Interest rate shocks andthe composition of sovereign debt
Eugenia Gonzalez-Aguado
Toulouse School of Economics

Fiscal Policy and Sovereign Debt
IMF-CARF-TCER-Waseda University Conference
June 2024, Tokyo

0 / 24

Motivation• Emerging countries borrow large share of their government debt from foreign investors→ they are exposed to world interest rate fluctuations• Increase in US interest rates associated with large declines in output in emerging countries• Why not borrow domestically instead?
- would avoid external shocks that aﬀect interest rates- but, domestic debt crowds out investment in capital

1 / 24

Motivation• Emerging countries borrow large share of their government debt from foreign investors→ they are exposed to world interest rate fluctuations• Increase in US interest rates associated with large declines in output in emerging countries• Why not borrow domestically instead?
- would avoid external shocks that aﬀect interest rates- but, domestic debt crowds out investment in capital• This paper:- quantitative sovereign default model with endogenous decision on debt composition- accounts for patterns observed in data
- quantify the role of financial development and domestic debt to mitigate exposure
1 / 24

Summary of empirical evidence• Panel of 14 emerging countries during 1960-2007 (some analyses restricted to 1969-1996)• Domestic debt and defaults data from Reinhart and Rogoﬀ (2011)
Main results:
1. Financial development positively related to share of domestic debt
- financial development measured as liquid liabilities to GDP (direct link to model)
2. Negative eﬀects of increase in U.S. interest rate on emerging economies output- larger drop in output if less financially developed
3. Domestic debt crowds out capital- Broner et al (2014): ↑ banks’ holdings of gov’t debt, ↓ private credit in Euro Area
- I document crowding out in emerging countries

2 / 24

Summary of empirical evidence• Panel of 14 emerging countries during 1960-2007 (some analyses restricted to 1969-1996)• Domestic debt and defaults data from Reinhart and Rogoﬀ (2011)
Main results:
1. Financial development positively related to share of domestic debt
- financial development measured as liquid liabilities to GDP (direct link to model)
2. Negative eﬀects of increase in U.S. interest rate on emerging economies output- larger drop in output if less financially developed
3. Domestic debt crowds out capital- Broner et al (2014): ↑ banks’ holdings of gov’t debt, ↓ private credit in Euro Area
- I document crowding out in emerging countries

2 / 24

Output response to increase in U.S. interest rate′
yit+h = βh urt + Γih Xit+ αih + εit+h(1)• Controls, Xit include:- lagged output, interest rates, exchange rates, and linear and quadratic time trends• After a shock that ↑ U.S. interest rate by 1 pp, real GDP ↓ 0.4% in emerging countries.20• Other specifications: [see]-.2• Romer-Romer shocks: 1969-1996-.4- other shocks-.6- real exchange rates- time period 1960-2007

-.8

%

.4

Output Emerging Countries

0

4

8

12
Quarters

16

20

24

3 / 24

Output response and financial development′
yit+h = βh urt + γh (urt × Fin Devit−1 ) + Γih Xit+ αih + εit+h(2)• Financial development: measure of liquid liabilities to GDP• If coeﬃcient γh is positive: financial dev. mitigates the drop in output after shock

4 / 24

Output response and financial development′
yit+h = βh urt + γh (urt × Fin Devit−1 ) + Γih Xit+ αih + εit+h(2)• Financial development: measure of liquid liabilities to GDP• If coeﬃcient γh is positive: financial dev. mitigates the drop in output after shock
Interaction coeﬃcient, γhQuarters after shock:

4

6

8

10

12

16

0.008

0.012

0.018∗

0.020∗∗

0.022∗∗

0.000(0.006)(0.008)(0.010)(0.009)(0.010)(0.008)Driscoll-Kray standard errors in parentheses.

