A Solution to the Default Risk-Business Cycle Disconnect

TL;DR: In this paper, the authors propose a solution to this default risk-business cycle disconnect based on a model of sovereign default with endogenous output dynamics, which replicates observed V-shaped output dynamics around default episodes, countercyclical sovereign spreads, and high debt ratios.

Abstract: Models of business cycles in emerging economies explain the negative correlation between country spreads and output by modeling default risk as an exogenous interest rate on working capital. Models of strategic default explain the cyclical properties of sovereign spreads by assuming an exogenous output cost of default with special features, and they underestimate debt-output ratios by a wide margin. This paper proposes a solution to this default risk-business cycle disconnect based on a model of sovereign default with endogenous output dynamics. The model replicates observed V-shaped output dynamics around default episodes, countercyclical sovereign spreads, and high debt ratios, and it also matches the variability of consumption and the countercyclical fluctuations of net exports. Three features of the model are key for these results: (1) working capital loans pay for imported inputs; (2) imported inputs support more efficient factor allocations than when these inputs are produced internally; and (3) default on the foreign obligations of firms and the government occurs simultaneously.

Summary

1 Introduction

• Three key empirical regularities characterize the relationship between sovereign debt and economic activity in emerging economies: (1) Output displays V-shaped dynamics around default episodes.
• Reinhart et al. (2003) report that the external debt ratio during default episodes averaged 71 percent of GDP for all developing countries that defaulted at least once in the 1824-1999 period.
• The authors extend the two classes of models (sovereign debt and business cycle models) by developing a framework in which the equilibrium dynamics of output and default risk are determined jointly, and influence each other via the interaction between foreign lenders, the domestic sovereign borrower, and domestic firms.
• These two inputs are perfect substitutes in the production technology, but imported inputs have a higher financing cost because they need to be paid in advance using working capital, while domestic inputs require costly reallocation of labor away from final goods production into intermediate goods production.

2 A Model of Sovereign Default and Business Cycles

• The authors study a dynamic stochastic general equilibrium model of sovereign default and business cycles.
• There are four groups of agents in the model, three in the "domestic" small open economy (households, firms, and the sovereign government) and one abroad (foreign lenders).

2.1 Households

• Households derive utility from consumption and disutility from labor.
• U is the period utility function, which is continuous, strictly increasing, strictly concave, and satisfies the Inada conditions.
• Following Greenwood, Hercowitz and Huffman (1988), the authors remove the wealth effect on labor supply by specifying period utility as a function of consumption net of the disutility of labor h(L t ), where h is increasing, continuously differentiable and convex.
• Households do not borrow directly from abroad, but they are still able to smooth consumption because the government borrows, pays transfers, and makes default decisions internalizing their utility function.
• With these functional forms, the optimality condition for sectoral labor supply allocations reduces to: EQUATION.

2.2 Final Goods Producers

• The f sector chooses optimally whether to import intermediate goods from abroad or buy them from the m sector at home.
• This interest rate is linked to the sovereign interest rate at equilibrium, as shown in the next section.
• Working capital loans satisfy the standard payment-in-advance condition: EQUATION Profit-maximizing firms choose κ t so that this condition holds with equality.
• As noted earlier, domestic inputs do not require working capital financing.
• When imported intermediate goods are used, the optimality conditions are EQUATION EQUATION Alternatively, when domestic inputs are used, the optimality conditions are: EQUATION ).

2.3 Intermediate Goods Producers

• At equilibrium, the m sector operates only if the market price of its output is positive, which occurs only if the f sector chooses to use domestic inputs.
• Given the domestic price of intermediate goods and the sectoral wage rate, they choose labor demand so as to solve the following profit maximization problem: EQUATION.
• If final goods producers demand domestic intermediate goods, optimal labor demand by producers of intermediate goods satisfies EQUATION.

2. The allocations

• Because, as the authors show later, the interest rate on foreign working capital loans is driven by the sovereign interest rate, these firms face higher financing costs when default risk rises, and so their factor demands and output fall.
• One special case of this situation is the state when default occurs, in which the country has no access to working capital because effectively r has gone to infinity.
• Firms cannot import inputs from abroad and switch to use domestic substitutes.
• Next the authors define the indicator function Φ(r, ε) to identify whether the f sector is using domestic or imported inputs at the current state of interest rates and TFP.

