One of my elderly relatives was in line at the grocery store one day and saw the person ahead of him, charging what looked like a cart full of junk food to her food assistance card. My relative was incensed: Why, should his hard-earned tax dollars be used to pay for someone’s Cheetos?

Currently, one in seven Americans receives some kind of government assistance to pay for food. The largest such program – called SNAP for “supplemental nutrition assistance program” – subsidizes a wide range of food purchases. No alcohol or tobacco, mind you, but as many Cheetos, Pepsi-colas, and hot dogs as a person can fit within their budget. Subsidizing such unhealthy foods is politically controversial, raising the question: What would happen if people were only allowed to use SNAP dollars to buy healthy food?

An important study out of Stanford and the University of California, San Francisco, set out to answer this question. The study tested two programmatic changes to food assistance.

1. For half the people in the study, their food assistance dollars could only be used to buy fruits and vegetables.

2. For half the people, the assistance money became available in full every month, whereas the other half, a quarter of their money became available every week.

The idea behind monthly versus weekly allotments of money comes out of behavioral economics. People getting a monthly lump sum may spend all that money quickly, forcing themselves to have limited money remaining at the end of the month. This kind of feast and famine cycle is bad for people’s health. It also encourages people to splurge on calorie-dense and unhealthy foods when they finally get their monthly funds, to make up for all the calories they’ve gone without at the end of the previous month. Weekly (versus monthly) funds may also promote fruit and vegetable purchases, because those products often have a short shelf life.

The researchers thought was that weekly funds would increase the number of fruits and vegetables that people bought.

The reality was that nothing changed. Zilch. Nada. Six months into the intervention, fruit and vegetable purchasing was unchanged.

Moreover, the group that was only allowed to buy healthy foods with their assistance dollars didn’t buy any more healthy foods than anyone else. They just used their own money to buy unhealthy foods and subsidy money to buy healthy ones. Those given more freedom to use the assistance dollars any way they wanted bought just as many healthy and unhealthy foods. Money is fungible, after all. And no one can stop people from buying unhealthy food with their own money.

I don’t want to say that food assistance didn’t do any good. It dramatically reduces people’s food insecurity. Receiving monthly or weekly food assistance is enormously helpful to people. Being able to buy health or unhealthy food with such money is beneficial.

Nevertheless, these programmatic changes failed to encourage people to buy healthier food. Why did it fail? I have a few ideas.

1. Habits are hard to change. I have a handful of “go-to meals” I can cook without effort or without making a separate trip to the grocery store. People in the study probably stuck with their go-tos, too.

2. Money is fungible. People who receive food assistance typically spend some of their own money on food, too. Only allow people to spend assistance dollars on fruits and vegetables, and they’ll simply shift which items they purchase with their own money.

3. We might be a bit obsessed with fruits and vegetables. Maybe reducing food insecurity is enough of an accomplishment. No one should worry whether they have enough money to pay for their next meal.

Peter Ubel is a physician and behavioral scientist who blogs at his self-titled site, Peter Ubel and can be reached on Twitter @PeterUbel. He is the author of Critical Decisions: How You and Your Doctor Can Make the Right Medical Choices Together. This article originally appeared in Forbes.

Image credit: Shutterstock.com