∗

p<0.1, ∗∗ p<0.05, ∗∗∗ p<0.01• At the 75th percentile of financial dev. (high FD), output drops less than 0.2pp• At the 25th percentile (low FD), output drops 0.6pp
4 / 24

Output response and financial development• Alternatively, consider two separate regressions: for low and high financial dev.
′
Low
Low
yit+h = βhLow urt + ΓLow
ih Xit + αih + εit+hif

Fin Devit < P50(Fin Devt )High′
yit+h = βhHigh urt + ΓHigh+ εHighih Xit + αih
it+h

if

Fin Devit > P50(Fin Devt )

-.6

-.4

%

-.2

0

.2

Output drop by financial development-.8

Low FDHigh FD[other specifications]04

8Quarters

12

16
5 / 24

Key ingredients and intuition for model• Emerging countries suﬀer output losses after increase in international interest rates- exposed through sovereign debt issued to external creditors→ important to consider sovereign debt composition

6 / 24

Key ingredients and intuition for model• Emerging countries suﬀer output losses after increase in international interest rates- exposed through sovereign debt issued to external creditors→ important to consider sovereign debt composition• Model introduces key trade-oﬀs between domestic and external debt
- domestic debt could mitigate exposure to international shocks- but, crowds out capital: especially costly if less financially developed

6 / 24

Key ingredients and intuition for model• Emerging countries suﬀer output losses after increase in international interest rates- exposed through sovereign debt issued to external creditors→ important to consider sovereign debt composition• Model introduces key trade-oﬀs between domestic and external debt
- domestic debt could mitigate exposure to international shocks- but, crowds out capital: especially costly if less financially developed• Main intuition in line with empirical results- financial development mitigates eﬀect on output of an increase in interest rates- because it allows countries to borrow more domestically- this mechanism is present in data: more financial dev., larger domestic debt share [see]→ model must introduce financial intermediaries to capture notion of financial development
6 / 24

Model Overview• Small open economy business cycle model that integrates- banking sector (financial intermediaries)- into sovereign default model with productivity and interest rate shocks- domestic and external government debt

7 / 24

Model Overview• Small open economy business cycle model that integrates- banking sector (financial intermediaries)- into sovereign default model with productivity and interest rate shocks- domestic and external government debt

• Households:- consume and save using deposits at banks- supply labor and pay taxes

7 / 24

Model Overview• Small open economy business cycle model that integrates- banking sector (financial intermediaries)- into sovereign default model with productivity and interest rate shocks- domestic and external government debt

• Households:- consume and save using deposits at banks- supply labor and pay taxes• Firms:- production: Y = zF (K, L)- z is aggregate productivity shock that follows AR1 process- working capital

7 / 24

Model Overview• Small open economy business cycle model that integrates- banking sector (financial intermediaries)- into sovereign default model with productivity and interest rate shocks- domestic and external government debt

• Households:- consume and save using deposits at banks- supply labor and pay taxes• Firms:- production: Y = zF (K, L)- z is aggregate productivity shock that follows AR1 process- working capital• Int’l creditors:- risk neutral and unconstrained, invest in external government debt
- stochastic international risk free rate, R∗[see details]
7 / 24

Model Overview• Banks:- financial intermediaries- receive deposits from households- invest in capital and domestic government debt
- collateral constraint limits borrowing from households→ financial development captured by collateral constraint→ domestic gov’t debt crowds out investment in capital due to collateral constraint

8 / 24

Model Overview• Banks:- financial intermediaries- receive deposits from households- invest in capital and domestic government debt
- collateral constraint limits borrowing from households→ financial development captured by collateral constraint→ domestic gov’t debt crowds out investment in capital due to collateral constraint• Government:- finances public expenditures using◦ distortionary taxes on labor income◦ government debt: external and domestic- can separately default on external and domestic debt

- note: bonds are long-term, but here for exposition show model with one-period bonds
8 / 24

Bank Problem• Aggregate state: S = (A, a, z, R∗ )- A = (B ∗ , B, K, D) are assets: bonds, capital, and deposits- a is default or autarky state (defined later)- z and R∗ are stochastic states

