The Substitutability of Labor of Selected Ethnic Groups in the US Labor Market

Transcription

1 DISCUSSION PAPER SERIES IZA DP No The Substtutablty of Labor of Selected Ethnc Groups n the US Labor Market Martn Kahanec January 2006 Forschungsnsttut zur Zukunft der Arbet Insttute for the Study of Labor

2 The Substtutablty of Labor of Selected Ethnc Groups n the US Labor Market Martn Kahanec IZA Bonn Dscusson Paper No January 2006 IZA P.O. Box Bonn Germany Phone: Fax: Emal: za@za.org Any opnons expressed here are those of the author(s) and not those of the nsttute. Research dssemnated by IZA may nclude vews on polcy, but the nsttute tself takes no nsttutonal polcy postons. The Insttute for the Study of Labor (IZA) n Bonn s a local and vrtual nternatonal research center and a place of communcaton between scence, poltcs and busness. IZA s an ndependent nonproft company supported by Deutsche Post World Net. The center s assocated wth the Unversty of Bonn and offers a stmulatng research envronment through ts research networks, research support, and vstors and doctoral programs. IZA engages n () orgnal and nternatonally compettve research n all felds of labor economcs, () development of polcy concepts, and () dssemnaton of research results and concepts to the nterested publc. IZA Dscusson Papers often represent prelmnary work and are crculated to encourage dscusson. Ctaton of such a paper should account for ts provsonal character. A revsed verson may be avalable drectly from the author.

3 IZA Dscusson Paper No January 2006 ABSTRACT The Substtutablty of Labor of Selected Ethnc Groups n the US Labor Market * Ths paper nvestgates the substtutablty of labor of selected ethnc groups n the US labor market. In the generalzed Leontef framework, the analyss of US census-based data reveals that labor of non-whte ethnc groups s complementary to that of Whte ethnc group. Ths fndng supports the vew that the negatve relatonshp between the relatve earnngs of an ethnc group and ts relatve sze s a labor market phenomenon. Moreover, t mples that ethnc dversty of labor force has postve effects on aggregate output. Whle the estmated elastctes of complementarty are relatvely small, they are shown to generate sgnfcant effects, gven the very uneven dstrbuton of ethnc groups across local labor markets, as resultng from long-run mgraton patterns. JEL Classfcaton: J15, J24 Keywords: substtutablty, elastcty of substtuton, ethnc group, labor market Correspondng author: Martn Kahanec IZA P.O. Box Bonn Germany Emal: kahanec@za.org * I thank Jan van Ours, Sak Smulders, Joshua Angrst, Frederc Vermeulen, Dmtrs Pavlopoulos, and the partcpants of varous semnars at CentER, Tlburg Unversty, and IZA Bonn for helpful comments on the earler drafts of ths paper. All remanng errors are mne. Fnancal support from Volkswagen Foundaton for the IZA proect on "The Economcs and Persstence of Mgrant Ethncty" s gratefully acknowledged.

4 1. Introducton Two man obectves have drven economsts to study the nature of labor market competton between dfferent ethnc groups. 1 Frst, we strve to understand the dfferences n the economc status of varous ethnc groups n the labor market. Second, we would lke to provde sound assessment of labor market and mmgraton polces that am at obectves concernng nteracton of ethnc groups n the labor market. Such obectves nclude reducton of nter-ethnc nequalty, elmnaton of socal excluson of some ethnc groups, or eradcaton of labor market dscrmnaton. The substtutablty of labor of dfferent ethnc group s the key characterstc of the ethncally dverse labor market. 2 Unsatsfactorly, so far there s no consensus n the lterature on the substtutablty of labor of dfferent ethnc groups. Grant and Hamermesh (1981) studed the substtutablty of youths, Whte women, Whte men, Black adults, and captal n producton, estmatng a translog econometrc model over 67 standard metropoltan statstcal areas (SMSAs). They found that Black adults were substtutes for Whte men and complements to Whte women and youths n producton, although the statstcal sgnfcance of the relatonshps of complementarty was low. In a smlar framework, Grossman (1982) nvestgated the substtutablty of natves and mmgrants n producton to fnd that both foregn-born workers and second-generaton natve workers were substtutes for natve workers. Boras (1983) utlzed Dewert s (1971) generalzed Leontef approxmaton to a producton functon to study substtutablty of Black, Hspanc, and Whte male workers. Boras suggested that Black male workers mght be substtutes for Whte male workers and found evdence for complementarty between Hspanc and Whte male workers. Usng a smlar methodology, Boras (1987) 1 Ethnc group s defned as a partcular group of people who share soco-cultural characterstcs such as culture, relgon, language, hstory, belefs, customs, values, and morals that make them dstnct from the rest of the populaton n ther habtat. 2 In ths study I do not dstngush the varous possble sources of mperfect substtutablty of labor of dfferent ethnc groups. Such sources nclude hstorcal reasons and soco-cultural dfferences as n Hofstede (1980) and Boras (1994), organzaton of socal nteracton n human captal acquston as n Kahanec (2004), or constrants mposed upon some ethnc groups by the socety as n the dscrmnaton lterature based on Becker (1957) and Arrow (1972a, 1972b, 1973, 1998). That ethnc groups tend to specalze n certan types of obs and educaton has been dscussed by e.g. Alton and Blank (1998:3153) and Chswck (1988), respectvely. 2

