Problem or opportunity? Immigration, job search, entrepreneurship and labor market outcomes of natives in Germany

I ikha , Zainab; Zaha ie a, Anna
Wo king Pape
P oblem o oppo uni y? Immig a ion, job sea ch,
en ep eneu ship and labo ma ke ou comes o na i es in
Ge many
Wo king Pape s in Economics and Managemen , No. 05-2024
P o ided in Coope a ion wi h:
Facul y o Business Adminis a ion and Economics, Biele eld Uni e si y
Sugges ed Ci a ion: I ikha , Zainab; Zaha ie a, Anna (2024) : P oblem o oppo uni y? Immig a ion,
job sea ch, en ep eneu ship and labo ma ke ou comes o na i es in Ge many, Wo king Pape s in
Economics and Managemen , No. 05-2024, Biele eld Uni e si y, Facul y o Business Adminis a ion
and Economics, Biele eld,
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Wo king Pape s in Economics and Managemen
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No. 5-2024
Decembe 2024
P oblem o oppo uni y? Immig a ion, job sea ch,
en ep eneu ship and labo ma ke ou comes
o na i es in Ge many
Zainab I ikha , Anna Zaha ie a
P oblem o oppo uni y? Immig a ion, job sea ch,
en ep eneu ship and labo ma ke ou comes o
na i esinGe many
∗
Zainab I ikha
†
Anna Zaha ie a
‡
No embe 20, 2024
Abs ac
In his s udy we e alua e he effec s o low-skilled immig a ion on small busi-
nesses, wages and employmen in Ge many. We de elop a sea ch and ma ching
model wi h he e ogeneous wo ke s, c oss-skill ma ching, and endogenous en y in o
en ep eneu ship. The model is calib a ed using Ge man Socio-Economic Panel
(SOEP) da a. Quan i a i e analysis shows ha low-skilled immig a ion benefi s
high-skilled wo ke s while nega i ely affec ing he wel a e o low-skilled wo ke s.
I leads o he endogenous expansion o immig an en ep eneu ial ac i i ies, gen-
e a ing posi i e spillo e s o all demog aphic g oups excep na i e en ep eneu s.
O e all, he e is a ma ginal loss o he economy in e ms o pe wo ke wel a e.
This loss is mi iga ed wi h inc eased skilled mig a ion om India. Policies es ic -
ing immig an en ep eneu ship elax compe i ion o na i e small businesses bu
educe wel a e o all o he wo ke g oups. E hnic seg ega ion o small businesses
benefi s low-skill na i e en ep eneu s.
Keywo ds: en ep eneu ship, small business, sel -employmen , sea ch ic ions,
immig a ion
JEL codes: J23, J31, J61, J64, L26
∗
We hank Michele Ba is i, Pa el B endle , He be Dawid, Guido F iebel, Leo Kaas, Kei h Kues e ,
Mo i z Kuhn, Joan Llull and Sebas ian O en o hei aluable commen s. Zainab I ikha would like o
hank he Joachim He z Founda ion, and he Deu sche Fo schungsgemeinscha (DFG, Ge man Resea ch
Founda ion), Ge many unde Ge many’s Excellence S a egy – EXC 2126/1-390838866 o financial
suppo . Anna Zaha ie a would like o hank he Leibniz Associa ion o p o iding financial suppo
o he Leibniz Science Campus “SOEPRegioHub” a Biele eld Uni e si y and he Ge man Resea ch
Founda ion (DFG) in he amewo k o he Resea ch T aining G oup RTG 2951.
†
Uni e si y o Bonn, CEPR, email: i ikha @uni-bonn.de
‡
Biele eld Uni e si y, Ge many, email: anna.zaha ie [email p o ec ed]
1 In oduc ion
In his pape we e isi he impac o immig a ion on ecei ing coun ies. We de elop a
mac oeconomic model wi h sea ch ic ions and endogenous en y in o en ep eneu ship.
The model is calib a ed o Ge man da a and makes ou con ibu ions o he li e a u e.
Fi s , we de elop a unified amewo k ha allows o he dual ole o immig an s as job
seeke s and as en ep eneu s o job c ea o s. By doing so, we cap u e he highe compe-
i ion na i e wo ke s ace due o immig a ion and he be e ou side op ions due o jobs
c ea ed by immig an en ep eneu s. Second, we p o ide a quan i a i e assessmen o he
model mechanism gene a ing new insigh s in o he he e ogeneous effec s o immig a ion
on wages, employmen oppo uni ies o na i es and incumben immig an s as well as job
c ea ion in small businesses in Ge many. Thi d, we e alua e he wel a e effec s o policies
acili a ing immig an s’ en y in o en ep eneu ship and analyze he ole o e hnic seg-
ega ion. Fou h, we quan i y he impac o ecen ly es ablished coope a ion on wo ke
mobili y be ween Ge many and India.1
On he one hand, he li e a u e p o ides e idence ha immig an en ep eneu s con-
ibu e o job c ea ion.2Fo example, Sachs e al. (2016) finds ha en ep eneu s wi h
mig a ion backg ound employed a leas 1.3 million people in Ge many in 2014, while
Leich and Langhause (2014) epo his numbe be ween 1.5 o 2 million. Ne e he-
less, his li e a u e does no explo e he gene al equilib ium consequences o immig a ion
in hos coun ies. On he o he hand, he la ge body o li e a u e dealing wi h di e se
aspec s o mig a ion in ecei ing coun ies igno es he immig an s’ en ep eneu ial ole de-
spi e i s di ec implica ions o he employmen oppo uni ies and wages o na i es. This
li e a u e ea s immig an s as wo ke s who compe e wi h na i es o jobs and influence
hei wel a e ia he effec s on wages, employmen and fiscal ans e s.3
In his pape we syn hesize he a o emen ioned s ands o li e a u e and add ess he
ollowing ques ions 1) does igno ing he ole o immig an s as en ep eneu s lead o biased
p edic ions conce ning he consequences o immig a ion o labo ma ke ou comes and
he wel a e o na i es? 2) whe he policies educing ba ie s o sel -employmen may
be beneficial in educing unemploymen and inc easing income/wel a e 3) which wo ke
g oups gain/lose om he e hnic seg ega ion o small businesses?
We de elop a sea ch and ma ching (SaM) model wi h ou demog aphic g oups: na-
i es/immig an s and high/low-skilled. Wi hin each demog aphic g oup he e a e indi-
iduals wi h a high en ep eneu ial spi i , called po en ial en ep eneu s, and indi iduals
wi h a low en ep eneu ial spi i , called egula wo ke s. This dis inc ion is mo i a ed by
1Ge many and India signed he “Mig a ion and Mobili y Pa ne ship Ag eemen ” (MMPA) in De-
cembe , 2022 o acili a e skilled mig a ion om India o Ge many. In Oc obe 2024 Ge many ag eed o
inc ease he numbe o isas g an ed o Indian skilled wo ke s and p omo e ai mig a ion.
2(Ke and Ke , 2020; Riillo and Pe oni, 2022; Li, 2001; Lo s om, 2002; Cons an and Zimme mann,
2006)
3(D’Amu i e al., 2010; Ben-Gad, 2008; Bo jas, 2003, 1999; Dus mann e al., 2017; Pischke and Velling,
1997; Busch e al., 2020; I ikha and Zaha ie a, 2019; Ba is i e al., 2018)
1
he SOEP da a, which shows ha egula wo ke s, making up he majo i y, emain in paid
jobs wi h an annual p obabili y o a leas 97% (see Appendix A.1 o de ails). Howe e ,
hose defined as po en ial en ep eneu s a e equen ly mo ing be ween paid jobs and
sel -employmen wi h annual p obabili ies in he ange o 15 −23%. This e idence shows
ha mos wo ke s do no conside sel -employmen as an al e na i e o hei job. Bu
also o hose who do, sel -employmen is no a “once and o all” decision and should be
modeled dynamically. Hence, po en ial en ep eneu s in ou model ha e se e al op ions:
hey can en e solo sel -employmen , egis e a small business wi h cowo ke s, o sea ch
and accep a egula paid job. En y in o hese s a es is endogenous and depends on he
labou ma ke condi ions. Regula wo ke s can be employed in egula jobs (la ge and
medium-size fi ms) o small businesses ope a ed by sel -employed en ep eneu s. La ge
and medium-size fi ms a e modeled in a classical SaM adi ion wi h ee en y.
Ou model has se e al no el ea u es. Fi s , we explici ly allow o he possibili y o
sel -employmen “ou o necessi y”, when sel -employed en ep eneu s con inue sea ching
o egula paid jobs, and sel -employmen “ou o oppo uni y”, when he income om
sel -employmen ac i i ies is high enough, and he e a e no gains om job sea ch. Sel -
employmen ou o necessi y is mo i a ed by he empi ical finding ha he unemploymen
a es o po en ial en ep eneu s a e lowe han hose o egula wo ke s. Also o he
s udies, o example, Poschke (2023) find e idence o sel -employmen ou o necessi y.
A he same ime, ou wage eg essions e eal ha he ea nings o business owne s a e
highe han he wages o compa able indi iduals employed in egula paid jobs, sugges ing
an impo an “oppo uni y” componen o en ep eneu ship. Second, he size dis ibu ion
o small businesses is endogenous. Thi d, we inco po a e he possibili y o c oss-skill
ma ching on a mic o-le el, whe eby small businesses ounded by high-skill en ep eneu s
hi e wo ke s om bo h skill g oups.
The model is calib a ed using he Ge man Socio-Economic Panel (SOEP), a com-
p ehensi e su ey o Ge man households. We combined his da a wi h in o ma ion on
acancies om he Fede al Employmen Office. The da a shows ha high-skill immig an
en ep eneu s a e mo e equen ly obse ed ope a ing small businesses a he han being
solo sel -employed, compa ed o all o he g oups o en ep eneu s. Mo eo e , immig an
businesses a e mo e p ofi able han he businesses o na i e wo ke s. Ano he ele an
empi ical ac is ha low-skill wo ke s a e o e ep esen ed in small businesses compa ed
o high-skill wo ke s, making hem mo e suscep ible o he en y o small businesses. Ou
modeling amewo k is well sui ed o cap u e hese empi ical ac s.
We use ou amewo k o s udy he implica ions o a 20% inc ease in he numbe
o low-skilled immig an s co esponding o he immig a ion wa e obse ed in Ge many
in 2012-2017.4In line wi h p e ious esea ch, we find ha ising low-skill immig a ion
4Du ing he Sy ian wa he numbe o immig an s o Ge many inc eased om 15 o 18 million. Also
he mos ecen immig an wa e in 2020-2024 (domina ed by he Russian-Uk ainian conflic ) is associa ed
wi h a simila inc ease om 20 o 23 million as epo ed by www.des a is.de
2