9 / 24

Bank Problem• Aggregate state: S = (A, a, z, R∗ )- A = (B ∗ , B, K, D) are assets: bonds, capital, and deposits- a is default or autarky state (defined later)- z and R∗ are stochastic states• Banks receive deposits, d, from households at price q D• Invest in: - capital with stochastic returns RK = zFK + 1 − δK
- defaultable domestic bonds, b, at price q• Collateral constraint: can only obtain fraction θ of net worth from deposits• Die with probability 1 − σ. If so, transfer net worth, n, to household- ensures banks build up of net worth limited, so collateral constraint binds
9 / 24

Bank Problem
Value of bank with net worth n:
󰁱
󰁲
′
b ′
′
V b (n; S) = max
βE[(1
−
σ)n
+
σV
(n
;
S
)]
′ ′ ′
k ,b ,ds.t.
• Budget constraint:k ′ + q(S)b′ = n + q D (S)d′• Collateral constraint:q D (S)d′ ≤ θn

• Evolution of net worth:n′ = RK (S ′ )k ′ + δ(S ′ )b′ − d′where δ(S) = {0, 1} is government repayment decision on domestic debt

10 / 24

Bank Problem
Value of bank with net worth n:
󰁱
󰁲
′
b ′
′
V b (n; S) = max
βE[(1
−
σ)n
+
σV
(n
;
S
)]
′ ′ ′
k ,b ,ds.t.
• Budget constraint:k ′ + q(S)b′ = n + q D (S)d′• Collateral constraint:q D (S)d′ ≤ θn

• Evolution of net worth:n′ = RK (S ′ )k ′ + δ(S ′ )b′ − d′where δ(S) = {0, 1} is government repayment decision on domestic debt
- note: assume households utility is U (C, L) = C + v(L), so, deposits price: q D (S) = β
10 / 24Government• Provides public goods G and maximizes utility by choosing- taxes on labor income: τ- domestic and external debt: B, B ∗- domestic and external repayment: δ, δ ∗• Resulting optimal program: smoothes tax distortions by borrowing• Exogenous default costs: identical for both types of default- autarky: lose access to credit market in which it defaults (re-enter with probability γ)- productivity during autarky: h(z) ≤ z• Autarky states a = {normal, domestic autarky, external autarky, both}

11 / 24Government Budget Constraint
Government budget constraint in four states:• Normal times:

G + δB + δ ∗ B ∗ = τ w(S)L + δq(S)B ′ + δ ∗ q ∗ (S)B ∗′• Domestic autarky: no B

G + δ ∗ B ∗ = τ w(S)L + δ ∗ q ∗ B ∗′12 / 24Government Budget Constraint
Government budget constraint in four states:• Normal times:

G + δB + δ ∗ B ∗ = τ w(S)L + δq(S)B ′ + δ ∗ q ∗ (S)B ∗′• Domestic autarky: no B
• External autarky: no B ∗G + δ ∗ B ∗ = τ w(S)L + δ ∗ q ∗ B ∗′G + δB = τ w(S)L + δq(S)B ′• Autarky in both markets: no B or B ∗G = τ w(S)L12 / 24

Markov Equilibrium• A Markov equilibrium consists of- policy functions π(S) = (δ ∗ , δ, B ∗′ , B ′ , τ )- allocation rules Y (S) = (C, L, B ∗′ , B ′ , K ′ , D′ )- pricing functions P (S) = (q, q ∗ , q D , RK , w)

such thati. associated outcomes are competitive equilibria [see definition]ii. given allocation rules, pricing rules, and future policy rules, then the current policy π(S)is optimal for the government

13 / 24

Markov Equilibrium• A Markov equilibrium consists of- policy functions π(S) = (δ ∗ , δ, B ∗′ , B ′ , τ )- allocation rules Y (S) = (C, L, B ∗′ , B ′ , K ′ , D′ )- pricing functions P (S) = (q, q ∗ , q D , RK , w)

such thati. associated outcomes are competitive equilibria [see definition]ii. given allocation rules, pricing rules, and future policy rules, then the current policy π(S)is optimal for the government• Use primal approach:- government directly chooses current allocations and policies- s.t. implementability constraints: constraints that summarize all FOC and budget
constraints of competitive equilibrium
13 / 24

