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https://doi.org/10.1007/s11187-018-0089-2
Cultural transmission and persistence of entrepreneurship
G. Olcina ·E. M. Tur ·L. Escriche
Accepted: 25 July 2018
© The Author(s) 2018
Abstract This paper contributes to explain the per-
sistence of differences in levels of entrepreneurship
within and across countries. We provide an expla-
nation based on the dynamic interplay between pur-
poseful intergenerational transmission of preferences
for entrepreneurship and public administration effi-
ciency. Individuals vote on taxes, and the collected
taxes fund the civil servants’ wages. The performance
of the administration generating an efficient norma-
tive and regulatory environment, affects the success
of entrepreneurship. We show that an economy can
G. Olcina
Faculty of Economics, University of Valencia and ERICES,
Avda dels Tarongers s/n, Valencia, Spain
e-mail: Gonzalo.Olcina@uv.es
E. M. Tur ()
School of Innovation Sciences, Eindhoven University
of Technology, Eindhoven, Netherlands
e-mail: E.M.Mas.Tur@tue.nl
E. M. Tur
INGENIO (CSIC- UPV), Universitat Polit`
ecnica de
Va l `
encia, Valencia, Spain
E. M. Tur
Institute of Innovation and Entrepreneurship,
School of Business, Law and Economics,
University of Gothenburg, Gothenburg, Sweden
L. Escriche
University of Valencia and ERICES, Valencia, Spain
e-mail: Luisa.Escriche@uv.es
reach two different long-run equilibria: a traditional
equilibrium, with a low proportion of entrepreneurs,
high taxes and an inefficient administration and, an
entrepreneurial equilibrium with a high proportion of
entrepreneurs and, lower taxes but enough to imple-
ment an efficient administration. The equilibrium
achieved depends on the tax policy followed by the
different generations. If decisions are made by major-
ity voting in a myopic way, then the initial conditions
of the society become crucial. This result explains per-
sistence: an economy evolves around similar levels
of entrepreneurship unless some reforms are imple-
mented.
Keywords Entrepreneurship ·
Cultural transmission ·Entrepreneurial preferences ·
Tax policy ·Public administration efficiency
JEL Classification L26 ·Z10 ·D01 ·H20
1 Introduction
Entrepreneurship is a key aspect of economic
dynamism as it determines productivity, innovation,
and economic growth (see Schumpeter 1934;Wen-
nekers and Thurik 1999; Minniti 1999; Audretsch and
Thurik 2001, for example).1Reynolds et al. (1999)
1See Wennekers and Thurik (1999) for a survey of how eco-
nomic growth is linked to entrepreneuship.
Small Bus Econ (2020) 54:155–172
/Published online: 24 August 2018
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G. Olcina et al.
show that variations in rates of entrepreneurship may
account for one third of the variation in economic
growth.
The persistent difference in entrepreneurship
within or across countries is a well-known stylized
fact. Comparing countries, Freytag and Thurik (2007)
show differences that endure for more than four
decades, so the ranking between countries is quite
stable (Reynolds et al. 2002).2Concerning regions,
Fritsch and Wyrwich (2014), for example, observe that
the regional differences in Germany tend to be per-
sistent as long as periods of 80 years, despite abrupt
and drastic changes in the political-economic envi-
ronment. This is not an isolated case since, as these
authors point out, the regional start-up rates tend to
be relatively persistent over periods of one or two
decades in other regions as the Netherlands (van Stel
and Suddle 2008), Sweden (Andersson and Koster
2011), the UK (Mueller et al. 2008), and the USA (Acs
and Mueller 2008).
This paper presents a theoretical model that
explains the persistence of differences in levels of
entrepreneurship among economies. Our model takes
into account the interaction between intergenerational
transmission of entrepreneurial traits (culture) and
efficiency of the administration (institutions). We
obtain that an economy can converge to two dif-
ferent long-run equilibria. The first one is a tradi-
tional economy, with few entrepreneurs, high taxes
and an inefficient administration. The second one
is an entrepreneurial economy with predominantly
entrepreneurial traits, lower taxes and a more effi-
cient administration and a higher per capita income.
We show that the equilibrium achieved depends com-
pletely on the tax policy followed by the different
generations.
1.1 Evidence and related literature
Culture and institutions play a crucial role in explain-
ing the level of entrepreneurship and especially
the persistence of entrepreneurship (Wennekers and
Thurik, 1999; Wennekers et al. 2005, for instance). As
Freytag and Thurik put it (2007, p.121), “the persistent
differences between countries point to non-economic
2Freytag and Thurik (2007) present an illustrative figure with
the development of the rate of entrepreneurship for six countries
of the 23 of the Compendia data set (van Stel et al. 2005) from
1973 to 2006.
causes, such as cultural factors, which have a tendency
to remain relatively stable over time.” We understand
culture as the prevailing norms or values of an econ-
omy, whereas the institutions refer to the rules and
laws of the environment where the businesses are
conducted.3
Entrepreneurship and culture. The values or pref-
erences of an individual affect the decision to become
an entrepreneur. These values can be risk tolerance,
autonomy, striving for independence, mastery, indi-
vidualism, or an aggregate trait that we will name
as preferences for entrepreneurship. Many studies
show that entrepreneurial preferences are transmit-
ted among generations (Chlosta et al. 2012; Dohmen
et al. 2011; Laspita et al. 2012). For example, a
crucial determinant of entrepreneurship, willingness
to take risk, is transmitted from parents to children
(Dohmen et al. 2011 and De Paola, 2012). Wyrwich
(2015) studies the relationship between entrepreneur-
ship and mastery, in the sense of challenging existing
conditions, finding evidence of an intergenerational
transmission of values from parents to children. Hund-
ley (2006) provides support for the effects of skills
and values that are specifically acquired from expo-
sure to a self-employed parent on the self-employment
choice. Lindquist et al. (2015) show that parental
entrepreneurship increases the probability of chil-
dren’s entrepreneurship by about 60% and present
suggestive evidence in favor of role modeling. Hoff-
mann et al. (2015) also found evidence about the
parental role models in entrepreneurship. Economic
theory also provides an extended literature on the
intergenerational transmission of values since the pio-
neering paper by Bisin and Verdier (2001).4Recently,
Chakraborty et al. 2016 have also considered this
framework to connect culture to entrepreneurship and
economic growth.
Entrepreneurship and institutions.Besides culture,
another determinant of entrepreneurship is the quality
of the institutions (Acs and Amor´
os 2008). Institu-
tions are crucial because of their role in ensuring the
protection of property rights, the objective resolution
3”Relevant institutions include fiscal legislation (tax rates
and tax breaks), the social security system influencing the
rewards and the risks of entrepreneurship, and the administra-
tive requirements for starting a new business.” (Wennekers et al.
2005, p. 300)
4See Bisin and Verdier (2011b) for a survey of this literature.
156
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Cultural transmission and persistence of entrepreneurship
of contracts and other legal disputes, and the govern-
ment’s transparency (van Stel et al. 2005). The OECD-
Eurostat Entrepreneurship Indicator Programme (EIP,
2009) indicates that entrepreneurship requires a good,
clear, and enforceable regulatory framework. Afonso
et al. (2005) elaborate an Administration Oppor-
tunity Indicator that takes into account corruption,
red tape (concerning regulatory environment), qual-
ity of the judiciary (concerning the confidence in
the Administration of justice), and the size of
the shadow economy. The correlation between the
entrepreneurship rate and this Administration Oppor-
tunity Indicator offers a positive and significant value
of 0.42.5Klapper et al. (2010) also find a posi-
tive and significant relationship between both the
“ease of doing business index” and the entry and
new firm density rates per country.6They estimate
that for every 10 percentage point decrease in entry costs,
density and entry rate increase by about 1%.
