Social Networks, Ethnicity, and Entrepreneurship

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1 Socia Networks, Ethnicity, and Entrepreneurship The Harvard community has made this artice openy avaiabe. Pease share how this access benefits you. Your story matters. Citation Accessed Citabe Link Terms of Use Kerr, Wiiam R., and Martin Mandorff. "Socia Networks, Ethnicity, and Entrepreneurship." Harvard Business Schoo Working Paper, No , October (NBER Working Paper Series, No , September 2015.) November 27, :40:59 PM EST This artice was downoaded from Harvard University's DASH repository, and is made avaiabe under the terms and conditions appicabe to Open Access Poicy Artices, as set forth at (Artice begins on next page)

2 Socia Networks, Ethnicity, and Entrepreneurship Wiiam R. Kerr Martin Mandorff Working Paper

3 Socia Networks, Ethnicity, and Entrepreneurship Wiiam R. Kerr Harvard Business Schoo Martin Mandorff Swedish Competition Authority Working Paper Copyright 2015 by Wiiam R. Kerr and Martin Mandorff Working papers are in draft form. This working paper is distributed for purposes of comment and discussion ony. It may not be reproduced without permission of the copyright hoder. Copies of working papers are avaiabe from the author.

4 Socia Networks, Ethnicity, and Entrepreneurship Wiiam R. Kerr Harvard University and NBER Martin Mandorff Swedish Competition Authority September 21, 2015 Abstract We study the reationship between ethnicity, occupationa choice, and entrepreneurship. Immigrant groups in the United States custer in specific business sectors. For exampe, Koreans are 34 times more ikey than other immigrants to operate dry ceaners, and Gujarati-speaking Indians are 108 times more ikey to manage motes. We deveop a mode of socia interactions where non-work reationships faciitate the acquisition of sector-specific skis. The resuting scae economies generate occupationa stratification aong ethnic ines, consistent with the reoccurring phenomenon of sma, sociay-isoated groups achieving considerabe economic success via concentrated entrepreneurship. Empirica evidence from the United States supports our mode s underying mechanisms. Key words: entrepreneurship, sef-empoyed, occupation, ethnicity, immigration, networks. JEL codes: L26; D21, D22, D85, F22, J15, L14, M13. Comments are appreciated and can be sent to wkerr@hbs.edu. We thank Gary Becker, Oa Bengtsson, Gustaf Bruze, Dennis Carton, Barry Chiswick, Matthew Gentzkow, Emi Iantchev, Svante Janson, Mini Kaur, Steven Laey, Ben Mathew, Andriy Protsyk, Jesse Shapiro, Rache Sooveichik, Chad Syverson, Robert Tope and Nick Wormad and seminar participants for very vauabe comments. We thank Meir Brooks and Rahu Gupta for exceent research support. This paper is a revised version of a paper initiay prepared for The Economics of Entrepreneurship: Bringing the Entrepreneur Back into Economics conference in Venice, Itay, during Juy The theory section of this paper draws heaviy from Mandorff s Ph.D. Dissertation at the University of Chicago. Financia support from the Marcus Waenberg Foundation, the Jan Waander and Tom Hedeius Foundation, the Esther and T.W. Schutz Dissertation Feowship, the Markovitz Dissertation Feowship, the Kauffman Foundation, and Harvard Business Schoo is gratefuy acknowedged. 1

5 1 Introduction Minority groups often concentrate in specific occupations and with a bent towards entrepreneurship. Kuznets (1960) observes that "a minorities are characterized, at a given time, by an occupationa structure distincty narrower than that of the tota popuation and the majority." Whie the particuar ethnic group and the particuar occupation in which the group speciaizes varies over time and with ocation, speciaization as a rue occurs in ethnic groups that are sociay cohesive and in occupations where sef-empoyment is the norm. Prominent exampes of such ethnic speciaizations are the Jewish merchants in Medieva Europe, the Chinese aunderers in eary twentieth century Caifornia, and more recenty the Korean dry ceaners and the Indian mote owners in the United States. Occupationa choice and entrepreneurship are correated with ethnicity even when accounting for differences in demographic characteristics and other quantifiabe attributes. The generating mechanism behind these sef-empoyment custers must therefore invove sorting based on unobservabe characteristics that are correated with ethnicity. Whie individua characteristics can be inked to ethnicity because of differences in the socia and ega status or the unique historica experiences of each ethnic group, choice behavior can aso generate group differences. Variation in occupationa structure need not aways resut from systematic differences between ethnic groups, but as we show in this paper, occupationa choice and entrepreneurship can aso be a stratifying force in itsef. 1 We contribute to the understanding of group differences by deveoping a theory of how economic behavior can ead to stratification. This theory is reated to the concept of ethnic capita as deveoped by Borjas (1992, 1995), but it emphasizes choice and interactions more expicity than does the standard treatment of ethnic capita. By tying together occupationa choice with socia interactions, entrepreneurship and ski acquisition, we show how socia reationships in effi cient markets can generate ong-run occupationa stratification, and as a consequence ead to persistent differences in economic outcomes between groups. We aso demonstrate how occupationa speciaization is especiay ikey to appear in sma groups, and, in direct contrast to the effects of discrimination in the marketpace as anayzed by Becker (1957), we show how socia interactions can sometimes favor minority groups over the majority. Beginning with occupationa concentration, minority groups that successfuy speciaize in business activities appear in many economies throughout history, and traditiona expanations focus on the temporary nature of some stays or expicit restrictions 1 In the context of this paper, the terms sef-empoyed, entrepreneur, and business owner have very simiar meanings and are used interchangeaby. In a simiar manner, it wi become evident that the ethnic speciaization we depict can be thought of in terms of occupationa or industry concentration (e.g., concentration of sef-empoyment for the taxi cab industry). 2

