RESEARCH ARTICLE

German cities with universities: Socioeconomic
position and university performance

Anthony F. J. van Raan

Centre for Science and Technology Studies, Leiden University, Leiden, Die Niederlande

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Tagebuch

Schlüsselwörter: bibliometric analysis, citation impact, Leiden Ranking, socioeconomic strength,
university cities, urban scaling

Zitat: van Raan, A. F. J. (2022).
German cities with universities:
Socioeconomic position and university
Leistung. Quantitative Science
Studien, 3(1), 265–288. https://doi.org
/10.1162/qss_a_00182

DOI:
https://doi.org/10.1162/qss_a_00182

Peer Review:
https://publons.com/publon/10.1162
/qss_a_00182

zusätzliche Informationen:
https://doi.org/10.1162/qss_a_00182

Erhalten: 10 Oktober 2021
Akzeptiert: 17 Januar 2022

Korrespondierender Autor:
Anthony F. J. van Raan
vanraan@cwts.leidenuniv.nl

Handling-Editor:
Vincent Larivière

Urheberrechte ©: © 2022 Anthony F. J. Transporter
Raan. Published under a Creative
Commons Attribution 4.0 International
(CC BY 4.0) Lizenz.

Die MIT-Presse

ABSTRAKT

A much-debated topic is the role of universities in the prosperity of cities and regions. Two major
problems arise. Erste, what is a reliable measurement of prosperity? And second, was sind die
characteristics, particularly research performance, of a university that matter? I focus on
this research question: Is there a significant relation between having a university and a city’s
socioeconomic strength? And if so, what are the determining indicators of a university; für
Beispiel, how important is scientific collaboration? What is the role of scientific quality
measured by citation impact? Does the size of a university, measured in number of publications
or in number of students matter? I compiled a database of city and university data: gross
urban product and population data of nearly 200 German cities and 400 districts. Universität
data are derived from the Leiden Ranking 2020 and supplemented with data on the number
of students. The socioeconomic strength of a city is determined using the urban scaling
methodology. My study shows a significant relation between the presence of a university
in a city and its socioeconomic indicators, particularly for larger cities, and that this
is especially the case for universities with higher values of their output, impact and
collaboration indicators.

1.

EINFÜHRUNG

1.1. Objective of the Study

Knowledge is the driving force of technological, socioeconomic, and healthcare innovations,
and therefore a crucial source of sustainable wealth. Cities, insbesondere, are centers of knowl-
edge production and innovation, especially when knowledge institutions such as a university
are present. Concentration of knowledge production increases the attractiveness of cities for
talented and entrepreneurial, highly skilled persons, and thus these urban centers continually
reinforce their socioeconomic strength (Bettencourt, Lobo, & Strumsky, 2007; Bettencourt, Lobo
et al., 2007; Glaeser, 1999). There is an extensive literature on the relation between human cap-
ital and innovation on the one hand, and the increase of socioeconomic welfare on the other.
Recent work focuses on the regional innovation impact of universities in Europe (Tijssen,
Edwards, & Jonkers, 2021). Drucker and Goldstein (2007) describe the growing interest in mea-
suring the impacts of higher education on regional economies and review the approaches used
to study the influence of research universities on regional economic development. These authors
focus on the methodological advantages and shortcomings of four major research designs:
single-university impact studies, surveys, knowledge production functions, and cross-sectional

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German cities with universities

designs. They conclude that knowledge-based activities such as teaching and basic research
have substantial positive effects on a variety of measures of regional economic progress.
Trotzdem, regional economies appear to vary considerably in their ability to convert
local academic research into local commercial innovation (Agrawal & Cockburn, 2003) Und
measuring the economic impact of university research proves difficult (Bessette, 2003).

Recent research on a worldwide scale based on an analysis of 15,000 universities in about
1,500 regions in 78 countries shows that increases in the number of universities are positively
associated with future growth of GDP per capita and that there appear to be positive spillover
effects from universities to geographically close neighboring regions. This effect is not simply
driven by direct expenditures of the university, its staff, and its students but also through an
increased supply of human capital and greater innovation (Valero & van Reenen, 2019). Dort
is a need for a study that looks more closely at the direct socioeconomic effects of universities.
In this study I investigate whether there is a significant relation between the mere presence of a
university in a city and a city’s socioeconomic strength, the growth of its gross urban product,
and its population size. And if so, what are the characteristics of a university that matter?

As in many countries, in Germany almost all major cities do have institutions of higher educa-
tion, but these can differ enormously, both in type of institution, ranging from large research-
intensive universities to small, specialized colleges, without the formal status of a university, als
well as in size (Lepori, 2021). In der Tat, in the approximately 650 higher education institutions in
Germany I find large universities with more than 40,000 students as well as colleges with fewer
als 100 students (German Federal Bureau of Statistics, 2021). To illustrate this, I show in the Sup-
plementary Material Figure S6 the ranking of these higher education institutions by number of stu-
dents. Only a small proportion of these higher education institutions can be characterized as major
universities with a large research output of international level and a large number of students. To
work with clear criteria on these aspects, the decision about whether or not a city has a major
university is based on the Leiden Ranking (Waltman, Calero-Medina et al., 2012), Ausführung
2020. A short discussion of this choice is given in the Supplementary Material Text S1.

The structure of this paper is as follows. Erste, I discuss how I measure the socioeconomic
strength of a city or district on the basis of the urban scaling methodology. I present the results
of these measurements for German cities in different regions of the country. The second part of
the paper focuses on the socioeconomic position of university cities compared to other cities
and which characteristics of universities play a significant role.

1.2. What Is Urban Scaling?

Recent studies show a more than proportional (superlinear) increase of the socioeconomic
performance of cities (measured by the gross urban product) in relation to population size
(Bettencourt, 2013; Bettencourt, Lobo et al., 2010; Lobo, Bettencourt et al., 2013). This urban
scaling relation is described by a power law dependence of the gross urban product on pop-
ulation size given by the relation

G Nð

Þ ¼ aN β

(1)

where G is the gross urban product1 and N the population size of a city. The exponent β
follows from the measurement; in most cases, values of the exponent are between 1.10 Und

1 Throughout the text, I use the abbreviation GUP for the gross urban product. In the case of mathematical

Gleichungen, I use the shorter symbol G.

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1.20. I refer to my recent work on urban scaling for further details (van Raan, 2020). The urban
scaling relation implies that a city twice as large (in population) as another city can be
expected to have approximately a 21.15 = 2.22 greater socioeconomic performance (in terms
of the gross urban product). Urban scaling behavior is also found for human interactions in
general for knowledge production activities in cities (Arbesman, Kleinberg, & Strogatz,
2009; Bettencourt et al., 2007; Nomaler, Frenken, & Heimeriks, 2014; Schläpfer, Bettencourt
et al., 2014) and universities also show scaling behavior similar to cities (van Raan, 2013).

A simple way to understand this phenomenon is by seeing cities as a complex network. Der
larger the city in population size, the more network nodes. The nodes in the urban system are
the inhabitants, social and cultural institutions, centers of education and research, firms, usw.
The number of nodes has a linear dependence on size, but the links between nodes depend on
size in a superlinear way. The links between these (clustered) nodes are crucial for new devel-
opments, reinforcement of urban facilities, and innovation. Because they increase superli-
nearly, the socioeconomic strength of cities increases more than proportionally with increasing
population size.

In this paper I build on my recent empirical work on urban scaling of German cities (Transporter
Raan, 2020), which implies that I use the term city only for cities defined as municipalities and
not for the entire urban agglomerations, such as the U.S. metropolitan statistical areas
(Bettencourt et al., 2010) or the European functional urban agglomerations (Bettencourt &
Lobo, 2016; Eurostat, 2019; OECD, 2019) which consist of many independent municipalities
that may or may not cooperate optimally.

