchmark results. In Col. ( ), we exclude repeat movers. In Col. ( ), we randomly assign repeat movers to a single university that they visited. In Col. ( ), we estimate Equation ( ) with a mixed logit; the six variance parameters are estimated as well, four of them exhibit a variance that signi cantly di ers from zero (variance of the coe cients of d ik , D kt , d ik Q, and Q kt Q). In Col. ( ), we estimate a nested logit model, with nest de ned as quartiles of universities in terms of notability. The estimated coe cients ψ m are the within-nest dissimilarity parameters.

		Benchm	Removing	Repeat movers	Mixed	Nested
					repeat movers linked to univ.	logit	logit
			( )		( )				( )		( )	( )
	d ik	-. ★★★	-. ★★★		-. ★★★	-. ★★★	-. ★★★
		( . )	Benchm ( . )	Sample	Adding ( . )	Limited cov. ( . )	( . )
	Q kt(i)		. ★★★	Unknown partial cov. . ★★★ . ★★★	Λ kt ≥ . ★★★	. ★★★
		( .	)	( ) ( . )	( )	( .	( ) )	( .	)	( )	( . )
	P kt	d ik	. ★★★ ( . )	-. ★★★ -. ★★★ . ★★★ ( . ) ( . ) ( . )	-. ★★★ . ★★★ ( . ) ( . )	-. ★★★ . ★★★ ( . ) ( . )	. ★★★ ( . )
	D kt	Q kt(i)	. ★★★ ( . )	. ★★★ . ★★★ ( . ) ( . )	. ★★★ ( . )	. ★★★ . ★★★ ( . ) ( . )	. ★★★ . ★★★ ( . ) ( . )	. ★★★ ( . )
	d ik q i	P kt	. ★★★ ( . )	. ★★★ . ★★★ ( . ) ( . )	. ★★★ ( . )	. ★★★ . ★★★ ( . ) ( . )	. ( . ) . ★★★ ( . )	. ★★★ ( . )
	Q kt(i) q i	D kt	. ★★★ ( . )	. ★★★ . ★★★ ( . ) ( . )	. ★★★ ( . )	. ★★★ . ★★★ ( . ) ( . )	-. . ★★★ ( . ) ( . )	. ★★★ ( . )
	ψ (low)	d ik q i			. ★★★ ( . )	. ★★★ ( . )		. ★★★ ( . )	. ★★★ ( . )	. ★★★ ( . )
	ψ	Q kt(i) q i			. ★★★ ( . )	. ★★★ ( . )		. ★★★ ( . )	. ★★★ ( . )	. ★★★ ( . )
	ψ	FE			yes	yes			yes	yes	. ★★★
		N. Obs.			,	,				,	,	( . )
	ψ (high)	Log Likelihood -,	-,			-,	-,	. ★★★
											( . )
	FE		yes		yes				yes		yes	yes
	N. Obs.		,		,				,		,	,
	Log Likelihood -,		-,			-,		-,	-,

Notes: * p < . , * p < . , * * * p < . .

Table :

Notes: * p < . , * p < . , * * * p < . .

  Our classi cation of academic scholars by scienti c eld is mostly based on teaching. A scholar may act in more than one " eld". FigureC. shows the share of elds by period.

		barycenter of places of birth
		All universities / Thu Jul 08 10:17:12 2021
		60°N
	law 36%		theology 20.6%			theology 20.9%
					law 40.5%
		55°N
							sciences 3%
				sciences 5.5%
		50°N	medicine 12.9%			medicine 16.3%
	arts 25%	Latitude			arts 19.2%
		45°N
	law 32.8%				law 28.8%
		40°N	theology 12.2%			theology 11.5%
				sciences 5.8%			sciences 6%
		35°N
	arts 31.9%	10°W barycenter of places of birth 0°10°E medicine 17.3% Longitude All universities / Thu Jul 08 10:17:12 2021 arts 42%	20°E	30°E medicine 11.7%
		60°N	Periods	1200-1348 1000-1199	1440-1526 1348-1439	1618-1685 1537-1617	1734-1800 1686-1733
	law 28.3%				law 21.7%
		55°N	theology 19%			theology 21.8%
		50°N
		Latitude		sciences 6.9%	arts 32.5%		sciences 11.7%
	arts 33.2%	45°N	medicine 12.6%			medicine 12.3%
	law 18%	40°N				law 18.2%
			theology 22%
							theology 17.2%
		35°N
		10°W		0°10°E	20°E	30°E
					Longitude arts 36%
	arts 35.5%		sciences 12.8%			sciences 14.9%
			Periods	1000-1199 1200-1348	1348-1439 1440-1526	1537-1617 1618-1685	1686-1733 1734-1800
		medicine 11.7%			medicine 13.7%
	Figure B. : Barycenter of places of birth, by period. Top: unweighted. Bottom: quality weighted

