Social Discrimiatio ad Occupatioal Specializatio arti ador August 9, 2005 Abstract Ethic miorities have specialized i shopkeepig, moeyledig ad other middlema activities throughout history. Small groups such as the Jews ad the overseas Chiese have frequetly prospered. While it is well-kow that market discrimiatio hurts miorities more tha the majority, this paper shows how social discrimiatio ca result i the opposite. The complemetary role of social iteractio i productio gives miorities a absolute advatage i some occupatios. I additio to historical accouts this theory is applied to Cesus data o ethic groups i the Uited States. It is explaied why specializatio is more commo for the self-employed tha for wage-earers. Graduate Studet, Departmet of Ecoomics, Uiversity of Chicago. Prelimiary ad icomplete. E-mail: mador @uchicago.edu.
1 Itroductio Ethic miorities have specialized as shopkeepers ad moeyleders throughout history. It has occurred with such regularity that some groups i diaspora have developed a reputatio as middleme miorities. This was historically the case for the Jews i Christia Europe ad the Christia Armeias i the Ottoma Empire; ad more recetly the Idias ad the Chiese i Southeast Asia, Africa ad the Americas. ot oly do these groups specialize as middleme, they are also strikigly successful i doig so. 1 Sowell [10] demostrates how widespread the pheomeo of middleme miorities is i history, ad how commo is their success. 1.1 Social discrimiatio It is a corerstoe i the ecoomics of discrimiatio that market discrimiatio results i greater ecoomic losses for the miority tha for the majority, just as a small coutry su ers more from a trade embargo tha does a large coutry, Becker [1]. The more itriguig the, the extraordiary ecoomic success of the Jews ad other middleme miorities. The aalysis here di ers from the stadard theory of discrimiatio by studyig what happes whe a miority group is culturally isolated but ecoomically itegrated with the majority. The miority is discrimiatig or discrimiated agaist i the cotext of social ad cultural iteractio, but its members are fully participatig 1 These groups have bee successful to the extet that they are free to compete ad ot legally discrimiated agaist that is. The hatred towards ad persecutio of these groups is aother early uiversal pheomeo, likely i tur to be liked to their ecoomic success. 2
i the market ecoomy. o discrimiatio coe ciet, Becker [1], taxes the market trasactios betwee miority ad majority members. As a illustratio of how social discrimiatio ad market discrimiatio ot always go had i had, cosider Shakespeare s cotroversial The erchat of Veice. As the Jews are forced to live withi the co es of the Ghetto, the Jewish moeyleder Shylock tells the Christia Atoio: "I will buy with you, sell with you, talk with you, walk with you, ad so followig; but I will ot eat with you, drik with you, or pray with you." It is demostrated i what follows that social discrimiatio, as opposed to market discrimiatio, ca result i a favorable ecoomic outcome for the miority. It is importat to stress that this applies oly to the ecoomic aspects of well-beig sice, depedig o the degree of edogeeity of social iteractio, the overall situatio is likely still to be worse for the miority. 1.2 Iteractio as a factor i productio There are two fudametal buildig blocks of the theory. First, the productivity of middleme icreases whe culturally ad socially iteractig with other middleme. Secod, a miority populatio has a absolute advatage i the iteractig activities coductive for middleme. The former is dealt with brie y i this subsectio whereas the latter is discussed extesively i the remaider of the paper. The rst questio is thus why middleme bee t from iteractig socially with other middleme. Social iteractio here deotes o-ecoomic activities such as family gatherigs, religious activities, leisurely discussios ad more. 3
