## _wp16186 ## Source details **Canonical URL:** [_wp16186](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2016/_wp16186.pdf) ## Other formats - [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2016/_wp16186.pdf.md) - [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2016/_wp16186.pdf.json) --- ### 1. Introduction — motivation, focus, and model setup - Motivation and context - The global financial crisis revealed limitations of a nation-bound supervisory architecture overseeing integrated financial markets and institutions. - Supervisory fragmentation: - hindered monitoring and understanding of cross-border linkages before the crisis; - led to often locally-driven and globally-inefficient policy actions after the crisis began. - Policy debate: need for greater cross-border integration of financial regulation and supervision; recent regulatory reform in Europe is an example. - Focus of the paper - The paper is a theoretical exploration of tensions in a “hub-and-spokes” supervisory regime: a centralized agency has legal power over all bank decisions but must rely on local supervisors to collect information. - Central question: how does this institutional design affect supervisors’ incentives to collect information and how does that influence bank behavior? - Stylized framework and applicability - Settings with conflicts among multiple agencies or hierarchical supervision/regulation (e.g., Eurozone banking union; state-chartered banks in the U.S.). - Model intentionally simple; does not capture all real-world checks and balances. - Model setup (high-level) - Banks choose portfolio risk quality θ on an efficient frontier: higher risk (lower θ) yields higher return R − 1/2 χ θ. - Banks have capital κ ∈ [0,1]; deposits finance 1 − κ; κ assumed uniform on [0,1] for tractability. - Deposits fully insured, r_D = 1; opportunity costs normalized to 1. - Local supervisor inspects with effort ε at cost δ/2 ε^2 (inspection reveals θ and κ with probability ε). - Conditional on inspection, supervisor can intervene; if intervened, with probability × the bank is put under receivership and supervisor chooses the socially optimal portfolio at cost A_L. - Bank failure imposes per-dollar cost ψ_L ≥ 1 borne by the supervisor. - Timing: stage 0 bank chooses θ and supervisor chooses ε; stage 1 inspection with prob ε, possible intervention and receivership with prob ×; stage 2 returns realized and payoffs distributed. - Mechanisms emphasized - Limited liability and asymmetric information generate moral hazard: banks do not internalize depositor/taxpayer losses. - Supervisory intervention corrects risk-taking but intervention is costly (reputational, fiscal, inefficiencies). - Under centralized supervision local supervisors still collect information but may have different objectives and be less inclined to intervene. - Principal-agent problem between central and local supervisors can induce local supervisors to prefer ignorance (lower ε). - Ambiguity of centralization effects - Centralization effects: - Tougher central standards and lower thresholds for intervention can reduce bank risk. - Distorted information collection by local supervisors (lower ε) can increase undetected risk-taking. - Net effect depends on severity of principal-agent problem between central and local supervisors. - Main contributions - Endogenous supervisor behavior and banks’ risk-taking incentives generate risk-based capital standards: supervisors tolerate greater portfolio risk for better-capitalized banks; banks choose safer portfolios as capital at risk increases. - Introduces centralized supervision and analyzes interaction of agency problems with bank incentives. - Relevance and policy implications - Relevant to the European banking union and multi-agency supervision. - Empirical reference: as of November 2014, the Single Supervisory Mechanism (SSM) within the ECB became primary supervisor of the Eurozone’s biggest banks; supervises directly the largest 128 banks, accounting for approximately 85 percent of banking assets of the area, and indirectly all banks in the Eurozone. - Practical implication: central agency must ensure spokes (local supervisors) act according to the centralized mandate; institutional responses include ECB’s right to bring any bank under direct supervision and multi-country teams headed by ECB officials conducting on-site inspections. - Literature connections - Builds on literature on bank risk-taking under limited liability and asymmetric information (Hellmann et al., 2000; Matutes and Vives, 2000; Repullo, 2004; Dell’Ariccia and Marquez, 2006). - Relates to centralized regulation/supervision and multinational bank regulation literature and delegation/authority literature. ### 4.1 Intervention choice of the local supervisor — structure and equilibrium - Supervisor payoff: no intervention vs intervention - No intervention payoff (equation (2)): - μ[θ( R − 1/2 χ θ − (1 − κ) )] − (1 − θ)(1 − κ) ψ_L − κ - Intervention payoff (equation (3)): - × μ[−A_L + θ*_L μ( R − 1/2 χ θ*_L − (1 − κ) ) − (1 − θ*_L)(1 − κ) ψ_L] - + (1 − ×) μ[θ μ( R − 1/2 χ θ − (1 − κ) ) − (1 − θ)(1 − κ) ψ_L] − κ - Supervisor’s optimal implemented portfolio upon intervention (equation (4)): - θ*_L(κ) = (R + (1 − κ)(ψ_L − 1)) / χ - Properties: - for κ < 1, θ*_L > bθ(1) = R/χ; - ∂θ*_L/∂κ < 0; - if κ = 1 then θ*_L = bθ and no intervention needed. - Net gain from intervention I_L(θ*_L, θ, κ) (equation (5)): - I_L = × [−A_L + θ*_L μ( R − 1/2 χ θ*_L − (1 − κ) ) − (1 − θ*_L)(1 − κ) ψ_L] - − × [θ μ( R − 1/2 χ θ − (1 − κ) ) − (1 − θ)(1 − κ) ψ_L] - Assumption ensuring intervention can be socially beneficial: - −A_L + θ*_L [ R − 1/2 χ θ*_L − 1 ] − (1 − θ*_L) ψ_L > 0 for some banks. - Intervention always desirable for banks with zero capital: I_L(θ*_L, θ, κ) > 0 for κ = 0. - Implies ψ_L > √(2 χ A_L). - Intervention threshold (Proposition 1) - Supervisor intervenes