Forbearance and Broken Credit Cycles

1. Forbearance and Broken Credit Cycles Tomohiro Ota Bank of England 15th December 2013 15th Macro Conference at the University of Tokyo • * The views expressed in this presentation are mine and not necessarily those of the Bank of England.

2. Forbearance and Broken Credit Cycle 1. Introduction Motivations: from crisis to post-crisis • Low Productivity (except for US) • Unusual fall in the level of productivity after the crisis • Property Price Puzzle (except for US etc) • Property price shows resilience after the crisis • Slow Deleverage (except for US) • Especially in less-performing sectors such as real-estate • Broken Credit Cycle • Especially in less-performing sectors such as real-estate

3. Forbearance and Broken Credit Cycle 1. Introduction Motivations: from crisis to post-crisis • Broken credit cycle in Japan • Correlation of land price and GDP (1st order difference) was 0.49 from 1956 till 1991, but -0.15 from 1991 till 2005. • Looks like the correlation recovers after 2005

4. Forbearance and Broken Credit Cycle 1. Introduction Motivations: Can forbearance be an answer? • Forbearance: • Banks do not liquidate less-performing borrowers by revising terms of the contracts • Also called: Zombie lending, evergreening loans • Why banks forbear • Liquidating bad borrowers need capital (or bankrupt) • Liquidation value could be higher in the future (gamble for resurrection) • Impacts to macroeconomy • Production capitals are wasted on the hand of ‘zombies’ • Forbearance hinders new lending (and new investments) • New entrants are especially penalised • But forbearance can also boost investment if the financial accelerator of the economy is high

5. Forbearance and Broken Credit Cycle 1. Introduction Literature • Forbearance (theory) • Kocherlakota and Shim (2007) • Caballero Hoshi and Kashyap (2008) • Philippon and Schnabl (2013) • Forbearance (empirical) • Peek and Rosengren (2005) • Saita et. al. (2003) • Relevant theories • Credit Cycles: • Kiyotaki and Moore (1997) • Krishnamurthy (2003) • Korineck and Jeanne (2011) • Optimal bubbles: • Martin and Ventura (2013)

6. Forbearance and Broken Credit Cycle 1. Introduction Overview • Introduction • Defining baseline model • Mechanism of leverage and de-leverage • Financial accelerator and “crisis” • Modelling forbearance • Impacts of forbearance • Banks’ incentive and coalition • Policy discussions • Welfare analysis (simplistic) • Implementing efficient outcome

7. Forbearance and Broken Credit Cycle 2. Benchmark model Assumptions • 3 sets of players: • Firms (atomless): better stochastic production technology at={aH, aL} • Banks (many, but finite): collect deposit to lend or invest directly • Dealers (atomless): with less profitable non-stochastic technology Banks Depositors Wealth ωt Collateral land Liquidate Seized collateral Loans Dt Firms Dealers Asset Market (qt) Buy /sell kft Buy /sell kbt

8. Forbearance and Broken Credit Cycle 2. Benchmark model Timeline Firms and banks sell land to outsiders at q2 They consume all the wealth and die Land price q0 is determined t = 3 t = 0 t = 1 t = 2 • Land (K) is supplied by outsiders • Firms receive endowment ω0 • Banks receive endowed ‘capital’ W0

9. Forbearance and Broken Credit Cycle 2. Benchmark model Firm’s problem • Budget constraint • Collateral constraint • Demand function • (constrained) • Harvest (at t+1): firms obtain at+1 kft • at+1 = {aH, aL} withprobπand1-π • Bankruptcy: Firms cannot harvest any with Probγ • Updating wealth ωt+1:

10. Forbearance and Broken Credit Cycle 2. Benchmark model Firms’ problem: one more assumption • Do firms realise all capital gains from their asset holding? • Firms realise a fraction ηof the capital gain • Firms’ demand function and financial accelerator

11. Forbearance and Broken Credit Cycle 2. Benchmark model Dealers’ problem • Dealers’ payoff function • Dealers’ demand function (downward sloping) • Market Clearing condition

12. Forbearance and Broken Credit Cycle 2. Benchmark model Banks’ problem • Banks determine loan size Dt and repayment Rt to maximise their next period payoff • Each bank lends to many firms • Banks make a take-it-or-leave-it offer to firms and take all excess profits • Borrowing firms’ default risks are perfectly correlated: • i.e. with probability γ, a bank receives no repayment

