Foster, along with a former student, evaluates how race-based preferences and geographical distance affect nursing home sorting. He finds that the resulting segregation exacerbates racial disparities in the quality of nursing-home care. In addition to peer-reviewed academic papers, this project resulted in a repository of long-term care data and state policies, and a Web site providing access to policies, provider data, and a quality-based map of LTC providers by location.

Foster has several projects looking at the relationship between air quality and health. In Delhi, India, he has a project that was initially directed at identifying the effects of a court mandate to enforce vehicle regulations with regard to the use of compressed natural gas (CNG). This study involved the systematic collection of ground data on air quality in combination with a household-level survey that included spirometry-based measures of respiratory health.

Foster has a series of projects on groundwater in rural India that also focus on issues of scale in agriculture. A central question in this body of work is how the spatial distribution of the population affects the rate of aquifer depletion. In joint work with a former student he finds surprisingly that water markets are more likely to arise in areas where water is not scarce. He also finds that whether water buying or selling increases or decreases aquifer depletion depends in part on the relative sizes of neighboring farms.