Efficient Bailouts? Javier Bianchi. Wisconsin & NYU

Efficient Bailouts? Javier Bianchi Wisconsin & NYU

Motivation Large interventions in credit markets during financial crises Fierce debate about desirability of bailouts Supporters: salvation from a deeper credit crunch Critics: sowing the seeds of future financial crises Frank-Dodd act attempts to end bailouts

Questions What are the implications of bailouts for the stability of the financial sector? Is it desirable to prohibit government bailouts? Quantitatively: What are the effects over risk-taking and the severity of crises? What is the optimal size of government intervention? What are the features of policies to prevent excessive risk taking?

What I do Propose a quantitative equilibrium model: Liquidity constraints generate occasional credit crunches This leads to precautionary behavior during normal times Inefficiency and Policy Response: Collective transfer to firms increase dividend payments and wages But households do not internalize these GE effects Ex-post: welfare improving bailouts Ex-ante: insurance and moral hazard effects Solve for optimal intervention

What I find Bailouts are ex-ante welfare improving Optimal bailout: 2% points of GDP on average and increasing in leverage Severity of recession falls by 4% with the optimal intervention Role for macro-prudential policy to correct private cost of borrowing Size of optimal bailout is reduced by half when bailout is not anticipated

Relationship to the Literature Credit crunches and credit policy in DSGE models: (Gertler-Karadi (JME, 211); Del Negro et al. (21); Gertler-Kiyotaki-Queralto (211)) They mostly focus on policy response to unanticipated credit crunches or log-linear dynamics. I analyze moral hazard effects. Moral hazard and incentive effects of bailouts: (Schneider-Tornell (RES, 24); Farhi-Tirole (AER, 212); Chari-Kehoe (21), Keister (21)) They study theoretically how bailouts increase risk-taking and moral hazard. I conduct a quantitative assessment. Externalities and macro-prudential regulation (Lorenzoni (RES, 28); Bianchi (AER, 211); Bianchi-Mendoza (21); Jeanne-Korinek (21)) They study prudential measures to address systemic risk. I study the role of bailouts and the implications for prudential regulation.

External Creditors Households Government Firms Households Households

Limited enforcement External Creditors Credit flows Households Government Firms Labor-Wages Equity payouts Households Households Agency Problems

Households Preferences: Budget constraint: E β t u(c t G(n t )) t= s t+1 p t + c t = w t n t + s t (d t + p t ) d t dividends, s t equity shares, p t price of shares FOC: w t = G (n t ) p t = E t m t+1 (d t+1 + p t+1 ) where m t+j β j u (c t+j G (n t+j ))/u (c t G (n t ))

Firms Continuum of firms with revenue given by F (z, k, h) = zk α h 1 α z t is an exogenous aggregate productivity shock Flow-of-funds constraint: b t + d t + k t+1 + φ(k t, k t+1 ) k t (1 δ) + F (z t, k t, h t ) w t h t + b t+1 R φ( ) capital adjustment costs b t non-state contingent one-period debt Remark: stock of shares is fixed and normalized to 1

Financial constraints Collateral constraint on debt financing: b t+1 κ t k t+1 Equity constraint: d t d Investment is constrained by internal and external funds: k t+1 k t (1 δ) + ψ(k t, k t+1 ) }{{} Investment = F (z t, k t, h t ) w t h }{{} t b t + b t+1 R d t }{{} profits new ext. funds FF data i t F (z t, k t, h t ) w t h t b t + κtk t+1 R d

Recursive Problem V (k, b, X) = max d,h,k,b { d + Em (X, X )V (k, b, X ) X } s.t. b + d + k + ψ(k, k ) (1 δ)k + F (z, k, h) w(x)h + b R b κk (µ) d d (η) X (K, B, κ, z)

Optimality conditions (Labor demand) F h (z t, k t, h t ) = w t (EE for bonds) 1 + η t = RE t m t+1 (1 + η t+1 ) + Rµ t (EE for capital) 1 + η t = E t m t+1 R k t+1(1 + η t+1 ) + κ t µ t R k t+1 1 δ + F k(z t+1, k t+1, h t+1 ) ψ 1,t+1 1 + ψ 2,t

Competitive Equilibrium Definition Given an interest rate R and stochastic processes for z t and κ t, a competitive equilibrium is defined by a set of prices {w t, p t } t, allocations {c t, k t+1, b t+1, d t, h t, n t, s t } t and a SDF {m t } t : 1 Households maximize utility 2 Firms optimize and discount dividends at β j u (t + j))/(u (t)) 3 All market clears: RCE Equity markets: s t = 1 Labor markets: h t = n t Resource constraint: b t + c t + k t+1 + ψ(k t, k t+1 ) = k t (1 δ) + F (z t, k t, n t ) + bt+1 R

