Breaking the feedback loop: macroprudential regulation of banks' sovereign exposures

Breaking the Feedback Loop:
Macroprudential Regulation of Banks’
Sovereign Exposures
Jorge Abad
<jorge.abad@cemﬁ.edu.es>
CEMFI
ADEMU Conference
April, 2018
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Motivation
Recent European crisis featured the so-called negative feedback loop between
banks and sovereigns (“diabolic loop”, “deadly embrace”, ...)
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Motivation
• Government bailouts increased debt burden and sovereign yields
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Motivation
• Banks increased their holdings of high-yield, risky sovereign debt
2 / 38

Motivation
→ Mutually reinforcing effects of sovereign and bank risk
→ Negative effect on financial intermediation and economic activity
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Motivation
→ Mutually reinforcing effects of sovereign and bank risk
→ Negative effect on financial intermediation and economic activity
• Several voices called for a change in the way banks’ exposure to sovereign
risk is regulated
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This paper
Negative feedback loop in a dynamic general equilibrium framework, with both
endogenous bank failure risk & sovereign default risk
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This paper
• Financial condition of banks aﬀects economic activity
• Bank risk and sovereign risk are interdependent
→ Sovereign risk as a source of ampliﬁcation and systemic spillovers
• Banks’ exposure to sovereign risk might be excessive
→ Room for macroprudential regulation
Some facts
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This paper
• Financial condition of banks affects economic activity
• Bank risk and sovereign risk are interdependent
→ Sovereign risk as a source of amplification and systemic spillovers
• Banks’ exposure to sovereign risk might be excessive
→ Room for macroprudential regulation
Some facts
Two main questions:
• Contribution of the feedback loop as an amplification mechanism
• Role of regulation and welfare trade-offs in mitigating these effects
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Regulatory framework
k
b
e
d
e: equity
d: deposits
b: sovereign bonds
k: other risky assets
Figure 1: A simpliﬁed bank balance sheet
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k
b
e
d
e: equity
d: deposits
b: sovereign bonds
Bank capital regulation: e ≥ γ(k + ιb)
• A fraction γ of banks’ risk-weighted assets has to be ﬁnanced with equity
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k
b
e
d
e: equity
d: deposits
b: sovereign bonds
Bank capital regulation: e ≥ γ(k + ιb)
• A fraction γ of banks’ risk-weighted assets has to be ﬁnanced with equity
• Domestic sovereign bonds are treated as riskless (risk weight ι = 0)
Policy debate
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Related literature
• Theoretical literature on the feedback loop: Cooper, Nikolov (2013); Acharya et al.
(2014); Broner et al. (2014); Brunnermeier el al (2016), Farhi, Tirole (2017); Leonello (forthcoming)
→ Typically static or partial equilibrium: do not provide quantitative answers
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Related literature
• Strategic default and banks: Genniaoli et al. (2014); Mallucci (2015); Perez (2015); Thaler
(2017); Sosa-Padilla (2017)
→ Focus on default incentives, abstracting from banks’ risk shifting
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Related literature
• Role of bank capital dynamics in macro: Gertler, Kiyotaki (2010, 2015); Gertler, Karadi
(2011); Brunnermeier, Sannikov (2014)
• Bank risk-taking and capital requirements in macro models: Martinez-Miera, Suarez
(2014); Begenau (2016); Mendicino et al. (forthcoming)
→ Abstract from sovereign default
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Related literature
• Role of bank capital dynamics in macro: Gertler, Kiyotaki (2010, 2015); Gertler, Karadi
(2011); Brunnermeier, Sannikov (2014)
• Bank risk-taking and capital requirements in macro models: Martinez-Miera, Suarez
(2014); Begenau (2016); Mendicino et al. (forthcoming)
→ Abstract from sovereign default
• Eﬀect of sovereign risk on banking sector: Bocola (2016), Ari (2017)
→ Exogenous shocks to sovereign risk: no two-way loop
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The model
• Parsimonious model
Keeping it simple helps understanding the mechanisms at play
Computationally intensive (global) solution method restricts what can be
feasibly solved (curse of dimensionality)
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The model
• Parsimonious model
Keeping it simple helps understanding the mechanisms at play
Computationally intensive (global) solution method restricts what can be
feasibly solved (curse of dimensionality)
• Rich enough to provide quantitative answers
Contribution of the feedback loop to the crisis
Eﬀects of regulatory changes
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Model overview
Government
Banks
International
investors
Firms
Bankers
Households
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Model overview
Government
Banks
International
investors
Firms
Bankers
Households
Deposits
(Dt)
Capital
(Kt)
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Model overview
Government
Banks
International
investors
Firms
Bankers
Households
Deposits
(Dt)
Equity
(Et)
Capital
(Kt)
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Model overview
Government
Banks
International
investors
Firms
Bankers
Households
Deposits
(Dt)
Equity
(Et)
Capital
(Kt)
Deposit
insurance
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Model overview
Government
Banks
International
investors
Firms
Bankers
Households
Deposits
(Dt)
Equity
(Et)
Capital
(Kt)
Bonds
(Bt)
Bonds
(Bt)Deposit
insurance
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Model overview
Discrete time, inﬁnite horizon model of a small open economy
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Model overview
• Households:
Workers: supply labor, intertemporal consumption-savings problem
Bankers: only providers of banks’ inside equity
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Model overview
• Households:
Workers: supply labor, intertemporal consumption-savings problem
Bankers: only providers of banks’ inside equity
• Banks:
Intermediate funds between households and ﬁrms, and hold sovereign bonds
Limited liability + ex post heterogeneous returns → endogenous failure risk
Subject to regulatory capital requirements
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Model overview
• Firms:
Combine labor and physical capital to produce consumption good
Operate a Cobb-Douglas production function under perfect competition
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Model overview
• Firms:
• Government:
Issues debt subject to default risk
Guarantees bank deposits (provided that the govt. does not default)
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Model overview
• Firms:
• Government:
• International investors:
Overlapping generations of risk-averse foreign lenders
Invest in sovereign debt
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Model overview
• Firms:
• Government:
• International investors:
Overlapping generations of risk-averse foreign lenders
Invest in sovereign debt
Two sources of aggregate risk: bank failure shock and sovereign default
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Key ingredients
Sovereign default:
• Government guarantees deposits
→ An increase in bank failure increases debt and sovereign risk
• If the government defaults:
It inﬂicts losses on bond holders
It cannot honor deposit guarantees
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Key ingredients
Sovereign default:
• Government guarantees deposits
→ An increase in bank failure increases debt and sovereign risk
• If the government defaults:
It inflicts losses on bond holders
It cannot honor deposit guarantees
Banks’ risk-taking incentives distorted by:
• Limited liability:
Banks do not internalize the social cost resulting from their failure
• Opaque balance sheets: Example
Individual banks do not internalize the effect of their risk profile on the
funding costs of the whole banking sector
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Notation
• Promised (gross) returns: Rd
t , Rb
t known ex-ante
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Notation
• Promised (gross) returns: Rd
t , Rb
t known ex-ante
• Realized (gross) returns: Rd
t+1, Rb
t+1 depend on the realization of aggregate
uncertainty
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Households
A representative household chooses Ct, Dt, Kh
t to maximize:
Et
∞
i=0
βi (Ct+i )1−ν
1 − ν
subject to the budget constraint:
Ct + Dt + Kh
t + h(Kh
t ) = Wt + Rd
t Dt−1 + Rk
t Kh
t−1 + Πt − Tt
Nt : relevant state variable for the household
(1)
• Ct: consumption; Dt: deposits; Kh
t : physical capital
• Capital management cost: h(Kh
t ) = κ(Kh
t )2
(as in Gertler and Kiyotaki, 2015)
• Wt: labor income; Πt: dividend payments from bankers; Tt: lump-sum taxes
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Bankers
Continuum of bankers with aggregate net worth Et:
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Bankers
• Linear utility function over dividend payments transferred to the household
• Allocate their net worth across banks taking returns Re
t+1 and the household
SDF Λt+1 as given
• Prob. of retirement 1 − ϕ (iid); new bankers’ initial endowment Nt
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Bankers
SDF Λt+1 as given
vt: value of one unit of bankers’ net worth at t
vt = Et Λt+1(1 − ϕ + ϕvt+1)
Ωt+1: bankers’ SDF
Re
t+1
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Bankers
SDF Λt+1 as given
vt: value of one unit of bankers’ net worth at t
vt = Et Λt+1(1 − ϕ + ϕvt+1)
Ωt+1: bankers’ SDF
Re
t+1
Aggregate law of motion: Et+1 = ϕRe
t+1Et
Cont. bankers
+ (1 − ϕ) Nt
New bankers
Dividend payments: Πt+1 = (1 − ϕ) Re
t+1Et − Nt
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Banks
Continuum of one-period lived, ex-ante identical banks
• Objective function (choose kt, bt, dt, et):
EtΩt+1max Rk
t+1ωkt + Rb
t+1bt − Rd
t dt − m(dt, bt), 0 − vtet
• Balance sheet constraint: kt + bt = dt + et (2)
• Regulatory capital requirement: et ≥ γ(kt + ιbt) (3)
• kt: physical capital; bt: govt. bonds; dt: deposits; et: equity
• Liquidity mgmt. cost m(dt, bt) = φ(dt )2