I the ecoomic theory of trade ad iteractio it has bee commo for some time to stress the importace of cotractability. For example, Greif [3] ad Greif, ilgrom ad Weigast [4] iterpret traders coalitios ad merchat guilds i the iddle Ages as clubs eablig cotract eforcemet. I this cotext social iteractio ca be see as stregtheig eforcemet; it icreases the cost of breakig a cotract by addig social repercussio to ecoomic pealty. A secod aspect, which is ofte overlooked i favor of cotractual issues, is the iformatio cotet of iteractio. For middleme this ivolves exchagig iformatio about the chages i supply ad demad for all the various goods they trade i. Which model to choose is a questio of whether the asymmetry or the dispersio of iformatio is stressed. Sice these two approaches are either mutually exclusive or ideti ed here, i the remaider of the paper it su ces to postulate that social iteractio i some way icreases the productivity of middleme. A middlema s productivity bee ts the from iteractig socially with other middleme. ore speci cally, as will be formalized i subsequet sectios, the more middleme he iteracts with, the higher is his productivity. 1.3 The miority advatage The secod questio is why miorities have a absolute advatage i iteractio that is coductive to middleme. The hypothesis i this paper is that small groups come to egage i close-kit social iteractio more aturally. If iteractio is limited to a socially isolated miority, the ki-of-ki is more likely to be immediate ki as well. 4
I a group where iteractio is structured i this way it is less costly, i terms of the social utility forgoe, to create a group of middleme where every middlema socializes oly with other middleme. The structure of social iteractio chages i respose to the productive value of middlema iteractio. evertheless, groups with aturally close-kit iteractio exhibit a complemetarity betwee social iteractio ad middlema activities that other groups do ot. This otio is formalized i the followig sectios. First a theory is developed where social iteractio takes place o a radom ecouter basis, a simplifyig assumptio frequetly used i the iteractio literature. This shows oe aspect of the relatioship betwee group size ad iteractio itesity, but it does ot deal with issues of group formatio. The subsequet sectio therefore edogeizes iteractio. The al sectio applies the theory to prelimiary data o ethic specializatio i the Uited States. 2 A theory of exogeous iteractio The labor market is composed of two professios; agricultural workers ad middleme. The populatio is divided ito two ethicities with people belogig to the miority, say Jews, ad people to the majority, say Christias, where <. The two groups iteract with each other i the market but ot otherwise; each perso iteracts socially with a represetative sample of his ow ethic group oly. Let x be the fractio of Jews workig as middleme. A fractio x of the frieds of ay Jew are cosequetly middleme. The correspodig fractio for a Christia is X. 5
iddlema activity is iformatio itesive ad iformatio exchage ad social iteractio are complemetary. Idividual productivity i the middlema sector varies positively with the umber of middleme a perso kows. The productivity of a Jewish middlema is (x), ad of a Christia middlema (X), where 0 > 0 ad (0) > 0. The fact that everyoe has the same productio fuctio implies that there is o market discrimiatio ad that both groups are equally skilled as middleme. Wages i the agricultural sector are ormalized to zero which implies that the middlema professio is always more productive. The demad for middleme is xed at where 0 < < +. The exact structure of aggregatio is abstracted from. It is postulated istead that the ecoomy is Pareto e ciet. A e ciet ecoomy allocates Jews ad Christias betwee the two sectors, choosig x ad X to maximize total productio Y (x; X) = x (x) + X (X) (1) subject to x + X ad x; X 2 [0; 1]. Sice the middlema professio is more productive tha farmig it follows that as may as possible, idividuals, will be allocated to the middlema sector. To determie what fractio x of Jews ad what fractio X of Christias that will work as middleme, begi by cosiderig the chage i total productio from a margial icrease i x at the expese of X dy dx x; x = (x) (X) + x 0 (x) X 0 (X) (2) 6
