Education and Migration: The Role of Zhaosheng in China

Education and Migration: The Role of Zhaosheng in China Pei-Ju Liao y Ping Wang z Yin-Chi Wang x Chong Kee Yip { Preliminary February 2014 Abstract China has implemented a unique household registration system, or hukou system, since early 1950s. The system was served not only for collecting household information but also for controlling population movement and determining citizens social bene ts. Since urban hukou comes with more social bene ts, having an urban hukou implies having a better life in the future. This paper focuses on one of the formal channels to obtain an urban hukou: zhaosheng. To better caputre the reality, we also consider the migration of rural workers to cities. A general equilibrium model with endogenous education migration decision is employed. The framework is calibrated to data from China and then counterfactual experiments are conducted. In particular, the abolishment of joint job assignment for college graduates in 1994 is examined in this paper. Our counterfactual experiments indicate that (1) If the policy of joint job assignment had been continued, average output would increase by about 0.8 percent during 1995-2007; (2) If rural workers were prohibited from migrating to cities to work, the total output would decrease by 20 percent in 2007; (3) If rural migrant workers job opportunity in 1980-1994 were the same as that after 1994, the average output would increase by 4.95 percent for 1980-2007; (4) If China had not loosened the population movement control, the average output would decrease by 2.07 percent. JEL Classi cation: Keywords: Rural-urban migration, education, urbanization, China development. Acknowledgment: y Institute of Economics, Academia Sinica. E-mail: pjliao@econ.sinica.edu.tw z Washington University in St. Louis. E-mail: pingwang@wustl.edu x Chinese University of Hong Kong. Email: ycwang@cuhk.edu.hk { Chinese University of Hong Kong. Email: chongkeeyip@cuhk.edu.hk

1 Introduction China introduced the unique hukou registration system in the early 1950s. Di erent from other countries, China used the hukou registration for government control and to de ne a citizen s job, grain rations, education for children, health care, and obligations. Therefore, having an urban hukou implied enjoying better bene ts, having a good life, and a future for children. Besides, after the economic reform, potential job opportunities in urban areas were much more than that in rural areas. These motivated people to migrate to urban areas. The in uences of the hukou system on the Chinese economy have drawn economists attention. For example, Cooney and Li (1994) and Liang, Yi, and Sun (2013) both link the hukou registration system to fertility. They show that, among all factors, hukou registration type was the most important reason in explaining fertility behaviors. Liu (2005) and Whalley and Zhang (2007) examine the rural-urban income inequality and the increasing rural-urban gap by looking at the restrictions on labor mobility in China. Furthermore, Nielsen, Nyland, Nyland, Smyth, and Zhang (2006) and Liang and Chen (2007) study the less education opportunities of migrant children under the hukou registration system. However, the hukou-related literature studies this issue by an empirical approach. This paper, instead, attempts to explore its in uence on the Chinese economy by constructing a general equilibrium model. In particular, our model focuses on zhaosheng and study the role and the impacts of zhaosheng on the aggregate economy. According to China s hukou registration system, zhaosheng was one of the formal channels to obtain an urban hukou: a student attended college by passing the gaokao (National College Entrance Examination). At the beginning of entering a college, a freshman could choose to change his hukou registration place to urban area. Therefore, entering college implied obtaining an urban hukou, having a bright future, and moving upward in the society. Wu and Treiman (2004) show that education was one of the main determinants of the upward mobility in China. To capture the spirit of zhaosheng, this paper employs a general equilibrium model with an endogenous decision on children s education migration. To capture more of the reality, we also include another migration channel migration through working as a rural migrant workers. 1 Then, the model is calibrated to data from China. Speci cally, two regimes are considered for the abolish- 1 We dismiss the discussion of whether rural migrant workers have urban hukou or not as it is impossible for us to distinguish migrant workers with urban hukou from migrant workers without urban hukou in the data. 1

ment of government job assignment (GJA) in 1994: pre-1994 and post-1994. Before 1994, a college graduate would be assigned to a stable government job and kept his urban hukou. After 1994, jobs are not guaranteed. Instead, a college graduate has to nd a job by himself. If he cannot get a job in urban areas, he may choose to move back to his hometown in rural areas. By comparing these two regimes, the e ects of GJA can be explored. We nd that if the abolishment of GJA only creates minor negative impacts on the economy. If the GJA were not abolished, the output level will only be 0.8 percent higher in 1995-2007, and the urbanization rate is almost not a ected. We also consider other policy experiments. First, if rural workers were prohibited from migrating to cities to work, the urbanization rate and the total output level would be 40 percent and 20 percent lower than those in 2007, respectively. If China had promoted more job opportunities for rural migrants and permitted more rural migrant workers to work in cities in 1980-1994 in a way such that the urban job opportunity for rural workers are the same as that in the post 1994 era, the average output level would increase by 4.95 percent in 1980-2007, and the urbanization rate would increase by 4.45 percent by the end of 2007. On the contrary, if China had not been loosening the control over the hukou system and promoting more job opportunities for rural migrant workers, the urbanization rate would be 4.63 percent lower by the end of 2007 and the average output level would decrease by 2.07 percent in 1995-2007. Finally, if China had been loosening control over population movement and promoting rural-urban migration in a way such that the urban job opportunities were doubled in 1980-2007, the urbanization rate would be 12.35 percent higher in 2007, and the average output level would increase by 7.27 percent in 1980-2007. The rest of this paper is organized as follows. Section 2 summaries the basis of China s hukou system, its reforms, and the role of zhaosheng. Section 3 mentions the model and the theoretical analysis. The calibration strategy, the simulation and counterfactual experiments are provided in Section 4. Finally, Section 5 concludes this paper. 2 Hukou System and Zhaosheng in China China implemented the unique hukou system in 1958 in order to solve the serious problem of the blind ows" (rural labor to cities) in the early 1950s. The system was still the basis of China s registration system in the last decade. The power of China s hukou system did not come from the regulation of migration itself. Instead, 2

