Billions of dollars are lost through unemployment fraud yearly.

In one sensational case, over $1 million of unemployment benefits was paid to prisoners in Arizona. The Arizona Department of Economic Security discovered the mistake after cross-checking its unemployment-benefit rolls with the Arizona Department of Corrections' inmate list, azcentral.com reported.

After finding that 475 prisoners had been cut checks from January 2010 to January 2012, it started trying to get the money back.

"Collections will take some time, as some individuals may not have any income that we can attach a claim against," Tasya Peterson, DES communications director, told azcentral.com.

"Given the overwhelming number of people our agencies are dealing with, sometimes things may not be as efficient as they could be," Mark Darmer, a corrections department official, told azcentral. "It would have been nice to identify this a little bit earlier."

About $3.3 billion was spent on unemployment fraud, estimate economists in a report done for the St. Louis Federal Reserve.

The bulk of that is concealed earnings, benefits paid to people who are employed but hiding their earnings, according to economists David L. Fuller, B. Ravikumar and Yuzhe Zhang.

That type of fraud accounted for about $2.2 billion in 2011, the most recent year for which data are available, they say. Of all the people collecting unemployment, 88,000 committed concealed earnings fraud.

Concealed earnings fraud is not evenly distributed across income groups: 18,000, or about 20 percent, earned less than $300 per week; and 12,000, about 14 percent, earned more than $900 per week.

Almost half a billion dollars of the fraudulent payments went to those earning more than $900 per week and $210 million went to those earning less than $300 a week.

"Given limited resources to deter fraud and to recover overpayments," the report says, "the unemployment insurance system faces a trade-off between the number of individuals versus the dollar amounts."

Not everyone who is unemployed collects benefits, the researchers note. Some are not eligible, and some choose not to collect. In 2011, the number of unemployed collecting benefits was 3.7 million, just 27 percent of unemployed individuals.