Overborrowing, Financial Crises and Macro-prudential Policy. Macro Financial Modelling Meeting, Chicago May 2-3, 2013

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2 Overborrowing, Financial Crises and Macro-prudential Policy Javier Bianchi University of Wisconsin & NBER Enrique G. Mendoza Universtiy of Pennsylvania & NBER Macro Financial Modelling Meeting, Chicago May 2-3, 2013

3 Financial Crises and Macro-Prudential Policies Evidence credit booms typically precede financial crises Wide consensus on the need to use Macro-Prudential Policy: Prevent overborrowing ex ante to make economy less vulnerable to crises ex post...but yet quantitative models helpful for the optimal design of macro-prudential policy are scarce Need models that can generate financial crises and evaluate the role for policy

4 Financial Crises and Macro-Prudential Policies Evidence credit booms typically precede financial crises Wide consensus on the need to use Macro-Prudential Policy: Prevent overborrowing ex ante to make economy less vulnerable to crises ex post...but yet quantitative models helpful for the optimal design of macro-prudential policy are scarce Need models that can generate financial crises and evaluate the role for policy

5 Financial Crises and Macro-Prudential Policies Evidence credit booms typically precede financial crises Wide consensus on the need to use Macro-Prudential Policy: Prevent overborrowing ex ante to make economy less vulnerable to crises ex post...but yet quantitative models helpful for the optimal design of macro-prudential policy are scarce Need models that can generate financial crises and evaluate the role for policy

6 Financial Crises and Macro-Prudential Policies Evidence credit booms typically precede financial crises Wide consensus on the need to use Macro-Prudential Policy: Prevent overborrowing ex ante to make economy less vulnerable to crises ex post...but yet quantitative models helpful for the optimal design of macro-prudential policy are scarce Need models that can generate financial crises and evaluate the role for policy

7 Key Questions: 1 How does Macro-Prudential Policy affect: The incidence and the severity of financial crises, The behavior of asset prices (excess returns, volatility), Welfare? 2 What are the features of macro-prudential instruments: How should these policies be implemented along the business cycle Their magnitudes Time consistency?

8 Key Questions: 1 How does Macro-Prudential Policy affect: The incidence and the severity of financial crises, The behavior of asset prices (excess returns, volatility), Welfare? 2 What are the features of macro-prudential instruments: How should these policies be implemented along the business cycle Their magnitudes Time consistency?

9 Contribution Answer these questions using an equilibrium model of business cycles and asset prices with a collateral constraint: Binding constraint triggers Fisherian deflation and deep recessions fire sale externality (e.g. Lorenzoni, 2007) Characterize constrained efficient allocations under commitment and discretion Quantitatively, evaluate outcomes of decentralized equilibrium and time consistent solution Examine simple tax schemes & conditional efficient outcomes

10 Contribution Answer these questions using an equilibrium model of business cycles and asset prices with a collateral constraint: Binding constraint triggers Fisherian deflation and deep recessions fire sale externality (e.g. Lorenzoni, 2007) Characterize constrained efficient allocations under commitment and discretion Quantitatively, evaluate outcomes of decentralized equilibrium and time consistent solution Examine simple tax schemes & conditional efficient outcomes

11 Contribution Answer these questions using an equilibrium model of business cycles and asset prices with a collateral constraint: Binding constraint triggers Fisherian deflation and deep recessions fire sale externality (e.g. Lorenzoni, 2007) Characterize constrained efficient allocations under commitment and discretion Quantitatively, evaluate outcomes of decentralized equilibrium and time consistent solution Examine simple tax schemes & conditional efficient outcomes

12 Contribution Answer these questions using an equilibrium model of business cycles and asset prices with a collateral constraint: Binding constraint triggers Fisherian deflation and deep recessions fire sale externality (e.g. Lorenzoni, 2007) Characterize constrained efficient allocations under commitment and discretion Quantitatively, evaluate outcomes of decentralized equilibrium and time consistent solution Examine simple tax schemes & conditional efficient outcomes

