Last Name Analysis of Mobility, Gender Imbalance, and Nepotism Across Academic Systems

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STATISTICS SOCIAL SCIENCES areas of research. Using the distribution of first names, we show In the second randomization (by city), we shuffle the last strong gender imbalance in science, technology, engineering, and names of academics within each city. That is, for each depart- mathematics (STEM) disciplines in all systems. Finally, we show ment, we assign researchers at random from those working in that nepotism is present (but declining) in Italy. the same city. As such, names that are common at the city level but rare nationwide (reflecting, for example, geographic, linguis- Results tic, or cultural barriers) will be sampled with high probability, Data. We collected four datasets for the Italian academic sys- increasing the expected number of IPs. tem, including the names of all professors holding permanent (or In the third randomization (by field), last names are shuffled since they were introduced in 2010, temporary “tenure-track”) within field. This procedure allows us to test the existence of positions along with their institution, academic field (area; 14 field-specific names (for instance, as a consequence of immigra- coarse-grained fields), rank (which we coarse-grained into assis- tion targeting a specific field). For example, a recent National tant, associate, and full professor), and gender. We enriched the Science Foundation survey (12) found that, of 5.2 million immi- data by adding a city and region to each record. The number of grant scientists and engineers in the United States, 57% were professors is 52,004 for year 2000, 60,288 for 2005, 58,692 for born in Asia and that immigrants targeted disproportionately 2010, and 54,102 for 2015. computer science, mathematics, and engineering. For France, we collected the names, unit, and region for all Randomizing by nation, we find that, in all systems, at least a of the researchers affiliated with CNRS (Chercheurs CNRS) or few sectors (Fig. 1) and regions (Fig. 2) have a significant excess working at a mixed CNRS–university research unit (Chercheurs of IPs (with stronger deviations in Italy and France). non-CNRS). Each unit is associated with a scientific field and This excess of IPs could be caused by region-specific distri- a location. Whenever available, we stored the self-reported butions of last names, in which case the difference between maiden names. The database contains 44,860 researchers. local and national distributions would drive the results. Ran- For the United States, we collected from state records the domizing by city, we observe a large drop in the ratio between names of professors at selected R1 institutions (research univer- observed and expected IPs in Italy and France (i.e., blue vs. red sities—highest research activity according to the Carnegie Clas- bars in Fig. 1), meaning that, in these systems, the excess of sification of Institutions of Higher Education). We collected data IPs for many fields and regions is likely due to the geographic on 38 institutions, privileging the states in which more than one R1 operate. Because the data do not contain a disciplinary field, we associated professors with a discipline using the Scopus Italy, 2015 database. We were able to successfully match 36,308 professors in this way. 4 Details on data collection and processing are reported in SI 3 Appendix. The data are publicly available. 2 1 Isonymous Pairs. Each researcher is associated with an institution 0 Observed/Expected Agr Bio and field. Two researchers with the same last name working at Geo Law Med Ped Soc Econ Hum Math Phys Chem the same institution and in the same field form an isonymous CivEng IndEng pair (IP). As a shorthand, we define the “department” d as the France CNRS using maiden names, 2016 set of all researchers working in a certain field at a given institu- 2 tion. For each last name i, nid measures how many researchers with that name work in department d. The number of IPs in a 1 P nid given department is pd = i 2 . For example, if in department d, we find three researchers whose last name is Hopper 0 fo ys Observed/Expected and four called Pollock, we have that pd = 3 + 6 = 9 IPs. This Cell Eng Env Geo In Hum Math Ph Chem Genet Neuro measure can be interpreted as the number of edges connect- HE Phys ing researchers with the same name in a network where the US public research institutions, 2016 nodes are the researchers working in the same department (SI 3 Appendix, Fig. S1), and it has excellent statistical properties compared with other quantities (SI Appendix, Fig. S2). 2 Given that each department belongs to a geographic region 1 and a discipline, we can sum the number of IPs by region (pr = P P 0 pd ) or field (pf = pd ). Using randomizations, we d∈r d∈f Observed/Expected Agr Bio hys Geo Med Ped Soc Econ Hum Math P Chem probe whether the observed pr (or pf ) is significantly different IndEng from what we would expect at random. randomization nation city field Three Randomizations. p p For each dataset, we calculate r and f Fig. 1. Ratio between observed and expected numbers of IPs for each for each region and field. We then repeatedly randomize the data academic system and field. Different colors stand for three randomiza- in three different ways, each time recording the values of pr and tions explained in the text; saturated colors mark fields in which the pf for the randomized data. In this way, we obtain an approxi- probability of finding a higher or equal number of IPs by chance is ≤ mate P value measuring the probability of finding a number of 0.05 per number of fields (i.e., significant after applying a Bonferroni cor- IPs greater than or equal to what was observed empirically in a rection for multiple hypothesis testing). Agr, agriculture; Bio, biological sci- given region or field. Importantly, each randomization provides ences; Cell, cell and molecular biology; Chem, chemistry and pharmaceutical us with a different angle to probe the data, unveiling distinctive sciences; CivEng, civil engineering and architecture; Econ, economics and patterns of mobility and immigration. statistics; Eng, engineering; Env, environmental sciences; Genet, genetics; 106 Geo, geology and Earth sciences; HE Phys, high-energy physics; Hum, philol- In the first randomization (by nation), we simply shuffle ogy, literature, archeology; IndEng, industrial, electronic, and electric engi- times the last names in the database, each time tracking pr and neering; Info, information and communications sciences; Law, law; Math, pf . This randomization tells us whether the empirical data con- mathematics and computer science; Med, medical sciences; Neuro, neuro- tain more IPs at the regional or field level than we would expect science; Ped, pedagogy, psychology, history, philosophy; Phys, physics and when resampling all academics at random. astrophysics; Soc, social and political sciences.

