Debt Management, Fiscal Vulnerability Debt Management, Fiscal Vulnerability and Fiscal Solvency: and Fiscal Solvency:

The Recent Mexican ExperienceThe Recent Mexican Experience

XXII Meeting of the Latin American Network of Central XXII Meeting of the Latin American Network of Central Banks and Finance MinistriesBanks and Finance Ministries

October 2005October 2005

Marco OviedoMarco OviedoAlejandro WernerAlejandro Werner

IntroductionIntroduction

The Mexican 1994-1995 crisis introduced the discussion The Mexican 1994-1995 crisis introduced the discussion about debt management against self fulfilling crises.about debt management against self fulfilling crises.

This work is an attempt to provide an analytical study on This work is an attempt to provide an analytical study on debt management under debt sustainability criteria.debt management under debt sustainability criteria.

We start by including risk in the definition of debt We start by including risk in the definition of debt sustainability and analyze debt management from a solvency sustainability and analyze debt management from a solvency point of view. The approach is particularly useful since we point of view. The approach is particularly useful since we can measure the effect of debt management policies, such as can measure the effect of debt management policies, such as debt composition and maturity in probabilities of insolvency.debt composition and maturity in probabilities of insolvency.

The question is if the existing levels of public debt and its The question is if the existing levels of public debt and its current conditions could lead to unsustainable paths, and current conditions could lead to unsustainable paths, and what elements of debt management could break potential what elements of debt management could break potential unbalances.unbalances.

Thus, by introducing debt management with solvency criteria Thus, by introducing debt management with solvency criteria we can evaluate the effectiveness of debt policy under the we can evaluate the effectiveness of debt policy under the Mexican experience.Mexican experience.

11*

11** )1()1( tttttttttt SBrBerBBeB

YYeY ttt *

Debt Sustainability with external debtDebt Sustainability with external debt

Debt accumulation equation with external debt:Debt accumulation equation with external debt:

Decomposition of GDP in its tradable and its non-tradable Decomposition of GDP in its tradable and its non-tradable components:components:

(1)(1)

tttt BBeB *

Debt Sustainability with external debtDebt Sustainability with external debt

Equation (1) can be written in terms of GDP ratiosEquation (1) can be written in terms of GDP ratios

(2)(2)

1

*11

1

1*

11

1

1*

11

*11*

*

*

)1()1(

)1()1(

ttt

t

ttt

tt

ttt

tttt

ttt

tttttt

YYe

S

YYe

Br

YYe

Beer

YYe

BBeb

Define: Define:

t

ttt B

Be *

t

ttt Y

Ye *

andand

Policy question: how much foreign borrowing the government Policy question: how much foreign borrowing the government should issue each period, given the observed values of foreign should issue each period, given the observed values of foreign and domestic interest rates and the depreciation of the real and domestic interest rates and the depreciation of the real exchange rate?exchange rate?

Debt Sustainability with external debtDebt Sustainability with external debt

If there is a mismatch, the elasticity of the GDP ratio to a If there is a mismatch, the elasticity of the GDP ratio to a change of the real exchange rate is not zero.change of the real exchange rate is not zero.

,ttb

e

e

b

The equation that defines the sustainable level of debt isThe equation that defines the sustainable level of debt is

(4)(4) grggerer

sb

~)( *

111*

1*

11 )1()1()1(1~~1 tttttttttttttt sbdrbereberbggege

Equation (2) can be rewritten as:Equation (2) can be rewritten as:

(3)(3)

Recent Mexican debt policyRecent Mexican debt policy

Public sector net debt has been reduced since the 1980s. The Public sector net debt has been reduced since the 1980s. The currency composition includes lower proportion of external currency composition includes lower proportion of external debt since the 1994-1995 crisis.debt since the 1994-1995 crisis.

