I think an officer with executive powers is effectively a government or part of one. Judicial powers are a grey area perhaps, but in my strong opinion there is no difference between a government and a magistrate telling everyone what to do.
People do "regulate" the economy, but the impact of any one individual's 'regulation' is too insignificant to really qualify for the term. If any one individual's effect as a regulator began to be noticeable, I submit that would mean that they had judicial or executive powers.
For Regulated I would have:
"A body/entity with powers of enforcement regulates the economy". You can't assume any degree of freedom in the economy, you can't make any assumptions about public and private ownership, and you can't assume that the body means to protect consumers, or even pretends to. I maintain that you can assume powers of enforcement, because unenforced regulations are simply not regulations.
If you want Magistrates to be compatible with Anarchy you definitely (imo) need to omit executive powers, but as I say above, if lawmaking and enforcement is done by some subset of the populace, the difference between that and government is negligible