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

Iftikhar, Zainab; Zaharieva, Anna Working Paper Problem or opportunity? Immigration, job search, entrepreneurship and labor market outcomes of natives in Germany Working Papers in Economics and Management, No. 05-2024 Provided in Cooperation with: Faculty of Business Administration and Economics, Bielefeld University Suggested Citation: Iftikhar, Zainab; Zaharieva, Anna (2024) : Problem or opportunity? Immigration, job search, entrepreneurship and labor market outcomes of natives in Germany, Working Papers in Economics and Management, No. 05-2024, Bielefeld University, Faculty of Business Administration and Economics, Bielefeld, https://doi.org/10.4119/unibi/2999443 This Version is available at: https://hdl.handle.net/10419/308760 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Faculty of Business Administration and Economics www.wiwi.uni−bielefeld.de 33501 Bielefeld − Germany P.O. Box 10 01 31 Bielefeld University ISSN 2196−2723 Working Papers in Economics and Management ➔ No. 5-2024 December 2024 Problem or opportunity? Immigration, job search, entrepreneurship and labor market outcomes of natives in Germany Zainab Iftikhar, Anna Zaharieva Problem or opportunity? Immigration, job search, entrepreneurship and labor market outcomes of nativesinGermany ∗ Zainab Iftikhar † Anna Zaharieva ‡ November 20, 2024 Abstract In this study we evaluate the effects of low-skilled immigration on small businesses, wages and employment in Germany. We develop a search and matching model with heterogeneous workers, cross-skill matching, and endogenous entry into entrepreneurship. The model is calibrated using German Socio-Economic Panel (SOEP) data. Quantitative analysis shows that low-skilled immigration benefits high-skilled workers while negatively affecting the welfare of low-skilled workers. It leads to the endogenous expansion of immigrant entrepreneurial activities, generating positive spillovers for all demographic groups except native entrepreneurs. Overall, there is a marginal loss to the economy in terms of per worker welfare. This loss is mitigated with increased skilled migration from India. Policies restricting immigrant entrepreneurship relax competition for native small businesses but reduce welfare for all other worker groups. Ethnic segregation of small businesses benefits low-skill native entrepreneurs. Keywords: entrepreneurship, small business, self-employment, search frictions, immigration JEL codes: J23, J31, J61, J64, L26 ∗ We thank Michele Battisti, Pavel Brendler, Herbert Dawid, Guido Friebel, Leo Kaas, Keith Kuester, Moritz Kuhn, Joan Llull and Sebastian Otten for their valuable comments. Zainab Iftikhar would like to thank the Joachim Herz Foundation, and the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), Germany under Germany’s Excellence Strategy – EXC 2126/1-390838866 for financial support. Anna Zaharieva would like to thank the Leibniz Association for providing financial support to the Leibniz Science Campus “SOEPRegioHub” at Bielefeld University and the German Research Foundation (DFG) in the framework of the Research Training Group RTG 2951. † University of Bonn, CEPR, email: [email protected] ‡ Bielefeld University, Germany, email: anna.zahariev[email protected] 1 Introduction In this paper we revisit the impact of immigration on receiving countries. We develop a macroeconomic model with search frictions and endogenous entry into entrepreneurship. The model is calibrated to German data and makes four contributions to the literature. First, we develop a unified framework that allows for the dual role of immigrants as job seekers and as entrepreneurs or job creators. By doing so, we capture the higher competition native workers face due to immigration and the better outside options due to jobs created by immigrant entrepreneurs. Second, we provide a quantitative assessment of the model mechanism generating new insights into the heterogeneous effects of immigration on wages, employment opportunities of natives and incumbent immigrants as well as job creation in small businesses in Germany. Third, we evaluate the welfare effects of policies facilitating immigrants’ entry into entrepreneurship and analyze the role of ethnic segregation. Fourth, we quantify the impact of recently established cooperation on worker mobility between Germany and India.1 On the one hand, the literature provides evidence that immigrant entrepreneurs contribute to job creation.2For example, Sachs et al. (2016) finds that entrepreneurs with migration background employed at least 1.3 million people in Germany in 2014, while Leicht and Langhauser (2014) report this number between 1.5 to 2 million. Nevertheless, this literature does not explore the general equilibrium consequences of immigration in host countries. On the other hand, the large body of literature dealing with diverse aspects of migration in receiving countries ignores the immigrants’ entrepreneurial role despite its direct implications for the employment opportunities and wages of natives. This literature treats immigrants as workers who compete with natives for jobs and influence their welfare via the effects on wages, employment and fiscal transfers.3 In this paper we synthesize the aforementioned strands of literature and address the following questions 1) does ignoring the role of immigrants as entrepreneurs lead to biased predictions concerning the consequences of immigration for labor market outcomes and the welfare of natives? 2) whether policies reducing barriers to self-employment may be beneficial in reducing unemployment and increasing income/welfare 3) which worker groups gain/lose from the ethnic segregation of small businesses? We develop a search and matching (SaM) model with four demographic groups: natives/immigrants and high/low-skilled. Within each demographic group there are individuals with a high entrepreneurial spirit, called potential entrepreneurs, and individuals with a low entrepreneurial spirit, called regular workers. This distinction is motivated by 1Germany and India signed the “Migration and Mobility Partnership Agreement” (MMPA) in December, 2022 to facilitate skilled migration from India to Germany. In October 2024 Germany agreed to increase the number of visas granted to Indian skilled workers and promote fair migration. 2(Kerr and Kerr, 2020; Riillo and Peroni, 2022; Li, 2001; Lofstrom, 2002; Constant and Zimmermann, 2006) 3(D’Amuri et al., 2010; Ben-Gad, 2008; Borjas, 2003, 1999; Dustmann et al., 2017; Pischke and Velling, 1997; Busch et al., 2020; Iftikhar and Zaharieva, 2019; Battisti et al., 2018) 1 the SOEP data, which shows that regular workers, making up the majority, remain in paid jobs with an annual probability of at least 97% (see Appendix A.1 for details). However, those defined as potential entrepreneurs are frequently moving between paid jobs and self-employment with annual probabilities in the range of 15 −23%. This evidence shows that most workers do not consider self-employment as an alternative to their job. But also for those who do, self-employment is not a “once and for all” decision and should be modeled dynamically. Hence, potential entrepreneurs in our model have several options: they can enter solo self-employment, register a small business with coworkers, or search and accept a regular paid job. Entry into these states is endogenous and depends on the labour market conditions. Regular workers can be employed in regular jobs (large and medium-size firms) or small businesses operated by self-employed entrepreneurs. Large and medium-size firms are modeled in a classical SaM tradition with free entry. Our model has several novel features. First, we explicitly allow for the possibility of self-employment “out of necessity”, when self-employed entrepreneurs continue searching for regular paid jobs, and self-employment “out of opportunity”, when the income from self-employment activities is high enough, and there are no gains from job search. Selfemployment out of necessity is motivated by the empirical finding that the unemployment rates of potential entrepreneurs are lower than those of regular workers. Also other studies, for example, Poschke (2023) find evidence for self-employment out of necessity. At the same time, our wage regressions reveal that the earnings of business owners are higher than the wages of comparable individuals employed in regular paid jobs, suggesting an important “opportunity” component of entrepreneurship. Second, the size distribution of small businesses is endogenous. Third, we incorporate the possibility of cross-skill matching on a micro-level, whereby small businesses founded by high-skill entrepreneurs hire workers from both skill groups. The model is calibrated using the German Socio-Economic Panel (SOEP), a comprehensive survey of German households. We combined this data with information on vacancies from the Federal Employment Office. The data shows that high-skill immigrant entrepreneurs are more frequently observed operating small businesses rather than being solo self-employed, compared to all other groups of entrepreneurs. Moreover, immigrant businesses are more profitable than the businesses of native workers. Another relevant empirical fact is that low-skill workers are overrepresented in small businesses compared to high-skill workers, making them more susceptible to the entry of small businesses. Our modeling framework is well suited to capture these empirical facts. We use our framework to study the implications of a 20% increase in the number of low-skilled immigrants corresponding to the immigration wave observed in Germany in 2012-2017.4In line with previous research, we find that rising low-skill immigration 4During the Syrian war the number of immigrants to Germany increased from 15 to 18 million. Also the most recent immigrant wave in 2020-2024 (dominated by the Russian-Ukrainian conflict) is associated with a similar increase from 20 to 23 million as reported by www.destatis.de 2 benefits high-skill regular workers with a corresponding gain in welfare equal to 1%, but there is a reduction in the welfare of low-skill regular