Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics Dean Corbae
Pablo D’Erasmo
University of Wisconsin - Madison and NBER Federal Reserve Bank of Philadelphia
June 25, 2017
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Questions
I
How does bankruptcy law affect the financial decisions of corporations and firm dynamics?
I
What are the positive and normative consequences of an American Bankruptcy Institute proposal (similar to AHM (1992)) which amounts to a “fresh start” for bankrupt firms?
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Current Bankruptcy Options I
Liquidation (Chapter 7) I
The proceeds of liquidating the corporation’s assets (k with fire-sale price s) are used to repay debt (b) after which the firm exits.
I
Limited liability for corporate shareholders max{sk − b − c7 , 0} where s < 1 is firesale value and c7 are bankruptcy costs.
I
Reorganization (Chapter 11) I
Bankruptcy law determines the negotiation rules over the fraction φ of debt that is repaid and cash flow to shareholders
I
After paying c11 bankruptcy costs, the reorganized corporation retains its assets and continues to operate.
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
What we do 1. Document capital structure facts for non-bankrupt vs Ch. 7 vs. Ch. 11 firms from Compustat. 2. Extend structural corporate finance models to include bankruptcy selection and endogenous entry/exit in a GE framework. 3. After estimating the parameters of the model to match item 1 facts, conduct policy counterfactual to assess variant of current American Bankruptcy Institute reform proposal (similar to Aghion, Hart, Moore (1992)). I
“fresh start” for bankrupt firms: after declaring bankruptcy, debt is canceled and creditors receive the rights to an all-equity firm
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Preview of Results I
Counterfactual yields sizable drop in borrowing costs leading to increased investment, a shift in the size distribution of firms, higher measured aggregate productivity and allocative efficiency.
I
Welfare gains from higher consumption.
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Preview of Results I
Counterfactual yields sizable drop in borrowing costs leading to increased investment, a shift in the size distribution of firms, higher measured aggregate productivity and allocative efficiency.
I
Welfare gains from higher consumption.
Intuition I
After the reform, absolute priority is enforced (lenders get full payment unless equity is wiped out)
I
Reduction in dead-weight losses associated with inefficient liquidation (most bankruptcies result in reorganization)
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Some Previous Literature I
Cooley and Quadrini (2001, AER), Hennessy and Whited (2007, JF) assume positive cash flows so Ch. 11 is a dominant strategy and there is no exit via Ch. 7. Further, creditor take-it-or-leave-it bargaining in renegotiation. More general bargaining problem in Eraslan (2008, IER).
I
Gomes (2001, AER) allows negative cash flows (due to fixed costs) so has endogenous exit via Ch. 7 but no Ch. 11 in an industry equilibrium. Khan, et. al. (2014) also consider a version of Ch. 7 in GE with aggregate shocks.
I
Broadie, et. al. (2007, JF) study Ch. 7 vs. Ch. 11 decision problem but with exogenous cash flows and initial bond finance of fixed investment.
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Compustat Data I
Annual observations from 1980-2014.
I
Medians (means) are time series averages of the cross-sectional median (mean) obtained for every year in our sample. Consistent with definitions in Duffie, et. al.:
I
I
I
Ch. 7 is value for final observation of a firm that exits via DLRSN code 03 (Liquidation) (nobs=315). Ch. 11 is value for initial period observation of a DLRSN code 02 (Bankruptcy) (nobs=1,319).
I
Non-bankrupt identifies annual observations (nobs=173,617) of firms that are not in the state of bankruptcy (i.e. firms which never declare bankruptcy as well as observations of firms before they declare bankruptcy excluding the above).
I
To be consistent with the way that the U.S. Census constructs exit statistics, a deleted firm is counted as a firm that exits if its deletion code is not 01 (e.g. M&A), 02 (Ch.11), 04 (Reverse A), 07&10 (other), 09 (private).
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Compustat Data Facts 1980-2014 Moment Frequency of Exit (%) Fraction of Exit by Ch 7 (%) Frequency of (all) Bankruptcy (%) Fraction of Chapter 11 Bankruptcy (%)
Capital (millions 1983$) Cash (millions 1983$) Assets (millions 1983$) Op. Income (EBITDA) / Assets (%) Net Debt / Assets (%) Total Debt / Assets (%) Frac. Firms with Negative Net Debt (%) Secured Debt / Total Debt (%) Interest Coverage (EBITDA/Interest) Equity Issuance / Assets (%) Fraction Firms Issuing Equity (%) Net Investment / Assets (%) Dividend / Assets (%) Z-score DD Prob. of Default (%)
Non-Bankrupt Avg. Median 917.05 33.21 119.18 9.06 1036.22 53.26 11.13 15.89 26.08 15.79 57.38 35.47 26.26 43.78 40.65 13.88 4.78 8.10 0.09 27.62 1.43 0.62 5.92 3.12 3.77 3.21 2.20 0.00
1.10 19.83 0.96 79.15 Chapter 11 Avg. 405.71∗,∗∗∗ 65.86∗,∗∗∗ 471.69∗ -12.67∗,∗∗∗ 58.05∗,∗∗∗ 79.51∗,∗∗∗ 17.49∗ 50.26∗ -1.76∗ 4.82∗ 35.22∗ -4.37∗,∗∗∗ 3.34∗,∗∗∗ -0.93∗,∗∗∗ 3.27∗,∗∗∗
Median 108.47 10.90 123.56 -2.05 36.50 53.87 49.66 -0.20 0.00 -4.73 1.32 0.43 0.72
Chapter Avg. 78.21∗∗ 11.55∗∗ 89.76∗∗ -16.16∗∗ 49.42∗∗ 77.46∗∗ 18.37∗∗ 48.85 -6.29∗∗ 5.21∗∗ 14.11∗∗ -4.29∗∗ 4.37 -1.05 ∗∗ 4.54∗∗
7 Median 21.33 2.75 27.04 -2.89 38.12 55.79 47.84 -0.31 0.00 -3.44 1.64 0.63 1.75
Test Mean Differences Distn
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Summary Data Facts I
Exit rates (fraction of deletions classified as exit to all firms in a given year) are small (1.10%).
