Financial Institution Dynamics and Capital Regulations

Transcription

1 Financial Institution Dynamics and Capital Regulations José-Víctor Ríos-Rull Tamon Takamura Yaz Terajima University of Minnesota Bank of Canada Bank of Canada Mpls Fed, CAERP Preliminary Macroeconomic Stability, Banking Supervision and Financial Regulation European University Institute, Florence, Italy September 18, 2014 The views expressed are those of the authors and not of the Bank of Canada, the Federal Reserve Bank of Minneapolis or the Federal Reserve System.

2 Motivation Regulatory discussions during the financial crisis: - insufficient capitalization of banks; - bank dividend payouts (Acharya, Gujral, Kulkarni and Shin 2011); - executive compensation (Financial Stability Forum 2009). Basel III capital regulations include: - Capital conservation buffer (2.5%) + min. capital requirement (4.5%). - Distribution of earnings will be restricted if the buffer is drawn down. Financial Institution Dynamics and Capital Regulations 2/20

3 Objective and Issues with Existing Macro-Banking Models Our goal: Analysis of macroeconomic implications of minimum capital requirement and conservation buffer in Basel III. To do so, we need a model environment whereby over-payment of dividends and executive bonuses naturally arise. Existing macro-banking models typically have - no outside equity issuance, and/or - manager s incentive perfectly aligned with shareholders interests. For today, focus on analyzing an equilibrium without capital regulations to discuss why they may be necessary. Financial Institution Dynamics and Capital Regulations 3/20

4 Our Paper A macro-banking model featuring a manager who controls the bank and: 1 issues outside equity and dividends (time inconsistency problem); 2 is impatient; and 3 faces moral hazard through limited liability. These elements allow us to analyze capitalization and risk taking of banks simultaneously. Financial Institution Dynamics and Capital Regulations 4/20

5 Main Results Under-capitalization due to time-inconsistency problem. Time inconsistency problems exist because of: - Reoptimization of dividend payment, and - Dilution of existing equities. Excessive leverage by banks due to moral hazard. Need for both capital conservation buffer and minimum capital requirement. Financial Institution Dynamics and Capital Regulations 5/20

6 Bank Manager s Problem with Implicit Loans Time-inconsistency issue subject to In equilibrium, Bonus incentive V (n) = Anti-dulition protection max {u (c) + χv (f (y))} {c,z,y,e,m} c + z + y = n + αm m = eβω (f (y)). Ω (n) = z (n) + β [1 e (n)] Ω (f (y (n))). e c ψz m (n γc z) + m Financial Institution Dynamics and Capital Regulations 6/20

7 Bank Manager s Problem with Implicit Loans Time-inconsistency issue subject to In equilibrium, Bonus incentive V (n) = Anti-dulition protection max {u (c) + χv (f (y))} {c,z,y,e,m} c + z + y = n + αm m = eβω (f (y)). Ω (n) = z (n) + β [1 e (n)] Ω (f (y (n))). e c ψz m (n γc z) + m Financial Institution Dynamics and Capital Regulations 7/20

8 Bank Manager s Problem with Implicit Loans Time-inconsistency issue subject to In equilibrium, Bonus incentive V (n) = Anti-dulition protection max {u (c) + χv (f (y))} {c,z,y,e,m} c + z + y = n + αm m = eβω (f (y)). Ω (n) = z (n) + β [1 e (n)] Ω (f (y (n))). e c ψz m (n γc z) + m Financial Institution Dynamics and Capital Regulations 8/20

9 Markov Perfect Equilibrium Generalized Euler Equation: u c = χ (1 α) f y 1 + αβγψf y z n αβf y u c. Knowing that tomorrow s manager will have his own interests, today s manager takes it into account through z n z n. GEE collapses to a usual Euler equation when α = 0: u c = χf y u c. The manager considers the cost of increasing y through Ω (f (y)) = ψγz (f (y)) + f (y). Financial Institution Dynamics and Capital Regulations 9/20

10 Under-Capitalization in MPE (Steady State) Markov Perfect Equilibrium: f ME y = Commitment Equilibrium: 1 χ (1 α) + αβ ( γψz n + 1) f CM y = 1 χ (1 α) + αβ Social Planner f SP y = 1 β Insufficient capitalization if z n > 0. y SP > y CM > y ME. Financial Institution Dynamics and Capital Regulations 10/20

11 Numerical Results (Steady State) Functional forms: u (c) = log (c), f (y) = y ν. Parameter values: α β γ χ ψ ν Results: z n = > 0. Thus, y CM > y ME. Commitment Equilibrium vs Markov Perfect Equilibrium y z Ω z/ω m/ω Commitment Markov Perfect Financial Institution Dynamics and Capital Regulations 11/20

