Fiscal policy and the output costs of sovereign default

Leyre Gómez-Oliveros Durán; Stefan Niemann; Paul Pichler

doi:10.1515/bejm-2017-0236

Article

Fiscal policy and the output costs of sovereign default

Leyre Gómez-Oliveros Durán , Stefan Niemann and Paul Pichler

Published/Copyright: December 7, 2019

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From the journal The B.E. Journal of Macroeconomics Volume 20 Issue 1

Abstract

We introduce fiscal policy into a sovereign debt model with endogenous default costs and examine the implications for the determination of the output costs of default. We find that the quantitative properties of the output costs of default, and their dependence on primitives such as the elasticity of labor supply, are distinctly different depending on the margin of fiscal adjustment. The consideration of fiscal policy thus has potentially important implications for the quantitative properties of models of sovereign debt and default.

Keywords: fiscal policy; output costs of default; sovereign debt

JEL Classification: E62; F34; H63

Acknowledgement

We are grateful to the editor, Davide Debortoli, and an anonymous referee for their detailed feedback. The content of this article does not reflect the official opinion of the European Union. Responsibility for the information and views expressed therein lies entirely with the authors.

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Appendix

Appendix A.1 Optimal tax and spending policy

Proof of Proposition Proposition 1.

Given some debt policy, the optimal tax and spending policy must satisfy (5) and

uc∂c∂τ−ul∂L∂τ+ug∂g∂τ=0.

Using (1) and (2), the optimality condition for taxes becomes

0=uc[∂gdp∂τ(1+τ)−gdp(1+τ)2]−ucv′(L)∂L∂τ+ug[(gdp+τ∂gdp∂τ)(1+τ)−τgdp(1+τ)2],

or equivalently,

uc{−∂11+τ∂τgdp−11+τ∂gdp∂τ+v′(L)∂L∂τ}=ug{−∂11+τ∂τgdp+τ1+τ∂gdp∂τ}.

From the definition of GDP as the value of the output of final goods net of the costs of imported intermediate inputs, gdp = y − P^*(r^*)m^*, and since factors earn their marginal products, while the price for imported inputs is exogenous, we have

∂gdp∂τ=∂gdp∂L∂L∂τ+∂gdp∂m∗∂m∗∂τ=w∂L∂τ+[P∗(r∗)−P∗(r∗)]∂m∗∂τ=w∂L∂τ.

Hence, the optimality condition for consumption-leisure (2) implies

−11+τ∂gdp∂τ+v′(L)∂L∂τ=[−w1+τ∂gdp∂τ+v′(L)]∂L∂τ=0,

so that the the optimality condition for taxes becomes

uc{−∂11+τ∂τgdp}=ug{−∂11+τ∂τgdp+τ1+τ∂gdp∂τ}.

This condition has an interpretation in terms of marginal benefits and marginal costs of changing the tax rate. Accordingly, variations in the government’s tax policy are seen to have two effects: a direct reallocation effect (−∂11+τ∂τgdp>0), and a budgetary effect (τ1+τ∂gdp∂τ<0). In detail, for given GDP, an increase in the tax rate allows to reallocate resources from private to public consumption. However, this causes tax distortions which work to reduce GDP, the relevant tax base for the consumption tax, and thus has negative implications for the government’s budget. In conjunction, this implies that the optimal fiscal policy limits distortions by keeping public expenditure below its first-best level, that is, u_c < u_g. ⊡

Appendix A.2 Business cycle implications under different fiscal policies

Table 2:

Statistical moments.

	(I)	(II)	(III)
Statistic	FP	exog. g	exog. τ
Standard deviation relative to standard deviation of GDP
C	1.09	1.23	1.00
G	1.34	0	1.63
Correlation with GDP
default	−0.12	−0.13	−0.12
spreads	−0.17	−0.17	−0.00
TB/GDP	−0.46	−0.49	−0.37
G	0.73	0	0.83
τ	−0.40	−0.65	0
Correlation with spread
TB/GDP	0.09	0.16	0.05
G	0.01	0	−0.03
τ	0.25	0.15	0
Mean debt-to-quarterly GDP	23.7%	25.1%	28.2%
Mean annualized spread	0.43%	0.34%	0.18%
Std. dev. of spreads	0.44%	0.37%	0.34%
Mean output drop at default	13.8%	16.3%	14.6%

Baseline parameterization from Table 1. The simulated statistics are computed as averages over N = 20.000 simulations of length T = 500, with the first 100 observations truncated. The simulated series are logged and filtered.

Published Online: 2019-12-07

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https://doi.org/10.1515/bejm-2017-0236

Keywords for this article

fiscal policy; output costs of default; sovereign debt