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American Economic Association
The Economic Benefits from Immigration
Author(s): George J. Borjas
Source: The Journal of Economic Perspectives, Vol. 9, No. 2 (Spring, 1995), pp. 3-22
Published by: American Economic Association
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JournalofEconomicPerspectives-Volume9, Number2-Spring 1995-Pages 3-22
The Economic Benefits
from Immigration
George J. Borjas
T he rapidincreasein the size of the immigrantflowreachingthe United
States, the major changes in the national origin composition of the
immigrant population, and the decline in the skills of immigrants
relative to the skills of native workers have rekindled the debate over immigration
policy. The current debate revives the old concerns over immigrants
"taking jobs away" from native workers and finding it difficult to adapt in the
American economy, as well as questions whether immigrants pay their way in
the welfare state.
A large literature investigates each of these issues in detail; Borjas (1994)
offers a survey. The empirical evidence indicates that more recent immigrant
waves will remain economically disadvantaged throughout their working lives;
that this disadvantage may be partly transmitted to their offspring; that recent
immigrants are more likely to participate in welfare programs than natives; and
that immigration may have contributed to the increase in wage inequality
observed during the 1980s.
Table 1 summarizes some of the key trends in immigrant skills and welfare
participation. The relative educational attainment of successive immigrant waves
fell dramatically in recent decades. In 1970, the typical immigrant who had just
arrived in the United States had 11.1 years of schooling, as compared to 11.5
years for the typical native worker. By 1990, the typical immigrant who had just
*George J. Borjasis Professorof Economics,Universityof Californiaat San Diego, La
Jolla, California, and Research Associate, National Bureau of Economic Research,
Cambridge,Massachusetts.
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4 Journal of Economic Perspectives
Table 1
Socioeconomic Characteristics of Immigrants and Natives
in the United States, 1970-1990
Group/ Variable 1970 1980 1990
Natives:
Mean Educational Attainment (in years) 11.5 12.7 13.2
Percent of Households Receiving Public 6.0 7.9 7.4
Assistance
All Immigrants:
Mean Educational Attainment (in years) 10.7 11.7 11.6
Percent Wage Differential Between + .9 - 9.2 - 15.2
Immigrants and Natives
Percent of Households Receiving Public 5.9 8.7 9.1
Assistance
Recent Immigants (< 5 years in U.S.):
Mean Educational Attainment (in years) 11.1 11.8 11.9
Percent Wage Differential Between -16.6 -27.6 -31.7
Immigrants and Natives
Percent of Households Receiving Public 5.5 8.3 8.3
Assistance
Source: Author's tabulations from 1970, 1980, and 1990 Public Use Samples of U.S. Census.
Educational attainment and relative wages are calculated in the sample of working men aged
25-64. The fraction of households receiving public assistance is calculated in the sample of
households where the household head is at least 18 years old.
arrived in the United States had 11.9 years of schooling, as compared to 13.2
years for natives. The data also reveal a corresponding decline in the relative
wage of immigrants. The most recent arrivals enumerated in the 1970 Census
earned 16.6 percent less than natives. By 1990, the wage disadvantage between
the most recent immigrant wave and natives had grown to 31.7 percent.
Because less-skilled workers tend to qualify for and participate in public
assistance programs, the deteriorating skill composition of the immigrant flow
may have increased the fiscal costs of immigration substantially. Table 1 shows
that immigrants were less likely than natives to receive public assistance in
1970. By 1990, the welfare participation rate of immigrant households had
risen to 9.1 percent, or 1.7 percentage points higher than the participation rate
of native households.
Overall, the available evidence extensively documents the various costs that
immigration imposes on native workers and taxpayers. Surprisingly, the literature
does not address an equally important set of issues: Do natives benefit
from immigration? Where do these benefits come from? How are these benefits
dispensed to the native population? And how large are the benefits? The
absence of any serious discussion regarding the gains from immigration is
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GeorgeJ. Borjas 5
puzzling because costs must be contrasted with benefits before we conclude that
immigrants are a "boon or bane" for the United States.' If the economic
benefits from immigration are sufficiently large, for example, the costs resulting
from increased expenditures in social programs can be reinterpreted as the
outlay on an investment that has a very high rate of return.
This paper uses a simple economic framework to describe how natives
benefit from immigration, provides a back-of-the-envelope calculation of these
benefits, and suggests the parameters of an immigration policy that would
maximize the economic benefits. The discussion indicates that natives do
benefit from immigration mainly because of production complementarities
between immigrant workers and other factors of production, and that these
benefits are larger when immigrants are sufficiently "different" from the stock
of native productive inputs. The available evidence suggests that the economic
benefits from immigration are relatively small, on the order of $7 billion, and
almost certainly less than $25 billion, annually. The discussion also indicates,
however, that these gains could be increased considerably if the United States
pursued an immigration policy that attracted a more skilled immigrant flow.
The analysis presented below discusses the impact of immigration on a host
country within a competitive, market-clearing framework. In this context, as
long as there are no externalities, an application of the fundamental theorems
of welfare economics and the principles of free trade suggests that allowing
factors of production to move from one country to another increases total
welfare and efficiency. Because of the potential implications of the results,
however, it is important to point out at the outset that the discussion ignores
some very important issues. For example, by focusing on the economic benefits
accruing to natives residing in the host country, the study ignores the impact of
immigration both on the immigrants themselves and on the persons who
remain in the source countries. Similarly, by focusing on a competitive economy
with market-clearing and full employment, the analysis ignores the potentially
harmful effects of immigration when there is structural unemployment in
the host economy, and jobs might be a "prize" that are captured partly by
immigrants.
