We consider monetary-fiscal interactions when the monetary authority is more conservative than the fiscal. With both policies discretionary, (1) Nash equilibrium yields lower output and higher price than the ideal points of both authorities, (2) of the two leadership possibilities, fiscal leadership is generally better. With fiscal discretion, monetary commitment yields the same outcome as discretionary monetary leadership for all realizations of shocks. But fiscal commitment is not similarly negated by monetary discretion. Second-best outcomes require either joint commitment, or identical targets for the two authorities - output socially optimal and price level appropriately conservative - or complete separation of tasks.
Dixit, Avinash and Luisa Lambertini.
2003."Interactions of Commitment and Discretion in Monetary and Fiscal Policies."American Economic Review,
93(5): 1522-1542.DOI: 10.1257/000282803322655428