workers equal to −1.3%. The results for potential entrepreneurs are novel and reveal asymmetric effects. Immigrant entrepreneurs (high and low-skilled) experience higher profits and their business entry is reinforced by immigration, generating a welfare gain of 3.1%. There is a reduction in welfare (−2%) of low-skilled native entrepreneurs due to the reduced profits and a rise in the probability of staying in solo self-employment without coworkers. Thus, and contrary to the previous studies (e.g., D’Amuri et al. (2010), Ottaviano and Peri (2012)), we find that some groups of incumbent low-skill immigrants are gaining from new immigration. The underlying reason for this finding is that immigrant businesses are more profitable on average, making them more sensitive to the improved chances of hiring coworkers in response to the immigration increase. In contrast, we find that the expected profits of native entrepreneurs are less sensitive on the recruitment margin and fall due to the lower marginal productivity of their low-skill coworkers. In a nutshell, our results show that low-skill immigration reduces the welfare of an average incumbent individual by 0.4%, but there is pronounced heterogeneity in this effect across demographic groups. A skill-neutral immigration scenario emerging in a preview of the recent German-Indian cooperation to promote skilled migration from India to Germany will reduce the losses of the incumbent to 0.27%. Addressing the second question, we conduct a counterfactual experiment by introducing legal barriers to self-employment and entrepreneurship for immigrant individuals. This experiment sheds light on the spillover effects of immigrant entrepreneurship for regular workers and native entrepreneurs. We find that immigrant entrepreneurship has moderate positive spillovers in the range 0.2−0.4% for regular workers. On the one hand, immigrant potential entrepreneurs entering self-employment out of opportunity reduce competition for regular jobs; on the other hand, immigrant entrepreneurs operating small businesses create additional workplaces. On the contrary, our model indicates substantial negative spillovers for native potential entrepreneurs (1.1−1.6% of welfare). This is intuitive since the business entry of immigrant entrepreneurs creates additional competition in recruiting and reduces the hiring chances of native small businesses. Our findings suggest that policies restricting immigrant entrepreneurship shield native small businesses from competition but reduce welfare for all other worker groups. Considering the last question, we allow for ethnic segregation in small businesses such that job matches between workers and business owners of the same ethnicity become more likely compared to random matching. Ethnic segregation benefits low-skill native entrepreneurs by increasing the profits associated with hiring high-productivity native workers but it is detrimental for the profits of immigrant low-skill businesses and welfare of regular workers. Reduced business entry of low-skill immigrant entrepreneurs suggest that their entrepreneurial potential could be underutilized in the presence of ethnic segregation. The outline of the paper is as follows. Section 2 positions our study in the related 3 literature. Section 3 describes the theory. Section 4 presents the data and the calibration strategy, while section 5 discusses the results, and section 6 concludes the paper. 2 Related Literature Our paper contributes to the literature concerning the impact of (low-skilled) migration on the labor market outcomes and welfare of natives in developed countries. The seminal paper by Borjas (1999) and later Ben-Gad (2004) show that an influx of immigrants in the US creates an immigration surplus, assuming homogeneous labour and imperfect substitution between labor and capital. Subsequent papers with heterogeneous labour support varied conclusions regarding wages of competing workers and immigration surplus (Borjas, 2003; Ben-Gad, 2008). Literature on wage effects of immigration is inconclusive, vastly empirical, and assumes perfectly competitive labor markets (Altonji and Card, 1991; Borjas et al., 1997; Card, 2001; Borjas, 2006; D’Amuri et al., 2010). Goldin (1994), Borjas (2003), Aydemir and Borjas (2007), and Aydemir and Borjas (2011) find a negative effect of immigration on native wages. Several papers report a negligible effect.5 More recent studies provide evidence for heterogeneous wage effects. For example, the wage effects are considerably larger for younger natives (Dustmann et al., 2017) in Germany, while in the UK, migration negatively affects the wages of low earners but increases the wages of high earners (Dustmann et al., 2013). Our framework accommodates the heterogeneity in immigration’s effects by assuming different skill groups and occupation choices between paid employment and entrepreneurship. D’Amuri et al. (2010), Felbermayr et al. (2010), and Ottaviano and Peri (2012) further find that migration adversely affects the wages of the incumbent immigrants when immigrants are imperfect substitutes to natives in the same skill group. We follow a parsimonious approach in assuming perfect substitution between immigrants and natives in the same skill group. However, assuming productivity differences between ethnic groups with the same skills allows us to compute the effects of migration for incumbent immigrants and natives. There are mixed findings in the literature discussing the employment consequences of immigration. Some papers find a substantial adverse effect of immigration on native employment (Borjas, 2003, 2006; Dustmann et al., 2017). Others find either a positive, negligible, or no effect of migration on native employment in receiving countries.6Only Dustmann et al. (2017) discuss the interaction between wage and employment effects. Our theoretical framework incorporates interactions between wage and job creation, and the quantitative analysis provides insights into the distributional consequences of migration shock to the German labor market. 5Card (2001), Card (2005), Friedberg (2001), D’Amuri et al. (2010), Felbermayr et al. (2010), Ottaviano and Peri (2012), Busch et al. (2020) 6(Altonji and Card, 1991; Hunt, 1992; Pischke and Velling, 1997; D’Amuri et al., 2010; Scharfbillig and Weissler, 2019; Friedberg, 2001; Malchow-Møller et al., 2009; Felbermayr et al., 2010) 4 Several papers employ SaM models to analyze the general equilibrium effects of immigration. Ortega (2000) is one of the first papers studying the effects of migration in a frictional labor market. However, this paper is theoretical and lacks a detailed data-based quantitative analysis. Liu (2010) develops a dynamic search and matching model with heterogeneous labor but focuses solely on the consequences of illegal migration for the US economy. Chassamboulli and Palivos (2014) extend Liu’s framework with a nested CES production function, low and high-skilled labor, and capital to study the impact of immigration on the US economy. Battisti et al. (2018) calibrate a SaM model featuring two skill types, wage bargaining and a redistributive welfare state for 20 OECD countries. Iftikhar and Zaharieva (2019) extend the framework of Battisti et al. (2018) by considering a two-goods economy and endogenous price setting. Their framework identifies additional effects of immigration on Germany through its impact on domestic demand. Nanos and Schluter (2014) and Moreno-Galbis and Tritah (2016) also use the SaM model to analyse consequences of migration in selected European economies. Our framework borrows several elements from these frameworks but substantially deviates and innovates by adding entrepreneurship and cross-skill matching into the model. Our paper also addresses how small businesses respond to migration shocks. Papers on this topic suggest positive contributions of migrants to entrepreneurship in receiving countries (Kerr and Kerr, 2020; Riillo and Peroni, 2022). Duleep et al. (2021) find that immigrant entrepreneurs facilitate innovation and entrepreneurship among natives.7None of these papers consider entrepreneurship’s spillovers on the job market for workers in paid jobs. Entrepreneurs contribute to job creation (Kerr and Kerr, 2020; Azoulay et al., 2022) as well as job destruction (Georgarakos and Tatsiramos, 2009), resulting in direct consequences of immigrant entrepreneurship for employment opportunities of workers in regular employment. Provided this evidence, we propose a unified framework for the entrepreneurial pursuits of natives and immigrants and regular employment activities. Finally, our paper builds on a traditional SaM framework (Mortensen and Pissarides (1994), Pissarides (2000)) and augments it with entrepreneurship. An early search model with occupational choice between paid employment and entrepreneurship is by Fonseca et al. (2001). Rissman (2007) and Kredler et al. (2014) extend this setup to a “business idea ladder”, where entrepreneurs generate business ideas and implement those of them that are more profitable. We contribute to this literature by combining the approach of a “business idea ladder” with endogenous business creation in the spirit of Masters (2016). 7An interesting strand of literature focuses on comparing characteristics of native and immigrant entrepreneurs in terms of earnings, human capital, likelihood, and reasons to start a business (Li, 2001; Lofstrom, 2002; Constant and Zimmermann, 2006). 