The Immigration Surplus
We begin by specifying the production technology in the host country
(which, for concreteness, will be the United States throughout the discussion).
Suppose that the technology can be summarized in terms of an aggregate
production function with two inputs, capital (K) and labor (L), so that
output Q = f(K, L). The workforce is composed of N native workers and M
IA number of theoretical models in the international trade literature explore how immigrants affect
the welfare of natives; see, for example, Bhagwati and Srinivasan (1983) and Ethier (1985). A rare
empirical analysis is given by Svorny (1991), who estimates the gains to American consumers from
the immigration of physicians.
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6 Journal of Economic Perspectives
immigrant workers. Initially, let's assume that all capital is owned by natives, so
that we ignore the possibility that immigrants might augment the host country's
capital stock. We will also ignore skill differentials among immigrant and native
workers and assume that all workers are perfect substitutes in production
(hence L = N + M). Finally, we will assume that the supplies of capital and of
both native- and foreign-born labor are perfectly inelastic.2
The aggregate production function exhibits constant returns to scale. As a
result, the entire output is distributed to the owners of capital and to workers.
The equilibrium in this economy prior to the admission of M immigrants
requires that each factor price equals the respective value of marginal product.
Suppose that the price of capital is initially ro and the price of labor is wo. The
price of the output is the numeraire (so that the input prices are measured in
units of output). Before the admission of immigrants, therefore, the national
income accruing to natives, QN' is the price of capital times the quantity used,
plus the price of labor times the number of workers hired, or QN = roK + woN.
Figure 1 illustrates this initial equilibrium in the labor market. Because the
supply of capital is inelastic, the area under the marginal product of labor curve
(MPL) gives the economy's total output. Prior to the entry of immigrants,
therefore, the national income accruing to natives QN is given by the trapezoid
ABNO.
What happens to national income when immigrants enter the country?
The supply curve shifts, and the market wage falls to w1. National income is
now given by the area in the trapezoid ACLO. Part of the increase in national
income, however, is distributed directly to immigrants (who get w1M in labor
earnings). Inspection of Figure 1 thus reveals that the increase in national
income accruing to natives, or the immigration surplus, is given by the triangle
BCD. Because the market wage equals the productivity of the last immigrant
hired, immigrants increase national income by more than what it costs to
employ them.
Note that if the demand curve for labor were perfectly elastic, so that
immigrants had no impact on the wage rate, immigrants would receive the
entire additional product, and natives would gain nothing from immigration.
An immigration surplus arises only when the native wage falls as a result of
immigration. Although native workers get a lower wage rate, these losses are
more than offset by the increase in income accruing to capitalists, through a
higher rental price of capital r.
The immigration surplus is given approximately by the area of the triangle
BCD, which can be calculated as X (w - W1) X M. By manipulating this
formula, it is easy to show that the immigration surplus, as a fraction of national
2It is easy to relax the assumption of inelastic supply curves. However, the calculation of the gains
from immigration would be more cumbersome because we would have to account for the change in
utility experienced by native workers as they move between the market and nonmarket sectors.
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The Economic Benefitsfrom Immigration 7
Figure I
The Immigration Surplus
Dollars
A
B
D C
MP/,
I Employment
0 N L=N+M
income, equals:3 1
- = - 2sem
Q 2
where s is labor's share of national income; e is the elasticity of factor price for
labor (that is, the percentage change in the wage resulting from a 1 percent
change in the size of the labor force); and m is the fraction of the workforce that
is foreign born (m = M/ L).
What does this formulation imply about the size of the immigration surplus
in the United States? The share of labor income is on the order of 70 percent,
and the fraction of immigrants in the workforce is slightly less than 10 percent.
The vast empirical evidence on labor demand, surveyed recently by
Hamermesh (1993), suggests that the elasticity of factor price for labor is on the
order of -.3, so that a 10 percent increase in the number of workers reduces
the wage by 3 percent.4 The immigration surplus, therefore, is only on the
order of .1 percent of GDP (that is, one-tenth of 1 percent!). The economic
gains from immigration in a $7 trillion economy, therefore, are relatively small,
about $7 billion per year or less than $30 per native-born person in the United
States. Even if we assume that the elasticity of factor price is - 1 (so that a 10
percent increase in labor supply decreases the native wage rate by 1Opercent),
the gains from immigration would still be on the order of $25 billion per year.
It is important to note that the immigration surplus is proportional to the
elasticity of factor price for labor e. If the increase in labor supply greatly
3In particular, note that if we let (w, - wo) (Aw/ AL) X M, the immigration surplus can be
rewritten as:
AQN I AW M ( wL Aw L M M
Q 2 L Q 2 Q AL ) L L
4If there are only two factors of production, the elasticity of factor price for labor must equal
(1 - s)2/ 71, where Y7is the output-constant elasticity of labor demand (Hamermesh, 1993,
pp. 26-29). There is some consensus that Y7is about -.3. Because the share of labor income is .7,
the elasticity of factor price is also -.3.