This shows that there is o asymmetry o the margi betwee the miority ad the majority. I fact, whe both groups are equally active as middleme, x = X, there is o chage i productio at all from a margial shift betwee the two groups. Addig a additioal middlema to the miority raises the group s fractio of middleme more, ad cosequetly raises idividual output more, tha it would for the majority. But this advatage of the miority is o set by the fact that the absolute umber of middleme i the miority is smaller, ad cosequetly so is the umber of people who bee t from a icrease i idividual output. Sice this is a o-covex optimizatio problem a margial aalysis does ot su ce for determiig the most productive allocatio. The asymmetry betwee the groups lies i the feasible levels of x ad X ad ot i their margial e ects. I fact, for a give size of the middlema sector there is a optimal group size, ad this size is trivially sice such a group ca achieve the greatest cocetratio of middleme. Therefore, if the Jews are ot too few relative to the middlema sector, this professio will be the exclusively Jewish. Propositio 1: If the miority specializes as middleme. Proof: Cosider total productio i a miority-oly middlema sector, which ca be expaded ad writte as Y ; 0 = = ( X) + X (3) Compare this to productio whe at least some majority members are 7
ivolved too Y X ; X = ( X) X + X (X) (4) where X > 0. Comparig the rst term i (4) with the rst term i (3), ad the secod term with the secod term, it is clear that miority-oly productio is more e ciet sice is strictly icreasig ad is greater tha both X ad X for all feasible X (at most X ca be ). This is the cetral result, the miority domiates the middlema professio sice the feasible cocetratio of middleme is greater for the miority tha for the majority. It is the cultural isolatio of the miority which eables or forces it to achieve such a high degree of specializatio. The miority therefore has a absolute advatage as middleme ad is also more productive tha the majority. Returig to the otio of optimal group size, the followig corollary establishes that if there are too few Jews relative to the size of the middlema sector, the it is the Christia majority istead who will domiate the busiess. Corollary: If = the majority specializes as middleme. The proof is similar to the proof above ad show i the appedix. I this case it is the Christias who are more adept at creatig a eviromet of dese social iteractio ad iformatio exchage. Ay Jewish presece would just serve to dilute the Christia middlema etwork. This corollary shows that it is ot the smalless of a group, but its size per se, which determies whether it has a absolute advatage as middleme. 8
The exogeously imposed radomess of iteractio is usatisfactory sice there are strog icetives to choose who to socialize with. It is for example to be expected if Christias would wat to covert to Judaism. Which was ot ucommo i the early iddle Ages before the Catholic Church reversed the icetives. Aother likely outcome is for Christias to simply form subgroups of optimal size. A theory of edogeous iteractio is eeded to deal with these questios. I the ext sectio iteractio is cosequetly edogeized, but rst the full implicatios of exogeous iteractio are derived. These are summarized i the gure o page 12. Results for other combiatios of (; ; ) deped o whether productio is covex i the iteractio desity or ot. Too see this, assume rst that the fuctio is covex, 00 0, which gives the followig useful lemma. Lemma: If is covex there is always specializatio i the sese that if both x ad X are positive, the either x = 1 or X = 1. Proof: It is equivalet to prove that e ciet productio requires a corer solutio. Take the secod derivative of productio, di eretiatig (2) oce more. d 2 Y dx 2 x; x = 2 0 (x) + x 00 (x) + (20 (X) + X 00 (X)) (5) With both 0 (x) > 0 ad 00 (x) > 0, the secod derivative is strictly positive ad productio is strictly covex i x. Sice dy x; x dx is zero at x = X, this is the global miimum; icreasig x decreases Y if x < X ad icreases Y if x > X. As a result, there ca be o iterior 9
