Question about careers in govermental policy/monetary policy

Hey, WSO. First time posting on here, so apologies if I havent gotten any of the ettequite or this seems ill informed. just want to ask a question the relationship of IB/PE/HF/ER in terms of recruitment pipelines towards central banks (Fed, RBA, BAE) and other government institutions (hell even regualtory authorities but honestly I'm not that dense to ask about that relationship). As well, I'm generally interested in what IB/HF deseginated "economists" roles are in these companies, and their expected path towards recruitment. I'm generally interesred in the formulation of macroeconomic policy, and want to be in that policy-centred environment. Any insight would be greatly appreciated, thanks for any replys.