Financial Regulation in a Quantitative Model of the Modern Banking System Juliane Begenau HBS Tim Landvoigt UT Austin CITE August 14, 2015 1
Flow of Funds: total nancial assets 22 20 18 16 $ Trillion 14 12 10 Shadow Banks Depository Institutions 8 6 Jun98 Jun00 Jun02 Jun04 Jun06 Jun08 Jun10 Jun12 Jun14 2
Motivation Financial sector: many dierent institutions Regulation may aect each institutions dierently Unintended consequences of regulating a subset of banks This paper: develops general equilibrium model to study & quantify eects of capital regulation on dierent intermediaries provides framework for designing optimal capital requirement 3
Quantitative GE model Main features endowment economy with two trees households own one tree but need intermediaries to access the other households' preference for safe & liquid bank liabilities two types of banks (regulated & unregulated) regulated banks face constant lev. constraint unregulated face endogenous lev. constraint idiosyncratic default risk 4
Eect of capital requirements Static eects for lower values: increase shadow activity and their risk regulated banks become less risky for higher values: regulated banks risk-free, higher share Dynamic eects of positive shock to banks' asset values Case: low capital requirement (less than 8%) increase in regulated bank activity Case: high capital requirement lower sensitivity of system to shocks decrease in regulated bank activity 5
Outline Model Comparative statics Parametrization Capital requirement experiment 6
Environment Discrete time, innite horizon Endowment: 2 trees produce Y t F Y and Z t F Z Households owny t, need banks for Z t Intermediaries invest in Zt tree & issue debt that provides liquidity service exposed to idiosyn. & agg. shocks have limited liability can default, results in deadweight loss C banks debt insured, risk-free for households S banks debt not insured, not risk-free for households 7
C-Banks A C t,i shares of Z tree, price p t Raise funds with debt Bt,i C at qc t,i & equity EC t,i at pc t,i Idiosyncratic risks ρ C t,i Fρ C proportional to assets, ρ C t,i Z t, i.i.d across banks & time Liabilities insured: qt,i C independent of capital structure Market value balance sheet: Capital requirements: p t A C t+1,i = B C t,i + p C t,ie C t,i (1 θ)p t A C t+1,i B C t,i. 8
Problem of C-Banks Homogeneous of degree one in A C t,i Dene b C t = Bt 1/A C C t (book-leverage) & a C t+1 = A C t+1/a C t (asset growth) Value function v C (b C t,i, Z t, ρ S t,i) = +a C t+1,i subject to max a C t+1,i,bc t+1,i Z t + p t ρ C t,i b C t,i... ( (q C t κ)b C t+1,i p t + E t [ Mt,t+1ˆv C (b C t+1,i, Z t+1 ) ]) (1 θ)p t b C t+1,i where κ is deposit fund fee, M t,t+1 is SDF & ˆv C (b C t+1,i, Z t+1 ) continuation value conditional on survival 9
Idiosyncratic default Continuation value of bank i ṽ C (b C t,i, Z t, ρ C t,i) = max{0, v C ( b C t,i, Z t ) ρ C t,i } With ρ C t,i Fρ C, taking expectations w.r.t ρ ṽ C (b C t,i, Z t ) = F C ρ ( v C ) }{{} prob surv v C ρ ( v C) }{{} loss cdt. on surv Banks of C type (and S type) identical, drop i 10
Bankruptcy & Insurance Fund Dene ρ ( + v ( )) C b C t, Z t average loss cdt on default Creditors recover r C (b C t ) = (1 ξ C ) Z t + p t ρ ( + v ( )) C b C t, Z t with ξ C bankruptcy costs b C t Insurance fund budget constraint for B C t = b C t A C t q C t G t + ( 1 F C ρ ( v C )) ( 1 r C ( b C t )) B C t 1 = G t 1 + κb C t 11
S-Banks Invest in Z & issue liquidity services providing liabilities Problem looks very similar to C banks But debt not insured not subject to capital requirements ( ) endogenous leverage constraint through q S t b S t+1 12