-

  Cathedral school of Liège ( ): Renardy ( ). Another famous cathedral school, already active before our sample starts. Did not transform into a university (not in Frijho ()).

	Key Suppressed in -University of Catania ( O cial E ect. End Tot. nb. . ): Sabbadini ( ), Carnazza Amari ( known -University of Sassari ( ): Mattone ( ).	Share max median ).
	Key -University of Cambridge ( O cial E ect. End Tot. nb. start start profs birth pl. obscure Q kt known Share max median Q kt ): Walker ( ), Venn ( ), Lamb and Masters ( ). -University of Valence ( ): Brun-Durand ( ), Nadal ( ). Suppressed in . More details in De -University of Mantua ( ): Grendler ( ), Sommervogel ( ).
	start -University of Naples ( Uvalencia-la Croix and Fabre ( b). ): Origlia Paolino ( start -University of Trnava ( ): Sommervogel (	profs birth pl. obscure Q kt . . ). ).	Q kt .
	Echartres-Eliege-Ctoledo-Umodena-Uoxford-Uparis-Uwittenberg-Ufrankfurt--University of Toulouse ( -University of Greifswald ( -University of Abo ( ): Jensen ( ): Deloume ( ): Jensen ( ). Cpoznan-. -University of Freiburg im Breisgau ( ): Bauer ( ), Barbot ( ), Junius Institute ( ), Ferté ( . . . . . . . . ). . ), Kurrus ( ). -University of Kassa ( ): Sommervogel ( ). Czurich-. -University of Salerno ( ): De Renzi ( ), Sinno ( ). School of medicine active before o cial foun-. . . . . . . . . . . . . . . ), Gilles ( ). Suppressed in . . . . -University of Basel ( ): Herzog ( ), Schwinges and Hesse ( ), Rosen ( ). -University of Lund ( ): Delen and Weibull ( ). More details in De la Croix ( d). . Ucoimbra-. . dation date. Unequal coverage over time, continuation of university unclear for some periods. -University of Zaragoza ( ): Catalán ( ) , Borao ( ). First century of existence remains obscure. -University of Linz ( ): Sommervogel ( ). . Ukonigsberg-. . . -University of Orléans ( ): Bimbenet ( ), Duijnstee ( ), Fournier ( ). Decent coverage of law -University of Uppsala ( ): Von Bahr ( ), Astro.uu.se ( ), Jensen ( ). The rst century remains -University of St Petersburg ( ): Shemivot ( ). A university created within the Academy of Sciences.
	Ucambridge-Umessina-faculty. Suppressed in quite badly covered (but university was closed for some time). . More details in De la Croix and Doraghi ( ).	.	.	.	.	. .
	Unapoli-Ureims--Univerity of Angers ( -University of Alcala (	): Rangeard and Lemarchand ( ): Torrecilla, Arboniés, and Torres (	. ), De Lens ( . . . ).	. ), Denéchère and Matz .
	Utoulouse-Udillingen-( ). Suppressed in -University of Valencia (		.	): Piñero (	), Guerau de Montmajor (	.	.	. ), O ce of the principal ( . . .	).
	Usalerno-Uevora--University of Montpellier ( Unequal coverage.	): Astruc (	), Dulieu (	. ) (Dulieu ( .	. . ), Dulieu (	. .	), Dulieu (	)),
	Uorleans-Udouai-Germain ( -University of Wittenberg ( ). Uncertain foundation date. Excellent coverage of faculty of medicine (the most renowned . . . . . . ): Kohnle and Kusche ( ). Excellent coverage of faculty of theology.
	Uangers-Uolmutz-one) and law. Weak coverage of faculty of arts. Suppressed in -University of Frankfurt ( ): No speci c source so far.	.	. .	. .	.	.
	Umontpellier-Ualtdorf--University of Avignon ( -Lubransky Academy in Poznan ( ): Nowicki ( ): Laval ( ), de Teule (	. . ). A university-level college, mentioned in Frijho . . . . ), Fournier ( ), Bénézet ( ), Barjavel (	),
	Uavignon-Upalermo-Duhamel ( ( ) as a colony of Cracow. More details in De la Croix ( ). Suppressed in .		a).	.	.	. .	.	.
	Uroma-Uvilnius--University of Roma 'Sapienzia' ( -Collegium Carolinum in Zurich ( ): Junius Institute ( ): Renazzi ( ).	. ), Godet, Türler, and Attinger ( . . . . .	).
	Uperugia-Aherborn--University of Perugia ( -University of Coimbra ( ): Sommervogel ( ): Frova, Catoni, and Renzi ( ). More sources will be exploited. . . . . ), Zucchini ( ), Quaresima ( . .	). Com-
	StudFlorence-Ufraneker-prehensive coverage of the medieval period. Broad coverage of the early modern period. . . . . . . -University of Konigsberg ( ): Schwinges and Hesse ( ) for the beginning, Naragon (	) for the
