We provide an analysis of the impact of migration on the skilled- unskilled wage gap. In particular, we show the possibility of a rise in the wage gap following the migration of skilled (unskilled ) labor.

Hamid Beladi

Reza Oladi

English

Research Papers in Economics

International Migration and Real Wages 
Reza Oladi Hamid Beladi
Utah State University University of Texas at San Antonio
Abstract
We provide an analysis of the impact of migration on the skilled- unskilled wage gap. In
particular, we show the possibility of a rise in the wage gap following the migration of skilled
(unskilled ) labor.
Citation: Oladi, Reza and Hamid Beladi, (2007) "International Migration and Real Wages." Economics Bulletin, Vol. 6, No. 30
pp. 1-8
Submitted: December 5, 2006.  Accepted: August 13, 2007.
URL: http://economicsbulletin.vanderbilt.edu/2007/volume6/EB-06F20009A.pdf1. Introduction
International migration of labor has always been an area of great concern for
policy makers and researchers. There is considerable academic research that relate
international migration to skilled ￿unskilled wage gap in an economy. A notable
sample can be drawn from Davis (1998), Feenstra (2000), Feenstra and Hanson
(2003), Jones and Marjit (2003), Kar and Beladi (2004) and Marjit and Kar (2005)
and Marjit, Beladi, and Chakrabarty (2003).
It is worth noting that most of the research to date looking for consequences
of international migration on wage gap has been done using models that focus
on traded goods and neglect the role of non-traded goods. In many developed
countries the majority of low-wage unskilled labor are predominately employed
in non-traded goods sector. In the U.S., 73.4 percent of low-wage workers are
employed in the non-traded service sector while only 26.6 percent are employed
in the traded goods industries. The statistics are similar for the European Union
where 73.6 percent of low-wage employment is concentrated in the non-traded
industries whereas only 26.4 percent is found in the traded-goods sector.1
Our purpose in this paper is to highlight the role of non-traded goods, as in
Beladi and Batra (2004), and explore the consequences of international migration
on the wage gap as both skilled and unskilled labor immigrate. We show, among
other things that migration of unskilled labor lowers both skilled and unskilled
wages in the host country and the wage gap widens between the wages of skilled
and unskilled workers under a fair condition.
2. The Model
We assume a small open economy with three production sectors: exportable,
importable, and non-traded. The production technology of the exportable sector is
represented by the production function Xe = Fe(Ke;Le), where Xe is the quantity
of production in the exportable sector, and Ke and Le are the capital and skilled
labor usage in this sector, respectively. Similarly, the production function for
the importable sector is given by Xi = Fi(Ki;Li), where Xi is the quantity of
importable good, Ki is the capital used in the production of importable good,
and Li denotes the skilled labor used by the importable sector. Finally, capital
and unskilled labor are used as inputs in the production of the non-traded good
with the production technology Xn = Fn(Kn;Lu), where Xn, Kn, and Lu denote
1For more details, see Beladi and Batra (2004) and OECD (2001).
2the quantity of production in the non-traded good sector, capital employed by
non-traded sector, and unskilled labor used in this sector, respectively. Following
Beladi and Batra (2004) and consistent with their observation, we assume that
the unskilled labor is used only in the non-traded sector. All the neoclassical
assumptions are imposed on the above production functions.
We assume that all markets are perfect competitive, according to which we
have the following zero pro￿t conditions:
aLew + aKer = pe (2.1)
aLiw + aKir = pi (2.2)
aLnwu + aKnr = pn (2.3)
where aLj, aKj, and pj are the labor-output ratio, capital-output ratio, and the
price in sector j = e;i;n, respectively. Moreover, w, wu, and r are the skilled
wage, unskilled wage, and the return to capital, respectively. Full employment of
all factors requires the following additional conditions:
aLeXe + aLiXi = ￿ L (2.4)
aKeXe + aKiXi + aKnXn = ￿ K (2.5)
aLnXn = ￿ Lu (2.6)
where ￿ L, ￿ K,￿ Lu are the ￿xed endowments of skilled labor, capital, and unskilled la-