1.2 Key features of the model
Our model explicitly analyzes the interaction among
preferences and institutions when preferences are het-
erogeneous in the population and evolve over time. In
this Section, we describe its key features.
Concerning the first element, preferences, we con-
sider that each adult chooses between becoming an
entrepreneur or not, in which case, he will work as
a civil servant or as a routine producer. The choice
depends on his preferences. Preferences are trans-
mitted among generations during the socialization
process. As in Bisin and Verdier (2011b), the model
considers that the values or attitudes may be transmit-
5Correlation between Total Entrepreneurial Activity Rate
(TEA) and Administration Opportunity Indicator for those
countries that appear in both sources of data in 2000. Source:
own elaboration based on data from Afonso et al. (2005)and
Global Entrepreneurship Monitor, GEM (Autio, 2005). TEA:
proportion of adults involved in creation of nascent firms
(3 months) and proportion involved in surviving firms (42
months).
6The Doing Business Report includes a ranking of this “ease
of doing business index” . A high position in the ease of doing
business ranking means that the regulatory environment is more
conducive to the starting and operation of a local firm. The
index is constructed as the simple average of the countries’
percentile rankings on 10 topics: Starting a business, Dealing
with licenses, Employing workers, Registering property, Get-
ting credit, Protecting investors, Paying taxes, Trading across
borders, Enforcing contracts, and Closing a business.
ted (at a cost) from parents to children or by society
at large, in other words, there exists direct transmis-
sion and oblique transmission. Parents try to shape the
preferences of their children taking into account the
potential gains of the children’s occupational choice
when they become adults. If parents do not succeed
in transmitting their chosen preferences, then chil-
dren acquire preferences from the social environment
where they grow up.
Concerning the second element, the quality of
institutions, we consider that the efficiency of the
administration determines the expected profits from
entrepreneurial activity. Specifically, if an individ-
ual decides to become an entrepreneur and start a
risky project, the probability of success will cru-
cially depend on the level of efficiency and the size
of the administration. By efficiency of the admin-
istration, we mean the effort made to generate a
friendly normative and regulatory framework for busi-
ness, although it can have other alternative inter-
pretations, such as the absence of corruption in
the public sector.7Bureaucracy (and civil servants)
will make its decision on efficiency pursuing its
own interests depending on the total payoff they
obtain. Wages of civil servants are paid with col-
lected taxes; it is assumed that there is a balanced
public budget. Specifically, the model assumes that
only entrepreneurs are net contributors. Therefore,
entrepreneurs face a trade off: high taxes mean that
they appropriate a low proportion of their income,
but it also means that the efficiency of the administration
is high. Consequently, the expected gross profits can
be high. The level of taxation is decided by some polit-
ical process. In this paper, it will be chosen by majority
voting, but obviously, we can also make clear predic-
tions to political situations where the decisive political
agent is not necessarily the median voter.
7To interpret the efficiency of the Administration as absence of
corruption, the distribution of ethics among the officials should
be considered. This can be implemented by considering that
civil servants could be either honest or dishonest as in Hauk
and Saez-Marti (2002) or that they may exhibit public service
motivation or not as in Delfgaauw and Dur (2008). A more
general model will analyze the coevolution of these traits and
the preferences for entrepreneurship. In this paper we focus on
the efficiency of the Administration as observable and valuable
items which can be measured by indicators such as for instance,
the ”easy doing business”.
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G. Olcina et al.
1.3 Main findings
The main result of the paper is that the persistent
differences in entrepreneurship across economies can
be explained by two factors: the initial conditions of
the economy and the taxation level on entrepreneurial
earnings. We first show that an economy can reach
two different long-run equilibria where the socializa-
tion efforts of entrepreneurs and non-entrepreneurs
parents to transmit their preferences are balanced. The
first equilibrium is a traditional economy, with a low
proportion of entrepreneurs, high confiscatory taxes,
and an inefficient administration. The second possi-
ble equilibrium is an economy with predominantly
entrepreneurial traits, lower taxes (but high enough to
implement an efficient administration), and a higher
per capita income. Taxes will be higher and the public
sector will be less efficient in a traditional equilibrium,
corroborating that high levels of taxation, corruption,
and bureaucratic obstacles to start a business can
discourage entrepreneurship (Lee and Gordon, 2005;
Klapper et al. 2006,2010; Ciccone and Papaioannou,
2007; Cullen and Gordon, 2007; Djankov et al. 2010).
Our model shows that the tax rate on entrepreneurial
profits implemented by the previous generations com-
pletely determines whether an economy achieves a tra-
ditional equilibrium or an entrepreneurial equilibrium.
If tax decisions are made by majority voting in a myopic
way, then the initial conditions of the economy become
crucial. That is, for an economy with an initial major-
ity of non-entrepreneur individuals, the dynamics will
move the economy towards the non-entrepreneurial
steady state, as they will vote for the highest taxes.
These confiscatory tax policy reinforces the supe-
rior incentives of non-entrepreneurs to transmit their
preferences consolidating their majority. Conversely,
an economy with a majority of entrepreneurs will set up a
moderate tax on entrepreneurial profits just high enough
to afford an efficient administration, and the dynamics
will move the economy towards the entrepreneurial
steady state. This efficient tax policy guarantees that
entrepreneurs have enough incentives to transmit their
preferences.
In the end, if individuals vote myopically, the
ultimate determinant of where the economy estab-
lishes in the long run is the initial proportion of
entrepreneurs and productivity. This fact explains per-
sistence: an economy evolves around similar levels of
entrepreneurship as in the initial situation unless some
structural changes are implemented.
However, if individuals are forward-looking and
they are concerned about the welfare of future gen-
erations, they might try to implement some tax
reform in order to drive the economy towards an
entrepreneurial society. In the entrepreneurial equilib-
rium, both entrepreneurs and non-entrepreneurs obtain
a higher payoff than in the traditional one. We discuss
different alternatives in order to establish a credi-
ble intergenerational commitment to never set con-
fiscatory taxes in the future and to compensate the
short-run losses for non-entrepreneurs with a subsidy.
The paper is organized as follows. Section 2intro-
duces the static model, describing the game played
by each generation. Section 3characterizes the dif-
ferent equilibria of the game played within a gen-
eration between administration and voters. Section 4
describes the cultural transmission of preferences and
the evolution of the proportion of entrepreneurs in the
population. Section 5characterizes the long-run equi-
libria of the society. Section 6compares the levels of
income and social welfare obtained in the different
steady-state equilibria. Finally, Section 7concludes
and discusses some policy proposals.
2 The model
We consider overlapping generations of individuals
that live two periods. During the first period, each
individual is socialized in some cultural traits and, at
the beginning of the second period, as an adult, he
becomes active and enters the labor market.
A proportion q∈[0,1]of the individuals are of
entrepreneurial type (E), and the rest, (1−q) ∈
[0,1], are of non-entrepreneurial type (N). The non-
entrepreneurs work as civil servants or in a traditional
sector with a fixed payoff. The civil servants are a pro-
portion αof the population and, therefore, α∈(0,1)
denotes the size of the administration.
