Medicare spending exceeds 4% of GDP in the US each year, and there are concerns that moral hazard problems have led to overspending. This paper considers whether hospitals that treat patients more aggressively and receive higher payments from Medicare improve health outcomes for their patients. An innovation is a new lens to compare hospital performance for emergency patients: plausibly exogenous variation in ambulance-company assignment among patients who live near one another. Using Medicare data from 2002-2010, we show that ambulance company assignment importantly affects hospital choice for patients in the same ZIP code. Using data for New York State from 2000-2006 that matches exact patient addresses to hospital discharge records, we show that patients who live very near each other but on either side of ambulance service area boundaries go to different types of hospitals. Both identification strategies show that higher-cost hospitals achieve better patient outcomes for a variety of emergency conditions. Using our Medicare sample, the estimates imply that a one standard deviation increase in Medicare reimbursement leads to a 4 percentage point reduction in mortality (10% compared to the mean). Taking into account one-year spending after the health shock, the implied cost per at least one year of life saved is approximately $80,000. These results are found across different types of hospitals and patients, as well across both identification strategies.