Main mechanisms of the model
1. Main trade-oﬀs in sovereign debt compostion: [see FOC]
- cost of domestic debt: it crowds out investment in capital◦ bank budget + collateral constraint: K ′ = (1 + θ)N − qB ′→ crowding out eﬀect

14 / 24

Main mechanisms of the model
1. Main trade-oﬀs in sovereign debt compostion: [see FOC]
- cost of domestic debt: it crowds out investment in capital◦ bank budget + collateral constraint: K ′ = (1 + θ)N − qB ′→ crowding out eﬀect- benefit of domestic debt: lower default probability on domestic ⇒ lower interest rate
◦ domestic default hurts own banks as it decreases its net worth
N = σ(RK K + δB − D) + (1 − σ)n̄14 / 24

Ex-post incentives to default
Default decisions for a given amount of external and domestic debt

.01

.01

.02

Default bothDefault both

.03

.04

Default
only external.02

External debt

.03

Default
only external

No default

No default

0

.01

.02

.03

Domestic debt

.04

0

Only domestic →0External debt

.04

.05

High productivity.05

Low productivity

.05

0

.01

.02

.03

.04

.05

Domestic debt

15 / 24Government borrowing decisions
External borrowing
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

.01

.02

.03

.04

.05

0

1.105

3.79

Optimal00.01External borrowing, B*'

.02

.03

.04

.05

0

.01

External borrowing, B*

.02

.03

.04

.05

.04

.05

External borrowing, B*'

Domestic borrowing
qB'
.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

.01

.02

.03

.04

.05

0

1.105

3.79

Optimal
0

0

.01

.02

.03

.04

.05

0

.01

.02

.03

16 / 24

Main mechanisms of the model
1. Main trade-oﬀs in sovereign debt compostion: [see FOC]
- cost of domestic debt: it crowds out investment in capital◦ bank budget + collateral constraint: K ′ = (1 + θ)N − qB ′→ crowding out eﬀect- benefit of domestic debt: lower default probability on domestic ⇒ lower interest rate
◦ domestic default hurts own banks as it decreases its net worth
N = σ(RK K + δB − D) + (1 − σ)n̄2. How does an increase in interest rate aﬀect output?
- gov’t budget constraint:

G + B + B ∗ = T (L) + qB ′ + ↓ q ∗ B ∗′- substitute external debt with taxes (↓ L) and domestic debt (↓ K ′ )16 / 24

Quantitative analysis• Set model parameters to match features of emerging economies on average [see all]- government expenditures to GDP, total debt to GDP, default rates, and- share of domestic rate and deposits to GDP

17 / 24

Quantitative analysis• Set model parameters to match features of emerging economies on average [see all]- government expenditures to GDP, total debt to GDP, default rates, and- share of domestic rate and deposits to GDP
Results:
1. Model can generate drop in output after increase in R∗- role of domestic debt: mitigates the decrease in output
2. The role of financial development:- change collateral constraint parameter θ to capture low and high financial development- model accounts for key empirical findings on debt composition and financial dev.
3. Pecking order of default: in mild recessions default only on external
17 / 24

Output response to ↑ R∗
• Impulse response to shock that increases R∗ by 100 basis points• Conterfactuals: only allow for domestic or external debt (keeping parameters the same)- domestic debt mitigates drop in output

external
baseline
domestic

0

-.4

.2

.4

pp

.6

percentage points
-.3
-.2

-.1

.8

0

Output1

Interest rate

0

4

8

12

Quarters after shock

16

20

0

4

8

12

16

20

Quarters after shock

18 / 24

Output response to ↑ R∗
• Domestic debt mitigates drop in output
External Debt
0.006

Domestic Debt

debt
-.004

.004
0

-.008

-.006

.002

debt

external
baseline
domestic-.002

external
baseline
domestic

4

8

12

16

20

0

4

8

12

Quarters after shock

Quarters after shock

Tax Rate

Capital

16

20

0

.4

0

.1

-.1

capitalpercentage points
.2

-.05

.3

external
baseline
domestic

0-.15

external
baseline
domestic

0

4

8

12

Quarters after shock

16

20

0

4

8

12

16

20

Quarters after shock

19 / 24

The role of financial development• Bank collateral constraint: βD′ ≤ θN
• Level of financial development captured by θ
- baseline: choose θ to match average deposits to GDP- now: change only θ to match low (25th perc.) and high (75th) deposits to GDP from data
Data