6 on activity. 2 These earier expanations do not appy very we to the United States today, however, and yet we continue to observe many speciaized ethnic groups that have setted permanenty. Prominent exampes incude ethnic groups from Korea, Greece, India, and the Midde East. This concentration can be very sharp, with a striking 45% of adut Korean maes being sef-empoyed, in contrast to 15% of the adut mae immigrant popuation as a whoe. Furthermore, different groups custer in different business sectors: Yemeni are 75 times more ikey to own grocery stores than other immigrants, and Gujarati-speaking Indians are 108 times more ikey to operate motes. Likewise, Greeks concentrate in the restaurant sector, and Midde Eastern immigrants custer in grocery stores and iquor stores. We consider in this paper how socia interactions can prompt this reguar feature across many diverse groups. Turning to socia interactions and ski acquisition, we use the term "socia interaction" here to describe interaction that takes pace outside of work: famiy gatherings, reigious and cutura functions, meetings with friends, and simiar. A considerabe iterature anayzes the importance of socia interactions for economic behavior outside of the workpace (e.g., Gaeser et a., 1996; Bertrand et a., 2000; Gaeser and Scheinkman, 2002). A smaer iterature ooks at the roe of socia interactions for workpace outcomes. In the context of occupationa choice, Granovetter (1973) finds that jobs often are found through referras, and that these tend to come from more casua acquaintances, so-caed "weak ties." Montgomery (1991) provides a comprehensive survey of the incidence of jobs found through referras, and Durauf and Fafchamps (2006) and Durauf and Ioannides (2010) are broader reviews. Ski acquisition is potentiay an even more important aspect of reationships in determining occupationa choice. Private information and tacit knowedge are instrumenta to productivity in many occupations. For exampe, sef-empoyed entrepreneurs in the sma business sector are their own managers, and they must rey on their own judgment to make business decisions. Skis in this sector may come in the form of knowedge of how to start or take over a business; information about market conditions (e.g., demand eves, pricing); knowedge of how to estabish suppier, customer, 2 Exampes incude the Jews in Medieva Europe and around the Mediterranean, the Armenians in the Ottoman Empire, the Jains and the Parsis in India, the Lebanese in West Africa, the Indians in East Africa, the Japanese in South America, and the Chinese in Southeast Asia and the Caribbean. Severa works in socioogy anayze this phenomenon, with Baock (1967) appying the term "middeman minorities" to these groups. Bonacich (1973) put forward what is known as the "sojourner theory," expaining speciaization as the outcome of temporary residence; more recenty, Botticini and Eckstein (2005) study path dependence and Jewish occupationa speciaization, which they propose is the outcome of a reigious iteracy requirement. More broady, Adrich and Wadinger (1990) review the socioogy iterature on ethnic entrepreneurship, and Sowe (1981) anayzes the roe of cuture more generay. Reated cassic work aso incudes Migram (1967), Light (1977), Thernstrom (1980), Landa (1981), Migrom et a. (1990), Meton (1990), Sowe (1996), Cohen (1997), Greif (1993), and Greif et a. (1994). 3

7 and empoyee reationships; and insights into ega and tax-reated issues. These skis are vauabe and cannot be instantaneousy transferred from one entrepreneur to another. Chung and Kanins (2006) further trace out resource access through ethnic networks in the case of Gujarati hote owners. Socia interaction with peope in the same industry can reduce the cost of ski acquisition. Industry information and professiona advice can be exchanged at itte or no time cost whie attending a famiy gathering or a reigious ceremony, and interaction can therefore be compementary to ski acquisition. 3 This roe of socia interaction is diffi cut to measure directy since few datasets contain information about horizonta reationships such as friendship and extended famiy. Fairie and Robb (2007) document from the Characteristics of Business Owners database that more than haf of business owners have cose reatives who are sef-empoyed, and a quarter of business owners have worked for these reatives. Datasets inking verticay across generations are more common. Dunn and Hotz-Eakin (2000) find that the incidence of sef-empoyment, controed for other factors, doubes when an individua s parents are sef-empoyed. We unite these features by making an important distinction between market interaction and socia interaction that is centra to our anaysis. The socia interaction theory that we deveop differs from the standard theory of discrimination. We anayze the case when groups are economicay integrated but cuturay isoated; groups are assumed to be excusive in their socia interactions, whie fuy participating in the market economy. In this case, no discrimination coeffi cient as in Becker (1957) taxes the market transactions between groups. To iustrate how market interaction can take pace without socia interaction, consider a scene from Shakespeare s The Merchant of Venice (Act 1, Scene III) depicting the socia divide between the Christians and Jews in Renaissance Europe. Foowing a negotiation over a arge oan to a Christian man who has aways scorned him, the Jewish moneyender Shyock comments: "I wi buy with you, se with you, tak with you, wak with you, and so foowing; but I wi not eat with you, drink with you, nor pray with you." Both market interaction and socia interaction generate stratification, but in different forms and with different economic consequences. Minorities are put at a disadvantage in industries where market interaction is important, and are consequenty driven out of these sectors; a group speaking ony a minority anguage woud for exampe have a hard time competing in an industry such as academia. 4 Discrimination 3 The compementarity between socia interaction and ski acquisition can be derived in severa ways. First, if peope derive utiity from spending time in the presence of friends, mentoring friends may provide more utiity than mentoring non-friends. Second, peope spend significant time at socia events, and business knowedge can diffuse among participants. Third, peope may trust the reciprocity of friends and therefore share knowedge, expecting future favors in return. 4 Market interaction can aso generate speciaization at the estabishment eve. For exampe, kitchen workers in the restaurant business might stratify aong ethnic ines. The resut is that each 4