5 3 The Model 3.1 The environment The labour market is populated by four demographic groups: low-skill immigrants dIL, low-skill natives dNL, high-skill immigrants dIH and high-skill natives dNH. All individuals are risk-neutral and discount future income flows at the rate r. Labour supply is inelastic, and the total labour force is normalized to 1: dIL +dNL +dIH +dNH =1 idenotes the origin of the individual {I,N}and jindicates the skill level {L, H}. Within each demographic group ij, there are two subgroups: potential entrepreneurs with high entrepreneurial spirit lij and regular workers with low entrepreneurial spirit dij −lij.This group distinction is exogenous and based on innate ability, attitudes, and personality traits, which we do not model explicitly.8Being a potential entrepreneur does not imply being an active entrepreneur at a given point in time. Potential entrepreneurs can also be observed in paid employment or unemployment. However, their entrepreneurial spirit may lead them to switch from these states to starting a solo self-employment or business with coworkers. This group distinction is motivated by the SOEP data, which shows that 85% of individuals in our sample were never observed in self-employment over 18 years and remain in paid employment with an annual probability of at least 97%. On the contrary, there are 15% of individuals actively moving between paid jobs and selfemployment with an average annual probability equal to 15 −23% and a similarly high transition probability back to a paid job (see Appendix A.1 for details). Regular workers. There are two employment states for regular workers. First, regular workers can be employed in a regular job ¯eij, producing output ¯yij and receiving a wage ¯wij. Regular jobs are positions in medium and large-size firms. Second, potential entrepreneurs can employ them in a small business ¯eij 0. Hence, we have: ¯eij +¯eij 0+¯uij =dij −lij Where ¯uij is a state of involuntary unemployment for regular workers associated with a flow income ¯zij −h.Variable¯zij is the unemployment benefit, whereas h– is the disutility from unemployment (e.g., the stigma of failure). The exogenous shock of job destruction arrives to all employees in regular jobs at rate ¯γij, rendering them unemployed. Potential entrepreneurs. Potential entrepreneurs have a high entrepreneurial spirit, so they can be solo self-employed sij or operating small businesses with coworkers bij.The decision to become self-employed and start a business is endogenous and driven by mar8Intuitively, individuals with high managerial and organizational skills, low risk-aversion, extroverted, and communicative are more likely to be potential entrepreneurs. 6 where w(1−t) is the after tax labour income and ¯γis the job destruction rate. This relationship shows that employed potential entrepreneurs continue generating new business ideas and may voluntarily quit the job and enter self-employment (out of opportunity) or start a new business. At α>α s, self-employed entrepreneurs stop searching and applying for regular paid jobs. This is because the quality of their product/service becomes sufficiently high, which is associated with a relatively high income σα(1 −t). So the cut-off value of αsis given by the following indifference condition: E(αs)=W. It then holds that Es(αs)=E(αs) since the option of searching for a regular job has zero value for α=αs. Proposition 2:The endogenous threshold αsseparating solo self-employed out of necessity and opportunity can be obtained from the following indifference condition: Es(αs)= E(αs)=W, which yields: σαs=w−(¯γ−γ) r+¯γ+Xλ(θ)w−z−h 1−t−δαs αu (1 −F(x))σ r+γ+Xλ(θ)+δ(1 −F(x))dx(9) The cutoff αsis increasing in the wage w. It is convex in wif γ>¯γand concave otherwise. The slope is given by: ∂αs ∂w =(r+γ+Xλ(θ)+δ(1 −F(αs))) σ(r+¯γ+Xλ(θ)+δ(1 −F(αs))) (10) Proof: appendix A.3 Equation (9) is an explicit form of a shorter expression σαs(1 −t)=w(1 −t)− (¯γ−γ)(W−U). First, self-employed entrepreneurs compare their flow incomes σα(1 − t)andw(1 −t). Second, they also consider the risk of dropping back to the state of unemployment, which is ¯γin a regular job and γin self-employment. In the special case ¯γ=γwe would get αs=w/σ. Equation (10) implies that a higher wage wmakes regular jobs even more valuable and gives rise to a higher threshold αs. The threshold value αuis given by the indifference condition Es(αu)=U.Es(α)isan increasing convex function of αwith a slope E s(α)=σ(1−t)/(r+γ+Xλ(θ)+δ(1−F(α))) as shown on figure 2. Comparing the present value from solo self-employment Es(αu)and the present value of unemployment Ugives the following result: Proposition 3: The endogenous threshold αudriving the entry into solo self-employment can be obtained from condition Es(αu)=U, which yields: σαu(1 −t)=z−h. Proof: appendix A.3 Potential entrepreneurs entering self-employment keep the option of searching for regular jobs, and they also keep the option of starting a small business, so there are no costs of starting self-employment apart from losing the flow income in unemployment z−h. The additional gain from self-employment is the flow income σα(1−t), which leads to the finding αu=(z−h)/(σ(1 −t)). Even though parameters z,h,t are exogenous, the productivity in self-employment is a product of the quantity and the endogenous price 13 (σ=ςP), making the entry cut-off αuendogenous as well. Hence, if the output price P is increasing, more potential entrepreneurs decide to enter self-employment. 3.4 Steady-state distribution The firm size distribution. In this section we discuss the steady-state distribution of the number of employees in small businesses. We start by analyzing low-skill small businesses. Let pI k– be the number of small businesses with kimmigrant coworkers and and pN m= be the number of businesses with mnative coworkers. In proposition 4 we characterize these distributions and show that they do not depend on α: Proposition 4: The numbers of immigrant and native coworkers in low skill businesses are given by geometric densities with parameters γ/(γ+¯q(θ0)(1 −μ)) and γ/(γ+ ¯q(θ0)μ)respectively. The number of all employees in low-skill businesses has a geometric density with parameter γ/(γ+¯q(θ0)).Proof: Appendix A.4. This proposition allows us to infer the average number of immigrant/native coworkers per low skill business which is given by ¯q(θ0)μ/γ and ¯q(θ0)(1 −μ)/γ respectively. So the average size of a small business is ¯q(θ0)/γ. The size distribution of small businesses (pn) is also given by the geometric density with parameter γ/(γ+¯q(θ0)): pn=¯q(θ0) γ+¯q(θ0)nγ γ+¯q(θ0) This density is decreasing in the whole support, implying that a vast majority of businesses are small and only very few of them survive for a long period of time and become large. We find that this decreasing pattern is consistent with the empirical evidence observed in Germany. For example, according to Leicht and Langhauser (2014) the share of native-owned businesses with less than 5 employees is 59%, the share of businesses with 6-10 employees is 21%, with 11 −19 employees – 10%, with 20 −49 employees – 6% and more than 50 employees – 3%. A similar decreasing pattern is also reported for immigrant businesses and it is well captured by the geometric distribution function. Considering high-skill businesses, the average number of type ij employees, i=I,N, j=L, H, is given by ¯q(θ0)μij/γ. Moreover, the unconditional distribution of employees ij in these businesses also has a geometric density with parameter γ/(γ+¯q(θ0)μij). The distribution of entrepreneurs. Variables suand seare the numbers of necessity and opportunity entrepreneurs, respectively, so that s=su+seis a total number of solo-entrepreneurs. Given that the total number of potential entrepreneurs (in the group ij, which we omit for the ease of exposition) is denoted by l,weget:su+se+e+u+b=l. Potential entrepreneurs, who are not business owners l−b, register start-up firms at rate δf(α)ifα>α 0. At the same time, businesses are destroyed at rate γ, which gives rise to the following dynamics: ˙ b(α)=δf(α)(l−b)−γb(α). Imposing the steady state condition 14 ˙ b(α) = 0 and integrating b(α) we can find the total number of 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 condition postulates a negative monotonous relationship between the entry threshold α0and the stock of small businesses b. Intuitively, a higher cut-off α0leadstoalower probability of starting a business 1 −F(α0), so the stock of small businesses bdeclines. Let G(α) be the equilibrium distribution of solo self-employed out of opportunity with respect to the quality of their product α. More precisely it is the accumulated stock of self-employed entrepreneurs with a product quality in the range [αs..α]. The dynamic equation for G(α) is given by: ˙ G(α)=(su+e+u)   =l−b−se δ(F(α)−F(αs)) −(γ+δ(1 −F(α)))G(α) (11) Unemployed entrepreneurs u, and those self-employed out of necessity su, stop searching for regular jobs, if they develop a product/service with quality above αs. Also employees in regular employment equit their jobs and become self-employed out of opportunity if they get a realization of αabove αs. So the first term in equation (11) is the inflow of entrepreneurs into solo self-employment out of opportunity. The second term is the outflow consisting of unsuccessful entrepreneurs dropping back into unemployment (at rate γ) and those who develop a better product (at rate δ(1 −F(α))). Imposing the steady state condition ˙ G(α) = 0 and taking into account that se=G(α0)weget: se=G(α0)= δ(F(α0)−F(αs)) [γ+δ(1 −F(α0))] γl [γ+δ(1 −F(αs))] (12) Next, consider the steady-state equation for employed potential entrepreneurs: ˙e=(u+su)Xλ(θ)−(¯γ+δ(1 −F(αs)))e=0 where the first term is the inflow which corresponds to all searching potential entrepreneurs (u+su) starting a regular job at rate Xλ(θ). Again, the second term is the outflow consisting of those losing regular jobs at rate ¯γor quitting their jobs voluntarily and becoming solo self-employed out of opportunity. Taking into account that u+su=l−b−se−e we get the equilibrium expression for e: e=Xλ(θ) [¯γ+Xλ(θ)+δ(1 −F(αs))] γl [(γ+δ(1 −F(αs))] (13) Further, let H(α) be the equilibrium distribution of solo self-employed out of necessity with respect to the quality of their product or service α. It is the accumulated stock of 15 self-employed with product qualities in the range [αu..