2.1 Payoffs
The workers that join the traditional sector will
receive a fixed monetary payoff denoted by R>
0. However, entrepreneurship is a risky activity. The
income is H>Rin case of success and zero in case
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Cultural transmission and persistence of entrepreneurship
of failure. If the entrepreneur fails, his payoff is lower
that the wage in a routine production activity R.
The success of the entrepreneurial activity depends
on the legal and normative framework where this
activity is conducted, and the institutional environ-
ment depends on the efficiency of the administration,
denoted by e. oWe consider that the administration
efficiency ecrucially affects the probability of suc-
cess denoted by pand for the activity to be risky
indeed; this probability of success phas to be lower
than 1. Additionally, there is some interaction between
the level of efficiency and the size of the administra-
tion. We assume that the success of the entrepreneurial
activity depends both on the efficiency and the size
of the administration, with an inverted-U relation-
ship. Thus, very small or very big administrations will
lead to lower probabilities of success.8Summariz-
ing, we assume that the probability of success of the
entrepreneurial activity is given by the following:
p=eα(1−α).
Therefore, the expected income πof the risky activ-
ity is π=pH,whereHcan be interpreted as the
productivity of the entrepreneurial sector. Moreover,
entrepreneurs pay taxes, τ, so that the net monetary
income of an entrepreneur is as follows:
yE=(1−τ)Hp. (1)
Collected taxes fund the public administration. We
consider that only entrepreneurs pay taxes. It could be
considered that all workers pay taxes and receive ser-
vices in return but, in any case, there would be net
contributors and net beneficiaries. Under our assump-
tion, the entrepreneurs are net contributors. Moreover,
the tax rate is decided by majority, through a voting
process.
We consider that the public administration is run by
a single entity, and we assume that its managers decide
on the level of efficiency and size of the administration
(e, α) with the objective of maximizing the income of
civil servants or bureaucrats. There is no agency prob-
lem within the administration, whoever holds power
on behalf of the bureaucracy cares about the average
welfare of the group as a whole. The level of efficiency
8Even if the administration is efficient, if civil servants are very
few the support given to the entrepreneurs activity is likely to
remain limited. Similarly, an oversized public sector would not
contribute to the success of entrepreneurial activity.
can be achieved at a cost which increases in the size of
the administration, that is, the number of civil servants
α. In particular, it has a cost given by c(e) =αβe2
2,
∀e∈[0,1). Therefore, the managers of the adminis-
tration choose the level of efficiency eand the size of
the administration αthat maximize the following:
τHqeα(1−α) −αβe2
2(2)
which is the difference between public income and the
cost to implement the regulatory framework. For sim-
plicity, we assume that the collected taxes minus the
cost of efficiency is divided equally among the civil
servants. Therefore, officials’ wage is given by the
following:
yC=τHqe(1−α) −βe2
2.
Civil servants’ wages increase with three factors: (i)
the level of taxes, τ, (ii) the level of expected profits
which, in turn, depends on the administration effi-
ciency e, and (iii) the proportion of entrepreneurs q
. If there is a high proportion qof entrepreneurs, the
proportion of taxpayers will increase. However, if the
size of the administration αincreases, the number of
recipients also increases: each civil servant receives a
smaller fraction of the collected taxes.
We abstract from the free-riding problem of civil
servants effort and consider that there is a minimum
observable effort that is enforceable and that if it is
not met by the civil servant, he will be fired. Then,
the public agency offers an enforceable contract in
which a wage level yCis specified, along with a min-
imum effort level. (See Delfgaauw and Dur, 2008,
or Forquesato, 2016, for an analysis on the incen-
tives and workers’ motivation in the public sector or
organizations).
Finally, the monetary payoff of an on-
entreprepreneurial individual is given by the following:
yN=α
1−qyC+1−α
1−qR(3)
where yCand Rare the payoffs as civil servants
and routine producers, respectively; and the fractions
α
1−qand 1 −α
1−qare the probabilities of a non-
entrepreneurial individual to work as civil servant or
routine producer, respectively, when (1−q) > α.If
(1−q) ≤α, the probability of a non-entrepreneurial
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G. Olcina et al.
individual to work as civil servant will be one and,
therefore yN=yC.
2.2 Preferences
Entrepreneurs positively value the participation in
a risky activity and obtain a psychological pay-
off denoted by γ>0. This non-pecuniary bene-
fit may correspond to social status, the satisfaction
of starting your own business, the flexibility and
autonomy of self-employment, etc. Moskovitz and
Vissing-Jorgensen (2002) estimate that entrepreneurs
non-pecuniary benefits amount on average to some
150% of the entrepreneur’s annual income. The non-
entrepreneurial individuals, in contrast, obtain a psy-
chological disutility γ>0 from undertaking a risky
activity. This type of individuals has a negative view
of things, such as taking risks, not having a permanent
job, etc.9
We use a simple kind of preferences to characterize
the types Eand N. In particular, we consider that the
individuals have a linear utility function that depends
on both the expected monetary payoff and on the non-
pecuniary benefit they obtain for their activity:
UE=yE+γ1E,(4)
UN=yN−γ1E(5)
where yi,i ∈{E, N},denotes the expected mon-
etary payoff and 1Eis the indicator function of
entrepreneurial activity (1E=0 if the individual is
type Nand 1E=1 if he is type E).
A priori, both types could choose to carry out either
the risky or the non-risky activity. However, taking
into account the evidence about the intergenerational
transmission of entrepreneurship, we consider that the
individual’s type determines the activity he chooses.
We make an assumption on the relationship between
the wage in the traditional sector Rand the psycho-
logical payoff γof entrepreneurship. In particular, we
establish a lower bound on this psychological payoff:
(1−α)R < γ Assumption 1
9We assume that the two psychological payoffs are the same.
That is, the utility of engaging in the risky activity for the
entrepreneurs is the same as the disutility of this activity for the
non-entrepreneurs. Although this assumption is not strictly nec-
essary, it simplifies the process of obtaining and interpreting the
results.
Assumption 1 implies that we will not consider in
our analysis the less interesting case where the psy-
chological payoff from entrepreneurship is so low
compared with the payoff in the traditional sector that
parents will always prefer that their offspring become
non-entrepreneurs under any circumstance.
2.3 The game between administration and voters
The timing of each generation’s game is as follows.
First, taxes are decided by majority voting, that is,
individuals vote for the level of taxes τ∈[0,1]
that will fund the administration. After voting, the
administration decides about efficiency and size of the
administration. Then, the entrepreneurial individuals
start their business and the non-entrepreneurial indi-
viduals find a job in either the public or the traditional
sector. Finally, all agents receive the payoffs.
There is a strategic interaction between the admin-
istration and entrepreneurs. The administration needs
the success of the entrepreneurs to guarantee the pub-
lic income and, obviously, the salary of the officials.
And in turn, entrepreneurs need the efficiency of the
administration to be successful in their activity.
3 Equilibria in each generation
In this section, we analyze the equilibrium of the
game played in each generation between administra-
tion and voters. Firstly, we obtain both the level of
efficiency and size of the administration given any tax
rate decided by the voters and, secondly, we analyze
the tax rate that each type will vote anticipating these
administration decisions.
The administration chooses the level of efficiency and
size of the public sector (e, α) that ensures the maxi-
mum total payoff of the bureaucracy. Maximizing (2)
with respect to eand α, subject to (1−q) ≥α, it
follows that the interior solution of each variable as a func-
tion of the other variable, is given by the following:
e(α) =τqH(1−α)
β,
α(e) =τ2qH −βe
4τHβ .
Notice that the smaller the size of administration,
the higher is the level of efficiency chosen by its
manager and vice versa.
