Consumers who mismanage their finances and consequently lose their bank accounts are getting a lot of attention from regulators these days. The government's message to the industry is: Give these folks a second chance.

In response, some banks have loosened their account-screening practices. While these banks are generally still weeding out known fraudsters, they are taking a more lenient approach when it comes to customers whose blemished records appear to reflect mistakes rather than intentional misbehavior.

But the risk associated with these once-banished customers – their earlier accounts were typically closed because they racked up unpaid fees – remains a source of concern inside the industry. So banks are taking a variety of steps to protect themselves, according to new survey data from Aite Group.

One specific option for banks – making these customers ineligible for any overdrafts – is the choice preferred by regulators and consumer advocacy groups.

"Oftentimes consumers don't want overdraft fees, whether they've had problems with them in the past or not," said Thaddeus King, a member of the consumer banking project at the Pew Charitable Trusts.

But other steps that banks are taking to guard against losses have not gotten a warm embrace from the industry's critics. In many cases, these policies render second-chance accounts less useful than other accounts.

For example, some institutions are making second-chance customers ineligible for a debit card, or barring them from depositing checks via a mobile phone, for a certain period of time. And some banks are placing holds on all checks deposited in second-chance accounts until the funds are collected.

"By their very nature, these are high-risk accounts," said Shirley Inscoe, a senior analyst with Aite Group.

Inscoe's recent report on second-chance accounts was based on a survey of 69 anonymous executives at financial institutions.

More than one-third of those executives said that their firms open accounts for consumers with checkered banking histories, though the institutions' specific policies varied.

Some respondents said that their firms are either planning to start offering second-chance accounts or discussing that option. Others said they will only change their policies if regulators require them to do so.

"Regulators are strongly encouraging large banks to decrease or eliminate reliance on industry databases to decline new accounts for former account abusers," the report stated. Those databases have come under scrutiny regarding the accuracy of the information they contain.

Federal and state regulators are trying to bring more Americans into the banking system, and they need the cooperation of banks to make that happen.

In February, the Consumer Financial Protection Bureau sent letters to the nation's 25 largest retail banks, encouraging them to offer overdraft-free accounts and to market their availability. Today, all five of the largest U.S. banks by deposits offer an overdraft-free option.

In 2014 and 2015, the New York Attorney General's office reached account-screening agreements with five banks – Capital One Financial, JPMorgan Chase, Santander, Citigroup and Amalgamated.

At its New York branches, Capital One agreed to approve consumers who had failed to pay back a negative balance, unless there was a hint of past fraudulent behavior. Santander agreed not to screen out New York applicants who had run up unpaid fees at other banks.

And in October 2015, New York Attorney General Eric Schneiderman sent a letter to nearly 100 banks urging them to adopt specific account-screening procedures that would result in the approval of more consumers.

For example, he asked the banks to consider approving customers who have a history of unpaid bank fees in circumstances where the chargeoffs were not recent and fell below a certain dollar amount.

Across the industry, it is not clear how many checking-account applications get rejected each year. But 7% of U.S. households did not have a bank account in 2015, according to a speech Thursday by Martin Gruenberg, chairman of the Federal Deposit Insurance Corp. That was an improvement from two years earlier, when 7.7% of households were unbanked.

Gruenberg said that "the change from 2013 outpaces what one would expect even in light of improving economic conditions during the two-year period," according to a prepared version of his remarks.

Today, more and more banks are only rejecting customers who have a history of fraudulent behavior, according to Robin Love, a vice president at Early Warning Services, which offers account-screening products to banks.

In other words, people who have tried to deposit counterfeit checks are still being screened out. But frequently, individuals who lost their bank accounts because of unpaid fees are being approved.

Love said that pressure from regulators is not the only reason that banks are becoming more lenient. Banks are also hoping to develop long-term relationships with consumers who, following some missteps, have gotten their financial lives in order.

"They don't want to exclude people," she said. "They're looking to get the younger people in the door."

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