α]. So we get: ˙ H(α)=uδ(F(α)−F(αu)) −(γ+δ(1 −F(α)) + Xλ(θ))H(α) The first term is the inflow and includes unemployed individuals developing product qualities above αuand starting self-employment. The second term is the outflow consisting of self-employed entrepreneurs taking a regular job (at rate Xλ(θ)), dropping back into unemployment (at rate γ) and developing a better product quality (at rate δ(1 −F(α))). Imposing again the steady state condition ˙ H(α) = 0 and taking into account that su=H(αs) we can find the equilibrium stock of potential entrepreneurs out of necessity suandinunemploymentu. We summarize these results in proposition 5: Proposition 5: The equilibrium number of solo self-employed out of necessity suand the number of unemployed potential entrepreneurs uare given 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))] Proposition 5 shows that, other things being equal, the stock suis decreasing in the cut-off αu. On the contrary, a higher αuis associated with a higher stock of unemployed entrepreneurs u. The distributions of solo self-employed with respect to the quality of their products αcan be found due to the fact that su(α)=H(α)andse(α)=G(α). The exact expressions are delegated to appendix A.4. 3.5 Wage setting In this section we address the determination of wages. Regular firms can be matched with regular workers or potential entrepreneurs seeking to take a paid job, however, small businesses only hire regular workers. This gives rise to several types of wage negotiations which we model by means of Nash bargaining. First, we describe the wage bargaining between regular firms and potential entrepreneurs. Bargaining with potential entrepreneurs: Consider a match between a regular firm and a potential entrepreneur and let the corresponding present value of a job be denoted by J, it becomes: rJ =y−¯ck−w−¯γ(J−V)−δ(1 −F(αs(w)))(J−V) where ¯ckcorresponds to the flow cost of capital for regular firms. This equation shows that the total job destruction rate associated with potential entrepreneurs is relatively high since there is a positive probability δ(1 −F(αs(w))) that they will quit the job and 16 enter self-employment. This reduces the value of the job surplus to the firm. In order to model wage bargaining between job applicants and regular firms we follow the approach in Gautier (2002). This approach assumes that applicants matched with an employer and negotiating over the wage stop searching for alternative jobs. In addition, we assume that they also disregard their activities in self-employment out of necessity, since paid employment is a superior state of income (i.e Es(α)<W ∀α<α s). However, they continue considering self-employment out of opportunity and the possibility of starting a business (which happens for α>α s) while negotiating with a regular employer. The advantage of this approach is that labour contracts are renegotiation proof, meaning that potential entrepreneurs receive the same wage win paid employment irrespective of their previous income in self-employment. Assuming additionally that potential entrepreneurs still enjoy the unemployment benefit zwhile bargaining, but no longer the stigma of failure h, gives rise to the following Nash bargaining problem:9 max ww(1 −t)−z r+¯γβ(y−¯ck−w) r+¯γ+δ(1 −F(αs(w)))1−β This equation shows that higher wages have an ambiguous effect on the present value of firms’ profits. On the one hand, there is the direct effect of higher labour costs reducing profits. But on the other hand, paying a higher wage reduces the probability that the potential entrepreneur employed in a regular job will quit into self-employment (i.e. higher αs(w)). This reduces the overall job destruction rate from the perspective of the firm and has a positive effect on the present value of profits. Proposition 6: The wage of potential entrepreneurs in paid employment is given by: w(1 −t)=β(y−¯ck)(1 −t)+(1−β)z+(1−β)(y−¯ck−w)(w(1 −t)−z)δf(αs) r+¯γ+δ(1 −F(αs)) ∂αs ∂w where ∂αs/∂w is given by equation (10). If the distribution of product qualities is uniform (f(α)=1)andγ≤¯γthen the wage is increasing in the productivity yand in the bargaining power βsuch that z≤w(1 −t)≤(y−¯ck)(1 −t). Proof: appendix A.5 This proposition presents conditions which are sufficient for the wage wto be increasing in the productivity yand the bargaining power β, however, these conditions are strong and the described properties of the wage hold for a broader range of parameter values. We follow the same approach and use the renegotiation-proof Nash bargaining for determining wages of regular workers in large and medium-size firms ( ¯w) and in small businesses (w0N,w0I,wCN,wCI). The subindex referes to the type of small business, for example, 0Nindicates wages paid by native small businesses to their employees, while the subindex 0Iindicates wages paid by immigrant small businesses. Further, the 9The present value of potential entrepreneurs in paid jobs Wand their disagreement value WDare presented in appendix A.5 17 subindex CN indicates wages paid by native high-skill businesses to low-skill employees, while the subindex CI indicates wages paid by immigrant high-skill businesses to their low-skill workers (engaged in cross-skill matching). In appendix A.5 we show that each wage is a weighted average of the respective productivity (¯y,y0N,y0I,yCN,yCI)andthe unemployment benefit ¯z. We use parameter β0for the bargaining power of workers in small businesses. All wages and productivities are specific to a particular demographic group of the individual ij, where the superscript ij was omitted for the ease of exposition. 3.6 Matching and free-entry In this section we describe matching between searching workers and vacancies in the market for regular jobs, as well as matching between searching workers and openings in small businesses. Figure 3 illustrates all the states and transitions of regular workers. Figure 3: Labour market states and transitions of regular workers ҧ݁௜ு ҧ݁௜௅ തݑ௜ு തݑ௜௅ ݁ைே ௜௅ ݁ைூ ௜ு ݁஼ூ ௜ ݁஼ே ௜݁ைே ௜ு ݁ைூ ௜௅ ܾூ௅ ݒ௅ݒு ܾேு ܾூு ܾே௅ Low-skill vacancies in regular firms High-skill vacancies in regular firms Low-skill small businesses High-skill small businesses Low-skill workers High-skill workers ܺ௜௅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 part of the diagram (red) corresponds to the cross-skill matching whereby low-skill regular workers apply for positions in high-skill small businesses. We use parameter κto describe the intensity of cross-skill matching.10 This parameter allows us to determine the number of regular workers searching and applying for positions in small businesses given by Σj 0.Σ L 0consists of unemployed regular low-skill workers ¯uiL weighted by their search intensities xiL,whereasΣ H 0consists of unemployed regular high-skill workers ¯uiH weighted by their search intensities xiH as well as regular low-skill workers weighted by their search intensities κxiL. With this notation we get: Σj 0=xIj¯uIj +xNj¯uNj +1Hκ(xIL¯uIL +xNL¯uNL) where 1Htakes value 1 for j=Hand value 0 for j=L. 10A doctor hiring a receptionist or a tax-consultant hiring a secretary are the real life examples of the type of cross-skill matching our model captures. 18 Next, consider low-skill small businesses. From proposition 4 we know that the average number of immigrant employees per small business is given by ¯q(θL 0)μ/γiL,whereireflects the ethnic group of the business owner. At the same time, the average number of native employees is ¯q(θL 0)(1−μ)/γiL. Given that the number of small businesses in this group is equal to biL, we can find the number of immigrant and native workers employed in these businesses eIL 0iand eNL 0i: ¯q(θL 0) γiL biL =eIL 0i μ=eNL 0i 1−μwhere μ=xIL¯uIL xNL¯uNL +xIL¯uIL (14) Here the superscript i=N,I refers to the ethnic background of the worker, while the subscript refers to the ethnic background of the entrepreneur and 0 stands for small businesses. Next consider high-skill businesses. Here the average number of immigrant high-skill employees is given by ¯q(θH 0)μIH/(γiH ), while the average number of native high-skill workers is ¯q(θH 0)μNH/(γiH ). In a similar way, we can use information about the average number of immigrant and native low-skill employees. Multiplying the average number of employees per business with the number of businesses biH yields the following: ¯q(θH 0) γiH biH =eIH 0i μIH =eNH 0i μNH =eI Ci μIL =eN Ci μNL (15) where the probabilities of hiring an employee of type iH and iL from the perspective of the business owner are given by: μiH =xiH ¯uiH i=I,N xiH ¯uiH +κxiL ¯uiL and μiL =κxiL ¯uiL i=I,N xiH ¯uiH +κxiL ¯uiL These probabilities do not depend on the ethnic background of the business owner. Further, we write down the steady state equation for employees in regular jobs: Xijλ(θj)¯uij =¯γij ¯eij and take into account that the total number of workers employed in small businesses is given by: ¯eij 0=eij 0N+eij 0I+1L(ei CN +ei CI), where the indicator function 1Ltakes value one for j=Land zero otherwise. This allows us to find the equilibrium unemployment rate of regular workers given by: ¯uij =dij −lij −¯eij −¯eij 0.Theexact expression is presented in appendix A.6. Finally, we consider the vacancy posting conditions for regular jobs. Recall that ¯c=¯ch+¯ckis the total cost of capital and posting facing regular firms. Using this notation we write down the present value equation for V, which is the present value of expected profits associated with an open vacancy, and impose the free-entry condition V= 0 to get: ¯c q(θ)= i=I,N Xi¯ui i=I,N Xi(¯ui+ui+si u)   matching with regular workers (¯ Ji−V)+ Xi(ui+si u) i=I,N Xi(¯ui+ui+si u)   matching with pot. entrepreneurs (Ji−V) (16) 19 Thus, regular firms create vacancies up to the point, where the expected cost of an open vacancy is equal to the expected present value of profits from a filled job. Writing down these equations for j=L, H allows us to find the equilibrium vacancies vLand vH. 3.7 Production of the final good and welfare The final good is produced using capital Kand a composite good Zusing the constant returns to scale technology (1). The composite good Zis produced using two intermediate inputs, YLand YHaccording to the CES production function (2), where Yjis a linear aggregate of output quantities produced by regular workers and potential entrepreneurs of type j, so it can be calculated 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) where the first three terms include output quantities of self-employed entrepreneurs and business owners, ϕij eij is the output produced by potential entrepreneurs employed in regular jobs, ¯ϕij ¯eij – output produced by workers in regular jobs, and the remaining terms constitute the output produced by workers employed in small businesses. Finally, theindicatorvariabletakesvalue1forj=Land value zero for j=H. Since capital as well as the two intermediate goods are supplied in competitive markets, their prices Rand Pjare equal to the marginal productivities: 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) where Ris the exogenous price of capital including the risk-free interest rate and the cost of capital depreciation. Finally, let ¯ Ωij, denote social welfare of regular workers and Ωij denote the welfare of potential entrepreneurs in the demographic group ij,where i=I,N,j=L, H. Since potential entrepreneurs are characterized by various qualities of the product α, we calculate an average product quality in each group: ¯αus =αs αu αsu(α) su dα ¯αs0=α0 αs αse(α) se dα ¯α01 =¯α α0 αb(α) bdα Variable ¯αus stands for the average product quality of solo self-employed out of necessity distributed in the range [αu...