conditional occupational segregation of minorities in the us

J Econ InequalDOI 10.1007/s10888-012-9229-0

Conditional occupational segregationof minorities in the US

Carlos Gradín

Received: 25 January 2011 / Accepted: 16 August 2012© Springer Science+Business Media, LLC 2012

Abstract We analyze the role of the demographic and human capital characteristicsof minorities in the US in explaining their high occupational segregation with respectto whites and the extent to which they are locked into low-paying jobs. We measureconditional segregation based on an estimated counterfactual distribution in whichminorities are given the relevant characteristics of whites. Our results show thatthe different levels of attained education by ethnicity and race explain a substantialshare of occupational segregation among non-whites in the US, while English skillsor immigration status are especially relevant for explaining segregation amongHispanics and Asians.

Keywords Conditional occupational segregation · Immigration ·Race and ethnicity · United States

JEL Classification D63 · J15 · J16 · J71 · J82

1 Introduction

Racial/ethnic minorities in the United States face high levels of segregation in theiremployment opportunities and in some cases such segregation implies an exclusionfrom better jobs, thus reducing their labor market opportunities.1 Alonso-Villar

1Albelda [1], King [35], Spriggs and Williams [50], Rawlston and Spriggs [42], Queneau [41], Alonso-Villar et al. [3].

Electronic supplementary material The online version of this article(doi: 10.1007/s10888-012-9229-0) contains supplementary material,which is available to authorized users.

C. Gradín (B)Departamento de Economía Aplicada, Universidade de Vigo,Facultade de CC. Económicase Empresariais, Campus Lagoas-Marcosende, 36310 Vigo,Galicia, Spaine-mail: [email protected]

http://dx.doi.org/10.1007/s10888-012-9229-0

C. Gradín

et al. [3] recently showed that Hispanic and Asian men faced the highest levels ofsegregation (compared with the total employment distribution). Less clear is theextent to which these high levels of segregation can be fully explained by differencesin the attributes of these groups with respect to whites. The uneven geographicaldistribution of minorities or differences in their age might be important factors.But more relevance should be given to workers’ skill-related characteristics suchas attained levels of education, the ability to speak English, or immigrants’ laborexperience in the host country (due to limited transferability of skills). Such levelsof human capital determine the types of jobs that a worker qualifies for. Exclusionfrom certain jobs on the basis of lacking the necessary skills leads to segregation of adifferent nature, based on the unequal access to pre-labor market conditions (supply-side), which should be treated differently from segregation that persists even whenthese variables are taken into account (demand-side).

Little has been done so far, however, to measure occupational segregation condi-tioned by these covariates in a sufficiently general way, or to quantify the individualcontribution of each of these differential characteristics in explaining observed levelsof segregation. Aslund and Skans [4] have recently proposed a method for the casein which segregation is measured considering the random case as the referencefor the absence of segregation [9]. This approach is thus especially appropriate forthe analysis of segregation over small units in which the conventional approach,that takes the even distribution as the reference for minimum segregation, wouldbe biased (measured segregation could be just the result of random assignment ofworkers to units rather than of systematic segregation).

The aim of this paper is to propose a new flexible framework to deal withconditional segregation when units are large and thus the conventional segregationapproach is a good approximation. Adapting the DiNardo et al. [16] re-weightingtechnique, we construct counterfactual employment distributions in which minoritiesare given the relevant characteristics of whites. We also use stochastic dominanceto analyze the extent to which these minorities are locked into low-paying jobsand whether this is explained by their attributes. Based on this setting, we analyzeoccupational segregation among minorities in the United States using the AmericanCommunity Survey 2005–07.

2 The literature on conditional segregation

The extent to which observed levels of segregation (of any type) can be explainedby the groups’ having different characteristics has already been addressed in variousways. For example, computing segregation by specific partitions of the populationaccording to some relevant characteristics.2 This alternative does not allow theresearcher to control for many attributes at the same time or to consider continuousvariables. For that, several approaches have estimated multivariate regressionsexploiting variability, either over time (e.g. [1, 51], or across local markets [3]).Carrington and Troske [10] estimated different OLS and ordered probit models ofracial composition, while other papers have used the information of multivariate

2E.g. Massey [37], Hellerstein and Neumark [24], Alonso-Villar et al. [3].

Conditional occupational segregation of minorities in the US

regressions to construct specific indices accounting for conditional segregation.3

Aslund and Skans [4] developed a more general approach in which they firstestimated non-parametrically the propensity of individuals holding jobs with somediscrete characteristics to be immigrants, and used these estimates to achieve acounterfactual distribution by means of simulations that randomly allocate minoritystatus to individuals within each cell resulting from crossing these characteristics,using the probability of being an immigrant as equal to the fraction of immigrants inthe cell. This approach is an extension, conditioning on covariates, of the notion ofsegregation developed by Carrington and Troske [9] in which the reference case forthe absence of segregation is the random distribution of groups across units ratherthan the even distribution on which the conventional approach is based -and thatwe will follow in this paper. Thus, the Aslund-Skans approach is especially suitablefor cases in which units are small and, thus, the use of the conventional evennessapproach would produce a biased estimation of segregation.

Most of the previous papers on occupational segregation of minorities in the UShave focused on unconditional segregation. An exception to this is Alonso-Villaret al. [3], whose main result was that most segregation of Asians and Hispanics is seento be driven by their different distribution of educational attainment, lack of Englishproficiency, and recent immigration into the US.4 However, they could not quantifyeither the level of conditional segregation at the national level, nor the individualcontribution of each explicative factor to overall segregation.

Occupational segregation measures the degree to which people work in differentoccupations on the basis of ascribed characteristics such as their gender or race.However, standard measures of occupational segregation, such as the populardissimilarity index and others, do not take into account the status or prestige ofjobs. Thus, high levels of segregation do not necessarily imply that some groupsare locked into jobs with low social recognition. Segregation could be neutral fromthe point of view of the status of occupations. The measurement of segregationincorporating the prestige of occupations has been the issue of some recent papers.5

The scarce empirical evidence available show that African-Americans and Hispanicsare overrepresented at low-paid occupations, while Asians are bipolarized betweenlow and highly paid jobs [3, 15], but we do not know to what extent this is the resultof workers’ characteristics.

