Transcript pptx - Tony Yates

Lecture 8: Sovereign debt and
default
MSc International Macro
Birmingham, Autumn 2015
Tony Yates
[Material from Uribe/S-G and Uribe/Woodford]
What is a sovereign default
• Government sells bonds to finance current
spending or investment project on behalf of
citizens [hopefully].
• Circumstances change and govt can no longer
raise the taxes to pay back the debt, or issue
further bonds to roll over the debt that is due.
• Could be resolved by partial default ‘hair-cut’.
• Or via inflation, which lowers real value of
outstanding nominal debt, a form of default.
Sovereign default very topical
• Eurozone crisis precipitated by threat of
default by the small ‘peripheral’ sovereigns of
Greece, Ireland, Portugal, Cyprus.
• Many defaults documented in, eg, Reinhardt
and Rogoff: ‘This time it’s different’.
• Russian default in 1997.
• Argentinian default in 2000.
• UK ‘austerity’ motivated initially by a desire to
avoid risk of default.
Plan
• Informal discussion of some issues in
sovereign debt
• Small formal model of sovereign default to
introduce you to the theoretical literature.
Issues raised by sovereign default
•
•
•
•
Orderly workouts, holdouts.
Empirical work on defaults.
Optimal sovereign debt contracts
Shilller agenda for financial reform, eg GDP linked
bonds
• Political economy of sovereign debt and
sovereign obligations
• Monetary-fiscal coordination
– Fiscal theory of the price level
– Unpleasant monetarist arithmetic
Workouts and holdouts
• If government defaults, negotiation proceeds
on a haircut.
• Holdouts are those who ‘hold out’ for the best
possible deal, potentially against the interests
of a majority of others, who favour a quick
settlement.
• Anticipating holdout problems, this makes
sovereign debt finance expensive at the
outset.
Optimal sovereign debt contracts
• How to structure the debt offering so that it
maximises welfare of borrower and lender.
• Remember debt, just as for our private
optimising consumers, can be the means for
consumption-smoothing undertaken by govts.
[eg automatic stabilisers]
• We will explore this a little, formally, later.
Shiller and financial reform
• We have index linked bonds issued by
developed economies.
• Why not GDP-linked bonds?
• Devices to diversify state out of volatile
‘strategic’, ‘nationalist’ assets like commodity
extraction…
• …whose returns are typically very volatile….
• Which mitigates against consumptionsmoothing.
Shiller and financial reform: (2)
• Elaborate debt contracts give rise to more
questions about enforcement…
• … and about truth-telling in the indices, like GDP,
and performance of state industries.
• Eg Argentinian inflation statistics, widely assumed
now to be falisified by state stats agency…
• …Venezuela, which now has stopped publishing
GDP… probably because it’s too embarrassing to
report sharp declines.
Political economy of sovereign debt
• How either success or failure of democracy
can give rise to inefficient debt accumulation
[which in turn could be too much or too little]
• How anti-democratic debt accumulation
involves subsequent trade-off between rights
of future cohorts, and financial terms they
might expect in the markets.
M and F policy coordination: fiscal
theory
• Politics can make taxes and spending
unresponsive to debt targets.
• Cochrane/Woodford; prices may jump to
revalue outstanding nominal debt…
• …how sharply depending on maturity
structure of outstanding debt.
M and F policy coordination:
unpleasant monetarist arithmetic
• Alternative explanation for how fiscal
‘misbehaviour’ leads to inflation
• As expected/actual gap opens up between
spending and revenue plans…
• People expect seigniorage [money printing] to be
used to make up the difference
• Expected inflation rises….
• Inevitable inflation increase cemented by fact
that it would be recessionary not to supply the
inflation expected.
Definition of default
• Doesn’t mean pay back 0. Average
‘haircut’=40%.
– Uribe cites: Sturzeneger and Zettelmeyer, 2008;
Cruces and Trebesch, 2014 and Benjamin and
Wright, 2008.
• Standard&Poor definition:
– Failure to meet a principal or interest payment on
the date it was due.
Empirics of default
• Output/financing spread/trade/financial
exclusion costs of default
• Identification problems
Source: slides by Schmitt-Grohe and Uribe [linked to in reading list]
The financing costs of default for
defaulters
Source: slides by Schmitt-Grohe and Uribe, linked to in reading list.
