Michael R Carter, Elena Serfilippi, and Catherine Guirkinger presented on this topic of risk and index insurance in November of 2015.

1. Discontinuous Preference for Certainty and
Insurance Demand:
Results From a Framed Field Experiment in Burkina Faso
Elena Serfilippi1
Michael R Carter2
Catherine Guirkinger1
1University of Namur
2University of California, Davis & NBER
November 8, 2015
Serfilippi, Carter & Guirkinger Certainty Preference

2. Logic of Insurance as a Development Tool
Decades of evidence that risk
Makes people poor by reducing incomes & destroying assets;
and,
Keeps people poor, by discouraging investment & distorting
patterns of asset accumulation)
The development impacts of risk reduction through insurance
should therefore be significant:
By protecting households against the worst consequences of
adverse climatic shocks, index insurance should in principal
allow households to prudentially invest more in risky, but high
returning agricultural activities.
That is, if insurance has ex post protection effects, then it
should also have ex ante investment effects
Serfilippi, Carter & Guirkinger Certainty Preference

3. Evidence on Insurance Impacts
Evidence on the ex ante and ex post effects is just emerging:
Satellite-based Livestock Insurance (IBLI) protected
consumption (for poorer households) and assets (for less poor
households) after a drought in Northern Kenya (Janzen &
Carter 2014)
’Two-trigger’ area yield contract in Mali induced 30% increases
in borrowing and cotton plantings by small-scale farmers
(Elabed & Carter 2014)
Karlan et al. study in Ghana finds impacts of a similar order of
magnitude
But despite this evidence, insurance demand is in many pilots
has been sluggish (see for example (Gine and Yang, 2009; Cole
et. al., 2013; Hill and Robles, 2011, Dercon et al. 2011)
Serfilippi, Carter & Guirkinger Certainty Preference

4. Behavioral Economics Insights into Insurance Demand
Multiple conventional (EU-compliant) explanations for this
sluggish demand:
Understanding and trust
Pricing
Contract quality
While insurance demand often approached through the lens of
standard expected utility theory (Clarke, forthcoming), decades
of behavioral experiments suggest systematic deviations
between actual behavior and expected utility theory
We have begun to see the application of behavioral insights to
the demand for insurance:
Petruad 2014 utilizes the Prospect Theory of Kahneman and
Tversky,1979 to study insurance preferences & demand
Elabed & Carter (2015) and Bryan (2014) similarly utilize the
notion of Ambiguity Aversion of Ellsberg (1961)
Today explore Andreoni and Sprenger’s (2009; 2012)
“Discontinuous Preference for Certainty” and its implications
for insurance contract design & demandSerfilippi, Carter & Guirkinger Certainty Preference

5. Outline for Today
1 The Allais paradox & the logic of a “Discontinuous Preference
for Certainty” (DPC)
2 Measuring the extent of DPC with cotton farmers in Burkina
Faso
3 Eliciting farmer willingness to pay for insurance under a
standard & a DPC-sensitive insurance contract framing
4 Econometric analysis of the the differentiated impact of the
DPC-sensitive framing
5 Robustness Checks & Alternative Explanations
6 Welfare implications
Serfilippi, Carter & Guirkinger Certainty Preference

6. The Allais Paradox
Consider the following lotteries:
Experiment 1
Lottery 1A Lottery 1B
Pay-offs Prob. Pay-offs Prob.
0 1%
$1 million 100% $1 million 89%
$5 million 10%
Under standard expected utility theory, preferring 1A to 1B
implies that
1u($1m) > 0.01u(0)+ 0.89 ∗ u($1m) + 0.10u($5m)
which by subtracting 0.89u($1m) we can rewrite as:
0.11u($1m) > 0.01u(0) + 0.10u($5m)
Serfilippi, Carter & Guirkinger Certainty Preference

7. The Allais Paradox
Now consider the following alternative lotteries:
Experiment 2
Lottery 2A Lottery 2B
Pay-offs Prob. Pay-offs Prob.
0 89% 0 90%
$1 million 11%
$5 million 10%
Under standard expected utility theory, preferring 2B to 2A
implies that
0.89u(0) + 0.11u($1m) < 0.90 ∗ u(0) + 0.10u($5m)
which by subtracting 0.89u(0) we can rewrite as:
0.11u($1m) < 0.01u(0) + 0.10u($5m)
which of course directly contradicts prior result
Serfilippi, Carter & Guirkinger Certainty Preference

