The U.S. government is losing billions of dollars in paid benefits to people who are still working, no longer alive or are behind bars, according to a report on unemployment fraud by the St. Louis Federal Reserve.

The study released last week found that of the $108 billion paid out in unemployment benefits in 2011, some $3.3 billion was paid out dishonestly - including $2.2 billion going to people who were still working.

According to the study, individuals with relatively low earnings constitute a larger fraction of those committing fraud. High-earnings individuals, however, account for larger dollar amounts of fraud.

Breaking down the $2.2 billion shows that nearly half a billion in dollars when to the category of workers earning at least $900 a week. Those earning less than $300 a week got $210 million of the fraudulent payments.

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