it was from its integration with other social and economic controls. In the rural areas, with the commune system, all rural residents in communes had to participate in agricultural production to receive food rations for their households. In the urban areas, most recruitment and job transfers were controlled by the state government. There were few jobs outside the state enterprises. Danwei was the basic administrative unit for most urban adults. It assigned most social services for its employees, such as the access to good jobs, grain rations, education for children, health bene ts, and purchasing house. Without a work unit, it was di cult to survive in a city. Therefore, in the pre-reform period, it was hard for people to survive outside their hukou registration place without permissions. However, in the late 1970s, because of the development of the market-oriented economy, more people stayed (i.e., actually worked and lived) outside their hukou registration place (so-called the oating population"). This resulted in a series of hukou reforms since 1980. In this session, rst the basis of China s hukou system and the role of zhaosheng are summarized. The second part describes the hukou reforms since the 1980s. 2.1 The basis of Hukou system and zhaosheng A citizen s hukou was classi ed by two part: hukou suozaidi (the place of hukou registration) and hukou leibie (the type or status of hukou registration). 2 Hukou suozaidi was a person s presumed regular residence. Everyone was required to register in one and only one place of his residence. The common categories of place of hukou registration were cities, towns, villages, and state farms. It determined where a person would receive his bene ts and social welfare. Hukou leibie referred to agricultural" and non-agricultural" hukou. It was used to determine a person s entitlements to state-subsidized food grain (commodity grain). A citizen with nonagricultural" hukou status would lose the right of land rental and the right of inheriting the land that his parents rented. The above two classi cations were di erent. Urban areas contained both agricultural and nonagricultural hukou population. Non-agricultural hukou population may exist in both urban and 2 Before 1997, hukou registration place and status were inherited from a person s mother. Since 1997, they can be inherited from a person s mother or father. 3

rural areas. Hukou registration place and status mattered because it determined, for example, access to good jobs, grain rations, education for children, health bene ts, and purchasing house. 3 A formal rural-urban migration involved both a change in hukou residential place and in entitlement status. In order to complete the process, a person had to satisfy both the migration requirements and obtained a space under the quota control. Changing from agriculture to non-agriculture was commonly known as nongzhuanfei. The annual quota was controlled by the central government at about 0.15-0.2 percent of the non-agricultural hukou population in each area. The regular channels of nongzhuanfei included recruitment by a state-owned enterprise (zhaogong), enrollment in an institution of higher education (zhaosheng), and promotion to a senior administrative job (zhaogan). Therefore, zhaosheng, i.e., entering college through gaokao, was one of the formal channels for rural students to obtain an urban hukou. The system of gaokao was established at the beginning of the 1950s. It was abolished for several years during the periods of Cultural Revolution and then was restored in 1977. Because of the scarcity of education resources, the acceptance rates were very low, especially in the 1980s. Students who passed gaokao enjoyed lots of social bene ts and were expected to become a pillar of society in the future. At the beginning of entering an university or a college, a freshman could be voluntary to change his own hukou registration place to his school (a collective joint household). This would also change his hukou status to become non-agricultural. During the periods with the implementation of Government Job Assignment (GJA, 1951-1994), a graduate would be distributed to a stable government job. Thus, a graduate simply moved his hukou to the working unit after graduation. He still kept the non-agricultural status. 4 In the periods that the GJA was abolished, a graduate could move his hukou to the working unit, temporarily put to the collective joint household of personal exchange center, or moved back to his own hometown. 5 Thus, under China s hukou system, entering college through gaokao implied an upward mobility in the society. 6 3 See Whalley and Zhang (2007) for the detail. 4 The reform of the GJA started in 1989; but was o cially abolished in 1996. Tibet, which abolished the system in 2007, was the last place to terminate the distribution system of graduation. 5 Even though a graduate moved his hukou back to his hometown, he still kept the non-agricultural status. This implied that he could not rent land and inherit the land rented by his parents. 6 Since 1996, China has introduced a series of education reforms. In particular, since 2003, universities in Hong Kong are allowed to enroll new students in Mainland China. Attending universities in Hong Kong is getting popular. 4

