Hukou system reforms and skilled-unskilled wage inequality in China

China Economic Review 41 (2016) 90–103

Contents lists available at ScienceDirect

China Economic Review

Hukou system reforms and skilled-unskilled wage inequality in China Jiancai Pi ⁎, Pengqing Zhang Department of Economics, School of Business, Nanjing University, 22 Hankou Road, Nanjing 210093, PR China

a r t i c l e

i n f o

Article history: Received 1 March 2016 Received in revised form 25 August 2016 Accepted 25 August 2016 Available online 30 August 2016 Keywords: Rural migrant workers Wage inequality General equilibrium approach Urban unemployment Informal sector

a b s t r a c t In China, rural migrant workers usually cannot get fair treatment due to the hukou system. This paper investigates how hukou system reforms affect the skilled-unskilled wage inequality through the general equilibrium approach. In the basic model, we find that an increase in the strength of hukou system reforms will narrow down the wage inequality if the urban skilled sector is more capital intensive than the urban unskilled sector. In addition, we separately extend the basic model by introducing the endogenous minimum wage and an informal sector, and find that in these two extended cases the main results of the basic model will conditionally or unconditionally hold. When we consider some empirical evidences in China, our models predict that an increase in the strength of hukou system reforms will reduce the wage inequality. © 2016 Elsevier Inc. All rights reserved.

1. Introduction The Chinese household or residential registration (hukou) system plays an important role in controlling and restricting ruralurban migration in China. Hukou determines the legitimate residences of Chinese rural and urban people. Generally, rural people have a rural hukou, and urban people have an urban hukou. The initial aim of the hukou system is to prevent rural residents leaving the agricultural sector and to protect urban residents to enjoy the basic amenities and social welfare provision. Hukou is not only a population registration system, but also a differential treatment of different residents in the sense of guaranteeing basic living and public services. During the course of the Chinese economic marketization, hukou system reforms are carried out to respond to the changing conditions in different ways. Along the way, the hukou system's functions of resource allocation and subsidization to urban residents have been greatly reduced and partially replaced. Although many reforms of the hukou system have been launched, there still exist two main roles (see Cai, 2011, pp.37–38). Firstly, the hukou system gives the priority of being employed by the urban sector to urban residents. That is to say, urban governments can protect workers who have an urban hukou and discriminate against workers who have a rural hukou. Secondly, the hukou system can exclude rural migrant workers from acquiring urban social welfare (e.g., access to public schools, health services, low-cost housing, and attractive jobs). In the new wave of hukou system reforms, many forms of institutional arrangements are introduced, and many rural migrant workers gradually obtain some urban social welfare that is excluded from them before. There are many studies exploring the evolution of the hukou system, especially from the perspective of hukou system reforms. Wang and Zuo (1999) hold that the hukou system can assure a steady labor flow from the rural area to the urban area and at the same time assure that rural migrants do not settle permanently in the urban area. Wang (2004) finds that the reformed hukou ⁎ Corresponding author. E-mail addresses: [email protected] (J. Pi), [email protected] (P. Zhang).

http://dx.doi.org/10.1016/j.chieco.2016.08.009 1043-951X/© 2016 Elsevier Inc. All rights reserved.

J. Pi, P. Zhang / China Economic Review 41 (2016) 90–103

91

system plays a crucial role in controlling internal migration and maintaining socio-political stability. Zhao (2005) reports that the changing hukou policies are employed to respond to the changing macro environment. Chan and Buckingham (2008) point out that the effect of recent reforms is not to abolish the hukou system, but to transfer the responsibility for hukou policies to local governments. Bao, Bodvarsson, Hou, and Zhao (2011) find that migration is significantly responsive to hukou system reforms. Cai (2011) argues that both central and local governments have incentives to carry out hukou system reforms because China has met the Lewis turning point. Wu (2013) holds that local governments have more flexibility to practice hukou system reforms during the course of political and economic decentralization. Song (2014) provides a literature review on the evolution of the hukou system and its reforms. On the one hand, many current studies investigate the effects of the hukou system, especially of hukou system reforms. Wang (2005) argues that the hukou system has created deep and rigid divisions and exclusions, which exerts both positive and negative impacts on Chinese society. Au and Henderson (2006) analyze how migration restrictions affect spatial agglomeration and productivity in China. Zhang (2010) explores how the hukou system generates an effect on migrant workers' job mobility. Bao et al. (2011) investigate how the hukou system influences the scale and structure of migration. Vendryes (2011) examines how migration constraints affect capital accumulation in China. Bosker, Brakman, Garretsen, and Schramm (2012) analyze how hukou system reforms generate an impact on China's internal economic geography, and find that an increase of the strength of hukou system reforms leads to more pronounced core-periphery outcomes. More importantly, many studies focus on the impacts of the hukou system on inequality from different perspectives. Liu's (2005) data support that the hukou system is a major force that leads to rural-urban inequality. Whalley and Zhang (2007) conduct a numerical simulation analysis of migration restrictions, and find that hukou restrictions play a significant role in supporting inequality. Wan and Li's (2013) evidence shows that the hukou system produces significant discriminatory effects on urban-rural income inequality. Afridi, Li, and Ren (2015) conduct an experimental study, and find that the hukou system reduces the performance of rural migrant workers and increases urbanrural inequality. However, the existing studies neglect to investigate how hukou system reforms affect the skilled-unskilled wage inequality in China, especially through the general equilibrium approach. This paper tries to fill the current research gap. On the other hand, the literature on skilled-unskilled wage inequality is very plentiful. The existing studies analyze such an issue from different perspectives. The perspective that is most closely related to this paper highlights the role of public inputs, institutional arrangements, and economic policies in affecting the skilled-unskilled wage inequality (see e.g., Anwar, 2008; Anwar & Sun, 2015; Chaudhuri & Yabuuchi, 2007; Mandal & Marjit, 2010; Pi & Chen, 2016; Pi & Zhou, 2012, 2013, 2014, 2015; Sun & Anwar, 2015). This strand of literature identifies different channels through which governmental behaviors and related institutions exert effects on wage inequality. For example, Mandal and Marjit (2010) and Pi and Zhou (2015) find that corruption influences the wage rates of skilled and unskilled workers and thus the wage inequality. Anwar and Sun (2015) and Sun and Anwar (2015) find that the taxation of labor in different sectors may generate different impacts on wage inequality via different economic mechanisms. However, the current studies on skilled-unskilled wage inequality fail to take China's hukou system reforms into consideration. This paper tries to explore how hukou system reforms affect the skilled-unskilled wage inequality, which is greatly different from the existing literature. In order to bridge the gap between the aforementioned two strands of literature, we build several general equilibrium models under the framework of Harris and Todaro (1970) to conduct our analysis. In the basic model, we find that the wage inequality will be reduced if the urban skilled sector is more capital intensive than the urban unskilled sector when the government increases the strength of hukou system reforms. In order to reflect the reality in China, we extend our basic model by considering two different cases with the urban endogenous minimum wage and an urban informal sector. In these two extended models, we find that the main results of the basic model will conditionally or unconditionally hold. Specifically, in the extended case where we introduce the urban endogenous minimum wage, when the elasticity of the urban minimum wage with respect to urban unemployment is large enough, our main results in the basic model will still hold; however, when the elasticity is small enough, these results will not hold. That is to say, our main results only conditionally hold in this situation. In the extended case where we introduce an urban informal sector into our basic model, our main results unconditionally hold. To the best of our knowledge, this paper is the first one to incorporate hukou system reforms into the Harris-Todaro framework. We also provide some empirical evidences to show that the urban skilled sector is more capital intensive than the urban unskilled sector, and that the condition of a large enough elasticity of the urban minimum wage with respect to urban unemployment can be satisfied with large probability. Thus, on the basis of these estimations, our models predict that an increase of the strength of hukou system reforms will narrow down the skilled-unskilled wage inequality. The rest parts of this paper are organized as follows. We build the basic model in Section 2. Section 3 gives two extended models. Section 4 offers some empirical discussions. Concluding remarks are provided in Section 5. 2. The basic model Consider a semi-open economy concluding three formal sectors, an urban skilled sector, an urban unskilled sector and a rural sector. All sectors produce final goods and sell them at given world prices. The urban skilled sector employs urban skilled labor LSX and capital KX to produce an exportable manufacturing good X. The urban unskilled sector employs urban unskilled labor (or rural migrant labor) LUY and capital KY to produce an import-competing manufacturing good Y. The rural sector employs rural labor LUZ and land T to produce an exportable agricultural good Z. X, Y, and Z also denote the total quantities of goods that these sectors produce, respectively. In the factor market, capital can move freely between the urban skilled sector and the urban unskilled sector, land is specific to the rural sector, and urban skilled and unskilled workers are specific to the urban skilled sector and the

