In this paper, we study the implications of a vacant home tax for housing availability and affordability. We develop a model with owner-occupied homes, tenanted rental units, and empty houses. Housing units are constructed by competitive developers and supplied to local households, but can also be sold to investors as a store of wealth. Empty homes held by investors are classified as speculative vacancies. Frictional vacancies, on the other hand, are the equilibrium result of search-and-matching frictions in the owner-occupied market. A tax on empty homes can improve housing availability and affordability in the rental market by reducing speculative vacancies, but can dis- tort the incentives to supply vacant homes for sale in the owner-occupied market (i.e., frictional vacancies), thereby increasing house prices and lowering home-ownership. Empirical predictions derived from the calibrated model are consistent with the pat- terns we observe for listings, sales, prices and rents in Vancouver following the recent implementation of an empty homes tax.