αs]. Variable ¯αs0denotes the average product quality of solo self-employed out of opportunity distributed in the range [αs...α0] and, finally, ¯α01 corresponds to the average product quality of business owners distributed in the range 20 [α0...¯α]. Based on these definitions, the welfare values for all worker groups can be obtained as (we suppress the upper index ij for the ease of exposition): ¯ Ω= 1 d−l(¯u(¯z−h)+(1−t)(¯e¯w+e0Nw0N+e0Iw0I+1L(eCNwCN +eCIwCI))) + T Ω=1 lu(z−h)+(1−t)(ew +suσ¯αus +seσ¯αs0+bσ¯α01)+b−c+¯q(θ0) γπ(r+γ)   net profit from coworkers +T where the indicator function 1Ltakes value one for j=Land zero otherwise and variable Tis the lump-sum transfer from the public budget. The cash inflow into the public budget consists of revenues from labour income taxes of regular workers and potential entrepreneurs BRtand corporate taxes paid on flow profits by small businesses and regular jobs BRτ. The outflow from the public budget consists of expenses for unemployment benefits for all demographic groups BE. Given that total revenues exceed substantially the expenses for unemployment benefits, the surplus of the budget is equally split and distributed as a lump-sum transfer Tacross all worker groups. The revenues and expenses are calculated as follows: BRt=t ij ¯e¯w+e0Nw0N+e0Iw0I+1L(eCNwCN +eCIwCI)   income taxes of regular workers +ew +suσ¯αus +seσ¯αs0+bσ¯α01   income taxes of potential entrepreneurs  BRτ=τ ij b¯q(θ0) γ π(r+γ) 1−τ   small businesses +(¯y−¯ck−¯w)¯e+(y−¯ck−w)e   regular jobs  BE = ij zu +¯z¯uT=1 ij dBRt+BRτ−BE(20) where ij dis the total size of the population. It is normalized to 1 in the benchmark calibration, but will be larger than 1 upon the immigration shock. 4Data We use data from the German Socio-Economic Panel (SOEP) waves 2000-2017. SOEP is a representative panel of households and individuals in Germany. It provides detailed information about the respondent’s ethnicity, qualifications, wages, size of employer firm, employment status, and the possibility of self-employment and entrepreneurship. Moreover, it contains information about self-employed entrepreneurs’ business size (i.e., the number of coworkers). We restrict the sample to labour force participants working full/part-time or actively searching for jobs (workers who report being registered as unemployed at the federal employment agency). Non-participants, retired, marginally employed or military 21 personnel and those below 17 years of age are dropped from the sample. This yields an unbalanced panel with 302686 person-year observations over the spell of 18 years. We define as native (N) an individual who is born in Germany or has German nationality since birth and is not an ethnic German from Eastern Europe. All second-generation immigrants born in Germany are considered natives. Workers with at least 13 years of schooling are defined as high-skilled (H) while others are considered low-skilled (L). 13 years of schooling correspond to the upper secondary schooling degree (”Abitur”) and grant direct access to tertiary education in Germany. High-skilled immigrants form the smallest fraction of the sample. The average share of high and low-skilled natives in the sample is 32.6% and 51.0%, respectively. In comparison, the high and low-skilled immigrants form 13.7% and 2.7% of the sample. Table 1 provides the sample profile. We define as potential entrepreneurs the individuals who are observed at least once in the data as self-employed, freelance professionals, or as small business owners (with or without coworkers). Their stock is denoted by lij in the model. Individuals who are never observed as business owners or in self-employment are considered regular workers (low entrepreneurial spirit). Their stock is denoted by dij −lij . We may underestimate the share of potential entrepreneurs as some individuals may have been in entrepreneurship before participating in the survey, while other potential entrepreneurs may have dropped out of the sample before being observed in an entrepreneurial state. The attrition rates could be particularly high for immigrants due to return migration. However, it is a reasonable measure given that there is no other way to deduce entrepreneurial abilities due to the lack of detailed information about the interest in entrepreneurship or efforts (both successful and unsuccessful) to open up a business. Table 1 shows the distribution of all workers in the sample across the four demographic groups and labour market states. High-skill native workers are least likely to be employed in small businesses (15.3%). This share is slightly higher for high-skill immigrant workers (18.3%), whereas it is much higher for low-skill workers (22.5−23.5%). It is interesting that potential entrepreneurs have much lower unemployment rates than workers without entrepreneurial abilities. Low-skilled immigrant workers have the highest unemployment rates. Both natives and immigrants in the high-skill group have the highest shares of active entrepreneurs (bij +sij)/lij. Further, SOEP provides information on solo self-employed entrepreneurs sij +bij 0and business owners with coworkers bij −bij 0. The last group is split into business owners with less than nine coworkers 9 n=1 bnand those with more than nine coworkers. 59 −60% of native and immigrant potential business people with low skills are solo entrepreneurs, and 36 −37% of them manage small businesses with 1 to 9 coworkers. This differs in the high-skill group, where only 46% of immigrant entrepreneurs are self-employed, and 43% are managing small businesses. 22 This development comes along with a lower welfare of low-skill individuals ΩiL and ¯ ΩiL and an increase in welfare of high-skill individuals ΩiH and ¯ ΩiH,i=I,N (Table 3, row-A). Moreover, it fosters the reallocation of native potential entrepreneurs with low skills from regular paid jobs to solo self-employment. Table 4 column (2) shows that the fraction of native potential entrepreneurs employed in regular jobs falls by 5.7%, and their wages also fall substantially in column (3). At the same time, their fraction in solo self-employment (column (4)) is increasing by 8.9%. The losses in the welfare of lowskill entrepreneurs (Table 3, row-A) are smaller compared to regular workers because the probability of hiring employees ¯q(θL) is increasing (note a lower θL 0), which moderates the negative effect of lower productivity on business profits. For the same reason, high-skill entrepreneurs’ welfare gains are higher than high-skill regular workers. In step (B), capital Kadjusts endogenously. Firms in the final goods sector increase capital K, which has a positive effect on the productivity and welfare of all worker groups via changes in prices and market tightness. Due to capital adjustment, the welfare losses in step (A) are slightly compensated for low-skill workers. In step (C), we update the lump-sum budget transfer Tand welfare values. This transfer is measured per person and is lower in the post-immigration equilibrium. There are two reasons for this reduction. First, a composition effect is emerging because the net fiscal contribution of an average low-skill immigrant is lower than that of an average native. Second, there is an endogenous adjustment of equilibrium variables described in table 2 reducing wages of low-skill workers and their net fiscal contribution below the pre-immigration level. A combination of these effects leads to a lower lump-sum transfer per person 0.486 <0.493 in the post-immigration equilibrium, reducing the welfare of all worker groups (Table 3, row-C). In the final step (D), we allow endogenous adjustment of the entrepreneurial business entry cutoffs αij 0. This is the novel part of our model, so we zoom in on the job creation process and potential entrepreneurs’ business entry decisions in table 4 starting with the low-skill submarket. On the one hand, hiring workers for open positions becomes easier (d¯q>0). However, on the other hand, a drop in the price of the low-skill intermediate good makes workers in low-skill businesses less productive and leads to a lower profit per person (dπi<0, i=I,N). Table 4 shows that the first effect is dominating for businesses operated by immigrant entrepreneurs. Their profits in column (8) increase, making such businesses more attractive for their owners: d¯qπI=πId¯q+¯qdπI>0 As a response, we observe a 13% increase in the fraction of immigrant potential entrepreneurs operating small businesses in column (6), inducing a reallocation of immigrant potential entrepreneurs away from regular jobs and solo self-employment towards operating small businesses. These effects are associated with a sizable increase in the 29 Table 3: Increase in immigration by 20%, low-skill scenario Low-skilled High-skilled Regular workers Pot. entrepreneurs Regular workers Pot. entrepreneurs 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 adjustment (D) -1.27% -1.37% -2.04% +3.15% +1.00% +1.08% +0.34% +3.10% Representative worker: -1.59% Representative worker: +0.9% Incumbent worker: -1.27% Representative worker: -0.88% Incumbent immigrant: -0.47% Incumbent worker: -0.37% Note: The table decomposes the impact of low-skill migration on welfare