bt
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Banks’ liquidity management
As shown in Repullo and Suarez (2004):
• One-period, limited liability banks that can invest in two diﬀerent risky assets
would optimally specialize in one of them (two types of banks in equilibrium)
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• ...unless there exist intermediation costs that imply some complementarity
between the two assets
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• Here: complementarity comes from diﬀerent degrees of liquidity of each
asset (maturity transformation of banks as in Diamond and Dybvig, 1983)
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• Here: complementarity comes from diﬀerent degrees of liquidity of each
asset (maturity transformation of banks as in Diamond and Dybvig, 1983)
Role of government bonds in reducing banks’ liquidity management costs:
• Assume banks receive a random stream of intra-period liquidity shocks
• Having access to a liquid asset (gov. bonds) allows banks to meet
withdrawals without having to liquidate assets
• Liquidity role of public debt analyzed in the theoretical literature (Woodford,
1990; Holmstrom and Tirole, 1998)
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Bank failure
• Banks have access to a capital production technology subject to
idiosyncratic risk
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Bank failure
idiosyncratic risk
• Idiosyncratic shock ω (as in Bernanke, Gertler and Gilchrist, 1999)
iid across banks and across time
Log-normally distributed with cdf F(ω). Also Γ(ω) =
ω
0
ω dF(ω)
Unit mean and cross-sectional dispersion σ
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Bank failure
idiosyncratic risk
• Idiosyncratic shock ω (as in Bernanke, Gertler and Gilchrist, 1999)
iid across banks and across time
Log-normally distributed with cdf F(ω). Also Γ(ω) =
ω
0
ω dF(ω)
Unit mean and cross-sectional dispersion σ
• Banks with ω < ωt default on their deposits:
ωt =
Rd
t−1dt−1 + m(dt−1, bt−1) − Rb
t bt−1
Rk
t kt−1
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Bank failure shocks
• Bank failure shocks take the form of infrequent, aggregate depreciation
shocks ψt ∈ {0, 1}, with Prob(ψt = 1) = π, that aﬀect banks’ return of
capital
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Bank failure shocks
capital
• When it realizes (ψt = 1) a fraction λ of banks suﬀer the full depreciation of
their stock of capital after production takes place
If ψt = 1, Rk
t =
rk
t + 1 − δ w.p. 1 - λ
rk
t w.p. λ
}
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Bank failure shocks
capital
• When it realizes (ψt = 1) a fraction λ of banks suﬀer the full depreciation of
their stock of capital after production takes place
If ψt = 1, Rk
t =
rk
t + 1 − δ w.p. 1 - λ
rk
t w.p. λ
}
• Similar to capital quality shocks in Gertler, Karadi (2011); or systemic
shocks in Martinez-Miera, Suarez (2014)
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Government
• The government finances its primary deficit by issuing one-period bonds with
promised return Rb
t :
Bt = (1 − θst)Rb
t−1
=Rb
t
Bt−1 + Gt − Tt + (1 − st)DIt
Primary deficit
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Government
promised return Rb
t :
Bt = (1 − θst)Rb
t−1
=Rb
t
Bt−1 + Gt − Tt + (1 − st)DIt
Primary deﬁcit
• Spending rule: Gt = gY (constant fraction of steady state level of output)
• Tax rule: Tt = τy Yt + τbBt−1
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Government
promised return Rb
t :
Bt = (1 − θst)Rb
t−1
=Rb
t
Bt−1 + Gt − Tt + (1 − st)DIt
Primary deﬁcit
• Default (st = 1) implies writing oﬀ a fraction θ of outstanding obligations
and not being able to honor deposit insurance
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Government
promised return Rb
t :
Bt = (1 − θst)Rb
t−1
=Rb
t
Bt−1 + Gt − Tt + (1 − st)DIt
Primary deﬁcit
• Default (st = 1) implies writing oﬀ a fraction θ of outstanding obligations
and not being able to honor deposit insurance
• It occurs randomly as in Bi and Traum (2012) and Bocola (2016):
pt ≡ Prob(st+1 = 1|Bt/Yt) =
exp(η1 + η2Bt/Yt)
1 + exp(η1 + η2Bt/Yt)
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Deposit insurance scheme
The government:
• Takes over the assets of failed banks
• Incurs in repossession costs: fraction µ of the failed banks’ assets
• Repays principal + promised return of insured deposits, provided that the
govt. does not default (st = 0)
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The government:
DIt = [Rd
t−1dt−1 + m(dt−1, bt−1) − Rb
t bt−1]F(ωt) − µRk
t kt−1Γ(ωt)
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The government:
DIt = [Rd
t−1dt−1 + m(dt−1, bt−1) − Rb
t bt−1]F(ωt) − µRk
t kt−1Γ(ωt)
The loss for depositors due to banks’ failure is ΨtDt−1 = stDIt
Rd
t Dt−1 = (Rd
t−1 − Ψt)Dt−1
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International investors
Overlapping generations of risk-averse international investors (Aguiar el al, 2016)
• Start every period with exogenous endowment W f
• Can invest in government bonds and a risk-free asset with exogenous gross
return Rf
(or borrow at the same rate)
• Exit the market after one period, replaced by new generation
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International investors