2. DATA AND ANALYTICAL METHOD

For my analysis I apply the same approach as described in my recent paper on urban scaling
and for the explanation I largely follow the relevant text in that paper (van Raan, 2020). Ger-
viele, mit 83 million inhabitants, consists of 16 federal states. These federal states have a
specific administrative structure in which cities and districts (Kreise) play a central role. In con-
nection with the availability of data on the gross urban product (GUP) at the German Federal
Statistical Bureau, I discuss this administrative structure in and around German cities in more
detail. Most larger cities (über 100,000 inhabitants) are kreisfrei (“district-free” (d.h., cities of
which the surrounding urban area belongs to the municipality of the city), and therefore I have
in these cases a one-governance urban area (which is in fact the definition of the concept
kreisfrei ). Germany currently has 107 kreisfreie cities, with a total population of about
27,000,000. Kreise are districts around mostly smaller cities consisting of between 10 Und
50 municipalities; together the Kreise (in Summe 294) have about 56,000,000 inhabitants. In
Kreise the administrative and economic centers are cities that are non-kreisfreie cities (Weil
they formally belong to a Kreis) although they can be larger than smaller kreisfreie cities2.
These central cities within a Kreis are called Kreis-city.

Most university cities are kreisfrei, but several German university cities (as far as included
in the Leiden Ranking) are Kreis-cities. This is the case for Hanover, Aachen, Göttingen,
Tübingen, Paderborn, Saarbrücken, Marburg, Giessen, Konstanz, Greifswald, and Freiberg
(not to be confused with Freiburg). Although these cities are similar to a kreisfreie city in every
respect, for curious local political reasons they are not kreisfrei, and thus these cities belong to

2 An example is Neuss (Nord Rhine-Westphalia) with about 155,000 inhabitants, but this city is not kreisfrei. Es
is the administrative center (Kreis-city) of the Rhein-Kreis Neuss which has a population of about 450,000.
The Bavarian city Schwabach, andererseits, with about 41,000 inhabitants, is a kreisfreie city.

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a specific Kreis (Göttingen, Tübingen, Paderborn, Marburg, Giessen, Konstanz, Greifswald,
and Freiberg) or to an ad hoc defined urban administrative district (Hannover, Aachen,
Saarbrücken). This has consequences for data collection. At the city level, the German Federal
Bureau of Statistics has GUP data available for the 107 kreisfreie cities. For the non-kreisfreie
cities GUP data are available at the level of the Kreis. daher, I collected for all kreisfreie
cities and for all Kreise (period 1992–2017) data on the gross urban product (GUP). Der
German Federal Bureau of Statistics (2021) also provided data on the population size (number
of inhabitants) for all cities and for all Kreise (period 1970–2019) and data on the number of
students in all German universities and other higher education institutions (1992–2019).

In this study I characterize universities with a series of bibliometric indicators. These indi-
cators are calculated with the data from the Leiden Ranking 2020. I refer to the Leiden Ranking
website (Leiden Ranking, 2020) for details on the data collection, data analysis and calculation
of the indicators, particularly the impact indicators. In Summe, 54 German universities are
included in the Leiden Ranking. I consider these as Germany’s major universities. Diese sind
the universities that meet the selection criterion for the Leiden Ranking: at least an annual
Durchschnitt von 200 Web of Science indexed publications in the period 2015–2018. Only research
articles and review articles published in international journals (“core publications”) are taken
into account. Other types of publications are not considered. The Leiden data include at least
the major universities but, Natürlich, the selection criterion is rather arbitrary. In der Tat, just
below the threshold of the selection criterion there are several other universities of consider-
able size in output, impact, and student numbers. Trotzdem, alle 80 Max Planck Institutes
and main research centers are located in or nearby universities covered by the Leiden
Ranking3.

In Table 1 I give an overview of the data sets of cities used in this study. Zum Beispiel, Dort
are in total 81 cities in Germany with more than 100,000 inhabitants, Und 44 of these cities
have a university included in the Leiden Ranking. Of these cities, 69 (84%) are kreisfrei and 39
of them have a university included in the Leiden Ranking. I remark that the 54 universities do
not always correspond one-on-one to cites: Large cities like Berlin, München, and Hannover
have more than one university included in the Leiden Ranking, and some universities are
located in two cities, such as Erlangen-Nurnberg and Duisburg-Essen. In Summe, Die 54 univer-
sities relate to 51 cities4.

3. URBAN SCALING OF GERMAN CITIES

3.1. Scaling of the Gross Urban Product

I refer to my recent publication (van Raan, 2020) for an extensive analysis of urban scaling in
the western, southern, Mitte, nördlich, and eastern regions5 of Germany and in the country
as a whole. For this study, I updated the data up to and including 2017. Figur 1 zeigt die
results of the analysis, where I compare the scaling of the southern cities to those of the other

3 Siehe https://www.mpg.de/17039558/annual-report-2020-structures.pdf, P. 167.
4 In the case of more than one university in a city, I characterize the city with the maximum indicator values of
the universities, see footnote 10, Abschnitt 4.2. In the case of a university located in two cities, I assign the
university to both cities.

5 North Rhine-Westphalia: western region of Germany; Baden-Württemberg and Bavaria: southern region;
Hesse, Rhineland-Palatinate, and Saarland: middle region; Bremen, Hamburg, Lower Saxony, Und
Schleswig-Holstein: northern region; Berlin, Brandenburg, Mecklenburg-Vorpommern, Saxony, Saxony-
Anhalt and Thuringia: eastern region.

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Tisch 1. Overview of the kreisfreie and non-kreisfreie cities with more than 100,000 inhabitants
and between 50,000 Und 100,000 inhabitants. Numbers in square brackets indicate the number
of cities with a university (as far as included in the Leiden Ranking). Es gibt 16 kreisfreie cities
with fewer than 50,000 inhabitants. There is one non-kreisfreie university city with fewer than
50,000 inhabitants

Cities >100,000

Cities 50,000–100,000

kreisfrei
68 [39]

23 [1]

Non-kreisfrei
13 [5]

87 [5]

Total
81 [44]

110 [6]

regions of Germany. In all cases the GUP scales superlinearly with population: The scaling
exponent ranges between and 1.03 Und 1.34. As I clearly see, in urban scaling not only is
the power law exponent a crucial parameter but so also is the absolute difference in GUP
between two sets of cities (d.h., the distance between the regression lines).

This difference in GUP is clearly visible in the lower right panel of Figure 1, where I com-
pare the urban scaling of the southern region to the eastern region. The southern cities are
generally at a considerably higher GUP level compared with the cities in the eastern region,
which is the former German Democratic Republic. But the difference between the wealthy
southern region of Germany and the old industrial western region is also striking. For an exten-
sive discussion of this issue, explanations of how individual cities influence the measured scal-
ing exponents, and for confidence intervals of the measured scaling exponents, I refer to van
Raan (2020). Remarkably, if I join all regions and calculate the urban scaling of the entire
country, I find a low superlinear scaling exponent 1.03, lower than most of the separate

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Figur 1. Scaling of the gross urban product (GUP) for German (kreisfreie) cities. Upper left panel: western and southern region of Germany;
upper right panel: middle and southern region; lower left panel: northern and southern region; lower right panel: eastern and southern region.
(GUP in units of A1,000; data average 2015–2017; data source: German Federal Bureau of Statistics).

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Scaling of the gross urban product (GUP) for German (kreisfreie) cities. Left panel: all west regions versus east; right panel: alle
Figur 2.
regions together (d.h., whole country) (GUP in units of A1,000; data average 2015–2017; data source: German Federal Bureau of Statistics).

regions of the country (siehe Abbildung 2). This phenomenon highlights an often neglected issue in
urban studies: The scaling of GUP with population size of cities in a country may depend
heavily on the regional economy within the country. This must be taken into account when
the scaling exponent of an entire country is calculated. Notice that the double-logarithmic
presentation might suggest a strong similarity of the distributions, but the calculations show
significant differences in coefficients and exponents which also persist over time.