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Cultural transmission and persistence of entrepreneurship
Solving for the optimal levels (e∗,α
∗),we obtain
that for 1 −q≥1/3,
e∗=τ2qH
3β,(6)
α∗=1
3.(7)
In the case that 1−q<1/3, then all non-entrepreneurs
work as civil servants: α∗=1−qand e∗=τq2H
β.
Therefore, there exists an optimal size of the
administration, while its efficiency increases (i) with
the tax rate τ, since bureaucrats acquire a higher pro-
portion of the entrepreneurs’ profits, (ii) with the pro-
portion entrepreneurs q(because they are tax payers)
and, finally (iii) with the productivity H.
Second, we analyze the results of the voting process
on taxes. Entrepreneurs face a trade off: high taxes
mean that they appropriate a low proportion of their
income but high taxes also improve the efficiency of
the administration, and then increase the probability of
success of the entrepreneurial activity. Consequently,
even if they do not appropriate all the benefits of
the risky activity, they vote for an intermediate tax
rate. Nonetheless, the earnings of non-entrepreneurs
depend positively on taxes, since a share of those
non-entrepreneurs are civil servants. Consequently,
non-entrepreneurs prefer a higher tax compared to
entrepreneurs.
Formally, each type votes the tax rate that maxi-
mizes his payoff, anticipating the efficiency chosen by
the bureaucracy. Entrepreneurs choose the tax rate that
maximizes
yE=(1−τ)π =τ(1−τ)4qH2
27βif q≤2/3,
τ(1−τ)H2q3(1−q)
βif q>2/3.
These payoff functions have a maximum in τ=1/2.
On the other hand, the non-entrepreneurs vote for the
tax rate τ∈[0,1], which maximizes their expected
payoff
yN=α∗
(1−q) yC+(1−α∗
(1−q) )R =2τ2H2q2
9β+2−3q
3(1−q) Rif q≤2/3,
yC=τ2q4H2
2βif q>2/3.
These payoffs are increasing with τand, conse-
quently, the non-entrepreneurs vote for τ=1.As it
can be expected, the non-entrepreneur individuals vote
for the maximum level of taxes, that is, confiscatory
taxes.
The main result of this section is stated below and
described formally in the Appendix.
Proposition 1 There are two possible equilibria in
each generation depending on which of the two types
is prevalent in the population, (i) an entrepreneurial
equilibrium if entrepreneurs are majority (q ≥1/2)
with a low tax rate τ=1/2and (ii) a traditional equi-
librium if non-entrepreneurs are majority (q < 1/2)
with a high tax rate τ=1.
Proof See Appendix.
If non-entrepreneurs are the majority of the pop-
ulation, they win the voting process and taxes will
be confiscatory. In this case, bureaucracy appropriates
the whole entrepreneurs’ earnings and entrepreneurs
obtain only their psychological payoff. Conversely, if
entrepreneurs are the majority of the population, they
will vote for an intermediate tax rate and the monetary
profits from entrepreneurship will be shared between
entrepreneurs and the bureaucracy.
4 Cultural transmission process
As obtained in the previous section the equilibrium
played by each generation is fully determined by the
existing distribution of preferences in the population.
But this distribution might change over time because
of a process of intergenerational cultural transmission
of preferences. Having established the payoff of indi-
viduals with different preferences in the equilibria,
parents face the problem of choosing to transmit his
cultural trait (preferences for entrepreneurship or not)
to his offspring.
4.1 The socialization process and the dynamics
of preferences for entrepreneurship
We draw from the model of cultural transmission by
Bisin and Verdier (2001), which is the economic ver-
sion of the anthropological model by Cavalli-Sforza
and Feldman (1981). The type of an individual (i.e.,
entrepreneur or not) will be an acquired trait derived
from the socialization process. Individuals will live
through two periods: as children and as adults. During
their childhood, each individual’s preference is shaped
by both his parents and society at large. As an adult,
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G. Olcina et al.
he enters the labor market and becomes part of the
productive economy in his generation’s game.
Each adult has one child in the second period of
his life and tries to transmit the values or preferences
that he believes are the most valuable. Therefore, each
adult makes a decision on a costly socialization effort
to influence his child’s preferences.
Let di
t∈[0,1)be the socialization effort made by
a parent of type iat generation t, i ∈{E, N}.Social-
ization occurs in two steps. A child is first directly
exposed to the parent’s preferences and is social-
ized to these preferences with probability di
t(vertical
transmission). If this direct socialization is not suc-
cessful, with probability 1 −di
t, she is socialized to
the preferences of a role model picked at random in
the population (oblique transmission). The transition
probabilities Pij
tthat a parent of type iwill have a
child of type j, if the proportion of entrepreneurs is qt,
are given by the set of equations:
PEE
t=dE
t+(1−dE
t)qt
PEN
t=(1−dE
t)(1−qt)
PNN
t=dN
t+(1−dN
t)(1−qt)
PNE
t=(1−dN
t)qt.(8)
For instance, PEE
tis the probability that a child of
an entrepreneur parent is socialized to entrepreneurial
preferences. Namely, with probability dE
t, he adopts
his parent preferences and with probability (1−dE
t)
he adopts these preferences of other entrepreneurial
individual with whom he is randomly matched.
Given the transition probabilities Pij
t, the propor-
tion qt+1of entrepreneurs in periodt+1 is described
in equation (9) and the dynamic evolution of the
distribution of preferences is given by (10):
qt+1=qt+qt(1−qt)(dE
t−dN
t), (9)
qt=qt(1−qt)(dE
t−dN
t). (10)
Notice that the proportion of entrepreneurs will
increase from one generation to another if, and only
if, the socializing effort of the entrepreneur par-
ents is greater than that of the non-entrepreneur
parents (equation 11). Likewise, the proportion of
entrepreneurs will fall if, and only if, the socializing
effort of the entrepreneur parents is lower than that of
the non-entrepreneur parents (equation 12).
qt>0⇐⇒ dE
t−dN
t>0 (11)
qt<0⇐⇒ dE
t−dN
t<0 (12)
4.2 The socialization effort choice of parents
Parents are imperfect altruists towards their chil-
dren, according to the notion of “imperfect empathy”
described by Bisin and Verdier (2001). That is, they
are concerned about their children’s welfare, but they
evaluate the utility that their children will receive
through the lens of their own preferences. We denote
Vij the utility a type iparent assigns to a child of type
j. This utility will depend on the expectation about the
distribution of preferences in the next generation. We
will assume that parents have adaptive or backward-
looking expectations, believing that the proportion of
entrepreneurs will be the same in the next generation
as in the current generation.
The socialization effort has a cost: parents have
to invest in their children’s education, spend time
with them, choose the appropriate neighborhood, or
school, etc. For simplicity, we consider that the cost is
quadratic c(di
t)=k(di
t)2
2, with k>0, even though the
results are qualitatively identical with any increasing
convex function. Parents of type ichoose the social-
ization effort di
tat generation tthat maximizes the
following:
max
di
t{Pii
tVii +Pij
tVij −c(di
t)}.(13)
The optimal parents’ socialization efforts are as
follows:10
d∗E
t=1
kV E(1−qt)(14)
d∗N
t=1
kV Nqt.(15)
As in the literature, we call V i=Vii −Vij the value
of cultural assimilation. This value of cultural assim-
ilation is the net gain from socializing your child to
your own preferences. Hence, the parents’ socializa-
tion effort depends on two factors: (i) the probability
of oblique transmission and (ii) the value that parents
10See Appendix for the proof.