Overlapping generations of risk-averse international investors (Aguiar el al, 2016)
• Start every period with exogenous endowment W f
• Can invest in government bonds and a risk-free asset with exogenous gross
return Rf
(or borrow at the same rate)
• Exit the market after one period, replaced by new generation
The representative investor solves a conventional static portfolio problem. It
chooses Bf
t to maximize:
Et
(Cf
t+1)1−νf
1 − νf
subject to Cf
t+1 = Rf
(W f
− Bf
t ) + Rb
t+1Bf
t
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Equilibrium
An equilibrium is deﬁned by a set of policy functions for all agents in the
economy such that, given prices and the realization of the shocks:
1. All agents optimize.
2. All markets clear.
3. All endogenous state variables evolve according to their respective law of
motion.
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Key equations
Households’ optimality condition for deposit holdings:
EtΛt+1 (Rd
t − Ψt+1)
=Rd
t+1
= 1
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Key equations
EtΛt+1 (Rd
t − Ψt+1)
=Rd
t+1
= 1
Value of bankers’ net worth:
vt = Et Λt+1(1 − ϕ + ϕvt+1)
=Ωt+1 (bankers’ SDF)
Re
t+1,
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Key equations
EtΛt+1 (Rd
t − Ψt+1)
=Rd
t+1
= 1
Value of bankers’ net worth:
vt = Et Λt+1(1 − ϕ + ϕvt+1)
=Ωt+1 (bankers’ SDF)
Re
t+1,
Banks’ optimality conditions for sovereign bond holdings:
EtΩt+1[Rb
t+1 − Rd
t (1 − γι) − mb
t ] (1 − F(ωt+1)) = vtγι,
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Quantitative results
• Numerical solution method
• Calibration strategy
• Results for the baseline parameterization
• Counterfactuals and welfare analysis
Counterfactual 1: contribution of the feedback loop
Counterfactual 2: macroprudential implications of bank capital requirements
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Solution method
Global solution method:
• Policy function iteration with linear interpolation
• Important to capture relevant non-linearities and time-varying risk premia
• High computational costs
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Solution method
Global solution method:
• Policy function iteration with linear interpolation
• Important to capture relevant non-linearities and time-varying risk premia
• High computational costs
Sketch of the algorithm: Details
• Discretize the state space [E × B × N]
• Guess policy functions
• Solve the system equilibrium equations at each point of the state space,
integrating over each possible realization of the shocks and using linear
interpolation to obtain t + 1 variables
• Update policy functions and repeat until convergence
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Calibration strategy
Two sets of parameters:
1. Calibrated outside the model:
Generally agreed values for standard parameters
Parameter values taken from related references
2. Calibrated inside the model
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Table 1: Parameters calibrated outside the model
Parameter Value Target
β Subjective discount rate 0.99 Standard
ν Risk aversion 2 Standard
ϕ Bankers’ survival rate 0.96 Bocola (2016)
γ Capital requirement 0.08 Basel II (Clerc et al, 2015)
ι Risk weight of sov. bonds 0.0 Basel II
µ Bankruptcy cost 0.3 Mendicino et al (2017)
α Elasticity of physical capital 0.33 Standard
δ Depreciation rate of capital 0.025 Standard
θ Write-oﬀ parameter 0.55 Bocola (2016)
νf
Intl. investors’ risk aversion 2 Same as ν (Aguiar et al, 2016)
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Table 2: Parameters calibrated inside the model
Parameter Value Target
κ Capital mgmt. cost 2.5e-4 Share of K held by households
New bankers’ endowment 0.005 Average bank return on equity
φ Liquidity mgmt. cost 1e-6 Average bank exposure to sov. debt
σ Dispersion of iid shock 0.03 Average bank failure rate (1)
λ Fraction aﬀected if ψt =1 0.10 Fiscal cost of crises (2)
π Prob(ψt =1) 0.0076 Systemic shock frequency (2)
g Govt. spending 0.25 Govt. ﬁnal consumption expenditure
τy Automatic stabilizer 0.20 Tax revenues
τb Debt stabilizer 0.06 Debt over GDP
η1 Sovereign default parameter 1 -12 Average default probability (3)
η2 Sovereign default parameter 2 15 Sov. yield sensitivity to B/Y
Rf
Intl. risk-free rate 1.0088 Yield on German bonds
W f
Intl. investors’ endowment 3 Share of debt held abroad
(1) Mendicino et al, 2017; (2) Laeven and Valencia (2013); (3) Bocola (2016)
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Table 3: Endogenous variables at the stochastic steady state
(baseline parameterization)
Variable Model Data (1)
Annualized intl. risk-free rate Rf
(2) 3.5% 3.25%
Annualized return on equity Re
14.88% 11.13%
Annualized sov. bond yield Rb
3.81% 3.38%
Annualized deposit rate Rd
3.72% 3.02%
Sovereign debt (% of GDP) (3) 28.74% 31.51%
Share of sov. debt held abroad 61.06% 64.02%
Annualized sov. default probability (4) 0.18% 0.19%
Share of Kt held by banks 84.7% ≈ 85%
Banks’ leverage (assets/equity) 13.23 13.92
Banks’ sovereign exposure (% of assets) 5.49% ≈ 5%
(1) Data for Spain (2000Q1-2008Q3), unless otherwise indicated; (2) Yield on 1Y German bond
(2000Q1-2008Q3); (3) Total outstanding debt held by banks and foreign investors; (4) Data for Italy (Bocola,