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8 Journal of Economic Perspectives
reduces the wage, natives as a whole gain substantially from immigration. If the
native wage is not very sensitive to the admission of immigrants, the immigration
surplus is nearly zero. The elasticity of factor price is small (in absolute
value) when the labor demand curve is elastic. In other words, the immigration
surplus is small when labor and capital are easily substitutable. The elasticity of
factor price is large (in absolute value) when the labor demand curve is
inelastic, implying that natives have much to gain from immigration when labor
and capital are more complementary. The immigration surplus, therefore,
arises because of the complementarities that exist between immigrants and
native-owned capital.5
Even though the immigration surplus is small, immigration has a substantial
economic impact. In particular, immigration causes a large redistribution of
wealth from labor to capital. In terms of Figure 1, native workers lose the area
in the rectangle woBDwl, and this quantity plus the immigration surplus
accrues to capitalists. Expressed as a fraction of GDP, the net change in the
incomes of native workers and capitalists are approximately given by:6
Change in Native Labor Earnings
2 ~~~~=sem(l1m) ,
Q
Changein Income of Capitalists- ( -
2 ~ ~~ --sem1- mJQ2
If the elasticity of factor price is -.3, native workers lose about 1.9 percent of
GDP, or $133 billion in a $7 trillion economy; native capital gains about 2.0
percent of GDP, or $140 billion. The small immigration surplus of $7 billion
thus disguises a sizable redistribution of wealth from workers to the users of
immigrant labor.
The relatively small size of the immigration surplus-particularly when
compared to the very large wealth transfers caused by immigration-probably
explains why the debate over immigration policy has usually focused on the
5It is easy to see this point with a CES production function, so that Q = [8IKP + 82LP]I'P. The
immigration surplus is then given by:
AQN 1 s(1 - s)m2
Q 2 owhere
(T is the elasticity of substitution between labor and capital. Natives have less to gain from
immigration when the elasticity of substitution is large.
6To calculate the total losses accruing to native workers, again let (w, - wo) = (Aw/ AL) X M. The
reduction in total labor income, as a fraction of GDP, can then be written as:
(w1-wo)N ( Aw M N wL Aw L M N
= *M . _ = _ . _ -._
Q AL Q Q ALw L L
T he gains accruing to capitalists are calculated by adding the absolute value of this expression to
the immigration surplus (that is, to the area of the triangle).
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GeorgeJ. Borjas 9
potentially harmful labor market impacts rather than on the overall increase in
native income. In other words, the debate stresses the distributional issues (the
transfer of wealth away from workers) rather than the efficiency gains (the
positive immigration surplus). If the social welfare function depends on both
efficiency gains and the distributional impact of immigration, the slight benefits
arising from the immigration surplus may well be outweighed by the substantial
wealth redistribution that takes place, particularly since the redistribution goes
from workers to owners of capital (or other users of immigrant services).
Putting aside the distributional impact of immigration, it is of great interest
to compare the immigration surplus with estimates of the fiscal cost of immigration.
Recent estimates of the net fiscal benefits (that is, of the difference between
the taxes paid by immigrants and the cost of services provided to immigrants)
range from a positive net fiscal benefit of about $27 billion calculated by Passel
and Clark (1994), to a $16 billion net loss reported by Borjas (1994), to a net
loss of over $40 billion estimated by Huddle (1993).
It is doubtful, however, that any of these numbers estimates accurately the
gap between the taxes paid by immigrants and the cost of services provided to
immigrants. For example, Passel and Clark conclude that immigrants pay their
way in the welfare state and contribute a net of $27 billion to native taxpayers
by assuming that immigrants do not increase the cost of most government
programs other than education and social welfare programs. In contrast,
Borjas assumes that the marginal cost of providing immigrants with a vast array
of public services equals the average cost of providing these same services to
natives. We do not know by how much immigrants increase the cost of
freeways, national parks, and even national defense. As a result, accounting
exercises that claim to estimate the net fiscal impact of immigration should be
viewed with a great deal of suspicion. Because the immigration surplus is only
on the order of $7 billion, however, it is evident that the net economic benefits
from immigration are very small and could even be negative.
Some Problems with the Calculation of the Immigration Surplus
A number of restrictive assumptions are built into the calculation of the
immigration surplus.
For example, the analysis assumes that immigration augments only the
economy's labor endowment. What if immigration also augments the host
country's capital stock? Interestingly, the immigration surplus might be even
smaller if immigrants bring in capital. To see why, suppose that immigrants
increase both the size of the labor force and the capital stock by 100 percent
(perhaps through the use of "investor visas" requiring that immigrants invest
in the host country). Because the production function has constant returns to
scale, this type of immigration would not change the factor prices r and w. As a
result, immigration would have no impact on the national income accruing to
natives. As long as immigrants replicate the existing economy, therefore,
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10 Journalof EconomicPerspectives
immigrants get the total returns from their product, and the immigration
surplus is zero.
'I'he calculation of the immigration surplus also assumes that immigrants
do have an impact on the earnings of native workers. This assumption seems to
contradict much of the available empirical evidence (Borjas, 1994; Friedberg
and Hunt, this issue). Many studies have found a negative, but weak, correlation
between the native wage in a particular labor market and the immigrant
share of the workforce in the locality. This weak correlation is then interpreted
as evidence that immnigrantsdo not reduce the earnings of native workers.