3.2. Scaling Residuals as Indicator of Socioeconomic Strength

As can be expected, and also clearly visible in the empirical results (Figuren 1 Und 2), Die
observed positions of cities will deviate from the expected positions given by the regression line
through all measuring points of a specific set. These deviations can be measured by the resid-
uals: Using Eq. 1 (which is the scaling relation for a set of cities) I find that G(Ni) is the expected
gross urban product of an individual city (ich) with population Ni. By denoting the observed (real)
value of the gross urban product of a city as Gi, I calculate the residuals ξi of the scaling
distribution for each of the (kreisfreie) cities (and similarly for the Kreise) as follows:

ξ
ich

¼ ln Gi=G Ni

D

½

Þ

(cid:1)
(cid:2) ¼ ln Gi=aNi

(cid:3)

β

(2)

Positive residuals indicate that a city performs better than expected. Daher, from the urban scal-
ing measurements of cities or districts (Kreise) residuals for individual cities or Kreise can be
determined directly from the empirical regression data and these residuals are considered as
an indicator of socioeconomic strength. In der Tat, I find a strong correlation of residuals with other
measures of socioeconomic strength; see van Raan (2020). Given the considerable economic
differences between the different regions of Germany, I calculated the residuals both in relation
to the regional (ξr) as well as the national context (ξn). Zum Beispiel, for cities in the western
region of Germany the regional residuals are calculated with the relevant scaling law as pre-
sented in Figure 1, upper left panel, d.h., on the basis of

D
Gi;r Ni

Þ ¼ 555:31Ni

1:34;

whereas their national residuals are calculated with the scaling law in Figure 2, right panel, d.h.,
on the basis of

D
Gi;n Ni

Þ ¼ 34034:96Ni

1:03:

Cities in the eastern part of Germany, such as Leipzig, Dresden, and Jena, do not yet have the
same socioeconomic strength as many cities in other parts of Germany, but within their own

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region Leipzig, Dresden, and Jena show a strong position. There is no rational basis on which to
assign specific weights to the national and the regional residual as components in the calcula-
tion of an overall socioeconomic strength indicator. daher, I give both components equal
weight and take as a measure for the relative socioeconomic strength S of a city the average
value of the national and the regional residuals:

S ¼ ξ
D

þ ξ

R

N

Þ=2

(3)

The statistical uncertainty in this measure is determined by the uncertainty in the measured
residuals, and these are determined by the standard error values of the measured scaling coef-
ficient and scaling exponent. On the basis of earlier discussion on confidence levels of scaling
Parameter (van Raan, 2020) I estimate the uncertainty in S to be ±0.03. An important char-
acteristic of urban residuals is that they are quite stable and vary little over a long period,
often on timescales of several decades (Alves, Mendes et al., 2015; Bettencourt, Yang
et al., 2020). Daher, scaling residuals can be seen as reliable indicators of the socioeconomic
strength of cities.

The full list for all kreisfreie cities with their national residuals ξn, regional residuals ξr, Und
socioeconomic strength S is presented in Table S1. In Figure S1 I show the normal distribution
of these parameters calculated on the basis of their respective means and standard deviations.

In Figure S2 I show the rank-distribution of the national residual in comparison with the
regional residual. In Table 2 I show as an example the top 25 cities ranked by their socioeco-
nomic strength S.

At the top of the S ranking I see the cities Wolfburg and Ingolstadt, with extraordinary
high socioeconomic strength. Wolfsburg (um 125,000 inhabitants) is the location of the
Volkswagen ( VW) headquarters with the world’s biggest car plant, producting 815,000 cars
per year (2015) and with 70,000 employees in Wolfsburg alone. The city even owes its origins
entirely to VW: When founded in 1938 it had only 1,000 inhabitants. Jetzt, measured in GUP
per capita, Wolfsburg is one of the richest cities in Germany. Ingolstadt (um 140,000 inhab-
itants) is partly a similar case: This city is home to the headquarters of the automobile manu-
facturer Audi. Jedoch, in strong contrast to Wolfsburg, Ingolstadt was already an important
city in Germany in the early Middle Ages. Neither city has a major university: Wolfsburg has a
college with a focus on vehicle technology, while Ingolstadt had a university from 1472–1800,
but from 1980 it has had a small Catholic university focusing mainly on social sciences and
humanities (not considered as a major university in this study) as well as a technical college.
As a result of the huge automobile companies, both cities have an extraordinarily large urban
scaling residual.

I have already noted that not all university cities are kreisfreie cities. daher, they are not
present in Tables S1 and S2. As discussed in Section 2, this is the case for Hanover, Aachen,
Göttingen, Tübingen, Paderborn, Saarbrücken, Marburg, Giessen, Konstanz, Greifswald, Und
Freiberg. This means that no GUP data are directly available for these cities, only for their total
Kreis. Trotzdem, all the abovementioned cities are (often by far) the largest cities in the
Kreis (and that is why they are called a Kreis-city) and they will largely determine the socio-
economic position of their Kreis. daher, I use the data of their Kreis to determine the
socioeconomic strength of these cities. I calculated the Kreis residuals in the same way as I cal-
culated the residuals of the kreisfreie cities, both in relation to the regional as well as in the
national context, and determine the socioeconomic strength also in the same way as for the
kreisfreie cities. In Table S2 I list all of the Kreise with their national residuals ξn, regional

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German cities with universities

Tisch 2. Deutsch (kreisfreie) cities ranked by S, top 25 (university cities, as far as present in the
Leiden Ranking, in bold)

Kreisfreie city
Wolfsburg

Ingolstadt

Schweinfurt

Erlangen

Coburg

Ludwigshafen

Regensburg

Bonn

Düsseldorf

Koblenz

Emden

Darmstadt

Stuttgart

Frankfurt

Aschaffenburg

Ulm

Passau

München

Münster

Bayreuth

Speyer

Memmingen

Leverkusen

Bamberg

Zweibrücken

S
1.20

0.90

0.68

0.56

0.56

0.49

0.48

0.43

0.42

0.38

0.38

0.37

0.37

0.35

0.35

0.34

0.25

0.24

0.21

0.20

0.18

0.17

0.16

0.16

0.15

residuals ξr, and socioeconomic strength S. Kreise with university cities (as far as these univer-
sities are present in the Leiden Ranking) sind in der Tabelle aufgeführt 3.

Using the residual calculations for the kreisfreie cities and for the Kreise as discussed above,
I analyze in the next section all 191 German cities with more than 50,000 inhabitants. Fifty of
them are university cities, with a special focus on cities with more than 100,000 inhabitants,
because the vast majority of university cities (44) are in this group.

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Tisch 3. German Kreise with university cities ranked by S

(Non-kreisfreie) city
Saarbrücken (Kreis Regionalverband Saarbrücken)

Hannover (Kreis Region Hannover)

Paderborn (Kreis Paderborn)

Aachen (Kreis Städteregion Aachen)

Marburg (Kreis Marburg-Biedenkopf )

Göttingen (Kreis Göttingen)

Giessen (Kreis Giessen)

Tübingen (Kreis Tübingen)

Konstanz (Kreis Konstanz)

Freiberg (Kreis Mittelsachsen)

Greifswald (Kreis Vorpommern-Greifswald)

S
0.23

0.15

0.10

0.09

0.08

0.06

0.03

−0.02

−0.03

−0.05

−0.15

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4. UNIVERSITY PERFORMANCE AND THE SOCIOECONOMIC CHARACTERISTICS OF
THEIR CITIES

4.1. University Cities Compared to Other Cities

In this section I compare university cities to other cities on the basis of three different socio-
economic indicators: the socioeconomic strength S; the growth of the gross urban product
over the last 20 Jahre (T ); and the growth in population in the last 20 Jahre (U ). I make this
comparison for cities with between 50,000 Und 100,000 inhabitants, and for cities with more
als 100,000 inhabitants. I calculated the socioeconomic strength S in Section 3, und in
Figur 3 I show the normal distribution of S for cities with more than 100,000 inhabitants.
In this figure, the four quartiles of the distribution are marked.