92

J. Pi, P. Zhang / China Economic Review 41 (2016) 90–103

urban unskilled sector, respectively. However, rural people can work in the urban unskilled sector, so they can move between the urban unskilled sector and the rural sector. Furthermore, all economic endowments are assumed to be exogenous. There is no capital inflow or outflow from the economy to other economies. Total amounts of land and labor remain unchanged. Such kinds of settings are reasonable in our analysis and prevalent in the existing literature (e.g., Beladi, Chaudhuri, & Yabuuchi, 2008; Chaudhuri & Yabuuchi, 2007; Marjit & Kar, 2005). In addition, both input and output markets are perfectly competitive. The production functions are X = F X(LSX, KX), Y= FY(LUY, KY), and Z = F Z(LUZ, T), where strict quasi-concavity and linear homogeneity are satisfied. Profit maximization of the three sectors yields: pX ¼ aSX wS þ aKX r;

ð1Þ

pY ¼ aUY wU þ aKY r;

ð2Þ

1 ¼ aUZ wR þ aTZ τ;

ð3Þ

where the price of the agricultural good is normalized to unity. pX and pY are the prices of the final products of the urban skilled sector and the urban unskilled sector, respectively. wS, wU, and wR are the wage rates of labor employed in the urban skilled sector, the urban unskilled sector and the rural sector, respectively. r indicates the interest rate in the economy. τ represents the rent of land. aij(i = S, U,K,T; j = X,Y,Z,I) is the envelope solution of the quantity of factor i employed in sector j in order to produce one unit of the final product. As a consequence, aij is the function of the factors' prices (e.g., aSX = aSX(wS, r)). S, U, K, and T stand for skilled labor, unskilled labor, capital, and land, respectively. In the economy, we assume that any worker involved in any formal sector can not only get his corresponding wage, but also obtain an explicit or implicit subsidy in the sense of public services adhering to the hukou system. The amount of subsidy depends on a worker's hukou. On the one hand, an urban worker who has an urban hukou can get the government subsidy g3 N 0. On the other hand, the amount of subsidy to a worker who has a rural hukou is related to the sector in which he works. Concretely, a rural-hukou worker employed in the rural sector can get a wage rate wR and a government subsidy g1 N 0. If a rural-hukou worker is employed in the urban unskilled sector, he becomes a rural migrant worker and gets a wage rate wU and a government subsidy g2 N 0. If an urban-hukou unskilled worker is employed in the urban unskilled sector, he gets a wage rate wU and a government subsidy g3 N 0. If an urban-hukou skilled worker is employed in the urban skilled sector, he gets a wage rate wS and a government subsidy g3 N 0. Here, g3 N g2, which reflects the fact that there exists discrimination against rural migrant workers due to the hukou system. Our setting reflects the fact that rural migrant workers usually get less public services than city residents in China. For example, comparing to urban residents, rural migrant workers cannot get equal treatment in social security coverage, the education of their children and so on. According to Bao et al. (2011, p.564), “Access to public schools, health services, low-cost housing, and attractive jobs by those who do not have local registration (Hukou) is often limited.” To measure the strength of hukou system reforms, we have: g ¼ g 3 −g 2 :

ð4Þ

So a larger (resp. smaller) g implies that the strength of hukou system reforms is smaller (resp. larger). To concentrate on our main topic, we take g1 and g3 as exogenously determined, but treat g2 as an endogenous variable.1 g is a policy variable that is controlled by the government. Through hukou system reforms, the government can reduce g, and thus decrease the barriers for rural migrant workers. Although hukou system reforms are multi-dimensional, reducing discrimination in the sense of public services is a major dimension. So, it is reasonable for us to use g to depict the strength of hukou system reforms. Since rural labor can choose to work in the rural sector or the urban unskilled sector. When a rural worker makes a decision, he will compare his total expected payoffs, which includes corresponding wage rates and subsidies. If the total expected payoff of becoming a rural migrant worker is higher, he will enter the urban unskilled sector. Otherwise, staying in the rural sector will be more attractive. Thus, in equilibrium, it is indifferent for rural labor to work in the rural sector or in the urban unskilled sector, which yields the rural-urban migration equilibrium condition as follows: wU þ g 2 ¼ wR þ g 1 ;

ð5Þ

where the left-hand side is the total expected payoff of being a rural migrant worker, while the right-hand side is the total expected payoff of staying in the rural sector. In addition, the full employment of economic endowments yields: aSX X ¼ LUS ;

ð6Þ

1 According to institutional facts in China, we can easily know that g2 b g1 b g3. This shows that rural migrant workers get a least subsidy in the sense of public services adhering to the hukou system. In Subsection 4.1, we will provide two illustrative tables to support this relationship.

J. Pi, P. Zhang / China Economic Review 41 (2016) 90–103

93

aUY Y ¼ LUU þ LRT ;

ð7Þ

aUZ Z ¼ LRU −LRT ;

ð8Þ

aKX X þ aKY Y ¼ K;

ð9Þ

aTZ Z ¼ T;

ð10Þ

where LUS, LUU, LRU , K, and T are the total amounts of urban skilled labor, urban unskilled labor, rural labor, capital and land, respectively. LRT is the total quantity of rural migrant workers. So far, the basic general equilibrium model with full employment has been constructed. Eqs. (1)–(10) determine ten endogenous variables, wS, wU, wR, r, τ, X, Y, Z, LRT, and g2. g is the policy variable, which is controlled by the government. Other variables are exogenously determined. Next, we will solve the economic system above to implement a comparative static analysis on how hukou system reforms affect skilled-unskilled wage inequality. Substituting Eqs. (4), (5), (6), (7), (8), and (10) into Eq. (9), and substituting Eq. (5) into Eq. (3), totally differentiating Eqs. (1)–(3) and (9), and rewriting the results into the matrix form, we obtain: 0

θSX B 0 B @ 0 wR λKX λUY σ X

10 1 0 1 0 θKX 0 ŵ S CB ŵ C B C 0 θKY 0 CB U C ¼ B Cĝ ; A@ r̂ A @ A gθUZ 0 wR θTZ −B −wR λKY λUZ σ Z gλUZ λKY σ Z τ̂

0 θUY wU θUZ A

ð11Þ

where A = λKY(wRλUYσY + wUλUZσZ) N 0, and B = wRλUY(λKXσX + λKYσY) N 0. θij(i = S, U, K, T; j = X, Y, Z, I) represents the distributive share of factor i employed in sector j (e.g., θSX ¼ aSXp wS ). σj(j = X, Y, Z, I) indicates the substitution elasticity of corresponding labor X

(e.g., skilled labor) and capital (or land) in sector j. λij(i = U, K; j = X, Y, Z, I) is the allocative share of factor i employed in sector j (e.g., λUY ¼

aUY Y ). LUU þLRU

S The notation “^” denotes the relative change in a variable (e.g., ŵ S ¼ dw wS ). Here, it should be noted that the

notations above is in accordance with Jones (1965, 1971). At the beginning, we will judge the sign of the determinant of the coefficient matrix of Eq. (11) (denoted as Δ1). The economic system constructed above is locally stable and exists a unique solution, if and only if Δ1 has an unambiguous non-zero sign. Because Eq. (11) is essentially a linear equation system, the conditions that ensure the stability and the existence of a unique solution of linear equation system can be used in Eq. (11). By matrix calculation and simplification, we have: 2

2

Δ1 ¼ wR λKX λUY θTZ θUY σ X þ wR λKY λUY θSX θTZ σ Y þ wR wU λKY λUZ θKY θSX σ Z N0; where Δ1 is unambiguously positive, which confirms that the economic system above is stable and has a unique solution. Now we establish Proposition 1 to illustrate how hukou system reforms generate an impact on skilled-unskilled wage inequality. Proposition 1. : In a three-sector economy with full employment, an increase of the strength of hukou system reforms will reduce the skilled-unskilled wage inequality if the urban skilled sector is more capital intensive than the urban unskilled sector, and expand the skilled-unskilled wage inequality if the urban skilled sector is less capital intensive than the urban unskilled sector. Proof: Using the Cramer's rule to solve Eq. (11), we obtain:

ŵ S gwR λKY λUZ θKX θUY σ Z ¼ N0; Δ1 ĝ ŵ U gwR λKY λUZ θKY θSX σ Z ¼ N0: ĝ Δ1 Thus the skilled-unskilled wage inequality can be expressed as: ŵ S −ŵ U gwR λKY λUZ ðθKX −θKY Þσ Z ¼ : ĝ Δ1 ̂

̂

U U Therefore, if θKX N θKY, then wS −w N 0; and if θKX b θKY, then wS −w b 0. ■ ĝ ĝ The economic intuition behind Proposition 1 can be explained as follows. When the government increases the strength of hukou system reforms, rural labor will find that becoming a rural migrant worker is more profitable. As a result, more rural people ̂

̂

94

J. Pi, P. Zhang / China Economic Review 41 (2016) 90–103

are attracted into the urban unskilled sector. Thus the marginal productivity of unskilled labor employed in the urban unskilled sector will fall, and the value of marginal product of unskilled labor will also fall as the price of the final product is exogenous. So the wage rate of unskilled labor in the urban unskilled sector will decrease. In addition, more unskilled workers employed in the urban unskilled sector will increase the marginal productivity of capital employed in this sector. Since the price of the final product remains unchanged, the value of marginal product of capital in this sector will increase. As a consequence, the urban unskilled sector is willing to pay a high interest rate in order to attract more capital to flow into this sector. So the amount of capital employed in the urban unskilled sector will increase, while that employed in the urban skilled sector will decrease. Consequently, the interest rate in the economy will rise. For the urban skilled sector, less capital employed in this sector will reduce the marginal productivity of skilled labor employed in this sector, and thus reduce the value of marginal product since the price of the final product remains unchanged. As a result, the wage rate of skilled labor will fall. If the urban skilled sector is more capital intensive than the urban unskilled sector (i.e., θKX N θKY), the decline of the wage rate of skilled labor employed in the urban skilled sector is more serious than that of unskilled labor employed in the urban unskilled sector. Thus the skilled-unskilled wage inequality will be narrowed down. Otherwise, if the urban skilled sector is less capital intensive than the urban unskilled sector (i.e., θKX b θKY), the decline of the wage rate of skilled labor employed in the urban skilled sector is less serious than that of unskilled labor employed in the urban unskilled sector, which expands skilled-unskilled wage inequality. 3. The extended models In this section, we will separately extend the basic model by introducing the urban endogenous minimum wage and an informal sector, respectively. 3.1. Economy with the urban endogenous minimum wage In this subsection, we will relax the full employment assumption in the basic model and introduce the urban endogenous minimum wage and urban unemployment, which are the typical characteristics in China. Now the wage rate of the urban unskilled sector is determined by the endogenous minimum wage.2 As we know, the endogenous minimum wage is influenced by labor protection and the government's willingness to reduce unemployment. It is in this sense that the endogenous minimum wage will not be in force in the urban skilled sector and the rural sector.3 In addition, though there exists the minimum wage in the urban unskilled sector, urban unemployment only exists among rural migrant workers. The jobs of urban unskilled labor are better protected by the government so that they will not lose their jobs. Such a treatment is greatly different from that of rural migrant workers, which reflects the discrimination against rural migrant workers. Here it is worth pointing out that such a setting of the unskilled labor market in developing countries is prevalent in the existing literature (e.g., Beladi, Chakrabarti, & Marjit, 2010; Chaudhuri, 2008). The difference is that we assume that unemployment only exists among rural migrant workers, which can capture the reality of China to some degree. Denoting the Harris-Todaro type unemployment rate of rural migrant workers as λ (see Harris & Todaro, 1970),4 we can rewrite the market clearing condition Eq. (7) for the urban unskilled sector as: aUY Y ¼ LUU þ

LRT : 1þλ

ð12Þ

The reason why there exists the endogenous minimum wage is that labor protection and the government's willingness to reduce unemployment will play an important role in determining the minimum wage. Similar to Pi and Zhou (2012), the urban endogenous minimum wage can be expressed as: wU ¼ wU ðwR ; λ; V Þ;

ð13Þ

where V is exogenously determined and represents the efficiency of the local government's labor protection.5 In addition, we aswR ∂wU U U U U N0, ∂w b0, ∂w N0, eR ¼ w  ∂w N0, and eλ ¼ wλU  ∂w b0, which are consistent with the existing literature (see e.g., Calvo, sume that ∂w ∂wR ∂λ ∂V ∂λ U R 1978; Pi & Zhou, 2012; Stiglitz, 1974; Yabuuchi & Chaudhuri, 2007). The economic intuition behind such a setting is clear and reasonable. Because rural migrant workers may be unemployed in the urban area, when rural labor decides whether to migrate to the urban area, he should take the probability of unemployment into consideration. Thus the rural-urban migration equilibrium 2

When the minimum wage is determined exogenously, we can find that the skilled-unskilled wage inequality will remain unchanged. The wage rates of the urban skilled sector and the rural sector are the outcomes of perfect competition, so they are equal to the corresponding values of marginal products. However, the endogenous minimum wage is usually higher than the value of marginal product. 4 The Harris-Todaro type unemployment rate of rural migrant workers can be understood in the sense of the probability that a typical peasant with a rural hukou cannot find a job in the urban unskilled sector. It has nothing to do with whether migrants stay in urban cities or go back to rural areas if they have no jobs. Thank two anonymous reviewers for reminding us to clarify this point. 5 In China, trade unions don't play a role as their counterparts in developed countries. Their role is replaced by local governments. The minimum wages are endogenously adjusted by local governments according to jurisdictional conditions. 3

J. Pi, P. Zhang / China Economic Review 41 (2016) 90–103

95

condition Eq. (5) will be replaced by: wU þ g 2 ¼ ðwR þ g 1 Þð1 þ λÞ:

ð14Þ

So far, the extended general equilibrium model with the urban endogenous minimum wage has been constructed. Eqs. (1)–(4), (6), (8)–(10), and (12)–(14) determine eleven endogenous variables, wS, wU, wR, r, τ, X, Y, Z, λ, LRT, and g2. g is still a policy variable, which is controlled by the government. Other variables are exogenously determined. Next, we will solve the economic system with the urban endogenous minimum wage in order to undertake a comparative static analysis on how hukou system reforms affect wage inequality. Substituting Eq. (4) into Eq. (14), totally differentiating Eqs. (1)–(3), (6), (8)–(10), and (12)–(14), and rewriting the results into the matrix form, we obtain: 0

0 0 0 0 0 1

B B B B B B B B B B B B 0 B B 0 B @λ

KX

0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

1

0

−F

0 λKY 0

1 0 1

G 0 0

0 0 0 −eλ −C 0 λ F 1þλ 0 0 0

0 0 −θUZ −eR −wR ð1 þ λÞ 0

−θKX −θKY 0 0 0 θKX σ X

−θKY σ Y

0

θKY σ Y

0

0 θUY λKY σ Y 0

−θTZ σ Z 0 θUZ σ Z

0 −D 0

θTZ σ Z 0 −θUZ σ Z

−θSX 0 0 0 0 −θKX σ X

0 −θUY 0 1 wU 0

0 0 θSX λKX σ X 0

where C =(g1 + wR)λ N 0, D = θSXλKXσX +θUYλKYσY N 0, F ¼

LRT LRT þð1þλÞLUU

N0, and G ¼

0 0 −θTZ 0 0 0

LRT LRU −LRT

10

1 0 1 ^ 0 CB X B0C ^ CB Y C B C CB ^ C B 0 C CB Z C B C CB ^ C B C CB LRT C B 0 C C CB B C CB λ ^ C C ¼ B g Cg^; CB C B0C CB w B C CB ^^ S C B0C CB w U C B C CB ^ C C 0C CB w R C B C C@ ^ A B @0A A r 0 τ^

ð15Þ

N0.