5 examned the substtutablty of Whte, Black, Hspanc, and Asan male workers by mmgrant status over 84 SMSAs. In ths study he found that all mmgrant groups were substtutes for natve Whtes; however, ths evdence was not robust wth respect to endogenety of labor supply. Furthermore, he found that Black natves were substtutes for Whte natves, but dd not fnd such evdence for Hspanc and Asan natves. These studes are summarzed n Table 1 n the Appendx. The nconclusveness of ths evdence s startlng. Several results pont at substtutablty, but some suggest that labor of dfferent ethnc groups s complementary. Clearly, substtutablty and complementarty have very dfferent effects on the labor market. To llustrate ths, f labor of ethnc groups A and B s complementary n producton, ncrease n the relatve number of workers of ethnc group A ncreases the margnal product of workers from ethnc group B and vce versa. 3 As a consequence, assumng that changes n margnal products are reflected n wages, relatve earnngs of workers from group A vs-à-vs workers from group B decrease n the relatve number of workers from group A, ceters parbus. In contrast, f labor of ethnc groups A and B s substtutable, ncrease n the relatve number of workers of group A ncreases ther relatve wages vs-à-vs Whte workers. These dstrbutonal consequences of mperfect substtutablty of labor of dfferent ethnc groups make the queston of substtutablty of labor of dfferent ethnc groups hghly relevant. The general observaton that the elastctes reported n the abovementoned lterature are numercally small does not undermne the relevance of ths queston. The reason s that even small elastctes may generate sgnfcant effects when the varaton of ethnc composton of the labor force s hgh. And t s very hgh ndeed. To wt, n the US, the percentage of Blacks s about 33 tmes larger n the 75 th percentle than n the 25 th percentle school dstrct. Smlarly, there are about 10 tmes more Asans and 22 tmes more Hspanc per one hundred nhabtants n the respectve 75 th and 25 th percentle 3 There s robust emprcal evdence, ncludng the studes by Blalock (1956, 1957), Heer (1959), Brown and Fugutt (1972), Frsbe and Nedert (1977) and Tenda and L (1987), that non-whte ndvduals n regons wth a hgher non-whte share earn relatvely less than non-whte ndvduals n regons wth a smaller non-whte share. Ths evdence s summarzed n Kahanec (2004). 3

6 school dstrcts. 4 Such hghly uneven dstrbuton of ethnc groups across US local labor markets, manly resultng from long-run mgraton patterns, s argued below to explan a sgnfcant share of nterethnc earnngs dfferental. Ths study contrbutes to the substtutablty debate dscussed above by sheddng lght on the queston whether labor of the largest non-whte ethnc groups and the Whte ethnc group n the US s complementary or substtutable n producton. The practcal contrbuton s twofold. Frst, we learn about the drecton of the effects of ncreasng presence mmgrants and ther descendants n the US labor market on earnngs nequalty. Second, we learn about the effects of ethnc dversty of the labor force on aggregate output. To acheve ths obectve, ths study nvestgates a US Census-based dataset descrbed below that offers two man advantages. Frst, t permts a relatvely fne partton of the labor force nto ethnc groups, such that we can study labor market nteracton of fve non-whte and the Whte ethnc groups. Second, ths dataset permts a relatvely large varaton of the key explanatory varable the ratos of labor supples of dfferent ethnc groups. In partcular, gven that the baselne unt of observaton n the dataset (and of ths study) s the school dstrct, ths dataset has nformaton about more than 14,000 local labor markets. 5 Prevewng the man results of ths study, I emprcally establsh that the largest US non- Whte ethnc groups are complementary to the Whte ethnc group n producton. Ths fndng s robust wth respect to a number of alternatve specfcatons of the unt of study, sample, and producton technology. Gven ths result, ths study suggests that labor market forces dsadvantage members of those ethnc groups n terms of ther (relatve) earnngs per effcency unt of ther labor that form a large proporton n a local labor market. In addton, t suggests that ethnc dversty n the labor market exhbts complementartes that postvely affect aggregate output. 4 Percentles n ths secton refer to rankng of school dstrcts accordng to the respectve percentage of non-whte populaton. 5 The key queston concernng the choce of the unt of observaton s what the proper geographc defnton of the local labor market s. Senstvty analyss reveals that the results of ths study are robust n ths respect. See the dscusson below. 4

7 To establsh ths result, I proceed n a number of steps. In the followng two sectons I develop the baselne analytcal framework and provde the descrpton of the data. In the next secton I outlne the estmaton methods and establsh the man results. Then I test the valdty of the man results wth respect to some alternatve explanatons and specfcatons. In the fnal analytcal secton I study the substtutablty ssue n the constant elastcty of substtuton framework and estmate ths elastcty. Then I conclude and suggest ssues for further research. 2. The Model To nvestgate the producton relatonshps among non-whte and Whte ethnc groups, I assume a generalzed Leontef producton functon: = ( X X ) 1 2 C β (1) where C stands for output, X and X are, respectvely, the quanttes of labor nputs of ethnc groups and n the labor market and β s the technology parameter, whch s restrcted such that β = β. 6 Labor nputs and are complements whenever β > 0 and substtutes whenever β < 0. Assumng that frms n the labor market operate n a perfectly compettve ndustry, the system of labor demands derved from the producton functon (1) s: ( X X ) 1 2 W = β + β, (2) where W s the wage of ndvduals from group. Ths system of labor demands s partcularly useful for emprcal analyss, as t s lnear n parameters β and thus can be estmated by conventonal least squares methods. The nterpretaton of β s also straghtforward: β s postve (negatve) and the wage of group ncreases (decreases) n the number of type- ndvduals per type- ndvdual whenever type- and type- 6 Generalzed Leontef producton functon s a second order approxmaton to any arbtrary producton functon and the parametrc restrcton should be seen as an ntegral part thereof. See Dewert (1971) for a dscusson of the propertes of ths producton functon and Boras (1987) for a note on the choce between the generalzed Leontef and translog functonal forms. 5