It is important to note, however, that the weak correlation between the
native wage and the immnigrantshare need not indicate that immigrants have
little impact on native earnings opportunities. In particular, the interpretation
of this correlation as a causal relationship between immigration and native
wages presumes that the local labor markets are closed (once immigration takes
place). Metropolitan areas in the United States, however, are not closed
economnies; labor, capital, and goods flow freely across localities and tend to
equalize factor prices in the process. As long as native workers and firms
respond to the entry of imumigrantsby moving to areas offering better opportunities,
there is no reason to expect a correlation between the wage of natives in
a particular locality and the presence of immigrants. As a result, the crosssection
or time-series comparison of local labor markets may be masking the
"macro" effect of immnigration.
A number of recent studies suggest that natives respond to immigration by
"voting with their feet" (Filer, 1992; Frey, 1994). In particular, natives tend to
move out of areas where immnigrantschoose to live, and this migration flow
nmayhave accelerated during the 1980s, resulting in what has been called "the
new white flight." To the extent that these migration flows (as well as flows of
capital and goods) disperse the adverse impact of immnigration on the wage
over the entire economy, the weak correlations reported in the literature bear
no relationship to the structur'al parameter required to estimate the immigration
surplus. Moreover, some recent empirical studies that look more closely at
the imnpact of inmigration on the aggregate economy (rather than on a
particular locality) find that immigration may have had a significant impact on
the relative wage of unskilled workers during the 1980s (Borjas, Freeman, and
Katz, 1992; Topel, 1994).
The conclusion that the immigration surplus is .1 percent of GDP assumes
that the elasticity of factor price for labor is -.3, so that a 10 percent increase in
the size of the labor force reduces the wage level by about 3 percent. If the
native wage is less responsive to immigration, the immigration surplus would be
correspondingly smaller.If we wish to believe that native workers are unaffected
by immigration, therefore, we would also be forced to conclude that immigrants
get the entire fruits of their labor and that there is no immigration
surplus. Ironically, even though the debate over immigration policy views the
possibility that immigrants lower the wage of native workers as a harmful
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The EconomicBenefitsfrom Immigration 11
consequence of immigration, the economic benefits from immigration arise
only when immigrants do lower the wage of native workers.7
External Effects and the Immigration Surplus
A number of recent studies have argued that an increase in trade generates
external returns in the aggregate economy (see, for example, Helpman and
Krugman, 1985). Immigration expands the size of the market. It can introduce
many new interactions among workers and firms, so that both workers and
firms might "pick up" knowledge without paying for it. As a result, even
though the production technology at the firm level has constant returns to
scale, the external effects resulting from immigration might lead to increasing
returns on the aggregate.
To represent these external effects, suppose that the firm's production
function is given by QF = f(K, L)Qy, where QF is the representative firm's
output and QE is the aggregate output in the economy (which the firm takes as
given). As immigrants expand the scale of the economy, the marginal product
of both labor and capital increases (assuming y > 0). The parameter y gives
the percentage increase in the marginal product of labor or capital resulting
from a 1 percent increase in aggregate output.
As illustrated in Figure 2, the external effects of immigration can increase
the size of the immigration surplus substantially. As the economy expands, the
marginal product of labor curve shifts from MPL to MPI. The change in
national income accruing to natives is then given by the sum of the triangle
BCD and the area of the trapezoid ABEF, which measures the impact of
immigration on natives' total product. The Appendix shows that the immigration
surplus, as a fraction of GDP, in the presence of external effects is
approximately given by:
/\QN 1 2 ysm
_QN= - -sem2 + 1 (1-sm),
Q 2
where the first term gives the area of the triangle, and the second term gives
the change in the value of natives' total product attributable to external effects.
As before, suppose that the share of labor income is approximately .7, and
that immigrants make up 10 percent of the workforce. If we assume that the
elasticity of marginal product with respect to aggregate output (or -y)is .05, the
external effects increase the national income accruing to natives by about .3
percent of GDP, or $21 billion. If y is .1, external effects increase the immigration
surplus by .7 percent of GDP, or about $49 billion. Adding the $7 billion
7This implication is analogous to the result from international trade theory, which shows that cheap
foreign imports, typically seen as having harmful and disruptive effects, often benefit the importing
country.
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12 Journal of Economic Perspectives
Figure 2
The Immigration Surplus in the Presence of External Effects
Dollars
As
F
B
I ~~D
W()
~E
MP1'
Employment
0 N L=N+M
surplus resulting from the triangle implies that the total contribution of immigrants
to native income would be between $30 billion and $55 billion.
Although models that incorporate external effects in the aggregate economy
are used frequently in modern discussions of the gains from trade, there is
little empirical evidence supporting the existence, let alone measuring the
magnitude, of the external effects (for an exception, see Dekle and Eaton,
1994). As a result, the numerical exercise presented here should not be
interpreted as indicating that immigrants contribute substantially to the incomes
of natives, but rather as giving a ballpark estimate of what the gains
would be if immigration indeed generated increasing returns in the aggregate
economy. Despite the current popularity of external effect models in the
theoretical international trade literature, it is difficult to imagine that immigrants
entering an economy as large as that of the United States could generate
these types of externalities. Most likely, immigration would lead to increased
congestion and decreasing returns to scale because other factors of production
remain fixed.
