Interest Rate Shocks andthe Composition of Sovereign Debt
Eugenia Gonzalez-Aguado∗
October, 2023

Abstract
There has been a growing concern about the vulnerability of emerging countries to fluctuations ininternational interest rates. Here, I show that the ability of countries to issue debt domestically
can mitigate this vulnerability. The model integrates a domestic banking sector into a sovereigndefault model where governments can issue domestic and external debt and selectively default.
Issuing domestic debt crowds out investment, but as financial markets develop, the share ofdomestic debt increases. The quantitative analysis is consistent with two novel facts: lessfinancially developed countries issue relatively more external debt and are more vulnerable toexternal shocks.

Keywords: Sovereign debt, Interest rates, International spillovers, Financial development
JEL codes: E44, F34, F42∗

Toulouse School of Economics. E-mail: eugenia.gonzalez@tse-fr.eu

1Introduction

A large body of empirical evidence shows that emerging countries suffer significant output drops
when international interest rates increase.1 This paper asks why do countries choose to expose
themselves to such suffering by borrowing large amounts of external debt. By doing so, an increasein the international interest rate raises the amount of debt that these countries owe to their foreign
creditors which in turn has negative effects on their economies. An obvious alternative is to eschew
such foreign debt and instead borrow from domestic agents. The thesis of the paper is that thisalternative has costs because domestic debt crowds out investment. Hence, governments choose toexpose themselves to international interest rate fluctuations in a way that optimally balances thecosts from such exposure from external debt against the crowding-out costs of domestic debt.
These trade-offs imply that the vulnerability of countries to fluctuations in the international
interest rate depends critically on the government’s choice of domestic versus external debt and on
how easily they can raise funds domestically. Since the literature mostly abstracts from the choiceof domestic versus foreign debt, I fill this void by developing a model that focuses on the decision of
how a country finances its debt, show that it can account for the key patterns of the data, and use
it to conduct counterfactual exercises. The main result of the paper is that it shows that financial
development is crucial in explaining the different degrees of vulnerability to external shocks that
we see in the data among emerging countries. In particular, an important feature of the data
documented here is that less-financially developed countries tend to both finance a large fractionof their debt with foreigners and suffer larger losses in output for a given increase in international
interest rates. The model is able to capture this crucial pattern of the data and is used to understandthe forces behind it.
To analyze how governments balance the costs and benefits of domestic and external debt, themodel has to include two key ingredients that highlight the costs and benefits of doing so. The
first one is that it introduces a crowding-out effect of domestic debt stemming from a friction in
the way that financial intermediaries, namely banks, can raise funds from domestic agents. This
creates a cost of domestic debt relative to external debt. Intuitively, the degree of such frictions in
the economy determines the level of financial development of the country: the larger these frictions
are, the more difficult it is for countries to raise funds domestically. Given the scarce amount offunds that banks can borrow from domestic consumers when governments increase their sales ofdomestic bonds, which are held precisely by those banks, investment in domestic capital by banks
is crowded out. The second feature of the model is that, as in the data, governments can default on
their debt. Moreover, as shown in Reinhart and Rogoff (2011) they often do so selectively, that is,they discriminate between domestic and external debt when they choose to default. In the sampleof emerging countries analyzed here, defaults only on external debt represent around 70% of all
1

See, for instance, Neumeyer and Perri (2005), Canova (2005), Uribe and Yue (2006), Maćkowiak (2007), Banerjee,
Devereux, and Lombardo (2016), Dedola, Rivolta, and Stracca (2017) , Iacoviello and Navarro (2019) for papers thatstudy the effects of increases in the U.S. interest rates on other developed countries and on emerging countries.

1the default events. Despite this evidence, existing models in the literature either abstract from thedistinction between domestic and foreign debt or assume non-discriminatory default. In the model
proposed in this paper, I allow governments to decide every period, not only whether to default
or repay as is standard in sovereign default models, but also on what type of debt they choose todefault. Governments take into account that defaulting on domestic debt directly hurts their own
citizens so, for similar amounts of debt, they endogenously prefer to default on external rather thanon domestic debt. This, in turn, gives an advantage to domestic debt relative to foreign, as it lowers
the risk premium governments have to pay on debt.
The quantitative results show that the model is successful in accounting for the drop in output
in emerging countries after a shock that increases international interest rates as in the data. In
addition, by changing a parameter in the model that controls the degree of financial development of
the economy, the model can account for the heterogeneity in the share of domestic sovereign debt
across emerging countries as well as for the differences in vulnerability to external shocks in suchcountries. An additional result from the model is that, by allowing selective default, it generates
the pattern of default observed in the data, that is, countries tend to default most of the time only
on external debt.
In order to understand the vulnerability of emerging countries to shocks to the world interest
rate, the first thing that the model has to rationalize is why emerging countries suffer output losses
after an increase in the world interest rates. In the model, this happens due to the increase in thecost of financing government expenditures. Every period, governments must decide how to financetheir exogenously given stream of expenditures: issuing external debt, domestic debt, or using taxes
on labor income. After an increase in the international interest rate, external debt becomes more
expensive. In this situation, the government could do any of the following. First, it could keep
the same amount of borrowing and taxes, but given the increase in interest rate, that would imply
higher taxes in the future to repay the debt, which through its distortionary effect on labor would
decrease future output. Second, it could substitute the now more expensive external borrowing
with higher taxes. Similarly, this would have a negative effect on today’s output. And, third, it
could substitute external borrowing with domestic borrowing. However, domestic debt reduces theresources that domestic banks have to invest in capital, that is it crowds out investment. Thisturns into lower future capital and thus lower future output. In any of these cases, regardless ofwhat the government chooses to do, the economy suffers a decrease in output after the increase ininternational interest rate.
These forces explain why emerging countries experience output losses due to external shocks.
But what determines the degree of vulnerability to these external shocks? I show that financial
development is key in explaining this vulnerability. In the model, a higher level of financial development allows governments to finance a larger share of their expenditures using domestic debt. Thisimplies that when an interest rate shock hits the economy and makes external debt more expensive,countries with higher financial development are less exposed to these changes. First, because they2

do not rely so heavily on external debt, and second, because the crowding out effects of substituting external debt with domestic debt are not as large as in countries with a low level of financial
development.
I document two new empirical findings for a panel of 14 emerging countries that motivate themain exercise in the paper. I first show a significant positive relationship between the share of domestic debt in a country and its financial development measured as the ratio of liquid liabilities overGDP. This measure of financial development quantifies the degree to which financial institutions
in a country can raise liquid funds in the economy. I find that a higher level of financial development is associated with a larger share of domestic sovereign debt. Intuitively, higher financial
development decreases the crowding out costs and allows governments to issue a higher fractionof their debt domestically. Second, following this argument, it should be true that when countries
are less financially developed, they find it more costly to substitute external debt with domestic
debt, which makes them more vulnerable to a shock that increases the world interest rate. In thedata, I show that this is indeed what happens: after a shock that increases the U.S. interest rate by
100 basis points, countries that are less financially developed and, therefore, have a larger share ofexternal debt suffer on average a 0.6 percent decrease in output. However, when countries are morefinancially developed, their output drop is only 0.2 percent.
Now, I turn to elaborate on the main forces in the model. Two ingredients are crucial for
explaining the results of the model. First, the model needs to incorporate a clear concept of financial
development, in the sense that domestic banks that act as the financial intermediaries in the economy
are constrained on the resources that they can obtain. I model these constraints in the traditionof Gertler and Kiyotaki (2010) and Gertler and Karadi (2011) in that banks have limited access tohouseholds’ savings due to an agency problem. I assume that the level of these frictions, captured
by a parameter in the collateral constraint reflecting the enforceability of contracts, represents
the financial development of the country. The idea is that in less financially developed countries,
the ability to enforce contracts is weak in that banks suffer only a small punishment when they
break financial contracts such as repaying their depositors. Hence, in such countries, consumers
are willing to lend to banks relatively small amounts of resources, the ratio of deposits to output
is relatively low, and banks can fund relatively small amounts of investment. As countries become
more developed in their financial markets, these costs are lowered, which translates into an increasein the amount of resources that banks can borrow. Banks then use these resources to invest in
capital and government bonds.2
Second, in the model, consistent with the data, governments can default selectively between domestic and foreign creditors. Differences in the costs of default between these types of debt affect therelative probability of default and cost of debt. In the model, the costs of default are a combinationof the standard exogenous costs of default, adopted from the sovereign default literature and, criti2

This mechanism is in line with empirical evidence that shows the relation between domestic debt held by banks
and a crowding-out effect on corporate lending from these banks. See, for instance, Becker and Ivashina (2018).

3

cally, the endogenous cost of defaulting on domestic debt in a model with financial intermediation.
These exogenous costs are that upon default on either type of debt, countries experience an output
loss and enter an autarky state in which they do not have access to that type of debt market for arandom number of periods. To focus attention on the differential endogenous cost of defaulting on
domestic and external debt, these exogenous costs are assumed equal across the two types of default.
The differential endogenous cost naturally arises because when the government defaults on domestic
debt, it defaults on its citizens rather than on foreigners. In particular, a default on domestic debt
reduces the net worth of domestic banks and, hence, the amount of resources that they have forinvestment, which then reduces future output in the economy. This endogenously larger ex-post
cost for domestic default, in turn, leads domestic agents to expect that, for the same amounts ofdomestic and external debt, the government has less of an incentive to default on domestic debt.
Therefore, all else equal, this endogenous force tends to lower expected default rates and thus thepremium on domestic debt over the world rate relative to that on foreign debt.3
Then, I use the model to quantitatively assess the role of domestic debt and financial development in mitigating shocks to international interest rates. Specifically, I assume that external
creditors have access to an international risk-free asset, the return on which evolves stochastically,
and that is calibrated to match the features of the U.S. Federal funds rate. Critically, the model
is able to generate the main features of the data in emerging countries in terms of the characteristics of sovereign debt and default in these countries, and its relation with their level of financial
development.
When there is an unexpected increase in the international risk-free rate, the model generates adrop in output similar to what we observe in the data. How does domestic debt mitigate the drop in
output? First, I show that in a counterfactual economy where only external debt is allowed, output
decreases almost 0.2 percentage points more after an increase in world interest rates than in thebaseline economy where the government has access to both, domestic and external debt. This is so
because the government responds to the interest rate shock by increasing the share of domestic debt.
In the absence of domestic debt, the government needs to raise taxes further to meet its payments.
Because labor income taxes are distortionary, they push output to decrease even more. Second,
the model predicts that more financially developed economies suffer less from external shocks inline with what happens in the data. I model a country’s increase in financial development as anincrease in its ability to enforce contracts which manifests itself as a parameter in the collateral
constraint that implies a better ability by the government to borrow from domestic residents. Asa country’s ability to enforce contracts increases, the balance of the relative benefits and relative
costs of domestic debt shifts, and the government endogenously chooses to issue a higher share ofdomestic debt. The quantitative model captures the same patterns as in the data: more financiallydeveloped countries tend to have higher shares of domestic debt.
3

The decrease in net worth and private lending from banks after default is observed in the data as shown in
Gennaioli et al. (2018) and Baskaya and Kalemli-Ozcan (2016), which provide evidence that after a domestic default,
banks holding government debt experience a large decrease in their net worth and aggregate lending.

4Interestingly, the model has three additional implications that are consistent with the evidence
in the data that it was not explicitly designed to address. The first feature is that the ratio ofdomestic to external debt is countercyclical in the data and model. This occurs because, on themargin, banks must be indifferent between investing a unit of their resources in domestic debt andinvesting a unit in physical capital and lending it to firms. When domestic productivity is highso is the return on capital and, hence, governments must pay a relatively high return on domestic
debt. This discourages issuing domestic debt in periods of high productivity. The second featureis related to the frequency of the different types of default. In the data, we observe that most of
the time governments default only on external debt, sometimes on both domestic and external, andalmost never default only on domestic debt. The quantitative model is able to reproduce thesepatterns: due to the endogenously different cost of default, default only on external debt is more
frequent than default on both types of debt.
The third feature is a pattern of discriminatory default in the data, that I refer to as the pecking
order of default: in moderate recessions, countries tend to default only on external debt, and only
in severe recessions do they default on both domestic and external debt. That the model also
generates this feature is connected to the model’s implied countercyclicality of the domestic debt
share. If a country starts in a relatively productive state, it tends to have a relatively high shareof external debt. If following such a state the economy experiences a drop in productivity, giventhat defaulting on domestic debt is more costly than on external, the government chooses to default
only on external debt. If instead, the adverse shock happens during a period when the economy
is already experiencing low to moderate productivity, the government tends to have a much higher
share of domestic debt. Hence, even if it defaults on external debt it does not generate much revenue
from it and, hence, it chooses to default on both types of debt.
Finally, to keep the analysis of the baseline model relatively simple, I abstracted from realexchange rates as another external shock in addition to international interest rates. I show thatthe model mechanisms and quantitative predictions are robust to the introduction of real exchange
rates. This is important because one might worry that the co-movements of international interest
rates and real exchange rates affect the attractiveness of each type of debt if we consider that usually
domestic debt is denominated in local currency and external debt in foreign currency. Although
in the data analysis in this paper, domestic debt is considered as debt issued under domestic
jurisdiction and external debt as issued under foreign jurisdiction, in general domestic-law debt
tends to be denominated in local currency, and foreign-law debt tends to be denominated in foreign
currency. That is why the decision on the type of debt to issue might be influenced by shocks to
the real exchange rate, as this would affect the cost of borrowing externally. Moreover, as shown for
instance in Eichenbaum and Evans (1995), shocks to the U.S. interest rate change the real exchange
rate, and so the effect on output in emerging countries after such a shock depends on the evolutionof the real exchange rate.
To assess the role of real exchange rates both in the decision of the government about what type5

of debt to issue and on the effect of an increase in the international interest rate, I extend the model
to incorporate an exogenous process for the real exchange rate, possibly correlated to the process
for the international interest rate. I use the data to estimate these processes and show that, once
those are incorporated into the model, the main mechanisms hold and are quantitatively similar tothe baseline model. I find that a shock that increases interest rates has a positive effect on future
real exchange rates defined as local over foreign units of goods. In the model, this makes repaymentof foreign credit more expensive, and so the same mechanisms apply by which the government
substitutes external debt with domestic debt and taxes, implying, therefore, a decrease in total
output.
Related Literature. This paper combines elements of the sovereign default and the financial
intermediation literature to study the government’s decision on whether to borrow domestically or
externally in an economy that is subject to international interest rate shocks. It contributes tothe standard sovereign default literature, such as Aguiar and Gopinath (2007) and Arellano (2008),
by introducing two types of debt, external and domestic, on which the government can selectively
default.
The model in this paper is related to Gennaioli, Martin, and Rossi (2014), Sosa-Padilla (2018),
and Bocola (2016). They incorporate financial intermediation and domestic debt to analyze theeffect of sovereign default on domestic banks’ balance sheets. However, they assume either that
there is only domestic debt, or that default is non-discriminatory. I argue, based on the evidence in
Reinhart and Rogoff (2011), Erce, Mallucci, and Picarelli (2022), and other literature that focuseson the legal aspects of sovereign default, such as Gelpern and Setser (2003), that governments can,and actually do, discriminate between domestic and foreign creditors. More similar to this paper are
Mallucci (2022) and Perez (2015) which include both domestic and external debt in the decision of
the government. However, they assume that governments cannot selectively default on domestic andexternal debt, which is at odds with what we observe in the data. Therefore, this paper contributes
to the sovereign default literature by introducing a new framework where governments can optimallychoose their debt issuance on both domestic and external debt and can default selectively. Allowing
for selective default as in the data is key in explaining the trade-offs the government faces when
deciding between domestic and external debt. This is due to the different costs of default between
each type of debt that arise endogenously in the model, which will affect the price of debt.
Arellano, Atkeson, and Wright (2016) include both types of debt, domestic and external, and thepossibility of selective default in a two-period theoretical model. Assuming exogenous costs of default
in each type of debt, they then study how public debt crises may have spillover effects on the private
sector in scenarios with differences in the level of government’s interference in private contracts andfiscal flexibility. Broner, Erce, Martin, and Ventura (2014) consider the role of domestic debt ina model where debt has a crowding-out effect on domestic banks and allow governments to also
selectively default on creditors. This paper differs from theirs mainly in two respects: first, thedefault decision is essentially exogenous in their case, whereas the model presented here considers
6the endogenous decision of default with endogenous default costs on domestic debt. Second, theirmodel only considers one type of debt that can be held both by domestic or international creditors,
whereas I consider a segmented market between domestic and international creditors. The data
support this assumption, as the characteristics of debt issued under domestic law are different fromthose of debt issued under foreign law—which is the definition used here of domestic and foreigndebt—especially regarding default probabilities.4
This paper also contributes to the growing literature on the spillover effects that financial conditions in developed countries have on the rest of the world. On the theoretical side, Bai et al. (2023)
develop a model which can account for the co-movements of emerging countries spreads with thosein develop economies, and hence co-move with a global financial cycle. On the empirical side, Rey(2015), Miranda-Agrippino and Rey (2015), and Bruno and Shin (2015) provide evidence on theexistence of a global financial cycle and argue that this cycle is largely driven by monetary policies
in the United States, which is unrelated to the economic conditions in developing countries. Other
papers that find a strong response of emerging countries to interest rate shocks are Dedola, Rivolta,
and Stracca (2017), and Maćkowiak (2007). Here, I show that the spillover effects in emerging
countries are related to their level of financial development. My results are in line with the empirical literature that indicates that an important mechanism of transmission of international shocks
is the financial channel (e.g., Canova, 2005 and Georgiadis, 2016), and that countries differ in their
response depending on how vulnerable they are to external conditions as shown in Iacoviello andNavarro (2019). I add to this empirical literature by providing a new mechanism of transmissionthat relates to the level of financial development of the country and the borrowing decisions of its
government. In my framework, these two factors capture endogenously the level of vulnerabilityof countries to external shocks. Banerjee, Devereux, and Lombardo (2016) also associate financial
intermediation with the response of countries to external shocks. However, they ignore the role of
the government and focus mostly on the transactions of domestic banks with international banks.
The effect of international interest rates on emerging countries is studied in Neumeyer and Perri(2005). In relation to this literature, recent papers have also explored the role of international
interest rate shocks in emerging countries through its effect on sovereign debt. Almeida, Esquivel,
Kehoe, and Nicolini (2019) study the impact of changes in the international rate on the default
probability and renegotiation costs in emerging countries. Similarly, Johri, Khan, and Sosa-Padilla(2022) also introduces fluctuations in the international interest rate in a sovereign default model,
which in addition features an economy with stochastic volatility. However, these papers only include
external debt, and therefore abstract from the decision of governments between issuing domestic
and external debt, and the role of domestic debt in mitigating such fluctuations in the international
interest rate.
4

Using data from Arslanalp and Tsuda (2014), I show in Section E.1 that indeed debt issued under domestic law
largely coincides with debt held by domestic residents. This reinforces the idea that debt markets are segmented.
Unfortunately, the data on who holds the debt is only available for recent years, so it is not suitable for the analysis
on this paper.