when θ < eθ_L(κ), where (equation (6)): - eθ_L(κ) = (1/χ) [ R + (1 − κ)(ψ_L − 1) − √(2 χ A_L) ] - Comparative statics: - ∂ eθ_L(κ) / ∂ κ < 0 - ∂ eθ_L(κ) / ∂ ψ_L > 0 - ∂ eθ_L(κ) / ∂ A_L < 0 - Interpretation: - Supervisor is more lenient with better-capitalized banks (higher κ). - Higher ψ_L raises the intervention threshold. - Higher A_L lowers tendency to intervene; as A_L → 0, eθ_L → θ*_L. - Bank profit under threat of intervention (equation (7)) - Bank profit Π: - For θ ≥ eθ_L: Π = θ[ R − 1/2 χ θ − (1 − κ) ] − κ - For θ < eθ_L: Π = (1 − ε ×) θ[ R − 1/2 χ θ − (1 − κ) ] − κ - Threat of intervention reduces expected payoff for risky portfolios. - Interaction of bank choice and intervention threshold - Unique capital level eκ_L where eθ_L(κ) = bθ(κ): - eκ_L = 1 − (1/ψ_L) √(2 χ A_L) (equation (8)) - Under ψ_L > √(2 χ A_L), eκ_L ∈ (0,1) - Banks with κ ≥ eκ_L choose laissez-faire bθ(κ); banks with κ < eκ_L may be induced to choose eθ_L(κ) to avoid intervention. - Bank expected profits comparing choices for κ < eκ_L: - Π(bθ) | κ 0 - ∂ κ_L(ε) / ∂ A_L < 0 - Interpretation: - Higher supervisory effort ε induces banks with lower capital to meet supervisory standards. - Feasibility condition for positive κ_L(ε) - To have κ_L(ε) > 0, supervisor chooses inspection effort ε < ε_L where (equation (12)): - ε_L = (ψ_L − √(2 χ A_L))^2 × (R − 1)^2 / 4 - Bank reaction function to supervisory effort - bθ_L(κ, ε): - bθ_L = bθ(κ) for ε < bε(κ) and κ < eκ_L - bθ_L = eθ_L(κ) for ε ≥ bε(κ) and κ < eκ_L - bθ_L = bθ(κ) > eθ_L(κ) for κ ≥ eκ_L - Supervisor’s inspection effort objective (equations (13) and (14)) - ΣΩ_L given (equation (13)); simplified dependence on ε (equation (14)): - ΣΩ_L = E[θ( R − 1/2 χ θ − (1 − κ) ) − (1 − θ)(1 − κ) ψ_L − κ] + ε Pr(θ < eθ_L) E[I_L(θ*_L, θ, κ) | θ < eθ_L] − δ/2 ε^2 - Supervisor’s optimal effort reaction (Lemma 2) - Given bank behavior, local supervisor chooses effort ε_L(κ_L) that satisfies (equation (15)): - ε_L(κ_L) = ∫_0^{κ_L} I_L(θ*_L, bθ, κ) f(κ) dκ < ε_L - Comparative statics: ∂ ε_L(κ_L) / ∂ κ_L > 0 - Interpretation: supervisor effort increases with κ_L. - Equilibrium with local supervision (Proposition 2) - Unique equilibrium (ε*_L, κ*_L, eθ_L, bθ_L) exists such that: 1) Supervisor intervenes any bank with θ < eθ_L(κ) (eθ_L as in (6)); 2) Banks that do not meet eθ_L(κ) choose laissez-faire portfolios bθ(κ); 3) Fixed point conditions: ε_L(κ*_L) = ε*_L and κ_L(ε*_L) = κ*_L - Equilibrium implications: - Supervisor exerts strictly positive effort ε*_L > 0. - Threshold κ*_L is strictly less than eκ_L, so supervision induces some banks to move toward regulatory standard eθ_L. ### 5.1 An unambiguously tougher central supervisor — framework and measures - Setup and threshold at which banks self-comply - Central regulator tougher so eθ_C(κ) > eθ_L(κ) (either A_C < A_L or ψ_C > ψ_L). - Threshold at which bank independently chooses bθ(κ) safe enough to avoid central intervention: - eκ_C = μ (1 − 1/ψ_C p 2 χ A_C ). (20) (preserved expression from source) - eκ_C > 0 if ψ_C > √(2 χ A_C). - eκ_C > eκ_L if ψ_C > ψ_L or A_C < A_L. - Banks' portfolio choice under a tougher central supervisor (Lemma 4) - For given supervisory effort ε, there exists κ_C(ε) such that: - Banks with κ < κ_C(ε) choose laissez-faire bθ(κ). - Banks with κ ∈ [κ_C(ε), eκ_C] switch to eθ_C(κ) > bθ(κ). - κ_C(ε) = μ (1 − √(ε× + √(2 χ A_C)/ψ_C + √(ε×) ) ) < eκ_C. (21) - Comparative statics: - ∂κ_C(ε)/∂ε < 0 - ∂κ_C(ε)/∂ψ_C > 0 - ∂κ_C(ε)/∂A_C < 0 - Range of banks affected by supervisory threat - eκ_C − κ_C(ε) = √(ε×)(R ψ_C − √(2 χ A_C)) / [ψ_C(ψ_C + √(ε×))]. (25) - eκ_L − κ_L(ε) = √(ε×)(R ψ_L − √(2 χ A_L)) / [ψ_L(ψ_L + √(ε×))]. - If ψ_C = ψ_L and A_C < A_L, then eκ_C − κ_C(ε) > eκ_L − κ_L(ε): more banks adjust portfolios under centralization. - Local supervisor's effort problem under central oversight - Local supervisor maximizes ΣΩ_Λ incorporating central thresholds eθ_C, implemented portfolio θ*_C, and local payoff differences I_Λ(θ*_C, θ, κ); reduced expression (23) preserves dependence on ε and I_Λ. - Key inequalities: - E[I_Λ(θ*_C, θ, κ) | θ < eθ(θ*_C)] < E[I_Λ(θ*_Λ, θ, κ) | θ < eθ(θ*_C)] if θ*_C ≠ θ*_Λ. - E[I_Λ(θ*_C, θ, κ) | eθ(θ*_C) ≤ θ < eθ_C] < 0. - Local supervisor reaction function under centralization (Lemma 6) - Define eκ(θ*_C) where bθ(κ) = eθ(θ*_C). - If A_C < A_L for ψ_C = ψ_L, or ψ_C > ψ_L for A_C = A_L, so eθ_C(κ) > eθ_L(κ) and θ*_C ≥ θ*_Λ, then: - ε_C(κ_C) = ∫_0^{min(κ_C, ε_κ(θ*_C))} I_Λ(θ*_C, bθ, κ) φ(κ) dκ + (1/κ_C) ∫_{ε_κ(θ*_C)}^{κ_C} I_Λ(θ*_C, bθ, κ) φ(κ) dκ < ε_κ(θ*_C) < ε_C, - and ε_C(κ) ≤ ε_Λ(κ). - Decomposition (25) preserved from source; signs and slopes of I_Λ described. - Interpretation: centralization makes local supervisor (weakly) less diligent in uncovering bank risk compared with independence because uncovered information enables central intervention the local supervisor may dislike. - Equilibrium cases and measures of portfolio quality - Two cases when central regulator tougher: 1) A_C < A_L with ψ_C = ψ_L ⇒ θ*_C = θ*_Λ. 2) ψ_C > ψ_L with A_C = A_L ⇒ θ*_C > θ*_Λ. - Measures: - Ex ante average portfolio quality Q_j (j = Λ, C) (equation (26)) preserved. - Ex post average portfolio quality Q*_j (equation (27)) preserved. ### 5.2 Lower intervention cost for the central supervisor — small and large conflict cases - Setup and comparative statics - Case: eθ_C > eθ_L but θ*_C = θ*_L (central tougher because A_C < A_L, ψ_C = ψ_L). - Local supervisor’s reaction function under centralization coincides with independent one for κ_C ≤ e κ_L. - Bank reaction κ_C(ε) under centralization remains strictly above κ_L(ε). - Proposition 3 — small conflict case - Assume ψ_C = ψ_L. - There exists ζ > 0 such that, for 0 < A_L − A_C < ζ: - Local supervisor exerts more effort under centralization: ε*_C > ε*_L. - Banks’ average portfolio quality higher under centralization ex ante and ex post: Q_C > Q_L and Q*_C > Q*_L. - Mechanism: tighter central standards induce safer bank portfolios and higher local effort to catch banks that prefer to risk intervention rather than meet standards. - Proposition 4 — large conflict and multiple equilibria - Assume ψ_C = ψ_L and A_C ≤ 1/(8χ) ( sqrt{3 (8χ A_L − ψ_L^2)} − ψ_L )^2 (expression preserved). - Results: - There exists an equilibrium with ε*_C = 0, κ_C = e κ_C, and lower bank portfolio quality: Q_C < Q_L and Q*_C < Q*_L. - As divergence increases, local supervisor’s incentives to exert effort decrease. - Multiple equilibria can arise: at least one positive-effort and one zero-effort equilibrium. - In positive-effort equilibrium, effort can be greater or lower than under local supervision depending on intersection. - In zero-effort equilibrium, local supervisor chooses no information collection; banks prefer this equilibrium; both supervisors prefer positive-effort equilibrium. - Parameter space for zero inspection equilibrium increases with A_L and decreases with ψ_L. - If conflict increases further, unique equilibrium is ε*_C = 0 and κ_C = e κ_C; supervision ineffective and banks choose laissez-faire portfolios. - Implication: centralization may require aligning incentives of local supervisors or improving monitoring (e.g., joint supervisory teams). - Delegation of supervision (section 5.2.1) - Central supervisor cannot commit beyond subgame perfect strategy; delegation to local supervisor considered. - Total surplus to central supervisor Σ_W_C expression preserved. - Proposition 5: - If ψ_C = ψ_L and A_C such that subgame optimal equilibrium with ε*_C = 0 exists, central supervisor is better off delegating supervision entirely to local supervisor. - Interpretation: when conflict is severe, delegation yields higher surplus for center. - Numerical examples (section 5.2.2) — parameter set and equilibria - Parameters: - R = 2.5, χ = 3, δ = 0.04, × = 0.2. - Local supervision: A_L = 0.25, ψ_L = 1.5. - Centralized supervision: A_C = 0.12637, ψ_C = ψ_L = 1.5. - Equilibrium under local supervision: - ε*_L = 0.04085. - Banks with κ ∈ [κ*_L = 0.08782, e κ_L = 0.18350] choose eθ_L; others choose laissez-faire. - Q_L = 0.66895. - Q*_L = 0.67159. - Equilibria under centralized supervision: - Three equilibria: two with positive effort and one with zero effort. - In all equilibria, inspection effort and average bank portfolio quality lower than under local supervision. - Highest-effort centralized equilibrium: - ε*_C = 0.01514 < ε*_L. - κ*_C = 0.35158 > κ*_L. - Q_C = 0.66782 < Q_L. - Q*_C = 0.66826 < Q*_L. - Other positive-effort equilibrium: - ε*' _C = 0.01509, κ*' _C = 0.35166. - Q' _C = 0.667817 and Q*' _C = 0.668254. - Zero-effort equilibrium: - ε*'' _C = 0 and κ*'' _C = e κ_L. - Q'' _C = Q*'' _C = 0.6. - Surplus comparisons for central supervisor: - Centralization increases surplus by ΔΣ_W_C = 0.000014 and ΔΣ_W'_C = 0.0000137 in the two positive-effort equilibria. - Delegation increases surplus by ΔΣ_W'' _C = 0.000122 in the zero-effort equilibrium. - Conclusion: centralization preferred if it yields positive effort; delegation preferred when centralization yields no effort. - Policy implications and takeaways - Centralization can improve outcomes when conflict is small. - When conflict is large, centralization can worsen outcomes due to reduced information collection and multiple equilibria including no-inspection equilibria. - To make centralization effective, align incentives and improve monitoring of local supervisors (e.g., joint supervisory teams); in extreme conflict, delegation may yield higher surplus. ### 5.3 Higher cost of bank failure for the central supervisor — effects and example - Setup and comparative statics - Case: A_C = A_L but ψ_C > ψ_L. - Implications: - eθ_C > eθ_L and θ*_C > θ*_Λ (center tougher both in threshold and standard conditional on intervention). - Local supervisor’s reaction function under centralization lies strictly below independent one for κ_C ≤ e κ_L because I_Λ(θ*_C; bθ; κ) < I_C(θ*_Λ; bθ; κ). - Bank reaction κ_C(ε) under centralization remains strictly above κ_Λ(ε). - Lemma 7 — local supervisor reaction under centralization - When A_C = A_L and ψ_C > ψ_L, local supervisor’s reaction under centralization strictly below independence: ε_C(κ) < ε_Λ(κ) for all κ < e κ_C. - Intuition: local supervisor cannot implement her preferred portfolio upon intervention, reducing incentives to exert effort to identify high-risk banks. - Net effects and equilibrium dependence - Banks adopt higher quality portfolios for given effort; supervisors exert less effort. - Equilibrium depends on size of conflict: - If conflict small, equilibrium effort may be higher under centralization. - If conflict large, inspection effort may be lower under centralization. - Condition for existence of equilibrium with zero supervisory effort under centralization still holds when ψ_C > ψ_L (expression preserved). - Numerical example — parameters and equilibrium outcomes - Parameters: - R = 2.5, χ = 3, δ = 0.04, × = 0.2. - A_L = A_C = 0.13. - ψ_L = 1.15. - ψ_C = 1.45. - Equilibrium under local supervision: - ε*_Λ = 0.03716. - κ*_Λ = 0.11124. - Q_Λ = 0.66946. - Q*_Λ = 0.67256. - Equilibrium under centralization: - ε*_C = 0.03081 < ε*_Λ. - κ*_C = 0.29380 > κ*_Λ. - Q_C = 0.66895 < Q_Λ. - Q*_C = 0.66969 < Q*_Λ. - Welfare comparison: - Central supervisor prefers subgame optimal solution under centralization rather than delegation: increase in surplus equals ∆Σ_W = 0.0000994. - Interpretation: centralization can entail lower inspection effort and higher bank risk, but can still be welfare-improving when inspection effort remains positive. - Key theoretical conclusions (excerpted) - Centralization can reduce local supervisors’ incentives to collect information because collected information might be used by the center to take actions the local supervisor dislikes. - Tougher central standards may paradoxically