Immigrant Skills and the Immigration Surplus
The previous section illustrates how and why the gains from immigration
arise in competitive economies. Perhaps the most restrictive aspect of the model
is that it ignores the skill differentials that exist both within and across the
native and immigrant populations. Because immigration policy can encourage
or prevent the admission of certain classes of workers, it is of interest to
investigate the relationship between the immigration surplus and the skill
composition of the immigrant flow. In other words, which type of immigrant
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GeorgeJ. Borjas 13
flow, a skilled flow or an unskilled flow, generates the largest increase in
national income for native workers?
A Simple Case: Ignoring Capital
To illustrate how the skill composition of the immigrant flow affects the
economic gains from immigration, consider the case where there are only two
skill classes in the workforce, skilled workers (Ls) and unskilled workers (Lu),
and initially ignore the role of capital in the production process. The fraction of
skilled workers in the native population is b, and the respective fraction among
immigrants is /3. We assume that the supply of workers to the labor market is
perfectly inelastic. Finally, suppose that the aggregate production function
is linear homogeneous and that there are no external effects, so that
Q =f(Ls, Lu).
Under these conditions, the immigration surplus is positive as long as the
skill composition of the immigrant flow differs from that of native workers (that
is, as long as /3 is not equal to b). If the skill composition of immigrants were
the same as that of natives, the constant returns to scale production function
implies that the wages of skilled and unskilled workers are unaffected by
immigration, and hence natives have nothing to gain from immigration. (This
result, of course, parallels our earlier discussion where the production function
depends on labor and capital, and immigrants increase both labor and capital
by the same proportion.) As stressed earlier, a key lesson of economic analysis is
that natives benefit from immigration only if immigrants are different from
natives.
If the skill composition of immigrants differs from that of natives, the
magnitude of the immigration surplus depends on exactly how different immigrants
are. Figure 3 illustrates the relationship between the immigration surplus
and the skill composition of the immigrant flow (as measured by /3, the
fraction of immigrants who are skilled).8 The left panel shows the situation
when 50 percent of the native workforce is skilled (or b = 1/ 2). As noted
above, there is no immigration surplus if half of the immigrant flow is also
composed of skilled workers. Natives do gain, however, whenever the skill
composition of immigrants differs from that of natives. In fact, the immigration
surplus is maximized when the immigrant flow is composed of exclusively
8The immigration surplus, as a fraction of GDP, is given by:
AQN 1 ssess(/8 -b)2
Q 2 p2(1 _pS)2 (1 m)2m2,
where ss is the share of national income accruing to skilled workers; ess is the elasticity of factor
price for skilled workers (that is, the percentage change in the skilled wage with respect to a
1 percent change in the number of skilled workers); and Ps is the fraction of the labor force that is
composed of skilled workers. Figure 3 is obtained by differentiating the immigration surplus with
respect to I8 and assuming that immigration is "small" so that the fraction of the workforce that is
skilled is not affected by immigration (that is, dpsl/ d, = 0).
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14 Journal of EconomicPerspectives
Figure 3
The Immigration Surplus and Immigrant Skills, in a Model Without Capital
Assumes 50% of Assumes 35% of Assumes 65% of
Natives Are Skilled Natives Are Skilled Natives Are Skilled
0 0.5 1 0 0.5 1 0 0.5 1
Fraction of Immigrants Who Are Skilled
unskilled or exclusively skilled workers. Either policy choice generates an
immigrant flow that is very different from the native workforce, and hence
maximizes the immigration surplus. Because 50 percent of natives are skilled,
there is no particular advantage (from the point of view of maximizing the
immigration surplus) to admitting either an all-skilled or an all-unskilled
immigrant flow.9
Economic incentives for pursuing an immigration policy that selects either
an all-skilled or an all-unskilled immigrant flow arise when the native workforce
is predominantly skilled or predominantly unskilled. Suppose, for example,
that the native workforce is relatively unskilled (or b < 1/ 2). As illustrated in
the middle panel of Figure 3, the immigration surplus is maximized by
admitting immigrants who complement the native workforce, and this is accomplished
by admitting only skilled workers. If, in contrast, the native workforce is
relatively skilled (as illustrated in the right panel of the figure), the immigration
surplus is maximized when immigrants are unskilled.
The United States presumably has a relatively skilled workforce. Economic
analysis thus implies that, in the absence of capital, the immigration surplus
would be maximized by pursuing an immigration policy that only admitted
unskilled workers. This type of immigration policy maximizes the economic
gains to natives by fully exploiting the production complementarities between
immigrants and natives.
Capital and the Skills of Immigrants
The conclusion that an unskilled immigrant flow maximizes the immigration
surplus in the United States hinges crucially on the assumption that capital
plays no role in the production process. To see how the existence of a
native-owned capital stock affects the relative gains to skilled and unskilled
migration flows, suppose that the technology in the host country is given by the
9This conclusion is closely related to the result from international trade theory that the benefits
from trade are larger when the trading countries differ greatly in their factor endowments.
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The EconomicBenefitsfrom Immigration 15
linear homogeneous production function Q = f(K, Ls, Lu). As before, we assume
that all factors of production are supplied inelastically to the economiy.
