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Industrial upgrade, employment shock, and land centralization in china.

I. INTRODUCTION

Traditional development economics considers the transfer of rural labor into the industrial sector the only way to balance the economic development in urban and rural areas. Chang (1949) mentioned that rural labor will not always stand in a static state on farms but that part of it will transfer into factories to engage in industrial production. Lewis (1954) established a dual-sector model and argued that the transfer of rural surplus labor from traditional sectors into modern industries is imperative. Later, Harris and Todaro (1970) changed the term of the industrial sector into urban sector by assuming that the former mainly exists in the cities. Since then, the dual-sector model has become a classical approach used in economic development research.

A closer look at coastal China, however, shows a more complex picture than the one predicted by a simple transfer of rural labor into the urban sector. In recent years, facing international competition, coastal China made great efforts to upgrade its industries; such efforts generate an adverse employment shock on peasant workers, forcing some of them to return to the countryside. For example, according to Zheng et al. (2007), the City of Suzhou upgrades its industries by attracting foreign manufacturers who possess more advanced technology and management. Many town-village enterprises (TVEs) and some State-owned enterprises (SOEs) lost their competition to foreign enterprises. Some had to close their businesses and others moved their production to inland areas. As a result, a significant portion of previous TVE and SOE employees was laid off. Peasant workers, especially those mid-aged workers who worked in TVEs, often find themselves lacking adequate skills to find new jobs in the industrial sector that now demand less unskilled workers. Many mid-aged peasant workers have to return to their villages and become farmers again. Worse, some returned peasant workers found little land left in their home villages because of the vast amount of land converted for urbanization and industrial uses (Zheng et al. 2007). For these land-lost peasants. survival becomes a challenge.

A new land conversion system, called land cooperation. seems to help peasant workers deal better with the adverse employment shock caused by China's industrial upgrading. Under the conventional land conversion system, local governments get land from peasants with one-time lump-sum compensations. which are often significantly lower than the fair market values. Once land is transferred to local governments. peasants lose both their land ownership and use rights. Under the new system. that is. the land cooperation system. peasants in the same village pool land together. invest land cooperatively into industrial and urban uses, and share returns jointly. Such land cooperation could mitigate the negative impact of employment shock because it not only allows peasants to keep their land ownership but also generates income 1-low for them. At the same time, the system could help local government centralize land because of better investment returns on land for urban and industrial uses.

Generally. China's rural labor transfer includes two groups: those who migrate to other cities and those who stay in local areas. In absolute numbers, the latter group is dominant. A number of studies have examined why farmers migrate into cities and become industrial workers (e.g., Zhao 1999; Zhang and Song 2003; Lu and Song 2006). They concluded that pushing factors include loss of land and high burden of taxes and lees in the countryside and pulling factors include higher income, better opportunities. better quality of life. and better education in cities. The backflow of rural migrants has not been studied by as many researchers. Hare (1999) and Zhao (2002) are exceptions. Hare (1999) belie% ed that the urban admittance system and immature factor market are two key factors of labor backflow in China. Zhao (2002) examined causes and consequences of return migration. Using the 1999 data of rural families From six provinces in China, she concluded that the factors influencing migration decisions include the unstable condition of land ownership, the urban admittance system, spouses leaving to work in other big cities. the proportion of adult labor in a family, and the development of nonagricultural sectors in rural areas.

Although cross-region rural-to-urban migration is important, this article focuses on the local rural-labor transfer, particularly in the coastal China where numerous farmers work in local TVEs. For local peasant workers, Hukou and high urban housing price are no longer the main challenges. In fact, more and more farmers want to keep their rural Hukou status because of the land entitlements and their ownership of dwellings in their villages or at the outskirts of their cities. Some peasant workers even own multiple housing units that are provided by the local government as compensation of land acquisition. However, many local peasant workers, especially those who are mid-aged TVE employees, now experience greater risk of being laid off and have more difficulties in finding new jobs because of the downsizing of the TVE sector and lack of skills for new positions in China's upgraded industrial sector.

We do not see any theoretical analysis on the relationship between backflow of peasant workers, the recent promotion of industrial upgrade. and rural land conversion systems. This article attempts to fill this gap. Inspired by a recent case study in Suzhou. China, about challenges faced by peasant workers in the era of industrial upgrading, done by Zheng et al. (2007). we develop a theoretical model to investigate how industrial upgrading generates adverse employment shocks on mid-aged blue-collar workers and make them return to the countryside. This article addresses age-related unemployment shock caused by efforts of industrial upgrading. not the employment condition of the general migrant population. We also show that. one-time compensation of land conversion is inferior because of the low compensation and the risk of backflow caused by adverse employment shocks. Consequently, such land compensation system would slow clown the pace of land conversion and hinder industrial upgrading in China. One possible solution, as theoretically proved in this article, is to have a land cooperation system in rural areas. Under this system, local governments do not acquire farmers land with low compensations. Instead. farmers keep their land ownership by investing land into urban-sector uses. Through such land investment, rural land is centralized for industrial purposes; it also generates incomes for rural laborers, helping them face employment shocks brought by industrial upgrading.