162
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Cultural transmission and persistence of entrepreneurship
confer to have a child of their own type instead of the
other type. Concerning the first one, optimal social-
ization efforts vary according to the probability of
oblique transmission. That is, the more individuals of
a type there are in the society, the lower the effort these
parents invest in vertical socialization. Since oblique
socialization is not costly, the parents of the predomi-
nant type can trust that their children will be socialized
toward their own type by other individuals in the soci-
ety. This is a standard property of the Bisin and Verdier
(2001) model of transmission of preferences.
With respect to the second factor, expressions (14
and 15) show that the value of cultural assimilation
influences the socializations efforts of parents. The
level of cultural assimilation for the different types
depends on the fiscal regime, which is decided by the
majority type in the population. These values of cul-
tural assimilation are computed in the Appendix and
are presented here to facilitate the explanation. In a
non-entrepreneurial economy (qt<1/2), where the
majority of non-entrepreneurs vote for confiscatory
taxes τ=1,the values are as follows:
V E=γ−yNand V N=γ+yN.
For instance, the value of cultural assimilation of an
entrepreneur V Ein an economy with a majority
of non-entrepreneurs will be the difference between
the value of having a child with his own prefer-
ences, γand the value of having a child with non-
entrepreneurial preferences, yN.
In an entrepreneurial economy (qt≥1/2), where
the majority of entrepreneurs vote for nonconfiscas-
tory taxes τ=1/2,the values of cultural assimilation
are now given by the following:
V E=γ+yE−yNand V N=γ−yE−yN.
In these expressions, we can see that the value for a
parent to transmit their own preferences depends cru-
cially on the expected payoff for their children. In
the next section, we explain in greater detail how the
values of cultural assimilation favors the spread of a
particular trait.
In short, preferences for entrepreneurship evolve
over time depending on the relative optimal effort
of both types of parents. Likewise, these optimal
efforts are determined by the expected payoffs as
entrepreneurs or not entrepreneurs which, in turn, are
Proportion of
ENTREPRENEURS
qt
Administration
EFFICIENCY
et
Socialization process
CULTURE
dit
Proportion of
ENTREPRENEURS
qt+1
Voting process t
Fig. 1 The dynamical links between the Proportion of
entrepreneurs, administration efficiency and Socialization
process
determined by taxes and administration efficiency. A
schematic illustration of the whole dynamic setting is
presented in Fig. 1.
The state variable of the dynamics is the proportion
of entrepreneurs in the population, qtin period t.This
proportion determines the tax rate decided through
the voting process, which in turn, determines the col-
lected taxes and the level of efficiency and size of the
administration. Efficiency and size of the administra-
tion determine the probability of success of the risky
entrepreneurial activity. This probability of success
together with the proportion of entrepreneurs qtand
the entrepreneurial productivity H, jointly determine
the monetary income obtained by both types in the
population: entrepreneurs and non-entrepreneurs. The
different types’ revenues, together with the psycholog-
ical payoff, determine the adults’ direct socialization
incentives, since they affect the net gains for transmit-
ting your own preferences. Finally, the effect of both
direct transmission incentives and oblique transmis-
sion of preferences, captured by the current distribu-
tion of preferences qt, leads to the next generation’s
proportion of entrepreneurs qt+1. In the next Section,
the pattern of the distribution of preferences in the
long run is analyzed.
163
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G. Olcina et al.
5 Preferences for entrepreneurship in the long run
The force that drives the change of the distribution of
preferences is the socialization effort of both types of
parents. Formally, the dynamics of the distribution of
preferences is derived by substitution of the optimal
education effort d∗E
tand d∗N
t, from (14) and (15), into
expression (10):
qt=qt(1−qt)d∗E
t−d∗N
t.(16)
A long-run equilibrium (steady state of the dynam-
ics) is a situation in which the proportion of
entrepreneurs remains constant over time, qt=0.
This can occur for two reasons. First, in a trivial way,
because the society is made of a single type (qt=0or
qt=1), although these solutions lack interest because
they are not stable.11 Second, because the socializing
efforts of the two types are balanced, d∗E
t−d∗N
t=0.
As explained in the previous section, if the social-
ization effort of entrepreneurial parents is greater
(smaller) than the effort of non-entrepreneurial, the
proportion of entrepreneurial individuals will increase
(decrease) from one generation to another. However,
if socialization efforts equals, i.e., d∗E
t−d∗N
t=0,
the distribution of preferences among the population
remains stable.
Next, we characterize the long-run equilibria of the
dynamics starting from a society with a majority of
non-entrepreneurs or from a society with a majority of
entrepreneurs.
5.1 The long-run equilibrium of a non-entrepreneurial
society
In a society with a majority of non-entrepreneurs,
where this majority holds up all the profits from
entrepreneurship through confiscatory taxes and
receive them as civil servants’ income, the dynamics
converges to a steady state equilibrium with a low pro-
portion of entrepreneurs, which we call as a traditional
equilibrium. The superscript cis used for traditional
equilibrium.
Proposition 2 Fo r al l q0<1/2the dynamics con-
verges to a traditional equilibrium (qc<1/2), with a
majority of non-entrepreneurs and a tax rate τ=1.
11This a property of this kind of dynamics, see Bisin and
Ver d i e r ( 2011b).
Proof See Appendix.
In a society with a majority of non-entrepreneurs,
the value of cultural assimilation and therefore
the incentives for direct socialization are always
higher for non-entrepreneurs than for entrepreneurs.
The intuition behind this result is quite obvi-
ous: non-entrepreneurs hold up all the profits from
entrepreneurship through confiscatory taxes and
receive them as civil servants’ income.
Nevertheless, given assumption 1 ((1−α)R < γ ),
for low values of the level of entrepreneurship qt,
the income of civil servants will also be very low
and so will be the difference between the values
of cultural assimilation of both types. On the other
hand, non-entrepreneurs trust on oblique transmis-
sion and will exert a low socialization effort, while
the minority of entrepreneurs will try to compensate
the effects of oblique transmission with an increased
socialization effort. As a result, for low values of qt,
the optimal socialization effort of the entrepreneurs
dE
twill be higher than the one of non-entrepreneurs
dN
t,and the share of entrepreneurship preferences
will increase in the next generation. For the rest of
the non-entrepreneurial region, oblique transmission
is not strong enough to compensate for the increas-
ing difference on the values of cultural assimilation
V N−V E.All the previous discussion explains
the directional arrows on Fig 2for qt<1/2. In Fig. 2,
we can see the direction of changes in the proportion
of entrepreneurs for different values of qt. The arrows
show the direction of intergenerational change.
5.2 The long-run equilibrium of an entrepreneurial
society
In a society with a majority of entrepreneurs where
they vote for intermediate taxes and thus share the
profits from entrepreneurship with civil servants, the
dynamics converges either to (i) the entrepreneurial
equilibrium, denoted by qe, with a relatively high
proportion of entrepreneurs and a high administra-
tion efficiency, if entrepreneurial productivity is high
enough, or to (ii) the traditional equilibrium, qc,if
entrepreneurial productivity is low. Formally,
Proposition 3 1. For all q0≥1/2and productiv-
ity H<H
the dynamics converges to a traditional
164
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Cultural transmission and persistence of entrepreneurship
Fig. 2 The dynamics of the
proportion of entrepreneurs
qt
0,5 1
qe
t
qt
0,5 1
qc
t
H < H
qc
equilibrium (qc<1/2), with a majority of non-
entrepreneurs and a tax rate τ=1.
