Having analyzed the moral hazard problem in a regime of tough bankruptcy law in section 3.4.1, we now move to a regime of soft bankruptcy law characterized by α > 0. This regime enables the debtor of a bankrupt rm to always keep a fraction of the rm's value, even if the creditors are not paid in full. In other words, the soft law enables violation of APR.
An often-cited example of a soft bankruptcy law is the U.S. Bankruptcy Code, es- pecially its reorganization chapter, Chapter 11. There is substantial evidence that the APR is often violated in Chapter 11 cases. Longhofer and Carlstrom (1995), for exam- ple, survey the existing empirical literature on APR violations and nd, based on that literature, that in a sample of large corporations with publicly traded securities, APR violations occur in 75% of reorganizations.
We model the soft law by assuming exogenously given α > 0 (the extensive form representation of this game is shown in Figure 3.2 in Appendix 3.A.1). As before, we are particularly interested in the eects on the debtor's strategy choice in state L and, implicitly, on the level of investment K and interest rate r.
18A testable hypothesis would be that in countries with tough bankruptcy laws, we should observe
The dierence from the case of α = 0 analyzed in section 3.4.1 is that if the debtor gambles on resurrection in state L and this gamble fails, she still keeps fraction α > 0 of the rm's remaining value. Thus her expected payo from continuation is larger by (1 − π)αV, which is added to the right hand side of ICC (3.11). To induce her to choose
SQ in state L for K = KF B and r = 0 the following modi ed ICC must hold:
V + γKF B − KF B ≥ π[V + B ln(KF B + 1) − KF B] + (1 − π)αV. (3.20)
In this case, by increasing the payo from continuation in the bad state, the soft law makes the gambling on resurrection more attractive.
For K = KF B and r = 0 to be the solution, the value kept by the debtor after out-
of-bankruptcy liquidation and full repayment must be larger than what she could obtain from ling for bankruptcy, i.e., the following must hold
V + γKF B − KF B ≥ α(V + γKF B). (3.21)
If the condition of having both (3.20) and (3.21) hold is violated, the solution with
K = KF B and r = 0 cannot be achieved. It may still be possible to achieve a solution
with K = KF B and r > 0, provided α is high enough to induce the debtor to choose S Q,
i.e., provided that
α(V + γKF B) ≥ π[V + B ln(KF B + 1) − (1 + rS)KF B] + (1 − π)αV, (3.22) where rS is given by solving the bank's participation constraint (holding with equality)
as rS = 1 − p p · 1 − (1 − α)V + γKF B KF B ¸ . (3.23)
In this case, as in the case with endogenous α, the debtor obtains a large enough share of the pie to induce him to act in the socially optimal way and to liquidate the project in the bad state. The bank, although not repaid in full in state L, is willing to nance the project at the socially e cient level because it is compensated by a higher payo in state H.
When the project upside given by B is high and the law's degree of softness given by
α is low (both (3.20) and (3.22) are violated), the rst best cannot be achieved for the
{KS, rS, S
i} will be determined as the solution to one of the following maximization
problems:
1. Quitting in state L. In the optimal contract, r = 0 and the investment K is such that the debtor prefers SQ in state L so that the creditor gets repaid in full. The
maximization problem then becomes
max
K p[V + B ln(K + 1)] + (1 − p)(V + γK) − K (3.24)
s.t.
V + γK − K ≥ π[V + B ln(K + 1) − K] + (1 − π)αV. (3.25) The optimal K is obtained by solving (3.25) held with equality, i.e., KS is given by
(γ + π − 1)KS− πB ln (KS+ 1) + (1 − α)(1 − π)V = 0. (3.26)
2. Continuation in state L. K and r are such that in the bad state the debtor prefers to continue the project. The maximization problem becomes:
max
K,r [p + (1 − p)π][V + B ln(K + 1) − (1 + r)K] + (1 − p)(1 − π)αV (3.27)
s.t.
[p + (1 − p)π](1 + r)K + (1 − p)(1 − π)(1 − α)V − K ≥ 0. (3.28) Here, the optimal investment is K = [p+(1−p)π]B−1 = KF B
C < KF B. The optimal
interest rate is positive and is obtained by substituting KF B
C in the participation
constraint (3.28) holding with equality.
When deciding which of the two possible contracts described above is the best, the debtor compares the expected payos from each, i.e., the values of the objective function at the optimal solution, and chooses the one with the highest payo.
We now summarize the above derivations in the following proposition.
Proposition 3. Under the soft law with exogenously given α, the optimal levels of K and
• If (3.20) and (3.21) hold, KS = KF B, rS = 0, SS
i = SQ.
• If (3.20) and (3.22) hold but (3.21) does not hold, KS = KF B, rS is given by (3.23),
and SS
i = SQ.
• If neither (3.20) nor (3.22) hold, then the rst best is not attainable and K < KF B.
The debtor will decide between a contract involving quitting in the bad state (case 1 above) and a contract involving continuation in the bad state (case 2 above), depending on which of the contracts yields her higher expected pro t in period 0. The key conclusion of the soft law analysis is that if the law is not soft enough (if the constraint (3.22) is violated), it further worsens the gambling on resurrection problem observed under tough law by making the continuation strategy in the bad state more attractive for the debtor. The consequence is higher ine ciency given by the higher dierence between the feasible (KS) and the optimal (KF B) investment level. If, on the
other hand, the law is soft enough (if the constraint (3.22) holds), then the debtor behaves in the socially optimal way, liquidating the project in the bad state. The practical question is when the law is soft enough. For the parameters here, this is the case for α = 0.5, meaning that the debtor would have to retain 50% of the rm's value in bankruptcy. Compared to the empirically observed values of the degree of softness under Chapter 11 which range from 0% to 26.5%, with an average below 10% (as discussed in section 3.2.2) this seems to be unrealistically high. If such a high level cannot be achieved in practice, then tougher law will produce better results.