2.5 Endogenous Output Cost of Default

• The decision by firms in the f sector to shift between foreign and domestic inputs depends on the states of the interest rate and TFP.
• Hence, firms choose to use domestic inputs (and bear the efficiency loss) rather than paying this financing cost.
• The switch from imported to domestic inputs that occurs at high interest rates has important implications for the output cost of default.
• This property of the output cost of default is key for the model's ability to support high debt levels together with observed default frequencies, because it makes the default option more attractive to the country at lower states of productivity, and works as a desirable implicit hedging mechanism given the incompleteness of asset markets.

2.6 The Sovereign Government

• The sovereign government trades with foreign lenders one-period, zero-coupon discount bonds, so markets of contingent claims are incomplete.
• As in the Eaton-Gersovitz model, the authors assume that when the country defaults it does not repay at date t and the punishment is exclusion from the world credit market in the same period.
• It chooses a debt policy (amounts and default) that maximizes the households' welfare subject to the constraints that: (a) the private sector allocations must be a competitive equilibrium; and (b) the government budget constraint must hold.
• The authors assume that during the exclusion stage the economy cannot build up its own stock of savings to supply working capital loans to firms, which could be used to purchase imported inputs.
• The authors also studied an alternative setup in which they allowed for a domestic financial market to operate during the exclusion stage.

2.7 Foreign Lenders

• International creditors are risk-neutral and have complete information.
• They invest in sovereign bonds and in private working capital loans.
• Foreign lenders behave competitively and face an opportunity cost of funds equal to the world risk-free interest rate.
• This condition implies that at equilibrium bond prices depend on the risk of default.
• This result, formalized in Theorem 2 below, is consistent with the empirical evidence documented by Edwards (1984) .

2.8 Country Risk & Private Interest Rates: Some Empirical Evidence

• The result that the interest rates on sovereign debt and private working capital loans are the same raises a key empirical question:.
• The authors then constructed the corresponding aggregate country measure as the median across firms.
• The comparison of this measure of interest rates faced by private firms with the standard EMBI+ measure of interest rates on sovereign debt shows two striking facts (see Table 1 ): First, the two interest rates are positively correlated in most countries, with a median correla-tion of 0.7, and in some countries the relationship is very strong .
• Condition 2 requires that the private consumption allocations implied by these optimal borrowing and default choices be both feasible and consistent with a competitive equilibrium (recall that the resource constraint of the sovereign's optimization problem considers only private-sector allocations that are competitive equilibria).

3.1 Calibration

• The authors study the quantitative implications of the model by conducting numerical simulations setting the model to a quarterly frequency and using the following benchmark calibration.
• Hence, setting α m = 0.4 would match the share of total intermediate goods but overestimate the fraction of them that are imported, while α m = 0.15 would match the share of imported inputs but underestimate the share of total intermediate goods.
• The standard deviation and first-order autocorrelation of the cyclical component of H-P filtered GDP are 4.7 percent and 0.79 respectively.
• The target statistic for default frequency is 0.69 percent because Argentina has defaulted five times on its external debt since 1824 (the average default frequency is 2.78 percent annually or 0.69 percent quarterly).

3.2 Results of the Benchmark Simulation

• This subsection examines the model's ability to account for the three key empirical regularities of sovereign debt highlighted in the Introduction: V-shaped output dynamics with deep recessions that hit bottom at times of default, countercyclical country interest rates, and high debt ratios.
• Table 3 compares the moments produced by the model with moments from Argentine data.
• Moreover, their model also produces a closer approximation to the actual correlation between bond spreads and GDP than other models of sovereign default, which do yield acyclical or countercyclical spreads but miss the actual correlations by wide margins.
• The sovereign borrows less when the economy faces an adverse productivity shock, and thus households adjust consumption by more than in the absence of default risk.
• If the authors aggregate the quarterly simulation data into an annual frequency and recalculate these statistics, they find that 22 percent of defaults occur in "good times" (i.e. with GDP above trend), 78 percent occur in bad times, and only about 6 percent of them occur when GDP is two standard deviations or more below trend.