Coordination Problem During a credit crunch, funds are more valuable inside firms Households do not internalize benefits of unilateral transfers to firms Free-rider problem inefficient level of investment Bailouts force households to transfer funds to firms solve free-rider problem and improve welfare ex-post Bailouts reduce perceived cost of borrowing Need for tax on debt ex-ante

Limited enforcement External Creditors Credit flows Households Government Firms Labor-Wages Equity payouts Households Households Agency Problems

Limited enforcement External Creditors Credit flows Households Bailout Government Firms Labor-Wages Lump-sum Tax Equity payouts Households Households Agency Problems

Normative Analysis 1 Set-up a constrained social planner s problem 2 Identify possible instruments that decentralize optimal allocations (debt-relief, equity injections, lump-sum transfers) 3 Quantitative analysis

Constrained Social Planner Problem Chooses investment, borrowing and dividends subject to liquidity constraints Choose transfers between firms and households subject to iceberg costs Lets labor markets, equity markets, and goods market clear competitively

Admissible Allocations (Resource Const.) b t + c t + k t+1 + ϕυ t = (1 δ)k t + F (z, k t, h t ) + b t+1 R (Equity Const.) (1 δ)k t +F (z t, k t, h t ) w t h t + b t+1 R +Υ t b t k t+1 d Υ t are transfers from households to firms, ϕ is iceberg cost of transfers (Collateral Constraint) b t+1 κ t k t+1 (Stock market clearing) p t = E t m t+1 (d t+1 + p t+1 ), s t = 1 (Labor Market clearing) w t = G (n t ) = F h (k t, h t )

Some characterization η t ϕu (t) with equality if Υ t > Remarks: If ϕ =, d d does not bind. If d =, the competitive equilibrium and the social planner s solution coincide planner s problem

Decentralization I: Debt relief, debt-tax Households finance bailout with lump-sum tax: s t+1 p t + c t w t n t + s t (d t + p t ) T t Firms receive debt relief: (1 γ t )b t + d t + i t F (z t, k t, h t ) w t n t + b t+1 R (1 τ t) + T f t Remark: Debt relief is executed only if equity constraint binds

Decentralization I: Debt relief, debt-tax Households finance bailout with lump-sum tax: s t+1 p t + c t w t n t + s t (d t + p t ) T t Firms receive debt relief and pay tax on debt: (1 γ t )b t + d t + i t F (z t, k t, h t ) w t n t + b t+1 R (1 τ t) + T f t Remark: Debt relief is executed only if equity constraint binds Remark: Tax on debt is set when debt releaf only if equity constraint is expected to bind policies

Decentralization II: Equity injections, debt-tax Government purchases equity and transfer them to households: s t+1 p t + c t w t n t + (s t + s g t )(d t + p t ) T t Firms s problem is: E t m t+j (d t+j e t b t ) j= s.t. b t + d t + i t F (z t, k t, h t ) w t n t + e t b t + b t+1 R (1 τ t) + T f t d t d, b t+1 κ t k t+1 where number of shares are re-normalized to one and equity injections are set to a fraction of debt

Decentralization III: Helicopter Drop Bailout implemented through lump sum transfers conditional on aggregate variables First-order conditions remain unaffected No tax on debt is required to implement planner s allocations Best case to prevent moral hazard as individual outcomes are independent of individual choices

Quantitative Analysis

Numerical Method Challenges Financial constraints impose significant non-linearities State variables are not confined to a small region Changes in consumption lead to large changes in firms s choices Approach: Iterates jointly on equilibrium policy functions on entire state space Allows for occasionally binding liquidity constraints Full-equilibrium dynamics

Functional Forms and Distribution Assumptions u(c G(n)) = ψ(k t, k t+1 ) = φ k 2 [ ] 1 σ c χ n1+ ω 1 1 1+ 1 ω, F (z, k, h) = zk α h 1 α 1 σ ( ) kt+1 k 2 t k t k t TFP shocks and financial shocks are independent processes: log(z t ) = ρ log(z t 1 ) + ɛ t, ɛ t N(, σ ɛ ) Financial shocks follow a two-state Markov chain with values given by { κ L, κ H} and transition matrix: P = P L,L 1 P L,L 1 P H,H P H,H

Calibration Parameters set independently Value Source/Target Interest rate R 1 =.2 Interest rate mid 2 Discount factor β =.97 Capital-output= 2.5 Share of capital α K =.33 Average Labor Share Depreciation rate δ =.1 Standard value Labor disutility coefficient χ =.67 Normalization Risk aversion σ = 1.5 Benchmark value Frisch elasticity parameter ω = 2. Benchmark value Efficiency cost ϕ = 1bps Benchmark value

Calibration Parameters set by simulation Value Target TFP shock Financial shock σ ɛ =.1 ρ =.24 κ L =.43 κ H =.54 P HH =.9 P LL =.1 SD of GDP=2. Autocorrelation of GDP=.45 Average leverage =45 percent Non-binding collateral constraint Probability of credit crunch=4 percent Duration of credit crunch=3 years Adjustment cost φ k = 2. SD of investment =9 percent Dividend threshold d =.5 Equalize prob. binding constraints Definition of credit crunch: Fall in credit of more than 2SD

How does a typical crisis look like in the decentralized equilibrium without intervention?