benefi s high-skill egula wo ke s wi h a co esponding gain in wel a e equal o 1%, bu
he e is a educ ion in he wel a e o low-skill egula wo ke s equal o −1.3%. The
esul s o po en ial en ep eneu s a e no el and e eal asymme ic effec s. Immig an
en ep eneu s (high and low-skilled) expe ience highe p ofi s and hei business en y is
ein o ced by immig a ion, gene a ing a wel a e gain o 3.1%. The e is a educ ion in
wel a e (−2%) o low-skilled na i e en ep eneu s due o he educed p ofi s and a ise in
he p obabili y o s aying in solo sel -employmen wi hou cowo ke s. Thus, and con a y
o he p e ious s udies (e.g., D’Amu i e al. (2010), O a iano and Pe i (2012)), we find
ha some g oups o incumben low-skill immig an s a e gaining om new immig a ion.
The unde lying eason o his finding is ha immig an businesses a e mo e p ofi able
on a e age, making hem mo e sensi i e o he imp o ed chances o hi ing cowo ke s in
esponse o he immig a ion inc ease. In con as , we find ha he expec ed p ofi s o
na i e en ep eneu s a e less sensi i e on he ec ui men ma gin and all due o he lowe
ma ginal p oduc i i y o hei low-skill cowo ke s.
In a nu shell, ou esul s show ha low-skill immig a ion educes he wel a e o an
a e age incumben indi idual by 0.4%, bu he e is p onounced he e ogenei y in his effec
ac oss demog aphic g oups. A skill-neu al immig a ion scena io eme ging in a p e iew
o he ecen Ge man-Indian coope a ion o p omo e skilled mig a ion om India o
Ge many will educe he losses o he incumben o 0.27%.
Add essing he second ques ion, we conduc a coun e ac ual expe imen by in o-
ducing legal ba ie s o sel -employmen and en ep eneu ship o immig an indi iduals.
This expe imen sheds ligh on he spillo e effec s o immig an en ep eneu ship o
egula wo ke s and na i e en ep eneu s. We find ha immig an en ep eneu ship has
mode a e posi i e spillo e s in he ange 0.2−0.4% o egula wo ke s. On he one
hand, immig an po en ial en ep eneu s en e ing sel -employmen ou o oppo uni y
educe compe i ion o egula jobs; on he o he hand, immig an en ep eneu s ope a -
ing small businesses c ea e addi ional wo kplaces. On he con a y, ou model indica es
subs an ial nega i e spillo e s o na i e po en ial en ep eneu s (1.1−1.6% o wel a e).
This is in ui i e since he business en y o immig an en ep eneu s c ea es addi ional
compe i ion in ec ui ing and educes he hi ing chances o na i e small businesses. Ou
findings sugges ha policies es ic ing immig an en ep eneu ship shield na i e small
businesses om compe i ion bu educe wel a e o all o he wo ke g oups.
Conside ing he las ques ion, we allow o e hnic seg ega ion in small businesses such
ha job ma ches be ween wo ke s and business owne s o he same e hnici y become
mo e likely compa ed o andom ma ching. E hnic seg ega ion benefi s low-skill na i e
en ep eneu s by inc easing he p ofi s associa ed wi h hi ing high-p oduc i i y na i e
wo ke s bu i is de imen al o he p ofi s o immig an low-skill businesses and wel a e o
egula wo ke s. Reduced business en y o low-skill immig an en ep eneu s sugges ha
hei en ep eneu ial po en ial could be unde u ilized in he p esence o e hnic seg ega ion.
The ou line o he pape is as ollows. Sec ion 2 posi ions ou s udy in he ela ed
3
li e a u e. Sec ion 3 desc ibes he heo y. Sec ion 4 p esen s he da a and he calib a ion
s a egy, while sec ion 5 discusses he esul s, and sec ion 6 concludes he pape .
2 Rela ed Li e a u e
Ou pape con ibu es o he li e a u e conce ning he impac o (low-skilled) mig a ion
on he labo ma ke ou comes and wel a e o na i es in de eloped coun ies. The seminal
pape by Bo jas (1999) and la e Ben-Gad (2004) show ha an influx o immig an s
in he US c ea es an immig a ion su plus, assuming homogeneous labou and impe ec
subs i u ion be ween labo and capi al. Subsequen pape s wi h he e ogeneous labou
suppo a ied conclusions ega ding wages o compe ing wo ke s and immig a ion su plus
(Bo jas, 2003; Ben-Gad, 2008). Li e a u e on wage effec s o immig a ion is inconclusi e,
as ly empi ical, and assumes pe ec ly compe i i e labo ma ke s (Al onji and Ca d,
1991; Bo jas e al., 1997; Ca d, 2001; Bo jas, 2006; D’Amu i e al., 2010). Goldin (1994),
Bo jas (2003), Aydemi and Bo jas (2007), and Aydemi and Bo jas (2011) find a nega i e
effec o immig a ion on na i e wages. Se e al pape s epo a negligible effec .5
Mo e ecen s udies p o ide e idence o he e ogeneous wage effec s. Fo example, he
wage effec s a e conside ably la ge o younge na i es (Dus mann e al., 2017) in Ge -
many, while in he UK, mig a ion nega i ely affec s he wages o low ea ne s bu inc eases
he wages o high ea ne s (Dus mann e al., 2013). Ou amewo k accommoda es he
he e ogenei y in immig a ion’s effec s by assuming diffe en skill g oups and occupa ion
choices be ween paid employmen and en ep eneu ship. D’Amu i e al. (2010), Felbe -
may e al. (2010), and O a iano and Pe i (2012) u he find ha mig a ion ad e sely
affec s he wages o he incumben immig an s when immig an s a e impe ec subs i-
u es o na i es in he same skill g oup. We ollow a pa simonious app oach in assuming
pe ec subs i u ion be ween immig an s and na i es in he same skill g oup. Howe e ,
assuming p oduc i i y diffe ences be ween e hnic g oups wi h he same skills allows us
o compu e he effec s o mig a ion o incumben immig an s and na i es.
The e a e mixed findings in he li e a u e discussing he employmen consequences
o immig a ion. Some pape s find a subs an ial ad e se effec o immig a ion on na i e
employmen (Bo jas, 2003, 2006; Dus mann e al., 2017). O he s find ei he a posi i e,
negligible, o no effec o mig a ion on na i e employmen in ecei ing coun ies.6Only
Dus mann e al. (2017) discuss he in e ac ion be ween wage and employmen effec s. Ou
heo e ical amewo k inco po a es in e ac ions be ween wage and job c ea ion, and he
quan i a i e analysis p o ides insigh s in o he dis ibu ional consequences o mig a ion
shock o he Ge man labo ma ke .
5Ca d (2001), Ca d (2005), F iedbe g (2001), D’Amu i e al. (2010), Felbe may e al. (2010), O a-
iano and Pe i (2012), Busch e al. (2020)
6(Al onji and Ca d, 1991; Hun , 1992; Pischke and Velling, 1997; D’Amu i e al., 2010; Scha billig
and Weissle , 2019; F iedbe g, 2001; Malchow-Mølle e al., 2009; Felbe may e al., 2010)
4
Se e al pape s employ SaM models o analyze he gene al equilib ium effec s o im-
mig a ion. O ega (2000) is one o he fi s pape s s udying he effec s o mig a ion in a
ic ional labo ma ke . Howe e , his pape is heo e ical and lacks a de ailed da a-based
quan i a i e analysis. Liu (2010) de elops a dynamic sea ch and ma ching model wi h
he e ogeneous labo bu ocuses solely on he consequences o illegal mig a ion o he
US economy. Chassamboulli and Pali os (2014) ex end Liu’s amewo k wi h a nes ed
CES p oduc ion unc ion, low and high-skilled labo , and capi al o s udy he impac o
immig a ion on he US economy. Ba is i e al. (2018) calib a e a SaM model ea u ing
wo skill ypes, wage ba gaining and a edis ibu i e wel a e s a e o 20 OECD coun ies.
I ikha and Zaha ie a (2019) ex end he amewo k o Ba is i e al. (2018) by consid-
e ing a wo-goods economy and endogenous p ice se ing. Thei amewo k iden ifies
addi ional effec s o immig a ion on Ge many h ough i s impac on domes ic demand.
Nanos and Schlu e (2014) and Mo eno-Galbis and T i ah (2016) also use he SaM model
o analyse consequences o mig a ion in selec ed Eu opean economies. Ou amewo k
bo ows se e al elemen s om hese amewo ks bu subs an ially de ia es and inno a es
by adding en ep eneu ship and c oss-skill ma ching in o he model.
Ou pape also add esses how small businesses espond o mig a ion shocks. Pape s
on his opic sugges posi i e con ibu ions o mig an s o en ep eneu ship in ecei ing
coun ies (Ke and Ke , 2020; Riillo and Pe oni, 2022). Duleep e al. (2021) find ha
immig an en ep eneu s acili a e inno a ion and en ep eneu ship among na i es.7None
o hese pape s conside en ep eneu ship’s spillo e s on he job ma ke o wo ke s in
paid jobs. En ep eneu s con ibu e o job c ea ion (Ke and Ke , 2020; Azoulay e al.,
2022) as well as job des uc ion (Geo ga akos and Ta si amos, 2009), esul ing in di ec
consequences o immig an en ep eneu ship o employmen oppo uni ies o wo ke s in
egula employmen . P o ided his e idence, we p opose a unified amewo k o he
en ep eneu ial pu sui s o na i es and immig an s and egula employmen ac i i ies.
Finally, ou pape builds on a adi ional SaM amewo k (Mo ensen and Pissa ides
(1994), Pissa ides (2000)) and augmen s i wi h en ep eneu ship. An ea ly sea ch model
wi h occupa ional choice be ween paid employmen and en ep eneu ship is by Fonseca
e al. (2001). Rissman (2007) and K edle e al. (2014) ex end his se up o a “business
idea ladde ”, whe e en ep eneu s gene a e business ideas and implemen hose o hem
ha a e mo e p ofi able. We con ibu e o his li e a u e by combining he app oach o a
“business idea ladde ” wi h endogenous business c ea ion in he spi i o Mas e s (2016).
7An in e es ing s and o li e a u e ocuses on compa ing cha ac e is ics o na i e and immig an
en ep eneu s in e ms o ea nings, human capi al, likelihood, and easons o s a a business (Li, 2001;
Lo s om, 2002; Cons an and Zimme mann, 2006).
5
3 The Model
3.1 The en i onmen
The labou ma ke is popula ed by ou demog aphic g oups: low-skill immig an s dIL,
low-skill na i es dNL, high-skill immig an s dIH and high-skill na i es dNH. All indi iduals
a e isk-neu al and discoun u u e income flows a he a e . Labou supply is inelas ic,
and he o al labou o ce is no malized o 1:
dIL +dNL +dIH +dNH =1
ideno es he o igin o he indi idual {I,N}and jindica es he skill le el {L, H}. Wi hin
each demog aphic g oup ij, he e a e wo subg oups: po en ial en ep eneu s wi h high
en ep eneu ial spi i lij and egula wo ke s wi h low en ep eneu ial spi i dij −lij.This
g oup dis inc ion is exogenous and based on inna e abili y, a i udes, and pe sonali y
ai s, which we do no model explici ly.8Being a po en ial en ep eneu does no imply
being an ac i e en ep eneu a a gi en poin in ime. Po en ial en ep eneu s can also
be obse ed in paid employmen o unemploymen . Howe e , hei en ep eneu ial spi i
may lead hem o swi ch om hese s a es o s a ing a solo sel -employmen o business
wi h cowo ke s. This g oup dis inc ion is mo i a ed by he SOEP da a, which shows
ha 85% o indi iduals in ou sample we e ne e obse ed in sel -employmen o e 18
yea s and emain in paid employmen wi h an annual p obabili y o a leas 97%. On
he con a y, he e a e 15% o indi iduals ac i ely mo ing be ween paid jobs and sel -
employmen wi h an a e age annual p obabili y equal o 15 −23% and a simila ly high
ansi ion p obabili y back o a paid job (see Appendix A.1 o de ails).
Regula wo ke s. The e a e wo employmen s a es o egula wo ke s. Fi s ,
egula wo ke s can be employed in a egula job ¯eij, p oducing ou pu ¯yij and ecei ing
a wage ¯wij. Regula jobs a e posi ions in medium and la ge-size fi ms. Second, po en ial
en ep eneu s can employ hem in a small business ¯eij
0. Hence, we ha e:
¯eij +¯eij
0+¯uij =dij −lij
Whe e ¯uij is a s a e o in olun a y unemploymen o egula wo ke s associa ed wi h a
flow income ¯zij −h.Va iable¯zij is he unemploymen benefi , whe eas h– is he disu ili y
om unemploymen (e.g., he s igma o ailu e). The exogenous shock o job des uc ion
a i es o all employees in egula jobs a a e ¯γij, ende ing hem unemployed.
Po en ial en ep eneu s. Po en ial en ep eneu s ha e a high en ep eneu ial spi i ,
so hey can be solo sel -employed sij o ope a ing small businesses wi h cowo ke s bij.The
decision o become sel -employed and s a a business is endogenous and d i en by ma -
8In ui i ely, indi iduals wi h high manage ial and o ganiza ional skills, low isk-a e sion, ex o e ed,
and communica i e a e mo e likely o be po en ial en ep eneu s.
6
whe e w(1− ) is he a e ax labou income and ¯γis he job des uc ion a e. This ela-
ionship shows ha employed po en ial en ep eneu s con inue gene a ing new business
ideas and may olun a ily qui he job and en e sel -employmen (ou o oppo uni y)
o s a a new business.
A α>α
s, sel -employed en ep eneu s s op sea ching and applying o egula paid
jobs. This is because he quali y o hei p oduc /se ice becomes sufficien ly high, which
is associa ed wi h a ela i ely high income σα(1 − ). So he cu -off alue o αsis gi en
by he ollowing indiffe ence condi ion: E(αs)=W. I hen holds ha Es(αs)=E(αs)
since he op ion o sea ching o a egula job has ze o alue o α=αs.
P oposi ion 2:The endogenous h eshold αssepa a ing solo sel -employed ou o ne-
cessi y and oppo uni y can be ob ained om he ollowing indiffe ence condi ion: Es(αs)=
E(αs)=W, which yields:
σαs=w−(¯γ−γ)
+¯γ+Xλ(θ)w−z−h
1− −δαs
αu
(1 −F(x))σ
+γ+Xλ(θ)+δ(1 −F(x))dx(9)
The cu off αsis inc easing in he wage w. I is con ex in wi γ>¯γand conca e
o he wise. The slope is gi en by:
∂αs
∂w =( +γ+Xλ(θ)+δ(1 −F(αs)))
σ( +¯γ+Xλ(θ)+δ(1 −F(αs))) (10)
P oo : appendix A.3
Equa ion (9) is an explici o m o a sho e exp ession σαs(1 − )=w(1 − )−
(¯γ−γ)(W−U). Fi s , sel -employed en ep eneu s compa e hei flow incomes σα(1 −
)andw(1 − ). Second, hey also conside he isk o d opping back o he s a e o
unemploymen , which is ¯γin a egula job and γin sel -employmen . In he special case
¯γ=γwe would ge αs=w/σ. Equa ion (10) implies ha a highe wage wmakes egula
jobs e en mo e aluable and gi es ise o a highe h eshold αs.
The h eshold alue αuis gi en by he indiffe ence condi ion Es(αu)=U.Es(α)isan
inc easing con ex unc ion o αwi h a slope E
s(α)=σ(1− )/( +γ+Xλ(θ)+δ(1−F(α)))
as shown on figu e 2. Compa ing he p esen alue om solo sel -employmen Es(αu)and
he p esen alue o unemploymen Ugi es he ollowing esul :
P oposi ion 3: The endogenous h eshold αud i ing he en y in o solo sel -employmen
can be ob ained om condi ion Es(αu)=U, which yields: σαu(1 − )=z−h.
P oo : appendix A.3
Po en ial en ep eneu s en e ing sel -employmen keep he op ion o sea ching o
egula jobs, and hey also keep he op ion o s a ing a small business, so he e a e
no cos s o s a ing sel -employmen apa om losing he flow income in unemploymen
z−h. The addi ional gain om sel -employmen is he flow income σα(1− ), which leads
o he finding αu=(z−h)/(σ(1 − )). E en hough pa ame e s z,h, a e exogenous, he
p oduc i i y in sel -employmen is a p oduc o he quan i y and he endogenous p ice
13