3.3 Dynamics of Output Around Default Episodes

• The authors illustrate the model's ability to match V-shaped dynamics of output around default episodes using event study techniques.
• Figure 4 plots the model's average path of output around default events together with the data for Argentina's HP detrended GDP around the 2001 default (1999Q1 to 2004Q2).
• In default events, however, the Solow residual overestimates the true adverse TFP shock by a large margin (on average, s falls by nearly twice as much as ε when the economy defaults).
• Labor and the allocation of intermediate goods also fall sharply when the economy defaults.
• The sharp declines in GDP, consumption, labor and intermediate goods, together with the large reversal in the current account, indicate that the model yields predictions consistent with the sudden stop phenomenon observed in emerging economies around financial crises.

3.4 Key Features of the Equilibrium with Default

• The value of default increases with working capital because the government transfers the repayment of working capital loans to households when it defaults.
• The lower-left panel of Figure 8 shows that the country borrows less (i.e. chooses a higher asset position) when it experiences a low TFP shock.
• Finally, the lower-right panel of Figure 8 shows that the relationship between output and foreign assets follows "almost" a two-step function.
• The higher step pertains to the range of debt positions when the country has access to world credit markets and firms use imported inputs.

4.1 Working capital

• The working capital constraint plays an important role in the quantitative performance of the model.
• The model without working capital performs much worse in terms of its ability to match all of the important features of the data that the benchmark model mimicked well.
• In contrast, the variability of GDP, the probability of default, and the mean and standard deviation of spreads all increase as θ rises.
• On the other hand, default leads to a lower fraction of output loss at default on average because the TFP shock that triggers default is smaller than in the benchmark case with a lower θ.
• The overall quantitative effects of tightening the working capital constraint on the debt/GDP ratio and the default frequency are particularly large, and the authors get these results even though average sovereign spreads, and hence the average interest rate on working capital, do not deviate sharply from the one-percent risk free rate.

4.2 Costly Labor Reallocation

• As the authors explained earlier, the shift from imported to domestic inputs that occurs when the economy defaults reduces production efficiency because of the costly reallocation of labor away from final goods production.
• The results show that the value of ν directly affects the fraction of output loss at default, as would be expected.
• In addition, the volatility of spreads falls from 2.8 percent with higher ν to 0.71 percent in the benchmark case and 0.35 percent with lower ν.
• Lower and higher ν produce a higher correlation between GDP and spreads than in the benchmark case, but the correlation is always negative.
• Aggregating to an annual frequency, the authors find that with ν = 0.43 half of the defaults occur with output above trend, and no defaults occur with GDP more than two standard deviations below trend (compared with 6 percent of defaults in the benchmark case).

4.3 Intermediate Inputs Share

• In the benchmark calibration, the authors set the share of intermediate goods in final goods production α m at 30 percent, and noted that this value is lower than the typical 40 percent share of total intermediate goods to gross output in the data but higher than the 12-15 percent share of imported intermediate goods.
• Clearly, changes in the value of α m have important quantitative implications: Higher α m sharply the output cost of default and the mean debt ratio, while it significantly the frequency of default and the standard deviation of spreads.
• By contrast, the volatility of output and the correlations shown in the Table are relatively unaffected.
• Thus, the model can generate defaults in good times even at the quarterly frequency.
• Aggregating to an annual frequency, α m = 0.35 yields almost 26 percent of defaults with output above trend, 74 percent with output below trend, and 3.4 percent of defaults occur with GDP more than two standard deviations below trend.

5 Conclusions

• This paper proposed a model of strategic sovereign default with endogenous output dynamics and examined its quantitative predictions.
• The model is consistent with three key stylized facts of sovereign debt: (1) the V-shaped dynamics of output around default episodes, (2) the negative correlation between interest rates on sovereign debt and output, and (3) high debt-output ratios on average and when defaults take place.
• This result follows from the fact that the financing cost of working capital when default occurs rises too much for firms to find it profitable to use imported inputs, and hence they optimally switch to domestic inputs and suffer the corresponding efficiency loss.
• Without the first two features, output would not respond to changes in country risk.
• The authors acknowledge, however, that the linkages between sovereign default and private sector borrowers, and the mechanisms by which default induces economy-wide efficiency losses, should be the subject of further research.