3 Methodology

3.1 Measuring unconditional segregation

The measurement of occupational segregation is still a controversial issue in laboreconomics. In order to approach racial/ethnic segregation by occupation, most often,

3E.g. Spriggs and Williams [50], Kalter [33], Bayer et al. [6]. Other statistical procedures can be foundin Sethi and Somanatham [46] and Mora and Ruíz-Castillo [40].4Similar results for workplace segregation were found by Hellerstein and Neumark [24].5See Reardon and Firebaugh [43], Hutchens [28, 29], Reardon [44], Del Río and Alonso-Villar [15].The use of indices that jointly combine standard segregation and economic disadvantage is howevercontentious (e.g. [30, 32]).

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segregation has been measured in pair-wise comparisons between two given groups,typically a non-white minority (blacks or Hispanics) and whites. Most recently,the study of multigroup segregation has allowed the measurement of the overallsegregation of all racial groups considered together.6 In our empirical application wechose pairwise-comparisons because we wanted to show how conventional measuresof segregation can be conditioned on characteristics in an easy way, and measuringthe segregation between two groups is the most common approach in the literature sofar. Additionally, our main empirical interest here is to show the heterogeneity in thesegregation profiles of US racial/ethnic minorities with respect to the majoritarianwhites.7

With respect to measurement, several indices can be found in the literature, withthe dissimilarity index [18] being, by far, the most popular in empirical analysisdespite its well-known limitations. Other indices have been proposed verifyingbetter properties, most of them borrowed from measurements of income inequality.Examples of these are the Gini index or the Generalized Entropy family of indices,which embrace the Theil index or the Hutchens square root as particular cases[18, 26, 27]. For this reason, in our empirical analysis, we will use a bundle of indicesin order to check the sensitivity of our results.

For simplicity, let us consider a population of size N divided into two groups: N1,whites, and N0, non-whites. We are interested in measuring the segregation of thispopulation across Toccupations in the economy. Let us denote by ni = (

ni1, . . . , ni

T

)

the distribution for one group across occupations, such that Ni =T∑

j=1ni

j, i = {0,1}.

Then, based on the proportions of whites and non-whites in each occupation, wedefine the following segregation indices:

D(n0, n1

) = 12

T∑

j=1

∣∣∣∣∣

n1j

N1 − n0j

N0

∣∣∣∣∣

H(n0, n1

) = 1 −T∑

j=1

√n0

j

N0

n1j

N1

T(n0, n1

) =T∑

j=1

n0j

N0 ln

⎛

⎝n0

j

/N0

n1j

/N1

⎞

⎠ (1)

D is the dissimilarity index proposed by Duncan and Duncan [18]. H is the Hutchenssquare root index, whose appealing properties are well-described in Hutchens [26,27] and was later generalized by Chakravarty and Silber [11], and T is the Theil

6Some well-known binary indices have been generalized to the multigroup case, such as the indexproposed by Karmel and MacLachlan [34] that was generalized by Silber [49], or the Gini index,generalized by Chakravarty et al. [12]. More recently, Frankel and Volij [21], in the context of schoolsegregation, characterized the Atkinson and Mutual Information indices. Reardon and Firebaugh[43] surveyed several multigroup indices, mainly from sociological literature, and evaluated theirproperties. In some cases, this overall segregation can be interpreted as the weighted sum ofsegregation of each group with respect to the whole economy [2].7Note, however, that our methodology can easily accommodate multigroup segregation measures.


index.8 Additionally, if occupations are sorted by the increasing magnitude of theratio n1

j

/(n0

j + n1j

), then we can write the Gini index, introduced as a measure of

segregation by Jahn et al. [31], as:

G(n0, n1) = 1 −

T∑

j=1

n1j

N1

⎛

⎝n0

j

N0 + 2T∑

h= j+1

n0h

N0

⎞

⎠ (2)

Note that D, G, and H are bounded between 0, when there is no segregationbecause whites and non-whites have the same distribution across occupations, and1, when segregation is at its maximum because there is no overlap between the twodistributions (whites and non-whites work in different occupations).

An alternative and more robust approach to ranking two distributions accordingto their level of segregation is to directly compute the segregation curves (Duncanand Duncan [18]; see a formalization in Hutchens [26]) that represent the cumulativeproportion of whites on the ordinate, and the cumulative proportion of non-whites onthe abscissa when occupations are ordered in increasing values of n1

j

/(n0

j + n1j

). The

45◦ line indicates the case of no segregation and, thus, nonintersecting segregationcurves for two distributions indicate a lower level of segregation for the one with thecurve lying closer to the 45◦ line. A variety of segregation indices will be consistentwith this partial ordering, including those discussed above.9

3.2 Segregation into low-paying jobs

The implications of high segregation for welfare vary depending on the nature ofoccupations into which segregated workers are confined, being definitively nega-tive when segregated groups are locked into less-valued jobs that are frequentlycharacterized by very low pay, little or no job or income security and lower socialprotection. To analyze this, we use stochastic dominance10 to rank employmentdistributions of racial/ethnic minorities according to their degree of segregation intolow-paid occupations. We will compare the employment distributions of Americandemographic groups, with occupations ordered by ascending median hourly wage,used here as a measure of their prestige or status.

We are interested in measuring which group in a population is more segregatedinto low-paid occupations. If occupations are ordered in ascending value of theirmedian hourly wage, w1 ≤ . . . ≤ wT , let us denote by f i(w) the corresponding(non-continuous) density for the ith group, i = {0,1}. The cumulative distribution

function (CDF) is then given by Fi (w) =w∫

of i(s)ds. We will say that one distribution

8Note that H (multiplied by 4) is a member of the family of Generalized Entropy GE(c) measureswhen c = 0.5, while T corresponds to c = 1. T is not defined if n1

j = 0 for any j.9Note that D indicates the maximum vertical distance between the 45◦ line and the segregation curve,while G is twice the area between the 45◦ line and the segregation curve.10Stochastic dominance was discussed by Atkinson [5] and Foster and Shorrocks [19] in the incomedistribution setting.

