Credit Booms, Financial Crises and Macroprudential Policy Mark Gertler, Nobuhiro Kiyotaki, Andrea Prestipino NYU, Princeton, Federal Reserve Board 1 March 219 1 The views expressed in this paper are those of the authors and do not necessarily reflect the views of the Federal Reserve Board or the Federal Reserve System
What We Do We develop a model of banking panics in which: 1. Banking crises are usually preceded by credit booms 2. Credit booms often do not result in crises, i.e. good booms We study macroprudential regulation in this model: How does optimal policy weigh the benefits of preventing a crisis against the costs of stopping a good boom? What are the features of optimal regulation? Countercyclical buffers
these variables). Spreads are normalized by dividing by the unconditional mean consistent with our normalization in the main text. All variables are demeaned at the country level. Banking We use crisis dates Crises from Schularick the Data and Taylor. (Krishnamurthy and Muir) Spread Path Credit Path -.2.2.4.6 Crisis 1 2 3 4 5-5 5 time -5 5 time GDP Path -8-6 -4-2 2-5 5 time
Credit Growth (" Mean) at t-1 Banking Crises in the Data (Schularick and Taylor) 1.5 No Crisis at t Crisis at time t Run Frequency after boom: 5.3 pct; After no boom: 2.5 pct. (Boom: top right quadrant) 1.5 -.5-1 -1.5-1.5-1 -.5.5 1 1.5 Credit Growth (" Mean) at t-2
Framework Starting point: GKP (218) Macro model of banking panics that disrupt real activity Nonlinearity: likelihood of panics depends on bank financial health Also captures credit booms preceding crises Buildup of credit generates vulnerability to run Optimistic beliefs lead to credit boom Belief dynamics consistent with survey evidence (Bordalo et al) Differences from GKP: Endowment economy (for simplicity) Recurrent booms that may or may not result in banking crises Study macroprudential regulation
Model Overview Two goods: consumption C t and capital K t K t fixed: K t = K = 1 ( Kt b ) ( ) intermediated by banks; K h t directly held by households : 1 = K h t + K b t Households direct finance entails a management cost α 2 Resource constraint : C t = Y t = Z t K t α ( ) 2 Kt h 2 where Z t is an exogenous productivity shock ( K h t ) 2
Marginal Rates of Return on Capital Q t price of capital Intermediated capital Directly held R b t+1 = Z t+1+q t+1 Q t R h t+1 = 1 1+α Kh t Qt R b t+1 i.e. increasing marginal cost of direct finance
Household and Bank Intermediation NO BANK RUN EQUILIBRIUM Q K b t t D t CAPITAL K N t! " #$ % h Q K t t HOUSEHOLDS CAPITAL K BANK RUN EQUILIBRIUM Q * t K HOUSEHOLDS
Households Structure Within each household, 1 f workers and f bankers Workers receive endowment Bankers manage financial intermediaries and pay dividends Perfect consumption insurance within the family Bankers have finite expected horizons With i.i.d. prob. 1 σ, a banker exits next period. expected horizon = 1 1 σ (Run leads to earlier exit) Replaced by new bankers who receive start-up transfer from the family
Household Optimization Choose {C t, D t, K h t } to maximize s.t. U t = E t i= β i [ ln Ct+i h ] C t + D t + Q t K h t + α 2 ( K h t ) 2 = (Zt + Q t )K h t 1 + R td t 1 + T t FONC : Λ t,t+1 β Ct C t+1 E t (Λ t,t+1 R t+1 ) = 1 (Deposits: D t ) Z t+1 + Q t+1 E t {Λ t,t+1 Q t + αkt h } = 1 (Capital: Kt h )
Bankers Bankers are part of the household and exit w.p. 1 σ Objective V t = E t Λ t,t+1 [(1 σ)n t+1 + σv t+1 ] Net worth n t+1 accumulated via retained earnings - no new equity issues n t+1 = R b t+1q t k b t R t+1 d t Balance sheet Q t k b t = d t + n t
Deposit Contract R t deposit rate; R t+1 return on deposits p t run probability; x t+1 < 1 recovery rate Deposit contract: (One period) { Rt with prob. 1 p R t+1 = t x t+1 R t with prob. p t where: x t+1 = min (( ) ) Q t+1 + Z t+1 k b t, 1 d t R t