13 Contribution Answer these questions using an equilibrium model of business cycles and asset prices with a collateral constraint: Binding constraint triggers Fisherian deflation and deep recessions fire sale externality (e.g. Lorenzoni, 2007) Characterize constrained efficient allocations under commitment and discretion Quantitatively, evaluate outcomes of decentralized equilibrium and time consistent solution Examine simple tax schemes & conditional efficient outcomes

14 Main Findings Planner can achieve significant reduction in financial fragility: Probability of financial crises decreases by a factor of 3 Asset prices fall 17 ppts less (7% v. 24%) Overall cyclical variability is also lower Mean excess return and Sharpe ratio decrease by factors of 6 and 10 Planner s allocations implementable with state-contingent taxes on debt ( 1% on average and positively corr. with leverage). Simpler tax schemes also deliver significant gains

15 Main Findings Planner can achieve significant reduction in financial fragility: Probability of financial crises decreases by a factor of 3 Asset prices fall 17 ppts less (7% v. 24%) Overall cyclical variability is also lower Mean excess return and Sharpe ratio decrease by factors of 6 and 10 Planner s allocations implementable with state-contingent taxes on debt ( 1% on average and positively corr. with leverage). Simpler tax schemes also deliver significant gains

16 Related Literature Overborrowing Externalities and Macroprudential Policy: Caballero and Krishnamurthy (2001), Lorenzoni (2008), Bianchi (2011), Jeanne and Korinek (2011), Benigno et al. (2010), Stein (2012), Kashyap et al. (2012), Gertler, Kiyotaki and Queralto (2012)... Quantitative Models of Macro-Financial Linkages: Financial Accelerator Models: Bernanke-Gertler-Gilchrist (1999); Kiyotaki-Moore (1997); Jermann and Quadrini (2012); Gertler and Kiyotaki (2010)... Non-Linear (systemic risk) models: Mendoza (2010), Bianchi (2012), He-Krishnamurthy (2012), Brunnermeier-Sannikov (2011)

17 Plan of the Talk 1 Analytics of fire-sale externality 2 Quantitative implications 3 Concluding Remarks

18 Decentralized Competitive Equilibrium Households solve: max {c t,k t+1,b t+1 } t 0 E t β t u(c t ) t=0 s.t. c t + q t k t+1 + b t+1 R b t+1 R z t follows a Markov process, κ < 1 = k t (q t + z t ) + b t κq t Non-state contingent bonds only Capital is unit fixed supply K = 1 Interest rate is exogenous. We look at equilibrium, where households are generally borrowers and constraint binds occasionally

19 Excess Returns E t [R k t+1] R = µ t(1 κ) Cov t (βu (c t+1 ), R k t+1 R) βe t u (c t+1 )

20 Excess Returns A tightening of the constraint leads to increase in excess returns E t [R k t+1] R = µ t(1 κ) Cov t (βu (c t+1 ), R k t+1 R) βe t u (c t+1 ) causing asset prices to fall z t+j+1 q t = E t j j=0 E t+i Rt+1+i k i=0 tightening the constraint and feeding back to asset prices Ex-ante, leverage magnifies Fisherian deflation systemic risk externality

21 Excess Returns A tightening of the constraint leads to increase in excess returns E t [R k t+1] R = µ t(1 κ) Cov t (βu (c t+1 ), R k t+1 R) βe t u (c t+1 ) causing asset prices to fall z t+j+1 q t = E t j j=0 E t+i Rt+1+i k i=0 tightening the constraint and feeding back to asset prices Ex-ante, leverage magnifies Fisherian deflation systemic risk externality

22 Excess Returns A tightening of the constraint leads to increase in excess returns E t [R k t+1] R = µ t(1 κ) Cov t (βu (c t+1 ), R k t+1 R) βe t u (c t+1 ) causing asset prices to fall z t+j+1 q t = E t j j=0 E t+i Rt+1+i k i=0 tightening the constraint and feeding back to asset prices Ex-ante, leverage magnifies Fisherian deflation systemic risk externality

