On the Existence and Duration "Wait" Migration in a Generalized Model

Recently Wang and Wirjanto (1997) proposed a simple dynamic model to study the optimal timing strategy for an individual's migration decision, using the theory of the optimal timing of investment under uncertainty, reviewed in Dixit (1992), Dixit and Pindyck (1994), and Pindyck (1991). It is shown that as a result of the individual's following the optimal timing strategy, there is a "waiting" phenomenon on the part of the potential migrant, giving rise to so-called wait migration observed in the data for Germany following the unification, and that the duration of this waiting behavior is affected by a number of economic factors such as uncertainty with respect to income in Western Germany, the individual's attitude toward risk, etc. In this note we extend the model in Wang and Wirjanto (1997) by generalizing the form of the individual's utility function and the stochastic processes of the wage income in Eastern and Western Germany respectively. In particular, we only restrict the utility function to be continuous in its argument without specifying a particular functional form, and allow the wage incomes to be characterized by general diffusion processes with possibly correlated Brownian motions. In this general setting we establish the existence of wait migration, and obtain an analytic expression for an optimal stopping strategy that yields the shortest waiting time among all optimal stopping strategies.