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CHAPTER 9:FISCAL SUSTAINABILITY

This section examines public debt dynamics. Starting from the governments cash-flow

constraint, it examines the factors affecting fiscal sustainability and shows how a stream

of budget deficits can, over time, lead to unsustainable public debt levels and their

macroeconomic consequences. Both the closed and open economy cases are considered.

9.1. Debt Dynamics in a Closed Economy

Consider first an economy that does not trade with the rest of the world. Denote by Ytthe

economys real GDP in year tandPtthe GDP deflator. Nominal GDP is the product PtYt.

Let tdenote the rate of increase in prices between years t-1and t, expressed as 11

=

t

t

tP

P .

Similarly, letgtdenote the real growth rate of output, expressed as 1

1

=

t

tt

Y

Yg .

LetMt-1denote the stock of money at the end of year t-1and assume, for simplicity, that all

interest-bearing government debt has one-year maturity. Denote byDt-1the stock of one-

period government bonds outstanding at the end of year t-1.The average nominal interest rate

on government debt issued at t-1is it. The governments expenditure in year tconsists of two

components, non-interest spending, denoted Gt, and interest payments on the debt, itDt-1.

Next consider the governments cash-flow constraint in year t. As a matter of accounting,

government expenditure must be financed by raising tax and nontax revenues net of transfers

to the private sector, denotedRt, through money issuance,MtMt-1 (=Mt), and by issuinginterest-bearing securities,DtDt-1.

Gt+ itDt-1=Rt + (Dt-Dt-1) + (Mt-Mt-1). (9.1)

The governments overall budget balance is the difference between revenue and expenditure,

Rt(Gt+ iDt-1). The primary budget balance,PBt, is the difference between revenue and non-

interest expenditure,Rt - Gt. As we are interested in the evolution of the stock of interest-

bearing public debt, we solve (9.1) forDt, yielding

( ) ( )11t t t t D i D PB M= + + .t (9.2)

To derive an expression for the stock of public debt in relation to GDP, we divide

equation (9.2) by nominal GDP:

This training material is the property of the International Monetary Fund (IMF) and is intended for us in IMF

Institute courses. Any reuse requires the permission of the IMF Institute.

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( )

( )

( )( )

1

1

1 1

1

1.

1 1

t tt t t

t t t t t t t t

t t t

t t t t t t t t

i DD PB M

PY PY PY PY

i D PB M t

P Y PY PY

+ = +

+ =

+ + +

t

(9.3)

Denote by lower-case letters the stock of debt, primary balance, and seignorage expressed as

shares of GDP: / ,/ ,t t td D PY t 1 1 1/ ,t t t t d D P Y 1 t t tpb PB PY and /t t t t PY . The

parameter multiplying , denoted t, is key in debt sustainability analysis.1td

Use the Fisher equation linking the nominal and real interest rate, 1 (1 ) /(1 )t tr i t+ + + , to

write t as the ratio of one plus the real rate of interest on government debt over one plus the

real rate of GDP growth:

( ) ( )( ) ( ) ( )1 /[ 1 1 ] 1 / 1t t t t t i g r + + + = + + tg . (9.4)

With this notation, the government budget constraint can now be rewritten as:

( )1 .t t t t t d d pb = + (9.5)

We can draw equation (9.5) in a phase diagram as shown in Figure 9.1 to examine how the

debt-to-GDP ratio evolves over time. The horizontal axis plots the debt-to-GDP ratio in year

t-1, , while the vertical axis shows the resulting value of in year t. The 45line shows

debt-to-GDP ratios that do not change over time. Suppose, for simplicity, that the parameters

1td td

t , tpb , and t are constant over time at , , andpb , respectively, so that andtd 1td

have a linear relationship.

Whether the public debt-to-GDP ratio is explosive or not depends on the value of the

parameter . The non-explosive case 1< is shown on the left-hand side panel of

Figure 9.1. In this case, the initial level of debt-to-GDP ratio eventually falls to and

stays at that level forever. The explosive debt case

0d*

d

1> is shown on the right-hand side

panel of Figure 9.1. Here, the real interest rate which the government pays on its debt

exceeds the real GDP growth rate

tr

t. Starting from any positive initial level of debt-to-GDP

ratio d0> d*in year 0, the debt to GDP ratio grows without bound, which is obviously

unsustainable.