8 in the marketpace, whether in the form of outright prejudice or simpy the inabiity to communicate in other anguages, imposes greater economic cost on the minority than on the majority (Becker, 1957), just as a sma country is more dependent on trade than a arge country. 5 This paper describes how socia interactions can work in the opposite direction of market interactions. Socia compementarities in industries where sector-specific skis are important can drive otherwise simiar groups to speciaize in different sectors, and these socia compementarities can resut in a favorabe economic outcome for some minority groups. 6 The next three sections formaize this conceptua structure. Section 2 deveops a two-group, two-sector mode of identica agents where socia interactions are random within groups and where socia reationships and production are compementary in one sector. We characterize the effi cient outcome and show that different groups shoud speciaize in different sectors, with sma groups having an absoute advantage in sectors where the compementarity between interaction and production is strongest. Section 3 characterizes the competitive equiibrium. We introduce dynamics to demonstrate how socia interactions ampify initia group differences and resut in ong-run occupationa speciaization (Pate and Vea, 2013). We aso show that under identica ski distributions for groups, mean earnings are positivey reated to a group s equiibrium eve of speciaization. Section 4 anayzes reationships in a socia network where interactions are endogenousy determined as the outcome of effi cient matching. Reating socia networks to empoyment is akin to Cavo-Armengo and Jackson (2004), who deveop a socia network mode of job referras that generates persistent empoyment differences. But whie they take the socia network as given, we derive the properties of a socia network that is endogenousy determined. We show that the resuts of the random interaction mode in Section 2 are strengthened, provided that socia reationships are not cose substitutes to one another. Section 5 anayzes the mode s predictions using Census Bureau data for the United States in Entrepreneuria activities and socia interactions are ceary correated, but identifying interaction effects is notoriousy diffi cut. Unobservabe characteristics estabishment wi have a homogenous workforce, but the ethnic composition at the industry eve is not affected. Market interaction at the estabishment eve such as in the restaurant exampe generates speciaization at the estabishment eve, whereas market interaction at the industry eve such as in academia generates speciaization at the industry eve. 5 Simiar resuts are derived in a mode of random encounters by Lazear (1999), who anayzes the effects of group size on assimiation. If ethnicity were endogenous in the mode deveoped in this paper, then assimiation pressures simiar to those in Lazear (1999) woud arise, athough this coud be counterbaanced by the economic benefits of beonging to a speciaized minority group, as is made cear ater on in this paper. 6 The favorabe economic outcome does not necessariy carry over to utiity. Depending on the degree of endogeneity of socia interaction, the overa situation for minority groups may sti be worse than the overa situation for the majority. 5

9 can give rise to the refection probem described by Manski (1993). For exampe, since peope have a procivity for cuisine from their home country, Greek restaurateurs wi sort into Greek restaurants and Chinese restaurateurs wi sort into Chinese restaurants, independent of socia reationships. This sorting mechanism is we-understood and very ikey at work in some occupations. The interaction theory deveoped in this paper has particuar impications, however, that are suitabe for testing. First, if socia interaction effects are important, speciaization shoud appear strongest in groups that are sociay isoated from the majority popuation. Case studies on successfu entrepreneuria groups show that indeed these groups tend to be sociay cohesive, as for exampe Indians in East Africa (Morris, 1956) and Lebanese in West Africa (Winder, 1962). Second, predictions exist for the earnings of sef-empoyed groups. We first provide extensive evidence of occupationa custering and entrepreneurship among ethnic groups, reated to Pate and Vea (2013). We show how the size of groups and their socia isoation, which we measure using in-marriage rates, strongy predict occupationa concentration for entrepreneurs from the ethnic group. A 10% decine in group size raises entrepreneuria concentration in one industry by 6%, and a 10% increase in group isoation boosts concentration by 5%. We show that these resuts are robust under many specification variants. These resuts coud be biased, however, by omitted factors or reverse causaity (e.g., occupationa concentration eading to higher in-marriage rates). We consider two instrument variabe specifications to address this issue. One approach uses the 1980 group sizes and in-marriage rates in the United States. Our second approach instruments US ethnic group size with the predictions from a gravity mode for migration to the United States and instruments US in-marriage rates with those observed for the same ethnic group in the United Kingdom. These estimations confirm the OLS resuts. We finay provide earnings estimations consistent with the mode s predictions. Our fina section concudes. Cassic accounts of the nature of entrepreneurship emphasize in equa measure disruptive forces that entrepreneurs generate (Schumpeter, 1942, 1988) and their roe in reducing price gaps and arbitrage opportunities (Kirzner, 1972, 1979). These theories rarey provide specific pressures or predictions for one group to become an entrepreneur versus another, except aong defined traits ike abiity to navigate uncertainty (Knight, 1921), risk toerance (Kihstrom and Laffont, 1979), business acumen (Lucas, 1978), and ski mix (Lazear, 2005). Connections of entrepreneurship to migration status have been frequenty noted but poory expained. A centra concusion from this paper is that socia interactions can generate groupeve effects towards entrepreneurship and occupationa choice that are important for expaining, today and in times past, why some popuations show a greater tendency to sef-empoyment, above and beyond other features that promote entry decisions. Further research needs to continue buiding out these connections from socia net- 6

