This dissertation consists of three papers studying existing practices in measuring quality of care for Medicare beneficiaries that warrant further examination. Quality of diabetes care is currently reported at the practice or plan level as a composite, summarizing multiple binary measures in the diabetes measure set. Medicare's Accountable Care organization demonstration uses an all-or-none approach deeming only diabetics who receive all measures in the diabetes care measure set to have met the quality threshold. This approach while simple might not be as meaningful as a graduated approach. Other approaches to composite quality measurement, like Medicare's value based payment system for physicians, add up binary measures in the diabetes care measure set, weighting them equally. But all measures in the set might not be equally important for quality, making the case for weighting measures accordingly. Finally, Medicare's Physician Quality Reporting System (PQRS) offers incentive payments to physicians for reporting quality for their patients. In the absence of incentives for outcomes, the impact of reporting on outcomes is questionable. The dissertation employs Medicare administrative claims to answer the above questions. Paper 1 compares prediction of subsequent outcomes for Medicare beneficiaries using all-or-none approach against a graduated approach to quality measurement. Paper 2 compares measure weights for diabetes care processes obtained using three alternate approaches to weighting composites, to study whether equal weighting is justified in practice. Paper 3 studies whether PQRS quality reporting for diabetics is linked to receipt of more recommended diabetes care processes and better outcomes. This dissertation ultimately emphasizes the need to better understand quality mechanisms to measure it appropriately for quality improvement.