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Figure 9.1. Debt Dynamics

a. Stable debt dynamics b. Explosive debt dynamics

dt 45o line

The speed at which debt can explode in realistic cases is surprisingly fast. Suppose the public

debt-to-GDP ratio is initially = 50 percent. Assume a nominal interest rate, =14 percent,

real GDP growth rate

0d i

= 4.0 percent, annual inflation = 4.3 percent, primary deficit

= -2.7 percent of GDP, and seignorage,pb = 1.1 percent of GDP. Applying the Fisher

equation, the real interest rate is 9.3 percent (= (1.14/1.043-1)100 percent), which exceeds

real GDP growth, implying 1 > . The debt-to-GDP ratio is explosive (see Figure 9.2) and

reaches 80 percent of GDPsometimes considered the threshold for severe

indebtednessin about five years.

Figure 9.2. The Debt-to-GDP Ratio in a Closed Economy

0%

20%

40%

60%

80%

100%

120%

140%

160%

180%

200%

2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024

dt= dt-1 (pb+)where < 1 orr< g

(pb+)

d d0

dt

45o line

dt= dt-1 (pb+)

where < 1 or r< g

d d0 (pb+)dt

dt

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The explosive nature of the governments debt dynamics can also been seen by differencing

equation (9.5) to calculate the change in the debt-to-GDP ratio, . Subtracting

dt-1from both sides of equation (9.5) yields the following

1t t td d d =

( ) ( )11t t t t t d d pb = + . (9.6)

Equation (9.6) underscores the factors that affect the change in the debt-to-GDP ratio: the

size of the primary budget balance tpb , seignorage t , and the built-in momentum of

debt, . If the real interest rate on government debt exceeds real GDP growth, debt

becomes explosive. Primary surpluses are then needed to offset the automatic debt dynamics.

The size of the primary surplus in relation to GDP,

( ) 11t d t

tpb , is a good indicator of the

governments fiscal adjustment effort.131Equation (9.6) is useful in calculating the primary

surpluses needed to achieve specific objectives, such as stabilizing the debt at its existinglevel or even reducing it to a lower level, as needed, for example, to meet the criteria of the

Maastricht Treaty for European Union member countries.

As a first step to fiscal sustainability, the authorities may pick fiscal targets with a view to

halt further increases in the public debt to GDP ratio. This requires raising the primary

balance to GDP ratio sufficiently to stabilize the debt-to-GDP ratio. To obtain thedebt-

stabilizing primary balance, set dt= 0 in equation (9.6) to obtain:

( ) .1 1 = ttt dpb (9.7)

Continuing with our earlier example, if the country is to avoid the ever-rising debt path

shown in Figure 9.2, the primary balance surplus needs to be at least 1.45 percent of GDP

{[((1.093 1.04)/1.04) 0.5] 0.011} 100 percent instead of 2.7 percent of GDP in deficit.

The debt-stabilizing primary balance depends on several factors. First, if the existing level of

debt is large, large primary surpluses are needed to prevent it from growing further. Second,

if the difference between the real interest rate and real GDP growth is large, then the primary

surplus also needs to be large. Third, if seignorage or other sources of government finance

are available (such as privatization receipts), these can be used to pay off the debt and will

result in lower debt-stabilizing values for the primary surplus. Of course, many countries

likely would like to reduce their stock of debt relative to GDP, rather than just stabilize it.

Those countries must then achieve a primary surplus in excess of the debt-stabilizing level.

131The government can manipulate the money growth rate to increase revenue from money creation, or

seignorage. But raising money growth and inflation leads to currency substitution, which places limits on the

amount of real resources the government can obtain from seignorage.