I
20% of exits are by Chapter 7 liquidation.
I
Fraction of all firms declaring bankruptcy is also relatively small (0.96%).
I
79% of bankruptcies are by Chapter 11 (similar to BWZ who have data on recovery rates). I
I
Note: Statistics on all business filings from the U.S. Courts suggests a lower fraction of Ch. 11, roughly 25% in 2013.
Creditors in Chapter 11 recover considerably more than creditors in Chapter 7 BWZ
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Summary Data Facts (cont.) On average, Nonbankrupt firms: I
Are bigger than Ch 11 which are bigger than Ch 7.
I
Are profitable while bankrupt firms are not
I
Have lower leverage than bankrupt firms
I
Have lower interest expenses relative to their cash flow.
I
Have higher equity issuance
I
Have positive net investment as opposed to negative net investment for bankrupt firms.
I
Have higher dividend payouts than bankrupt firms.
I
In terms of statistical significance, there are many instances where there are differences between Chapter 11 versus Chapter 7 (despite small sample size).
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Environment Basics I
General equilibrium model with a representative household but a distribution of heterogeneous firms with idiosyncratic productivity shocks and fixed operating costs.
I
Firms finance investment with internal funds, debt or costly equity.
I
Firms can choose Ch.7 liquidation and exit or Ch. 11 renegotiation of debt burden via Nash Bargaining.
I
Competitive lenders price debt taking into account bankruptcy choices.
I
Entry and exit generates an endogenous firm size distribution.
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Environment - Technology I
I
Competitive firms produce a homogeneous good that can be consumed by households or can be used as capital. Firms have access to a decreasing returns to scale production technology α 1−α ν yjt = zjt kjt njt , α ∈ (0, 1), ν ∈ (0, 1)
(1)
where I
I I
zjt is an idiosyncratic productivity shock, i.i.d. across firms, drawn from Markov process G(zjt+1 |zjt ), njt is labor input, and kjt is capital input.
I
There is a fixed cost of production cf , measured in units of output.
I
Firms own their capital and choose investment igjt = kjt+1 − (1 − δ)kjt with quadratic adjustment costs.
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Environment - Financing and Entry I
Inputs can be financed by: 1. One period non-contingent debt bjt+1 at discounted price qjt which can depend on firm characteristics, 2. Current cash flow and savings, 3. External equity at cost λ(ejt ) depending on equity amount ejt raised.
I
Firms can enter by paying a fixed cost κ after which they draw an initial level of productivity zj0 from the stationary distribution G(z) derived from G(zjt+1 |zjt ).
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Environment - Cash Flow I
Firm j’s operating income (EBITDA) is given by πjt = yjt − wt njt − cf
(2)
where wt is the competitively determined real wage. I
Taxable income is Υjt = πjt − δkjt −
I
Corporate taxes are
1 qjt
bjt+1 − 1 (1+r)
c Tjt = 1{Υjt ≥0} τc · Υjt
(3)
where 1{·} is an indicator function (note tax benefits of debt).
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Environment - Firm Objective I
Firm j maximizes the expected discounted value of dividends E0
∞ X
(1 + r)−t djt
(4)
t=0 I
The after-tax net cash flow to equity holders is given by (1 − τd )ejt if ejt ≥ 0 djt = ejt − λ(ejt ) if ejt < 0
(5)
where c ejt = πjt − Tjt − ijt − bjt + qjt bjt+1 − Ψ(kjt+1 , kjt ).
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
(6)
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Environment - Bankruptcy I
Firms have 2 possible default options: 1. Chapter 7 liquidation: Firm j liquidates its assets at firesale discount s < 1 which it uses to pay debts subject to limited liability: I I I
Firm incurs a bankruptcy cost c7 and exits. Shareholders obtain (pre-tax): max{skjt − bjt − c7 , 0}. Lenders obtain: min{bjt , max{skjt − c7 , 0}}.
2. Chapter 11 reorganization: Firm j and lender renegotiate the defaulted debt: I I I I
I
I
Nash bargain over the repayment fraction φjt (firm weight θ), Firm pays bankruptcy cost c11 , debt reduced to φjt bjt (where φjt ∈ [0, 1]), net payouts to shareholders restricted to be non-positive, faces equity finance cost λ11 (ejt ), continues operating (i.e. does not exit).
A firm can choose to exit (without default) at any point in time.
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Environment - Households I
HHs choose a stream of consumption Ct , shares {Sjt+1 }j of incumbent and entrant firms, and risk free bonds Bt+1 to maximize the expected present discounted value of utility given by "∞ # X t max E0 β U (Ct ) (7) t=0
subject to Z Ct +
pjt Sjt+1 dj + qtB Bt+1 = (1 − τi )wt Z + (pjt + djt ) Sjt dj + Bt + Tth
(8)
where pjt is the after dividend stock price of firm j, qtB is the after-tax price of the risk free bond, and Tth are lump sum taxes/transfers for households. Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Timing 1. Productivity zjt is realized. 2. Bankruptcy decision for incumbent firms. I
I
If the firm chooses to repay debt (to avoid bankruptcy costs), it chooses whether or not to exit. If the firm chooses to default, it chooses whether to exit by Ch. 7 (incurring c7 and s) or not by Ch. 11 (incurring c11 , λ11 , and θ)).
3. Potential entrants decide whether to start a firm or not. 4. Households choose shares and bonds, which given earnings and taxes determines their consumption.