(σ=ςP), making he en y cu -off αuendogenous as well. Hence, i he ou pu p ice P
is inc easing, mo e po en ial en ep eneu s decide o en e sel -employmen .
3.4 S eady-s a e dis ibu ion
The i m size dis ibu ion. In his sec ion we discuss he s eady-s a e dis ibu ion
o he numbe o employees in small businesses. We s a by analyzing low-skill small
businesses. Le pI
k– be he numbe o small businesses wi h kimmig an cowo ke s and
and pN
m= be he numbe o businesses wi h mna i e cowo ke s. In p oposi ion 4 we
cha ac e ize hese dis ibu ions and show ha hey do no depend on α:
P oposi ion 4: The numbe s o immig an and na i e cowo ke s in low skill busi-
nesses a e gi en by geome ic densi ies wi h pa ame e s γ/(γ+¯q(θ0)(1 −μ)) and γ/(γ+
¯q(θ0)μ) espec i ely. The numbe o all employees in low-skill businesses has a geome ic
densi y wi h pa ame e γ/(γ+¯q(θ0)).P oo : Appendix A.4.
This p oposi ion allows us o in e he a e age numbe o immig an /na i e cowo ke s
pe low skill business which is gi en by ¯q(θ0)μ/γ and ¯q(θ0)(1 −μ)/γ espec i ely. So he
a e age size o a small business is ¯q(θ0)/γ. The size dis ibu ion o small businesses (pn)
is also gi en by he geome ic densi y wi h pa ame e γ/(γ+¯q(θ0)):
pn=¯q(θ0)
γ+¯q(θ0)nγ
γ+¯q(θ0)
This densi y is dec easing in he whole suppo , implying ha a as majo i y o busi-
nesses a e small and only e y ew o hem su i e o a long pe iod o ime and become
la ge. We find ha his dec easing pa e n is consis en wi h he empi ical e idence ob-
se ed in Ge many. Fo example, acco ding o Leich and Langhause (2014) he sha e
o na i e-owned businesses wi h less han 5 employees is 59%, he sha e o businesses
wi h 6-10 employees is 21%, wi h 11 −19 employees – 10%, wi h 20 −49 employees –
6% and mo e han 50 employees – 3%. A simila dec easing pa e n is also epo ed o
immig an businesses and i is well cap u ed by he geome ic dis ibu ion unc ion.
Conside ing high-skill businesses, he a e age numbe o ype ij employees, i=I,N,
j=L, H, is gi en by ¯q(θ0)μij/γ. Mo eo e , he uncondi ional dis ibu ion o employees
ij in hese businesses also has a geome ic densi y wi h pa ame e γ/(γ+¯q(θ0)μij).
The dis ibu ion o en ep eneu s. Va iables suand sea e he numbe s o neces-
si y and oppo uni y en ep eneu s, espec i ely, so ha s=su+seis a o al numbe o
solo-en ep eneu s. Gi en ha he o al numbe o po en ial en ep eneu s (in he g oup
ij, which we omi o he ease o exposi ion) is deno ed by l,wege :su+se+e+u+b=l.
Po en ial en ep eneu s, who a e no business owne s l−b, egis e s a -up fi ms a a e
δ (α)i α>α
0. A he same ime, businesses a e des oyed a a e γ, which gi es ise o
he ollowing dynamics: ˙
b(α)=δ (α)(l−b)−γb(α). Imposing he s eady s a e condi ion
14
˙
b(α) = 0 and in eg a ing b(α) we can find he o al numbe o small businesses b:
b=¯α
α0
b(α)dα =δ(1 −F(α0))(l−b)
γ⇒b=δ(1 −F(α0))l
γ+δ(1 −F(α0))
This condi ion pos ula es a nega i e mono onous ela ionship be ween he en y h eshold
α0and he s ock o small businesses b. In ui i ely, a highe cu -off α0leads oalowe
p obabili y o s a ing a business 1 −F(α0), so he s ock o small businesses bdeclines.
Le G(α) be he equilib ium dis ibu ion o solo sel -employed ou o oppo uni y wi h
espec o he quali y o hei p oduc α. Mo e p ecisely i is he accumula ed s ock o
sel -employed en ep eneu s wi h a p oduc quali y in he ange [αs..α]. The dynamic
equa ion o G(α) is gi en by:
˙
G(α)=(su+e+u)
 
=l−b−se
δ(F(α)−F(αs)) −(γ+δ(1 −F(α)))G(α) (11)
Unemployed en ep eneu s u, and hose sel -employed ou o necessi y su, s op sea ching
o egula jobs, i hey de elop a p oduc /se ice wi h quali y abo e αs. Also employees
in egula employmen equi hei jobs and become sel -employed ou o oppo uni y
i hey ge a ealiza ion o αabo e αs. So he fi s e m in equa ion (11) is he inflow
o en ep eneu s in o solo sel -employmen ou o oppo uni y. The second e m is he
ou flow consis ing o unsuccess ul en ep eneu s d opping back in o unemploymen (a
a e γ) and hose who de elop a be e p oduc (a a e δ(1 −F(α))). Imposing he
s eady s a e condi ion ˙
G(α) = 0 and aking in o accoun ha se=G(α0)wege :
se=G(α0)= δ(F(α0)−F(αs))
[γ+δ(1 −F(α0))]
γl
[γ+δ(1 −F(αs))] (12)
Nex , conside he s eady-s a e equa ion o employed po en ial en ep eneu s:
˙e=(u+su)Xλ(θ)−(¯γ+δ(1 −F(αs)))e=0
whe e he fi s e m is he inflow which co esponds o all sea ching po en ial en ep eneu s
(u+su) s a ing a egula job a a e Xλ(θ). Again, he second e m is he ou flow con-
sis ing o hose losing egula jobs a a e ¯γo qui ing hei jobs olun a ily and becoming
solo sel -employed ou o oppo uni y. Taking in o accoun ha u+su=l−b−se−e
we ge he equilib ium exp ession o e:
e=Xλ(θ)
[¯γ+Xλ(θ)+δ(1 −F(αs))]
γl
[(γ+δ(1 −F(αs))] (13)
Fu he , le H(α) be he equilib ium dis ibu ion o solo sel -employed ou o necessi y
wi h espec o he quali y o hei p oduc o se ice α. I is he accumula ed s ock o
15
sel -employed wi h p oduc quali ies in he ange [αu..α]. So we ge :
˙
H(α)=uδ(F(α)−F(αu)) −(γ+δ(1 −F(α)) + Xλ(θ))H(α)
The fi s e m is he inflow and includes unemployed indi iduals de eloping p oduc
quali ies abo e αuand s a ing sel -employmen . The second e m is he ou flow con-
sis ing o sel -employed en ep eneu s aking a egula job (a a e Xλ(θ)), d opping
back in o unemploymen (a a e γ) and de eloping a be e p oduc quali y (a a e
δ(1 −F(α))). Imposing again he s eady s a e condi ion ˙
H(α) = 0 and aking in o ac-
coun ha su=H(αs) we can find he equilib ium s ock o po en ial en ep eneu s ou
o necessi y suandinunemploymen u. We summa ize hese esul s in p oposi ion 5:
P oposi ion 5: The equilib ium numbe o solo sel -employed ou o necessi y suand
he numbe o unemployed po en ial en ep eneu s ua e gi en by:
su=δ(F(αs)−F(αu))
[γ+Xλ(θ)+δ(1 −F(αu))]
(¯γ+δ(1 −F(αs)))
[¯γ+Xλ(θ)+δ(1 −F(αs))]
γl
[γ+δ(1 −F(αs))]
u=γ+Xλ(θ)+δ(1 −F(αs))
[γ+Xλ(θ)+δ(1 −F(αu))]
(¯γ+δ(1 −F(αs)))
[¯γ+Xλ(θ)+δ(1 −F(αs))]
γl
[γ+δ(1 −F(αs))]
P oposi ion 5 shows ha , o he hings being equal, he s ock suis dec easing in he
cu -off αu. On he con a y, a highe αuis associa ed wi h a highe s ock o unemployed
en ep eneu s u.
The dis ibu ions o solo sel -employed wi h espec o he quali y o hei p oduc s
αcan be ound due o he ac ha su(α)=H(α)andse(α)=G(α). The exac
exp essions a e delega ed o appendix A.4.
3.5 Wage se ing
In his sec ion we add ess he de e mina ion o wages. Regula fi ms can be ma ched
wi h egula wo ke s o po en ial en ep eneu s seeking o ake a paid job, howe e , small
businesses only hi e egula wo ke s. This gi es ise o se e al ypes o wage nego ia ions
which we model by means o Nash ba gaining. Fi s , we desc ibe he wage ba gaining
be ween egula fi ms and po en ial en ep eneu s.
Ba gaining wi h po en ial en ep eneu s: Conside a ma ch be ween a egula
fi m and a po en ial en ep eneu and le he co esponding p esen alue o a job be
deno ed by J, i becomes:
J =y−¯ck−w−¯γ(J−V)−δ(1 −F(αs(w)))(J−V)
whe e ¯ckco esponds o he flow cos o capi al o egula fi ms. This equa ion shows
ha he o al job des uc ion a e associa ed wi h po en ial en ep eneu s is ela i ely
high since he e is a posi i e p obabili y δ(1 −F(αs(w))) ha hey will qui he job and
16
en e sel -employmen . This educes he alue o he job su plus o he fi m.
In o de o model wage ba gaining be ween job applican s and egula fi ms we ollow
he app oach in Gau ie (2002). This app oach assumes ha applican s ma ched wi h an
employe and nego ia ing o e he wage s op sea ching o al e na i e jobs. In addi ion,
we assume ha hey also dis ega d hei ac i i ies in sel -employmen ou o necessi y,
since paid employmen is a supe io s a e o income (i.e Es(α)<W ∀α<α
s). How-
e e , hey con inue conside ing sel -employmen ou o oppo uni y and he possibili y o
s a ing a business (which happens o α>α
s) while nego ia ing wi h a egula employe .
The ad an age o his app oach is ha labou con ac s a e enego ia ion p oo , meaning
ha po en ial en ep eneu s ecei e he same wage win paid employmen i espec i e
o hei p e ious income in sel -employmen . Assuming addi ionally ha po en ial en-
ep eneu s s ill enjoy he unemploymen benefi zwhile ba gaining, bu no longe he
s igma o ailu e h, gi es ise o he ollowing Nash ba gaining p oblem:9
max
ww(1 − )−z
+¯γβ(y−¯ck−w)
+¯γ+δ(1 −F(αs(w)))1−β
This equa ion shows ha highe wages ha e an ambiguous effec on he p esen alue o
fi ms’ p ofi s. On he one hand, he e is he di ec effec o highe labou cos s educing
p ofi s. Bu on he o he hand, paying a highe wage educes he p obabili y ha he
po en ial en ep eneu employed in a egula job will qui in o sel -employmen (i.e. highe
αs(w)). This educes he o e all job des uc ion a e om he pe spec i e o he fi m and
has a posi i e effec on he p esen alue o p ofi s.
P oposi ion 6: The wage o po en ial en ep eneu s in paid employmen is gi en by:
w(1 − )=β(y−¯ck)(1 − )+(1−β)z+(1−β)(y−¯ck−w)(w(1 − )−z)δ (αs)
+¯γ+δ(1 −F(αs))
∂αs
∂w
whe e ∂αs/∂w is gi en by equa ion (10). I he dis ibu ion o p oduc quali ies is uni o m
( (α)=1)andγ≤¯γ hen he wage is inc easing in he p oduc i i y yand in he
ba gaining powe βsuch ha z≤w(1 − )≤(y−¯ck)(1 − ).
P oo : appendix A.5
This p oposi ion p esen s condi ions which a e sufficien o he wage w o be inc eas-
ing in he p oduc i i y yand he ba gaining powe β, howe e , hese condi ions a e s ong
and he desc ibed p ope ies o he wage hold o a b oade ange o pa ame e alues.
We ollow he same app oach and use he enego ia ion-p oo Nash ba gaining o
de e mining wages o egula wo ke s in la ge and medium-size fi ms ( ¯w) and in small
businesses (w0N,w0I,wCN,wCI). The subindex e e es o he ype o small business,
o example, 0Nindica es wages paid by na i e small businesses o hei employees,
while he subindex 0Iindica es wages paid by immig an small businesses. Fu he , he
9The p esen alue o po en ial en ep eneu s in paid jobs Wand hei disag eemen alue WDa e
p esen ed in appendix A.5
17
subindex CN indica es wages paid by na i e high-skill businesses o low-skill employees,
while he subindex CI indica es wages paid by immig an high-skill businesses o hei
low-skill wo ke s (engaged in c oss-skill ma ching). In appendix A.5 we show ha each
wage is a weigh ed a e age o he espec i e p oduc i i y (¯y,y0N,y0I,yCN,yCI)and he
unemploymen benefi ¯z. We use pa ame e β0 o he ba gaining powe o wo ke s in
small businesses. All wages and p oduc i i ies a e specific o a pa icula demog aphic
g oup o he indi idual ij, whe e he supe sc ip ij was omi ed o he ease o exposi ion.
3.6 Ma ching and ee-en y
In his sec ion we desc ibe ma ching be ween sea ching wo ke s and acancies in he
ma ke o egula jobs, as well as ma ching be ween sea ching wo ke s and openings in
small businesses. Figu e 3 illus a es all he s a es and ansi ions o egula wo ke s.
Figu e 3: Labou ma ke s a es and ansi ions o egula wo ke s
ҧ݁௜ு
ҧ݁௜௅
തݑ௜ு
തݑ௜௅
݁ைே
௜௅
݁ைூ
௜ு
݁஼ூ
௜
݁஼ே
௜݁ைே
௜ு
݁ைூ
௜௅
ܾூ௅
ݒ௅ݒு
ܾேு
ܾூு
ܾே௅
Low-skill acancies
in egula i ms
High-skill acancies
in egula i ms
Low-skill small
businesses
High-skill small
businesses
Low-skill wo ke s High-skill wo ke s
ܺ௜௅ߣ(ߠ௅)
ҧߛ௜௅ ܺ௜ுߣ(ߠு)
ҧߛ௜ு
ߛே௅ ߛேு ߛேு
ߛூு
ߛூு
ߛூ௅
ݔ௜௅ ҧ
ߣ(ߠை
௅)Ɉݔ௜௅ ҧ
ߣ(ߠை
ு)ݔ௜ு ҧ
ߣ(ߠை
ு)
The middle pa o he diag am ( ed) co esponds o he c oss-skill ma ching whe eby
low-skill egula wo ke s apply o posi ions in high-skill small businesses. We use pa am-
e e κ o desc ibe he in ensi y o c oss-skill ma ching.10 This pa ame e allows us o de-
e mine he numbe o egula wo ke s sea ching and applying o posi ions in small busi-
nesses gi en by Σj
0.Σ
L
0consis s o unemployed egula low-skill wo ke s ¯uiL weigh ed by
hei sea ch in ensi ies xiL,whe easΣ
H
0consis s o unemployed egula high-skill wo ke s
¯uiH weigh ed by hei sea ch in ensi ies xiH as well as egula low-skill wo ke s weigh ed
by hei sea ch in ensi ies κxiL. Wi h his no a ion we ge :
Σj
0=xIj¯uIj +xNj¯uNj +1Hκ(xIL¯uIL +xNL¯uNL)
whe e 1H akes alue 1 o j=Hand alue 0 o j=L.
10A doc o hi ing a ecep ionis o a ax-consul an hi ing a sec e a y a e he eal li e examples o he
ype o c oss-skill ma ching ou model cap u es.
18

