Week 7: Insurance
ECON2111
Dr. Hasin Yousaf
Learning goals
• Identify 3 sources of income/consumption risk for the poor.
• Define risk aversion.
• Outline the model of perfect insurance AND
• Identify 3 reasons why this model fails in developing countries.
• Identify 2 ways in which households in developing countries self-
insure.
• Explain how households use credit as insurance.
• Identify 2 reasons why insurance programs for the poor have not
been successful.
Source: Jayachandran (2006)
Coping with Risk
• The poor often find clever ways to cope with risk:
1. Diversify: many occupations, other than agriculture
2. Holding multiple plots
3. Migration
4. Marriage
5. Risk-sharing
• ROSCAs
• (informal) Insurance
• Credit
Insurance is welfare-improving because
people are risk averse
•What is risk aversion?
• It is the reluctance of a person to accept a bet with an
uncertain payoff rather than another bet with a more
certain, but possibly lower, expected payoff.
Gamble A Gamble B
50% chance: $50 $10
50% chance: $50 $100
Expected value: $50 $55
Why are people risk averse?
• Decreasing marginal utility:
• Utility from a dollar when you are poor is much
higher than the utility from a dollar when you
are rich.
Decreasing marginal utility and risk aversion
Consumption
Utility
Decreasing marginal utility and risk aversion
Consumption
Utility
100 500
U(100)
U(500)
• Marginal utility is the
slope of the curve
• MU at U(500) < MU
at U(100)!
Decreasing marginal utility and risk aversion
•Assume a 50-50 chance of a random shock:
• 50% chance that consumption = 100
• 50% chance that consumption = 500
•Expected value (of consumption) = (0.5*100) +
(0.5*500) = 300
•Expected utility = 0.5*U(100) + 0.5*U(500)
Decreasing marginal utility and risk aversion
Consumption
Utility
100 500
U(100)
U(500)
300
(Expected value)
0.5*U(100) + 0.5*U(500)
(Expected Utility)
Decreasing marginal utility and risk aversion
Consumption
Utility
100 500
U(100)
U(500)
300
(Expected value)
Expected Utility
Utility of Exp. Value: U(300)
Utility of Expected Value
>
Expected Utility
Decreasing marginal utility and risk aversion
Utility of Exp. Value: U(300)
Indifferent between Y*
and the expected value,
because they both give the
same utility
Consumption
Utility
100 500
U(100)
U(500)
300
(Expected value)
Expected Utility
Y*
The cost of the risk: Part 1
Utility of Exp. Value: U(300) •Y* is the certainty equivalent
•300 – Y* is the “cost of risk”
• what you would be
willing to pay to insure
against the risk
Consumption
Utility
100 500
U(100)
U(500)
300
(Expected value)
Expected Utility
Y*
Why insurance is welfare-improving
• Suppose a good outcome is H and a bad outcome L
• H occurs with probability p, and L with probability 1-p
• Expected utility under this framework:
• EU = p*U(H) + (1-p)*U(L)
• If you get insurance that guarantees you the expected value of
income:
• EV = p*H+(1-p)*L
• And there is decreasing marginal utility of income:
• U(EV) > EU 
• U(p*H+(1-p)*L) > p*U(H) + (1-p)*U(L)
Why insurance is welfare-improving
Consumption
Utility
L H
U(L)
U(H)
p*H + (1-p)*L
(Expected value)
EU = p*U(H) + (1-p)*U(L)
U(EV) = U(p*H + (1-p)*L)
U(EV) > EU!!!!
Insurance
• Insurance: the ability to smooth unanticipated shocks in
income
• Self-insurance: the ability to use one’s own wealth to
smooth such shocks
• Mutual insurance: a contract between members of a
group such that individuals experiencing negative shocks
are compensated by those who are receiving positive
shocks
Perfect insurance model
• Y = A + e + π
• Y is consumption
• A is each farmer’s average income
• e is a random shock that affects each farmer independently
(idiosyncratic risk)
• π is all sources of risk that are shared by farmers in a village
(covariate risk)
• What are examples of e? What are examples of π?
Perfect insurance model
• Suppose farmers agree to compensate each other when their
incomes are higher or lower than average
• People who earn unexpectedly more share with those who earn
unexpectedly less
• Example: Suppose five farmers with idiosyncratic shocks:
• e1 = 10
• e2 = -10
• e3 = 12
• e4 = -6
• e5 = -6
• If there is perfect insurance, who should compensate whom?
Perfect insurance model conclusions
• With perfect insurance, consumption is: Yinsured=A+π
• If farmers are risk averse, they prefer this to Y
• What does this tell us about the fluctuation of
consumption under perfect mutual insurance?