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i dominates another distribution k stochastically at first order if, for any w, Fi(w) ≤Fk(w).11 That is, for any possible wage used as a cut-off for defining a low-paidjob, the proportion of workers from group k in occupations below that level (low-pay head count) is no smaller than the proportion of such individuals in group i.This condition is very stringent, but if satisfied leads to a very robust ordering.12

In some cases, this partial ordering will be enough to rank two given distributions.In some other cases, however, the corresponding CDFs will cross at least onceand the dominance criterion will not be satisfied. In such cases, however, we cansay that there is dominance over a restricted domain of wages, what is usuallyreferred to as restricted stochastic dominance.13 In these last cases, we can be furtherinterested in ranking both distributions, but give more weight to the proportion oflow-paid workers in occupations with smaller median wages. This entails weightingeach proportion of workers in a given low-paid occupation according to the gapbetween their median wage and the cut-off used to define a low-paid job. Thisis what second order stochastic dominance does, by integrating the area of theCDF for each wage level.14 We will say that one distribution i dominates another

distribution k stochastically at second order if, for any w,w∫

oFi (s) ds ≤

w∫

oFk (s) ds.15

This implies that distribution k has a higher average gap between the low-paid jobcut-off and the median wage of each occupation than distribution i regardless of thecut-off.16 In other words, in the case of, for instance, one single-cross, the first areabetween both curves in which one distribution dominates the other is larger than thesecond one in which the ordering is reversed. This dominance can also be definedover a restricted domain. Similarly, if we require an increasing sensitivity to thebottom of the distribution, higher orders of dominance can be defined by successivelyintegrating the CDFs.

It is important to note that dominance in one order implies dominance in higherorders, but the reverse is not true. Thus, for example, second-order dominance isa weaker condition than first-order dominance and, as a consequence, the partialordering is more complete, as we will be able to rank more pairs of distributions aswe move to higher orders. In dominance analysis it is also important to undertakeinference tests to check whether the lack of dominance is due only to samplevariability.

11This is the weak version, with strong dominance further requiring that the strict inequality holdsfor some w.12In welfare analysis this implies that welfare is larger in group i for any social welfare function thatobeys the monotonicity (in w), the anonymity and the population invariance principles.13See Duclos and Makdissi [17] for a formal analysis of its relationship with welfare in the context ofincome distribution.14Second order stochastic dominance is univocally related to the well-known Generalized LorenzCurve in welfare analysis [19].15Again, this is the weak version, with strong dominance further requiring that the strict inequalityholds for some w.16In welfare analysis, this implies that welfare is larger in group i for any social welfare functionthat obeys the monotonicity, the anonymity, the population invariance and the Pigou-Daltonprinciples.


3.3 Measuring conditional segregation

In this section, we adapt the approach of DiNardo et al. [16] to the measurementof occupational segregation when units are large.17 This propensity score techniquewas initially proposed in the context of decomposing the wage differential betweentwo given populations across the entire distribution. In presenting the procedure,we first need to reformulate the notation. Each individual observation belongs to ajoint distribution F(e, z, W) of occupations e ∈ {1, 2. . . ,T}, (continuous or discrete)individual characteristics z = (z1, z2, . . ., zk, . . ., zK) defined over the domain �z, anda dummy W indicating group membership. The joint distribution of occupationsand attributes of each group is the conditional distribution F (e, z| W). The discretedensity function of occupations for each group, f i(e), can be expressed as the productof two conditional distributions:

f i (e) ≡ f (e|W = i) =∫

z

dF (e, z|W = i) dz =∫

z

f (e|z, W = i) · f (z|W = i) dz,

(3)where i = 1 for whites and 0 for non-whites.

Then, under the general assumption that the structure of occupations of non-whites, represented by the conditional density f (e| z, W = 0), does not dependon the distribution of attributes, we can define the hypothetical counterfactualdistribution fz(e):

fz (e) =∫

z

f (e|z, W = 0) · f (z|W = 1) dz

=∫

z

f (e|z, W = 0) · ψz · f (z|W = 0) dz

=∫

z

ψz f (e, z|W = 0)dz (4)

as the density that would prevail if the population of non-whites kept their ownconditional probability of being in a given occupation, f (e|z, W = 0), but had thesame characteristics of whites given by their marginal distribution f (z|W = 1).Expression 4 shows that this counterfactual distribution can be produced by properlyreweighting the original distribution of the target group.

From Bayes’ Theorem we know that f (z|W = 1) = Pr(W=1|z) Pr(z)

Pr(W=1)and f (z|W =

0) = Pr(W=0|z) Pr(z)

Pr(W=0). Thus, the reweighting scheme ψz, which is just the ratio of the last

two expressions, can be obtained as the product of two probability ratios:

ψz = f (z|W = 1)

f (z|W = 0)= Pr (W = 0)

Pr (W = 1)

Pr (W = 1|z)

Pr (W = 0|z). (5)

The first ratio is given by the unconditional probabilities of group membership and isa constant. The second ratio is given by conditional probabilities and can be obtained

17The approach presented here can, obviously, be applied to segregation across other types of units(such as workplaces or schools, for example).

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by pooling the samples for whites and non-whites and estimating a logit (or probit)model for the probability of being white conditional on z. We will estimate thefollowing logit model:

Pr (W = 1|z) = exp(zβ̂

)

1 + exp(zβ̂

) , (6)

where β̂ is the associated vector of estimated coefficients. Alternatively, one couldthink in terms of using a nonparametric approach estimating the weights based onthe empirical distribution of characteristics in both groups, that is, by computingthe proportion of both populations in each cell that result from crossing all discretecharacteristics (for example, the proportion of native-born whites and Hispanics witha university degree).18 However, this approach could be difficult to implement whena large number of covariates are involved (many cells will be zero or will have asmall number of observations), or when some factors are approached by continuouscovariates. Our approach overcomes these problems and makes it easy to identifythe individual contribution of each factor.