Figur 3. Normal distribution of the socioeconomic strength (S ).

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German cities with universities

I have GUP values for kreisfreie cities and Kreise available from 1992 Zu 2017 and calculate

the ratio T between the average GUP value for 2015–2017 and for 1995–1997:

D
T ¼ GUP 2015–2017

½

(cid:2):
Þ
Þ=GUP 1995–1997

D

This indicator defines the growth of the gross urban product over the last 20 Jahre. I consider T as
the indicator of socioeconomic strengthening. I present this indicator for all cities with between
50,000 Und 100,000 inhabitants and all cities above 100,000 inhabitants in Table S3. I see high T
values in the car industry cities Ingolstadt and Wolfsburg. This is also the case for the former East
German cities Jena, Potsdam, Dresden, and Leipzig, indicating the socioeconomic strength-
ening of these cities. Of the 10 lowest ranked cities above 100,000 inhabitants the majority
are in the old industrial region (Ruhr Area) in Nord Rhine Westphalia. In Abbildung 4 I present the
normal distribution of T for the 81 cities with more than 100,000 inhabitants, where the first two
quartiles are marked.

The third socioeconomic city indicator is population growth. Using the data on city pop-

ulation I calculate the ratio U between the number of inhabitants in 2019 und in 2000:

½
U ¼ N 2019

D

(cid:2):
Þ
Þ=N 2000
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I present this ratio for all cities with between 50,000 Und 100,000 inhabitants and all cities
with more than 100,000 inhabitants in Table S3, where S values and number of inhabitants
N are included. Some cities, such as Potsdam, show relatively strong growth, while a consid-
erable part of the cities (35%) did not grow at all or even decreased in population. In Abbildung 5 ICH
present the normal distribution of U for the 81 cities with more than 100,000 inhabitants, wieder
with the first quartiles of the distribution indicated.

I analyze the data as follows and take the socioeconomic strength S as an example. Der
independent variable concerns cities, namely university cities versus other cities. I rank all cit-
ies by their S value and divide this ranking into quartiles to have a reasonable number of cities
(20) per unit of division. Daher, the first quartile S(Q1) are the cities in the top 25% of the S
distribution, und so weiter. Zum Beispiel, S(Q1) of all cities with more than 100,000 inhabitants
covers the values 1.20 Zu 0.15, the second quartile S(Q2) the values 0.14 to −0.04, und so weiter,

Figur 4. Normal distribution of the GUP increase over 20 Jahre (T ).

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Figur 5. Normal distribution of the city population growth over 20 Jahre (U ).

and in a similar way for the two other distributions; see Figures 3–5 (the relevant data are in
Table S3).

For each quartile I count the number of cities with universities as well cities without (Leiden
Ranking) universities. The result of this analysis is presented in two contingency tables (sehen
Tisch 4): left-hand side for the 81 cities with more than 100,000 inhabitants and the right-hand
side for the 110 cities with 50,000–100,000 inhabitants. A chi-squared test of the data for S
(Q1, Q2, Q3, and Q4) renders a p-value of 0.010 in the case of the cities with more than
100,000 inhabitants. Taking the conventionally accepted significance level p < 0.05 I find a significant difference in the distribution of cities according to the presence of universities. Further inspection of the contingency table reveals more information. I see that it is partic- ularly the fourth quartile S(Q4) distribution that makes the difference: Universities are signifi- cantly absent in cities with the lowest socioeconomic strength. By distinguishing between the first half of the S distribution at the high values side, S(Q1 + Q2), and the low values second half S(Q3 + Q4), 28 of the 44 university cities with more than 100,000 inhabitants (64%) are in S(Q1 + Q2), which means that they are cities with an above-average socioeconomic strength ( p = 0.011, the probability that no difference exists). For the group of 110 cities with 50,000– 100,000 inhabitants the significance disappears. But as is clear from Table 4, the number of university cities in this group is very low (six) and one cannot expect significant results. I performed a similar analysis for the two other city indicators: socioeconomic growth T and population growth U. The results are shown in Table S4. For the cities with more than 100,000 inhabitants I find that the university cities are significantly present in T(Q1 + Q2). For the pop- ulation growth U I find that for the cities with more than 100,000 inhabitants, as well as for the cities with 50,000–100,000 inhabitants, the university cities are significantly present in U(Q1 + Q2). Just like in the case of the socioeconomic strength S, the significance is mainly due to the low number of university cities in the fourth quartile. For the cities with between 50,000 and 100,000 inhabitants I also find that the university cities are significantly in U(Q1 + Q2). Table 5 gives an overview of my findings. I conclude that for all three socioeconomic indica- tors (socioeconomic strength, socioeconomic growth, and population growth) university cities with more than 100,000 inhabitants are predominantly present in the better half of these indicators. Quantitative Science Studies 275 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u q s s / a r t i c e - p d l f / / / / 3 1 2 6 5 2 0 0 8 2 6 5 q s s _ a _ 0 0 1 8 2 p d / . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 German cities with universities Table 4. Number of university cities and other cities for each quartile of the socioeconomic strength (S ) distribution (left: the 81 cities with more than 100,000 inhabitants; right: the 110 cities with 50,000–100,000 inhabitants) S Q1 Q2 Q3 Q4 p = S University cities 12 16 11 5 44 0.010 Other cities 8 5 9 15 37 University cities Other cities Q1 + Q2 Q3 + Q4 28 16 44 13 24 37 20 21 20 20 81 41 40 81 S Q1 Q2 Q3 Q4 p = S University cities 1 2 2 1 6 0.871 Other cities 26 26 25 27 104 University cities Other cities Q1 + Q2 Q3 + Q4 3 3 6 52 52 104 p = 0.011 p = 1.000 I find a positive relation between having a major university and being a city with a relatively strong socioeconomic position. However, I must be cautious with my conclusions. I certainly did not find an iron law for each university city, nor can I make a statement about causality. An indication of a possible causal relation is that most of the major universities are centuries old, whereas my socioeconomic indicators relate to recent times. This temporal precedence could suggest that cities with a major university had a higher probability than cities without a major university to develop into a socioeconomically strong position. Next to the data on socioeconomic strength, socioeconomic growth, and population growth used so far in the study, there is a further important source of data. The German socio- economic research agency Prognos AG (Prognos, 2021) evaluates the future opportunities and risks of all (kreisfreie) cities and Kreise. Prognos has published the results every three years since 2004 in the report Zukunftatlas. The latest edition is from 2019. The evaluation of the future perspectives of cities and Kreise is based on 29 macro- and socioeconomic indicators to assess strength and dynamism. These indicators cover the fields of demographics, labor mar- ket, social welfare, competition, and innovation. No scaling approaches were applied. These indicators are discussed in detail in the Zukunftatlas (Prognos Zukunftatlas, 2019). On the basis of these assessments, a ranking (Future Index) of all cities and Kreise is created. The Prognos Future Index is the only nationwide German ranking that shows urban regional developments over a period of 15 years. I used the publicly available6 overview of all rankings since 2004 to calculate for all German cities with a population greater than 100,000 the difference in Prog- nos ranking positions between the years 2004 and 2019. For instance, the Prognos ranking position of Berlin was 262 in 2004, and 93 in 2019. So Berlin improved its ranking position by +169. In sharp contrast, the traditional old industry city Essen fell in ranking position from 121 in 2004 to 239 in 2019, a difference of −131. 6 https://de.wikipedia.org/wiki/ Zukunftsatlas. I checked the reliability of the data in this Wikipedia page with the original data in the Prognos Zukunftatlas 2016 and 2019. Quantitative Science Studies 276 27 28 27 28 110 55 55 110 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u q s s / a r t i c e - p d l f / / / / 3 1 2 6 5 2 0 0 8 2 6 5 q s s _ a _ 0 0 1 8 2 p d / . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 German cities with universities Table 5. Overview of the significance tests for university cities with respect to the three socioeconomic city indicators Cities N = 50,000–100,000 Population growth U Significant Socioeconomic strength S Not significant Socioeconomic growth T Not significant Cities N > 100,000

Significant

Significant

Significant

After distinguishing between university cities and other cities, I calculated for both groups
the normal distribution of ranking position differences. Figure S3 presents the results. I tested
the difference between the two means of both distributions and found that at the 95% confi-
dence interval level p = 0.041. I conclude that university cities improved their ranking posi-
tions in the 15 years period between 2004 Und 2019 significantly more than the other cities.