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Recursive Representation of the Firm Problem The value of the firm V (z, k, b) is defined as follows: I
It can choose to declare bankruptcy (∆ = 1) or not (∆ = 0): V (z, k, b) = max V∆ (z, k, b)
(9)
∆∈{0,1}
I
Conditional on the bankruptcy choice it must decide whether to exit (x = 1) or not (x = 0): V∆ (z, k, b) = max V∆x (z, k, b)
(10)
x∈{0,1}
I
Conditional on ∆ = 1, the exit decision determines chapter choice: I I
Exit (i.e. (∆ = 1, x = 1)) implies a Ch 7 liquidation Continue (i.e. (∆ = 1, x = 0)) implies a Ch 11 reorganization.
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Firm Problem if no default I
No exit: V00 (z, k, b) =
max 0
n≥0,k
≥0,b0
n o d + (1 + r)−1 Ez0 |z [V (z 0 , k 0 , b0 )]
(11)
s.t. e = π − T c (k, z, k 0 , b0 ) − ig − Ψ(k 0 , k) − b + q(b0 , k 0 , z)b0 (1 − τ d )e if e ≥ 0 d= e − λ(e) if e < 0 I
Exit: V01 (z, k, b) =
(1 − τd )(sx k − b) if sx k ≥ b . (k − b) − λ(sx k − b) if sx k < b
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
(12)
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Firm Problem if defaults I
No exit (Ch 11 reorganization):
V10 (z, k, b) =
max 0
{n,k }≥0,d≤0,b
n o −1 0 0 0 0 d + (1 + r) E [V (z , k , b )] z |z 0
(13)
s.t. e = π − T c (k, z, k 0 , b0 ) − 1{ig ≥0} ig − 1{ig <0} s11 ig − Ψ(k 0 , k) −φ(z, k, b)b + q(k 0 , b0 , z)λb11 b0 − c11 d = e − λ11 (e)
I
Exit (Ch 7 liquidation): V11 (z, k, b) = (1 − τd ) max{s7 k − b − c7 , 0}.
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
(14) Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Firm Entry
I
The value of creating a new firm is o n X 0 −1 0 0 ) VE = max d + (1 + r) V (z , k , 0)G(z E 0 0 k ≥0,b
(15)
z0
where 0 0 0 0 dE = −kE + q(kE , b0E )b0E − κ − λE (−kE + q(kE , b0E )b0E − κ). (16)
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Lenders’ Profits Ω(b0 , k 0 , z)
=
−q(b0 , k 0 , z)b0 + q B [1 − Λ(b0 , k 0 , z)]b0 (17) X 0 B 0 0 +q min b , max{s7 k − c7 , 0}}G(z |z) z 0 ∈D7 (k0 ,b0 )
+q B
X
φ(k 0 , b0 , z 0 )b0 G(z 0 |z).
z 0 ∈D11 (k0 ,b0 )
where the expected default probability is given by: X Λ(b0 , k 0 , z) =
G(z 0 |z),
(18)
z 0 ∈{D7 (k0 ,b0 )}∪{z 0 ∈D11 (k0 ,b0 )}
with default intervals: D7 (k, b) D11 (k, b)
z ∈ Z : ∆(z, k, b) = 1 & x(z, k, b) = 1 , = z ∈ Z : ∆(z, k, b) = 1 & x(z, k, b) = 0 .
=
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Reorganization I
Upon reorganization, the value of defaulted debt is reduced to a fraction ϕ of the unpaid debt b.
I
The value of an agreement of size ϕ to the firm is n o −1 0 0 0 0 |z [V (k , b , z )] V R (z, k, b; ϕ) = max d + (1 + r) E z 0 0 n,b ,k ,d≤0
s.t. e = π − T c (k, z, k 0 , b0 ) − 1{ig ≥0} ig − 1{ig <0} s11 ig − Ψ(k 0 , k) −ϕb + q(k 0 , b0 , z)λb11 b0 − c11 d = e − λ11 (e)
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Reorganization: Nash Bargaining Solution The recovery rate is the solution to the following Nash Bargaining problem: φ(z, k, b) ≡ arg max [W R (z, k, b; ϕ)]θ [W L (z, k, b; ϕ)]1−θ
(19)
ϕ∈[0,1]
s.t. W R (z, k, b; ϕ) ≥ 0, W L (z, k, b; ϕ) ≥ 0. where I The surplus for the firm reflects a threat point of Ch.7 given by W R (z, k, b; ϕ) = V R (z, k, b; ϕ)−(1−τd ) max{s7 k −b−c7 , 0}. (20) I
The surplus for the lender is given by W L (z, k, b; ϕ) = ϕb − min b, max{s7 k − c7 , 0}}.
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
(21)
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Definition of Steady State Equilibrium ∗ V ∗ , w∗ , r∗ , q B∗ , q ∗ , φ∗ , p∗ , D7∗ , D11 , Λ∗ , Γ∗ , M ∗ , C ∗ , B 0∗ , S 0∗ , T ∗ such that:
1. Given w, r, q, φ, firm’s optimize yielding V ∗ . 2. Given V, w, r, q, the recovery rate φ∗ (k, b, z) solves the bargaining problem. 3. The prob. of default Λ∗ is consistent with firm decision rules. 4. Loan prices q ∗ are such that lenders expect to earn zero profits. 5. Entry condition VE∗ ≤ 0 is satisfied with = when M > 0. 6. Γ∗ (z, k, b) and M ∗ is a fixed pt. of the LOM of firm distribution. 7. Given (w, q B , p) and taxes/tansfers T h , households optimize. 8. Goods, Labor, Bond and Stock markets clear at w∗ , q B∗ , p∗ . 9. Taxes/Transfers satisfy the government budget constraint. Household Problem
Cross-Sectional Distribution
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Taxes
Market Clearing
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Model Parameters Our model has 21 parameters, 11 of which we estimate within the model. Parameter Risk Free Rate Dep. rate Cap. share Ret. to scale Corporate Tax Dividend Tax Income Tax Autocorr. z Std. Dev. Price k liq. Price k reorg.
