Technological advances in health care have been shown to yield large average health benefits for the U.S. elderly population. However, less is known about the marginal or incremental benefits of health care spending. We use geographical variations in health care spending to measure the marginal value of greater health care intensity among the elderly Medicare population. To correct for the reverse causation problem -- that sicker areas tend to require more health care -- we use regional averages of physician visits in the last six months of life as a natural randomization for health care intensity. Using linear and semiparametric instrumental variables, we find that a large component of Medicare expenditures -- $26 billion in 1996 dollars, or nearly 20 percent of total Medicare expenditures -- appears to provide no benefit in terms of survival, nor is it likely that this extra spending improves the quality of life. While secular trends in health care technology have delivered large health benefits, variation in health care intensity at a point in time have not.