Section II elaborates how industrial upgrading causes adverse employment shocks on mid-aged peasant workers. Section III first discusses the influence of adverse shock on mid-aged peasant workers under the one-time lump-sum compensation system and then examines how a land cooperation system could reduce the impact of adverse shock and help land centralization for industrial uses. Section IV concludes.

II. INDUSTRIAL UPGRADING AND ADVERSE EMPLOYMENT SHOCK

In recent years, in order to raise its international competitiveness, China has made great efforts to promote industrial upgrading by providing enterprises with free or low-cost land, direct subsidies, and tax breaks. For example, in the coastal region, local governments often use the guidelines developed by the central government to attract foreign enterprises only if they help to upgrade industries. In consequence, investment in local TVEs and SOEs decreases relatively to those in foreign enterprises. Furthermore, local governments encourage early-attracted processing and assembling foreign direct investment enterprises to move to less developed inland areas. With such a switch from low-value-added activities to high-value-added and more sustainable industries. east China sees sectoral shifts and employment shocks on workers, especially on low-skilled and mid-aged peasant workers who work in the TVE sector. New positions in the upgraded industries now demand better-educated and more-skilled workers who tend to be younger, making less educated and mid-aged peasant workers face more difficulty in finding new jobs.

This study theoretically investigates how the promotion of industrial upgrading affects a firm's hiring decisions. For this purpose, we classify workers into two general groups, blue-collar and white-collar workers. We further divide blue-collar workers into young and mid-aged workers. Because the legal retirement ages for blue-collar workers in China are 50 years for female workers and 55 years for male workers, one possible cut-off age could be 40 years. Throughout this article, we will use a firm-level employment model, which assumes (a) the difference in age determines the difference in physical labor supplied and (b) the industrial upgrading within a company is driven by endogenous reasons such as profit maximization and exogenous reasons including government subsidies and tax breaks.

Specifically, we assume that a company uses three inputs in production, namely blue-collar labor input as [n.sub.1]l, white-collar worker input as [n.sub.2]t and capital input as K, with [n.sub.1] representing the number of blue-collar workers hired, I the amount of labor provided per blue-collar worker, [n.sub.2] the number of white-collar workers hired, t the amount of labor input provided per white-collar worker, and [bar.K] the fixed amount of capital. For simplicity, blue-collar workers are all from rural areas, as a result of migrants' lack of education and job-training. We further assume that l is a function of worker's age, b, with [l.sub.1] for young workers (such as 40-year-old or younger) and [l.sub.2] for mid-aged workers (above 40-year-old). Because young workers offer more physical labor input than mid-aged workers, we have [l.sub.1] > [l.sub.2]. Therefore, the firm's production function becomes f([l.sub.1]l(b), [l.sub.2]t, [bar.K]). which satisfies [f.sub.1], [f.sub.2] [greater than or equal to] 0, [f.sub.11], [f.sub.22] [greater than or equal to] 0. We also assume that product price, P. depends on a, the value-added of production, with P'(*) [greater than or equal to] 0, P"(*) [less than or equal to] 0. We let [alpha] = [n.sub.2]t +d, the value-added, be a function of white-collar labor input, where d is a parameter that measures the level of industry's technology upgrading.

In this article, to make our model workable, we assume fixed capital because our analysis attempts to examine how industrial upgrading adversely affects employment of mid-aged peasant workers. Hence, our model is a partial equilibrium model. However, our assumption of fixed capital also helps to derive important implications. In the value-added formula, we did not include [n.sub.1] because it represents the amount of blue-collar labor, which is abundant in China, with wages being stagnated at a very low level, implying that the marginal effect of [n.sub.1] remains little change. In other words, we consider the concept of value added with a perspective of the industrial upgrading and try to measure the dynamic marginal effects of [n.sub.2] and d on [alpha].

Currently, the movement of industrial upgrading is directed largely by the government through land provision and tax subsidies. Such movement, many policy-makers believe, will help local governments increase fiscal revenues through enhancing the profits of local enterprises and their international competitiveness. Industrial upgrading is also a very important measure for the upper-level government to assess the local government officials. Therefore, local governments have strong incentives to promote industrial upgrading through various programs, such as by providing enterprises with a research and development (R&D) subsidy of s per white-collar worker. In reality, local Chinese governments apply various instruments to promote industrial upgrading, including tax reduction, R&D subsidies, and technical training. In our model. we use s to proxy the combined local government efforts.