Limits to Bank Arbitrage Moral Hazard Problem: After banker borrows funds at t, it may divert fraction θ of assets for personal use. If bank does not honor its debt, creditors can recover the residual funds and shut the bank down. Incentive constraint (IC) θq t k b t V t
Solution Can show V t = ψ t n t with ψ t 1 and: ψ t increasing in excess returns E t R b t+1 R t+1 ψt independent of n t Combine with IC endogenous capital requirement : κ t n t Q t k b t θ ψ t Note: ψ t countercyclical market capital requirements relaxed in bad times nt bank cannot operate (key for run equilbria)
Bank Runs A run is a rollover panic as in Cole and Kehoe (2) Self-fulfilling bank run equilibrium (i.e. rollover crisis) possible if: A depositor believes that if other households do not roll over their deposits, the depositor will lose money by rolling over. Condition met iff banks net worth nt goes to zero during a run n t = banks cannot operate
Conditions for Bank Run Equilibrium (BRE) Run equilibrium exists at t + 1 if recovery rate x t+1 < 1 ( Q t+1 + Z t+1 ) K b t < D t R t (1) where Qt+1 is the liquidation price: Q t = E t {Λ t,t+1 (Z t+1 + Q t+1 )} αk h t evaluated at K h t = 1 Run occurs if (i) equation (1) is satisfied and (ii) ι t+1 = 1 ιt+1 sunpot variable
Run probability p t and the role of leverage Assume sunspot occurs with probability κ. The time t probability of a run at t + 1 is p t = κ Pr t {Z t+1 < Z R t+1} Z R t+1 is the threshold value below which a run is possible Q t+1 ( ) Zt+1 R + Zt+1 R = D t R t Kt b Higher leverage ratios Dt R t K b t increase run probability
Calibration Parameter Description Value Target Model Calibrated Parameters θ Share of Divertible Assets.22 Leverage =1 φ = 9.9 σ Banker Survival Rate.935 Quarterly Spread=5 bps ER b R = 45 bps W New Banker Endowmnet 1 pct of SS Net Worth HH Share of Interm.=.5 K h =.49 α Marginal HH Intermediation Costs.6 Output Drop During Run=6 pct pct y during run =6 pct ι Sunspot Probability 1 pct Run Probability= 1 pct quarterly Run Prob=1.1 pct σ(ɛ Z ) Standard Dev. of Innovation to Z 1 pct Standard Dev. of Output= 1.9 pct σ(y ) = 1.7 pct Fixed Parameters β Impatience.99 - - ρ Z Serial Correlation of Z.95 - - W h HH Endowment 2 Z - -
Level Annual Basis Points Level (pct) Run After a Large Negative Shock Run after a sequence of bad shocks Sunspot No Sunspot Productivity 3 Run Probability Bank Net Worth -.2 -.4 -.6 -.8-1 -1.2 2.5 2 1.5 1.5-2 -4-6 -8-1.4 1 2 3 4 5 6 1 2 3 4 5 6-1 1 2 3 4 5 6 Bank Intermadiation Excess Return: ER b -R free (1 years) 25 Output -2 24 23-1 -2-4 22-3 -6 21-4 -8 2 19-5 -6-1 1 2 3 4 5 6 Quarters 18 1 2 3 4 5 6 Quarters -7 1 2 3 4 5 6 Quarters
Boom leading to the bust: news driven optimism Productivity: Z t+1 = ρz t + ɛ t+1 Occasionally, bankers receive news about future productivity If news at t, bankers learn that unusually large realization ɛ t B B > will happen at t B {t + 1,..., t + T } with prob. P B t < 1 of size Time t prob. of Z boom at t + i is P B t Pr t {t B = t + i} Pr t {t B = t} is a truncated Normal (discrete approx.) Agents update Pr t+i {s} and P B t+i by observing ɛ t+i
Level Beliefs Driven Credit Boom Calibration of News Prior cond. prob. of shock happening at time t.2 1 Beliefs Evolution 2 Expected VS Realized Productivity P B t Pr tft b = t + 1g Z t.15.8 1.5 E t Z t+4.6.1 1.4.5.2.5 t=1 t=1.5 Time t=21 t=1 t=1.5 Time t=21 t=1 t=1.5 t=21 1 Output 3 Bank Intermediation: S b.6 Probability of being in crisis zone 25.5.5 2.4 15.3 1.2 5.1 -.5 t=1 t=1.5 t=21 t=1 t=1.5 t=21 t=1 t=1.5 t=21
Level Annual Basis Points Level (pct) Boom Leading to a bust Survey Evidence on Credit Spreads Survey RunEvidence After on Credit GDP Boom Sunspot observed No Sunspot observed 2 Expected Productivity 2 Realized Productivity 8 Run Probability (if no boom) Z t 1 1 Z R t+1 6 4-1 -1-2 -2 2-3 1 2 3 4 5 6-3 1 2 3 4 5 6 1 2 3 4 5 6 4 Bank Intermediation Excess Return: ER b -R free (1 yrs) 26 2 Output 2 24-2 22-2 -4 2-4 -6-8 18-6 -1 1 2 3 4 5 6 Quarters 16 1 2 3 4 5 6 Quarters -8 1 2 3 4 5 6 Quarters
