monetary policy and sovereign debt vulnerability€¦ · government renounces the ability to...
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Monetary Policy and Sovereign Debt Vulnerability1
Galo Nuño & Carlos Thomas
Banco de España
XVII Annual Inflation Targeting Seminar, Banco Central do BrasilMay 21 2015
1These slides represent the authors’views and does not necessarily represent those ofBanco de España
Nuño & Thomas (BdE) Monetary Policy and Sovereign DebtXVII Annual Inflation Targeting Seminar, Banco Central do Brasil May 21 2015 1
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Motivation: European debt crisis
Legacy of 2007-9 financial crisis: large fiscal deficits and soaringgovernment debt
Before summer 2012, sovereign yields rose sharply in EMU periphery(GR, IR, IT, PT, SP) ...
... but not in other highly indebted countries (US, UK, etc.)
Many argue a key difference is: US-UK can deflate debt away, EMUperiphery countries cannot
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Motivation: role of monetary policy
What role, if any, should monetary policy play in guaranteeingsovereign debt sustainability?
Arguments for and against monetary policy involvement:
provide ’monetary backstop’against default fearscreating inflation also entails costseffect on inflation expectations (and yields) if low monetary credibility
This paper: analyze trade-offs between price stability and sovereigndebt sustainability...
... when gov’t cannot make credible commitments
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Framework of analysis
Small open-economy, continuous-time model
Benevolent government issues nominal defaultable debt to foreigninvestors
Gov’t may default on debt at any time
costs of default: exclusion from capital markets + output loss
Government chooses fiscal (primary deficit) and monetary policy(inflation) under discretion
Benefits and costs of inflation:
debt can be deflated awaydirect welfare losses
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Preview of results
Calibrate to average peripheral EMU economy
Analyze two monetary regimes:1 inflationary regime: benevolent gov’t chooses inflation discretionarily2 no inflation regime: zero inflation at all times
In (2), government gives up option to deflate debt away
issue foreign currency debtjoin monetary union with strong anti-inflation mandate
Main result: Welfare is higher in no inflation regime, for any debtratio and on average
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Literature review
Links between sovereign debt vulnerability and monetary policy
Aguiar et al. (2013, 2015), Corsetti and Dedola (2013): self-fulfillingdebt crises (à la Calvo,1988; Cole and Kehoe, 2000)
Optimal fundamental sovereign default in quantitative models
Aguiar and Gopinath (2006), Arellano (2008), etc.
Extend literature on continuous-time models of default to the pricingof defaultable nominal sovereign debt
Merton (1974), Leland (1994)
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The model: output, prices and debt
Single consumption good with int’l price = 1. Exogenous outputendowment,
dYt = µYtdt + σYtdWt .
Local currency price,dPt = πtPtdt.
Sovereign debt,dBt = Bnewt dt − λdtBt .
λ : amortization rate; fully held by foreign investorsGovernment’s flow of funds
QtBnewt = (λ+ δ)Bt + Pt (Ct − Yt ) .
δ : coupon rate
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The model: output, prices and debt
Single consumption good with int’l price = 1. Exogenous outputendowment,
dYt = µYtdt + σYtdWt .
Local currency price,dPt = πtPtdt.
Sovereign debt,dBt = Bnewt dt − λdtBt .
λ : amortization rate; fully held by foreign investorsGovernment’s flow of funds
QtBnewt = (λ+ δ)Bt + Pt (Ct − Yt ) .
δ : coupon rate
Nuño & Thomas (BdE) Monetary Policy and Sovereign DebtXVII Annual Inflation Targeting Seminar, Banco Central do Brasil May 21 2015 7
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The model: output, prices and debt
Single consumption good with int’l price = 1. Exogenous outputendowment,
dYt = µYtdt + σYtdWt .
Local currency price,dPt = πtPtdt.
Sovereign debt,dBt = Bnewt dt − λdtBt .
λ : amortization rate; fully held by foreign investors
Government’s flow of funds
QtBnewt = (λ+ δ)Bt + Pt (Ct − Yt ) .
δ : coupon rate
Nuño & Thomas (BdE) Monetary Policy and Sovereign DebtXVII Annual Inflation Targeting Seminar, Banco Central do Brasil May 21 2015 7
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The model: output, prices and debt
Single consumption good with int’l price = 1. Exogenous outputendowment,
dYt = µYtdt + σYtdWt .
Local currency price,dPt = πtPtdt.
Sovereign debt,dBt = Bnewt dt − λdtBt .
