# Public debt dynamics

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## Abstract

In this chapter, we will address the last economic question resulting from the chosen model framework: how does public indebtedness evolve and how does fiscal policy and financial market interaction influence this evolution? We will take ‘public debt per output’ (i.e. the debt ratio) as the appropriate measure for public indebtedness. The debt ratio is usually associated with the question whether a present stock of public debt is compatible with default-free future debt service which would guarantee intertemporal solvency of the government. This solvency question itself does, however, not stand in the foreground of this chapter. The reason is that we always assume that the tax rate and the public expenditure ratio are subject to those fiscal policy constraints developed in Chapter 3. These conditions were shown to fulfill the transversality condition, thereby ruling out Ponzi-game dynamics of public debt as pointed out by Obstfeld/Rogoff (1996, p. 717) ^{1}. Thus, the main purpose in this chapter is to analyze the model dynamics of the debt ratio, especially with regard to the underlying parameters and variables characterizing fiscal policy and financial market behavior.

## Keywords

Interest Rate Fiscal Policy Capital Accumulation Public Debt Debt Ratio## Preview

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## Notes

- 1.This argumentation need no longer hold in an overlapping generations model as Buiter/Kletzer (1997) discuss in a recent paper.Google Scholar
- 2.A possible way out of this dilemma could be the following: one postulates a specific functional form of k depending on r
_{D}and substitutes it into the dynamics of k, i.e. (5.2b). Simultaneously, one calculates the dynamics of k applying Ito’s Lemma to the postulated functional form of k. The parameter coefficients of the postulated functional form can then be obtained by comparing the two dynamics to each other and equalizing the parameters in front of the lowest order expressions of r_{D}. The problem with this approach is, however, that the computations involved get highly complicated. The reason for this is that one needs nonlinear specifications of k in terms of r_{D}when one focuses on functional forms that aim to yield good approximations. We thus refrain from this approach and postpone it to future work.Google Scholar - 3.Note that we have shown in Proposition 6.1 that for values of r
_{D}smaller than becomes negative, banning the danger of an exploding debt ratio.Google Scholar - 4.For our parameter constellation, the debt ratio would have to exceed 300% by far in order to yield explosive debt ratio paths. Additionally, this explosion could only happen for short-term interest rates always remaining higher than.Google Scholar
- 5.It is noteworthy that this negative short run effect on the drift of d may also exist in the medium run although tax revenues then get smaller compared to the short run since higher tax rates harm wealth accumulation. Simultaneously, however, less wealth implies less resources for capital accumulation which reduces government expenditure. If this decreasing effect on government expenditure is stronger than the loss in tax revenues than the primary deficit improves. This slows down debt accumulation so that the negative sign of the drift effect may remain even in the medium run.Google Scholar