In this paper we investigate Oswald's hypothesis according to which higher homeownership rates increase aggregate unemployment rates. To this end, we develop a matching model à la Pissarides (2000) in which homeowners are assumed to be less mobile than tenants. Based on numerical simulations, we analyze both macroeconomic and microeconomic labour market outcomes following an (exogenous) increase in homeownership rates. We show that (1) Oswald's hypothesis does not always hold as it depends crucially on the importance of mobility costs; (2) while higher homeownership may harm macroeconomic labour market performances, individual performances always improve following an increase in homeownership rates.