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

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 1 / 38
Motivation Recent European crisis featured the so-called negative feedback loop between banks and sovereigns (“diabolic loop”, “deadly embrace”, ...) 2 / 38
Motivation Recent European crisis featured the so-called negative feedback loop between banks and sovereigns (“diabolic loop”, “deadly embrace”, ...) • Government bailouts increased debt burden and sovereign yields 2 / 38
Motivation Recent European crisis featured the so-called negative feedback loop between banks and sovereigns (“diabolic loop”, “deadly embrace”, ...) • Government bailouts increased debt burden and sovereign yields • Banks increased their holdings of high-yield, risky sovereign debt 2 / 38
Motivation Recent European crisis featured the so-called negative feedback loop between banks and sovereigns (“diabolic loop”, “deadly embrace”, ...) • Government bailouts increased debt burden and sovereign yields • Banks increased their holdings of high-yield, risky sovereign debt → Mutually reinforcing effects of sovereign and bank risk → Negative effect on financial intermediation and economic activity 2 / 38
Motivation Recent European crisis featured the so-called negative feedback loop between banks and sovereigns (“diabolic loop”, “deadly embrace”, ...) • Government bailouts increased debt burden and sovereign yields • Banks increased their holdings of high-yield, risky sovereign debt → 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 2 / 38
This paper Negative feedback loop in a dynamic general equilibrium framework, with both endogenous bank failure risk & sovereign default risk 3 / 38
This paper Negative feedback loop in a dynamic general equilibrium framework, with both endogenous bank failure risk & sovereign default risk • 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 3 / 38
This paper Negative feedback loop in a dynamic general equilibrium framework, with both endogenous bank failure risk & sovereign default risk • 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 3 / 38
Regulatory framework k b e d e: equity d: deposits b: sovereign bonds k: other risky assets Figure 1: A simplified bank balance sheet 4 / 38
Regulatory framework k b e d e: equity d: deposits b: sovereign bonds k: other risky assets Figure 1: A simplified bank balance sheet Bank capital regulation: e ≥ γ(k + ιb) • A fraction γ of banks’ risk-weighted assets has to be financed with equity 4 / 38
Regulatory framework k b e d e: equity d: deposits b: sovereign bonds k: other risky assets Figure 1: A simplified bank balance sheet 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 4 / 38
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 5 / 38
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 • 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 5 / 38
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 • 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 • 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 5 / 38
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 • 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 • 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 5 / 38
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) 6 / 38
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 6 / 38
Model overview Government Banks International investors Firms Bankers Households 7 / 38
Model overview Government Banks International investors Firms Bankers Households Deposits (Dt) Capital (Kt) 7 / 38
Model overview Government Banks International investors Firms Bankers Households Deposits (Dt) Equity (Et) Capital (Kt) 7 / 38
Model overview Government Banks International investors Firms Bankers Households Deposits (Dt) Equity (Et) Capital (Kt) Deposit insurance 7 / 38
Model overview Government Banks International investors Firms Bankers Households Deposits (Dt) Equity (Et) Capital (Kt) Bonds (Bt) Bonds (Bt)Deposit insurance 7 / 38
Model overview Discrete time, infinite horizon model of a small open economy 8 / 38
Model overview Discrete time, infinite horizon model of a small open economy • Households: Workers: supply labor, intertemporal consumption-savings problem Bankers: only providers of banks’ inside equity 8 / 38
Model overview Discrete time, infinite horizon model of a small open economy • 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 8 / 38
Model overview • Firms: Combine labor and physical capital to produce consumption good Operate a Cobb-Douglas production function under perfect competition 9 / 38
Model overview • Firms: Combine labor and physical capital to produce consumption good Operate a Cobb-Douglas production function under perfect competition • Government: Issues debt subject to default risk Guarantees bank deposits (provided that the govt. does not default) 9 / 38
Model overview • Firms: Combine labor and physical capital to produce consumption good Operate a Cobb-Douglas production function under perfect competition • Government: Issues debt subject to default risk Guarantees bank deposits (provided that the govt. does not default) • International investors: Overlapping generations of risk-averse foreign lenders Invest in sovereign debt 9 / 38
Model overview • Firms: Combine labor and physical capital to produce consumption good Operate a Cobb-Douglas production function under perfect competition • Government: Issues debt subject to default risk Guarantees bank deposits (provided that the govt. does not default) • International investors: Overlapping generations of risk-averse foreign lenders Invest in sovereign debt Two sources of aggregate risk: bank failure shock and sovereign default 9 / 38
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 10 / 38
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 10 / 38
Notation • Promised (gross) returns: Rd t , Rb t known ex-ante 11 / 38
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 11 / 38
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 12 / 38
Bankers Continuum of bankers with aggregate net worth Et: 13 / 38
Bankers Continuum of bankers with aggregate net worth Et: • 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 13 / 38
Bankers Continuum of bankers with aggregate net worth Et: • 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 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 13 / 38
Bankers Continuum of bankers with aggregate net worth Et: • 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 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 13 / 38
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 14 / 38
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) 15 / 38
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) • ...unless there exist intermediation costs that imply some complementarity between the two assets 15 / 38
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) • ...unless there exist intermediation costs that imply some complementarity between the two assets • Here: complementarity comes from different degrees of liquidity of each asset (maturity transformation of banks as in Diamond and Dybvig, 1983) 15 / 38
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) • ...unless there exist intermediation costs that imply some complementarity between the two assets • 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) 15 / 38
Bank failure • Banks have access to a capital production technology subject to idiosyncratic risk 16 / 38