23 Excess Returns A tightening of the constraint leads to increase in excess returns E t [R k t+1] R = µ t(1 κ) Cov t (βu (c t+1 ), R k t+1 R) βe t u (c t+1 ) causing asset prices to fall z t+j+1 q t = E t j j=0 E t+i Rt+1+i k i=0 tightening the constraint and feeding back to asset prices Ex-ante, leverage magnifies Fisherian deflation systemic risk externality

24 Normative Analysis Planner chooses borrowing and transfers proceeds of credit market operations Land market remains competitive Commitment versus Discretion Equivalent approach: Ramsey planner choosing debt taxes

25 Normative Analysis Planner chooses borrowing and transfers proceeds of credit market operations Land market remains competitive Commitment versus Discretion Equivalent approach: Ramsey planner choosing debt taxes

26 Private Choices in Constrained Efficient Equil. Taking planner s policies {b t+1, T t } t 0 and asset prices as given, households solve: max E 0 {c t,k t+1 } t 0 t=0 β t u(c t ) s.t. c t + q t k t+1 = k t (q t + z t ) + T t First order condition and key implementability condition: q t u (c t ) = βe t [ u (c t+1 ) (z t+1 + q t+1 ) ]

27 Commitment Case Planner solves: max {c t,q t,b t+1 } E 0 β t u(c t ) t=0 s.t. c t + b t+1 R t = z t + b t b t+1 R t κq t q t u (c t ) = βe t u (c t+1 )(z t+1 + q t+1 )

28 Commitment Case Planner solves: max {c t,q t,b t+1 } E 0 β t u(c t ) t=0 s.t. c t + b t+1 R t = z t + b t (λ t ) b t+1 R t κq t (µ t ) q t u (c t ) = βe t u (c t+1 )(z t+1 + q t+1 ) (ξ t )

29 Optimality Conditions b t+1 :: λ t = βr t E t λ t+1 + µ t t 0 c t : λ t = u (c t ) ξ t q t u (c t ) + u (c t )ξ t 1 (q t + z t ) t > 0 q t :: ξ t = ξ t 1 + µ tκ u (c t ) t > 0

30 Optimality Conditions b t+1 :: λ t = βr t E t λ t+1 + µ t t 0 c t : λ t = u (c t ) ξ t q t u (c t ) + u (c t )ξ t 1 (q t + z t ) t > 0 q t :: ξ t = ξ t 1 + µ tκ u (c t ) t > 0 Current consumption raises current asset prices

31 Optimality Conditions b t+1 :: λ t = βr t E t λ t+1 + µ t t 0 c t : λ t = u (c t ) ξ t q t u (c t ) +u (c t )ξ t 1 (q t + z t ) t > 0 q t :: ξ t = ξ t 1 + µ tκ u (c t ) But current consumption also lowers previous asset prices Solution is time inconsistent t > 0

32 Optimality Conditions b t+1 :: λ t = βr t E t λ t+1 + µ t t 0 c t : λ t = u (c t ) ξ t q t u (c t ) +u (c t )ξ t 1 (q t + z t ) t > 0 q t :: ξ t = ξ t 1 + µ tκ u (c t ) But current consumption also lowers previous asset prices Solution is time inconsistent t > 0

33 Euler Equation for Bonds Decentralized Equilibrium (µ t = 0) u (c t ) = βre t u (c t+1 ) 1 ξ t 1 = 0, µ t = 0 ( u (c t ) = βre t u (c t+1 ) µ ) t+1κ u (c t+1 ) q t+1u (c t+1 )

34 Euler Equation for Bonds Decentralized Equilibrium (µ t = 0) u (c t ) = βre t u (c t+1 ) 1 ξ t 1 = 0, µ t = 0 ( u (c t ) = βre t u (c t+1 ) µ ) t+1κ u (c t+1 ) q t+1u (c t+1 ) Positive wedge between social and private marginal benefits from borrowing. Fire sale externality: Borrow less today to avoid sharp drop in asset price tomorrow

35 2 ξ t 1 > 0, µ t = 0 u (c t ) + ξ t 1 (z t u (c t ) E t u (c t+1 )z t+1 ) = ( βre t u (c t+1 ) µ ) t+1κ u (c t+1 ) q t+1u (c t+1 ) Theoretically ambiguous current wedge between private and social benefit from borrowing due to effects on previous constraints.