For any given segregation index S, we can measure unconditional segregationdefined over the distributions of occupations for whites and non-whites, S (e) ≡S ( f (e|W = 1) , f (e|W = 0)), and define segregation conditional on z to be thesame index computed after replacing the density of non-whites by the counter-factual: S (e|z) ≡ S ( f (e|W = 1) , fz (e)). This is the amount of (unexplained) seg-regation that remains after controlling for characteristics. The difference betweenunconditional and conditional segregation (counterfactual) provides a measure ofsegregation that is actually explained by our covariates z. This is in line with howwage differentials are usually decomposed into their characteristics (explained) andcoefficients (unexplained) effects. Then, unconditional segregation can be dividedinto its explained and unexplained parts:

S (e) = [S (e) − S (e|z)

] + S (e|z) . (7)

One advantage of this method is that it preserves the metric of segregation indices,unlike the Aslund-Skans set-up based on the Carrington-Troske index of systematicsegregation, that uses a transformation that redefines the metric into a measure basedon the deviation of the segregation index from that of a random allocation as a frac-tion of the maximum possible deviation from the random allocation. Additionally,our method permits the gathering of additional information using the counterfactualdistribution. For example, we can construct the conditional segregation curve orestimate the conditional density for any occupation in which we are interested. Inparticular, this can be applied to analyze stochastic dominance among conditional

18Note that Aslund and Skans [4], in their general case, estimate nonparametrically the proportion ofemployment represented by the minority in each type of jobs (resulting from crossing characteristics).However, their algorithm then uses these weights in a different way. Instead of reweighting, they usesimulations. That is, they replicate the sample a large number of times and assign the minority statusrandomly based on these estimated weights. Segregation is then computed in each replication andaveraged afterwards to compute conditional segregation. This makes this approach a procedure tocondition the notion of segregation developed by Carrington and Troske [9] that takes the randomcase as reference for the absence of segregation, as opposed to the even distribution of employmentin which the conventional approach is based—and we follow here.


distributions. Note, however, that the main limitation of our method is that it inheritsthe same bias of the conventional evenness approach when units are small, in whichcase methods based on the Carrington-Troske approach, such as Aslund-Skans,would be more suitable.

Furthermore, the explained term can be additionally disaggregated into thedetailed contribution of each covariate (or subset of covariates) zk in order to identifywhich factors are more explicative. With s(zk) being the relative contribution ofcovariate k,

S (e) − S (e|z) =∑

k

s (zk)[S (e) − S (e|z)

]. (8)

In order to obtain this detailed decomposition, we need to compute a new counterfac-tual distribution fzk (e) in which the corresponding reweighting factor ψzk is obtained,setting all of the other logit coefficients but this one to zero [36]. Alternatively, we canshift all of the coefficients in a specific sequence, computing the contribution of eachfactor as the result of changing its associated coefficients. This recalls the well-knownpath-dependency problem in inequality decomposition, because the contribution ofa factor to the overall differential in income will depend on the order in whichwe consider them. This difficulty will be overcome in the empirical analysis bycomputing the Shapley decomposition that results from averaging over all possiblesequences [13, 47].19 Thus, the contribution of a given factor (i.e. education) will bethe average of the contribution of education for all possible paths: when educationcoefficients are changed in the first case, in the second, and so on.20

4 Empirical analysis

4.1 Data

The data used in the empirical analysis comes from the 2005–07 release of the PublicUse Microdata Sample (PUMS) file of the American Community Survey (ACS)conducted by the US Census Bureau, thus reflecting the pre-recession situation inthe US labor market. This survey is the result of pooling a series of monthly samplesjointly accounting for 3 % of the overall population living in the US in housingunits during the period (and 2 % of those living in group quarters during 2006–7).The sample amounts to 4,123,320 observations21 of employed workers for whicha variety of information is provided about their socio-demographic characteristicsand labor market performance. In particular, we will analyze five different possible

19See Gradín [22] for an application of a similar procedure for the decomposition of incomedistribution differentials across racial groups. Statistical inference for both the aggregate and thedetail decompositions can be executed using bootstrapping. However, in the empirical analysisshown in the next section, no inference was made because the large dimension of the dataset makesbootstrapping too time-consuming a task.20See Sastre and Trannoy [45] for the exact formula used to implement this average in a simplemanner.21After a check to prevent the influence of outliers, four Hispanic male observations withPr (W = 0| z) close to zero were discarded. Their inclusion would lead to disproportionally largecounterfactual weights, according to expression 5.

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explicative factors: i) education, 16 groups defined by the census according to thelevel attained (going from no schooling to doctorate degree); ii) the ability to speakEnglish, chosen among five categories (speaks only English, speaks English very well,well, not well, not at all); iii) immigrant status, distinguishing between those bornin the US and immigrants of different periods after arrival in the US (less than ayear, 1 to 5, 5 to 15, more than 15 years); iv) geographical location, defined as 158metropolitan/nonmetropolitan areas of work;22 and v) age, measured in years andage squared.

Regarding race and ethnicity, people are asked in the survey to choose therace(s) with which they most closely identify and to answer whether they have ornot Spanish/Hispanic/Latino origin. Based on self-reported identity, we identifiedthe following mutually exclusive groups of workers: i) the four major single-racenon-Hispanic groups, that is, whites, African Americans/blacks, Asians, and NativeAmericans (who could be American Indian, Alaskan, Hawaiian, or Pacific Islandnatives); ii) Hispanics of any race, but distinguishing whites from non-whites; andiii) others (non-Hispanics choosing other races or more than one race). Segregationwill be measured separately for each gender, due to the evidence of differentoccupational distributions among women and men of the same group membership.Regarding occupations, we have considered the detailed list of 469 occupationsprovided in the public PUMS files, which is based on the 2000 Standard OccupationalClassification (SOC) System. Median hourly wage for each occupation is estimatedbased on reported wage and number of hours worked.

4.2 Unconditional segregation

It is well known that there are high levels of occupational segregation of minoritieswith respect to whites in the US. The first four columns of Table 1 report foreach demographic group (race or ethnicity by gender) the corresponding level ofunconditional segregation as measured by the four indices described in the previoussection. For all minorities, it is true that men are always more segregated than womenwith respect to (non-Hispanic) whites of the same gender.23

The ranking of groups according to their level of segregation is generally the sameregardless of the index we use. In fact, most minorities can be ranked accordingto their segregation level using the segregation curves. These curves for men aredepicted in Fig. 1 (for women see Fig. A1 in the Online Appendix). Here occupations

22We considered 140 MSA with at least 4,000 sample observations. Workers were assigned tothe MSA using the information from Public Use Microdata Area corresponding to the place ofwork (POWPUMA) available in publicly accessible ACS files, which, in some cases, required theassignment of a given POWPUMA to the MSA in which it has a larger population, according to thecensus. Workers with a job abroad were removed from the sample, and workers with a job but notcurrently working were assigned according to their area of residence. The remaining metropolitanand non-metropolitan areas were categorized, respectively, into the nine US geographical regions,resulting in a total of 158 areas. This allows our results to be representative of the whole country.Note, however, that our results are generally robust to the elimination of workers out of the main 140Metropolitan Areas, although some differences exist especially for Native Americans, the minoritywith the largest proportion of workers (45 %) in the aggregated areas.23In contrast, Alonso-Villar et al. [3] found that Hispanic females are more segregated than Hispanicmales when they are compared with the economy as a whole (instead of with white females).


