Raising the eligibility age for Medicare, the third largest program in the federal budget, could lead to a large reduction in the federal budget deficit; however, the effect of this change on the welfare and the health of the near-retirement population is unclear. Using Health and Retirement Study (HRS) dataset, I measure the effect of a change in Medicare eligibility age on the welfare of the elderly population by estimating a dynamic discrete choice model of health and retirement that endogenizes health investment decisions. The empirical model allows for tracking the health behavior, labor supply, and health status among the other key variables. Using Forward Simulation and Conditional Choice Probability estimator (CCP), I incorporate a large, multidimensional state space that includes fixed unobserved heterogeneity. I find that labor supply, life expectancy, and mental health will be affected positively in response to an increase in the Medicare eligibility age. The welfare effect, however, is negative and there is some evidence of cost transfers from Medicare to the Social Security Program.