λ : amortization rate; fully held by foreign investorsGovernment’s flow of funds
QtBnewt = (λ+ δ)Bt + Pt (Ct − Yt ) .
δ : coupon rate
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The state variable: debt-to-GDP ratio
Debt-to-GDP ratiobt ≡ Bt/ (PtYt )
Applying Itô’s lemma
dbt =
rt (yield)︷ ︸︸ ︷λ+ δ
Qt− λ+ σ2 − µ− πt
bt + ctQt
dt − σbtdWt ,
wherect ≡ (Ct − Yt ) /Yt
is primary deficit ratio
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The state variable: debt-to-GDP ratio
Debt-to-GDP ratiobt ≡ Bt/ (PtYt )
Applying Itô’s lemma
dbt =
rt (yield)︷ ︸︸ ︷λ+ δ
Qt− λ+ σ2 − µ− πt
bt + ctQt
dt − σbtdWt ,
wherect ≡ (Ct − Yt ) /Yt
is primary deficit ratio
Nuño & Thomas (BdE) Monetary Policy and Sovereign DebtXVII Annual Inflation Targeting Seminar, Banco Central do Brasil May 21 2015 8
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Preferences
Household preferences,
U0 = E0
[∫ ∞
0e−ρt
(log(Ct )−
ψ
2π2t
)dt].
ψ > 0 : distaste for inflation, reduced-form π-disutility followingAguiar et al. (2013)
Using Ct = (1+ ct )Yt ,
U0 = E0
[∫ ∞
0e−ρt
(log(1+ ct )−
ψ
2π2t
)dt]+ V aut0 ,
where V aut0 = E0[∫ ∞0 e
−ρt log(Yt )dt]is the (exogenous) autarky
value
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Preferences
Household preferences,
U0 = E0
[∫ ∞
0e−ρt
(log(Ct )−
ψ
2π2t
)dt].
ψ > 0 : distaste for inflation, reduced-form π-disutility followingAguiar et al. (2013)
Using Ct = (1+ ct )Yt ,
U0 = E0
[∫ ∞
0e−ρt
(log(1+ ct )−
ψ
2π2t
)dt]+ V aut0 ,
where V aut0 = E0[∫ ∞0 e
−ρt log(Yt )dt]is the (exogenous) autarky
value
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Fiscal and monetary policy
At each point in time, choose
default or continue repaying debt ⇔ optimal default threshold b∗
primary deficit ratio (ct ), inflation rate (πt )
under discretion (take investor’s pricing scheme Q (b) as given)
First analyze default scenario
Then lay out general optimization problem
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The default scenario
Default (at a debt ratio b) implies
exclusion from capital markets (reenter at rate χ)and contraction in output endowment (in logs, εmax{0, b− b})
At end of exclusion period, gov’t reenters markets with debt ratio θb
Value of defaulting (net of autarky value),
V def (b) = −εmax{0, b− b}ρ+ χ
+χ
ρ+ χV (θb) .
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The general problem
Let T (b∗) be time-to-default. Government value function,
V (b) = maxb∗,{ct ,πt}
E
{ ∫ T (b∗)0 e−ρt
(log(1+ ct )− ψ
2π2t
)dt
+e−ρT (b∗)Vdef (b∗)|b0 = b
}
subject to b’s law of motion, and
V (b∗) = Vdef (b∗),
V ′ (b∗) = V ′def (b∗),
i.e. value matching & smooth pasting conditions
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The ’no inflation’regime
Consider an alternative scenario where
π (b) = 0
for all b.
Government renounces the ability to deflate debt away
Possible interpretations:
Issue foreign currency debtJoin a monetary union with a strong anti-inflationary stance(Appoint extremely conservative central banker)
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International investors (bond pricing)
Risk-neutral investors can invest elsewhere at riskless real rate r
Unit price of the nominal non-contingent bond
Q(b) = E
∫ T ∗0 e−(r+λ)t−
∫ t0 πsds (λ+ δ) dt
+e−r (T∗+τ)−λT ∗−
∫ T ∗0 πsdsθ
YT ∗+τ
YT ∗Q (θb∗) |b0 = b
,T ∗ ≡ T (b∗), with boundary condition
Q(b∗) = E
[e−rτθ
Yτ
Y0Q (θb∗)
]=
χ
r + χ− µθQ (θb∗) .
