Yes, the states have the autonomy to carry out fiscal and monetary policy but the regional leaders have turned it into a way to embezzle money from state covers despite being regulated by centrally. In Nigeria, State government are given autonomy but state government deny local government the right.
In India a mixed structure is in place. The fiscal policy at the broad level is centralized whereas the states do have their own state budgets. The resources are contributed singly by states, or singly by the centre or by the joint contribution. The monetary policy is in the hands of the central bank i.e. the Reserve Bank of India.
POLICY by its nature and definition is centralized. IMPLEMENTATION may be localized. At a macro-level, it is all centralized; otherwise, it cannot be a policy. At state or local level, the central government may give some leeway in policy implementation as to process, but the policy outcome would still remain a central mandate.