Household Preferences HH derive utility from C and liquidity services H U (C t, H t ) = C1 γ t 1 + ψ (H t/c t ) 1 η 1 γ 1 η with η > 1 (complementarity b/w C and H) Liquidity services H created with intermediary debt H t (N S t 1, N C t 1) = [ (N C t 1) α + F S ρ ( v S ( b S t, Z t )) ν (N S t 1 ) α] 1/α with ν > 0 liquidity factor and α = 1 1/ELS 13
Households' Problem Household wealth: W t+1 = j=s,c + N S t + N C t F j ρ ( v j ) ( D j t+1 + p j t+1)s j t [ F S ρ ( v S ) + ( 1 F S ρ ( v S )) r S (b S t+1) ] Given wealth and bank liquidity, maximize discounted expected utility subject to the budget constraint W t + Y t = C t + p j ts j t + q j t N j t j=s,c j=s,c 14
Recursive Equilibrium State vars: tree Y, HH wealth, liquid bank debt N j j {C, S}, banks' capital structure b j j {C, S} Exog. shocks to log Y & log Z Given prices, households & intermediaries optimize Policies satisfy market clearing for consumption and both intermediaries debt, equity shares & asset shares N S = B S and N C = B C G Deposit fund budget constraint holds 15
Outline Model Mechanism & Comparative Statics Parametrization Capital requirement experiment 16
Liquidity provision by C vs S banks Liquidity benet: H(N S, N C ) = [ (N C ) α + (Fρ S ) ν (N S ) α] 1/α lever up as much as possible C banks: N C = b C A C G restricted by capital req (1 θ) p b C q C independent of b C default cost borne by insurance fund S banks' debt price set by HH's FOC q S = β(f S + (1 F S )r S + MRS S ) 17 Can show that q S / b S < 0 endog. leverage constraint q S + b S q (b S ) = βf S To increase N S = B S = b S A S need larger share of Z (higher A S )
Liquidity factor ν Governs usefulness of N S for liquidity generation Larger ν, higher sensitivity w.r.t survival probability F S ρ S banks internalize their eect on changes in liquidity provision to households: νmrs S /F S Case eect taken into account: higher ν increases price of N S as S banks lower F S Case eect ignored: higher ν lowers price of N S as S banks lower F S not strong enough 18
Liquidity factor eect on H NS FS ν 0.35 0.3 0.25 LF=0 LF=1 BS/(AS*p) 0.22 0.2 0.18 0.2 0 50 100 150 0.16 0 50 100 150 0.9985 0.9799 FS 0.998 0.9975 qs 0.9798 0.9797 0.9796 19 0.997 0.9795 0 50 100 150 0 50 100 150 ν ν Red: S banks takes liquidity aect of its capital structure choice into account Blue: not taken into account
Elasticity of substitution Governs demand for type of intermediary debt α 0: complements, HH need H to be composed of intermediary debt mix α 1 : substitutes, HH care more about quantity, not specic mix Pins down share of shadow banking activity Increasing α liquidity demand eect: shift to commercial banks leverage externality eect: default risk & insurance fund increase, less H desired as consumption falls 20
Liquidity demand vs leverage externality eect 1 0.8 0.8 0.7 AS 0.6 BS 0.6 0.5 0.4 0.4 0.2 0.2 0.4 0.6 0.8 1 0.3 0.2 0.4 0.6 0.8 1 0.25 0.4 BS/(p*AS) 0.2 0.15 G 0.3 0.2 0.1 21 0.1 0.2 0.4 0.6 0.8 1 α 0 0.2 0.4 0.6 0.8 1 α
Comparative Statics: Capital Requirement Increasing the capital requirements: for lower values increase in value of Z lowers leverage constraint for S banks share of shadow banks increases higher survival probability of C banks and default risk of S banks as θ becomes larger, drive down DWL, increase C higher C want more H if θ large enough, G 0 need less H relative less demand for deposits C banks debt becomes relatively more attractive 22
Increase in capital requirement 4.936 0.75 4.934 0.7 p 4.932 4.93 AC 0.65 0.6 4.928 4.926 0.05 0.1 0.15 0.55 0.5 0.05 0.1 0.15 1.5 1 1 0.995 G 0.5 FC 0 0.99 23-0.5 0.05 0.1 0.15 θ 0.985 0.05 0.1 0.15 θ
Eect on Shadow Banks 0.5 0.215 NS FS ν 0.4 0.3 BS/(AS*p) 0.21 0.205 0.2 0.05 0.1 0.15 0.2 0.05 0.1 0.15 0.9977 0.5 FS 0.9976 0.9975 AS 0.45 0.4 0.35 0.3 0.9974 0.05 0.1 0.15 θ 0.25 0.05 0.1 0.15 θ 24