8 ndvduals are complements (substtutes) n producton. Thus, accordng to the system of labor demands (2), the wage of members of ethnc group s affected by the numbers of members of other groups per member of group, X X. A useful transformaton of the coeffcent β s the one that lnks t to the Hcks partal elastcty of complementarty: e = CC CC, where C = C X and C = 2 C X X. 7 Namely, t can be shown that under the Generalzed Leontef producton functon the elastctes of complementarty are gven by: e and e β = for ( s s WW ) W =, = β for 2sW where s = W X C s the relatve share of ncome accrung to labor nput. The Hcks elastcty of complementarty measures the effect of a change n the relatve supply of nput on the relatve prce of nput, holdng the quanttes and margnal costs of other nputs constant. A useful property of the elastcty of complementarty s that ( ) d ln W d ln ( X ) = s e. In consequence, these elastctes completely descrbe the changes n wages resultng from changes n supples of labor nputs for any gven share of ncome accrung to the respectve labor nput. Estmaton of the demand system (2) nvolves three maor econometrc ssues. Frst, labor force s not necessarly homogenous across labor markets. Certanly, members of group may earn dfferent average wages n some regons than n others not as a result of regonal dfferences n relatve supples of labor nputs, but as a result of varaton of ther average sklls. To solve ths ssue, I adopt an analogue of the technque customary n the 7 See Hcks (1970). 6

9 lterature. 8 In partcular, I assume that the average earnngs of members of group n labor market n, E,n, depend on () the market-determned wage for the average member of group n labor market n, W, and () the dfference between the average skll level of members of group n labor market n and the average skll level of all members of group. Ths dfference,,n f,n f, n, s treated as a fxed effect such that, formally, a representatve member of group from labor market n earns wage E = W +,n,n f,n. It s assumed that f,n = Z + ε, where s the vector of observable characterstcs of,n,n Z,n ndvduals of type n labor market n and ε,n s the respectve random uncorrelated error. Assumng that n each labor market wages are determned accordng to the demand system (2), t follows that 1 2 ( X n X n ) + βz n n E, n β + β,,, + ε, =, (3) whch s the specfcaton of the system of labor demands used throughout the paper. Second, the relatve supples of labor nputs, X,n X, n, may be endogenous. Therefore, whle n the baselne analyss of ths paper the assumpton of nelastc labor supply s adopted, I extend the analyss to more complex supply condtons n Secton 5.1. In partcular, I adopt the conventonal approach to ths problem and address the endogenety ssue n the nstrumental varable framework. Fnally, although the focus of the analyss s on labor nputs, other nputs such as captal, land, and technology enter producton. In the lterature, ths ssue has often caused dffcultes. Scholars who attempt to account for captal admt that the measures of captal that they use are unsatsfactory or of lmted use. 9 Land and technology have not been, to my knowledge, addressed n ths context at all. Despte the lmtatons gven by the avalable data, n Secton 5.3 I address ths ssue and test the robustness of the predctons of ths paper usng the degree of urbanzaton and farmng as ndcators of captal and land utlzaton. The analyss s based on the assumpton that urbanzaton (farmng) s postvely (negatvely) related to captal 8 See Boras (1983) and Boras (1987). 9 See e.g. Grant and Hamermesh (1981), Grossman (1982), Boras (1983), and Boras (1987). 7

10 utlzaton and technologcal advancement and negatvely (postvely) to land utlzaton n producton. 3. Data The emprcal analyss s conducted on the dataset that contans data about 14,405 school dstrcts of the US, as compled n the Census 2000 School Dstrct Tabulaton (STP2) by the Natonal Center for Educaton Statstcs (NCES) of the US. 10 The auxlary data from the year 1990 are compled from the SDDB-School Dstrct Database (NCES ) as avalable at the Natonal Bureau for Economc Research. 11 Ths dataset contans economc and demographc nformaton about the Whte (non-hspanc) ethnc group, hereafter Whte, and fve non-whte ethnc groups: () Black or Afrcan Amercan, hereafter Black, () Amercan Indan or Alaska natve, hereafter Amercan Indan, () Asan, (v) Natve Hawaan or other Pacfc Islander, hereafter Pacfc Islander, and (v) Hspanc or Latno. Two ponts are worth mentonng n regard of ths partcular partton of the labor force. Frst, t covers most of the US labor force as dentfed n the 2000 Census. 12 Second, ths partton s approprate n the lght of the man nterest of ths study: the substtutablty of labor of dfferent ethnc and racal groups. In partcular, although further sub-parttons of workers of dfferent ethnctes based on age, mmgrant status, or gender certanly deserve further research, they are not the focus of ths study. 13 The school dstrct, a specal purpose admnstraton dstrct n the US n whch publc schools are admnstered, was chosen as the baselne unt of observaton. School dstrcts reflect the organzaton of socal and economc lfe of the populaton and thus provde a reasonable geographcal representaton of the local labor market. Nevertheless, t s necessary to evaluate senstvty of the results of ths study wth respect to the choce of The two remanng groups not covered here are Some other race and Two or more races. 13 See Grossman (1982) and Boras (1987) for a partton based on mmgrant status, Grant and Hamermesh (1981) and Boras (1987) for a partton based on gender, and Grant and Hamermesh (1981) for a partton based on age. The data does not permt partton by mmgrant status, age, or any other. It does permt partton by gender (and race), however. Supplementary nvestgaton shows that the man predctons of ths study are robust wth respect to restrctng the analyss to men. 8

11 the geographcal defnton of the local labor market. The robustness check that was conducted n ths matter nvolved estmaton of the model only for school dstrcts wth relatvely large populaton, thus more smlar to SMSAs. It turned out that the man results reported below are robust wth respect to such exercse. 14 For ths study, the most relevant nformaton n the NCES dataset nvolves earnngs and ncome, educatonal attanment, employment status and tme worked, and age structure of members of each racal and ethnc group mentoned above. The man statstcs for the key varables are depcted n Tables 2 to 4. As one can see, the average school dstrct has 7,768 full-tme workers of all races combned, whle the medan school dstrct has 2,325 full-tme workers. The relatvely large dscrepancy s due to a number of relatvely large dstrcts,.e. 113 school dstrcts have full-tme workng populatons above 100,000 and 6 out of these are above 500,000, but n more than 91 percent of school dstrcts the number of full-tme workers s between 100 and 30,000. Table 2 also reveals very large dscrepances between mean and medan numbers of non-whte full-tme workers, whch suggests concentraton of non-whte ethnc groups n subsets of school dstrcts. Table 2: Numbers of full-tme workers, by race. Race Mn Max Mean Medan All races 8 2,313,825 7,768 2,325 Whte 0 922,630 4,944 1,685 Black 0 528,105 1, Amercan Indan 0 11, Asan 0 228, Pacfc Islanders 0 27, Hspanc or Latno 0 630, Note: Computed for school dstrcts wth postve total populaton (14,375). Table 3 depcts that, as concerns medan earnngs, each non-whte ethnc group earns less than the Whte ethnc group. Ths s also true for average earnngs, wth the excepton of Asan workers. The reason that Asans on average earn more and n the medan school dstrct less than Whtes s also apparent n Table 3: the share of school dstrcts wth medan earnngs above 100,000 US dollars per year s by far the largest for 14 Results avalable upon request. The robustness check nvolved sample reductons such that the analyss was lmted to school dstrcts wth populaton larger than 30, 50, and 100 thousand nhabtants. 9

