Why Do Governments Borrow so Much?
Michel Habib (UZH, SFI, and CEPR) and Jean-Charles Rochet (UZH, SFI, and TSE)
Outline
Motivation
Main Insight and Results
Literature Review
Model: One Term in Office
Calibration: One Term in Office
Model: Many Terms in Office
Calibration: Many Terms in Office
Conclusion
ii
Motivation
Starting with Eaton and Gersovitz’s (1981) seminal work, many papers have attempted to
reproduce prevailing country debt/GDP ratios.
These papers make two central assumptions:
(i) governments have infinite horizon
(ii) governments may default strategically, in which case they are excluded from future access to
capital markets
In these papers, governments borrow in order to insure their population against output shocks;
they default when the expected benefits of future insurance are smaller than the gains from
reneging on debt service commitments.
1
Neither assumption is entirely natural.
Assumption (i) contrasts with the widely-held view that a government’s horizon extends only as
far as the government’s expected term in office: après moi le déluge.
Assumption (ii) is belied by the empirical evidence: Levy Yeyati and Panizza (2011) find precious
little evidence of strategic default. Moreover, sanctions toward countries that default are
typically very short lived (Bulow-Rogoff 1989): they are quickly able to borrow again. Moreover,
existing papers generate debt/GDP ratios that are too low.
The higher calibrated debt/GDP ratio found in this literature is 30%: Hatchondo et al. (2010). As
we know, actual ratios are often markedly higher.
2
Debt/GDP Ratios, Selected Countries
Country Average Debt/GDP , 1980-2011, % Debt/GDP 20 11, %
Argentina
73
45
Australia
20
24
Austria
64
72
Canada
78
85
France
50
86
Germany
61
80
Greece
85
165
Italy
108
120
Japan
117
229
Spain
47
69
Sweden
55
38
Switzerland
50
47
Turkey
53
39
U. Kingdom
45
82
U. States
65
103
3
Main Insight and Results
We replace Assumptions (i) and (ii) by their more or less exact opposites:
(I) Government has horizon limited to its expected term in office.
(II) Government defaults only when unable to service their debt.
A government whose horizon is limited to its expected term in office naturally neglects negative
consequences of borrowing that occur beyond that term. Such a government can be expected to
borrow more.
Investors anticipate that governments will do everything possible not to default. Thus, provided
that spreads are high enough, investors are willing to accommodate large levels of borrowing.
There is therefore higher debt than in existing models.
4
We derive an estimate of maximum sustainable government debt as a function of:
(a) three variables that are specific to every country:
(1) the mean level of GDP growth
(2) the volatility of GDP growth
(3) the ratio of government income to GDP
(b) two parameters that are common to all countries
(4) the risk-free rate
(5) the ratio of government disposable income to total government income (should be
country-specific, but data not available)
We calibrate maximum debt/GDP ratios and default probabilities for a wide cross-section of
countries.
We provide some further insights into the notion of debt intolerance (Reinhart, Rogoff, and
Sevastiano, 2003; Catão and Kapur, 2004).
5
The prospect of reelection prompts politicians to choose government debt levels below the
maximum sustainable level: politicians realize that default jeopardizes future terms in office.
The difference between prevailing and maximum debt levels provides governments with a
‘margin of safety:’ negative output shocks can be accommodated by increasing government debt
towards its maximum sustainable level.
The probability of default increases slowly as long as there remains a margin of safety; it
increases very quickly once that margin has been exhausted and prevailing debt exceeds its
maximum sustainable level.
6
Literature Review
Eaton and Gersovitz (1981) + …
Aguiar and Gopinath (2006) and Arellano (2008): study interactions of default risk, output,
consumption, the trade balance, interest rates, and foreign debt in setting of small open
economy.
Mendoza and Yue (2012): endogenize output and collapse of output in default.
Cuadra and Sapriza (2008): consider the role of political risk.
Yue (2009) and Benjamin and Wright (2009): consider the role of renegotiation in default.
7
Literature Review (2)
Hatchondo and Martinez (2009) and Chatterjee and Eyigungor (2012): consider the role of debt
maturity.
Fink and Scholl (2011): consider the role of conditionality.
Cohen and Villemot (2013): develop a model in which the cost of default is borne ‘in advance.’
Note that our assumption of non -strategic default is not subject to the Bulow and Rogoff (1989)
critique of Eaton and Gersovitz (1981).
8
Model: One Term in Office
For simplicity we only consider one period debt
Notation:
yt = government “disposable” income in period t : tax revenues minus unavoidable public