2016)
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Counterfactual exercises
1. Contribution of the feedback loop:
Switching oﬀ time-varying sovereign default risk:
Constant default risk equal to the average default rate under baseline
parameterization
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parameterization
2. Macroprudential regulation of banks’ sovereign exposures
Positive risk-weights for sovereign bond holdings (ι > 0)
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parameterization
2. Macroprudential regulation of banks’ sovereign exposures
Positive risk-weights for sovereign bond holdings (ι > 0)
Measuring welfare in equivalent constant consumption units C:
E0
∞
t=0
βt
u(Ct) = (1 − β)u C
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Contribution of the feedback loop
Figure 1: Response to a bank failure shock
0 10 20 30 40 50 60
-40
-30
-20
-10
0
0 10 20 30 40 50 60
0
20
40
60
80
0 10 20 30 40 50 60
-5
-4
-3
-2
-1
0
0 10 20 30 40 50 60
-5
0
5
10
15
0 10 20 30 40 50 60
0
100
200
300
0 10 20 30 40 50 60
-100
0
100
200
300
0 10 20 30 40 50 60
-40
-20
0
20
0 10 20 30 40 50 60
0
100
200
300
0 10 20 30 40 50 60
0
100
200
300
400
500
Red lines: constant sov. default risk
Black lines: baseline parameterization (table 1)
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Model data points correspond to observations during an average crisis (as displayed in the previous IRFs)
Some facts
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The feedback loop has dramatic eﬀects on ﬁnancial stability and economic
activity even if default does not materialize
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• Higher yields make banks increase their sovereign exposures (and their
leverage), increasing their expected probability of failure
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• Since, in the event of default, deposits cease to be insured, this translates
into higher funding costs for banks to compensate for potential losses
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→ Initial shock translates into further declines in aggregate equity, with an
associated decrease in economic activity
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→ Initial shock translates into further declines in aggregate equity, with an
associated decrease in economic activity
Compared to the constant risk counterfactual case, the feedback loop implies a
welfare loss of 1.3% in equivalent constant consumption units
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Capital requirements for sovereign exposures
0 10 20 30 40 50 60
-40
-30
-20
-10
0
0 10 20 30 40 50 60
0
20
40
60
80
0 10 20 30 40 50 60
-5
-4
-3
-2
-1
0
0 10 20 30 40 50 60
-5
0
5
10
15
0 10 20 30 40 50 60
0
100
200
300
0 10 20 30 40 50 60
-100
0
100
200
300
0 10 20 30 40 50 60
-40
-20
0
20
0 10 20 30 40 50 60
0
100
200
300
0 10 20 30 40 50 60
0
100
200
300
400
500
Blue lines: higher risk weights for sov. debt (from 5% to 70%)
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0 10 20 30 40 50 60
-40
-30
-20
-10
0
0 10 20 30 40 50 60
0
20
40
60
80
0 10 20 30 40 50 60
-5
-4
-3
-2
-1
0
0 10 20 30 40 50 60
-5
0
5
10
15
0 10 20 30 40 50 60
0
100
200
300
0 10 20 30 40 50 60
-100
0
100
200
300
0 10 20 30 40 50 60
-60
-40
-20
0
20
0 10 20 30 40 50 60
0
100
200
300
0 10 20 30 40 50 60
0
100
200
300
400
500
Blue lines: higher risk weights for sov. debt (from 5% to 70%)
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Risk weights on sovereign exposures mitigate the negative eﬀects of two
externalities:
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externalities:
• Limited liability: banks’ do not internalize the bankruptcy costs associated
to their failure
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externalities:
to their failure
• Opaque balance sheets: individual banks do not internalize the eﬀect of
their risk proﬁle on the funding costs of the banking system as a whole
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externalities:
to their failure
• Opaque balance sheets: individual banks do not internalize the eﬀect of
their risk proﬁle on the funding costs of the banking system as a whole
Higher capital requirements imply:
• skin in the game ↑ → risk-shifting incentives ↓
• leverage ↓ → bank failure risk ↓
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Optimal risk weight
Increasing sovereign debt risk weights does not come at no cost:
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Optimal risk weight
• Sov. bond holdings require using scarce equity
→ Share of physical capital directly held by banks decreases (↓ output)
→ Contractions are sharper at the beginning of crises
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Optimal risk weight
• Share of sov. debt held abroad increases
→ Increase in govt. borrowing costs
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Optimal risk weight
• Share of sov. debt held abroad increases
→ Increase in govt. borrowing costs
Welfare does increase, but gains stop increasing after certain point
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Figure 3: Welfare gains for diﬀerent risk weights
0 10 20 30 40 50 60 70
0
0.1
0.2
0.3
0.4
0.5
0.6
36 / 38