2.2 Hukou reforms Since the late 1970s, due to the economic reform, people have become easier to survive outside their hukou registration place. The economic reform relaxed the administrative control, such as the abolition of the commune system, the introduction of the household responsibility system, and the erosion of the rigid danwei-based rationing system. Furthermore, the growing market-oriented economy demanded more cheap labor. Both the push and pull factors increased migrations from rural to urban areas. It was noted that in 1995 there was a oating population" of some 80-100 million, who stayed outside their own hukou registration place. 7 The increase in mobility had forced the government to change its hukou policies. The main parts of hukou reforms were to relax the migration requirements. For example, state governments implemented a new type of urban hukou with self-supplied food grain" in 1984. People actually living in urban areas other than their place of hukou registration were required to apply for a temporary residence certi cate. In addition, due to the demand of economic development, some local governments introduced the blue-stamp" urban hukou in the early 1990s in order to attract professional workers and investors. 8 The blue-stamps hukou system allowed them to obtain a temporary urban hukou. It could be upgraded to a formal urban hukou after some years. However, applying the blue-stamp hukou required an urban infrastructure construction fee for any new comer, ranging from a few thousand to some fty thousand yuans. Blue-stamps hukou was di erent from the urban hukou obtained through nongzhuanfei that it only had limited rights and obligations compared to regular urban residents. In a statement of 2005, the deputy minister of public security stated that eleven provinces had begun or would soon begin to implement uni ed urban-rural household registration system, removing the distinctions between agricultural and non-agricultural hukou status. 9 aim is to abolish the regulations of migration in the hukou system. The ultimate 7 See Chan and Zhang (1999) for the detail. 8 This was distinguished by a blue stamp, di erent from the formal urban hukou book with a red stamp. 9 However, Beijing was tentatively excluded. See Chan and Buckingham (2008) for the detail. An updated statement in 2007 repeated the same points and included a list of twelve provincial-level units. 5

3 The model We use (i; j; k) to denote three consecutive generations and let (H; L) denote high skill and low skill respectively. Our optimization problem focuses only on the decision of rural parents (generation i) in sending their children to urban area to get education. So our speci cation of the urban households is rather simple. There is an initial mass of workers in urban area given by (N H ; N L ), where N H (N L ) denotes the total number of high (low) skilled workers. Occupations of urban households are passed from one generation to another. 3.1 Production Urban output is produced with a constant-return Cobb-Douglas technology, using skilled and unskilled labor as inputs: Y U = A (N H h) N 1 L ; (1) where h is the level of human capital associated with the high-skilled worker, A is the technology scaling factor in urban area, or urban TFP, and is the income share of high-skilled labor. The urban wage rates are determined competitively: And the skilled-unskilled wage ratio is given by w H = A (N H h) 1 N 1 L ; (2) w L = A (1 ) (N H h) N L : w H w L = N L 1 N H h (3) Rural production uses raw (or unskilled) labor only and constant returns requires a linear production technology: Y R = BN R ; (4) where N R is the number of raw-labor workers in rural area and B is the technology scaling factor in rural area. Competitive labor market implies that the rural wage rate is w R = B: (5) 6

3.2 Rural households Rural households (generation i) are altruistic and derive utility from both their own consumption (c i ) and their children s consumption (c j ). There is no fertility decision and each agent gives birth to a child when he/she turns adult. Assuming the utility function u () is strictly increasing and strictly concave, then the representative household objective is: i I j ji i = 0; I k ; x j = max u c i + E X u c j (6) I j where is the altruistic factor on children and I j is an indicator function such that 8 < I j 0 if the household does not send children to college in urban area = : 1 if the household sends children to college in urban area. We assume constant child-rearing cost i. Education of the children only takes place in urban area with cost x j, which is a random variable that is inversely related to the talents of the child z j, i.e., z j 1=x j. We note that z j is drawn from a distribution with cdf G z j. Finally, the migration cost (settle-down cost in cities) of moving from rural to urban is. Then the budget constraint for a rural parent is c i + I j x j + + i = w R : (7) Children become skilled workers after receiving education in urban area. They can either get high (low) skilled job in urban area, earning a skilled wage income w H (w L ) with probability H ( L ), or otherwise are forced to move back to rural area, earning a rural wage income of w R. Children that remain in the rural area do not incur any cost in education or migration. They either get recruited to serve as low skilled worker in urban area and earn w L (with probability ), or otherwise work as unskilled labor in rural area and earn w R. The income for the children (generation j) when they become adults is W j = I j [ H w H + L w L + (1 H L ) w R ] + 1 I j [(1 ) w R + (w L )] : (8) Then the children s budget constraint is given by c j + I k I j (1 H L ) + 1 I j x k + + j = W j (9) where 8 < I k 0 if children do not send their kids (grandchildren) to college in urban area = : 1 if children send their kids (grandchildren) to college in urban area 7

and x k is the education cost of grandchildren going to college in cities. When households of generation i decide I j, x k is unknown to them. We use X to denote the random variable of education cost. An agent s discrete-choice problem is to decide whether to send his or her child to urban area to attend college (I j = 1; I j = 0). That is, the agent compares i 1j0; I k ; x j to i 0j0; I k ; x j and chooses the highest value among the two. By substituting c i = W R I j x j + i and c j = W j I k I j (1 H L ) + 1 I j x k + j into the value functions, with W j given by (8), we have: i 1j0; I k ; x j = u W R x j i 0 +E X u @ Hw H + L w L + (1 H L ) (w R ) I k (X) (1 H L ) (X + ) j 1 A and i 0j0; I k ; x j = u W R i + E X u (1 ) w R + (w L ) I k (X) (X + ) j : De ning i I k ; x j i 1j0; I k ; x j i 0j0; I k ; x j, we have: i I k ; x j = u W R x j i u W R i (10) 8 < u H w H + L w L + (1- H - L ) w R -I k (X) (1- H - L ) (X+) - j 9 = +E X : -u (1-) w R + (w L -) -I k (X) (X+) - j ; : To proceed further, we make an assumption that wage is a positive function of the education/skill level: Assumption 1: w H > w L > w R. We also impose a condition that the relative probability of getting an urban job through education cannot be too low so that there is enough incentive to get education: Condition S: H + L > max (0; 1 2). Then we are able to present our rst nding on parents decision for their children s education choice: 8

