IMMIGRATION AND THE ECONOMIC STATUS
OF AFRICAN-AMERICAN MEN

George J. Borjas, Harvard University
Jeffrey Grogger, University of Chicago
Gordon H. Hanson, University of California, San Diego

January 2009

1
CIMMIGRATION AND THE ECONOMIC STATUS
OF AFRICAN-AMERICAN MEN

George J. Borjas, Jeffrey Grogger, and Gordon H. Hanson
Abstract

The employment rate of black men, and particularly of low-skill black men, fell
precipitously from 1960 to 2000. At the same time, the incarceration rate of black men rosemarkedly. This paper examines the relation between immigration and these trends in black
employment and incarceration. Using data drawn from the 1960-2000 U.S. Censuses, we find astrong correlation between immigration, black wages, black employment rates, and blackincarceration rates. As immigrants disproportionately increased the supply of workers in aparticular skill group, the wage of black workers in that group fell, the employment rate declined,
and the incarceration rate rose. Our analysis suggests that a 10-percent immigrant-induced
increase in the supply of a particular skill group reduced the black wage by 2.5 percent, lowered
the employment rate of black men by 5.9 percentage points, and increased the incarceration rateof blacks by 1.3 percentage points.

2
IMMIGRATION AND THE ECONOMIC STATUS
OF AFRICAN-AMERICAN MEN
George J. Borjas, Jeffrey Grogger, and Gordon H. Hanson*
After a wave of raids by federal immigration agents on Labor Day weekend, alocal chicken-processing company called Crider Inc. lost 75% of its mostly
Hispanic 900-member work force. The crackdown threatened to cripple theeconomic anchor of this fading rural town. But for local African-Americans, thedramatic appearance of federal agents presented an unexpected opportunity.
Crider suddenly raised pay at the plant. An advertisement in the weekly ForestBlade newspaper blared “Increased Wages” at Crider, starting at $7 to $9 anhour—more than a dollar above what the company had paid many immigrant
workers. (The Wall Street Journal, January 17, 2007)
I. Introduction
The employment rate of African-American men—defined as the fraction of weeks
worked during a calendar year by the typical black male—fell from 73.2 percent in 1960 to 64.3
percent in 2000.1 This drop stands in sharp contrast to the slight decline observed among whitemen during that period, from 85.4 to 83.7 percent. The racial employment gap widened evenmore for low-skill persons: the employment rate of black high school dropouts fell by over 30
percentage points, from 71.3 to 39.1 percent, as compared to a 20-percentage point drop for
white high school dropouts, from 80.8 to 60.5 percent.
The decline in labor market participation among black men was accompanied by a rapid
increase in the number of black men in correctional institutions. As recently as 1980, 3.8 percent* Borjas: John F. Kennedy School of Government, Harvard University, and National Bureau of Economic
Research; Grogger: Harris School of Public Policy Studies, University of Chicago, and National Bureau of
Economic Research; Hanson: School of International Relations and Pacific Studies and Department of Economics,
University of California, San Diego, and National Bureau of Economic Research. We thank Eli Berman, Donald
Cox, Melissa Famulari, Peter Gottschalk, Richard Freeman, Larry Katz, and seminar participants at Boston College,
Harvard University, and UCSD for helpful comments.
1 Throughout the paper, the “employment rate” gives the average fraction of weeks worked during thecalendar year prior to the Census (i.e., the ratio of weeks worked, including zeros, to 52). The “incarceration rate”
gives the fraction of persons who are institutionalized at the time of the Census. The data will be described in greater
detail in the next section.

3of black men (and 5.6 percent of black high school dropouts) were incarcerated. By 2000, 9.8
percent of black men (and 21.2 percent of black high school dropouts) were incarcerated.2
A large academic literature examines these trends. One strand of the literatureemphasizes the impact of government programs, such as the Social Security disability programor the minimum wage, in driving black men out of the labor market (Bound and Freeman, 1992;
Bound, Schauenbaum, and Waidmann, 1995; Parsons, 1980; Stern, 1989; and Welch, 1990).
Another focuses on the possibility that the changes in the wage structure, and particularly the
decline in the real wage of low-skill workers, may have discouraged low-skill black men fromentering the labor market (Juhn, 1992, 2003). Finally, some analysts note that the trend in blackincarceration rates was shaped by the crack epidemic of the 1980s and early 1990s. The
invention of crack cocaine in the early 1980s represented a technological innovation that greatly
increased the profitability of the cocaine trade. As illegal drug markets expanded, crime rose
(Grogger and Willis, 2000). Many jurisdictions responded by increasing both drug arrests andthe likelihood of imprisonment for convicted arrestees (Boggess and Bound, 1997). Crack and its
consequences were concentrated in African-American communities, in part because pre-existing
black gangs acted to profit from the expanding drug trade (Fryer et al, 2005).
Although immigration has disproportionately increased the number of low-skill workers
in the United States, only a few studies (Altonji and Card, 1991; LaLonde and Topel, 1991) havesought to estimate the effect of immigration on the wages of African Americans, who aredisproportionately represented among the low skilled.3 This paper extends the literature by

2 Western and Pettit (2000) show that ignoring the prevalence of incarceration rates provides a very

misleading picture of employment trends in the black population.
3 We are aware of two studies that suggest a potential link between immigration and incarceration. Using
cross-section data from the 1980s, Butcher and Piehl (1998) find that metropolitan areas with larger immigrant
populations had higher crime rates, but this relationship disappears once they control for the demographic
characteristics of the underlying populations. In their replication of the Borjas (2003) study, Raphael and Ronconi(2005) claim that adding incarceration rates as an explanatory variable in a regression of wages on immigrant sharesattenuates the wage impact of immigration in national-level data. The Raphael-Ronconi empirical exercise,

4
examining the relation between immigration and black wages, employment, and incarceration.
We use data drawn from the 1960-2000 U.S. Censuses. The data reveal a strong correlation
between immigration and black wages, black employment rates, and black incarceration rates.
As immigrants disproportionately increased the supply of workers in a particular skill group, wefind a reduction in the wage of black workers in that group, a reduction in the employment rate,
and a corresponding increase in the incarceration rate.
Our study suggests that a 10-percent immigrant-induced increase in the supply of aparticular skill group is associated with a reduction in the black wage of 2.5 percent, a reductionin the black employment rate of 5.9 percentage points, and an increase in the black
institutionalization rate of 1.3 percentage points. Among white men, the same ten-percent
increase in supply reduces the wage by 3.2 percent, but has much weaker employment andincarceration effects: a 2.1 percentage point reduction in the employment rate and a 0.2
percentage point increase in the incarceration rate. It seems, therefore, that black employment
and incarceration rates are more sensitive to immigration than those of whites.
These findings can obviously generate a great deal of controversy in the immigration
debate and can be easily misinterpreted. As a result, we are extremely cautious in both thepresentation and interpretation of the evidence. Although we have attempted to control for otherfactors that may account for the large shifts in black employment and incarceration rates over the
four-decade period that we examine, it should be obvious that no study can control for all
possible factors. It is equally important to emphasize that although the evidence suggests that
immigration played a role in generating these trends, much of the decline in employment orincrease in incarceration in the black population remains unexplained. Put differently,
immigration seems to have an effect and this effect seems to be numerically important, but we

however, may have the logic backwards: shifts in incarceration rates are likely endogenous and may be partly

5
would have witnessed a sizable decline in black employment and the concurrent increase inblack incarceration rates even if there had been no immigration in the past few decades.

II. Data and Descriptive Trends
Our data are drawn from the 1960, 1970, 1980, 1990 and 2000 Integrated Public Use
Microdata Samples (IPUMS) of the decennial Censuses. The 1960 file represents a 1 percent
sample of the U.S. population, the 1970 file represents a 3 percent sample, and the 1980 through2000 files represent 5 percent samples. The empirical analysis is restricted to men aged 18 to 64.
The Data Appendix describes the construction of the sample extracts and variables used in the
study.
We define an immigrant as someone who is either a noncitizen or a naturalized U.S.
citizen. All other persons are defined as natives. Similarly, we use information contained in thecensus race variable to classify persons as “black” or “white.” Unless otherwise specified,persons whose race is neither black nor white are excluded from the analysis.
As in Borjas (2003), skill groups are defined in terms of both educational attainment andyears of labor market experience. We classify workers into four distinct education groups: (1)high school dropouts (workers who have less than 12 years of completed schooling); (2) highschool graduates (workers who have exactly twelve years of schooling); (3) workers who havesome college (thirteen to fifteen years of schooling); and (4) college graduates (workers who
have at least sixteen years of schooling).
We group workers into a particular years-of-experience cohort by using potential years ofexperience. We assume that age of entry into the labor market is 17 for high school dropouts, 19
for high school graduates, 21 for persons with some college, and 23 for college graduates, andcaused by immigration.