7

Finally, this paper complements the literature that studies the implications of an increasinguse of domestic debt in developing countries. Bua, Pradelli, and Presbitero (2014) documents thistrend in low-income countries, and show that this increase has been associated with a decrease inborrowing costs. Panizza (2008) finds similar trends and studies the potential trade-offs that thisswitch to domestic debt may have in their economies. I contribute to this literature by providing
a new framework to analyze the costs and the benefits of domestic debt, and to understand the
incentives of governments that led them to issue more domestic debt over the last years.

2

Empirical Evidence

In this section, I provide the evidence that motivates this paper on the vulnerability of countries
to interest rate shocks, and on the composition of sovereign debt. This section also shows evidenceof selective default on sovereign debt that is used to discipline the model. In particular, there arethree main facts documented in this section for a sample of 14 emerging countries. First, countries
often default in a discriminatory way against external debt. In more than 70% of the default events
during the years analyzed here, countries defaulted only on external debt and not on domestic
debt. Second, countries issue on average 54% of their sovereign debt domestically, and this share ofdomestic debt increases with financial development. And, third, emerging countries suffer output
drops after a shock that increases the U.S. interest rate, and this effect is bigger for less financiallydeveloped countries.
The main data analysis focuses attention on 14 developing countries and the choice of countries
is given by the availability of data. In the main analysis, I restrict attention to the period 1969-1996.
This is because the identification of the interest rate shock is known to be consistent for this period.
However, I show that all results are robust to extending the period to 1960-2007. Next, the sourcesand definitions for the main data variables used in this paper are discussed.
Domestic Debt. There are different definitions that can be used for domestic debt. In the model,
domestic debt refers to debt held by residents of the country as opposed to foreigners. However,there is no long-time series data available for this definition. I use data on domestic debt from
Reinhart and Rogoff (2011) which uses the definition of domestic debt based on the market where
it is issued: under the own country’s jurisdiction, or under foreign jurisdiction. In general, indeveloping countries, the debt issued in domestic debt is held by residents of the country, and thedebt issued abroad by foreigners. For instance, the World Bank and IMF (see Arslanalp and Tsuda(2014)) have recently released new data on domestic debt where they can differentiate between debt
based on whether holders are residents or foreigners. While this time series is too short to be usedin my analysis, I find it reassuring that these series display similar levels and trends to those basedon the market of issuance.5
5

Appendix E.1 shows a comparison of these series for the time period where there is data on both.

8Default Events. The list of historical default events across developing countries is also taken from
Reinhart and Rogoff (2011). Moreover, I use their classification between defaults that involve only
external debt and those that involve both, domestic and external debt. They classify all default
episodes between those involving external debt only, and overt defaults that involve both domestic
and external defaults. Their classification of overt defaults includes cases where the government
forced conversions of deposits, bank deposits were frozen, imposed lower coupon rates, there was a
unilateral reduction of principal, or suspension of payments.
Financial Development. I use data on liquid liabilities to GDP from the World Bank Financial
Structure and Development Dataset as a measure of financial development. In particular, liquidliabilities consist of a broad definition of money including demand and interest-bearing liabilities,
such as deposits, at domestic financial institutions. This has been one of the main measures offinancial development in the literature (see for example, King and Levine (1993)). This variablemeasures the size of the financial sector relative to economic activity, which is known as financial
depth. Intuitively, when liquidity is high, it is easier to trade among agents in the economy. Low
liquidity may indicate the presence of financial frictions that prevent agents from transforming theirassets, or that prevent resources from flowing between savers and borrowers.
Other Variables. The main analysis also uses data on real GDP in each country. For this, I use
data from Iacoviello and Navarro (2019) which extends annual data from the World Bank’s World
Development Indicators. Other variables used in the analysis are U.S. interest rates, which aretaken as the Fed Funds Rate, and the bilateral real exchange rates, for which I use data from the
U.S. Department of Agriculture.

2.1

Selective Default

Table 1 shows descriptive statistics for each country on the sample. It documents that based on thedata from Reinhart and Rogoff (2011) these countries experienced a total of 22 defaults over theperiod 1960 to 1996 which represents a 4% annual frequency. Of those default events, 73% of themwere only in external debt. In their database, none of the defaults are labeled as “only domestic
debt” defaults. Therefore, those defaults that are not external debt-only are assumed to be defaults
on both external and domestic debt.
Countries not only default selectively on their debt, but also the economic conditions around an
external default are different from those around a default on both types of debt. For instance, taking
data since the year 1960 up to 2007, the average real GDP in the sample of emerging countries usedhere in the year before default is 0.8% below trend if the default was only on external debt and1.9% below trend if the default was on both types of debt. Similarly, in the year of default, real
GDP was 0.7% below its trend during external-only defaults, whereas it was 4.2% below trend when9

Table 1: Descriptive Statistics
LiquidDomestic

Total

External

liabilities

debt sharedefaults

defaults

Argentina

0.172

0.449

2

0

Brazil

0.172

0.848

2

0

Chile

0.267

0.489

1

1

China

0.636

0.359

0

0

Colombia

0.189

0.398

0

0

Ecuador

0.177

0.418

1

1

India

0.297

0.761

2

2

Indonesia

0.194

0.034

1

1

Malaysia

0.632

0.762

0

0

Mexico

0.222

0.562

1

0

Peru

0.186

0.186

6

5

South Africa

0.514

0.958

3

3

Thailand

0.474

0.752

0

0

Turkey

0.195

0.526

2

2

Total

0.312

0.540

22

16

Sources: World Bank Financial Structure and Development, andReinhart and Rogoff (2011).
Notes: The last row shows the average liquid liabilities to GDP
and domestic debt share for the countries in the sample. Total
defaults refers to the number of years a given country defaulted
on either type of debt, and External defaults refers to the numberof years a country defaulted only on external debt.

the default was on both types of debt.6 I refer to this difference in the patterns around default asa pecking order of default in that we observe moderate output drops if countries default only on
external debt but severe drops if countries default on both types of debt.

2.2

The Composition of Sovereign Debt and Financial Development

I turn now to describing the empirical patterns related to the share of domestic sovereign debt
and its relationship with financial development. As shown in Table 1, domestic debt accounts on
average for 54 percent of the total amount of sovereign debt in these countries, although there issome variation across countries: Peru and Indonesia have shares of domestic debt of only 18% and
3% respectively, whereas other countries such as India and South Africa have shares over 75%.
At the same time, countries also display heterogeneity in their level of financial development. On
average liquid liabilities are about 30 percent of their GDP with a large dispersion across countries.
6Here, the data used is extended to year 2007 in order to include more default observations, as the number ofdefaults on both types of debt in the baseline period is only 6, and therefore the statistics on these could havesignificant noise. However, the patterns remain the same when focusing on the baseline period only. Deviations fromtrend are measured using the Hodrick-Prescott filter on quarterly GDP, and then taking the annual average.

10Malaysia
China

60

70

coeff = 0.358
p-val = 0.062

SouthAfrica

40

50

Thailand

20

30

Chile

Indonesia
Peru

MexicoTurkeyEcuadorColombia
Argentina

India

Brazil10

Average financial development, %80

Figure 1: Average Domestic Debt and Financial Development

0

20

40

60

80

100

Average domestic debt share, %Next, I explore the relationship between these two variables: domestic debt share and financial
development.
Table 2: Financial Development and Domestic Debt: Data

Financial development
Total debt to GDP
Log GDP per capita
Country Effects
Year Effects
Observations(1)
0.466∗∗∗(0.070)-0.250∗∗∗(0.059)0.754(1.581)
No
No
365

(2)
0.487∗∗∗(0.078)-0.297∗∗∗(0.035)-31.573∗∗∗(3.399)
Yes
No
365

(3)
0.389∗∗∗(0.088)-0.263∗∗∗(0.043)-16.273∗∗∗(5.956)
Yes
Yes
365

Notes: Driscoll-Kraay standard errors in parentheses.
∗ p<0.1, ∗∗ p<0.05, ∗∗∗ p<0.01.

Figure 1 shows the relationship between average financial development and share of domestic
debt across countries. There is a strong positive relationship between these variables, that is,countries with higher levels of financial development tend to have on average higher shares ofdomestic debt. This positive link between financial development and domestic debt might be driven
by many factors, such as the level of income per capita or total amount of debt that these countries
are able to issue. To control for these factors, I consider the following regression
Domestic Debtit = αi + δt + βFDit−1 + ΓXit−1 + εit(1)where the dependent variable is the share of domestic debt in the country i at time t. The regressors
11include the main variable of interest, namely financial development measured as the ratio of liquidliabilities to GDP, which is lagged by one period to avoid endogeneity, as well as other regressors
in Xit−1 including the total amount of public debt and log GDP. In this regression, I also allow
for country and time-fixed effects. Results are reported in Table 2 for countries in our sample.
On average, an increase of 10 points in the ratio of liquid liabilities to GDP, that is, the measureof financial development, is associated with an increase in the share of domestic debt of around 4
percentage points. Moreover, this positive relationship is statistically significant.

2.3

Effect of Interest Rate Shocks on Emerging Countries

Here, I study how shocks to world interest rates affect economic outcomes in developing countries.
First, I show that after a shock that increases the U.S. interest rate, emerging countries experiencea drop in their real GDP. Second, I show how this drop depends crucially on the level of financial
development of these countries, where financial development is measured by the amount of liquidliabilities in the country.
Baseline Specification. In the baseline specification, shocks to the U.S. interest rates are takenfrom Romer and Romer (2004) on their original sample which covers 1969 to 1996. They identify
monetary policy shocks using a narrative approach. This identification strategy has been used in themost recent literature and is known for capturing well the main features of responses to monetary
policy shocks.7 Then, to see the effect of these shocks on the the output of emerging countries, I
use the local projection method proposed in Jordà (2005). In particular, consider the following setof regressions
yit+h = βh ut +

4
X

2 2
∗
1
ti + αi + εit+hti + δih
γ1ijh yit−j + γ2ih eit−1 + γ3ih eit+h + ρih Rt−1
+ δih

(2)

j=1

for h = {0, ..., H}, where, yit+h is the real GDP in country i in quarter t + h and ut is the RomerRomer monetary policy shock. The parameter of interest in this regression is β which estimatesthe effect of a monetary policy shock that increases the U.S. interest rate on the GDP of emerging
countries. This specification also controls for the effect that real exchange rates of the emerging
country with respect to the U.S. in the periods before the shock, ei,t , has on output growth, as wellas output in previous quarters. Parameters δj capture a linear and quadratic time trend. I allow
these trends to be country-specific, as the different countries in my sample experienced different
growth trends. Other controls included in the regression are lagged values of GDP, lagged value of∗ , as well as a country fixed effect captured by α .
the level of interest rate in the United States, Rt−1
iFigure 2 shows the estimated coefficient βbh for each quarter after the shock. The left panel shows
the specification in (2) without real exchange rates and the right panel with the same specification
but adding exchange rates as a control. Dotted lines represent the confidence interval of one standard
7

See Ramey (2016) for a discussion on these methods.

12Figure 2: Output Response to an Increase in US Interest Rates

.2
0
-.2
-.8

-.8

-.6

-.4

Output change, %

0
-.2
-.4
-.6

Output change, %.2.4With Exchange Rates.4

Without Exchange Rates

0

4

8

12

16

20

24

0

Quarters after shock

4

8

12

16

20

24

Quarters after shock

Notes: This figure shows the coefficient βh from regression (2). The left panel corresponds to the coefficientwhen exchange rates are not included as regressors in (2), and the right panel includes exchange rates.
Dashed lines are 68% confident intervals. Standard errors are computed using the Driscoll-Kraay method.

deviation, computed using the Driscoll and Kraay (1998) estimation that allows to control forheteroskedastic, autocorrelated, and possibly correlated errors across countries. The drop in output
in emerging countries after a shock that increases interest rates by 100 basis points is about 0.6
percent when exchange rates are not considered and 0.4 percent once we include real exchange rates
in the estimation. The peak effect happens 8 quarters after the shock. The delay in the response tothis type of shock is standard in the literature. Note that the specification without exchange rates(left panel) shows an even larger delay in the response, possibly due to a delayed transmission of
exchange rates themselves.8
Alternative Specifications. The original series of monetary shocks developed by Romer andRomer (2004) is estimated until 1996. This is the series that we use in the baseline specifications.
More recently, Wieland and Yang (2020) extended this series to more current dates using the same
methodology. The left panel of Figure 3 compares results using the two series, where I consider
periods up to 2007 to avoid the Great Recession period where interest rates were at the zero lower
bound. Results are very similar: it shows a similar fall in output of around 0.4%.
The right panel of Figure 3 compares the results of the baseline specification with those that
result from using different monetary policy shocks. I assume that the US interest rate depends
on output, inflation, and other real and nominal variables from the US economy, as in a Taylor
rule specification, and consider the residuals from a regression on these variables the unexplained
variation in the US interest rate, that is a monetary policy shock. In particular, I estimate by OLS
8
Other papers in the literature have analyzed the spillover effects of U.S. monetary policy using different methods.
See for instance: Banerjee et al. (2016), Canova (2005), Dedola et al. (2017), Iacoviello and Navarro (2019), andMaćkowiak (2007). The results shown here on the effect on output of an external shock align with those reported in
the literature.

13

Figure 3: Output Response to US Interest Rates: Alternative Specifications

.2
0
-.2
-.6

-.4

Output change, %

0
-.2
-.4

0

4

8

12

16

until 1996

Romer-Romer (baseline)

until 2007

Ramey/Coibon

20

-.8

-.8

-.6

Output change, %.2.4Different Monetary Shocks.4

Different Time Periods

240Quarters after shock

4

Iacoviello-Navarro
Ramey/Coibon (no reserves)

8

12

16

20

24

Quarters after shock

Notes: The left panel of this figure shows the coefficient βh from regression (2) computed for two different
time periods: baseline (blue line) and extended time period until 2007 (red line). The right panel compares
the baseline (blue line) with alternative specifications as explained in the main text.

the following regression
rtU S =

4
X
j=1

US
βir rt−j+4XUS
βiy yt−j
+

j=1

4
X

US
βiπ πt−j+ γXt−1 + ut ,j=1

and consider ût as the monetary policy shock that I then use in equation (2). The right panel of
Figure 3 shows the results of using these shocks with different control variables included in Xt .
Following Iacoviello and Navarro (2019), one of the specifications includes as controls corporate
spreads in the US and a measure of the world GDP. I also consider the specification in Ramey(2016) and Coibion (2012) which includes as controls the unemployment rate, commodity prices,money and reserves. Finally, I also show results with the Ramey/Coibon setup excluding reserves
from the regression. The baseline specification is similar to what one would obtain if using othershocks. The output response of emerging countries to a Romer and Romer monetary policy shocks
lies in between the response obtained by monetary shocks obtained from different Taylor rules
specifications.
Other robustness exercises are provided in Appendix E.3, which includes robustness on thesample of countries considered (Latin American or East Asian countries). I also show that the dropin output is not driven by the Volcker period which was a time in which both the interest rates
in the United States were high and many emerging countries experienced years of severe recessions(what is known as the lost decade in Latin America).
External Vulnerability and Financial Development. The magnitude of the output drop after
an increase in the U.S. interest rate varies with the level of financial development in the country. To
see this, first I show the results of running the same regressions as in (2) but for two separate samples
14

Figure 4: Output Response by Level of Financial Development

0
-.2

%
-.4
-.6

-.6

-.4

%

-.2

0

.2

By median in year.2

By median in sample

0

4

8

12

Low FDHigh FD-.8-.8

Low FDHigh FD
16

0

Quarters

4

8

12

16

Quarters

Notes: This figure shows the coefficient βh from regression (2) computed for two different samples: observations for which the level of financial development is above the median (dashed green line) and thosebelow the median (solid red line). The median used as a threshold to divide observations is computed in
the whole sample in the left panel and year by year in the right panel.

of observations: high and low financially developed countries. Another way of providing evidenceof the difference in response by financial development is to add an interaction term in (2) between
the monetary policy shock and the level of financial development. I show that both methods imply
a negative relationship between the level of financial development and the vulnerability to external
shocks.
First, observations are divided into two groups depending on their level of financial development.
Here, I consider two possible classifications: 1) a country-year observation is high financial development if its level is above the median level in the sample, and low financial development otherwise,and 2) a country-year observation is high financial development if its level is above the median levelin that year, and low financial development otherwise. Note that with these definitions a country
might be low-financially developed in some years, but switch to high-financially developed in otheryears. The second definition takes into account that the level of financial development changes overtime. Then, regression (2) is run separately in each of these groups so that we obtain the responseof output for high, βbhigh , and for low financially developed, βblow . Results are shown in Figure 4.
When the country’s level of financial development is low, output drops by more than 0.6 percent,but countries with high financial development are barely affected, with a drop in output of about
0.2 percent.
To further analyze the role of financial development, consider now the same local projections asin (2), but adding an interaction between the monetary policy shock and the financial development

15

Table 3: Output Response and Financial Development

Quarters after shock:Interaction coefficient, γh
6
8
10
12

4
0.008
(0.006)0.012(0.008)0.018∗(0.010)0.020∗∗(0.009)0.022∗∗(0.010)16
0.000(0.008)Notes: Driscoll-Kraay standard errors in parentheses. ∗ p<0.1, ∗∗ p<0.05, ∗∗∗ p<0.01.

measure, that is,
yit+h =βh ut + γh ut × FDit−1 +4X∗
γ1ijh yit−j + γ2ih eit−1 + γ3ih eit+h + ρih Rt−1

j=1
1
2 2
+ δih
ti + δihti + αi + εit+h ,(3)where, FDit−1 is our measure of financial development. Therefore, our object of interest is theestimate γ̂h . If positive, it represents how much an increase in the level of financial development
mitigates the drop in output from an external monetary policy shock. Table 3 shows the estimates
for the coefficient on the interaction between financial development and the U.S. monetary policy
shock, γ̂. The coefficient is estimated to be positive and significantly different from zero. This implies
that higher financial development decreases the output drop after an expansionary monetary policy
shock in the United States.9
In summary, the main empirical finding of the paper is that emerging countries suffer large output
losses from international interest rate shocks, especially so if they are less financially developed.
Moreover, it is precisely the less financially developed countries the ones that tend to have higher
shares of their government debt held by foreign creditors rather than domestic creditors. In thefollowing section, I present a general equilibrium model that captures the main empirical findings
and is then used to analyze the decision of governments on their sovereign debt composition as wellas the effect of a shock to international interest rates.

3

Model

I consider a small open economy model with infinitely lived consumers. The model incorporates abanking sector along the lines of Gertler and Kiyotaki (2010) and Gertler and Karadi (2011) into asovereign default model with discriminatory default on domestic and foreign debt. The economy iscomposed of a representative household whose members can be workers or bankers, a representative
firm, international creditors, and a government. Households consume and save by holding deposits
at banks. Banks are the financial intermediaries in the economy: they use deposits from households
9

Appendix E.4 shows that this finding is robust to the use of different samples, both relative to the countries andto the time periods considered in the analysis.