q˜B δ α ν τc τd τi ρz σ s7 s1 1
Value 1.02−1 0.150 0.330 0.850 0.300 0.120 0.250 0.657 0.199 0.400 0.869
Parameter Fixed Cost Ch. 7 cost Ch. 11 cost Firm’s Barg. Power Equity Cost Equity Cost Borrowing Cost Adj. Cost Price k exit Entry cost
cf c7 c11 θ λ1 λ11 1 λ11 b ψ sx κ
Value 0.051 0.001 0.160 0.968 0.010 0.440 0.880 0.297 0.724 0.174
log(z 0 ) = ρ log(z) + , ∼ N (0, σ )
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Baseline Moments
Parameterization
Model Definitions
Moment (%) Exit Rate Frequency of all Bankruptcy Fraction of bankruptcy Reorganization Recovery rate by Liquidation Recovery rate Reorganization Equity issuance Non-Bankrupt Equity issuance Reorganization Debt to Assets Non-bankrupt Debt to Assets Reorganization Net Investment/Assets Non-Bankrupt Net Investment/Assets Reorganization
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Positive Results
Normative Results
Other Moments
Data 1.10 0.96 79.15 5.80 49.09 0.06 0.01 28.31 41.99 1.16 -2.94
Conclusion
Algorithm
Model 1.19 0.88 72.61 4.23 57.91 0.00 0.01 28.97 43.15 0.89 -6.22
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Decision Rules - Default (∆) and Exit (x) Firms with I
High Productivity I I I
I
Low debt/capital, continue (∆ = 0, x = 0) High debt/capital, Ch. 11 (∆ = 1, x = 0) None choose exit (either Ch. 7 (∆ = 1, x = 1) or (∆ = 0, x = 1))
Low Productivity I I I I
Cash (b < 0 and low capital, continue (∆ = 0, x = 0) Low debt/capital, exit (∆ = 0, x = 1) Medium debt/capital, Ch. 11 (∆ = 1, x = 0) High debt/capital, Ch. 7 (∆ = 1, x = 1)
Figures
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Debt Price Menus
I
For a given level of capital (collateral), lenders recover less the higher is debt
I
For a given level of debt/capital, the higher the productivity the more lenders recover
I
Thus, firms with high debt to assets face higher interest rates and more productive firms face lower interest rates
Figures
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
NonBankrupt/Non-exiting Debt Dynamics and Dividend/Equity Policy Firms with Median to High productivity I
and low debt/capital ratio, accumulate debt to finance positive net investment (collateral serves to lower interest rates) and issue dividends (e > 0).
I
and high debt/capital, lower debt holdings (some median issue equity (e < 0))
Firms with low productivity (the few with negative net debt who don’t exit or declare bankruptcy) I
Reduce cash holdings and continue to pay dividends
0 Figure b
Figure Div/Equity
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Cross-Sectional Distribution of Firms Panel (i): Dist. of capital (cond. on z)
Fraction of Firms
1
zL
0.8
zM zH
0.6 0.4 0.2 0 0
0.5
1
1.5
2
2.5
3
3.5
4
Capital (k) Panel (ii): Dist. of debt (cond. on z) 1
Fraction of Firms
zL
0.8
zM zH
0.6 0.4 0.2 0 -0.5
0
0.5
1
1.5
2
2.5
Debt (b)
Mass of high (low) productivity firms on high (low) capital and debt. Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
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Parameterization
Positive Results
Normative Results
Conclusion
Test: Reorganization Event Analysis Panel (ii): Debt/Assets Data
Panel (i): Debt/Assets Model 1
0.8 avg model +/− σ
avg data +/− σ
0.6
0.5 0.4 0 −5
0 period Panel (iii): Int. Rate Model
0.2 −5
5
0 period Panel (iv): Int. Rate Data
5
0 period Panel (vi): Sales/Assets Data
5
0 period Panel (viii): Net Inv./Assets Data
5
0 period
5
0.3 0.4 0.2
0.3 0.2
0.1
0.1 0 −5
0 period Panel (v): Sales/Assets Model
0 −5
5
1.5 Sales/Assets
3 2 1 0 −5
0 5 period Panel (vii): Net Inv./Assets Model
1
0.5 −5
0.05 0.4 0.2
0
0 −0.2 −5
0 period
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
5
−0.05 −5
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Test: Liquidation Event Analysis Panel (i): Debt/Assets Model 0.7 0.6
Panel (ii): Debt/Assets Data 0.4
avg model +/− σ
0.35
avg data +/− σ
0.5 0.3
0.4 0.3 −4
−3
−2 −1 period Panel (iii): Int. Rate Model
0
0.25 −4
−3
−2 −1 period Panel (iv): Int. Rate Data
0
−3 −2 −1 period Panel (vi): Sales/Assets Data
0
−3 −2 −1 period Panel (viii): Net Inv./Assets Data
0
0.2 0.2 0.1
0.1 0 −4
−3 −2 −1 period Panel (v): Sales/Assets Model
0
0 −4
1
2
0.5
1.5
0 −4
−3 −2 −1 period Panel (vii): Net Inv./Assets Model
0
0.5
1 −4
0.01
0
0
−0.5
−0.01
−1 −4
−3
−2 period
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
−1
0
−0.02 −4
−3
−2 period
−1
0
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Policy Counterfactual: AHM Proposal
Aghion, Hart, and Moore (1992, Journal of Law, Economics, and Organization, p.524): I
Western bankruptcy procedures “are thought either to cause the liquidation of healthy firms (as in Chapter 7 of the U.S. Bankruptcy Code) or to be inefficient and biased toward reorganization under incumbent management (as in Chapter 11 in the United States).”
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Policy Counterfactual: AHM - cont. AHM proposed the following bankruptcy reform: I
When a firm goes bankrupt, all of the firm’s existing debts are canceled.
I
Bids are solicited for the “new” all-equity firm in order to value it and rights to the equity in this new firm are allocated among the former debt holders.
