This paper examines the implications of central bank independence for equilibrium macroeconomic performance. The focus is on institutional arrangements governing financial relationships between central banks and ministries of finance, in the presence of competing objectives and constraints across institutions. Abstracting from long-run considerations, higher central bank independence increases fiscal discipline and results in lower inflation and growth, generating a short-run institutional Phillips curve. In the presence of sufficiently strong negative long-run externalities of inflation onto growth, higher CBI also increases fiscal discipline and generates lower inflation, however, it also yields higher growth and generates an inverted institutional Phillips curve. Strikingly, higher central bank independence is found to be frequently sub-optimal for a wide set of stylized economies. Whether these economies are empirically relevant is an open question.