In financial and economic policy circles concerned with public debt in developing countries, a rising debt-GDP ratio is interpreted as a signal of overborrowing, warning of debt defaults if strong fiscal corrections are not adopted in time. This paper shows why this interpretation is incorrect by building a simple model of fiscal policy in which upward-sloping debt paths are observed even though the probability of default is ``almost surely" equal to zero.public debt; fiscal policy; debt sustainability; debt limits

Oviedo, P. Marcelo

English

Research Papers in Economics

 
IOWA STATE UNIVERSITY 
Department of Economics 
Working Papers Series 
 
Ames, Iowa 50011 
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Sustainable Fiscal Policy with Rising Public Debt-to-
GDP Ratios  
P. Marcelo Oviedo  
November  2006  
Working Paper # 06040  Sustainable Fiscal Policy with Rising
Public Debt-to-GDP Ratios ¤
P. Marcelo Oviedoy
Iowa State University
November 17, 2007
Abstract
In ¯nancial and economic policy circles concerned with public debt in developing
countries, a rising debt-GDP ratio is interpreted as a signal of overborrowing, warn-
ing of debt defaults if strong ¯scal corrections are not adopted in time. This paper
shows why this interpretation is incorrect by building a simple model of ¯scal policy in
which upward-sloping debt paths are observed even though the probability of default
is \almost surely" equal to zero.
JEL classi¯cation codes: E62, F34, F37, H63
Key words: public debt, ¯scal policy, debt sustainability, debt limits
¤I am grateful to Enrique Mendoza for helpful discussions and to Rajesh Singh for thoughtful suggestions
and comments on an earlier draft. All remaining errors are mine.
yEconomics Department, 279 Heady Hall, Ames, IA 50010, oviedo@iastate.edu; tel.: +1 (515) 233-56511 Motivation
The literature on public debt sustainability is largely silent about when an indebtedness level
becomes unsustainable. The empirical evidence seems not to be helpful either: the median
public debt-GDP ratio among countries that defaulted on their public debt during the last
30 years is about 50 percent; 35 (30) percent of the defaults happened at debt ratios of less
(more) than 40 (80) percent (IMF, 2003a, Ch.III). The lack of sustainability benchmarks
leads policymakers and debt analysts to focus on other aspects of public debt to assess its
sustainability.
Following the tradition started with Blanchard (1990) and Blanchard et al. (1990), one
of the most common practices points out that upward-sloping time paths of public debt signal
¯scal policy unsustainability. For instance, the slope of the debt path is a key component
of a framework elaborated by the IMF and the World Bank for assessing debt sustainability
(see IMF, 2003b), and as documented by IMF (2003b), investment houses and risk-rating
agencies also based their ¯scal sustainability analyses on the short-term dynamics of public
debt.1 By building a model in which rising debt paths are consistent with an almost surely
nil probability of default, this paper shows why it is misleading to assess ¯scal sustainability
by focusing on the slopes of debt-paths.
2 The Basics
Debt sustainability analyses focus on the government budget constraint, which takes the
following form in a non-monetary economy:
bt = bt¡1Rt + gt ¡ ¿t (1)
where all variables except the growth-adjusted interest rate Rt ´ Rt=¡t are measured as
GDP ratios; here, Rt and ¡t are the gross rates of interest and GDP growth; ¿t and gt
represent ¯scal revenues and non-interest ¯scal outlays; and bt the public debt issued at the
1For recent applications of this approach, see Celasun et al. (2006) and the references therein.
1end of period t. Hereafter, Rt, ¡t, and ¿t are assumed to be exogenous and stochastic with
their dynamics governed by a Markov chain Q(qt+1;qt), where qt ´ [¿t;Rt;¡t]0.
Seeking to identify unsustainable debt ratios, Mendoza and Oviedo (2006a, 2006b)
adopt the notion of the natural debt limit (NDL) of the precautionary-savings literature
(Aiyagari, 1994; see also Aiyagari, et al. 2002) to pinpoint the maximum sustainable level of
public debt that a country can support. Levels of debt that exceed the NDL are inconsistent
with solvency (i.e. debt repayment) in all states of nature. In Mendoza and Oviedo (2006a)
the NDL on public debt, Á, depends on the \worst" state of the Markov chain Q, as well as
the minimum level of gt, say gmin, considered as socially or politically tolerable:
Á ´ min
©
R
¡1
t (¿t ¡ g
min)
ª
; (2)
By never borrowing more than Á a country guarantees its ability to pay even under the most
