Insurance Flashcards
First: what are the ways for people to be less risk-averse?
- self-insurance
- mutual insurance
- credit
Self-insurance?
Individuals (with the wealth to do it) protect themsleves rom exogenous uncertainties
Examples of self-insurance
Cash, savings, stocks of food grain (but less durable than money), durable goods (jewellery, animals (bullocks)…)
- probability to keep bullock increased when wealth increased
Stocks of food grain can be useful to smooth consumption inside the year, but not across years!
Mutual insurance
A and B are farmers, harvest can be 1000$ or 2000$
4 possibilities of distribution:
if one get 1000 and other one 2000. A and B prefer insurance to no insurance, because promise of 1500 if the other gets 2000.
Mechanism: the lucky one gives 500$ to the unlucky one.
Implications of mutual insurance?
- idiosyncratic (individual) shocks are insurable (disease, festivities, local damage…)
- common shocks to the village are non-insurable (climate…)
- possible (even better) with a larger group: lucky one gives 500$ to the common pot, unlucky take 500$.
- independence of shocks ensures that on average, surplus=deficit.
- so no need for perfect negative correlation (always 2000;1000, 1000;2000), only independence of shocks!
Credit
Credit may smooth income shocks over time: borrow when face negative shock, lend when face positive shock
Conclusion of perfect insurance model?
- thanks to: self-insurance, mutual insurance, and credit; individual shocks may be completely insured.
- Implication: household consumption should depend ONLY on village income, not on household income!!
Regression implications? (e.g. how to test this?)
Ch= a+b*Yh+c*Yh+... Ch: household consumption Yh: household income Yv: village income b should be 0, c should be 1
Criticisms of this study/finding?
- What is the relevant group…? Caste, village, occupation, household….
- Yh is in Yv (counted twice). Should rather consider Yv-h.
- Reverse causality: if my Ch goes up, then Yv increases (villlage income), positive externality
- OMV: common group shocks
- And hidden cost of lack of insurance? Farmers might choose safer in the first place, but lower returns to crops?
Conclusion: if we believe the estimates, NO COMPLETE INSURANCE is possible.
Why is no complete insurance possible?
Information problems:
1: Information problem about the final outcome
Individuals lie about the final outcome!
Information problem about the final outcome, an individual may lie about how much he got from the harvest! Impossible in small communities, but possible in larger more anonymous areas. Might explain low take-up rates of formal insurance in developing countries!
= EX-POST MORAL HAZARD
More on information problems: what led to the final outcome in the first place?
2: Information problem about what led to the final outcome (effort or no effort?)
No incentive to exert effort if people are insured!
- We always assumed an exogenous shock!
- What if it depends on an endogenous decision: effort?
- The harvest could be good or bad only because the farmer has not exerted enough effort…
- If under complete insurance one earns 1500$ for sure. Why ever bother to work at all?
Proof of why information problems occur:
- H with prob p if high effort (with a cost of C)
- H with prob q( qU(H)+(1-q)U(L)
- (p-q)*[U(H) - U(L)] > C
- Intuition: the farmer needs p and H to be more than q and L by a lot, so that it’s worth working
… assuming everyone works hard?
- then average total income is: pH+(1-p)L (chances of getting a high payoff plus the remaining chances of not getting one)
- then everybody gets the utility of that: U[pH+(1-p)L]
Payoffs of that..?
- If effort: U[pH+(1-p)L]-C
- If not effort: U[pH+(1-p)L]
- Always better to not work (because you would never have to pay the cost of effort!)
- But then contradiction: Average total income (will never be) pH+(1-p)L (if no one works)!
- ex-ANTE moral hazard: the mere fact of offering insurance to an agent modifies his behaviour, even before the harvest is realised
3: Information problem about what types if the agent
Now assume there are two types of agents:
People are different and don’t want to work with people with lower payoffs than themselves!
- type P: high probability of success (= low risk)
- type q (q<p): low probability of success (=high risk)
Average income of the group is then:
½[pH+(1-p)L]+½[qH+(1-q)L]
Implications…?
P type (high chances of receiving success): has a LOWER chances of success than he would have had on his own (with an income of pH+(1-p)L ) Hence, the p-types do not want to participate, only the q-types are interested in insurance.
This is: ADVERSE SELECTION!
Adverse selection:
Only the risky types are interested in insurance
Analogy with smoking and insurance, an ex-ante and ex-post moral hazard:
- Adverse selection:
Only the smokers are interested - Premiums increase, further driving out the non-smokers
- Moral hazard: once covered, the non-smokers might as well smoke!
- Ex-ante moral hazard: people start smoking
- Ex-post moral hazard: after they smoke, they lie about smoking
Enforcement problems of mutual insurance:
A participant to mutual insurance should pay if he gets 2000$. Why would he want to pay? Suppose he gets a High payoff (H).
If he participates in a mutual insurance, he would get
pH+(1-P)L
If he deviates, he gets:
- G: U(H) - U(pH+(1-p)L]
(which is more than what he would have gotten if he did not deviate?)
Sanctions of deviation?
- Excluded forever from the mutual insurance
If the person participates: U[pH+(1-p)L]
If the person does not participate: pU(H)+(1-p)U(L)
For N periods
So Loss = N* ( U[pH+(1-p)L] - pU(H) - (1-p)U(L))
To be more rigorous, it should be the DISCOUNTED SUM OF ALL FUTURE LOSSES.
This loss has to be compared to the one-time gain for it to be worthwhile deviating.
- Social sanctions S
Ostracisation, gossip stigma, social capital goes down.
So person deviates only if…
Gains are greater than loss
G > L.
U(H) - U[pH+(1-p)L] > N* ( U[pH+(1-p)L] - pU(H) - (1-p)U(L)) + S
If social capital (s) goes up, less deviation.
If number of period goes up (n), less deviation..