expenditures.
bt yt = government borrowing at date t and

dt yt = debt level (promised repayment) at date t+1.



Let the growth rate in government income g  yt 1 / yt be lognormally distributed F  , 2 .
A government that remains only a single term in office maximizes borrowing bt yt .
This is true for all increasing government utility functions uyt  bt yt  dt 1yt 1  .
9
Under the assumption of non-strategic default, a government will go so far as to use all
government disposable income and all new borrowing proceeds in order to service existing debt.
Under the additional assumption that there is a ‘sudden stop’ to lending in default, the maximum
amount lenders are willing to provide is
bt yt 


1
Pr 1  bt 1 yt 1  dt yt dt yt  0d y / 1b  yt 1dF yt 1 
1r
 bt 
t

t 1
t

1
xt 1  F xt 1  bt 1   0x gdF g 
1r
t
where xt  dt / 1  bt 1  . Note the ‘bubble-like’ property of debt: the amount lenders are willing
to provide in period t depends on the amount that will be provided in period t  1 .
10
The only bounded equilibrium is the fixed point bt  bt 1  bM such that
bM  max BbM , z 
z
where


e 
z
2  z   


BbM , z  

1

b

e

1


z


e


M
1  r 

ln x   
z

2

We have made use of the lognormality of g .
11
Proposition 1: If E g   1  r ,  bM   max z BbM , z  is a contraction mapping and the
government’s maximization problem has a unique solution.
Proposition 2: Maximum government borrowing bM is increasing in the mean growth rate  and
decreasing in its volatility  and in the risk-free rate r .
Proposition 3: The probability of default  z  is decreasing in the mean growth rate  and
increasing in its volatility  (for  z   1 / 2 ) and in the risk-free rate r .
12
b,τ(b)
b
τ(b)
bM
b
Maximum Sustainable Borrowing bM
13
The expressions for maximum government debt dM , interest factor R , and expected loss given
default LGD are
dM  exp  zM 1  bM 
R
dM exp  zM  zM 

bM
 1   zM 
and


z
 exp   zg d zg 
LGD  1 
 zM exp  zM 1  bM 
where zM  arg max z BbM , z .
We can obtain comparative statics results about the variations in  ,  , and r of these
quantities.
14
Calibration: One Term in Office
We estimate  and  from IMF data over the period 1980-2011 and set r  6.9%, the average US
TB rate over that period.
Recalling that d denotes the debt to government disposable income ratio, we transform dM into
its corresponding debt/GDP ratio by multiplying it by the product of the ratio of government
income to GDP and the ratio of government disposable income to government income.
Debt
Debt
Gvt .Disp.Inc. Gvt .Inc.