solutio. This is a lemma about how the ecoomy tries to achieve as ethically homogeous a middlema sector as possible. It is iformative sice it rules out mixed solutios with some Jews workig as middleme ad some i agriculture, ad some Christias as middleme ad some i agriculture. The followig shows that give this drive for homogeeity there is a poit at which the ecoomy abruptly switches from Jewish to Christia specializatio. Propositio 2: If is covex there is a with < < such that for < the miority specializes as middleme, ad for > the majority specializes as middleme. Proof: Propositio 1 demostrates that the miority specializes whe. What remais to aalyze is <. Cosider rst < <. Give the lemma it su ces to compare miority with majority specializatio. De e a ew fuctio F () as the di erece betwee the two. F () = Y 1; Y 0; = (1) + ( ) (6) If F is positive the miority specializatio is more productive ad vice versa. Clearly, F () > 0 ad F () < 0. To determie what happes i 10
the iterval < <, cosider the derivative of F which is F 0 () = + 0 0 (7) This derivative is strictly egative sice is icreasig ad covex. It follows that miority specializatio is more productive iitially but becomes less so as the middlema sector grows. At some poit, where < <, it is idi eret which group specializes as F ( ) = 0. Beyod this poit majority specializatio is more productive. This proves the case for < <. The corollary proved the case for =. It remais to be show that the majority cotiues to specialize also for <. This proof is similar to the oe above ad is show i the appedix. The ituitio is quite straightforward. At rst, as the middlema sector grows beyod the extreme over-represetatio of Jews cotiues, x = 1, while the additioal positios are lled with Christias. The few Christia middleme eterig the idustry are extremely ie ciet sice the Christia desity is so low; but this is still better tha the alterative which, accordig to the lemma, is to give up o high desity Jewish iteractio ad replace it with medium desity Christia iteractio. As the middlema sector cotiues to grow however, so does the potetial desity of Christia-oly iteractio, ad evetually the ecoomy switches abruptly at. 11
x 1 + 0 0 + ( ) The fractio of middleme who are Jews ( x ) as a fuctio of the size of the middlema sector ( ). Whe a fractio + of middleme are Jews, x = X. For large eough a Jewish populatio, the miority domiates the middlema sector. Productivity is covex. Fially, to see that covexity is eeded for the lemma o ethic homogeeity to hold, cosider a o-covex productio fuctio where a threshold fractio must work as middleme for iteractio to have ay value; = 0 > 0 if x > b ad zero otherwise (ad equivaletly, X > b for Christias). 2 I this case, if the middlema sector is so large that o sigle group ca completely domiate it, <, ad if (; ; ; b) is such that b + b < b +, the both the miority ad the majority must work as middleme; but either group 2 This fuctio violates the assumptio that productivity is strictly icreasig, 0 > 0, but it is easy to imagie a reshaped versio that would coform to this while still maitaiig the step-property assumed here. 12
specializes i the sese that some people of both groups work as agricultural workers as well. This goes agaist the lemma. The reaso for this is that if oe group specializes completely, x = 1 or X = 1, the there are fewer middleme i the other group tha the threshold b, so that their productivity reaches zero. Therefore, istead of wastig the e ort of these zero-productivity middleme, at o loss of idividual productivity some middleme positios ca be trasferred from oe group to the other, allowig both groups to exceed the threshold b. 3 A theory of edogeous iteractio This sectio develops a model of social iteractio determied by prefereces for kiship, or friedship more geerally. The objective is to characterize the structure of iteractio give a limited amout of time available for socializig. As i the previous sectio the focus is o Pareto e ciet outcomes. These are oly cojectured sice the formal structure is a complicated object. 3.1 Describig the social structure Let be the set of all the L idividuals i the ecoomy. People egage i two activities, labor ad social iteractio. iteracts socially with d > 2 others. Leisure time is limited ad every perso These d idividuals ca be thought of as close ki or frieds. The social structure is aalyzed by choosig a perso i ad iteratively examiig his iteractios through a brachig process. Take a idividual ad de e the sigleto set (0) as that perso. Let (1) be the set of 13
