The White House Office of Management and Budget did not respond to repeated requests to specify which other income support programs it's being compared to, or which impact and performance measures it's being evaluated on. So we're left to puzzle through this on our own.

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And the claim is something of a puzzle. A 2014 paper in the journal Contemporary Economic Policy by economists at Virginia Tech and the USDA noted that while the program has been under "significant scrutiny" from Congress in recent years, "no one has explicitly put forth" the argument that "the program does not work."

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On the contrary, a number of federal and private academic reports on the program's efficacy have had generally positive things to say about the program's efficacy.

For instance, the whole purpose of LIHEAP is to provide energy assistance to the most vulnerable households, reducing overall energy insecurity. On those terms, it appears to be working: LIHEAP's most recent report to Congress, for fiscal year 2014, shows that the program helped 5.7 million households with their heating bills, 673,000 with cooling, and another 1.7 million or so households with "crisis" situations where the program intervened when power to the house was about to be shut down.

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There's some overlap between these categories, but it's not clear how much since all states don't track them separately. But we can say that the program kept millions of families warm, hundreds of thousands cool, and helped 1.7 million avoid termination of their utilities. That's a pretty big footprint.

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What do we know about households that receive LIHEAP? The most recent federally-funded survey of recipients was conducted in 2011. At that time, more than 90 percent of LIHEAP households include either children, disabled people or senior citizens -- individuals at particular risk for temperature-related health issues. One-fifth of LIHEAP households are home to military veterans.

Recipient families are low income, and tend to skimp on spending elsewhere to keep the lights on. "Nearly one third reported that they went without food, over 40 percent sacrificed medical care, and one quarter had someone in the home become sick because the home was too cold."

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LIHEAP is also associated with better health among poor children (Frank et. al., 2006). Young children living in LIHEAP households were less likely to be undernourished, as well as less likely to require emergency hospitalization, than young kids in economically similar non-LIHEAP households.

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Does LIHEAP actually reduce energy insecurity overall? Yes (Murray and Mills, 2014). This analysis of 2005 federal survey data found, not surprisingly, "participation in LIHEAP significantly increases energy security in low-income households."

The authors also ran some economic simulations and found that "eliminating LIHEAP decreases the number of energy-secure households by 17%, significantly changing the size and composition of the energy secure population within the United States."

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In other words, getting rid of LIHEAP as Trump proposes will have a big impact on low-income families in the U.S.

Is the program perfect? No (Hernandez and Bird, 2006). Based on interviews with 72 low-income households, this study argues LIHEAP could be improved by placing more emphasis on weatherization ( it doesn't make sense to pay for heat that's just going to leak out of a drafty house), energy literacy (close the vents in rooms you're not using), and smarter energy billing policies from utility companies.

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That's not to say LIHEAP is perfect. The program could also be doing more to combat fraud and abuse, according to a 2010 GAO report. The GAO looked at LIHEAP payouts in seven states and found that "about 9 percent of households receiving benefits—totaling $116 million—in the selected states contained invalid identity information, such as Social Security numbers, names, or dates of birth." Much of this, of course, could have been from clerical errors or typos. But the GAO recommended HHS take a number of steps to "better prevent fraud in LIHEAP."