The existence of transaction taxes reduces transactions, and in the case of housing, reduces household mobility and affects the costs of downsizing in dire times. We construct and estimate an overlapping generation model in which households are heterogeneous in age and earnings, and prudential regulation and the tax system are modeled in fine detail. These housing and public policies are likely to affect markets globally, and clearing both rental and property markets is important when evaluating them. We use the institutional and data setting of France, where transactions taxes are some of the highest in Europe, and evaluate the counterfactual impact of reducing transaction taxes from 14% to 6%, similar to US levels. The impact on transactions is strong, but the impact on welfare remains limited.