10 works and occupationa structures to entrepreneurship given the genera appicabiity of these phenomena to many ethnic groups and their persistent roes in many cutures and economies. 2 A Mode of Speciaization The theory in this paper consists of two fundamenta buiding bocks. First, socia interactions and production are compementary. Second, different socia reationships are not cose substitutes for one another. The former is deat with in this section, whie the atter is discussed extensivey in Section 4 where reationships are anayzed in a socia network with endogenous matching. 2.1 Socia Interaction as a Factor in Production Consider a popuation where everyone has equa innate abiity, divided into two ethnic groups, A and B. Group A is in the minority, with a continuum of individuas of tota mass N A, and group B is the majority, with a continuum of individuas of tota mass N B, where N A < N B. Members of A and B interact in the marketpace but are sociay segregated and spend their eisure time separatey. Assume that socia interaction is random within groups; each person interacts with a representative sampe of individuas in their own group ony. 7 This assumption of random interaction is reaxed in Section 4. There are two occupations in our mode: workers and entrepreneurs. Workers produce goods and entrepreneurs produce services in the form of seing the goods. Industry knowedge is important to entrepreneurs but not to workers, since entrepreneurs (as opposed to workers) are their own managers and have to rey on their own judgment when they make business decisions. When sociaizing during famiy gatherings and reigious/cutura functions, entrepreneurs mentor each other and exchange industry knowedge and professiona advice. 8 The more an entrepreneur sociaizes with other entrepreneurs, the more knowedge is exchanged. Socia interaction and production are therefore compementary in the entrepreneuria sector and entrepreneuria productivity increases with the number of friends and famiy members in that sector. Define X for {A, B} as the fraction of the popuation in group who are entrepreneurs. This fraction is referred to as the group s degree of speciaization. Since socia interaction is random within groups, a fraction X of the friends and famiy 7 The terms "representative sampe" and "random sampe" are used interchangeaby. They coincide conceptuay if the random sampe is arge enough, which is assumed to be the case. 8 In addition to mentoring, socia reationships can aso improve the abiity to extend credit. Socia ties increase the cost of breaking a contract, adding socia repercussions to economic and ega penaties. 7

11 members of every individua in group are entrepreneurs as we. Denote individua entrepreneuria productivity in group as θ (X ). Given that productivity increases when sociaizing with other entrepreneurs, it foows that: Assumption 1a Entrepreneuria productivity increases in speciaization: θ > 0. This is the centra component of the theory. Proceeding to specify a compete economic environment, denote Q 1 as the aggregate suppy of services produced by entrepreneurs. Aggregate suppy can be written as a function of the occupationa distribution (X A, X B ): Q 1 (X A, X B ) = X A N A θ (X A ) + X B N B θ (X B ) (1) Since socia interaction is assumed to pay no productive roe for workers, et the goods sector exhibit constant returns to scae with worker productivity normaized to one. Defining Q 0 as the aggregate suppy of goods, write this as: Q 0 (X A, X B ) = (1 X A ) N A + (1 X B ) N B (2) Moving from the suppy-side to the demand-side, services and goods shoud be compementary enough to avoid the compications of mutipe optima possiby generated by non-convexities. To simpify the exposition, et services and goods be perfect compements. Consumers then have Leontief preferences with the utiity function: ( U (q 0, q 1 ) = min q 0, q ) 1 (3) v where v > 0 is a preference parameter and q 0 and q 1 are individua consumption of goods and services, respectivey. 2.2 The Pareto Probem Since both commodities have unitary income easticities, distributiona aspects can be ignored when characterizing the effi cient outcome. The probem simpifies to choosing an occupationa distribution (X A, X B ) that maximizes a representative utiity function U (Q 0 (X A, X B ), Q 1 (X A, X B )). A margina anaysis is inappropriate since this is a non-convex optimization probem. Consider instead the most speciaized occupationa distributions, where either as many individuas as possibe in group A or as many individuas as possibe in group B are entrepreneurs. Figure 1 depicts the production possibiities for the two most speciaized distributions. Define V (X A, X B ) Q 1 Q 0 as the ratio of the suppy of services to goods under the distribution (X A, X B ). Aong the curve with the kink V (1, 0) in the figure, group A speciaizes as entrepreneurs. Starting from a position with ony workers furthest to 8

12 the right, As are added to the entrepreneuria sector moving eftward aong the x-axis. When reaching the kink V (1, 0), a As are entrepreneurs. Thereafter, continuing to move eftward, Bs are aso added to the sector unti when reaching Q 0 = 0, there are no more workers in the economy. Simiary, aong the curve with the kink V (0, 1), group B speciaizes as entrepreneurs. Bs are added moving eftward aong the x-axis unti reaching the kink V (0, 1), where a Bs are entrepreneurs. Thereafter aso As are added unti reaching Q 0 = 0. {Insert Figure 1} The curve with minority speciaization is above the curve with majority speciaization, so ong as the entrepreneuria sector is suffi cienty sma. A arge fraction of As are entrepreneurs when the minority speciaizes, aowing minority entrepreneurs to sociaize mosty within their own occupation, greaty improving productivity. The same is not true for the majority when they speciaize, since even if a arge fraction of entrepreneurs are Bs, most Bs are nevertheess workers. As a resut, majority entrepreneurs spend their time sociaizing with workers instead of with other entrepreneurs. The argument can be generaized to show that minority speciaization is Pareto effi cient so ong as the entrepreneuria sector is sma enough. Perfect compementarity simpifies the probem of soving for the optima aocation, since any bunde where goods and services are in the exact ratio v of the Leontief preferences (3) is stricty preferabe to a other bundes that do not incude at east as much of both goods and services. The Pareto optima distribution (X A, X B ) must therefore satisfy v = V (X A, X B ). Define the tota number of entrepreneurs in the popuation as M X A N A + X B N B. It foows that: Proposition 1 If v V (1, 0), a entrepreneurs beong to minority A. Proof: Take the distribution (X A, 0) where X A is such that v = V (X A, 0). This is feasibe since v V (1, 0). Assume by contradiction that it is not the uniquey effi cient distribution. Then there exists an aternative distribution (X A, X B ) with Q 1 Q 1 and Q 0 Q 0. Given Q 0 Q 0 it foows that M M, or equivaenty, X A N A + X B N B X A N A, which impies X A X A and X B < X A, with X A < X A if X B = 0. Manipuating the expression for Q 1: This contradicts Q 1 Q 1. Q 1 = (M X BN B ) θ (X A) + X BN B θ (X B) (4) < (M X BN B ) θ (X A ) + X BN B θ (X A ) = Q 1 Consequenty, the effi cient outcome requires that a singe group speciaizes as entrepreneurs, and importanty, which group speciaizes is not arbitrary. Minority speciaization is more effi cient since the minority s socia isoation enabes entrepreneurs 9

