Economic Modelling 38 (2014) 367–371

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Economic Modelling

j ourna l homepage: www.e lsev ie r .com/ locate /ecmod

Environment and labor movement of skilled labor and unskilled laborbetween sectors

Xiaochun Li ⁎, Yuanting Xu 1, Dianshuang Wang 2

Department of Economics, Nanjing University, 22 Hankou Road, Nanjing, Jiangsu Province 210093, China

⁎ Corresponding author. Tel.: +86 13814097480.E-mail addresses: xiaochun@nju.edu.cn (X. Li), xuyuan

wangds07@126.com (D. Wang).1 Tel.: +86 13914729811.2 Tel.: +86 18251930335.

0264-9993/$ – see front matter © 2014 Elsevier B.V. All rihttp://dx.doi.org/10.1016/j.econmod.2014.01.018

a b s t r a c t

a r t i c l e i n f o

Article history:Accepted 17 January 2014Available online 15 February 2014

JEL classification:O24Q56R23

Keywords:EnvironmentHeterogeneous labor movementAgricultural product price

In this paper, we divide the labor into skilled and unskilled labor to investigate the impact that the heterogeneouslabor movement between sectors has on the environment under the international skilled and unskilled laborflows and the price change of the agricultural products. The main conclusions are: under certain conditions,skilled labor inflow deteriorates the environment while its outflow improves the environment; unskilled laborinflow improves the environment while its outflow deteriorates the environment; the increasing price of theagricultural products improves the environment while the decreasing price deteriorates the environment.

© 2014 Elsevier B.V. All rights reserved.

1. Introduction

The movement of heterogeneous labor force between different sec-tors is often considered in studies of income disparity and employment.Marjit and Kar (2005) divided the labor force in an economy into skilledand unskilled labor, and established a general equilibrium model of atwo-sector economy. They studied the income disparity under the as-sumption that there is no unemployment or capitalmovement betweensectors. Yabuuchi and Chaudhuri (2007) took skilled labor as a specificfactor whereas unskilled labor could move freely between sectors.Based on the assumption of non-existence of unemployment in eithersector, they analyzed the impact of international factors on changesof income. Beladi et al. (2008) analyzed the impact of inflow of interna-tional factors on the wage disparity between the skilled labor and un-skilled labor through a two-sector general equilibrium model. Thispaper is based on the assumptions of full employment and free move-ment of skilled labor between sectors, and existence of unemploymentof the unskilled labor. Gupta and Dutta (2010) made an assumptionthat skilled labor moves between trade and non-trade sectors, whileunskilled labor does not, uponwhich they established a general equilib-rium model and studied the impact of changes in factor endowmentsand in the price of tradable goods on unemployment and the relative

tingcindy@126.com (Y. Xu),

ghts reserved.

wages of skilled and unskilled labor. Chaudhuri and Banerjee (2010) di-vided the rural sector into the advanced and the backward subsectorsand established a general four-sector equilibrium model. They studiedthe income effect of capital inflow under the premise of existenceof unemployment of skilled labor and immobility of them betweensectors, as well as full employment and full mobility of the unskilledlabor between the two rural sectors and immobility of unskilled laborbetween the rural and urban sectors. However, with regard to thereal-world economic activities in the developing countries, the impactof the heterogeneousmovement labor is not limited to incomedisparityand employment.

On the other hand, since the 1990s, there have beenmany studies inacademia on the impact of inter-sector labor movement in developingcountries on the environment from different perspectives, particularlythe impact of labor movement on pollution based on the Harris-TodaroModel, such as Beladi and Rapp (1993), Beladi and Frasca (1999),Daitoh (2003), Daitoh (2008), Tawada and Sun (2010), Daitoh andOmote (2011) and Kondoh and Yabuuchi (2012), which involve taxa-tion, environmental policy and improvement of labor market. However,we note that all the aforesaid studies on the labor movement and envi-ronment are based on a common premise, namely, labor is homoge-neous, which is different from the reality where labor is actuallyheterogeneous. In fact, the impact of labor quality on environment is afocus of academic studies in developing countries. Some Chinesescholars (Li and Ding, 2012; Peng, 2008) pointed out that increasingskilled labor endowment would have an impact of improving the envi-ronment. Therefore, wewould like to study the impact of heterogeneouslabor movement between sectors on the environment.