4.2. Bibliometric Performance Indicators of German Universities

In the previous section I compared university cities with other cities. I found that university
cities are predominantly present in the better half of the S, T, and U distributions but not all
cities with a major university belong to the socioeconomically strong cities. Could this be due
to characteristic differences between universities? Mit anderen Worten, how do the university cities
in the first quartile or first two quartiles of the S, T, and U distributions differ from the university
cities in the second, dritte, and fourth quartiles, or in the third and fourth quartiles, jeweils?
To investigate this, I have to categorize the university cities in such a way that I can distinguish
them from one another. I do this with help of bibliometric7 indicators. Before I perform the
Analyse, I must first discuss the basic elements of bibliometric indicators.

Distinguishing between universities is the core business of university rankings. On the basis
of survey data or bibliometric data, oder beides, several organizations produce annual rankings of
universities. Frequently used rankings are the Academic World Universities Ranking (Shanghai
Ranking) (ARWU, 2020), the Times Higher Education ranking (THE, 2020), the Leiden Ranking
(Leiden Ranking, 2020), the QS ranking (QS, 2020), the Scimago ranking (Scimago, 2020), Und
the U-Multirank (U-Multirank, 2020). For an extensive discussion of the problems related to
university rankings, I refer to van Raan (2005, 2019) and Waltman et al. (2012). Here I briefly
outline several important issues. The combination of scores for teaching and research perfor-
mance into one final score is methodologically incorrect because teaching and research are
different tasks and also different missions of universities. In research rankings it is incorrect to
combine size-dependent (z.B., number of papers in specific journals such as Nature and Sci-
enz) and size-independent measures (z.B., publications per staff member). Indicators based
on citation analysis must be field normalized, otherwise universities with a focus on engineer-
ing, or on social sciences and humanities, will be systematically disadvantaged. Often citation
indicators are based on averages. But average-based indicators are very sensitive to outliers,
thus they are not the best statistic in the case of skewed distributions, such as the distribution of
citations over publications. A further problem is that comparison of ranking scores in a time
series can be affected seriously if, meanwhile, the number of universities covered by the rank-
ing is increased substantially, for instance by lowering the required threshold for the number of
publications. Last, but not least, the definition of a university, particularly the relation with
medical schools and hospitals, is a cumbersome task.

7 The quantitative study of science, mostly referred to as scientometrics, aims at the advancement of our
knowledge on the development of science and its communication structure, in relation to social, techno-
logical, and socioeconomic aspects. Within scientometrics, research on scientific communication, particu-
larly with data from publications, citations, and journals is called bibliometrics (van Raan, 2019).

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9

Tisch 6. University indicators considered in this study

Number of fractionally counted publications (Pfrac)

Number of fractionally counted publications in the top 1, 5, 10, 50% (Pt1frac, Pt5frac, Pt10frac, Pt50frac)

Same as 2, now relative ( pt1frac=[Pt1frac/Pfrac]), similar for pt5frac, pt10frac, pt50frac)

Number of fully counted publications (Pfull )

Number of fully counted publications in the top 1, 5, 10, 50% (Pt1full, Pt5full, Pt10full, Pt50full )

Same as 5, now relative ( pt1full=[Pt1full/Pfull]), similar for pt5full, pt10full, pt50full )

Number of fractionally counted citations (Cfrac)

Number of fully counted citations (Cfull )

Number of collaborative publications (total Pcoll, within this total: international Pintcoll, with business

companies Pb, and of these latter with local business companies PbL) (fully counted)

10

Number of students (Ns) and the increase of this number in the last 20 Jahre (V )

All of the above issues, including a well-defined uncertainty measure, are dealt with metic-
ulously in the Leiden Ranking (Waltman et al., 2012). For this paper I use the 2020 version of
the Leiden Ranking (Leiden Ranking, 2020). In this version publication data relate to the period
2015–2018 and the citation data to 2015–2019; author self-citations are excluded. Universi-
ties are included if they have more than 200 publications covered by the Web of Science
( WoS)8 on average per year in the period 2015–2018. I consider this also as the definition
for a major university. This does not mean that universities with a publication output below
the abovementioned threshold are low-performance institutions, but they are not a major uni-
versity in terms of scientific productivity. For a detailed discussion of all bibliometric indicators
I refer to the Leiden Ranking methodology.

I consider in my analysis the indicators given in Table 6. In the Leiden Ranking publications
and citations can be fractionally or fully counted9. I distinguish 10 indicator families consisting
of one to at most four subindicators. Zum Beispiel, the second indicator family contains four
subindicators: Die (absolute) number of fractionally counted publications in the worldwide top
1, 5, 10, Und 50% of the citation-impact distribution of the relevant field (Pt1frac, Pt5frac,
Pt10frac, Pt50frac). The first nine indicator families are available in the Leiden Ranking, Die
tenth (number of students, Jahr 2020, and the increase of the number of students in the last 20
Jahre) was obtained from the German Federal Bureau of Statistics. I have 26 (sub)indicators

8 Web of Science, published by Clarivate Analytics; siehe https://clarivate.com/webofsciencegroup.
9 The scientific impact indicators in the Leiden Ranking are calculated using either a full or a fractional count-
ing (at the institutional level) method. The full counting method gives equal weight (with value 1) to all
publications of a university, regardless of collaboration. The same goes for the citations received by these
publications. The fractional counting method, Jedoch, gives less weight to collaborative publications than
to noncollaborative ones. Genauer, publications as well as their citations are divided over the col-
laborating institutes. The fractional counting method leads to a more proper field normalization of impact
indicators (Waltman & van Eck, 2015). Because of the better normalization properties, fractional counting is
regarded as the preferred method in the Leiden Ranking, but both modalities are available in this ranking.
The advantage in having both is that it provides a good idea of the robustness of the outcomes. At high
aggregation levels such as universities, the correlation between the ranking based on full counting and that
based on fractional counting is high.

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which means that each university (ich) is characterized by the set of indicators {i1, i2, …, i26}.
Folglich, the university city is also characterized by these indicators10.

The pt10frac indicator (third indicator family, third subindicator) is generally considered as
the main research performance indicator. This indicator gives the fraction of publications that
are in the top 10% of their fields11 in the case that publications are fractionally counted. Also, Wenn
for a university this fraction is 0.100, this university performs according to the expected value;
if the fraction is above 0.100, the university performs better, and below 0.100 die Performance
is lower than the expected value. The indicator values of the universities have, to a good
approximation, a normal distribution. Als Beispiel, I show in Figure S4 this distribution
of the pt10frac indicator for all German universities covered by the Leiden Ranking.

In Table 7 I present German universities cities (as far as included in the Leiden Ranking
2020) ranked by the pt10frac indicator of their university (in the case of more than one uni-
Vielseitigkeit, see footnote 10). I show the first 25 cities (two of which have a population below
100,000) and given the large amount of data I limit the table to the first nine indicators (indi-
cator families 1 Zu 3) and the last two indicators (indicator family 10), as well as the population
of the city (N, Jahr 2019) and the values of the three socioeconomic indicators S, T, and U. Der
complete set of data (all university cities, all indicators) is available in my data repository12.