Proposition 1 Under Assumption 1, if Condition S is satis ed, it must be the case that parents decide to send their children to urban area to attend college. Proof. Sending children to urban area to attend college incurs cost x j +. Hence, for a parent who decides to send his or her child to urban area to attend college, it must be that E X u c j U u c j R > 0; where c j U denotes the consumption of children if sending children to urban area, and cj R denotes the consumption of children if keeping children in rural area. Since u () is strictly increasing and strictly concave, the above inequality implies that E X c j U c j R > 0: The above inequality will de nitely be satis ed if c j U > cj R for all x k 2 (0; x max ]. By substituting c j U and cj R have: into the above inequality using (8) and (9) we c j U > cj R, Hw H + L w L + (1 H L ) (w R ) I k (X) (1 H L ) (X + ) j > (1 ) w R + (w L ) I k (X) (X + ) j, H w H + L w L + (1 H L ) (w R ) + I k (X) ( H + L ) (X + ) > (1 ) w R + (w L ), H w H + L w L w L ( H + L ) (w R ) + I k (X) ( H + L ) (X + ) + (2 1) > 0(11) Applying Condition S to (11), we have H w H + L w L w L ( H + L ) (w R ) + I k (X) ( H + L ) (X + ) + (2 1) > ( H + L ) w L ( H + L ) (w R ) + I k (X) ( H + L ) (X + ) + (2 1) = ( H + L ) (w L w R + ) + I k (X) ( H + L ) (X + ) + (2 1) > ( H + L ) (w L w R ) + (1 2) + I k (X) ( H + L ) (X + ) + (2 1) = ( H + L ) (w L w R ) + I k (X) ( H + L ) (X + ) > 0: 9

The results follow. The intuition of the above proposition is straightforward. If the probability of nding a higherpaid job in cities is reasonably high (Condition S), then it pays the parents to send their children to urban college. Otherwise, the presence of the zhaokong system captured by the probability (1 H L ) would make urban education unattractive. 3.3 Comparative statics In the following, we examine how i I k ; x j responds to changes in the parameterization, i.e. we examine whether the marginal parent (parent who is indi erent between sending children to attend college in urban area or keeping children in rural area) will send her children to urban area or keep the children in rural area. Denote u i c U = u c c i U as the marginal utility, we have d i I k ; x j = u i c dx U < 0 j d i d i d i I k ; x j n = E X d H I k ; x j n = E X d L I k ; x j d We have the following proposition: io u j c U h[w H (w R )] + I k (X) (X + ) io u j c U h[w L (w R )] + I k (X) (X + ) = E X u j c R [w R (w L )] > 0 > 0 Proposition 2 Under Assumption 1, 1. Parents will be more willing to send their children to urban area to attend college when their children become more talented (x j #). 2. Parents will be more willing to send their children to urban area to attend college when the chances for the children to obtain a job in cities are higher ( H ", L "). 3. When the rural wage income is lower than the net low-skilled urban wage income (net o migration cost), parents will be less willing to send their children to urban area when the chance of zhaokung becomes higher ( "). To examine how changes in migration cost () a ect parents decision, we compute d i I k ; x j d h i = u i c U E X nu j c U (1 H L ) 1 + I k (X) 10 o u j c R + I k (X) :

Then we have Proposition 3 Under Condition S, when the migration cost increases, parents may still be willing to send children to attend college in urban area. Proof. Under Condition S, c j U > cj R and uj c U < u j c R. De ne u j c U (1 H L ) 1 + I k (X) u j c R + I k (X). Also, h i u j c U (1 H L ) 1 + I k (X) u j c R + I k (X) = u j c U (1 H L ) u j c R + u j c U (1 H L ) u j c R I k (X) < u j c R (1 H L ) + u j c U (1 H L ) u j c R I k (X) < u j c R [1 (1 ) ] + u j c U (1 H L ) u j c R I k (X) < 0 where the second-last inequality follows from Condition S. Therefore, if > u i c U, di (I k ;x j ) d > 0. ( ) ( ) 3.4 Population Since only adult agents supply labor to the market and each agent gives birth to only one child, the whole population participates in the labor market. Denote N t H ; N t L as the skilled and unskilled workers in the city and N t R as the rural labor force at time t. Given the initial labor force in the city and in the countryside, N 0 H ; N 0 L and N 0 R respectively, the population of skilled, unskilled and rural laborers evolve according to the following law of motion equations: Z 1 N t+1 H = NH t + NR t Z 1 N t+1 L = NL t + NR t N t+1 R = N t R Z 1 z min I j z min I j z min I j z j ; I k H dg(z j ) (12) z j ; I k Z 1 h L dg(z j ) + 1 I j z j ; I ki dg(z j ) z min Z 1 h z j ; I k (1 H L ) dg(z j ) + z min (13) 1 I j z j ; I ki (1 ) dg(z j )(14) where G(z j ) is the cdf of the Pareto distribution (with the tail parameter and the minimum value z min ). We note that the last term in the RHS bracket of (13) represents the zhaokong channel of urban labor force adjustment, whereas the zhaosheng channel is given by the last term on the RHS 11