Table 4: Endogenous variables at the stochastic steady state
(counterfactual exercise)
ι = 0 ι = 40% Diﬀ.
Annualized return on equity Re
14.88% 14.96% 8 bps
Annualized sov. bond yield Rb
3.81% 3.91% 10 bps
Annualized deposit rate Rd
3.72% 3.75% 3 bps
Welfare (= equiv. constant consumption units) 1.449 1.458 0.57%
GDP 2.964 2.959 -0.17%
Sovereign debt (% of GDP) 28.74% 28.28% -46 bps
Share of sov. debt held abroad 61.06% 77.49% 16.4 pps
Annualized sov. default probability 0.18% 0.17% -1 bps
Share of Kt held by banks 84.7% 84.3% -40 bps
Banks’ leverage (assets/equity) 13.23 12.75 -3.63%
Banks’ sovereign exposure (% of bank assets) 5.49% 3.22% 2.3 pps
Annualized default rate of banks 0.92% 0.81% -11 bps
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Conclusions
• Dynamic general equilibrium model of the sovereign-bank feedback loop
• Excessive sovereign exposures translate into system-wide instability
• There is room for macroprudential regulation, which generates non-trivial
welfare trade oﬀs
• (Preliminary) quantitative results: optimal risk weight for sov. exposures
38 / 38