6then calculate years of experience accordingly. The analysis is restricted to persons who have
between 1 and 40 years of experience. Workers are aggregated into five-year experiencegroupings (i.e., 1 to 5 years of experience, 5 to 10 years, and so on) to capture the notion thatworkers who have roughly similar years of experience are more likely to affect each other’slabor market opportunities than workers who differ significantly in their work experience. The
resulting data set contains 160 observations (4 education groups, 8 experience groups, and 5
years).
The cell corresponding to educational attainment (e), experience level (x), and calendar
year (t) defines a skill group at a point in time for the U.S. labor market. The immigrant supply
shock experienced by a particular skill group is given by:(1)

where Mext gives the total number of work hours provided by immigrants in the particular skill
group; and Next gives the corresponding number of work hours provided by native workers.4 The
variable pext then gives the immigrant share (i.e., the fraction of total supply that is foreign-born).
Figure 1 summarizes some of the (well-known) information regarding trends in theimmigrant share, by education and experience group, for the 1960-2000 period. The fraction ofthe (hours-weighted) workforce that is foreign-born increased most for high school dropouts.
Within any given census year, the immigration-induced increase in supply is largest for workers
with lower levels of labor-market experience, due to the preponderance of young adults in theimmigrant population. By 2000, 13.8 percent of the male workforce and 40.4 percent of high

4 The counts of immigrants and natives for skill group (e, x, t) include persons of all races.

7school dropouts were foreign-born. Among high-school dropouts with 10 to 15 years ofexperience, 48.0 percent of the workforce was foreign born.
It is useful to begin by illustrating racial differences in national-level trends in
employment and incarceration across race, education, and experience groups.5 The top panel of
Figure 2 reports the education-and-experience-specific trends for the black employment rate,
while the bottom panel presents the corresponding figure for white men. As noted above, theemployment rate is defined as the average fraction of weeks worked during the preceding
calendar year (including non-workers). Both figures are drawn to the same scale so that the large
racial differences can be grasped easily. Since employment rates and incarceration rates tend tobe lower for men in their mid-50s or older, our discussion focuses on the trends for those with up
to 30 years of labor market experience.
In 1960, the employment rate hovered around 70 to 75 percent for black workers who
were high school dropouts and had between 5 and 30 years of experience. By 2000, theemployment rate for these black high school dropouts had fallen to around 40 to 45 percent. In
contrast, the employment rate of black college graduates with 5 to 30 years of experience
hovered around 85 to 90 percent in 1960 and remained in that range by 2000.
The bottom panel of Figure 2 shows the corresponding trend for white men. As withblacks, there has been a decline in employment propensities for the least educated workers, but
the decline is modest relative to that seen in the black population. Among the most educatedwhites, average employment rates remain very high for all but the oldest workers. For college
graduates with up to 30 years of experience, the average employment rate was essentially flat
during the four-decade period, at around 90 to 95 percent. Among white high school dropouts
5 To provide some context to the discussion, it is instructive to report the share of black and white workers
in each of the education groups. In 2000, 18.8 (8.9) percent of blacks (whites) were high school dropouts, 43.7

8
with 5 to 30 years of experience, however, the average employment rate fell from around 85
percent in 1960 to around 68 percent in 2000, about a 17-percentage point drop. This is a large
and important decline, but it is much smaller than the 30 to 35-percentage point drop observed
among black high school dropouts with similar levels of work experience.
The rapid disappearance of a large segment of black high school dropouts from theworkforce was accompanied by a large increase in the number of black high school dropouts in
the institutionalized population. We use information on residence in group quarters available inthe decennial censuses to enumerate the number of persons in institutions. These institutions
include jails, prisons, and mental hospitals.6 For young men, the 1980 Census shows that the
majority of persons institutionalized are, in fact, incarcerated. Furthermore, the growth ininstitutionalization in Census data closely tracks the growth in incarceration apparent in
Department of Justice data from correctional facilities (Western and Pettit, 2000). For
expositional convenience, therefore, we will refer to the fraction of persons institutionalized as
the “incarceration rate.”
Figure 3 presents the trends in the incarceration rate, by race, education, and experience,over the 1960-2000 period. We again use the same scale in the two graphs so that the very large
racial differences can be easily seen. The average incarceration rate among white male highschool dropouts with 1 to 30 years of experience increased from around 2 percent in 1960 tobetween 5 and 10 percent in 2000. For whites with at least a high school diploma, theincarceration rate remained small even by 2000.

(33.2) percent were high school graduates, 26.4 (29.0) percent had some college, and 11.1 (28.9) percent werecollege graduates.
6 Although it is possible to differentiate between correction facilities and mental hospitals before 1990,
there is no such information in the 1990 and 2000 census data. To keep the variable definitions constant over time,
we focus on the number of persons who are in institutions.

9
In contrast, the incarceration rate for black men increased rapidly beginning after 1980
for all groups except college graduates. Among high school dropouts with 1 to 30 years ofexperience, for example, the incarceration rate hovered around 5 to 7 percent in 1960. By 2000,
however, some of the groups of younger black high school dropouts had astoundingly highincarceration rate. The incarceration rate of black high school dropouts with 5 to 15 years ofexperience had increased to around 35 percent.
This paper examines if these trends are related to the increases in immigration
experienced by the specific skill cohort at a particular point in time. To visually illustrate thenature of this link, Figure 4 presents a scatter diagram relating decadal changes in the immigrantshare and decadal changes in employment rates for blacks and whites, after removing decade
effects. Figure 5 presents the corresponding scatter diagrams relating decadal changes in theimmigrant share and decadal changes in incarceration rates. By removing decade effects, we
control for features of the economic environment that are common to all education andexperience groups in any given decade, but that might vary over time.
The graphical evidence is striking. Each point in the scatter diagram in Figure 4
represents the change in employment rate for an (e, x, t) cell and the corresponding change in theimmigrant share of the workforce for that cell. It is evident that there is a negative correlation
between changes in employment propensities and the immigrant share, and that the correlation isstronger for black men. Similarly, Figure 5 shows a corresponding positive correlation betweenchanges in incarceration rates and the immigrant share, with the correlation again being stronger
for black men. The remainder of this paper examines if these correlations persist after we control
for other factors that affected the trends in male employment and incarceration propensities overthis time period.

10III. Theory
To understand how immigration could reduce employment and increase incarceration
among native-born persons, with possibly larger effects among African-Americans, consider atwo-sector model of a national labor market. Native labor consists of black and white workers,
who are perfectly mobile between a formal sector (i.e., the “market” sector) and a sector
dedicated to crime.
We use this framework to investigate the consequences of an exogenous shift in the
supply of immigrant labor. We are interested in determining whether immigration induces some
native workers to exit market employment and engage in other activities. The mechanism
through which this might occur is straightforward. A positive immigrant supply shift puts
downward pressure on the wage in the market sector, causing native workers to substitute out ofmarket work and into either crime or leisure. One can think of the model as a generalequilibrium extension of Gronau (1977), in which individuals allocate time between work,
leisure, and home production. Our framework reinterprets home production as crime (as in
Grogger, 1998) and endogenizes the wage.7
The specification of the model presented in this section relies on three key assumptions.
First, we assume that all workers (i.e., immigrants, black natives, and white natives) are perfect
substitutes in the market sector.8 Although the assumption of perfect substitutability is notessential for deriving our theoretical results, it greatly simplifies the analysis.9 More important,
we will test for the empirical validity of this assumption in the next section.

7 The resulting framework is similar to the specific-factors model of a small open economy (e.g., Feenstra,
2004), extended to allow for the endogenous supply of labor to wage employment.
8 The race of immigrant workers is left unspecified.
9 We also solved a model in which black, white, and immigrant labor are imperfect substitutes in the
production of formal-sector output. All of the qualitative results of the simpler model presented here carry throughto the more general framework (one minor difference is that imperfect substitutability produces slightly different
estimating equations than those reported below in (6a)-(6d)).

