Nixon and Carter had two of the most incompetent Fed Chairs in history in Burns and Miller. Inflation took off under Nixon and continued under Ford and Carter because the FOMC sent mixed messages to the business community and nobody was sure what the Fed was trying to do. Paul Volker was a much stronger Fed chair and the proof is in the fact that inflation averaged 7.4% per year the ten years before Volker became Fed Chair and has averaged 2.9% per year the ten years after Volker's term ended.
Paul Volcker should get credit for the nasty recession we had in the early 80’s. Reagan should get credit for the lower inflation due to his pro economic growth policies.