An illustration of the differences in student numbers (Ns) and growth in student numbers (V )
for universities in the Leiden Ranking (LR) and universities/other higher education institutions
not in the LR is given in Figure S5. I find a significant difference in student numbers between
the top universities (d.h., LR universities in the first quartile of the pt10frac distribution) and all
LR universities ( p = 0.012), and also a significant difference between all LR universities and the
non-LR universities ( P < 0.000). For the growth in student numbers there is no significant dif- ference between the top universities and all LR universities, but there is a significant difference between all LR universities and the non-LR universities ( p = 0.002): Non-LR universities show a larger increase of student numbers compared with LR universities. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u q s s / a r t i c e - p d l f / / / / 3 1 2 6 5 2 0 0 8 2 6 5 q s s _ a _ 0 0 1 8 2 p d . / 4.3. University Performance and Socioeconomic Indicators of Cities I am now ready to address the question how the university cities (>100,000 inhabitants) im
first quartile (Q1) or first two quartiles (Q1 + Q2) of the S, T, and U distributions differ from the
other university cities. The S, T, and U distributions are based on all 81 cities with more than
100,000 inhabitants. I apply two data-analytical methods. In the first method the city indicators
are leading, whereas in the second method the university indicators are leading.

I start with the first method. University cities are ranked by a specific city indicator (I do this
successively for S, T, and U ). Als Beispiel, I take the S distribution. For the university cities
in the first quartile S(Q1) as well as for those in the other quartiles S(Q2 + Q3 + Q4) I calculate
the mean and standard deviation of all university indicators and of the city indicators as well.
With a test of the difference between the means I am able to find which indicators differ sig-
nificantly when comparing the university cities in S(Q1) with those in S(Q2 + Q3 + Q4). I repeat
the same procedure for the university cities in S(Q1 + Q2) (above average socioeconomic
Stärke) versus those in S(Q3 + Q4) (below average socioeconomic strength). This analysis

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10 In the case of, zum Beispiel, two universities a and b in one city, I characterize that city as if it has one uni-

versity with the set of indicators {max(a1, b1), max(a2, b2), …, max(a26, b26)}.

11 I use here the indicator symbol pt10frac; in the Leiden Ranking this indicator has the symbol PP(top 10%)

calculated in the fractional counting modality.

12 Siehe https://osf.io/4ru96/.

Quantitative Science Studies

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Tisch 7. German university cities with the first three bibliometric indicator families (nine indicators) and indicator family 10 (number of students and growth of the
number of students, main text), as well as city population (N ) and the three socioeconomic indicators S, T, and U, ranked by the pt10frac indicator (I show the first 25)

Universität
city
Göttingen

N
118,911

Ns
30,162

S
0.06

U
0.96

T
1.51

V
1.32

Pfrac
4872

Pt1frac
60

Pt5frac
346

Pt10frac
664

Pt50frac
2,838

pt1frac
0.012

pt5frac
0.071

pt10frac
0.136

pt50frac
0.582

München

1,484,226

48,697

0.24

1.23

1.75

1.53

8142

101

Bonn

329,673

38,481

0.43

1.09

1.42

1.04

4819

70

Heidelberg

161,485

25,986

−0.01

1.15

1.74

1.26

7744

100

Würzburg

127,934

27,552

0.14

1.00

1.52

1.68

3622

Münster

315,293

45,022

0.21

1.19

1.53

1.03

4707

Mainz

218,578

29,907

0.04

1.20

1.46

1.11

3817

Stuttgart

635,911

24,153

0.37

1.09

1.60

1.71

2697

Frankfurt

763,380

45,179

0.35

1.18

1.50

1.26

4462

Erlangen

112,528

37,575

0.56

1.12

2.02

1.92

5939

Nürnberg

518,370

37,575

0.00

1.06

1.65

1.92

5939

Freiburg

231,195

24,028

−0.10

1.13

1.74

1.37

4923

Aachen

248,960

45,945

0.09

1.02

1.60

1.58

6146

Karlsruhe

312,060

23,616

0.12

1.12

1.54

1.73

5527

Berlin

Köln

3,669,491

37,312

−0.17

1.08

1.57

1.05

5284

1,087,863

54,105

0.05

1.13

1.57

0.91

4029

Regensburg

153,094

20,584

0.48

1.22

1.99

1.44

2856

Essen

582,760

43,029

Duisburg

498,686

43,029

−0.19

−0.36

0.98

1.37

1.15

3424

0.97

1.43

1.15

3424

Darmstadt

159,878

25,170

0.37

1.16

1.59

1.57

2517

Kassel

202,137

22,786

Dresden

556,780

29,148

−0.05

−0.09

1.04

1.45

1.49

863

1.17

1.87

1.28

4933

Bayreuth

74,783

12,931

0.20

1.01

1.60

1.85

1629

Kiel

246,794

27,101

Tübingen

91,506

26,842

−0.07

−0.02

1.06

1.47

1.35

3087

1.13

1.90

1.45

5148

45

52

48

29

51

74

74

56

64

55

57

39

29

32

32

23

7

45

13

40

47

498

287

492

215

309

229

153

264

351

351

279

344

313

278

217

157

186

186

129

45

262

86

161

254

1,000

4,681

0.014

0.066

0.133

0.575

590

946

441

565

443

310

510

678

678

561

694

618

570

447

314

375

375

274

92

520

171

324

539

2,734

0.015

0.060

0.122

0.567

4,374

0.013

0.064

0.122

0.565

2,020

0.012

0.059

0.122

0.558

2,579

0.011

0.066

0.120

0.548

2,098

0.012

0.060

0.116

0.550

1,499

0.011

0.057

0.115

0.556

2,443

0.011

0.059

0.114

0.548

3,198

0.013

0.059

0.114

0.538

3,198

0.013

0.059

0.114

0.538

2,809

0.011

0.057

0.114

0.570

3,280

0.010

0.056

0.113

0.534

3,021

0.010

0.057

0.112

0.547

2,868

0.011

0.057

0.111

0.548

2,177

0.010

0.054

0.111

0.540

1,576

0.010

0.055

0.110

0.552

1,835

0.009

0.054

0.109

0.536

1,835

0.009

0.054

0.109

0.536

1,349

0.009

0.051

0.109

0.536

418

0.009

0.053

0.106

0.484

2,584

0.009

0.053

0.105

0.524

851

0.008

0.053

0.105

0.522

1,639

0.013

0.052

0.105

0.531

2,776

0.009

0.049

0.105

0.539

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answers the question: Are the university cities in the “top” of a specific city indicator also the
cities that have (on average) a significantly higher score for one or more university indicators,
and which indicators are they?

The results of method 1 are presented in Table 8. To keep the table clear, I only show the p-
values for the significant results (d.h., indicators with p-value <0.050). The basic data and the calculations of the statistical significance are available in my data repository. I first give an example how to read this table. The left-hand side of Table 8 relates to the university cities within U(Q1), the first quartile of the population growth distribution U of all 81 cities >100,000. I find that for these cities, the marked indicators have significantly larger vales com-
pared with the university cities in the rest of the U distribution (d.h., in U(Q2 + Q3 + Q4)). Das
difference is given by the ratio in the second column, and the p value in the third column gives
the probability within the 95% confidence interval. Daher, for university cities in U(Q1) Die
pt10frac indicator value of their universities is 1.12 larger than the same indicator for the uni-
versities of the cities in U(Q2 + Q3 + Q4), with p = 0.009.

I conclude from Table 8 that universities in cities with above-average population growth
are in general universities with a higher performance in scientific output (publication-based
indicators), in scientific impact (citation-based indicators), and in scientific collaboration. ICH
also see in Table 8 that particularly the number of publications with local companies (d.h.,
companies in these cities and in their urban region (indicator PbL)) is almost a factor two
higher (1.72 in the case of U(Q1), p = 0.048; Und 2.08 in the case of U(Q1 + Q2), p =
0.029). Given that the number of publications of a university correlates quite well (van Raan,
2006) with the size of the academic research staff, the significantly higher scores for the abso-
lute number of publications Pfrac and Pfull suggest that the size of the staff, which can be
regarded as a pool of innovative people, could be a significant parameter in relation to the
population growth of the city.