Figures

Table 2: Benchmark Model Calibration

Figure 8: Value Function and Decision Rules

Table 6: Changes in Share of Intermediate Goods

Table 3: Model Simulation and Statistics in the Data

Figure 3: Sovereign Bond Interest Rates and Median Firm Financing Costs

Figure 5: Growth Rates of GDP, True TFP and Solow Residual around Default

Figure 6: Dynamics of Output and Sovereign Spreads before a Debt Crisis

Table 4: Changes in the Working Capital Constraint

Figure 2: Output and the Output Cost of Default as Functions of TFP

Figure 4: Output around Default Events

Figure 1: The Intermediate Goods Market

Table 5: Changes in Sectoral Labor Elasticity

Figure 7: Macro Dynamics around Default Episodes

Table 1: Sovereign Interest Rates and Firm Financing Cost

Full text

Board of Governors of the Federal Reserve System
International Finance Discussion Papers
Number 924
March 2008
A Solution to the Default Risk-Business Cycle Disconnect
Enrique G. Mendoza
And
Vivian Z. Yue
NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate
discussion and critical comment. References in publications to International Finance Discussion
Papers (other than an acknowledgment that the writer has had access to unpublished material)
should be cleared with the author or authors. Recent IFDPs are available on the Web at
www.federalreserve.gov/pubs/ifdp/.

A Solution to the D efault R isk-Bu siness C ycle Disconn ect
∗
Enrique G. Mendoza
Universit y of M aryland and NBE R
Vivian Z. Yue
New York University
March 2008
Abstract
Models of business cycles in emerging economies explain the negative correlation be-
tween country spreads and output by modeling default risk as an exogenous interest rate
on working capital. Models of strategic default explain the cyclical properties of sovereign
spreads by assuming an exogenous output cost of default with special features, and they
underestimate debt-output ratios by a wide margin. This paper proposes a solution to
this default risk-business cycle disconnect based on a model of sovereign default with
endogenous output dynamics. The model replicates observed V-shaped output dynamics
around default episodes, countercyclical sovereign spreads, and high debt ratios, and it
also matches the variability of consumption and the countercyclical fluctuations of net ex-
ports. Three features of the model are key for these results: (1) working capital loans pay
for imported inputs; (2) imported inputs support more efficient factor allocations than
when these inputs are produced internally; and (3) default on the foreign obligations of
firms and the governm ent occurs simultaneously.
JEL Code: E32, E44, F32, F34
Key Words: Business
cycles, so vereign default, emerging economies
∗
We thank Cristina Arellano, Andy Atkeson, Fernando Broner, Jonathan Eaton, Jonathan Heathcote, Pat
Keho e, Naraya na Kocherlakota, Guido Lorenzoni, Andy Neumeyer, Victor Rios-Rull, Mark Wright, and Tom
Sargent for helpful comments and suggestions. We also acknowledge comments by participants at seminars
and conferences at NYU, CUNY, Federal Reserve Bank of Kansas City, SUNY-Albany, Federal Reserve Bank
of Minneapolis, SED 2007 Annual Meeting in Prague, LACEA 2007 Annual Meeting in Bogota, and the
CREI-CEPR 2007 Conference o n Sovereign Risk in Barcelona.

