Models Of Credit Markets Flashcards
Intertemporal substitution model (why demand is high despite high interest
What is our maximum utility function
W₁ - income in period 1
W₂ - income in period 2
Can borrow (or lend) amount L at gross interest rate R in period 1.
Discount factor δ (for period 2)
Maximising utility for both periods:
Max u(c₁) + δu(c₂)
We get the Euler equation - and what does this mean
u’(c₁) = δRu’(c₂)
Add R to 2nd period as we have either borrowed or lent at rate R!
Consumption smoothing - Marginal utility constant
What does this become with credit constraints
w₁>=c₁ or L=0
u’(c₁) >= δRu’(c₂)
(Marginal utility today>marginal utility tomorrow)
So we are consuming less today!
Add possibility to invest amount I , with returns f(I) in period 2.
What is our c₁ and c₂ equations
C₁ = w₁ + L - I
(Consumption is out wage + amount we borrow - amount we invest)
C₂ = w₂ + f(I) - RL
(Consumption is our wage in p2 + returns from investment - loan cost
Sub into our utility maximisation (FC1)
Max u(c₁) + δu(c₂) becomes
Max u(w₁ + L - I) + δu(w₂ + f(I) - RL)
Solving the problem (F.O.C) with respect to investment what do we get
Intuition:
f’(I) = R
R (interest rate) determines optimal investment! (Think, keep adding £1 to invest as long as the return is greater than the interest rate, cos then better off saving in banks!)
From then we can use optimal investment I to find optimal loan L we should take out using c₁=w₁ +L - I
So with credit constraints what are the 2 equations (THEY ARE INEQUALITIES)
u’(c₁) >= δRu’(c₂)
f’(I)>=R (Return is higher than the interest rate which is good, but credit constraint so can’t access more loans)
Why is loan demand high despite R: (3)
Indiviudals may discount future heavily - δ is low offsetting high R
u’(c₁) >= δRu’(c₂)
Low δ means marginal utility in period 2 is low i.e consumption is high so need to borrow despite the high R
Or if w₂ is high. so consume more in future too c₂,so borrow more
If return f’(I) is high, so consume more too, so borrow more!!
What can explain low consumption today (c₁) but high marginal utility today?
Give an example
Transitory shocks
E.g health emergencies - will have a high marginal utility from spending
What has to be true for reality to fit the neoclassical model I.e why demand is high despite high R (4)
Poor may be myopic (do not think about tomorrow) ,
Or cannot reduce consumption due to subsistence constraints i.e need it to survive)
Or they are becoming non-poor very quickly
Or do not understand compound interest (hence why demand high still)
Or model is missing something
Thus what do lenders face? (2) (Hint: financial markets module!!)
Adverse selection - in choosing non-risky borrowers
Moral hazard - how they will spend the money is unknown
How can they lend effectively
Screening for safe/risky and monitoring actions.
And lenders differ in their ability to this (formal banks vs moneylenders) , and so does the cost (moneylenders typically can screen cheaper and less restrictions, SHOWN IN ENFORCEMENT MODEL NEXT!)
As a result they set interest rates high:
Lemons adverse selection problem
Higher interest rates mean safe borrowers drop out, so left with only riskier borrowers.
So what is the correlation between default and interest rate
Positive - more likely to default if interest rate is high
Karlan/Zinman (Karlan same person who tried paying off debt experiment, didn’t work, people still went back into debt - behavioural constraints etc)
Aim to distengle selection from incentive effect
Select in based on an offered interest rate, but incentives determines by contract interest rate.
50% were given a low offered interest rate. Who stuck with lower contract rate.
Other 50% given high offer rates, among them 50% given low contract rate anyways
How can we measure selection effects?
Default in high offer low contract - Default in low low
(to see purely effects from just selection choices as taken)
((DOUBLE CHECK THO!!)
How can we measure incentive effects?
Default in high offer high contract - default of high offer low contract (the 50% within the high offer rate that was given low rate!!)
see the effect of the incentive shifting since half were stilll given a low rate! we would expect higher default from the high high group!!
they added a dynamic rate too: All groups were promised future loans conditional on repayment
They were split into 2 groups
One group were offered future rates the same as current (contract) rate
Other were offered future rates higher than current rate
Regression
Defaulti =α+βoffer+βCcontract+βOdynamic+γXi +εi
Karlan/Zinman’s findings
Mild evidence for selection effects influencing default
Dynamic rate (moral hazard) - explains 22% of defaults. (people given the future rate equal to contract rate default less than the ones given the higher future rate!)
Huge caveat to these results that lessen the validity
Letters sent to former borrowers in good standing - we have pre-screened good borrowers, so reduced the selection effect
How do prices have selection and incentive effects
Selection - higher prices mean those who need it the most receive it. (Benefit of a free market - shows preferences)
Incentive - value more when paid for it.
