Shapley Value for A Differential Game of Monetary and Fiscal Economic Policy

This paper implements a dynamically stable cooperative mechanism for allocating economic-policy costs between fiscal and monetary authorities in the context of public debt stabilization. The mechanism is implemented in the debt-stabilization game proposed by Tabellini [1986] [Money, debt and deficits in a dynamic game, J. Econ. Dyn. Control 10(4), 427–442] and computed using the algorithm developed by Petrosyan and Zaccour [2003] [Time-consistent Shapley value allocation of pollution cost reduction, J. Econ. Dyn. Control 27(3), 381–398]. Based on the resulting parameter equations, two institutional settings are considered: first, a setting in which both authorities are equally sensitive — in absolute terms — to movements in public debt; and second, a setting in which the monetary authority is fully conservative, assigning no weight to public debt dynamics, while the fiscal authority does. The main findings are as follows. (i) A higher discount factor slows down the adjustment of public debt toward its steady state. (ii) A larger joint weight attached to public debt speeds up the adjustment of public debt. (iii) Under the first institutional setting, both authorities share the economic-policy costs equally, and this allocation lies between the two asymmetric allocations obtained in the second setting, where the monetary authority bears lower costs than the fiscal authority. (iv) Under the first setting, both authorities face lower long-run economic-policy costs when the tension in the economic-policy environment is smaller.