16

to invest in capital and government domestic bonds, but they are constrained on how much they
can invest. Firms use capital supplied by banks, and labor supplied by workers to produce a single
good, and are subject to an aggregate productivity shock. The government finances a constantamount of public expenditures using taxes on labor income, and issuing domestic bonds that arebought by banks, and external bonds that are bought by international creditors. The government
can decide whether to default on each type of debt separately.
Households. There is a representative household composed of a measure 1 of workers and ameasure 1 of bankers. Households maximize their utility function defined over consumption, Ct ,and labor Lt , and discount the future at rate β.10 Their preferences are given by∞X

β t [Ct − v(Lt )] ,

(4)

t=0

where v(Lt ) represents the disutility of working and is assumed to be such that v ′ > 0 and v ′′ > 0.11
Households can only save by using deposits at banks at price qtD , that is, they deposit qtD Dt+1 units
today and get back Dt+1 units tomorrow. A measure 1 − σ of workers randomly become bankers
every period. The household transfers n̄ to these new bankers so that they can start their activity
at the bank. Households receive dividends, Xt from existing banks, and maximize their utility bychoosing how much to consume, Ct , how much to save in deposits, Dt+1 , and how many hours towork, Lt+1 , at wage wt , subject to their budget constraint
Ct + qtD Dt+1 ≤ (1 − τt )wt Lt + Dt + Xt − (1 − σ)n̄,(5)where τt is the labor income tax.12
In order for the household to be willing to supply deposits to the bank, it has to be that the priceof deposits is at least as large as the rate at which they discount the future, so that, in equilibrium,
it must be that qtD = β. Moreover, households choose their supply of labor such that the following
condition holdsv ′ (Lt ) = (1 − τt )wt .
(6)
10

Alternatively, we could include the consumption of public goods, G, in the utility of the households as Ut =Ct + Gt + v(Lt ). Notice, however, that given that public goods are assumed to be an exogenous constant in themodel, that would not imply any difference in the model.
11Here, I assume that households have linear utility in consumption for tractability. However, as it will be clear
below, the government still wants to smooth consumption due to the curvature in the v(.) function. In particular,
the incentives of the government to smooth consumption are given by its incentives to smooth tax distortions that
affect the amount of labor supplied. Therefore, the introduction of risk aversion on private consumption would notchange the main mechanisms of the model.
12
An implicit assumption in the problem of the households is that they cannot hold domestic debt. This allows
us to focus on the role of financial development. One of the key elements in the model is the need for financial
intermediaries to capture the concept of financial development and how changes in financial development in a given
country can affect government decisions regarding the denomination of debt. That is why in this economy all domestic
financial transactions are intermediated through domestic banks and households are purposely left out of the domestic
debt market. Using data from Arslanalp and Tsuda (2014), banks’ holdings of domestic debt account for more than
35% of all domestic debt in emerging countries.

17

Banks. At the beginning of the period, the aggregate productivity shock, zt , is realized, andbankers collect returns from their last period investments. Each period bankers learn whether they
will continue their activity as a banker in the following period or not. In particular, with probability
σ they learn that they will continue as bankers next period and with probability 1 − σ they learn
that they will return to the household as a worker. In this latter case, bankers transfer all their net
worth to the household. Notice that 1 − σ < 1 is required because otherwise, banks would build up
enough net worth to make financial constraints not binding, and therefore, irrelevant. Every period,a measure 1 − σ of new bankers replace the banks that do not survive.
Bankers that survive, decide on their new investments by choosing investment in capital, kt+1 ,K , and government bonds bwith return Rt+1
t+1 at price qt . Government bonds are long-term bonds,
and it is assumed that payments on debt decay at a geometric rate in case of no default: a bankthat buys one unit of debt today will receive, λ units tomorrow, λ(1 − λ) in two periods, λ(1 − λ)2 inthree periods, and so on.13 The government can default in its debt, in which case it returns nothing
to the bank. The repayment decision on domestic debt is denoted by δt , which takes value 1 if it
repays and 0 otherwise.14
Let the value of an existing bank be denoted by Vtb (nt ), where nt is the bank’s current net worth,nt = RtK kt + δt [λ + (1 − λ)qt ] bt − dt . Hence, current net worth is the sum of the returns on capitaland the returns from government bonds, net of the payments to the household from their deposits,
dt . When a banker returns to the household, it transfers its current net worth to the household.
Then, the objective of a bank is to maximize the value that it will transfer to the household. We
can write the value of a bank as
Vtb (nt ) =max{bs+1 ,ks+1 ,ds+1 ,xs }

Et

∞
X



β s−t+1 σ s−t xs + σ s−t (1 − σ)ns ,

(7)

s=t

where xt are the dividends that surviving banks can transfer to households every period. In equilibrium, we can show that xt = 0 in every period, so from now on, we impose this equilibrium outcome.
The intuition for this result is that, by paying low dividends, banks can finance more capital andbonds issuing fewer deposits, thus relaxing the collateral constraint. Surviving banks choose their
13
This follows the way of modeling long-term debt as in Hatchondo and Martinez (2009), which retains tractability
as it does not require to keep track of the whole sequence of debt issued in each period: a bank that had bt amounts ofbonds from the previous period, today receives λbt from the government and will carry on as claim to the next period
the remaining (1 − λ)bt units. Then, the bank buys new debt this period by an amount of b̃t+1 = bt+1 − (1 − λ)bt
units, so that it starts period t + 1 with a total claim on bt+1 .
14
In this model domestic banks can only buy domestic bonds and have no access to external bonds and all theexternal resources have to come in through the government. One way to rationalize this is to assume that foreign
creditors do not trust private domestic banks enough to lend them resources, due to their inability to properly monitor
their activities. Following this argument, relaxing this assumption and allowing banks to borrow externally would
require the inclusion of an additional collateral constraint on the resources that they can get from abroad (similar
to the collateral constraint on domestic deposits). Therefore, in this alternative scenario, the banks would still be
constrained on how much they can borrow—so, the crowding out effect would still be in place— and changes in theinternational interest rate will now directly affect them, and thus, the effect of a shock to the interest rate will prevailor could even be amplified.

18

capital investment, bond purchases, and how much to borrow from households using deposits, dt+1 ,subject to their budget constraint
kt+1 + qt bt+1 − qtD dt+1 ≤ nt .

(8)

The key financial constraint is a collateral constraint. Banks are constrained on how much they canborrow using deposits from households. In particular, they can not borrow more than a fraction θof their current net worth, that is
qtD dt+1 ≤ θnt .
(9)This constraint arises endogenously from an agency problem between banks and households,
in which bankers can divert a fraction of their assets. Assume that the bank, after receiving thedeposits from households can run away with a fraction 1/ (1 + θ) of its total assets at that point,
nt + qtD dt+1 , which will return to its household, and start as a new banker with that given new
net worth. In
to not have incentives to divert, it must be the case that
 order for the banker
1
1
D
b
b
(nt + qtD dt+1 ),Vt (nt ) ≥ Vt 1+θ (nt + qt dt+1 ) . Given monotonicity of Vtb , this implies nt ≥ 1+θ
which gives rise to collateral constraint (9).
The problem for the bank in recursive formulation is thenVtb (nt ) =max

bt+1 ,kt+1 ,dt+1hib
Et β σVt+1(nt+1 ) + (1 − σ)nt ,(10)

subject to the evolution of net worth,K
nt+1 = Rt+1
kt+1 + δt+1 [λ + (1 − λ)qt ] bt+1 − dt+1 ,(11)

the budget constraint (8), and the collateral constraint (9).
Firms. Firms rent capital from banks at rate RK,t , and demand labor from workers at price wt .
Following Neumeyer and Perri (2005), we assume that, within a period, firms need to borrow to pay
for a fraction κ of workers’ wage, that is, they need to borrow working capital. Then, the problemof the firm is
max zt F (Kt , Lt ) − RK,t Kt − wt Lt − rt∗ κwt Lt ,Kt ,Ltso the first-order conditions are
RK,t = zt FK,t (Kt , Lt )wt (1 + rt∗ κ) = zt FL,t (Kt , Lt ).
I assume that the intra-period borrowing market is frictionless, and firms always repay at theend of the period. Moreover, the rate at which they borrow is given by the international interest
rate, rt∗ . This assumption allows the model to capture a way in which the private sector is also19

directly affected by changes in the world interest rate, not only indirectly through its effect on thecost of borrowing of the government, which affects only the quantitative results of the model.15
International Creditors. The government borrows from risk-neutral international creditors whose
one-period risk free rate is rt∗ . There are external shocks that can affect the interest rate on theworld risk-free asset, which is characterized by the following stochastic process:∗rt∗ = (1 − ρr )µr + ρr rt−1
+ ϵr,twhere ϵrt ∼ N (0, σr ).

(12)

The problem of international creditors is to maximize their expected stream of discounted conPt+s c∗
sumption, Et ∞t+s subject to
s=0 β
c∗t +

1 ∗
a
+ qt (b∗t+1 − (1 − λ)b∗t ) = y + a∗t + λb∗t ,Rt∗ t+1

where y is their income, a∗ is the one-period international asset which is bought at price 1/Rt∗ andreturns one unit in the next period, where Rt∗ = 1 + rt∗ denotes the gross interest rate. It is assumed
that the endowment y is large enough to cover all possible supply of bonds, that is, international
creditors are assumed to have deep pockets.
In equilibrium, international creditors make zero profits. Therefore, the expected return on
bonds has to be equal to the return on the international asset, that is:
 ∗

∗ )
Et δt+1(λ + (1 − λ)qt+1= Rt∗ .
qt∗

(13)This equation defines the bond price schedule that the government faces. Conditionally on not
defaulting in period t + 1, the government repays λ on each unit of external debt that it borrows in∗ , where q ∗period t. The value of each unit of the remaining debt is then (1 − λ)qt+1
t+1 refers to thebond price schedule given the government’s borrowing decision in period t + 1, which in equilibrium
is a function of today’s borrowing decisions and the aggregate state of the economy.
Government. The government starts each period with a given amount of outstanding externaland domestic debt, {B ∗ , B}, on which it owes a fraction λ. It can decide whether to repay eachtype of debt or to default on it, and it can do so in a discriminatory way. The difference between
defaulting on domestic debt and defaulting on external debt arises because domestic debt is heldby residents of the country: when the government defaults on domestic debt, it defaults on its own
citizens. In order to emphasize this feature, I assume that all exogenous costs of defaulting on debt
are identical between defaulting on domestic and external debt. The only difference comes fromthe endogenous effect that defaulting on domestic debt has on the economy. In particular, domestic
15
In Section 6.2, I show that the main results hold when there is no working capital in the model, and therefore
firms are not directly affected by fluctuations in the world interest rate.

20

default affects banks’ investment decisions because it decreases their net worth, and therefore, itwill affect the total output of the country.
Defaulting on either debt implies immediate exclusion from that credit market. Once the government is excluded from a given market, it regains access to it with probability γ every period.
I refer to these periods as autarky periods, and, given that the government can default separately
on domestic and external debt, there are three possible autarky states in which a country can be:
domestic autarky, when it defaults on domestic debt, and has access only to external debt, external
autarky, when it defaults on external debt and has only access to domestic debt, and autarky in bothmarkets, that is, when the government has defaulted on both debts and has no access to borrowing.
In all these autarky periods, the economy experiences an exogenous productivity loss, such that
productivity in these periods is h(z) ≤ z.
The government has to provide a constant amount of public goods G every period t, and itchooses labor income taxes, τt , and new debt to issue (if it has access to credit). Therefore, thegovernment budget constraint when the country is not in autarky is∗G + δt λBt + δt∗ λBt∗ = τt wt Lt + δt qt (Bt+1 + (1 − λ)Bt ) + δt∗ qt Bt+1
+ (1 − λ)Bt∗ ,(14)

where, δt and δt∗ are the current period default decisions on domestic and external debt respectively.
When the country is in one of the three autarky states defined before, the budget constraint issimilarly defined, but it does not include the market to which the country does not have access.
In this model, the government has incentives to issue debt to smooth taxes over the cycle. When
productivity is low, labor is reduced, and therefore, the tax revenues that the government can getfrom taxing labor income at a given tax rate are low. That is, if there was no debt, the government
would have to raise taxes significantly during downturns in order to finance its expenditures G.
Given that taxes are distortionary, the government wants to avoid sharp increases in taxes, andthus, when productivity is low it prefers to issue debt instead, which it will repay during booms.
Finally, the country-level budget constraint for the economy in normal times, defined before
government default decisions, is∗
Ct + Gt + Kt+1 − (1 − δK )Kt + δt∗ λBt∗ − qt+1 Bt+1
+ (1 − λ)Bt∗= δt∗ δt zt F (Kt , Lt ) + (1 − δt∗ δt ) h(zt )F (Kt , Lt ).



+

rt∗
κzt FL (Kt , Lt )Lt
1 + rt∗(15)

This constraint aggregates the budget constraint of households, banks, and the government, suchthat aggregate consumption in private and public goods, and investment, plus net exports—measured
as, payments to foreigners minus transfers from foreigners—must be equal to the production in theeconomy.16 If the government defaults on either debt, production is affected by the default produc16

See Appendix B for the derivation of the country-level budget constraint.

21

tivity cost, h(z).
Next, I turn to defining the Markov equilibrium for this economy. For that, we need first to
define the equilibrium of the private agents of this economy, who take as given a set of government
policies.
Competitive Equilibrium
Let S = (B ∗ , B, K, D, z, a, R∗ ) denote the aggregate state of the economy, where a is an indicator of the current financial state of the country, that is, a = {n, d, e, b} indicates non-autarky,domestic autarky, external autarky, and autarky in both markets, respectively. Given a government policy π(S) = (δ ∗ , δ, B ∗′ , B ′ , τ ), a competitive equilibrium is an allocation Y (S, π) =(C, L, B ∗′ , B ′ , K ′ , D′ ), households and banks’ value function V h (d; S), V b (n; S), and pricing func
tions P (S, π) = q, q ∗ , q D , RK , w , such thati. given prices and government policy, households’ allocations, (C, l, d′ ), and value function,
V h (d; S), solve the household problem;
ii. given prices and government policy, banks’ allocations, (b′ , k ′ , d′ ), and value function, V b (n; S),solve the bank problem;iii. given prices and government policy, demand for capital, and labor, solve the firm problem;
iv. international lenders break-even condition is satisfied;v. government policy satisfies the government budget constraint;
vi. allocation is feasible: it satisfies the country-level budget constraint.
Lemma 1 (Characterization of the Bank’s Problem). The value function of banks is linear
in net worth
V b (n; S) = ν(S)nwhere
ν(S) = βE
1 − σ + σν(S ′ ) (1 + θ)RK (S ′ ) − θ/q D .

(16)Moreover, banks prefer not to pay dividends, x = 0 if they continue as bankers. They only transfer
their net worth to the household when they have to switch back to being workers.
The proof for this lemma can be found in Appendix A and follows Gertler and Kiyotaki (2010).
Intuitively, all the choices for banks enter linearly in the problem, due to linearity of the budget
constraint and the collateral constraint in n. An implication of this lemma is that the aggregate
state S does not need to include the measure over the state variables of individual banks but rather
only the aggregate net worth.

22

The function ν(S) is interpreted as the marginal value of an additional unit of net worth at thebank. The intuition is the following: if the constraint binds, an extra unit of net worth increases
deposits by θ/q D and investment by 1+θ. The net return on this investment is then RK (S ′ ) (1 + θ)−
θ/q D , which is the second term in brackets in (16). When banks collect their returns from theinvestment in the previous period, with probability 1 − σ they have to return to the household,and they give to their household their entire net worth. With probability σ they continue asbankers, and their value per unit of net worth is ν(S ′ ). Then, the effective discount rate of banks
is m(S ′ ) ≡ βE (1 − σ + σν(S ′ )), which is the first term in brackets in equation (16).
I now characterize the set of allocations that constitute a competitive equilibrium. Define theproductivity in the economy as a function of the current autarky state of the economy as z̃(S) = z
if δ(S) = δ ∗ (S) = 1 and a = n, that is, normal times, and z̃ = h(z) otherwise. Also, for notation
convenience, let δ(·, a = {d, b}) = 0 and δ ∗ (·, a = {e, b}) = 0, which just indicates that there is no
repayment of the debt if the government is already in an autarky situation for that type of market.
From the bank’s first order condition, and substituting the RK from the firm problem, theschedule of prices that the government offers to the bank must be such that for any choices A′ ≡(B ∗′ , B ′ , K ′ , D′ ) and given current productivity, z, and autarky state, a, banks’ expected value ofthe return on bonds must be equal to the expected value of the marginal product of capital:E m(S ′ )δ(S ′ )(λ + (1 − λ)q(A′′ ; S ′ )) S
′
K
′
S
=
E
m(S
)R
(S
)
q(A′ ; S)(17)

where m(S ′ ) = βE (1 − σ + σν(S ′ )), and RK (S) = z̃(S)FK (S) + 1 − δK . That is, for banks to
be willing to hold government debt they have to be indifferent between investing in bonds and incapital. Notice from this condition that the interest rate the government has to offer to banks is
positively related to the returns that they get from investing in capital. Therefore, in periods whenreturns on capital are high, it is more costly for the government to borrow from banks.
Given that the value of a unit of net worth at the bank is always higher than the value of that
unit for the households, banks always borrow to the maximum from households, that is, q D D′ = θN .
Then, aggregating budget constraints of newborn and continuing banks, and substituting the binding
collateral constraint, we get that the aggregate budget constraint of the bank is:
K ′ + δ(S)q(S)B ′ = (1 + θ) [σ (z̃(S)FK (S)K + (1 − δK ) K + δ(S)B − D) + (1 − σ) n] .

(18)

International creditors’ break-even condition implies that the bond price schedule that the government offers is such thatE δ ∗ (S ′ ) (λ + (1 − λ)q ∗ (A′′ ; S ′ )) S
= R∗
(19)
q ∗ (A′ ; S)
Finally, from the labor supply condition of workers, we can write total tax revenues of the government as T (S) = (z̃(S)FL (S) − v ′ (L)) L. Therefore, substituting this condition in the government
23

budget constraint we get:δ(S)q(S)(B ′ − (1 − λ)B) + δ ∗ (S)q ∗ (S)(B ∗′ − (1 − λ)B)
=G + δ(S)λB + δ ∗ (S)λB ∗ − z̃(S)FL (S) − v ′ (L) L(20)

We refer to the resource constraint (15) together with constraints (17)—(20) as the implementability
constraints.
Lemma 2 (Characterization of Competitive Equilibrium).
An allocation Y = (C, L, B ∗′ , B ′ , K ′ , D′ ) constitute a competitive equilibrium if and only if itsatisfies the implementability constraints.
Given that the implementability constraints were derived using the equilibrium conditions ofbanks, households, and firms, and that they satisfy the government, bank, and country-level budget
constraints, it is immediate that if Y is a competitive equilibrium then it has to satisfy the implementability constraints. To proof sufficiency we can construct taxes such that τ = 1 − v ′ (L)/zFL ,and prices, w = zFL , RK = zFK + 1 − δK , qD = β, so if Y satisfies the implementability constraints,
then Y is part of the competitive equilibrium for these prices and tax rates.
Markov Equilibrium
A recursive Markov equilibrium is policy functions π(S; a) = (δ, δ ∗ , B ∗′ , B ′ , τ ), a set of allocation
rules Y (S, π; a) = (C, L, B ∗′ , B ′ , K ′ , D′ ), and pricing functions q(S, π; a), q ∗ (S, π; a) such thati. the associated outcomes constitute a competitive equilibrium for all S and π, and autarky
state a;ii. given S, and taking as given future policy functions, allocation rules, and pricing rules, thecurrent policy π(S; a) is optimal for the government.
Let V (S) be the value function of the government when the country is not in autarky, and let
Wa (Sa ) be the value when it is in one of the three possible autarky states, a = {d, e, b}. The primalMarkov problem is to choose current allocations Y = (C, L, B ∗′ , B ′ , K ′ , D′ ), and current policies
δ, δ ∗ , taking as given future policy functions δ(S ′ ),δ ∗ (S ′ ), pricing functions q(S ′ ), value functionof the bank, ν(S ′ ), and value functions of the government, V (S ′ ), Wa (Sa′ ), with the objective of
maximizing the utility of the representative household. That is, the value of the government innormal times isn
V (S) = max∗ C + v(L)
Y,δ,δ


o
+ βE δδ ∗ V (S ′ ) + δ(1 − δ ∗ )We (S ′ ) + (1 − δ)δ ∗ Wd (S ′ ) + (1 − δ)(1 − δ ∗ )Wb (S ′ )

24

(21)

subject to the implementability constraints (15), (17)–(20) conditional on a = n.17 When the
country is in domestic or external autarky it can only issue and default on one type of debt. Let
δa denote the relevant default decision for each type of autarky state. Then, the value of thegovernment in either external autarky or domestic autarky, a = {d, e}, isnWa (S) = max C + v(L)
Y,δa



o
+ βE δa γV (S ′ ) + (1 − γ)Wa (S ′ ) + (1 − δa )Wb (S ′ )(22)subject to the implementability constraints, where, γ is the probability of exiting the autarky state.
Finally, when the government is in complete autarky, there are no default or debt-issuing decisions,so the problem for the government isnoWb (S) = max C + v(L) + βE γV (S ′ ) + (1 − γ)Wb (S ′ )
Y,δa

(23)

subject to the implementability constraints.

