Transitional Dynamics in Monetary Economies: Numerical Solutions

In the previous chapter we have characterized dynamic optimality conditions for monetary economies, but we have only evaluated the steady-state effects of monetary policy. To complete the analysis, this chapter is devoted to characterizing the transitional dynamics of a monetary economy, as it moves from the initial condition to the steady-state. In particular, we examine the evolution of a given economy following a monetary policy intervention. We start by discussing the possible instability of the stock of debt, an issue that conditions the set of feasible policies which needs to be taken into consideration in the type of policy analysis which is undertaken in this chapter. As an example, we saw in the previous chapter how a policy of choosing the rate of money growth and the lump-sum transfer to consumers would lead to a well-defined steady-state, with stable inflation and a finite stock of debt. That is a not trivial result, since interest payments on outstanding debt have a feedback effect on the deficit and hence, on financing requirements, producing a tendency for the stock of debt to increase over time. Hence, when the government changes the inflation rate or the size of the lump-sum transfer, the service of outstanding debt could take the stock of debt to diverge from its steady-state level along an explosive path. This possibility can be avoided by linking the size of the lump-sum transfer to the level of outstanding debt each period t. The implication is then that the government can only freely choose monetary policy, fiscal policy being constrained to satisfy the government budget constraint.