Nex , conside low-skill small businesses. F om p oposi ion 4 we know ha he a e age
numbe o immig an employees pe small business is gi en by ¯q(θL
0)μ/γiL,whe ei eflec s
he e hnic g oup o he business owne . A he same ime, he a e age numbe o na i e
employees is ¯q(θL
0)(1−μ)/γiL. Gi en ha he numbe o small businesses in his g oup is
equal o biL, we can find he numbe o immig an and na i e wo ke s employed in hese
businesses eIL
0iand eNL
0i:
¯q(θL
0)
γiL biL =eIL
0i
μ=eNL
0i
1−μwhe e μ=xIL¯uIL
xNL¯uNL +xIL¯uIL (14)
He e he supe sc ip i=N,I e e s o he e hnic backg ound o he wo ke , while he
subsc ip e e s o he e hnic backg ound o he en ep eneu and 0 s ands o small
businesses. Nex conside high-skill businesses. He e he a e age numbe o immig an
high-skill employees is gi en by ¯q(θH
0)μIH/(γiH ), while he a e age numbe o na i e
high-skill wo ke s is ¯q(θH
0)μNH/(γiH ). In a simila way, we can use in o ma ion abou he
a e age numbe o immig an and na i e low-skill employees. Mul iplying he a e age
numbe o employees pe business wi h he numbe o businesses biH yields he ollowing:
¯q(θH
0)
γiH biH =eIH
0i
μIH =eNH
0i
μNH =eI
Ci
μIL =eN
Ci
μNL (15)
whe e he p obabili ies o hi ing an employee o ype iH and iL om he pe spec i e o
he business owne a e gi en by:
μiH =xiH ¯uiH
i=I,N xiH ¯uiH +κxiL ¯uiL and μiL =κxiL ¯uiL
i=I,N xiH ¯uiH +κxiL ¯uiL
These p obabili ies do no depend on he e hnic backg ound o he business owne .
Fu he , we w i e down he s eady s a e equa ion o employees in egula jobs:
Xijλ(θj)¯uij =¯γij ¯eij and ake in o accoun ha he o al numbe o wo ke s employed in
small businesses is gi en by: ¯eij
0=eij
0N+eij
0I+1L(ei
CN +ei
CI), whe e he indica o unc ion
1L akes alue one o j=Land ze o o he wise. This allows us o find he equilib ium
unemploymen a e o egula wo ke s gi en by: ¯uij =dij −lij −¯eij −¯eij
0.Theexac
exp ession is p esen ed in appendix A.6.
Finally, we conside he acancy pos ing condi ions o egula jobs. Recall ha
¯c=¯ch+¯ckis he o al cos o capi al and pos ing acing egula fi ms. Using his
no a ion we w i e down he p esen alue equa ion o V, which is he p esen alue o
expec ed p ofi s associa ed wi h an open acancy, and impose he ee-en y condi ion
V= 0 o ge :
¯c
q(θ)=
i=I,N
Xi¯ui
i=I,N Xi(¯ui+ui+si
u)
 
ma ching wi h egula wo ke s
(¯
Ji−V)+ Xi(ui+si
u)
i=I,N Xi(¯ui+ui+si
u)
 
ma ching wi h po . en ep eneu s
(Ji−V) (16)
19
Thus, egula fi ms c ea e acancies up o he poin , whe e he expec ed cos o an open
acancy is equal o he expec ed p esen alue o p ofi s om a filled job. W i ing down
hese equa ions o j=L, H allows us o find he equilib ium acancies Land H.
3.7 P oduc ion o he inal good and wel a e
The final good is p oduced using capi al Kand a composi e good Zusing he cons an
e u ns o scale echnology (1). The composi e good Zis p oduced using wo in e media e
inpu s, YLand YHacco ding o he CES p oduc ion unc ion (2), whe e Yjis a linea
agg ega e o ou pu quan i ies p oduced by egula wo ke s and po en ial en ep eneu s
o ype j, so i can be calcula ed as:
Yj=
i=I,Nςij αij
s
αij
u
αsij
u(α)dα +ςij αij
0
αij
s
αsij
e(α)dα +ςij ¯α
αij
0
αbij(α)dα
+ϕijeij +¯ϕij ¯eij +ϕij
0Neij
0N+ϕij
0Ieij
0I+1L(ϕi
CNei
CN +ϕi
CIei
CI)
whe e he fi s h ee e ms include ou pu quan i ies o sel -employed en ep eneu s and
business owne s, ϕij eij is he ou pu p oduced by po en ial en ep eneu s employed in
egula jobs, ¯ϕij ¯eij – ou pu p oduced by wo ke s in egula jobs, and he emaining
e ms cons i u e he ou pu p oduced by wo ke s employed in small businesses. Finally,
heindica o a iable akes alue1 o j=Land alue ze o o j=H.
Since capi al as well as he wo in e media e goods a e supplied in compe i i e ma -
ke s, hei p ices Rand Pja e equal o he ma ginal p oduc i i ies:
R=AηKη−1[aY ρ
L+(1−a)Yρ
H]
1−η
ρ(17)
PL=a(1 −η)AKηYρ−1
L[aY ρ
L+(1−a)Yρ
H]
1−η−ρ
ρ(18)
PH=(1−a)(1 −η)AKηYρ−1
H[aY ρ
L+(1−a)Yρ
H]
1−η−ρ
ρ(19)
whe e Ris he exogenous p ice o capi al including he isk- ee in e es a e and he
cos o capi al dep ecia ion. Finally, le ¯
Ωij, deno e social wel a e o egula wo ke s and
Ωij deno e he wel a e o po en ial en ep eneu s in he demog aphic g oup ij,whe e
i=I,N,j=L, H. Since po en ial en ep eneu s a e cha ac e ized by a ious quali ies
o he p oduc α, we calcula e an a e age p oduc quali y in each g oup:
¯αus =αs
αu
αsu(α)
su
dα ¯αs0=α0
αs
αse(α)
se
dα ¯α01 =¯α
α0
αb(α)
bdα
Va iable ¯αus s ands o he a e age p oduc quali y o solo sel -employed ou o necessi y
dis ibu ed in he ange [αu...αs]. Va iable ¯αs0deno es he a e age p oduc quali y o
solo sel -employed ou o oppo uni y dis ibu ed in he ange [αs...α0] and, finally, ¯α01
co esponds o he a e age p oduc quali y o business owne s dis ibu ed in he ange
20
[α0...¯α]. Based on hese defini ions, he wel a e alues o all wo ke g oups can be
ob ained as (we supp ess he uppe index ij o he ease o exposi ion):
¯
Ω= 1
d−l(¯u(¯z−h)+(1− )(¯e¯w+e0Nw0N+e0Iw0I+1L(eCNwCN +eCIwCI))) + T
Ω=1
lu(z−h)+(1− )(ew +suσ¯αus +seσ¯αs0+bσ¯α01)+b−c+¯q(θ0)
γπ( +γ)
 
