The provision of owner-occupied versus rental houses is modeled as a competitive search economy where households have private information over their expected duration. With public information, households with low vacancy hazard rates pay lower rents and search in thicker rental markets. With private information, rentals are under-provided to long-duration households to discourage short-duration households from searching there. Ownership is attractive in part because it cures the private information problem. Using a novel data set of rental listings, we show that homeownership rates are high where rent-to-price ratios are low but rentals are scarce and that long-duration households sort into scarce rental markets. These patterns are consistent with the model only under private information.