The right-hand side of Table 8 shows my findings with city indicator S, the distribution of
the socioeconomic strength of cities. In this case I find that fewer university indicators than in
the case of population growth correlate with the socioeconomic strength of a city. Jedoch, Die
universities in cities in the first two quartiles S(Q1 + Q2) in particular show a higher perfor-
mance compared with the universities in cities in S(Q3 + Q4) für, remarkably, especially the
fractionally counted top 1, 5, 10 Und 50% impact indicators, both in absolute terms (z.B.,
Pt10frac, p = 0.017) as well as relative terms (z.B., pt10frac, p = 0.003). These fractionally
counted relative top impact indicators are a particularly strong indicator of scientific quality.
These findings suggest that for university cities with above-average socioeconomic strength
the probability that their university is a top university is higher compared with cities with
below-average socioeconomic strength. As I see in the results, it is possible that one or more
of the pt1, 5, 10, 50frac indicators is (sehr) significant and another is less or not significant. Ein
explanation for this is that a university can have an overall performance with most of the work in
the better half (top 50%) but much less work is, zum Beispiel, in the top 10%, or top 5% or top
1%. Also, this university performs—in terms of citation impact—quite well, but there are just a
few or no really outstanding groups13.

Table S5 presents my findings for the third city indicator T, the growth in socioeconomic
Stärke. In this table I also show for clarity only the p-values for the significant results (d.h.,

13 By selecting the German universities in the Leiden Ranking one finds that, zum Beispiel, the top 10 univer-
sities are not the same for pt1, 5, 10, 50frac, and by selecting also the field, for instance Biomedical and
Health Sciences, it becomes clear that these differences are field dependent.

Quantitative Science Studies

281

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Tisch 8.
100,000 inhabitants compared with the rest of this distribution. In the case of these distributions I do not have a ratio but a difference.

The shaded indicators are significantly larger for the first quartile (Q1) or first half (Q1 + Q2) of the U and S distributions for the 81 cities with more than

U(Q1 + Q2)
S

Ratio or diff:
(Q1 + Q2)/
(Q3 + Q4)
0.25

Ratio or diff:
Q1/(Q2 +
Q3 + Q4)
0.43

P

0.0000

S(Q1 + Q2)
S

Ratio or diff:
(Q1 + Q2)/
(Q3 + Q4)
0.37

Ratio or diff:
Q1/(Q2 +
Q3 + Q4)
0.15

1.15

1.15

1.59

1.79

1.78

1.71

1.63

1.18

1.16

1.12

1.04

1.58

1.69

1.69

1.67

1.61

U(Q1)
S

U

T

V

Pfrac

Pt1frac

Pt5frac

Pt10frac

Pt50frac

pt1frac

pt5frac

pt10frac

pt50frac

Pfull

Pt1full

Pt5full

Pt10full

Pt50full

2
8
2

P

0.037

0.000

0.000

U

T

V

0.002

Pfrac

0.003

Pt1frac

0.001

Pt5frac

0.002

Pt10frac

0.003

Pt50frac

0.030

pt1frac

0.005

pt5frac

0.009

pt10frac

0.021

pt50frac

0.006

Pfull

0.015

Pt1full

0.008

Pt5full

0.008

Pt10full

0.007

Pt50full

1.14

1.14

1.56

1.82

1.68

1.63

1.60

1.20

1.13

1.04

1.66

1.88

1.80

1.76

1.71

P

0.000

0.000

0.000

S(Q1)

S

U

T

V

0.011

Pfrac

0.009

Pt1frac

0.015

Pt5frac

0.017

Pt10frac

0.011

Pt50frac

0.018

pt1frac

0.027

pt5frac

pt10frac

0.012

pt50frac

1.04

0.046

pt50frac

0.008

Pfull

0.013

Pt1full

0.011

Pt5full

0.011

Pt10full

0.008

Pt50full

Pfull

Pt1full

Pt5full

Pt10full

Pt50full

U

T

V

Pfrac

Pt1frac

Pt5frac

Pt10frac

Pt50frac

pt1frac

pt5frac

pt10frac

P

0.000

0.017

0.045

0.031

0.017

0.014

0.017

0.024

0.012

0.004

0.003

0.002

1.06

1.08

1.44

1.70

1.67

1.61

1.51

1.21

1.17

1.13

1.05

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pt1full

pt5full

pt10full

pt50full

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Cfull

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Pintcoll

Pb

PbL

pt1full

pt5full

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pt10full

0.027

pt50full

0.005

Cfrac

0.016

Cfull

0.009

Pcoll

0.005

Pintcoll

0.018

Pb

0.048

PbL

1.09

1.04

1.67

1.64

1.59

1.65

1.61

1.73

pt1full

pt5full

pt10full

0.021

pt50full

0.031

Cfrac

0.021

Cfull

0.008

Pcoll

0.007

Pintcoll

0.012

Pb

0.029

PbL

1.04

1.57

1.73

1.71

1.75

1.80

2.08

pt1full

pt5full

pt10full

pt50full

Cfrac

Cfull

Pcoll

Pintcoll

Pb

PbL

1.63

0.017

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German cities with universities

