We examine the effect of emigration of skilled and unskilled labor on pre-existing wage gap between the skilled-unskilled labor. The results by Marjit and Kar (2005) will be confirmed also in a dual economy setup.International factor mobility, Wage inequality, Unemployment, Harris-Todaro model

Shigemi Yabuuchi

English

Research Papers in Economics

     
 
 
  
  
Volume 29, Issue 3 
  
Emigration and wage inequality in a dual economy  
  
 
 
Shigemi Yabuuchi  
Aichi University 
Abstract 
We examine the effect of emigration of skilled and unskilled labor on pre-existing wage gap between the skilled-
unskilled labor. The results by Marjit and Kar (2005) will be confirmed also in a dual economy setup.
The author would like to thank two anonymous referees for many useful and constructive comments on the earlier version of this note. This 
research was financially supported by the Grants-in-Aid for Scientific Research (c-19530255 and a-21243023) from the Japan Society for the 
Promotion of Science. 
Citation: Shigemi Yabuuchi, (2009) ''Emigration and wage inequality in a dual economy '', Economics Bulletin, Vol. 29 no.3 pp. 1549-1554. 
Submitted: Apr 26 2009.   Published: July 01, 2009. 
 
        
1.  Introduction 
 
  There have been extensive studies on the effects of economic liberalization on the 
skilled-unskilled wage inequality. Recently, Marjit and Kar (2005) examined the effect of 
skilled and unskilled labor emigration on wage gap in the developing world by using a simple 
two good-three input specific-factor model like Jones (1971).
1 Their model differs from 
Jones (1971) in that labor is specific in the Marjit-Kar model while capital is specific in the 
original Jones’ model. Their important result is that emigration of unskilled as well as skilled 
workers would increase (decrease) the wage gap if capital’s income share in the skilled sector 
is larger (smaller) than that in the unskilled sector, in other words, if the skilled (unskilled) 
sector is capital intensive. 
   
  They assume that the economy is a developing country. Then, our first innovation in 
this note is that it introduces unemployment into the two-good-three input specific factor 
model. The justification for this stems from Marjit and Kar’s (2005) paper where it is 
assumed that the economy is a developing economy. Thus incorporating unemployment into 
the model serves a useful purpose since unemployment is a characteristic feature of 
developing economies. This is achieved by the labor allocation mechanism in the model 
where the wage rate in the agricultural sector equals the wage rate in the manufacturing 
sector times the probability of finding a job in the manufacturing sector. This is based on the 
Harris-Todaro model where the wage rate in the manufacturing sector is relatively higher and 
more rigid than the agricultural sector’s wages which are more flexible. 
 
The second innovation in the present model is a direct extension of Marjit and Kar’s 
(2005) model on the mobility of unskilled labor between the sectors. We extend the model so 
that unskilled labor is mobile between the sectors while both unskilled and skilled labor are 
specific in Marjit and Kar’s model. This setup captures the real economy more accurately. 
 
2. The model and assumptions 
Let us consider a small open economy in which there are two sectors.  One sector 
produces good 1, , and the other sector produces good 2,  .  For simplicity, we label 
sectors 1 and 2 as agricultural and manufacturing sectors, respectively. Production of good 1 
requires unskilled-labor ( ), and capital ( ), while production of good 2 requires 
unskilled-labor ( ), capital ( ), and skilled-labor ( ). Thus, the production functions are 
as follows: 
1 X 2 X
1 L 1 K
2 L 2 K 2 H
 
  2
)
2
        ,                  ( 1 )   , ( 1 1
1
1 K L F X =
          
2
22 2 (, , ) X FLKH = .       ( 2 )  
 
It is assumed that    has positive and diminishing marginal products and it is homogeneous 
of degree one.     
j F
  Under perfect competition, we have 
  
  r a w a p K L 1 1 1 1 + = ,               (3) 
                                                           
1 Other studies on wage inequality include Davis (1998), Feenstra and Hanson (1997, 2003), Jones and Marjit 
(2003), Kar and Beladi (2004), and Chaudhuri and Yabuuchi (2007), among others.    
          22 22 2 LK H p aw ar as =+ + ,         ( 4 )  
 
where    is the amount of the ith factor used in the jth industry to produce one unit of the 
output,   is the wage rate of unskilled labor in the jth sector, s is the wage rate of skilled 
labor,  r  is rental of capital, and    is the price of the jth good (j  = 1,2).  In order to 
simplify the analysis, we assume that sector 2 employs a constant amount of skilled labor to 
produce one unit of the output, i.e., 
ij a
j w
j p
2 H a  is constant. We also assume that all goods are 
tradable and then their prices are exogenously given. 
 