of (12) together with the rst term in the RHS bracket of (13): Z 1 zhaosheng = NR t z j ; I k ( H + L ) dg(z j ); 3.5 Equilibrium zhaokung = N t R I j z Z min 1 z min h 1 I j z j ; I ki dg(z j ): First, all labor markets must be clear under the factor prices fw H ; w L ; w R g given by (2) and (5): where N dt J each period: N dt J = N t J; J = H; L; R (15) denotes labor demand of type J. Finally, there is the overall population restriction for where N is the constant population size in each period. We are now ready to de ne the equilibrium for our model. N t H + N t L + N t R = N (16) De nition 1 A competitive equilibrium of the model consists of consumption, migration choice and wage rates, c i ; c j ; I j ; w H ; w L ; w R, such that fw H ; w L ; w R g are given by (2) and (5), and the parents (generation i) solve (6) subject to (7), (8) and (9), given initial distributions of population, N 0 H, N 0 L and N 0 R, in the two locations. In addition, fw H; w L ; w R g are such that labor markets clear in all locations as given by (15) and (16). 4 Numerical Analysis China started a series of economic reform in December 1978, right after the 11th Central Committee of the Communist Party of China. The reform in 1994 abolished the system of joint job assignment for college graduates, and obtaining a college degree in cities does not guarantee an urban job with an urban hukou for rural college graduates anymore. We thus examine the period of 1980 to 2007 and divide the period of 1980 to 2007 into two regimes: (1) pre-1994 regime, spanning from 1980 to 1994, and (2) post-1994 regime, for the years of 1995 to 2007. The model is then calibrated to t the data from China for the two regimes respectively. Based on the calibrated parameters, we back out the urban TFP for 1981 2007 and decompose the e ects of zhaosheng and zhaokong on urbanization rates and income levels for both regimes. Experiments of varying policies on zhaosheng and zhaokong are performed as well. 12

4.1 Calibration For calibration purpose, we assume that the utility function takes the CRRA form: u (c) = c1 " 1 1 " ; where " is the inverse of the elasticity of intertemporal substitution. The distribution of children s talents is assumed to be Pareto, since it is a distribution commonly associated with wealth and income, which may be correlated with talents. The cdf is given by: G z j = 1 zmin z j ; z j z min ; where z min and are the location and shape parameter of Pareto distribution. Denote ^z as the threshold of children s talent. When children are talented enough (z j 1=x j ^z), their parents are willing to send them to cities to attend college ( i (I k ; x j ) 0 ), and vice versa. The relative wages in urban area, the job opportunities for college graduates and the migration cost thus determine the threshold talent ^z, which then decides the rural out ow (or urban in ow), the urbanization rate, the output levels in urban and in rural areas, and the relative wages in urban area in the next period. We assume that the parameters for preference (" and ), child-rearing cost (), migration cost (), talent distribution (z min and ) and urban high-skilled labor income share () are deep parameters and are common between the two regimes. The abolishment of the joint job assignment for college graduate in 1994 justi es that the job nding rates for college graduates ( H and L ) are di erent in two regimes. We also allow that the urban TFP (A), the level of human capital associated with the high-skilled worker (h), the zhaokong rates () and hence the endogenous threshold of talents (^z) are di erent across the two regimes. In the following, we rst decide the parameter values for the common parameters in both regimes, and then we proceed on pinning down the parameter values for pre-1994 regime and post-1994 regime. Common parameters The model period is set to be 25 years. Normalize total population to one as there is no population growth for the whole economy, and adjust all numbers of population ow and stock in the data accordingly. We normalize the rural TFP (B) to be one, and the rural wage rate, w R, is equal to one from (5). Following the literature, the annual time preference rate is set at 4.75%, and the parental altruistic factor on children is equal to 0.3134; the inverse of the intertemporal elasticity of substitution " is set at 2. According to Liu (2011), based on the estimates in Zhao 13

(1999b), the migration cost roughly amounts to 15% of annual income. We thus set the migration cost to be 0.15 because the total wage income for rural household equals to one. There is no nationwide survey on rural child-rearing cost in China. Zhu and Zhang (1996) estimate the childrearing cost in some rural villages in Xianyang, Shaanxi province. The average child-rearing cost for an age 0-16 child in 1995 was 17.4% of family income, and education cost only amounted to 9% of total child-rearing cost. Ye and Ding (1998) study the child-rearing cost for age 0-16 children in Xiamen Special Economic Zone in 1996. They nd that average child-rearing cost in Xiamen accounted for 34% of annual family income, and the number for Beijing in 1995 was roughly 20%. We thus set child-rearing cost to be 0.2. For Pareto distribution location parameter z min and the shape parameter, as far as we know, there is no available estimates on the talent distribution in China. Bajona and Locay (2009) model the distribution of managerial ability of entrepreneurs with a Pareto distribution, setting the Pareto location parameter to be one and calibrating the Pareto shape parameter to be 1.35 so as to match the Gini coe cient in the data. In the literature of rm productivity, rm size distribution and international trade, Pareto distribution is often used to model the rm productivity (which could represent the managerial ability of entrepreneurs) because it provides a good t to the rm size distribution in the data. Several researchers have estimated or calibrated the Pareto shape parameter and found that the range of the Pareto shape parameter falls between 3.6 and 4. 10 We thus choose to set at 3.8 and calibrate the location parameter z min. The high-skilled wage to total wage ratio for year 2003-2007 based on the data of total wage bill of employed persons in urban units is 0.31, and hence the high-skilled labor income share is set accordingly. Pre-1994 regime In the pre-1994 regime, most college graduates were assigned to serve in the government sector, and H = 1 and L = 0 follow as a result, i.e. there is no mismatch for high-skilled laborers in the market. We need to search the values for h, A, z min, ^z, and. From (3), h = N L w L 1 N H w H. From urban low-skilled to rural wage ratio, the urban TFP can be derived as A = B (1 ) 1 wl w R wh wl. The average high-low skilled workers ratio in 1980-1994 is 10 Melitz and Ghironi (2005) set the Pareto shape parameter at 3.4; Melitz and Redding (2014) set the Pareto parameter at 4.25; Mayer, Melitz, and Ottaviano (2014) report the estimates of the Pareto shape parameter between 1.34 and 4.87; Bernard et al (2003) set the shape parameter at 3.6 so that their simulated data match the actual productivity advantage and size advantage of exporters; Eaton and Kortum (2002) estimate the dispersion parameter at the values of 3.60, 8.28 and 12.86. 14