11
We also assume that immigrants do not participate in crime. One could generalize themodel to allow immigrant labor to be employed in either the market or crime sector. Our results
would hold as long as the elasticity of labor demand in crime is larger for natives than
immigrants (or, alternatively, if the elasticity of substitution between native and immigrant laboris higher in market employment than in crime). Since criminal penalties are larger for
immigrants than natives (for non-citizens, the penalties for criminal activity are incarceration andpossible deportation), it seems reasonable to assume immigrants are less likely than natives tosubstitute into crime in response to a negative wage shock. In fact, relative to observationallyequivalent natives, immigrants are much less likely to be incarcerated (Butcher and Piehl, 1998,
2000).
Finally, we assume that there are race-specific crime production functions, effectively
implying that black and white criminals tend to operate in separate markets.10 This assumption
allows immigration to have different effects by race on employment and incarceration, even if it
has the same effects on wages. Black men, by virtue of being relatively concentrated in innercities, may have more opportunities to engage in criminal activity. Grogger (1998) finds thatblack men are more likely to participate in crime than white men even after controlling foralternative labor market options. Further, black-white differences in criminal propensities may
have been exacerbated by the advent of crack cocaine. Fryer et al (2005) argue that pre-existinggang organizations, which controlled street corners and other outdoor spaces in many urban
areas, gave blacks an advantage in creating and controlling crack distribution networks.11 Other

10 This assumption, like the other two, simplifies the discussion but is not essential for the results. What isessential for immigration to have different effects on black and white workers is that the elasticity of labor demandin crime differs between the two groups.
11 Responses to a survey of 27 large-city police chiefs administered by Grogger and Willis (2000) indicatedthat crack was concentrated among blacks or minorities in all but four jurisdictions.

12
evidence suggests criminal gangs tend to be organized along racial lines and operate in spatiallysegmented markets (Venkatesh, 1997; Grogger and Willis, 2000).
Let Lfs = Nbfs + Nwfs + Ms, where Nbfs denotes employment of native black workers in the(formal) market sector who have skill s; Nwfs denotes the corresponding employment of native
white workers; and Ms denotes the corresponding number of immigrants. For workers of race iand skill group s, the wage in the market sector is:(2),

where Xfs is a labor demand shifter for the market sector; i is a parameter that captures
preferences for discrimination on the part of employers, with w = 0 and 1 > b  0, so that black
workers may face a lower market wage as a result of discrimination; and f < 0 is the inverse of
the labor demand elasticity in the market sector (or the factor price elasticity in this simple
framework). Equation (2) assumes that all workers in skill group s are perfect substitutes in termsof their contribution to market sector output.
The marginal product of labor in the crime sector for workers in racial group i with skill s
is:

(3)

,

where Xics is a demand shifter for criminal activity, Nics gives employment of native workers ofrace i and skill group s in crime, and ic < 0 is the inverse of the labor demand elasticity in thecrime sector.

13Black-white wage differences are determined by the extent of discrimination in themarket sector, with wb/ww = (1 - b)  1.12 Inter-sectoral labor mobility transmits thediscrimination-driven market racial wage gap to the crime sector. The demand shifters, Xfs andXics, embody capital, TFP, and the output price in each sector. Our empirical analysis will allow
for changes in sectoral demand shifters by controlling for race-specific changes in the returns toskill over time.
The supply of labor to paid employment (i.e., employment in either the market or crime
sectors) is elastic, with the inverse demand for leisure given by:(4),

where Xihs is a leisure demand shift parameter, Nihs gives the number of natives consuming
leisure, and ih < 0 is the inverse of the demand elasticity for leisure.
Finally, the allocation of native labor to employment in the market sector, employment in
the crime sector, and leisure is subject to the constraint:

(5)

where

,

is the (constant) population of native-born persons of race i and skill s.
Equations (2)-(5) represent a system of seven equations in seven unknowns. For

simplicity, we neglect the impact of immigration on capital accumulation, which would tend to

12 For simplicity, we assume that the discrimination coefficient is independent of skills. Relaxing thisassumption does not change any of the results of the model.

14dampen the wage effects of immigration over time.13 Figure 6 illustrates the equilibrium of themodel for black workers of skill group s. There is an analogous, and interdependent, set of
equilibrium conditions for white workers. The equalization of wages for black workers between
the formal sector and the crime sector is shown by the intersection of the two sectoral labordemand schedules at point 1. The allocation of labor to leisure is implicit, since the endogenous
leisure allocation defines the value, which is total black labor available

for employment in either the market or crime sector. Solving for Nbhs defines the width of thebox in Figure 6. The sensitivity of leisure to wages will become apparent once we consider alabor-supply shock due to immigration.
Figure 7 shows the labor-market consequences of an increase in immigrant labor supply.
The immediate direct effect is a contraction in the demand for native labor.14 The contraction inmarket-sector labor demand puts downward pressure on the market wage, inducing native labor
to increase leisure and decrease labor supplied to the market. The increase in leisure implies thatlabor available for either the market or crime sectors falls fromto, whichimplies the right vertical axis in Figure 7 shifts to the left, inducing a corresponding leftward
shift, from Dc to, in the demand for labor in the crime sector (whose horizontal position isdetermined by the position of the right axis).
The net effect of the immigrant labor supply shock is a new equilibrium at point 2, in
which the black wage is lower, black employment in the market sector is lower, black
employment in the crime sector is higher, and black leisure is higher. Market employment falls

13 We have worked out an extension of the model where the market sector employs both labor and capitalin production, with the supply of capital adjusting over time in response to deviations in the return to capital from its
long-run rate. As long as complete adjustments in the capital stock are not immediate, the short-run consequences ofimmigration are qualitatively the same as those implied by the simpler model summarized in this section.
14 For black workers, part of the inward shift in formal-sector labor demand is mitigated by the exit ofwhite workers from the formal sector. In the graphical analysis, this adjustment is implicit.

15
because immigrant labor substitutes for black labor; black employment in crime rises because
lower market-sector labor demand induces blacks to shift into crime; and black leisure rises
because the black wage falls.
The model has similar qualitative predictions for the wage and sectoral distribution ofwhite workers. The model, in addition, yields an important and testable quantitative prediction.
Since black and white workers are perfect substitutes in the market sector, the percent impact ofimmigration on the black and white wage is the same. As long as the discrimination parameter b
is invariant to labor-market conditions, immigration changes black and white wages by the same
percentage amount, leaving the racial wage differential unchanged. However, racial differencesin the demand elasticities of crime and leisure imply that the employment effects of immigrationneed not have the same magnitude.
Let
and letbe the wage for race group i and skill group s in the pre-immigration equilibrium,
give the corresponding number of native workers in the market sector at that time
. We measure the immigrant supply shock by, the immigrant-

induced percent increase in labor supply to the market sector. The Mathematical Appendix
shows that the race-specific equations relating post-immigration wages, native labor allocations,and the immigrant supply shock are given by:

(6a)
(6b)

,

(6c)

,

16

(6d)

.

As shown in the Mathematical Appendix, the parameter  is a positive constant that lies between
zero and one and is defined by:

(7)

where

is the average number of type-j natives across skill groups in the pre-immigration

equilibrium.
The parameter  gives an elasticity-adjusted measure of the market sector participation
rate of natives in the pre-immigration equilibrium. Consider, for instance, the special case where
the demand elasticities are equal in all activities, so that f = ic = ih. Equation (7) shows that 
is then exactly equal to the fraction of natives participating in the market sector in the preimmigration period. It is also worth noting that if the demand for labor in both the crime andleisure sectors is perfectly inelastic (so that the ratios 1/ic and 1/ih are equal to zero), theparameter  is then equal to one. In this extreme case, the relative number of native workers ineach of the sectors is effectively fixed.
Equation (6a) implies that more immigration lowers wages (f  < 0), with the wage
impact being greater the larger the factor price elasticity in the market sector. Two points areworth emphasizing about the wage impact of immigration. First, as noted above, the wage