2. For all q0≥1/2and productivity H≥Hthe
dynamics converges to an entrepreneurial equilibrium
(qe>1/2), with a majority of entrepreneurs and a
tax rate τ=1/2.
The critical value is H=6√βR.
Proof See Appendix.
In a society with a majority of entrepreneurs
voting for nonconfiscastory taxes τ=1/2,the
relationship between the values of cultural assim-
ilation depend now on the difference in monetary
payoffs obtained between entrepreneurs and non-
entrepreneurs. Namely, notice that V E>V
Nif
and only if yE>y
N.
For low values of the proportion of entrepreneurs
qt,but higher than 1/2, the relation between yEand
yNand the relative incentives for socialization depend
on the level of entrepreneurial productivity H.Letus
denote as Hthe value of Hthat equalizes yEand yN
when q=1/2.Straightforward calculation yields that
H=6√βR.
Therefore, when the productivity from
entrepreneurship is very low, H<H
,the socializa-
tion effort of non-entrepreneurs parents is higher than
that of entrepreneur parents even when taxes are non-
confiscatory. Preferences for non-entrepreneurship
spread in the population until eventually qtwill fall
below 1/2 and non-entrepreneurs will become the new
majority. In this case, there will be no steady-state
equilibrium where entrepreneurial preferences are
majority.
But for high enough levels of productivity, H
≥H,and qthigher and close to 1/2,the
income obtained by entrepreneurs will be higher
than the income obtained by individuals of the non-
entrepreneur type. Consequently, the socialization
effort of entrepreneurs will be higher than that of
non-entrepreneurs, resulting in an increase in the next
generation’s proportion of entrepreneurs. Intuitively,
only if the productivity of entrepreneurship His suf-
ficiently high, entrepreneur parents will have stronger
incentives to socialize their children than the incen-
tives non-entrepreneurial parents have.
However, once high values of qtare reached,
the monetary payoff for a non-entrepreneur becomes
greater than the one obtained by an entrepreneur.
The reason is that in an economy with high levels
of entrepreneurship, the few existing civil servants
share half of the aggregate profits from entrepreneurial
activity, which are collected through taxes, obtain-
ing very high wages. Moreover, for high values of
qt, oblique transmission also favors the spread of
non-entrepreneurial preferences.
In Fig. 2, we can see the direction of changes in the
proportion of entrepreneurs for different values of qt
and H.
Summarizing, the results obtained in the two pre-
vious propositions show how the persistence of the
levels of entrepreneurship is determined by the initial
proportion of entrepreneurs in the society and by the
productivity of the entrepreneurial sector. If the econ-
omy starts with a low proportion q0of entrepreneurs
in the population, or with an initial low level of pro-
ductivity H(H<H
), then it will get trapped in the
165
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G. Olcina et al.
long run in a traditional steady state equilibrium (qc).
The persistence of high levels of entrepreneurship in
an economy can also be explained by our results.
If entrepreneurs are the majority in the population
(q0>1/2) and the productivity is sufficiently high,
the economy will settle down in an entrepreneurial
equilibrium.
5.3 The role of taxes
The deep determinants driving the convergence to
one steady-state equilibrium or the other are the
level of taxes and the level of productivity of the
entrepreneurial sector. If the level of productivity His
very low (H < H ), then the society will get trapped
in the long run in a traditional steady-state equilib-
rium (qc). However, when productivity is sufficiently
high (H≥H), the introduction or not of confisca-
tory taxes in some generation is driving the dynamics.
More precisely, if confiscatory taxes are set by some
generation and maintained over time, the economy
converges to the traditional steady state. Alternatively,
if non-confiscatory taxes are implemented by all gen-
erations along the trajectory of the dynamics, the
economy converges to the entrepreneurial steady state.
Remark 1 The tax policy path implemented by all
generations determines the convergence to a tradi-
tional or entrepreneurial equilibrium.
In order to see the intuition, let us consider that
the same tax policy is implemented for any distribu-
tion of preferences in the population. For instance, if
confiscatory taxes are set for any qtin all periods,
the traditional equilibrium with qc<1/2 becomes
the global attractor of the dynamics. That is, for any
initial condition of the economy q0the dynamical
system converges to the steady state qc. Similarly,
for a permanent non-confiscatory tax policy (τ=
1/2), the entrepreneurial equilibrium with qe>1/2
becomes the global attractor of the dynamics. Obvi-
ously, an exogenous and permanent change in tax
policy can move the economy from one steady state
to the other. For instance, suppose that an economy
is trapped in a traditional equilibrium because of a
confiscatory tax policy. A permanent change to a
non-confiscatory tax policy will drive the economy
to an entrepreneurial equilibrium with high levels of
productivity and entrepreneurship.
6 Comparison of the traditional
and entrepreneurial equilibria
In this Section, we compare the two steady states,
focusing on the aggregate income of the economy,
as well as the incomes obtained by entrepreneurs
and non-entrepreneurs. That is, we will analyze the
size and distribution of aggregate welfare. We use
again the superscript eto denote the characteristics of
the entrepreneurial equilibrium, and the superscript c
stands to denote those of the traditional equilibrium.
Let us assume that the psychological payoff from
entrepreneurship has an upper bound,
γ<H2
81β+10
9R (Assumption 2)
Assumption 2 implies that we do not consider
in our analysis the case where the psychological
payoff from entrepreneurship is so high that par-
ents will always prefer that their offspring become
entrepreneurs under any circumstance.
Proposition 4 Suppose that Assumption 2 holds,
1. The administration is more efficient in the
entrepreneurial equilibrium than in the traditional
equilibrium: ee>e
c. 2. Civil servants’ payoff is
higher in the entrepreneurial equilibrium than in the
traditional equilibrium: ye
C>y
c
C.
3. Entrepreneurs’ payoff is higher in the
entrepreneurial equilibrium than in the traditional
equilibriumA: ye
E>y
c
E.
Proof See Appendix.
Thus, in the entrepreneurial equilibrium, the
Administration is more efficient. Hence, the proba-
bility of success of risky entrepreneurship is higher
than in the traditional equilibrium. In addition, pay-
offs are higher both for entrepreneurs and for civil
servants. Since in the traditional sector the payoff Ris
always the same, per capita incomes are higher in the
entrepreneurial equilibrium. The social welfare func-
tion is given by the aggregation of the income obtained
by each type: qyE+(1−q)1
3(1−q)yC+2−3q
3(1−q)R.
Therefore, it easily follows that social welfare is
higher in the entrepreneurial equilibrium. Given the
choice, both civil servants and entrepreneurs would
prefer to be in an entrepreneurial equilibrium. Thus
Corollary 1 follows from Proposition 4.
166
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Cultural transmission and persistence of entrepreneurship
Corollary 1 Social welfare is higher in the entreprene-
urial equilibrium than in the traditional equilibrium.
If Assumption 2 does not hold, the incentives for
socialization of entrepreneurial parents, even in a soci-
ety with a majority of non-entrepreneurs, would be so
high that the traditional equilibrium would be charac-
terized by a relatively high proportion of entrepreneurs
(although in a minority) and, given the confiscatory taxes,
the administration might show a high level of efficiency and
obtain a high monetary income for the bureaucracy.
Another issue is the distribution of this welfare among
the different types of individuals in each steady state.
In the traditional equilibrium non-entrepreneurs will
be better off than entrepreneurs because they appro-
priate all the profits generated by the entrepreneurial
sector through confiscatory taxes. The opposite hap-
pens in the entrepreneurial equilibrium.
