Property transaction taxes—also known as stamp duty—are widely viewed as an inefficient form of taxation. In this paper, we examine the welfare implications of removing stamp duty in a general equilibrium overlapping generation model with heterogeneous agents. Our model features an idiosyncratic shock to housing preferences, which may create mismatch or induce households to move. We calibrate the model to the Australian housing market, and conduct counterfactual policy experiments where stamp duty is replaced with recurrent property or consumption taxes. We find that removing stamp duty raises household mobility and reduces the degree of housing mismatch substantially. When examining steady states, we find that newborn households prefer entering an economy with a recurring property tax rather than one with stamp duty. In contrast, when examining the transition we find that existing households prefer replacing stamp duty with a consumption tax.