I
The new shareholders –that is, the former debt holders– decide whether to continue or liquidate the firm.
I
After these steps the firm exits from bankruptcy (given a “fresh start”).
Their policy is very similar to a recent proposal by the American Bankruptcy Institute. Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Implementing AHM I
No default (∆ = 0), no real changes in continuation (V00 (z, k, b)) or exit (V01 (z, k, b)).
I
However, in the event the firm declares bankruptcy (∆ = 1), the value is: V1 (z, k, b) = max {W (z, k, 0) − b − cB , 0} , where the value of the all equity firm is W (z, k, 0) = max{V (z, k, 0), sk}. since the new claimholders have the option to liquidate.
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Implementing AHM - cont.
I
The lender’s profit function reflects the fact that the bondholders receive the value of the all-equity firm in return for debt forgiveness: Ω(b0 , k 0 , z)
= −q(b0 , k 0 , z)b0 + q B [1 − Λ(b0 , k 0 , z)]b0 X +q B min b0 , max{W (z 0 , k 0 , 0) − cB , 0}}G(z 0 |z) z 0 ∈D1 (k0 ,b0 )
I
The different recovery rate (W (z 0 , k 0 , 0)) will play an important role in the GE effects of the policy.
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
AHM Reform: Main Findings I
Ceteris paribus, new recovery procedure reduces the need for the firm to hold as much capital (collateral) against loans and puts downward pressure on interest rate menu. Fig. q
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
AHM Reform: Main Findings I
Ceteris paribus, new recovery procedure reduces the need for the firm to hold as much capital (collateral) against loans and puts downward pressure on interest rate menu. Fig. q
I
Nonbankrupt and bankrupt firms increase borrowing (to assets) and Dist. Debt/Assets decrease equity issuance considerably. Table Moments Dist. k/Assets
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
AHM Reform: Main Findings I
Ceteris paribus, new recovery procedure reduces the need for the firm to hold as much capital (collateral) against loans and puts downward pressure on interest rate menu. Fig. q
I
Nonbankrupt and bankrupt firms increase borrowing (to assets) and Dist. Debt/Assets decrease equity issuance considerably. Table Moments Dist. k/Assets
I
This increased demand for debt increases equilibrium real interest rates (GE effect) for nonbankrupt firms but lowers interest rates for bankrupt firms.
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
AHM Reform: Main Findings (cont.) I
Net investment to assets increases 19% on average for non-bankrupt firms and there’s a 76% decrease in negative net investment by bankrupt firms.
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
AHM Reform: Main Findings (cont.) I
Net investment to assets increases 19% on average for non-bankrupt firms and there’s a 76% decrease in negative net investment by bankrupt firms.
I
There is a considerable reduction of the bankruptcy rate (-51%) and a jump in the fraction of bankruptcy via reorganization (via the new policy) while leaving the exit rate almost unaffected (-4%).
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
AHM Reform: Main Findings (cont.) I
Net investment to assets increases 19% on average for non-bankrupt firms and there’s a 76% decrease in negative net investment by bankrupt firms.
I
There is a considerable reduction of the bankruptcy rate (-51%) and a jump in the fraction of bankruptcy via reorganization (via the new policy) while leaving the exit rate almost unaffected (-4%).
I
The reform economy exhibits a lower mass of entrants M (-3%), but the reduction in exit rates results in a higher total mass of firms (+2%).
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
AHM Reform: Main Findings - Cohorts I
Can track the evolution of a given cohort of M entering firms.
I
Entrants’ size rises by 8% while mature firms exhibit higher net investment in the reform economy than the benchmark. Fig. Net Inv., k, z
I
Since firms enter bigger in the reform economy, if they experience a low productivity draw they are less likely to exit by selling off their capital.
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
AHM Reform: Main Findings - Cohorts I
Can track the evolution of a given cohort of M entering firms.
I
Entrants’ size rises by 8% while mature firms exhibit higher net investment in the reform economy than the benchmark. Fig. Net Inv., k, z
I
Since firms enter bigger in the reform economy, if they experience a low productivity draw they are less likely to exit by selling off their capital.
I
A firm is less likely to exit or declare bankruptcy early in its lifecycle. Survival, exit, bankruptcy over age
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
AHM Reform: Main Findings - Cohorts I
Can track the evolution of a given cohort of M entering firms.
I
Entrants’ size rises by 8% while mature firms exhibit higher net investment in the reform economy than the benchmark. Fig. Net Inv., k, z
I
Since firms enter bigger in the reform economy, if they experience a low productivity draw they are less likely to exit by selling off their capital.
I
A firm is less likely to exit or declare bankruptcy early in its lifecycle. Survival, exit, bankruptcy over age
I
While the technology shock process doesn’t change, selection effects imply young firms have lower average productivity with reform which reverses when mature.
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
AHM Reform: Main Findings Aggregates/Welfare I
Measured aggregate total factor productivity (TFP) rises by 0.43%.
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
AHM Reform: Main Findings Aggregates/Welfare I
Measured aggregate total factor productivity (TFP) rises by 0.43%.
I
Aggregate consumption rises 0.54%.
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Aggregates
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
AHM Reform: Main Findings Aggregates/Welfare I
Measured aggregate total factor productivity (TFP) rises by 0.43%.
I
Aggregate consumption rises 0.54%.
I
Olley-Pakes decomposition: Z X zb ≡ zj ωj dj = [z + cov(z, ω)] K×B
Aggregates
z
where zb is the average of firm level productivity weighted by output share, ωj is the output share ofPeach firm j, and z is the unweighted R mean productivity (i.e., K×B z zΓ(dk, db, z)).
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
AHM Reform: Main Findings Aggregates/Welfare I
Measured aggregate total factor productivity (TFP) rises by 0.43%.
I
Aggregate consumption rises 0.54%.
