It’s a plausible and widely-believed hypothesis: Poor people in the United States suffer from measurably worse nutrition because they have such limited access to good food. Confronted with a high concentration of poor diet choices (like fast food, and processed food in convenience stores) and with few markets offering fresh fruit and vegetables, the poor end up eating a less healthy diet. In this view, bad diets are a problem of the urban environment—the lack of good food in poor neighborhoods.

But while there are certainly urban neighborhoods that lack good grocery options, is there any evidence that close physical access to food—as opposed to other factors like income or education—are big determinants of healthy eating? We’ve been skeptical of that view for some time.

A new study by researchers at the University of Pennsylvania, Princeton and the US Department of Agriculture summarized in the Chicago Policy Review concludes that after controlling for differences in educational attainment and income, variations in physical access to food explain less than ten percent of the variation in consumption of healthy foods. They also find that the opening of new, healthier supermarkets in neighborhoods has very little effect on food consumption patterns of local residents.

This new study confirms earlier research that questioned whether the physical proximity to healthier eating choices is the big driver of our hunger and nutrition problems.

Studies show that there is no apparent relationship between a store’s mix of products and its customer’s body/mass index (BMI) (Lear, Gasevic, and Schuurman, 2013). Limited experimental evidence suggest that improving the supply of fresh foods seems to have limited impacts on food consumption patterns. Preliminary results of a study of consumers in a Philadelphia neighborhood that got better supermarket access showed no improvement in fruit and vegetable consumption or body mass index even for those who patronized the new store.

In January, we observed that physical proximity alone is not likely to be a strong explanation of variations in diet. Judged by proximity to grocery stores nearly all of rural America is a food desert. Nathan Yau at FlowingData uses Google maps data to construct a compelling map of how far it is to the nearest grocery store across the entire nation. The bleakest food deserts are the actual deserts of the American West, in Nevada and Wyoming.

City dwellers, particularly those in the biggest, most dense cities tend to live closest to supermarkets and have the best food access. WalkScore used their data and modeling prowess to develop some clear, objective images of who does (and doesn’t) have a good grocery store nearby. They estimate that 72 percent of New York City residents live within a five-minute walk of a grocery store. At the other end of the spectrum, only about five percent of residents of Indianapolis and Oklahoma City are so close. If you want to walk to the store, this data shows the real food deserts are in the suburbs.

There are other ways of measuring food access and mapping food deserts. The U.S. Department of Agriculture and PolicyMap have both worked to generate their own maps of the nation’s food deserts. They use a combination of physical proximity (how far it is to the nearest grocery store) and measurements of neighborhood income levels.

While it’s clear that income plays a big role in food access, it’s far from clear how to combine income and proximity to define food deserts. The USDA uses an overlay which identifies low-income neighborhoods with limited food access. PolicyMap has a complicated multi-step process that compares how far low-income residents have to travel to stores compared to higher income residents living in similarly dense neighborhoods.

In practice, combining neighborhood income and physical proximity actually muddles the definition of food access. First, and most important, it acknowledges that income, not physical distance, is the big factor in nutrition. Both of these methods imply that having wealthy neighbors or living in the country-side means than physical access to food is not a barrier. Second, it is your household’s income, not your neighbor’s income, that determines whether you can buy food. Third, these methods implicitly treat low income families differently depending on where they live. For example, PolicyMap excludes middle income and higher income neighborhoods from its definition of “limited supermarket access” areas—and therefore doesn’t count lower income families living in these areas as having poor food access.

The fact that both of these systems use a different yardstick for measuring accessibility in rural areas suggests that proximity isn’t really the issue. Rural residents are considered by USDA to have adequate food access if they live within ten miles of a grocery story, whereas otherwise identical urban residents are considered to have adequate access only if they live within a mile or half-mile of a store.

If we’re concerned about food access, we probably ought to focus our attention on poverty and a lack of income, not grocery store location. The argument here parallels that of Nobel Prize-winning economist Amartya Sen, who pointed out that the cause of starvation and death in famines is seldom the physical lack of sufficient food, but is instead the collapse of the incomes of the poor. Sen’s conclusion was that governments should focus on raising incomes if they wanted to stave off hunger, rather than stockpiling or distributing foodstuffs

It’s tempting to blame poor nutrition and obesity on a lack of convenient access to healthier choices, but the problem is more difficult and complex than that. Poverty and poor education are strong correlates of poor nutrition and obesity.

Of course, we have good reasons to believe that the built environment does play an important role in obesity—but as the Surgeon General’s report implies that may have more to do with how easy it is to walk to all our daily destinations, and not just the distance to the fresh food aisle.

(Portions of this post appeared originally on City Observatory in a January commentary “Where are the food deserts.”)