At the beginning, we will judge the sign of the determinant of the coefficient matrix of Eq. (15) (denoted as Δ2). Unfortunately, the sign of Δ2 cannot be judged by direct calculation. With the help of the dynamic adjustment process, the local stability of the extended model in this subsection can be achieved if Δ2 N 0 (see Appendix A). Now we will establish Proposition 2 to illustrate how hukou system reforms exert their effects on skilled-unskilled wage inequality. Proposition 2. : In a three-sector economy with the urban endogenous minimum wage, (i) if the elasticity of the urban minimum wage with respect to urban unemployment is large enough relative to the elasticity of the urban minimum wage with respect to the wage rate of the rural sector, an increase of the strength of hukou system reforms will generate almost the same impact on skilled-unskilled wage inequality as that in Proposition 1; and (ii) if the elasticity of the urban minimum wage with respect to urban unemployment is small enough relative to the elasticity of the urban minimum wage with respect to the wage rate of the rural sector, an increase of the strength of hukou system reforms will reduce the skilled-unskilled wage inequality when the urban skilled sector is less capital intensive than the urban unskilled sector, and will raise the skilled-unskilled wage inequality when the urban skilled sector is more capital intensive than the urban unskilled sector. Proof: Using the Cramer's rule to solve Eq. (15), we obtain: ^S FgλKY θKX θUY ðeλ ð1 þ λÞσ Z þ eR λθTZ GÞ w ¼− ; g ð1 þ λÞΔ2 ^U FgλKY θKY θSX ðeλ ð1 þ λÞσ Z þ eR λθTZ GÞ w ¼− : ð1 þ λÞΔ2 ĝ Thus the skilled-unskilled wage inequality can be expressed as: ^ S −ŵ U FgλKY ðθKX −θKY Þðeλ ð1 þ λÞσ Z þ eR λθTZ GÞ w ¼− : ð1 þ λÞΔ2 ĝ ̂

λθTZ G U U  eR , if θKX N θKY, then wS −w N0; and if θKX b θKY, then wS −w b0; and (ii) suppose that Therefore, (i) suppose that −eλ N ð1þλÞσ ĝ ĝ Z 6 ŵ S −ŵ U ŵ S −ŵ U λθTZ G  e , if θ b θ , then N0; and if θ N θ , then b0. ■ −eλ b ð1þλÞσ R KX KY KX KY ĝ ĝ Z The economic mechanism behind Proposition 2 is as follows. When the government increases the strength of hukou system reforms, rural labor will find that becoming rural migrant workers is more profitable. As a result, more rural people will swarm into the urban area. On the one hand, since less rural people work in the rural sector, the marginal productivity of rural labor employed in the rural sector will increase. With the fixed price of the agricultural good, the value of marginal product of rural labor will rise. Thus the ̂

6

̂

Remember that eλ b 0 and eR N 0. We compare these two kinds of elasticities by their absolute values.

̂

96

J. Pi, P. Zhang / China Economic Review 41 (2016) 90–103

wage rate of the rural sector will increase. According to the determination mechanism of the urban minimum wage, the urban minimum wage will tend to increase, and the incremental wage rate is dependent on eR. On the other hand, since there exists the restriction of the urban minimum wage, it is profitable for the urban unskilled sector to employ more rural migrant workers only when this sector can be allowed to pay a lower wage rate for unskilled labor. Thus, more rural migrant workers increase the urban unemployment rate. On the basis of the determination mechanism of the urban minimum wage, the urban minimum wage will tend to decrease, and the descending wage rate is dependent on eλ. Therefore, if eλ is large enough relative to eR, the urban minimum wage will go down, and more rural migrant workers will be employed. So the following economic explanations are similar to what we have discussed behind Proposition 1. On the other hand, if eλ is small enough relative to eR, the urban minimum wage will increase. As a consequence, less rural migrant workers will be employed, which will reduce the marginal product of capital employed in this sector and thus make this sector willing to pay a lower interest rate. So a portion of capital flows into the urban skilled sector, and the interest rate in the economy will decrease. More capital employed in the urban skilled sector will increase the marginal productivity of skilled labor. So the skilled wage rate will rise when the value of marginal product of skilled labor increases. If the urban skilled sector is less capital intensive than the urban unskilled sector (i.e., θKX b θKY), the increase of the wage rate of skilled labor employed in the urban skilled sector will be less than that of unskilled labor employed in the urban unskilled sector. Thus the skilled-unskilled wage inequality will be reduced. Otherwise, if the urban skilled sector is more capital intensive than the urban unskilled sector (i.e., θKX N θKY), the increase of the wage rate of skilled labor employed in the urban skilled sector will be greater than that of unskilled labor employed in the urban unskilled sector. Thus the skilled-unskilled wage inequality will be expanded. 3.2. Economy with an urban informal sector In this subsection, we will introduce an urban informal sector into our basic model. The urban informal sector is another crucial characteristic in China. The importance of the urban informal sector has been widely analyzed by the existing literature (e.g., Chandra & Khan, 1993; Chaudhuri, 2000; Chaudhuri, Yabuuchi, & Mukhopadhyay, 2006; Grinols, 1991; Gupta, 1993, 1997). In general, the urban informal sector provides opportunities for peddlers, small business owners, housekeepers, and others, which can support their daily life and their family. We assume that only rural migrant workers may work in the urban informal sector. When they work in the urban informal sector, they cannot get any subsidy in the sense of public services from the government. Urban skilled labor and urban unskilled labor who have an urban hukou are well protected by the government so that they will surely work in the corresponding formal sectors. Here we also assume that the job opportunities in the urban unskilled sector for rural migrant workers are limited and exogenously determined (denote the amount as LUR). Rural migrant workers who cannot be employed in the urban unskilled sector will choose to work in the urban informal sector in order to wait for a job in the urban unskilled sector, or go back to the rural area. Such settings can be referred to Grinols (1991), Chandra and Khan (1993), Gupta (1997) and others.7 Furthermore, the urban informal sector also employs capital KI from the competitive capital market in the production, and the urban informal sector is perfectly competitive. Denoting total rural migrant workers in this sector as LUI, we can write the production function as I = F I(LUI, KI), where I is the total output of this sector and the strict quasi-concavity and linear homogeneity are satisfied. Profit maximization of the urban informal sector yields: pI ¼ aUI wI þ aKI r;

ð16Þ

where pI is the exogenous price of the final product in the urban informal sector. wI is the wage rate in this sector. Since rural migrant workers may work in the urban informal sector, when rural people decide whether to migrate to the urban area, they should take their expected payoffs into consideration. Thus the rural-urban migration equilibrium condition Eq. (5) will be replaced by: P ðwU þ g 2 Þ þ ð1−P ÞwI ¼ wR þ g 1 ;

ð17Þ

UR where P¼L LRT N0 is the probability that rural migrant workers can work in the urban unskilled sector. Here we assume that LRT NLUR , because if LRT ≤LUR rural migrant workers will surely work in the urban unskilled sector and no one will work in the urban informal sector, which has been discussed in the basic model. In addition, the full employment conditions Eqs. (7) and (9) will be replaced by:

7

aUY Y ¼ LUU þ LUR ;

ð18Þ

aKX X þ aKY Y þ aKI I ¼ K:

ð19Þ

There may be another situation that the urban informal sector and urban unemployment coexist (see e.g., Chaudhuri, 2000; Chaudhuri et al., 2006).

J. Pi, P. Zhang / China Economic Review 41 (2016) 90–103

97

The full employment condition of the urban informal sector yields: aUI I ¼ LRT −LUR :

ð20Þ

So far, the extended general equilibrium model with an urban informal sector has been constructed. Eqs. (1)–(4), (6), (8), (10), and (16)–(20) determine twelve endogenous variables, wS, wU, wI, wR, r, τ, X, Y, I, Z, LRT, and g2. g is still a policy variable, which is controlled by government. Other variables are exogenously determined. Next, we will solve the economic system with an urban informal sector to explore how hukou system reforms influence the skilled-unskilled wage inequality. Substituting Eq. (4) into Eq. (17), totally differentiating Eqs. (1)–(3), (6), (8), (10) and (16)–(20), and rewriting the results into the matrix form, we obtain: 0

0 B 0 B B 0 B B 0 B B 0 B B 1 B B 0 B B 0 B B 0 B @λ KX 0

0 0 0 0 0 0 1 0 0 λKY 0

0 0 0 0 0 0 0 1 0 λKI 0

−θSX 0 0 0 0 −θKX σ X 0 0 0 λKX θSX σ X 0

0 0 0 0 0 0 0 0 0 −PJ 0 0 0 0 0 −M 1 N 0 0 1 0

0 −θUY 0 0 PwU 0 −θKY σ Y 0 0 λKY θUY σ Y 0

0 0 −θUI 0 ð1−P ÞwI 0 0 −θKI σ I 0 λKI θUI σ I 0

0 0 0 −θUZ −wR 0 0 0 −θTZ σ Z 0 θUZ σ Z

where H =λKXθSXσX + λKYθUYσY + λKIθUIσI N 0, J= (wU +g3) − (wI + g) N 0, M ¼

−θKX −θKY −θKI 0 0 θKX σ X θKY σ Y θKI σ I 0 −H 0 LRT LRT −LUR

10 1 0 1 ^ 0 0 X CB Y^ C B 0 C 0 CB C B C CB ^I C B 0 C 0 CB C B C B^ C B C −θTZ C CB Z C B 0 C CB ^L C B Pg C 0 CB RT C B C CB w C B Ĉ 0 CB ^ S C ¼ B 0 Cg; CB w C B C 0 ^ CB U C B 0 C CB w C B C 0 CB ^ I C B 0 C C B C Bw θTZ σ Z C ^ CB R C B 0 C A@ ^r A @ 0 A 0 0 −θUZ σ Z τ^

N0, and N ¼

LRT LRU −LRT

ð21Þ

N0.

