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2017 | OriginalPaper | Buchkapitel

Government Debt, Fiscal Rules and Singular Growth Dynamics

verfasst von : Paulo Brito

Erschienen in: Inequality and Finance in Macrodynamics

Verlag: Springer International Publishing

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Abstract

A fiscal rule controlling the government surplus as a function of the deviation of the actual debt ratio from a target level is introduced in an otherwise benchmark endogenous growth model in which productive government expenditures are financed by taxes and government debt. This generates a feedback mechanism from the government debt ratio to expenditure that can generate impasse-singular dynamics, in the sense that rates of growth can become locally infinitely valued. We characterize locally the different impasse-singular dynamics that can exist and discuss their consequences for the existence and characterization of general equilibrium endogenous growth paths, for different parameterizations of the fiscal rule. We present some consequences of impasse-singular dynamics generated by particular fiscal rules, which are not present in regular models: existence of multiple over-determinate balanced growth paths (BGP), existence of constraints in the domain of existence of determinate equilibrium paths converging to a regular BGP, and the existence of singular BGP’s.

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In both papers we deal with implicit differential equations by using the approach and terminology presented in Zhitomirskii (1993) and Llibre et al. (2002) and extending to cases in which there are steady states. See also Riaza (2008).

The proofs are assembled at the Appendix.

Greiner and Fincke (2015, p. 169–173) assume that only the income generated by private sources is taxed. That is, there are no taxes over the return on the private investment on government bonds. This assumption changes significantly the types of dynamics that can occur.

All the proofs are in the Appendix.

As function δ(g) can only be equal to zero at a specific value for the state variables and not for a particular value of the parameters we have impasse-singularities and not fast-slow singularities (see Brito et al. (2017a)).

Using the analogy with fast-slow singularities, we can see desingularization as a device to uncover the singularities by locally changing the time scale such that the speed of the trajectories close to the singular surface becomes finite.

See Brito et al. (2017a) for further details. There is another type of impasse point, impasse-tangent points at which a tangent trajectory passes through \(\mathcal{S}\). In the present model there are no impasse-tangent points.

Observe that given the constraint introduced by the singularity condition, the set of singular steady states has a higher co-dimension in the joint space of the variables and the parameters.

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Titel: Government Debt, Fiscal Rules and Singular Growth Dynamics
verfasst von: Paulo Brito
Verlag: Springer International Publishing
Buch: Inequality and Finance in Macrodynamics
Print ISBN: 978-3-319-54689-6

Electronic ISBN: 978-3-319-54690-2

Copyright-Jahr: 2017
DOI: https://doi.org/10.1007/978-3-319-54690-2_3