Lack of access to nutritious and affordable food has become an important public policy issue in the U.S.: various interest groups are seeking to reverse a trend whereby certain areas lack larger, full-service grocery stores that provide “higher” quality foods. Based on game-theoretic findings suggesting that lack of food access can be an equilibrium outcome, we specify a model relating access to higher quality food stores to a vector of supply and demand factors, using seven years of county-level data for the contiguous U.S., and a constrained generalized ordered logit estimator. Our results suggest that demand side factors, especially market size (total income and SNAP funds) play an important role in determining food access, and that large food stores avoid areas with higher poverty. Some cost determinants, such as the ratio of building costs to the total site cost, home price index (for counties with higher poverty rates than the average) and ease of recruiting labor, affect the probability of observing areas with no access. A more favorable business tax regime has no impact on access, while better transportation infrastructure reduces rather than improves food access. Our results shed new light on the determinants of food access in addition to highlighting what policy can and cannot accomplish to improve food access.