bor, respectively. Equations (2.4)-(2.6) imply that skilled labor is mobile between
the exportable and the importable sectors, while capital is mobile across all three
sectors and that unskilled labor is speci￿c to the non-traded good sector. Due
to our assumption of a small open economy, pe and pi are given by international
markets. As for the price of the non-traded good, it is determined by the domestic
market clearing condition, i.e.:
Xn = D(pn;pe;pi;I) (2.7)
where D is the demand for the non-traded good and the left-hand side of equation
(2.7) is the supply of the non-traded good. I denotes national income, de￿ned as:
I = ￿j=e;i;npjXj (2.8)
The system of equations (2.1)-(2.8) is a complete general equilibrium system with
eight endogenous variables. We normalize all (input) prices to have initial value
of unity.
3Now, using the linear homogeneity of the unit cost function, we can rewrite
equations (2.1)-(2.3) using real factor prices. Then, by di⁄erentiating these equa-
tions, and denoting proportional changes by a circum￿ ex we get:
(aLe^ ! + aKe^ ￿)= ^ Xn = ￿1=￿n (2.9)
(aLi^ ! + aKi^ ￿)= ^ Xn = ￿1=￿n (2.10)
aLn^ !u + aKn^ ￿ = 0 (2.11)
where ! , !u and ￿ denote the real skilled wage, real unskilled wage, and real
return to capital, respectively, all in terms of non-traded good and ￿n < 0 is the
price elasticity of demand for the non-traded good.
Now we turn to the questions we have raised in the next two sections.
3. The impact on the host country
In this section we explore the impact of unskilled and skilled labor migration
on real skilled and unskilled wages as well the gap between them for the host
country. First, assume that the endowment of unskilled labor increases as a result
of migration, resulting in an increase in marginal product of capital in the non-
traded sector. This brings about movements of capital from both importable and
exportable sectors to non-traded sector. Thus, the output of non-traded sector
rises, i.e., ^ Xn > 0. On the other hand, the marginal product of labor falls in both
of the trading sectors, lowering the real skilled wage, that is, ^ ! < 0. This, along
with equation (2.9) and ^ Xn > 0, imply that the real return to capital increases
across the economy, i.e., ^ ￿ > 0. Consequently, all this along with equation (2.11),
indicate that the real unskilled wage must fall, ^ !u < 0:
The most interesting issue is however the impact of this type of migration on
the gap between skilled and unskilled wages. To investigate this, we substitute
equation (2.11) in equation (2.10) to obtain ^ ! > ((ki)=(kn))^ !u. This implies that
^ ! > ^ !u if ki < kn. Note that, as the changes in both real wages are negative, this
indicates that the absolute value of the change in unskilled real wage is greater
than the absolute value of the change in skilled wage. Therefore, we have the
following proposition.
Proposition 3.1. Migration of unskilled labor decreases both skilled and un-
skilled real wages in the host country. Moreover, such migration widens the gap
between skilled and unskilled wages if the importable sector is less capital intensive
than the non-traded sector.
4Now let the endowment of skilled labor increase as a result of migration. This
increases the marginal product of capital in both the exportable and importable
sectors, causing movements of capital from the non-traded sector to exportable
and importable sectors. This, in turn, leads to a decrease in production of the non-
traded good, i.e. ^ Xn < 0, as well as a decrease in marginal product of unskilled
labor. The latter implies that unskilled wage falls, i.e. ^ !u < 0. This and equation
(2.11) imply that return to capital increase across the economy, that is, ^ ￿ > 0.
Finally, equation (2.10) and ^ ￿ > 0 imply that ^ ! < 0 as we already concluded that
^ Xn < 0.
Next, we investigate the impact of skilled labor migration on skilled-unskilled
wage gap. We substitute equation (2.11) in equation (2.10) and use ^ Xn < 0 to
conclude that (kn=ki)^ ! < ^ !u. With this the following result is in order.
Proposition 3.2. Migration of skilled labor decreases both skilled and unskilled
real wages in the host country. However, the skilled-unskilled wage gap reduces
as a result of such migration if the non-traded sector is less capital intensive than