12 the Asan ethnc group. As concerns the relatve standng of the non-whte ethnc groups vs-à-vs the Whte ethnc group, non-whte people earn between 33.9 percent less and 2.8 percent more and between 31.8 percent and 2.5 percent less than Whte ndvduals, measured by mean and medan earnngs, respectvely. Table 3: Medan earnngs of full tme workers, by race. Race Percent of school dstrcts wth yearly medan earnngs Medan earnngs <2, ,000 Mean Medan Whte ,612 34,768 Black ,255 27,589 Amercan Indan ,125 25,661 Asan ,660 33,900 Pacfc Islanders ,714 28,572 Hspanc or Latno ,196 23,729 Note: Computed for school dstrcts wth postve total populaton (14,375). Mean and medan weghted by the respectve populatons of workers. In US dollars. Table 4: Percentages of people above 25 wth unversty educaton. Race Graduate or professonal degree Bachelor s degree Mean Medan Mean Medan Whte Black Amercan Indan Asan Pacfc Islanders Hspanc or Latno Note: Computed for school dstrcts wth postve total populaton (14,375). Mean and medan weghted by respectve populatons. Fnally, n Table 4 one can observe that some of the varaton of earnngs s due to varaton n educatonal levels. In partcular, each non-whte ethnc group has a lower educatonal level than the Whte ethnc group, measured by mean and medan percentages of respectve populatons wth graduate and undergraduate degrees. The only excepton are Asans, who attan a hgher educatonal level than Whtes. The 10

13 extraordnarly hgh educatonal achevement of Asans appears to be the explanaton of why ther earnngs more or less match the earnngs of Whtes. A note concernng the numbers of observatons s due before I proceed to the results. Whle there are 14,375 school dstrcts wth postve total populaton, n the analyss below observatons are lost due to two man reasons. Frst, a large number of observatons are lost as a result of the structure of the model. Namely, estmaton of a smultaneous equaton model wth each equaton representng one socal group mples that one can estmate the system only for those school dstrcts that contan all these socal groups. Second, a relatvely small number of observatons contan mssng nformaton, whch precludes ther ncluson n the analyss. To llustrate, n the baselne model of the next secton that nvolves the Whte ethnc group as well as all fve non- Whte ethnc groups, the frst restrcton reduces the number of school dstrcts to 2,009. Further 66 observatons are lost due to mssng nformaton, resultng n 1,943 observatons ncluded n the baselne model. Table 5: Numbers and medan earnngs of full-tme workers, by race. Dstrcts wth all socal groups present. Number of workers Medan earnngs Race Mean Medan Mean Medan Whte 19,623 9,700 38,312 36,562 Black 3, ,537 27,883 Amercan Indan ,746 26,516 Asan 1, ,715 33,514 Pacfc Islanders ,790 28,572 Hspanc or Latno 4, ,065 23,750 Note: Computed for the 1,949 school dstrcts ncluded n the analyss of Secton 4.4. Mean and medan weghted by respectve populatons of workers. In US dollars. To understand the consequences of such reductons of the sample, Table 5 lsts the basc statstcs of the sample of the baselne model. As one can observe comparng Table 5 to Tables 2 and 3, sample reducton has a mnor effect on mean and medan earnngs. The effect of sample reducton on mean and medan numbers of full-tme workers s one of a substantal ncrease of these numbers n the reduced sample. Ths s a natural consequence of the fact that sample reducton nvolved elmnaton of school dstrcts that 11

14 do not contan workers of each race, whch are typcally small school dstrcts. Straghtforward calculatons show, however, that the relatve numbers of non-whte workers between the full sample and the reduced sample are much more smlar than the absolute numbers. Aggregaton of ethnc groups nto one (multethnc) group ncreases the lkelhood that at least one of the aggregated ethnc groups s present n a school dstrct, thereby permttng ncluson of more school dstrcts n the analyss. Droppng a relatvely small ethnc group from the analyss has smlar effect. To wt, aggregaton of Asans and Amercan Indans and omttng Pacfc Islanders permts ncluson of 7,878 school dstrcts. Aggregaton of all non-whte ethnc groups but the Pacfc Islanders permts ncluson of as many as 13,335 school dstrcts. 15 In Secton 5.2 I nvestgate ths ssue further and establsh robustness of the results of the baselne analyss wth respect to aggregaton of non-whte groups. 4. Estmaton Methods and Results The NCES dataset contans all the necessary nformaton for the estmaton of the econometrc model (3). Labor nput X,n s defned as the number of full-tme workers from group that are 15 years old and over. Correspondngly, medan earnngs of fulltme workers older than 15 s the baselne measure of E. 16 The vector of observable,n characterstcs Z,n comprses educatonal ndcators measurng the percentages of adult members of group n school dstrct n wth () hgh school dploma, () some college but no degree, () assocate degree, (v) bachelor s degree, and (v) graduate or professonal degree. 17 Besdes these varables, regonal dummes are ncluded n every regresson 15 It turns out that these aggregatons are statstcally sensble. See Secton As an alternatve specfcaton, I re-estmated the model usng the weghted average of medan earnngs of full-tme and part-tme workers as the explaned varable and the ratos of the numbers of all non-whte and Whte workers as the explanatory varable. The results were very smlar to those obtaned for full-tme workers. 17 Further analyss showed that ncluson of () relatve numbers of workers that worked full-tme less than the whole year by weeks worked and race or () varables depctng the age structure of populaton by race n the vector Z,n does not affect the man results, whle reducng sample sze sgnfcantly. 12