Table 1 Conditional and unconditional white/nonwhite occupational segregation in the US, 2005–07

Group Unconditional Conditional

Duncan Gini Theil Hutchens Duncan Gini Theil Hutchens

BlacksMales 0.280 0.383 0.242 0.060 0.255 0.347 0.202 0.050Females 0.245 0.333 0.192 0.046 0.220 0.306 0.163 0.039

AsiansMales 0.323 0.447 0.367 0.086 0.228 0.324 0.181 0.045Females 0.244 0.351 0.253 0.056 0.169 0.239 0.115 0.027

Native AmericansMales 0.241 0.334 0.185 0.047 0.170 0.252 0.120 0.030Females 0.211 0.294 0.156 0.038 0.171 0.249 0.121 0.030

HispanicsMales 0.327 0.444 0.347 0.082 0.162 0.234 0.100 0.024Females 0.265 0.371 0.270 0.060 0.121 0.173 0.062 0.015White males 0.308 0.420 0.318 0.074 0.167 0.239 0.105 0.025White females 0.244 0.345 0.247 0.054 0.116 0.170 0.066 0.016Nonwhite males 0.351 0.476 0.389 0.095 0.201 0.291 0.166 0.039Nonwhite females 0.292 0.405 0.308 0.070 0.205 0.290 0.176 0.039

Other racesMales 0.167 0.236 0.091 0.023 0.126 0.180 0.055 0.014Females 0.142 0.200 0.068 0.017 0.118 0.167 0.053 0.013

Fig. 1 Unconditionaloccupational segregationcurves for whites/nonwhites inthe US, 2005–07: men

0.1

.2.3

.4.5

.6.7

.8.9

1

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1cumulative proportion of nonwhite men

Other races Native A.

Black White Hisp.

Asian Nonwhite Hisp.

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are ranked in increasing values of n1j

/(n0

j + n1j

), with no need to use indices. In

the case of men, all distributions can be ranked despite some overlap between thecurves of the most highly segregated minorities. Non-white Hispanic males show ahigher level of segregation than any other group according to all indices, followedby Asian males and Hispanic white males. Workers of other races present the lowestlevel of segregation among men, followed by Native Americans and blacks. Whenno distinction is made among Hispanic males regarding their race, Asian males areslightly more highly segregated than they are, except for the dissimilarity index.

Regarding women, there are also clear dominance relationships for their segrega-tion curves, but the curves are closer to one another, and the curve of white Hispanicscrosses the corresponding curve for blacks and can hardly be distinguished fromthat of Asians. According to all indices, non-white Hispanics and Asians also showthe highest levels of segregation for women, but with white Hispanics and blackshaving similar levels to those of Asians, especially for the dissimilarity index. Thus,Native American women and those of other races tend to show the lowest levels ofsegregation.

4.3 Conditional segregation

It seems natural to ask to what extent the specific attributes of racial/ethnic groupsin the US along relevant dimensions such as education, geographic or demographiccharacteristics can explain their high occupational segregation levels. It is clearthat groups such as Hispanics and Asians, which have in common a large share ofrecent immigration, tend to be far more segregated than groups with more native-born workers.24 Indeed, groups with many immigrants tend to have different educa-tional profiles, being either less educated (Hispanics) or more educated (Asians),than whites and any other group. To a lesser extent, other minorities, such asblacks and Native Americans, have traditionally faced lower educational outcomescompared with whites.25 Furthermore, immigrants face a series of barriers causingmismatches of educational attainment and occupation of employment (over- andunder-education) more often than the native-born population: limited internationaltransferability of skills, selectivity to migration, and labor-market discrimination[14]. English proficiency tends to be more limited,26 especially among Hispanics,considerably narrowing the range of available jobs and making promotion moredifficult. Very often, jobs requiring low English skills are also those demanding lownon-language skills [39]. Hispanics are younger than any other group in age and, thus,have less experience, while Asians are similar in age to other minorities but are still

24While foreign-born workers comprised 82 % of Asians of any sex, 65 % of Hispanics males, and53 % of Hispanic females, they accounted for 5 % of whites and less than 15 % of blacks and NativeAmericans.25For example, 39 % of Hispanic men working have attained less than a secondary education(compared to 9 % of whites and Asians, 13 % of blacks, and 15 % of Native Americans). Similarly,54 % of Asian male workers have achieved a bachelor’s degree or higher compared to 32 % ofwhites, 18 % of blacks, and 11 % of Latinos. Differences among women are similar.26Among Hispanics, about 32 % of men and 22 % of women lack English skills (speak the languagenot well or not at all). This compares with 12 % of Asian men (women: 14 %), 4 % of men of otherraces (women: 2 %), and less than 1 % in the rest of groups.


Table 2 Explainingwhite/nonwhite occupationalsegregation in the US, 2005–07

Percentage of change in unconditional segregationdue to characteristics

Group All characteristics

Duncan Gini Theil Hutchens

BlacksMales −8.8 −9.4 −16.5 −17.3Females −10.2 −7.9 −15.2 −14.8

AsiansMales −29.5 −27.7 −50.8 −46.9Females −30.8 −31.8 −54.6 −51.0

Native AmericansMales −29.7 −24.5 −34.9 −35.4Females −18.8 −15.2 −22.2 −19.8

HispanicsMales −50.5 −47.3 −71.1 −70.5Females −54.2 −53.3 −77.0 −75.7White males −45.9 −43.1 −67.1 −65.5White females −52.5 −50.7 −73.1 −70.9Nonwhite males −42.8 −38.7 −57.2 −58.7Nonwhite females −29.9 −28.3 −43.0 −43.6

OtherMales −24.5 −23.6 −39.6 −39.1Females −16.8 −16.5 −22.4 −23.2

younger than whites.27 Minorities additionally tend to be located in specific areas ofthe country, with Asians and Hispanics being concentrated in geographical regionssuch as the Pacific, Middle Atlantic (Asians), and West South Central (Hispanics).Similarly, blacks are more overrepresented in the South Atlantic region and NativeAmericans in the West South Central area.