indicators with p-value <0.050). Remarkably, for university cities in T(Q1) as well as in T(Q1 + Q2) I do not find any university indicator that scores significantly higher compared with the cities in T(Q2 + Q3 + Q4) and T(Q3 + Q4), respectively. I do see, however, that socio- economic growth and city population growth correlate significantly. This is to be expected, given the urban scaling relation between city population and the gross urban product of a city. I find that cities in the first quartile of the socioeconomic growth distribution have a 1.09 larger population growth compared with the other cities ( p = 0.001). The student population of a city can also be regarded as a pool of innovative people. So, does the number of students (Ns, not included in Table 8) relate to one or more city indicators? I do not find a significant relation between number of students and city indicators. This does not mean that the size of student population does not matter: Our group of universities consists of mostly large universities with high numbers of students (the average number of students is around 30,000). Apparently, within that order of magnitude, further differences in student population do not give significant correlations with city indicators. In the second method the university indicators are leading: the university cities are ranked by a specific university indicator and I do this successively for all 26 university indicators. The data-analytical and statistical procedures are the same as in the first method. As an example, I take the pt10frac distribution. For the university cities in the first quartile pt10frac(Q1) as well as for those in the other quartiles pt10frac(Q2 + Q3 + Q4) I calculate the mean and standard deviation of all university indicators and also of the city indicators. With a test of the difference between the means I am able to find which indicators differ significantly when comparing the university cities in pt10frac(Q1) with those in pt10frac (Q2 + Q3 + Q4). I repeat the same procedure for the university cities in pt10frac(Q1 + Q2) versus those in pt10frac(Q3 + Q4). This analysis answers the question: are the university cities that are “top” in a specific university indicator, for instance pt10frac, also the cities with a significantly higher S, T, and U? Table 9 presents the results of method 2. I again see that the indicator PbL, the absolute number of scientific collaboration publications with local companies, has a significant relation with city indicator for population growth U: University cities in the first quartile PbL(Q1) have a significantly ( p = 0.019) larger city population growth compared with the university cities in PbL(Q2 + Q3 + Q4). A further analysis shows that also the relative number of scientific col- laboration papers in general pcoll and particularly for international collaborations pintcoll relate to city growth. For the socioeconomic strength indicator S I find that cities of which the university is in the first quartile of the pt10frac distribution have, on average, a significantly larger socioeconomic strength indicator value S (with p = 0.002). This is also the case for the other relative numbers of fractionally counted publications in the top 1% and top 5%. This is largely similar to what I found with method 1, although there also the absolute numbers of fractionally counted top publications showed a significant relation. Whereas with method 1 no university indicator appeared to relate significantly to the socioeconomic growth T of the university cities, with method 2 I find a significant relation for relative number of scientific collaboration papers in general pcoll. I cannot expect that all the results will be the same for both methods: In method 1 city indicators are leading and thus their quartiles are based on the entire city indicator distribution for the 81 cities with more than 100,000 inhabitants, whereas in method 2 the university indi- cator quartiles are based on the university indicator distributions of the 44 university cities. I illustrate the effect of this difference with an example in Table S6. Quantitative Science Studies 284 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u q s s / a r t i c e - p d l f / / / / 3 1 2 6 5 2 0 0 8 2 6 5 q s s _ a _ 0 0 1 8 2 p d . / f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Q u a n t i t a i t i v e S c e n c e S u d e s t i Table 9. University indicators with a significant relation with city indicators S, U, and T. pt1frac(Q1) Ratio or diff: Q1/(Q2 + Q3 + Q4) S 0.17 pt5frac(Q1) Ratio or diff: Q1/(Q2 + Q3 + Q4) S 0.18 p 0.041 p 0.027 pt10frac(Q1) Ratio or diff: Q1/(Q2 + Q3 + Q4) p pt10frac(Q1 + Q2) Ratio or diff: (Q1 + Q2)/(Q3 + Q4) S 0.25 0.002 S 0.16 pt50frac(Q1 + Q2) Ratio or diff: (Q1 + Q2)/(Q3 + Q4) S 0.17 pt50full(Q1 + Q2) Ratio or diff: (Q1 + Q2)/(Q3 + Q4) S 0.15 Pt5frac(Q1) Ratio or diff: Q1/(Q2 + Q3 + Q4) S PbL(Q1) U 0.17 Ratio or diff: Q1/(Q2 + Q3 + Q4) 1.07 pcoll(Q1) Ratio or diff: Q1/(Q2 + Q3 + Q4) U T 1.08 1.09 p 0.043 p 0.019 p 0.006 0.026 pintcoll(Q1) Ratio or diff: Q1/(Q2 + Q3 + Q4) p pintcoll(Q1 + Q2) Ratio or diff: Q1/(Q2 + Q3 + Q4) U 2 8 5 1.06 0.045 U 1.06 p 0.021 p 0.014 p 0.025 p 0.014 G e r m a n c i t i e s w i t h u n i v e r s i t i e s l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u q s s / a r t i c e - p d l f / / / / 3 1 2 6 5 2 0 0 8 2 6 5 q s s _ a _ 0 0 1 8 2 p d . / f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 German cities with universities I also investigated how the Prognos Future Index relates to my city indicators S, T, and U. To this end I used the ranking for all cities and Kreise of 2019 from which I deduced the ranking of the 81 cities with more than 100,000 inhabitants. Next, I determined the quartiles of the dis- tribution of this ranking (P distribution, in which rank 1 is given the value 100, and so on). Then I calculated for P(Q1) of the 44 university cities the average values of S, T, and U and compared these values with those for P(Q2 + Q3 + Q4). I did a similar comparison for P(Q1 + Q2) and P(Q3 + Q4). I find a significant relation between the P distribution and the average values of all three indicators S, T, and U with probabilities p < 0.010 in all cases14. So I con- clude that the Prognos Future Index ranking correlates well with each of my socioeconomic and population indicators. A final remark. An interesting issue is the possible influence of the age of a university on the socioeconomic position of the university city15. This topic is outside the context of the current study but is certainly worth investigating further. In the Supplementary Material text S1 I provide a short discussion of initial observations based on my data. 5. CONCLUDING REMARKS The study of the role of universities in the prosperity of cities and regions encounters two major problems. First, what is a reliable measurement of the diverse elements of prosperity? And sec- ond, given the wide variety of types of universities, what are the characteristics, particularly research performance, of a university that really matter? In this study I focus on the research question: Is there a significant relation between having a university and a city’s socioeconomic strength, growth of the gross urban product, and population size? And if so, what are the deter- mining indicators of a university? To investigate this, I compiled a large database of city and university data: gross urban product and population data of nearly 200 German cities and 400 districts for the period 1997–2017. Data for the universities are derived from the CWTS bibliometric data system and supplemented with data on the number of students 1995–2020. Performance characteristics of universities are derived from the Leiden Ranking 2020. The socioeconomic strength of a city is determined with the urban scaling methodology. My study shows a significant relation between the presence of a university in a city and its socioeconomic indicators, particularly for larger cities. I find that for all three city indicators (socioeconomic strength, socioeconomic growth, and population growth) university cities are predominantly in the better half of the distribution function of these indicators. To find which university indicators do have a significant relation with city indicators I devel- oped two complementary data-analytical methods. In the first method the city indicators are lead- ing and the analysis is focused on the question whether the university cities that are in the “top” of a specific city indicator also are the cities that have a significantly higher score for one or more university indicators. In the second method the university indicators are leading; here the focus is on the question of whether the cities of which the universities are “top” in a specific university indicator also are the cities with significantly higher values for one or more the city indicators. I find that universities in cities with above-average population growth are in general univer- sities with a higher performance in scientific output (publication-based indicators), in scientific impact (citation-based indicators) and in scientific collaboration. Particularly collaboration with “local” companies (i.e., companies in these cities and in their urban region relate to population growth). I also find indications that the number of staff, which can be regarded as a pool of 14 Data and calculations are available at https://osf.io/4ru96/. 15 This valuable suggestion was made by one of the reviewers. Quantitative Science Studies 286 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u q s s / a r t i c e - p d l f / / / / 3 1 2 6 5 2 0 0 8 2 6 5 q s s _ a _ 0 0 1 8 2 p d . / f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 German cities with universities innovative people, could be a significant parameter in relation to the population growth of the city. For the socioeconomic strength of a city I find a relation with the fractionally counted top impact indicators in particular, both in absolute as well as in relative terms. These fractionally counted relative top impact indicators are a strong indicator of scientific quality. I conclude that university cities with above-average socioeconomic strength have a higher probability that their university is a top university compared with cities of below-average socioeconomic strength. Socioeconomic growth and city population growth appear to correlate significantly. This is to be expected, given the urban scaling relation between city population and the gross urban prod- uct of a city. Moreover, I find for socioeconomic growth of university cities a significant relation with the relative number of scientific collaboration papers. I do not find a significant correlation between number of students and city indicators. This does not mean that the size of the student population does not matter: My group of universities consists of mostly large universities with high numbers of students (the average number of students is around 30,000). Apparently, within that order of magnitude, further differences in student population do not give significant correlations with city indicators. An interesting additional socioeconomic city indicator is provided by the ranking of cities and Kreise in the Prognos Future Index. This ranking index correlates well with each of my socioeconomic and population indicators. I find that university cities improved their socioeco- nomic ranking positions in the 15-year period between 2004 and 2019 significantly more than the other cities. In conclusion, I have found a positive relation between having a major uni- versity and being a city with a relatively strong socioeconomic position and that this is espe- cially the case for universities with higher values of their output and impact indicators. But this is certainly not an iron law for each university city, nor do I make a statement about causality. An indication of a possible causal relation is that most of the major universities are centuries old, whereas my socioeconomic indicators relate to recent times. This temporal precedence could suggest that cities with a major university will have a higher probability than cities with- out a major university to develop into a socioeconomically strong position. Finally, I note that high-quality research, particularly applied research (including medical research) and related technological developments, will probably also play an important role in the socioeconomic position of cities. To this end, I am currently investigating patenting activities in cities together with a focus on the question of whether university indicators based specifically on applied research may relate more strongly to the socioeconomic city indicators than the same university indicators based on all university research. ACKNOWLEDGMENTS I thank my colleagues Jos Winnink for the calculation of the bibliometric indicators for the German universities that are not included in the Leiden Ranking and for preparation and first analyses of the relevant patent data, and Robert Tijssen for the calculation of university collaboration indicators. I also acknowledge the reviewers for their stimulating comments, particularly on the possible influence of the age of a university. FUNDING INFORMATION The author did not receive funding for this research. DATA AVAILABILITY Data is available at https://osf.io/4ru96, in files: QSS-data1-20220201 for city indicators and university indicators; QSS-data2-20220201 for GUP and population size data; and QSS-data3- 20220201 for data on student numbers. 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