lead to greater aggregate risk-taking if agency conflicts reduce information collection. - Agency problems are larger when the local supervisor is laxer; the mismatch problem may be most severe for those cases that stand to benefit most from centralization. - Design features that mitigate conflicts (as in the SSM) include: - ECB retaining the right to take any bank under direct supervision (threat increases local payoff from effort). - Putting locally systemic banks and euro-level systemic banks under direct ECB supervision (minimizes differences in utility). - Internal governance practices such as ECB staff leading on-site inspections and rotating staff of different nationalities to limit conflicts. *Source: _wp16186 - 1. Introduction; 4.1 Intervention choice of the local supervisor; 5.1 An unambiguously tougher central supervisor; 5.2 Lower intervention cost for the central supervisor; 5.3 Higher cost of bank failure for the central supervisor.* ### 1. Introduction ........................................................................................................ ### 1 Introduction ### Motivation and context - The global financial crisis revealed limitations of a nation-bound supervisory architecture overseeing integrated financial markets and institutions. - Supervisory fragmentation: - hindered monitoring and understanding of cross-border linkages before the crisis; - led to often locally-driven and globally-inefficient policy actions after the crisis began. - Policy debate: need for greater cross-border integration of financial regulation and supervision; recent regulatory reform in Europe is an example. - Centralization raises new questions about: - internal governance of a centralized supervisory agency; - relationship with local supervisors; - effects on behavior of financial institutions under its jurisdiction. ### Focus of the paper - The paper is a theoretical exploration of tensions in a “hub-and-spokes” supervisory regime: - a centralized agency has legal power over all bank decisions but must rely on local supervisors to collect information. - Central question: how does this institutional design affect supervisors’ incentives to collect information and how does that influence bank behavior? ### Stylized framework and applicability - Broadly applicable to settings with: - conflicts among multiple agencies; or - hierarchical supervision/regulation. - Relevant to: - centralization across national borders (e.g., Eurozone banking union); - multiple-agency structures (e.g., state-chartered banks in the U.S.). - Model limitations: intentionally simple; does not capture all real-world checks and balances or corrective procedures. ### Model setup (high-level) - Banks are levered, protected by limited liability, and operate under asymmetric information, leading to excessive risk without effective supervision. - Key features: - Banks choose portfolio risk (quality θ) on an efficient frontier: higher risk (lower θ) yields higher return R − 1/2 χ θ. - Banks are endowed with capital κ ∈ [0,1]; deposits finance 1 − κ. - Capital κ distributed according to F(κ); for tractability κ assumed uniform on [0,1]. - Deposits fully insured, r_D = 1; opportunity costs normalized to 1. - Local supervisor can inspect with effort ε at cost δ/2 ε^2 (inspection reveals θ and κ with probability ε). - Conditional on inspection, supervisor can intervene; if intervened, with probability x the bank is put under receivership and supervisor chooses the socially optimal portfolio at cost A_L. - Bank failure imposes per-dollar cost ψ_L ≥ 1 borne by the supervisor (deposit insurance/social externality). - Timing: stage 0 bank chooses θ and supervisor chooses ε; stage 1 inspection with prob ε, possible intervention and receivership with prob x if intervened; stage 2 returns realized and payoffs distributed. ### Mechanisms emphasized - Limited liability and asymmetric information generate moral hazard: banks do not internalize depositor/taxpayer losses, producing excessive risk taking. - Supervisory intervention corrects risk-taking but intervention is costly (reputational, fiscal, loss of national champion, inefficiencies from public takeover). - Under centralized supervision: - local supervisors still collect information but must transmit it to a central agency; - local supervisors may have objectives different from the central agency and are generally less inclined to intervene (higher local intervention costs or regulatory capture). - This creates a principal-agent problem between central and local supervisors (in addition to supervisor–bank agency problems). - Local supervisors may prefer ignorance (lower inspection effort) to avoid triggering central interventions contrary to local interests. ### Ambiguity of centralization effects - Centralization has two opposing effects: - Tougher central standards (lower tolerance for risk) and lower thresholds for intervention can reduce bank risk. - Distorted information collection by local supervisors (lower ε) can increase undetected risk-taking, worsening outcomes. - Net effect depends on severity of principal-agent problem between central and local supervisors: - If problem not too severe → centralization tends to yield stricter supervision and a safer banking sector. - If problem severe → centralization can increase overall banking sector risk despite higher standards. ### Main contributions - Develops a model where supervisor behavior and banks’ risk-taking incentives are endogenous, generating: - risk-based capital standards: supervisors tolerate greater portfolio risk for better-capitalized banks; - banks choose safer portfolios as capital at risk increases. - Introduces centralized supervision and analyzes interaction of agency problems (central vs local supervisors) with bank incentives. ### Relevance and policy implications - Relevant to the European banking union and