All of these factors together could differentially affect the opportunities of work-ers belonging to these minorities in the labor market, thus influencing segregationacross occupations. For this reason, applying the methodology described in theprevious section, we compute segregation conditional on a number of covariates,accounting for geographical location, education, English proficiency, immigration,and age, as explicated in the data description. Conditional segregation for each groupis reported in the four last columns of Table 1, while Table 2 reports the change inthe percentage of unconditional segregation after conditioning for all characteristicsin the first block in the table.28

Segregation is, generally, reduced after accounting for covariates, even if theextent varies significantly across groups and indices. These reductions are slightly

27The median Hispanic male worker is 35 years old (36 in the case of females), compared with 42 forwhites, 39 for blacks and Asians, and 38 for Native Americans (the corresponding figures for womenare roughly similar).28Estimates of the logit regressions for the probability of being white used in the computation ofconditional segregation are reported in Table A1 in the Online Appendix. The extent to whichthese regressions are able to balance covariates for minorities and whites can be evaluated by thelarge reduction in the pseudo-R2 [48] after replacing the original distribution of each minority by itscounterfactual. There persists a weak relationship between covariates and minority status, however,as the use of LR tests [7] suggest.

C. Gradín

higher in relative terms for women than for men in the cases of white Hispanics andAsians, of a similar magnitude in the case of blacks, and lower in the other cases(non-white Hispanics, Native Americans, and workers of other races). Taking theDuncan and Duncan dissimilarity index as a reference, it turns out that conditioningon covariates reduces more significantly the level of segregation for Hispanics thanfor any other group: about 47 % for males and 54 % for females. However, it isnoteworthy that these reductions are similar for white and non-white Hispanic menbut substantially lower for non-white females of the same ethnicity. The reductionsfor Asians (men and women) and Native American men are also high, around 30 %.The lowest reductions are found in the case of blacks (9–10 %). Native Americanfemales reduce segregation by 19 % and people of other races by 17 % (females)and 24 % (males). The results from the Gini index are pretty similar to the those ofthe dissimilarity index, while those arising from using the Theil and Hutchens indicesare qualitatively similar even if they differ in magnitude. For example, the reductionfor white Hispanic males is about 65–67 % and around 71–73 % for females.

Consequently, after controlling for covariates, according to conditional segrega-tion, black males turn to be, now, the most segregated group of workers, followed byAsian males.29

The most salient downward movement in the ranking after controlling for covari-ates according to segregation indices is observed in the case of white and non-whiteHispanic males. The former has, now, a similar or lower level compared to those ofNative Americans and Asian women. Similarly, white Hispanic women have become,along with workers of other races, the group with the lowest segregation levels. Still,female groups have lower levels of segregation than men’s groups, except for NativeAmericans and non-white Hispanics, where they have similar levels.

4.4 Main explicative factors of segregation

Ethnic and racial groups differ not only as to the magnitude of the reduction obtainedby controlling for characteristics, but also in the nature of the underlying factors. Thepercentage of reduction in unconditional segregation induced by each set of variables(using the Shapley decomposition) is shown in Table 3. Here, we discuss the case ofthe dissimilarity index.30

The most relevant factors underlying segregation are the ability to speak Englishand educational attainment. Each of these factors alone accounts for a reductionin the dissimilarity index of about 20–30 % in the segregation of Latino workers.While education seems to be more relevant in explaining the segregation of non-white Hispanics, English proficiency appears to be more relevant for whites of thesame origin. This compares to values ranging from about 3–7 % for the reductiondue to immigration status among the same groups. Thus, the time of arrival in the

29See Fig. A4 in the Online Appendix. Clearly, in the case of men, the segregation curve for blacks isbelow the others, while the curves for Asians and non-white Hispanics cross each other at the bottomof their employment distributions, and Native American and white Hispanics overlap for most of therange. In the case of women, segregation curves intersect in several cases, and there is a great rangeof overlap among them, indicating that the segregation levels are close.30Note that, again, the Gini index provides similar results to those of the dissimilarity index, whilethe Theil and Hutchens indices provide similar qualitative results.


Tab

le3

Fac

tors

expl

aini

ngw

hite

/non

whi

teoc

cupa

tion

alse

greg

atio

nin

the

US,

2005

–07

Per

cent

age

ofch

ange

inun

cond

itio

nals

egre

gati

ondu

eto

each

seto

fcha

ract

eris

tics

(Sha

pley

valu

es)

Gro

upG

eogr

aphi

car

eaE

duca

tion

Eng

lish

prof

icie

ncy

Imm

igra

tion

Age

DG

TH

DG

TH

DG

TH

DG

TH

DG

TH

Bla

cks

Mal

es4.

84.

69.

68.

8−1

4.6

−14.

0−2

5.2

−25.

30.

60.

61.

51.

30.

1−0

.6−2

.8−1

.90.

30.

00.

5−0

.2F

emal

es8.

87.

316

.113

.9−2

1.6

−16.

5−3

1.3

−29.

60.

91.

12.

62.

2−0

.3−1

.7−5

.9−4

.62.

01.

93.

33.

3A

sian

sM

ales

10.1

9.3

18.5

17.1

−10.

1−1

0.1

−14.

4−1

6.9

−10.

9−9

.7−2

0.7

−17.

3−1

0.9

−11.

1−2

4.7

−20.

2−7

.7−6

.1−9

.4−9

.7F

emal

es9.

98.

817

.315

.7−6

.5−6

.6−1

1.9

−10.

8−1

6.0

−15.

2−2

6.9

−25.

1−1

4.2

−15.

2−2

9.9

−27.

0−3

.9−3

.6−3

.3−3

.8N

ativ

eA

.M

ales

−2.8

−1.8

−2.5

−1.6

−23.

8−2

0.0

−27.

9−3

0.1

−2.6

−2.4

−4.4

−3.3

0.3

0.3

0.6

0.6

−0.8

−0.6

−0.7

−1.0

Fem

ales

0.6

2.0

4.7

5.6

−16.