ne p o i om cowo ke s +T
whe e he indica o unc ion 1L akes alue one o j=Land ze o o he wise and a iable
Tis he lump-sum ans e om he public budge . The cash inflow in o he public
budge consis s o e enues om labou income axes o egula wo ke s and po en ial
en ep eneu s BR and co po a e axes paid on flow p ofi s by small businesses and egula
jobs BRτ. The ou flow om he public budge consis s o expenses o unemploymen
benefi s o all demog aphic g oups BE. Gi en ha o al e enues exceed subs an ially
he expenses o unemploymen benefi s, he su plus o he budge is equally spli and
dis ibu ed as a lump-sum ans e Tac oss all wo ke g oups. The e enues and expenses
a e calcula ed as ollows:
BR = 
ij ¯e¯w+e0Nw0N+e0Iw0I+1L(eCNwCN +eCIwCI)
 
income axes o egula wo ke s
+ew +suσ¯αus +seσ¯αs0+bσ¯α01
 
income axes o po en ial en ep eneu s 
BRτ=τ
ij b¯q(θ0)
γ
π( +γ)
1−τ
 
small businesses
+(¯y−¯ck−¯w)¯e+(y−¯ck−w)e
 
egula jobs 
BE =
ij
zu +¯z¯uT=1
ij dBR +BRτ−BE(20)
whe e ij dis he o al size o he popula ion. I is no malized o 1 in he benchma k
calib a ion, bu will be la ge han 1 upon he immig a ion shock.
4Da a
We use da a om he Ge man Socio-Economic Panel (SOEP) wa es 2000-2017. SOEP is a
ep esen a i e panel o households and indi iduals in Ge many. I p o ides de ailed in o -
ma ion abou he esponden ’s e hnici y, qualifica ions, wages, size o employe fi m, em-
ploymen s a us, and he possibili y o sel -employmen and en ep eneu ship. Mo eo e ,
i con ains in o ma ion abou sel -employed en ep eneu s’ business size (i.e., he numbe
o cowo ke s). We es ic he sample o labou o ce pa icipan s wo king ull/pa - ime
o ac i ely sea ching o jobs (wo ke s who epo being egis e ed as unemployed a he
ede al employmen agency). Non-pa icipan s, e i ed, ma ginally employed o mili a y
21
pe sonnel and hose below 17 yea s o age a e d opped om he sample. This yields an
unbalanced panel wi h 302686 pe son-yea obse a ions o e he spell o 18 yea s.
We define as na i e (N) an indi idual who is bo n in Ge many o has Ge man na ion-
ali y since bi h and is no an e hnic Ge man om Eas e n Eu ope. All second-gene a ion
immig an s bo n in Ge many a e conside ed na i es. Wo ke s wi h a leas 13 yea s o
schooling a e defined as high-skilled (H) while o he s a e conside ed low-skilled (L).
13 yea s o schooling co espond o he uppe seconda y schooling deg ee (”Abi u ”) and
g an di ec access o e ia y educa ion in Ge many. High-skilled immig an s o m he
smalles ac ion o he sample. The a e age sha e o high and low-skilled na i es in
he sample is 32.6% and 51.0%, espec i ely. In compa ison, he high and low-skilled
immig an s o m 13.7% and 2.7% o he sample. Table 1 p o ides he sample p ofile.
We define as po en ial en ep eneu s he indi iduals who a e obse ed a leas once
in he da a as sel -employed, eelance p o essionals, o as small business owne s (wi h o
wi hou cowo ke s). Thei s ock is deno ed by lij in he model. Indi iduals who a e ne e
obse ed as business owne s o in sel -employmen a e conside ed egula wo ke s (low
en ep eneu ial spi i ). Thei s ock is deno ed by dij −lij . We may unde es ima e he
sha e o po en ial en ep eneu s as some indi iduals may ha e been in en ep eneu ship
be o e pa icipa ing in he su ey, while o he po en ial en ep eneu s may ha e d opped
ou o he sample be o e being obse ed in an en ep eneu ial s a e. The a i ion a es
could be pa icula ly high o immig an s due o e u n mig a ion. Howe e , i is a
easonable measu e gi en ha he e is no o he way o deduce en ep eneu ial abili ies
due o he lack o de ailed in o ma ion abou he in e es in en ep eneu ship o effo s
(bo h success ul and unsuccess ul) o open up a business.
Table 1 shows he dis ibu ion o all wo ke s in he sample ac oss he ou demog aphic
g oups and labou ma ke s a es. High-skill na i e wo ke s a e leas likely o be employed
in small businesses (15.3%). This sha e is sligh ly highe o high-skill immig an wo ke s
(18.3%), whe eas i is much highe o low-skill wo ke s (22.5−23.5%). I is in e es ing
ha po en ial en ep eneu s ha e much lowe unemploymen a es han wo ke s wi hou
en ep eneu ial abili ies. Low-skilled immig an wo ke s ha e he highes unemploymen
a es. Bo h na i es and immig an s in he high-skill g oup ha e he highes sha es o
ac i e en ep eneu s (bij +sij)/lij.
Fu he , SOEP p o ides in o ma ion on solo sel -employed en ep eneu s sij +bij
0and
business owne s wi h cowo ke s bij −bij
0. The las g oup is spli in o business owne s wi h
less han nine cowo ke s 9
n=1 bnand hose wi h mo e han nine cowo ke s. 59 −60%
o na i e and immig an po en ial business people wi h low skills a e solo en ep eneu s,
and 36 −37% o hem manage small businesses wi h 1 o 9 cowo ke s. This diffe s in he
high-skill g oup, whe e only 46% o immig an en ep eneu s a e sel -employed, and 43%
a e managing small businesses.
22
This de elopmen comes along wi h a lowe wel a e o low-skill indi iduals ΩiL and
¯
ΩiL and an inc ease in wel a e o high-skill indi iduals ΩiH and ¯
ΩiH,i=I,N (Table 3,
ow-A). Mo eo e , i os e s he ealloca ion o na i e po en ial en ep eneu s wi h low
skills om egula paid jobs o solo sel -employmen . Table 4 column (2) shows ha
he ac ion o na i e po en ial en ep eneu s employed in egula jobs alls by 5.7%, and
hei wages also all subs an ially in column (3). A he same ime, hei ac ion in solo
sel -employmen (column (4)) is inc easing by 8.9%. The losses in he wel a e o low-
skill en ep eneu s (Table 3, ow-A) a e smalle compa ed o egula wo ke s because he
p obabili y o hi ing employees ¯q(θL) is inc easing (no e a lowe θL
0), which mode a es he
nega i e effec o lowe p oduc i i y on business p ofi s. Fo he same eason, high-skill
en ep eneu s’ wel a e gains a e highe han high-skill egula wo ke s.
In s ep (B), capi al Kadjus s endogenously. Fi ms in he final goods sec o inc ease
capi al K, which has a posi i e effec on he p oduc i i y and wel a e o all wo ke g oups
ia changes in p ices and ma ke igh ness. Due o capi al adjus men , he wel a e losses
in s ep (A) a e sligh ly compensa ed o low-skill wo ke s.
In s ep (C), we upda e he lump-sum budge ans e Tand wel a e alues. This
ans e is measu ed pe pe son and is lowe in he pos -immig a ion equilib ium. The e
a e wo easons o his educ ion. Fi s , a composi ion effec is eme ging because he
ne fiscal con ibu ion o an a e age low-skill immig an is lowe han ha o an a e age
na i e. Second, he e is an endogenous adjus men o equilib ium a iables desc ibed in
able 2 educing wages o low-skill wo ke s and hei ne fiscal con ibu ion below he
p e-immig a ion le el. A combina ion o hese effec s leads o a lowe lump-sum ans e
pe pe son 0.486 <0.493 in he pos -immig a ion equilib ium, educing he wel a e o all
wo ke g oups (Table 3, ow-C).
In he final s ep (D), we allow endogenous adjus men o he en ep eneu ial business
en y cu offs αij
0. This is he no el pa o ou model, so we zoom in on he job c ea ion
p ocess and po en ial en ep eneu s’ business en y decisions in able 4 s a ing wi h he
low-skill subma ke . On he one hand, hi ing wo ke s o open posi ions becomes easie
(d¯q>0). Howe e , on he o he hand, a d op in he p ice o he low-skill in e media e
good makes wo ke s in low-skill businesses less p oduc i e and leads o a lowe p ofi pe
pe son (dπi<0, i=I,N). Table 4 shows ha he fi s effec is domina ing o businesses
ope a ed by immig an en ep eneu s. Thei p ofi s in column (8) inc ease, making such
businesses mo e a ac i e o hei owne s:
d¯qπI=πId¯q+¯qdπI>0
As a esponse, we obse e a 13% inc ease in he ac ion o immig an po en ial en-
ep eneu s ope a ing small businesses in column (6), inducing a ealloca ion o immi-
g an po en ial en ep eneu s away om egula jobs and solo sel -employmen owa ds
ope a ing small businesses. These effec s a e associa ed wi h a sizable inc ease in he
29