Some facts
Source: Eijﬃnger, Kobielarz, Uras (2015) Back (intro) Back (results)
2 / 10

Some facts
Source: Merler and Pisani-Ferry (2012) Back (intro) Back (results)
3 / 10

Some facts
Source: Altavilla, Pagano and Simonelli (2017) Back (intro) Back (results)
4 / 10

Some facts
Bank interest rates - deposits from households with agreed maturity of up to one year
Source: ECB Statistical Data Warehouse - MFI Interest Rate Statistics Back (intro)
Back (results)
5 / 10

Some facts
Share of debt held abroad
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
0.25
0.3
0.35
0.4
0.45
0.5
0.55
Spain
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
0.35
0.4
0.45
0.5
0.55
Italy
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
Portugal
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
0.5
0.6
0.7
0.8
0.9
Ireland
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
0.45
0.5
0.55
0.6
0.65
0.7
France
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
0.4
0.45
0.5
0.55
0.6
0.65
Germany
Source: Bruegel (2016) Back (intro) Back (results)
6 / 10

Ongoing debate
“The current regulation’s assumption that government bonds are risk-free has
been dismissed by recent experience. The time is ripe to address the regulatory
treatment of sovereign exposures. Without it, I see no reliable way of breaking
the sovereign-banking nexus” (Weidmann, 2013)
“If sovereign exposures are in fact subject to default risk, consistency with a
risk-focused approach to prudential regulation and supervision requires that this
default risk is taken into account” (ESRB, 2015)
“It is essential to move away from the present favourable treatment of sovereign
exposures in bank regulation to a framework that more accurately reﬂects
sovereign risk.The current prudential treatment of sovereign exposures is no
longer tenable” (BIS, 2016)
“I doubt that further changes in prudential regulation are the right instrument for
addressing the sovereign-bank nexus. The potential beneﬁts of a reform are
uncertain, while the potential costs could be sizeable.” (Visco, 2016)
Back
7 / 10

Opaque balance sheets
“(In 2011), the EBA decided to give full and very granular disclosure of
information on individual banks’ exposures to each sovereign. Using the very
granular information provided by the EBA, analysts calculated the capital position
of each bank participating in the stress test when all sovereign exposures were
valued at market prices. The first casualty was Dexia, which had significant
exposures to sovereigns and municipalities in stressed countries. The bank started
experiencing difficulties in accessing market funding and the liquidity problems led
very fast to a crisis that quickly drove the bank into resolution.”
(Enria, Farkas and Overby, 2016)
Back
8 / 10

Solution method
Policy function iteration / time iteration (Coleman, 1990; Judd, 1996)
1. Initial step (Set grid, initial policy and error tolerance)
1.1 Set equidistant grids for state variables S
1.2 Set guess policy functions x(S)
1.3 Set error tolerance for time iteration ¯ > 0
2. Main step (Update policy functions)
2.1 Solve for t + 1 state S given the current guess for the policy functions
2.2 Compute time t + 1 values of policy functions x(S )
2.3 Find the values ˜x(S) that solve the system of equilibrium conditions
3. Final step (Check error criterion)
3.1 Compute maximum error: = max|x(S) − ˜x(S)|, for each policy x(S)
3.2 Set x(S) = ˜x(S)
3.3 If max( ) < ¯, stop and report results; otherwise go back to step 2.
9 / 10

Solution accuracy
-10 -8 -6 -4 -2 0
0
0.05
0.1
0.15
0.2
-10 -8 -6 -4 -2 0
0
0.05
0.1
0.15
0.2
0.25
-10 -8 -6 -4 -2 0
0
0.02
0.04
0.06
0.08
0.1
-10 -8 -6 -4 -2 0
0
0.05
0.1
0.15
0.2
0.25
Back
10 / 10

Breaking the feedback loop: macroprudential regulation of banks' sovereign exposures

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