36 2 ξ t 1 > 0, µ t = 0 u (c t ) + ξ t 1 (z t u (c t ) E t u (c t+1 )z t+1 ) = ( βre t u (c t+1 ) µ ) t+1κ u (c t+1 ) q t+1u (c t+1 ) Theoretically ambiguous current wedge between private and social benefit from borrowing due to effects on previous constraints. Normally, a positive wedge if constraints are expected to bind.

37 Decentralized Equilibrium (µ t > 0) u (c t ) = βre t u (c t+1 ) + µ t 3 ξ t 1 = 0, µ t > 0 βre t ( u (c t+1 ) u (c t ) µ tκq t u (c t ) u (c t ) ) + µ t µ t+1κ u (c t+1 ) q t+1u (c t+1 ) + u (c t+1 )µ t z t+1 =

38 Decentralized Equilibrium (µ t > 0) u (c t ) = βre t u (c t+1 ) + µ t 3 ξ t 1 = 0, µ t > 0 βre t ( u (c t+1 ) u (c t ) µ tκq t u (c t ) u (c t ) ) + µ t µ t+1κ u (c t+1 ) q t+1u (c t+1 ) + u (c t+1 )µ t z t+1 = Time consistency problem: Promise lower consumption tomorrow to relax constraint today

39 Time Consistent Planner s Problem Taking as given future policies C, planner solves: subject to V (b, z) = max c,b,q u(c) + βev (b, z ) c + b R = b + z t (λ) b R κq (µ) q = βeu (C(b, z )(Q(b, z ) + z ) u (c) (ξ) Foc

40 Euler Equation Comparison Under discretion: u (c) ξ t u ( (c t )q t = βre t u (c t+1 ) ξ t+1 u ) (c t+1 )Q t+1 + ( βe t u (c t+1 )C b (t + 1)(Q t+1 (t + 1)) + z t+1 ) + Q b (t + 1)u (c t+1 ) ) + µ t ξ t = κµ t u (c t )

41 Euler Equation Comparison Under discretion: u (c) ξ t u ( (c t )q t = βre t u (c t+1 ) ξ t+1 u ) (c t+1 )Q t+1 + ( βe t u (c t+1 )C b (t + 1)(Q t+1 (t + 1)) + z t+1 ) + Q b (t + 1)u (c t+1 ) ) + µ t ξ t = κµ t u (c t )

42 Under discretion: Euler Equation Comparison u (c) ξ t u (c t )q t = βre t ( u (c t+1 ) ξ t+1 u (c t+1 )Q t+1 ) + βe t ( u (c t+1 )C b (t + 1)(Q t+1 (t + 1)) + z t+1 ) + Q b (t + 1)u (c t+1 ) ) + µ t Under commitment ξ t = κµ t u (c t ) u (c t ) ξ t q t u (c t ) + u (c t )ξ t 1 (q t + z t ) = βre t ( u (c t+1 ) ξ t+1 q t+1 u (c t+1 ) + u (c t+1 )ξ t (q t+1 + z t+1 ) ) + µ t ξ t = ξ t 1 + µ tκ u (c t )

