Sustainable Fiscal Policy: Numerical Computation Of Markov Equilibria In A Dynamic Game

We characterize the optimal fiscal policy in a dynamic stochastic general equilibrium model of an economy consisting a government and the continuum of consumers. The key features of the model are the optimizing government unable to commit itself to ex-ante optimal policies and individually rational competitive consumers. The model demonstrates that the debt reduction policy may be a better alternative to immediate tax reduction because of the possibility of multiple Markov equilibria. In such equilibria, for every state in the space of aggregate capital and public debt, both the government and the consumers make sequentially rational decisions given inferred responses of the other participants. The equilibria are characterized by the regions in the state of public debt levels for which the optimal tax rates depend on the aggregate stock of capital. When the government choses debt in excess of this level, multiple Markov equilibria may realize. In order to compute the equilibrium in this economy, we emplyed both analitical and numerical methods. For simple cases of zero probability and probability one sunspots, the extrinsic stochastic variables that coordinate the equilibrium, both methods are applicable. For non trivial distribution of the sunspots, only numerical methods allow to find the equilibrium. The model is calibrated to the US data.