Table 3: Inc ease in immig a ion by 20%, low-skill scena io
Low-skilled High-skilled
Regula wo ke s Po . en ep eneu s Regula wo ke s Po . en ep eneu s
NINI NINI
¯
ΩNL ¯
ΩIL ΩNL ΩIL ¯
ΩNH ¯
ΩIH ΩNH ΩIH
(0) 1.552 1.405 1.523 1.497 1.988 1.641 1.970 1.810
Keeping K,Tand αij
0
(A) -2.05% -2.21% -1.09% -0.92% +0.28% +0.29% +0.34% +0.76%
Keeping Tand αij
0fixed
(B) -0.94% -1.03% -0.54% -0.36% +1.26% +1.39% +0.77% +0.83%
Keeping αij
0fixed
(C) -1.36% -1.50% -0.97% -0.80% +0.78% +0.93% +0.44% +0.47%
Full adjus men
(D) -1.27% -1.37% -2.04% +3.15% +1.00% +1.08% +0.34% +3.10%
Rep esen a i e wo ke : -1.59% Rep esen a i e wo ke : +0.9%
Incumben wo ke : -1.27%
Rep esen a i e wo ke : -0.88%
Incumben immig an : -0.47%
Incumben wo ke : -0.37%
No e: The able decomposes he impac o low-skill mig a ion on wel a e o diffe en demo-
g aphic g oups in se e al s eps. Row (D) shows he change in wel a e a e a ull adjus men o
endogenous a iables in he pos -mig a ion equilib ium. The second las panel epo s wel a e
changes o a ep esen a i e/incumben wo ke in a gi en skill g oup. The las panel epo s
wel a e changes o a ep esen a i e/incumben wo ke in he economy.
wel a e o immig an po en ial en ep eneu s ΩIL in able 3.
Conside ing he si ua ion o na i e businesses, we find ha he d op in p oduc i i y
is domina ing and leads o a sligh dec ease in p ofi s in column (8):
d¯qπN=πNd¯q+¯qdπN<0
Thus, ope a ing small businesses becomes less a ac i e o na i e en ep eneu s. Thei
ac ion in column (6) is alling by 3.2% inducing a ealloca ion away om egula em-
ploymen and businesses owa ds solo sel -employmen . These effec s a e associa ed wi h
a dec ease in he wel a e o na i e po en ial en ep eneu s ΩNL. The asymme ic esponse
o small businesses owa ds he immig a ion shock can be explained by he ac ha im-
mig an businesses a e mo e p ofi able on a e age, meaning ha he expec ed p ofi s pe
ec ui men a e also highe (πI>π
N, inline wi h he empi ical da a in able 11 in he
appendix). This makes immig an businesses mo e sensi i e o he job-filling a e since
πId¯q>π
Nd¯q. The p ofi s o na i e en ep eneu s a e lowe , making hem less esponsi e
o changes in he p obabili y o filling posi ions.
Nex , we conside he high-skill subma ke . High-skill wo ke s become mo e p oduc-
i e, eflec ed in he highe p ice o he high-skill in e media e good PH.Thisboos sjob
c ea ion in he high-skill subma ke , leading o a highe ma ke igh ness θHand a highe
30
Table 4: De ailed changes in he s eady-s a e dis ibu ion o po en ial en ep eneu s
upon a 20% inc ease in low-skill immig a ion
(1) (2) (3) (4) (5) (6) (7) (8)
G oup u/l e/l w (su+se)/l σ¯αu0b/l σ¯α01 ¯q(θ0)π/γ
Low-skill
Na i es 0.035 0.418 1.222 0.259 1.145 0.288 1.291 1.971
Change +0.001 -0.057 -0.019 +0.089 +0.019 -0.032 -0.004 -0.001
Low-skill
Immig . 0.049 0.426 1.245 0.251 1.100 0.274 1.314 2.077
Change +0.001 -0.054 -0.019 -0.077 -0.102 +0.130 -0.019 +0.01
High-Skill
Na i es 0.014 0.418 1.884 0.290 1.883 0.277 1.953 3.763
Change -0.001 +0.072 +0.030 -0.070 +0.010 -0.001 +0.014 -0.000
High-Skill
Immig . 0.039 0.384 1.309 0.206 1.199 0.370 1.374 5.270
Change -0.001 +0.056 +0.026 -0.093 -0.092 +0.037 +0.006 +0.004
No e: ¯αu0is he a e age en ep eneu ial abili y in he ange [αu..α0], calcula ed as (su¯αus +
se¯αs0)/(su+se). ¯α01 is he a e age en ep eneu ial abili y in he ange [α0..¯α].
job-finding a e. Thus, he e is a sizable inc ease in he ac ion o high-skill po en ial
en ep eneu s employed in egula paid jobs in column (2): 7.2% o na i es and 5.6% o
immig an po en ial en ep eneu s. This p ocess is accompanied by inc easing wages in
column (3) o able 4 and leads o he inc eased wel a e o egula high-skill wo ke s ¯
ΩIH
and ¯
ΩNH in able 3.
Highe p oduc i i y o cowo ke s is also beneficial o high-skill small businesses, bu
he p oduc i i y o low-skill cowo ke s employed in high-skill businesses is dec easing.
We find ha he second effec domina es, so he a e age p oduc i i y o cowo ke s in
small businesses ope a ed by high-skill en ep eneu s dec eases mode a ely. Howe e , a
he same ime, filling posi ions becomes easie , especially low-skill posi ions; hus, he
ma ke igh ness θH
0is dec easing, while he job-filling a e is inc easing. Again, we
find ha immig an and na i e en ep eneu s ope a ing businesses a e asymme ically
affec ed. Column (8) o able 4 shows ha he posi i e effec o a highe job-filling
a e is domina ing o immig an en ep eneu s, and he e is a sligh inc ease in hei
p ofi s. This makes immig an businesses mo e a ac i e o hei owne s and induces
he ealloca ion o immig an en ep eneu s om solo sel -employmen o ope a ing small
businesses equal o 3.7%. O e all, we obse e a sizable inc ease in he wel a e o high-
skill immig an en ep eneu s ΩIH in able 3. This is pa ially due o highe p ofi s
om ope a ing small businesses and he ealloca ion om low-income ac i i ies in solo
sel -employmen o egula jobs. Mo e specifically, able 4 shows ha he income o
immig an sel -employed (1.199) is well below hei wages in egula paid jobs (1.309).
Fo na i e high-skill en ep eneu s, he si ua ion is diffe en . The lowe p oduc i i y
o an a e age cowo ke neu alizes he posi i e effec o a highe job-filling a e. Thus,
31
he p ofi s and he ac ion o na i e high-skill business owne s a e ha dly changing, and
he only meaning ul change is a shi owa ds egula jobs. Howe e , he diffe ence in
income be ween hese wo s a es is negligibly iny, compa e columns (5) and (3) in able
4, so he e is only a sligh inc ease in he wel a e o na i e en ep eneu s ΩNH in able 3.
De ailed wage and employmen changes o egula wo ke s a e p esen ed in able 14
in appendix C. Wages o low skill egula wo ke s all (column (3)); mo eo e , finding
jobs becomes mo e difficul since bo h ma ke igh ness a iables θL
0and θLa e alling due
o he s onge compe i ion among wo ke s. This leads o sligh ly highe unemploymen
a es in column (1) o able 14 and a mode a e educ ion in wel a e ¯
ΩNL and ¯
ΩIL.
Ou esul s sugges a ma ginal dec ease o abou 0.5% in he wel a e o an incumben
immig an . A mode a e decline o 0.88% is obse ed in he wel a e o a ep esen a i e
wo ke . I eflec s a combina ion o lowe wel a e o incumben wo ke s educed by 0.37%
and a composi ion effec since a ep esen a i e wo ke becomes “mo e immig an ” and
“mo e low skilled” on a e age. A he same ime, we find ha he a e age es ima e
hides subs an ial he e ogenei y o he effec ac oss wo ke g oups. Con a y o he p e-
ious s udies epo ing wage and wel a e losses o he incumben immig an popula ion
(D’Amu i e al. (2010), O a iano and Pe i (2012)), we find ha immig an en ep eneu s
expe ience sizable wel a e gains om a new immig a ion wa e equal o 3.1%.
5.2 Coope a ion wi h India
Ge many signed he “Mig a ion and Mobili y Pa ne ship Ag eemen ” (MMPA) wi h
India in Decembe 2022. I is he fi s mig a ion ag eemen be ween Ge many and a
non-EU coun y. The ag eemen aims o p omo e he mobili y o high-skill immig an s
om India o Ge many. Recen de elopmen s in Oc obe , 2024 led Ge many o ag ee
o inc ease he annual numbe o isas g an ed o skilled Indian wo ke s om 20,000 o
90,000. Gi en he inc easing e ugee mig a ion o he de eloped wo ld, we expec he
low-skill scena io o domina e. Howe e , policies acili a ing high-skill immig a ion in
Ge many may, a bes , esul in skill-neu al immig a ion. These de elopmen s mo i a e
he expe imen o a skill-neu al immig a ion scena io o analyze he possible effec s o
inc eased Indian immig a ion o Ge many. The e o e, able 15 in appendix C.1 epo s
he implica ions o a 20% skill-neu al mig an influx.
Ou analysis sugges s ha in he case o skill-neu al immig a ion an incumben
wo ke will expe ience a smalle wel a e loss (−0.27%) compa ed o he low skill sce-
na io (−0.37%). Mo eo e , he wel a e o incumben immig an wo ke s will inc ease
(+0.38%). The eason is ha hi ing cowo ke s becomes easie o all ypes o small busi-
nesses, boos ing immig an en ep eneu s’ wel a e. Combined wi h highe wages and he
wel a e o high-skill immig an wo ke s, his effec is domina ing despi e a sligh educ ion
in he wel a e o low-skill immig an s. The wel a e loss o a ep esen a i e wo ke will
also be smalle (−0.66%) han he one expe ienced in a low-skill scena io (−0.88%).
32
5.3 Value o immig an en ep eneu ship
In his sec ion, we conduc a coun e ac ual expe imen on he legal ba ie s o sel -
employmen and en ep eneu ship o immig an s. We se δIL =0andδIH = 0, implying
ha he legal en y ba ie in o sel -employmen and business owne ship is infini ely high
o immig an po en ial en ep eneu s so ha none o hem a e obse ed in he s a es sIj
and bIj,j=L, H. We conside he benchma k model wi hou an immig a ion shock and
analyze how he lack o immig an en ep eneu ial ac i i y affec s he wel a e o wo ke s
compa ed o he benchma k model wi h he op ion o en ep eneu ship.
The goal o his expe imen is wo old. Fi s , i allows us o es ima e he op ion
alue o en ep eneu ship o immig an s. Second, we can es ima e he spillo e effec s
o immig an en ep eneu ship o all o he g oups p oducing insigh s abou he en y
ba ie s policies o immig an small businesses. The esul s a e summa ized in able 5,
whe e line (0) co esponds o he benchma k equilib ium and line (E) con ains wel a e
changes o all wo ke g oups in he coun e ac ual se ing wi h en y ba ie s.
Table 5: Wel a e changes in he coun e ac ual scena io wi hou immig an
en ep eneu ship
Low-skilled High-skilled
Regula wo ke s Po . en ep eneu s Regula wo ke s Po . en ep eneu s
NI NINI NI
¯
ΩNL ¯
ΩIL ΩNL ΩIL ¯
ΩNH ¯
ΩIH ΩNH ΩIH
(0) 1.552 1.405 1.523 1.497 1.988 1.641 1.970 1.810
(E) -0.35% -0.43% +1.62% -15.2% -0.17% -0.18% +1.08% -30.5%
No e: Row (0) shows he wel a e o wo ke s in he benchma k model. Row (E) shows he
change in wel a e in he coun e ac ual case o a comple e ban on immig an en ep eneu ship.
Table 5 shows ha he wel a e losses o high-skill po en ial en ep eneu s a e d a-
ma ic and amoun o 30.5% o hei wel a e. This is p ima ily d i en by unemploymen
inc easing om 3.9% o 11% (see able 16 in he appendix). The losses o low-skill po-
en ial en ep eneu s a e also la ge, eaching 15.2% and caused by he co esponding
inc ease in unemploymen om 4.9% o 18%. These findings indica e a e y high alue o
he en ep eneu ship op ion o immig an indi iduals wi h a high en ep eneu ial spi i .
They also sugges ha en ep eneu ship is an efficien way o educing unemploymen o
immig an s.
Fu he , we obse e mode a e nega i e spillo e s o egula wo ke s wi h educed
wel a e. These wel a e losses sugges ha policies educing en y ba ie s o immig an
en ep eneu s a e likely o be beneficial o egula wo ke s (na i e and immig an ). Thei
wel a e is highe in he benchma k scena io wi h immig an en ep eneu ship. The ea-
sons o highe wel a e a e h ee old: fi s , immig an po en ial en ep eneu s en e ing
sel -employmen educe compe i ion o egula jobs; second, immig an small businesses
c ea e new wo king places o all wo ke g oups; and hi d, he lump-sum ans e T
33
is highe due o highe ne fiscal con ibu ions o immig an s. A he same ime, able
5 e eals ha he wel a e o na i e po en ial en ep eneu s is lowe in he benchma k
scena io wi h immig an en ep eneu ship. The eason is s onge compe i ion wi h im-
mig an businesses, sugges ing ha en y ba ie s o immig an en ep eneu s shield
na i e businesses om compe i i e o ces. Ge many in oduced se e al amendmen s in
i s Residence Ac o non-Ge man en ep eneu s be ween 2004 and 2012. These amend-
men s elaxed he condi ions equi ed o en ep eneu ial en u es and offe ed incen i es
o o eigne s o in es in Ge many.16 Ou expe imen helps e alua e he effec i eness o
hese policies.
5.4 E hnic seg ega ion in small businesses
The li e a u e on social ne wo ks documen s e hnic homophily, meaning a highe p oba-
bili y o c ea ing social ies wi h indi iduals o he same e hnic o igin (McPhe son e al.
(2001)). Dus mann e al. (2016) epo s o Ge many ha a new hi e is mo e likely
o be an immig an i he e is al eady a la ge sha e o immig an wo ke s in he fi m.
Ala e dyan and Zaha ie a (2022) show ha 44% o immig an s in Ge many find hei
jobs ia social con ac s. Addi ionally, e hnic seg ega ion could be an ou come o hi ing
disc imina ion. A field expe imen conduc ed by Kaas and Mange (2012) finds ha a
o eign name educes he a e age p obabili y o a callback and ha diffe en ial ea men
o na i e and immig an wo ke s is pa icula ly s ong and significan in smalle fi ms.
Ye ano he eason o e hnic seg ega ion could be ha small fi ms a e o en amily busi-
nesses. This sec ion in es iga es he implica ions o e hnic seg ega ion in small businesses.
Gi en he empi ical e idence in Kaas and Mange (2012) ha hi ing disc imina ion is
s onge in small fi ms and he findings in Goldbe g e al. (1995) ha i is mo e (less)
p onounced in low (high) skill jobs, we ocus on he e hnic seg ega ion in low-skill small
businesses o he ollowing analysis.
Remaining agnos ic abou he eason o e hnic seg ega ion, we in oduce pa ame e
ψ>0, cap u ing he co-e hnic bias in ma ching. Table 6 shows ha highe alues o ψ
inc ease he sha e o ma ches be ween na i e wo ke s and na i e-owned small businesses
and he sha e o ma ches be ween immig an wo ke s and immig an -owned businesses
(on he ma ix’s main diagonal). A he same ime, i educes he sha e o ma ches
be ween wo ke s and business owne s wi h diffe en e hnic o igins (off he diagonal). The
benchma k equilib ium wi h unbiased ma ching can be eco e ed when ψ=0,whe eμ
is he p obabili y o hi ing an immig an cowo ke iden ical o bo h ypes o businesses,
and 1 −μis he p obabili y o hi ing a na i e cowo ke . No e ha pa ame e ψonly
influences he sha es o ma ches o a pa icula ype bu does no en e he exp ession
o he o al numbe o ma ches c ea ed pe uni ime.
16Residence Ac 2004, Ac o Implemen Residence- and Asylum-Rela ed Di ec i es o he Eu opean
Union 2007, Labou Mig a ion Con ol Ac 2009, Residence Ac 1s Augus 2012
34