17
impact is predicted to be the same for black and white workers.15 Second, the reduced-form
regression of the log wage on the immigrant supply shock m does not identify the factor priceelasticity, f . Rather, it identifies the product of the factor price elasticity and , the parameterthat roughly indicates the sectoral allocation of the native population (up to a linear
approximation). The parameter  equals one when the supply of native labor to the market sector
is perfectly inelastic. It is only in this case that the regression coefficient identifies the factor
price elasticity. If native labor supply to the market sector is elastic, however, the reduced-form
impact of immigration is numerically smaller than the factor price elasticity. The intuition forthis result is obvious: Native opportunities to substitute into crime or leisure dampen the impactof immigration on the market wage, relative to the case of inelastic labor supply. Figure 7
illustrates the result. If the demand for leisure were perfectly inelastic the post-immigration
equilibrium would be at point 1, instead of point 2. The fall in the native wage would be larger
and the fall in native formal employment would be smaller. We will refer to the product f  as
the “reduced-form wage elasticity.”
Equation (6b) shows that a larger immigrant supply shock increases the number ofnatives participating in the crime sector (f /ic > 0), with the impact of immigration being
larger the more elastic is the demand for crime labor relative to the demand for formal labor. The
immigration-induced change in crime employment for blacks relative to whites depends on theratio of the elasticities wc/bc. Even though the wage impact of immigration is predicted to be
the same for blacks and whites, black employment in the crime sector is more responsive toimmigration if the elasticity of labor demand in crime is larger for blacks than whites.
15 As shown by equation (2), the market sector wage for both black and white workers (who are perfect

substitutes in production) is determined by the equilibrium size of the workforce in that sector. As a result, the18Equation (6c) indicates that more immigration is associated with greater native demand
for leisure (f /ih > 0), with the impact of immigration on leisure being larger the more elastic
is the demand for leisure relative to the demand for formal labor. Similar to participation incrime, the immigration-induced change in leisure for blacks relative to whites depends on theratio of elasticities wh/bh, indicating that black leisure time is more responsive to immigration
if the elasticity of demand for leisure is larger for blacks than whites.
Finally, equation (6d) implies that a larger immigrant supply shock is associated withlower native market sector employment, with the impact of immigration being larger the moreelastic is the demand for formal labor relative to the demands for crime labor or leisure. The
impact of immigration depends on the pre-existing employment shares in the various sectors,
where(the pre-immigration share of race i persons in the crime sector),(the pre-immigration share of race i persons in the leisure sector), and(the pre-immigration share of race i persons in the market sector).16 If, forexpositional convenience, we ignore the skill subscript, equation (6d) implies that the change inmarket employment for blacks relative to whites is given by the ratio wf(bc/bc + bh/bh)/bf(wc/wc + wh/wh), which shows that black market employment is more responsive toimmigration if the elasticities of demand for crime labor and for leisure are larger for blacks thanwhites (as long as the market participation rate of whites is at least as high as that of blacks).17

manner in which native substitution across sectors mitigates the wage consequences of immigration is common to
all native workers, regardless of race.
16 Note that none of the coefficients in equations (6a)-(6d) depend on the extent of discrimination in thelabor market because the discrimination coefficient is assumed to be constant over time.
17 The condition for immigration to affect black market sector employment more than for whites depends
on initial black-white relative employments in crime and leisure. If the initial black shares of employment in crime
and leisure are higher than the white shares (bc > wc, bh > wh), immigration can then induce relatively larger
reductions in market sector employment for blacks even if the black crime and leisure demand functions are lesselastic than those for whites.

19This model helps us understand the source of racial differences in the consequences ofimmigration and motivates why the empirical analysis presented in the subsequent sections
allows the impact of immigration on wages, employment, and incarceration rates to differ
between black and white men. As we have seen, if the demand for labor in the crime sector ismore elastic for blacks than for whites, immigration will have a larger negative impact on black
market employment and a larger positive impact on black crime employment.
Our empirical analysis uses data on wage and employment rates for education-experience
cohorts by year. Although we do not have data on participation rates in crime, we do haveinformation on incarceration rates for the various groups.18 These data constraints require that we
estimate the reduced-form expressions, as summarized by equations (6a)-(6d), rather than astructural model of sectoral time allocation.

IV. Evidence
The estimating equations implied by the theory built in the assumption of perfect
substitution between black and white native workers, as well as perfect substitution between
native and immigrant workers. Before proceeding to a discussion of the empirical link between
immigration and black economic status, therefore, it is important to test for the validity of these
two assumptions using the data set of 160 skill groups (defined by education, experience, andtime) introduced in Section II.
Consider a generic two-level nested CES production function (as in Card and Lemieux,
2001), where the first level defines the size of the native-born workforce as a CES aggregate of
the number of black (b) and white (w) workers, and the second level defines output as a function

18 The National Longitudinal Survey of Youth (NLSY) has information on participation in criminal
activities, but only for a single cross-section.

20of the (CES-weighted) native-born workforce and immigrants. By equating the wage to themarginal product of labor for each native worker type, it is easy to derive the relative demand
function:

(8)

1
1 
ln ( wbst / wwst ) =  ln ( N bst / N wst ) +ln ( bst /  wst ) ,where  is the elasticity of substitution between black and white native workers; wist is the wageof race group i and skill group s at time t; Nist is the total number of manhours provided by thegroup; and ist is a parameter measuring relative efficiency. We proxy the relative efficiency termin equation (8) by introducing vectors of fixed effects indicating education, experience, and timeeffects, their interactions, and a random error term. The null hypothesis of perfect substitution
between black and white native workers states that the coefficient 1/ equals zero.
The first row of the top panel of Table 1 reports the OLS coefficient that examines theextent of substitutability between black and white native labor (i.e., the dependent variable is thelog wage ratio between black and white workers and the independent variable is the log ratio of
the total number of work hours supplied by black relative to white workers). The results do notprovide much support for the hypothesis that black and white workers are imperfect substitutes(within these narrowly defined skill groups). The coefficient is most negative in the specification
reported in column 4 of the table (which is the most general specification). In this case, theestimated coefficient is -.045 with a standard error of .027. The implied elasticity of substitution
between black and white native workers is 22.2, which for most practical purposes is equivalent
to perfect substitution.

21
One potential problem with the least squares estimates is that the relative size of the black
workforce in the right-hand-side of equation (8) may be endogenous. The estimated elasticity of
substitution between white and black workers, therefore, may be contaminated by labor supply
decisions at both the intensive and extensive margins. We use instrumental variables to correct
for the possible endogeneity bias. In particular, we instrument the relative number of manhours
worked by blacks with the relative number of men in the particular skill group who are black.19
Row 2 of the top panel of Table 1 shows that the IV estimates of the elasticity of substitution
between black and white workers also provide little evidence that the assumption of perfect
substitution between black and white native workers is soundly rejected by the data.
Once we have established that black and white native workers are perfect substitutes, we
can then move to the next level of the nested CES system, and derive an analogous relative
demand equation that relates the relative log wage of immigrants to the log of the relative supplyof immigrants. The bottom panel of Table 1 reports both OLS and IV estimates of the coefficientfrom regressions that relate the relative wage of immigrant workers to their relative quantity (i.e.,the dependent variable is the log wage ratio between immigrant and native workers and the
independent variable is the log total hours ratio).20 Again, there is no evidence to reject the null
hypothesis that immigrants and natives are perfect substitutes.21 For the remainder of the

19 More precisely, the instrument is the ratio of the number of black persons in a skill group to the numberof white persons in that skill group. The counts of persons in the instrument include both workers and non-workers.
20 The instrument is given by the ratio of the number of foreign-born persons in a skill group to the total
number of native persons in that skill group. The counts of persons in the instrument include both workers and nonworkers.
21 It is worth emphasizing that the literature provides mixed evidence on the extent of substitution between
immigrant and native workers, with Jaeger (1996) finding that immigrants and natives are perfect substitutes but
Ottaviano and Peri (2006) finding strong complementarities between immigrants and natives. However, Borjas,
Grogger, and Hanson (2008) show that the complementarity results in Ottaviano and Peri result from a flaw in theconstruction of their sample, particularly the classification of currently enrolled junior and senior high school
students as high school dropouts. If these students are dropped from the data, the Ottaviano-Peri finding ofcomplementarity vanishes.

