Estimating Loan-to-Value and Foreclosure Behavior

We develop and estimate a unified model of house prices, loan-to-value ratios (LTVs), and trade and foreclosure behavior. House prices are only observed for traded properties, and trades are endogenous, creating sample-selection problems for traditional estimators. We develop a Bayesian filtering procedure to recover the price path for each individual property and produce selection-corrected estimates of historical LTVs and foreclosure behavior, both showing large unprecedented changes since 2007. Our model reduces the index revision problem by nearly half, and has applications in economics and finance (e.g., pricing mortgage-backed securities).