13 in A to sociaize mosty within their own occupation. Proposition 1 impies that, for v V (1, 0), the transformation curve and the curve with minority speciaization in Figure 1 coincide. Group A has absoute and comparative advantages as entrepreneurs. If the demand for services is suffi cienty great, however, then the minority is too sma to satisfy demand by themseves. Instead, there is now a trade-off between few, highy-speciaized minority entrepreneurs, or many unspeciaized majority entrepreneurs. In the specia case when v = V (0, 1), the demand for services is great enough for group B to speciaize competey. In this case minority invovement woud just serve to diute majority entrepreneurship, and the Pareto effi cient soution is for Bs to speciaize. Coroary If v = V (0, 1), a entrepreneurs beong to the majority, B. The proof is anaogous to the proof of Proposition 1. As the coroary shows, the reationship between group size and productivity is not monotonic. Rather, the group with the absoute advantage is the group with a popuation size that most cosey adheres to the size of the sector where socia interaction and production are compementary. Other production possibiities generated by more unspeciaized occupationa distributions, such as X A = X B, are not dispayed in Figure 1. Since some of these production pans coud be above the two speciaized curves in the Figure, the transformation frontier cannot be fuy characterized at this stage. The production function must be restricted further to aow a compete characterization. 2.3 Quaity and Convex Productivity In addition to the quantity of friends that are entrepreneurs, the quaity of these friends coud aso matter for productivity. Let individua productivity increase both in the quantity and in the average productivity of feow entrepreneurs. Write this as: θ = φ + δx θ (5) where φ > 0 is a productivity term, 0 < δ < 1 is a socia mutipier, X is the fraction of entrepreneurs in group, and θ is the average productivity of these entrepreneurs. Soving for equiibrium productivity by setting θ equa to θ, individua productivity is a function: φ θ (X ) = (6) 1 δx It foows that productivity is convex in the degree of speciaization, when taking both the quantity and the quaity of interaction into account. 9 With this resut in mind, 9 This specification highights the differences from a standard interaction mode. The standard mode is generay specified so that individua productivity is a function of a group-specific term φ and the discounted mean of the group, δθ. Soving θ = φ + δθ, interaction exacerbates the difference in φ across groups, θ = φ 1 δ > φ, but the degree of speciaization X has no effect on productivity. 10

14 assume for now that productivity is indeed convex. Assumption 1B Productivity is convex in speciaization: θ > 0. Assumption 1B is unnecessary for the resuts in the next sections, but it is usefu now to aow a fu characterization of the effi cient soution without having to resort to expicit functiona form. Convex productivity gives the foowing resut: Lemma If productivity is convex, both groups never work in both sectors. Proof: Assume by contradiction that an effi cient distribution (X A, X B ) exists where 0 < X < 1 for = {A, B}. Consider a margina change ɛ in the ethnic composition of entrepreneurs whie hoding fixed the overa number of entrepreneurs M (and therefore aso the suppy of goods). Taking the derivative of Q 1 with respect to ɛ, and evauating it at ɛ = 0: Q 1 ɛ ( X A + ɛ N A, X B ɛ N B ) = θ (X A ) + X A θ (X A ) θ (X B ) X B θ (X B ) (7) Since (X A, X B ) is effi cient, and since X is interior, this derivative has to be zero. 10 But with convex productivity the derivative is zero ony at X A = X B, which is the goba minimum. This contradicts effi ciency. The effi cient economy aims for maximum ethnic homogeneity in entrepreneurship. Ruing out that both groups work in both sectors impies that ony the speciaized distributions aong the two curves depicted in Figure 1 coud possiby coincide with the transformation frontier. The shape of the entire transformation frontier can therefore be deduced by tracing out the maximum of the two curves in that Figure. Proposition 2 If productivity is convex, there is a cutoff vaue v such that for v < v, the minority speciaizes as entrepreneurs, whereas for v > v, the majority speciaizes. Figure 2 shows how the degree of speciaization varies with the size of the entrepreneuria sector, as governed by v, and the cutoff vaue v for primary group speciaization. {Insert Figure 2} The greater the vaue of v, the greater is the demand for services and the more peope work in the entrepreneuria sector. As the sector increases in size in Figure 2, the interaction externaity generates a characteristic discrete jump from one type of equiibrium to another. At the point v, where many from group B have aso joined the entrepreneuria sector, the economy abrupty moves from minority speciaization to majority speciaization. 10 If the derivative is nonzero, then the suppy of services coud increase whie keeping the suppy of goods constant. By subsequenty increasing the number of workers marginay, a Pareto improvement is feasibe, thus contradicting effi ciency. 11