Table 6: Ma ching bias ψgi ing ise o e hnic seg ega ion in small businesses
Biased pai wise ma ching Immig an cowo ke Na i e cowo ke Sum
Immig an business owne (μ+ψ)bIL
bNL+bIL (1 −μ−ψ)bIL
bNL+bIL
bIL
bNL+bIL
Na i e business owne (μ−ψ)bNL
bNL+bIL (1 −μ+ψ)bNL
bNL+bIL
bNL
bNL+bIL
We augmen he co esponding equa ions o he p ofi s o small businesses in he
ollowing way:
πI=(μ+ψ)ΔI
I+(1−μ−ψ)ΔN
IπN=(μ−ψ)ΔI
N+(1−μ+ψ)ΔN
N
whe e he uppe (lowe ) index indica es he ype o he wo ke (business owne ). In
addi ion, we adjus equa ions o he numbe s o wo ke s employed in small businesses:
¯q(θL
0)
γIL bIL =eIL
0I
μ+ψ=eNL
0I
1−μ−ψand ¯q(θL
0)
γNL bNL =eIL
0N
μ−ψ=eNL
0N
1−μ+ψ
We conside a ma ginal change in e hnic seg ega ion equal o 1% and se ψ=0.01.
The implica ions o e hnic seg ega ion o low-skill businesses a e as ollows. Fi s , na i e
wo ke s a e mo e p oduc i e on a e age. So, i leads o a highe specializa ion on he mo e
p oduc i e g oup o na i e wo ke s in na i e businesses. This is associa ed wi h highe
p ofi s, highe business en y and highe wel a e o na i e en ep eneu s (see able 7 o
wel a e effec s and able 17 in Appendix C.2 o u he de ails). Second, he e is a highe
specializa ion o immig an businesses on he less p oduc i e g oup o immig an wo ke s
leading o lowe p ofi s. As a esul immig an en ep eneu s mo e in ensi ely o solo sel -
employmen , which is associa ed wi h lowe wel a e. Thi d, changes in he composi ion
o small businesses a e associa ed wi h lowe ea nings o na i e egula wo ke s and lowe
wel a e despi e a highe p obabili y o ge ing jobs in na i e businesses.
Fu he mo e, we find mode a e spillo e s o e hnic seg ega ion o high-skill busi-
nesses. On he one hand, c oss-skill ma ching implies ha high-skill businesses compe e
wi h low-skill businesses o low-skill wo ke s. Tigh e compe i ion o low-skill na i e
wo ke s educes p ofi s and wel a e o na i e high-skill en ep eneu s. On he o he hand,
difficul ies in hi ing los skill na i e wo ke s imply ha acancies in high-skill businesses
a e inc easingly filled wi h high-skill applican s aising he p oduc i i y o an a e age
employee. The la e effec is domina ing o immig an high-skill businesses leading o
highe p ofi s and a sizable inc ease in hei wel a e ΩIH.
O e all, ou findings in his sec ion indica e ha e hnic seg ega ion could be ben-
eficial o na i e low-skill businesses bu i seems o be de imen al o he p ofi s and
en y o immig an businesses in he same subma ke leading o he unde u iliza ion o
en ep eneu ial po en ial in his g oup.
35
Table 7: Wel a e changes upon a ma ginal inc ease in e hnic seg ega ion, ψ=0.01
Low-skilled High-skilled
Regula wo ke s Po . en ep eneu s Regula wo ke s Po . en ep eneu s
NI NININI
¯
ΩNL ¯
ΩIL ΩNL ΩIL ¯
ΩNH ¯
ΩIH ΩNH ΩIH
(0) 1.552 1.405 1.523 1.497 1.988 1.641 1.970 1.810
(F) -0.18% -0.07% +1.74% -7.63% -0.12% -0.14% -0.15% +0.95%
No e: Row (0) shows he wel a e o wo ke s in he benchma k model. Row (F) shows he
change in wel a e upon e hnic seg ega ion in low-skill businesses, ψ=0.01.
6Conclusion
In his pape , we de elop a unified amewo k ha inco po a es he dual ole o immi-
g an s as wo ke s and en ep eneu s. As wo ke s, mig an s compe e wi h na i e wo ke s
o jobs in he egula job ma ke . In con as , as en ep eneu s, hey compe e wi h na-
i e en ep eneu s bu c ea e employmen oppo uni ies o o he na i es and mig an s
looking o jobs. The heo e ical se up combined wi h su ey da a om he SOEP is used
o quan i y he impac o low-skill immig a ion on small businesses, unemploymen a es,
wage s uc u e, and wel a e o na i e and incumben immig an s in Ge many.
We conside a low-skilled mig a ion shock simila in in ensi y o he e ugee wa e o
2012 −2017. Consis en wi h he li e a u e, we find ha i is associa ed wi h inc eased
unemploymen and educed wages o all low-skilled wo ke s, nega i ely affec ing hei
wel a e. Simila ly, he high-skilled wo ke s gain om such an inflow. None heless, we
ex end he li e a u e by p o iding a mo e de ailed pic u e o he effec s o mig a ion
on small businesses and en ep eneu s. Con a y o he exis ing li e a u e, sugges ing
a nega i e impac o mig a ion on incumben mig an s, we find ha incumben immi-
g an en ep eneu s in bo h skill g oups gain om immig a ion and expand hei en-
ep eneu ial ac i i ies. This amplifies he wel a e gains o high-skill egula wo ke s and
educes he wel a e losses o he low-skilled. Ye , we documen an ad e se effec on na-
i e en ep eneu s, especially he low-skilled, losing wel a e om he lowe p oduc i i y o
hei cowo ke s and acing s onge ec ui men compe i ion om immig an small busi-
nesses. We also find ha ecen Ge man-Indian coope a ion on skilled-wo ke mobili y
can educe he losses om low-skilled mig a ion.
The coun e ac ual expe imen sugges s ha es ic ing he en y o immig an s in o
en ep eneu ship leads o an o e all wel a e loss o he economy. All demog aphic g oups
incu wel a e losses excep o he na i e en ep eneu s who gain om educed compe-
i ion wi h immig an businesses. Finally, quan i ying he impac o e hnic seg ega ion
in small businesses, we find ha low-skill na i e en ep eneu s and high-skill immig an
en ep eneu s gain while all o he g oups o wo ke s lose wel a e om such seg ega ion.
36
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38
ob ained as wCI(1− )=β0yCI(1− )+(1−β0)¯zand wCN(1− )=β0yCN(1− )+(1−β0)¯z
whe e he subindex Cs ands o c oss-skill ma ching.
A.6 Unemploymen o egula wo ke s
The equilib ium unemploymen o egula wo ke s ¯uij,i=I,N,j=L, H is gi en by:
¯uij =dij −lij −μij ¯q(θH
0)bNH
γNH +bIH
γIH −1LM¯q(θL
0)bNL
γNL +bIL
γIL¯γij
¯γij +Xijλ(θj)
whe e a iable M akes alue μ o immig an low-skill wo ke s and 1 −μ o na i e
low-skill wo ke s.
B Empi ical da a
B.1 Mince ea nings eg essions
The in o ma ion on g oss mon hly wage/income o egula wo ke s and po en ial en-
ep eneu s is a ailable in SOEP. We use da a o 2000-2017 and un he ollowing Mince
ea nings eg essions o egula wo ke s:
ln wi =φ0+φ1Ni +φ2FSi +φ3HSi +φ4Ni ×FSi +φ5Ni ×HSi
+φ6HSi ×FSi +φ7Ni ×HSi ×FSi +φ8 +ςi
Whe e wi is he wage o wo ke iobse ed in yea .Ni is he indica o unc ion ha
akes he alue 1 o na i es, FSi is he indica o unc ion wi h alue 1 o la ge fi ms,
HSi akes alue 1 o high-skill wo ke s. We in oduce in e ac ion e ms (Ni ×FSi )and
(HSi ×FSi ) in o de o cap u e a ia ion in he effec o fi m size on wages by e hnici y
and skill. Simila ly, (Ni ×HSi ) cap u es he ac ha he e u n o schooling could be
diffe en o na i e and immig an wo ke s.
Fo he po en ial en ep eneu s we un he ollowing eg ession
ln wi =φ0+φ1Ni +φ2HSi +φ3Ni ×HSi +
3

l=1
φ4lPEl
i +
3

l=1
φ5lNi ×PEl
i
+
3

l=1
φ6lHSi ×PEl
i +
3

l=1
φ7lHSi ×PEl
i ×Ni +φ8 +i
whe e PEl
i is he indica o unc ion, such ha l= 1 o po en ial en ep eneu s in solo
sel -employmen , l= 2 o business owne s wi h less han 9 cowo ke s, l= 3 o business
owne s wi h mo e han 9 cowo ke s. Po en ial en ep eneu s in paid employmen se e
as a e e ence ca ego y. The in e ac ion e ms Ni ×PEl
i and HSi ×PEl
i cap u e he
e hnici y specific and skill specific fixed effec s o en ep eneu s i diffe en economic
s a es. Ni ×HSi cap u es he skill fixed effec s specific o he wo e hnic g oups. The
coefficien s om bo h eg essions a e summa ized in ables 10 and 11 espec i ely. We use
hese esul s o p edic g oss ea nings o diffe en wo ke g oups. These a e used as a ge
momen s o he calib a ion o p oduc i i ies o wo ke s and he ela ed pa ame e s.
45

Table 10: Wage eg ession o egula wo ke s, SOEP 2000-2017
Va iable Coefficien S anda d e o P edic ed ln(w) No malized wage
Na i e 0.142∗∗∗ (0.012) ¯eNH
0: 7.25 wNH
0=1.295
Fsize 0.609∗∗∗ (0.012) eNH:7.93 ¯wNH =2.557
Na i e ×Fsize -.064∗∗∗ (0.014) ¯eNL
0: 6.99 wNL
0=1
HSkill 0.251∗∗∗ (0.029) ¯eNL:7.53 ¯wNL =1.715
Na i e ×HSkill 0 .008 (0.030) ¯eIH
0: 7.10 wIH
0=1.120
Fsize ×HSkill 0.048 (0.330) ¯eIH:7.76 ¯wIH =2.158
Na i e ×Fsize ×HSkill 0.086∗∗ (0.034) ¯eIL
0: 6.85 wIL
0=0.870
Cons an 6.779∗∗∗ (0.013) ¯eIL:7.46 ¯wIL =1.599
Obse a ions 180699
∗p<0.05, ∗∗ p<0.01, ∗∗∗ p<0.001
Fsize = 1 o la ge fi m wi h mo e han 20 wo ke s
Table 11: Wage eg ession o po en ial en ep eneu s, SOEP 2000-2017
Va iable Coefficien S anda d e o P edic ed ln(w) No malized wage/p ofi
PE ype1-0.009 (0.043) sNH: 7.43 1.551
PE ype20.770∗∗∗ ( 0.048) sNL: 7.26 1.309
PE ype31.078∗∗∗ (0.119) bNH
<9: 8.34 3.854
HSkill 0.049 (0.060) bNL
<9: 7.89 2.458
PE ype1×HSkill 0 .131 (0.082) bNH
>9: 8.71 5.580
PE ype2×HSkill 0 .460∗∗∗ (0.091) bNL
>9: 8.37 3.972
PE ype3×HSkill 0.182 (0.191) eNH: 7.62 1.876
Na i e -0.018 (0.034) eNL: 7.19 1.220
PE ype1×Na i e 0.081∗(0.046) sIH: 7.38 1.476
PE ype2×Na i e -0.077 (0.052) sIL: 7.20 1.232
PE ype3×Na i e 0.101 (0.126) bIH
<9: 8.50 4.523
HSkill ×Na i e 0.383∗∗∗ (0.063) bIL
<9: 7.99 2.716
PE ype1×HSkill ×Na i e -0.398∗∗∗ (0.085) bIH
>9: 8.52 4.614
PE ype2×HSkill ×Na i e -0.443∗∗∗ (0.095) bIL
>9: 8.29 3.666
PE ype3×HSkill ×Na i e -0.272 (0.199) eIH: 7.26 1.309
Cons an 7.111∗∗∗ (0.038) eIL: 7.21 1.245
Obse a ions 37831
∗p<0.05, ∗∗ p<0.01, ∗∗∗ p<0.001
PE ype1= Solo sel -employed o helpe s in amily business, PE ype2= sel -employed wi h less han 9 cowo ke s
PE ype3= sel -employed wi h mo e han 9 cowo ke s, PE ype4=inpaidemploymen
Table 12: A e age enu e o diffe en demog aphic g oups o wo ke s
G oup Tenu e
Regula wo ke s, immig an s a e age enu e 8.781
Regula wo ke s, na i e a e age enu e 11.547
Regula wo ke s, a e age enu e (na i e and immig an s combined) 8.237
Regula wo ke s, small fi ms na i es a e age enu e 8.504
Regula wo ke s, small fi ms na i es a e age enu e 6.750
B.2 Ba gaining powe in small i ms
Combining in o ma ion on wages o wo ke s in small fi ms and he co esponding p ofi s
o small businesses we ob ain he ba gaining powe pa ame e β0. Mo e specifically, o
low-skill businesses we se he ollowing exp essions equal o he p e- ax p ofi s p edic ed
om a Mince eg ession:
σ1
α0
(α)
1−F(α0)dα −c
 