13. Forbearance and Broken Credit Cycle 2. Benchmark model Equilibrium (when η is low) Firms’ unconstrained demand fn Firms’ constrained demand fn qt dealers’ demand fn (horizontally inverted) (1 – h)Et[qt+1] ktf ktb K

14. Forbearance and Broken Credit Cycle 2. Benchmark model Equilibrium with negative macro shock (at+1 = aL) • When η is small: Unique equilibrium qt Negative macro shock (1 – h)Et[qt+1] ktf ktb K

15. Forbearance and Broken Credit Cycle 2. Benchmark model Equilibrium Price (output) Dynamism qt aH aH aL q0 E0[q1] aH aL E1[q2] aL t=0 t=1 t=2 t=3 Time Proposition: In the baseline model, the asset price qt follows a process with (nearly) zero drift.

16. Forbearance and Broken Credit Cycle 1. Introduction Overview • Introduction • Defining baseline model • Mechanism of leverage and de-leverage • Financial accelerator and “crisis” • Modelling forbearance • Impacts of forbearance • Banks’ incentive and coalition • Policy discussions • Welfare analysis (simplistic) • Implementing efficient outcome

17. Forbearance and Broken Credit Cycle 3. Forbearance model What happens to the ‘stricken’ banks under neg. shock • Asset price plunge creates loan loss of the banks • Banks with capital Wt below a regulatory threshold are penalised • Banks can ‘make up’ their capitals if they can contain the plunge • … but how?

18. Forbearance and Broken Credit Cycle 2. Benchmark model Forbearance: a basic structure failed firms Collateral Banks Depositors repayment Liquidate a fraction (1 – θ) of seized collateral Liquidate Seized collateral Survived firms Dealers Asset Market Buy /sell Buy /sell

19. Forbearance and Broken Credit Cycle 3. Forbearance model Forbearance: definitions • Renegotiation of terms and conditions of loan contracts • LTV covenant breach • Interest / debt service breach • Maturity extension • Payment holiday • Creating new loans to help borrowers service their debts • “snowballing loans” (Japan) • Foreclosing borrowers, but not liquidating collateral assets • Spanish banks till 2011

20. Forbearance and Broken Credit Cycle 3. Forbearance Forbearance: assumptions • Bad borrowers (fraction γ)’ productivity is fixed at zero throughout the periods • Ie they do not recover, nor deteriorate further • The value of bad borrowers is measured by the value of their collateral (ie banks have to write off all negative equities) • Banks can forbear only at t=1, and have to unwind at t=2 • Banks have a chance to collude (not to liquidate bad borrowers)

21. Forbearance and Broken Credit Cycle 3. Forbearance model Forbearance: impact on price and investment • bad borrowers stay at their land without producing any • … and squeeze total available production capital • Asset price should be pushed up in any equilibrium q1 q1s.t. W1=W K k1f k1b θγk0f

22. Forbearance and Broken Credit Cycle 3. Forbearance model Equilibrium Price Dynamism qt aH aH aL E0[q1] q0 aL aL Time t=0 t=1 t=2 t=3 Pre-crisis crisis Post-crisis

23. Forbearance and Broken Credit Cycle 3. Forbearance model Equilibrium Investment Dynamism (when η is low) kft aH aH aL E0[kf1] kf0 aL aH Time t=0 t=1 t=2 t=3

24. Forbearance and Broken Credit Cycle 3. Forbearance model Forbearance: impact on k1f • Firms’ demand function: • Higher land price lowers firms’ purchasing power directly • But the collateral value of land does not increase as the unwinding of forbearance is expected • i.e. the ‘haircut’ of collateral land increases by forbearance • Higher land price increases firms’ wealth • Total supply of land decreases to K – θγkf0 . • θγkf0 is left unused

25. Forbearance and Broken Credit Cycle 3. Forbearance model Forbearance (when η is high) • Forbearance could increase or decrease firms’ land holding k1f • Depend on parameters, particularly higher η • Difficult to solve analytically – numerical exercise needed • Increase of k1f is not the sufficient condition of higher output qt ktf ktb K

26. Forbearance and Broken Credit Cycle 3. Forbearance model Forbearance: impact on k1f (new entrants) • Firms’ demand function: • Survived (incumbent) firms’ purchasing power is supported by the wealth effect to some extent • If we introduce new entrants with higher productivity possessing ω0 at t=1, their land holding decreases further than the incumbents

