NEW YORK — Home-efficiency measures such as installing new windows or replacing insulation deliver such a small fraction of their promised energy savings that they may not save any money in the long run, according to the conclusion of a University of Chicago study.

The study, which used data from a random sample of 30,000 low-income Michigan households eligible for an Energy Department home-weatherization program, found that the projected energy savings were 2.5 times greater than actual savings. As a result, energy bills didn’t decline nearly enough to pay for the initial cost of the upgrades.

“The problem is that the real world is screwy,” said Michael Greenstone, an energy economist and head of the Energy Policy Institute at the University of Chicago. “The models project much larger savings than are realized by homeowners.”

The study, conducted by Mr. Greenstone and University of California at Berkeley economists Meredith Fowlie and Catherine Wolfram, has not yet been reviewed by a panel of peers. And energy-efficiency experts who were shown the study say the authors’ broad conclusions about energy efficiency in general aren’t justified after studying a single program in a single state focused only on low-income households.

But Mr. Greenstone said he is finding similar results in a second study of middle-income homes in Wisconsin. If correct, the findings could undermine the rationale for billion-dollar federal and state efficiency programs and call into question the understanding that making homes and businesses more energy-efficient are among the cheapest ways to cut carbon dioxide emissions.

States are expected to expand efficiency programs such as the federal weatherization program in the coming years to meet regulations in development at the Environmental Protection Agency to reduce emissions from power generation.

The researchers found that the energy use of these homeowners fell by 10 percent to 20 percent after the upgrades, saving them just $2,400 in energy expenses, far less than the $5,000 the upgrades in the study cost on average. They figured that it cost the federal program $329 for every ton of carbon dioxide it saved. The government estimates the cost to society of a ton of carbon dioxide is $38.

The Energy Department’s Weatherization Assistance program has upgraded 7 million homes since going into effect in 1976. The Energy Department did not respond to requests for comment on the study.

Steven Nadel, chief of the American Council for an Energy-Efficient Economy, said that weatherization programs for low-income households are typically among the least cost-effective energy-efficiency measures. That’s partly because it is so hard to get low-income homeowners to sign up. Once they do, workers are urged to do as much as possible, even if it has only marginal benefits.

The study, Mr. Nadel said, neglects to factor in other benefits for homeowners, including lower maintenance bills, cutting the chance of missed utility payments, and having a more comfortable home.

Other fixes, such as patching leaks in ducts and replacing lightbulbs, have shown a clear benefit. And it is still almost certain that buying more efficient windows and appliances or lightbulbs when it’s time to replace them pays off in the long run.

First Published June 28, 2015, 4:00 a.m.