4

Model Forces

Before turning to the quantitative results, it is useful to explain here the main forces in the modelthat determine the composition of sovereign debt, and the effect on output of an increase in theinternational interest rate.

4.1

Sovereign Debt Composition

In the decision of what type of debt to issue, the government balances the costs and benefits ofdomestic debt relative to external debt. On one hand, the main cost of issuing domestic debt isthat it crowds out investment in capital, whereas external debt does not have that negative effecton domestic capital. On the other hand, the relative benefit of domestic debt is that, due to lower
ex-post default incentives, it becomes relatively cheaper than external debt, especially in bad times.
This generates a trade-off for the government between domestic and external debt, which I illustratein this section using the government’s first-order conditions.
When choosing how much to borrow, the government equates the revenues of issuing an additional unit of each type of debt to the costs. As in standard models of external sovereign debt,
the benefit of an additional unit of debt is that it increases the revenues for the government by∂(q ∗ B ∗′ )/∂B ∗′ units, and thus relaxes its budget constraint. The cost of issuing an additional unit
17
To solve the model computationally, it is assumed that the government receives every period idiosyncratic preference shocks on the amount of borrowing (B ∗′ , B ′ ) that it chooses. This assumption is standard in the sovereign
debt with long-term bonds literature, and it facilitates the stability and convergence of the model. For simplicity of
exposition, here I present the model without such shocks. The details of the model with preference shocks can befound in Appendix D.

25

of debt is that it has to be repaid in the future, and therefore tightens the future government budget
constraint.
In addition to these standard effects of borrowing, in this model, there are two additional factors.
First, an increase in one type of debt affects the price of the alternative debt. That is, increasing
external debt results in a higher external default probability and so decreases its price, but it also
generally increases the probability of defaulting on domestic debt, so it also decreases the price ofdomestic debt. Therefore, there is a cross-price effect given by ∂q/∂B ∗′ in the case of externalborrowing. Using a similar logic, an increase in domestic debt changes the price of external debt
by ∂q ∗ /∂B ′ . Second, because in this economy there are domestic financial intermediaries holding
government bonds, changes in domestic borrowing will directly affect the investment decisions on
capital, generating a crowding-out effect when domestic debt increases. However, the effect on
capital is indirect in the case of external borrowing as it is present only through the cross-priceeffect ∂q/∂B ∗′ .
To simplify the exposition of the government first-order conditions, the case with one-period
debt, λ = 1, full capital depreciation, δK = 1, and no working capital, κ = 0, is considered here.
Under those simplifications, the problem of the government when it is not in autarky as in (21) isnoV R (S) = max zF (K, L) + q ∗ B ∗′ − G − K ′ − B ∗ + v(L) + βE δ̃(S ′ )V R (S ′ ) + ΓD (S ′ )subject toµ:

G + B + B ∗ − qB ′ − q ∗ B ∗′ − T̂ (L)L ≤ 0

ρ:K ′ + qB ′ − σ (zFK K + B − D) − βD′ − (1 − σ)n̄ ≤ 0

η:βD′ − θσ (zFK K + B − D) − θ(1 − σ)n̄ ≤ 0

and the pricing equations. Here, T̂ = FL − v ′ (L) is the tax revenue per unit of labor. Let µ, ρ, andη be the Lagrange multipliers with respect to the government budget constraint, the bank’s budget
constraint, and the bank’s collateral constraint, respectively. Assuming that the price functions, q
and q ∗ , are differentiable, and letting δ̃=δδ ∗ denote the joint repayment of both types of debt, thefirst-order conditions of the government with respect to external debt is


h
i
∂q ′
∂q ∗ ∗′∂q ∗ ∗′
∗
′
′
∗
B
+
B
+
q
+
B
=
βE
δ̃
µ
+
1
+
µ q +
∂B ∗′
∂B ∗′
∂B ∗′
|
{z
}
|
{z
}

∂q ′
ρ
B
∗′
| ∂B
{z }

+ X ∗,

(24)





h
i
∂q ′ ∂q ∗ ∗′∂q ∗ ∗′
∂q ′
′
′
′
˜
µ q+
B +
B +
B = βE δ µ − σ ρ + θη+ρ q+
B + X,
∂B ′
∂B ′
∂B ′
∂B ′
|
{z
}
|
{z
}
|
{z
}

(25)

repayment effectrevenue effectinvestment effectand, the first-order condition for domestic debt isrevenue effect

repayment effectinvestment effectwhere X ∗ and X capture additional terms corresponding to the non-repayment continuation value
26

for the government.18
We can classify the terms in both of the first-order conditions into three groups: a revenue effect,a repayment effect, and an investment effect of increasing borrowing. On the left-hand side, there is
the revenue effect from borrowing today, which comes from a relaxation of the budget constraint,µ, and an increase in consumption. The first term reflects that each additional unit of borrowing
increases resources by ∂(qB ′ +q ∗ B ∗′ )/∂B ∗′ if external, and ∂(qB ′ +q ∗ B ∗′ )/∂B ′ if domestic borrowing,
and so the government budget constraint is relaxed, as captured by the term multiplying µ. In thecase of external debt, issuing debt has a direct positive effect on consumption due to additional
external resources, ∂(q ∗ B ∗′ )/∂B ∗′ , coming into the economy from abroad, whereas this effect isonly indirect through the change in external prices from increasing domestic debt ∂(q ∗ B ∗′ )/∂B ′ .
This is captured by the second terms outside the brackets on the revenue effect.
Then, the government equates this marginal revenue from borrowing to the marginal cost of
repaying tomorrow and from a change in the investment in capital, that is, the right-hand sideof equations (24) and (25). Repayment of either external or domestic debt implies a tighteningof tomorrow’s government budget constraint, µ′ . Moreover, external debt is repaid to external
creditors, and therefore implies a direct decrease in consumption due to resources flowing out of
the economy, whereas domestic debt is repaid to domestic banks, which increases their net worth.
These terms correspond to what is labeled as the repayment effect. Finally, increasing borrowing
has


∂q
∂q
′
an investment effect captured by the term ρ ∂B ∗′ B in the case of external debt, and ρ q + ∂B ′ B ′in the case of domestic debt. This corresponds to an important distinction between external anddomestic debt, which will be analyzed below.
There are two main differences in the first-order conditions (24) and (25) that affect the composition of debt. First, the sensitivity of prices to an increase in debt, ∂q ∗ /∂B ∗′ and ∂q/∂B ′ , isgenerally higher for external debt than for domestic debt. This corresponds to the relative benefitof domestic debt. Second, the effect on capital from increasing debt is positive for external borrowing and negative for domestic borrowing. This represents the relative costs of domestic debt.
Importantly, these differences depend on the business cycle, as they are affected by the current
productivity in the economy. I analyze these differences in detail in what follows.
Benefit of Domestic Debt. First, we want to analyze the benefit of domestic debt relative tothat of external debt. For this, we focus on the left-hand-side of equations (24) and (25), that is,on the revenue effects. Then, by dividing the revenue effect of external debt by the revenue effectof domestic debt, we get∂q ∗∗′ + ∂q B ′ + ∂q ∗ B ∗′ + q ∗µ q ∗ + ∂B
∗′ B
∗′
∂B
∂B ∗′


Relative marginal revenue =.
∂q∂q ∗ ∗′∂q ∗ ∗′′µ q + ∂B
+ ∂B
′ B + ∂B ′ B
′B
18

(26)

Details about the derivation of this problem and the equations that solve µ, ρ, and η can be found in Appendix

C.

27

Figure 5: Laffer Curve for Borrowing.035

High productivity

.03

qB'

.025

.025

.03

.035

Low productivity

.02
.01

.015

q*B*'

.005

.005

.01

.015

.02

qB'

0

0

q*B*'
0

.01

.02

.03

.04

.05

0

Borrowing, B' and B*''

.01

.02

.03

.04

.05

Borrowing, B' and B*''

Notes: This figure plots qB ′ (solid green line) and q ∗ B ∗′ from the numerical solution of the model explained in
Section 5. The values q and q ∗ are for a chosen asset state space, (B ∗′ , B ′ , K ′ , D′ ), the interest rate R∗ is set to
1, and productivity z is set to be below the mean in the left-panel, and above the mean in the right-panel. In thex-axis, domestic borrowing B ′ is used for the qB ′ line, and external borrowing B ∗′ is used for the q ∗ B ∗′ line.

From (26) it is clear that what determines the relative marginal revenue is the shape of the pricefunctions of each type of debt, q and q ∗ . In particular, it is important to understand the differencesin the sensitivity of each price to changes in the amount of borrowing, that is, the derivative of
prices with respect to borrowing, which captures changes in the default probability on that debt.
Then, changes in default probability affect the price at which the government issues an extra unitof borrowing, which in turn affects the marginal revenue that the government gets from issuing thatextra unit of borrowing. But incentives to default on external debt are different from incentives todefault on domestic debt, and thus the shape of the price function of external and domestic debt
can be different. When the government defaults on external debt, the only costs that it faces are
the exogenous decrease in productivity and autarky from external markets for an exogenous amountof time. In contrast, when the government defaults on domestic debt, it faces an additional costbecause it defaults on its own domestic banks. In particular, aggregate banks’ net worth is givenby
N = σ [zFK (K, L) + δB − D] + (1 − σ)n̄,(27)
so upon default, net worth decreases by σ, which is the survival rate of banks. This additional
endogenous effect is not present when defaulting on external debt, and thus makes the government
more reluctant to default on domestic than on external debt, which in turn makes the price ofdomestic debt less sensitive than the external debt price for the same amount of debt. This implies
that for similar levels of prices, q and q ∗ , the increase in available resources from an increase indomestic debt is in general bigger than from an increase in external debt.
This effect can be seen in Figure 5, which plots the total resources obtained qB ′ and q ∗ B ∗′ fromborrowing B ′ and B ∗′ units of bonds respectively, that is, the Laffer curve for borrowing on each typeof debt. This figure uses the numerical results obtained in the quantitative analysis of the model that28

will be shown below. As external borrowing increases, q ∗ quickly decreases, especially in periods oflow productivity, z (left panel), and so the increase in total resources q ∗ B ∗′ becomes lower.19 This
happens at a much lower rate in the case of domestic borrowing. Due to the higher sensitivity of
external debt prices to increases in debt, the increase in the amount of resources, q ∗ + ∂q ∗ /∂B ∗′ , islower for external than for domestic debt, and so the relative marginal gain decreases for high levelsof external debt.
Cost of Domestic Debt. The second main difference between the decision of domestic andexternal borrowing comes from the investment effect: domestic debt crowds out investment, andexternal debt has, in general, a positive effect on investment. In the first order conditions(24)and∂q∂q′(25) these effects are captured by the term ρ ∂B ∗′ B for external borrowing, and ρ q + ∂B ′ B ′ fordomestic borrowing, where ρ is the multiplier on the banks budget constraint. That is, ρ captures
the positive effect of capital investment in the economy, and mainly represents the increase in
output in future periods due to an increase in future capital.20 Importantly, the sign of these effects
is different for external and domestic debt: an increase in external borrowing increases investment∂q′in capital by − ∂B∗′ B , which in general is positive because more external debt tends to increase
the default probability on both types of debt. In the case of domestic borrowing, an increase in∂q′borrowing changes investment by −q − ∂B
′ B , which is negative, reflecting thus the crowding out
of investment in capital.
These effects can be understood from the aggregate banks’ budget constraint: K ′ = (1 + θ)N −qB ′ . Domestic debt is held by domestic banks, so increasing B ′ directly decreases the resources
available to the bank to invest in capital. The effect of external borrowing on investment is given
through the cross-price effect: increasing external debt generally decreases the price of domestic
bonds, ∂q/∂B ∗′ < 0, due to a higher probability of default. Therefore, for a given amount ofdomestic debt, it increases the resources available to the bank to invest in capital.
Cyclicality of Domestic Debt. So far we have analyzed the relative benefits and costs of eachtype of debt for a given state of the economy. However, the state of the domestic economy—theaggregate productivity level in the country—also affects the decision on what type of debt to issue.
In the model, when productivity is low, the share of domestic debt will tend to increase. Thisis because when productivity is low, expected returns to capital, RK , are also low. Therefore, first,
the price of domestic debt, aside from default risk, is higher as banks’ incentives to invest in capitaldecrease, and second, the cost of crowding out capital is lower, as the increase in output from using
capital is lower when productivity is low, making then domestic debt more attractive. Moreover,in low productivity periods, the incentives to default on external debt increase—and, it does so
19Note that the government will never optimally choose to borrow on the decreasing side of the Laffer curve ofq B ∗′ , as it can get the same amount hof resources by borrowing less, as shown in Arellanoi(2008).

∗

20

∗

∂q
∗′
′ ′
′ ′
′
′
′
′
′
′
′
In particular, ρ = ∂K
′ B −1+βE z FK + µ T̂K L + [ρ + θη ] σz (FKK K + FK ) +µT̂ are tax revenues per unit of labor.

29

∂q ∗
∂q
′
B ∗′ + ∂K′B∂K ′, whererelatively more than for domestic debt—which, therefore, decreases the price of external debt.
These two factors, more incentives to issue domestic debt and higher default risk on external debt
during periods of low productivity, are what make the share of domestic debt to be countercyclical.

4.2

The Effects of a Shock to the Interest Rate

An increase in the international interest rate increases the cost of borrowing externally. Here, I
provide intuition on how the increase in the cost of borrowing translates into a decrease in output,
and how the government chooses to substitute the relatively costlier external debt with higher taxes
or higher domestic debt to mitigate the drop in output.
Consider the case where the government only has access to external debt and bonds are oneperiod bonds. Intuitively, the increase in interest rates increases the cost of borrowing externallyas it decreases q ∗ , and therefore increases the cost for the government of financing its expenditures.
To see this consider the government budget constraint under repayment,g + B ∗ = T (L) + q ∗ B ∗′ ,where T (L) = (zFL − v ′ (L))L are total tax revenues. The left-hand side of the budget constraint
is given at the beginning of the period and therefore, the government has no further choice on it.
Suppose, for the sake of argument, that after the increase in R∗ —that is, a decrease in q ∗ —thegovernment decides not to change its external borrowing B ∗′ . Then, an increase in the international
interest rate implies that, for the same amount of debt issued, the government gets a lower amountof resources q ∗ B ∗′ , and therefore has to increase tax revenues in order to make its payments g + B ∗ .
The total effect on labor is then,−1∂q ∗ ∗′ 
∂L
′′
=
−
B
zF
−
v
(L)
L
+
T
(L)/L
< 0.
LL
∂R∗
∂R∗

(28)

The first term ∂q ∗ /∂R∗ B ∗′ represents the change in total external resources from increasing R∗ .
As can be seen from the external creditors pricing equation (13), the change in prices due to anincrease in the interest rate captures both, the direct decrease in q ∗ from the better outside optionof external creditors, and from a change in the probability of default. The second term in square
brackets represents how much total tax revenues decrease given an increase in labor, ∂T /∂L < 0.
Then the effect on output after an increase in R∗ is given by zFL ∂L ∂R∗ . After the initial
impact on output, the effect carries on to future periods through the net worth of banks. This isbecause the decrease in labor affects negatively the returns on capital, and hence decreases the total
net worth of banks. This implies that banks have fewer resources to invest in capital, so capital
available to produce in future periods decreases, and so does output. This example illustrates how
the increase in interest rates is propagated to output in emerging countries, but it is an extreme casewhere the government does not optimally change its decision on how much to borrow externally, so
B ∗′ is fixed. In equilibrium, the government will generally prefer to lower the amount of external
30

debt due to its higher costs, up to the point where it equates the marginal gain of external debt to its
marginal cost of repaying it. To see this, notice that the relative marginal revenue of external debt
in equation (26) is now affected by a decrease in q ∗ which, for a given amount of debt, decreases themarginal revenue of external debt relative to domestic, so that, in general, the government would
prefer to substitute away from external borrowing and into domestic borrowing.
In fact, domestic debt can mitigate the drop in output after an increase in external interest
rates. To avoid the output cost of increasing taxes as seen in equation (28), the government can
substitute external debt for domestic debt if the crowding out cost of domestic debt is not larger
than the higher costs of borrowing externally. This can be seen from the relative marginal gain of
issuing external debt in equation (26). In equilibrium, the government equates the relative marginal
gain of external debt to the relative marginal cost of repayment net of the effect on capital, thatis, the right-hand side of (24) relative to the right-hand side of (25). These forces are analyzed
quantitatively in the following section.

5

Quantitative Analysis

This section presents the numerical solution of the model in which data on a sample of emerging
countries is used to set the parameters of the model. The numerical solution is then used toevaluate the predictions of the model regarding the effects of shocks to the international interest
rate on emerging countries, the role of sovereign debt composition, and the patterns of default.
Appendix D contains the details on the computational algorithm used to solve the equilibrium.