It is instructive to compare the immigration surplus resulting from two
alternative policy choices. Suppose initially that the United States decides to
admit only skilled immigrants. As shown in the Appendix, the immigration
surplus (as a fraction of GDP) would then be given by:
AQN if U.S. admits only skilled immigrants 1 ssess 2
Q = 2 p
where ss is the share of income that goes to skilled workers, ess is the elasticity
of factor price for skilled workers (that is, the percentage change in the wage of
skilled labor resulting from a 1 percent chanige in the inumber of skilled
workers); and Ps is the fraction of the workforce that is skilled.'0
If the United States instead pursues an immigration policy that admits
only unskilled workers, the immigration surplus is given by a parallel
formulation:
AQN if U.S. admits only unskilled immigrants 1 sue UU 2
Q 2 Pu
where su is the share of income that goes to unskilled workers; euu is the
elasticity of factor price for unskilled workers (that is, the percentage change in
the wage of unskilled labor resulting from a 1 percent change in the numnberof
unskilled workers); and Pu is the fraction of the workforce that is unskilled.
Note that each immigration surplus is proportional to the relevant elasticity
of factor price. As long as the immigration of skilled workers reduces the
wage of skilled workers or the immnigrationof unskilled workers reduces the
wage of unskilled workers, there is a positive immigration surplus regardless of
whether the United States admits exclusively skilled or exclusively unskilled
workers.
Which immigration policy leads to a larger iniunigration surplus? Although
there is a great deal of dispersion in the esti-nated elasticities, many studies
surveyed in Hamermesh (1993, ch. 3), suggest that the elasticity of factor price
is greater (in absolute value) for skilled workers than for unskilled workers. The
fact that the wages of skilled workers are more responsive to a shift in supply
than the wages of unskilled workers (that is, e s < euu) introduces a new set of
incentives that suggest the immigration surplus mnaybe larger when the
immigrant flow is composed of skilled workers.
10The reader will note that this formulation is closely related to the original calculation of the
immigration surplus in the model that had only an aggregate labor input and capital. Instead of
depending on the share of income going to all workers, the immigration surplus now depends on
the share going to skilled labor. Similarly, instead of depending on the elasticity of factor price for
all labor, the formula now depends on the elasticity of factor price for skilled workers (as well as on
the fraction of the workforce that is skilled).
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16 Journal of Economic Perspectives
To see this point, suppose that the fraction of skilled workers in the native
workforce is one-half. Suppose also that immigration is relatively small, so that
the fraction of skilled workers in the population (Ps) is approximately one-half.
Our earlier discussion indicated that as long as we ignored capital, the immigration
surplus was maximized whenever the immigrant flow was either exclusively
skilled or unskilled. The introduction of capital, however, implies that as
long as ess < euu the United States is better off admitting an exclusively skilled
immigrant flow."
A skilled immigrant flow generates a larger immigration surplus partly
because of the production complementarities that exist between skilled labor
and capital. A very negative elasticity of factor price for skilled workers implies
that skilled workers are highly complementary with other factors of production.
In contrast, a numerically small elasticity of factor price for unskilled workers
implies that unskilled workers are not highly complementary with other factors
of production. Because the complementarities across factors play a central role
in generating the gains from immigration, the immigration surplus is maximized
when the immigrant flow is skilled. In other words, the complementarity
between capital and skills provides an economic rationale for admitting skilled
workers. 12
Of course, this conclusion is reinforced if we allow for the possibility that
the human capital imported by immigrants has external effects in production.
It is also reinforced by the fact that unskilled immigrants are more likely to
increase expenditures on such government programs as unemployment compensation
and means-tested entitlement programs, and are less likely to pay
sufficient taxes to offset those costs.
Figure 4 illustrates the relationship between the immigration surplus and
the fraction of the immigrant flow that is skilled in an economy with capital
(assuming that 50 percent of the native workforce is skilled). As drawn, the
immigration surplus is at a minimum when the immigrant flow is "mixed" in
terms of skilled and unskilled workers.'3 Because skilled workers are more
complementary with other inputs than unskilled workers, however, the host
country benefits more from the admission of an exclusively skilled immigrant
IIBecause Ps = 1/2, the share of income accruing to skilled workers ss exceeds the share of
income accruing to unskilled workers su.
l2The empirical evidence supporting the capital-skill complementarity hypothesis reflects an
important property of technology in the postwar era. Because the production function is not stable
over time, the technology available in earlier time periods may reflect different relationships among
the various inputs. For instance, it seems plausible that unskilled workers and some fixed factors of
production (such as land) were complements in the U.S. economy at the end of the nineteenth
century. In fact, there is some empirical evidence (James and Skinner, 1985) suggesting that,
around 1850, skilled labor and capital were better substitutes than unskilled labor and capital. As a
result, the theoretical implication that the immigration surplus is maximized by admitting a skilled
immigrant flow might not have applied to the United States in earlier time periods.
13If skilled workers and unskilled workers are sufficiently "strong" substitutes (in the sense that an
increase in the quantity of one of the inputs reduces the wage of the other), it is possible for the
minimum point to occur at the corner where the immigrant flow is exclusively unskilled.
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GeorgeJ. Borjas 17
Figure 4
The Immigration Surplus and Immigrant Skills, in a Model With Capital
(assuming50 percentof natives are skilled)
0 0.5 1
Fraction of Immigrants Who Are Skilled
flow. This conclusion, of course, may change if the native workforce is predominantly
skilled. In particular, when the native workforce is predominantly
skilled, the gains from admitting a skilled immigrant flow resulting from
capital-skill complementarity might be outweighed by the gains from admitting
immigrants who differ from native workers.