0.17, the weighted average skilled premium (w H =w L ) in 1980-1994 11 is 1.53, and the urban lowskilled to rural wage ratio in the pre-1994 regime is 2.46. h and A are computed and equal to 1.6987 and 5.2055, respectively. The values of two parameters z min and and one endogenous variable ^z are left unknown. Rearrange (12) and (13) to arrive at: N t H N t R N t L N t R N t+1 H N t+1 L N t H NR t NL t NR t zmin = H (17) ^z zmin zmin = L + 1 (18) ^z ^z We already set H = 1 and L = 0, and hence the above two equations become: zmin zmin = ; = 1 : N t H N t R ^z N t L N t R By setting the indi erence boundary equation (10) to zero ( i two equations, z min, ^z and are solved as 34.0954, 201.0861 and 0.0054. 12 Post-1994 regime ^z I k ; x j = 0), together with the above Without loss of generality, the distribution of talents is assumed to be stationary over time, and hence values for the Pareto distribution parameters z min and are the same as that in the pre-1994 regime. The average high-low skilled workers ratio in urban units in 2003-2007 is 0.3, the weighted average skilled premium (w H =w L ) in urban units in 2003-2007 is 1.44, 13 and the urban low-skilled to rural wage ratio in the post-1994 regime is 2.93. h and A are computed and equal to 1.0464 and 6.1024, respectively. The remaining unknown parameters are H, L and, and the endogenous threshold of children s talent ^z for parents to send children to cities to accept college education. De ne H + L as the urban employment rate. In this way we can write H = L and once L is pinned down, H is found immediately. The average employment rate in city districts in 1995-2007 is 0.9627. 14 11 The weights are based on the numbers of workers. 12 When computing the population ow in the data, 13 The categorization of industrial sectors has changed in 2003, and wage and employment data in urban units are available only after 2003. Before 2003, only nationwide wage and employment data by sector are available. Therefore, we choose to use the wage and employment data in urban units in 2003-2007 to calibrate the post-1994 regime. 14 In the model, refers to the employment rate for college graduates migrating from rural area. However, there is no counterpart in the data. Thus we have to use urban employment rate, computed by the formula: 1 total registered unemployed persons (with urban non-agricultural hukou)/total work force in urban area. We are aware that the actual employment rate in urban area should be lower, but this is the best data we have. 15

Thus, (17), (18) and the indi erence boundary equation ( i I k ; x j = 0) pin down the values for L, and ^z. The calibrated values for H, L, and ^z are 0.9586, 0.0041, 0.0103 and 168.223, respectively. Table 1 summarizes the calibration results for the two regimes. Since we are interested in learning the e ects of the policy change in the job assignment for college graduates and the easiness for rural migrants to nd jobs in urban area on the urbanization rates and income levels, based on the calibrated parameters in the two regimes, we next turn to calibrate the urban TFP from 1980 to 2007. Based on the the calibrated urban TFP series, we then decompose the e ects of zhaosheng and job opportunities for rural migrants in cities. Policy experiments, such as keeping implementing GJA, subsidies on college education, and widen the door of urban job opportunities for rural non-college graduate migrants, will be performed and discussed. 4.2 Simulation and policy experiments Before proceeding to simulating the model, we need to calibrate the urban TFP for the period of 1980-2007. The urban TFP a ects relative wage rates in urban area, which then determine the in ow of population from rural area to cities. Based on the data on population in ow to urban area in 1980-2007 and the calibrated parameters from pre-1994 and post-1994 regimes, we can back out the TFP in cities for the entire period. In the model, the urban TFP and the stocks of urban high and low skilled workers govern the urban high and low skilled wage rates and subsequently impact parents decision whether to send children to cities to attend college. The threshold of children s talents ^z is being determined by the indi erence boundary equation ( i I k ; x j = 0). The zhaosheng to rural population ratio and the urban in ow through the working-migration channel to rural population ratio can thus be readily computed from (17) and (18) once ^z is known. 15 Therefore, given the initial stocks of urban high and low skilled workers and the data on migration through zhaosheng or workingmigration channel, we can solve a series of urban TFP using the indi erence boundary equation ( i I k ; x j = 0) and either equation (17) or (18). The current project focuses on studying the impacts of policy change in GJA for migrant college graduates, and formally model rural parents decision whether to send children to accept college education in urban area. We thus choose to target the urban zhaosheng in ow to rural population ratio to back up urban TFP series. The 15 The rural out ow rates can also be computed from (14). 16