5.1

Parameterization

A period in the model is one quarter. I assume that the disutility of working for households takes
1+ϕ
the following form: v(L) = ξ L1+ϕ , where ϕ is the inverse of the Frisch elasticity, and the production
function is Cobb-Douglas, F (K, L) = K α L1−α where α is the capital share of production. In normal
times, the total output produced at the firm is then zK α L1−α , where z is the aggregate productivity
shock. When the economy is in autarky, however, productivity becomes h(z) < z. As standard in
the literature literature on sovereign default, I assume that this productivity cost is nonlinear and ishigher for high realizations of z. Specifically, following Chatterjee and Eyigungor (2012), I assume
h(z) = z − max{ζ0 z + ζ1 z 2 , 0}, with ζ0 < 0 and ζ1 > 0, which implies that defaulting is relatively
more costly at higher levels of productivity.
Assigned Parameters. The parameters used in the baseline model are reported in Table 4.
Some parameters, Θ1 = {µR , ρR , σR , ρz , α, δK , λ, γ, ϕ, κ} are taken directly from the data or fromthe literature, and the rest of parameters are set using a moment matching procedure so that themodel is able to reproduce crucial targets in the data. Most of the parameters assigned from the dataor literature are standard. For the parameters regarding the international interest rate process (12),31Table 4: Parameter Values
Assigned parameters
Average world risk free rate
Risk free rate autocorrelation
Risk-free rate standard dev.
Productivity autocorrelation
Capital share
Capital depreciation
Debt decay rate
Autarky duration
Inverse Frisch elasticity
Working capitalµR = 0.017
ρR = 0.955
σR = 0.003
ρz = 0.95
α = 0.3
δK = 0.05
λ = 0.05
γ = 0.063
ϕ = 0.5
κ = 0.26

Parameters from matching moments
Discount factor
β = 0.986
Banks survival rate
σ = 0.92
Collateral constraint
θ = 0.46
Banks initial net worthn̄ = 0.70
Gov. expenditures
G = 0.035
Disutility of working
ξ = 2.15
Productivity standard dev.
σz = 0.009
Productivity cost of default
ζ0 = −0.182
Productivity cost of default
ζ1 = 0.195

SourceAverage US interest rate (quarterly rate)
AR(1) on US interest rate
AR(1) on US interest rate
Neumeyer and Perri (2005)
Standard capital shareStandard capital depreciation
Average maturity
Gelos et al. (2011)
Keane and Rogerson (2012)
Neumeyer and Perri (2005)
Moment matched
Default probability
Deposits to GDP
Share of domestic debt
Returns on equity
Government expenditures to GDP
Hours worked
Volatility of GDP
Debt to GDP
Standard deviation spread

I estimate an AR(1) process using data on the U.S. Federal Funds rate. The process is persistent,with the autocorrelation coefficient being ρR = 0.955, and a standard deviation of the error term
σR = 0.003. As for the productivity process, I follow the same strategy as in Neumeyer and Perri(2005). Due to a lack of available data, it is not possible to construct a reliable series of productivity
from the Solow residual. Because of this, I simply fix the autocorrelation parameter ρz to 0.95 asin the U.S. data, and choose σz so as to match the average volatility of the HP-filtered log output
in the countries in the sample, which is 3.08%. Regarding the production technology of firms, thecapital share is set to 0.3 and the depreciation rate of capital to 0.05. The parameter λ refers in
the model to the debt decay rate and therefore is related to the average maturity of long-term debt.
This parameter is set to match an average maturity of 4 years, in line with the standard maturity
used in the literature (see Chatterjee and Eyigungor, 2012). The period of autarky after default isassumed to last on average almost 4 years, to match the estimates in Gelos et al. (2011). Finally, theFrisch elasticity is set equal to 2, so ϕ = 0.5, which is in the range of the macroeconomic estimates(see for instance Keane and Rogerson, 2012).
Parameters From Moment Matching. The remaining eight parameters from the model, Θ2 ={β, σ, θ, n̄, G, ξ, σz , ζ}, are set to match eight moments from the data. Some of them are standard
in the sovereign default literature: average default probability, total debt to GDP, and average

32

Table 5: Model Fit

Default probability, annual %Debt to GDP, %Deposits to GDP
Share of domestic debt
Return on equity, %Government expenditures to GDP
Hours worked
Output volatility
Spread volatility

Data
4.51
32.5
0.32
0.54
12.5
0.14
0.22
3.08
2.45

Model
1.05
30.9
0.33
0.52
16.5
0.13
0.22
3.11
1.55

spread on external debt.21 To assign the value of government expenditures, G, I target the average
government expenditures to GDP in the data, and for the disutility of working, ξ, I target the
average total hours worked. Three parameters are left that are related to the bank’s problem,
θ, σ, n̄. The fraction of net worth that the banks can borrow from households, θ, is directly related
to the amount of deposits or, more broadly liquidity, in the economy. For this reason, I use theaverage ratio of liquid liabilities to GDP as a target. The remaining two parameters are the survival
rate of banks, σ, and the net worth transferred from households to newborn banks, n̄. To set theseparameters, I use two moments: the share of domestic debt over total debt, and the average returnon equity for banks. Intuitively, the average duration of banks affects the decision of the government
on how much domestic debt to issue, as repayment of the debt will last for longer at the bank, andwill allow for a higher accumulation of capital. The initial net worth at the bank, n̄, affects theoverall resources of banks and therefore the total capital in the economy, which in turn affects thereturns to capital. With this calibration, the value of θ is then set to 0.46, which means that, if thebank were to run away with the deposits of the households, it would get a fraction of 0.68 of its
current net worth, that is, 1/(1 + θ). The value of σ is set to 0.92, that is, banks survive on average
12.5 years.

5.2

Results in the Baseline Economy

Table 5 compares the targeted moments in the data and in the model. Overall the model can reproduce the main features of the data. Next, I show the trade-off of the government between the benefitof domestic debt, that is, its lower default risk, and the cost of domestic debt, that is its crowdingout effect on investment, in the calibrated model. Let the value for the government of choosing agiven combination of external and domestic borrowing (B ∗′ , B ′ ) be denoted by Ṽ (S; B ∗′ , B ′ ), suchthat, the problem for the government is V (S; B ∗′ , B ′ ) = maxB ∗′ ,B ′ Ṽ (S; B ∗′ , B ′ ). Figure 6 showsthese values as a function of B ∗′ (top panels), and B ′ (bottom panels) together with the implied
new capital in the economy, K ′ , and total resources from debt that the government obtains from
21
The average default probability is computed using the default events documented in Reinhart and Rogoff (2011).
I compute the average default probability for each country in the sample (including countries that never defaulted),
and take the average across developing countries.

33

Figure 6: Government Borrowing Decisions
q*B*'
.04

1.13

Capital Investment, K'

.03
.01

1.11

3.8

1.115

.02

3.81

1.12

3.82

1.125

3.83

Value Function

.03

.04

.05

0

1.105

.02

0

.01

.02

.03

.04

.05

0

.01

.02

.03

External borrowing, B*'

External borrowing, B*

External borrowing, B*'

Value Function

Capital Investment, K'

qB'

.05

.04

.05

.04

.04

.03
.01

1.11

3.8

1.115

.02

3.81

1.12

3.82

1.125

3.83

.01

1.13

3.79

Optimal
0

.01

.02

.03

Domestic borrowing, B'

.04

.05

0

1.105

3.79

Optimal
0

0

.01

.02

.03

Domestic borrowing, B'

.04

.05

0

.01

.02

.03

Domestic borrowing, B'

Notes: The upper panels of this figure show the implied value function for the government (right-panel), new capital(middle-panel), and external resources obtain from borrowing q ∗ B ∗′ as a function of new external borrowing B ∗′ . Thisis computed for a given state space (B, B ∗ , K, D, z, R) and for a given amount of domestic borrowing B ′ , which is set
to be the optimal one. The black dot in each figure indicates the optimal amount of external borrowing B ∗′ , that is,
the one that maximizes the value function. The bottom panels show the equivalent plots as a function of new domestic
borrowing B ′ .

borrowing such quantities qB ′ . The optimal decision is indicated in the plots with a black dot.
For the chosen level of the state of the economy, S, the optimal amount of domestic and externalborrowing is the same, such that, B ′ = B ∗′ = 0.016.
The crowding-out cost of domestic debt can be seen in the middle panels of Figure 6: as thegovernment increases domestic debt the amount of capital available for the next period K ′ decreases.
This is the opposite in the case of external debt: increasing external borrowing increases future
capital, except for values of debt that are higher than is ever optimal for the government. This is
why the value for the government of issuing more domestic debt sharply decreases for high amountsof domestic debt even if qB ′ , that is, the revenue from borrowing more, does not decrease. On theother hand, the relative benefit of domestic debt can be seen precisely from the difference in the
total amount of resources that the government gets from borrowing domestically, qB, and externally,q ∗ B ∗′ . As will be clear below, external prices are more sensitive to an increase in borrowing thandomestic borrowing, as default risk increases more rapidly. As a consequence, the slope of q ∗ B ∗′starts decreasing for low amounts of external borrowing. This contrasts with the slope of qB ′ , whichis always increasing in the amount of domestic borrowing. Therefore, as the amount of externalborrowing increases the relative marginal revenue defined in equation (26) starts decreasing.
To explain the difference in the sensitivity of prices to changes in borrowing, Figure 7 plots the34

Figure 7: Ex-post Default Decisions

.01

.02

Default bothDefault both

.03

.04

Default
only external.02

External debt

.03

Default
only external.01

External debt

.04

.05

High productivity.05

Low productivity

No default

No default

0

.01

.02

.03

.04

0

0

Only domestic →.05

0Domestic debt

.01

.02

.03

.04

.05

Domestic debt

default decisions of the government as a function of (B, B ∗ ). Defaulting on domestic involves anadditional endogenous cost because it directly decreases the net worth of domestic banks, as canbe seen in equation (27). This implies that, for the same amount of debt, the government will havemore incentives to default on external than on domestic debt. When domestic debt is relatively low,
the government defaults only on external debt when B ∗ is high enough. Similarly, when external
debt is very low, the government defaults only on domestic debt when domestic debt, B, is verylarge. However, it is clear from the graph that the government is more tolerant of domestic debt:
the region of only external default is larger both in terms of the minimum B ∗ for which it defaults,
and because it requires a higher B for defaulting on both. As debt becomes larger for both typesof debt, the government has more incentives to default on both. As productivity increases, thedefault set shrinks and the no-default area becomes larger, as can be seen in the right panel of
Figure 7. Moreover, when productivity is high, there is no region (B, B ∗ ) on which the government
defaults only on domestic debt. In this case, the incentives of the government to repay domestic
debt increase because, by repaying, it increases the total net worth of the banks, which then canbe used to invest in high-productivity capital. Section 5.5 elaborates on the patterns of default andthe differences between the conditions under which the government chooses to default on domestic
or external debt. Moreover, it shows that these patterns are consistent with what we observe in the
data.

5.3

Vulnerability to External Shocks

This section shows the effects of an increase in the international interest rate in output, and how
the decisions of the government change after such a shock. In the model, international interest
rates are assumed to follow a stochastic process as in equation (12). Figure 8 plots the response

35

Figure 8: Response to a Positive Interest Rate ShockExternal Debt

12

16

20

0

4

8

12

16

-.008

-.4

8

-.006

debt
-.004

percentage points
-.3
-.2

.6
pp
.4
.2

external
baseline
domestic

0

20

0

4

8

12

Quarters after shock

Quarters after shock

Tax Rate

Capital020-.05capital

.1

-.1

debt
.002

16

external
baseline
domestic

percentage points
.2

.004

external
baseline
domestic.4

Quarters after shock

Domestic Debt

.3

4

.006

0

external
baseline
domestic

-.002

-.1

.8

0

0

Output1

Interest rate

-.15

0

0

0

4

8

12

Quarters after shock

16

20

external
baseline
domestic

0

4

8

12

Quarters after shock

16

20

0

4

8

12

16

20

Quarters after shock

Notes: The solid blue lines in this figure show the response of each of the variables in the baseline economy, that is when
the government has access to both domestic and external borrowing. The dashed green lines show the case when thegovernment can only borrow externally, and the dashed red lines show the case when the government can only borrow
domestically.

to a shock that increases the international interest rate by 100 annual basis points. Output in thebaseline economy (solid blue line) drops about 0.3 percentage points, close to what we observe inthe data which is around 0.4 percentage points. Notice that none of the parameters of the model
are set to match the output drop as in the data. The drop in output after an increase in interest
rates is a consequence of higher costs of external borrowing. Given higher interest rates, it is now
more costly for the government to finance its expenditures, especially if it finances it using external
debt. As shown in Figure 8, in order to balance the higher cost of external debt, the government
chooses to decrease its external borrowing and increase domestic debt. In addition, it also needs toincrease tax rates to compensate for the decrease in external borrowing. Higher taxes, through its
distortionary nature, and higher domestic debt, through its crowding out effect, will decrease bothlabor and capital in this economy, and thus output drops.
Domestic debt helps mitigate the drop in output. To see this, consider the case where there is
only external debt in the economy. In this exercise, I keep the same parameters as in the baseline
economy and solve the equilibrium of the model where I constrain the government to have no accessto domestic debt. The output response in the economy with only external debt is shown in Figure
8 represented by the dashed green lines. In this case, output drops more than in the baseline
economy where the government has access to both types of debt. When the government does nothave access to domestic debt, most of the substitution of external debt after the increase in theinterest rates is done via an increase in taxes. Therefore, even though there is no crowding out effectand capital does not decrease as much, the large increase in taxes implies a significant decrease in36

Table 6: Financial Development and Domestic Debt
Data
Low θ

Model

High θLow θHigh θ

Deposits to GDP

0.20

0.45

0.22

0.42

Domestic debt share

0.36

0.68

0.18

0.71

labor. This causes a larger decrease in output in the economy with only external debt. The effect of
an increase in interest rates in the economy with only domestic debt comes only from the working
capital mechanism, as in this case the cost of borrowing is not directly affected by international
prices. Therefore, the drop in output is relatively small in the case of only domestic debt.

5.4

Financial Development and Domestic Debt

Now, I analyze how the share of domestic debt and the vulnerability to interest rate shocks dependon the level of financial development of the economy. In the model, the level of financial developmentof a country is controlled by the parameter θ in the collateral constraint (9). The higher θ is thelower the frictions in the financial sector. Specifically, higher θ is associated with a lower fractionof assets that banks can divert. This can be interpreted as improving the monitoring technologythat depositors have over banks’ behavior, which is linked to the level of development of domestic
financial markets.
To see the implications of the model regarding the level of financial development, I perform thefollowing quantitative exercise. First, I divide countries between low and high financial development
depending on whether their average level of financial development is above or below the medianlevel in the sample. Then, I vary the parameter θ so as to match the average level of deposits to
GDP in each of the groups: low and high financial development. Importantly, in this exercise, theonly parameter changing is the value of θ and the rest of the parameters are kept fixed at their level
as in Table 4. The average share of domestic debt for countries that are less financially developedin the data is 0.36, whereas in countries that are more financially developed this share is 0.68.
Moreover, the difference in the means across these two groups is significantly different from zero.
The re-calibrated parameter θ is 0.36 for low financially developed and 0.65 for high financiallydeveloped (in the baseline economy it is 0.46).
Table 6 compares the levels of financial development and shares of domestic debt in the data andthe ones generated by the model. The model captures the differences in the share of domestic debt
between high and low-financially-developed countries. In particular, it captures quantitatively wellthe higher share of domestic debt in relatively high financially developed economies, and the drop
in domestic debt in lower financially developed economies, although it overstates such drop relative
to the data. Note that none of the domestic shares in this exercise are targeted moments. There are
two main mechanisms in the model that generate this result. First, when banks face less stringent
constraints, that is countries are more financially developed, the interest rate that the government
37

Figure 9: Response to a Positive Interest Rate Shock: Model
low FDhigh FD.004

0

low FDhigh FD

-.002

8

12

16

20

debt
.001

0

4

8

12

16

20

0

4

8

12

Quarters after shock

Quarters after shock

Quarters after shock

CapitalLabor

Tax rate

16

20

low FDhigh FD

48

12Quarters after shock

16

20

low FDhigh FD

-.004

-.15

low FDhigh FD
0

0

4

8

12

Quarters after shock

16

20

0

-.003

-.1

.1

pp

labor
-.002

capital

.2

-.05

-.001

0

.3

4

0

0

0

-.4

low FDhigh FD

-.008

-.3

-.006

.002

%
-.2

debt
-.004

.003

-.1

Domestic Debt

.005

External Debt0

Output

0

4

8

12

16

20

Quarters after shock

Notes: The dashed blue lines in this figure show the response of each of the variables for the economy with a high level offinancial development (high θ). The solid red lines show the case when the economy is low financially developed (low θ).

has to pay on domestic debt decreases. Lower constraints imply lower returns to capital due tolower marginal product of capital, and thus lower interest rates on domestic debt. Similarly, whenconstraints are more relaxed, the crowding-out cost from issuing domestic debt is lower. Therefore,
domestic debt becomes more attractive relative to the case where financial constraints are tighter,and governments issue more domestic debt.
The response to a shock that increases the interest rate for the low- and high-financially developed economies is shown in Figure 9. After the shock, in both economies, there is a decrease inexternal debt, due to its increase in cost, an increase in domestic debt, and an increase in taxes, tosubstitute for the decrease in external debt. However, the magnitude of these changes is different
for low and high-financially developed economies, which in turn affects the magnitude of the drop
in total output.
The main difference between the two economies is that, in low financially developed countries, thegovernment mostly substitutes external debt for higher taxes, whereas in high financially developed
countries, the government substitutes into higher domestic debt instead of taxes. To understandthese decisions, it is useful to consider the effect of each of these policies on capital through the bankaggregate budget constraint when the collateral constraint is binding, that is, K ′ = (1 + θ)N − qB ′ .
An increase in domestic debt, B ′ , has a direct negative effect on capital that depends on the price of∂q′domestic debt. In particular, the effect of increasing debt on capital is given by ∂B′ B + q. On theother hand, increasing taxes have an effect on today’s aggregate net worth of banks, N . An increasein taxes translates into a decrease in total labor, which in turn decreases the return on capital and38

Table 7: Private Credit From Banks and Domestic Debt
(1)
Domestic debt to GDP
Total debt to GDP
Financial development
Log GDP per capita
Country Effects
Year Effects
Observations

(2)
∗∗∗

-0.140(0.026)-0.122∗∗∗(0.031)1.083∗∗∗(0.038)5.259∗∗∗(0.853)
No
No
272

∗∗∗

-0.145(0.041)-0.053∗∗∗(0.029)0.636∗∗∗(0.075)20.990∗∗∗(4.351)
Yes
No
272

(3)
-0.156∗∗∗(0.043)-0.073∗∗∗(0.033)0.666∗∗∗(0.078)8.092(5.586)
Yes
Yes
272

Standard errors in parentheses. * p<0.1, ** p<0.05, *** p<0.01

Ktherefore, the bank’s net worth. The effect on capital is then, (1 + θ)σ ∂R∂τ . Notice that, for a given∂RK∂τ , this effect will be larger the higher θ is, that is, the more financially developed the economy is.
The reason is that higher financial development implies that a higher fraction of banks’ net worth
can be invested in capital.