As noted above, there is a great deal of uncertainty regarding the values
of the elasticities that determine the immigration surplus in this model.
Nevertheless, the simulations reported in Table 2 show that altering the skill
composition of the immigrant flow can generate sizable gains for natives. If half
of the natives are skilled, and if the elasticities of factor price are -.4 and -.75
for unskilled and skilled workers, respectively, the immigration surplus would
be $14 billion if only unskilled immigrants are admitted, but would jump to
$47.3 billion if only skilled immigrants are admitted. Even if the native workforce
were predominantly skilled (so that 75 percent of the natives are skilled),
these elasticity values suggest that the immigration surplus would increase from
$22.4 to $28.0 billion if the United States pursued a more selective immigration
policy. The complementarities in production between skilled workers and
capital, therefore, may be sufficiently strong to suggest that natives gain if the
immigrant flow is composed of exclusively skilled workers, even if the native
workforce is predominantly skilled.
It is important to stress that the simulation results reported in Table 2 only
suggest how a shift in the skill composition of the immigrant flow influences the
immigration surplus. To calculate or predict the immigration surplus resulting
from particular immigration policies, we would have to provide a much more
complete description of what is meant by "skilled" and "unskilled" workers, as
well as obtain robust estimates of the elasticities of factor price, which ultimately
determine the size of the immigration surplus.
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18 Journalof EconomicPerspectives
Table2
Estimates of Immigration Surplus
(in billionsof dollars)
25% of Natives 50% of Natives 75% of Natives
are Skilled; are Skilled; are Skilled;
30% of National 45% of National 60% of National
IncomeGoesto IncomeGoesto IncomeGoesto
SkilledWorkers SkilledWorkers SkilledWorkers
Admit Only Unskilled
Imninigrants:
Elasticity of Factor
Price for Unskilled
Workers is:
-.2 5.0 7.0 11.2
-.4 10.0 14.0 22.4
- .6 14.9 21.0 33.6
Adniit Only Skilled
Immigrants:
Elasticity of Factor
Price for Skilled
Workers is:
-.5 84.0 31.5 18.7
- .75 126.0 47.3 28.0
- 1.0 168.0 63.0 37.3
Notes: The calculations assume that the GDP in the United States equals $7 trillion; that the share
of niationalincome accruing to capital is 30 percent; and that immigrants make up 10 percent of the
workforce.
Conclusion
The family of economic models summarized in this paper provides the
foundation for a positive theory of immigration policy. If we are willing to
maintain the hypothesis that immigration policy should increase the national
incomiieof natives, the government's objective function in setting immigration
policy is well defined: maximize the immigration surplus net of the fiscal
burden imposed by immigrants on native taxpayers. The optimal size and skill
comiiposition of the immigrant flow would equate the increase in the immigration
surplus resulting from admitting one more immigrant to the marginal cost
of the iinmnigrant.
It is reasonable to suppose that the net fiscal costs of immigration are
larger for unskilled immigrant flows. After all, unskilled immigrants are more
likely to use many government services and pay lower taxes. In addition, there
are economic reasons, arising mainly from the complementarity between capital
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The EconomicBenefitsfrom Immigration 19
and skills, that suggest that the immigration surplus might be larger when the
immigration flow is composed exclusively of skilled workers. It seems, therefore,
that on purely efficiency grounds there is a strong economic case for an
immigration policy that uses skill filters in awarding entry visas.
The analysis, however, also revealed that these efficiency considerations
may not be the most important consequences of choosing among alternative
immigration policies. Immigration also generates a sizable redistribution of
wealth in the economy, reducing the incomes of natives who are now competing
with immigrant workers in the labor market and increasing the incomes of
capitalists and other users of immigrant services.
It is worth stressing that the discussion in this paper considers only the
"demand side" of the immigration market. The United States can attract only
those immigrants who wish to enter the country.'4 If economic conditions in
the United States are particularly attractive to unskilled workers from other
countries, the demand side of the immigration market might only grant visas to
skilled workers, but the supply side suggests that only unskilled workers are
willing to make the move. It is possible, therefore, that ruling out the immigration
of unskilled workers may greatly reduce the size of (and perhaps even cut
off) the immigrant flow.
Finally, the positive theory of immigration policy suggested by the discussion
is based on the idea that, distributional issues aside, the main objective of
immigration policy should be to increase the national income accruing to
natives. It is far from clear that immigration policy should pursue this objective.
The immigration statutes reflect a political consensus that incorporates the
conflicting social and economic interests of various demographic, socioeconomic,
and ethnic groups, as well as political and humanitarian concerns.
Nevertheless, the economic approach is useful because it tells us what we are
giving up by pursuing immigration policies that minimize or ignore economic
considerations.
Appendix
The Mathematics of Calculating Surplus
The Immigration Surplus
To show how the immigration surplus can be calculated in more complicated
models, it is instructive to provide an algebraic derivation of the surplus
given by the triangle BCD in Figure 1. The linear homogenous production
function is given by Q= f(K, L), where L = N + M. The national income
accruing to natives is QN = wN + rK. Assuming that native workers and capital
are inelastically supplied to the economy, immigration increases QN by the
1See Borjas (1987) for an analysis of the immigration decision.