7−1

5.8

−23.

6−2

3.9

−6.6

−5.8

−11.

8−9

.70.

30.

40.

60.

73.

63.

98.

07.

4H

ispa

nics

Mal

es7.

67.

010

.39.

6−2

3.3

−21.

8−3

1.1

−30.

9−2

3.4

−22.

0−3

2.8

−31.

7−6

.9−6

.6−1

2.4

−11.

5−4

.4−3

.9−5

.1−6

.0F

emal

es5.

95.

911

.39.

7−2

7.9

−26.

7−3

7.1

−37.

0−2

8.5

−28.

5−4

4.6

−41.

9−4

.9−5

.0−1

0.5

−9.2

1.4

0.9

3.9

2.7

Whi

tem

ales

7.6

7.0

9.3

9.0

−19.

7−1

8.5

−27.

6−2

6.9

−22.

1−2

0.8

−30.

8−2

9.7

−6.6

−6.3

−11.

8−1

1.0

−5.1

−4.6

−6.3

−6.9

Whi

tefe

mal

es6.

16.

411

.410

.1−2

4.5

−23.

1−3

2.7

−32.

2−2

8.8

−28.

3−4

3.1

−40.

4−4

.6−4

.6−9

.4−8

.3−0

.7−1

.00.

7−0

.1N

onw

hite

mal

es8.

68.

414

.112

.7−2

4.8

−23.

1−3

3.1

−34.

0−2

1.0

−19.

3−3

0.6

−29.

0−5

.1−4

.9−9

.6−8

.8−0

.50.

12.

00.

3N

onw

hite

fem

ales

10.1

9.8

17.6

15.9

−31.

1−2

9.9

−54.

0−5

0.2

−20.

8−1

9.4

−30.

4−2

9.4

−2.6

−2.3

−5.2

−4.6

14.4

13.5

28.9

24.7

Oth

erM

ales

4.1

4.3

7.2

7.4

−8.4

−8.6

−14.

5−1

4.5

−2.0

−1.7

−3.0

−2.9

−1.4

−1.2

−1.7

−1.7

−16.

8−1

6.4

−27.

6−2

7.3

Fem

ales

10.6

8.8

16.6

15.2

−12.

9−1

2.9

−21.

1−2

0.5

−1.3

−1.4

−2.9

−2.6

0.3

0.0

−1.4

−0.7

−13.

5−1

1.1

−13.

6−1

4.6

D=

Dun

can

and

Dun

can

diss

imila

rity

,G=

Gin

i,T

=T

heil,

H=

Hut

chen

ssq

uare

root

C. Gradín

US seems to be of little importance in explaining the segregation of Latinos, oncethe gap in observed skills (language and education) has been taken into account.

English proficiency, education, and immigration status explain about 10 % of thesegregation of Asian men, and 16, 14, and 6.5 % respectively for women of the samerace. Thus, education and language skills are much less relevant in explaining thesegregation of Asians than of Hispanics, while immigration status is more relevant,especially for Asian women. Age seems also to play a role in segregation for Asians(8 % of reduction for men and 4 % for women).

For Native Americans and blacks, most explained segregation can be attributed toeducational gaps: 15 and 22 % reduction, respectively, for black males and females,24 and 17 % in the case of Native Americans. Among the other factors, only Englishproficiency appears to be relevant, for Native American females (7 %).

Unlike the other attributes, controlling for geographical location generally in-creases rather than decreases the segregation of Hispanics, Asians, and blacks. Thatis, segregation would be larger (by 6–10 %), had Latinos the same geographicaldistribution as whites. Comparable percentages apply to the other groups, exceptNative Americans.31 This means that segregation of these minorities cannot beexplained by them living in areas where the occupations in which they are typicallyfound are overrepresented. On the contrary, they tend to live in areas where thoseoccupations are underrepresented and, thus, after equalizing the spatial distributionwith that of whites segregation turns to be higher. Similarly, controlling for ageincreases the segregation of non-white Hispanic women (14 %), while it decreasessegregation for white Hispanic men, having no effect on others of the same ethnicity.

4.5 Segregation into low-paying jobs

The previous results have shown that racial/ethnic minorities and whites in the USdo work in different occupations, but to what extent are the former being confined tolow-paid jobs? In order to rigorously assess whether or not we can generally say thatminorities in the US work in less-valued occupations, we undertake the dominanceanalysis described previously. As Fig. 2 shows, the unconditional CDFs for Hispanic,black and Native American men generally lie above those of whites (Fig. A2 in theOnline Appendix shows the same for women). Thus, the employment distributionsof these minorities are first-order stochastically dominated by those correspondingto whites over a wide range of wages. It becomes clear that, compared to whites,Hispanics, blacks and Native American workers tend to be overrepresented intothose occupations reporting a lower median hourly wage.

There is unrestricted dominance of white workers over Native American workersof any gender, as well as over Hispanic females.32 In the remaining cases, Hispanicmales and black male and females, there is only a short range of very low-paidoccupations where we find a statistically significant larger accumulated proportion

31This exception for Native Americans is linked to their larger presence in small or non-Metropoltanareas. If the analysis is done only for the largest 140 MAs, equalizing the geographical distributionalso increases segregation for this minority.32Table A2 in the Online Appendix summarizes the inference over dominance results implementedusing the Distributive Analysis Stata Package (DASP) authored by Araar and Duclos.


Fig. 2 First orderstochastic dominance in USunconditional employmentdistributions by race andethnicity: men

0.1

.2.3

.4.5

.6.7

.8.9

1

CD

F0 5 10 15 20 25 30 35 40 45 50 55 60 65

median wage of occupation

Hispanics Blacks Native A.Whites Asians

CDFs by ethnicity/race: malesFirst order stochastic dominance

of white workers (there is at least one significant cross from above).33 Thus, onlyrestricted first order stochastic dominance does apply, even if for a wide rangeof median wages. There is, however, unrestricted stochastic dominance for higherorders in the case of Hispanic males. As a result, one can generally assess for a broaddefinition of low-wage occupations, that Hispanics are more segregated into low-paidoccupations than any other group, followed by blacks and Native Americans, whosecorresponding distributions can hardly be distinguished from one another.

