Article I expressly states the legislative branch "consist of a Senate and House of Representatives." So the fed can't be part of the legislative branch.

Agencies can exist under the bailiwick of Congress, e.g.:

* https://en.wikipedia.org/wiki/Congressional_Budget_Office

Further, having a bank that is not directly controlled by Government dates back to the first Congress (Washington, Hamilton):

> The suspicion of this would most probably be a canker, that would continually corrode the vitals of the credit of the Bank, and would be most likely to prove fatal in those situations, in which the public good would require, that they should be most sound and vigorous. It would indeed be little less, than a miracle, should the credit of the Bank be at the disposal of the Government, if in a long series of time, there was not experienced a calamitous abuse of it. It is true, that it would be the real interest of the Government not to abuse it; its genuine policy to husband and cherish it with the most guarded circumspection as an inestimable treasure. But what Government ever uniformly consulted its true interest, in opposition to the temptations of momentary exigencies? What nation was ever blessed with a constant succession of upright and wise Administrators?

* https://founders.archives.gov/documents/Hamilton/01-07-02-02...

Alright, you have a point here, as rayiner also pointed out.

The legislative powers more accurately are vested in only congress and senate, and not only that are defined as consisting of the house and senate.

Therefore the CBO exists in a rather odd area, where it cannot exercise any power unless it moves into the execute branch, or it somehow uses executive power.