15 2.4 The Case of Non-Convex Productivity Finay, to see that convexity is needed for the Lemma on ethnic homogeneity to hod, consider a non-convex production function where a threshod fraction must work as entrepreneurs for interaction to have vaue: θ > 0 if X b and zero otherwise. This specification vioates the assumption that productivity is stricty increasing in the degree of speciaization. Then, if the demand for services is so great that a singe group cannot satisfy it entirey, v > V (0, 1), and if in addition V (b, b) < v < V (b, 1), effi ciency requires that both groups work in both sectors, contradicting the Lemma. To see why, consider what woud happen if one of the groups speciaized competey. In this case the non-speciaized group s degree of speciaization woud be positive but beow b, causing entrepreneurs in that group to have zero productivity. If, however, the occupationa distribution was unspeciaized instead, with X A = X B, then entrepreneurs in both groups woud be as productive as those in the most productive group were under the aternative. Ceary this woud be Pareto superior, contradicting the Lemma. This specia case shows how the Lemma fais for non-convex productivity, and how in this case the quaitative features of speciaization wi depend on specific functiona form assumptions. Reca however that the resuts for both v V (1, 0) and v = V (0, 1) are more genera and appy both for convex and non-convex productivity. 2.5 Ski-Specificity and Muti-Sector Extension The two-sector mode can be directy appied to data if entrepreneuria skis are sufficienty genera to encompass a forms of entrepreneuria activity: if, for exampe, operating a dry ceaning shop requires simiar skis as operating a mote or a iquor store. If skis are more sector-specific, then a mutisector framework is more appropriate. Athough we do not deveop a muti-sector mode here, simiar principes appy as in the two-sector mode. In some specia cases the effi cient outcome is aso intuitivey simiar to the two-sector mode. For exampe, consider an economy with two entrepreneuria sectors instead of just one, with equa demand for both services, and where there are two minority groups instead of just one, both equa in size. If the demand for entrepreneuria services is suffi cienty sma, then the effi cient outcome is for one minority group to speciaize in one entrepreneuria sector, and for the other minority group to speciaize in the other sector. Which minority group speciaizes in which sector is arbitrary. In this muti-sector economy with sector-specific skis, otherwise-simiar groups consequenty speciaize in different business sectors. An interesting extension for future work is to incude both genera and specific skis in the same framework. In such a mode of spiovers between sectors, it shoud be possibe to derive stratification in overa entrepreneuria activity as we as stratification 12

16 between different forms of entrepreneurship at the same time. This woud correspond to the current situation in the United States, where groups ike the Koreans are strongy custered in a few business sectors, whie at the same time being overrepresented in amost a other business activities as we. 3 The Price Equiibrium The previous section characterized the effi cient outcome. The focus now turns to the competitive outcome. An equiibrium anaysis wi yied two insights into how socia interaction affects the occupationa distribution. First, it shows how stratifying forces act to make groups more and more different, and second, how group earnings are positivey reated to the degree of speciaization. To see how socia interaction works as a stratifying force, begin by introducing time into the anaysis, with t = 0, 1,...,. Dynamics are buit into the mode by making the interaction effect work with a ag. Denote by X t the degree of speciaization in period t for group, and et individua entrepreneuria productivity in period t be a function θ ( ) X t 1. This one-period ag specification for the interaction effect coud easiy be generaized to a distributed ag. Interaction now effectivey works as a form of socia capita, with the group s occupationa activities in the previous period benefiting individua productivity today. Let p t 1 and p t 0 be the prices of services and goods respectivey. Entrepreneuria earnings are y1, t = pt 1θ ( ) X t 1 and worker earnings are y0, t = p t 0. Competitive occupationa choice is straightforward to derive in this setting; defining the reative price of goods to services as p t = pt 0, an individua in p t 1 group joins the entrepreneuria sector if: θ ( ) X t 1 p t (8) and favors being a worker if θ ( ) X t 1 p t. Since individuas have identica skis, aggregate abor suppy for group is discontinuous, with: 1 if θ ( ) X t 1 X t > p t = [0, 1] if θ ( ) X t 1 = p t 0 if θ ( (9) ) X t 1 < p t. Avoid for now the knife-edge unspeciaized case where X t 1 A = X t 1 B. Since there is a singe price of abor, p t, at east one of the two groups A and B must then be in a corner: { ( X t (X A, XB) t t = A = 1, 0 < XB t ) or (Xt A 1, Xt B (0 < XA t, Xt B = 1) or (Xt A = 0, Xt B = 0) if Xt 1 A 1) if Xt 1 A > Xt 1 B < Xt 1 B (10) 13