Assume that an enterprise receives an allowance of s per white-collar worker and labor total cost [n.sub.1][sigma][omega] + [n.sub.2][omega]. where [omega] is the wage rate received by white-collar workers and 0< [sigma] < 1. meaning that blue-collar workers get a proportion of the wage rate received by white-collar workers. Then, the profit maximization of the enterprise becomes:

(1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The first-order conditions are:

(2) [f.sub.1](+)I(b)P([n.sub.2]t + d) - [lambda][sigma][omega] = 0

(3) [[f.sub.2](+)P([n.sub.2]t + d) + f(+)P([n.sub.2]t + d)]t + st - [lambda][omega] =0

Combining Equations (2) and (3) and simplifying them. we have

(4) (I(b)/[sigma])[f.sub.1](*) - t[f.sub.2](*)- (If(*)P'(([n.sub.2]t + d) + s]t)/P([n.sub.2]t + d) = 0.

We want to examine the impact of industrial upgrading on the employment of mid-aged peasant workers. For this, we investigate two relationships. The first one is between a and [n.sub.1]l, assuming that industrial upgrading will increase the level of value-added in production and thus the demand for blue-collar workers. The second relationship is between the government efforts to promote industrial upgrading and the demand for blue-collar workers.

Taking the derivative of [OMEGA] = [n.sub.1]l(b) with respect to d on Equation (4), we get

(5) [sigma][OMEGA]/[sigma]d [greater than or equal to] 0

The proof of Equation (5) is straightforward: because [f.sub.1] > 0 and [f.sub.12] > 0, industrial upgrading will raise the marginal benefit of employing physical labor and thus leads to a larger [OMEGA]. Equation (5) suggests that the amount of blue-collar labor input, [n.sub.1] l, would increase with industrial upgrading. In turn, the demand for l will increase if [n.sub.1] is fixed. This implies that the enterprise will replace part or even all of [l.sub.1] with [l.sub.2]. Accordingly. the enterprise would lay off some mid-aged workers and replace them with young employees. Therefore, we have proved the following proposition.

PROPOSITION 1. When enterprises are in the process of industrial upgrading and if the number of blue-collar workers is fired, they replace part or all of the mid-aged workers with young workers, creating an adverse employment shock on mid-aged peasant workers.

Similarly, by providing subsidies to enterprises, government's efforts to promote industrial upgrading also create an adverse employment shock on mid-aged peasant workers. Taking the derivative of [OMEGA] = [n.sub.1] l(b) with respect to s on Equation (4), we get

(6) [sigma][OMEGA]/[sigma] s [greater than or equal to] 0.

The above equation demonstrates that the demand for blue-collar labor input, [n.sub.1] l. would increase with government subsidy on industrial upgrading. It the number of blue-collar workers is fixed. Equation (6) suggests that l will increase, which means that enterprises will replace mid-age workers with young workers. In turn. we have derived the following proposition.

PROPOSITION 2. If the number of blue-collar workers. is fixed, local government subside on industrial upgrading would make enterprises substitute more young workers for mid-aged workers, causing an adverse employment shock on mid-aged peasant workers.

Several points are worth mentioning. First. the above propositions have different emphases. Proposition I, through the impacts of industrial upgrading on the level of value-added in production and thus the price of industrial products, shows how industrial upgrading creates an adverse employment shock on mid-age blue-collar workers. It tells how the market force determines the demands for various types of workers. Proposition 2, by relating government's subsidy to the amount of blue-collar labor input, shows how government efforts to promote industrial upgrading causes an adverse employment shock on mid-age blue-collar workers. It shows the direct impact of government policy on enterprises' demand for various types of workers. Second. in the above analysis. we treated peasant workers as pure physical workers in a static state. In reality, however. some migrant workers could he white-collar workers and more will become white-collar workers through education and job-training. But this should not change our general conclusions. especially because enterprises may make more efforts to train young workers than to train mid-aged workers. Third, in the above analysis, we only considered the impact of industrial upgrading on the value-added of product. However, industrial upgrading also improves production efficiency. Yet, our general conclusions remain the same because our production function is in its general form, which already captures the efficiency improvement through changes of various labor inputs. Finally, in proving Propositions 1 and 2, we assumed that the number of blue-collar workers is fixed. This assumption should be considered as a necessary condition but not a sufficient condition for the two propositions, because increasing [n.sub.1] l could also suggest an increase in [n.sub.1] l or both [n.sub.1] and I. Increasing both [n.sub.1] and l will not change our general conclusions in Propositions 1 and 2.