multi-agency supervision (e.g., U.S.). - Empirical reference: as of November 2014, the Single Supervisory Mechanism (SSM) within the ECB: - became the primary supervisor of the Eurozone’s biggest banks; - supervises directly the largest 128 banks, accounting for approximately 85 percent of banking assets of the area, and indirectly all banks in the Eurozone. - Practical implication: central agency must ensure spokes (local supervisors), which may have different objectives, act according to the centralized mandate. - Institutional responses noted in the source: ECB’s right to bring any bank under direct supervision; multi-country teams headed by ECB officials conducting on-site inspections. ### Literature connections - Builds on literature on bank risk-taking under limited liability and asymmetric information (Hellmann et al., 2000; Matutes and Vives, 2000; Repullo, 2004; Dell’Ariccia and Marquez, 2006). - Relates to literature on centralized regulation/supervision and multinational bank regulation (Acharya, 2003; Dell’Ariccia and Marquez, 2006; Morrison and White, 2009; Calzolari and Loranth, 2011; Calzolari, Colliard, and Loranth, 2015; Goyal et al., 2013; Beck and Wagner, 2014; Beck, Todorov, and Wagner, 2013; Basel Committee on Banking Supervision, 2010; IMF, 2010). - Connects to delegation/authority literature (Aghion and Tirole, 1997) and models of informational transmission to central agencies (Holthausen and Rønde, 2004). - Distinction from related work: focuses on intervention policies to keep banks running with safer portfolios rather than bank closure/resolution. ### Paper structure (as stated) - Section 2: basic model with a local independent supervisor. - Section 3: bank’s portfolio choice under no supervision. - Section 4: equilibrium with an independent local supervisor (inspection and intervention). - Section 5: effects of centralizing supervision. - Section 6: conclusion. *Source: _wp16186 - 1. Introduction (PDF chapter).* ### 4.1 Intervention choice of the local supervisor ### 4.1 Intervention choice of the local supervisor ### Supervisor payoff: no intervention vs intervention - No intervention payoff (equation (2)): - μ[θ( R − 1/2 χ θ − (1 − κ) )] − (1 − θ)(1 − κ) ψ_L − κ - Intervention payoff (equation (3)): - × μ[−A_L + θ*_L μ( R − 1/2 χ θ*_L − (1 − κ) ) − (1 − θ*_L)(1 − κ) ψ_L] - + (1 − ×) μ[θ μ( R − 1/2 χ θ − (1 − κ) ) − (1 − θ)(1 − κ) ψ_L] − κ - Supervisor’s optimal implemented portfolio upon intervention (equation (4)): - θ*_L(κ) = (R + (1 − κ)(ψ_L − 1)) / χ - Properties: for κ < 1, θ*_L > bθ(1) = R/χ; ∂θ*_L/∂κ < 0; if κ = 1 then θ*_L = bθ and no intervention needed. ### Net gain from intervention and constraints - Net gain from intervention I_L(θ*_L, θ, κ) (equation (5)): - I_L = × [−A_L + θ*_L μ( R − 1/2 χ θ*_L − (1 − κ) ) − (1 − θ*_L)(1 − κ) ψ_L] - − × [θ μ( R − 1/2 χ θ − (1 − κ) ) − (1 − θ)(1 − κ) ψ_L] - Assumption to ensure intervention can be socially beneficial (text): - −A_L + θ*_L [ R − 1/2 χ θ*_L − 1 ] − (1 − θ*_L) ψ_L > 0 for some banks - Intervention is always desirable for banks with zero capital: I_L(θ*_L, θ, κ) > 0 for κ = 0 - This implies ψ_L > √(2 χ A_L) ### Intervention threshold (Proposition 1) - Supervisor intervenes when θ < eθ_L(κ), where (equation (6)): - eθ_L(κ) = (1/χ) [ R + (1 − κ)(ψ_L − 1) − √(2 χ A_L) ] - Comparative statics: - ∂ eθ_L(κ) / ∂ κ < 0 - ∂ eθ_L(κ) / ∂ ψ_L > 0 - ∂ eθ_L(κ) / ∂ A_L < 0 - Interpretation: - Supervisor is more lenient with better-capitalized banks (higher κ) — they can operate riskier portfolios. - Higher per-dollar cost of failure ψ_L raises the intervention threshold (more precaution). - Higher intervention cost A_L lowers the tendency to intervene; as A_L → 0, eθ_L → θ*_L. ### Bank profit under threat of intervention (equation (7)) - Bank profit Π: - For θ ≥ eθ_L: Π = θ[ R − 1/2 χ θ − (1 − κ) ] − κ - For θ < eθ_L: Π = (1 − ε ×) θ[ R − 1/2 χ θ − (1 − κ) ] − κ - Consequence: threat of intervention reduces expected payoff for risky portfolios and may change bank choice. ### Interaction of bank choice and intervention threshold - There exists unique capital level eκ_L where eθ_L(κ) = bθ(κ): - eκ_L = 1 − (1/ψ_L) √(2 χ A_L) (equation (8)) - Under ψ_L > √(2 χ A_L), eκ_L ∈ (0,1) - Banks with κ ≥ eκ_L choose laissez-faire bθ(κ); banks with κ < eκ_L may be induced to choose eθ_L(κ) to avoid intervention. - Bank expected profits comparing choices for κ < eκ_L: - Π(bθ) | κ 0 - ∂ κ_L(ε) / ∂ A_L < 0 - Interpretation: - Higher supervisory effort ε induces banks with lower capital to meet supervisory standards. - Decrease in ψ_L or increase in A_L lowers the capital level at which banks meet standards. ### Feasibility condition for positive κ_L(ε) - To have κ_L(ε) > 0, parameters must satisfy supervisor chooses inspection effort ε < ε_L where (equation (12)): - ε_L = (ψ_L − √(2 χ A_L))^2 × (R − 1)^2 / 4 - (text expression: ε_L = (ψ_L − √(2 χ A_L))^2 × (R − 1)^2 / 4) ### Bank reaction function to supervisory effort - Bank reaction bθ_L(κ, ε): - bθ_L = bθ(κ) for ε < bε(κ) and κ < eκ_L - bθ_L = eθ_L(κ) for ε ≥ bε(κ) and κ < eκ_L - bθ_L = bθ(κ) > eθ_L(κ) for κ ≥ eκ_L - Less-capitalized banks have riskier laissez-faire portfolios but are forced into safer portfolios eθ_L once supervised. ### Supervisor’s inspection effort objective (equations (13) and (14)) - Supervisor total surplus ΣΩ_L (equation (13)): - Pr(θ > eθ_L) E[θ( R − 1/2 χ θ − (1 − κ) ) − (1 − θ)(1 − κ) ψ_L − κ | θ > eθ_L] - + ε × Pr(θ < eθ_L) E[−A_L + θ*_L( R − 1/2 χ θ*_L − (1 − κ) ) − (1 − θ*_L)(1 − κ) ψ_L − κ | θ < eθ_L] - + (1 − ε ×) Pr(θ < eθ_L) E[θ( R − 1/2 χ θ − (1 − κ) ) − (1 − θ)(1 − κ) ψ_L − κ | θ < eθ_L] - − δ/2 ε^2 - Simplified form highlighting dependence on inspection effort (equation (14)): - ΣΩ_L = E[θ( R − 1/2 χ θ − (1 − κ) ) − (1 − θ)(1 − κ) ψ_L − κ] + ε Pr(θ < eθ_L) E[I_L(θ*_L, θ, κ) | θ < eθ_L] − δ/2 ε^2 ### Supervisor’s optimal effort reaction (Lemma 2) - Given bank