of different demographic groups in several steps. Row (D) shows the change in welfare after a full adjustment of endogenous variables in the post-migration equilibrium. The second last panel reports welfare changes for a representative/incumbent worker in a given skill group. The last panel reports welfare changes for a representative/incumbent worker in the economy. welfare of immigrant potential entrepreneurs ΩIL in table 3. Considering the situation of native businesses, we find that the drop in productivity is dominating and leads to a slight decrease in profits in column (8): d¯qπN=πNd¯q+¯qdπN<0 Thus, operating small businesses becomes less attractive for native entrepreneurs. Their fraction in column (6) is falling by 3.2% inducing a reallocation away from regular employment and businesses towards solo self-employment. These effects are associated with a decrease in the welfare of native potential entrepreneurs ΩNL. The asymmetric response of small businesses towards the immigration shock can be explained by the fact that immigrant businesses are more profitable on average, meaning that the expected profits per recruitment are also higher (πI>π N, inline with the empirical data in table 11 in the appendix). This makes immigrant businesses more sensitive to the job-filling rate since πId¯q>π Nd¯q. The profits of native entrepreneurs are lower, making them less responsive to changes in the probability of filling positions. Next, we consider the high-skill submarket. High-skill workers become more productive, reflected in the higher price of the high-skill intermediate good PH.Thisboostsjob creation in the high-skill submarket, leading to a higher market tightness θHand a higher 30 Table 4: Detailed changes in the steady-state distribution of potential entrepreneurs upon a 20% increase in low-skill immigration (1) (2) (3) (4) (5) (6) (7) (8) Group u/l e/l w (su+se)/l σ¯αu0b/l σ¯α01 ¯q(θ0)π/γ Low-skill Natives 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 Immigr. 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 Natives 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 Immigr. 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 Note: ¯αu0is the average entrepreneurial ability in the range [αu..α0], calculated as (su¯αus + se¯αs0)/(su+se). ¯α01 is the average entrepreneurial ability in the range [α0..¯α]. job-finding rate. Thus, there is a sizable increase in the fraction of high-skill potential entrepreneurs employed in regular paid jobs in column (2): 7.2% for natives and 5.6% for immigrant potential entrepreneurs. This process is accompanied by increasing wages in column (3) of table 4 and leads to the increased welfare of regular high-skill workers ¯ ΩIH and ¯ ΩNH in table 3. Higher productivity of coworkers is also beneficial for high-skill small businesses, but the productivity of low-skill coworkers employed in high-skill businesses is decreasing. We find that the second effect dominates, so the average productivity of coworkers in small businesses operated by high-skill entrepreneurs decreases moderately. However, at the same time, filling positions becomes easier, especially low-skill positions; thus, the market tightness θH 0is decreasing, while the job-filling rate is increasing. Again, we find that immigrant and native entrepreneurs operating businesses are asymmetrically affected. Column (8) of table 4 shows that the positive effect of a higher job-filling rate is dominating for immigrant entrepreneurs, and there is a slight increase in their profits. This makes immigrant businesses more attractive for their owners and induces the reallocation of immigrant entrepreneurs from solo self-employment to operating small businesses equal to 3.7%. Overall, we observe a sizable increase in the welfare of highskill immigrant entrepreneurs ΩIH in table 3. This is partially due to higher profits from operating small businesses and the reallocation from low-income activities in solo self-employment to regular jobs. More specifically, table 4 shows that the income of immigrant self-employed (1.199) is well below their wages in regular paid jobs (1.309). For native high-skill entrepreneurs, the situation is different. The lower productivity of an average coworker neutralizes the positive effect of a higher job-filling rate. Thus, 31 the profits and the fraction of native high-skill business owners are hardly changing, and the only meaningful change is a shift towards regular jobs. However, the difference in income between these two states is negligibly tiny, compare columns (5) and (3) in table 4, so there is only a slight increase in the welfare of native entrepreneurs ΩNH in table 3. Detailed wage and employment changes for regular workers are presented in table 14 in appendix C. Wages of low skill regular workers fall (column (3)); moreover, finding jobs becomes more difficult since both market tightness variables θL 0and θLare falling due to the stronger competition among workers. This leads to slightly higher unemployment rates in column (1) of table 14 and a moderate reduction in welfare ¯ ΩNL and ¯ ΩIL. Our results suggest a marginal decrease of about 0.5% in the welfare of an incumbent immigrant. A moderate decline of 0.88% is observed in the welfare of a representative worker. It reflects a combination of lower welfare of incumbent workers reduced by 0.37% and a composition effect since a representative worker becomes “more immigrant” and “more low skilled” on average. At the same time, we find that the average estimate hides substantial heterogeneity of the effect across worker groups. Contrary to the previous studies reporting wage and welfare losses for the incumbent immigrant population (D’Amuri et al. (2010), Ottaviano and Peri (2012)), we find that immigrant entrepreneurs experience sizable welfare gains from a new immigration wave equal to 3.1%. 5.2 Cooperation with India Germany signed the “Migration and Mobility Partnership Agreement” (MMPA) with India in December 2022. It is the first migration agreement between Germany and a non-EU country. The agreement aims to promote the mobility of high-skill immigrants from India to Germany. Recent developments in October, 2024 led Germany to agree to increase the annual number of visas granted to skilled Indian workers from 20,000 to 90,000. Given the increasing refugee migration to the developed world, we expect the low-skill scenario to dominate. However, policies facilitating high-skill immigration in Germany may, at best, result in skill-neutral immigration. These developments motivate the experiment of a skill-neutral immigration scenario to analyze the possible effects of increased Indian immigration to Germany. Therefore, table 15 in appendix C.1 reports the implications of a 20% skill-neutral migrant influx. Our analysis suggests that in the case of skill-neutral immigration an incumbent worker will experience a smaller welfare loss (−0.27%) compared to the low skill scenario (−0.37%). Moreover, the welfare of incumbent immigrant workers will increase (+0.38%). The reason is that hiring coworkers becomes easier for all types of small businesses, boosting immigrant entrepreneurs’ welfare. Combined with higher wages and the welfare of high-skill immigrant workers, this effect is dominating despite a slight reduction in the welfare of low-skill immigrants. The welfare loss of a representative worker will also be smaller (−0.66%) than the one experienced in a low-skill scenario (−0.88%). 32 5.3 Value of immigrant entrepreneurship In this section, we conduct a counterfactual experiment on the legal barriers to selfemployment and entrepreneurship for immigrants. We set δIL =0andδIH = 0, implying that the legal entry barrier into self-employment and business ownership is infinitely high for immigrant potential entrepreneurs so that none of them are observed in the states sIj and bIj,j=L, H. We consider the benchmark model without an immigration shock and analyze how the lack of immigrant entrepreneurial activity affects the welfare of workers compared to the benchmark model with the option of entrepreneurship. The goal of this experiment is twofold. First, it allows us to estimate the option value of entrepreneurship for immigrants. Second, we can estimate the spillover effects of immigrant entrepreneurship for all other groups producing insights about the entry barriers policies for immigrant small businesses. The results are summarized in table 5, where line (0) corresponds to the benchmark equilibrium and line (E) contains welfare changes for all worker groups in the counterfactual setting with entry barriers. Table 5: Welfare changes in the counterfactual scenario without immigrant entrepreneurship Low-skilled High-skilled Regular workers Pot. entrepreneurs Regular workers Pot. entrepreneurs 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% Note: Row (0) shows the welfare of workers in the benchmark model. Row (E) shows the change in welfare in the counterfactual case of a complete ban on immigrant entrepreneurship. Table 5 shows that the welfare losses of high-skill potential entrepreneurs are dramatic and amount to 30.5% of their welfare. This is primarily driven by unemployment increasing from 3.9% to 11% (see table 16 in the appendix). The losses of low-skill potential entrepreneurs are also large, reaching 15.2% and caused by the corresponding increase in unemployment from 4.9% to 18%. These findings indicate a very high value of the entrepreneurship option for immigrant individuals with a high entrepreneurial spirit. They also suggest that entrepreneurship is an efficient way of reducing unemployment for immigrants. Further, we observe moderate negative spillovers for regular workers with reduced welfare. These welfare losses suggest that policies reducing entry barriers for immigrant entrepreneurs are likely to be beneficial for regular workers (native and immigrant). Their welfare is higher in the benchmark scenario with immigrant entrepreneurship. The reasons for higher welfare are threefold: first, immigrant potential entrepreneurs entering self-employment reduce competition for regular jobs; second, immigrant small businesses create new working places for all worker groups; and third, the lump-sum transfer T 33 is higher due to higher net fiscal contributions of immigrants. At the same time, table 5 reveals that the welfare of native potential entrepreneurs is lower in the benchmark scenario with immigrant entrepreneurship. The reason is stronger competition with immigrant businesses, suggesting that entry barriers for immigrant entrepreneurs shield native businesses from competitive forces. Germany introduced several amendments in its Residence Act for non-German entrepreneurs between 2004 and 2012. These amendments relaxed the conditions required for entrepreneurial ventures and offered incentives to foreigners to invest in Germany.16 Our experiment helps evaluate the effectiveness of these policies. 