This paper analyzes global dynamics in an overlapping generations general equilibrium model with housing-wealth effects. It demonstrates that monetary policy cannot burst rational bubbles in the housing market. Under monetary policy rules of the Taylor-type, there exist global self-fulfilling paths of house prices along a heteroclinic orbit connecting multiple equilibria. From bifurcation analysis, the orbit features a boom (bust) in house prices when monetary policy is more (less) active. The paper also proves that booms or busts cannot be ruled out by interest-rate feedback rules responding to both inflation and house prices.