Model

Low FDHigh FDLow θHigh θ

Deposits to GDP

0.20

0.45

0.22

0.42

Domestic debt share

0.36

0.68

0.18

0.71

• Model predicts: less financial development, lower share of domestic government debt
- consistent with data [see]20 / 24

Financial development and output response• Impulse response to shock that increases R∗ by 1pp

-.3

%
-.2

-.1

0

Output-.4

low FDhigh FD
0

4

8

12

16

20

Quarters after shock• When financial development is low, output drop is larger, as in data
- low financial development: larger crowding out eﬀect of domestic debt
- more costly to replace external debt by domestic debt due to crowding out
21 / 24

Output response to ↑ R∗
• Impulse response to shock that increases R∗ by 1pp
Domestic Debt

External Debt

-.002
%
-.004

%

8

12

16

20

-.006

0

4

8

12

16

20

0

4

8

12

Quarters after shock

Quarters after shock

Tax rate

Labor

Capital

0

%

%
-.002

.2

-.003

-.1

.1

pp

20

-.05

-.001

low FDhigh FD

16

0

Quarters after shock

.3

4

0

-.4

low FDhigh FD
0

-.008

.001

-.3

.002

%
-.2

.003

-.1

low FDhigh FD0low FDhigh FD

.004

0

.005

Output4

8

12

Quarters after shock

16

20

0

4

8

12

Quarters after shock

16

20

low FDhigh FD-.15

low FDhigh FD

-.004

0

0

0

4

8

12

16

20

Quarters after shock

22 / 24

Patterns of discriminatory default• In mild recessions: default only on external debt
• In severe/long recessions: default on both
Data
Output deviation from trend:

Model

External only

Both

External only

Both

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:

74%

26%

67%

33%

Note: the periods before and after default correspond to the average over the previous andfollowing year of default, respectively.

• Key for this result: model generates countercyclical share of domestic debt (as in the data)
23 / 24

Conclusions• This paper develops a business cycle model of sovereign default with- endogenous debt composition- separate default by type of debt
- theory of vulnerability by level of financial development• Model consistent with- relationship btw financial development and vulnerability of countries to external shocks- patterns of discriminatory default and pecking order to default• Evaluate policies to limit vulnerability- domestic debt mitigates eﬀect of external shocks: but only if financially developed- restricting external debt could depress economy by crowding out capital
24 / 24

24 / 24Comparison of domestic debt databases

1980

2000

Arslanalp-Tsuda

2020

1
.8
0

.2

domestic debt share
.4
.6

.8
0

.2

domestic debt share
.4
.6

.8
domestic debt share
.4
.6
.2
0

1960

1960

Reinhart-Rogoff

1980

2000

Arslanalp-Tsuda

2020

2020

1
domestic debt share
.4
.6
.2
0

1960

Reinhart-Rogoff

1980

2000

Arslanalp-Tsuda

2020

1980

2020

1
0

.2

domestic debt share
.4
.6

.8

1
.8
.2

Reinhart-Rogoff

2020

Reinhart-Rogoff

Philippines

0

2000

2000

Arslanalp-Tsuda

domestic debt share
.4
.6

.8
domestic debt share
.4
.6
.2
0

1980
Arslanalp-Tsuda

1960

Reinhart-Rogoff

Mexico1

Malaysia

1960

2020

Reinhart-Rogoff

.8

1
.8
.2

2000

2000

Indonesia

01980
Arslanalp-Tsuda

1980
Arslanalp-Tsuda

domestic debt share
.4
.6

.8
domestic debt share
.4
.6
.2
0

1960

1960

Reinhart-Rogoff

India

1

Ecuador[back]