1 TFP Shock TFP κ t 2 t 1 t t+1 t+2 Multipliers 1 η µ.5.5 t 2 t 1 t t+1 t+2 Output 1 1 2 t 2 t 1 t t+1 t+2 1 2 3 4 t 2 t 1 t t+1 t+2 1.35 1.3 1.25 1.2 1 Investment Credit 1.15 t 2 t 1 t t+1 t+2 t 2 Employment.5 1 1.5 2 t 2 t 1 t t+1 t+2

Comparison with Data Model Data 28-29 Output 1.5% 2.6% Consumption 1.1% 1.2% Investment 27.% 22.6% Debt-repurchase/GDP 6.6% 8.1% Hours 1.% 6.7% Note: Data corresponds to US data 28-29. Model corresponds to average crisis in decentralized equilibrium. second moments

Ergodic Distribution of Bailouts.15.1.5.5 1 1.5 2 2.5 3 3.5 4 4.5 Percentage points of GDP

( Laws of motion for leverage Bt+1 K t+1 ), borrowing and capital as a function of current debt, for mean values of productivity and mean value of capital OBP denote optimal bailout policy NBP denote no bailout policy

.5 Leverage (κ H ).5 Leverage (κ L ).45.45.4.4.35 1.4 Next Period Debt (κ H ).35 1.4 Next Period Debt (κ L ) 1.2 1.2 1 1 3 3 2.75 2.5 2.75 2.5 NBP

.5 Leverage (κ H ).5 Leverage (κ L ).45.45.4.4.35 1.4 Next Period Debt (κ H ).35 1.4 Next Period Debt (κ L ) 1.2 1.2 1 1 3 3 2.75 2.75 2.5 NBP 2.5 BP

.5 Leverage (κ H ).5 Leverage (κ L ).45.45.4.4.35 1.4 Next Period Debt (κ H ).35 1.4 Next Period Debt (κ L ) 1.2 1.2 1 3 Next Period Capital (κ H ) 1 3 Next Period Capital (κ L ) 2.75 2.75 2.5 NBP 2.5 BP

.4 Investment (κ H ).4 Investment (κ L ).2.2.2.15.12.9.6.3 Dividends (κ H ) Consumption (κ H ).9.2.15.12.9.6.3 Dividends(κ L ) Consumption (κ L ).9.8.8 NBP

.4 Investment (κ H ).4 Investment (κ L ).2.2.2.15.12.9.6.3 Dividends (κ H ) Consumption (κ H ).9.2.15.12.9.6.3 Dividends(κ L ) Consumption (κ L ).9.8.8 NBP OBP

Ergodic Distribution Leverage.4 NBP.3.2.1.38.4.42.44.46.48.5.52.54.56.4 OBP.3.2.1.38.4.42.44.46.48.5.52.54.56

Non-linear impulse response What is the economy s response to a negative financial shock? Simulate economy for a long period of time for a sequence of TFP shocks equal to the average and positive financial shocks Hit the economy with a one-time negative financial shock Compare economy without intervention to economy with anticipated and unanticipated bailouts Role for macro-prudential policy

1.3 Credit 2.9 Capital 1.25 2.85 1.2 2.8.55 Financial Shock 1 TFP Shock.5.5.45.5 1 NBP

1.3 Credit 2.9 Capital 1.25 2.85 1.2 2.8.55 Financial Shock 1 TFP Shock.5.5.45.5 NBP 1 UBP

Credit 2.9 Capital 1.3 2.85 1.25 2.8 1.2.55 Financial Shock 1 TFP Shock.5.5.45.5 1 NBP OBP UBP

Leverage Investment.46 1.43 2 3 1 Output.5 Employment.5 1 1 2 1.5 NBP

Leverage Investment.46 1.43 2 3 1 Output.5 Employment.5 1 1 2 NBP 1.5 OBP

Leverage Investment.46 1.43 2 3 1 Output.5 Employment.5 1 1 2 1.5 NBP OBP UBP

1 Consumption.7 Dividends.65 1.6.55 2.5 3.45.7 Equity Constraint Multiplier.5 Collateral Constraint Multiplier.6.5.4.4.3.3.2.2.1.1 NBP