	Emallorca-Udublin--Studium in Florence ( ): Prezziner ( end.	), Cerracchini (		. ). No university status, but important and . . . . .
	Ucahors-Uprague-Uperpignan-Uvienna-Ucologne-Uwurzburg-Uaix-Cwarsaw-Uaixbourbon-well documented. -University of Messina ( Ucagliari--The Mallorcan School of Cartography ( ): Collective ( -University of Reims ( ): Sommervogel ( Cpoznan-higher learning. Not in Frijho ( ). -University of Dillingen ( ): Fischer ( Usassari--University of Cahors ( ): Ferté ( ), Baudel ( ). ): Pastor and Camarero ( . . . . . . . . . . ). More sources will be exploited. Suppressed in . . . . . . . . . . . . . . . . . . . ). An informal institution of . . . . ), Sommervogel ( ). . . . ). Suppressed in . -University of Evora ( ): Nunes and Silva ( ), Sommervogel ( ). . Umantua-. . -University of Prague ( ): Svatoš and Čornejová ( ), Čornejová and Fechtnerová ( ). -University of Douai ( ): Soetaert and Soen ( ), Sommervogel ( ). Suppressed in . . Utrnava-. . . -University of Perpignan ( ): Carmignani ( ), Capeille ( ),Izarn ( ). Suppressed in . -University of Olmutz ( ): Sommervogel ( ). Suppressed in .
	Ustandrews-Uabo--University of Vienna ( -University of Altdorf (		): Lackner ( ): Flessa (	. . ). Low coverage, except for medicine. . . . . ), Schwinges and Hesse ( ), von Aschbach ( ), Köbler (	).
	Ulouvain-Ukassa--University of Cologne ( -University of Palermo (			. . ). Low coverage after . . ), Sommervogel ( ): Schwinges and Hesse ( ): Cancila ( ).	. . Suppressed in .	.
	Upoitiers-Ulund--University of Wurzburg ( -University of Vilnius (	. . ). Disappeared quickly after founda-. . . . ), Sommervogel ( ), Sommervogel ( ): Bumblauskas et al. ( ): Walter ( ).
	Ubordeaux-Ulinz-tion, resurrected with the Jesuits ( ). -Herborn Academy ( ): Junius Institute (	. ). Not a university, not in Frijho ( . . .	.	.	), but an impor-
	Ucatania-Ustpetersburg--University of Aix-en-Provence ( tant institution of higher learning. Low coverage so far. ): Belin ( ), Belin (		. . ), Fleury and Dumas ( . . . .	), De la Croix
	Uglasgow-and Fabre ( -University of Franeker ( ): Feenstra, Ahsmann, and Veen ( Table D. : Universities with broad coverage ( ) . ). Several schools active before o cial creation of university. Suppressed in . . ), Napjus and Lindeboom (	. More ).
	Uvalence-details in De la Croix and Fabre ( -University of Dublin ( ): Kirkpatrick ( ), Burtchaell and Sadleir ( . a).	. ).	.
	Ugreifswald--Toledo School of Translators ( -University of St Andrews ( ): Junius Institute ( ): González ( ). A famous place of high learning. Did not transform . . . ), Smart ( ). The rst two centuries remain -College of Warsaw ( ): Sommervogel ( ). A Jesuit college providing university level education (not
	Ufreiburg-Ubasel-into a university (not in Frijho ( quite badly covered. in Frijho ( )). Uzaragoza--University of Modena ( ): Mor and Di Pietro ( )). -University of Louvain ( ): Ram ( ), Nève ( -University of Aix-Bourbon ( ): Méchin ( ), Sommervogel ( ). For Frijho ( . . . ), Schwinges and Hesse ( . . . ). Suppressed in . . ), Brants ( . More details ), Lam-), started as a Studium in . Uuppsala-. . berts and Roegiers ( ). Suppressed in . in De la Croix and Fabre ( a). only. . Ualcala-. . -University of Oxford ( ): Emden ( -University of Poitiers ( ): Boissonade ( ). Suppressed in . -University of Cagliari ( ): Pillosu ( ), Tola ( ). Low coverage. ), Foster ( ). Uncertain foundation date. . -University of Paris ( ): Antonetti ( ), Courtenay ( ), Hazon and Bertrand ( ), Feret ( -University of Bordeaux ( ): Gaullieur ( ), Pery ( ). Low coverage and little hope to do better. -College of Poznan ( ): Sommervogel ( ). A Jesuit college providing university level education (not ), Table D. : Universities with broad coverage ( ) Gorochov ( ), Genet ( ). Uncertain foundation date. Loose and complex university structure. Suppressed in . in Frijho ( )).

