The short answer is I'm not sure. For me, it depends on several things about which I am completely ignorant. Nevertheless, I have an opinion or two.
Where does the FED derive it's authority to set salaries?
If the authority derives from agreements (made at the time the FED loaned money to them) with the corporations, then yes they have the authority. If the corporations don't like that, then they shouldn't have agreed to it and faced the consequences of not getting a loan from the FED. Someone who loans you money has the right to set conditions upon the loan. If you don't like the conditions, either don't agree to the conditions or borrow the money elsewhere. Once you agree, you have no standing to complain about what you agreed to.
If the FED has invented its authority that's another story. They should not.
If Congress has passed legislation giving the FED the authority, that's wrong too.
But, to me, none of those things are the issue here.
There's a lot of talk right now about how offended the public is over the outrageous salaries and bonuses of management in some companies.
Publically held corporations are funded by shareholders, bonds and loans. Ultimately the control of the corporations rests in the hands of the shareholders. Any members of the public who are not shareholders should mind their own business and businesses in which they don't hold shares are not their "business". If non-shareholders are offended by the way a business is run they can express their dissatisfaction by not buying products from those businesses. if you don't like the way a business is run, don't invest in it or don't buy their products, or don't do business with them. On the other hand, if you are a shareholder, it is certainly your right to be concerned about the way your company is being run. Speak up. Form, or join, some sort of group whose collective share of the company is significant enough to effect the outcome of elections of Boards of Directors and vote in Directors who will direct the officers of the company in a way which meets your needs. Alternatively, sell your shares and invest your money in a company which operates the way you think it should - or put your money under your mattress.
The problem I have noticed over the last 15-20 years is that Directors are hand-picked by CEOs in order to authorize what the CEO wants to do. So shareholders have two major problems, the CEO and the Board. Shareholders can vote out the Board and the Board can control the CEO. But shareholders go along with the company by signing proxies for their votes and then complain when they don't like the way the company is run or the compensation of its employeees. Quit whining shareholders. You have a say/vote and if you don't like something don't give your vote away to management. On one hand you're telling management to vote for you and on the other hand you're compaining about what they do with your vote.
All that is to say that if you (shareholders) hadn't enabled these companies to function immorally, pay themselves obscene salaries/bonuses, fly around the world in private jets, have board meeting in exotic locations and generally live the high life on your money we wouldn't be having this discussion.
Read more of what I have to say at chuck-thompson.com