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9.2. Debt Dynamics in an Open Economy

The analysis of public debt sustainability is similar when the government can borrow from

international financial markets to cover part of its budget deficit. Now public debt

sustainability depends on the path of the nominal and real exchange rate and foreign

interest rates.

When the government borrows abroad, a distinction needs to be made between domestic

currency-denominated debt htD and foreign-currency denominated debtf

tD . Letting be

the nominal exchange rate (local currency per unit of foreign currency), the debt stock is

te

h

t t t

f

tD D e D= + and the government budget constraint can be written

( ) ( )* 11t t t t D i D PB M= + + .t (9.8)

In equation (9.8), , the effective nominal interest rate, is a weighted sum of the domesticand foreign interest rates and , and also depends on the exchange rate

*

tih

ti f

ti

( )( ) ( )* 1 h f ft t t t i i i = + + +1 ,ti (9.9)

where ( ) /ft t te D D = is the portion of foreign currency denominated debt, and t is the rateof depreciation of the currency. It can be shown that the public debt to GDP ratio evolves

according to the following equation, which is analogous to (9.5):

( )* 1t t t t t d d pb = + , (9.10)

In equation (9.10), ( ) ( )( )* *1 /[ 1 1t t ti g + + +*

]t

is analogous to t , and*

t , the GDP deflator,

depends on domestic inflation ht , foreign inflationf

t , and exchange rate movements:

( )( ) ( )* 1 h f ft t t t = + + +1 ,t (9.11)

where is the output share of tradables in GDP.( ) /f ft t t t t e P Y PY =

The intuition discussed in the closed economy case still holds: Debt dynamics are explosive

if the real interest rate ( ) ( )* * *1 / 1t t tr i + + 1 is greater than real GDP growth t . In theopen economy the interest rate relevant for the DSA calculation depends on domestic and

foreign interest rates and inflation, on exchange rate movements, and on the size of foreign

borrowing and foreign trade.

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In terms of our earlier example, suppose =14 percent, =8 percent,di fi =0.5, =0, and

=0. Then the effective nominal interest rate is 11 percent = (0.5*i 14 percent + 0.5

8 percent)+0.501.08), and the effective real interest rate is 6.4 percent

(= (1.11/1.043-1) 100 percent), which is greater than the real GDP growth rate of 4.0

percent. As in the closed economy case, the debt-to-GDP ratio is explosive (see Figure 9.3).Moreover, if the exchange rate depreciates by 30 percent, the effective nominal interest rate

and the effective real interest rate become as high as 27.2 percent and 22.0 percent. The debt-

to-GDP ratio rises much more rapidly and exceeds the 80 percent threshold in less than

5 years, assuming a crisis does not force an adjustment first (see Figure 9.3). The debt

stabilizing primary balance in this case rises to 7.6 percent of GDP (= (22.0 percent

4.0 percent)/1.04 0.5 1.1 percent).

*r

Figure 9.3. The Debt-to-GDP Ratio in an Open Economy

0%

20%

40%

60%

80%

100%

120%

140%

160%

180%

200%

220%

240%

2005

2006

2007

2008

2009

2010

2011

2012

2013

2014

2015

2016

2017

2018

2019

2020

2021

2022

2023

2024

d

d* with 30% depreciation

d* with no depreciation

9.3. The IMFs Approach to Public Debt Sustainability

Basic macroeconomic assumptions

In this section, we focus on public DSAs relevant for countries with access to international

capital markets. The fiscal DSA framework consists of a baseline scenario and sensitivity

tests of debt dynamics to a number of assumptions.

There are many difficulties in constructing realistic projections of public debt and debt

service. In particular, three important risks need to be assessed. A first risk comes from

contingent liabilities (Box 9.1). Many contingent liabilities, by nature, go unnoticed in

normal times but are more likely to emerge in crises. Contingent liabilities are exceedingly

difficult to measure in practice, both because the amounts involved are often unknown and

because the precise circumstances under which they would turn into actual liabilities are

often unknowable.