I
Olley-Pakes decomposition: Z X zb ≡ zj ωj dj = [z + cov(z, ω)] K×B
Aggregates
z
where zb is the average of firm level productivity weighted by output share, ωj is the output share ofPeach firm j, and z is the unweighted R mean productivity (i.e., K×B z zΓ(dk, db, z)). I
A larger value for the covariance term captures an improvement in allocative efficiency. It rises 2.58% with the reform.
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Concluding Remarks
I
We build a general equilibrium model of firm dynamics with both Ch 7 and Ch 11 bankruptcy choices.
I
We find that if reforms proposed by legal and economic scholars are followed, there can be significant changes in borrowing costs, capital structure and investment decisions, as well as the cross-sectional distribution of firms.
I
The GE consequences of such reforms can actually lead to a rise in consumer welfare, measured TFP, and allocative efficiency.
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Parameterization
Positive Results
Normative Results
Conclusion
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Data Facts: Dist. Debt / Assets & EBITDA / Assets Distribution Debt / Assets Non−Bankrupt Chapter 11 Chapter 7
debt/assets
3 2 1 0 1
5
10 25 median 75 90 percentiles distribution Debt/Assets
95
99
95
99
Distribution EBITDA / Assets
EBITDA/assets
1
Non−Bankrupt Chapter 11 Chapter 7
0.5 0 −0.5 −1 −1.5 1
Return
5
10 25 median 75 90 percentiles distribution EBITDA/Assets
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Data Facts: Dist. Net Inv / Assets & z-scores
Net Inv./assets
Distribution Net Inv. / Assets Non−Bankrupt Chapter 11 Chapter 7
0.2 0 −0.2 1
z−scores
20
5
10 25 median 75 90 95 percentiles distribution Net Inv./Assets Distribution z−scores
99
Non−Bankrupt Chapter 11 Chapter 7
10 0 −10 1
5
10 25 median 75 90 percentiles distribution z−scores
95
99
Return
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Equilibrium
Parameterization
Exit/Bankruptcy Rules 4
0.8
2 0.4
1
0
0 0
1
2
0.8 0.6
2 0.4
1
0.2
0
0.4
0.8
2 0.4
0.8 0.6
2 0.4
0
0
0
0
0
0.8
0
0
2 0.4
1
0.2 0
0
0.8
2 0.4
1
0.2 0
0
3
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
0
1
2
debt (b)
2
3
4
1
0.6
debt (b)
1
debt (b)
3
capital (k)
0.6
2
3
4
1
3
1
2
0.2
debt (b)
4
0
1
0.8
0.4
1
0
1
0.6
0.2
3
3
2
1
2
2
3
0.2
debt (b)
1
4
1
1
1
0
0
debt (b)
3
capital (k)
0.6
0
0.2
0
3
4
1
3
capital (k)
2
0.6
2
debt (b)
4
capital (k)
1
0.8
1
0
debt (b)
Conclusion
1
3
0.2
0
3
4
1
3
capital (k)
capital (k)
0.6
Normative Results
return
4
1
3
Positive Results
capital (k)
Environment
capital (k)
Data
3
1 0.8
3
capital (k)
Motivation
0.6
2 0.4
1
0.2 0
0 0
1
2
3
debt (b)
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Recovery and Bond Price Functions 4
Return
1 0.8
3
capital (k)
Conclusion
0.6
2 0.4
1 0 -0.5
0.2 0
0
0.5
1
1.5
2
2.5
3
debt (b)
future capital (k )
4
1 0.8
3
0.6
2 0.4
1 0 -0.5
0.2 0
0
0.5
1
1.5
2
2.5
3
future debt (b )
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Debt Choice b0 (k, b, z) Non-Bankrupt 0.6
0.5
0.4
0.3
0.2
0.1
0
-0.1
-0.2 0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
capital (k) Return
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Dividend / Equity Issuance Policy 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
capital (k) Return
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Counterfactual: Debt to Asset Ratios I
Debt to asset ratios are higher with no Chapter 11 reorganization Distribution Debt / Assets
0.3
Benchmark Reform
0.25
Fraction of Firms
0.2
0.15
0.1
0.05
0 0
0.1
0.2
0.3
Return Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
0.4
0.5
0.6
0.7
0.8
0.9
1
Debt/Assets Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Mean test I
For each variable of interest xt , we run the following regressions: xit = a0 + a1 dch11 + a2 dch7 it it + bt + uit
I
I
I
(22)
where dch11 = 1 if the firm/year observation corresponds to the start it of a Chapter 11 bankruptcy; dch7 it = 1 if the firm/year observation corresponds to a Chapter 7 bankruptcy; and bt corresponds to a full set of year fixed effects. A significant coefficient a1 reflects that average xt is significantly different for firms in Chapter 11 bankruptcy than that of Non-bankrupt firms. Similarly, a significant coefficient a2 reflects that average xt is significantly different for firms in Chapter 7 bankruptcy than that of Non-bankrupt firms. To test whether a1 is significantly different than a2 we perform an F-test.
Return Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Model Definitions Variable Book Value Assets Capital Net Debt Total Debt Operating Income Taxable Income Cash Flow Equity Issuance Dividends Gross Investment Net Investment Secured Debt Unsecured Debt Market Value Assets
Model Expression k + I{b<0} (−b) k b I{b≥0} b π = zkα n1−α − cf − wn 0
b π − δk − 1q − 1 (1+r) π − 1q − 1 b0 − T
I{e<0} e I{d≥0} (1 − τ d )d ig = k0 − (1 − δ)k in = ig − δk I{b≥0} min{sk, b} I{b≥0} max{0, b − sk} V (k, b, z) + qb0
Return Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Computational Algorithm 1. Guess initial wage rate w0 , price schedule q 0 (k 0 , b0 , z), recovery rate schedule φ0 (k 0 , b0 , z). Solve the Firm Problem. Obtain Recovery Schedule φ1 (k 0 , b0 , z). Obtain Bond Price Schedule q 1 (k 0 , b0 , z). If ||φ1 (·) − φ0 (·)|| < φ and ||q 1 (·) − q 0 (·)|| < q , continue to the next step. If not, update the price and recovery schedule and return to point 2. 6. Evaluate the free entry condition V E at w0 . If it holds with equality, continue. If it does not, update w0 and return to point 2. 7. Clear the Labor Mkt: Set M = 1 and compute the stationary distribution associated with this mass of entrants. Denote this ˆ b, z; M = 1). Given homogeneity, set M 0 to distribution Γ(k, 2. 3. 4. 5.
