Equilibrium selection and stability in dynamic core-periphery models with heterogeneous preferences

In New Economic Geography, recent models have shown that idiosyncratic preferences of workers for locations act as a dispersion force affecting the number and stability of equilibrium population distributions. Yet those models are based on ad hoc deterministic adjustment procedures that have two shortcomings. Firstly, they remove the aggregate effect of idiosyncratic preferences on the collective spatial dynamics of workers, whose study would require the use of specific notions of equilibrium stability. Secondly, these adjustment dynamics lack an explicit time unit that prevents adjustment trajectories to be expressed as dynamic scenarios. Those two shortcomings strive against the use of New Economic Geography models to support policy recommendations. Starting from a classic core-periphery model of New Economic Geography, this paper proposes a novel approach to adjustment dynamics, based on stochastic migration models, by which the dynamics of the population distribution is a continuous-time Markov chain. Using a diffusion approximation, the dynamic system is reduced to a set of Itô stochastic differential equations, which is an original contribution to New Economic Geography. In those equations, deterministic and stochastic effects are still distinct at the aggregate scale, which enables to numerically compute equilibrium population distributions as well as to evaluate their stability and selection under stochastic perturbations generated by idiosyncratic preferences. Those equations also enable to complete expected adjustment trajectories with an explicit time unit and with confidence intervals, for different scenarios. Hence this paper is a substantial improvement of the capacity of New Economic Geography models to support policy recommendations.