III. LAND CENTRALIZATION AND MITIGATION OF ADVERSE EMPLOYMENT SHOCK

In many Chinese cities, a vast amount of rural land is centralized and used for industrialization and urbanization, through either government's acquisition, land leasehold, or land cooperation. In this article, inspired by Yao (2004), we develop a model to analyze how a peasant household arranges production factors when it faces an adverse employment shock. Specifically, in Section III.A, we assume that local governments acquire land from peasants with lump-sum compensations but that they cannot force peasants to sell their land. In Section III.B, we will generalize our analysis by including the option of land cooperation in rural areas.

It is worth mentioning that land ownership in rural areas belongs to collectives. Individual farmers only have the right to use the land, on 30-year contracts. Land acquisitions are made between the government and collectives through village committees. Once land is acquired for nonagricultural uses, land ownership goes to the government and farmers lose the land forever. By law, individual farmers are compensated, mostly with monetary lumpsums, which are often greatly under paid. In some cities, instead of paying money, local governments provide land-lost farmers with free apartments or consider acquired land as investment from farmers. In these cases, farmers will be able to receive rents from their apartments if they rent them out or land that is used for industrial purposes.

A. One-Time Lump-Sum Land Compensation

Assume peasant workers face a two-stage life-cycle decision process. At the first stage, in ages below or equal to 40 and with an employment level [L.sub.1], peasant workers arrange their initial resources. Between stage 1 and stage 2, they face an adverse employment shock caused by industrial upgrading, as discussed in Section II. At the second stage, peasant workers are in mid-ages and the adverse employment shock has taken place. The employment becomes [L.sub.2] = [L.sub.1][theta], where [theta] is a nonnegative random variable representing the adverse employment shock on peasant workers. Over [0, [L.sub.1]], [theta] is distributed with a probability density function [PHI]([theta]|[epsilon]) and a cumulative distribution function [PHI], with a conditional parameter [epsilon] representing the scale of industrial upgrading and thus [partial derivative][PHI](theta]|[epsilon])/[partial derivative][epsilon] [less than or equal to] 0.

Let [bar.L] and [bar.T] be the initial peasant's endowments of labor and land, respectively. Under the one-time lump-sum compensation system, peasant workers have three income sources. One is the farming income, with an agricultural production function F([T.sup.f], [L.sup.f]), where [T.sup.f] is the land input and Ll is the labor input. In the following analysis, we let the unit price of agricultural product equal 1 and all other prices be relative to this price. The second source is the wage income from the industrial sector, with an exogenous wage rate [omega]. The third source is a one-time lump-sum compensation from a local government in a land transaction [T.sup.b]([r.sup.b] - [c.sup.b]), with [T.sup.b], [r.sup.b], and eh being the amount of land transferred, unit land price, and unit transaction cost, respectively.

We use a Cobb--Douglas production function F([T.sup.f], [L.sup.f]) = [([T.sup.f]).sup.[alpha]][(L.sup.f]).sup.[beta]] to describe the agricultural production. Later in Section III.B, we will add the commonly used term A into the production function for efficiency improvement. To ensure the concavity of function and based on empirical finding of decreasing return to scale in agricultural production (Hayami and Ruttan 1985; Kamat, Tupe, and Kamat 2007; Shi, Meng, and Wang 2008), we assume that [alpha] < 1, [beta] < 1, and [alpha] + [beta] < 1. Therefore, in the first stage, a peasant worker is to

(7) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

[L.sub.1.sup.[omega]] [less than or equal to] [L.sub.1.sup.[omega]]:

[L.sub.1.sup.f], [L.sub.1.sup.[omega]], [L.sub.1.sup.f], [L.sub.1.sup.b] [greater than or equal to] 0

where [L.sub.1.sup.f], [L.sub.1.sup.[omega]], [L.sub.1.sup.f], [L.sub.1.sup.b] represent the labor input used in the agriculture production, labor input supplied to the industrial production, the land used in the agricultural production, and the land transferred to the local government, respectively. [mu] is the discount factor with [mu] < 1. [[pi].sub.2.sup.*] is the optimal value of peasant income in the second stage. Assuming an optimal interior solution exists, we get the following first-order conditions:

(8) [beta][([T.sub.1.sup.f].sup.[alpha[([L.sub.1.sup.f].sup.[beta]-1 - w = 0

(9) -[alpha] ([bar.T] - [[[T.sub.1].sup.b].sup.[alpha]-1]][alpha[([L.sub.1.sup.f].sup.[beta]] + ([r.sub.b] - [c.sub.b] + [mu]([partial derivative]E[[pi].sub.2].sup.*]([[T.sub.1].sup.b])]/[partial derivative][[T.sub.1].sup.b] = 0.