Firstly, we will judge the sign of the determinant of the coefficient matrix of Eq. (21) (denoted as Δ3). Unfortunately, the sign of Δ3 cannot be judged by direct calculation. With the help of the dynamic adjustment process, the local stability of the extended model in this subsection can be achieved if Δ3 b 0 (see Appendix B). Now we will establish Proposition 3 to summarize the main results. Proposition 3. : In a four-sector economy with an urban informal sector, an increase of the strength of hukou system reforms will generate almost the same impact on skilled-unskilled wage inequality as that in Proposition 1. Proof: Using the Cramer's rule to solve Eq. (21), we obtain: ŵ S gMPλKI θKX θUI θUY σ Z ¼− N0; Δ3 ĝ

ŵ U gMPλKI θKY θSX θUI σ Z ¼− N0: Δ3 ĝ Thus the skilled-unskilled wage inequality can be expressed as: ŵ S −ŵ U gMPλKI θUI ðθKX −θKY Þσ Z ¼− : Δ3 ĝ U U N0; and if θKX b θKY, then wS −w b0. ■ Therefore, if θKX N θKY, then wS −w ĝ ĝ The economic mechanism behind Proposition 2 is as follows. When the government increases the strength of hukou system reforms, more rural people are attracted to flow into the urban area. However, the urban unskilled sector can only employ a certain quantity of rural migrant workers. So, more rural migrant workers will reduce the probability of working in the urban unskilled sector. That is to say, more rural migrant workers will be employed in the urban informal sector and wait for the opportunities to work in the urban unskilled sector. As a consequence, the wage rate of the urban informal sector will decrease. At the same time, more rural migrant workers employed in the urban informal sector will increase the marginal productivity of capital employed in this sector, which finally leads to the increase of the interest rate in the economy and the decrease of capital employed in both the urban unskilled sector and the urban skilled sector. Thus, the marginal productivity of skilled labor and unskilled labor employed in the corresponding sectors will decrease. Due to the fixed price of the final product, the wage rates of the urban skilled sector and the urban unskilled sector will fall. Here, economic explanations are similar to those behind Proposition 1. If the urban skilled sector is more capital intensive than the urban unskilled sector (i.e., θKX N θKY), the skilled-unskilled wage inequality will be reduced. Otherwise, if the urban skilled sector is less capital intensive than the urban unskilled sector (i.e., θKX b θKY), the skilled-unskilled wage inequality will be expanded. ̂

̂

̂

̂

98

J. Pi, P. Zhang / China Economic Review 41 (2016) 90–103

Table 1 The coverage of five insurances for urban workers and migrants in 2014.Data source: China's National Bureau of Statistics and the Ministry of Human Resources and Social Security.

Urban workers Migrants Gap

Pension insurance

Medical insurance

Unemployment insurance

Employment injury insurance

Maternity insurance

65.0% 16.7% 48.3%

53.5% 17.6% 35.9%

43.4% 10.5% 32.9%

52.5% 26.2% 26.3%

43.4% 7.8% 35.6%

Note: The retirees can also receive the pension insurance and medical insurance, but we don't mention them in the table. In order to save space, the data from 2009 to 2013 is not provided since the change of the gap is small.

4. The empirical discussions In this section, we will provide some empirical discussions for our theoretical analyses. Firstly, we discuss the cohering welfare for the hukou system, which offers a more detailed support for g2 b g1 b g3 and g. Secondly, we assess the capital intensities of the urban skilled and unskilled sectors in China, which helps us to draw some more definite conclusions. Thirdly, we discuss the urban minimum wage and its elasticities in China, which gives the related justification and judgment to Subsection 3.1. Fourthly, we analyze the applicability of our theoretical models to Chinese economy.

4.1. The cohering welfare of the hukou system In China, the hukou system coheres tightly with the allocation of social welfare. For rural residents who have a rural hukou, they usually possess the rights to use a piece of residential land and farmland. They can also enjoy the government's subsidy to agriculture. For urban residents who have an urban hukou, they can enjoy the comprehensive benefits in job, education for children, social security and so on, although they cannot possess the usufruct of residential land and agricultural land. From Table 1, we can see that the coverage of five insurances for urban-hukou workers is relatively high. As for migrants, on the one hand, they partly lose the benefits in the rural region (e.g., the local and central governments' subsidies to agriculture). On the other hand, they can hardly get access to social welfare in the urban region like urban residents with an urban hukou. Some jobs are limited to urban-hukou residents and so migrants are excluded (Meng & Manning, 2010; West & Zhao, 2000). The children of migrants usually should go back the registered residence to take the college entrance examination. Comparing to urban workers with an urban hukou, social security for migrants is very limited (see Table 1). It is convincing that there are different welfare levels for migrants in different regions, since there exists unbalanced development in China (e.g., the eastern is better developed comparing to the middle and the western).8 We will observe the coverage of five insurances in the eastern, the middle and the western of China.9 From Table 2, we know the coverage is higher in the eastern than the middle and the western. However, there exists a great gap of coverage between migrants and urban workers. It is always hard to access social security for migrants, and this is a common phenomenon in China. To promote equality between migrants with a rural hukou and urban residents with an urban hukou, the central and local governments in China have implemented some reforms on the hukou system. These reforms mainly focus on two aspects. The first aspect is about how migrants can get an urban hukou. In the hukou system reforms of 2001 and 2014, the central government relaxed the constraints for migrants to obtain an urban hukou in the small and middle towns, but the restrictions in the semilarge and large cities are still strict. In some large cities (e.g., Shanghai, Guangzhou and Shenzhen), migrants can get an urban hukou if they can accrue a certain point. The point is dependent on the working experience, the education or skill background, the engagement in social insurances, and so on. The second aspect of hukou system reforms is about the decrease of the connection between hukou and social welfare. In 2008, China enacted the new Labour Contract Law and one of the purposes of the law is to increase the fair treatment for migrants. In 2015, the central government formally abolished the temporary residence permit, and replaced it with the residence permit. The latter bears more social welfare functions than the former. If migrants have the residence permit for a certain number of years, they can enjoy most of urban welfare even if they have no urban hukou. Take Shenzhen for example. Migrants who have the residence permit can let their children receive the compulsory education in Shenzhen. Besides, migrants who have the residence permit for 10 years will be accepted in the system of social security in Shenzhen. Guangdong, one of the provinces with most migrants in China, has promulgated several policies on how to realize that the children of migrants can take part in the college entrance examination in Guangdong instead of their domicile province. These reforms indeed make the access to urban welfare less relevant to hukou, although there are still some constraints on migrants to share identical urban welfare.

8

We would like to thank an anonymous reviewer for encouraging us to consider the different treatments for migrants in different regions. The eastern region includes Beijing, Tianjin, Hebei, Liaoning, Shanghai, Jiangsu, Zhejiang, Fujian, Shandong, Guangdong and Hainan. The middle region consists of Shanxi, Jilin, Heilongjiang, Anhui, Jiangxi, Henan, Hubei and Hunan. The western region includes Inner Mongolia, Guangxi, Chongqing, Sichuan, Guizhou, Yunnan, Tibet, Shaanxi, Gansu, Qinghai, Ningxia and Xinjiang. 9

J. Pi, P. Zhang / China Economic Review 41 (2016) 90–103

99

Table 2 The coverage of five insurances for urban workers and migrants in the eastern, middle and western China in 2014.Data source: China's Ministry of Human Resources and Social Security and China Labour Statistical Yearbook.