M0 = R
1 ˆ n(z, k, b)dΓ(z, k, b; M = 1)
Return Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Goods Market Clearing C = Y − CF − I − Λ + X − BC − E
(23)
where aggregate output is Z X Y = (1 − x(k, b, z))z(k α n1−α )ν Γ(dk, db, z), K×B
z
aggregate operating costs are Z X CF = (1 − x(k, b, z))cf Γ(dk, db, z), K×B
z
aggregate investment plus adjustment costs are Z X I= (1 − x(k, b, z)) [k 0 − (1 − δ)k + Ψ(k 0 , k)] Γ(dk, db, z), K×B
z
aggregate equity issuance costs are Z X Λ= (1−x(k, b, z))1{e(k,b,z)<0} (1{ζ=0} λ(e)+1{ζ=11} λ11 (e))Γ(dk, db, z K×B
z
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Goods Market Clearing - cont. where final distributions from exiting firms are Z n X X= x(k, b, z) 1{ζ=0} (k − b) K×B
z
o +1{ζ=7} max{sk − b − c7 , 0} Γ(dk, db, z), aggregate bankruptcy costs are Z Xn (1 − x(k, b, z))1{ζ=11} c11 BC = K×B
z
o +x(k, b, z)1{ζ=7} max{c7 , sk} Γ(dk, db, z), and entrants’ investment and costs are E = M {k e + κ + λ(−k e + q(k e , be )be − κ)} . Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Labor, Bond, and Stock Market Clearing
B 0∗
h
i 1{∆(k,b,z)=J } hn J (z, k, b) Γ(dk, db, z) h i R P P = K,B Z (1 − x(z, k, b)) J =0,1 1{∆(k,b,z)=J } hbJ (z, k, b) Γ(dk, db, z)
1=
R
K,B
P
Z
(1 − x(z, k, b))
P
J =0,1
1 = S 0∗ Return
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Taxes Total Household Taxes are Th =
T dZ+ T B + T 7 + T i X + (1 − x(k, b, z))T c (k, z)Γ(dk, db, z) + T L K×B
z
d
Dividend taxes T are Z X T d = τd (1 − x(k, b, z))1{e(k,b,z)≥0} e(k, b, z)Γ(dk, db, z), K×B
z
Taxes on interest earnings T B are 1 − 1 B0, T B = τi qeB qeB Taxes to cover bankruptcy cost of liquidated firms T 7 are Z X 7 T = x(k, b, z)1{ζ=7} max{c7 , sk}Γ(dk, db, z), K×B
z
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Taxes (cont.) Income taxes on the final distribution by exiting firms T i are Z n X Ti = τi x(k, b, z) 1{ζ=0} (k − b) K×B
z
o +1{ζ=7} max{sk − b − c7 , 0} Γ(dk, db, z), Taxes to cover ex-post losses associated with bankruptcy T L are Z X TL = qB {−Λ(z, k, b)b K×B
z
+ min b, max{sk − c7 , 0}} + φ(z, k, b)b}Γ(dk, db, z). Return
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
AHM Reform: Price Schedules Future capital (k )
2.5
Normative Results
Conclusion
Return
1
2
0.8
1.5
0.6
1
0.4
0.5
0.2 0
-0.5
0
0.5
1
Future debt (b )
Future capital (k )
2.5
1
2
0.8
1.5
0.6
1
0.4
0.5
0.2 0
-0.5
0
0.5
1
Future debt (b )
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
AHM Reform: Distribution Debt/Assets Distribution Debt / Assets
0.3
Benchmark Reform
0.25
Fraction of Firms
0.2
0.15
0.1
0.05
0 0
0.1
0.2
0.3
Return
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
0.4
0.5
0.6
0.7
0.8
0.9
1
Debt/Assets Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
AHM Reform: Capital to Assets 0.45 Benchmark Reform
0.4 0.35
cdf Firms
0.3 0.25 0.2 0.15 0.1 0.05 0 0
0.2
0.4
0.6
0.8
1
Note: truncated the frequency at capital to assets at 1 (zero cash holdings). The mass of firms with capital to asset equal to 1 in the
Capital/Assets
figure is 73.43% and 75.50% in the benchmark and the reform economy respectively. Return Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
AHM Bankruptcy Reform: Main Findings Return
Exit Rate Frequency of all Bankruptcy Fraction of bankrupty Reorganization Recovery rate by Liquidation Recovery rate Reorganization Equity issuance Non-Bankrupt Equity issuance Reorganization Debt to Assets Non-bankrupt Debt to Assets Reorganization Net Investment/Assets Non-Bankrupt Net Investment/Assets Reorganization Fraction of exit by Liquidation Frac. Firms issuing equity Non-Bankrupt Frac. Firms issuing equity Reorganization Spread all firms Spread Non-Bankrupt Spread Reorganization Avg Size (k) / Prod. z Non-Bankrupt Avg Size (k) / Prod. z Ch 11 Avg Size (k) / Prod. z Ch 7 Avg Size (k) / Debt b Entrant Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Data 1.10 0.96 79.15 5.80 49.09 0.06 0.01 28.31 41.99 1.16 -2.94 19.83 22.04 13.14 1.30
Benchmark 1.19 0.88 72.61 4.23 57.91 0.00 0.01 28.97 43.15 0.89 -6.22 20.18 26.72 9.75 0.50 0.43 13.86 0.642 / 1.015 1.978 / 1.561 0.010 / 0.645 0.674 / 0.475
Reform 1.14 0.43 99.99 14.51 88.04 0.00 0.65 36.63 89.06 1.06 -13.55 0.00 25.70 50.88 0.051 0.052 0.000 0.633 / 1.021 0.433 / 0.619 0.010 / 0.589 0.729 / 0.649 Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