Equation (8) shows that peasant's marginal benefit from agricultural production equals the wage rate working in an enterprise. Equation (9) demonstrates that the current and expected losses in agricultural production be compensated by the one-time lump-sum compensation. This condition suggests that a peasant worker make land transfer decision by considering both current and future agricultural profits. We regard the third term of Equation (9) as the shadow price of land transfer. P, which depends on peasant's expected income from the second stage and affects positively the amount of land transferred in the first stage, that is,

(10) ([partial derivative][[T.sub.1].sup.b]/[partial derivative]P > 0.

In the second stage, facing the adverse employment shock caused by industrial upgrading, a peasant worker is to

(11) Max [[pi].sub.2] = [([bar.T] - [[T.sub.1].sup.b]).sup.[alpha] [([[L.sup.2].sup.f]).sup.[beta] +[omega][[L.sub.2].sup.w][[L.sub.2].sup.f][L.sub.2.sup.f], [L.sub.2.sup.[pi]] s.t. [[bar.L].sub.2.sup.f] + [[bar.L].sub.2.sup.[omega]]; [L.sub.2.sup.f], [L.sub.2.sup.[omega]

Accordingly, we get Kuhn-Tucker conditions:

(12) [beta][([bar.T - [[bar.T].sub.1].sup.b]).sup.[alpha]] [([bar.L] - [L.sub.2.sup.[omega]]).sup.([beta]-1)] - [omega] + [lambda] = 0.

(13) [lambda]([bar.L].sub.2.sup.[omega]] - [L.sub.2.sup.[omega]] [greater than or equal to] 0.

Denote [L.sub.2.sup.[omega]]* to be the solution of the above equation. When [lambda] > 0, we have [beta][([bar.T] - [T.sub.1.sup.b]).sup.[alpha]] [([bar.L] - [L.sub.2.sup.[omega]]).sup.([beta] - 1) - [omega] < 0 and possibly [[bar.L].sub.2.sup.[omega]] - [L.sub.2.sup.[omega]]* = 0, implying that enterprises are offering wthzes much higher than the agricultural income and thus virtually all peasants are eager to enter the industrial sector. In this case, we use [[bar.L].sub.2.sup.[omega]], to substitute for [L.sub.2.sup.[omega]]*. Let [bar.[theta]] be the maximum of O. We can rewrite the shadow price of land transfer as follows:

(14) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Integrating by parts of Equation (14), we get

(15) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

To investigate the impact of industrial upgrade scale [epsilon] on the shadow price of land transfer, we take the derivative of the above function with respect to [epsilon]. We obtain

(16) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

because of ([partial derivative][PHI]([partial derivative][epsilon])) [less than or equal to] 0 and d ([([bar.T] - [T.sub.1.sup.b]).sup.([alpha] - 1)])([([bar.L] - [L.sub.2.sup.[omega]]).sub.[beta]] > 0. Combining Equations (10) and (16), we derive the following relationship between the amount of land transferred in the first period and the scale of industrial upgrading.

(17) ([partial derivative][T.sub.1.sup.b]|[partial derivative][epsilon]) = ([partial derivative][T.sub.1.sup.b]|[partial derivative]P)([partial derivative]P|[partial derivative][epsilon]) < 0.

Therefore, we conclude that industrial upgrading (thus higher E) will cause less land voluntarily transferred by peasant workers, leading to a slower pace of land centralization for industrial and urban uses.

The above conclusion, however, is not surprising. With industrial upgrading, an adverse employment shock exists for mid-age peasant workers, resulting in a higher possibility for peasant workers to return to home villages and lower incentive for them to sell their land. In other words, the relative marginal return of land would increase with peasant workers flowing back to villages. To balance the marginal land return of the two stages, peasant workers will reduce land transfer in the. first stage.

One possible solution to help land centralization is to lower the unit land transaction cost by better defining rights of land for peasants. Mathematically, based on Equation (9), we can prove that a lower land transaction cost will lead to more land transferred in the first period, because

(18) ([partial derivative][T.sub.1.sup.b]|[partial derivative][c.sup.b]) = (1/(([[alpha].sup.2] - [alpha])[([bar.T] - [T.sub.1.sup.b]).sup.([alpha] - 2)] [([L.sub.1.sup.f]).sup.[beta]] + [mu][([L.sub.2.sup.f]).sup.[beta]])) < 0

where [[alpha].sup.2] - [alpha] < 0, given 0 < [alpha] < 1.

The above discussions allow us to state the following proposition.

PROPOSITION 3. Facing an adverse employment shock caused by industrial upgrading, peasant workers have a higher possibility of returning to rural land and thus less motivation to sell their land under the one-time lump-sum compensation system. This slows down the pace of land centralization for industrial purposes. However, lower transaction cost could promote land transfers and help land centralization.

