Modelling Long Bonds - The Case of Optimal Fiscal Policy

We show how to model portfolio models in the presence of long bonds. Specifically we study optimal fiscal policy under incomplete markets where the government issues bonds of maturity N > 1. Assuming the existence of long bonds introduces an additional intertemporal mechanism that makes taxes more volatile in order to achieve lower debt management costs. In other words, fiscal policy is secondary to debt management. Modelling optimal policy with long term bonds is computationally demanding because of the promises made to cut future taxes. The longer the maturity of bonds the more promises need to be monitored and the larger the state space. We consider three means of overcoming this problem - a computational method using the “condensed PEA”, an approximation whereby long bonds are modelled as a sequence of geometrically declining coupons and a model of independent powers where the fiscal authority and interest rate setting authority are separate. We compare the accuracy and properties of solutions across these three approaches and examine how the properties of optimal fiscal policy differ in the case of long bonds compared to one period debt.

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