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STATISTICS SOCIAL SCIENCES Italy (first names), 2015 category is assigned to all of the researchers (e.g., academic rank, gender, hired, or retired). Second, IPs for a certain combination 1.5 of categories are computed (e.g., IPs of the type male–female or 1.0 retired–not retired). Third, the categories are repeatedly scram- 0.5 bled within each department to estimate a P value. 0.0 For example, if the excess number of IPs was caused by nepo-

Observed/Expected aw tism, we would expect many of the pairs of isonyms within the Agr Bio Geo L Med Ped Soc Econ Hum Math Phys Chem CivEng IndEng same department to have different ranks because of the age difference between fathers and children. We thus measure the num- randomization nation city field ber of IPs of the kind full professor↔not full professor and com- pute the probability of observing a higher or equal number of IPs of this kind when shuffling the ranks within departments. In all four Italian datasets, we find a significant excess of IPs of this type (P value <0.01 for all years, computed out of 104 randomizations). Similarly, given that last names are inherited by line of father, in the case of nepotistic hires, we would expect an excess of male↔male IPs (or equivalently, fewer IPs involving a woman). Measuring the number of IPs of this kind, we find that, in all cases, the number of male↔male IPs is higher than expected by chance, with 2 years yielding significant results (2005: P value < 0.01; 2010: P value < 0.03) and two differences that are not sig- Fig. 4. (Upper) The same as in Fig. 1 but using first names instead of last nificant (2000: P value = 0.13; 2015: P value = 0.07). names. (Lower) Ratio between observed and expected number of IPs vs. pro- If nepotistic hires were orchestrated by senior faculty mem- portion of women for all years (national randomization). Some of the fields bers, we would expect retirees to be more likely to share names are highlighted for reference. Saturated colors mark significant results once with the remaining faculty than expected by chance. Take two accounted for multiple hypothesis testing. Agr, agriculture; Bio, biological consecutive periods (for example, 2000 and 2005). Some names sciences; Chem, chemistry and pharmaceutical sciences; CivEng, civil engineering and architecture; Econ, economics and statistics; Geo, geology and appear in the 2000 database but do not appear in the 2005 Earth sciences; Hum, philology, literature, archeology; IndEng, industrial, database: these faculty members have retired or exited the sys- electronic, and electric engineering; Law, law; Math, mathematics and com- tem in the meantime—we mark these as “retired.” All of those puter science; Med, medical sciences; Ped, pedagogy, psychology, history, who did not retire are marked as “remained.” Measuring the philosophy; Phys, physics and astrophysics; Soc, social and political sciences. number of IPs of the type retired↔remained and computing the probability of observing a larger or equal number of IPs of this kind when shuffling the labels retired/remained within One caveat on the analysis of first names is that, contrary to each department, we see that, in all years, the number of IPs last names, first names can fluctuate widely from year to year, of this type is significantly higher than expected (2000 and 2005: sometimes following specific events (16). For example, in SI P value < 0.01; 2010: P value < 0.02). Appendix, Fig. S6, we show that the frequency of newborns Similarly, we can find new hires for the years 2005–2015 and named Francesco (the most common first name among Italian test whether new hires are more or less likely to share names boys born in the last decade) increased of about 40% after the with the professors already in the system. This test is interest- election of Pope Francis. Because of these idiosyncratic trends, ing, because a “natural experiment” was carried out during these researchers of the same age would be more likely to share first years: the Italian law 240 of 2010, which reformed the university names than those of different ages—a problem that is absent in system, included a provision (article 18) preventing departments the study of last names. from hiring relatives of their faculty, with the explicit intent of curbing nepotism. Our results show that the effects of this law Time Evolution. For the Italian system, we have collected four can be detected in the data. Measuring the number of IPs of snapshots between 2000 and 2015 in intervals of 5 years. We can, the kind hired↔already present, we find that, in 2005 and 2010, therefore, repeat the randomizations for all datasets and track the evolution of the system in time. Earlier years yield a higher number of significant results, with one-half of the fields testing

signiﬁcantly (randomization by city) in 2000 and 2005; there were 2.0 2000 2005

five significant fields in 2010 and only two significant fields in 2010 1.5 2015 2015 (Fig. 5). The results by region follow a similar pattern (SI Appendix, Figs. S8 and S9). 1.0 0.5

