DISCUSSION OF CAPITAL REQUIREMENTS, RISK CHOICE, AND LIQUIDITY PROVISION IN A BUSINESS CYCLE MODEL

Transcription

1 DISCUSSION OF CAPITAL REQUIREMENTS, RISK CHOICE, AND LIQUIDITY PROVISION IN A BUSINESS CYCLE MODEL BY JULIANE BEGENAU Dmitriy Sergeyev Bocconi University and IGIER Structural Changes in the Banking Sector October 24,

2 SUMMARY This paper solves for optimal bank capital requirement in a DSGE model shows that capital requirements can be expansionary 2

3 SUMMARY This paper solves for optimal bank capital requirement in a DSGE model shows that capital requirements can be expansionary Approach build a DSGE model with various imperfections calibrate it to match macro and financial moments study optimal capital requirements conditional on other policies 2

4 SUMMARY This paper solves for optimal bank capital requirement in a DSGE model shows that capital requirements can be expansionary Approach build a DSGE model with various imperfections calibrate it to match macro and financial moments study optimal capital requirements conditional on other policies Important question. Very nice paper. 2

5 SUMMARY This paper solves for optimal bank capital requirement in a DSGE model shows that capital requirements can be expansionary Approach build a DSGE model with various imperfections calibrate it to match macro and financial moments study optimal capital requirements conditional on other policies Important question. Very nice paper. Discussion A Simple two-period model Variation in government debt Other frictions 2

6 Time: t = 0, 1 SIMPLE MODEL Goods (that enter utility function) Assets perishable consumption: c0, c 1 bank debt: s c 0, s b 0 Agents Markets physical capital (not traded): k0 bank equity (not traded) bank debt households: bankers and consumers (a.k.a. Lucas family) goods market: p = 1 bank debt market: R0 Technology: y 1 = zk0 ν, ν (0, 1) Uncertainty: No Endowment: E 0, E 1 3

7 BANKER-CONSUMER PROBLEM max c 0,c 1,s c 0,sb 0,k 0 c 0 + βc 1 + θ ( s c 0 ) 1 η 1 η s.t.: k 0 + c 0 + s c 0 E 0 + s b 0 c 1 + T 1 E 1 + R 0 s c 0 + zkν 0 R 0s b 0 + τsb 0 }{{} TR 1 s b 0 (1 ξ)k 0 (ψ) Notation s c 0 s b 0 - consumer choice of bank debt - banker choice of debt TR 1 = τs b 0 - tax benefits of debt issuance ξ (0, 1) - capital requirements T 1 - taxes Observe: no government debt 4

8 BANKER-CONSUMER PROBLEM SOLUTION 5

9 BANKER-CONSUMER PROBLEM SOLUTION θ (s c 0 ) η = 1 βr 0 (debt demand) 5

10 BANKER-CONSUMER PROBLEM SOLUTION θ (s c 0 ) η = 1 βr 0 (debt demand) ( ) s b ν 1 1 = βzν 0 + [1 β(r 1 0 τ)] (1 ξ) (debt supply) ξ }{{}}{{} =ψ>0 =k0 ν 1 5

11 BANKER-CONSUMER PROBLEM SOLUTION θ (s c 0 ) η = 1 βr 0 (debt demand) ( ) s b ν 1 1 = βzν 0 + [1 β(r 1 0 τ)] (1 ξ) (debt supply) ξ }{{}}{{} =ψ>0 =k0 ν 1 An equilibrium is (c 0, c 1, s c 0, sb 0, k 0, T, τ) and R 0 such that agents maximize given R 0, T, τ markets clear bank debt: s b 0 = s c 0 consumption goods: c0 + k 0 = E 0, c 1 = E 1 + zk ν 0 government respects T = τs b 0 5

12 EQUILIBRIUM k 0 = s 0 1 ξ 6

13 INCREASE IN CAPITAL REQUIREMENTS 7

14 INCREASE IN CAPITAL REQUIREMENTS dr 0 dξ < 0, ds 0 dξ < 0, dk 0 dξ = d ( ) s0 0 dξ 1 ξ 7

15 INCREASE IN CAPITAL REQUIREMENTS dr 0 dξ < 0, ds 0 dξ < 0, dk 0 dξ = d ( ) s0 0 dξ 1 ξ [ ] dk0 dξ > 0 iff η > 1 7

16 OPTIMAL CAPITAL REQUIREMENTS Household utility = regulator s objective Regulator s optimum W = E 0 k 0 + β (E 1 + zk ν 0 ) + v(s 0) dw = βτ ds 0 ψk 0 = 0 dξ eq um dξ }{{} <0 Intuition: higher ξ reduces bank debt s 0 which (+) reduces social losses due to government subsidy ( ) increases social losses due to capital requirements constraint 8

17 1. VARIATION IN GOVERNMENT DEBT Source: Krishnamurthy, Vissing-Jorgensen (2013) 9

18 1. VARIATION IN GOVERNMENT DEBT Empirical regularity is consistent with the model Government debt is an important state variable for regulators How does capital requirement varies with government debt? Should the policy be stricter after QE? Government debt is not included in the utility function Why? Does it matter? 10

19 2. OTHER FRICTIONS? In the paper: government transfers is the friction to be corrected There are other frictions in the literature Pecuniary externalities [Stein (2012)] Limited commitment [Gertler, Kiyotaki (2010)] Asymmetric information [Christiano, Ikeda (2013)] Which one is the most important? 11

20 SUMMARY 1. Very nice paper on extremely important topic 2. Key contributions of the paper optimal capital requirements in a DSGE model capital requirements can be expansionary 3. Main comments variation in government debt why present friction is the most important? 12