When lenders screen, what do they look at/do? (3)
Where they live
Nature and scale of borrower’s business
Get references from others
(Imagine i do this on depop too when buying!)
What do they do for monitoring once they have screened and lent the money? (3)
Visit borrower
Check how loan is being used as intended, and if profitable
Chase loans if required
What is the problem with screen and monitoring
Costs time and money - and these expenses ARE FIXED i.e need basic info even for tiny loans.
Smaller the loan, larger the proportional screening cost, so higher the interest rate to compensate
What does screening and monitoring cost mean for the cost of loan
Smaller the loan, larger the proportional screening cost, so higher the interest rate to compensate.
How big of an issue is this? Aleem
lenders charge equal to their average cost (P=AC so 0 profit!!)
Enforcement (and moral hazard) model
Assumption :
Loan repayment is imperfectly enforceable (delays, non-repayment etc)
Borrower invest k dollars, gross return of F(k) (output)
Loan size is k - w at gross interest r repayed end of period. r(k-w)
Opportunity cost of pw
Hide entire capital from lender at cost nk.
When will borrower repay (maths expression)
B) what is the loan size formula k-w
C) amount invested k
F(k) - r(k-w) - pw > F(k) - nk - pw
(So if return from borrowing>return of hiding)
B) Leaves us with a loan size of:
K-W<= n/r-n x W
Or
K = r/r-n x W
Maximum loan size depends on wealth and diversion cost, negatively on r
So what does maximum loan size depend on, and relationship? (3)
Positively on wealth and diversion cost
negatively on r (borrowing cost)
Intuition
The richer you are, the more difficult to hide. So more wealth, higher n and higher max loan size (since collateral!)
A lot of capital, and small loan, it is not worth hiding capital to avoid paying the loan, because more difficult to hide.
Or if little to no wealth, better to hide at cost n rather than pay it all back.
What if there is no monitoring cost
A competitive lender could offer r=p as long as L<=Lbar
(Interest rate = opportunity cost)
This would be in a perfect capital market
In reality monitoring costs (M) exists.
What is the lenders break-even constraint, and what do we have to assume
Constraint for break even is
r(k-w)>= p(k-w) + M
M is fixed monitoring cost
(Loan repayment i.e what lenders receive)>opportunity cost i.e where (k-w) couldve been used elsewhere + monitoring costs
So now we include monitoring costs: What does the lender set the interest rate r, with competition?
Key finding:
r*= p + M/k-w
Which is opportunity cost + monitoring cost which is spread across the loan size (k-w) !!
We can see interest increases for small loans (when k-w is small) (explains why interest falls as loan size increases!)
What are final equations for interest rate r* and optimal investment k* with monitoirng costs
Remember
K-w = n/r-n x W
Sub into lenders interest rate equation on previous slide.
r* = p + M p-n/nw-M
And
K=pw-M/p-n
2 Implications of this final equation of the interest rate the lender sets (accounting for monitoring costs)
r* = p + M p-n/nw-M
Monitoring explains a large difference between cost of capital (p) and lending rate. (Under perfect competition they set r=p!)
Explains why interest decreases with loan size (FC 34 IF INSURE - why rich borrow more and pay less interest, key stylised fact)
When can the poorest not borrow at all?
When pw<M (monitoring cost>opportunity cost)
Since they would not repay (use FC 35 loan size equation - it becomes negative when M>pw)
Solution to access to credit for these poor people
Subsidy to monitoring cost (or wealth - even more efficient but harder to target since going around giving people money - hard to decide who to give to!)
Why don’t formal banks lend to the poor (4)
Far away from villages
Legal interest ceiling
Screening and monitoring info expensive
Cannot easily threaten people - threatening is effective since decrease monitoring costs, and so can offer lower interest rates (since people more likely to repay)
Why do moneylenders thrive (4)
Live close to people (unlike formal banks previously)
Better connected to locals - can get references without substantial cost (unlike banks)
(No legal restrictions on snooping too!)
Their ability to empose larger social penalities e.g reputation etc - allows them to lower interest rates!
(More effective than financial penalties with banks!)
Repayment is flexible - so thrive more
Issue moneylenders face
Refinancing cost is higher than banks - which increases their interest rates
Do moneylenders abuse monopoly power?
What is it known as?
Despite ex ante competition of moneylenders in villages(stylised fact) , people dont switch often.
“Ex post lock in” - costly to switch borrowers. Others lenders may refuse you if you try to leave old moneylenders.
Thus able to exercise monopoly power and leave interest high (despite having covered the lenders fixed cost of monitoring already)
