A DISSERTATION SUBMITTED TO THE GRADUATE FACULTY in partial fulfillment of the requiriments for the degree of DOCTOR OF PHILOSOPHY Finally, we consider the case where the housing market gives parents few options, with only three equally-sized districts ( J = 3, n = N 3 ). This corresponds roughly to the 40th percentile of the . distribution. Suppose here that 3 j μ j = , j = 1, 2, 3 . When there are no peer effects (Panel E), equilibrium is again unique and is perfectly sorted on effectiveness