368 X. Li et al. / Economic Modelling 38 (2014) 367–371

In this paper, wewill divide the entire labor force into the skilled andunskilled and study the impact of heterogeneous labor movement be-tween sectors on the environment under the conditions of free flow ofinternational labor factors and a change in the agricultural productsprice. The main conclusion of this paper is that, under certain circum-stances, the inflow of skilled labor could deteriorate the environment;on the other hand, the outflow of labor could improve the environment.The inflow of unskilled labor would, however, improve the environ-ment; and the outflow would deteriorate the environment. In thefollowing, we will establish a theoretical model in the second section,made a theoretical analysis in the third section, and draw a conclusionthereupon the last section would.

2. The model

We consider a small open developing economy with two sectors,namely, the urban sector and the agricultural sector. The economyuses four production factors, which are skilled labor LS, unskilled laborLU, capital K and land N. The urban sector uses skilled labor, unskilledlabor and capital to produce import-competing goods. The agriculturalsector uses skilled labor, unskilled labor and land to produce exportablegoods. The urban sector is skilled labor intensive and the agriculturalsector is unskilled labor intensive. The production functions of theurban and agricultural sectors are given by:

X1 ¼ F1 LS1; LU1;Kð Þ ð1Þ

X2 ¼ eF2 LS2; LU2;Nð Þ ð2Þ

F1 and F2 are production functions increasing corresponding to eachfactor and satisfying linear homogenous and strictly quasi-concaveproperties.

In the production function of the agricultural sector,

e ¼ E−μX1

Eð3Þ

where e represents the environment of the economy. When e = 1, theenvironment is in the best condition. It becomes worse when e de-creases. E represents the environment endowment when there is nopollution in the economy. μ is the pollution that the urban sectordischarges for producing oneunit of good.We assume that only the pro-duction of the urban sector causes pollution emission to make the envi-ronment worse. The harmful substance emitted, such as waste gas,waste residue and waste water, pollute water and soil for agriculturaluse through atmosphere, rivers and other media. Hence, the productefficiency of the agricultural sector decreases.

Under the condition that the markets are perfectly competitive, wecould obtain that:

p1 ¼ aS1wS1 þ aU1wU þ aK1r ð4Þ

p2 ¼ aS2wS2 þ aU2wU2 þ aN2R ð5Þ

where aij(i= S, U, K, N; j=1, 2) represents the factor i used in produc-ing one unit of goods in the jth sector. wS1 is the wage rate of skilledlabor in the urban sector. wS2 is the wage rate of skilled labor in theagricultural sector. wU is the wage rate of unskilled labor in the urbansector. wU2 is the wage rate of unskilled labor in the agricultural sector.r is the interest rate of capital in the urban sector. R is the rent ofland used in the agricultural sector. pj(j = 1, 2) represents the productprices of the urban sector and the agricultural sector, respectively. Inthis paper, we assume that all the products are tradable and hence theproduct prices are given internationally.

Generally, developing countries lack skilled labor. Therefore, we as-sume that skilled labors are fully employedwith no unemployment andtheymove freely between the urban and agricultural sectors. This paper

assumes that the wage rate of unskilled labor in the urban sector isgiven exogenously, which means that it is downward rigid. However,in the agricultural sector, thewage rate of unskilled laborw is fully elas-tic. We use LUU to denote the number of unemployed unskilled labor inthe urban sector and λ to denote the unemployment rate of unskilledlabor in this sector. Hence, λ = LUU/LU1 = LUU/aU1X1. Therefore, in theunskilled labor market equilibrium, the wage rate in the agriculturalsector equals the expected wage income in the urban sector, whichequals to the downward rigid wage rate wU multiplied by the probabil-ity of obtaining a job in this sector LU1/(LU1 + LUU). Thus, the allocationmechanism of the skilled labor and unskilled labor are shown as:

wS1 ¼ wS2 ð6Þ

wU2 ¼ LU1LU1 þ LUU

wU ð7Þ

or:

1þ λð ÞwU2 ¼ wU : ð7′Þ

The market clearing conditions of the four production factors: skilledlabor, unskilled labor, capital and land, could be shown as follows:

aS1X1 þ aS2X2 ¼ LS ð8Þ

aU1X1 þ aU2X2 þ λaU1X1 ¼ LU ð9Þ

aK1X1 ¼ K ð10Þ

aN2X2 ¼ N ð11Þ

where LS, LU, K, N represent the endowment of skilled labor, unskilledlabor, capital and land, respectively.

The basic theoretical model has been built, which consists of nineEqs. (3)–(11). Nine endogenous variables are determined, and theyare wS1, wS2, wU2, r, R, λ, e, X1 and X2.

3. Environment and labor movement between sectors

Differentiating the Eqs. (4)–(11) and writing in a matrix notation,we can obtain the following equation:

θS1 0 θK1 0 0 0θS2 θU2 0 θN2 0 0

A λS2S2SU λS1S

1SK λS2S

2SN λS1 λS2

B C D λU2S2UN 1þ λð ÞλU1 λU2

S1KS 0 S1KK 0 1 0

S2NS S2NU 0 S2NN 0 1

0BBBBBBBB@

1CCCCCCCCA

wS1wU2rRX1

X2

0BBBBBB@

1CCCCCCA

¼

p1p2LSLUKN

0BBBBBB@

1CCCCCCA

ð12Þ

and differentiating the Eq. (3), we can get the following:

eeþ 1−eð ÞX1 ¼ 0 ð13Þ

where “^” represents the rate of change, θij(i = S, U, K, N; j = 1, 2) isthe distributive share of factor i in the jth sector (e.g. θS1 = aS1wS1/p1),λij(i = S, U, K, N; j = 1, 2) is the allocated share of factor i in thejth sector (e.g. λS1 = aS1X1/LS), Sijh(i, j = S, U, K, N; h = 1, 2) is the par-tial elasticity of substitution between factors i and j in the hth sector

(e.g. S2SU ¼ ∂aS2∂wU2

wU2

aS2), Sijh N 0(i ≠ j) and Sij

h b 0(i = j). We also have:

A ¼ λS1S1SS þ λS2S

2SS b0;B ¼ 1þ λð ÞλU1S

1US þ λU2S

2US N 0;

C ¼ λU2S2UU− 1þ λð ÞλU1b0;D ¼ 1þ λð ÞλU1S

1UK N 0:

3 See: Frédéric Docquier and Hillel Rapoport, 2012. Globalization, Brain Drain and De-velopment. Journal of Economic Literature 50, 681-730.

369X. Li et al. / Economic Modelling 38 (2014) 367–371

The partial elasticity of substitution between factors plays an impor-tant role in the following discussion. Therefore, in this paper, we makethe following assumptions:

Assumption 1.

S1UKθK1

NS1USθS1

Assumption 1 implies that unskilled labor ismore substitutable withcapital than with skilled labor in the urban sector.

Assumption 2.

S2SNθN2

NS2SUθU2

Assumption 2 implies that skilled labor is more substitutable withland than with unskilled labor in the agricultural sector.

3.1. Labor movement between sectors under an international skilled laborflow

Skilled labor in developing countries will sometimes leave becauseof low wages. In reality, there are also some situations in which skilledlabor move to developing countries from outside. Recently, high unem-ployment rate in some developed countries results in unemployed andretired skilled labor moving to the developing countries to find jobopportunities. Therefore, in this paper we not only consider skilledlabor outflow, but also their inflow.