  Cluny Abbey ( ): a key center of knowledge. Lack of sources. University of Grenoble ( ): Guénée ( ). Lack of sources. Suppressed / transferred to Valence in .

	Key -College Royal Dauphin ( O cial E ect. End Tot. nb. ): Sommervogel ( ). Jesuit college of university status. known Share max median
	-University of Munster (	start	start ): Sommervogel (	profs birth pl. obscure Q kt ).	Q kt
	Ecluny--University of Nimes (		): Sommervogel (	).	.	.	.
	Usiena-Ulerida--University of Duisburg ( Ugrenoble--University of Nijmegen ( ): Suppressed in ): (Junius Institute Uerfurt--University of Lwow ( ): Sommervogel ( ). Uferrara--University of Innsbruck ( ): Sommervogel ( Utorino--University of Besancon ( ): Beaune and d'Arbaumont ( ), Köbler ( . ). Low coverage which can be further improved. . . . . . ). Low coverage. . . . . . . . . . . . ), Lavillat ( ). Suppressed in .
	Uparma--University of Breslau (		): Fischer (	), Sommervogel (	).	.	.	.
	Udole--Collegium Carolinum in Kassel (	): The university of Kassel (	-	.	. ) mentioned in Frijho ( .	)
	Ucaen-had an ephemeral existence. More important is the Collegium Carolinum founded in . .	.	.
	Ubarcelona--University of Fulda (		): Sommervogel (	).	.	.
	Utrier--Collegium Nobilium of Warsaw (	): college of university level.	.	.	.
	Unantes-							.	.
	Ubourges-							.	.	.
	-University of Siena ( Usiguenza-		): Frova, Catoni, and Renzi (	). Low coverage after . .	.
	-University of Lerida (Lleida) ( Ugandia-pressed in Umilano-. CClermontParis---University of Erfurt ( ): Schwinges and Hesse ( ): Lladonosa ( Uorange--University of Ferrara ( ): Borsetti ( ),Pardi ( Uoviedo-Ufermo-	), Lladonosa ( ). Lower coverage after ), Esteve i Perendreu ( . . . . . . . . . . . . . . ). Not fully exploited yet. . . .	). Sup-
	-University of Torino ( Uaberdeennew-		): Vallauri (	).	.	.
	-University of Parma ( C eche-		): Rizzi ( ). More details in Rolla and Vitale (	.	).	.
	-University of Dole ( Cdauphin-		): Beaune and d'Arbaumont (	). Transferred to Besançon in . .	.
	-University of Caen ( Umunster-		): de Pontville (	), Boisard (	). Guerrin ( .	), Carel ( .	.	). Coverage can
	be improved further. Suppressed in Unimes-	.	.	.	.
	-University of Barcelona ( Uduisburg-	): no good source found yet. Suppressed in .	.	.	.
	-University of Trier ( Unijmegen-		): Sommervogel (	). Low coverage before the Jesuits came. Schwinges and . . .
	Hesse ( Ulwow-	) not exploited yet. Suppressed in	.	.	.
	-University of Nantes ( Uinnsbruck-		): Chenon (	), Grünblatt (	).	.	.
	-University of Bourges ( Ubesancon-		): Arabeyre, Halpérin, and Krynen (	), Fournier ( . .	). Decent coverage
	of top lawyers. Suppressed in Ubreslau-	.		.	.	.
	-University of Siguenza ( Ckassel-		): Sanz Serrulla (	).	.
	-University of Gandia ( Ufulda--University of Milano ( ): Sommervogel ( ): Sommervogel ( Cwarsaw-	. ). Jesuit college of university status (Frijho . ). .	).
	-College of Clermont / Louis-le-Grand ( Table D. : Universities with partial coverage ) : Sommervogel ( ). Jesuit college of university status (not
	in (Frijho	)).
	-University of Orange ( ): Bourchenin ( -University of Fermo ( ): Brizzi ( ), Curi ( ). First university from ). More details in Di Caprio and Vitale ( to with almost no data. ).
	Second university founded in -University of Aberdeen (new) -Marishal College ( ): Anderson ( . Suppressed in .	).
	-University of Oviedo ( -College La Fleche (	): Canella Secades ( ): Sommervogel ( ). Jesuit college of university level. ).

