A federal program that helps low-income families pay for things like energy-efficient replacement windows might have upfront costs that far exceed the actual savings.

A study from the University of Chicago and the University of California, Berkeley looked at 30,000 homes in Michigan that took part in the Department of Energy’s Weatherization Assistance Program. It found that upfront costs for efficiency upgrades averaged about $5,000 per house, but the estimated energy savings over the lifetime of the upgrades was only about $2,400 per household. Researchers took into account the possibility of a “rebound effect,” in which households increase energy usage because bills are lower. But they found no evidence for that.

The study found that the Weatherization Assistance Program did save energy – often up to 20 percent per household. But that was only about 39 percent of the projected savings.

“We were very surprised by the result,” Michael Greenstone of the University of Chicago told the explanatory-journalism website Vox.

However, the researchers said the results might not be representative of all such programs across the country.

“This is one study in one state looking at one subpopulation and one type of measure,” Meredith Fowlie of the University of California, Berkeley told The Washington Post. “I would not feel comfortable generalizing from our study in Michigan.”

In a follow-up on Friday, Vox noted that the study generated strong responses from those involved in energy-efficiency projects. They point out that while current techniques for predicting energy efficiency often over-sell potential cost savings, there are many benefits from low-income weatherization projects. Those include making homes more comfortable, removing hazards such as mold or asbestos, and eliminating dangerous carbon monoxide leaks from old heating systems.