They are private corporations operating under a federal charter. That's why they are called Government Sponsored Entities. They stopped being government owned once government sold their shares.
private company and the 2010++ definition of GSE are not contradiction
FNMA was a GOV agency like FDCI or lots
At some point - around when Freddie was introduced as a competitor - they stopped being a GOV agency (easy to understand)
They were then called GSE --- Gov Sponsored Entities
But they were private companies - so understood and so declared by say 10 courts over last 10 years
one issue was did they carry a GOV (Treasury - Congress) guarantee on the bonds they issued like GNMA clearly does !!!
but nope - their bonds did not have such true explicit Treasury guarantee but only a market assume implicit guarantee from a history of ONCE being an agency and that amorphous description of GSE but with shareholders !!!
the conservatorship with the various documents -- NOW does provide such Treasury guarantee !!--- and that guarantee (which the GOV said was their reason to take over) ----- kept the Chinese Russians and mega rich people and institutions in USA - rom panic selling their paper in 2008 which would have been catastrophic - especially if done by those outside the company that owned a ton of such paper
but they are private
so would be a Federal Private Utility - argued by me and many smarter than me
GSE does not equate to or equal AGENCY ---- again see stuff like FDIC for a true agency