Accounting for fluctuations in social network usage and migration dynamics

In this paper, we examine network capital usage and migration patterns in a theoretical model. Networks are modeled as impacting the migration decision in many ways. When young, larger networks reduce the time lost moving from one region to another. In addition networks decrease the time spent searching for a job. Finally, when old, migrants receive transfer payments through the network. We show that the number and properties of steady state equilibria as well as the global dynamics depend crucially on whether the returns to network capital accumulation exhibit constant, increasing, or decreasing returns to scales relative to the level of network capital. With constant returns to scale, migration flows and network capital levels are characterized by either a unique steady state equilibria or by a two-period cycle. The fluctuations in network capital usage exhibited by our model are consistent with recent empirical data regarding the usage of networks by Mexican immigrants. In the case of increasing returns to scale, either there exists a unique, stable steady state equilibria or multiple equilibria which are characterized as either sinks or saddles. When the returns to scale are decreasing, there exists a unique, stable steady state equilibrium. Finally, we show that increasing barriers to migration will result in an increase in the flow of immigrants, contrary to the desired effect, in the constant and increasing returns to scale cases.