17 In equiibrium, suppy must satisfy (10) and production must meet demand so that markets cear. Because of perfect compementarity, meeting demand reduces to satisfying v = V (XA t, Xt B ). The resuting equiibrium distribution is unique. To see why, take the case when group is more speciaized than group in the previous period, with X t 1 > X t 1. Given that at east one of the two groups must be in a corner according to (10), the equiibrium distribution must either be of the type (X t, 0) or of the type (1, X t ). Since the function V is stricty increasing in both arguments, it foows that V (1, X t ) > V (Xt, 0). Ony one distribution can consequenty make V equa to v. The equiibrium distribution is therefore uniquey determined by the distribution in the previous period. Continuing to avoid the knife-edge unspeciaized case, define a function φ that maps every previous distribution into a new distribution: ( X t A, X t B) = φ ( X t 1 A, Xt 1 B Next, proceed to characterize stationary equiibrium distributions. Like other equiibrium distributions, stationary distributions must satisfy (10) and must meet demand. Foowing the same argument as above, based on V being stricty increasing in both arguments, it foows that there is a stationary equiibrium where each of the two groups speciaize. Denote the stationary distribution as ( X A A, XA B) when the minority speciaizes, and the stationary distribution as ( X B A, XB B ) when the majority speciaizes. {Insert Figure 3} Finay, returning for a moment to the unspeciaized knife-edge case where X t 1 A = X t 1 B, this type of initia condition is of measure zero and therefore not eaborated on. Note ony that since V is stricty increasing in both arguments, there can ony be one such stationary unspeciaized equiibrium distribution. Denote that equiibrium distribution as ( XA U, ) XU B. In the unspeciaized case, athough there is ony one stationary equiibrium, the uniqueness of equiibria no onger appies. To summarize, there are consequenty three stationary equiibrium distributions: two speciaized, ( XA A, B) XA and ( ) ( ) X B A, XB B, and one unspeciaized, X U A, XB U. Figure 3 above shows the two speciaized equiibria, as we as the knife-edge equiibrium, when v is ess than V (1, 0). ) (11) 3.1 Occupationa Stratification The foowing section shows that the dynamic system in (11) converges to a stationary speciaized equiibrium, so ong as the interaction externaity is not too strong. 11 Consider what happens to the aggregate production of entrepreneuria services when 11 This section ony deas with unspeciaized initia conditions, which estabishes convergence on measure one. 14

18 one (infinitesima) person in group joins the entrepreneuria sector. First, aggregate production increases by an amount equa to the individua productivity of that person, θ (X ). In addition, a other entrepreneurs in group benefit from the interaction externaity when sociaizing with this entrepreneur. Individua productivity therefore increases by 1 N θ (X ) for a X N entrepreneurs in group. Consequenty, the internaized effect on aggregate production of one person joining the entrepreneuria sector is θ (X ), and the externa effect is X θ (X ). Assume that the externa effect is smaer than the interna effect. 12 Assumption 2 The interna effect dominates: θ (X ) X < θ (X ). This condition is satisfied if productivity is concave in X, but it aso hods for some convexity as ong as θ (0) > 0. To see why the assumption is needed for the system to be stabe, consider the extreme case when group A has no mass at a, with N A = 0. Since the derivative of V with respect to XA t is zero in this case, group A can be ignored atogether in the genera equiibrium anaysis. There is then a singe stationary eve of speciaization for group B; denote this vaue as XB. Consider a perturbation in period t so that the majority starts out with too many entrepreneurs, XB t > X B, shown in Figure 4 beow. Such a deviation boosts the interaction effect in period t+1 reative to the stationary equiibrium, θ (XB t ) > θ (X B ). With perfect compementarity, the suppy of both goods and services must therefore increase reative to their stationary equivaents. Increasing the production of goods requires an increase in the number of workers, and consequenty, a decrease in the number of entrepreneurs to beow the stationary vaue XB. With fewer entrepreneurs in period t + 1 than the stationary number of entrepreneurs, the tabes turn in period t + 2, so that the interaction effect now is reduced to beow that in the stationary equiibrium. Reducing the production of both goods and services in period t + 2 in response, the number of workers in period t + 2 has to decrease and the number of entrepreneurs has to increase reative to the stationary equiibrium. These reversas repeat every period in cobweb-stye dynamics. 13 {Insert Figure 4} The question of whether the system is stabe reduces to whether the number of entrepreneurs in period t + 2 is ess than the number of entrepreneurs in period t, so that the degree of speciaization in group B gets coser and coser to the stationary vaue XB over time. Using the derived direction of the change in the production of services, 12 We thank Rache Sooveichik for this interpretation of Assumption The fip-fopping character of the equiibrium distribution is a resut of the one-period ag specification for the interaction effect. The occupationa distribution woud change more graduay with a more genera specification aowing for distributed ags. 15

19 Q t+1 1 > Q t+2 dividing the eft-hand side by XB t 1, this atter inequaity can be equivaenty expressed, after mutipying and, and dividing both sides by Xt+1 B N B, as: XB t θ (XB t ) > X t+2 θ ( ) X t+1 B XB t B (12) X t+1 B Given that productivity is not too convex, as stipuated by Assumption 2, it foows that θ(x ) X is stricty decreasing in X. Since XB t > Xt+1 B, equation (12) then estabishes that XB t > Xt+2 B. This proves convergence and the stabiity of group B s degree of speciaization around XB. Having estabished stabiity in the case of N A = 0, the same exampe aso serves to show how the stratifying force comes into pay. Let group B be in its stabe state, with XB t = X B, and perturb the minority s occupationa distribution so that Xt A > X B. Since group B is so much greater in size than group A, the former is unaffected by the perturbation and the price continues to be ocked in at p t+1 = θ (XB ). The interaction effect in period t+1, generated by the perturbation in period t, then resuts in everyone in group A becoming more productive as entrepreneurs than as workers, with θ (XA t ) > p t+1. Group A s degree of speciaization consequenty jumps from XA t to Xt+1 A = 1, and the occupationa distribution stays in this stratified state forever. This stratification resut is extended in the appendix for the genera case of any popuation size of the two groups, and it foows that for {A, B} and {A, B}: Proposition 3 Initia differences resut in ong-run speciaization: If group is more speciaized than group initiay, X 0 > X 0, then group speciaizes in the ong run and the imiting distribution is ( XA, B) X. This aso impies that the stationary unspeciaized equiibrium ( X U A, XU B ) is unstabe. If the minority is sighty more speciaized initiay, then the economy converges to minority speciaization ( X A A, XA B), and if the opposite is true, then the economy converges to majority speciaization ( X B A, XB B ). Over time, socia segregation ampifies initia group differences. 3.2 Initia Conditions and Mutipe Groups Depending on the initia conditions, as is cear from Proposition 3, either of the two groups A and B can speciaize as entrepreneurs. Socia interaction ampifies initia differences, but it does not expain why they are there to begin with. The difference in group size has some impications for what initia conditions to expect, however. Consider an economy with more than two groups. As before, the group that is most entrepreneuria initiay wi speciaize in the ong run. If the initia occupationa distribution is subject to randomness, one of the smaer groups is ikey to be the 16