5.4 Ethnic segregation in small businesses The literature on social networks documents ethnic homophily, meaning a higher probability of creating social ties with individuals of the same ethnic origin (McPherson et al. (2001)). Dustmann et al. (2016) reports for Germany that a new hire is more likely to be an immigrant if there is already a large share of immigrant workers in the firm. Alaverdyan and Zaharieva (2022) show that 44% of immigrants in Germany find their jobs via social contacts. Additionally, ethnic segregation could be an outcome of hiring discrimination. A field experiment conducted by Kaas and Manger (2012) finds that a foreign name reduces the average probability of a callback and that differential treatment of native and immigrant workers is particularly strong and significant in smaller firms. Yet another reason for ethnic segregation could be that small firms are often family businesses. This section investigates the implications of ethnic segregation in small businesses. Given the empirical evidence in Kaas and Manger (2012) that hiring discrimination is stronger in small firms and the findings in Goldberg et al. (1995) that it is more (less) pronounced in low (high) skill jobs, we focus on the ethnic segregation in low-skill small businesses for the following analysis. Remaining agnostic about the reason for ethnic segregation, we introduce parameter ψ>0, capturing the co-ethnic bias in matching. Table 6 shows that higher values of ψ increase the share of matches between native workers and native-owned small businesses and the share of matches between immigrant workers and immigrant-owned businesses (on the matrix’s main diagonal). At the same time, it reduces the share of matches between workers and business owners with different ethnic origins (off the diagonal). The benchmark equilibrium with unbiased matching can be recovered when ψ=0,whereμ is the probability of hiring an immigrant coworker identical for both types of businesses, and 1 −μis the probability of hiring a native coworker. Note that parameter ψonly influences the shares of matches of a particular type but does not enter the expression for the total number of matches created per unit time. 16Residence Act 2004, Act to Implement Residenceand Asylum-Related Directives of the European Union 2007, Labour Migration Control Act 2009, Residence Act 1st August 2012 34 Table 6: Matching bias ψgiving rise to ethnic segregation in small businesses Biased pairwise matching Immigrant coworker Native coworker Sum Immigrant business owner (μ+ψ)bIL bNL+bIL (1 −μ−ψ)bIL bNL+bIL bIL bNL+bIL Native business owner (μ−ψ)bNL bNL+bIL (1 −μ+ψ)bNL bNL+bIL bNL bNL+bIL We augment the corresponding equations for the profits of small businesses in the following way: πI=(μ+ψ)ΔI I+(1−μ−ψ)ΔN IπN=(μ−ψ)ΔI N+(1−μ+ψ)ΔN N where the upper (lower) index indicates the type of the worker (business owner). In addition, we adjust equations for the numbers of workers 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 consider a marginal change in ethnic segregation equal to 1% and set ψ=0.01. The implications of ethnic segregation for low-skill businesses are as follows. First, native workers are more productive on average. So, it leads to a higher specialization on the more productive group of native workers in native businesses. This is associated with higher profits, higher business entry and higher welfare of native entrepreneurs (see table 7 for welfare effects and table 17 in Appendix C.2 for further details). Second, there is a higher specialization of immigrant businesses on the less productive group of immigrant workers leading to lower profits. As a result immigrant entrepreneurs move intensively to solo selfemployment, which is associated with lower welfare. Third, changes in the composition of small businesses are associated with lower earnings of native regular workers and lower welfare despite a higher probability of getting jobs in native businesses. Furthermore, we find moderate spillovers of ethnic segregation for high-skill businesses. On the one hand, cross-skill matching implies that high-skill businesses compete with low-skill businesses for low-skill workers. Tighter competition for low-skill native workers reduces profits and welfare of native high-skill entrepreneurs. On the other hand, difficulties in hiring los skill native workers imply that vacancies in high-skill businesses are increasingly filled with high-skill applicants raising the productivity of an average employee. The latter effect is dominating for immigrant high-skill businesses leading to higher profits and a sizable increase in their welfare ΩIH. Overall, our findings in this section indicate that ethnic segregation could be beneficial to native low-skill businesses but it seems to be detrimental to the profits and entry of immigrant businesses in the same submarket leading to the underutilization of entrepreneurial potential in this group. 35 Table 7: Welfare changes upon a marginal increase in ethnic segregation, ψ=0.01 Low-skilled High-skilled Regular workers Pot. entrepreneurs Regular workers Pot. entrepreneurs 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% Note: Row (0) shows the welfare of workers in the benchmark model. Row (F) shows the change in welfare upon ethnic segregation in low-skill businesses, ψ=0.01. 6Conclusion In this paper, we develop a unified framework that incorporates the dual role of immigrants as workers and entrepreneurs. As workers, migrants compete with native workers for jobs in the regular job market. In contrast, as entrepreneurs, they compete with native entrepreneurs but create employment opportunities for other natives and migrants looking for jobs. The theoretical setup combined with survey data from the SOEP is used to quantify the impact of low-skill immigration on small businesses, unemployment rates, wage structure, and welfare of native and incumbent immigrants in Germany. We consider a low-skilled migration shock similar in intensity to the refugee wave of 2012 −2017. Consistent with the literature, we find that it is associated with increased unemployment and reduced wages for all low-skilled workers, negatively affecting their welfare. Similarly, the high-skilled workers gain from such an inflow. Nonetheless, we extend the literature by providing a more detailed picture of the effects of migration on small businesses and entrepreneurs. Contrary to the existing literature, suggesting a negative impact of migration on incumbent migrants, we find that incumbent immigrant entrepreneurs in both skill groups gain from immigration and expand their entrepreneurial activities. This amplifies the welfare gains of high-skill regular workers and reduces the welfare losses of the low-skilled. Yet, we document an adverse effect on native entrepreneurs, especially the low-skilled, losing welfare from the lower productivity of their coworkers and facing stronger recruitment competition from immigrant small businesses. We also find that recent German-Indian cooperation on skilled-worker mobility can reduce the losses from low-skilled migration. The counterfactual experiment suggests that restricting the entry of immigrants into entrepreneurship leads to an overall welfare loss for the economy. All demographic groups incur welfare losses except for the native entrepreneurs who gain from reduced competition with immigrant businesses. 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B Empirical data B.1 Mincer earnings regressions The information on gross monthly wage/income for regular workers and potential entrepreneurs is available in SOEP. We use data for 2000-2017 and run the following Mincer earnings regressions for regular workers: ln wit =φ0+φ1Nit +φ2FSit +φ3HSit +φ4Nit ×FSit +φ5Nit ×HSit +φ6HSit ×FSit +φ7Nit ×HSit ×FSit +φ8t+ςit Where wit is the wage of worker iobserved in year t.Nit is the indicator function that takes the value 1 for natives, FSit is the indicator function with value 1 for large firms, HSit takes value 1 for high-skill workers. We introduce interaction terms (Nit ×FSit)and (HSit ×FSit) in order to capture variation in the effect of firm size on wages by ethnicity and skill. Similarly, (Nit ×HSit) captures the fact that the return to schooling could be different for native and immigrant workers. For the potential entrepreneurs we run the following regression ln wit =φ0+φ1Nit +φ2HSit +φ3Nit ×HSit + 3  l=1 φ4lPEl it + 3  l=1 φ5lNit ×PEl it + 3  l=1 φ6lHSit ×PEl it + 3  l=1 φ7lHSit ×PEl it ×Nit +φ8t+it where PEl it is the indicator function, such that l= 1 for potential entrepreneurs in solo self-employment, l= 2 for business owners with less than 9 coworkers, l= 3 for business owners with more than 9 coworkers. Potential entrepreneurs in paid employment serve as a reference category. The interaction terms Nit ×PEl it and HSit ×PEl it capture the ethnicity specific and skill specific fixed effects for entrepreneurs if different economic states. Nit ×HSit captures the skill fixed effects specific to the two ethnic groups. The coefficients from both regressions are summarized in tables 10 and 11 respectively. We use these results to predict gross earnings of different worker groups. These are used as target moments for the calibration of productivities of workers and the related parameters. 