• Individual CONSUMPTION should track group CONSUMPTION
more closely than it tracks individual INCOME
How would you test this prediction?
Testing the perfect insurance model
• Regress household consumption on average community
consumption and household income, plus potential
consumption side shocks 
= + 1 + 2 + +
• With perfect insurance, should find no effect of
individual/household characteristics and a coefficient of 1 for
group average consumption 
= and =
This has been tested in a variety of ways
• Results have been mixed
• A variety of empirical studies (including Townsend in Thailand and
India) show a considerable amount of mutual insurance within
villages, but not perfect
• Jensen and Paxson’s work suggests that households may also be self-
insuring
• Mordoch finds significant evidence that consumption smoothing
seems to occur among richer farmers, but less among the poor
Why don’t households insure each other
perfectly? (3 Reasons)
1. Limited information about final outcome: perhaps
individuals lie about their actual income, and try to game
the system
• Not so likely in small villages and/or
• Places with high social capital
2. Limited information about the source of the outcome
• MORAL HAZARD: unobserved actions  people take more risks
because someone else bears the cost of those risks
• People change behavior once they know they will not bear the full
consequences
• What if people deliberately don’t work hard, or make important
investments?
• Mutual insurance creates this incentive
Mutual insurance & incentives to work
1. Suppose a good outcome is H and a bad outcome L
• Can exert high or low effort in achieving outcome
2. Probability of H with high effort is p; with low effort is q
• p > q
3. High effort costs C
WITHOUT INSURANCE, work hard if:
p*U(H) + (1-p)*U(L) - C > q*U(H) + (1-q)*U(L)
Expected utility
from High Effort
Expected utility
from Low Effort
Mutual insurance & incentives to work
WITH INSURANCE:
• Can easily imagine an insurance scheme that guarantees:
p*H + (1-p)*L  Expected income with high effort (without
the cost of working hard)
• Recall:
U(p*H + (1-p)*L) > p*U(H) + (1-p)*U(L)
so insurance is welfare-improving!
Utility of expected
income
Expected utility
The disincentive
• On the down side, if you receive guaranteed income, regardless of
whether or not you work hard, why work hard and incur C?
• A second best outcome can be achieved by offering slightly less than
perfect insurance.
• “Second best” insurance
• Household consumption moves partially with household shocks
Limits to insurance (3rd Reason):
3. Enforcement
• Informal insurance is…. informal
• There is an incentive to deviate from an “agreement” and
pocket output in a good year
• Why wouldn’t households do this?
Self-insurance – Jensen
• Examines how households change investments in the face of
agricultural shocks
• Setting: Ivory Coast, 1985-1988
• 70% of households depend upon agriculture as primary source of
income (primarily cocoa)
• 25% live below poverty line
• Research Question: Do households that experience adverse weather
shocks reduce investment in their children?


Weight-for-Height Densities: Boys
Conclusions -- Jensen
• Example of “self-insurance” in the face of covariate
(correlated) shocks
• Households “self-insure” by decreasing investment in
children.
• When households receive income shock, investment in
children is deferred
• Short or long term effects?
Credit as insurance – Udry
• Feb 1998 - Feb 1999 collect data from 198 random households in
4 villages in Northern Nigeria.
• Interviewed each adult male and each of his wives once a month.
• Asked questions about assets, loans, debt, credit, labor,
transactions, etc.
• Mostly Muslim households. Every HH in sample has a farm which
is typically multiple plots interspersed with other village members‘
plots.
• Interested in credit transactions. What is true about sharia law
and interest rates?
Lending is frequent
Wealthier HHs lend and borrow more
84% do not set an interest rate!
• Lending in private with
no contract
• No witnesses
• Paid and repaid in cash
• No collateral required
• Average nominal RoR is
-3.0% (-7.5% w/ inflation)
• So, why do people
repay?!
97% of informal sector loans are between
residents of the same village or relatives
Shocks to Borrowers: reduce interest rate
Shocks to Lenders: increase interest rate
What about formal insurance?
• Since there is so much potential benefit, it seems like
companies should be able to make some money off of
this!
• In addition to moral hazard, formal insurance has the
problem of ADVERSE SELECTION
• Unobserved type  demand for insurance is positively
correlated with the risk of loss
• If insurance not mandatory, risky people (who need
insurance) are likely to buy. The problem is when you can’t
tell who is risky
Formal Insurance
• What do you think could be done to increase the use of
insurance products in developing countries?
• How do we get around moral hazard in Australian
insurance markets?
• How do we get around adverse selection in Australian
insurance markets?