20 most speciaized initiay. To see why, et the initia distribution be generated by random draws, where each person becomes an entrepreneur with probabiity ρ. 14 This probabiity structure resuts in the same expected initia degree of speciaization for a groups, but since the popuation size varies across groups, the variance in the degree of speciaization aso varies. The smaest groups have the argest variance, and therefore, the smaest groups are most ikey to exhibit the owest and aso the greatest initia degrees of speciaization. Consequenty, with the smaest groups the most ikey to speciaize initiay, as interaction ampifies initia differences over time, the smaest groups are aso the most ikey to speciaize in the ong run. 3.3 Heterogeneity and Earnings Socia compementarities aso have impications for earnings. To examine how interaction effects woud show up in earnings data, it is necessary to move away from the framework of identica skis. Returning to a static environment, endow each person i with entrepreneuria skis s 1 (i) and worker skis s 0 (i). Entrepreneuria earnings are now a function of both interactions and skis. Denote the earnings of individua i in group when she is an entrepreneur as y 1 (X, i) = p 1 θ (X ) s 1 (i), and when she is a worker as y 0 (i) = p 0 s 0 (i). Defining the ratios s s 1 s 0, p p 0 p 1, and q p y 1 y 0, the earnings-maximizing occupationa choice of individua i is to consider becoming an entrepreneur if: q (X, i) p (13) and to consider being a worker if q (X, i) p. Here the term q (X, i) = θ (X ) s (i) summarizes the individua s comparative advantage in entrepreneurship, at parity prices, as a function of socia interaction and skis. When individuas have different skis, the character of the price equiibrium depends cruciay on the margina entrepreneur and how his comparative advantage changes as more and more untaented peope become entrepreneurs. If the benefits of interaction are weak and the margina entrepreneur "deteriorates" as the more intrinsicay untaented peope enter the business, then the economy reduces to a standard Roy mode, or sorting mode, with a unique unspeciaized equiibrium. Ony if the interaction effect is strong enough to overcome ski heterogeneity can interaction change the character of the equiibrium. {Insert Figure 5} Without oss of generaity, order individuas from the greatest to the smaest comparative advantage in entrepreneurship, so that the ski ratio is decreasing in 14 These draws can be partiay correated within groups with the assumption that the correation is the same for every group. 17

21 i, s (i) 0. The margina entrepreneur is then the individua indexed by i = X, and her comparative advantage is q (X, X ). To prevent the economy from reducing to a sorting mode, assume that the interaction effect trumps heterogeneity: Assumption 3 Interaction dominates at the margin: d dx q (X, X ) > 0. This assumption impies that the soid ine in Figure 5 is upward soping. The equiibrium distribution (X A, X B ) must be competitivey suppied and enough goods and services must be produced to meet demand. Using a simiar ine of reasoning as in the previous section, based on V being stricty increasing in both arguments, it foows from Assumption 3 that there are three equiibria: one unstratified, denoted ( ) ( ) X U A, XB U ; one where minority A speciaizes, denoted X A A, XB A ; and one where majority B speciaizes, denoted ( XA B, ) XB B. 15 In the equiibrium where minority A speciaizes as entrepreneurs, the mean earnings of As are higher than the mean earnings of Bs, and vice versa in the equiibrium where group B speciaizes. To see why, et y = max (y 0, y 1 ) be actua individua earnings, and denote mean group earnings as µ = 1 ydi. 0 Proposition 4 Earnings covary with entrepreneurship: µ (X ) > µ (X ) if X > X. Proof: Since peope sort into occupations, mean earnings can be rewritten as µ (X ) = 1 0 y 0 (i) di + X 0 (y 1 (X, i) y 0 (i)) di (14) Rearranging, the difference in mean earnings between the two groups is: µ (X ) µ (X ) = X 0 (y 1 (X, i) y 1 (X, i)) di + X X (y 1 (X, i) y 0 (i)) di (15) where both parts of the expression are positive. The first part is stricty positive due to the interaction effect, y 1(X,i) X > 0, and the second part is positive because of sorting, y 1 (X, i) y 0 (i) for a i X. This unequivoca effect on mean earnings at the group eve does not carry through to the sectora eve. Depending on the joint distribution of skis, mean earnings in either sector can increase or decrease as interaction increases entrepreneuria productivity and shifts peope of different abiity between sectors. The effect of interaction on sectora earnings is simiar to the effect of changing ski prices, which cannot be signed for a genera ski distribution (Heckman and Honore, 1990). 15 Note that Assumptions 2 and 3, when combined, put both an upper and a ower bound on the interaction effect: d n s dx < d n θ dx < 1 X. 18