B. Land Cooperation

In some Chinese cities such as Suzhou, an innovative approach to centralizing rural land is land cooperation (Zheng et al. 2007). Under this new system, rural land is centralized within a collective and managed jointly by peasants. The land cooperation system exhibits two main advantages. First, although peasants still keep their land ownership, they pool land together and rent bulk part of land for industrial and city uses. This will not only help peasants better plan for their land use but also enhance peasants' bargaining power in land transactions, thus better protecting their welfare in both long and short terms. Second, by pooling land together and managing land jointly, the new system helps to promote large-scale agricultural production and improve efficiency. In China, after the agricultural reform, land in rural areas has been divided into small pieces, making production and mechanization more difficult. Land cooperation would pool the small pieces of land together and make mechanization easier, helping agricultural output increase further.

How could the land cooperation system help to mitigate the adverse employment shock caused by industrial upgrading on mid-aged peasant workers? To answer this question, we acid a term A into the agricultural production function to capture the efficiency gain generated by land cooperation and large-scale production, thus A < l relative to the production function used in Section III.A. It is important to understand that A < 1 is not contradictory to the empirical evidence of decreasing return to scale in agricultural production, because A measures the efficiency gain of land pooling, not [alpha] + [beta]. Put differently, given the same amount of land and labor inputs, the term A tells the efficiency gain generated by land centralization.

Denote N to be the number of peasants in a land cooperation. Assume other factors remain the same as those in Section I1I.A, such as an individual peasant's labor and land endowments[bar.L] and [bar.T]. the Cobb--Douglas form of production function, and the industrial wage rate [omega]. Therefore, a land cooperation has a production function [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

For an individual peasant i, we denote [T.sup.g] and [L.sup.g] to be his land and labor inputs to the cooperation, respectively. For other peasants, j [member of] N and j [not equal to] i, we denote [T.sup.g]* and [L.sup.g]* to be the optimal land and labor inputs devoted by peasants j, respectively. Peasant's income from the cooperation is endogenous, with the wage [[omega].sup.g] and land rent [r.sup.g] depending on the marginal output of labor and land, as shown in the following equations:

(19) [[omega].sup.g] = ([partial derivative] G|[partial derivative][L.sup.g]) = A[[beta]l(N - 1)[T.sup.g]* + [T.sup.g]].sup.[alpha]][[(N- 1)[L.sup.g]* + [L.sup.g]].([beta] - 1)]

(20) [r.sup.g] = ([partial derivative] G|[partial derivative][L.sup.g]) = A[[alpha]l(N - 1)[T.sup.g]* + [T.sup.g]].sup.([alpha] - 1)][[(N- 1)[L.sup.g]* + [L.sup.g]].[beta]]

For a typical or average peasant, because of A > 1 and N > 1, we have A[N.sup.([alpha]+[beta]-1)] > 1. Therefore, the marginal income of labor in the cooperation is always higher than that of self-cultivated land, suggesting that peasants are willing to put more labor into the cooperation. In turn, this will increase the marginal return of land used in the cooperation, as seen in Equation (20). making peasants invest more land to the cooperation. In other words, land cooperation is able to absorb more workers and promote land centralization. Thus, it helps to mitigate the negative impact caused by exogenous adverse employment shock on peasant workers.

Under the land cooperation system, the optimization problem for a peasant becomes:

(21) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

In Appendix 1. we list all live first-order conditions with Equations (Al)-(A5). If all the peasants in the cooperation are assumed to he the same, we can use [L.sup.g], [T.sup.g] to replace all the [L.sup.g]*, [T.sup.g]* in the first-order conditions and simplify these equations. Specifically. by combining Equations ( Al) and (A3) and Equations (A2) and (A5). we get the following two results. respectively

(22) [alpha][L.sup.f]/[beta][T.sup.f] = [[lambda].sub.1]/[[lambda].2]

(23) [alpha][L.sup.g]/[beta][T.sup.g] = [[lambda].sub.1]/[[lambda].2]

From the above equations. we derive that,

(24) [L.sup.f][T.sup.f] = [L.sup.g]/[T.sup.g]

indicating that the optimal labor-to-land ratio is the same for self-cultivation and cooperation production. This interesting result. derived from the model. confirms our earlier argument that the efficiency gain from land pooling (A > 1) is not contradictory to the decreasing returns to scale in the production function ([alpha] + [beta] < 1)

To examine how the land cooperation affects land centralization for industrial uses. we discuss the ratio of [T.sup.g]/[T.sup.f] and investigate how this ratio changes with the scale of land cooperation. From Equations (A3) and (A5) in Appendix l. we obtain the following optimal ratio between land invested in cooperation and used for self-cultivation. A:

(25) A = [T.sup.g]/[T.sup.f] = [1/(A[N.sup.([alpha] + [beta] -2)](N + [alpha] + [beta] - 1)).sup.(1/[alpha] + [beta] -1)]

Appendix 2 derives the above equation. Given N > 1, the above ratio is strictly positive. meaning the amount of land invested in a cooperation from its peasants never equals to zero and thus our Laaange solution is the overall optimal solution. The result also shows that the cooperation has enhanced the welfare of its peasants.

On the basis of Equation (25). because of 0 < [alpha] + [beta] <1. it is not difficult to see that A increases along with the growth of A, because cat

(26) [partial derivative]A/[partial derivative]A = (1/(1 - [alpha] - [beta]))[A.sup.(([alpha] + [beta])/1 - [alpha] - [beta]) x l[N.sup.([alpha] + [beta] -2])(N + [alpha] + [beta] - 1)[l.sup.(l/(1 - [alpha] - [beta])] > 0

This result suggests that peasants are more willing to invest land in a cooperation with better production efficiency brought by a large-scale production. Again, we have proved that land cooperation not only improves efficiency but helps land centralization as well.

Appendix 3 proves that A decreases with N but NA increases with N for N > I. a given condition For any land cooperation. showing that individually the proportion of land invested in a land cooperation decreases with the number of peasants joining the cooperation, but collectively this proportion increases with the number of peasants joining the cooperation. Because many costs and problems arise with the size of an organization. such as transaction cost and the Free-ride problem. there could exist an optimal level of N. which could vary from one cooperation to another. Zheng et al. (2007) consider village as a good size for land cooperation, as evidenced by the experiences in south Jiangsu Province.

The above analyses allow us to give our last proposition.

PROPOSITION 4. When an adverse employment shock on peasants exists during industrial upgrading, land cooperation helps to mitigate the negative impact on the process of land centralization and the welfare of peasant workers. Peasants are more willing invest their lain] in a land cooperation because of better efficiency and higher returns. Also, the total amount of land invested in land coopercuion increases proportionally with the number of peasants joining the cooperation. thus promoting land centralization.

IV. CONCLUSIONS

Facing international competition, China made great efforts in recent years to upgrade its industries. These efforts, however. generate an adverse employment shock on peasant workers because of their lack of adequate skills to keep or rind jobs in the industrial sector. Many of them have to flow hack to their villages and become Farmers again. Some returned peasant workers even round that survival in the countryside becomes a challenge because or the amount of land converted for urbanization and industrial uses.

Using a firm-level employment model, this article has theoretically proved that firms would replace mid-aged peasant workers with younger workers, causing an adverse employment shock on peasant workers. This adverse employment shock would force some rural workers to return to their home villages, especially mid-aged workers. The current lump-sum land acquisition system, however, is unable to help peasant workers mitigate the negative impact of the employment shock when they face a risk of backflow to home villages, because peasants found it uneconomical to sell their land if the compensation was too low. Therefore, the current land acquisition system makes it more difficult to centralize rural land for industrial and urban uses.

This article has also proved that land cooperation could help peasant workers better deal with the adverse employment shock and centralize rural land for nonagricultural purposes. Under the land cooperation, peasants in the same village pool land together, invest part of the land for industrial and urban uses, and share profits jointly. Because of the large scale of production and higher returns from nonagricultural uses, land cooperation would not only improve agricultural efficiency but also increase peasants' incentive to invest their land for urban purposes. The former helps peasant workers mitigate the negative impact of employment shock, whereas the latter promotes land centralization for industrial and urban uses. Both improve peasant welfare.

On the basis of our theoretical findings, we propose two policy recommendations. First, to upgrade China's industries, it is important for the government to provide peasant workers with job-training and education opportunities. With the rapid pace of urbanization, more and more farmers will migrate into cities. Without adequate job-training and education, rural migrants, especially those mid-aged ones. would have a very low employability and thus many of them could become the urban poor. Second, China needs to further reform its rural land system. Under the current land expropriation system, local governments compensate farmers too little. It deprives peasants' interests and hinders land centralization. To better protect peasants' land rights and welfare, various land conversion systems could coexist, depending largely on peasants' choices rather than going with local governments' decisions. Given the huge rural population, China would not possess a harmonious society if peasants are left behind and unable to benefit from the overall economic development.

