Rural-urban wage differentials, unemployment, and efficiency wages: an open economy policy analysis.

• Author: Chin, Judith C.

1. Introduction

   In a competitive and perfectly functioning market economy with a homogeneous labor force, the equilibrium value of the marginal worker's output is equated across all sectors of the economy. Full employment is achieved, and the market's allocation of labor is efficient.

   In the real world, however, labor market outcomes often deviate sharply from this ideal. In particular, large intersectoral wage differentials accompanied by high urban unemployment are frequently observed in the economies of developing countries. When one sector's wage is markedly higher than another sector's wage, moving workers from the low-wage sector to the high-wage sector would increase the value of national output. Similarly, when there are unemployed workers, increasing employment in either sector would increase the value of national output. The existence of large wage differentials and urban unemployment thus suggests that these economies' labor markets are not functioning properly.

   Given this evidence of labor market failure, the question arises as to what a government can do to push such an economy toward an efficient allocation. International trade economists have partially addressed this question within the more general framework of the literature on policy and domestic distortions (see, e.g., Johnson 1965; Bhagwati 1971). This literature seeks to rank corrective trade and domestic policies in terms of their potential for improving welfare when an economy has a domestic distortion. The standard result is that the best policy instrument to correct a domestic distortion is the instrument that most directly addresses the distortion. Hence, a wage differential would be most efficiently corrected by direct intervention in the affected labor market.

   One shortcoming of the traditional policy ranking literature is that the models generally do not allow for unemployment. Recalling the original work of Harris and Todaro (1970), one might think that sector-specific policies would not improve welfare in the presence of urban unemployment; rural losses may offset the urban gains if more workers are drawn to the urban sector and become unemployed. Thus, perhaps even the most targeted policy instrument may not improve the allocation of resources when unemployment exists.

   Another problem with the traditional policy ranking literature is that the models used generally assume an exogenously determined distortion. Such an assumption of course precludes the possibility that policies may affect the size of the distortion. More recent work has considered various possible endogenous mechanisms through which an equilibrium wage differential may evolve (see, e.g., Stiglitz 1974, 1976; Calvo 1978; Calvo and Wellisz 1978; Bulow and Summers 1986). This literature, however, has not focused on the ranking of trade policies versus more targeted policies aimed at correcting the domestic distortion.

   In this paper, an efficiency wage model of the Bulow and Summers (1986) type is applied to a small, rural-urban open economy with urban unemployment to analyze the impact of various policies meant to improve the allocation of labor within the economy. With this model, the analysis incorporates each policy's potential impact both on the wage differential that exists in equilibrium and on the equilibrium level of urban unemployment. The policies explicitly considered are an urban wage subsidy, an urban production subsidy, and a tariff on the urban good. These policies are analyzed for their effects on the value of national output and for their distributional effects on the discounted lifetime expected utilities of different workers.

   The analysis shows that, while these policies are able to raise the value of national output, their distributional effects depend on the production technology of the rural sector. In some cases, these policies make every type of worker worse off. Here, redistribution effects may limit the viability of intervention. In most cases, however, these policies are Pareto improving.

   In related literature, others have explored the desirability of subsidies and tariffs in efficiency wage models of wage differentials with full employment. For a closed-economy, dual labor market model, Bulow and Summers (1986) find that subsidies to increase urban employment are Pareto improving policies. For the analogous small, open economy, however, Bulow and Summers only discuss the welfare-improving effects of protection over free trade; they do not discuss the role of more direct policies for countering the labor market distortion. Copeland (1989) analyzes a two-sector, two-country model in which workers are hired for two different types of jobs; again, one type of job can only be monitored imperfectly. However, in Copeland's model, both sectors of production hire workers for both types of jobs; migration between job types does not entail migration between production sectors. For this model, Copeland finds that a wage subsidy is better than a tariff and better than a production subsidy for national welfare; he also shows that, in certain circumstances, a small tariff will increase national income. However, neither of the above papers incorporates urban unemployment into an open-economy policy analysis, although Bulow and Summers model the case of urban unemployment for a closed economy.

   Two papers that incorporate unemployment into an open-economy efficiency wage model are Brecher (1992) and Hoon (1991). Brecher (1992) explores the role of unemployment in a two-factor, three-good model with an efficiency wage. However, unlike the present paper, workers are paid a uniform efficiency wage. Hoon (1991) also considers a model with a uniform efficiency wage and efficiency wage-driven unemployment; his purpose is to study the impact of trade on the equilibrium unemployment rate. Neither paper explores the wage gap problem, the sector-specific unemployment, or the sector-specific policies on which this paper focuses.(2)

   A paper more closely related to the present paper is the work of Matusz (1994), which examines the role of trade policy in a two-sector model with equilibrium unemployment and sector-specific wage differentials. The model, however, is somewhat different from the model in the present paper; Matusz assumes fully mobile capital and allows efficiency wages in both sectors. Also, Matusz's focus is on trade policies' effects on the levels of real wages and on output through changes in the level and composition of employment. He leaves open the question of whether or not policy affects workers in a Pareto improving manner when one considers the different workers' lifetime expected utilities. This distributional question is addressed in the present paper.

   The remainder of the paper is divided into four sections. The next section describes the assumptions of the model. Section 3 provides the policy analysis, and section 4 closes the paper with some concluding remarks.

2. The Assumptions

   The basic assumptions of the model are similar to those employed by Bulow and Summers (1986). However, the focus here is on the case of a small country that is open to international trade. It is assumed that the economy has N identical infinitely lived agents, each able to supply one unit of labor at any instant of time. An agent may be hired by one of two sectors, the urban sector or the rural sector. The urban wage is denoted [w.sub.u], while the rural wage is denoted [w.sub.r]. An important characteristic of the urban sector is that urban employers find it difficult to monitor their workers; rural employers do not have monitoring problems.

   Firms in each sector use labor and capital in production, but capital is fixed and the cost of capital is sunk. Thus, labor is the only variable factor. The number of workers employed in the urban sector is [E.sub.u], while the number of workers employed in the rural sector is [E.sub.r]. The urban output level can thus be expressed as a function of the number of employed urban workers only, or F([E.sub.u]), where F[prime]([E.sub.u]) [greater than] 0. The rural production function can be expressed as G([E.sub.r]), where G[prime]([E.sub.r]) [greater than] 0. Both sectors may exhibit either a decreasing or a constant marginal product of labor. To eliminate certain uninteresting equilibria, however, the analysis is restricted to situations where at least one sector exhibits a decreasing marginal product of labor: either F[double prime]([E.sub.u]) [less than] 0 or G[double prime]([E.sub.R}) [less than] 0.(3)

   The goods produced by the urban and rural sectors have identical counterparts on the world market. Hence, in an equilibrium with free trade, domestic prices equal world prices. The world price of the rural good is normalized to be one and the world price of the urban good is called [p.sub.w].

   Given these prices, agents act as consumers to maximize their discounted lifetime expected utility. In addition to the utility derived from consumption of the two goods, workers find disutility from working hard. To maintain simplicity, it is assumed that, at any particular time, a worker either works or shirks and that a shirking worker produces nothing. The latter assumption implies that, when an urban worker shirks, urban output falls by the marginal product of labor at the existing urban employment level. In terms of utility, shirking is a perfect substitute for consumption of the rural good. A shirking worker gains an increment of instantaneous utility equal to that which [Alpha] units of the rural good would provide.(4) It is further assumed that consumer preferences are homothetic in each time period and additively separable across time. Consumers are also...