5. Verifiable Income Flashcards
What makes a variable verifiable?
A court of law are able to enforce the execution of the contract agreement. So third parties can also verify terms written in the contract
Verifiable income
The principal of maximal insider incentives
Semiverifiable income
Audits and bankruptcy
Nonverifiable income
The threat of termination
How is income modelled in the principal agent model Innes (1990)?
Random variable R distributed on the interval (0, R bar) according to the distribution p(R|e) where e>0 denotes the entrepreneurs effort
How is the entrepreneur modelled in the principal agent model Innes (1990)?
Risk neutral, net worth A, disutility of effort, limited liability
How is the contract modelled in the principal agent model Innes (1990)?
W(R) is the entrepreneurs reward when realised income is R; R-w(R) is lenders reward
What does the monotone log likelihood ratio property (MLPR) state?
A higher income signals a higher effort
What does the objective function give?
The entrepreneurs expected compensation conditional on the level of effort
Integral of w(R)p(R|e)dR -g(e)
What is incentive compatibility constraint?
This is obtained after setting the derivative of the objective function wrt e equal to 0
Integral of w(R)dp(R|e)/de dR = g’(e)
What is the zero profit constraint?
This is the expected loan repayment
Integral of (R-w(R))p(R|e)dR= I-A
What is the monotonicity constraint?
It requires that the lender’s payoff is nondecreasing in the projects return.
R-w(R) is nondecreasing for all R
What do mu and lambda denote?
The non negative multipliers of the constraints (ICb) and (IR) and ignore the monotonicity constraint
Suppose mu >0, what does the monotone likelihood property imply?
That there exists a threshold income R* such that
W(R) = R if R>R*
W(R) = 0 if R<R*
Proposition 1 live or die contract
The solution generalises the maximal insider incentive principle: the borrower receives nothing for R<R* and the entire income for R>R*. These type of contracts are called live or die
What happens if we relax the lenders limited liability constraint
The solution would degenerate with W(R)=0 for R<R bar and spike at R bar
Proposition 2 when is the optimal reimbursement the standard debt contract?
When we add the monotonic constraint the optimal reimbursement is the standard debt contract. When monotonicity is imposed the lenders limited liability constraint isn’t binding
For a risk averse entrepreneur why is there a conflict in contract design?
Conflict between insuring the entrepreneur against income uncertainty and inducing effort
What reward does the borrower get?
W(R)
What reward does the lender get?
R-w(R)
What is the assumption of monotonic reimbursement and why is it needed?
R-w(R) is nondecreasing for all R. Otherwise the entrepreneur could borrow R2-R1 from a third party and increase her reward by w(R2)-w(R1) and then repay the third party and make a profit
If we impose the extra constraint that the lender has limited liability w(R)<=R then what is the solution?
W(R) = R if 1+ mu((dp(R|e)/de)/p(R|e)> lambda
W(R)= 0 if 1+ mu((dp(R|e)/de)/p(R|e) < lambda
If mu=0 what is the optimal effort given by?
g’(e)= integral of Rdp(R|e)/de dR
What is the correspondence between the fixed investment model and the verifiable income model?
The only differences are:
-In fixed investment there are only two states and in the verifiable income model there are a continuum of state.
-In fixed investment there is a benefit to working and in verifiable income there is a cost of working