    In the standard Harris-Todaro model (Harris and Todaro (1970)),
2 it is assumed that 
the wage rate in (manufacturing) sector 2 ( ) is set at a relatively high level, and it is rigid 
due to some political and/or institutional considerations, while the wage rate in (agricultural) 
sector 1 ( ) is flexible.    In this situation, the rural workers have two alternatives of staying 
in rural areas in order to obtain a job at a low wage rate or migrating to urban areas in order 
to seek a high wage income at the risk of unemployment.  Thus, the labor allocation 
mechanism between the sectors is shown as follows: 
2 w
1 w
 
       o r    ) /( 2 2 2 1 u L L L w w + = 2 1 ) 1 ( w w = +λ ,    (5) 
 
where   and   are the employed and unemployed labor in the urban area, respectively, 
and 
2 L u L
2 /L Lu = λ .  In the labor market equilibrium, therefore, the wage rate in sector 1 ( ) 
equals the expected wage income in sector 2, which equals the manufacturing wage rate ( ) 
times the probability of finding a job in the urban manufacturing sector ( ).  
1 w
2 w
) /( 2 2 u L L L +
 
  Exogenously given endowments impose the following resource constraints: 
 
  * 2 2 2 2 1 1 L L X a X a X a L L L + = + + λ ,               ( 6 )  
  , (7)  * 2 2 H H X aH + =
and 
  , (8)  11 22 * KK aX aX K K += +
 
where L, H, and K are the domestic endowments of unskilled labor, skilled labor, and capital, 
respectively, while L*, H*, and K* are the foreign inflows of unskilled labor, skilled labor, 
and capital, respectively.  This completes the specification of our model with the fixed 
endowment of factors and the internationally determined prices.  We have six unknown 
variables  , s, r,  , and  1 w 2 1,X X λ , which are solved by six equations (3)–(8) for given 
parameters,  , ,L, H, K, L*,H*, and K*.    2 w 2 1, p p
 
 
 
                                                           
  3
2 On the Harris-Todaro model and the extension, see Batra and Naqvi (1987), Beladi and Naqvi (1988), Beladi, 
Chaudhuri and Yabuuchi (2008), Chao and Yu (1996), Corden and Findlay (1975), Gupta (1993), Khan (1980), 
Neary (1981), Yabuuchi (2008) etc.    
3.International factor movement and wage inequality 
 
  Let us now analyze the consequences of international mobility of different factors of 
production on the skilled-unskilled wage inequality. Differentiating (3) to (8), we obtain 
 
1 2 22
1 11
1
12 1 2
2
1
12 1 1
11
ˆ ˆ 00 0 0
ˆ ˆ 00 0 0
ˆ ˆ ** 0( 1 )
ˆ ˆ 00 010 0 **
ˆ 00 ˆ **
(1 ) 0 0 0 0 ˆ 0
HK
LK
LL L L L L
KK L K K
w p
s p
r lL SA
X hH
SB X kK
ww
θθ
θθ
λλ λ λ λ λ
λλ λ
λλ λ
⎡⎤ ⎡ ⎤ ⎡⎤
⎢⎥ ⎢ ⎥ ⎢⎥
⎢⎥ ⎢ ⎥ ⎢⎥
⎢⎥ ⎢ ⎥ ⎢⎥ +
⎢⎥ ⎢ ⎥ = ⎢⎥
⎢⎥ ⎢ ⎥ ⎢⎥
⎢⎥ ⎢ ⎥ ⎢⎥
⎢⎥ ⎢ ⎥ ⎢⎥
⎢⎥ ⎢ ⎥ + ⎢⎥ ⎣⎦ ⎣ ⎦ ⎣⎦
 
          ( 9 )  
 
where      ** / ( * ) lLL L ≡+ ** / ( * ) hHH H ≡+** / ( * ) kKK K , , , + ij   ≡ λ  is the allocative 
share of factor i in the jth sector (e.g.,  11 1 /( *) KK aX K K λ = + ),  ij θ  is the distributive share 
of factor i in the jth sector (e.g.,  2 2 2 / p saH H = θ ),   , 
 and 
0 ) 1 (
1
1
2
2 > + + ≡ LK L LK L S S A λ λ λ
0
1
1
2
2 < + ≡ KK K KK K S S B λ λ
1
11 (/ ) ( / ) KK K K Sr a a r = ∂∂ and so on. 
  Solving (9) for   and  , we have    1 ˆ w ˆ s
 
