Optimal Deposit Insurance Eduardo D´ avila and Itay Goldstein Yale/NYU Stern/NBER and UPenn Wharton Diamond/Dybvig@36 Conference 3/30/2019 1 / 19
Motivation • Deposit insurance: main explicit financial guarantee • Significant effects • 4,000 bank failures only in 1933 • 4,000 bank failures between 1934 and 2014 Question What is the optimal level of deposit insurance? • Are existing coverage levels ( ✩ 250,000 or e 100,000) optimal? Figure 2 / 19
Motivation • Deposit insurance: main explicit financial guarantee • Significant effects • 4,000 bank failures only in 1933 • 4,000 bank failures between 1934 and 2014 Question What is the optimal level of deposit insurance? • Are existing coverage levels ( ✩ 250,000 or e 100,000) optimal? Figure • This paper 1. Characterize welfare impact of changes in the level of DI coverage dW dδ • Applies broadly 2. As a function of a small number of sufficient statistics • Connects theory and measurement 2 / 19
Main results 1. Welfare impact of change in level of coverage dW dδ = A × B − C × D • Marginal benefit • A -Sensitivity of bank failure probability to DI change • B Utility gain of preventing marginal failure • Marginal cost • C Probability of bank failure • D Expected marginal social cost of intervention in case of bank failure 3 / 19
Main results 1. Welfare impact of change in level of coverage dW dδ = A × B − C × D • Marginal benefit • A -Sensitivity of bank failure probability to DI change • B Utility gain of preventing marginal failure • Marginal cost • C Probability of bank failure • D Expected marginal social cost of intervention in case of bank failure 3 / 19
Main results 1. Welfare impact of change in level of coverage dW dδ = A × B − C × D • Marginal benefit • A -Sensitivity of bank failure probability to DI change • B Utility gain of preventing marginal failure • Marginal cost • C Probability of bank failure • D Expected marginal social cost of intervention in case of bank failure 2. Insights • Sufficient statistics • If C → 0 , unlimited DI is optimal (DD83) 3 / 19
Main results 1. Welfare impact of change in level of coverage dW dδ = A × B − C × D • Marginal benefit • A -Sensitivity of bank failure probability to DI change • B Utility gain of preventing marginal failure • Marginal cost • C Probability of bank failure • D Expected marginal social cost of intervention in case of bank failure 2. Insights • Sufficient statistics • If C → 0 , unlimited DI is optimal (DD83) 3. Ex-ante regulation • Focus on marginal fiscal externalities (not fairly-priced DI) • Both asset- and liability-side regulation are needed 3 / 19
Main results 1. Welfare impact of change in level of coverage dW dδ = A × B − C × D • Marginal benefit • A -Sensitivity of bank failure probability to DI change • B Utility gain of preventing marginal failure • Marginal cost • C Probability of bank failure • D Expected marginal social cost of intervention in case of bank failure 2. Insights • Sufficient statistics • If C → 0 , unlimited DI is optimal (DD83) 3. Ex-ante regulation • Focus on marginal fiscal externalities (not fairly-priced DI) • Both asset- and liability-side regulation are needed 4. Quantitative implications • Direct measurement • Model simulation 3 / 19
Outline 1. Basic framework • Positive analysis • Welfare analysis ⇒ dW dδ (main result) 2. Extensions 3. Measurement 4. Conclusion • Theoretical contribution: rich cross-section of depositors Literature 4 / 19
Environment • t = 0 , 1 , 2 • Aggregate state (profitability) s ∈ [ s, s ] , known at date 1 , cdf F ( · ) 5 / 19
Environment • t = 0 , 1 , 2 • Aggregate state (profitability) s ∈ [ s, s ] , known at date 1 , cdf F ( · ) • Depositors • Double continuum of depositors, mass D 0 i ∼ G ( · ) (cdf), • Fraction λ of early types • Endowments Y 1 i ( s ) (early), Y 2 i ( s ) (late) • Ex-ante expected utility E s [ λU ( C 1 i ( s )) + (1 − λ ) U ( C 2 i ( s ))] • Depositors choose D 1 i ( s ) ∈ [0 , R 1 D 0 i ] 5 / 19
Environment • t = 0 , 1 , 2 • Aggregate state (profitability) s ∈ [ s, s ] , known at date 1 , cdf F ( · ) • Depositors • Double continuum of depositors, mass D 0 i ∼ G ( · ) (cdf), • Fraction λ of early types • Endowments Y 1 i ( s ) (early), Y 2 i ( s ) (late) • Ex-ante expected utility E s [ λU ( C 1 i ( s )) + (1 − λ ) U ( C 2 i ( s ))] • Depositors choose D 1 i ( s ) ∈ [0 , R 1 D 0 i ] • Banks technology • − 1 → ρ 1 ( s ) (date 1) → ρ 2 ( s ) > 0 (date 2) • Returns ρ 1 ( s ) > 0 and ρ 2 ( s ) > 0 increasing in s 5 / 19