Empirical Evidence on Main Mechanisms. There are two main mechanisms in the modelthat explain the patterns observed in the data. First, the model assumes that default in domestic
debt implies an endogenous cost arising from a decrease in domestic banks’ net worth. And second,domestic debt crowds out investment in the private sector through the collateral constraint affecting
banks’ investment decisions. Here, I discuss and provide evidence on these mechanisms.
After default, as standard in the literature on sovereign default, an exogenous drop in productivity will prevail for a given amount of periods. This exogenous cost is modeled as exactly thesame for domestic and external defaults. However, the model also features an additional endogenous default cost when defaulting on domestic debt, that is not present when defaulting on external
debt. This happens because domestic banks’ net worth depends on the repayment of such debt,
and therefore default would imply a decrease in banks’ net worth. Empirically, we observe suchan effect. Gennaioli et al. (2018) use a panel of data on banks for different European countries
to analyze the relationship between government default risk, banks holding of domestic debt, andtheir loan-to-assets ratio. Baskaya and Kalemli-Ozcan (2016) estimate the impact of default risk
on domestic banks holding government debt using a natural experiment in Turkey. They find that
increases in default risk imply a significant reduction in bank credit supply and in net worth. Key
to this mechanism is also the introduction of selective default in the model. This is assumed following what is observed in the data, as there are indeed episodes of defaults where governments
discriminate between domestic and external creditors.
The second important mechanism in the model is the crowding out effect of domestic debt.

39

Becker and Ivashina (2018) show, for the Eurozone countries, that increases in banks’ government
bond holdings were associated with a decrease in their corporate lending. I show a similar result
using aggregate data on the sample of emerging countries studied here. Using data on total private
credit from banks, and total domestic government debt in a given country, consider the following
regression
Domestic Debtit
Private Creditit=β+ ΓXit + αi + δt εit ,
(29)
GDPit
GDPit
where the coefficient β is an indicator of the crowding out effect that domestic debt has on theamount of credit that banks are able to provide. The controls included in X in this regression arelog GDP per capita, level of financial development, and total debt. Table 7 reports the results andshows that when there is a high domestic debt to GDP ratio, the amount of private credit fromdomestic banks tends to significantly decrease, indicating a crowding out effect of domestic debt.

5.5

Patterns of Discriminatory Default

Here, I explain what are the patterns of default implied by the model, and I compare them with theones observed in the data. When do governments default on external debt and when in domestic
debt? There are three main points regarding the patterns of discriminatory default in the data.
First, governments tend to default more often on external debt alone. Second, the output drop after
a default only on external debt is lower than after a default on both types of debt. And third, before
defaulting, the patterns of output are already different between defaults only on external debt anddefaults on both types of debt. In particular, when output is moderately below trend countries
default only on external debt but when it is greatly below trend they tend to default on both typesof debt. I refer to this pattern as pecking order of default.
The model is able to generate the same patterns around default that we observe in the data.
First, regarding the frequency of each type of default, note that one crucial assumption in the modelis that governments can discriminate when they default between external and domestic creditors.
As it has been shown in Section 2, this is consistent with what we observe in the data, based on
Table 8: Pecking Order of Default
Data

Model

External only

Both

External only

Both

74%

26%

67%

33%

Before default

-0.8%

-1.9%

-0.3%

-2.5%

Default period

-0.7%

-4.2%

-2.9%

-2.9%

After default

-0.6%

-2.2%

-2.3%

-3.4%

Frequency of default
Output deviation from trend:

Note: Deviations from trend are measured using the Hodrick-Prescott filter on quarterly series
for real GDP. The periods before and after default correspond to the average over the previous
and following year of default, respectively. The data used here covers the period 1960 to 2007.

40

Figure 10: Output Deviation at the Time of Default: Data and Model.02.01
Output deviation-.05 -.04 -.03 -.02 -.01 0

Output deviation-.05 -.04 -.03 -.02 -.01 0

.01

.02

.03

Model

.03

Data

External
Both
-8

-6

-4

-2

0

2

4

6

8

External
Both-8

Quarters since default

-6

-4

-2

0

2

4

6

8

Quarters since default

Notes: In the data, output deviation is measured as deviations of the quarterly real GDP from its
HP-filtered series (smoothing parameter set to 1600)

the evidence, for instance, in Reinhart and Rogoff (2011). Table 8 shows the frequency of eachtype of default. As in the data, the model generates a higher fraction of external defaults thanof defaults on both types of debt, and it matches well the frequencies even though these are nontargeted moments. Second, Table 8 also presents the output patterns around a default event, whichshows that the circumstances under which governments default only on external debt and when theydefault on both, domestic and external, are very different. In particular, in the periods preceding
defaults, output is below trend, but it is much lower when the country defaults on both debts thanwhen it only defaults on external debt. This can also be seen in Figure 10, which shows the average
evolution of output around the time of default across all the events of default in the data (left panel)and in the simulations of the model (right panel). In the data, the year before defaulting on bothtypes of debt, output was already almost 2% below trend, and in the year of default it fell morethan 4% below trend, whereas for defaults on external debt, only the fall in output is much lower:
0.8% and 0.7% respectively. Similarly, in the model output is already very low in the year before
defaulting on both types of debt, and less so when defaulting only on external debt.
In order to understand why the model generates these patterns it is important to see what
are the cyclical properties of domestic debt. In the model, higher productivity today increases the
expected returns to capital, and therefore, given that the price of debt must be such that banks
are indifferent between investing in bonds or in capital, the interest rates that the government
has to offer are higher when productivity is high. Moreover, higher productivity implies that thecosts from the crowding effect of issuing debt are larger, because a high z today implies a highexpected marginal product of capital tomorrow, so that an additional unit of investment would beturned into relatively high output, and therefore consumption, tomorrow. These two effects, thatis, relatively higher interest rates on domestic debt and higher costs from issuing domestic debt,
makes this type of debt is less attractive to the government when productivity is high. This results
in a countercyclical share of domestic debt. Importantly, the same patterns hold in the data. Thisis shown in Figure 11 which displays the cross-correlation between the detrended series of GDP and

41

0
-.02
-.04
-.06

cross correlation (detrended series).02

Figure 11: Correlation GDPt+h and Domestic Debtt in Data

-4

-3

-2

-1

0

1

2

3

4

Years
Notes: This figure uses data on annual series of real GDP andshare of domestic debt for the countries in the sample used inthis paper (see Section 2). The series are detrended using the
Hodrick-Prescott filter with a smoothing parameter set to 100.

that of the share of domestic debt. In the sample of countries considered in this paper, periods
when GDP is below trend are associated with higher shares of domestic debt.
The countercyclicality of domestic debt explains the pecking order of default. When productivity
is not too low, like in the period before defaulting on external debt (see Figure 10), the government
has incentives to issue more external debt than domestic because it is relatively cheaper and it
does not crowd out capital at a time when investment in capital is very valuable. Then, a dropin productivity will induce defaulting only on external debt because defaulting on domestic debt ismore costly, and the share of domestic debt is low. On the other hand, if productivity is alreadyvery low, such as in the period before defaulting on both domestic and external debt, the priceof external debt becomes more expensive due to a relatively higher probability of defaulting on
external than domestic debt. Moreover, both the crowding cost and the interest rates from issuing
domestic debt are lower than when productivity is high. Therefore, the government starts issuing ahigher share of domestic debt. Then, when there is a sharp decrease in productivity the government
has to default on both types of debt, because, given the low shares of external debt, defaulting on
foreign creditors is not enough to solve the financing problems of the government.

6

Discussion

In this section, I discuss two main assumptions of the model and show quantitatively that the main
results of the paper continue to hold if we modify those assumptions. The first assumption is theabstraction from real exchange rate changes in the model. The second is the presence of working
capital through which firms are directly affected by fluctuations in the international interest rate.

42

Table 9: Parameters and Moments to Match: Model With Exchange Rates
Parameter
Discount factor
Banks survival rate
Collateral constraint
Banks initial net worth
Gov. expenditures
Disutility of working
Productivity standard dev.
Productivity cost of default
Productivity cost of default

6.1

β = 0.979
σ = 0.93
θ = 0.485n̄ = 0.70
G = 0.036
ξ = 2.30
σz = 0.009
ζ0 = −0.178
ζ1 = 0.188

Moment

Data

Model

Default probability
Deposits to GDP
Share of domestic debt
Returns on equity
Government expenditures to GDP
Hours worked
Volatility of GDP
Debt to GDP
Spread

4.51
0.32
0.54
12.5
0.14
0.22
3.08
32.5
2.45

0.96
0.33
0.53
16.9
0.11
0.22
3.24
29.9
1.67

The Role of Real Exchange Rates

A large literature has explored the effects of monetary policy on exchange rates. This literature findsthat a shock that increases the U.S. interest rate is associated with a significant appreciation of the
U.S. dollar.22 The decision of the government between domestic and external is affected by changes
in the exchange rate. Usually, external credit is issued in foreign currency, so an appreciation of
the dollar makes the repayment of dollar-denominated debt more expensive. Moreover, if changes
in the international interest rate are associated with changes in the real exchange rate, then thevulnerability of emerging countries to an increase in the international interest rate will also beaffected by the change in the exchange rate.
To explore the role of exchange rates both in determining the share of domestic and external
debt, and in the effects of an increase in the international interest rate, I introduce real exchange
rates in the model. Let et be the real exchange rate that expresses units of local goods in terms ofunits of foreign goods. Then, the government budget constraint when the economy is in non-autarky
times is∗∗
G + δt λBt + δt∗ λet Bt∗ = τt wt Lt + δt qt (Bt+1 + (1 − λ)Bt ) + δt∗ et qt+1
Bt+1
+ (1 − λ)Bt∗ .

(30)

An increase in the real exchange rate, et , implies that the cost of repaying the debt increases, as
more units of local goods are required to repay a given amount of foreign goods. This can be seenin the left-hand side of the government budget constraint (30). In periods of high exchange rates,
then, keeping everything else the same, the government will have more incentives to issue domestic
debt relative to external debt.
Exchange rates are affected by shocks to the exchange rate, ϵet , but also by shocks to theinternational interest rate, ϵrt . This allows to capture the idea that the exchange rate will beaffected by a shock increase in the international interest rate. In particular, the joint stochastic
22

See, for instance, Eichenbaum and Evans (1995), Faust and Rogers (2003).

43

Figure 12: Response to a Positive Interest Rate Shock: Model With Exchange Rates
Baseline
Ex. rates

Baseline
Ex. rates

-.3

-.006

.002

debt

debt
-.004

.004

-.002

0
-.1
%
-.2

Domestic Debt

.006

External Debt0

Output

8

12

16

20

0

0

4

8

12

16

20

0

4

8

12

16

Quarters after shock

Quarters after shock

Quarters after shock

CapitalTax rate

Real exchange rate

Baseline
Ex. rates

20

pp
.005
0

-.1

.1

pp

capital

-.05

.2

.01

0

.015

4

.3

0

-.008

-.4

Baseline
Ex. rates

4

8

12

16

0

20

0

Quarters after shock

Baseline
Ex. rates

-.005

-.15

Baseline
Ex. rates
0

4

8

12

16

20

0

Quarters after shock

4

8

12

16

20

24

28

32

36

Quarters after shock

Notes: The solid green lines in this figure show the response of each of the variables for the economy that includes
real exchange rate fluctuations, and the dashed lines correspond to the baseline economy without real exchange rate
fluctuations.

process for international interest rates and the exchange rate is
"

∗
rt+1
et+1

#

"
=A+B

rt∗
et

#

"
+Σ

ϵrt+1
ϵet+1

#
,

(31)

where Σ is the variance-covariance matrix, and A and B are matrices containing the constants andthe auto-regressive coefficients of the system. I estimate this system of equations using the data forthe countries in the sample and solve the model using by discretizing the vector of interest rates andexchange rates, following the methodology proposed in Terry and Knotek II (2011). This allows us
to capture the joint process for rt∗ and et . Then, the parameters of the model are set using the same
strategy as in the baseline economy without exchange rates. Appendix E.6 shows the details of theestimation and the corresponding results. The estimation shows that on impact after a shock that
increases the international interest rate, there is a decrease of around 0.8% in the real exchange rateof the emerging countries relative to the United States. However, after the initial negative impact,
relative exchange rates increase up to 2%.
Next, I show that the effect of an increase in the international rates—which now has also a direct
effect on the real exchange rates— is similar to the economy in which there are no fluctuations in thereal exchange rate. The model with exchange rates is then calibrated to match the same moments
as in the baseline economy. The parameters used and the model fit are shown in Table 9, andFigure 12 shows the response to an increase in the interest rate of 1 percentage point annualized.
In this case, the real exchange rate also responds to the shock to the interest rate, as specified by44

Figure 13: Response to a Positive Interest Rate Shock: No Working Capital
OutputExternal Debt
01Interest rate

0

8

12

16

20

-.006

debt
-.004

0

4

8

12

16

20

0

4

8

12

Quarters after shock

Tax Rate

Capital20

external
baseline
domestic

debt
-.05

.001

0

.002

debt
.003

percentage points
.1

0

.004

external
baseline
domestic

16.05

Quarters after shock.3

Quarters after shock

Domestic Debt

.2

4

.005

0

-.008

external
baseline
domestic

-.4

.2

-.3

.4

pp

.6

percentage points
-.2
-.1

-.002

.8

0

external
baseline
domestic

0

-.1

-.1

external
baseline
domestic

0

4

8

12

16

20

0

Quarters after shock

4

8

12

Quarters after shock

16

20

0

4

8

12

16

20

Quarters after shock

Notes: The solid blue lines in this figure show the response of each of the variables in the baseline economy, that is, when
the government has access to both domestic and external borrowing. The dashed green lines show the case when thegovernment can only borrow externally, and the dashed red lines show the case when the government can only borrow
domestically.

the estimated equation (31). The patterns are the same as in the baseline, with a similar decreasein output. To compensate for the higher cost of borrowing externally, the government substitutes
external debt by increasing taxes and domestic debt. External debt in Figure 12 is expressed ininternational goods units. Therefore, the increase in the real exchange rate causes external debt inlocal goods units to decrease even further.

6.2

The Role of Working Capital

The model assumes that the international interest rate has not only an effect through changes in
the cost of borrowing for the government, but it assumes that firms working capital is paid using
international frictionless intra-period borrowing. The objective of this assumption is to introduce a
direct effect on private agents in the domestic economy. Here, I show that dropping this assumption
by setting the amount of working capital to zero, that is κ = 0, implies no change in the mechanismsof the model, although it decreases the magnitude of the output drop after an increase in interest
rates.
Figure 13 shows the response to an increase in the international interest rate in such a case.
All parameters are kept the same as in the baseline calibration in 4 except for κ which is set tozero. I show the response in three different scenarios: when the government has access to both
domestic and external debt (solid dark line), when the government only has access to external debt
(dashed green line), and when the government only has access to domestic debt (dashed red line).

45

This figure shows the same patterns as those in the main analysis in Figure 8, although the drop in
output after the increase in interest rate is naturally smaller than in the case with working capital.
In particular, in the scenario with both types of debt, an increase in the interest rate of 1 percentage
point implies a decrease in output of 0.2 percent and 0.3 percent in the case with only external debt.
Clearly, when there is no working capital and the government has only access to domestic debt,
changes in the international interest rate have no effect on the domestic economy.

7

Conclusion

The key motivation in this paper is the evidence that the aggregate fluctuations and default rates
in emerging market economies are not driven solely by internal shocks, as is typically assumed, butalso by external shocks, such as movements in world interest rates. I argue that an omission in
the existing literature is the link between financial development, the share of domestic debt, andthe vulnerability of developing economies to fluctuations in world interest rates. I have shown that
empirically, countries that are less financially developed, as measured by their deposit-to-output
ratio, have low shares of domestic government debt to the externally issued government debt. Suchcountries are also more vulnerable to fluctuations in world interest rates.
I developed a model consistent with these features. By embedding a financial intermediation
sector into an otherwise standard model of sovereign default, I have a way of naturally model financial development as a strengthening of the ability to enforce contracts as measured by a parameter
governing the tightness of the resulting collateral constraint. As this ability to enforce contracts
increases so does the share of domestic debt and, through the equilibrium, the vulnerability toexternal shocks decreases. The model naturally also produces other key features of the data: thepecking order of default and the countercyclicality of the domestic debt share.

46

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50

Appendix A
A.1

Banks Problem

Proof of Lemma 1

Consider the recursive formulation of the bank problem. To write the problem of the bank it issufficient to have as an individual state variable its net worth, n, at the beginning of the period.
Then, the value of a bank is

h
i
b ′
′
′
V b (n; S) = β max
E
σV
(n
;
S
)
+
(1
−
σ)n
′ ′ ′
k ,b ,d(32)

subject to the budget constraint
k ′ + q(S)b′ − q D (S)d′ ≤ n(33)

q D (S)d′ ≤ θn

(34)



n′ = RK (S ′ )k ′ + δ(S ′ ) λ + (1 − λ)q(S ′ ) b′ − d′(35)collateral constraint,

and, evolution of net worth

We can rewrite the banks problem (32) by substituting in the evolution of net worth (35)V b (n; S) = max′ ′ ′k ,b ,dnoβσE V b (RK (S ′ )k ′ + δ(S ′ ) λ + (1 − λ)q(S ′ ) b′ − d′ ; S ′ )+ β(1 − σ)E RK (S ′ )k ′ + δ(S ′ ) λ + (1 − λ)q(S ′ ) b′ − d′subject tok ′ + q(S)b′ − q D (S)d′ ≤ n
q D (S)d′ ≤ θn
Let ρ(S) be the Lagrange multiplier on the budget constraint (33), and let µ(S) be the Lagrange
multiplier on the collateral constraint (34). Then,
FOC(k ′ ) :FOC(b′ ) :

βE

βE

nh
i
o
1 − σ + σVnb (n′ ; S ′ ) RK (S ′ ) − ρ(S) = 0

nh
i

o
1 − σ + σVnb (n′ ; S ′ ) δ(S ′ ) λ + (1 − λ)q(S ′ ) − q(S)ρ(S) = 0

51

(36)

(37)

h
i
−βE 1 − σ + σVnb (n′ ; S ′ ) + q D (S)ρ(S) − q D (S)µ(S) = 0,

FOC(d′ ) :(38)

where, Vnb denotes the derivative of the value function with respect to net worth, n.
Now, we guess that the value function is linear in net worth, that is, V b (n; S) = nν(S). Then,
optimality conditions are
FOC(k ′ ) :ρ(S) = βE
1 − σ + σν(S ′ ) RK (S ′ )FOC(b′ ) :q(S)ρ(S) =βE

FOC(d′ ) :q D (S) [ρ(S) − µ(S)] = βE 1 − σ + σν(S ′ ) ,



(39)



1 − σ + σν(S ′ ) λ + (1 − λ)q(S ′ ) δ(S ′ )

(40)

(41)

Substituting the guess into the value function, we get





1 − σ + σν(S ′ ) RK (S ′ ) k ′ + βE 1 − σ + σν(S ′ ) λ + (1 − λ)q(S ′ ) δ(S ′ ) b′
− βE 1 − σ + σν(S ′ ) d′ ,nν(S) =βE

and, using optimality conditions (39)-(41), we can rewrite it asnν(S) =ρ(S) k ′ + q(S)b′ − q D (S)d′ + µ(S)q D (S)d′=ρ(S)n + µ(S)q D (S)d′(42)

Then the guess is verified: if the constraint binds, q D (S)d′ = θn, so
ν(S) = ρ(S) + θµ(S),(43)

where, ρ(S) = βE [1 − σ + σn′ ν(S ′ )] RK (S ′ ) , andµ(S) = βE





 K ′
1 − σ + σν(S ) R (S ) −′1
q D (S)


,

(44)

so,
 


ν(S) = E β 1 − σ + σν(S ′ ) (1 + θ)RK (S ′ ) − θ/q D .