27. Forbearance and Broken Credit Cycle 3. Forbearance model Incentive of Forbearance • Authorities monitor banks’ W1 and force banks to close if W1 < 0 • Banks choose the fraction of zombie borrowers θ • Two symmetric equilibria: • θ*=0 • θ*such that W1=Wbar: minimum deviation by a bank triggers default q1 q1s.t. W1=W K k1f k1b θγk0f

28. Forbearance and Broken Credit Cycle 3. Forbearance model Discouraging forbearance • If W1 is increased by the government (capital injection), or the threshold Wbaris lowered, banks do not have to forbear • But if the injection is insufficient it could rather incentivise forbearance q1 q1s.t. W1=W K k1f k1b θγk0f

29. Forbearance and Broken Credit Cycle 4. Discussions Provisioning and capitalisation: Japan and Spain

30. Forbearance and Broken Credit Cycle 4. Discussions Policy implications • Externalities to healthy banks and healthy firms • Forbearance reduces new lending from healthy banks to healthy firms • Healthy banks’ capital accumulation would slow down • Explains the international productivity gap • The US: de-leveraging till 2010 • The UK: less de-leveraging in CRE sectors etc

31. Forbearance and Broken Credit Cycle 4. Discussions Directions for further works • Social planner’s optimal θ (regulatory forbearance) • Bank failure is currently costless in this model • Surviving banks replace loans without friction • Stricken banks do not internalise all negative effect on output • Another incentive of forbearance • Expected price recovery in the future can lead to forbearance • Externality creates a dynamic inconsistency • Endogenous interest rate

32. Forbearance and Broken Credit Cycle 4. Discussions Summary • Banks do forbearance to avoid liquidating collateral assets in the middle of the plunge of asset price (= realising a larger loan losses). • Higher asset price (than it should be) and expected price decline tightens healthy firms’ credit constraint (negative externality), which lowers the firms’ investments. • Healthy banks’ profit lowers as well, as they lose lending opportunities. • If financial accelerator effect is strong, higher asset price could boost firms’ investment. • Policy responses would be non-monotonic

33. Forbearance and Broken Credit Cycle 5. Appendix Appendix: revival of zombies? • During the “resolving NPL” stage from 2002 to 06, 10 tn Yen loans were downgraded and 10tn Yen were upgraded • Banks choose the fraction of zombie borrowers θ (collectively)

34. Forbearance and Broken Credit Cycle 2. Benchmark model Competitive equilibrium (at t > 0) • When η is larger: No equilibrium (crisis) qt HIDDEN CHARTS (1 – h)Et[qt+1] ktf ktb K

35. Forbearance and Broken Credit Cycle 1. Introduction Motivations: from crisis to post-crisis • Low Productivity (Hughes and Saleheen, 2012) • Unusual fall in the level of productivity after the crisis (except for US)

36. Forbearance and Broken Credit Cycle 1. Introduction Motivations: from crisis to post-crisis • Property Price Puzzle • Residential property price experienced 250% increase from 2000 till 2007, the price dropped by only 20% after the crisis +137% (‘00 – ’07) -10% (‘07 – ’12) +62% (‘00 – ’07) -19% (‘07 – ’12)

37. Forbearance and Broken Credit Cycle 1. Introduction Motivations: from crisis to post-crisis • Slow develerage (especially in less performing sectors) Japan UK

38. Forbearance and Broken Credit Cycle 1. Introduction Motivations: from crisis to post-crisis • Slow develerage (especially in less performing sectors) Spain US

39. Forbearance and Broken Credit Cycle 3. Forbearance model Forbearance: impact on price and investment • bad borrowers stay at their land without producing any • … and squeeze total available production capital • Asset price should be pushed up in any equilibrium q1 q1s.t. W1=W K k1f k1b θγk0f

40. Forbearance and Broken Credit Cycle 2. Benchmark model Static Equilibrium (when η is high) • When η is larger: Multiple equilibria • Demand curve becomes Z-shape • Focus only on the stable equilibrium qt (1 – h)Et[qt+1] ktf ktb K

41. Forbearance and Broken Credit Cycle 3. Forbearance model Is forbearance good or bad? • Forbearance is rational for ‘stricken’ banks • Forbearance lowers investment (and output) • Some production capital is wasted • Productive firms reduce investment • Healthy banks (and the stricken banks) reduce profit • Forbearance increases investment (and output) • If the economy is highly leveraged, the positive ‘wealth effect’ outweighs everything else