Environment • t = 0 , 1 , 2 • Aggregate state (profitability) s ∈ [ s, s ] , known at date 1 , cdf F ( · ) • Depositors • Double continuum of depositors, mass D 0 i ∼ G ( · ) (cdf), • Fraction λ of early types • Endowments Y 1 i ( s ) (early), Y 2 i ( s ) (late) • Ex-ante expected utility E s [ λU ( C 1 i ( s )) + (1 − λ ) U ( C 2 i ( s ))] • Depositors choose D 1 i ( s ) ∈ [0 , R 1 D 0 i ] • Banks technology • − 1 → ρ 1 ( s ) (date 1) → ρ 2 ( s ) > 0 (date 2) • Returns ρ 1 ( s ) > 0 and ρ 2 ( s ) > 0 increasing in s • Deposit contract • Banks offer noncontingent deposit rate R 1 • Pro-rata distribution after failure 5 / 19
Environment • t = 0 , 1 , 2 • Aggregate state (profitability) s ∈ [ s, s ] , known at date 1 , cdf F ( · ) • Depositors • Double continuum of depositors, mass D 0 i ∼ G ( · ) (cdf), • Fraction λ of early types • Endowments Y 1 i ( s ) (early), Y 2 i ( s ) (late) • Ex-ante expected utility E s [ λU ( C 1 i ( s )) + (1 − λ ) U ( C 2 i ( s ))] • Depositors choose D 1 i ( s ) ∈ [0 , R 1 D 0 i ] • Banks technology • − 1 → ρ 1 ( s ) (date 1) → ρ 2 ( s ) > 0 (date 2) • Returns ρ 1 ( s ) > 0 and ρ 2 ( s ) > 0 increasing in s • Deposit contract • Banks offer noncontingent deposit rate R 1 • Pro-rata distribution after failure • Deposit insurance • Government guarantees δ dollars • Fiscal shortfall is T ( s ) ; Cost of public funds κ ( T ( s )) • DWL 1 − χ ( s ) after bank failure 5 / 19
Environment • Taxpayers V τ ( δ, R 1 ) = E s [ U ( Y τ ( s ) − T ( s ) − κ ( T ( s )))] 6 / 19
Environment • Taxpayers V τ ( δ, R 1 ) = E s [ U ( Y τ ( s ) − T ( s ) − κ ( T ( s )))] • Timeline s is realized t = 0 t = 1 t = 2 Deposit insurance Deposit rate Depositors choose δ determined R 1 determined depositholdings D 1 i 6 / 19
Environment • Taxpayers V τ ( δ, R 1 ) = E s [ U ( Y τ ( s ) − T ( s ) − κ ( T ( s )))] • Timeline s is realized t = 0 t = 1 t = 2 Deposit insurance Deposit rate Depositors choose δ determined R 1 determined depositholdings D 1 i • Two possibilities at date 1 1. Bank failure 2. No bank failure � min { D 0 i R 1 , δ } + α F ( s ) max { D 0 i R 1 − δ, 0 } + Y 1 i ( s ) , Bank Failure C 1 i ( s ) = D 0 i R 1 + Y 1 i ( s ) , No Failure, � min { D 0 i R 1 , δ } + α F ( s ) max { D 0 i R 1 − δ, 0 } + Y 2 i ( s ) , Bank Failure C 2 i ( s ) = α N ( s ) D 0 i R 1 + Y 2 i ( s ) , No Failure , 6 / 19
Equilibrium: Definition • Equilibrium : depositors choose D 1 i ( s ) optimally, given other depositors choices and given values of R 1 and δ • Symmetric equilibria • Sunspot π ∈ [0 , 1] 7 / 19
Equilibrium: Definition • Equilibrium : depositors choose D 1 i ( s ) optimally, given other depositors choices and given values of R 1 and δ • Symmetric equilibria • Sunspot π ∈ [0 , 1] • Key assumptions 1. Restriction to deposit contract (noncontingent and demandable) 2. Single policy instrument (noncontingent deposit insurance with full commitmment) 7 / 19
Equilibrium: Definition • Equilibrium : depositors choose D 1 i ( s ) optimally, given other depositors choices and given values of R 1 and δ • Symmetric equilibria • Sunspot π ∈ [0 , 1] • Key assumptions 1. Restriction to deposit contract (noncontingent and demandable) 2. Single policy instrument (noncontingent deposit insurance with full commitmment) • Three scenarios 1. R 1 predetermined (baseline) 2. R 1 chosen by competitive banks 3. R 1 chosen by the planner (perfect regulation) 7 / 19
Equilibrium: Depositors’ behavior • Three types of depositor 1. Early depositors: withdraw all deposits 8 / 19
Equilibrium: Depositors’ behavior • Three types of depositor 1. Early depositors: withdraw all deposits 2. Full insured late depositors: leave all deposits 8 / 19
Equilibrium: Depositors’ behavior • Three types of depositor 1. Early depositors: withdraw all deposits 2. Full insured late depositors: leave all deposits 3. Partially insured late depositors: leave δ or all deposits (indeterminacy) 8 / 19
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