(45)

If the constraint does not bind, µ(S) = 0, and ν(S) = ρ(S).
Moreover, from the first order condition we get the pricing equation for domestic bonds. Combining (39) and (40):q(A′ ; S) =E {[1 − σ + σν ′ ] [λ + (1 − λ)q(A′′ ; S)]}′E [1 − σ + σν ′ ] RK
52

(46)

Appendix B

Aggregate Budget Constraint

Here we derive the country-level budget constraint under the case where the government repays its
debt and thus, it is in the no autarky state. Derivation of the autarky states country-level budget
constraint follow the same steps. To get the country’s aggregate budget constraint (15) we startwith the households budget constraint:
C + q D D′ + σn̄ = (1 − τ )wL + D + X.

(47)

From the firm’s first order condition, we can substitute w = zFL (K, L). Moreover, from the banks
net worth, the dividends that are transferred to the households are this period returns for the
fraction σ of bankers that do not survive to next period, so X = σ RK K + (λ + (1 − λ)q) B − D ,σ2σ
N − 1−σn̄.
which we can write in terms of N using the aggregate net worth definition as, X = 1−σSo, substituting w and X into (47) we get
C + qD D′ +σσn̄ = (1 − τ )zFL (K, L)L + D +
N.
1−σ
1−σ

(48)

Now, using banks aggregate net worth definition,
N = (1 − σ) RK K + (λ + (1 − λ)q)B − D + σn̄,(49)

we can substitute for D in (48), so
C + q D D′ = zF (K, L)L − T + RK K + (λ + (1 − λ)q) B − N,(50)

where T = τ wL, and substituting RK = zFK (K, L) + 1 − δK from firms first order condition, we
get,
C + q D D′ = zF (K, L) − T + (λ + (1 − λ)q) B − N,(51)
where we used the fact that zF (K, L) = zFL (K, L)L + zFK (K, L)K.
Now, from the government budget constraint under repayment we have,
G + λB + λB ∗ = T + q B ′ − (1 − λ)B + q B ∗′ − (1 − λ)B ∗ ,so we can substitute T into (51),C + N + q D D′ = zF (K, L) + (1 − δ K )K − G − λB ∗ + qB ′ + q B ∗′ − (1 − λ)B ∗ .

Finally, using the aggregate bank budget constraint,
N + q D D′ = K ′ + qB ′ ,

53

(52)

so, substituting N + q D D′ into (52) we get
C + K ′ − (1 − δK )K + G + λB ∗ = zF (K, L) + q B ∗′ − (1 − λ)B ∗ ,which is equation (15).

54

(53)

Appendix C

Government Problem

Consider the government of the problem deciding between domestic and external debt in the simpler
case with one-period bonds, no working capital, no capital adjustment costs, and no stochastic
international interest rate. Let the aggregate state of the economy be St = (At ; zt ), and At denotethe assets, that is, At = (Kt , Dt , Bt , Bt∗ ). The problem of the government if it repays its debt thisperiod is:

V R (S) =max′∗

B ′ ,B ,L,C,Kt+1no
C + v(L) + βE δ̃(S ′ )V R (S ′ ) + ΓD (S ′ )(54)

where, ΓD are the collected continuation values for the government in terms of default, and δ̃(St ) =δ(St )δ ∗ (St ). The government budget constraint under repayment isq(A′ , z)B ′ + q ∗ (A′ , z)B ∗′ = G + B + B ∗ − zFL + v ′ (L) L(55)

the banks budget constraint is
K ′ + q(A′ , z)B ′ = (1 + βθ) [σ (zFK K + B − D) + (1 − σ)n̄] ,(56)

where, FK is simplified notation for ∂F (K, L)/∂K; the country’s resource constraint is
C + G + K ′ + B ∗ = zF (K, L) + q(A′ , z)B ∗′ ;and, the pricing equations areEδ ∗ (S ′ )
,
R∗

(58)

E [m(S ′ )δ(S ′ )],E [m(S ′ )z ′ FK (S ′ )](59)

q ∗ (A′ , z) =for the external debt, and,q(A′ , z) =(57)

for domestic debt, where m(S) = βE(1 − σ + σν(S ′ )) and ν is the marginal value of net worth at
the bank, defined in (16).
Then, the problem of the government is to solve (54) subject to (55)-(59). We can rewrite thisproblem as
V R (S) = maxzF (K, L) − B ∗′ − G − K ′ (S, B ′ ) + q ∗ (A′ , z)B ∗′ + v(L)B ′ ,B ∗′no+ βE δ̃(S ′ )V R (S ′ ) + ΓD (S ′ )(60)

G + B + B ∗ − q(A′ , z)B ′ − q ∗ (A′ , z)B ∗′ − T̂ (L; S)L ≤ 0(61)subject toµ(S) :

55

ρ(S) :

K ′ + q(A′ , z)B ′ − σ (zFK (K, L)K + B − D) − βD′ − (1 − σ)n̄ ≤ 0(62)

η(S) :

βD′ − θσ (zFK (K, L)K + B − D) − θ(1 − σ)n̄ ≤ 0(63)and, to the pricing equations, where the function K ′ (S, B ′ ) is defined by the banks budget constraint,
and the function T̂ (S) is the tax revenues per unit of labor. Let µ(S) be the Lagrange multiplieron the government budget constraint, ρ(S) on the aggregate bank budget constraint, and η(S) on
the aggregate bank collateral constraint. Then, taking first order condition with respect to externalborrowing we get:∂q ′∂q ∗ ∗′∂q ′∂q ∗ ∗′∗
B + µ(S) q +B +B − ρ(S)
B
q +
∂B ∗′
∂B ∗′
∂B ∗′
∂B ∗′
n
o
∂E δ̃(S ′ )V R (S ′ ))=−β+ ∆∗ (S).
∂B ∗′
∗

(64)

To simplify the exposition of the model forces, we focus on the continuation value under repayment,so that we can ignore the extra terms involving default, ΓD , or changes in default probability, which
we collect with the variable, ∆∗ (S), and set to 0. Now, taking first order condition with respect todomestic debt we get:∂q ′ ∂q ∗ ∗′∂q ′∂q ∗ ∗′
B + µ(S) q +B +B− ρ(S) q +
B
∂B ′
∂B ′
∂B ′
∂B ′
n
o
∂E δ̃(S ′ )V R (S ′ )= −β+ ∆(S),∂B ′(65)

where, similarly to equation (64), ∆(S) captures the terms involving changes in default probability
and the default continuation values, after a change in Bt+1 . We can further derive (64) and (65),
to obtainhi∂q ∗ ∗′∂q ∗ ∗′
∂q ′
∂q ′
∗
∗
′
′
q +
B
+
µ(S)
q
+
B
+
B
=
βE
+ ρ(S)
B
(66)
δ̃(S
)
1
+
µ(S
)
∗′
∗′
∗′
∂B
∂B
∂B
∂B ∗′


∂q ∗ ∗′∂q ′ ∂q ∗ ∗′
B
+
µ(S)
q
+
B
+
B
∂B ′
∂B ′
∂B ′


h
i

∂q ′
′
′
′
′
= βE δ̃(S ) µ(S ) − ρ(S σ − η(S )θσ + ρ(S) q +
B .
∂B ′

(67)

To complete the problem of the government we need to specify the first order conditions withrespect to labor, L, capital, K ′ , and deposits D′ , which give us three additional conditions:µ(S) =(ρ(S) + θη(S)) σzFKL K + T̂ (L; S)
T̂L (L; S)L − T̂ (L; S)

56

,

(68)

i

ρ(S ′ ) + θη(S ′ ) − µ(S ′ )T̂K (L′ ; S ′ )L′


 ∗
∂q ∗′
∂q ′
1 ∂q ∗ ∗′
,
B
−
µ(S)
B
+
B
−
β ∂D′
∂D′
∂D′

ρ(S) + η(S) =σE

h

(69)

and,
ρ(S) = ∗∂q ∗ ∗′
∂q
∂q ′
∗′
B
−
1
+
µ(S)
B
+
B
∂K ′
∂K ′
∂K ′
h


i
′
′
′
+ βE z ′ FK
+ µ(S ′ )T̂K (L′ ; S ′ )L′ + ρ(S ′ ) + θη(S ′ ) σz ′ FKK
K ′ + FK

57

(70)

Appendix D

Computational Algorithm

The model is solved as the limit of a finite horizon model with a large enough number of periods,
T . Starting from the last period T , I solve the model backwards taking as given the value functions
and bond prices one period ahead until convergence. I use a grid search method to find the optimal
amount of borrowing B ′ , B ∗′ over a grid B of a total of 100 points. Moreover, in order to smooththe decision of the government, which is necessary computationally in the case of long-term debt, I
follow Dvorkin et al. (2021) and introduce i.i.d. shocks distributed as Extreme Value Type I into
the government decision on borrowing.
Notation. Aggregate state is S = (B ∗ , B, K, D, z, R∗ , a). Define for each autarky state:– Normal times: S n = (B ∗ , B, K, D, z, R∗ )– Domestic autarky: S d = (B ∗ , K, D, z, R∗ )– External autarky: S e = (B, K, D, z, R∗ )– Autarky in both markets: S b = (K, D, z)
Let V a,R (S a ) be the value of repaying in autarky state a = {n, d, e}, that is, normal times, domestic
autarky, and external autarky respectively; and V b (S b ) the value when in autarky in both (norepayment decision)
Discretize Space State. The state space is discretized as follows:– Aggregate endogenous state variables: B ∗ , B, K, D
– Productivity, z, process: AR1 discretized using Tauchen (1986) method– International interest rate, R∗ , process: AR1 discretized using Tauchen (1986) method

Solve Problem in the Last Period t = T
Here, I show how to solve the value functions and price functions in the last period. I assume thatin the last period there is no new borrowing and no investment in capital. First, I show how tocompute the repayment values in each of the autarky states: no-autarky, domestic autarky, external
autarky, and full autarky. Given the repayment values, we can compute the default decisions, andtherefore the prices.
Repayment Values.

581. Enter the last period in no-autarky state (normal times). The value of repaying both debts is
VTn,R (S n ) =zK α L(S n )1−α + (1 − δK )K − G − B ∗ + ψL(S n )1+ϕ
1+ϕ

where, L(S n ) solves
G + B + B ∗ = z(1 − α)K α L(S n )1−α + ψL(S n )1+ϕ
2. Enter the last period in domestic autarky state. The value of repaying external debt is
VTd,R (S d ) =zK α L(S d )1−α + (1 − δK )K − G − B ∗ + ψL(S d )1+ϕ
1+ϕ

where, L(S d ) solves
G + B ∗ = h(z)(1 − α)K α L(S d )1−α + ψL(S d )1+ϕ
3. Enter the last period in external autarky state. The value of repaying domestic debt isVTe,R (S e ) =zK α L(S e )1−α + (1 − δK )K − G + ψL(S e )1+ϕ
1+ϕ

where, L(S e ) solves
G + B = h(z)(1 − α)K α L(S e )1−α + ψL(S e )1+ϕ
4. Enter the last period in autarky in both markets. The value of full autarky is
VTb (S b ) =zK α L(S b )1−α + (1 − δ)K − G + ψL(S b )1+ϕ
1+ϕ

where, L(S b ) solves
G = h(z)(1 − α)K α L(S b )1−α + ψL(S b )1+ϕ − ξ bwhere ξ b is a fixed cost of defaulting on both. Note that this is only included in the lastperiod because absent this cost the government always wants to default on both rather thandefaulting only on domestic or external.
Default Decisions and Value Function.
1. If currently in normal times:(a) Default on external only if VTe,R (S e ) > VTn,R (S n ), and then δT (S n ) = 1, δT∗ (S n ) = 0
59

(b) Default on domestic only if VTd,R (S d ) > VTn,R (S n ), and then δT (S n ) = 0, δT∗ (S n ) = 1(c) Default on both if VTb (S b ) > VTn,R (S n ), and then δT (S n ) = 0, δT∗ (S n ) = 0(d) Otherwise, and then δT (S n ) = 1, δT∗ (S n ) = 1
and therefore value is VT (S n ) = max{VTn,R (S n ), VTd,R (S d ), VTe,R (S e ), VTb (S b )}2. If currently in domestic autarky default if VTb (S b ) > VTd,R (S d ), and then δd,T (S d ) = 0; otherwise δd,T (S d ) = 1
and therefore value is VTd (S d ) = max{VTd,R (S d ), VTb (S b )}∗ (S e ) = 0; otherwise
3. If currently in external autarky default if VTb (S b ) > VTe,R (S e ), and then δe,T
∗ (S e ) = 1
δe,T

and therefore value is VTe (S e ) = max{VTe,R (S e ), VTb (S b )}∗ ,δBond Prices. Given repayment decisions, (δT∗ , δT , δe,Td,T ), compute prices that creditors willoffer to the government at t = T − 1

qT∗ (B ∗′ , B ′ , K ′ , D′ ; z, R∗ ) =Ez ′ ,R∗′ δT∗ (B ∗′ , B ′ , K ′ , D′ , z ′ , R∗′ ) z, R∗
R∗



∗
qd,T
(B ∗′ , K ′ , D′ ; z, R∗ ) =∗ (B ∗′ , K ′ , D ′ , z ′ , R∗′ ) z, R∗
Ez ′ ,R∗′ γδT∗ (B ∗′ , 0, K ′ , D′ , z ′ , R∗′ ) + (1 − γ)δe,T



R∗


Ez ′ ,R∗′ δT (B ∗′ , B ′ , K ′ , D′ , z ′ , R∗′ ) z, R∗qT (B ∗′ , B ′ , K ′ , D′ ; z, R∗ ) =Ez ′ ,R∗′ FK (B ∗′ , B ′ , K ′ , D′ , z ′ , R∗′ ) z, R∗ )Ez ′ ,R∗′ γδT (0, B ′ , K ′ , D′ , z ′ , R∗′ ) + (1 − γ)δd,T (B ′ , K ′ , D′ , z ′ , R∗′ ) z, R∗qe,T (B ∗′ , K ′ , D′ ; z, R∗ ) =d (B ′ , K ′ , D ′ , z ′ , R∗′ ) z, R∗ )Ez ′ ,R∗′ γFK (0, B ′ , K ′ , D′ , z ′ , R∗′ ) + (1 − γ)γFKd (S d ) = h(z)αK α−1 L(S d )1−α . I set the marginal value
where, FK (S n ) = zαK α−1 L(S n )1−α and FK
of a unit in the bank in the last period, νT , to be 1, as it is immediately transfer to the household.

Iterate Backwards: t = T − 1
Taking as given the value functions and price functions from last period, T , we can iterate backwards
to compute the value functions and price functions at t = T − 1.
Value Functions Under Repayment.
1. Normal times (access to both credit markets)

60

Let Ṽtn,R (B ∗′ , B ′ ; S n ) be the value of repaying existing debt and issuing new debt (B ∗′ , B ′ ):Ṽtn,R (B ∗′ , B ′ ; S n ) =zK α L(B ∗′ , B ′ ; S n )1−α − K ′ (B ∗′ , B ′ ; S n ) + (1 − δK )K − G∗+ qn,t+1(B ∗′ , B ′ ; S n ) B ∗′ − (1 − λ)B ∗ − λB ∗L(B ∗′ , B ′ ; S n )1+ϕ
κr∗
α
∗′
′
n 1−α
z(1
−
α)K
L(B
,
B
;
S
)
+
ψ
1 + r∗
1+ϕ



∗′
′
′
∗′
′
n
′
∗′
+ βEz ′ ,R∗′ Vt+1 B , B , K (B , B ; S ), D (B , B ′ ; S n ), z ′ , R∗′ |z, R∗−

where functions L(B ∗′ , B ′ ; S n ), K ′ (B ∗′ , B ′ ; S n ), D′ (B ∗′ , B ′ ; S n ) solve the competitive equilibrium
conditions for given values (B ∗′ , B ′ ; S n ). That is, these functions solve the following system of
equations.
– Collateral constraintβD′ (B ∗′ , B ′ ; S n ) = θN
where aggregate net worth N is defined as
N = σ αzK α L(B ∗′ , B ′ ; S n )1−α + (1 − δK )K + B(λ + (1 − λ)B) − D + (1 − σ)n̄
– Bank aggregate budget constraint
K ′ (B ∗′ , B ′ ; S n ) = (1 + θ)N − q̂n,t+1 (B ∗′ , B ′ ; S n )B ′– Government budget constraint




∗
G + λB + λB ∗ = T + q̂(B ∗′ , B ′ ; S n ) B ′ − (1 − λ)B + q̂n,t+1(B ∗′ , B ′ ; S n ) B ∗′ − (1 − λ)B ∗where T are tax revenues
T = z(1 − α)K α L(B ∗′ , B ′ ; S n )1−α + ψL(B ∗′ , B ′ ; S n )1+ϕ
Solution method: Nelder-Mead algorithm to find (L, K ′ , D′ ) that solveK ′ (B ∗′ , B ′ ; S n ) − (1 + θ)N − q̂n,t+1 (B ∗′ , B ′ ; S n )B ′∗G + λB + λB ∗ − T − q̂(B ∗′ , B ′ ; S n ) [B ′ − (1 − λ)B] − q̂n,t+1(B ∗′ , B ′ ; S n ) [B ∗′ − (1 − λ)B ∗ ]





βD′ (B ∗′ , B ′ ; S n ) − θ σ αzK α L(B ∗′ , B ′ ; S n )1−α + (1 − δ)K + B(λ + (1 − λ)B) − D + (1 − σ)n̄where, q̂n,T (B ∗′ , B ′ ; S n ) is the value qT piecewise linearly interpolated at the points (K ′ , D′ ), and∗ .
similarly for qn,T

61

=0
=0
=0

Then, value of repaying both debts isnoVtn,R (S n ) =E max Ṽtn,R (B ∗′ , B ′ ; S n ) + ξB1/ηX
exp Ṽtn,R (B ∗′ , B ′ ; S n )=η log(B ′ ,B ∗′ )∈B

where η is the scale parameter of the Extreme Value Type I shocks, ξB , which I assume is equal to
0.0001. Note also that given the assumed distribution for the borrowing shocks, we can computethe probability of the government choosing a bond portfolio of (B ∗′ , B ′ ) as
1/η

exp Ṽtn,R (B ∗′ , B ′ ; S n )π(B ∗′ , B ′ ; S n ) =

1/η
P
n,R
∗′ , B̂ ′ ; S n )
exp
Ṽ
(
B̂
t
B̂ ∗′ ,B̂ ′2. Domestic autarky (no access to domestic borrowing)
Let Ṽtd,R (B ∗′ ; S d ) be the value of repaying existing debt and issuing new debt B ∗′ :L(B ∗′ ; S d )1+ϕṼtd,R (B ∗′ ; S d ) =h(z)K α L(B ∗′ ; S d )1−α − K ′ (B ∗′ ; S d ) + (1 − δK )K − G + ψ
1+ϕ


