7. Nonverifiable Income Flashcards
What do we aim to look at with nonverifiable income and what do we find?
We ask if it’s possible to have any loan agreements when the lenders are completely unable to verify project returns. We find that it might be possible to find solutions to the incentive problem as long as we extend the time horizon of projects. We also find that the problem has interesting applications for intermediate finance and sovereign debt
Summarise the model
-Date 1: investment I yields R1 with prob p and 0 with prob 1-p
-Date 2: the initial investment if not terminated yields expected income R2. If the project is liquidated at the end of date 1, lenders receive liquidation value L<I-A and the entrepreneur receives nothing
Remark 1 distribution of R2
Given that 0 is part of the distribution of R2 the entrepreneur repays nothing at date 2 since they claim they made 0
What do we assume about liquidation level?
Insufficient liquidation L<R2. The continuation value of the project is higher than its liquidation value
How is the contract modelled?
Repayment D<=R1; probability of continuation yo distributed [0,1] if D is not repaid; probability of continuation y1 distributed [0,1] if D is repaid
What does the incentive compatibility constraint require?
R1-D + y1R2>= R1 + yoR2
(y1-yo)R2>=D
What is the objective function?
P(R1-D+y1R2)+(1-p)(yoR2)
What is the incentive compatibility constraint?
(y1-yo)R2>=D
What is the zero profitability constraint?
P(D+(1-y1)L)+ (1-p)(1-yo)L>=I-A
Why do we assume the constraint D<=R1 isn’t binding?
If it was there would be no mechanism that could solve the incentive problem
Proposition 1 what does the optimal contract specify?
y1=1
1-yo= (I-A)/(pR2+(1-p)L and D=(1-yo)R2
In what cases does the stochastic contract dominate a deterministic one?
The optimal stochastic contract will dominate a deterministic contract where the project is always terminated when there is no repayment
How should the lender set the probability of termination 1-yo?
As long as the lender breaks even in expectation it is always better to set the probability of termination as low as possible given the liquidation is inefficient
Why is the zero profit incentive binding?
If not D could be lowered without effecting the two constraints
Why does the lender sometimes allow the project to continue under the optimal mechanism even when the borrower makes no repayment?
Stochastic contract. The lender tries to maximise the borrowers utility. Given continuation is always better than liquidation, the lender tries to maximise the probability that the project continues
