International Monetary Economics
Lecture 11: Debt Sustainability
Master d’Affaires Publiques SciencesPo Spring 2013
Pierre-Olivier Gourinchas
Slide 11-2
§ Public Debt Sustainability • What is the relevant concept? • Debt-sustainability analysis
§ External Debt Sustainability
Roadmap
Slide 11-3
§ Limitations of the analysis so far: • The AA-DD model does not incorporate explicitly
intertemporal constraints: public and external debts need to be repaid, borrowing today constrains behavior tomorrow…
Debt Sustainability
Slide 11-4
§ An important question for policymakers: what level of public debt is sustainable in the long run? • What do we mean by sustainable? • Key consideration: countries are growing over time.
Economic growth reduces debt burdens over time. § Often, we understand the concept of sustainability as the
ability to stabilize the public debt to GDP ratio D/Y. • Debt to GDP is the relevant economic concept (larger
countries can sustain larger debt) • Also as income grows, the ratio shrinks.
Public Debt Sustainability
Slide 11-5
§ Some simple accounting: • Denote nominal GDP $Y, (real GDP is denoted Y). • Denote nominal public debt $D • Denote the growth rate of nominal output $g • Suppose we want nominal public debt $D to grow at the
same rate as output: $Dt+1 – $Dt = $g $Dt
• $Dt+1 – $Dt = $deficit is the public deficit
Public Debt Sustainability
Slide 11-6
• Dividing by nominal output: $deficit/$Y = $g $D/$Y
• Equivalently, we can write: $surplus/$Y = -$g $D/$Y
Where $surplus is the nominal public surplus (the opposite of the public deficit). • Lesson: a country can run a permanent deficit and still
maintain a stable debt/output ratio as long as nominal output growth is high enough
• Ex: with $g=5% and $D/$Y=60%, $deficit/$Y = 3%
Public Debt Sustainability
Slide 11-7
§ This may still require an important fiscal effort. Why? Because part of the budget is beyond the control of the government: the interest payments on past debts.
§ Separate the budget surplus into a primary surplus and interest
payments: $Surplus = $Primary Surplus - i $D
§ Substitute into the previous expression and re-arrange:
$Primary Surplus/$Y = (i - $g) $D/$Y
Public Debt Sustainability
Slide 11-8
$Primary Surplus/$Y = (i - $g) $D/$Y
§ Interpretation • When interest rates are high, government needs to run a primary
surplus to stabilize the public debt/GDP ratio • With faster growth, government can run a smaller (or negative)
primary surplus and keep public debt/GDP ratio stable • Government needs to run sufficient surplus to cover interest
payments, with a correction term for output growth. • Typically, i > $g, so primary surpluses are necessary. Even if
there is a deficit, the government needs to run a primary surplus
§ Ex.: if i=7%, then with $D/$Y=60%, $primary/$Y = 1.2%
Public Debt Sustainability
Slide 11-9
$Primary Surplus/$Y = (i - $g) $D/$Y
§ The role of inflation • Observe that $g = g + π. • So it might seem that one way to make the debt sustainable is to
increase inflation. • However, this will also tend to increase the nominal interest rate: by
the Fisher relationship, i=r+πe
$Primary Surplus/$Y = (r – g- (π–πe)) $D/$Y
• If the debt is adjustable (or equivalently short maturity), then the
interest rate will quickly adjust and inflation will have a very limited effect.
Public Debt Sustainability
Slide 11-11
§ Debt Sustainability Analysis • Typically, calculate path of primary surpluses necessary to bring a
country back to some target level of $D/$Y over a certain horizon • In IMF or Troika analysis, magic number seems to be 120% by 2020?
2030? Little empirical support • Exercise is typically over-optimistic on
– Growth assumptions (especially the impact of fiscal consolidations) – Government revenues (primary surpluses) – Exceptional revenues (privatization….)
Public Debt Sustainability
Slide 11-16
§ Another important question: what level of external debt is sustainable in the long run?
§ Follow the same steps as before. • $B: nominal external debt • Concept of sustainable external debt: stable $B/$Y • $CA = $NX- i $B • [Note that $B<0 for creditor country]
§ Stable external debt when: $CA/$Y = - $g $B/$Y
$NX/$Y = (i - $g) $B/$Y
External Debt Sustainability
Slide 11-17
§ External and domestic debt problems often go hand in hand (witness Greece, Ireland, Spain etc…) • Governments issue both domestic debt (in domestic
currency and held by mostly by domestic residents) and foreign currency debt (held mostly by foreigners)
• Moreover, in times of crisis, private liabilities (e.g. foreign borrowing by domestic banks) becomes public liabilities (e.g. government is forced to bail out the banks).
External Debt Sustainability
Slide 11-18
§ If no adjustment in $CA, where does the external debt converge?
$CAt/$Yt = ($Bt+1- $Bt )/$Yt
$CAt/$Yt = (1+$g) $Bt+1/$Yt+1 - $Bt/$Yt
• $CA/$Y = -4% • $g = 5% • Converges to $B/$Y = -80%
§ Is this unsustainable? Not necessarily. If foreigners want to hold domestic debt, then this may be fine (e.g. US). • Potential problem is the stock, not the flow: The country needs to roll over
larger and larger amounts of debt. What happens if foreigners stop rolling over the debt? SUDDEN STOP.
– Asset prices collapse (stock and bond) – Collapse of the currency
External Debt Sustainability
Slide 11-20
§ Consider a mild scenario: suppose foreigners refuse to extend new debt, but accept to roll-over the principal on the existing debt, so that CA=0.
§ What happens? • Expenditure Approach: CA = NX(q,Y,Y*) + rB,
• Investment-Saving Approach: CA = S(r) – I(r)
A Sudden Stop
Slide 11-21
§ Three types of balance of payment crisis • First generation emphasizes bad fundamentals, often an
inconsistency between the requirements of a fixed exchange rate regime and the desired policies of local policymakers.
• Second generation emphasizes the self-fulfilling elements of many crisis and their unpredictability.
• Third generations emphasize the role of financial factors and the link between financial and balance of payment crisis.
Summary