Proposition 5 In the entrepreneurial equilibrium,
entrepreneurs have a higher utility than non-
entrepreneurs: Ue
E>U
e
N, and a higher monetary
payoff than civil servants, ye
E>y
e
C.
Proof See Appendix.
According to this proposition, entrepreneurs obtain
a higher expected utility than non-entrepreneurs in
the entrepreneurial equilibrium. This result is in
line with the theory of social legitimation (Etzioni
1987), according to which economies with more
entrepreneurs create an environment that is more
favorable to entrepreneurship. Notice additionally
that, in the entrepreneurial equilibrium, civil servants
have a lower income than entrepreneurs.
7 Concluding remarks and discussion
This paper presents a theory that explains the persis-
tence of differences between levels of entrepreneur-
ship across countries or regions. Empirical evidence
shows that the ranking of countries by level of
entrepreneurship does not change over the years for
long periods of time (Freytag and Thurik 2007). The
main result of the study is that taxes on entrepreneurial
profits are crucial to lead an economy towards either
an entrepreneurial or a traditional equilibrium. The
level of taxes, if decided by majority voting, depends
on the proportion of entrepreneurs among the popula-
tion. Due to the interdependence and the intertemporal
reinforcement among taxes, Administration perfor-
mance, productivity, and transmission of preferences,
the economy gets trapped close to the initial situation.
In an entrepreneurial equilibrium, there is a major-
ity of entrepreneurs in the population. The distribution
of preferences does not change because the socializa-
tion efforts are equal for both types of individuals. The
entrepreneur majority implements a tax policy that
maximizes their expected profits by giving the appro-
priate incentives for efficiency to the public administra-
tion. The high net payoff obtained b y the entrepreneuri al
activities provides strong incentives for cultural social-
ization to entrepreneurship preferences. But in this
steady state, there are also equally strong incentives for
socialization to non-entrepreneur preferences, because
the wage for civil servants (designed to sustain their
high level of efficiency) is very high. The high levels
of income obtained by entrepreneurs and civil servants
are sustained by a high efficiency of the bureaucracy.
In an traditional equilibrium, there is a majority
of non-entrepreneurs in the population. The non-
entrepreneur majority implements a confiscatory tax
policy. The socialization effort of entrepreneur par-
ents and non-entrepreneur parents equalize in this
steady state thanks to both oblique cultural transmis-
sion and the low income that can be obtained by
routine producers. Both factors provide incentives for
socialization effort to entrepreneurial preferences.
Social welfare is higher in an entrepreneurial equi-
librium. In line with studies that link entrepreneur-
ship to economic growth, both the efficiency of the
entrepreneurial sector and the per capita income will
be higher in the entrepreneurial equilibrium than in the
traditional equilibrium.
Therefore, if individuals are forward-looking and
are concerned about the welfare of future genera-
tions, they will try to implement some tax reform in
order to drive the economy to an entrepreneurial equi-
librium. Namely, a coalition between entrepreneurs
and civil servants could be formed to agree on a cred-
ible commitment to never set confiscatory taxes in the
future and to compensate the short-run losses for non-
entrepreneurs with a subsidy. Obviously this intergen-
erational and interclass coalition suffers from the usual
time-inconsistency problem. In other words, this com-
mitment or promise is clearly non-credible. However,
there are ways to establish credible commitments.
167
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G. Olcina et al.
For instance, constitutional limits on the tax rate pol-
icy and on the civil servants future wages can be
established. Alternatively, another way to build credi-
bility is the integration in a supranational organization
(international club), for instanc, the European Union,
where confiscatory taxes are not permitted. For dif-
ferent reasons, these mechanisms are very costly to
reverse. In case of a constitutional reform, because
it requires a qualified majority to do so. In case of
the participation in an international club, because exit
can be very costly in terms of losing the trading
advantages obtained from being a member of the club.
Another mechanism of commitment that operates
to guarantee the absence of confiscatory taxes is the
degree of external openness of the economy. Notice
that in our model a closed economy is implicitly
assumed. But if the economy is open (and in particular if
it belongs to a supranational economic region with free
trade and free movement of persons and capital), then
there will be an obvious restriction on the behavior
of a non-entrepreneur majority that puts a limit on
tax rates: talent and entrepreneurship can migrate to
another country. These possibleextensions of our model
highlight again the crucial role played by taxes on the
final long-run equilibrium achieved by an economy.
Acknowledgments G. Olcina and L. Escriche acknowledge
financial support from the Spanish Ministry of Economy and Com-
petitiveness project, ECO-2014-58297-R, ECO-2017-87245-R
and the ERC project-TECTACOM. E.M. Tur thanks the Broman
Foundation for financial support.
Open Access This article is distributed under the terms of the
Creative Commons Attribution 4.0 International License (http://
creativecommons.org/licenses/by/4.0/), which permits unre-
stricted use, distribution, and reproduction in any medium,
provided you give appropriate credit to the original author(s)
and the source, provide a link to the Creative Commons license,
and indicate if changes were made.
Appendix
The time subscript has been removed in the proofs
Proof of Proposition 1 The individuals of the major-
ity win the vote on taxes. The manager of the adminis-
tration decides on the level efficiency and the size of
the administration (e, α) with the objective of maxi-
mizing the total payoff of the bureaucracy: τHqeα(1−
α) −αβe2
2, subject to (1−q) ≥α. Let us denote this
function as f=τHqeα(1−α)−αβe2
2. The first-order
conditions for an interior solution are follows:
fe=0→τqH 1−α∗α∗−α∗βe∗=0→e∗=τqH(1−α∗)
β,
fα=0→τqHe1−2α∗−βe∗
2=0→α∗=τ2qH−βe∗
4τHβ .
Solving for the optimal levels (e∗,α
∗), we obtain
the following:
e∗(τ ) =τ2qH
3β,(17)
α∗=1
3.(18)
And, it is easy to check that it is a maximum since:
fee =−αβ < 0,f
αα =−2τHqe∗<0. Furthermore,
fee ×fαα >(f
eα)2since
2α∗βτHqe∗>τHq −2τHqα∗−βe∗2
→8
9(τHq)2>5
9(τHq)2.
If 1 −q<1/3,then the maximum is in the boundary
of the set of feasible solutions, α∗=1−qand the
effort level is e∗(τ ) =τqH2
β. Substituting the tax rate
(τ=1orτ=1/2), we obtain the administration
efficiency in each case. The payoffs for both types of
agents are determined by equations (1) and (3). There
are two possible equilibria within a generation:
1. Equilibrium if non-entrepreneurs are the majority,
q<1/2, characterized by the following:
τ=1,
e=2qH
3β,
yC=2q2H2
9β,
yE=0.
2. Equilibrium if entrepreneurs are the majority, q≥
1/2, characterized by the following:
τ=1/2,
e=qH
3βif q≤2/3
qH2
2βif q>2/3,
yC=q2H2
18βif q≤2/3
q4H2
8βif q>2/3,
yE=qH2
27βif q≤2/3
q3(1−q)H2
4βif q>2/3.
168
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Cultural transmission and persistence of entrepreneurship
Proof of the optimal socialization effort choice
of parents (subsection 4.2)
Parents of type ichoose the socialization effort di
tat
generation tthat maximizes the following:
max
di
t{Pii
tVii +Pij
tVij −c(di
t)}.
The first order condition is as follows :
∂Pii
t
∂di
t
Vii +∂Pij
t
∂di
t
Vij =kdi
t.