Colombia

1

Brazil1

Argentina

1960

1980
Arslanalp-Tsuda

2000
Reinhart-Rogoff

2020

1960

1980
Arslanalp-Tsuda

2000

2020

Reinhart-Rogoff

24 / 24

Output response: alternative specifications• Real exchange rates:- an increase in U.S. interest rates might cause a change in real exchange rates- this could aﬀect decision on domestic vs. external debt, and output response to the shock• Add current bilateral real exchange rates, eit in regressions′
yit+h = βh urt + ρih eit+h + Γih Xit+ αih + εit+h

(3)

-.6

-.4

-.2

%

0

.2

.4

Output Emerging Countries

0

4

8

12
Quarters

16

20

24

24 / 24

Output response: alternative specifications• Large literature on how to measure monetary policy shocks• In the baseline specification, I considered Romer and Romer shocks- most used in recent studies• Other shocks:- define shock to interest rate as residual from Taylor rule

rtUS =

4󰁛j=1

US
β1j yt−1
+

4
󰁛
j=1

US
β2j rt−1
+

4
󰁛
j=1

β3j pUS
t−1 +

4
󰁛

US
β4j Mt−1
+ ut

(4)

j=1

24 / 24

Output response: alternative specifications• Other shocks:- define shock to interest rate as residual from Taylor rule

-.5

-.4

-.3

-.2

%
-.1

0

.1

.2

.3

Output: Different Shocks

0

4

8

Romer-Romer

12
Quarters

16

Iacoviello-Navarro

20

24

Ramey/Coibon• Very similar results when using other shocks specifications[back]

24 / 24

Output response: alternative specifications• For the period 1969-2007: similar in magnitude but maximum response comes later

-.6

-.4

-.2

%

0

.2

.4

Output: Different Time Periods

0

4

8

12
Quarters

1969-1996[back]

16

20

24

1969-2007

24 / 24

Output response and financial development′
yit+h = βh urt + γh (urt × Fin Devit−1 ) + ρih eit+h + Γih Xit+ αih + εit+h(5)• If coeﬃcient γh is positive:- higher financial dev. mitigates the drop in output after a shock that ↑ U.S. interest rate

24 / 24

Output response and financial development′
yit+h = βh urt + γh (urt × Fin Devit−1 ) + ρih eit+h + Γih Xit+ αih + εit+h(5)• If coeﬃcient γh is positive:- higher financial dev. mitigates the drop in output after a shock that ↑ U.S. interest rate
Interaction coeﬃcient, γhQuarters after shock:

1

4

6

8

10

12

16

1969-1996

0.006

0.008

0.012

0.018∗

0.020∗∗

0.022∗∗

0.000(0.008)1969-2007(0.005)(0.006)(0.008)(0.010)(0.009)(0.010)0.004

0.014∗∗

0.024∗∗∗

0.021∗∗∗

0.018∗∗

0.010-0.006(0.003)(0.005)(0.008)(0.008)(0.008)(0.009)(0.010)Driscoll-Kray standard errors in parentheses.

∗

p<0.1, ∗∗ p<0.05, ∗∗∗ p<0.01• At the 75th percentile of financial dev. (high FD), output drops less than 0.2pp• At the 25th percentile (low FD), output drops 0.6pp

24 / 24

Household Problem• State of households: existing deposits, D• Aggregate state S = (A, a, z, R∗ ) where A = (B ∗ , B, K, D) are assets and a is default state• Value of the household:V h (D; S) = max′ {C + v(L) + G + βEV h (D′ ; S ′ )}L,Dsubject to budget constraint
C + q D (S)D′ = (1 − τ )w(S)L + D + X − (1 − σ)n̄where
• X are aggregate dividends from banks• w are wages• (1 − σ)n̄ are transfers s.t. each newborn bank has initial net worth n̄[back]
24 / 24

Firm Problem• Rent capital from banks at price RK , depreciates at rate δK• Hire workers at wage w• Working capital: pay a fraction κ of salaries in advancemax zF (K, L) + (1 − δK )K − RK K − wL(1 + r∗ κ)K,L• FOC:RK = zFK (K, L) + 1 − δKw(1 + r∗ κ) = zFL (K, L)[back]
24 / 24