1Introduction
Three key empirical regularities characterize the relationship between sovereign debt and
economic activity in emerging economies:
(1) Output displays V-shaped dynamics around default episodes. Recent default episodes
have been associated with deep recessions. Arellano (2007) shows that GDP deviations from
trend in the quarter in which default occurred were -14 percent in Argentina, -13 percent
in Russia and -7 percent in Ecuador. Using quarterly data for 39 developing countries over
the 1970-2005 period, Levy-Yeyati and Panizza (2006) show that the recessions associated
with defaults tend to begin prior to the defaults and generally hit bottom when the defaults
take place. Tomz and Wright’s (2007) study of the history of defaults for industrial and
developing countries during the period 1820-2004 reports that the frequency of defaults is
at its maximum when output is at least 7 percent below trend. They also found, ho wever,
that some defaults occurred with less severe recessions, or when output is not below trend in
annual data.
(2) Interest rates on sovereign debt and domestic output are negatively correlated. Neumeyer
and Perri (2005) report that the cyclical correlations between these interest rates and GDP
range from -0.38 to -0.7 in five emerging economies, with an average correlation of -0.55.
Uribe and Yue (2006) report correlations for seven emerging economies ranging from zero to
-0.8, with an average of -0.42.
1
(3) External debt as a share of GDP is high on average, and high when countries default.
Foreign debt was about a third of GDP on average over the 1998-2005 period for the en tire
group of emerging and developing countries as defined in IMF (2006). Within this group,
the highly indebted poor countr ies had the highest average debt ratio at about 100 percent
of GDP, followed by the Eastern European and Western Hemisphere countries, with averages
of about 50 and 40 percent of GDP respectively. Reinhart et al. (2003) report that the
external debt ratio during default episodes averaged 71 percent of GDP for all developing
countries that defaulted at least once in the 1824-1999 period. The default episodes of recent
years are in line with this estimate: Argentina defaulted in 2001 with a 64 percent debt ratio,
and Ecuador and Russia defaulted in 1998 with debt ratios of 85 and 66 percent of GDP
respectively.
These empirical regularities have proven difficult to explain. On one hand, quantitative
business cycle models can account for the negative correlation between country interest rates
and output if the interest rate on sovereign debt is introduced as the exogenous interest rate
faced by a small open economy in which firms require working capital to pay the wages bill.
2
On the other hand, quan titative models of sovereign default based on the classic setup of
1
Neumeyer and Perri used data for Argentina, Brazil, Ko rea, Mexico and the Philippines. Uribe and Yue
added E cuador, Peru and South Africa, but exclude d Korea.
2
See Neumeyer and Perri (2005), U ribe and Yue (2006) and O viedo (2005).
1

Eaton and Gersov itz (1981) can generate countercyclical sovereign spreads if the sovereign
country faces stochastic shocks to an exogenous output endowment.
3
These models require
exogenous output costs of default with special features in order to support non-trivial levels
of debt together with observed default frequencies, but ev en with these costs they either
produce mean debt ratios under 10 percent of GDP or underestimate default probabilities
by a wide margin.
4
Thus, there is a crucial disconnect between business cycle models and
sovereign default models: the former lack an explanation of the default risk premia that drive
their findings, while the latter lack an explanation of the business cycle dynamics that are
critical for their results.
The country risk-business cycle disconnect raises three important questions: Would a
business cycle model with endogenous default risk still be able to explain the stylized facts
that models with exogenous country risk have explained? Can a model of sovereign default
with endogenous output dynamics produce the large output declines needed to support high
ratios of defaultable debt as an equilibrium outcome? Would a model that endogenizes
both country risk and output dynamics be able to mimic the V-shaped dynamics of output
associated with defaults, and the countercyclical behavior of default risk?
This paper aims to answer these questions by studying the quantitative implications of a
model of sovereign default with endogenous output fluctuations. The model borrows from the
sovereign default literature the workhorse Eaton-Gersovitz recursive formulation of strategic
default in which a sovereign borrower makes optimal default c hoices by comparing the payoffs
of repayment and default. In addition, the model borrows from the business cycle literature
a transmission mechanism that links default risk with economic activity via the financing
cost of working capital. We extend the two classes of models (sovereign debt and business
cycle models) by developing a framework in which the equilibrium dynamics of output and
default risk are determined jointly, and influence each other via the interaction between
foreign lenders, the domestic sovereign borro wer, and domestic firms. In particular, a fall in
productivit y in our setup increases the likelihood of default and hence sovereign spreads, and
this in turn increases the firms’ financing costs leading to a further fall in output, which in
turn feeds back into default incentives and sovereign spreads.
We demonstrate via numerical analysis that the model can explain the three key empirical
regularities of sovereign debt mentioned earlier: The model mimics the V-shaped pattern
of output dynamics around defaults with large recessions that hit bottom during defaults,
yields countercyclical in terest rates on sovereign debt, and supports high debt-GDP ratios on
3
See, for example, Aguiar and Gopinath (2006), Arellano (2007), Yue (2006), and Bai and Zhang (2005).
4
Arellano (2 00 7 ) obtains a mean debt ratio of 6 pe r cent of GDP assuming an output cost of default such
that income is the maximum of actual output or 0.97 of average output while the economy is in financial
autarky. Aguiar and Gopinath (2006) obtain a m ean debt ratio of 27 percent assuming a cost of 2 percent of
output per qu arter, but the default freq uenc y is only 0.02 perce nt (in their m od el without tren d shocks and
debt bailouts). Yue (2006) assumes the same output cost in a mo del with renegotiation calibrated to observed
default frequ enc ies, but obtains a mean debt ratio of 9.7 percent of o utput.
2

