Skiba thresholds in a model of controlled migration

This paper presents a dynamic optimization model of a central challenge of US housing policy: deconcentrating poverty via housing mobility programs without inducing middle-class flight. We explore two versions both with and without the possibility that poor families assimilate into the middle class. Both demonstrate multiple equilibria with a Skiba point separating initial conditions for which the optimal strategy leads to substantial flight from those leading to a stronger middle-class population. We also find an interesting mathematical phenomenon of a “lens” focusing the trajectories in a sense that allows for the coexistence of three saddles and an unstable equilibrium.