This paper models the housing sector, mortgages and endogenous default in a DSGE setting with nominal and real rigidities. We use data for the period 1981-2006 to estimate our model using Bayesian techniques. We analyze how an increase in risk in the mortgage market raises the default rate and spreads to the rest of the economy, creating a recession. In our model two shocks are well suited to replicate the subprime crisis and the Great Recession: the mortgage risk shock and the housing demand shock. Next we use our estimated model to evaluate a policy that reduces the principal of underwater mortgages. This policy is successful in stabilizing the mortgage market and makes all agents better off. (C) 2017 Elsevier B.V. All rights reserved.