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Bruce Buchanan, a professor of government at the University of Texas, said Mr. Madison’s continued compensation from TIAA-CREF should not pose an ethics problem as long he and department ethics lawyers are careful about monitoring potential conflicts.

“You have a small talent pool, and you don’t want to tie the hands of the government,” he said. “You just have to be careful to run things through the legal department and have the relevant officers recuse themselves when it makes sense to.”

Over the past year, the company has lobbied Congress, Treasury, the White House and other agencies over issues involving TARP, executive-compensation rules, mark-to-market accounting, mortgage reform, stimulus spending and securities regulations, among other issues, according to U.S. Senate lobbying disclosures.

“An individual assuming a position in the federal government must understand the responsibility to the public in terms of trust,” said Marthena Cowart, a spokeswoman for the Project on Government Oversight, a nonpartisan watchdog group.

“Unlike the private sector, the public needs to be assured that the official making the decision on their behalf has no conflicts of interest, real or perceived,” she said.

Many of Mr. Obama’s top appointees have reported taking home millions of dollars in deferred-compensation arrangements from their private-industry jobs, though they generally reported taking the money before starting their government positions.

Attorney General Eric H. Holder Jr. reported receiving $3.3 million, including deferred compensation, from his previous job as a partner at the law firm Covington & Burling.

But arrangements like Mr. Madison’s aren’t unprecedented.

Dick Cheney continued getting deferred compensation from defense contractor Halliburton after he left the company to become vice president. In 2003, Sen. Frank R. Lautenberg, New Jersey Democrat, said in a press release that the nonpartisan Congressional Research Service researched the issue at his request and determined that the deferred compensation was a financial interest.