The eastern The middle The western

Urban workers Migrants Urban workers Migrants Urban workers Migrants

Pension insurance

Medical insurance

Unemployment insurance

Employment injury insurance

Maternity insurance

85.2% 20.0% 60.6% 10.7% 55.8% 11.4%

69.6% 20.4% 48.7% 11.8% 49.1% 13.6%

56.3% 12.4% 40.6% 6.9% 38.6% 7.7%

67.8% 29.8% 51.2% 17.8% 44.5% 21.9%

56.5% 9.1% 39.2% 4.9% 39.9% 5.8%

Note: The eastern region consists of Beijing, Tianjin, Hebei, Liaoning, Shanghai, Jiangsu, Zhejiang, Fujian, Shandong, Guangdong and Hainan. The middle region includes Shanxi, Jilin, Heilongjiang, Anhui, Jiangxi, Henan, Hubei and Hunan. The western region consists of Inner Mongolia, Guangxi, Chongqing, Sichuan, Guizhou, Yunnan, Tibet, Shaanxi, Gansu, Qinghai, Ningxia and Xinjiang.

4.2. The capital intensities of the urban skilled and unskilled sectors in China In this subsection, we will provide some empirical evidences to show that the urban skilled sector is in general more capital intensive than the urban unskilled sector in China. Our assessment is based on the available data from 2010 to 2013. In order to identify whether a sector is the urban skilled sector or the urban unskilled sector, we borrow from the experience of Galiani and Sanguinetti (2003), who take educational attainment of labor as the key characteristic to classify skilled labor and unskilled labor. They define the unskilled group as those who don't finish high school, and the semi-skilled group as those who have finished high school, and the skilled group as those who have obtained a tertiary degree. In this paper, we define the urban unskilled sector as a sector that is composed of the industries where the average education level is at most high school, and the urban skilled sector as a sector that is composed of the industries where the average education level is above high school. Different from Galiani and Sanguinetti (2003), we classify the semi-skilled group into the unskilled group. We use Chinese General Social Survey (CGSS) to promote the empirical division between the urban skilled sector and the urban unskilled sector. CGSS has finished the first wave survey (from 2003 to 2008), and now the second wave (from 2010 to 2019) is being implemented. The second wave survey data from 2010 to 2013 are available, on the basis of which we calculate the average education year from 2010 to 2013 across industries. Here, we don't employ the data in the first wave in order to maintain the consistency. The capital intensity can be measured by the ratio of capital stock to gross output, or by the capital stock per labor. The latter is very straightforward. The insight of the former is derived from the definition of θKX and θKY. With the help of China Statistical Yearbook, we estimate the capital stock across industries from 2010 to 2013 with the depreciation rate of 10% and the constant-price in 2004.10 Besides, both average gross outputs (constant-price in 2004) and average total labor across industries are derived from China Statistical Yearbook. According to these raw or estimated data, we can calculate the capital intensities of the urban skilled sector and the urban unskilled sector from 2010 to 2013. Table 3 shows the empirical results of the classification and the capital intensities of the skilled and unskilled sectors. No matter which method is used to estimate the capital intensity, we can find that in China the urban skilled sector is more capital intensive than the urban unskilled sector. 4.3. The urban minimum wage and its elasticities in China In China, the minimum wage was first introduced in 1993. However, its implementation is not effective until the promulgation of Minimum Wage Regulations by the Ministry of Labor and Social Security in 2004. In addition, the minimum wage is only applicable in the urban region, which is consistent with our first extended model. There are several empirical studies concerning how the Chinese minimum wage will generate an impact on employment. These studies show that the minimum wage may exert a more significantly negative impact on employment as time goes by (i.e., the elasticity of the urban minimum wage with respect to urban unemployment tends to become larger). On the one hand, Ni, Wang, and Yao (2011) employ the data from 2000 to 2005 to support that the minimum wage will not significantly do harm to employment overall. Wang and Gunderson (2011) separately investigate the impact across the eastern, middle and western regions in China with the data from 2000 to 2007, and find that the effect is relatively small and not very significant. On the other hand, using the survey data in 2007 and 2008, Ding (2010) draws the conclusion that the minimum wage generates a significantly negative impact on employment of migrant labor in 2008, comparing to that in 2007. Ding (2010) also shows that the impact on employment of urban-hukou residents is not significant due to the dual employment system. Such a characteristic has been embodied in one of our extended models. Comparing to the urban sectors, the wage rate in the rural sector is relatively low in the 2000s, and thus such a relatively low wage rate may not influence the making of the minimum wage policy. Knight, Deng, and Li (2011) show that in the China Household Income Project (CHIP) in 2007,11 migrants were asked how much they would have earned if they had remained in the rural region. It is found that the ratio of the average migrant wage rate to the average counterfactual rural income was 2.43. The great 10 11

Similar to Gong and Xie (2004) and Zhang, Wu, and Zhang (2004), we adopt the depreciation rate of 10%. The CHIP in 2007 is the latest that can be available.

100

J. Pi, P. Zhang / China Economic Review 41 (2016) 90–103

Table 3 The classification of the unskilled and skilled sectors and their corresponding capital intensities from 2010 to 2013. Data source: Authors' own calculation based on the data collected from Chinese General Social Survey and China Statistical Yearbook. Sector

Industry

Capital intensity

Agriculture, forestry, animal husbandry and fishery Construction Hotels and catering services Service to households, repair and other services Wholesale and retail trades Manufacturing Mining Urban skilled sector Transport, storage and post Management of water conservancy, environment and public facilities Leasing and business services Real estate Production and supply of electricity, heat, gas and water Culture, sports and entertainment Public management, social security and social organization Health and social service Financial intermediation Education Information transmission, software and information technology Scientific research and technical services

Urban unskilled sector

The ratio of capital stock to gross output

Capital stock per labor, thousand yuan

1.79

567.71

4.28

866.87

Note: The classification of industries is in accordance with China Statistical Yearbook, and the industries are under the title of the non-rural sector in the yearbook. The industry whose average education level is at most (resp. above) high school will be grouped in the unskilled (resp. skilled) sector. In the estimation of the capital intensity, the constant-price is in terms of 2004, and the capital stock is with the depreciation rate of 10%.

wage gap between rural and urban areas encourages rural labor to migrate to the urban sector, and thus migrants are oversupplied indeed. However, although whether the Lewis turning point has emerged is inconclusive (e.g., Meng & Bai, 2007; Zhang, Yang, & Wang, 2011), the competition for rural labor between urban and rural regions will become more and more intensive. The urban sector may gradually lose its attraction to migrants in future. As a result, the wage rate of the rural sector should be gradually taken into consideration when the government makes the minimum wage policy. The elasticity of the urban minimum wage with respect to the wage rate of the rural sector will become larger and larger. 4.4. The application to China There are many studies related to the hukou system and rural-urban inequality in China (see e.g., Hertel & Zhai, 2006; Liu, 2005; Meng, 2012; Yang, 1999), but only a few of them indirectly address the issue of hukou system and skilled-unskilled wage inequality in China. For example, Meng (2012) investigates the wage inequality among urban labor and finds that the inequality has increased greatly. He shows that the ratio of the real annual wage for the 90th to 10th decile increased from 3 to 6 between 1988 and 2009. He also shows that such a ratio declined between 2000 and 2002 and between 2008 and 2009. Although Meng (2012) doesn't directly analyze the skilled-unskilled wage inequality, it is reasonable to use the 90th to 10th decile in the urban region as a proxy variable to reflect the skilled-unskilled wage gap in China. On the one hand, the wage for the 90th decile can be interpreted as the income of urban skilled labor and the 10th decile can be regarded as the earning of urban unskilled labor. The 90th to 10th decile is also a common index to measure inequality. On the other hand, the wage in the rural sector is usually too low, as we have mentioned in Subsection 4.3 that the ratio of the average migrant wage rate to the average counterfactual rural income was 2.43. Thus, the rural-urban inequality is not a good proxy variable to reflect the skilled-unskilled wage inequality. The 90th to 10th decile shows that the skilled-unskilled wage inequality was expanded from 1988 to 2009 but slightly narrowed down from 2000 to 2002 and from 2008 to 2009 in China. Since we have discussed in Subsection 4.2 that the urban skilled sector is more capital intensive than the urban unskilled sector overall in China, in the basic model and the extended model with an informal sector we can infer that an increase of the strength of hukou system reforms will reduce the skilled-unskilled wage inequality. λ  θσTZZ  eR and As for the extended model with the minimum wage, the relevant conditions in Proposition 2 is −eλ N LRT  1þλ LRU −LRT

−eλ b

LRT LRU −LRT

λ  1þλ  θσTZZ  eR. According to CHIP in 2007 (see Knight et al., 2011), we can get

of Chinese economy, this value may become smaller and smaller. 12

migrants,

and it is relatively small (e.g.,

λ 1þλ

λ 1þλ

LRT LRU −LRT

¼ 0:28, and with the development

can be interpreted as the unemployment rate among

¼ 5%). So it is more likely that −eλ N

LRT LRU −LRT

λ  1þλ  θσTZZ  eR . Combining this condition

12 λ λ is the Harris-Todaro type unemployment rate, which is equal to the ratio of the amount of unemployment to the amount of employment. So 1þλ can be interpreted as the unemployment rate in the common sense.