average and in default episodes. These results are obtained requiring only a small fraction of
firms’ factor costs to be paid with working capital (only 10 percent of the cost of imported
inputs). Moreover, the model matches key business cycle features like the variability of
consumption and the countercyclical behavior of net exports.
These results hinge on three key assumptions of the model: First, producers of final
goods obtain w orking capital loans from abroad to finance purchases of imported intermediate
goods. Second, these producers can choose optimally to employ domestic intermediate goods
instead of imported inputs, but this shift entails an efficiency loss. Third, the gov ernme nt
can divert the firms’ repayment of working capital loans when it defaults on its own debt, so
that both agents default on their foreign obligations at the same time, and the interest rates
they face are equal at equilibrium.
The transmission mechanism that connects count ry risk and business cycles in our model
operates as follows: Final goods producers maximize profits and choose optimally whether
to use imported inputs or inputs produced in the domestic economy. These two inputs are
perfect substitutes in the production technology, but imported inputs have a higher financing
cost because they need to be paid in advance using working capital, while domestic inputs
require costly reallocation of labor away from final goods production into intermediate goods
production. Thus, a shift from imported to domestic inputs causes an efficiency loss in
production of final goods due to the reallocation of labor.
5
The choice of imported v. domestic inputs by final goods producers depends on the
country interest rate (inclusiv e of default risk), which drives the financing cost of working
capital, and on the state of total factor productivity (TFP). When the country has access
to world financial markets, they choose imported intermediate goods if the country interest
rate is low enough and/or TFP is high enough for the efficiency loss from using domestic
inputs to exceed the higher financial cost of imported inputs. That is, final goods producers
trade off the higher financing cost of imported inputs for the enhanced efficiency in the use
of labor services (which are fully allocated to final goods production). In this situation,
fluctuations in default risk affect the cost of working capital and thus induce fluctuations in
factor demands and output. Conversely, above (below) a threshold value of the interest rate
(TFP) firms choose to use domestic inputs because the financing cost of imported inputs
exceeds the efficiency loss due to domestic labor reallocation, with labor services now being
allocated to both final and intermediate goods production.
When the economy defaults, both the government and firms are excluded from world credit
markets for some time, with an exogenous probability of re-entry as is common in the recent
5
This efficiency loss can be mode led in different ways. We can obtain similar results as t he ones shown
in this paper by modeling the efficiency loss as resulting from costly sectoral reallocation of capital, given an
exogenous amount of aggregate capital, or from foreign inputs that are “superior” to d omestic inputs in the
sense that they support higher TFP. The efficiency loss can also result from changes in capacity utilization,
which can be linked to the choice of imp orted v. domestic inputs using Finn’s (1995) setup.
3

Frequently asked questions

Q1. What are the contributions in "A solution to the default risk-business cycle disconnect" ?

This paper proposes a solution to this default risk-business cycle disconnect based on a model of sovereign default with endogenous output dynamics. 

Q2. What are the future works mentioned in the paper "A solution to the default risk-business cycle disconnect" ?