behavior, local supervisor chooses effort ε_L(κ_L) that satisfies (equation (15)): - ε_L(κ_L) = ∫_0^{κ_L} I_L(θ*_L, bθ, κ) f(κ) dκ < ε_L - Comparative statics: - ∂ ε_L(κ_L) / ∂ κ_L > 0 - Interpretation: - Supervisor effort increases with κ_L: a larger set of banks that would be excessively risky raises inspection incentives. ### Equilibrium with local supervision (Proposition 2) - Unique equilibrium (ε*_L, κ*_L, eθ_L, bθ_L) exists such that: 1) Supervisor intervenes any bank with θ < eθ_L(κ) (eθ_L as in (6)); 2) Banks that do not meet eθ_L(κ) choose laissez-faire portfolios bθ(κ); 3) Fixed point conditions: ε_L(κ*_L) = ε*_L and κ_L(ε*_L) = κ*_L - Equilibrium implications: - Supervisor exerts strictly positive effort ε*_L > 0. - Threshold κ*_L is strictly less than eκ_L, so supervision induces some banks to move away from their laissez-faire portfolios toward regulatory standard eθ_L. *Source: _wp16186 - 4.1 Intervention choice of the local supervisor* ### 5.1 An unambiguously tougher central supervisor ### 5.1 An unambiguously tougher central supervisor ### Setup and threshold at which banks self-comply - Assume the central regulator has a tougher intervention policy, eθ_C(κ) > eθ_L(κ), either because of a lower intervention cost A_C < A_L or because she bears a higher cost of failure, ψ_C > ψ_L. - Threshold at which a bank independently chooses a portfolio bθ(κ) that is safe enough to avoid central intervention: - eκ_C = μ (1 − 1/ψ_C p 2 χ A_C ). (20) - Again assume eκ_C > 0, which holds if ψ_C > √(2 χ A_C). - eκ_C > eκ_L if either ψ_C > ψ_L or A_C < A_L. ### Banks' portfolio choice under a tougher central supervisor (Lemma 4) - For a given supervisory effort ε, there exists κ_C(ε) such that: - Banks with κ < κ_C(ε) choose the laissez-faire portfolio quality bθ(κ). - Banks with κ ∈ [κ_C(ε), eκ_C] switch to portfolio quality eθ_C(κ) > bθ(κ). - κ_C(ε) = μ (1 − √(ε× + √(2 χ A_C)/ψ_C + √(ε×) ) ) < eκ_C. (21) - Comparative statics: - ∂κ_C(ε)/∂ε < 0 - ∂κ_C(ε)/∂ψ_C > 0 - ∂κ_C(ε)/∂A_C < 0 ### Range of banks affected by supervisory threat - Range of banks who deviate from preferred portfolios to avoid intervention: - eκ_C − κ_C(ε) = √(ε×)(R ψ_C − √(2 χ A_C)) / [ψ_C(ψ_C + √(ε×))]. (25) - eκ_L − κ_L(ε) = √(ε×)(R ψ_L − √(2 χ A_L)) / [ψ_L(ψ_L + √(ε×))]. - If ψ_C = ψ_L and A_C < A_L, then eκ_C − κ_C(ε) > eκ_L − κ_L(ε): more banks adjust portfolios under centralization. ### Local supervisor's effort problem under central oversight - Local supervisor's total-return maximization under centralization: - max_ε ΣΩ_Λ = Pr(θ > eθ_C) E[θ(μ(R − 1/2 χ θ) − (1 − κ)) − (1 − θ)(1 − κ) ψ_Λ − κ | θ > eθ_C] + ε× Pr(θ < eθ(θ*_C)) E[−A_Λ + θ*_C(μ(R − 1/2 χ θ*_C) − (1 − κ)) − (1 − θ*_C)(1 − κ) ψ_Λ − κ | θ < eθ(θ*_C)] + ε× Pr(eθ(θ*_C) ≤ θ < eθ_C) E[−A_Λ + θ*_C(μ(R − 1/2 χ θ*_C) − (1 − κ)) − (1 − θ*_C)(1 − κ) ψ_Λ − κ | eθ(θ*_C) ≤ θ < eθ_C] + (1 − ε×) Pr(θ < eθ(θ*_C)) E[θ(μ(R − 1/2 χ θ) − (1 − κ)) − (1 − θ)(1 − κ) ψ_Λ − κ | θ < eθ(θ*_C)] + (1 − ε×) Pr(eθ(θ*_C) ≤ θ < eθ_C) E[θ(μ(R − 1/2 χ θ) − (1 − ε)) − (1 − θ)(1 − κ) ψ_Λ − κ | eθ(θ*_C) ≤ θ < eθ_C] − δ/2 ε^2. - Reduced expression: - max_ε ΣΩ_Λ = E[θ(μ(R − 1/2 χ θ) − (1 − κ)) − (1 − θ)(1 − κ) − κ] (23) + ε Pr(θ < eθ(θ*_C)) E[ I_Λ(θ*_C, θ, κ) | θ < eθ(θ*_C) ] + ε Pr(eθ(θ*_C) ≤ θ < eθ_C) E[ I_Λ(θ*_C, θ, κ) | eθ(θ*_C) ≤ θ < eθ_C ] − δ/2 ε^2, - where I_Λ(θ*_C, θ, κ) is expression (5) evaluated with θ*_C instead of θ*_Λ and captures the local supervisor’s payoff difference from intervention under centralization. - Key inequalities: - E[I_Λ(θ*_C, θ, κ) | θ < eθ(θ*_C)] < E[I_Λ(θ*_Λ, θ, κ) | θ < eθ(θ*_C)] if θ*_C ≠ θ*_Λ. - E[I_Λ(θ*_C, θ, κ) | eθ(θ*_C) ≤ θ < eθ_C] < 0. ### Local supervisor reaction function under centralization (Lemma 6) - Define eκ(θ*_C) where bθ(κ) = eθ(θ*_C). - If A_C < A_L for ψ_C = ψ_L, or ψ_C > ψ_L for A_C = A_L, so that eθ_C(κ) > eθ_L(κ) and θ*_C ≥ θ*_Λ, then the local supervisor’s reaction function satisfies: - ε_C(κ_C) = ∫_0^{min(κ_C, ε_κ(θ*_C))} I_Λ(θ*_C, bθ, κ) φ(κ) dκ + (1/κ_C) ∫_{ε_κ(θ*_C)}^{κ_C} I_Λ(θ*_C, bθ, κ) φ(κ) dκ < ε_κ(θ*_C) < ε_C, - and ε_C(κ) ≤ ε_Λ(κ). - Decomposition: - ε_C = { ∫_0^{κ_C} I_Λ(θ*_C, bθ, κ) φ(κ) dκ for κ_C ≤ eκ(θ*_C) ∫_0^{ε_κ(θ*_C)} I_Λ(θ*_C, bθ, κ) φ(κ) dκ + ∫_{ε_κ(θ*_C)}^{κ_C} I_Λ(θ*_C, bθ, κ) φ(κ) dκ for κ_C > eκ(θ*_C) } (25) - Signs of I_Λ: - I_Λ(θ*_C, bθ, κ) > 0 for κ_C ≤ eκ(θ*_C) - I_Λ(θ*_C, bθ, κ) < 0 for κ_C > eκ(θ*_C) - Slopes: - ∂ε_C / ∂κ_C = I_Λ(θ*_C, bθ, κ_C) φ(κ_C) > 0 for κ_C ≤ eκ(θ*_C) - ∂ε_C / ∂κ_C = I_Λ(θ*_C, bθ, κ_C) φ(κ_C) < 0 for κ_C > eκ(θ*_C) - Interpretation: for a given κ_C, centralization makes the local supervisor (weakly) less diligent in uncovering bank risk compared with independence because uncovered information enables central intervention, and the local supervisor may prefer to avoid generating such information. ### Equilibrium cases and measures of portfolio quality - Distinguish two cases where the central regulator is tougher (eθ_C > eθ_L): 1. A_C < A_L with ψ_C = ψ_L ⇒ θ*_C = θ*_Λ (supervisory portfolio quality unchanged by centralization). 2. ψ_C > ψ_L with A_C = A_L ⇒ θ*_C > θ*_Λ (supervisory portfolio quality increases under centralization). - Two measures of banks’ portfolio quality: - Ex ante average portfolio quality under regime j (j = Λ, C): - Q_j = ∫_0^1 bθ(κ) φ(κ) dκ + ∫_{ε_κ_j}^{κ_j} [ eθ_j(κ) − bθ(κ) ] φ(κ) dκ. (26) - Ex post average portfolio quality expected after regulatory intervention: - Q*_j = ∫_0^1 bθ(κ) φ(κ) dκ + ∫_{ε_κ_j}^{κ_j} [ eθ_j(κ) − bθ(κ) ] φ(κ) dκ + ε*_j × ∫_{κ_I}^0 [ θ*_j(κ) − bθ(κ) ] φ(κ) dκ. (27) - Q_j is an ex ante measure of portfolio risk; Q*_j is an ex post measure. *Source: 5.1 An unambiguously tougher central supervisor (excerpt).