the importable sector.
The following proposition formally addresses the fate of capital.
Proposition 3.3. Migration of unskilled or skilled labor increases the real return
to capital.
4. The impact on the source country
Turning to the source country in this section, let the endowment of unskilled labor
decrease due to migration. As a result, the marginal product of capital decreases
in the non-traded sector. This in turn leads to movements of capital from the non-
traded sector to both the importable and exportable sectors. Thus, the output of
non-traded good falls, i.e., ^ Xn < 0: Moreover, the movements of capital from the
non-traded sector to tradable sectors raise the marginal product of skilled labor
in the economy, which results in an increase in the skilled real wage, i.e., ^ ! > 0.
As ^ Xn < 0 and ^ ! > 0, it can be concluded from equation (2.10) that the return
to capital must fall across the economy, that is, ^ ￿ < 0. Finally, equation (2.11)
and ^ ￿ < 0 imply that ^ !u > 0, i.e., the unskilled wage must go up.
As in the preceding section, now we explore the gap between skilled and un-
skilled wages. Again, we conclude from ^ Xn < 0 as well as equations (2.10) and
(2.11) that ^ ! < ^ !u if ki < kn: Therefore we have the following proposition:
5Proposition 4.1. Migration of unskilled labor increases both skilled and un-
skilled real wages in the source country. Moreover, such migration reduces the
gap between skilled and unskilled wages if ki < kn.
Next assume that skilled labor migrates from the source country, resulting in
a decline in the marginal product of capital in the importable and exportable
sectors. This leads to movements of capital from the these two tradable sectors to
non-traded sector, raising the marginal product of unskilled labor and hence the
real unskilled wage, that is, ^ !u > 0: This and equation (2.11), in turn, imply that
^ ￿ < 0: Moreover, it clear that ^ Xn > 0. We then conclude from ^ ￿ < 0, ^ Xn > 0,
and equation (2.10) that ^ ! > 0: Once again, using ^ Xn > 0; and equations (2.10)
and (2.11), we obtain that ^ ! > ^ !u if ki > kn: Thus, we have the following result.
Proposition 4.2. Migration of skilled labor increases both skilled and unskilled
real wages in the source country. Moreover, such migration increases the gap
between skilled and unskilled wages if ki > kn.
As for the impact of migration, skilled or unskilled, on return to capital, we
have the following formal statement.
Proposition 4.3. Migration of unskilled or skilled labor decreases the real return
to capital in the source country.
5. Conclusion
The purpose of this paper was to analyze the impact of international migration of
skilled and unskilled labor on the wage gap. We show that factor intensities and
the output of the non-traded sector continue play a dominant role in explaining
the behavior of skilled and unskilled wages.
In particular, we point out that migration of both skilled and unskilled labor
would decrease skilled (unskilled) wages in the host country irrespective of capital
intensity ranking. However, migration of skilled (unskilled) labor would decrease
(increase) skilled￿ unskilled wage gap if importables are the most (least) capital-
intensive.
6References
[1] Beladi, H. and R. Batra, "Traded and Nontraded Goods and Real Wages,"
Review of Development Economics 8, 2004, 1-14.
[2] Davis, D., "Technology, Unemployment, and Relative Wages in a Global Econ-
omy," European Economic Review 42, 1998, 1613 ￿1633.
[3] Feenstra, R. C. (Ed.), The Impact of International Trade on Wages, University
of Chicago Press, Chicago, 171 ￿193.
[4] Feenstra, R. C. and G. H. Hanson, "Global Production Sharing and Rising
Inequality; a Survey of Trade and Wages, In: Choi, E. K. and J. Harrigan
(Eds.), Handbook of International Trade, Basil Blackwell, London, 2003.
[5] Kar, S. and H. Beladi, "Skill Formation and International Migration; Welfare
Perspective of Developing Countries, Japan and the World Economy 16, 2004,
35 ￿54.
[6] Marjit, S., Beladi, H. and A. Chakrabarty, "Trade and Wage Inequality in
Developing Countries," Economic Inquiry 42, 2003, 295 ￿303.
[7] Marjit, S. and S. Kar, "Immigration and Wage Inequality," Economics Letters
88, 2005, 141 ￿145.
[8] OECD, OECD Employment Outlook, 2001, Paris.
7

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