International Creditors• Competitive risk neutral international creditors can invest in- defaultable external government debt
- international risk free asset: return R∗ follows AR1• Given the repayment rule of the government, δ ∗ (·), schedule of bond prices q ∗ (·) oﬀered toa government depends on- new assets: A′ ≡ (B ∗′ , B ′ , K ′ , D′ )- productivity z, world interest rate, R∗ , and autarky state ã• Bond prices: lenders indiﬀerent risk free asset and lending to gov’t󰁫󰁬󰀏E δ ∗ (A′ ; a′ , z ′ , R∗′ )󰀏ã, z, R∗R∗ =q ∗ (A′ ; ã, z, R∗ )determines bond schedule q ∗ (·) [back]

24 / 24

Output response and financial development• Alternatively, consider two separate regressions: for low and high financial dev.
′
Low
Low
yit+h = βhLow urt + ΓLow
ih Xit + αih + εit+hif

Fin Devit < P50t (Fin Devt )High′
yit+h = βhHigh urt + ΓHigh+ εHighih Xit + αih
it+h

if

Fin Devit > P50t (Fin Devt )

-.6

-.4

%

-.2

0

.2

Output drop by financial development-.8

Low FDHigh FD[back]

0

4

8
Quarters

12

16
24 / 24Competitive Equilibrium
Given policy π(S) = (τ, B ′ , B ∗′ , δ, δ ∗ ) a competitive equilibrium consists of• allocations Y (S) = (C, L, A′ ),• value functions of households and banks, V h (S), ν(S)• pricing functions P (S) = (q, q ∗ , q D , RK , w)
such that:i. solve households, banks, and firms optimization problem
ii. international creditors’ condition is satisfied
iii. policy satisfies government budget constraint
iv. allocation satisfies country-level budget constraint[back]
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Parameters1+φ• Disutility of labor: v(L) = ψ L1+φ

• Exogenous productivity loss in autarky: h(z) = z − max{ζ0 z + ζ1 z 2 , 0}
Assigned parameters:
Parameter
Average world risk free rate
Risk free rate autocorrelation
Risk free rate standard dev.
Capital share
Debt decay rate
Autarky duration
Inverse Frisch elasticity
Productivity autocorrelation
Working capital[back]µR = 0.017
ρR = 0.955
σR = 0.003
α = 0.3
λ = 0.05
γ = 0.080
φ = 0.5ρz = 0.95
κ = 0.26

SourceAverage US interest rate (quarterly rate)
AR(1) on US interest rate
AR(1) on US interest rate
Standard capital share
Average maturity
Gelos et al 2011
Keane and Rogerson 2012
Neumeyer and Perri 2005
Neumeyer and Perri 2005
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Parameters
Parameters from Matching Moments:
Parameter
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

Moment matched
Default probability
Share of domestic debt
Deposits to GDP
Returns on equity
Government expenditures to GDP
Hours worked
Volatility of GDP
Debt to GDP
Average spread[back]

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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
Average spread

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
2.14

[back]
24 / 24

Financial development and domestic debt
• Panel regression: share of domestic debt on financial development + controls′
Dom Debtit = βFin Devit−1 + ΓXit−1+ αi + δt + εit(1)

1960-1996
(2)

(3)

(4)

1960-2007(5)(6)

Financial dev.
Debt to GDP
GDPCountry Eﬀects
Year Eﬀects

0.464***-0.247***-2.341*NoNo

0.399***-0.249***-17.781***
Yes
No

0.343***-0.255***-11.059**
Yes
Yes

0.331***-0.155***-0.023NoNo

0.388***-0.138***-10.091***
Yes
No

0.200***-0.105***-2.406
Yes
Yes

Observations

365

365

365

516

516

516

Standard errors in parentheses* p<0.1, ** p<0.05, *** p<0.01• A 10pp increase in financial dev., increases share of domestic debt by ≈ 2–4.6pp
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Problem with Only External Debt: FOCµ = Lagrange multiplier on government budget constraintµ(S) :
Only external debt:
󰀕
󰁿

q∗ +

G + B ∗ ≤ q ∗ (B ∗′ , K ′ , D′ ; z, R∗ )B ∗′ + T (L; S)