AHM Reform: Survival, Exit and Bankruptcy Prob. Survival (fraction survives) 1 benchmark reform
0.9 0.8 0.7 0.6 0.5 0
5
10
15
20
25
firm age Avg Exit Probability (fraction exit)
0.025
benchmark reform
0.02 0.015 0.01 0.005 0 0
5
10
15
20
25
firm age Avg Bankruptcy Prob. (fraction bankruptcy)
0.05
benchmark reform
0.04 0.03 0.02
Return
0.01 0 0
5
10
15
20
25
firm age
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
AHM Reform: Net Inv., k and z avg Net Inv. / Assets
0.05
0
-0.05 benchmark reform
-0.1 0
5
10
15
20
25
firm age avg k
0.75
benchmark reform
0.7
0.65
0.6 0
5
10
15
20
25
firm age avg z benchmark reform
1.04
1.02
Return 1 0
5
10
15
20
25
firm age
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
AHM Reform: Debt/Assets and Equity Issuance/Assets avg Debt/Assets
1
benchmark reform
0.8 0.6 0.4 0.2 0
5
10
15
20
25
firm age avg Equity Issuance/Assets
0.08
benchmark reform
0.06
0.04
0.02
0 0
5
Return
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
10
15
20
25
firm age
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
AHM Reform: Welfare and Aggregates Aggregate Consumption C Aggregate Output Y Fixed Cost CF Investment I Adjustment Costs Ψ Equity Issuance Λ Bankruptcy Costs BC c Bankruptcy Costs BC s Exit Value X Entry Costs E Equilibrium wage Capital to output ratio K/Y Measured TFP (= Y /K 1/3 ) Avg. Productivity z¯ Avg. (output weighted) Prod. zˆ Cov(z, ω) Mass Entrants Total Mass Firms
Benchmark Model 1.13 1.76 0.20 0.36 0.03 0.002 0.004 0.0001 0.01 0.04 1.00 1.46 1.28 1.02 1.24 0.22 0.05 3.97
Conclusion
Return
Bankruptcy Reform (∆%) 0.54 -0.04 1.87 -0.83 -5.49 -84.32 -99.75 -100.00 26.38 3.52 0.02 -1.35 0.43 -0.02 0.44 2.58 -2.78 1.80
Note: z is average firm productivity, zb is the (output weighted) average firm level productivity and ω is the output share of each firm. Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Household Problem I
The HHs f.o.c in a steady state implies qtB
=
β
(24)
pjt
=
βEt [pjt+1 + djt+1 ]
(25)
I
To characterize stock prices, consider an incumbent firm and let p(z, k, b) = V (z, k, b) − d(z, k, b) and (1 + r)−1 = β.
I
Then it is straightforward to show that (25) is equivalent to (9) or p(z, k, b)
= ⇐⇒
βEz0 |z [p(z 0 , k 0 , b0 ) + d(z 0 , k 0 , b0 )] V (z, k, b) − d(z, k, b) = (1 + r)−1 Ez0 |z [V (z 0 , k 0 , b0 )]
Return
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Cross-Sectional Distribution of Firms The law of motion for the cross-sectional distribution of firms is given by: Γ0 (K, B, Z; M, w) = ( Z X Z X K,B
Z
K,B
(26) h (1 − x(z, k, b)) 1{∆(k,b,z)=0} 1{k0 =hk (z,k,b),b0 =hb (z,k,b)} 0
0
Z
)
i +1{∆(k,b,z)=1} 1{k0 =hk (z,k,b),b0 =hb (z,k,b)} G(z 0 |z)Γ(dk, db, z) dk0 db0 1
+M
X
1
0 ,b0 } G(z) 1{kE E
Z
where M denotes the mass of new entrants.
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Return
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Other Moments Fraction of exit by Liquidation Frac. Firms issuing equity Non-Bankrupt Frac. Firms issuing equity Reorganization Dividend to Asset Non-Bankrupt Dividend to Asset Reorganization Net Debt / Assets non-Bankrupt Net Debt / Assets Reorganization Spread all firms Spread Non-Bankrupt Spread Reorganization Avg Size (k) / Prod. z Non-Bankrupt Avg Size (k) / Prod. z Ch 11 Avg Size (k) / Prod. z Ch 7 Avg Size (k) / Debt b Entrant
Data (%) 19.83 22.04 13.14 3.49 1.80 9.11 29.61 1.30
Model (%) 20.18 26.72 9.75 2.87 0.00 22.82 43.15 0.50 0.43 13.86 0.642 / 1.015 1.978 / 1.561 0.010 / 0.645 0.674 / 0.475
Return
Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
Motivation
Data
Environment
Equilibrium
Parameterization
Positive Results
Normative Results
Conclusion
Some Corporate Bankruptcy Facts BWZ (2006, JF) sample of 300 bankrupt public and private firms in AZ and NY from 1995-2001: I
Fraction of Ch 11 bankrupts in all bankruptcies is 80%. Note: Statistics on all business filings from the U.S. Courts suggests a lower fraction of Ch. 11, roughly 25% in 2013.
I
Ch. 11 are larger (assets) and have lower debt-to-asset ratios.
I
Creditors in Chapter 11 reorganizations recover considerably more than creditors in Chapter 7 liquidations
Mean Median = 0%
Chapter 7 27.4 5.8 43
Chapter 11 69.4 79.2 0
Table : BWZ (2006) Recovery Rates (% of initial claim) Return Reorganization or Exit: Bankruptcy Choice and Firm Dynamics
Dean Corbae, Pablo D’Erasmo