calibrated urban TFP series is directly computed from data and uctuates quite a bit. For the purpose of conducting counterfactual analysis and policy experiments, we smooth the series with a second degree polynomial. The smoothed and the non-smoothed urban TFP series are shown in Figure 1. 16 The rural migrants to rural stock ratio, both the data and the model (based on the calibrated urban TFP series) are plotted in Figure 2. It can be easily noticed from the data that there is a regime change between the year 1994 and 1995: there is a jump in rural migrants to rural population ratio between 1994 and 1995. For the pre-1994 regime, the rural migrants to rural population ratio uctuates greatly, maintains at a relatively low level, and reaches its trough in 1989, probably a consequence of the Tiananmen Square protests of 1989. After 1994, the rural migrants to rural population ratio is maintained at a relatively high level. Although not able to capture all the uctuations in the data, our model is able to capture the trend in the data quite well. De ne urbanization rate as the percentage of total population living in urban area. We perform the simulation using the smoothed urban TFP series. The simulation procedure goes as follows: given the initial urbanization rate (N R, as we already normalize N R in the way that total population in the economy is one), high and low-skilled worker ratios (N H =N L ), and high and low-skilled workers populations (N H and N L ) in 1980, based on the urban TFP, we simulate N R, N H and N L for 1981-1994 using (12)-(14). Ideally, we shall take the simulation result of that of 1994 as initial condition for the post-1994 regime simulation. Nevertheless, the simulation result gives us a low N H =N L in 1994 (0.25 in the data vs. 0.1918 for the model). With such a low N H =N L ratio, it is impossible for our model to have sensible result for the post-1994 simulation. 17 To x this problem, we thus use the simulated urbanization rate in 1994, the N H =N L data in 1994, and the N H and N L adjusted based on the N H =N L in the data as initial conditions. 18 When conducting experiments and decomposing 16 We have smoothed the urban TFP with HP- lter and polynomials of other degrees. Adding more degrees to curve tting polynomials does not give us much bene ts. The R-squares of the second, third and fourth degree polynomial are 0.7169, 0.7179 and 0.7182; the adjusted R-square of the second, third and fourth degree polynomial are 0.6942, 0.6826 and 0.6692. The simulation results of the model based on di erent curve tting for the urban TFP series are very similar. 17 The average N H=N L for 1995-2007 is 0.3027, and we based on this number to calibrated the post-1994 regime. 18 The adjusted 1994 N H is computed using the following formula: N H;adjusted = (1 N R;m o del ) NH N L data 1 + NH N L data The adjusted 1994 N L can thus be computed as 1 N R;m o del N H;adjusted : : 17

the channels in the model, we also apply the same procedure for the simulation in the post-1994 regime. The simulated urbanization rate and total output are plotted in Figure 3(a) and 3(b), respectively. The simulation result shows that, the urbanization rate in the baseline model is always slightly lower than the data. 19 Not surprisingly, since the technology in urban area is better, with a lower urbanization rate and a smaller population in urban area, the total output in the model is also slightly lower than that in the data. 20 Without much discrepancies between the simulation and the data, we now turn to examine the channels in the model, conduct di erent experiments, and compare the result to that of the benchmark model. Shut the door for rural migrant workers We rst shut the door for rural workers to migrate to cities in both regimes. College education becomes the only way for rural people to move to cities. In the pre-1994 regime, all migrant college graduates work as high-skilled laborers after graduation, and the population of low-skilled workers is kept constant. In the post-1994 regime, the newly added low-skilled workers in urban area are those college graduates with bad luck. The smaller low-skilled workers population and a larger high-to-low skilled workers ratio in cities result in a lower wage for urban high-skilled workers and decrease the incentive for rural parents to send their children to urban to attend college. urbanization rate becomes much lower than that in the baseline model, and the total output is lower as well. If rural workers were prohibited from migrating to cities, the model predicts that the urbanization rate would be 23.6944 percent by the end of 2007, while the urbanization rate in the benchmark model of 40.0948 percent; the total output would only be 81.0627 percent of that of the benchmark model in 2007. That is, shutting down the channel for rural migrant workers will result in roughly 40 percent lower in urbanization rate and 20 percent lower in total output of the economy in the end of the examining period. The comparisons in urbanization rates and total output levels between the benchmark model and this exercise are plotted in Figures 4(a)-(b). Continuation of the GJA in the post-1994 regime The next experiment conducted is to examine the case of continuation of the GJA policy. One would expect that the abolishment of the GJA scheme will make college education less attractable, 19 The simulated urbanization rate in the baseline model is lower than the data by 1.8719% for 1981-2007. 20 The data of total output is computed based on the model according to (1) and (4), using the data on urbanization rate and percentage of high- and low-skilled workers ratios out of total population. The average simulated output level is smaller by 2.9788 percent of that of the average output level of data for 1980-2007. The 18