adverse scenario. If borrowing more than Á is allowed, there are feasible scenarios in which
the country is unable to repay even setting gt = gmin forever.
3 A Model of Sustainable Fiscal Policy
Consider a government that seeks to provide a smooth path of ¯scal outlays without incurring
too large a debt or primary ¯scal de¯cits dt ´ gt ¡ ¿t, while ensuring the provision of the
minimum level of expenditures gmin. This can be the goal of a government interested in
meeting policy goals like those of the Maastricht ¯scal convergence criteria, which require
the primary de¯cit and the debt ratio to not exceed 3 and 60 percent of GDP, respectively.
Assume that the policy goals are summarized by the following in¯nite-horizon loss
function:
L0 =
1 X
t=0
¯
tE0
©
¡log(gt) + !
£
¶(dt ¸ ¹ d) + ¶(bt ¸ ¹ b)
¤ª
; (3)
subject to: (i) the budget constraint (1); (ii) bt · Á, according to the de¯nition of Á given in
(2) and a given gmin; (iii) the Markov chain Q(qt+1;qt); and (iv) b¡1 given . In (3), E0 is the
conditional expectation operator and ¯ 2 (0;1) a discount factor; ¶ is an indicator function
2equal to 1 if the condition stated in its argument occurs, and equal to 0 otherwise. The
parameters ¹ d and ¹ b are \upper desirable limits" on dt and bt, externally imposed to the ¯scal
authority, and ! ¸ 0 is a penalty parameter capturing the adverse political consequences of
exceeding those limits.
The term ¡log(gt) captures the perceived bene¯ts from government outlays and in-
duces an outlay-smoothing e®ect similar to the one that helps Mendoza and Oviedo (2006a)
to explain the procyclicality of ¯scal policy in developing countries. As in social choice the-
ory, concave preferences over gt re°ect either that opportunistic policymakers bene¯t from
rents that are proportional to ¯scal expenditures or that benevolent policymakers internalize
the welfare derived by residents from the consumption of public goods.
Calibration
The foregoing model is calibrated to the 1985-2006, Costa Rican ¯scal variables of the central
government. The starting point is ^ qt, the empirical counterpart of [¿t;Rt;¡t]0. By resort-
ing to Tauchen and Hussey's (1991) algorithm, a Markov chain of twelve states Q(qt+1;qt)
approximates the statistical properties of the exogenous state variables in actual data, i.e.,
f^ qtg2006
t=1985. Table 1 shows the implied statistical moments of ¿t and Rt.2
To guarantee that the unconditional mean values of bt and gt match their empirical
counterparts, ¯ is set equal to 0:981 and the mean value of Rt is set to 1.065. Following the
Maastritch ¯scal criteria and considering that the size of the central government is about
2/3 of the total size of the Costarrican government, ¹ d = 0:02 and ¹ b = 0:40. gmin is set equal
to two-and-a-half standard deviations below the mean in the data: the observed mean value
of gt is equal to 0.130 and gmin = 0:086. This value of gmin, along with the states of the
Markov chain, imply that Á = 0:502. Finally, ! = 0:01199 is the minimum value of the
penalty parameter that reduces to zero the probabilities Pr[dt > ¹ d] and Pr[bt > ¹ b], so bt ¿ ¹ b
and dt ¿ ¹ d almost surely 8t. As ¹ b < Á, the economy is always able to honor its public debt
and consequently, the ¯scal policy is sustainable.
2The Costa Rican data, along with the used Markov chain are available from the author upon request.
34 Rising Debt Ratios with Sustainable Fiscal Policy
The constrained loss-minimization problem is solved by formulating a discrete-state dynamic
programming problem. The state space are 500 equidistant values of bt 2 [0:1;Á], along with
the 12 triples of qt of the Markov chain. The controls are gt and bt; the pay-o® function is
the negative of the instantaneous loss function in (3); last, the budget constraint (1) and the
transition probability matrix of the Markov chain Q are the states' laws of motions.
Let ¼1 represent the limiting distribution of the states (bt;qt). Table 1 shows the
moment statistics implied by ¼1 and Figure 1a shows the induced marginal limiting distri-
bution of bt. The ¯gure shows that Pr[bt > ¹ b]=0, and therefore Pr[bt > Á]=0. Thus, by the
the de¯nition of the NDL, the ¯scal policy represented by gt = ~ g(bt¡1;qt) and bt = ~ b(bt¡1;qt)
poses no ¯scal risk: the government is always able to repay its debt!
Can this policy generate short- to midterm increasing public debt paths? Two com-
putable objects can answer this question: (a) the \forecasting functions" of bt, which repre-
sent the model implied conditional mean of the debt ratio given an initial state (b¡1;q0); and
(b) a fan chart, which was recently introduced in the literature by Celasun et al. (2006) to
represent the results of a large number of simulations of equation (1). Typically, the simula-
tions consider a distribution of shocks a®ecting the debt ratio and a reaction function of the
primary balance to the debt level, the latter being the empirical counterpart of ~ g(bt¡1;qt)
and ~ b(bt¡1;qt) in the model.
Starting with the ¯rst exogenous state and ¯ve initial debt ratios ranging between 0.2
and 0.4 (=¹ b), Figure 1b shows the corresponding forecasting functions. When b¡1 = 0:2
(b¡1 = 0:4), the model predicts a time-increasing (time-decreasing) debt ratio. More gen-
erally, as the forecasting functions represent conditional means, all these functions converge
to the unconditional mean of bt, ¹(b), shown in Table 1. Therefore, any initial debt ratio
such that b¡1 < ¹(b) generates time-increasing debt ratios. Increasing or decreasing ratios,
however, cannot be interpreted as signals of ¯scal policy unsoundness for it has been shown
that debt default is is an impossible event in the modelled economy.
The uninformativeness of the slope of the time-path of public debt to signal unsustain-
ability is not a result particular to the loss function speci¯ed in (3). Any ¯scal policy that
4generates a unique unimodal distribution of bt with a support included in (¡1;Á] can lead
to the same conclusion.
The fan chart in Figure 1c arises from 1000 simulations of Q and the use of the optimal
policy functions to describe the dynamics of the endogenous state variables. The initial debt
ratio is b¡1 = ¹ b=2 = 0:20. From lighter to darker, the colored areas show deciles at 20, 40,
60 and 80 percent con¯dence intervals around the median projection; it can be inferred from
the chart, for instance, that the probability of observing a rising debt ratio is approximately
equal to 90%.
The results depicted in Figures 1a to 1c lead to the conclusion of this paper. Public debt
ratios are expected to rise if the actual debt ratio is below its unconditional mean. Increasing
debt ratios are perfectly consistent with a sound ¯scal policy that, by construction, rules out
debt default.
References
Aiyagari, S. R., 1994. Uninsured idiosyncratic risk and aggregate saving. Quarterly Journal
of Economics 109 (3), 659{684.
Blanchard, O., 1990. Suggestions for a new set of ¯scal indicators.OECD Working Paper
No. 79, Organization for Economic Cooperation and Development.
Blanchard, O. J., Chouraqui, J.-C., Hagemann, R., Sartor, N., Autum 1990. The sustain-
ability of ¯scal policy: New answers to an old question. OECD Economic Studies (15),
7{36.
Celasun, O., Debrun, X., Ostry, J., 2006. Primary surplus behavior and risks to ¯scal sustain-
ability in emerging market countries: A "fan-chart" approach. IMF Sta® Papers 53 (3).
IMF, September 2003a. Public debt in emerging countries: Is it too high? World Economic
Outlook.
IMF, 2003b. Sustainability assessment -review of applications and methodological re¯ne-
ments. SM/03/206.
Mendoza, E. G., Oviedo, P.-M., October 2006a. Fiscal policy and macroeconomic uncertainty
in developing countries: The tale of the tormented insurer. NBER WP 12586.
Mendoza, E. G., Oviedo, P.-M., 2006b. Public debt, ¯scal solvency and macroeconomic
uncertainty in latin america: The cases of brazil, colombia, costa rica, and mexico. Mimeo,
Iowa State University.
5Rao, A. S., Marcet, A., Sargent, T., SeppÄ alÄ a, J., 2002. Optimal taxation without state-
contingent debt. Journal of Political Economy 110 (6), 1220{1254.
Tauchen, G., Hussey, R., 1991. Quadrature-based methods for obtaining approximate solu-
tions to nonlinear asset pricing models. Econometrica 59, 371{396.
6Table 1: Unconditional Moments Implied by the
Limiting Distribution of the State Variables
Variable (x) ¹(x) ¾(x) ½(x) ½(x;y)
(GDP ratios, except Rt) £100 £100
y = ¿ y = R
Fiscal revenue (¿t) 13.2 5.7 0.62 1.00 -0.19
Growth adjusted int. rate (Rt ¡ 1) 1.7 3.5 0.21 -0.19 1.00
Public debt (bt) 33.1 13.0 0.96 -0.24 0.02
Non-interest outlays (gt) 12.6 5.1 0.75 0.52 -0.42
Primary balance (¡dt) 0.6 125.3 0.54 0.61 0.18
Notes: ¹(x), ¾(x), and ½(x), stand for the mean, standard deviation, and
autocorrelation of x. ½(y;x) is the contemporaneous cross correlation between
y and x.
Figure 1: Public Debt-GDP Ratio: Limiting Marginal
Distribution, Forecasting Functions, and a Fan Chart
0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.01
φ
Public Debt−to−GDP Ratio
P
r
o
b
a
b
i
l
i
t
i
e
s
(a) Marginal Distribution of bt
2 4 6 8 10 12 14
0.1
0.15
0.2
0.25
0.3
0.35
P
u
b
l
i
c
 