15 throughout the analyss. 18 The purpose of these dummy varables s to pck the effect of nterstate varaton n development, nfrastructure, clmate, and other factors outsde the analyzed econometrc model that possbly affect the dstrbuton of earnngs. Econometrc model (3) s estmated usng the Zellner s seemngly unrelated regressons (SUREG) estmator, smultaneously mposng cross-equaton technologcal restrctons β = β mpled by the generalzed Leontef technology. Table 6 depcts the baselne estmates of the technologcal parameters. 19 The man result, showng up n column (1), s that labor of each non-whte ethnc group s complementary to that of the Whte ethnc group. Ths result s of substantal nterest, as t supports the vew that labor of non-whte and Whte workers s mperfectly substtutable n the labor market. Furthermore, that non-whte labor complements Whte labor n producton suggests that ethnc dversty s benefcal n terms of aggregate output, ceters parbus. And fnally, ths result s consstent wth the emprcal evdence of the drect relatonshp between Whte/non- Whte earnngs gaps and the relatve szes of the respectve non-whte ethnc groups. In partcular, complementarty mples that an ncrease n the relatve sze of a non-whte ethnc group ncreases Whte earnngs and decreases the earnngs of ths non-whte ethnc group, holdng the szes of other ethnc groups and the aggregate sze of the economy constant. As concerns the technologcal relatonshps among non-whte ethnc groups, there appears to be a sgnfcant complementary relatonshp between Pacfc Islanders and Asans, but all the other relatonshps are nsgnfcant. As concerns the educatonal varables, they are sgnfcant and have expected sgns and ther magntudes are ranked as expected These dummes represent school dstrcts accordng to the US Census Bureau Classfcaton: Md-West East North, Md-West West North, South Atlantc, South East Central, South West Central, North East New England, North East Md-Atlantc, West Pacfc except Hawa, West Mountan, and Overseas (Hawa and Puerto Rco). I oned Hawa and Puerto Rco to construct the Overseas category. 19 Technologcal parameters are reported only once; the restrcton β = β mples that the table of technologcal parameters s dagonally symmetrc. 20 In further analyss the parameters wth educatonal varables are not reported. 13

16 Table 6: Baselne estmates of the technologcal parameters. Medan earnngs of group, full-tme workers X X (1) (2) (3) (4) (5) (6) Whte Black Amercan Asan Pacfc Hspanc or Indan Islanders Latno Whte Black (5.9)** Amercan Indan (4.5)** (1.1) Asan (6.9)** (1.8) (0.0) Pacfc Islanders (2.2)* (1.5) (0.6) (3.4)** Hspanc or Latno (4.3)** (0.2) (1.8) (1.5) (0.9) Educaton (Group ): Hgh school 17, ,335 2,612 4,142 6,689 (3.9)** (0.5) (3.7)** (1.0) (2.5)* (3.7)** College, no degree 1,154 8,192 10,461 2,836 4,885 13,407 (0.3) (4.5)** (5.4)** (1.1) (3.0)** (8.1)** Assocate degree -4,684 11,195 13,142 12,060 5,973 5,922 (0.7) (4.1)** (4.5)** (3.1)** (2.6)* (1.7) Bachelor degree 59,341 21,875 16,297 25,783 16,962 31,042 (17.3)** (10.6)** (6.6)** (10.8)** (8.3)** (13.6)** Graduate or pro- 52,308 33,044 35,111 55,415 24,445 30,779 fessonal degree (11.7)** (12.6)** (10.8)** (24.3)** (10.5)** (11.8)** Constant 16,472 25,009 20,080 15,397 23,006 16,918 (6.4)** (18.0)** (12.4)** (8.6)** (12.3)** (20.5)** R-squared Observatons Absolute value of z statstcs n parentheses * sgnfcant at 5 percent; ** sgnfcant at 1 percent As concerns nterpretaton of the baselne results, t s nstructve to derve the crosselastctes of complementarty between the fve non-whte ethnc groups and the Whte ethnc group. Because these elastctes depend not only on the technologcal parameters e β but also on W and s, a decson has to be made about the values of W and s at whch these elastctes are evaluated. Means and medans are the natural 14

17 evaluaton ponts. Table 7 summarzes cross-elastctes of complementarty e and elastctes of factor prces s e between non-whte and Whte ethnc groups. Table 7: Cross-elastcty of complementarty and elastctes of factor prces. Cross-elastcty of complementarty Elastcty of factor prces (Change n the wage of Whte wth respect to the quantty of non-whte labor) Elastcty of factor prces (Change n the wage of non- Whte wth respect to the quantty of Whte labor) Mean Medan Mean Medan Mean Medan Black Amercan Indan Asan Pacfc Islander E Hspanc or Latno w Note: Evaluated at mean and medan and of the sample of Table 6, 1943 observatons. s These estmates confrm the fndngs of the prevous lterature that although the elastctes are statstcally sgnfcant, 21 the effects are not numercally large. As a consequence, short-run mgraton, whch nvolves relatvely small changes n ethnc composton of labor supply n a local labor market, has relatvely small effect on the relatve earnngs of dfferent ethnc groups. 22 When one compares school dstrcts wth markedly dfferent ethnc composton of labor, as resultng from long-run mgraton patterns, the mpled dfferences n earnngs dstrbutons may become substantal, however. To llustrate, consder the 20 th percentle school dstrct that has 9 and the 80 th percentle school dstrct that has 199 Black per 1,000 Whte full-tme workers. To estmate the dfference n Black-Whte earnngs dfferental between these school dstrcts, let us use 21 Concernng the sgnfcance levels of the respectve technologcal coeffcents from Table Gven the varaton of the earler results, drect comparson s almost mpossble. Among those results n the prevous lterature that establsh complementarty of non-whte and Whte labor, Boras (1983) fnds the elastcty of complementarty between Hspanc and Whte labor of about , thus slghtly hgher than my result of Grant and Hamermesh (1981) establsh somewhat hgher elastctes of factor prces for the substtutablty of Black workers wth Whte female workers, but ther results were not sgnfcant. 15

