Unfortunately, more fresh food closer to home likely does nothing for folks at the bottom of the socioeconomic ladder. Obesity levels don’t drop when low-income city neighborhoods have or get grocery stores. A 2011 study published in the Archives of Internal Medicine showed no connection between access to grocery stores and more healthful diets using 15 years’ worth of data from more than 5,000 people in five cities. One 2012 study showed that the local food environment did not influence the diet of middle-school children in California. Another 2012 study, published in Social Science and Medicine, used national data on store availability and a multiyear study of grade-schoolers to show no connection between food environment and diet. And this month, a study in Health Affairs examined one of the Philadelphia grocery stores that opened with help from the Fresh Food Financing Initiative. The authors found that the store had no significant impact on reducing obesity or increasing daily fruit and vegetable consumption in the four years since it opened.

Earlier research suggesting that better fresh-food access improves diet and would therefore improve the health of people living in poverty was drawn from small samples or looked at store availability in narrow geographical slices—often without information about how or where the people who lived there shopped. “They never link the neighborhood characteristics to actual individuals,” explains Helen Lee, author of the Social Science and Medicine study. “Without that, all you have is speculation.”

Lee also notes in her study that, on closer inspection, food deserts don’t actually exist in the U.S., at least not as a national problem—on average, poor neighborhoods have more grocery stores than wealthier neighborhoods. Even before Obama’s Healthy Food Financing Initiative was announced in 2010, studies suggested that the food desert explanation for obesity wasn’t right. A report from Department of Agriculture researchers presented to Congress in 2009 also showed more grocery stores in poor neighborhoods. In 2012, USDA researchers crunched the data again and found once more that low-income neighborhoods had more—not fewer—grocery stores.

Why, then, do campaigns like the Healthy Food Financing Initiative persist? The push for fresh food is usually considered a progressive cause, connected as it is to criticisms of processed foods’ effect on health. And the most prominent voices against the fresh-food push have been conservative, from Rush Limbaugh to Reason magazine. But look a little closer, and fresh-food financing initiatives are a pretty conservative idea. They offer a market-based opportunity for individuals to make better choices about health, leaving the impression that people living in poverty get sick for reasons that are within their control.

In fact, researchers who focus on health disparities have suspected for decades that people who live in poverty die early because of the stress of poverty itself rather than the poor health choices low-income people make. That’s not to say that poor people don’t make decisions about diet and exercise, but in general they are preoccupied with very different choices than wealthier people are: Should I pay my electricity or my water bill? Can I pay my rent and buy my kid a pair of school shoes? The immediacy of these pressures may make it more difficult to think about how eating choices today will affect health 10 or 20 years from now.