people that he iteracts with directly. The people i (1) i tur iteract ot oly with (0) but also with others, some of whom are potetially i (1) themselves. De e (2) as the set of those that iteract with (1) but who are ot i (0) or (1) themselves. The set (1) is the set of close ki ad the set (2) is the set of ki-of-ki that are ot immediate family themselves; all from the viewpoit of (0). Cotiuig by iteratio to more ad more distat relatios, de e (r) as the set of people kow rst after r steps. This is the set of people that iteract with those i (r 1) but that are ot i (r 1), or i (r 2), themselves. The variable r deotes what is sometimes called the degree of separatio betwee the iitial perso i (0) ad the people i (r), a measure of the social distace betwee idividuals. This is a brachig process. The sets are mutually exclusive, (r) \ (r 0 ) = ;, but they eed ot be exhaustive, lim r!1 [ r q=0 (q) 6=, sice there could be subsets of society that are ot iteractig either directly or idirectly. As a illustratio, take the experimetal results of ilgram [7] i the 1960 s, which showed that Americas were acquaited through at most six degrees of separatio. This is sometimes called the Small World problem. I the otatio of the curret paper this correspods to [ 6 r=0 (q) =. This is just to illustrate the otatio, to actually apply ilgram s result here would be misleadig sice the de itio of iteractio ad its applicatios di er. 3.2 Social prefereces There is social discrimiatio. People di er i their social characteristics ad i what characteristics they value i others. Iteractio betwee two people i ad j 14
geerates social utility u (i; j) which for simplicity is assumed to be trasferable. The populatio is divided i two ethic groups, Jews ad Christias where the Jews are i miority. There is a strog preferece for ethicity i the sese that it is always preferable to socialize withi ethic groups tha across groups. Assume that withi-group utility is etirely radom. Cosider what happes if the social structure is such that it maximizes total social utility. complexity. 3 Determiig this structure is a matchig problem of cosiderable Assumig that the ecoomy is very large, the followig is a cojecture of the properties of the geeric case. 3.3 Close-kit groups Deote by s (r) the cardiality of the set (r). Sice every perso i (r) by de itio iteracts with d idividuals, at least oe of whom is i (r 1), the process is bouded by s (r + 1) s (r) (d 1) (8) I geeral this equatio holds with iequality. The reaso for the slowdow of the expasio is threefold; rst, a perso i (r) ca iteract with more tha oe perso i (r 1), secod, a perso i (r) ca iteract with others i (r), ad ally, more tha oe idividual i (r) ca iteract with the same idividual i (r + 1). These three combie to prevet each perso i (r) from addig a full d 1 ew 3 I graph theory terms the matchig problem is to take a complete graph of order L, to assig umbers to each edge, i particular to assig the umber u (i; j) to the edge betwee vertices i ad j ad so o, ad the to choose the d-regular subgraph of order L whose edges sum to the greatest value. 15
idividuals to (r + 1). Give the ethic prefereces, the structure that maximizes social utility ivolves withi-ethic group iteractio oly. Sice the Jewish group is smaller tha the Christia group, the brachig process (r) expads less rapidly i the former. This is the precise meaig of close-kit iteractio. A cetral property of the brachig process is that it expads so that i the limit, lim r!1 [ r q=0 (q), it icludes everyoe with the same ethicity as (0). This implies that the ethic group is coected. Every idividual iteracts either directly or idirectly with the etire group. To see why, cosider a sketch of what happes if this were ot true, if the process i the limit stops short of icludig the etire ethic group. I this case, sice (r) evetually must become arbitrarily small relative to the ucoected set, the likelihood that someoe i (r) iteracts with others i (r), or that more tha oe perso i (r) iteract with the same idividual i (r + 1), is also arbitrarily small. But the the process i (8) holds with equality agai, ad the expasio gais speed so that s (r + 1) > s (r). This i tur cotradicts the assumptio that the process stops before everyoe is coected. Cojecture therefore that everyoe i the same ethic group is coected. This is the structure that maximizes social utility. 3.4 iddleme ad iteractio There are middleme, < L, the others work as farmers with productivity ormalized to zero. Every perso has the same iheret ability to be a middlema. Social iteractio complemets middlema activities; the more middleme a perso 16