GDP Gvt .Disp.Inc.
Gvt .Inc.
GDP
Gvt .Inc.
 dM   
GDP
where  is there ratio of government disposable income to government income.
We obtain Debt / GDP and Gvt .Inc. / GDP from IMF data and set   40% .
15
Debt/GDP, Max.Debt/GDP, Max.PD, Selected Countries
Country D, 80-11, % D, 11, % dM , % PDM , %
Argentina
73
45
61
3.01
Australia
20
24
166
0.62
Austria
64
72
224
0.58
Canada
78
85
168
0.86
France
50
86
222
0.53
Germany
61
80
172
0.82
Greece
85
165
107
1.28
Italy
108
120
171
0.73
Japan
117
229
106
1.06
Spain
47
69
150
0.84
Sweden
55
38
216
0.91
Switzerland
50
47
140
0.66
Turkey
53
39
97
2.04
U. Kingdom
45
82
148
0.89
U. States
65
103
135
0.81
16
Different countries clearly have different dM as well as PDM .
These can be viewed as defining a country’s tolerance for debt, with lower dM and/or higher PDM
countries being more debt-intolerant (Reinhart et al., 2003).
Debt intolerance tends to decrease in  and the ratio of government income to GDP; it tends to
increase in  (Catão and Kapur, 2004).
The results in  and  are perhaps not surprising.
Those in the ratio of government income to GDP reflect the dependence of government
creditworthiness on government income.
Government income and private income are not always positively related: John Kenneth
Galbraith (1958) contrasted “public squalor” with “private affluence.”
17
 ,  , Gov.Inc./GDP, Max.Debt/GDP, Max.PD, Selected Countries
Country
Argentina
Australia
Austria
Canada
France
Germany
Greece
Italy
Japan
Spain
Sweden
Switzerland
Turkey
U. Kingdom
U. States
 , %  , % Gvt.Inc., % dM , % PDM , %
2.5
3.1
2.1
2.5
1.8
1.7
1.4
1.3
2.1
2.5
2.3
1.8
4.1
2.3
2.6
6.0
1.6
1.5
2.1
1.4
2.0
2.9
1.8
2.5
2.1
2.2
1.7
4.4
2.2
2.0
28
33
49
41
49
45
34
44
30
37
56
34
32
38
32
61
166
224
168
222
172
107
171
106
150
216
140
97
148
135
3.01
0.62
0.58
0.86
0.53
0.82
1.28
0.73
1.06
0.84
0.91
0.66
2.04
0.89
0.81
18
Note that if the government were able to ‘sell’ its expected future disposable income to
investors, it would receive
 E g 

  yt  s

E g s
E 
y

y
1


...


...
t

s t
s
1

r


1

r
 s0 1  r  


yt

E g 
1
1r
E g  
The ‘price to disposable income’ ratio, PDIR   1 
 , expressed as a fraction of GDP, can be
 1r 
compared to maximum government debt dM .
1
19
Max.Debt/GDP, Price to Disposable Income Ratio, Max.PD, Selected Countries
Country dM , % PDIR , % PDM , %
Argentina
61
284
3.01
Australia
166
382
0.62
Austria
224
442
0.58
Canada
168
407
0.86
France
222
411
0.53
Germany
172
373
0.82
Greece
107
269
1.28
Italy
171
342
0.73
Japan
106
267
1.06
Spain
150
359
0.84
Sweden
216
524
0.91
Switzerland 140
282
0.66
Turkey
97
527
2.04
U. Kingdom 148
357
0.89
U. States
135
323
0.81
20
The difference between the two measures can be accounted for by

the annual income that remains for the government to dispose of in the case of debt
financing and

the ‘sudden stop’ in default, which prevents the ‘bringing forward’ of future income
through borrowing.
Income remains because debt financing implies an upper bound on payments to lenders.
There is no upper bound in the case of equity financing; no income therefore remains.
There is no default in the case of equity financing.
21
Model: Many Terms in Office
We now consider the case where the government is reelected with probability  to another term
in office.
The government’s value function V dt 1yt 1 ,yt  is such that
V dt 1yt 1 , yt   uyt  bt yt  dt 1yt 1  

1 r
E V dt yt ,yt 1 
The government recognizes that its choice of borrowing bt affects its debt dt .
c1a
We shall set uc  
. In this case V D ,Y  is homogenous:
1a
D
V D ,Y   V  ,1 Y 1a  v d Y 1a
Y 
22
The value function is obtained by iterating the contraction mapping
Tvd'   max u1  B x   d'  
x