* ### 5.2 Lower intervention cost for the central supervisor: ### 5.2 Lower intervention cost for the central supervisor: ### Setup and comparative statics - Consider the case where eθ_C > eθ_L (central supervisor is tougher because of a lower intervention threshold) but θ*_C = θ*_L (same portfolio chosen conditional on intervention). Formally, eθ_C > eθ_L and θ*_C = θ*_L. - From Lemmas 5 and 6: - The local supervisor’s reaction function under centralization coincides with the one under local supervision as in (15) for κ_C ≤ e κ_L. - The bank’s reaction function κ_C(ε) under centralization remains strictly above the one under local supervision κ_L(ε). - Goal: analyze equilibrium supervisory effort, banks’ portfolio choices, and equilibrium risk levels. ### Proposition 3 — small conflict case - Assumptions: ψ_C = ψ_L. - Claim: There is a value ζ > 0 such that, for 0 < A_L − A_C < ζ: - The local supervisor exerts more effort under centralization than when independent: ε*_C > ε*_L. - Banks’ average portfolio quality is higher under centralization, both ex ante and ex post: Q_C > Q_L and Q*_C > Q*_L. - Mechanism: - Tighter standards from the central supervisor require banks to choose safer portfolios to avoid intervention. - Some banks prefer to risk being intervened rather than meet tougher standards; the local supervisor responds by exerting more effort to catch these banks. - The upward shift in banks’ reaction function under centralization leads to greater inspection effort by the local supervisor in equilibrium. ### Proposition 4 — large conflict and multiple equilibria - Assumptions: ψ_C = ψ_L and A_C ≤ 1/(8χ) ( sqrt{3 (8χ A_L − ψ_L^2)} − ψ_L )^2 (expression preserved as in source). - Results: - There exists an equilibrium under centralization with supervisory effort ε*_C = 0, κ_C = e κ_C, and lower bank portfolio quality: Q_C < Q_L and Q*_C < Q*_L. - As divergence between local and central objectives increases, local supervisor’s incentives to exert effort decrease. - Over a region, reaction functions of banks and supervisor intersect before the tangency point → multiple equilibria: - At least one equilibrium with positive effort and one with zero effort. - In the positive-effort equilibrium, effort can be greater or lower than under independent local supervision depending on where intersection occurs. - In the zero-effort equilibrium, the local supervisor chooses no information collection; banks prefer this equilibrium; both supervisors prefer the positive-effort equilibrium. - Parameter space for equilibrium with zero inspection effort: - Increases in A_L. - Decreases with ψ_L. - Hence broader for laxer local supervisors. - If conflict increases further so reaction functions cross only beyond tangency, the unique equilibrium is ε*_C = 0 and κ_C = e κ_C; supervision is ineffective and banks choose laissez-faire portfolios. - Implication: centralization may require measures to better align incentives of local supervisors with central authority or improve monitoring of local supervisors (e.g., joint supervisory teams). ### Delegation of supervision (section 5.2.1) - Context: under centralization, central supervisor cannot commit beyond subgame perfect strategy. The equilibrium with lower inspection effort raises question of whether central supervisor can do better by committing to another strategy. - Consider credible alternative: central supervisor delegates intervention policy to the local supervisor (i.e., allow local operator to act as under full independence). - Total surplus to central supervisor when choosing regime (equation preserved as in source): - Σ_W_C = E[ θ μ R − 1/2 χ θ − (1 − κ) ] − (1 − θ)(1 − κ) − κ + ε_φ Pr(θ < eθ_φ) E[I_C(θ*_φ, θ, κ) | θ < eθ_φ] − δ/2 ε_φ^2, where φ = L, C. - Proposition 5: - Suppose ψ_C = ψ_L and A_C is such that a subgame optimal equilibrium under centralization with ε*_C = 0 exists. - In this equilibrium, the central supervisor is better off delegating supervision entirely to the local supervisor, allowing her to choose eθ_L and θ*_L. - Interpretation: when conflict is severe, centralization is so ineffective that delegation is the best option for the central supervisor. ### Numerical examples (section 5.2.2) - Purpose: illustrate that centralization may lead to less information collection and weaker intervention threat, producing worse outcomes than local supervision. - Parameters used in example: - R = 2.5, χ = 3, δ = 0.04, × = 0.2. - Under local supervision: A_L = 0.25, ψ_L = 1.5. - Under centralized supervision: A_C = 0.12637, ψ_C = ψ_L = 1.5. - These parameters ensure θ*_L = θ*_C is interior for κ ∈ [0,1], and eθ_L, eθ_C, and laissez-faire portfolios bθ are interior to [0,1]. - Equilibrium under local supervision: - Unique equilibrium with inspection effort ε*_L = 0.04085. - Banks with κ ∈ [κ*_L = 0.08782, e κ_L = 0.18350] choose intervention threshold eθ_L; banks with κ < κ*_L and κ > e κ_L choose laissez-faire bθ. - Average portfolio quality ex ante: Q_L = 0.66895. - Average portfolio quality ex post (after intervention): Q*_L = 0.67159. - Equilibria under centralized supervision: - Three equilibria: two with positive inspection effort and one with zero effort. - In all equilibria, inspection effort and average bank portfolio quality are lower than under local supervision. - Highest-effort centralized equilibrium: - ε*_C = 0.01514 < ε*_L. - κ*_C = 0.35158 > κ*_L. - Ex ante average portfolio quality: Q_C = 0.66782 < Q_L. - Ex post quality: Q*_C = 0.66826 < Q*_L. - Other positive-effort equilibrium: - ε*' _C = 0.01509, κ*' _C = 0.35166. - Average portfolio qualities: Q' _C = 0.667817 and Q*' _C = 0.668254. - Zero-effort equilibrium: - ε*'' _C = 0 and κ*'' _C = e κ_L (no banks are disciplined). - Given ineffective supervision, banks’ average portfolio qualities equal laissez-faire: Q'' _C = Q*'' _C = 0.6. - Surplus comparisons for central supervisor: - Centralization increases surplus by ΔΣ_W_C = 0.000014 and ΔΣ_W'_C = 0.0000137 in the two positive-effort equilibria (ε*_C, κ*_C) and (ε*' _C, κ*' _C), respectively. - Delegation increases surplus by ΔΣ_W'' _C = 0.000122 in the third equilibrium where centralization