20

30

40

50

60

70

80

90

1980

Q1

1981

Q2

1982

Q3

1983

Q4

1985

Q1

1986

Q2

1987

Q3

1988

Q4

1990

Q1

1991

Q2

1992

Q3

1993

Q4

1995

Q1

1996

Q2

1997

Q3

1998

Q4

2000

Q1

2001

Q2

2002

Q3

2003

Q4

2005

Q1

PUBLIC SECTOR NET DEBT(% of GDP)

40

45

50

55

60

65

70

75

80

85

90

1980

Q1

1981

Q2

1982

Q3

1983

Q4

1985

Q1

1986

Q2

1987

Q3

1988

Q4

1990

Q1

1991

Q2

1992

Q3

1993

Q4

1995

Q1

1996

Q2

1997

Q3

1998

Q4

2000

Q1

2001

Q2

2002

Q3

2003

Q4

2005

Q1

PUBLIC SECTOR EXTERNAL NET DEBT(% of public sector total net debt)

Recent Mexican debt policyRecent Mexican debt policy

Additionally, both duration and maturity has been Additionally, both duration and maturity has been considerably increased in the last years.considerably increased in the last years.

264

418 405

291230

288 283

380423

559 539

744

859908

1071

1148

0

200

400

600

800

1000

1200

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

*

AVERAGE MATURITY OF DOMESTIC PUBLIC DEBT

(days)

*Data from August.

329 331398

471

617

699

1095

0

200

400

600

800

1000

1200

2000 2001 2002 2003 2004 2005/e 2006/e

AVERAGE DURATION OF DOMESTIC PUBLIC DEBT

(days)

e/ Estimated

The Rigobon and Garcia methodology is applied. The external The Rigobon and Garcia methodology is applied. The external debt component, debt component, ηη, is incorporated. This will let us obtain , is incorporated. This will let us obtain every period the level of external debt as a function of the rest every period the level of external debt as a function of the rest variables and measure the impact of this variable in variables and measure the impact of this variable in sustainability.sustainability.

In equation (2) the rate of growth of GDP (In equation (2) the rate of growth of GDP (), the real exchange ), the real exchange depreciation (depreciation (), the external interest rate (r*), the domestic ), the external interest rate (r*), the domestic interest rate (r) and the primary surplus (s) and its different interest rate (r) and the primary surplus (s) and its different components are stochastic and are multi-normally distributed, components are stochastic and are multi-normally distributed, thenthen

MethodologyMethodology

),(~,,,,, * Nsrr tttttt

And using the observed components of the primary surplus And using the observed components of the primary surplus we can estimatewe can estimate

),,,,,,,,|Pr( *tttttttttt gntotrrbb

which is the probability of public debt of reaching a threshold which is the probability of public debt of reaching a threshold given the values of the relevant variables.given the values of the relevant variables.

Probability of debt to GDP ratio of reaching more than threshold in the Probability of debt to GDP ratio of reaching more than threshold in the following 5 yearsfollowing 5 years

0.0

0.2

0.4

0.6

0.8

1.0

82 84 86 88 90 92 94 96 98 00 02 04

100% of GDP83% of GDP

60% of GDP40% of GDP

Prob

abil

ity

ResultsResults

The probability of reaching a threshold of public debt to GDP ratio The probability of reaching a threshold of public debt to GDP ratio of 83 is in average 0.66 in the 1980s. This probability has of 83 is in average 0.66 in the 1980s. This probability has decreased to 0.21, on average, in the 1990s and 2000s.decreased to 0.21, on average, in the 1990s and 2000s.

In particular, during the 2000s the debt to GDP ratio was around In particular, during the 2000s the debt to GDP ratio was around the twenties, and the probability of attaining a threshold of 45 the twenties, and the probability of attaining a threshold of 45 percent of GDP in the next five years is less than 0.35.percent of GDP in the next five years is less than 0.35.

Initial debt composition and the probability of reaching debt 83 percent Initial debt composition and the probability of reaching debt 83 percent of GDPof GDP

There is a positive relationship between the probability of There is a positive relationship between the probability of reaching a threshold of 83 percent of GDP and the level of debt at reaching a threshold of 83 percent of GDP and the level of debt at the initial condition. The effect of the composition of debt in the the initial condition. The effect of the composition of debt in the probability of hitting the threshold in the next 5 years is about 0.3, probability of hitting the threshold in the next 5 years is about 0.3, which means that when the initial composition of external debt which means that when the initial composition of external debt increases 1 percentage point, the probability increases 0.003.increases 1 percentage point, the probability increases 0.003.