In order to guarantee di
t∈[0,1), a sufficient condi-
tion is k>max{V E,VN}, i.e., the marginal cost
of effort 1 is greater than the value of cultural assim-
ilation. In that case, the marginal cost for parents to
ensure that their child acquires the same preferences
as their own is too high.
Differentiating the transition probabilities in Eq. 8
and substituting in the first order condition, we obtain
the parents’ socialization efforts as follows:
d∗E
t=1
kVEE −VEN(1−qt)
d∗N
t=1
kVNN −VNEqt.
Hereafter, to simplify the notation, we do not
include this auxiliary parameter k, although it should
be remembered that it is implicit in the formulas.
When dE
t−dN
tis written, one should actually read
kdE
t−dN
t.
Proof of Proposition 2: Equilibrium in the long run
when non-entrepreneurs are majority.
In a non-entrepreneurial economy (q < 1/2),where
the majority of non-entrepreneurs vote for confisca-
tory taxes τ=1, the values of cultural assimilation
are follows:
V E=γ−yN→V E=γ−αyC+(1−α)R
V N=γ+yN→V N=γ+αyC+(1−α)R.
The difference between the socialization efforts of
the two types of parents is as follows:
dE−dN=(1−q)V E−qVN
=V E−qV E+V N=
=γ(1−2q) −yN.
If q<1/2, the payoffs are yC=2q2H2
9αβ ,yE=0(see
proof of Proposition 1), therefore
dE−dN=γ(1−2q)−2q2H2
27(1−q)β +2−3q
3(1−q)R.
We have to prove that qceffectively exists and that is
unique. If q<1/2, we have the following:
dE−dN=− q2H2
2(1−q)2αβ −2−3q
3(1−q)R
<0
+γ(1−2q)
>0
and substituting for q=1/2andq=0, the difference
between socialization efforts results:
dE−dNq=1/2=−
2H2
54β−5
6R<0
dE−dNq=0=γ−2
3R>0 under Assumption 1
As dE−dNis continuous in [0,1/2],∃qc∈(0,1/2):
dE−dN=0, and therefore at this point qt=0.
In addition, ∂dE−dN
∂q =−
2H2
27β
2(1−q)
(1−q)2−2γ−
R
3(1−q)2<0,∀qc∈[0,1/2],therefore dE−dNis
decreasing in [0,1/2]. Therefore, this qc∈(0,1/2)is
unique.
Proof of Proposition 2: Equilibrium in the long run
when entrepreneurs are majority,q≥1/2.
In an entrepreneurial economy (q≥1/2) where the
majority of entrepreneurs vote for non-confiscastory
taxes τ=1/2.The values of cultural assimilation if
qt<2/3 are now given by the following:
V E=γ+yE−yN→V E
=γ−1−1
3(1−q)R+yE−1
3(1−q)yC,
V N=γ−yE−yN→V N
=γ+1−1
3(1−q)R−yE−1
3(1−q)yC.
The differences between socialization effort, consid-
ering (14)and(15) are follows:
dE−dN=(1−q)V E−qVN
=V E−qV E+V N
=yE−1
3(1−q)yC−1−1
3(1−q)R
+γ(1−2q).
169
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G. Olcina et al.
If q>2/3then(1−q) < α∗=1/3 and all non-
entrepreneurs become civil servants and yN=yC.
Therefore,
dE−dN=γ(1−2q) +q3H2
8β(2−3q),
which is negative for all q>2/3.
However, if q<2/3then
dE−dN=qH2
27β−1
3(1−q)
q2H2
18β
−2−3q
3(1−q)R+γ(1−2q)
=2−3q
54(1−q)βqH 2−2−3q
3(1−q)R+γ(1−2q)
We have to prove that qeeffectively exists and that is
unique. We have that the first term is positive and the
second is negative if q<2/3.
dE−dN=2−3q
54(1−q)βqH 2
>0
−2−3q
3(1−q)R+γ(1−2q)
<0
Substituting for q=1/2andq=2/3inthis
expression, we have the following:
dE−dNq=1/2=−
1
3R−H2
36β
>0ifH≥H,whereH=6βR
dE−dNq=2/3=−
1
3γ<0.
As dE−dNis continuous in [1/2,2/3],∃qe∈
(1/2,2/3):dE−dN=0, and therefore at this point
qt=0.
In addition, ∂dE−dN
∂q =−2γ+R
3(1−q)2+
H2
54β
3q2−6q+2
(1−q)2<0∀q∈[1/2,2/3],taking into
account that 2
3R<γand that H≥H=6√βR;
therefore, dE−dNis decreasing in [1/2,2/3]. Hence,
this qe∈(1/2,2/3)is unique.
Nonetheless, if H<H
, the differences between
socialization efforts (dE−dN)is negative ∀qt∈
[1/2,1]and non-entrepreneurial traits spreads among
the population. Eventually, the proportion qtwill arise
to qt<1/2 and the economy converges to qcas
proved in Proposition 2.
Proof of Proposition 4 Comparison of the traditional
and entrepreneurial equilibria
Tabl e 1 Efficiency and payoffs at the steady state equilibria
Traditional equilibrium Entrepreneurial equilibrium
ec=2qcH
3βee=qeH
3β
yc
C=2(qc)2H2
9βye
C=(qe)2H2
18β
yc
E=0ye
E=qeH2
27β
Taking into account the steady state points qc
and qefrom Propositions 2 and 3, we calculate the
administration efficiency, civil servants’ payoff, and
entrepreneurs’ payoff in each equilibrium. Table 1
provides the results to facilitate the comparison
1. Comparing administration efficiency, we have
that ee>e
cif qeH
3β>2qcH
3β→qe>2qc.We
know that 1/2<q
e<2/3andqc<1/2. There-
fore, it must hold that 1/2>2qc.A sufficient
condition is qc<1/4.If dE−dNq=1/4<0,
then qc<1/4. The difference between social-
ization efforts for q<1/2isgivenbythe
following:
dE−dN=− 2q2H2
27β(1−q)−2−3q
3(1−q)R+γ(1−2q)
and evaluated in q=1/4is
dE−dNq=1/4=− H2
162β−5/9R+1/2γ.
Recall that for H<H
, there is only a steady
state qc.Therefore, we analyze the case where
H≥H. Substituting for H=6√βR, we obtain
that under Assumption 2, for any H≥H→
dE−dNq=1/4<0,which implies that ee>e
c.
2. Civil servants’ payoff is higher in the
entrepreneurial economy than in the traditional
economy: ye
C>y
c
Cif (qe)2H2
18β>(qc)2H2
9β→qe>
2qc, which holds if ee>e
cthat has been proved
above.
3. It is trivial because yc
E=0
Proof of Proposition 5 First, we compare the utilities
Ue
Eand Ue
N:
Ue
E=qeH2
27β+γ
Ue
N=(qe)2H2
54(1−qe)β +2−3qe
3(1−qe)R.
170
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Cultural transmission and persistence of entrepreneurship
Comparing the first terms, we obtain that qeH2
27β>
(qe)2H2
54(1−qe)2βif qe<2
3which holds because qe∈
(1/2,2/3). Moreover, γ> 2−3qe
3(1−qe)R∀qe∈
(1/2,2/3)as γ>2
3Rbecause of Assumption 1, then
Ue
E>U
e
N.
Second, we compare ye
Ewith ye
C. The payoff of
entrepreneurs is higher than the payoff of a civil ser-
vant if qeH2
27β>(qe)2H2
18β→qe<2/3 which holds
because qe∈(1/2,2/3).
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