18 the estmate of the technologcal parameter from Table 6. In addton, assume that relatve labor nput supples are the only determnants of earnngs and that, net of ther nfluence, workers earn the medan earnngs of ther socal group. Gven these smplfcatons, t turns out that Black workers earn about 6.1 percent more (29,687 vs. 27,990 US dollars per annum) and Whte workers about 0.2 percent less (34,787 vs. 34,868 US dollars per annum) n the 20 th percentle than n the 80 th percentle school dstrct. 23 Ths mples a substantal reducton of the Black-Whte earnngs dfferental from 6,877 to 5,099 US dollars per year, that s, by about a quarter. Ths example llustrates that even f the effects of mgraton over the short run on earnngs are perhaps numercally unmportant, long-run mgraton patterns and the resultng changes n the ethnc composton of labor supply matter substantally for the dstrbuton of earnngs. 5. Robustness of the Baselne Results 5.1. Supply Sde Whle n the prevous secton the assumpton of nelastc labor supply was adopted, t s possble that labor supply responds to wages. People may decde to mgrate for better obs, to work more (or less) n response to a hgher wage, or t may be that people wth hgher wages can afford better medcal care and thus be absent from work less often. Whenever any of such possbltes s operatve, labor nputs are endogenous and, as a result, the baselne estmates of Table 6 are based. To account for the possblty of endogenety of labor nputs, the nstrumental varable framework s adopted n ths secton. In partcular, I adopt the three-stage least square method (3SLS) to estmate the technologcal parameters of the system of demand equatons nvolved n the econometrc model (3). As above, the technologcal constrants β = β are mposed. The respectve ratos of populaton szes of dfferent ethnc groups from the year 1990 are used to nstrument X,n X, n. The assumpton that s made here s that these past ratos are related to current earnngs through current ratos of labor supples, X,n X, n, but not 23 Smlar computatons usng the estmated elastctes of factor prces lead to a varaton of even greater magntude, leadng to the estmates of 32.7 and 1.3 percent, respectvely. 16

19 drectly. Ths assumpton of ndrect relatonshp s capturng the dea that past presence of a non-whte n a school dstrct attracts mmgraton of smlar people through socal relatons, that people have ncentves to reman n the place of ther brth to avod the costs nvolved n relocaton, and that larger populatons contan more workers. 24 Table 8: 3SLS estmates of the technologcal parameters. Medan earnngs of group, full-tme workers X X (1) (2) (3) (4) (5) (6) Whte Black Amercan Asan Pacfc Hspanc or Indan Islanders Latno Whte Black (4.5)** Amercan Indan (3.7)** (1.3) Asan (4.8)** (2.4)* (1.1) Pacfc Islanders (0.2) (1.3) (0.0) (1.1) Hspanc or Latno (4.0)** (0.7) (0.6) (0.6) (0.8) Constant 19,241 23,450 17,914 17,805 25,892 17,562 (6.6)** (15.5)** (8.4)** (8.4)** (8.1)** (18.8)** R-squared Observatons Absolute value of z statstcs n parentheses * sgnfcant at 5 percent; ** sgnfcant at 1 percent The most mportant result of ths analyss, summarzed n Table 8, s that the sgns and magntudes of the coeffcents reman very smlar to those of Table To wt, comparng these two tables, the coeffcent n column (1) for the Black ethnc group changes from to and for the Asan non-whte from to In other words, these coeffcents almost do not dffer whether estmated usng the SUREG or 24 The exstence of such lnks s confrmed by the (non-reported) frst-step regressons of the 3SLS analyss, where the sets of nstruments are statstcally sgnfcant n each frst-step regresson. Reduced-form estmaton shows that the relatonshps between explaned varables and the exogenous varables are sgnfcant and have expected sgns. 25 Note that Table 7 contans about 380 observatons less than Table 5. Ths loss results from mssng observatons for the nstruments. 17

20 3SLS method. Coeffcents wth other non-whte ethnc groups even somewhat ncrease n magntude, n favor of the Whte/non-Whte complementarty hypothess. Whle the coeffcent wth Pacfc Islanders loses sgnfcance, ts sgn remans postve. These results suggest that the possble endogenety bas s n general nsgnfcant and the results of the baselne analyss of Table 6 are robust n ths respect. In other words, t s the demand sde that drves the relatonshp between relatve numbers of workers and ther earnngs Aggregaton As mentoned above, one of the ssues wth estmaton of the system of demand equatons nvolved n econometrc model (3) s that the number of observatons s lmted by the restrcton that only school dstrcts that contan workers of each ethncty can be ncluded n the analyss. In ths secton I nvestgate ths ssue. In general, from the prevous sectons t appears that each non-whte ethnc group s complementary to the Whte ethnc group, wth the excepton of the Pacfc Islanders, who seems not to have a sgnfcant effect on Whte earnngs. To evaluate the valdty of these observatons, I test two hypotheses concernng coeffcent restrctons. Frst, I test the hypothess that the coeffcents β for representng Amercan Indans and Asans and representng Whtes, Blacks, and Hspanc or Latno are equal and that the correspondng coeffcents for representng Pacfc Islanders s zero. The test of ths hypothess n the SUREG 2 model of Table 6 yelds χ =14.88, thus not reectng the null hypothess at 0.01 confdence level. In the 3SLS model of Table 8, ths hypothess s not reected at any conventonal confdence level, yeldng the test statstcs 2 χ = Second, smlarly, I test the hypothess that the coeffcents β for representng the Whte ethnc group are equal for all non-whte ethnc groups except for the coeffcent wth Pacfc Islanders 2 that s zero. The test of ths hypothess n the SUREG framework yelds χ = , whch s nsgnfcant at the 0.01 confdence level. Testng the same hypothess n the 3SLS framework yelds 2 χ = whch s nsgnfcant at any conventonal confdence level. 18