Rose’s gravity model and ‘trade
sanctions’
• Empirical ‘gravity’ model for trade.
• Trade increased by proximity, shared
language, colonial history, currency….
• Default status reduces trade significantly.
Output permanently lower than pre-default trend.
NPV of this would be huge.
Source: Slides from Schmitt-Grohe and Uribe, linked to in reading list
Note: relevant if we consider the model of sovereign debt and reputation; or
sanctions imposition.
Source: slides by Schmitt-Grohe and Uribe linked to in the reading list.
Simple model of sovereign debt
• Small economy
• Representative agent who is risk averse.
• Rest of world simply lends, and faces no
opportunity cost of funds.
• Finite number of states S, with prob pi_s
• Endowment y_s varies with the state.
• RA seeks insurance against endowment variation
[to do consumption smoothing] using debt
contracts.
Remarks about the model set up
•
•
•
•
•
•
Microfounded.
No production.
Representative agent.
Small open economy again.
Risk.
Benevolent government attempting
consumption-smoothing for its RA consumer.
y s y e s
Rep agents faces this random endowment
process.
S
 sd s 0
s1
And seeks an insurance contract d_S that
will remove uncertainty in its consumption
possibilities.
In good times, RA pays to the insurer [the
rest of world].
In bad times, RA collects a payment from
ROW.
S
max  
cs
s u
s1
Rep agent maximises consumption across
the different states of nature.
c s y e s d s , 
s
Subject to a budget constraint that holds
in each state.
d s , s 1. . . . S
And by choosing the d_s contracts in each
state too.
Limited commitment problem
• When the state is bad, our rep agent is due a
payout from the rest of world insurer.
• But when state is good, rep agent has to pay
out. This may be hard to commit to.
• For now we ignore the commitment problem.
• But will later return to it.
Lagrangian for rep agent consumer
S
L  
u
y e s d s d s 
s
s1
Here we have used the
state by state budget
constraint to substitute out
for consumption
Here we insert the constraint that
the debt payments have to add up
to zero in expectation. Lamda is the
LM on this constraint.
Note that summing over the S terms
weighted by their probability signals
that we are maximising expected
utility.
Optimal debt contract
dL  0  u 
c s 
s
s  0
dd s
 u 
c s 
c s y
d s e s
S first order conditions wrt the
choice variables d_s
MU is constant, since a fn of the
LM, which is independent of the
state.
Leads to observation that c_s=y.
All of uncertainty pushed onto
the lender.
dd s
de s
1
Ie insurance payout=shock.
Empirical relevance of commitment
• Assuming commitment begs q: how will it be
enforced?
• Elected governments can and are supposed to
do what they were elected to do. Which
might be to default.
• Many defaults in the past, so commitments
sometimes broken.
• Possible answers: constitutions; military or
economic sanctions; reputation.
No commitment
• Notion of ‘incentive compatability’
• Means: only payments allowed are ones that
an agent would not have an incentive to
renege on.
• Here, means: debt payments that are
payments from lender to borrower, or zero.
• We’ll see that without commitment, there is
no insurance.
Optimal debt with no commitment,
and no algebra either!
d s 0, 
s
Incentive compatability means that debt
payments have to be 0 or positive, or the
borrower will renege.
S
 sd s 0
s1
dd s
de s
0
But at the same time, for the lender to be
willing to participate, debt has to average zero
across states.
Only contract that satisfies both constraints is
d=0,all s.
So no insurance. C_s=y_s.
Sovereign debt with creditor sanctions
• We’ll assume the creditor can levy sanctions k
if the borrower reneges.
• And though these are harmful, ex post, if the
borrower reneges…
• Ex ante, the sanctions are a blessing….
• Since they permit partial insurance…
• And therefore lower consumption volatility
and higher utility for the representative agent.
Creditor sanctions and the Lagrangian
d s k
Debt payments can’t exceed the sanction
that the creditor can impose. If they did,
borrower better off reneging.
S
L  
u
y e s d s d s s 
k d s 

s
s1
New Lagrangian with sanctions.
Note 3 constraints appear. Period by period budget constraint has been
imposed by substituting out for consumption as before.