43 Under discretion: Euler Equation Comparison u (c) ξ t u (c t )q t = βre t ( u (c t+1 ) ξ t+1 u (c t+1 )Q t+1 ) + βe t ( u (c t+1 )C b (t + 1)(Q t+1 (t + 1)) + z t+1 ) + Q b (t + 1)u (c t+1 ) ) + µ t Under commitment ξ t = κµ t u (c t ) u (c t ) ξ t q t u (c t ) + u (c t )ξ t 1 (q t + z t ) = βre t ( u (c t+1 ) ξ t+1 q t+1 u (c t+1 ) + u (c t+1 )ξ t (q t+1 + z t+1 ) ) + µ t ξ t = ξ t 1 + µ tκ u (c t )

44 Remarks on Scope for Policy Two sources of welfare improving policies: 1 Make future constraints less binding Borrow less today to reduce fire sales in the future 2 Make current constraints less binding: (a) Lower future consumption raises current asset prices Requires commitment (b) Higher consumption raises current asset prices Non-feasible Remark: Conditional Efficiency Time Consistent Solution CE solution

45 Remarks on Scope for Policy Two sources of welfare improving policies: 1 Make future constraints less binding Borrow less today to reduce fire sales in the future 2 Make current constraints less binding: (a) Lower future consumption raises current asset prices Requires commitment (b) Higher consumption raises current asset prices Non-feasible Remark: Conditional Efficiency Time Consistent Solution CE solution

46 Remarks on Scope for Policy Two sources of welfare improving policies: 1 Make future constraints less binding Borrow less today to reduce fire sales in the future 2 Make current constraints less binding: (a) Lower future consumption raises current asset prices Requires commitment (b) Higher consumption raises current asset prices Non-feasible Remark: Conditional Efficiency Time Consistent Solution CE solution

47 Quantitative Model Introduce firms, labor supply and working capital Capital has individual value as collateral Model calibrated to industrialized countries Target of long-run moments include a 3 percent crisis probability Focus on time consistent solution

48 Representative Firm-Household Problem Maximize: [ ] E 0 β t u(c t G(nt s )) t=0 subject to budget constraint q t k t+1 + c t + b t+1 R = q tk t + b t + w t n s t + [ε t F(k t, n d t ) w t n d t ] and collateral constraint b t+1 R + θw tn d t κq t k t+1

49 Law of Motion for Bonds Next Periodt Bond Holdings Decentralized Equilibrium / 49

50 Law of Motion for Bonds Next Periodt Bond Holdings Financial Regulator Decentralized Equilibrium / 49

51 Law of Motion for Bonds Next Periodt Bond Holdings Financial Regulator Decentralized Equilibrium / 49

52 Debt Dynamics: Decentralized Equilibrium Next Periodt Bond Holdings Decentralized Equilibrium 45 Degree Line A Current Bond Holdings 25 / 49

53 Debt Dynamics when Bad Shock hits Next Periodt Bond Holdings A A Current Bond Holdings 26 / 49

54 Small diff. in debt in normal times Next Periodt Bond Holdings A 0.38 B 0.39 A Current Bond Holdings 27 / 49

55 Leads to large differences in crises Next Periodt Bond Holdings A 0.38 B B 0.39 A Current Bond Holdings 28 / 49

56 erian deflation and internalizing its price dynamics, the planner chose to borrow agents in the decentralized equilibrium a period earlier. Distribution of Leverage (measured as b t+1+θw t h t x 10 4 q t k t ) 5 4 Decentralized Equilibrium Social Planner Probability Leverage b t+1+θw th t 29 / 49

57 Comparison of Financial Crises: Event Analysis Use decision rules to simulate DE and SP for 100,000 periods Define a crisis event: binding credit constraint and a fall in credit of credit of more than 1 SD Isolate five-year event windows centered in financial crisis periods Compute median shocks in t 2, t 1, t, t + 1, t + 2 and median initial debt level at t 2 Simulate DE and SP given initial debt level and sequence of shocks 30 / 49

58 5 Credit Consumption % 10 % t 2 t 1 t t+1 t+2 t 2 t 1 t t+1 t+2 Decentralized Equilbirium Social Planner Fixed Price 31 / 49

