A stochastic model of macroeconomic equilibrium: capital accumulation, inflation, and fiscal policy

The purpose of this paper is to develop a stochastic macroeconomic model with a financial sector. All of the fundamental macroeconomic variables evolve according to a process combining a Brownian motion with Poisson jumps. Specifically, the Brownian motion reproduces the fluctuations that are observed every day and the Poisson process models atypical movements (booms or falls) that occasionally occur. The proposed model incorporates the exposure of the agents (consumers, firms, and government) to the different financial risks affecting their decision making processes and considers explicitly the effects of uncertainty on fiscal and monetary policy in the equilibrium. In the equilibrium, the inflation rate, the rate of capital accumulation, the tax rate on wealth, and the asset returns are endogenously determined.