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International Monetary Economics

Lecture 11: Debt Sustainability

Master d’Affaires Publiques SciencesPo Spring 2013

Pierre-Olivier Gourinchas

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§  Public Debt Sustainability •  What is the relevant concept? •  Debt-sustainability analysis

§  External Debt Sustainability

Roadmap

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§  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

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§ 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

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§  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


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•  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%


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§  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


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§  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%


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§  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.


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Primary Surplus/Y = (r - g) D/Y §  Plugging some numbers:


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§  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….)


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§ 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

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§  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).


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§  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


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§ 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

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§  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

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