leads to zero supervisory effort. - Conclusion: centralization is preferred as long as it leads to positive effort; delegation is better when centralization leads to no effort. ### Policy implications and takeaways - Centralization can improve outcomes (higher local effort, safer portfolios) when the conflict between central and local supervisors is small. - When conflict is large, centralization can worsen outcomes due to agency problems that reduce local supervisors’ incentives to collect actionable information, possibly producing multiple equilibria including no-inspection equilibria preferred by banks. - To make centralization effective, measures to align incentives and improve monitoring of local supervisors are important (e.g., joint supervisory teams). - In extreme conflict cases, full delegation of intervention to the local supervisor can yield higher total surplus for the central authority. *Source: 5.2 Lower intervention cost for the central supervisor (from the supplied IMF chapter content).* ### 5.3 Higher cost of bank failure for the central supervisor: ### 5.3 Higher cost of bank failure for the central supervisor: ### Setup and comparative statics - Case considered: central supervisor faces the same intervention cost as the local supervisor (  =  ), but bears a higher cost in case of bank failure (     ). - Implications: - againe   e  - supervisor is tougher in both dimensions: higher intervention threshold and higher standard conditional on intervention, so  ∗    ∗  - local supervisor’s reaction function under centralization lies strictly below the one under local supervision (15) for   ≤ e   because   ( ∗  ; b; )    ( ∗  ; b; ) for any   ≤ e   - bank’s reaction function   () under centralization remains strictly above the one under local supervision   () ### Lemma 7 — local supervisor reaction under centralization - Statement: When   =   and      , the local supervisor’s reaction function under centralization is strictly below the reaction function under independence:   ()    () for all   e   - Intuition: - Central supervisor internalizes a higher cost of bank failure, leading to different preferred portfolios conditional on intervention ( ∗  vs  ∗  ). - Even when the local supervisor would like to intervene, she cannot implement her preferred portfolio, reducing her incentives to exert effort to identify high-risk banks. ### Comparative dynamics (Figure 6 description) - Red curve labeled   : local supervisor’s reaction function for effort when the central supervisor bears a higher failure cost;   is strictly below   for all levels of the capital threshold . - Curve labeled   : banks’ reaction to tougher standards; shifted out relative to independent local supervisor (as in Section 5.2). - Net effect under centralization with higher failure-cost for center: - Banks adopt higher quality portfolios for a given level of effort. - Supervisor exerts less effort. - Equilibrium depends on size of conflict between local and central supervisor: - If conflict is small, equilibrium inspection effort may be higher under centralization than under local supervision. - If conflict is large enough, inspection effort may be lower under centralization. - Condition for existence of equilibrium with zero supervisory effort under centralization still holds when      : there exists an equilibrium with  ∗  = 0 if   ≤ 1 8 ³ q 3 ¡ 8  −  2  ¢ −   ́ 2 . - Reason: banks’ reaction function shifts further out while supervisor’s reaction function shifts further down. ### 5.3.1 Numerical example — parameters and equilibrium outcomes - Parameter set (modified from Section 5.2.2): -  = 25 -  = 3 -  = 004 -  = 02 -   =   = 013 -   = 115 -   = 145 - These parameters ensure all portfolio qualities ( ∗  , e  and b) are interior solutions for all  ∈ [0 1], with  = , . - Equilibrium under local supervision: - supervisory effort:  ∗  = 003716 - optimal threshold:  ∗  = 011124 - average portfolio quality chosen by banks (definition (26)):   = 066946 - portfolio quality after regulatory intervention (definition (27)):  ∗  = 067256 - Equilibrium under centralization: - supervisory effort:  ∗  = 003081   ∗  - optimal threshold:  ∗  = 029380   ∗  - average portfolio quality chosen by banks:   = 066895    - portfolio quality after intervention:  ∗  = 066969   ∗  - Welfare comparison: - Central supervisor prefers the subgame optimal solution under centralization rather than to delegate: increase in surplus equals ∆ = 00000994. - Interpretation: centralization can entail lower inspection effort and higher bank risk, but can still be welfare-improving when inspection effort remains positive. - Uniqueness: the equilibrium with lower but positive inspection effort under centralization is now unique in this example. ### Key theoretical conclusions (excerpted) - Centralization can reduce local supervisors’ incentives to collect information because collected information might be used by the center to take actions the local supervisor dislikes. - Tougher central standards may paradoxically lead to greater aggregate risk-taking if agency conflicts reduce information collection. - Agency problems are larger when the local supervisor is laxer; the mismatch problem may be most severe for those cases that stand to benefit most from centralization. - Design features that mitigate conflicts (as in the SSM) include: - ECB retaining the right to take any bank under direct supervision (threat increases local payoff from effort). - Putting locally systemic banks and euro-level systemic banks under direct ECB supervision (minimizes differences in utility). - Internal governance practices such as ECB staff leading on-site inspections and rotating staff of different nationalities to limit conflicts. *Source: _wp16186 - 5.3 Higher cost of bank failure for the central supervisor:* --- _Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2016/_wp16186.pdf_