J. Pi, P. Zhang / China Economic Review 41 (2016) 90–103

101

with the discussion of θKX N θKY in China, we can find that our first extended model with the minimum wage predicts an increase of the strength of hukou system reforms will reduce the skilled-unskilled wage inequality. 5. Concluding remarks This paper explores how hukou system reforms influence the skilled-unskilled wage inequality by building several general equilibrium models. In the basic model, we find that the wage inequality will be reduced if the urban skilled sector is more capital intensive than the urban unskilled sector when the government increases the strength of hukou system reforms. In the extended models, we separately introduce the endogenous minimum wage and the informal sector, and find that in both extended cases the main results of the basic model almost still hold. Future studies can extend our analysis in the following respects. Firstly, in this paper, an increase in the strength of hukou system reforms implies that rural migrant workers obtain more urban social welfare. We can use other variables to depict the strength of hukou system reforms if such variables have practical implications. Secondly, the public sector is very important in China, and thus we can divide the urban sector into the public sector and the private sector in future studies. Thirdly, there are many urban-hukou workers engaged in the urban informal sector in China. Hence, we should consider this point in the future research. Fourthly, there are several types of discrimination against rural migrant workers (e.g., discrimination in terms of the wage rate) (see Song, 2015), but this paper only analyze discrimination in the sense of public services adhering to the hukou system. We can take other types of discrimination (e.g., wage discrimination) into account. Fifthly, job search is an important and distinguishing feature in the real world, we can incorporate job search into our improved Harris-Todaro framework. Acknowledgements We thank two anonymous reviewers for their helpful comments and suggestions. Pi acknowledges the financial support provided by the Program for New Century Excellent Talents in University, the Fundamental Research Funds for the Central Universities, and the Collaborative Innovation Center for China Economy. Any remaining errors are our own. Appendix A. The dynamic adjustment process of the model with the urban endogenous minimum wage The dynamic adjustment process, consisting of the Marshallian quantity adjustment process and the Walrasian price adjustment process, is based on the idea of the excess demand function. Our methodology is in accordance with Beladi et al. (2008). According to the excess demand functions of the extended model in Subsection 3.1, the differential equations can be constructed as follows: X_ ¼ d1 ðpX −aSX wS þ aKX r Þ;

ðA1Þ

Y_ ¼ d2 ðpY −aUY wU þ aKY rÞ;

ðA2Þ

Z_ ¼ d3 ð1−aUZ wR þ aTZ τ Þ;

ðA3Þ

λ_ ¼ d4 ðwU −wU ðwR ; λ; V ÞÞ;

ðA4Þ

L_ RT ¼ d5 ðwU þ g 2 −ðwR þ g 1 Þð1 þ λÞÞ;

ðA5Þ

  _ S ¼ d6 aSX X−LUS ; w

ðA6Þ

   L _ U ¼ d7 aUY Y− LUU þ RT ; w 1þλ

ðA7Þ

   _ R ¼ d8 aUZ Z− LRU −LRT ; w

ðA8Þ

  r_ ¼ d9 aKX X þ aKY Y−K ;

ðA9Þ

  τ_ ¼ d10 aTZ Z−T ;

ðA10Þ

102

J. Pi, P. Zhang / China Economic Review 41 (2016) 90–103

where di N 0 (i = 1,2, … , 10) is the speed of adjustment. The notation “.” denotes the differentiation with respect to time (e.g., X_ ¼ dX ). The determinant of the Jacobian matrix of Eqs. (A1)–(A10) (denoted as Φ1) is as follows: dt

  0   0   0   0   0  Φ1 ¼ ε1  1    0   0    λKX  0

0 0 0 0 0 0

0 0 0 0 0 0

1

0 −F

0 λKY 0

0 0 0 0 0 0

1 0 1

G 0 0

0 0 0 −eλ −C 0 λ F 1þλ 0 0 0

10

where ε 1 ¼

∏ di pX pY LUS ðLUU þ

i¼1

−θSX 0 0 0 0 −θKX σ X

0 −θUY 0 1 wU 0

0 0 θSX λKX σ X 0

LRT ÞðL −LRT ÞK T 1 þ λ RU

wS wR rτλXYZLRT

0 0 −θUZ −eR −wR ð1 þ λÞ 0

−θKX −θKY 0 0 0 θKX σ X

−θKY σ Y

0

θKY σ Y

0

0 θUY λKY σ Y 0

−θTZ σ Z 0 θUZ σ Z

0 −D 0

θTZ σ Z 0 −θUZ σ Z

0 0 −θTZ 0 0 0

            ¼ ε 1 Δ2 ;         

N 0.

According to the Routh-Hurwitz theorem, the local stability can be achieved if Φ1 N 0, which implies that Δ2 N 0. Thus with the assumption that our economic system is locally stable, we need Δ2 N 0. Appendix B. The dynamic adjustment process of the model with an urban informal sector _ L_ RT , w _ U , r_ , and w _ I are as follows: The differential equations about I, İ ¼ d4 ðpI −ðaUI wI þ aKI r ÞÞ;

ðB1Þ

L_ RT ¼ d5 ðP ðwU þ g 2 Þ þ ð1−P ÞwI −ðwR þ g 1 ÞÞ;

ðB2Þ

   _ U ¼ d7 aUY Y− LUU þ LUR ; w

ðB3Þ

  r_ ¼ d9 aKX X þ aKY Y þ aKI I−K ;

ðB4Þ

   _ I ¼ d11 aUI I− LRT −LUR : w

ðB5Þ

The determinant of the Jacobian matrix of Eqs. (A1)–(A3), (A6), (A8), (A10), and (B1)–(B5) (denoted as Φ2) is as follows:   0   0   0   0   0  Φ2 ¼ ε2  1  0   0   0  λ  KX  0

0 0 0 0 0 0 1 0 0 λKY 0

0 0 0 0 0 0 0 1 0 λKI 0

0 0 0 0 0 0 0 0 0 −PJ 0 0 0 0 0 −M 1 N 0 0 1 0

−θSX 0 0 0 0 −θKX σ X 0 0 0 λKX θSX σ X 0

0 −θUY 0 0 PwU 0 −θKY σ Y 0 0 λKY θUY σ Y 0

0 0 −θUI 0 ð1−P ÞwI 0 0 −θKI σ I 0 λKI θUI σ I 0

0 0 0 −θUZ −wR 0 0 0 −θTZ σ Z 0 θUZ σ Z

−θKX −θKY −θKI 0 0 θKX σ X θKY σ Y θKI σ I 0 −H 0

  0   0   0  −θTZ   0  ¼ε Δ ; 0 2 3   0   0  θTZ σ Z   0  −θUZ σ Z 

11

where ε 2 ¼

∏ di pX pY pI LUS ðLUU þ LUR ÞðLRT −LUR ÞðLRU −LRT ÞK T

i¼1

wS wU wI wR rτXYIZLRT

N 0:

According to the Routh-Hurwitz theorem, the local stability can be achieved if Φ2 b 0, which implies that Δ3 b 0. Thus with the assumption that our economic system is locally stable, we need Δ3 b 0. References Afridi, F., Li, S. X., & Ren, Y. (2015). Social identity and inequality: The impact of China's hukou system. Journal of Public Economics, 123, 17–29. Anwar, S. (2008). Labour inflow induced wage inequality and public infrastructure. Review of Development Economics, 12(4), 792–802. Anwar, S., & Sun, S. (2015). Taxation of labour income and the skilled-unskilled wage inequality. Economic Modelling, 47, 18–22.