The case of Asians is a bit more complex due to the larger heterogeneity in skillsof workers in this group. There is an outstanding bipolarity with some Asian workersconfined into low-paid occupations, while others are segregated into highly paidjobs [3]. The employment distributions for Asians and whites have two statisticallysignificant crossings, such that one can say that Asians are more segregated into low-paid jobs than whites for median wages lying only between about 8 and 15 dollarshourly wage (restricted dominance), and this holds for higher orders of stochasticdominance.

4.6 Conditional segregation into low-paid occupations

Our final objective is to show to what extent the confinement of some racial/ethnicminorities into low-paid occupations can also be attributed to their specific character-istics. For that, we replicate the previous stochastic dominance analysis, based now onthe conditional distributions of employment. Figure 3 reports first-order stochasticdominance among male groups.34

Once we have conditioned by all human capital, demographic and geographicalcovariates, blacks and Native Americans still show higher segregation into low-wage occupations than whites, especially for males. Restricted stochastic dominance

33There are several occupations among those with the lowest median hourly wage reporting largerproportions of white workers than of any other group such as “motion picture projectionists,”“farmers and ranchers,” and “lifeguards and other protective service workers,” among others.34For females, see Fig. A3 in the Online Appendix. Table A2 also summarizes the inference analysisfor the conditional case.

C. Gradín

Fig. 3 First order stochasticdominance in US conditionalemployment distributions byrace and ethnicity: men

0.1

.2.3

.4.5

.6.7

.8.9

1C

DF

0 5 10 15 20 25 30 35 40 45 50 55 60 65median wage of occupation

Hispanics Blacks Native A.Whites Asians

conditional CDFs by ethnicity/race: malesFirst order stochastic dominance

applies in both cases for a wide range of wages, with unrestricted higher orderstochastic dominance observed only in the case of Native American females. Thus,in this case the specific attributes do not fully explain this confinement into low-paidjobs. This phenomenon, however, is no longer true for Hispanics, whose conditionaldistributions for males and females can hardly be distinguished now from thosecorresponding to whites. In fact, the dominance is now reversed, with whites showing(slightly) larger proportions of workers in occupations with low wages.

This result is consistent with a higher discrimination of blacks and Native Amer-icans in the US labor market compared with (predominantly) immigrant minorities.But it could also be driven by the several pre-labor market factors that have beenpointed out as being responsible for the generally bad performance of blacks,especially men, in the US labor market. These factors cannot be accounted for withthe available information: Statistical discrimination induced by disproportionallyhigh incarceration rates [25]; the difficulty of finding adequate jobs due to prevalentresidential segregation and the migration of jobs from inner cities to suburbs [20];the lower school quality affecting their achievement (i.e. [23]); their specific familybackground as a result of higher share of people living in single-mother families[8], phenomenon that could be induced by changes in social norms, declining wagesamong low-skilled men, or the unintended incentives of the welfare system [38].

5 Conclusions

In this paper, we have adapted a propensity-score technique, initially proposedin the literature with respect to wage differentials, for the analysis of conditionalsegregation when units are large and thus the evenness approach is a reasonableapproximation. By measuring the segregation of a counterfactual occupational dis-tribution in which non-whites are given the characteristics of whites, we quantifythe segregation that can and cannot be explained by individual characteristics.This counterfactual is simply constructed by reweighting the original distribution ofnon-whites using predictions from a logit model of the probability of being white.Furthermore, we are able to identify the individual contribution of each factor to


overall segregation by following a Shapley approach. Additionally, we used first andhigher order stochastic dominance in order to rank distributions of US racial andethnic groups according to the degree to which workers of each group are lockedinto low-paid occupations.

Our technique is used to measure the conditional segregation of various minoritiesin the US. Our results show that Hispanics and Asians exhibit the largest levels ofunconditional segregation. However, this high segregation can be, to a large extent,attributed to their specific characteristics, especially their lack of English proficiency,education attainment, and high percentage of recent immigration to the US. Thesethree factors explain at least 50–60 % of observed segregation for Hispanics and atleast 30–35 % for Asians. Among these factors, education and English proficiencyare more important among Hispanics, while immigration status is more relevant forAsians.

By contrast, blacks, with a larger share of native-born workers, show relatively lowsegregation levels compared to the other groups before conditioning, but a smallershare of that can be explained by their attributes, ending up with higher conditionalsegregation than any other group. In this case, education is the only salient factor.In all cases, except for Native American male workers, if minorities had the samegeographical distribution across the country as whites, their segregation would beeven larger; that is, the uneven geographical distribution mitigates the segregationthat would be observed otherwise.

We have shown that for almost the whole range of wages, one can assertthat Hispanic workers are more segregated than any other group into low-payingoccupations. Hispanics are followed by blacks and Native Americans. However,while segregation of Hispanics in low-paid jobs is mostly driven by the specificcharacteristics of workers such as attained education, language ability, or recentimmigration, this is not generally true for blacks and Native Americans. The case ofAsians is different from the other groups. We can say that Asians have more workersin low-paid occupations only up to a certain level, due to the fact that a significantpart of this group is confined within a few highly paid jobs.

The new technique proposed here allows us to say that ethnic and racial segrega-tion in the US is, to a large extent, explained by individual attributes of non-whites,especially those related to recent immigration that are expected to eventually vanishwith the progressive assimilation of foreign-born workers. However, a substantiallevel of segregation is explained by some minorities’ having low educational profilescompared to whites. This, remarkably, affects also those minorities with larger sharesof native-born workers. Further, a notable share of observed segregation still remainsunexplained and could be caused by any form of racial/ethnic discrimination facedby these groups in the labor market.

These empirical results highlight the existence of heterogeneous patterns ofoccupational segregation among US minorities with respect to the majoritarianwhites. These empirical findings contribute to proof the importance of controllingfor covariates in order to explain segregation, similarly to what is usual in themeasurement of wage differentials.

Acknowledgements I acknowledge financial support from the Spanish Ministerio de Ciencia eInnovación (grant ECO2010-21668-C03-03/ECON) and Xunta de Galicia (grant 10SEC300023PR).I would like to thank two referees for their very helpful suggestions that allowed me to substantiallyimprove the paper.

C. Gradín

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conditional occupational segregation of minorities in the us

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