iteracts with the greater is his potetial productivity as a middlema. Take a perso deoted by (0). Let x be the umber of middleme he kows, this is equivalet to the umber of middleme i (1). The potetial productivity of (0) as a middlema is the (x) where 0 > 0 ad (0) > 0. Cosider a social structure that maximizes productio. Clearly this structure is such that there are middleme ad every middlema iteracts with as may other middleme as possible, i other words with d other middleme. Total productio is the (d) ad it follows that all close ki (1) of a middlema (0) are middleme. Sice the close ki of (1) are middleme i tur, everyoe i (2) are middleme too. Cotiuig like this, for ay middlema (0), everyoe i the set lim r!1 [ r q=0 (q) are middleme as well. This is the social structure that maximizes productio. 3.5 iority specializatio Sice social utility is trasferable a social structure that maximizes both social utility ad productio is Pareto e ciet. If such a structure exists the all structures that do ot maximize both are ie ciet. Assume for simplicity that there are Jews ad L Christias. There are three possibilities, either all middleme are Jews, all are Christia or there are some from either group. Cosider what happes if all middleme are Jews. The trivially, sice all Jews are middleme, the structure that maximizes social utility also maximizes productio. Therefore, Jewish specializatio is Pareto e ciet. Cosider what happes if all middleme are Christia. Take the structure that 17
maximizes social utility, the all Christias are coected but this ecessarily implies that the cardiality of lim r!1 [ r q=0 (q) is greater tha sice the size of the Christia group is greater tha. Cosequetly, some Christia middleme must iteract with some farmers. This structure therefore does ot maximize productio, ad as a result it caot be Pareto e ciet. The same is trivially the case if some middleme are Jews ad some are Christias. Therefore, cojecture that, also i the case of edogeous iteractio, the e ciet outcome is for the miority to geerically specialize as middleme. ote that although the miority is likely to succeed better ecoomically tha the majority, it pays a social cost i the form of less choice ad, depedig o how u (i; j) is geerated, less social utility. A atural extesio of the curret model is to edogeize ethicity completely. I that case the miority would be more successful ecoomically, less fortuate socially, ad exactly as well-o i total as is the majority populatio. 4 Self-employmet clusters i the U.S. Ethic miorities i the Uited States as i other coutries specialize as shopkeepers ad moder day equivalets. Some of the most otable clusters are the Gujarati motel owers ad the Korea dry-cleaig etrepreeurs. The Chiese-America specializatio i lauderig a cetury before the preset day Korea domiace, ad the Jewish garmet idustry o ahatta s lower east side at that time, are well-kow historical examples of the same pheomeo (see table o page 26). 18
Self employmet clusters i 2000 Origi Laguage Idustry Total Ratio Idia Gujarathi Hotels 3,988 (71) Korea Korea Lauderig 12,106 (43) Idochia Arabic Food st. 1,015 (22) Ethiopia Amharic Taxicabs 1,139 (17) Greece Greek Restaurats 7,309 (16) Bagladesh Begali Taxicabs 1,199 (15) Korea Korea Liquor st. 1,782 (15) Vietam Vietamese Fisheries 1,033 (15) Pakista Urdu Taxicabs 2,307 (14) Korea Korea Dry goods 1,425 (14) ajor U.S. self employmet clusters i 2000. Total is the umber of self employed. Ratio is the fractio of the group s total workforce that is self employed i the idustry, divided by the correspodig fractio for immigrats who do ot speak the laguage of that group. Oly clusters with more tha 1000 self employed are show. Source: Cesus, IPUS. The theory i the previous sectios has di eret predictios for wage-earers ad self-employed. Although it is the case that a worker i geeral bee ts from workig with others of the same ethicity, this is a force towards ethically homogeeous workplaces but ot ecessarily towards large scale ethic specializatio. It is bee cial if all workers i a grocery store speak the same laguage, but the laguage spoke by workers i other grocery stores is ot very importat. It is a di eret situatio for the self-employed sice they are their ow maagers ad have to iteract with the outside. Here the ethicity of other shop-owers should matter more ad the theory of social iteractio is the relevat. 19