21 Gven these results, I mpose the abovementoned parametrc restrctons one by one on the model and treat the respectve non-whte ethnc groups as one homogeneous group n the labor market. Aggregaton of Asans and Amercan Indans permts ncluson of 7,878 school dstrcts n the analyss, that s, almost four tmes as many as n the baselne model. The model s estmated usng the Zellner s SUREG estmator wth the properly defned parametrc constrant β = β. The results are summarzed n Table 9. As one can observe, the man result remans ntact: non-whte ethnc groups are complementary to the Whte ethnc group n the labor market. The magntudes also reman very smlar to the baselne estmates of Table 6 and the 3SLS estmates of Table 8. The aggregate of Asans and Amercan Indans s also complementary to Whtes, although the magntude of ths effect and ts sgnfcance s not very large. Interestngly, ths aggregate appears to be complementary to Blacks. Table 9: Aggregaton. Medan earnngs of group, full-tme workers X X (1) (2) (3) (4) Whte Whte Black Hspanc or Latno Asan or Am. Indan Black (8.4)** Hspanc or Latno (9.5)** (0.9) Asan or Am. Indan (2.1)* (3.4)** (0.8) Constant 19,287 22,873 18,900 24,037 (18.4)** (33.9)** (39.5)** (27.5)** R-squared Observatons Note: Aggregate represents Asans and Amercan Indans. Absolute value of z statstcs n parentheses. * sgnfcant at 5 percent; ** sgnfcant at 1 percent Concernng the second parametrc restrcton, aggregaton of all non-whte ethnc groups but Pacfc Islanders, who are dropped from the analyss, permts ncluson of as many as 19

22 13,335 school dstrcts n the analyss. Usng the same methodology as n the prevous aggregaton, the estmate of the technologcal parameter β for Whtes and the aggregate of all Non-Whtes s wth the z statstcs of 12.3, whch s hghly sgnfcant and n the range of the values estmated n Tables 6 and 8, where only a smaller sample of school dstrcts was avalable. Gven the smlarty of the coeffcents estmated n these restrcted models to the baselne estmates, t turns out that aggregaton strengthens the man predcton of the baselne analyss that non-whte and Whte labor s complementary. 26 These results also suggest, although ths deserves further research, that one should not expect markedly dfferent predcton n ths respect by aggregatng and dsaggregatng non-whte ethnc groups, for example Asans nto Japanese, Chnese, Vetnamese, and other Asan ethnctes Non-Labor Inputs As mentoned above, land, captal, and technology typcally enter producton, alongsde labor. Unfortunately, t s mpossble to obtan measures of technology and the measures of land and captal are scarce and problematc. Nevertheless, I test the robustness of the baselne predctons wth respect to ncluson of varables measurng urbanzaton and farmng ntensty, whch are, by assumpton, correlated wth the use of captal, land, and technology n producton. Urbanzaton and farmng ntensty are measured as the shares of nhabtants of a school dstrct resdng n urban and farm areas, respectvely. Smlarly as n the case of educatonal varables, the fxed effects formalzaton s adopted such that a vector of measures of non-labor nputs s drectly ntroduced nto the econometrc model (3). Agan, the Zellner s SUREG estmator s used and β = β s mposed. 26 Gven the data avalable, aggregaton also permts 3SLS estmaton wth the values of the shares of Blacks and all other non-whte ethnc groups together n the populaton from the year 1870 as nstruments. Ths yelds the estmate of β for Whtes and Non-Whtes of wth the z statstcs Ths result further supports the complementarty predcton and suggests that even f there was an endogenety bas, t would work aganst the complementarty hypothess and, because of ths, the presented estmates of β are conservatve n ths respect. 20

23 Table 10: Non-labor nputs n producton. Medan earnngs of group, full-tme workers X X (1) (2) (3) (4) (5) (6) Whte Black Amercan Asan Pacfc Hspanc or Indan Islanders Latno Whte Black (4.6)** Amercan Indan (4.2)** (1.0) Asan (5.8)** (1.4) (0.4) Pacfc Islanders (2.0)* (1.4) (0.2) (3.6)** Hspanc or Latno (4.5)** (0.2) (2.1)* (1.2) (0.5) Non-Labor Inputs: Farmng Intensty -25,048 42,615-43,870 31,056-33,007-37,919 (2.5)* (2.7)** (2.3)* (1.6) (1.2) (3.2)** Urbanzaton 702 1,641-2,437 2,869-2, (1.0) (1.5) (1.8) (2.0) (1.4) (0.5) Constant 15,458 23,109 22,274 12,844 25,323 17,867 (5.8)** (13.8)** (11.5)** (5.5)** (10.1)** (15.1)** R-squared Observatons Absolute value of z statstcs n parentheses * sgnfcant at 5 percent; ** sgnfcant at 1 percent Table 10 summarzes the results. One observes that ncluson of the two varables that measure farmng ntensty and urbanzaton does not change the estmates of the technologcal parameters sgnfcantly, as compared to the baselne model of Table 6. Ths result supports the robustness of the baselne estmates vs-à-vs presence of nonlabor nputs. Both of these varables are sgnfcant, however (even for urbanzaton, whch s typcally only margnally sgnfcant n each regresson, excluson s reected). Further mprovement of the measures of non-labor nputs s necessary n future research, however. 21