Table E .

 E : Multinomial logit regressions: Robustness to identifying assumptions

		( )	( )	( )
	σ		.
	ω
	d ik	-. ★★★	-. ★★★ -. ★★★
	Q kt	. ★★★	. ★★★	. ★★★
	P kt	. ★★★	. ★★★	. ★★★
	D kt	. ★★★	. ★★★	. ★★★
	d ik q i	. ★★★	. ★★★	. ★★★
	Q ikτ (i) q i	. ★★★	. ★★★	. ★★★
	FE	yes	yes	yes
	N. Obs.	,	,	,
	Log likelihood	-,	-,	-,

Acknowledgements

We thank the research assistants who have been contributing to this adventure: Basile Burnet, Guillaume Catoire, Valentine Debois, Giovanni Di Caprio, Mehrdaad Doraghi, Julie Duchêne, Clémence and Timothée de la Croix, Thomas Einsfeld, Maximilian Ganterer, Hugo Jay, Soraya Karioun, Victoire Michel, Annika Onemichl, Fabian Fischer, Gaia Spolverini, Baptiste Standaert, Mara Vitale, Stefanija Veljanoska, and Pascaline Zwarts.

The rst two authors acknowledge nancial support from the EOS program of the Flemish (FWO) and French-speaking (FRS-FNRS) communities of Belgium (convention on "Winners and Losers from Globalization and Market Integration: Insights from Micro-Data"). David de la Croix thanks the European Research Council (ERC) under the European Union's Horizon research and innovation programme under grant agreement No "Did elite human capital trigger the rise of the West? Insights from a new database of European scholars." Alice Fabre thanks nancial support by the French National Research Agency Grant ANR--EURE-and by the Excellence Initiative of Aix-Marseille University -A*MIDEX. Robert Stelter acknowledges nancial support from the Max Geldner foundation.

for positive selection, the e ect is positive and signi cant in all cases, more prevalent for theology and sciences. Finally, the sorting term is positive and signi cant in most sub-samples as well. It is smaller and less signi cant in the rst periods, when agglomeration forces are stronger. Overall, despite smaller numbers of observations, our results are fairly robust across sub-samples.