22
analysis, therefore, we will maintain the assumption that different labor types (within the narroweducation-experience categories defined earlier) are perfect substitutes in the formal sector.
Let yext denote the mean value of a particular labor market outcome for native-born men
who have education e, experience x, and are observed at time t. As noted above, we calculated
yext using the sample of natives who are either black or white. The empirical analysis reported inthis section stacks these national-level data across skill groups and calendar years and estimates
the following regression model separately by race:(9)

yext =  pext + E + X + T + (E  T) + (X  T) + (E  X) + ext,

where E is a vector of fixed effects indicating the group’s educational attainment; X is a vector of
fixed effects indicating the group’s work experience; and T is a vector of fixed effects indicating
the time period. The linear fixed effects in equation (9) control for differences in labor market
outcomes across schooling groups, experience groups, and over time. The interactions (E  T)
and (X  T) control for the possibility that the impact of education and experience changed overtime, and the interaction (E  X) controls for the fact that the experience profile for a particularlabor market outcome may differ across education groups. The regression specification in (9)implies that the labor market impact of immigration-induced supply shifts is identified using
time-variation within education-experience cells. The regressions are weighted by the number ofobservations used to calculate the dependent variable yest.22 Finally, the standard errors are
clustered by education-experience cells to adjust for possible serial correlation.

22 We weigh the cells by the sample size to adjust for differences in precision. An alternative weighting

scheme would be to normalize the sum of weights in each cross-section to equal 1, so that each of the censuses“counts” equally in the estimation of the coefficients. This “rescaled” weighting scheme would lead to larger (andmore significant) wage effects. For example, the OLS coefficient in the log weekly wage regression reported in23
We examine the impact of immigration on three distinct outcomes. The alternative
dependent variables include: the log weekly earned income, the employment rate, and theincarceration rate.23 We estimate the employment and incarceration rate regressions using agrouped logit estimator.24 Let rext be the relevant employment or incarceration rate for cell (e, x,t). The grouped logit estimator is given by the weighted least squares regression of the log odds
model:(9)

To make the results more easily interpretable, we convert the estimated coefficient * (and its
standard error) into a marginal impact, which is given by, where we use the race-

specific sample mean of the employment or incarceration rate in the calculation.25
It is important to emphasize that the incarceration rate is an imperfect measure ofparticipation in crime, as individuals in prison today may have committed crimes several years in
the past when different labor market conditions prevailed. To control for lags between shocks to
the labor market and changes in the size of the prison population, we report results on
incarceration that use either the current share of immigrants in the workforce or the five-year lagof the immigrant share. Together, the contemporaneous immigrant share and the five-year lag

Panel A of Table 2 increases from -0.346 (0.137) to -0.617 (0.203) for blacks and from -0.522 (0.254) to -0.672(0.243) for whites.
23 Recall that the employment rate is defined by the average fraction of weeks worked during the calendar
year prior to the Census (including non-workers).
24 The use of logit versus a linear probability model leads to relatively similar marginal impacts for theemployment rates, but smaller marginal impacts for the incarceration rate. This is not surprising given the clusteringof incarceration rates at very small numbers near zero.

24
bracket the length of the average prison term, which is about two years (Raphael and Stoll,2005).
Table 2 reports our estimates of the adjustment coefficient  (or the corresponding
marginal impact in the grouped logit regressions). The top panel of the table reports the leastsquares estimates of the regression model. The first row of the panel reports the results for blackmen, while the second row reports the results for white men. Consider initially the results when
the dependent variable is the mean log weekly earnings of the skill group. The adjustment
coefficient  is -0.346 (with a standard error of 0.137) for blacks, and -0.522 (0.254) for whites.
These coefficients are easier to interpret if we convert them into an elasticity that gives thepercent change in wages associated with a percent change in labor supply. Let mext = Mext/Next, or
the percentage increase in the labor supply of group (e, x, t) attributable to immigration. We cancalculate the reduced-form wage effect (equivalent to the product of parameters f f in ourtheoretical framework) as:(10)

By 2000, immigration had increased the immigrant share in the total number of hours supplied to
the U.S. labor market to 13.8 percent. Equation (10) implies that the reduced-form wage
elasticity—evaluated at the mean value of the immigrant supply shift—can be obtained bymultiplying  by approximately 0.74. The reduced-form wage elasticity for weekly earnings isthen -0.26 (or -0.346  0.74) for blacks, and -0.39 for whites. Although the estimated elasticity is

25 The weighted least squares estimator for grouped logit uses a weight equal to, where the25higher for whites than blacks, the difference between the two estimates is not statisticallysignificant (t=0.6). This is additional evidence in favor of the assumption made in Section III
that equally skilled blacks and whites are perfect substitutes in production. The estimatedelasticities imply that a 10 percent immigrant-induced increase in the number of workers in aparticular skill group reduces the wage of that group by 3 to 4 percent.26 These results closely
match the estimated wage impacts of immigration across all workers reported in Borjas (2003).
Columns two through four of Table 2 show the relation between immigration andemployment and incarceration rates. There is a strong negative relation between immigration andemployment rates and a weaker positive relation between immigration and incarceration rates. A
10 percent increase in supply is predicted to reduce the employment rate of black men by 5.1
percentage points (-0.683  0.74) and that of white men by 1.6 percentage points. Similarly, a 10
percent increase in supply increases the incarceration rate of black men by 1.0 percentage point,
but has only a negligible effect on the incarceration rate of white men. Lagged immigration has aroughly similar effect on incarceration rates for blacks and a numerically small (but statisticallysignificant) effect on whites. It seems, therefore, that the impact of immigration at the extensive
margin of labor supply is far larger for blacks than for whites.
A potential problem with the least squares estimates is that the immigrant share includedin the right-hand-side of equation (9)—that is, the fraction of the total labor supply provided byforeign-born persons—may be endogenous. Although our theoretical model maintained theassumption of inelastic immigrant labor supply, it is important to relax that assumption in thepredicted probabilities are calculated from a first-stage unweighted regression on the log odds ratio and next is the
sample size in the cell.
26 The regression model in (7) uses the immigrant share, p, rather than the (more natural) relative numberof immigrants, m, as the regressor. The main reason for using p as the regressor is that the outcomes used in thispaper tend to be nonlinearly related to m, and p is approximately a linear function of log m. Rather than introducing
significant nonlinearity in the regression, we opted for the simpler approach of a generic regression of the outcomeon the immigrant share.

26
empirical work. We use instrumental variables to correct for the possible endogeneity bias,
where the instrument is the immigrant share in the population.27 Panel B of Table 2 reports theestimated IV coefficients. The wage effects from the IV specification are similar to those fromthe least squares regression. The least squares coefficient of the immigrant share on the log
weekly wage of black men, for example, is -0.346 (0.137), while the corresponding IV
coefficient is -0.314 (0.131). In addition, the estimated IV coefficients in the black employment
and black incarceration regressions are essentially the same as those obtained in the least squares
specification.
Another concern is that the measured effects of immigration may be contaminated byfactors that are driving employment and incarceration behavior for blacks and whites within
education-experience groups. These factors will not be absorbed by the fixed effects included in
the regression and may be correlated with the immigrant supply shifts. The potential existence of
these additional factors is not altogether surprising. As we discussed above, the wage structurechanged considerably during our sample period and the crack epidemic raised the return to crime
during the 1980s and 1990s. It is important, therefore, to examine the impact of various sourcesof bias on the magnitude of the estimated coefficients.
Consider initially how the crack epidemic may influence our results. In terms of themodel from the previous section, the invention of crack raises the marginal product of criminal
labor, shifting the curve labeled Dc in Figure 6 to the left. This leftward shift reduces native labor
supplied to the formal sector and raises native labor supplied to crime, just like an increase inimmigration. Unlike an increase in immigration, however, the increasing productivity of crimeshould raise equilibrium wages. This casts some doubt on the notion that the effects we attributeto immigration are entirely due to crack, since the data reveal that immigration reduced wages.
27 In other words, it is the ratio of the number of foreign-born persons in a skill group to the total number of27
Nevertheless, given the potential importance of crack as an alternative explanation, it isimportant to account for it explicitly in the regression model.
To do so we make use of the “crack index” developed by Fryer, Heaton, Levitt, andMurphy (2005). This index is a linear combination of several variables related to the crack
epidemic, including the share of arrests made for cocaine-related charges, the number of deaths
due to cocaine, the number of cocaine busts carried out by the federal Drug Enforcement
Administration, and the number of cocaine-related hospital emergency room incidents. Most ofthese measures can obviously be considered as outcomes of the crack epidemic, whereas theideal measures for our purposes would be indicators of the extent to which crack raised criminal
productivity and exogenous measures of the criminal-justice response to the crack problem. Thus
one could argue that the crack index is really an endogenous variable, particularly in theincarceration regressions. This possibility will affect the interpretation of our results.
The Fryer et al crack index varies only by time and race, meaning that its main effects are
subsumed by the year fixed effects included in our regression model.28 To include the index in
the model, we interact it with the education-experience fixed effects. In particular, consider thefollowing regression:(11)

yext =  pext + E + X + T + (E  T) + (X  T) + (E  X) + (E  X) Ct + ext,

where Ct is the value of the crack index at time t. Note that the specification in (11) essentiallyintroduces a specific type of time variation in the education-experience interaction fixed effects.
Obviously, a totally unrestricted type of variation would be impossible since there would then be

persons in that skill group.