Participation constraint by lenders with LM=lamda.
Incentive compatability constraint for borrowers, with LM=gamma_s.
First order conditions…
dL
dd s

0  u 
c s  s
s 0
s k d s 0
Marginal utility of c, hence c, has both a
part not related to the state, and a part
that is related to the state.
These two conditions that hold at the
optimum follow from the kuhn-Tucker
theorem.
First: just says ‘either constraint doesn’t
bind, or there will be some gain to the
rep agent from relaxing it.’
Second: we see that gamma_s can be
zero. In which case, second condition
satisfied by d_s<k.
Form of the optimal debt contract,
details to be derived later
d s d e s , e s e
d s k, e s e
Debt payment will be some constant, plus an
amount equal to the shock, provided the
endowment is not too positive.
In which case our rep agent would rather
renege and face the sanctions.
So above a certain value for the shock, the debt
payment simply equals the sanctions value.
Plan for next bit of analysis…
d e k, d 0
We are going to assume the first of these
[Uribe actually proves it to be the case].
First says: ‘constant bit of the insurance
payment, plus the cutoff value of the
endowment shock=level of sanctions that can
be levied by the lender’.
We will prove that d_bar is positive.
And that means that the rep agent gets less
insurance than under full commitment.
Under full commitment, when the endowment
is negative, agent receives e_s.
Now our rep agent receives e_s-d_bar
 sd es sk 0
e s e
e s e
 sd es sd e0
e s e
e s e
d  
 se 0
ses 
e s e
e s e
Split the zero average payments
condition into 2 parts, one including
shocks up to e_bar, and the other greater
than e_bar.
Here we substitute in d_bar+e_bar=k
Now collect terms in d_bar; note that
we have 1*d_bar since the prob weights
pi_s sum to 1.
Deducing d_bar>0
d  
 se 0
ses 
e s e
e s e
d  
e s e0
s
e s e
It turns out that we can write this
expression that we just derived on
last slide…..
….As this one, which will reveal
directly to us that d_bar must be
positive. [We’ll return to exactly why
this is true].
To see why this re-writing is possible,
expand this summation term…
Showing that d_bar>0
d
 s es  se
e s e
…to get this second line here…
0
e s e
 d  
 se 0
ses 
e s e
 ses  ses
e s e
e s e
e s e
We’ll see that this is what needs
to be true for our re-writing to be
valid. And this is true by the
assumption that the endowment
shock is mean zero.
‘Mean zero’ means the
probability weighted sum of the
endowment shock is zero.
Showing d_bar>0
d  
e s e
s
e s e
Probability weights pi_s are obviously>0.
Given RHS sum restricted to range where
e_s>=0, then terms in brackets either
zero, or >0.
So RHS >0.
Which means d_bar>0.
This means that come what may, our
borrower has to pay something to the
lender, even in bad states with e_s<0.
So outcome worse than full insurance.
But better than no insurance!
Benefits of partial insurance
dd s
0, e s e
de s
dd s
1, e s e
de s
We saw that with full insurance, the
debt payment moves 1 for 1 with the
endowment.
With no insurance, d is constant.
Here we have an intermediate case.
Below the cutoff level of the
endowment at which the incentive
compatability constraint binds, debt
payment behaves as under full
insurance.
Sanctions are a curse not a blessing
• Sanctions punishment against borrowers is
actually a blessing.
• The higher is k, the higher the endowment shock
can be before it’s worth the borrower reneging.
• This enlarges the region of the endowment for
which debt moves one for one with the
endowment
• …Reducing income and consumption risk…
• And therefore raising utility.
Recap
• We saw that default was costly.
– Reduces output, trade, increases borrowing costs
• Yet many instances of sovereign default.
• Sovereign debt an important device to smooth
consumption of a nation’s citizens.
• But difficult political economy issues [rights of
the unborn, or those who don’t vote in nondemocracies]
Recap: 2
• Studied a microfounded rep agent model of
sovereign debt as insurance.
• Full commitment leads to full insurance.
• No commitment leads to no insurance.
• No commitment plus credible sanctions leads
to partial insurance.
• The worse are the sanctions, the better the
insurance, and the better off is our rep agent
borrower.