The results by period can be used to consider the e ect of Protestantism on the academic market. The period ends with the creation of the rst Protestant university, Marburg. The period -covers a divided world, where many scholars had to change religions if they wanted to keep their positions, while others decided to migrate to a region where their religion was accepted. Others converted voluntarily and this changed their approach to science. In the period before the Reformation, the agglomeration force attracting all scholars to the most notable universities is very strong (coe cient of Q kτ (i) around . ). Positive sorting seems negligible then. In the post-Reformation period, it is the opposite. The agglomeration force weakens (the coe cient is about . ), but sorting is strong, indicating that the ability of top universities to attract professors became con ned to top scholars. It is as if the Reformation slowed down the mobility

Implications for the Scienti c Revolution

Firstly, we assess the estimated e ect of the determinants of location decisions (x ikt ) on individual choice probabilities by comparing simulated outcomes with counterfactual experiments. We focus on the role of agglomeration, positive selection, and positive sorting for two scholars who were born in the same region in the rst period (the period with the smallest choice set), but who exhibit di erent levels of human capital. We rst consider Thomas Aquinas ( -), who was born in Roccasecca and taught theology at Paris for twenty years ( -) and at Naples. Thomas Aquinas belongs to the very top of the ability distribution (ranked th, q = . ). Aquinas's choice set consists of universities. We then consider Ro redus Beneventanus ( -), who was born in Benevento, taught law at Naples ( -), and is in the middle of the distribution (q = . ). As he was born years before Thomas Aquinas, Ro redus Beneventanus's choice set consists of just universities. In Table , we compare the predicted location probabilities of the full speci cation of Table , with those of a restricted model in which the coe cients of the selection and sorting terms are set to zero. For both scholars, the set of universities is ranked by decreasing order of the predicted probability generated by the full speci cation.

Unsurprisingly, positive selection implies a broader menu of e ective options, whereas agglomeration forces and positive sorting increase the attractiveness of famous universities. The e ects are balanced by the extent of each scholar's notability. Our estimated model shows that the most likely locations for Thomas Aquinas are Bologna ( . %), Naples ( . %), Paris ( . %) and Padova ( . %). Neutralizing the positive selection term increases the probability of choosing a good location closest to his birthplace (Naples) to the detriment of Bologna and Paris. Neutralizing the positive sorting and agglomeration term drastically decreases the attractiveness of Paris. Overall, the basic gravity model predicts a low probability of choosing Paris ( . %). The combination of agglomeration, selection, and positive sorting increases this probability by a factor of , and increases the probability of choosing Bologna by a factor of .

For Ro redus Beneventanus, who has less human capital (q i ), the selection and sorting e ects are weaker.

Our estimated model shows that the most likely location is Naples ( . %). Compared to Thomas Aquinas, Ro redus Beneventanus is more sensitive to distance, and less sensitive to the notability of the university or to agglomeration e ects. Removing the sorting e ect or the agglomeration e ect increases the probability of choosing Padua, Salerno, and Pisa, at the expense of Bologna, Montpellier, and Paris. When removing the selection e ect, similar changes are obtained. The basic gravity model also predicts that Naples and Padua are the two most attractive universities, for both Ro redus Beneventanus and Thomas Aquinas, and that the probability of choosing Paris or Bologna, the best universities in this period, are similar for both (a bit higher in fact for Beneventanus, because his choice set is more limited). However, unlike for Thomas Aquinas, the combination of agglomeration, positive selection, and positive sorting increases the probability of choosing Paris and Bologna by a factor of to only.

It is also interesting to consider the case of Adam Smith. He was very down on the universities of his time -with the exception of Scottish universities. His estimated choice probabilities are quite consistent with his opinion: out of universities, the estimated "ranking" is: . University of Edinburgh ( . %), . University of Cambridge ( . %), . University of Oxford ( . %), . University of Glasgow ( . %), . University of Paris ( . %), ..., . University of Toulouse ( . %). He wrote about the university of Oxford, where he studied, that "the greater part of the public professors have, for these many years, given up altogether even the pretence of teaching" (Smith (

), Book V, part III, chap. ). Incentives to teach were too low. According

Appendix A Coverage

To show the current coverage of the database, Figure A. displays the place of origin of all identi ed scholars over the whole period.