Using unique data on reverse mortgage borrowers in the Home Equity Conversion Mortgage (HECM) program, we semiparametrically estimate a dynamic discrete choice model of borrower behavior. Our estimator is based on a new identification result we develop for models with multiple terminating actions. We show that the per-period utility functions and discount factor are identified without restrictive, ad hoc identifying restrictions that lead to incorrect counterfactual implications. Our estimates provide insights about factors that influence HECM refinance, default, and termination decisions and allow us to quantify the trade-offs involved for proposed program modifications, such as income and credit requirements.