Three musketeers: A dynamic model of capital inflow, the real wage rate and the net migration flow with empirical application

This paper first develops a dynamic model of a system of piecewise continuous differential equations to study the simultaneous interactions between three endogenous variables: Capital inflow (FDI), the real wage rate and the net migration flow into a region. Stability of the general model is compared with two special cases of either or both sticky real wages and fixed capital input. We add return migration and possible immobility (no one moves) to the dynamic equation of immigration to fully capture the determinants of net migration. Empirically, we apply this general model with Cobb-Douglas production and calibrate it for Guangdong over 1990-2010, a fast growing province with the highest volume of net migration flow in China. We claim three contributions: this paper is the first theoretical and empirical one to study these simultaneous interactions and innovates by recognising the inherent regime shifts due to migration costs and two way migration; we find that the wage elasticity plays a crucial role for stability condition; the results of calibration indicate that regions in Guangdong are heterogeneous but with positive simultaneous interactions between those three endogenous variables. Some policy implications and further research directions are also suggested.