Kenneth Feinberg, Treasury’s special master for executive pay at companies that received government bailout money, announced Tuesday that 84% of the top executives at American International Group, Bank of America, Citigroup, General Motors, Chrysler, Chrysler Financial and GMAC stayed in their jobs even though he cut their cash compensation by 90% and total pay more than 50% last year.

“There are always predictions that people will leave if they don’t get paid what they want,” says David Lewin, professor at the University of California-Los Angeles‘ Anderson School of Management. “It’s a bogus argument … folks are not going to be scrambling out the door.”

Feinberg imposed the pay restrictions last fall, responding to criticism that lavish pay packages encouraged CEOs to take big risks to reap short-term gains instead of looking out for the long-term health of their companies.

On Tuesday, Feinberg announced more pay rules for the 119 top executives at the five firms still on government life support. Citigroup and Bank of America have paid back the bailout money and escaped Feinberg’s jurisdiction. Feinberg:

•Cut their cash compensation by an average 33% this year from 2009.

•Reduced their total pay by an average 15%.

•Limited cash salaries to $500,000 for 82% of the executives.

•Limited GMAC chief Michael Carpenter to 100% stock compensation, no cash.

•Reaffirmed that most executive compensation be paid in stock.

Feinberg also has asked all 419 firms that received taxpayer money from the Troubled Asset Relief Program (TARP) before Feb. 19, 2009, to disclose how they paid top executives. If he determines that the pay packages were “contrary to public interest,” he’ll try to get some of the money back in the Treasury.

UCLA’s Lewin says that most academic studies have shown no link between executive pay and company performance. Instead, he says, executives earn higher pay when their companies are bigger and have more layers of bureaucracy. a lot of talented employees rank other factors above pay in deciding where to work. “Some people are motivated strictly by money,” he says. “Other people — millions — are motivated by something else. That something else usually has something to do with the meaningfulness of their work.”

Top execs didn’t leave firms over TARP pay cut rules