indi idual ea nings
+γ+¯q(θ0)
γ
(1 −β0)
β0(1 − )μ(wI
0(1 − )−¯zI)) + (1 −μ)(wN
0(1 − )−¯zN)
 
a e age p o i pe cowo ke
46
whe e (γ+¯q(θ0))/γ is he a e age numbe o cowo ke s condi ional on hi ing a leas one.
Fo high-skill businesses we ex end he exp ession o accoun o c oss-skill ma ching.
Based on hese a ge alues o p ofi s we find βL
0=0.456 and βH
0=0.422.
B.3 Ma ching unc ion
The Fede al Employmen Office (Bundesagen u ¨u A bei ) da a includes in o ma ion on
he absolu e numbe o unemployed, acancies and acancy du a ions (in days) which a e
no a ailable in he SOEP su ey. In o al he e 228 mon hly obse a ions. We use his
da a o cons uc an economy wide a e age ma ke igh ness (θ =V
U ) and he hi ing a e
(q(θ ). These a iables a e illus a ed on Fig 5. The uppe le panel o his figu e shows a
sha p inc ease o he a e age acancy du a ion be ween he yea s 2000 and 2018. Whe eas
i was only 41.5 days on a e age in he yea 2000, i almos ipled and eached a le el 112
days by 2018. The op igh panel o figu e 5 shows he co esponding Be e idge cu e o
Ge many showing a s able nega i e ela ionship be ween unemploymen and acancies.
The bo om le panel shows he ma ke igh ness, while he agg ega e job-filling a e q(θ)
is illus a ed in he bo om igh panel o figu e 5. Using his in o ma ion we es ima e
he ollowing eg ession:
ln q(θ )=cs −ζln θ +Yea +ι (22)
We con ol o ime fixed effec s by in oducing a dummy o each yea . This eg ession
gi es us a alue o he slope pa ame e ζequal o 0.47.
Figu e 5: Vacancy du a ion and ma ke igh ness.
No e: Au ho s’ calcula ions using s a is ical in o ma ion o he Fede al Employmen
Office (Bundesagen u ¨u A bei ) be ween Janua y 2000 and Decembe 2018.
47
Table 13: Pa ame e s calib a ed using SOEP da a 2000-2017
P m. Empi ical momen / a ge Defini ion and calib a ed alues
NL IL NH IH NL IL NH IH
¯γA e age enu e o egula wo ke s Regula job des uc ion a e
11.55 8.78 11.55 8.78 0.0198 0.0270 0.0206 0.0269
γSha e o wo ke s in small businesses e0/(e0+¯e)Business des uc ion/exi a e
0.265 0.270 0.165 0.212 0.0296 0.0358 0.0305 0.0292
δSha e o ac i e en ep eneu s (b+s)/l T ansi ion a e o en ep eneu ship
0.547 0.525 0.568 0.577 0.5893 0.5355 1.1149 0.5173
xUnempl. a e o immig an wo ke s ¯u/(d−l)Sea ch in ensi y o small businesses
- 0.141 - 0.091 1 0.5713 1 0.2851
XUnempl. a e o immig an po . en ep eneu s u/l Sea ch in ensi y o egula jobs
- 0.049 - 0.039 1 0.7593 1 0.2750
cSha e o solo-en ep eneu s (b0+s)/(b+s)Flow cos o a small business
0.586 0.607 0.591 0.459 1.1636 1.2919 2.2448 3.0985
ςBusinesses wi h 1-9 cowo ke s 9
n=1 bn/(b+s)En ep eneu ial p oduc i i y
0.366 0.362 0.326 0.425 0.2499 0.255 0.3703 0.2635
ϕ0NP ofi s o small businesses wi h cowo ke s Quan i ies in small (na i e) businesses
2.63 2.77 4.20 4.52 0.2973 0.2398 0.4109 0.3363
ϕ0IA . wages in small businesses ¯w0Quan i ies in small (immig an ) businesses
1 0.8674 1.2950 1.1144 0.3437 0.3097 0.5293 0.4227
¯ϕA . wages o wo ke s in egula jobs ¯wQuan i ies o wo ke s in egula jobs
1.625 1.492 2.940 2.630 0.9727 1 0.9157 1
ϕWages o po . en ep eneu s in egula jobs wQuan i ies o po . en ep . in egula jobs
1.222 1.246 1.884 1.309 0.8954 0.9004 0.8619 0.7440
z60% eplacemen a e in he 1s yea Unemploymen benefi s o po . en ep eneu s
and ALG II assis ance a e wo ds 0.3719 0.3723 0.3757 0.3709
¯z60% eplacemen a e in he 1s yea Unemploymen benefi s o egula wo ke s
and ALG II assis ance a e wo ds 0.3838 0.3809 0.3948 0.3869
MUnempl. a e o na i e en ep eneu s u/l Ma ching mul iplie , egula jobs
0.035 - 0.014 - 0.5319 0.9955
¯
MUnempl. a e o na i e wo ke s ¯u/(d−l)Ma ching mul iplie , small businesses
0.085 - 0.022 - 0.0748 0.1809
¯ckA e age job-filling a e q(θ)Capi al cos in egula fi ms
1.5500 1.2398 3.3821 2.5642
chRebien, S ops, Zaha ie a (2020) Vacancy pos ing cos
0.7431 2.3344
β0Assump ion wN
0I/wI
0I=¯wN/¯wIBa gaining powe o wo ke s in small fi ms
1.0819 1.1905 0.4564 0.4222
Annual discoun a e = 5% (Qua e ly) Discoun a e
0.0125
ηChassamboulli and Pali os (2014) Elas ici y o subs . be ween Kand Z
Ba is i e al. (2018) 0.350
ρO a iano and Pe i (2012) Elas ici y o subs . be ween YHand YL
Ba is i e al. (2018) 0.500
RChassamboulli and Pali os (2014) (Qua e ly) cos o capi al
Ba is i e al. (2018) 0.030
ANo maliza ion ¯yNH =PHTo al ac o p oduc i i y
2.5630
aNo maliza ion ¯yNL =PLIncome sha e o YL
0.5547
κA e age enu e in small fi ms C oss-skill ma ching pa ame e
8.2369 0.1700
ζReg ession ln q(θ)onlnθElas ici y o he ma ching unc ion
0.47
βRa io o nominal wages o GDP Ba gaining powe o wo ke s in egula jobs
0.28 0.9084
48
CResul s
C.1 Low-skilled immig a ion and skill-neu al immig a ion
We define e0=e0N+e0I– o al employmen o wo ke s in small businesses wi hin hei
own skill g oup wi h he co esponding a e age wage ¯w0=(w0Ne0N+w0Ie0I)/(e0N+e0I).
Fu he , eC=eCN +eCI – o al employmen o low-skill wo ke s in high-skill small
businesses wi h he co esponding a e age wage ¯wC=(wCNeCN +wCIeCI)/(eCN +eCI).
Table 14: De ailed changes o egula wo ke s upon a 20% inc ease in immig a ion,
low-skill immig a ion scena io.
(1) (2) (3) (4) (5) (6) (7)
G oup ¯u/(d−l) ¯e/(d−l)¯w e0/(d−l)¯w0eC/(d−l)¯wC
Low-skill
Na i es 0.085 0.680 1.718 0.135 1.002 0.100 0.997
Change +0.003 -0.003 -0.021 -0.001 +0.009 +0.002 -0.002
Low-skill
Immig . 0.141 0.634 1.588 0.129 0.871 0.096 0.862
Change +0.004 -0.004 -0.021 -0.002 +0.016 +0.001 -0.001
High-Skill
Na i es 0.022 0.825 2.544 0.153 1.295
Change -0.001 +0.007 +0.034 -0.007 +0.009
High-Skill
Immig . 0.091 0.726 2.163 0.182 1.120
Change -0.002 +0.010 +0.031 -0.007 +0.007
We now conside skill-neu al immig a ion and inc ease p opo ionally he numbe o
low and high-skill immig an s by 20%. Ou esul s a e summa ized in able 15.
Table 15: Inc ease in immig a ion by 20%, skill-neu al scena io
Low-skilled High-skilled
Regula wo ke s Po . en ep eneu s Regula wo ke s Po . en ep eneu s
NINI NINI
¯
ΩNL ¯
ΩIL ΩNL ΩIL ¯
ΩNH ¯
ΩIH ΩNH ΩIH
1.552 1.405 1.523 1.497 1.988 1.641 1.970 1.810
-0.77% -0.83% -1.56% +2.95% +0.52% +0.53% -0.08% +4.24%
Rep esen a i e wo ke : -1.05% Rep esen a i e wo ke : +0.24%
Incumben wo ke : -0.78%
Rep esen a i e wo ke : -0.68%
Incumben immig an : +0.38%
Incumben wo ke : -0.27%
The changes in wages, p oduc i i ies and wel a e o egula wo ke s a e less p o-
nounced compa ed o he low-skilled scena io. This holds o he losses o egula low-
skill wo ke s (app ox. −0.8% ins ead o −1.3%) and o he gains o he egula high-skill
wo ke s (app ox. +0.5% ins ead o +1%). The effec is also mo e mode a e o he wel a e
o low skill en ep eneu s, bu i is mo e p onounced o he p ofi s and wel a e (+4.2%)
49
o high-skill immig an en ep eneu s. This is in ui i e since hi ing high-skill cowo ke s
becomes easie in he case o skill-neu al immig a ion.
C.2 En ep eneu ship en y ba ie s and e hnic seg ega ion
Table 16: The dis ibu ion o po en ial en ep eneu s upon business en y ba ie s
(1) (2) (3) (4) (5) (6) (7) (8)
G oup u/l e/l w (su+se)/l σ¯αu0b/l σ¯α01 ¯q(θ0)π/γ
Low-skill
Na i es 0.035 0.418 1.222 0.259 1.145 0.288 1.291 1.971
Change -0.000 -0.002 -0.001 -0.052 -0.032 +0.054 -0.004 +0.003
Low-skill
Immig . 0.049 0.426 1.245 0.251 1.100 0.274 1.314 2.077
Change +0.132 +0.393 -0.001 -0.251 --0.274 --
High-Skill
Na i es 0.014 0.418 1.884 0.290 1.883 0.277 1.953 3.763
Change -0.000 +0.002 +0.001 -0.027 -0.005 +0.025 -0.001 +0.001
High-Skill
Immig . 0.039 0.384 1.309 0.206 1.199 0.370 1.374 5.270
Change +0.072 +0.504 +0.001 -0.206 --0.370 --
No e: ¯αu0is he a e age en ep eneu ial abili y in he ange [αu..α0], calcula ed as
(su¯αus +se¯αs0)/(su+se). ¯α01 is he a e age en ep eneu ial abili y in he ange [α0..¯α].
Table 17: The dis ibu ion o po en ial en ep eneu s upon e hnic seg ega ion
(1) (2) (3) (4) (5) (6) (7) (8)
G oup u/l e/l w (su+se)/l σ¯αu0b/l σ¯α01 ¯q(θ0)π/γ
Low-skill
Na i es 0.035 0.418 1.222 0.259 1.145 0.288 1.291 1.971
Change -0.000 +0.005 +0.001 -0.057 -0.035 +0.052 -0.003 +0.003
Low-skill
Immig . 0.049 0.426 1.245 0.251 1.100 0.274 1.314 2.077
Change -0.000 +0.004 +0.001 +0.247 +0.107 -0.251 +0.016 -0.006
High-Skill
Na i es 0.014 0.418 1.884 0.290 1.883 0.277 1.953 3.763
Change -0.000 -0.005 -0.002 +0.006 -0.001 -0.001 -0.001 -0.000
High-Skill
Immig . 0.039 0.384 1.309 0.206 1.199 0.370 1.374 5.270
Change +0.000 -0.004 -0.002 -0.010 -0.009 +0.014 -0.002 +0.001
50