We can obtain the following by solving the Eq. (12):

X1=LS ¼ θK1S1KS−θS1S

1KK

� �θU2λU2 S2UN−S2NN

� �−θN2 C−λU2S

2NU

� �h i=ΔN0

ð14Þ

wS1=LS ¼ −θK1 θU2λU2 S2UN−S2NN� �

−θN2 C−λU2S2NU

� �h i=Δb0 ð15Þ

r=LS ¼ θS1 θU2λU2 S2UN−S2NN� �

−θN2 C−λU2S2NU

� �h i=ΔN0 ð16Þ

where Δ is the determinant of the matrix in Eq. (12) and Δ N 0 (seeAppendix A).Differentiating the equation aS1X1 = LS1, we could obtainthe following from the Eqs. (14)–(16):

LS1LS

¼ X1

LSþ S1SS

wS1

LSþ S1SK

r

LSN0: ð17Þ

According to Eqs. (13), (17) andX1

LS¼ X1

LS1

LS1LS

, we could get that:

X1=LS1N0 ð18Þ

e=LS1b0: ð19Þ

Differentiating the equation aU1X1 = LU1, we could obtain the followingequation from the Eqs. (14)–(16) and Assumption 1:

LU1LS

¼ X1

LSþ S1US

wS1

LSþ S1UK

r

LSN0: ð20Þ

According to Eqs. (13), (20) andX1

LS¼ X1

LU1

LU1LS

, we could get that:

X1=LU1N0 ð21Þ

e=LU1b0: ð22Þ

With the six Eqs. (17)–(22) and Assumption 1, we can obtain thefollowing proposition:

Proposition 1. Under Assumption 1, the skilled labor inflow increasesemployment of skilled labor of the urban sector and causes the skilled andunskilled labor from the agricultural sector migrate to the urban sector,which deteriorates the environment. Conversely, the skilled labor outflowdecreases the employment of skilled labor of the urban sector and causesthe urban unskilled labor move to the agricultural sector, which improvesthe environment.

The urban sector is more skilled labor intensive than the agriculturalsector. Therefore, the skilled labor inflow increases the skilled laborendowment in the economy. According to the Rybczynski Theorem,skilled labor inflow leads to an expansion of the urban sector and a con-traction of the agricultural sector following the Rybczynski effect. Withthe unchanged capital endowment, the urban sector should employmore skilled and unskilled labor to increase the output. Hence, therural skilled and unskilled labor migrates to the urban sector. The in-creasing output of the urban sector increases pollution and deteriora-tion of the environment. Conversely, using the same method, wecould also analyze the impacts of the skilled labor outflow.

3.2. Labor movement between sectors under an international unskilledlabor flow

We consider the impacts of both the outflow and inflow interna-tional unskilled labor on the environment in the developing countries.Although the former situation (outflow) is common in developingcountries, the latter (inflow) also exists in real developing economies.3

Under Assumption 2, we could obtain the following by solving theEq. (12):

X1=LU ¼ λS2 θS1S1KK−θK1S

1KS

� �θU2S

2SN−θN2S

2SU−θU2S

2NN þ θN2S

2NU

� �=Δb0

ð23Þ

wS1=LU ¼ θK1λS2 θU2S2SN−θN2S

2SU−θU2S

2NN þ θN2S

2NU

� �=Δ N0 ð24Þ

r=LU ¼ −θS1λS2 θU2S2SN−θN2S

2SU−θU2S

2NN þ θN2S

2NU

� �=Δb0: ð25Þ

Differentiating the equation aS1X1 = LS1, we could obtain the fol-lowing from Eqs. (23)–(25):

LS1LU

¼ X1

LUþ S1SS

wS1

LUþ S1SK

r

LUb0: ð26Þ

According to Eqs. (13), (26) andX1

LU¼ X1

LS1

LS1LU

, we could get that:

X1=LS1N0 ð27Þ

e=LS1b0: ð28Þ

Differentiating the equation aU1X1 = LU1, we could obtain the fol-lowing equation from the Eqs. (23)–(25) and Assumption 1:

LU1LU

¼ X1

LUþ S1US

wS1

LUþ S1UK

r

LUb0: ð29Þ

370 X. Li et al. / Economic Modelling 38 (2014) 367–371

According to Eqs. (13), (29) andX1

LU¼ X1

LU1

LU1LU

, we could get that:

X1=LU1 N0 ð30Þ

e=LU1b0: ð31Þ

With the six Eqs. (26)–(31), Assumptions 1 and 2, we can obtain thefollowing proposition:

Proposition 2. Under Assumptions 1 and 2, the inflow of unskilled laborcauses the urban unskilled as well as skilled labor migrate to the agricul-tural sector, which improves the environment. Conversely, the outflow ofunskilled labor outflow increases the employment of unskilled labor of theurban sector, and causes the agricultural skilled labor migrate to theurban sector, which deteriorates the environment.

The agricultural sector is more unskilled labor intensive than theurban sector. Therefore, the unskilled labor inflow increases the un-skilled labor endowment in the economy. According to the RybczynskiTheorem, unskilled labor inflow leads to an expansion of the agri-cultural sector and a contraction of the urban sector following theRybczynski effect. With the unchanged land endowment, the agri-cultural sector should employ more skilled and unskilled labor toincrease the output. Hence, demand for both production factors in-crease, and both the urban skilled and unskilled labor migrate to theagricultural sector. The decreasing output of the urban sector decreasesthe pollution and improves the environment. Conversely, using thesame method, we could also analyze the situation of decreased un-skilled labor endowment.

3.3. Labormovement between sectors under the price change of agriculturalproducts

We consider the impacts that the labor movement between sectorshas on the environment under the condition of a change in the priceof agricultural products. We can obtain the following by solving theEq. (12):

X1=p2 ¼ λS2 θS1S1KK−θK1S

1KS

� �V=Δb0 ð32Þ

wS1=p2 ¼ λS2θK1V=Δ N0 ð33Þ

r=p2 ¼ −λS2θS1V=Δb0 ð34Þ

where V ¼ λU2 S2UN S2SU þ S2NS� �

−S2NN S2SU þ S2US� �

þ S2NUS2SN

h i

− 1þ λð ÞλU1S2NN−CS2SN N0:

Differentiating the equation aS1X1 = LS1, we could obtain the fol-lowing from the Eqs. (32)–(34):

LS1p2

¼ X1

p2þ S1SS

wS1

p2þ S1SK

rp2

b0: ð35Þ

According to Eqs. (13), (35) andX1

p2¼ X1

LS1

LS1p2

, we could get that:

X1=LS1N0 ð36Þ

e=LS1b0: ð37Þ

Differentiating the equation aU1X1 = LU1, we could obtain the followingequation from Eqs. (32)–(34) and Assumption 1:

LU1p2

¼ X1

p2þ S1US

wS1

p2þ S1UK

rp2

b0: ð38Þ

According to Eqs. (13), (38) andX1

p2¼ X1

LU1

LU1p2

, we could get that:

X1=LU1N0 ð39Þ

e=LU1b0: ð40Þ

With the six Eqs. (35)–(40) and Assumption 1, we can obtain thefollowing proposition:

Proposition 3. Under Assumption 1, increase of the agricultural productprice causes the urban skilled and unskilled labor to migrate to the agricul-tural sector, which improves the environment; conversely, the decrease ofagricultural product price causes the agricultural skilled and unskilledlabor migrate to the urban sector, which deteriorates the environment.