A prelimiary look at occupatioal data idicates that specializatio ideed is more importat for the self-employed tha for wage-earers. Below is data o selfemploymet ad employmet i some traditioal immigrat occupatios. Liquor stores Origi Laguage Wage Self Ratio Iraq Arabic 1000 734 (56) Syria Arabic 433 303 (43) Jorda Arabic 270 176 (20) Idia Gujarati 444 592 (17) Korea Korea 1318 1782 (15) Idia Pujabi 366 227 (11) Lebao Arabic 28 156 (10) Cambodia o Khm. 118 211 (10) Idia Hidi 262 180 (3) Vietam Vietam. 306 171 (.9) Immigrats 9,196 US bor 15,510 Gas statios Origi Laguage Wage Self Ratio Lebao Arabic 1,126 506 (30) Idia Pujabi 1,939 556 (25) Turkey Turkish 959 280 (21) Pakista Urdu 2,730 601 (17) Iraq Arabic 431 205 (14) Idia Gujarati 888 448 (11) Ira Farsi 882 496 (10) Idia Hidi 1,639 385 (6) Korea Korea 1,037 368 (2) exico Spaish 9,661 263 (.1) Immigrats 10,001 US bor 28,336 The ethic groups i the U.S. with the greatest umber of self employed i the idustry. Ordered accordig to ratio (right colum.) umber of wage earers (middle colum) ad self employed (secod from right) i 2000. 20
Lauderig Origi Laguage Wage Self Ratio Korea Korea 10,143 12,106 (43) Ira Farsi 426 566 (4) Idia Gujarati 671 414 (3) Chia Chiese 1,299 943 (2) Vietam Vietam. 2,682 990 (2) Italy Italia 361 294 (1) Russia Russia 686 339 (1) Philippies Tagalog 2,173 371 (.4) Cuba Spaish 1,612 273 (.4) exico Spaish 38,087 806 (.1) Immigrats 29,928 US bor 33,313 Hotels Origi Laguage Wage Self Ratio Idia Gujarati 4,195 3,988 (71) Idia Saskrit 1,329 707 (27) Taiwa Formosa 400 294 (12) Idia Hidi 2,046 678 (6) Taiwa Chiese 955 247 (3) Germay Germa 2,946 312 (2) Polad Polish 2,810 344 (2) Korea Korea 3,604 537 (2) Chia Chiese 5,055 280 (.8) exico Spaish 101,122 784 (.2) Immigrats 18,328 US bor 52,098 Taxicabs Origi Laguage Wage Self Ratio Ethiopia Amharic 1,408 1,139 (17) Bagladesh Begali 1,471 1,199 (15) Pakista Urdu 2,973 2,307 (14) igeria Kru 995 1,479 (12) Idia Pujabi 1,739 1,230 (12) Haiti Frech 2,891 1,989 (5) Russia Russia 2,862 2,294 (4) Dom. Rep. Spaish 4,832 2,924 (4) Ecuador Spaish 1,310 964 (3) exico Spaish 3,476 1,024 (.1) Immigrats 45,773 US bor 34,133 Persoal services Origi Laguage Wage Self Ratio Vietam Vietam. 28,262 14,436 (8) Italy Italia 2,803 2,715 (4) Korea Korea 8,808 4,197 (3) Germay Germa 1,594 1,514 (2) USSR/Rus. Russia 4,975 1,706 (1) Germay Eglish 2,314 2,001 (1) Jamaica Eglish 1,778 1,563 (1) Eglad Eglish 2,878 1,607 (.9) Cuba Spaish 3,651 1,656 (.8) exico Spaish 14,824 7,390 (.3) Immigrats 99,759 US bor 550,660 21
Food stores Origi Laguage Wage Self Ratio Idochia Arabic 1,521 1,015 (22) Iraq Arabic 2,245 1,088 (11) Korea Korea 12,188 8,018 (9) Pakista Urdu 4,319 1,751 (7) Idia Gujarati 3,517 1,734 (7) Italy Italia 5,093 1,390 (3) Dom Rep. Spaish 14,989 2,122 (2) Vietam Vietam. 10,189 1,730 (1) Chia Chiese 8,153 1,269 (1) exico Spaish 96,419 5,633 (.4) Immigrats 64,605 US bor 139,649 Restaurats Origi Laguage Wage Self Ratio Greece Greek 10,953 7,309 (16) Italy Italia 10,350 6,208 (6) Thailad Thai 8,685 1,709 (5) Taiwa Chiese 5,944 2,747 (5) Chia Chiese 58,061 11,893 (5) Korea Korea 23,522 10,715 (5) Japa Japaese 10,790 2,193 (3) Ira Farsi 5,264 2,123 (3) Vietam Vietam. 24,752 4,104 (1) exico Spaish 453,775 17,041 (.5) Immigrats 154,063 US bor 325,312 Refereces [1] Becker, Gary, The Ecoomics of Discrimiatio (Chicago: Uiversity of Chicago Press 1957). [2] Cohe, Robi, Global diasporas: a itroductio (Seattle: Uiversity of Washigto Press, 1997). [3] Greif, Aver, "Cotract Eforceability ad Ecoomic Istitutios i Early Trade: The aghribi Traders Coalitio," America Ecoomic Review, Vol. 83, o. 3 (Ju., 1993), 525-548. 22