Bank failure • Banks have access to a capital production technology subject to 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 16 / 38
Bank failure • Banks have access to a capital production technology subject to 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 16 / 38
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 17 / 38
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 • 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 } 17 / 38
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 • 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) 17 / 38
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 18 / 38
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 • Spending rule: Gt = gY (constant fraction of steady state level of output) • Tax rule: Tt = τy Yt + τbBt−1 18 / 38
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 • Spending rule: Gt = gY (constant fraction of steady state level of output) • Tax rule: Tt = τy Yt + τbBt−1 • Default (st = 1) implies writing off a fraction θ of outstanding obligations and not being able to honor deposit insurance 18 / 38
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 • Spending rule: Gt = gY (constant fraction of steady state level of output) • Tax rule: Tt = τy Yt + τbBt−1 • 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) 18 / 38
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) 19 / 38
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) DIt = [Rd t−1dt−1 + m(dt−1, bt−1) − Rb t bt−1]F(ωt) − µRk t kt−1Γ(ωt) 19 / 38
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) 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 19 / 38
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 20 / 38
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 20 / 38
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. 21 / 38
Key equations Households’ optimality condition for deposit holdings: EtΛt+1 (Rd t − Ψt+1) =Rd t+1 = 1 22 / 38
Key equations Households’ optimality condition for deposit holdings: 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, 22 / 38
Key equations Households’ optimality condition for deposit holdings: 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, 22 / 38
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 23 / 38
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 24 / 38
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 24 / 38
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 25 / 38
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) 26 / 38
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) 27 / 38
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) 28 / 38
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 29 / 38
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 2. Macroprudential regulation of banks’ sovereign exposures Positive risk-weights for sovereign bond holdings (ι > 0) 29 / 38
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 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 29 / 38
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) 30 / 38
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) 30 / 38
Model data points correspond to observations during an average crisis (as displayed in the previous IRFs) Some facts 31 / 38
Contribution of the feedback loop The feedback loop has dramatic effects on financial stability and economic activity even if default does not materialize 32 / 38
Contribution of the feedback loop The feedback loop has dramatic effects on financial stability and economic activity even if default does not materialize • Higher yields make banks increase their sovereign exposures (and their leverage), increasing their expected probability of failure 32 / 38
Contribution of the feedback loop The feedback loop has dramatic effects on financial stability and economic activity even if default does not materialize • Higher yields make banks increase their sovereign exposures (and their leverage), increasing their expected probability of failure • Since, in the event of default, deposits cease to be insured, this translates into higher funding costs for banks to compensate for potential losses 32 / 38
Contribution of the feedback loop The feedback loop has dramatic effects on financial stability and economic activity even if default does not materialize • Higher yields make banks increase their sovereign exposures (and their leverage), increasing their expected probability of failure • Since, in the event of default, deposits cease to be insured, this translates into higher funding costs for banks to compensate for potential losses → Initial shock translates into further declines in aggregate equity, with an associated decrease in economic activity 32 / 38
Contribution of the feedback loop The feedback loop has dramatic effects on financial stability and economic activity even if default does not materialize • Higher yields make banks increase their sovereign exposures (and their leverage), increasing their expected probability of failure • Since, in the event of default, deposits cease to be insured, this translates into higher funding costs for banks to compensate for potential losses → 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 32 / 38
Capital requirements for sovereign exposures Figure 2: 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) Blue lines: higher risk weights for sov. debt (from 5% to 70%) 33 / 38
Capital requirements for sovereign exposures Figure 2: 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 -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) Blue lines: higher risk weights for sov. debt (from 5% to 70%) 33 / 38
Capital requirements for sovereign exposures Risk weights on sovereign exposures mitigate the negative effects of two externalities: 34 / 38
Capital requirements for sovereign exposures Risk weights on sovereign exposures mitigate the negative effects of two externalities: • Limited liability: banks’ do not internalize the bankruptcy costs associated to their failure 34 / 38
Capital requirements for sovereign exposures Risk weights on sovereign exposures mitigate the negative effects of two externalities: • Limited liability: banks’ do not internalize the bankruptcy costs associated 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 34 / 38
Capital requirements for sovereign exposures Risk weights on sovereign exposures mitigate the negative effects of two externalities: • Limited liability: banks’ do not internalize the bankruptcy costs associated 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 ↓ 34 / 38
Optimal risk weight Increasing sovereign debt risk weights does not come at no cost: 35 / 38
Optimal risk weight Increasing sovereign debt risk weights does not come at no cost: • 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 35 / 38
Optimal risk weight Increasing sovereign debt risk weights does not come at no cost: • 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 • Share of sov. debt held abroad increases → Increase in govt. borrowing costs 35 / 38
Optimal risk weight Increasing sovereign debt risk weights does not come at no cost: • 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 • Share of sov. debt held abroad increases → Increase in govt. borrowing costs Welfare does increase, but gains stop increasing after certain point 35 / 38
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 37 / 38
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
Appendix 1 / 10
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

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