28
as many education-experience-time interactions as there are observations. Our specification
permits the effects of skill to vary over time in a manner that is related to the spread of crack,
while still enabling us to estimate the effects of immigration from changes over time within thesame skill groups.
The estimated adjustment coefficients  (and corresponding marginal impacts in thegrouped logit regressions) are reported in panel C of Table 2. It is evident that the estimatedmarginal effects on black wages, employment, and incarceration rates are not very sensitive tothe inclusion of the crack index. A ten-percent immigrant-induced supply shift still lowers thewage of blacks by -3.0 percent, lowers the employment rate by 4.1 percentage points, andincreases the incarceration rate by 0.9 percentage points.
There is an important sense, however, in which the Fryer et al crack index does not
capture how the crack epidemic affected the sectoral choices of the various skill groups. The
index, after all, takes on the same value for black high school dropouts as it does for blackcollege graduates. It is evident that the crack epidemic had a much greater impact on the
behavior of low-skill (and younger) persons. To incorporate this notion into our study, we reestimated the regression models using a “restricted” version of the Fryer et al crack index. In
particular, we reset the index to 0 for all persons who have at least a high school diploma or morethan 20 years of work experience. The restricted crack index, therefore, effectively assumes thatthe crack epidemic was mainly a demand shifter for younger, low-skill persons. Panel D of Table
2 reports the regression coefficients obtained from the use of the restricted crack index. Note that
this change in the way we account for the crack epidemic barely affects our results.

28 The index takes on a value of 0 for all cells drawn from the 1960, 1970, or 1980 Censuses. The index forthe 1990 cells is the average for 1988 and 1989 of the Fryer et al (2005) race-specific city-level crack index. The
index for the 2000 cells is the average of the 1998 and 1999 values.

29
The use of the crack index helps the regression model partly account for what has been
happening at the low-skill end of the U.S. labor market. A large research literature documentsthat there was also a substantial increase in the rate of return to skills and to labor market
experience beginning around 1980 (Katz and Murphy, 1992; Autor, Katz, and Kearny, 2008).
Our basic regression specification in equation (9) attempts to control for these changes by
including interactions of fixed effects between education and time, as well as interactions of
fixed effects between experience and time. As noted above, ideally we would control for changes
in the wage structure by including a complete set of three-way interactions between the
education, experience, and time fixed effects. Such a strategy is not feasible, however, because
the full set of interactions would be exactly collinear with the immigrant share variable. As aresult, we must balance the collinearity problem against the need to control for changes in thewage structure by allowing year effects to vary by education and experience in a limited way.
We attempt to capture the changes that occurred at both ends of the skill distribution byintroducing a set of dummy variables that allow for some interactions between education,
experience, and time. In particular, we introduce dummy variables indicating if the (e, x, t) cellrefers to a post-1980 observation of high school dropouts, a post-1980 observation of high school
graduates or those with some college, or a post-1980 observation of college graduates. Moreover,for each education group we categorize individuals into very young, young, and older experiencegroups (1-10, 11-20, or 20 plus years of experience). This set of dummy variables is specificallydesigned to capture changes that occurred at the extremes of the wage distribution (in terms ofboth education and experience) before and after 1980.
It is worth emphasizing that the inclusion of this restricted set of education-experiencetime interactions does not impose any structure on why these changes may have occurred. As aresult, the interactions capture not only the impact of the widening of the wage structure, but also

30
the impact of the crack epidemic, as well as any kinds of changes in the composition of particularskill groups over time (e.g., the possibility that younger low-skill workers may be selecteddifferently before and after 1980). In particular, one consequence of rising returns to skill may
have been to raise the incentive for workers at all ability levels to obtain more education. If,
within each skill group, more able workers are those more likely to complete additional
schooling, then over time we would observe a decline in the average ability of workers in all
education groups. Such an outcome would be more likely among the young, since their net
benefit to completing more schooling is relatively high. Declining average ability within skill
groups could result in all groups, and especially the young, exhibiting declining wages, declining
employment rates, and rising incarceration rates, which are the same patterns that would result
from an immigration-induced labor supply shock. The included set of additional educationexperience-time fixed effects allow for differential effects before and after 1980 among very
young, young, and older workers, with low, average, or high levels of education. Hence we canpartly control for changes in the average ability of individuals within experience-educationgroup, focusing on those cases where the ability changes are likely to have been mostpronounced.
The bottom panel of Table 2 reports the estimated coefficients from the specification withthe restricted set of education-experience-time fixed effects. The wage effect of immigration
remains negative and significant—even after controlling for these changes in the wage structure
at the extremes of the skill distribution. In fact, the adjustment coefficients are very similar forthe two race groups: -0.355 (0.171) in the black regression and -0.428 (0.233) in the white
regression. A 10-percent immigrant-induced increase in supply, therefore, reduces wages byaround 3.0 percent. Second, immigration reduces the employment rate of both black and white
workers. These effects are statistically significant, and the marginal impact on blacks is over

31
twice as large as the marginal impact on whites. Finally, immigration has a significant impact on
incarceration rates for both blacks and whites, with the marginal impact on blacks being 3.5
times as large as the marginal impact on whites. A 10-percent immigrant induced increase insupply raises black incarceration rates by 1.3 percentage points and that of whites by 0.2
percentage points.29
We conclude that our key findings are robust to a number of major specification changes.
The marginal wage effect of an immigration-induced increase in supply is never significantly
different between blacks and whites. Nevertheless, this supply shift always has a larger impact
on the employment and incarceration rates of blacks than of whites. The similar wage effects are
consistent with the assumption that equally skilled blacks and whites are perfect substitutes inmarket production. The larger quantity adjustments are consistent with the differential access tocriminal markets that has been reported in the literature (Fryer et al, 2005; Grogger and Willis,
2000).
One remaining question is whether our results would be substantially different if we cast
the analysis in terms of state-level labor markets, rather than a national-level labor market. In an
earlier draft of this paper (Borjas, Grogger, and Hanson, 2006), we addressed this issue by
allowing for natives to move across states in response to immigration from abroad. We show thatthe correct regression specification in such a model would be one that relates native labor market
outcomes to both state- and national-level immigration shares on the right hand side of ourregression models (where the national-level immigration share captures the “externality” that
immigration into one specific region imparts on the wage structure in other regions through29 We experimented with other specifications for the restricted set of education-experience-time

interactions (e.g., allowing a dummy variable for each experience cohort for high school dropouts after 1980). This
experimentation revealed that the evidence summarized in Table 2 adequately represent the results that can beobtained from a large family of alternative specifications—as long as the specifications include interactions thatdifferentiate younger versus older workers separately for the two extreme education groups in the study.

32
native internal migration). The total effect of immigration is then given by the sum of thenational- and state-level coefficients. Since the results of our state-level analysis were very
similar to those reported in this section, we refer the interested reader to our working paper draft
for more detail.

