Estimating Loan-to-value Distributions

We estimate a model of house prices, combined loan-to-value ratios (CLTVs) and trade and foreclosure behavior. House prices are only observed for traded properties and trades are endogenous, creating sample-selection problems for existing approaches to estimating CLTVs. We use a Bayesian filtering procedure to recover the price path for individual properties and produce selection-corrected estimates of historical CLTV distributions. Estimating our model with transactions of residential properties in Alameda, California, we find that 35% of single-family homes are underwater, compared to 19% estimated by existing approaches. Our results reduce the index revision problem and have applications for pricing mortgage-backed securities.