 1  bM x 
E g1av 

1r 
g



where
B x  


1
x1  F  x 1  bM   0xgdF g 
1r
denotes government borrowing as a fraction of government disposable income.
Note that x  xM  dM / 1  bM  and B x   BxM   bM for   0 .
Further note that v 0  PDIR for   1 and a  0 .
23
Proposition: Government borrowing B x  and government debt d are decreasing in  .
Corollary: B x   bM and d  dM for   0 .
The prospect of reelection decreases government borrowing and government debt: governments
realize that default jeopardizes their prospect of future terms in office; they decrease the
probability of default by decreasing borrowing.
We refer to  as ‘the patience of politicians.’
We expect patience to depend not only on the length of politicians’ expected term in office, but
also on politicians’ greater or lesser concern with developments beyond such term.
24
d
a0
dM
 1
 1
1
1  bM
d'
Debt Dynamics under Risk Neutrality
25
d
a0
dM
 1
 1
1  bM
d'
Debt Dynamics under Risk Aversion
26
Calibration: Many Terms in Office
Minimum debt, dm , prevails where politicians are least risk averse ( a  0 ) and most patient
(  1 ).
Low actual default probabilities may be explained by the ‘margin of safety’ due to the difference
between actual and maximum sustainable debt.
Default probabilities remain quite low on as long as government debt remains below its
maximum sustainable level. They increase rather quickly afterwards.
27
Debt/GDP, Max.Debt/GDP, Min.Debt/GDP, Selected Countries
Country D, 80-11, % D, 11, % dM , % dm , %
Argentina
73
45
61
7
Australia
20
24
166
21
Austria
64
72
224
43
Canada
78
85
168
24
France
50
86
222
61
Germany
61
80
172
24
Greece
85
165
107
15
Italy
108
120
171
23
Japan
117
229
106
20
Spain
47
69
150
27
Sweden
55
38
216
52
Switzerland
50
47
140
26
Turkey
53
39
97
13
U. Kingdom
45
82
148
21
U. States
65
103
135
25
28
Debt/GDP, PD, Max.Debt/GDP, Max.PD, Selected Countries
Country D, 80-11, % PD, 80-11, % D, 11, % PD, 11, % dM , % PDM , %
Argentina
73
82
45
0
61
3.01
Australia
20
0
24
0
166
0.62
Austria
64
0
72
0
224
0.58
Canada
78
0
85
0
168
0.86
France
50
0
86
0
222
0.53
Germany
61
0
80
0
172
0.82
Greece
85
0
165
100
107
1.28
Italy
108
0
120
0
171
0.73
Japan
117
96
229
100
106
1.06
Spain
47
0
69
0
150
0.84
Sweden
55
0
38
0
216
0.91
Switzerland
50
0
47
0
140
0.66
Turkey
53
0
39
0
97
2.04
U. Kingdom
45
0
82
0
148
0.89
U. States
65
0
103
0
135
0.81
29
Conclusion
Different countries have different degrees of debt (in)tolerance, represented in our model by the
maximum sustainable debt ratio bM .
A country’s debt tolerance depends on the mean and volatility of the country’s growth rate, its
government income to GDP ratio, its government disposable income to government income
ratio, and the world risk-free interest rate.
A country’s actual debt ratio differs from the country’s maximum sustainable ratio because

politicians realize that default jeopardizes their prospect of future terms in office

politicians may have concerns that extend beyond their expected term in office.
The difference between a country’s actual and maximum sustainable debt ratios provide the
country with a ‘margin of safety:’ a country that has not yet reached its maximum sustainable
debt ratio can increase debt at relatively little cost.
Such is no longer the case once the margin of safety has been exhausted and debt is larger than
its maximum sustainable level.
30
We believe our results may help shed some light on the recent experience of countries such as
Argentina on the one hand and France, the United Kingdom, and the United States on the other
hand.
If our calibration results are (approximately) true, then there is little justification for the recent
occasional spikes in Italy and Spain’s borrowing rates.
Matters in Greece and Japan may be different.
Note that an increase in debt towards its maximum sustainable ratio, although feasible, generally
is not desirable: it mortgages future government disposable income (and therefore may actually
invalidate the assumption of no strategic default).
31
v( d )
v( 0 )


1
E g1av 0   K
1r
1  bM
d
Default Payoffs for Country and for Government
32