V. Accounting for the Trends in Employment and Incarceration Rates
We now use the regression coefficients reported in Table 2 to determine the extent towhich the immigration-induced shift in supply accounts for the decline in black wages andemployment and the increase in black incarceration. In particular, we use the coefficients tosimulate the impact of the immigrant influx that entered the United States between 1980 and
2000. Suppose the estimated regression coefficient for a particular outcome y (and for aparticular race group) is. Equation (10) then implies that the reduced-form impact of an

immigrant influx that increases the supply of education group e by me percent can beapproximated by:(12)

where we evaluate the derivative in (10) at the mean value of the immigrant share observed in
2000. We define the immigration-induced labor-supply shock between 1980 and 2000 as:

(13)

33
so that the baseline population used to calculate the percent increase in labor supply averages out
the (changing) size of the native workforce during the 1980-2000 period and treats the preexisting immigrant population as part of the “native” stock.
Table 3 summarizes the results of the simulation. Column 1 of the table reports the actualchange in the log weekly wage, employment, and incarceration rates experienced by black men
during the 1980-2000 period. The changes in wages, employment and incarceration rates arequite large for black men, and particularly for low-skill black men. Between 1980 and 2000, forexample, the real wage of black high school dropouts (a group that made up around 25 percent of
the black male population in 1990) fell by 14.2 percent, the employment rate fell by 16.7
percentage points, and the incarceration rate rose by 15.6 percentage points.
Column 2 summarizes the results of the simulation when we use the adjustment
coefficients reported in Panel E of Table 2. Equation (12) predicts that, other things equal, the1980-2000 immigrant influx reduced the wage of black high school dropouts by 5.3 percent,reduced the employment rate by 12.6 percentage points, and increased the incarceration rate by
2.8 percentage points. These predicted impacts are sizable and account for about a third of theobserved reduction in wages, for over two-thirds of the observed decline in employment, and forabout 15 percent of the rise in incarceration rates. In other words, immigration contributed a
numerically significant amount to the trends among low-skill blacks, but much of the decline inblack economic status would have been observed even in the absence of the immigrant influx.
Table 3 shows that our approach cannot explain the observed changes in wages or
employment for high-skill blacks. In the sample of black college graduates, for example,
immigration is predicted to reduce wages by 2.9 percent and employment rates by 6.9 percent,whereas they rose by 13.1 percent and 0.1 percent, respectively. The key assumption of thesimulation—that “other things are equal” in the 1980-2000 period—obviously misses an34
important part of what was driving employment opportunities for high-skill workers at that time.
The simulation reported in Table 3 does not account for these shifts.
A second caveat is that the regression results reported above impose the restriction thatthe various demand elasticities are invariant to skill. We might imagine that the elasticity of labordemand in crime, in particular, varies by education level, with elasticities being larger for theless-educated. If the demand for highly educated labor in crime is in fact relatively inelastic, wewould overstate the impact of immigration on their employment and incarceration rates.
Finally, the “all other things equal” assumption ignores the capital adjustments inducedby the immigrant supply shock. If the aggregate production function had constant returns toscale, for example, the capital adjustments would eventually return the average wage in the labormarket to its pre-immigration equilibrium level. Even in the long run, however, immigration canhave distributional effects. In a CES framework, the long-run relative wage effects ofimmigration are obtained by differencing the effects across the different education groups
reported in Table 3 (Borjas and Katz, 2007). For example, the 1980-2000 immigrant influx
lowered the wage of black high school dropouts relative to that of college graduates by 2.4
percent (or –0.053 – (–0.029)). These relative wage effects suggest that there would also be
sizable relative employment effects and relative incarceration effects.
The last two columns of Table 3 report the simulation results for white men. The 19802000 immigrant influx reduced the wages of white high school dropouts by about 6.8 percent, or
about a third of the observed change. The influx also lowered the employment rate by 4.6
percentage points, or about 40 percent of the decline actually observed in the white sample.
Immigration also explains a smaller portion of the increase in incarceration rates observed
among low-skill white men.

35
VI. Summary
It is well known that black employment rates declined substantially over the past few
decades, and that this decline was accompanied by a rapid rise in the black incarceration rate.
This paper examines a simple yet potentially controversial question: has the resurgence of largescale immigration in the United States contributed to these trends?
We use data drawn from the microdata files of the 1960-2000 U.S. Censuses to examine
the trends in black wages, employment, and incarceration. Our empirical analysis examines thelink between immigration and the evolution of these variables over the four-decade period—after
adjusting for other factors that could account for shifts in the wage structure as well as shifts inopportunities in the “formal” labor market and in the crime sector. We find a numerically sizable
and statistically significant negative correlation between immigration and the wages of blackmen; a sizable and significant negative correlation between immigration and the employment
rate of black men; and a significant positive correlation between immigration and theincarceration rate of black men. It is important to emphasize that we find similar correlations forwhite men, but the magnitude of these correlations differ in important ways between the twogroups. Although the wage effect of immigration is similar for black and white men, the negative
employment effect and the positive incarceration effect are larger for blacks.
Our analysis suggests that a 10-percent immigration-induced increase in the supply of aparticular skill group reduced the black wage by about 3 percent, lowered the employment rate ofblack men by about 5 percentage points, and increased the incarceration rate of blacks by one
percentage point. Although these effects are statistically and numerically important, much of thedecline in employment or increase in incarceration in the black population remains unexplained.

36
DATA APPENDIX
The data are drawn from the 1960, 1970, 1980, 1990, and 2000 Integrated Public Use
Microdata Samples (IPUMS) of the U.S. Census. In the 1960 Census, the data extract forms a 1
percent sample of the population. In the 1970 Census, the data extract forms a 3 percent sample(formed by pooling the state, metropolitan area, and neighborhood samples). Finally, in the 1980,
1990, and 2000, the data extracts form a 5 percent sample. The analysis is restricted to men aged
18-64. A person is classified as an immigrant if he was born abroad and is either a non-citizen ora naturalized citizen; all other persons are classified as natives. We use the information containedin the census race variable to classify persons as “black” (IPUMS variable raced = 200) or“white” (raced = 100 or 110). Sampling weights are used in all calculations.
Definition of education and experience: We use the IPUMS variables educrec to classify
workers into four education groups: high school dropouts (educrec <= 6), high school graduates(educrec = 7), persons with some college (educrec = 8), college graduates (educrec = 9). We
assume that high school dropouts enter the labor market at age 17, high school graduates at age
19, persons with some college at age 21, and college graduates at age 23, and define work
experience as the worker’s age at the time of the survey minus the assumed age of entry into thelabor market. We restrict the analysis to persons who have between 1 and 40 years of experience.
Workers are classified into one of 8 experience groups, defined in five-year intervals.
Counts of persons in education-experience groups: The workforce counts are calculated
in the sample of men who worked at some point in the calendar year prior to the census and are
not enrolled in school. The workforce counts weigh each observation by the number of hours
worked in the previous calendar year (so that the total count of immigrants and natives in aparticular skill groups effectively represents the total number of hours worked by the group). The
population counts are calculated in the sample of men who are not enrolled in school.

37
Weekly earnings: We use the sample of men who do not reside in group quarters, report
positive weeks worked, are not enrolled in school, and report positive earnings. Our measure of
earnings is the sum of the IPUMS variables incwage and incbusfm in 1960, the sum of incearn,
incbus, and incfarm in 1970 and 1980, and is defined by incearn in 1990-2000. In the 1960,
1970, and 1980 Censuses, the top coded annual salary is multiplied by 1.5. All earnings are
deflated to 1990 dollars. In the 1960 and 1970 Censuses, weeks worked in the calendar year prior
to the survey are reported as a categorical variable. We imputed weeks worked for each worker
as follows: 6.5 weeks for 13 weeks or less, 20 for 14-26 weeks, 33 for 27-39 weeks, 43.5 for 4047 weeks, 48.5 for 48-49 weeks, and 51 for 50-52 weeks. The average log weekly earnings for aparticular education-experience cell is defined as the mean of log weekly earnings over all
workers in the relevant population.
Employment and incarceration rates: These variables are calculated in the total sample ofmen. The employment rate is the sample average of the ratio of weeks worked during thecalendar year prior to the Census, including zeros, to 52. A person is institutionalized if thegroup quarter variable gq takes on a value of 3 (indicating the person is in an institution). The
1990 and 2000 Censuses do not provide detailed information on the type of institution where an
institutionalized person resides.