󰀖
󰀅
󰀃
󰀄 󰀆
∂q ∗ ∗′
B(1 + µ) = βE δ ′ 1 + µ′∗′∂B󰁿 󰁾󰁽 󰂀
󰁾󰁽󰂀
repayment eﬀect+Xe (S ′ )revenue eﬀect• Revenue eﬀect: how much more government gets from increasing debt
- gets q ∗ but additional unit of borrowing decreases q ∗- increases consumption and relaxes gov’t budget constraint• Repayment eﬀect: cost of repaying debt tomorrow- decreases consumption and tightens gov’t budget constraint
24 / 24

Both External and Domestic Debt: FOCs
µ = Lagrange multiplier on government budget constraintρ = Lagrange multiplier on bank budget constraint
FOC(B ∗′ ):
󰀕
󰀖
󰁫 󰀃
󰀄󰁬
∂q ∗ ∗′∂q∂q ∗ ∗′′∗
˜′ µ′ + 1 + ρ ∂q B ′µ q∗ +
B
+
B
+
q
+
B
=
βE
δ
∂B ∗′
∂B ∗′
∂B ∗′
∂B ∗′

∂q
′
where ∂B∗′ B < 0 captures indirect eﬀect on the price of the other type of debt

24 / 24

Both External and Domestic Debt: FOCs
µ = Lagrange multiplier on government budget constraintρ = Lagrange multiplier on bank budget constraintη = Lagrange multiplier on bank collateral constraint
FOC(B ∗′ ):

󰀕
󰀖
󰁫 󰀃
󰀄󰁬
∂q ∗ ∗′∂q∂q ∗ ∗′′∗
˜′ µ′ + 1 + ρ ∂q B ′µ q∗ +
B
+
B
+
q
+
B
=
βE
δ
∂B ∗′
∂B ∗′
∂B ∗′
∂B ∗′

FOC(B ′ ):

󰀕
󰀖
󰀕
󰀖
󰁫 󰀃
󰀃
󰀄󰀄󰁬
∂q ′
∂q ∗ ∗′∂q ∗ ∗′∂q ′˜′ µ′ − σ ρ′ + θη ′
µ q+
B
+
B
+
B
=
βE
δ
+
ρ
q
+
B
∂B ′
∂B ′
∂B ′
∂B ′

󰀓
󰀔
∂q
′
where ρ q + ∂BB
> 0 captures crowding out eﬀect′[back]
24 / 24

Markov Problem
The problem for the government under repayment in normal times is thenV (S) = max

C + v(L) + βE max{V (S ′ ), W default (S ′ )}subject to the implementability constraints:• Country aggregate budget constraint: zF (K, L) = C + K ′ − (1 − δK )K + G + δ ∗ B ∗ − δ ∗ q ∗ B ∗′• Government budget constraint

G + δB + δ ∗ B ∗ = (zFL − v ′ (L))L + δq(S)B ′ + δ ∗ q ∗ (S)B ∗′󰁿󰁾󰁽󰂀T (L;S)• Bank aggregate budget constraint• Bank aggregate collateral constraint• And, pricing equations for domestic and external bonds
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Markov Problem• International lenders break-even condition󰁫󰁬󰀏E δ ∗ (S ′ )󰀏z, R∗q ∗ (A′ ; z, R∗ )• Domestic bank first order condition󰁫󰁬
E m(S ′ )δ(S ′ )q(A′ ; z, R∗ )

= R∗

󰀅
󰀆
= E m(S ′ )(z ′ FK (S ′ ) + 1 − δK )- where, m(S) = 1 − σ + σν(S)󰀅󰀃󰀄󰀆- and, ν(S) = E m(S ′ ) (1 + θ)(z ′ FK (S ′ ) + 1 − δK ) − θ

24 / 24