24 6. Constant Elastcty of Substtuton Aggregaton of non-whte workers nto one category yelds another nterestng possblty. Namely, t permts econometrc analyss of a two-factor constant elastcty of substtuton (CES) model of labor market competton. 27 In ths secton I estmate the elastcty of substtuton between labor of the Whte ethnc group and the aggregate of the labor nput of all non-whte ethnc groups but Pacfc Islanders, smlarly as n Secton 5.2. For ths purpose, assume that producton takes place accordng to the CES producton functon: C = I ( ρ 1 ) / ρ J ( ρ 1 ) / ρ ( X d) + ( X d) ) 0 0 ρ /( ρ 1 ), where ρ > 0 denotes the elastcty of substtuton between non-whte and Whte labor. Assumng a compettve labor market, from ths specfcaton t follows that 1 ( X X )ρ W W =. Takng the logarthm of both sdes and assumng that all factors affectng relatve wages n labor market n other than X X are fully accounted of by,n, n the fxed-effects approach descrbed n Secton 2, one obtans a CES econometrc model: Ln ( E n E, n ) = γ 0 + γ Ln( X, n X, n ) + γ 1Z n + ε n, (4) where Z n s the vector of factors affectng producton and relatve wages n partcular n labor market n and γ s the elastcty parameter of our nterest that has a convenent nterpretaton: t s the nverse of the elastcty of substtuton ρ. Table 11 summarzes the results of estmaton of the CES econometrc model (4). 28 Column (1) presents the OLS estmate of the coeffcent γ equal to It s sgnfcant at any conventonal sgnfcance level and ts magntude mples the elastcty of substtuton of To nvestgate the possblty of endogenety bas, a two-stage least square estmator was computed usng the past values of the rato of Whte and non- Whte populatons as nstruments from the year The results summarzed n column 27 The nonlnearty of the multple-factor CES models complcates econometrc analyss such that conventonal estmaton methods are unusable. 28 As above, coeffcents wth educaton varables and regonal dummes are not reported. 22

25 (2), gven ther smlarty to those n column (1), suggest that the possble endogenety bas s not severe and that the elastcty of substtuton between non-whte and Whte labor s about Table 11: Constant elastcty of substtuton. Logarthm of the Whte/non-Whte rato of medan earnngs, full tme workers (1) (2) Logarthm of the Whte/non-Whte rato of full-tme workers (16.7)** (15.3)** R-squared Observatons Robust t statstcs n parentheses * sgnfcant at 5 percent; ** sgnfcant at 1 percent The man message of ths secton s that t confrms the results obtaned n the generalzed Leontef framework: non-whte (Whte) relatve wage s ncreasng n the relatve number of Whte (non-whte) workers n the local labor market. In other words, t corroborates the fndng that Whte/non-Whte wage dfferental s ncreasng n the share of non-whte workers n producton. It s dffcult to compare the magntudes of the present results wth those of Sectons 4 and 5, especally because the cross elastctes of substtuton are not constant. One result s robust, however: a relatvely large change n labor supples corresponds to a relatvely small change n wages. 30 To conclude, the estmaton of the CES model further supports the hypothess that non-whte and Whte labor s not perfectly substtutable. Furthermore, t suggests that the emprcal evdence that t hurts to be a member of a large ethnc group n terms of relatve earnngs s, at least partly, a labor market phenomenon. 29 The model was estmated also usng the 1870 Whte/non-Whte populaton rato as nstrument, yeldng the estmate of equal to wth the z statstcs of 7.9, mplyng the elastcty of substtuton of 9.2. γ Ths result further supports that there s mperfect substtutablty between non-whte and Whte labor and suggest that the estmates of the elastcty of substtuton of Table 11 are conservatve. 30 Assumng that the Whte/non-Whte earnngs dfferental s fully explaned by non-whte percentage, computatons show that accordng to the CES specfcaton and the estmated elastcty coeffcent of about 0.04, Whte/non-Whte earnngs dfferental s by about one quarter smaller n school dstrcts wth non- Whte populaton 0.9 percent than n those wth 19.9 percent of non-whte workers. Ths example suggest that the results of ths secton are comparable to those based on the generalzed Leontef producton functon, see the example at the end of Secton 4. 23

26 7. Concluson Usng data from the US labor market, ths emprcal paper sheds lght on the substtutablty of labor of non-whte and Whte ethnc groups. In partcular, n the generalzed Leontef framework, t s emprcally establshed that non-whte and Whte labor exhbt complementarty n producton. Ths result suggests that the fndngs of the large body of emprcal lterature that observes a negatve relatonshp between non- Whte relatve earnngs and non-whte concentraton n a local labor market s a labor market phenomenon. In partcular, based on ths result t can be argued that concentraton of non-whte workers n the local labor market has a drect and causal negatve effect on non-whte relatve wage due to complementarty of non-whte and Whte labor n producton. Moreover, complementarty of Whte and non-whte labor n producton suggests that ethnc dversty of labor force has postve effects on aggregate output. That labor market competton between non-whte and Whte workers generates a negatve relatonshp between relatve earnngs of non-whte workers and ther proporton n the local labor market s corroborated n the CES framework. Two ssues should be noted concernng the results of ths study. Frst, n the lght of earler studes t appears that the defnton of socal groups competng n the labor market may affect the result as concerns the estmates of the substtutablty of labor. In partcular, whle ths study suggests that non-whte labor s complementary to Whte labor, other studes show that some subgroups of non-whte and Whte populatons, ncludng mmgrants, youths, or women, may be substtutes n producton. Certanly, the partcular partton of the labor force that one adopts s determned by the focus of the partcular study. In any case, further research s necessary to elucdate the substtutablty of labor of dfferent subgroups of non-whte and Whte workers. Second, t s desrable to study the supply sde of the labor market n a greater detal. Certanly, one would lke to understand the processes that determne the supply of labor n a local labor market as determned by mgraton and ndvdual labor supply decson, so that a rcher account can be taken of the wage determnaton process. 24