The authors acknowledge, however, that the linkages between sovereign default and private sector borrowers, and the mechanisms by which default induces economy-wide efficiency losses, should be the subject of further research. This suggests that introducing a mechanism to link political uncertainty to private sector decisions in a model with sovereign risk can be a promising line of research. Similarly, the findings of Bi ( 2008a and 2008b ) on debt dilution effects and dynamic renegotiation in endowment economy models suggest that adding these features to default models with endogenous output dynamics can also be important. Finally, results obtained by Arellano ( 2007 ), Lizarazo ( 2005 ) and Volkan ( 2008 ) suggest that adding risk-averse foreign lenders can also contribute to produce higher debt rations and break the one-to-one link between spreads and default probabilities, so that bond spreads include an additional risk premium and can get closer to the data. 

Q3. What are the key features of the model that are critical for the results?

Three features of the model are critical for the results: imported inputs require working capital, the government diverts the firms’ working capital repayment when it defaults, and production with domestic inputs entails an efficiency loss. 

Q4. What are the target moments used to set 2 and?

The target moments used to set σ2 and ρε are the variability and persistence of output, which the authors calibrate to quarterly data for Argentina. 

Q5. What should be the subject of further research?

The authors acknowledge, however, that the linkages between sovereign default and private sector borrowers, and the mechanisms by which default induces economy-wide efficiency losses, should be the subject of further research. 

Q6. What is the effect of the transmission mechanism linking country risk and business cycles?

The transmission mechanism linking country risk and business cycles generates an endogenous output cost of default that is larger in “better” states of nature (i.e., increasing in the state of TFP). 

Q7. Why is the debt ratio linked one-to-one with default probabilities?

Because the authors assume a zero recovery rate on defaulted debt and risk-neutral creditors, bond spreads are linked one-to-one with default probabilities (see 38). 

Q8. How much of the deviations from the benchmark are below trend?

The fraction of defaults that occur when output is more that two standard deviations below trend falls from 76 percent in the benchmark to 31 percent. 

Q9. Why does the model replicate the negative correlation between spreads and GDP?

The model replicates the negative correlation between spreads and GDP because sovereign bonds have higher default risk in bad states. 

Q10. What is the effect of the shift from imported to domestic inputs on production efficiency?

16As the authors explained earlier, the shift from imported to domestic inputs that occurs when the economy defaults reduces production efficiency because of the costly reallocation of labor away from final goods production. 

Q11. Why does the model simulation for average GDP weigh more the latter than the latter?

Since re-entry has a relatively low probability, however, the model simulation for average GDP weighs more the former than the latter. 

Q12. What is the effect of the feedback from country interest rates to output dynamics?

This feedback from country interest rates to output dynamics also affects the country’s incentives to default, reinforcing the reduction in default risk. 

Q13. Why is the Argentine bond spreads model able to mimic the negative correlation between GDP?

The model is able to mimic this stylized fact because the ability to share risk with foreign lenders is negatively affected by the higher interest rates induced by increased default probabilities. 

Q14. What is the probability of a country being excluded after default?

The probability of re-entry after default is 0.1, which implies that the country stays in exclusion for 2.5 years after default on average, in line with the finding of Gelos et al. (2003). 

Q15. How does the model produce a substantial output drop when the country defaults?

Figure 4 shows that the model produces a substantial output drop when the country defaults, equivalent to about 13 percent of the pre-default output level. 

Q16. What is the main reason why the model can account for the role of productivity shocks in explaining?

The model’s output dynamics also suggest that the model can account for the seemingly dominant role of productivity shocks in explaining output collapses during financial crises in emerging markets. 

Q17. How does the model keep the output loss at default?

To keep the results comparable, the authors introduce an exogenous output loss at default in this variant of their model and calibrate it so as to keep matching the average output loss in default of 13 percent observed in the data, which the authors used as a calibration target in the benchmark calibration. 

Q18. Why is the Solow residual so different from the real-world TFP?

The large difference between the two is due to the fact thatthe Solow residual treats the efficiency loss caused by the sectoral reallocation of labor and the lower use of intermediate goods as a reduction in TFP in final goods production. 

Q19. What is the average debt ratio for the three countries that defaulted?

Reinhart et al. (2003) report that the external debt ratio during default episodes averaged 71 percent of GDP for all developing countries that defaulted at least once in the 1824-1999 period.