J. Pi, P. Zhang / China Economic Review 41 (2016) 90–103

103

Au, C. -C., & Henderson, J. V. (2006). How migration restrictions limit agglomeration and productivity in China. Journal of Development Economics, 80(2), 350–388. Bao, S., Bodvarsson, Ö. B., Hou, J. W., & Zhao, Y. (2011). The regulation of migration in a transition economy: China's hukou system. Contemporary Economic Policy, 29(4), 564–579. Beladi, H., Chakrabarti, A., & Marjit, S. (2010). Skilled-unskilled wage inequality and urban unemployment. Economic Inquiry, 48(4), 997–1007. Beladi, H., Chaudhuri, S., & Yabuuchi, S. (2008). Can international factor mobility reduce wage rate inequality in a dual economy? Review of International Economics, 16(5), 893–903. Bosker, M., Brakman, S., Garretsen, H., & Schramm, M. (2012). Relaxing Hukou: Increased labor mobility and China's economic geography. Journal of Urban Economics, 72(2–3), 252–266. Cai, F. (2011). Hukou system reform and unification of rural-urban social welfare. China & World Economy, 19(3), 33–48. Calvo, G. A. (1978). Urban unemployment and wage determination in LDCs, trade unions in the Harris–Todaro model. International Economic Review, 19(1), 65–81. Chan, K. W., & Buckingham, W. (2008). Is China abolishing the hukou system? China Quarterly, 195, 582–606. Chandra, V., & Khan, M. A. (1993). Foreign investment in the presence of an informal sector. Economica, 60(237), 79–103. Chaudhuri, S. (2000). Rural–urban migration, informal sector, urban unemployment, and development policies: A theoretical analysis. Review of Development Economics, 4(3), 353–364. Chaudhuri, S. (2008). Wage inequality in a dual economy and international mobility of factors: do factor intensities always matter? Economic Modelling, 25(6), 1155–1164. Chaudhuri, S., Yabuuchi, S., & Mukhopadhyay., U. (2006). Inflow of foreign capital and trade liberalization in a model with an informal sector and urban unemployment. Pacific Economic Review, 11(1), 87–103. Chaudhuri, S., & Yabuuchi, S. (2007). Economic liberalization and wage inequality in the presence of labor market imperfection. International Review of Economics and Finance, 16(4), 592–603. Ding, S. (2010). Employment effects of minimum wage regulation and cross effect of the employment contracts law. Social Sciences in China, 31(3), 146–167. Galiani, S., & Sanguinetti, P. (2003). The impact of trade liberalization on wage inequality: Evidence from Argentina. Journal of Development Economics, 72(2), 497–513. Gong, L., & Xie, D. (2004). Factor mobility and dispersion in marginal products: A case on China. Economic Research Journal (Jingji Yanjiu), 39(1), 45–53. Grinols, E. (1991). Unemployment and foreign capital: The relative opportunity costs of domestic labour and welfare. Economica, 58(229), 107–121. Gupta, M. R. (1993). Rural–urban migration, informal sector and development policies: A theoretical analysis. Journal of Development Economics, 41(1), 137–151. Gupta, M. R. (1997). Foreign capital and the informal sector: Comments on Chandra and Khan. Economica, 64(254), 353–363. Harris, R., & Todaro, M. (1970). Migration, unemployment, and development: A two-sector analysis. American Economic Review, 60(1), 126–142. Hertel, T., & Zhai, F. (2006). Labor market distortions, rural-urban inequality and the opening of China's economy. Economic Modelling, 23(1), 76–109. Jones, R. W. (1965). The structure of simple general equilibrium models. Journal of Political Economy, 73(6), 557–572. Jones, R. W. (1971). A three-factor model in theory, trade, and history. In J. Bhagwati (Ed.), Trade, Balance of Payments and Growth. Amsterdam: North-Holland. Knight, J., Deng, Q., & Li, S. (2011). The puzzle of migrant labour shortage and rural labour surplus in China. China Economic Review, 22(4), 585–600. Liu, Z. (2005). Institution and inequality: The hukou system in China. Journal of Comparative Economics, 33(1), 133–157. Mandal, B., & Marjit, S. (2010). Corruption and wage inequality? International Review of Economics and Finance, 19(1), 166–172. Marjit, S., & Kar, S. (2005). Emigration and wage inequality. Economics Letters, 88(1), 141–145. Meng, X. (2012). Labor market outcomes and reforms in China. Journal of Economic Perspectives, 26(4), 75–101. Meng, X., & Bai, N. (2007). How much have wages of unskilled workers in China increased? In R. Garnaut, & L. Song (Eds.), China: Linking Markets for Growth. Canberra: Asian Pacific Press. Meng, X., & Manning, C. (2010). The great migration in China and Indonesia: Trend and institutions. In X. Meng, C. Manning, S. Li, & T. N. Effendi (Eds.), The Great Migration: Rural–Urban Migration in China and Indonesia. Cheltenham: Edward Elgar. Ni, J., Wang, G., & Yao, X. (2011). Impact of minimum wages on employment: Evidence from China. Chinese Economy, 44(1), 18–38. Pi, J., & Chen, X. (2016). The impacts of capital market distortion on wage inequality, urban unemployment, and welfare in developing countries. International Review of Economics and Finance, 42, 103–115. Pi, J., & Zhou, Y. (2012). Public infrastructure provision and skilled-unskilled wage inequality in developing countries. Labour Economics, 19(6), 881–887. Pi, J., & Zhou, Y. (2013). Institutional quality and skilled-unskilled wage inequality. Economic Modelling, 35, 356–363. Pi, J., & Zhou, Y. (2014). Foreign capital, public infrastructure, and wage inequality in developing countries. International Review of Economics and Finance, 29, 195–207. Pi, J., & Zhou, Y. (2015). The impacts of corruption on wage inequality and rural–urban migration in developing countries. Annals of Regional Science, 54(3), 753–768. Song, Y. (2014). What should economists know about the current Chinese hukou system? China Economic Review, 29, 200–212. Song, Y. (2015). Zhongguo Shouru Fenpei Geju de Xianzhang yu Gaige Cuoshi: Jiyu Laodongli Shichang de Lilun he Shizheng Fenxi. Beijing: China Renmin University Press. Stiglitz, J. (1974). Alternative theories of wage determination and unemployment in LDCs. Quarterly Journal of Economics, 88(2), 194–227. Sun, S., & Anwar, S. (2015). Taxation of labour, product varieties and skilled-unskilled wage inequality: Short-run versus long-run. International Review of Economics and Finance, 38, 250–257. Vendryes, T. (2011). Migration constraints and development: Hukou and capital accumulation in China. China Economic Review, 22(4), 669–692. Wan, H., & Li, S. (2013). The effects of household registration system discrimination on urban–rural income inequality in China. Economic Research Jounal (Jingji Yanjiu), 9, 43–55. Wang, F. -L. (2004). Reformed migration control and new targeted people: China's hukou system in the 2000s. China Quarterly, 177, 115–132. Wang, F. (2005). Organizing Through Division and Exclusion: China's Hukou System. Stanford: Stanford University Press. Wang, J., & Gunderson, M. (2011). Minimum wage impacts in China: Estimates from a prespecified research design, 2000–2007. Contemporary Economic Policy, 29(3), 392–406. Wang, F., & Zuo, X. (1999). Inside China's cities: Institutional barriers and opportunities for urban migrants. American Economic Review, 89(2), 276–280. West, L. A., & Zhao, Y. (2000). Rural Labor Flows in China. Berkeley, CA: University of California Press. Whalley, J., & Zhang, S. (2007). A numerical simulation analysis of (Hukou) labour mobility restrictions in China. Journal of Development Economics, 83(2), 392–410. Wu, L. (2013). Decentralization and hukou reforms in China. Policy and Society, 32(1), 33–42. Yabuuchi, S., & Chaudhuri, S. (2007). International migration of labor and skilled-unskilled wage inequality in a developing economy. Economic Modelling, 24(1), 128–137. Yang, D. T. (1999). Urban-biased policies and rising income inequality in China. American Economic Review, 89(2), 306–310. Zhang, H. (2010). The Hukou system's constraints on migrant workers' job mobility in Chinese cities. China Economic Review, 21(1), 51–64. Zhang, J., Wu, G., & Zhang, J. (2004). The estimation of China's provincial capital stock: 1952–2000. Economic Research Journal (Jingji Yanjiu), 39(10), 35–44. Zhang, X., Yang, J., & Wang, S. (2011). China has reached the Lewis turning point. China Economic Review, 22(4), 542–554. Zhao, Z. (2005). Migration, labor market flexibility, and wage determination in China. Developing Economies, 43(2), 285–312.