The agricultural sector is more unskilled-labor intensive than theurban sector. Therefore, according to the Stolper–Samuelson effects,the increase of the agricultural product price raises wage rate of the un-skilled labor in the agricultural sector, which attracts the unskilled laborin the urban sectormigrates to the agricultural sector. An increase of theunskilled labor employment of the agricultural sector raises the outputand the demand for skilled labor in this sector. This also attracts theskilled labor in the urban sector to migrate to the agricultural sector.The decrease of employment of both skilled and unskilled labor in theurban sector decreases the output of the urban sector as well as pollu-tion. Hence, the environment of the economy improves. Conversely,using the same method, we could analyze the impacts of decreasingthe agricultural product price.

4. Conclusion

This article analyzed the impact of the skilled and unskilled labormovement between sectors on the environment, considering free flowof international labor factor and price change of agricultural products.One of the characteristics of this paper is that labor force, as the researchobject in this article, is heterogeneous, which is different with existingpapers about environment pollution caused by labor movement. It isthe first time that the entire labor force has been divided into the skilledand the unskilled in the study of environmental pollution caused bylabor movement, which is closer to reality. Therefore, the results ofour research have more valuable reference to the real economy. For ex-ample, some scholars hold that an increase in skilled labor endowmentwill improve environment, and inflow of skilled labor from abroad is animportant channel to increase skilled labor endowment. However, thispaper shows that inflow of skilled labor could deteriorate the environ-ment. This conclusion reminds us that we could not improve environ-ment by increasing skilled labor endowment blindly. Nonetheless, it isjust a beginning, and we shall proceed to other related topics, such astaxation, environmental policies and labor market reform in our futurestudies.

Acknowledgements

Weexpress our thanks to the anonymous referees for their construc-tive comments and suggestions. Financial supports are provided by theNational Social Sciences Fund Project No.10BJL035.

371X. Li et al. / Economic Modelling 38 (2014) 367–371

Appendix A

Under the present model, the dynamic adjustment process for thesupply side is as follows:

X1 ¼ d1 p1−aS1wS1−aU1wU−aK1rð Þ ðA1Þ

X2 ¼ d2 p2−aS2wS1−aU2wU2−aN2Rð Þ ðA2ÞwS1 ¼ d3 aS1X1 þ aS2X2−LSð Þ ðA3Þ

wU2 ¼ d4 aU1X1 þ aU2X2 þwU−wU2

wU2aU1X1−LU

� �ðA4Þ

r¼ d5 aK1X1−Kð Þ ðA5Þ

R¼ d6 aN2X2−Nð Þ ðA6Þ

where “.” represents differentiation with respect to time and dj(j=1, 2,3, 4, 5, 6) is the positive coefficient measuring the speed of adjustmentand dj N 0.

Marshallian adjustment process is assumed for quantities when thedemand price differs from the supply price in the goods markets.A Walrasian adjustment mechanism is assumed for the factor priceswith the fixed endowment in the factor markets. The determinant ofthe Jacobian matrix of Eqs. (A1)–(A6) is:

Jj j ¼ d1d2⋯d6p1p2KNLSLU

0 0 −θS1 0 −θK1 00 0 −θS2 −θU2 0 −θN2λS1 λS2 A λS2S

2SU

λS1S1SK λS2S

2SN

1þ λð ÞλU1 λU2 B C D λU2S2UN

1 0 S1KS 0 S1KK 0

0 1 S2NS S2NU 0 S2NN

��������������

��������������

:

It can also be written as follows:

Jj j ¼ d1d2⋯d6p1p2KNLSLUΔ:

Therefore, according to the Routh–Hurwitz Theorem, a necessarycondition for the local stability of the system is that the determinant

of the Jacobian matrix is positive. Hence, it is assumed that the equilib-rium in this paper is stable under the condition that |J| N 0.We could ob-tain that Δ N 0.

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Xiaochun Li is a professor of Economics inNanjingUniversity and researcher in Centre forSocial and Economic Research on Yangtze River Delta, Nanjing University. His research in-terests include the Labor Economics and Development Economics. He has publishedmorethan 7 articles in journals.

Yuanting Xu is a graduate student in Nanjing University since 2012, major in economic.

Dianshuang Wang is a graduate student in Nanjing University since 2012, major ineconomic.