45 Table 10: Wage regression for regular workers, SOEP 2000-2017 Variable Coefficient Standard error Predicted ln(w) Normalized wage Native 0.142∗∗∗ (0.012) ¯eNH 0: 7.25 wNH 0=1.295 Fsize 0.609∗∗∗ (0.012) eNH:7.93 ¯wNH =2.557 Native ×Fsize -.064∗∗∗ (0.014) ¯eNL 0: 6.99 wNL 0=1 HSkill 0.251∗∗∗ (0.029) ¯eNL:7.53 ¯wNL =1.715 Native ×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 Native ×Fsize ×HSkill 0.086∗∗ (0.034) ¯eIL 0: 6.85 wIL 0=0.870 Constant 6.779∗∗∗ (0.013) ¯eIL:7.46 ¯wIL =1.599 Observations 180699 ∗p<0.05, ∗∗ p<0.01, ∗∗∗ p<0.001 Fsize = 1 for large firm with more than 20 workers Table 11: Wage regression for potential entrepreneurs, SOEP 2000-2017 Variable Coefficient Standard error Predicted ln(w) Normalized wage/profit PE type1-0.009 (0.043) sNH: 7.43 1.551 PE type20.770∗∗∗ ( 0.048) sNL: 7.26 1.309 PE type31.078∗∗∗ (0.119) bNH <9: 8.34 3.854 HSkill 0.049 (0.060) bNL <9: 7.89 2.458 PE type1×HSkill 0 .131 (0.082) bNH >9: 8.71 5.580 PE type2×HSkill 0 .460∗∗∗ (0.091) bNL >9: 8.37 3.972 PE type3×HSkill 0.182 (0.191) eNH: 7.62 1.876 Native -0.018 (0.034) eNL: 7.19 1.220 PE type1×Native 0.081∗(0.046) sIH: 7.38 1.476 PE type2×Native -0.077 (0.052) sIL: 7.20 1.232 PE type3×Native 0.101 (0.126) bIH <9: 8.50 4.523 HSkill ×Native 0.383∗∗∗ (0.063) bIL <9: 7.99 2.716 PE type1×HSkill ×Native -0.398∗∗∗ (0.085) bIH >9: 8.52 4.614 PE type2×HSkill ×Native -0.443∗∗∗ (0.095) bIL >9: 8.29 3.666 PE type3×HSkill ×Native -0.272 (0.199) eIH: 7.26 1.309 Constant 7.111∗∗∗ (0.038) eIL: 7.21 1.245 Observations 37831 ∗p<0.05, ∗∗ p<0.01, ∗∗∗ p<0.001 PE type1= Solo self-employed or helpers in family business, PE type2= self-employed with less than 9 coworkers PE type3= self-employed with more than 9 coworkers, PE type4=inpaidemployment Table 12: Average tenure for different demographic groups of workers Group Tenure Regular workers, immigrants average tenure 8.781 Regular workers, native average tenure 11.547 Regular workers, average tenure (native and immigrants combined) 8.237 Regular workers, small firms natives average tenure 8.504 Regular workers, small firms natives average tenure 6.750 B.2 Bargaining power in small firms Combining information on wages of workers in small firms and the corresponding profits of small businesses we obtain the bargaining power parameter β0. More specifically, for low-skill businesses we set the following expressions equal to the pre-tax profits predicted from a Mincer regression: σ1 α0 f(α) 1−F(α0)dα −c   individual earnings +γ+¯q(θ0) γ (1 −β0) β0(1 −t)μ(wI 0(1 −t)−¯zI)) + (1 −μ)(wN 0(1 −t)−¯zN)   average profit per coworker 46 where (γ+¯q(θ0))/γ is the average number of coworkers conditional on hiring at least one. For high-skill businesses we extend the expression to account for cross-skill matching. Based on these target values for profits we find βL 0=0.456 and βH 0=0.422. B.3 Matching function The Federal Employment Office (Bundesagentur f¨ur Arbeit) data includes information on the absolute number of unemployed, vacancies and vacancy durations (in days) which are not available in the SOEP survey. In total there 228 monthly observations. We use this data to construct an economy wide average market tightness (θt=Vt Ut) and the hiring rate (q(θt). These variables are illustrated on Fig 5. The upper left panel of this figure shows a sharp increase of the average vacancy duration between the years 2000 and 2018. Whereas it was only 41.5 days on average in the year 2000, it almost tripled and reached a level 112 days by 2018. The top right panel of figure 5 shows the corresponding Beveridge curve for Germany showing a stable negative relationship between unemployment and vacancies. The bottom left panel shows the market tightness, while the aggregate job-filling rate q(θ) is illustrated in the bottom right panel of figure 5. Using this information we estimate the following regression: ln q(θt)=cst −ζln θt+Year+ιt(22) We control for time fixed effects by introducing a dummy for each year. This regression gives us a value of the slope parameter ζequal to 0.47. Figure 5: Vacancy duration and market tightness. Note: Authors’ calculations using statistical information of the Federal Employment Office (Bundesagentur f¨ur Arbeit) between January 2000 and December 2018. 47 Table 13: Parameters calibrated using SOEP data 2000-2017 Prm. Empirical moment/target Definition and calibrated values NL IL NH IH NL IL NH IH ¯γAverage tenure of regular workers Regular job destruction rate 11.55 8.78 11.55 8.78 0.0198 0.0270 0.0206 0.0269 γShare of workers in small businesses e0/(e0+¯e)Business destruction/exit rate 0.265 0.270 0.165 0.212 0.0296 0.0358 0.0305 0.0292 δShare of active entrepreneurs (b+s)/l Transition rate to entrepreneurship 0.547 0.525 0.568 0.577 0.5893 0.5355 1.1149 0.5173 xUnempl. rate of immigrant workers ¯u/(d−l)Search intensity for small businesses - 0.141 - 0.091 1 0.5713 1 0.2851 XUnempl. rate of immigrant pot. entrepreneurs u/l Search intensity for regular jobs - 0.049 - 0.039 1 0.7593 1 0.2750 cShare of solo-entrepreneurs (b0+s)/(b+s)Flow cost of a small business 0.586 0.607 0.591 0.459 1.1636 1.2919 2.2448 3.0985 ςBusinesses with 1-9 coworkers 9 n=1 bn/(b+s)Entrepreneurial productivity 0.366 0.362 0.326 0.425 0.2499 0.255 0.3703 0.2635 ϕ0NProfits of small businesses with coworkers Quantities in small (native) businesses 2.63 2.77 4.20 4.52 0.2973 0.2398 0.4109 0.3363 ϕ0IAv. wages in small businesses ¯w0Quantities in small (immigrant) businesses 1 0.8674 1.2950 1.1144 0.3437 0.3097 0.5293 0.4227 ¯ϕAv. wages of workers in regular jobs ¯wQuantities of workers in regular jobs 1.625 1.492 2.940 2.630 0.9727 1 0.9157 1 ϕWages of pot. entrepreneurs in regular jobs wQuantities of pot. entrepr. in regular jobs 1.222 1.246 1.884 1.309 0.8954 0.9004 0.8619 0.7440 z60% replacement rate in the 1st year Unemployment benefits of pot. entrepreneurs and ALG II assistance afterwords 0.3719 0.3723 0.3757 0.3709 ¯z60% replacement rate in the 1st year Unemployment benefits of regular workers and ALG II assistance afterwords 0.3838 0.3809 0.3948 0.3869 MUnempl. rate of native entrepreneurs u/l Matching multiplier, regular jobs 0.035 - 0.014 - 0.5319 0.9955 ¯ MUnempl. rate of native workers ¯u/(d−l)Matching multiplier, small businesses 0.085 - 0.022 - 0.0748 0.1809 ¯ckAverage job-filling rate q(θ)Capital cost in regular firms 1.5500 1.2398 3.3821 2.5642 chRebien, Stops, Zaharieva (2020) Vacancy posting cost 0.7431 2.3344 β0Assumption wN 0I/wI 0I=¯wN/¯wIBargaining power of workers in small firms 1.0819 1.1905 0.4564 0.4222 rAnnual discount rate = 5% (Quarterly) Discount rate 0.0125 ηChassamboulli and Palivos (2014) Elasticity of subst. between Kand Z Battisti et al. (2018) 0.350 ρOttaviano and Peri (2012) Elasticity of subst. between YHand YL Battisti et al. (2018) 0.500 RChassamboulli and Palivos (2014) (Quarterly) cost of capital Battisti et al. (2018) 0.030 ANormalization ¯yNH =PHTotal factor productivity 2.5630 aNormalization ¯yNL =PLIncome share of YL 0.5547 κAverage tenure in small firms Cross-skill matching parameter 8.2369 0.1700 ζRegression ln q(θ)onlnθElasticity of the matching function 0.47 βRatio of nominal wages to GDP Bargaining power of workers in regular jobs 0.28 0.9084 48 CResults C.1 Low-skilled immigration and skill-neutral immigration We define e0=e0N+e0I– total employment of workers in small businesses within their own skill group with the corresponding average wage ¯w0=(w0Ne0N+w0Ie0I)/(e0N+e0I). Further, eC=eCN +eCI – total employment of low-skill workers in high-skill small businesses with the corresponding average wage ¯wC=(wCNeCN +wCIeCI)/(eCN +eCI). Table 14: Detailed changes for regular workers upon a 20% increase in immigration, low-skill immigration scenario. (1) (2) (3) (4) (5) (6) (7) Group ¯u/(d−l) ¯e/(d−l)¯w e0/(d−l)¯w0eC/(d−l)¯wC Low-skill Natives 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 Immigr. 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 Natives 0.022 0.825 2.544 0.153 1.295 Change -0.001 +0.007 +0.034 -0.007 +0.009 High-Skill Immigr. 0.091 0.726 2.163 0.182 1.120 Change -0.002 +0.010 +0.031 -0.007 +0.007 We now consider skill-neutral immigration and increase proportionally the number of low and high-skill immigrants by 20%. Our results are summarized in table 15. Table 15: Increase in immigration by 20%, skill-neutral scenario Low-skilled High-skilled Regular workers Pot. entrepreneurs Regular workers Pot. entrepreneurs 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% Representative worker: -1.05% Representative worker: +0.24% Incumbent worker: -0.78% Representative worker: -0.68% Incumbent immigrant: +0.38% Incumbent worker: -0.27% The changes in wages, productivities and welfare of regular workers are less pronounced compared to the low-skilled scenario. This holds for the losses of regular lowskill workers (approx. −0.8% instead of −1.3%) and for the gains of the regular high-skill workers (approx. +0.5% instead of +1%). The effect is also more moderate for the welfare of low skill entrepreneurs, but it is more pronounced for the profits and welfare (+4.2%) 49 of high-skill immigrant entrepreneurs. This is intuitive since hiring high-skill coworkers becomes easier in the case of skill-neutral immigration. C.2 Entrepreneurship entry barriers and ethnic segregation Table 16: The distribution of potential entrepreneurs upon business entry barriers (1) (2) (3) (4) (5) (6) (7) (8) Group u/l e/l w (su+se)/l σ¯αu0b/l σ¯α01 ¯q(θ0)π/γ Low-skill Natives 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 Immigr. 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 Natives 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 Immigr. 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 -- Note: ¯αu0is the average entrepreneurial ability in the range [αu..α0], calculated as (su¯αus +se¯αs0)/(su+se). ¯α01 is the average entrepreneurial ability in the range [α0..¯α]. Table 17: The distribution of potential entrepreneurs upon ethnic segregation (1) (2) (3) (4) (5) (6) (7) (8) Group u/l e/l w (su+se)/l σ¯αu0b/l σ¯α01 ¯q(θ0)π/γ Low-skill Natives 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 Immigr. 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 Natives 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 Immigr. 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