Level Annual Basis Points Level (pct) False Alarms False Alarms Boom Happens No Sunspot is Observed 2 Expected Productivity 2 Realized Productivity 6 Run Probability (if no boom) 1 1 Z t Z R t+1 5 4 3-1 -1 2-2 -2 1-3 1 2 3 4 5 6-3 1 2 3 4 5 6 1 2 3 4 5 6 3 Bank Intermediation Excess Return: ER b -R free (1 yrs) 2 1.4 Output 25 195 1.2 2 19 1 15 185.8.6 1 18.4 5 175.2 1 2 3 4 5 6 Quarters 17 1 2 3 4 5 6 Quarters 1 2 3 4 5 6 Quarters
Credit Growth (" Mean) at t-1-1.5-1.5-1 -.5.5 1 1.5 Credit Growth (" Mean) at t-2 Credit Growth (" Mean) at t-1-1.5-1.5-1 -.5.5 1 1.5 Credit Growth (" Mean) at t-2 Unpredictability of Crises: Data and Model No Crisis at t Run Frequency after boom: 5.3 pct; After no boom: 2.5 1.5 Crisis at time t Run Frequency after boom: 4 pct; After no boom: 2.4 1.5 1 1.5.5 -.5 -.5-1 -1
Regulation Macroprudential regulator sets time varying capital requirement κ t Equilibrium capital ratios are κ t = max { κ t, κ m t } where κ m t = θ ψ t are the market imposed capital ratios We restrict policy to be deteremined by simple rule κ t = { κ if Nt N if N t < N We look for ( κ, N ) that maximize welfare
Regulation Capital Ratio.1.5 Decentralized Equilibrium N DE SS Net Worth
Regulation.1.5 Decentralized Equilibrium Capital Requirement N N DE SS
Regulation.1.5 Decentralized Equilibrium Capital Requirement Regulated Equilibrium N N M P SS N DE SS
Level (pct) Avoiding a Run with Regulation Avoiding Runs with Macro Pru Regulated Unregulated 2 Expected Productivity 2 Realized Productivity 1 1 Z t 2 Capital Ratio: 5 Z R t+1 (Unregulated) -2-4 -1-1 -6-2 -2-8 -3 1 2 3 4 5 6-3 1 2 3 4 5 6-1 1 2 3 4 5 6 4 Bank Intermediation 8 Run Probability 2 Output 2 6-2 -4 4-2 -4-6 -8 2-6 -1 1 2 3 4 5 6 Quarters 1 2 3 4 5 6 Quarters -8 1 2 3 4 5 6 Quarters
Level (pct) Responding to False Alarms: No Sunspot Observed Response to News: Regulated VS Unregulated economy Regulated Unregulated 2 Expected Productivity 2 Realized Productivity 1 1 Z t 2 Capital Ratio: 5 Z R t+1 (Unregulated) -2-4 -1-1 -6-2 -2-8 -3 1 2 3 4 5 6-3 1 2 3 4 5 6-1 1 2 3 4 5 6 4 Bank Intermediation 8 Run Probability 2 Output 2 6-2 -4 4-2 -4-6 -8 2-6 -1 1 2 3 4 5 6 Quarters 1 2 3 4 5 6 Quarters -8 1 2 3 4 5 6 Quarters
Effect of Regulation Unregulated Economy = ; N = Optimal Regulation = :13; N = :85 N DE SS Fixed Capital Requirements = :13; N = Run Frequency :8 pct :45 pct :3 pct AVG Output Cond. No Run ( from Decentralized Economy) :4 pct 1:7 pct AVG Output ( from Decentralized Economy) :1 pct :9 pct Welfare Gain ( Permanent Consumption) :16 pct 1:16 pct
Recovery From a Run Recovery from a run: Forgiveness VS No Forgiveness Regulated Fixed Unregulated Regulated Countercyclical Asset Price Net Worth Output -1-2 -1-2 -4-3 -2-6 -4-3 -5-8 -6-4 -1-7 -5-8 -12-6 -9-14 1 2 3 4 5 6 Quarters -1 1 2 3 4 5 6 Quarters -7 1 2 3 4 5 6 Quarters
Conclusion Develop model of banking panics that captures boom-bust cycles and unpredictability of runs Study macroprudential policy Future work Ex-post intervention Equity injections
Calibration of News Go Back Parameter Description Value π n Prob of Receiving News.2 B Size of Productivity Boom 2 σ(ɛ Z ) T News Horizon 21 Quarters µ(t B ) Expected time of Z boom 1.5 Quarters ahead σ(t B ) Std Dev. of prior 2 Quarters P B Banker Prob. that Shock will happen.99 P TRUE True Prob. that Shock will happen.5
Forecast Errors for credit spreads from GKP (219) Go Back Financial Crisis: Forecast Error Forecast Errors: AAA-Treasury (4-Quarters Ahead) Bear Stearns Lehman Brothers Data (Bordalo-Gennaioli-Shleifer) Model 1 75 5 25-25 -5 Error (Next 4Q Average) = Actual - Forecast -75 24q3 27q3 28q4 213q4-1
Forecast Errors for GDP Go Back Forecast Errors 8 DATA: Consensus (Mean)* DATA 5-95 pctile MODEL 6 4 2-2 *Survey of Professional Forecasters, 1-year ahead GDP growth, forecast minus realized -4 24 25 26 27 28 29 21