[4] Greif, Aver, ilgrom, Paul; ad Weigast, Barry, "Coordiatio, Commitmet ad Eforcemet: The Case of the erchat Guild," Joural of Political Ecoomy, Vol. 102, o.4 (Aug., 1994), 745-776. [5] Lada, Jaet, "A Theory of the Ethically Homogeeous iddlema group: A Istitutioal Alterative to Cotract Law," Joural of Legal Studies, Vol. 10, o. 2, (Jue, 1981), 349-362. [6] Lazear, Edward, Culture ad Laguage, Joural of Political Ecoomy, Vol. 107, o. 6, (December 1999), 95-126. [7] ilgram, Staley, "The Small World Problem," Psychology Today, Vol. 22, (ay, 1967), 61-67. [8] ilgrom, Paul, orth, Douglass; ad Weigast, Barry, "The Role of Istitutios i the Revival of Trade: The edieval Law erchat, Private Judges, ad the Champage Fairs," Ecoomics ad Politics, Vol. 1, (ar., 1990), 1-23. [9] Sowell, Thomas, Ethic America (ew York: Basic Books, 1981). [10] Sowell, Thomas, igratios ad cultures: a world view (ew York: Basic Books, 1996). [11] Therstrom, Stepha (ed.), Harvard Ecyclopedia of America Ethic Groups (Cambridge: Harvard Uiversity Press, 1980). 23
5 Appedix Corollary: If = the majority specializes as middleme. Proof: Similar to Propositio 1, subtract the productio of a combiatio of miority ad majority middleme from the productio of majority-oly middleme. Y (0; 1) Y x; x = x (1) ( x) (1) (9) x x (x) ( x) where x > 0. It follows that majority-oly productio is greater sice is strictly icreasig ad 1 x ad 1 > x Propositio 2 (secod part): If is covex ad < the majority specializes as middleme. Proof: The lemma esures that it su ces to compare miority with majority specializatio. De e a fuctio G () as the di erece betwee the two. G () = Y 1; Y ; 1 (10) = (1) + ( ) ( ) (1) (11) With G ( + ) = 0, ad usig the fact that G () = F () < 0, it 24
follows that the majority specializes both whe = ad whe = +. To determie what happes i the itermediary case, cosider the derivative of G which is G 0 () = 0 + (12) 0 ote that > for < < +. To see why, apply the same reasoig oce more by de ig a fuctio H () = Evaluate it at the corers, H () = H 0 () = 1 Give 1 >. > 0 ad H ( + ) = 0. Sice < 0 it follows that H () > 0 i the relevat iterval. for < < + it the follows that the derivative G 0 () is strictly positive i the relevat iterval, ad as a result the fuctio G () is strictly egative i that same iterval. 25
Self employmet clusters 1910 Origi Laguage Idustry Total Ratio Germay Yiddish Retail st. 1,008 (110) Chia Chiese Lauderig 6,045 (99) Turkey Arabic dial. erchad. st. 3,274 (23) Yugoslavia Serbo Cr. erchad. st. 1,008 (18) Hugary agyar Coal miig 1,008 (17) Russia Russia Wholesale tr. 2,016 (15) Germay Germa eat prod. 1,259 (15) Russia Yiddish Build. mat. ret. 2,016 (14) Austria Yiddish Liquor st. 1,008 (14) Caada Germa Apparel st. 1,008 (13) Caada Eglish Legal services 1,512 (13) Russia Yiddish Wholesale tr. 8,315 (13) Filad Fiish Fisheries 1,008 (12) Eglad Eglish Egieerig 1,764 (11) Russia Yiddish Apparel 11,835 (11) Austria Yiddish Apparel st. 3,779 (10) Demark Germa Agriculture 1,006 (10) Switzerlad Germa Priv. househ. 1,511 (9) Russia Yiddish aufact. 1,008 (9) Russia Russia Retail st. 1,259 (8) Austria Yiddish Apparel 1,511 (8) Caada Gaelic edical 1,008 (8) Russia Yiddish Apparel st. 15,869 (7) Russia Yiddish erchad. st. 21,414 (7) Austria Yiddish erchad. st. 3,526 (7) Self employmet clusters 2000 Origi Laguage Idustry Total Ratio Idia Gujarati Hotels 3,988 (71) Lebao Armeia Jewelry st. 392 (66) Iraq Arabic Liquor st. 734 (56) Syria Arabic Liquor st. 303 (43) Korea Korea Lauderig 12,106 (43) Romaia Romaia Welfare ser. 507 (35) Yeme () Arabic Food st. 701 (34) Lebao Arabic Gasolie st. 506 (30) Idia Saskrit Hotels 707 (27) Idia Pujabi Gasolie st. 556 (25) Israel/Pal. Arabic Food st. 659 (22) Idochia Arabic Food st. 1,015 (22) Korea Chiese Restaurats 648 (21) Korea Korea Shoe repair 822 (21) Cambodia Chiese Restaurats 882 (19) Ira Farsi otor veh. 360 (18) Korea Korea Shoe stores 559 (18) Paraguay Spaish Priv. househ. 385 (18) Ethiopia Amharic Taxicabs 1,139 (17) Pakista Urdu Gasolie st. 601 (17) Idia Gujarati Liquor st. 592 (17) Greece Greek Restaurats 7,309 (16) Ira Farsi Dry goods 609 (15) Bagladesh Begali Taxicabs 1,199 (15) Korea Korea Liquor st. 1,782 (15) Clusters i the U.S. with more tha 1000 etrepreeurs (4 observatios) i 1910 ad 300 etrepreeurs (15 observatios) i 2000. 26