resulting in a lower incentive for rural parents to send their children to attend college in urban area and bringing negative impacts on the economic development through a lower urbanization rate and hence a smaller total output. The question concerned is the magnitude of the negative impact of the annulment of the GJA. If the impact is minor, it justi es the decision of the abolishment of the GJA scheme; on the contrary, if the impact is huge, it would be better to keep subsidizing college graduates and cancel the GJA scheme later when the economy is more matured. We thus conduct a policy experiment, assuming that the GJA had been implemented in the post-1994 regime. Figures 5(a)-(b) plot the comparisons in urbanization rates and total output levels between the benchmark model and the current experiment. It turns out that if the GJA were kept in practice, the urbanization rate in the post-1994 regime is almost no di erent from that in the benchmark model, the average total output level for 1995-2007 is 0.8431 percent more than that in the benchmark model, and the positive e ect ot the GJA on total output seems to gradually decrease. By the end of 2007, the output level is only 0.7668 percent higher than that in the benchmark model. Our result shows that the abolishment of the GJA scheme only bring small negative impact on the economy. More job opportunities for rural migrant workers in the pre-1994 regime We now come to the experiment, assuming that rural migrant workers have the same job opportunities as those workers in the post-1994 regime. Figures 6(a)-(b) plot the comparisons in urbanization rates and total output levels between the benchmark model and the current experiment. Not surprisingly, both the urbanization rates and the output are higher than that in the benchmark model for 1981-1994. The urban in ux of low-skilled rural workers in the pre-1994 regime continues to contribute to the economic development in the post-1994 regime. The urbanization rate keeps increasing but at a slower pace. The output level is higher than the benchmark model by roughly 6 percent throughout 1995-2007, but the e ects of the in ux of rural migrant workers gradually die out. To sum up, the average output level and the urbanization rates for 1981-2007 increase by 4.9364 and 4.4494 percent, respectively. Fewer job opportunities for rural migrant workers in the post-1994 regime What would happen if China had not loosened the control over the hukou system and did not allow more rural people to come to cities to work? In this counterfactual analysis, we consider the case where the China government does not widen the door for rural migrant workers in the post- 1994 regime. The job nding rate for rural migrant workers is kept at the pre-1994 regime level. 19

The results are shown in Figures 7(a)-(b). The gap in urbanization rate and output between the benchmark model and the current exercise widen as time goes by. The urbanization rate is 4.626 percent lower than the benchmark model and reaches only 35.47 percent by 2007. The output is roughly 5 percent lower than the benchmark model in 2007, and the average output is decreased by 2.0703 percent for the entire post-1994 regime. Double urban job opportunities for rural migrants in both regimes Finally, we consider the case that China loosens its population movement control and promotes rural-urban migration in a way such that the urban job opportunities are doubled for 1980-2007. Since urban high and low skilled workers are Pareto complements in urban production, the in ux of rural low-skilled workers results in a lower N H =N L ratio, a higher demand for high-skilled workers and a higher wages for high-skilled workers. Parents are thus more willing to send children to urban area to attend college. Our numerical results for urbanization rate and total output are plotted in Figures 8(a)-(b). The urbanization rate would be 12.3486 percent higher in 2007, and the average output level would increase by 7.2689 percent for 1980-2007. 5 Conclusion The unique household registration system (or hukou system) in China has aroused more and more interests in research recently. This paper attempts to explore the economic impact of the hukou system on the Chinese economy. Earning a college degree in urban area is one of the important channels for rural people to obtain urban hukou, which usually comes with better social welfare bene ts and better career prospects. For a rural agent not able to accept college education, there is still urban job opportunities in cities for him or her, although the job opportunities, social welfare bene ts and career prospects are not as good as those for college graduates. We provide a general equilibrium framework and formally model rural parents decision in whether to send children to cities to attend college. The framework is calibrated to data from China and then counterfactual experiments are conducted. The abolishment of the joint job assignment for college graduates in 1994 is examined as well. We nd that if rural workers were prohibited from migrating to cities to work, the urbanization rate and the total output level would be 40 percent and 20 percent lower than those in 2007, 20

respectively. The abolishment of joint job assignment almost exerts no e ect on urbanization rate, brings minor negative impact on the Chinese economy, and lowers the output level by 0.8431 percent for 1995-2007. If China had promoted more job opportunities for rural migrants and permitted more rural migrant workers to work in cities in 1980-1994 in a way such that the urban job opportunity for rural workers are the same as that in the post 1994 era, the average output level would increase by 4.9463 percent for 1980-2007, and the urbanization rate would increase by 4.45 percent by the end of 2007. On the contrary, if China had not been loosening the control over the hukou system and promoting more job opportunities for rural migrant workers, the urbanization rate would be 4.626 percent lower by the end of 2007 and the average output level would decrease by 2.0703 percent for 1995-2007. Finally, if China had been loosening control over population movement and promoting rural-urban migration in a way such that the urban job opportunities were doubled for 1980-2007, the urbanization rate would be 12.3486 percent higher in 2007, and the average output level would increase by 7.2689 percent for 1980-2007. Although the current research starts with the aim of examining the e ects of zhaosheng and the e ects of the abolishment of the GJA scheme, the framework developed in this paper can further be applied to study the optimal migration policy. In the current framework, we do not consider the side e ects of the in ux of rural migrants on the cities, such as crowdedness, slums, smuggling, crimes and others. Those side e ects is possible to exert negative impact on the development and the growth of cities, and therefore the development of an economy. This is left for the future extension of this project. 21