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20 Journal of EconomicPerspectives
amount:
dr dw
(Al) QN= K + Nd AL,
where A?L= M.
It is well known that when the derivatives in (Al) are evaluated at the
initial equilibrium (where L = N), the infinitesimal increase in national income
accruing to natives is zero (Bhagwati and Srinivasan, 1983, p. 294). To calculate
finite changes, therefore, we evaluate the immigration surplus using an "average"
rate for dr/ dL and dw/ dL, where the average is defined by:
I1 dr dr
2 dL L=N dL L=N+M)
with a similar definition for the average rate of change in the wage. Because
evaluating the immigration surplus at L = N leads to a zero value for ZQN,
this approximation implies that the finite change in the immigration surplus is
half the gain obtained when equation (Al) is evaluated at L = N + M. Using
this property and converting equation (Al) into percentage terms yields:
(A2) Q - [(1 - s)eKL + S(l - m)eLL]m,
Q 2
where s = wL/ Q;m = M/L; eLL = d log w/d log L; and eKL = d log r/d log L.
A weighted average of factor price elasticities adds up to zero (Hamermesh,
1993), so that (1 - s)eKL + seLL = 0. Substituting this fact into (A2) yields the
area of the triangle reported in the text.
If there are external effects, the production function for the representative
firm is given by QF = f(K, L)QFy.Because the firm ignores the external effects,
input prices are given by the marginal productivity conditions r = fK QEand
W = fL QE.Equation (Al) still gives the change in national income accruing to
natives. Immigration changes input prices, and these changes depend on the
external effects. To calculate the derivatives dr/dL and dw/vdL, therefore, we
use the equilibrium condition Q= f(K, L)'7U' 7. The equation in the text
reporting the magnitude of the immigration surplus in the presence of external
effects is obtained by evaluating the contributions of external effects to the
immigration surplus at the point where L = N + M.
The Surplus and Immigrant Skills
To conserve space, the immigration surplus is derived only for the model
that includes capital; a similar approach can be used to derive the equation
reported in note 8 in the text. The concave linear homogeneous production
function is given by:
(A3) Q =f(K,Ls,Lu) =f(K,bN+3M,(1 -b)N+ (1 - 3)M),
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GeorgeJ. Borjas 21
where b and ,3 denote the fraction of skilled workers among natives and
immigrants, respectively. The wage of each factor of production (capital, skilled
workers, and unskilled workers) is determined by the respective marginal
productivity condition. The increase in national income accruing to natives is:
dr dws dwu\
(A4) ?SQN= KdM +bNdM + (1-b)NDM )M.
Define eij = dlog w/ dlog X, (where X, = K, L , Lu), or the elasticity of factor
price. If we convert equation (A4) into percentage terms, evaluate the various
derivatives at the "average" point, and use the condition that a weighted
average of elasticities of factor price equals zero, we obtain:
()QN _ s ess /3m2 sueuu( 1- _3 )2m2
(A5)Q2p
ssesu13(l8 - 83)m2 sueus,83(l - 3)m2
2pspu 2PsPLJ
where ss and su are the shares of national income accruing to skilled and
unskilled workers, respectively, and ps and Pu are the shares of the workforce
that are skilled and unskilled. The equations reported in the text giving the
immigration surplus when the immigrant flow is exclusively skilled or unskilled
are obtained by evaluating the immigration surplus in (A5) at the values of
,3 = 1 or f3 = 0.
To show that the immigration surplus is positive, note that the elasticity of
factor price e,i = sjci,, where cij is the elasticity of complementarity (defined as
c,,j= fi . f/f fj). We can then rewrite(A5)as:
ZSQN_ S2C f2m2 s2cUU(I- _)2m2 s s c5 2(1-)m
(A6) 2pu PSPU
The concavity of f(K, Ls, Lu) implies that:
fss < 0, f f > 0, and fU5 fUU fuK < 0.
ft5 A~~fsKfK
U fK K
The linear homogeneity of the production function implies that the determinant
of the three-by-three matrix is zero. We can write the production function
in its intensive form as Q= K q(L / K, L / K). Assuming that q is strictly
concave implies that fss fuu - f2j > 0, so that CS5CU - C2 > 0. This assumption
guarantees that the isoquants between skilled labor and unskilled labor, for
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22 Journalof EconomicPerspectives
a given capital, have the usual convex shape. Using this restriction, it can be
shown that the immigration surplus in (A6) is positive. The relationship between
the immigration surplus and ,3 illustrated in Figure 4 is obtained by
differentiating (A6) twice with respect to ,3 (and evaluating these derivatives at
Ps = Pu = 1/ 2). Using various restrictions implied by css C,U - c2u > 0 and
assuming that css < cuu, it can be shown that the first derivative is positive at
,3 = 1 and that the second derivative is positive everywhere, so that (A6) is
convex. The relationship between the immigration surplus and ,3 therefore is
either upward-sloping (and convex) throughout or has the U-shape illustrated
in Figure 4.
n I amgrateful toJohn Conlisk,VincentCrawford,RichardFreeman,Claudia Goldin,
Daniel Hamermesh,ValerieRamey,James Rauch, Michael Rothschild,Carl Shapiro,
Joel Sobel, TimothyTaylor,and StephenTrejofor helpful comments,and to the Sloan
Foundationand theNational ScienceFoundationfor researchsupport.
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