WASHINGTON — A federal court judge on Tuesday posed several tough questions to parties involved in retailers' lawsuit against the Federal Reserve Board's implementation of a law setting a cap on debit interchange fees.

The case centers on whether the central bank appropriately set its cap of roughly 21 cents in line with a statutory directive in the so-called Durbin amendment of the Dodd-Frank reform law.

Merchants, the Fed and a coalition of banking trade groups participating as friends of the court made their case before Judge Richard J. Leon of the U.S. District Court for the District of Columbia during oral arguments.

Leon did not ask many questions, and gave little indication of his views on the case. But many of the queries he did pose went to the heart of the controversy: whether the Fed appropriately considered the proper costs to issuers in setting the cap, as directed by Congress.

"So Congress was basically going to rely on the Board to figure out what was basically a reasonable and fair fee model?" Leon asked Shannen Coffin, an attorney at Steptoe & Johnson representing retail groups including the National Association of Convenience Stores and the National Retail Federation.

"That's correct. But Congress didn't stop there," said Coffin, charging that the Fed improperly included costs in its calculation that lawmakers didn't intend.

The Fed was instructed to set a debit interchange limit that "shall be reasonable and proportional to the cost incurred by the issuer with respect to the transaction," according to the Durbin amendment. But the law also told the Fed not to include "other costs incurred by an issuer which are not specific to a particular debit transaction," in its calculations.

Retailers point to the discrepancy between the cap of about 12 cents set in the Fed's earlier proposal and the limit set in the final rule, which is almost double that amount.

"This is a case where an administrative agency … seeks to exploit the deference normally accorded to agencies," Coffin said during his arguments, adding that "in its final rule the Board dramatically changed course."

The Fed "found its way to shift … what we estimate to be about $3 billion a year from the pockets of merchants and their customers to the banks," he added.

Leon pressed attorneys representing the Fed about the agency's rule as well, asking why the limit changed between the proposed and final rules.

"So if the Board had read [the Durbin amendment] literally … then the interchange fee … would have been significantly smaller," Leon said, speaking to the Fed attorney Katherine Wheatley.

Wheatley said the Fed decided to incorporate additional costs into its calculations after taking comments on the proposed rule, noting the practical difficulties of assessing which costs were appropriate to consider. She said the agency received more than 11,000 comments on the rule.

Leon also raised concerns about the potential impact on some merchants, like convenience stores, that typically handle small-dollar purchases. In some cases, such merchants have argued that they are paying a larger proportion of the ticket sale on each purchase towards interchange and that their interchange fees may actually increase as issuers and networks seek to offset revenue losses elsewhere from the rule.

"It has that consequence if the Board reads the statute in a more expansive way as opposed to a more narrow way," Leon said.

But Wheatley argued that the "Board's rule does not set a floor, only a ceiling" on interchange fees, meaning the companies could charge such merchants less if they chose. Nevertheless, she acknowledged that potential impact of the rule.

Meanwhile, banking groups including the Clearinghouse Association, the American Bankers Association and the Consumer Bankers Association argued that the Fed didn't go far enough in considering various issuer costs associated with debit card transactions. They claim that the fee cap is actually below cost for debit transactions and needs to be set higher.

"What are the practical consequences if the court were to agree" with the trade groups, Leon asked attorney Seth Waxman, of Wilmer, Cutler, Pickering, Hale & Dorr, who represented the groups. "Would that not have a practical effect on the Board?" he added.

Waxman said it could potentially impact the Fed, noting that the agency "did make clear" that it is monitoring the actual costs of debit card transactions and could even make changes based on that data down the road.

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