The federal government does a poor job of keeping tabs on money wired abroad. That increases the risk of illegal immigrants and criminals abusing the system, according to a new watchdog report.

Requested by Sen. David Vitter, R-La., and Rep. Tom Price, R-Ga., the General Accountability Office report questions the methods used by the Bureau of Economic Analysis to estimate that the amount of money sent abroad totaled $40 billion in 2014. Citing data from the World Bank, auditors said the true figure likely was $54.2 billion.

Residents of the United States send more money to other countries than any other nation, according to the report. The biggest recipient countries include Mexico (the destination of an estimated $25 billion), China ($15 billion) and India ($10 billion).

“The Obama administration has shown a complete lack of both competence and interest when it comes to securing our borders and enforcing our immigration laws,” Vitter said in a prepared statement. “And that’s costing us a lot of money. Billions, in fact. The GAO reports I have requested and made public today help us determine how massive the remittances problem is with illegal immigrants sending billions out of the U.S. — money they likely haven’t paid income taxes on.”

Various studies have demonstrated that illegal immigrants account for a large share of the funds sent abroad. The Center for Immigration Studies in 2010 estimated the total at $25 billion a year, a figure that has since almost certainly grown.

Vitter has sponsored legislation that would tighten regulation of remittances and pay for those controls and stronger border security by fining senders who cannot prove they were legal U.S. residents.

The GAO estimated that Vitter’s bill could generate $1 billion a year for increased border enforcement but cautioned that uncertainties make it hard to predict. For instance, it is unknown how many illegal immigrants used regulated money transfers and how many used informal networks.

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“What my legislation would do is basically improve on our border security while making illegal immigrants pay for it,” Vitter stated.

The GAO noted objections from representatives of the money-transfer industry, who complained that businesses could face increased compliance costs under Vitter’s bill.

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David North, a fellow at the Center for Immigration Studies, said Vitter could avoid those concerns by copying a model adopted by Oklahoma. That state imposes a 1 percent fee on all transactions and then allows people to write off the cost on their income taxes.

“I like the thrust,” he said, assessing Vitter’s bill. “I don’t like the technique.”

North said collecting the fee from all customers is simpler and invites less objection than creating a system where clerks are in the position of determining which customers are legal residents and which are not.

Oklahoma raises some $11 million a year from its fee, a figure that has been growing year by year. North said only about 10 percent of customers claim the fee on their taxes, indicating a large sum is from income earned under the table.

“They’re tapping into untaxed income,” he said. “It’s easier to lay on a blanket requirement.”