59 5 Asset Price 0 Output % % t 2 t 1 t t+1 t+2 7 t 2 t 1 t t+1 t+2 Decentralized Equilbirium Social Planner Fixed Price 32 / 49

60 0 Employment 3 Tax on Debt % 3 % t 2 t 1 t t+1 t+2 0 t 2 t 1 t t+1 t+2 Decentralized Equilbirium Social Planner Fixed Price 33 / 49

61 counted when the planner implements the constrained-efficient equilibrium in a competitive economy. Intuitively, the tax represents the additional premium that the social planner im- Fat poses so Tail as to equalize in Land the social benefits Returns of investing in bonds (ergodic and land. The unconditional CDFs of average of the tax is 1.07 percent, v when the constraint binds and 1.09 when it does not. 1 returns) 0.8 Decentralized Equilibrium Social Planner 0.6 Probability 0.4 Social Planner 0.2 Decentralized Equilibrium / 49

62 2 Excess Return 1.5 Decentralized Equilibrium Financial Regulator Current Bond Holdings 35 / 49

63 0.4 Sharpe Ratio 0.3 Decentralized Equilibrium Financial Regulator Current Bond Holdings 36 / 49

64 Welfare Analysis Welfare effects calculated as increase in permanent consumption that renders DE and SP in terms of utility: E 0 t=0 β t u(c DE t (1 + γ) G(n DE t )) = E 0 t=0 β t u(c SP t Two sources of welfare effects from the externality: Production efficiency is affected when constraint binds Larger drops in consumption when constraint binds 0.05 percentage points on average G(n SP t )) Higher in the run-up to a financial crisis (about 1.5 times higher) 37 / 49

65 Conclusions Fire-sale externalities increase magnitude and incidence of financial crises, mean excess returns, volatility of returns and Sharpe ratios State contingent taxes on debt can implement the constrained efficient allocations. Simple policies are also effective. MPP has to adapt to fin. innovation and differences in information/beliefs (Bianchi, Boz & Mendoza (2012)) Road ahead: value of commitment

66 Optimality Conditions b t+1 :: λ t = βr t E t λ t+1 + µ t t 0 c t : λ t = u (c t ) ξ t q t u (c t ) + u (c t )ξ t 1 (q t + z t ) t > 0 q t :: ξ t = ξ t 1 + µ tκ u (c t ) t > 0 commitment

67 Optimality Conditions b t+1 :: λ t = βr t E t λ t+1 + µ t t 0 c t : λ t = u (c t ) ξ t q t u (c t ) + u (c t )ξ t 1 (q t + z t ) t > 0 q t :: ξ t = ξ t 1 + µ tκ u (c t ) t > 0 ξ t is a positive non-decreasing sequence

68 Optimality Conditions b t+1 : λ t = βre t λ t+1 + βe t ( u (c t+1 )C b (t + 1)(Q t+1 (t + 1)) + z t+1 ) + Q b (t + 1)u (c t+1 ) ) + µ t c t : λ t = u (c t ) ξ t u (c t )q t q t : κµ t = ξ t u (c) discretion

69 Calibration Source / target Interest rate R 1 = U.S. data Risk aversion σ = 2 Standard DSGE value Share of labor α n = 0.64 U.S. data Labor disutility coefficient χ = 0.64 Normalization Frisch elasticity parameter ω = 1 Kimball and Shapiro (2008) Supply of land K = 1 Normalization Working capital coefficient θ = 0.14 Working Capital-GDP=9% Discount factor β = 0.96 Debt-GDP ratio= 38% Collateral coefficient κ = 0.36 Frequency of Crisis = 3% Share of land α K = 0.05 Housing-GDP ratio = 1.35 TFP process σ ε = 0.014, ρ ε = 0.53 Std. dev. and autoc. of U.S. GDP

70 Conditional Efficiency [ ] V (B, z) = max u(c) + βe z B,c zv (B, z ) c + B R = z + B B R Taking as given q(b, z) = q DE (B, z), κq(b, z) back