   (10)  11 1 2 1 1 ˆˆ ˆ ( / ){( * *) ( * *) ( * *)} KH K L K L ww l L h H k K λθ θ λ λ =Δ + Λ − ˆ
ˆ
 
    (11)  11 2 1 1 ˆˆ ˆ ( / ){( * *) ( * *) ( * *)} LK K L K L sw l L h H k K λθ θ λ λ =Δ+ Λ −
 
where  12 1 2 (1 ) LK L K K L λ λλ λ λ Λ= − + , and  Δ  is the value of the determinant of the coefficient 
matrix of the system, 
  . 
2
112 2 1 1
11 1
11 1 1
[(1 ) ( )
{( ) }] 0
KH L K LL K
L L LK K KL K LL
wS
SS S
λλ θ λ λθ θ
λθ θ θ
Δ=− + +
++ − <
)
 
Subtraction of (10) from (11) yields 
 
    11 1 1 ˆˆ ˆ ˆˆ ( ) ( / ){( * *) ( * *) ( * *)} KL K L sw w l L h H k K λλ λ −= Θ Δ +Λ −
           ( 1 2 )  
 
where  21 1 2 ( KL KH θ θθ θ Θ= − . We suppose that the model satisfies the Khan-Neary stability 
condition, i.e.,  12 1 2 (1 ) 0 LK L K K L λ λλ λ λ Λ= − + > . This leads to the following proposition. 
 
Proposition 1.  Emigration (Immigration) of skilled or unskilled labor will increase 
(decrease) the wage inequality if sector 2 is capital intensive in the sense that 
21 1 2 () KL KH 0 θ θθ θ Θ= − > . 
 
  4   
  Emigration of unskilled labor increases the wage rate ( ). This causes the induced 
change in the wage rate of skilled labor (s). In order to examine the effect on s, we obtain by 
differentiating (3) and (4), 
1 w
 
   11 1 ˆˆ 0 LK wr θ θ +=       ( 1 3 )  
     22 ˆˆ 0 KH rs θ θ += .       ( 1 4 )  
 
Thus, we have 
 
   12 211 ˆ (/) LK H K sˆ w θ θθ θ =   .      ( 1 5 )  
 
Therefore, the skilled wage rate also increases due to the outflow of unskilled labor and 
induced increase in . The effect on the wage inequality depends on the relative magnitude 
of the changes in the wage rates, that is, on the factor intensity condition. The condition 
provided in Proposition 1 is formally the same as that derived by Marjit and Kar (2005) 
except that unskilled labor is used in both sectors in our model, so that it cannot be simplified 
in the form shown in their paper (i.e., 
1 w
21 K K θ θ >  in the present notations). However, this 
shows the robustness of the result of Marjit and Kar (2005). 
 
  Finally, let us make a brief remark on the effect of capital inflow on the wage 
inequality. It can be seen from (12) that capital inflow has exactly the opposite effect than the 
effects of the inflow of skilled and unskilled labor. The inflow of foreign capital decreases its 
rental. This, in turn, increases the wage rates of skilled and unskilled labor to restore the 
competitive profit conditions under the fixed commodity prices as shown in (13) and (14). If 
sector 2 is capital intensive, skilled wage rate increases more than the unskilled wage rate. 
Thus, capital inflow increases the wage inequality sector 2 is capital intensive while the 
inflow of skilled and unskilled labor decrease it. This implies that the policy makers in 
developing countries must consider this effect when they induce foreign capital as a 
development strategy. 
 
4. Concluding remarks 
 
  In this paper, we have extended the Marjit-Kar model to include sectorally-mobile 
unskilled labor and urban unemployment, and examined the effects of labor movements on 
the skilled-unskilled wage inequality. The results obtained are exactly the same as that 
derived in Marjit and Kar (2005, Proposition 1) in that immigration of skilled or unskilled 
labor will decrease the wage gap if the manufacturing sector is capital intensive. The analysis 
shows robustness of the results by Marjit and Kar (2005) in a general setup of developing 
countries. This has an important policy implication for the policy makers in developing 
countries who suffer from chronic unemployment as well as serious wage inequalities. That 
is, the immigration policy suggested by Marjit and Kar (2005) can be applied to address the 
wage gap problem in many developing countries with unemployment. The effect of 
international capital movement has also been examined and compared with that of labor 
movement. 
 
 
  5   
  6
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Emigration and wage inequality in a dual economy

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Emigration and wage inequality in a dual economy

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