38
MATHEMATICAL APPENDIX
Derivation of equations (6a)-(6d)Equate equations (2) and (3) in the text. This yields:(A1)

We linearize equation (A1) using a multivariate first-order Taylor series approximation. The
linearization is conducted at the arbitrary point:(A2)

where the asterisks indicate the values of the variables in the pre-immigration equilibrium and S
gives the number of skill groups. Recall that Lf gives the sum of natives (Nf) and immigrants (M)in the market sector. In the pre-immigration equilibrium, it must be the case that Lf = Nf. The
first-order approximation of (A1) can then be written as:(A3)

N ics = g( X f / X ic , N f ) + g1 ( X f / X ic , N f )( X fs / X ics  X f / X ic )+ g 2 ( X f / X ic , N f )(L fs  N fs ),where g1 = g/(Xfs/Xics) and g2 = g/Lfs. Given (A1) these derivatives are:

39

(A4)

If we evaluate these derivatives at the points defined in (A2), the first-order approximation is:(A5)

Nics = ics + ic Lfs ,where:(A6)

 ics = g( X f / X ic , N f )  g1 ( X f / X ic , N f ,) X f / X ic + g1 ( X f / X ic , N f )( X fs / X ics )g 2 ( X f / X ic , N f )N f ,Note that the intercept in (A5) is a function of the skill level s, but the slope ic is not. By using asimilar method, we can derive the analogous linear approximation for Nihs:(A7)

Nihs = ihs + ih Lfs ,In the post-immigration equilibrium, the total number of persons participating in themarket sector can be written as:

(A8)

40

where

gives the number of native persons of race i and skill s in the population. By

substituting equations (A5) and (A7) into (A8), and solving for Lfs we obtain:(A9)

where  is a constant that is not race-specific and that does not depend on skills. In fact, it
follows from the definition of g2 that:

(A10)

.

where

and

is defined analogously. The intercept s in equation (A8)does depend on skills and is defined by:

(A11)

.

It follows from equation (A9) thatin the pre-immigration

equilibrium. Substituting this into equation (2) in the text implies that the pre-immigration
equilibrium wage is:

41
(A12)

.

Suppose immigrant supply increases from 0 to Ms. The post-immigration wage is:ln wis = ln[ X fs (1  i )] +  f ln[ s + ( N bs + N ws + M s )]

(A13)

where

= ln[ X fs (1  i )] +  f ln[N *fs + M s ]= ln wis* +  f  ms ,, which produces the result in equation (6a). Equations (6b) and (6c) in the

text follow from combining (A5) with equations (2) and (3). To derive equation (6d), write
equation (5) in terms of rates of change as

(A14)

where

,

, and

substituting equations (6b) and (6c) into (A14).

. Equation (6d) follows after42
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45
Figure 1. The share of immigrants in the workforce

46
Figure 2. Trends in employment rates, by race, education and experience
A. Blacks

B. Whites

47
Figure 3. Trends in incarceration rates, by race, education and experience
A. Blacks

B. Whites

48
Figure 4. Relation between decadal changes in employment and immigration(removing decade effects)
A. Blacks

B. Whites

49
Figure 5. Relation between decadal changes in incarceration and immigration(removing decade effects)
A. Blacks

B. Whites

50

Figure 6. Initial equilibrium: allocation of labor across sectors

w
Dc

Df

1

NativeCrime
Employment

NativeMarketEmployment

Nbfs

Nbcs

51
Figure 7. Impact of immigration on sectoral allocation of labor

w
Dc

Df

1
2

1

NativeCrime
Employment

NativeMarketEmployment

Pre-immigration Nbfs

Post-immigration Nbfs

Pre-immigration Nbcs

Post-immigration Nbcs

52
Table 1. Tests for perfect substitution
Specification

A. Testing perfect substitution between black
and white native workers.
OLS estimate of 1/IV estimate of 1/Includes time fixed effects
Includes education-experience fixed effects
Interacts education and time fixed effects
Interacts experience and time fixed effects

A. Testing perfect substitution between
immigrant and native workers
OLS estimate of 1/IV estimate of 1/Includes time fixed effects
Includes education-experience fixed effects
Interacts education and time fixed effects
Interacts experience and time fixed effects

1

2

3

4

0.013
(0.012)0.011(0.012)-0.003(0.008)-0.005(0.009)0.033(0.026)0.019(0.034)-0.045(0.027)-0.054(0.032)

No
No
No
No

Yes
No
No
No

Yes
Yes
No
No

Yes
Yes
Yes
Yes

-0.016(0.008)-0.019(0.008)0.019(0.008)0.018(0.008)-0.002(0.014)-0.002(0.014)0.047(0.042)0.035(0.043)

No
No
No
No

Yes
No
No
No

Yes
Yes
No
No

Yes
Yes
Yes
Yes

Notes: Standard errors are reported in parentheses and are adjusted for clustering within education-experience cells.
All regressions have 160 observations and are weighted by the total number of observations used to calculate thedependent variable. The dependent variable in panel A is the difference between the mean log weekly wage of black
and white workers, and the independent variable is the difference between the log of the number of black workers
and the log of the number of white workers. The dependent variable in panel B is the difference between the mean
log weekly wage of immigrant and native workers, and the independent variable is the difference between the log of
the number of immigrant workers and the log of the number of native workers.

53
Table 2. Estimates of the impact of immigration
Dependent variable
Log weekly
earnings

Employment
rate

Incarceration
rate-0.346(0.137)-0.522(0.254)-0.683(0.183)-0.222(0.097)0.135(0.078)0.003(0.025)0.086(0.012)0.026(0.009)-0.314(0.131)-0.444(0.243)-0.683(0.183)-0.222(0.097)0.135(0.079)0.003(0.025)0.086(0.012)0.026(0.009)-0.410(0.258)-0.332(0.135)-0.557(0.248)-0.231(0.137)0.116(0.067)0.039(0.035)0.070(0.029)0.028(0.008)-0.432(0.166)-0.434(0.280)-0.655(0.176)-0.272(0.105)0.113(0.052)0.030(0.028)0.066(0.025)0.025(0.008)

E. IV, with restricted education-experience-time interactions
Blacks-0.335-0.792(0.171)(0.193)
Whites-0.428-0.287(0.233)(0.074)0.176(0.047)0.033(0.015)0.072(0.015)0.020(0.005)

A. Least squares
BlacksWhitesB. Instrumental variables
BlacksWhitesC. IV, with crack index
BlacksWhitesD. IV, with restricted crack index
BlacksWhitesIncarceration rate,using lagged
immigration

Notes: Standard errors are reported in parentheses and are adjusted for clustering within education-experience cells.
All regressions have 160 observations and include education, experience, and period fixed effects, and interactions
between education and experience fixed effects, education and period fixed effects, and experience and period fixed
effects. Regressions on employment and incarceration rates use a grouped logit specification; reported coefficientsare marginal effects evaluated at the mean employment and incarceration rates in the particular sample. Instrumental
variable regressions instrument the immigrant share in the workforce with the immigrant share in the population.
The restricted crack index sets the value of the Fryer et al (2005) crack index to zero if the skill cell has at least ahigh school education or more than 20 years of experience. The restricted education-experience-time interactions
include a vector of fixed effects indicating if the cell refers to a post-1980 observation of high school dropouts with
1-10, 11-20, or more than 20 years of experience; a post-1980 observation of workers with a high school diploma orsome college with 1-10, 11-20, or more than 20 years of experience; or a post-1980 observation of college graduateswith 1-10, 11-20, or more than 20 years of experience. The lagged immigration variable gives the immigrant sharefor the particular skill group measured five years prior to the Census.

54
Table 3. The impact of the 1980-2000 immigrant influx

Black Men
1. Actual change 2. Predicted(1980-2000)
impactLog weekly wage
High school dropouts
High school graduates
Some college
College graduates
Employment rate
High school dropouts
High school graduates
Some college
College graduates
Incarceration rate
High school dropouts
High school graduates
Some college
College graduates

White Men
1. Actual change 2. Predicted(1980-2000)
impact-0.142-0.0760.018
0.131-0.053-0.020-0.022-0.029-0.205-0.133-0.0340.114-0.068-0.025-0.028-0.037-0.167-0.0980.001
0.010-0.126-0.046-0.051-0.069-0.110-0.0480.000-0.003-0.046-0.017-0.018-0.025

0.156
0.065
0.031
0.005

0.028
0.010
0.011
0.015

0.032
0.014
0.005
0.001

0.005
0.002
0.002
0.003

Notes: The education-specific immigrant supply shock is defined as the number of immigrants arriving between
1980 and 2000 divided by a baseline population equal to the average size of the native workforce (over 1980-2000)
plus the number of immigrants in 1980. The education-specific supply shocks are: 0.214 for high school dropouts;
0.079 for high school graduates; 0.087 for persons with some college; and 0.118 for college graduates. The predicted
impacts use the coefficients reported in Panel E of Table 2.