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Box 9.1. Contingent Liabilities

The governments contingent liabilities are potential claims on the government that may or may not be

incurred depending on macroeconomic conditions and other events. Unlike direct liabilities, such as

pension obligations, which are predictable and will arise in the future with certainty, contingent

liabilities are obligations triggered by discrete but uncertain events. By nature, contingent liabilities aredifficult to measure. While information is usually available on debt formally guaranteed by the central

government, debt not explicitly guaranteed has often been an important contributor to public debt build-

up.

Contingent liabilities, especially those arising from the need to rescue banks, were responsible for large

jumps in the public debt to GDP ratio in several countries affected by past financial crises. Capturing the

hidden fiscal risks arising from contingent liabilities is therefore an important task for public DSAs.

One of the stress tests in the public debt sustainability template examines the effect on the public debt

dynamics of the realization of contingent liabilities, specified as an exogenous increase in the debt ratio

of 10 percent of GDP. This shock is exogenous and is not linked to the countrys financial sector

vulnerabilities and other shocks examined in the template (e.g., to growth, interest rates, or the exchange

rate).

Explicit liabilities are those recognized by a law or contract, such as government guarantees for non-

sovereign borrowing and obligations issued by subnational governments and public or private sector

entities or trade and exchange rate guarantees.Implicit liabilities are obligations that may be assumed by

government due to public and interest-group pressures, such as financial sector bailouts, or bailouts of

non-guaranteed social insurance funds.

A second risk is an abrupt change in financing conditions in international markets affecting

both the availability and the cost of funds. Such changes may reflect developments in the

financial markets, such as contagion, or funding difficulties specific to the country. These

changes may give rise to a liquidity crisis if the country is unable to rollover its maturing

obligations or result in sharply higher interest rates, calling into question the long-term

solvency of the borrower.

A third risk is a depreciation of the exchange rate, possibly in the aftermath of the collapse of

an exchange rate peg, which increases the domestic currency value of the stock of external

public debt. A key factor in determining the post-crisis evolution of the exchange rate is the

extent of initial overvaluation and the extent of possible exchange rate overshooting. As

some cases have shown, once a crisis erupts, the capital outflows can result in exchange rate

adjustments far in excess of any initial estimates of overvaluation.

To stress test the baseline projections against these and other risks, the IMF DSA:

calibrates the size of shocks (reasonable but not extreme; use historical standarddeviations or absolute deviations for global shocks),

assesses interdependencies (perturb correlated parameters at the same time),

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sets durations of shocks (use shock sequences for serially correlated parameters), and assesses the effect of other debt-creating flows (e.g., contingent liabilities). 132The public sector DSA template

The public sector debt template tracks the behavior of the gross debt-to-GDP ratio shown in

equation (9.9). The definition of debt used in the IMFs DSA is based on gross liabilities

that is, public sector liquid or other assets are not netted out. The coverage of public debt is

as broad as possible and it includes public enterprises as well as local governments.

Based on equation (9.9), the template identifies the different channels that contribute to the

evolution of the debt to GDP ratio, including the primary deficit and endogenous/automatic

factors related to interest rates, growth rates and exchange rate changes. The template also

includes other debt-creating operations, such as would result from the recognition by the

government of contingent liabilities, as well as debt-reducing operations, such asprivatizations whose proceeds are used to pay down public debt.

The gross financing needs of the public sector are defined as the sum of the public sector

deficit and all debt maturing over the following 12 months. The template also calculates the

debt-stabilizing primary balance which would be needed to keep the debt-to-GDP ratio

constant if all the variables in the debt dynamics equation remained at the level reported in

the last year of the projection.

As discussed in Chapter 8, in the IMFs public debt sustainability framework, the baseline

paths of the public debt-to-GDP ratio and the variables on which it depends are projected byIMF staff in consultation with country authorities. The baseline projections are conditional in

the sense that they assume that the authorities will fully implement the announced fiscal,

monetary, exchange rate, and structural policies.

In addition, the public debt sustainability template presents projections under a historical

scenario. This is an alternative path of the debt ratio, constructed under the assumption that

all key variables stay at their historical averages throughout the projection period. This

scenario is a test of the realism of baseline projections: if the deviations of assumed

policies and macroeconomic developments in the baseline are very different from those in

the historical scenario, these will need to be justified by referring to credible changes inpolicies.