APPENDIX 1

Using Lagrange's theorem to Equation (21). we get the following five first-order conditions:

(Al) [alpha][([T.sup.f]).sup.([alpha] - 1)][([L.sup.f]).sup.[beta]] - [[lambda].sub.1] = 0

(A2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(A3) [beta][([T.sup.f]).sup.[alpha]][([L.sup.f]).sup.([beta] - 1)] - [[lambda].sub.2] = 0

(A4) [omega] - [[lambda].sub.2] = 0

(A5) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [[lambda].1] and [[lambda].2] are Lagrange multipliers.

APPENDIX 2

Dividing Equation (A3) by the simplified Equation (A5), we get:

(A6) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Because of [L.sup.f]|[T.sup.f] = [L.sup.g][T.sup.g], we rewrite the right side of the above equation as:

(A7) 1 = (I/(A[N.sup.([alpha] + [beta] -2])(N + [alpha] + [beta] -1)[(T.sup.f]/[T.sup.g]).sup.([alpha] + [beta] -1)]

Solving the ratio of [T.sup.g]/[T.sup.f], we obtain:

(A8) A = [T.sup.g]/[T.sup.f] = [(1/(A[N.sup.([alpha] + [beta] -2)](N + [alpha] + [beta] -1)).sup.(I/([alpha] + [beta] - 1)]

APPENDIX 3

Let [alpha] + [beta] - 1 = x and thus x<0. Equation (A8) becomes

(A9) A = [(1/(A[N.sup.(x-1)(N + x)).sup.1/x].

Taking the partial derivative of Equation (A9) with respect to N. we get:

(A10) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Similarly.

(All) l) NA = N[(I/(A[N.sup.(t-1)(N + x)).sup.1/x]

Taking the partial derivative of Equation (All) with respect to N. we get:

(A12) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Therefore. A decreases with N but NA increases with N for N > 1. This result shows that individually the proportion of land invested in a land cooperation decreases with the number of peasants joining the cooperation. but collectively this proportion increases with the number of peasants joining the cooperation.

ABBREVIATIONS

R&D: Research and Development

SOE: State-Owned Enterprise

TVE: Town-Village Enterprise

REFERENCES

Chang, P. K. Agriculture and Industrialization. Cambridge. MA: Harvard University Press. 1949.

Hare. D. "'Push' versus Tull' Factors in Migration Outflows and Returns: Determinants of Migration Status and Spell Duration among China's Rural Population." Journal of Development Studies. 35(3). 1999. 45-72.

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Kamat. M., S. Tupe, and M. Kamat. "Indian Agriculture in the New Economic Regime, 1971-2003: Empirics Based on the Cobb Douglas Production Function." MPRA Paper No. 6150. 2007. Accessed September 29. 2010. http://mpra.ub.uni-muenchen.de/6150/.

Lewis. W. A. "Economic Development with Unlimited Supplies of Labour." Manchester School. 28(2). 1954. 139-91.

Lu. Z., and S. Song. "Rural-Urban Migration and Wage Determination." China Economic Review, 17. 2006. 337 -45.

Shi. H.. L. Meng, and H. Wang. "Regional Differences and fluctuations of China's Agricultural Productivity: A Stochastic Frontier Production Function Analysis." Economic Science. 3, 2008. 20-33.

Yao, Y. Land. Institution and Agricultural Development. Beijing. China: Peking University Press. 2004.

Zhang. K. H., and S. Song. "Rural-Urban Migration and Urbanization in China: Evidence from Time-Series and Cross-Sectional Analyses." China Economic Review, 14(4). 2003. 386-400.

Zhao. Y. "Leaving the Countryside: Rural to Urban Migration Decisions in China." American Economic Review. 89(2). 1999. 281-6.

--."Causes and Consequences of Return Migration: Recent Evidence from China." Journal of Comparative Economics. 30. 2002. 376-94.

Zheng.J., H. Zhao. C. Wang, and C. Chen. "Building Up the Status of Peasants and Eliminating the Development Diversity." Journal of Northwest University. 95(3), 2007. 12-18.

Sang: Department of Economics, University of Nevada. Reno, NV 89557-0207; School of Economics. Zhejiang University. Hangzhou, China. Phone 775-784-6860, Fax 775-784-4728, E-mail song@unr.edu

Wang: School of Economics, Australia School of Business, University of New South Wales. Sydney NSW 2052, Australia. Phone 61-2-9385 9903. Fax 61-2-9313 6337. E-mail chengsi.wang@unsw.edu.au

Zheng: Department of Industrial Economics, Nanjing University. Nanjing, Jiangsu 210093. China. Phone 86-13337811016. Fax 86-25-83595262, E-mail zhengjh@nju.edu.cn

doi:10.1111/j.1465-7287.2011.00266.x
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Author:Song, Shunfeng; Wang, Chengsi; Zheng, Jianghuai
Publication:Contemporary Economic Policy
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Date:Oct 1, 2012
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