Politicians across the spectrum like to fret about fraud in anti-poverty programs, but the biggest problem isn't too many people getting benefits: It's too few people getting benefits. Underclaiming rates for major safety net programs are substantial: In 2013, 15 percent of people eligible for food stamps didn't get them — down from a whopping 31 percent in 2007. In 2012, 20 percent of people eligible for the earned income tax credit (EITC) didn't get it.

A new paper in the American Economic Review suggests that making more people aware of these programs — and offering simpler ways of accessing them — could help substantially. Carnegie Mellon's Saurabh Bhargava and University of Texas Austin's Dayanand Manoli conducted an experiment in conjunction with the IRS in which they sent mailings to 35,050 tax filers in California who didn't claim the EITC in 2009, despite their tax returns indicating that they were eligible and despite an initial reminder notice from the IRS. Collectively, these filers had left $26 million to which they were entitled on the table. Bhargava and Manoli wanted to see if giving them a second chance to claim the money would increase uptake.

Overall, 22 percent of people getting the survey responded and claimed their money. But Bhargava and Manoli tried a bunch of different tactics to try to determine the most effective way of reaching people. Their "control" mailing offered a simple notice and a simple worksheet, but they also sent out more complicated notices and worksheets:

Some of the mailings warned recipients of the time needed to complete the worksheet (either "less than 60 minutes" or "less than 10 minutes," with the two randomly alternated); some listed possible benefit sizes (up to $457, $3,043, $5,057, or $5,567; again, randomized). Some of the mailings included informational flyers explaining how the EITC works. Some included language in bold print indemnifying the recipients against legal retaliation if they accidentally made an error. Some included a note saying, "Important — Good News for You" on the envelope. And some notices included lines to reduce social stigma involved in claiming a credit — one saying, "You may have earned a refund due to your many hours of employment," (a personal stigma reducer), and one saying, "Usually, four out of every five people claim their refund" (a social stigma reducer).

As you'd expect, complex mailings got fewer responses. But so did ones with informational flyers, and ones including the social stigma line. Giving cash benefit size numbers ($457, $3,043, etc.), by contrast, led to a big increase in uptake:

Interestingly, lower benefit estimates seemed to lead to higher take-up than bigger numbers. Ultimately, the best intervention, with simple notices and worksheets plus the benefit number, led 31 percent of respondents to respond and claim their benefits. Bhargava and Manoli estimate that you could reduce EITC underclaiming by 3 percentage points, and distribute an additional $503 million, if this approach were done nationally.

That's an impressive result for a simple mailing. But it's still pretty small in the scheme of things. The really important findings of the study are that lack of information about the size of the benefits offered by the EITC and complexity of tax documents deter people from getting all the benefits they're eligible for.

What would really make a difference, and unlock billions in currently unclaimed money, is a system of automatic dispersal. The IRS typically knows most people's wage income from W-2s filed by employers, and so can probably guess who's eligible for the EITC and file those people's returns for them, ensuring they get the benefits. Hell, the IRS could file returns for everybody. It only doesn't because of an unholy alliance with Intuit, H&R Block, and other tax preparation companies and anti-tax conservatives who want people to be annoyed by taxes annually so as to hate them more: