We introduce scal policy into a sovereign debt model with endogenous default costs and examine the im-
plications for the determination of the output costs of default. We nd that the quantitative properties of the
output costs of default, and their dependence on primitives such as the elasticity of labor supply, are distinctly
dierent depending on the margin of scal adjustment. The consideration of scal policy thus has potentially
important implications for the quantitative properties of models of sovereign debt and default.
scal policy, output costs of default, sovereign debt
E62, F34, H63
10.1515/bejm-2017-0236
The dening feature of sovereign debt is the absence of legal enforcement mechanisms. The presumption un-
derlying formal models in the tradition of Eaton and Gersovitz (1981) is that sovereign debt can nevertheless be
sustained via direct costs of default and the threat of nancial autarky. The empirical literature, however, nds
limited support for external punishment following default; instead, defaults appear to be deterred by domes-
tic costs (Borensztein and Panizza 2009; Panizza, Sturzenegger, and Zettelmeyer 2009). These costs have been
found to be sizeable and potentially long-lasting. For example, De Paoli, Hoggarth, and Saporta (2009) estimate
a median output loss relative to pre-crisis output of at least 5% per year.
On the theoretical front, output costs of default are often incorporated in an ad hoc fashion (Aguiar and
Gopinath 2006; Arellano 2008). More recently, Mendoza and Yue (2012) endogenize the output costs of default
in the context of a production economy with trade in intermediate inputs; this approach thus facilitates an
integrated assessment of business cycles and sovereign default risk.
Importantly, however, Mendoza and Yue (2012) completely abstract from scal policy. Fiscal policy is dis-
tortionary, but also oers margins of adjustment that may constitute alternatives to outright sovereign default.
Given the endogenous nature of the output costs of default, it is thus a priori unclear to what extent the nd-
ings in Mendoza and Yue (2012) are robust to the explicit consideration of scal policy. This note makes a rst
pass at assessing the role of scal policy for the determination of the output costs of default.
1
This is impor-
tant because their structure in terms of magnitude and dependence on the underlying state of productivity
has been identied as a key determinant of sustainable debt levels and macroeconomic dynamics predicted by
quantitative models.
2
We nd that the output costs of default are critically dependent on the margin of scal adjustment. In a
partial equilibrium analysis based on exogenous debt levels and default decisions, we uncover the following
results. When adjustment in the wake of default comes exclusively via changes in public spending, the resulting
output losses are identical to those obtained in the model without scal policy. The quantitative insights from
Mendoza and Yue (2012) are thus robust to this scenario. However, when adjustment comes in the form of tax
changes instead, the associated reduction in distortions implies output costs of default that are signicantly
lower and more sensitive to the underlying productivity state. This makes it interesting to further examine the
dependence of the output costs of default on the elasticity of labor supply. Absent scal policy, the output costs
are increasing in the elasticity of labor supply. But this comparative-static eect is actually reversed once scal
policy is taken into account. This nding is therefore relevant for the assessment of default models where labor
market dynamics play an important role.
3
1
Konstanzer Online-Publikations-System (KOPS)
URL: http://nbn-resolving.de/urn:nbn:de:bsz:352-2-pthg0qdafi3j9
Output costs of default materialize as a consequence of two competing eects. On the one hand, default
induces a misallocation of resources due to the unavailability of working capital loans for imported intermediate
inputs the working capital channel. On the other hand, due to the scal relief through default there is potential
scope for tax cuts with favorable eects on labor supply the tax channel. Based on the full model where debt
dynamics, interest rate spreads and sovereign default all arise endogenously, we are able to quantify the direct
consequences of default through these channels relative to the counterfactual where debt is repaid. Our results
largely conrm the ndings from the partial equilibrium analysis. The margin of scal adjustment matters for
the magnitude of the output costs of default and their incidence over time. Moreover, as long as the tax channel
is active, it dominates the working capital channel so that, on impact, the output costs of default are decreasing
in the elasticity of labor supply.
Mendoza and Yue (2012) consider a small, open production economy with endogenous output costs of default
driven by disruptions to the import of intermediate inputs. A sovereign government issues debt to international
investors, and default wipes out the entirety of the maturing liabilities. We extend the model by introducing
scal policy in the form of a linear consumption tax τ and government expenditure g.
4
Otherwise our model is
identical; our exposition is thus conned to essential and new elements.
As is standard in the sovereign debt literature, households face a static problem and do not participate in
international nancial markets. Decisions about consumption c and labor supply L are taken subject to a budget
constraint linking private expenditure to income (gdp),
1 (1)
where the latter is given by the value of the output of nal goods net of the costs of imported intermediate
inputs. Preferences have a GHH-structure (Greenwood, Hercowitz, and Human 1988) and are specied as
1
1
1
1
1
Accordingly, the contributions of public expenditures and the consumption-leisure composite to utility have an
additively-separable CES structure and are aggregated with relative weights (1 π) and π. The labor supply
schedule is given by
1
(2)
As seen, the consumption tax distorts labor supply, which can be devoted to the production of nal (f ) or inter-
mediate (m) goods, L = L
f
+ L
m
. The nal goods production function is Cobb-Douglas and subject to productivity
shocks ε,
(3)
where M are intermediate inputs; k is the time-invariant capital stock; α
M
, α
L
, α
k
(0, 1) and α
M
+ α
L
+ α
k
= 1.
The mix of intermediate inputs is determined by a CES Armington aggregator combining domestic (m
d
) and
imported (m
*
) inputs,
1
1
with λ, μ (0, 1), implying an elasticity of substitution of
1
1
. Domestic inputs are produced according
to the production function
2
where A > 0 and γ [0, 1]. Imported inputs, in turn, are given by a Dixit-Stiglitz aggregator combining a
continuum of dierentiated varieties
, j [0, 1],
∫
01
1
(4)
where ν (0, 1). Thus, there is a nite elasticity of substitution of
1
1
across imported input varieties.
A subset Ω of the imported input varieties, dened by the interval 0 with θ (0, 1), must be nanced
in advance via working capital loans κ. The availability of working capital loans to rms conditions on the
governments access to international nancial markets. When the government repays its maturing debt, rms
can contract loans at the risk-free world interest rate r
*
; in this case, their demand for working capital κ satises
1
∫
0
where
denotes the exogenous, time-invariant price of the imported input variety j. Following a sovereign
default, instead, working capital loans become unavailable (κ = 0), preventing nal goods rms from sourcing
the optimally desired mix of imported inputs in (4). Since varieties in Ω must be replaced by imperfect substi-
tutes, this induces an eiciency loss. The resulting output costs of default are increasing in productivity. This is
because the complementarity embodied in the Cobb-Douglas production function (3) implies that distortions
to rms
optimal factor demand are more costly at higher levels of productivity.
Given productivity ε and some specication of scal policy (τ, g), factor allocations, factor prices and output
in a competitive equilibrium can be determined from the above conditions. In order to quantify the output costs
of default, numerical values must be assigned to the model parameters. Our assignment, detailed in Table 1,
introduces π as a new parameter but is otherwise identical to the one in Mendoza and Yue (2012) who calibrate
their model to data from Argentina (1980Q12005Q4). Parameters below the line are relevant only to the full
dynamic model discussed in Section 4.
Table 1: Parameter values.
Parameter Value Description
ω 1.455 Frisch elasticity 1/(ω 1) = 2.2
σ 2 intertemporal elasticity 1/σ = 0.5
π 0.9 utility weight
α
M
0.43 intermed. input share
α
L
0.40 nal sector labor share α
L
/(1 α
M
) = 0.7
α
k
0.17 nal sector capital share α
k
/(1 α
M
) = 0.3
γ 0.7 intermed. sector labor share
A 0.31 intermed. sector productivity
λ 0.62 Armington weight of domestic inputs
μ 0.65 between elasticity η
d
= 1/(1 μ) = 2.86
ν 0.59 within elasticity η
j
= 1/(1 ν) = 2.44
θ 0.7 working capital parameter
r
*
0.01 risk-free interest rate
β 0.88 discount factor
ϕ 0.083 reentry probability
ρ
ε
0.95 autocorrelation of productivity shock
σ
ϵ
0.017 standard deviation of productivity shock
In order to assess the importance of scal policy for the determination of the output costs of default, we subject
the model economy to a comparative experiment under an exogenous, possibly suboptimal debt policy (cf. the
partial equilibrium exercise in Section III of Mendoza and Yue 2012). Given an amount b of maturing debt
and the issuance of new debt b’, taxes and spending must satisfy the government budget constraint, τc = g +
3
(1 d) [b qb’], where d {0, 1} is a default indicator and q denotes the price for sovereign debt placed on
international nancial markets. Substituting from (1), the government budget constraint can be rewritten as
1
1
1
(5)
where
1
denotes the debt interest burden when a stationary level of debt
is rolled over at the risk-free
world interest rate r
*
. This is actually without loss of generality: What matters for the determination of taxes
and spending are not interest rates and debt separately, but only the resulting debt interest burden.
5
Conditional
on
1
, (5) therefore captures the implications for taxes and spending under any admissible debt policy. We
then have the following result, which extends that of Cuadra, Sanchez, and Sapriza (2010) to an environment
with endogenous default costs along the lines of Mendoza and Yue (2012).
Proposition 1
Given some debt policy, the governments optimal tax and spending policy is characterized by
1
1
1
1
1
(6)
which implies underprovision of public spending, u
c
< u
g
.
Given a debt interest burden of 3% of GDP, the preference weight π = 0.9 has been chosen such as to induce
a level of public spending of 15% of GDP when the government honors its liabilities and productivity is at ε
= 1. These numbers correspond roughly to their empirical counterparts in Argentina. Starting from there, we
compare the output of nal goods under default (y
d
) and repayment (y
nd
) for varying productivity. The output
costs of default are then computed as 1 y
d
/y
nd
, whereby we contrast between three alternatives that dier in
the scal adjustment in response to changing productivity and the exogenous repayment decision:
(i) the repayment regime (d = 0) where both τ and g are adjusted optimally in line with (6);
(ii) the default regime (d = 1) where both instruments are again adjusted optimally;
(iii) the default regime (d = 1) where one of the scal instruments is constrained to replicate the state-contingent
level chosen in regime (i) while the other one must adjust residually to satisfy (5).
6
The dierences across scal regimes are most readily seen in the two panels of Figure 1, which plot the tax rate
τ and the level of public spending relative to GDP, g/gdp, against productivity.
Figure 1: Fiscal instruments under dierent modes of scal adjustment. (A) Taxes. (B) Public spending
Under repayment, τ is decreasing in ε, while g/gdp is increasing. The reason is that higher productivity
induces a higher tax base, which allows a more favorable reallocation from private to public consumption by
means of taxation. By comparison, in regime (ii) τ is lower but g/gdp is higher for all productivity states. This is
because of the scal relief coming from sovereign default. For the same reason, since tax revenues are no longer
needed to nance the debt interest burden but used exclusively to provide public spending, both τ and g/gdp
are now independent of ε.
7
Finally, scal relief through default is also present in regime (iii), but there are two
distinct cases. When only taxes adjust (panel (a)), τ is lower than in regime (i) and increasing in ε. When only
spending adjusts (panel (b)), g/gdp is higher than in regime (i) and decreasing in ε.
What does this imply for the output costs of default? Figure 2 plots these costs, contrasting the dierent
scenarios for scal adjustment.
4
Figure 2: Output costs of default under dierent modes of scal adjustment.
We begin with the case of regime (iii) when taxes remain unchanged so that scal adjustment is exclusively
in the form of changes in public spending. The resulting output costs of default are identical to those obtained
in the model without scal policy studied by Mendoza and Yue (2012). This is because tax distortions are
kept constant, while public spending enters utility in an additively-separable fashion and hence does not aect
allocations. Next, consider the case of regime (iii) when public expenditure is xed and scal adjustment comes
entirely in the form of tax changes. Compared to the other case and thus also to the model without scal policy
the output costs of default are lower, and for suiciently low productivity shocks even negative; moreover,
the output costs schedule is now steeper in ε. These two features are again due to the fact that debt repudiation
through default relaxes the government budget constraint so that tax distortions are reduced. The relevance of
this mechanism is higher in low productivity states because the underlying tax base is smaller so that default
allows for a greater reduction of the tax rate. Finally, regime (ii) where both instruments are adjusted optimally
generates output costs of default that average out the previous two scenarios both in terms of level and slope.
As seen, the consideration of scal policy in general, and the specication of details about the scal ad-
justment process in particular, have quantitatively relevant implications for the output costs of default. Fiscal
activity matters due to its distortionary eect on labor supply. It is therefore interesting to examine the sensi-
tivity of our ndings to changes in the elasticity of labor supply
1
1
.
8
Figure 3 does this for regime (ii) where
both scal instruments are adjusted optimally. In Mendoza and Yue (2012), a higher elasticity of labor supply
dampens the wage response in the event of default, which implies stronger intersectoral reallocation eects and
ultimately higher output costs of default. This comparative-static eect is actually reversed once scal policy is
taken into account: a higher Frisch elasticity is now associated with lower (possibly even negative) output costs
of default. To understand this, recall that default induces lower tax rates (cf. Figure 1). This has a positive eect
on labor supply which is more pronounced the higher the elasticity of labor supply. In addition to their level
eect on the output costs of default, induced changes in taxation can hence also aect important qualitative
lessons from the model where scal policy is absent.
Figure 3: Regime (ii): Output costs of default under dierent labor supply elasticity.
5