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Calibration
Calibrate to the average peripheral EMU economy, time unit = 1 year
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Equilibrium: inflationary regime
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40.1
0
0.1
0.2
0.3
debttogdp ratio, b
Value function, V
In.ationary
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40.4
0.5
0.6
0.7
0.8
0.9
1
debttogdp ratio, b
Bond price, Q
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.41
0.5
0
0.5
debttogdp ratio, b
Primary decit to gdp, c
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40
0.05
0.1
0.15
debttogdp ratio, b
In.ation, :
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40
10
20
30
40
debttogdp ratio, b
Expected time to default, T e
year
s
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40
0.05
0.1
0.15
0.2
0.25
0.3
debttogdp ratio, b
Nominal interest rate, r
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Equilibrium: inflationary vs no-inflation regime
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40.1
0
0.1
0.2
0.3
debttogdp ratio, b
Value function, V
No in.ation
In.ationary
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40.4
0.5
0.6
0.7
0.8
0.9
1
debttogdp ratio, b
Bond price, Q
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.41
0.5
0
0.5
debttogdp ratio, b
Primary decit to gdp, c
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40
0.05
0.1
0.15
debttogdp ratio, b
In.ation, :
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40
10
20
30
40
debttogdp ratio, b
Expected time to default, T e
year
s
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40
0.05
0.1
0.15
0.2
0.25
0.3
debttogdp ratio, b
Nominal interest rate, r
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Risk premia & inflation premia
Nominal bond yield r (b) can be decompose as risk premium +inflation premium
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40
0.01
0.02
0.03
0.04
0.05
0.06
debttogdp ratio, b
Risk premium
In.ationary
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40
0.01
0.02
0.03
0.04
0.05
0.06
debttogdp ratio, b
In.ation premium
No in.ation
In.ationary
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Average performance
Inflationary regime yields lower value function V (b) at any debtratio, but...
... If it delivers suffi ciently lower debt ratio most of the time, averagewelfare could be higher
Compute stationary debt distribution so as to calculate unconditionalaverage values
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Stationary debt distribution
Inflationary regime shifts distribution to the left (debt deflation)...
0.34 0.345 0.35 0.355 0.36 0.365 0.37 0.375 0.380
20
40
60
80
100
120
140
debttogdp ratio, b
No in.ation
In.ationary
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Average performance (cont’d)
... but not enough to make inflationary policy better on average
Data Model1995-2012 No inflation Inflationary
debt-to-GDP, b (%) 35.6 35.6 35.6primary deficit ratio, c (%) -4.1 -0.01 -0.12inflation, π (%) 0.4 0 3.20bond yields (net of r ), r − r (bp) 187 154 448risk premium, r − r (bp) 154 154 139inflation premium, , r − r (bp) 33 0 309Exp. time to default, T e (years) - 29.4 37.1Welfare loss, V − Vπ=0 (% cons.) - 0 -0.25
Again, ↑ in mean risk premia dominated by ↓ in mean inflationpremia & direct utility costs
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Robustness
Investigate robustness to alternative calibrations of:
bond amortization rate (λ)bond recovery parameter (θ)output loss from default (b)
For all parameter values, we continue to find higher average welfare inno-inflation regime
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Monetary policy delegation
’No inflation’regime equivalent to appointing an extremelyconservative central banker
Consider intermediate arrangement: appoint a central banker...
who dislikes inflation more than society...... but not so much as to set π = 0 at all times
Given government’s c (b) and b∗, central banker chooses π ...
to maximize its value function V , defined similarly to V , but withψ ≥ ψ
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Monetary policy delegation: results
Average welfare increases monotonically with ψ/ψ but never reachesE (Vπ=0)
0 10 20 30 40 500.25
0.2
0.15
0.1
0.05
0
eA / A
Welfare, V
0 10 20 30 40 500.3
0.32
0.34
0.36
0.38
0.4
eA / A
Default threshold, b$
0 10 20 30 40 500.075
0.08
0.085
0.09
0.095
0.1
eA / A
Average time in exclusion
No in.ation
In.ationary
0 10 20 30 40 500
0.005
0.01
0.015
0.02
0.025
0.03
eA / A
In.ation, :
0 10 20 30 40 508
6
4
2
0
2x 104
eA / A
Primary decit, c
0 10 20 30 40 50
0.075
0.08
0.085
0.09
0.095
0.1
eA / A
Nominal interest rate, r
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Conclusions
Analyzed trade-offs between price stability and sovereign debtsustainability...
... in an open-economy model with nominal debt and optimal default
Welfare is higher if gov’t renounces the option to deflate debt away,e.g. by
issuing foreign currency debtjoining an anti-inflationary monetary union
Intuition: benefits (lower inflation premia, no direct welfare costs)outweigh costs (higher risk premia)
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