A Dynamic Migration Model with Uncertainty

We study a dynamic version of the Harris-Todaro migration model where a finite population of infinitely lived Bayesian agents choose consumption and migration decision rules as a function of their histories. The agents do not know the production functions in the two sectors and learn about them through wage draws that they receive from the stochastic production functions. The government knows the true production functions but is uninformed about the agents' beliefs, and the actual wage draws they observe. The government maximizes its welfare function- using wage subsidies in the two sectors, and a migration tax. We solve the agents' dynamic programming problem, and then use the solution to solve the government's dynamic programming problem. We study the effects of government policies on the population distribution, and illustrate the model by numerically solving a particular parametric example.