Outline Model Mechanism Parametrization Capital requirement experiment 25
Parametrization Parameters Function Value Target β discount rate 0.98 P/D C banks (Compustat) α maps into CES par. 1 1/Elast = 0.875 S bank activity share GS report, 41% ν liquidity factor 40 S bank book leverage 30 κ deposit insurance fee 0.0006168 FDIC assessment rates (25 bp p.a) θ C bank capital req. 0.06 Basel III Tier 1 cap req ξρ C bankruptcy loss 0.625 Moody Fin Sec. recovery rate (37.1%) ξρ S bankruptcy loss 0.15 Moody Fin Sec. recovery rate (37.1%) µ C ρ mean of ρ shock 0 assumption µ S ρ mean of ρ shock 0 assumption σρ C vol of ρ shock 0.15 FDIC default rate 0.42 % σρ S vol of ρ shock 1.42 q S : averg. (99-15) ON CP AA n. sector other parameters 26
Outline Model Mechanism Parametrization Capital requirement experiment 27
Response to Z shock Solution: local approximation method, 2nd order Get policies for benchmark θ = 6% and other levels Compute IRF for dierent θ levels 28
IRF to Z-shock 2 AC 0.4 C % rel. Z shock 1 0-1 -2 θ = 5.7% θ = 8.3% θ = 11% θ = 15% % rel. Z shock 0.3 0.2 0.1 0 5 10 15 20 25 30 Quarters 5 10 15 20 25 30 Quarters 10 NC 20 p % rel. Z shock 5 0-5 % rel. Z shock 15 10 5 0 5 10 15 20 25 30 Quarters 5 10 15 20 25 30 Quarters 29
IRF to Z-shock ctd qs qc % rel. Z shock 0.6 0.4 0.2 % rel. Z shock 0.6 0.4 0.2 0 0 5 10 15 20 25 30 Quarters 5 10 15 20 25 30 Quarters 0.15 FS 2.5 FC % rel. Z shock 0.1 0.05 0-0.05 5 10 15 20 25 30 Quarters % rel. Z shock 2 1.5 1 0.5 0 5 10 15 20 25 30 Quarters 30
Conclusion Quantitative dynamic model general equilibrium model with two nancial institutions Static eects shadow bank activity increases for low θ and decreases for high θ S bank demand increases valuation of Z despite higher θ risky activity shifts to shadow banks for higher θ, eliminates idiosyncratic risk & DWL, reduces insurance fund size higher consumption Dynamic eects of positive shock to banks' asset values, case θ low more C banks & higher responsiveness to shocks under 31
Parametrization ctd Parameters Function Value Target γ risk aversion 2 η compl. bw cons & safe assets 2 vol(c/h) ψ utility weight on safe assets 0.85 TBD µ Z mean of Z 0.1 normalization σ Z vol of Z shock 0.01 assumption µ Y mean of Y 0.1 normalization σ Y vol of Y shock 0.0071 agg. TFP vol δ persistence of Y shock 0.95 agg. TFP persistence ρ Y Z covariance between Y and Z 0 assumptions back 32
Transition to new capital requirement Simulate the economy under benchmark capital requirement θ = 6% Change in cap req: simulate economy starting at benchmark with policies for new requirement compare path to the new steady state under the new requirement to the benchmark path 33
Transition: from benchmark θ = 6% to new level 0-0.2 AC 0 FC Percent -0.4-0.6-0.8-1 θ = 8.3% θ = 11% θ = 15% Percent -0.05-0.1-0.15 θ = 8.3% θ = 11% θ = 15% 5 10 15 20 25 30 Quarters 5 10 15 20 25 30 Quarters 0 p 0 C -1-0.5 Percent -2-3 -4 θ = 8.3% θ = 11% θ = 15% Percent -1-1.5-2 θ = 8.3% θ = 11% θ = 15% 5 10 15 20 25 30 Quarters 5 10 15 20 25 30 Quarters 34
Related literature Households' demand for money like claims Diamond & Dybvig 1983; Gorton & Winton 1995; Diamond & Rajan 2000; Kashyap, Rajan & Stein 2002; Van Den Heuvel 2008; Williamson 2012; Dang, Gorton, Holmström & Ordonez 2013; DeAngelo & Stulz 2013 Bansal & Coleman 1996; Kacperczyk & Schnabl 2010, Krishnamurthy & Vissing-Jørgensen 2013; Greenwood, Hanson & Stein 2014 Financial sector with shadow banks Plantin 2014; Kashyap, Tsomocos & Vardoulakis 2014 Adrian & Shin 2010, Pozsar 2014, Quantitative models Gertler, Kiyotaki, Prespitino 2015 35