Is Italian Academia Nepotistic? As shown above, the geographic 0.0 distribution of last names as well as field-specific immigration Observed/Expected Agr Bio hys Geo Law Med Ped Soc Econ Hum Math P can greatly affect the number of IPs within departments. In Italy, Chem CivEng IndEng even when accounting for these factors, we do observe significant results. Previous studies (7, 8) have suggested that the excess IPs Fig. 5. Evolution of the ratio between observed and expected number of observed in Italian academia could be caused by nepotistic hires, IPs in Italy between 2000 and 2015. Saturated colors mark significant results with fathers hiring their children and siblings for academic posts once accounted for multiple hypothesis testing. Agr, agriculture; Bio, bio- (mothers hiring their children would be undetectable, because logical sciences; Chem, chemistry and pharmaceutical sciences; CivEng, civil engineering and architecture; Econ, economics and statistics; Geo, geology they would have different last names). Although proving this and Earth sciences; Hum, philology, literature, archeology; IndEng, indus- hypothesis would require access to data on actual family ties, trial, electronic, and electric engineering; Law, law; Math, mathematics and which are not available, in this section, we present four statis- computer science; Med, medical sciences; Ped, pedagogy, psychology, his- tical tests probing whether our results are compatible with the tory, philosophy; Phys, physics and astrophysics; Soc, social and political hypothesis of nepotism. All tests have the same structure. First, a sciences.

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STATISTICS SOCIAL SCIENCES Randomizations. In all datasets, for each researcher, we have information The maximum likelihood estimate αˆ can be found by maximizing this on first name, last name, institution, and field of study as well a geographic quantity. By taking the logarithm of the likelihood and neglecting the terms information (city and region). The department is obtained by combining independent of α, one obtains institution and field. For each department, we count the number of pairs X d απ(d) + − α π(c) . of researchers with the same last name (IPs). We then sum the IPs by region mj log j (1 ) j [2] or field. The three randomizations are obtained by (i) randomizing all last j names (randomized by nation), (ii) randomizing last names within each city (d) We determined πj as the frequency of last name j in department d at (by city), and (iii) randomizing last names within each field (by field). the beginning of the period (e.g., in 2000 if the period 2000–2005 is considered) and π(c) as the frequency in the city (removing the department) at the Modeling Nepotism. We consider a simple mixture model, in which the prob- j beginning of the period. One special case that needs to considered is that ability of choosing to hire a researcher with name j in the department d and (d) (c) (d) in which the name of the new hire is not present in the department or the city c is qj = απj + (1 − α)πj , where πj is the frequency of name j in (d) (c) city, in which case πj = πj = 0. In such cases, we postulate that the name is π(c) the department, and j is the frequency in the general population from present in the city at an unknown (low) frequency. This assumption is quite which the new researcher is sampled. The parameter α can be interpreted convenient, because for π(d) = 0, the exact value of π(c) does not impact the as the probability of a nepotistic hire. For instance, in a perfectly nonnepo- j j maximum likelihood estimate of α. In fact, the term log((1 − α)π(c)) appear- tistic system, α would be equal to zero, and all of the last names of new j (d) (c) hires are random samples from the general population. Note that, even if ing in Eq. 2 in the case of πj = 0 can be written as log(1 − α) + log πj , α = 0, it is possible to hire a person with a last name that is already present and therefore, the second additive term does not impact the maximum like- in the department. The parameter α quantifies, therefore, the probability lihood estimate. of a nepotistic hire using the excess of IPs. Note that, given the finiteness of the data, a maximum likelihood esti- For a given period (e.g., 2000–2005), we compile a list of all new hires for mate αˆ > 0 could be a consequence of fluctuations and not nepotistic hires. d each department, obtaining mj : the number of people hired in department To assess the importance of these fluctuations, we compared the maximum d with last name j. Under our model, the probability of observing a set of likelihood estimate of αˆ with the one obtained by randomizing the names new hires with last names {md} is given by the multinomial distribution of new hires within a department.

ACKNOWLEDGMENTS. We thank M. J. Michalska-Smith for comments. Data P d mj ! md were provided by Scopus.com. J.G. was supported by the Human Frontier d j Y (d) j P({m }) = qj . [1] Science Program; S.A. was supported by National Science Foundation Grant Q md! j j j DEB 1148867.

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