∗
(B ∗′ ; S d ) B ∗′ − (1 − λ)B ∗ − λB ∗+ qd,t+1n+ βEz ′ ,R∗′ γVt+1 B ∗′ , 0, K ′ (B ∗′ ; S d ), D′ (B ∗′ ; S d ), z ′ , R∗′ +od+ (1 − γ)Vt+1
B ∗′ , K ′ (B ∗′ ; S d ), D′ (B ∗′ ; S d ), z ′ , R∗′ z, R∗ ,where functions L(B ∗′ ; S d ), K ′ (B ∗′ ; S d ), D′ (B ∗′ ; S d ) solve the competitive equilibrium conditions forgiven B ∗′ ; S d , that is summarize by the following system of equations:– Collateral constraintβD′ (B ∗′ ; S d ) = θN
where aggregate net worth N is defined ashi
N = σ αh(z)K α L(B ∗′ ; S d )1−α + (1 − δK )K − D + (1 − σ)n̄
– Bank aggregate budget constraint
K ′ (B ∗′ ; S d ) = (1 + θ)N– Government budget constraint∗
G + λB ∗ = T + q̂d,t+1(B ∗′ ; S d ) B ∗′ − (1 − λ)B ∗62

where T are tax revenues
T = h(z)(1 − α)K α L(B ∗′ ; S d )1−α + ψL(B ∗′ ; S d )1+ϕ
Solution method: Nelder-Mead algorithm to find (L′ , K ′ ) that solveK ′ (B ∗′ ; S d ) − (1 + θ) σ αh(z)K α L(B ∗′ ; S d )1−α + (1 − δ )K − D + (1 − σ)n̄
K
∗′
d
∗′
∗
G + λB ∗ − T − q̂ ∗(B ; S ) [B − (1 − λ)B ]
d,t+1

=0
=0

∗
∗
where, qd,t+1(B ∗′ , S d ) is the value of qd,Tpiecewise linearly interpolated at the points (K ′ , D′ )
and
i
o
θn h
σ αh(z)K α L(B ∗′ ; S d )1−α + (1 − δK )K − D + (1 − σ)n̄D′ =βThen, value of repayment isnoVtd,R (S d ) =E max Ṽtd,R (B ∗′ ; S d ) + ξB1/ηX
exp Ṽtd,R (B ∗′ ; S d )=η logB ∗′ ∈Bd

3. External autarky (no access to external borrowing)
Let Ṽte,R (B ′ ; S e ) be the value of repaying existing debt and issuing new debt B ′ :Ṽte,R (B ′ ; S e ) =h(z)K α L(B ′ ; S e )1−α − K ′ (B ′ ; S e ) + (1 − δ)K − G
L(B ′ ; S e )1+ϕ1+ϕn+ βEz ′ ,R∗′ γVt+1 0, B ∗′ , K ′ (B ′ ; S e ), D′ (B ′ ; S e ), z ′ , R∗′oe+ (1 − γ)Vt+1
B ′ , K ′ (B ′ ; S e ), D′ (B ′ ; S e ), z ′ , R∗′ z, R∗+ψwhere functions L(B ′ ; S e ), K ′ (B ′ ; S e ), D′ (B ′ ; S e ) solve the competitive equilibrium conditions
for given(B ′ ; S e ), that is summarize by the following system of equations:– Collateral constraintβD′ (B e′ ; S e ) = θN
where aggregate net worth N is defined as
N = σ αh(z)K α L(B ′ ; S e )1−α + (1 − δK )K + B(λ + (1 − λ)B) − D + (1 − σ)n̄63

– Bank aggregate budget constraint
K ′ (B e′ ; S e ) = (1 + θ)N + q̂e,t+1 (B ′ ; S e )B ′– Government budget constraint
G + λB = T + q̂e,t+1 (B ′ ; S e ) B ′ − (1 − λ)B
where T are tax revenues
T = h(z)(1 − α)K α L(B ′ ; S e )1−α + ψL(B ′ ; S e )1+ϕ
Solution method: Nelder-Mead algorithm to find (L, K ′ ) that solve
K ′ (B ′ ; S e ) − (1 + θ)N − q̂e,t+1 (B ′ ; S e )B ′G + λB − T − q̂(B ′ ; S e ) [B ′ − (1 − λ)B]βD′ (B ′ ; S e ) − θ σ αh(z)K α L(B ′ ; S e )1−α + (1 − δ )K + B(λ + (1 − λ)B) − D + (1 − σ)n̄
K

=0
=0
=0

where, q̂e,t+1 (B ′ ; S n )B ′ is the value qe,T piecewise linearly interpolated at the points (K ′ , D′ ); and D′ = θ σ αh(z)K α L1−α + (1 − δK )K + B − D + (1 − σ)n̄

Then, value of repayment isnoVte,R (S e ) =E max Ṽte,R (B ′ ; S e ) + ξB
1/ηX=η logexp Ṽte,R (B ′ ; S e )(B ′ )∈B⌉

4. Autarky in both markets: no debt issuance or default decision

Vtb (S b ) =h(z)K α L(S b )1−α − K ′ (S b ) + (1 − δ)K − G
L(S b )1+ϕ
1+ϕ
n


+ βEz ′ ,R∗′ γVt+1 0, 0, K ′ (S b ), D′ (S b ), z ′ , R∗′ +ob+ (1 − γ)Vt+1
K ′ (S b ), D′ (S b ), z ′ , R∗′ z, R∗+ψwhere functions L(S b ), K ′ (S b ), D′ (S b ) solve the competitive equilibrium conditions for givenS b ,that is summarize by the following system of equations:64

– Collateral constraintβD′ (S b ) = θN
where aggregate net worth N is defined ashi
N = σ αzK α L(S b )1−α + (1 − δK )K − D + (1 − σ)n̄
– Bank aggregate budget constraint
K ′ (S b ) = (1 + θ)N– Government budget constraint
G = h(z)(1 − α)K α L(S b )1−α + ψL(S b )1+ϕ
Default Decisions and Value Function.
1. If currently in normal times:(a) Default on external only if Vte,R (S e ) > Vtn,R (S n ), and then δt (S n ) = 1, δt∗ (S n ) = 0(b) Default on domestic only if Vtd,R (S d ) > Vtn,T (S n ), and then δt (S n ) = 0, δt∗ (S n ) = 1(c) Default on both if Vtb (S b ) > Vtn,R (S n ), and then δt (S n ) = 0, δt∗ (S n ) = 0(d) Otherwise, , and then δt (S n ) = 1, δt∗ (S n ) = 1
and therefore value is Vt (S n ) = max{Vtn,R (S n ), Vtd,R (S d ), Vte,R (S e ), Vtb (S b )}2. If currently in domestic autarky default if Vtb (S b ) > Vtd,R (S d ), and then δd,t (S d ) = 0; otherwise
δd,t (S d ) = 1
and therefore value is Vtd (S d ) = max{VTd,R (S d ), VTb (S b )}∗ (S e ) = 0; otherwise
3. If currently in external autarky default if Vtb (S b ) > Vte,R (S e ), and then δe,t
∗ (S e ) = 1
δe,t

and therefore value is Vte (S e ) = max{Vte,R (S e ), Vtb (S b )}∗ , δ ), compute prices that creditors will offer
Bond Prices. Given repayment decisions, (δt∗ , δt , δe,td,t
to the government at t = T − 1qt∗ (B ∗′ , B ′ , K ′ , D′ ; z, R∗ ) =

n
o


1
∗
∗′
′
′
′ ′
∗′
∗
′
∗
′ ,R∗′
(S
)
z,
R
E
δ
(B
,
B
,
K
,
D
,
z
,
R
)
λ
+
(1
−
λ)q
z
t
T
Rt∗

65

∗
qd,t
(B ∗′ , K ′ , D′ ; z, R∗ ) =




1
′
∗′
E
γδt∗ (B ∗′ , 0, K ′ , D′ , z ′ , R∗′ ) λ + (1 − λ)qT∗ (S ′ )
z ,R
∗
Rt



∗
∗
+ (1 − γ)δe,t(B ∗′ , K ′ , D′ , z ′ , R∗′ ) λ + (1 − λ)qd,T(S ′ ) z, R∗Ez ′ ,R∗′ νT (S ′ )δT (S ′ ) [λ + (1 − λ)qT (S ′ )] z, R∗qt (B ∗′ , B ′ , K ′ , D′ ; z, R∗ ) =Ez ′ ,R∗′ νT (S ′ )FK (B ∗′ , B ′ , K ′ , D′ , z ′ , R∗′ ) z, R∗ )1
qe,t (B ∗′ , K ′ , D′ ; z, R∗ ) =d (S e′ )′′′′Ez ′ ,R∗′ γνT (S )FK (0, B , K , D , z ′ , R∗′ ) + (1 − γ)νe,T (S ′ )FK(
× Ez ′ ,R∗′ γνT (S ′ )δt (0, B ′ , K ′ , D′ , z ′ , R∗′ ) λ + (1 − λ)qT (S ′ )+ (1 − γ)νe,T (S ′ )δd,t (B ′ , K ′ , D′ , z ′ , R∗′ ) λ + (1 − λ)qd,T (S ′ ) z, R∗)d (S d ) = h(z)αK α−1 L(S d )1−α .
where, FK (S n ) = zαK α−1 L(S n )1−α and FK

Value of the Bank. Finally, we need to compute the marginal value of a unit in the bank ν,which is given by (16). In particular,
νt (S) = βEz ′ ,R∗′Xhπ(B ∗′ , B ′ ; S) FK (B ∗′ , B ′ , K ′ , D′ , z ′ , R∗′ )(B ∗′ ,B ′ )∈Bi+ θνT (B ∗′ , B ′ , K ′ , D′ , z ′ , R∗′ ) z, R∗ ,and similarly for the other autarky states.

Iterate Backwards and Check Convergencee |, |V d − V d |, |V b − V b | , andCheck value function convergence: d = max |Vnt − Vt−1 |, |Vte − Vt−1
t
t
t−1
t−1
o
q
∗
∗
∗
∗
bond price schedule convergence, d = max |qt − qt−1 |, |qe,t − qe,t−1 |, |qt − qt−1 |, |qd,t − qd,t−1| ,update them and iterate until convergence.

Simulate Equilibrium Results
1. Start from a given initial state S0 = (B0∗ , B0 , K0 , D0 , z0 , R0∗ , a0 )2. Using value functions, policy functions in equilibrium, and extreme value shocks for the determination of borrowing, find new assets, A1 ≡ (B1∗ , B1 , K1 , D1 ); given repayment decision
δ(S0 ), δ ∗ (S0 ), update (intra-period) autarky state
3. Realization of new shocks: productivity, z1 , international interest rate, R1∗ , and, if intra-period
autarky-state ã = {d, e, b}, re-enter credit markets with probability γ, and updated autarky
state, a1 correspondingly.
66

4. Start with new state S1 = (B1∗ , B1 , K1 , D1 , z1 , R1∗ , a1 ), and iterate for T = 50000 periods.

67

Appendix E
E.1

Additional Empirical Evidence

Domestic Debt Definition

The definition used in the empirical evidence for domestic vs. external debt is by the jurisdiction
where the debt is issued. This data is taken from Reinhart and Rogoff (2011). The definition in
the model is based on who holds the debt: domestic vs. foreign investors. However, in the data
the two definitions align in most cases. Using data from Arslanalp and Tsuda (2014), I compare
these two definitions for the years in which we have information on both series and for the countries
in the sample (for most countries, this time period is 1999-2010). Figure 14 compares the shareof domestic debt using each definition, and it can be seen that the correlation is high for the twoseries. Moreover, Table 10 compares the main statistics of the series for the overlapping periods,
and we can see that they are remarkably similar.

.8
.6
.4

correlation = 0.871.2Domestic share: by holder

1

Figure 14: Domestic debt share by definition

.2

.4

.6

.8

Domestic share: by jurisdiction

Table 10: Domestic debt definition
By holderBy jurisdiction

Mean

0.547

0.549

Median

0.577

0.570

P25

0.341

0.360

P75

0.752

0.780

68

1

E.2

Descriptive Statistics: Different Time Periods

Table 11 shows the same descriptive statistics as in the main text in Table 1, but compares two
different periods in time: the period 1969-1996 is the one used in the main analysis as is the relevant
one for analyzing the monetary shocks to the U.S. interest rate, and the period 1960-2007 for whichdata is available.
Table 11: Descriptive Statistics
1969-1996

1960-2007

LiquidDomestic

Total

External

LiquidDomestic

Total

External

liabilities

debt sharedefaults

defaults

liabilities

debt sharedefaults

defaults

Argentina

0.172

0.449

2

0

0.184

0.306

3

0

Brazil

0.172

0.848

2

0

0.275

0.787

4

2

Chile

0.267

0.489

1

1

0.340

0.583

4

4

China

0.636

0.359

0

0

0.849

0.443

0

0

Colombia

0.189

0.398

0

0

0.189

0.406

0

0

Ecuador

0.177

0.418

1

1

0.194

0.219

2

1

India

0.297

0.761

2

2

0.389

0.797

2

2

Indonesia

0.194

0.034

1

1

0.261

0.126

4

4

Malaysia

0.632

0.762

0

0

0.868

0.759

0

0

Mexico

0.222

0.562

1

0

0.223

0.460

2

1

Peru

0.186

0.186

6

5

0.245

0.179

6

5

South Africa

0.514

0.958

3

3

0.483

0.937

3

3

Thailand

0.474

0.752

0

0

0.665

0.773

0

0

Turkey

0.195

0.526

2

2

0.239

0.553

2

2

Total

0.312

0.540

22

16

0.370

0.581

31

23

Sources: World Bank Financial Structure and Development, and Reinhart and Rogoff (2011).
Notes: Last row shows the average liquid liabilities to GDP and domestic debt share for the countries in the sample.
Total defaults refers to the number of years a given country defaulted on either type of debt, and External defaults
refers to the number of years a country defaulted only on external debt.

69

E.3

Effect of Interest Rates on Emerging Countries: Robustness Exercises

Sample of Countries. In the baseline sample there are 7 countries from Latin America and 4
East Asian, as well as Turkey and South Africa. Here, I show that the negative output response
after a shock to the U.S. interest rates is present regardless of the sub-sample of countries that we
consider. The left panel of Figure 15 shows the estimated response of real GDP when only countries
in Latin America are considered in equation (2), and the right panel shows the response for East
Asian countries. Real GDP drops around 0.6 percent in Latin America, and around 0.4 percent inEast Asia.
Figure 15: Output response by sample of countries
East Asia

0
-.2
-.4
-1

-1

-.8

-.6

Output change, %

0
-.2
-.4
-.6
-.8

Output change, %

.2

.2

.4

.4

Latin America

0

4

8

12

16

20

24

0

4

Quarters after shock

8

12

16

20

24

Quarters after shock

Volcker Period. Another potential concern about the results on the effect of interest rate shocks
on emerging countries is whether results are partially driven by the Volcker shock. The beginningof 1980s was a period characterized by large increases in the U.S. interest rates which was followed
by several crisis in developing countries. To see the effect of this period in the main results, I run
regression (2) taking out the years of the Volcker shock: 1980-1985. Figure 16 shows the results
for the two sample periods considered in the paper. The results do not change if we exclude theVolcker shock years.
Figure 16: Output response excluding Volcker shock periods
1960-2010

0
-.2
-.8

-.6

-.4

Output change, %

0
-.2
-.4
-.6
-.8

Output change, %

.2

.2

.4

.4

1969-1996

0

4

8

12

16

20

24

0

Quarters after shock

4

8

12

16

Quarters after shock

70

20

24

E.4

Financial Development and External Shocks: Robustness

In this section, I show robustness exercises regarding the results on the difference in the vulnerabilityof emerging countries to interest rate shocks by their level of financial development. To this end,
regression (3) is estimated in a number of different sub-samples including different time period,
countries, and excluding the Volcker shock periods. Table 12 shows the results for all sub-samples.
The main result prevails: the coefficient γh is positive and significantly so for many quarters after
the shock. This indicates that a higher level of financial development, measured as liquid liabilities
to GDP, mitigates the drop in output in emerging countries from a shock that increases U.S. interest
rates.
Table 12: Output response and financial development: Robustness
Interaction coefficient, γhQuarters after shock:

4

6

8

10

12

16

All countries 1960-2007

0.015∗∗∗

0.026∗∗∗

0.023∗∗

0.019

0.010

-0.004(0.006)(0.008)(0.009)(0.008)(0.009)(0.008)

0.024

0.037

0.055

0.082∗

0.095∗-0.008(0.036)(0.033)(0.041)(0.047)(0.051)(0.043)0.051

0.102∗∗∗

0.117∗∗∗

0.101∗∗

0.065∗∗

0.007(0.034)(0.035)(0.042)(0.041)(0.044)(0.041)0.010

0.014∗

0.020∗

0.013

0.021∗-0.001(0.007)(0.008)(0.011)(0.010)(0.011)(0.008)0.019∗∗∗

0.030∗∗∗

0.024∗∗

0.014

0.009

-0.009(0.007)(0.011)(0.012)(0.010)(0.011)(0.011)All countries 1969-1996

0.008

0.015

0.030∗

0.024

0.036∗-0.006

excluding Volcker shock(0.012)(0.013)(0.017)(0.018)(0.021)(0.013)All countries 1960-2007

0.015∗

0.027∗∗∗

0.031∗∗

0.020

0.013

0.002

excluding Volcker shock(0.009)(0.010)(0.011)(0.013)(0.012)(0.013)Latin America 1969-1996

Latin America 1960-2007

East Asia 1969-1996

East Asia 1960-2007

Driscoll-Kraay standard errors in parentheses.

E.5∗

p<0.1, ∗∗ p<0.05, ∗∗∗ p<0.01

Financial Development and Domestic Debt: 1960-2007

Here, I consider the same regression as in (1) but focus on the broader sample period from 1960 to2007. Results are reported in Table 13, which shows that higher financial development is associatedwith a larger share of domestic debt. The magnitudes are also similar to the baseline sample
1969-1996.

71

Table 13: Domestic debt and financial development
(1)

(2)

(3)

0.332∗∗∗

0.420∗∗∗

0.189∗∗∗(0.045)(0.070)(0.076)-0.156∗∗∗-0.168∗∗∗-0.103∗∗∗(0.046)(0.032)(0.035)0.432*-16.497∗∗∗-1.409(1.316)(3.236)(5.130)Country Effects

No

Yes

Yes

Year Effects

No

No

Yes

Observations

516

516

516

Financial development

Total debt to GDP

Log GDP per capita

Standard errors in parentheses. * p<0.1, ** p<0.05, *** p<0.01

E.6

U.S. Interest Rate and Real Exchange Rate

Here I show the results for the estimation of the bivariate process for the U.S. interest rate and thereal exchange rate between the United States and each of the emerging countries considered in thesample, as specified in equation (31). I estimate the process for each country separately and thentake averages of each of the coefficients. The estimation is done using the average quarterly U.S.
Federal funds rate, and the average quarterly log real exchange rates. The estimated coefficients
are
"
# "
# "
#"
# "
#"
#
∗
rt+1
0.00110.933 0.000
rt∗
0.00001 0.00000
ϵrt+1
=
+
+
. (71)
et+1−0.0198
1.237 0.967
et−0.00002 0.01076
ϵet+1
Figure 17 plots the resulting impulse response of a shock that increases the annualized interest
rate by 100 basis points.
Figure 17: Bivariate VAR process for r∗ and eReal exchange rate

%
0

-1

.2

0

.4

%

.6

1

.8

2

1

International interest rate

0

10

20

30

40

0

Quarters since shock

10

20

Quarters since shock

72

30

40