132In 2005, the IMF reviewed its DSA framework and revised the size and duration of the shocks used in the

stress tests. The new approach considers the effects of smaller but more persistent shocks.

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The template also contains a no-policy-change scenario. This is derived under the assumption

that the primary balance is constant in the future and equal to the projection for the current

year. The no-policy-change scenario can be modified to assume an unchanged cyclically

adjusted primary position, or to make adjustments for the expiration of one-off measures, as

necessary.

The baseline scenario is also stress-tested using different assumptions on key parameters.

Permanent shocks equal to one-half standard deviation are applied to the baseline projections

of each of the parameters, and paths of debt ratios are then derived. One-quarter standard

deviation shocks are applied in the combined shock test. These shocks are applied to the

interest rate, growth rate, and primary balance. In addition, the template examines the debt

trajectory in the case of a 30 percent depreciation of the local currency and a contingent

liabilities shock of 10 percent of GDP. The latter is presented as a rough measurement of an

increase in debt-creating flows, given the difficulties in discussing contingent liabilities risk.

If better measures are available, the staff is encouraged to use them in stress tests.

Table 9.1 lists the data inputs needed to calculate the debt-to-GDP ratio in the IMFs DSA.

Table 9.1. Data Input Requirements for DSA

Fiscal Variables Macroeconomic Variables

Public sector debt, Nominal GDP,

Public sector balance, Real GDP,

Public sector expenditure,

Public sector interest expenditure,

Exchange rate, national currency per U.S.

dollar, end of period,

Public sector revenue (and grants),

Foreign-currency denominated debt

Exchange rate, national currency per U.S.

dollar, period average,

(expressed in local currency), GDP deflator

Amortization on medium- and long-

term public sector debt,

Short-term public sector debt,

Interest payments on foreign debt

It is also desirable to have data on privatization receipts, recognition of implicit or contingent

liabilities, and other liabilities (e.g., bank recapitalization). While this data is much harder to

collect, it greatly improves the quality of the baseline projection and the stress tests.

Once input data are filled in, the baseline and stress test results are automatically calibrated

and presented in a summary table and in charts representing the outcomes of the stress tests,

also known as bound tests. See Table 9.2 and Figure 9.4 for an example.

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Table 9.2 summarizes the baseline scenario. Lines 1 and 2 show how the debt-to-GDP ratioevolves over time. The key macroeconomic assumptions underlying the baseline are reported

at the bottom of the table. The different channels that contribute to the evolution of the debt-

to-GDP ratio are: the primary deficit (line 4), the automatic debt dynamics (line 7), and otheridentified debt-creating flows(line 12), which include privatization receipts, recognition ofimplicit or contingent liabilities, and other obligations such as bank recapitalization. Theseflows are assumed zero in this particular example.

The automatic debt dynamics, in turn, is broken down into contributions from the real

interest rate, real GDP growth, and exchange rate. This decomposition allows an assessment

of the importance of different factors in the buildup of public debt and also serves as the

basis for stress tests, the results of which are summarized together with the baseline

projections in Figure 9.3.

Changes in gross debt arising from other below-the-line operations, such as repayment of

debt financed by a reduction in financial assets, and cross-currency movements are includedin a residual (line 16). It is critical to monitor the behavior of this residual, as it may highlight

errors in implementing the approach. A large residual may, in particular, signal a breach of

the flow-stock identity linking the deficit to changes in debt. The residual should be small

unless it can be explained by specific factors. The gross financing needs of the public sector,

in percent of GDP and in billions of dollars, are also calculated.

Table 9.2 also reports the paths of debt to GDP ratio under the historical scenario and undertheno-policy-change scenario. These scenarios test the realism of the baseline scenario.Finally, the template also calculates the debt-stabilizing primarybalance (last column ofTable 9.2).

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Figure 9.4 Country: Public Debt Sustainability: Bound Test1

(Public debt in percent of GDP)