12 Model with Loan, Deposit and Default V (n; Ω) = subject to { max u (c)+χ V ( F ( d, y, η ) ; Ω ) G ( dη ) +χ V G ( η (d, y) )} {c,z,y,l,d,e,m} η (d,y) c + z + y = n + αm l = d + y m = e β η (d,y) Ω ( F ( l, y, η )) dg ( η ) Budget Constraint Balance Sheet Equity Issuance c ψz Compensation Constraint m e = (n γc z) + m [ ] Dilusion Constraint F (d, y, η ) = R(d + y) 1 ν η R d + h(d) d Loan Return η (d, y) given by F (d, y, η = η ) = 0 Default Threshold Financial Institution Dynamics and Capital Regulations 12/20

13 The model simplifies to... { ( V (n) = max u(ψz) + χ V F ( d(z, )) y, n), y, η G(dη ) z,y η ( d(z,y,n),y) ( )} + χ V G η ( d(z, y, n), y) Deposit, d, is determined through the bud. const. given (z, y, n): [1 + ψ α (1 + γψ)] z + y = (1 α) n + αβ η ( d,y) αβγψ z η ( d,y) F ( d, ) y, η G ( dη ) ( F ( d, )) y, η G ( dη ) Financial Institution Dynamics and Capital Regulations 13/20

14 Optimality conditions [z] [ ] ψu c + χ V nf d G(dη ) + [V V (0)] G(η )η d d z = 0 η ( d,y) [y] V n η ( d,y) ) ] (F d dy + F y G(dη ) + [V V (0)] G(η ) [η d dy + η y = 0 [envelope] [ V n (n) = χ V nf d G ( ] dη ) + [V V (0)] G (η ) η d d n η ( d,y) Financial Institution Dynamics and Capital Regulations 14/20

15 Generalized Euler Equations [y] dy ψ (1 α) ψu c = χ d z η ( d,y) 1 + ψ α (1 + γψ) u cf y G(dη ) χ [V V (0)] G(η )η y [z] [ ψu c = χ η ( d,y) V nf d G(dη + [V (0) V ] G(η )η d ] d z Financial Institution Dynamics and Capital Regulations 15/20

16 GEEs continued [y] 0 = ψ u c { 1 1+ψ α(1+γψ) 1 +αβ η ( d,y) (1 γψz n)f y G(dη ) } +αβγψz(0)g(η )η y +χ η ( d,y) ψ(1 α) 1+ψ α(1+γψ) u cf y G(dη ) direct loss in consumption from y gain in equity valuation from more loans gain in equity valuation from lower default gain in future (consumption) from more loans +χ [V (0) V ] G(η )η y gain in continuation value from lower default Financial Institution Dynamics and Capital Regulations 16/20

17 Two State Example Suppose η {0, 1} and h = κ (l y). Let p 1 = Pr (η = 1). Long-surviving bankers leverage and capital can be orderd as leverage ME > leverage CM > leverage SP, y ME < y CM < y SP. Financial Institution Dynamics and Capital Regulations 17/20

18 Proof (Step 1) Compare a Markovian manager and a committed manager. Regardless of com. tech., l (y) is the same under moral hazard. D l F (l (y), y, 1) = 0. DRS implies dl (y) /dy < 1 and leverage is decreasing in y. Again, y ME < y CM due to time inconsistency. Hence, leverage ME > leverage CM. Financial Institution Dynamics and Capital Regulations 18/20

19 Proof (Step 2) Compare a committed banker and the social planner. Only the banker is protected by limited liability. Solutions to d and l satisfy d CM > d SP and l CM < l SP : d CM = p 1 1 [χ (1 α) + αβ] 1 R d 2κ > β 1 R d 2κ = d SP, l CM = [[χ (1 α) + αβ] p 1 (1 γ) R] 1/γ < [βp 1 (1 γ) R] 1/γ = l SP This implies that y CM < y SP. As a result, leverage CM > leverage SP, Financial Institution Dynamics and Capital Regulations 19/20

20 Conclusion Time inconsistency problem regarding outside equity issuance leads bankers to pay excessive dividends and accumulate insufficient capital. Moral hazard problem leads to too much borrowing and thus excessive leverage of banks. Minimum capital requirement alone may not be adequate to promote capital accumulation. Capital conservation buffer may be an effective policy instrument. What s next? - Global solution (non-steady-state analysis). - Quantitative analysis of capital regulations. - Markovian evolution of banking industry. - Aggregate shocks. - General equilibrium. Financial Institution Dynamics and Capital Regulations 20/20

21 Equity Issuance by Banks in Canada Financial Institution Dynamics and Capital Regulations 21/20

22 Dividend Payout by Banks in Canada Financial Institution Dynamics and Capital Regulations 22/20