D
e
b
t
−
t
o
−
G
D
P
 
R
a
t
i
o
Years
(b) Forecasting Functions of bt
1 2 3 4 5 6 7 8 9 10
0.18
0.2
0.22
0.24
0.26
0.28
0.3
0.32
Years
P
u
b
l
i
c
 
D
e
b
t
−
t
o
−
G
D
P
 
R
a
t
i
o
(c) Fan-Chart of bt
7

Fiscal policy and macroeconomic uncertainty in developing countries: The tale of the tormented insurer.

Optimal taxation without statecontingent debt.

Primary surplus behavior and risks to ¯scal sustainability in emerging market countries: A &quot;fan-chart&quot; approach.

Public debt in emerging countries: Is it too high? World Economic Outlook.

Public debt, ¯scal solvency and macroeconomic uncertainty in latin america: The cases of brazil, colombia, costa rica, and mexico.

Quadrature-based methods for obtaining approximate solutions to nonlinear asset pricing models.

Suggestions for a new set of ¯scal indicators.OECD Working Paper No. 79, Organization for Economic Cooperation and Development.

Sustainability assessment -review of applications and methodological re¯nements.

The sustainability of ¯scal policy: New answers to an old question.

Uninsured idiosyncratic risk and aggregate saving.

Sustainable Fiscal Policy with Rising Public Debt-To-Gdp Ratios

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Sustainable Fiscal Policy with Rising Public Debt-To-Gdp Ratios

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