ResultsResults

0.4

0.5

0.6

0.7

0.8

0.9

0.0 0.2 0.4 0.6 0.8 1.0

Probability of debt reaching 83% of GDP

Ex

tern

al d

ebt

to t

ota

l ra

tio

Probability of reaching a threshold of 60 percent of GDP in the following Probability of reaching a threshold of 60 percent of GDP in the following 5 years with a constant decrease in the proportion of external debt5 years with a constant decrease in the proportion of external debt

.25

.30

.35

.40

.45

.50

.55

1996 1997 1998 1999 2000 2001 2002 2003 2004

0% reduction2% reduction

4% reduction6% reduction

Prob

abil

ity

Effects of a currency composition debt policyEffects of a currency composition debt policy

We introduce an explicit debt composition policy that decreases the We introduce an explicit debt composition policy that decreases the proportion of external debt each period. Increasing the rate of reduction proportion of external debt each period. Increasing the rate of reduction of the proportion of of the proportion of from zero to 2 percent, reduces the probability of from zero to 2 percent, reduces the probability of a crisis in 0.02 and from zero to four percent, it reduces the probability a crisis in 0.02 and from zero to four percent, it reduces the probability in 0.025. Finally, the increase of the rate of reduction from zero to six in 0.025. Finally, the increase of the rate of reduction from zero to six percent reduces, on average, this probability in 0.032. percent reduces, on average, this probability in 0.032.

Debt term structure and the probability of a crisisDebt term structure and the probability of a crisis

We include a maturity index in our model and an explicit policy for We include a maturity index in our model and an explicit policy for that parameter by incorporating an explicit constant increase of the that parameter by incorporating an explicit constant increase of the maturity index. In the data, this index is increased in 3.9 percent per maturity index. In the data, this index is increased in 3.9 percent per quarter. In our exercise we incorporate zero, two, four and six quarter. In our exercise we incorporate zero, two, four and six percent increment.percent increment.

If the average maturity of the domestic debt increases from zero to If the average maturity of the domestic debt increases from zero to two percent every quarter, on average the probability of reaching the two percent every quarter, on average the probability of reaching the specified threshold is 0.02. Similarly, increasing the rate of the term specified threshold is 0.02. Similarly, increasing the rate of the term structure of debt from zero to four percent reduces the probability in structure of debt from zero to four percent reduces the probability in 0.037, increasing it at 6 percent per quarter decreases the probability 0.037, increasing it at 6 percent per quarter decreases the probability in 0.054.in 0.054.

To have an idea of this impact, if the average maturity of domestic To have an idea of this impact, if the average maturity of domestic debt increases from 1000 days to 1060, and then to 1123 so on, the debt increases from 1000 days to 1060, and then to 1123 so on, the probability of attaining an unsustainable path will be reduced in probability of attaining an unsustainable path will be reduced in 0.054 every quarter, thus reducing it in 0.2 in a year.0.054 every quarter, thus reducing it in 0.2 in a year.

Debt term structure and the probability of a crisisDebt term structure and the probability of a crisis

The effect of an increment in maturity in the probability of reaching a The effect of an increment in maturity in the probability of reaching a threshold of 60 percent of GDP in the following 5 yearsthreshold of 60 percent of GDP in the following 5 years

.1

.2

.3

.4

.5

.6

1996 1997 1998 1999 2000 2001 2002 2003 2004

0% increment2% increment

4% increment6% increment

Prob

abil

ity

Sustainability is redefined when debt management is Sustainability is redefined when debt management is considered. According to the Mexican experience, both considered. According to the Mexican experience, both currency composition and maturity affect the probability of a currency composition and maturity affect the probability of a crisis.crisis.

On average, higher proportions of external debt increases the On average, higher proportions of external debt increases the probability of a debt crisis.probability of a debt crisis.

Similarly, increasing the average maturity of domestic debt has Similarly, increasing the average maturity of domestic debt has a considerable effect in the reduction of the probability of a considerable effect in the reduction of the probability of insolvency.insolvency.

These estimated impacts supports the beliefs of the potential These estimated impacts supports the beliefs of the potential benefits of increasing the maturity on public debt. More analysis benefits of increasing the maturity on public debt. More analysis should be done in terms of potential costs to provide more light should be done in terms of potential costs to provide more light on this matter to policy makers.on this matter to policy makers.

ConclusionsConclusions