A utility function based approach towards the modeling of migration in village equilibrium models

Village equilibrium models are computable general equilibrium (CGE) implementations of agricultural household models in a village equilibrium framework which have the salient feature of being able to capture general equilibrium effects arising at the level of rural communities. Due to the important role migration plays for livelihoods in developing countries, the approach has been successfully applied to analyze aspects related to migration and village economies. However, the depiction of migration in village equilibrium models is not carried out in a way that captures interactions between migration and household consumption demand while at the same time allows for an endogenous adjustment of the level of migration by the households themselves. Furthermore, approaches to modeling migration are purely demand side oriented. Supply side factors, such as differences between households, which may influence household responses to changes in incentives to migrate, cannot be accommodated in a theoretically convincing manner. To address these issues, a nonseparable household model with endogenous migration decisions and feedback to the consumption sphere is proposed as the theoretical foundation for a village equilibrium model. A composite utility function captures utility which accrues to the household through per capita household consumption of goods and leisure, on the one hand, and utility stemming directly from participation in different activities by the household including migration, on the other hand. It is shown that the allocation of labor among different activities is governed by the size of marginal returns to labor in terms of market returns, changes in household demand and (dis)utility of labor market participation relative to the household shadow wage. The practical implementation of the theoretical framework is achieved by the derivation of two independent demand systems from the composite utility function. A per capita linear expenditure system is proposed to depict household consumption demand. The allocation of labor to migration is assumed to follow a factor demand specification using power functions which translate utility considerations made by the household into imperfectly elastic responses to changes in incentives for participation in the labor market.