1 Consumption.7 Dividends.65 1.6.55 2.5 3.45.7 Equity Constraint Multiplier.7 Collateral Constraint Multiplier.6.6.5.5.4.4.3.3.2.2.1.1 NBP OBP

.3 Tax on Debt Percentage.2.1 Bailout Percentage points of GDP 2 1 OBP UBP

No Prudential Tax on Debt Leverage Investment.46 1 2.43 3 1 Output.5 Employment.5 1 1 2 NBP 1.5 BP (no debt tax)

Prudential Tax on Debt Leverage Investment.46 1 2.43 3 1 Output.5 Employment.5 1 1 2 NBP 1.5 OBP

Welfare Gains of Optimal Policy 1.4 1.2 Percentage points 1.8.6.4.2 1.4 1.3 1.2 1.1 Current debt 1.9 2.5 2.6 2.7 3 2.9 2.8 Current capital 3.1 3.2

Conclusions Substantial effects of bailouts on risk-taking and on recovery from recession Part of the increase in leverage is socially desirable (insurance effects) Best approach is to complement bailouts with prudential policy This offsets moral hazard effects Delivers time-consistent policy Moving forward: foundations for financial shocks and equity constraint, crowding-out effects of bailouts

Extra Slides

minus net proprietor s investment in noncorporate businesses. This captures the net payments to business owners (shareholders of corporations and noncorporate business owners). Debt is defined as Credit Market Instruments which include only liabilities that are directly related to credit markets transactions. Debt Financial Flows back repurchases are simply the reduction in outstanding debt (or increase if negative). Both variables are expressed as a fraction of business GDP. See the online appendix for a more detailed description. Figure 1. Financial flows in the nonfinancial business sector (corporate and noncorporate), 1952.I-21.II. See the online appendix for data sources. Source: Jermann and Quadrini (AER, 212) from Flow of Funds Two patterns are clearly visible in the figure, very strongly so for the second half of the sample period. First, equity payouts are negatively correlated with debt repurchases. This suggests that there is some substitutability between equity and debt financing. Second, while equity payouts tend to increase in booms, debt repurchases increase during

Equity Injections back e t b t = Υ t T t = Υ t (1 + ϕ) τ t = E t m t+1 (1 + η t+1 ) + µ t E t m t+1 (1 + η t+1 (1 e t+1 )) + µ t 1 T f t = b t+1τ t R

Debt Relief back γ t b t = Υ t T t = Υ t (1 + ϕ) τ t = E t m t+1 (1 + η t+1 ) + µ t E t m t+1 (1 + η t+1 )(1 γ t+1 ) + µ t 1 T f t = b t+1τ t R

Recursive Competitive Equilibrium { firms policies ˆd(k, b, X), ĥ(k, b, X), ˆk(k, b, X), ˆb(k, } b, X) and firm s value V (k, b, X) households s policies {ŝ(s, X), ˆn(s, X)} and SDF m(x, X ) prices for labor and stocks w(x), p(x) a law of motion of aggregate variables X = Γ(X) back i ii households solve their optimization problem firms s policies and firm value solve their Bellman equation iii markets clear in equity and labor market (ŝ(1, X) = 1), (ĥ(k, B, X) = ˆn(1, X)) iv the law of motion is Γ( ) is consistent with individual policy functions and stochastic processes for κ and z.

Binding Region 3.5 3 2.95 2.9 Capital 2.85 2.8 2.75 2.7 2.65 2.6 1 1.5 1.1 1.15 1.2 1.25 1.3 1.35 both constraint bind dividend constraint binddebt none binding not feasible

Planner s problem back max k t+1,b t+1,d t,c t,υ t,h t,p t E β t u(c t G(h t )) t= b t + c t + k t+1 + Υ t ϕ = (1 δ)k t + F (z t, k t, h t ) + b t+1 R d (1 δ)k t + F (z, k t, h t ) w t h t + b t+1 R + Υ t b t k t+1 b t+1 κk t+1 where h t, wt wt =G (h t ) = F L (z t, kt, h t ) p t u (t) = βe t u (t + 1)(d t + p t+1 ) Remark: similar results if planner internalizes wage effects

The nation must work together to strike the right balance between our need to promote the public trust and using taxpayer money prudently to strengthen the financial system...to get credit flowing to working families and businesses. Geithner, T. (29): My Plan for Bad Bank Assets,.Wall Street Journal, March 23

Table: Second Moments No Bailout Policy Optimal Bailout Policy Data Output 2.3 2.2 2.3 Consumption 2. 2.1 1.6 Employment 1.5 1.5.8 Investment 9.9 9.6 9. Note: Moments in the model correspond to the stochastic steady state. Moments in the data correspond to annual data from 195-21. back