8. The Allais Paradox
So what explains this fatal (for EU theory) attraction to
Lottery 1A?
Experiment 1 Experiment 2
Lottery 1A Lottery 1B Lottery 2A Lottery 2B
Pay-offs Prob. Pay-offs Prob. Pay-offs Prob. Pay-offs Prob.
0 1% 0 89% 0 90%
$1 million 100% $1 million 89% $1 million 11%
$5 million 10% $5 million 10%
Prospect theory manages this departure from expected utility
theory with a probability weighting function that overweights
small probabilities relative to their objective likelihood
Serfilippi, Carter & Guirkinger Certainty Preference

9. The Allais Paradox
Allais himself made two observations about this paradoxical
result:
Expected utility theory is ‘incompatible with the preference for
security in the neighborhood of certainty’ (Allais, 2008)
But ‘far from certainty’, individuals act as expected utility
maximizers, valuing a gamble by the mathematical expectation
of its utility outcomes (Allais, 1953)
Andreoni & Sprenger propose a parsimonious approach to
capture these two observations:
Suppose we simply discontinuously value probability one
outcomes with a more favorable utility function; for example:
v(y) = yα
if y is certain; and,
u(x) = xα−β
if x is uncertain, where β ≥ 0 is a measure of a
discontinuous preference for certainty
Andreoni and Sprenger go on to implement lab experiments
that confirm that expected utility works if comparing uncertain
things, but breaks down in the neighborhood of certainty
Serfilippi, Carter & Guirkinger Certainty Preference

10. What’s Insurance Got to Do with It?
Insurance is an alien commodity precisely because it (usually)
has a certain cost (the premium), but an uncertain benefit
(the indemnity)
In explaining insurance to the never before insured, I have in
fact strongly emphasized this point so that farmers understand
they may not in any particular year receive anything in return
for their insurance purchase
At least one farmer was provoked into asking if the premium
had to be paid even in a bad, drought year
But if Allais/Andreoni & Sprenger are right, then in making
insurance purchase decisions, do we overweight the certain
cost (the negative element of the contract) relative to the
uncertain benefits of the contract, implying lower than
expected insurance demand?
Serfilippi, Carter & Guirkinger Certainty Preference

11. What’s Insurance Got to Do with It?
The Andreoni & Sprenger formulation does not adapt easily to
payoff structures that include certain and uncertain thing, but
consider the following variant which preserves their intuition:
w(x, y) = (αy+x)1−γ
1−γ where y is certain and x is uncertain and
α ≥ 1
In this ’bird in the hand is worth two in the bush’ specification,
α is the constant marginal rate of substitution of a uncertain
for a certain dollar
Relative to expected utility (with α = 1), this formulation
would lead to an undervaluation of insurance (with α > 1),
unless the premium could itself be made uncertain ...
Serfilippi, Carter & Guirkinger Certainty Preference

12. Field Experiment in Burkina Faso
Working with 577 farmer participants in the area where we are
working with Allianz, HannoverRe, EcoBank, Sofitex and
PlaNet Guarantee to offer area yield insurance for cotton
farmers, played two incentivized behavioral games:
Tested for existence of a discontinuous preference for certainty
(α > 1)
Measured willingness to pay for insurance under two randomly
offered alternative, actuarially equivalent contract framings:
Standard framing (certain premium)
Novel framing (premium rebate in bad years)
Found that:
One-third of farmers exhibit certainty preference
Average willingness to pay for insurance is 10% higher under
rebate framing
Certainty preference farmers willing to pay 25% for insurance
with rebate framing
Serfilippi, Carter & Guirkinger Certainty Preference

13. Testing for Discontinuous Preferences for Certainty
Choose between 8 binary lotteries with pb = pg = 1/2
Initially lottery R stochastically dominates lottery S, but R becomes
riskier as move down table
Where the individual switches from R to S brackets their risk
aversion parameter, γ.
Pair Riskier Lottery (R) Safer Lottery (S) E(R)-E(S) CRRA
Bad Good Bad Good
outcome outcome outcome outcome
1 90,000 320,000 80,000 240,000 45,000 –
2 80,000 320,000 80,000 240,000 40,000 –
3 70,000 320,000 80,000 240,000 35,000 1.58 < γ
4 60,000 320,000 80,000 240,000 30,000 0.99 < γ < 1.58
5 50,000 320,000 80,000 240,000 25,000 0.66 < γ < 0.99
6 40,000 320,000 80,000 240,000 20,000 0.44 < γ < 0.66
7 20,000 320,000 80,000 240,000 10,000 0.15 < γ < 0.44
8 0 320,000 80,000 240,000 0 0 < γ < 0.15
Serfilippi, Carter & Guirkinger Certainty Preference

14. Playing the Game
Serfilippi, Carter & Guirkinger Certainty Preference

15. Testing for Discontinuous Preferences for Certainty
Replace safer lottery with a degenerate lottery D with certain payoff
(risky lottery R is the same)
The value of the degenerate lottery at each row equals the certainty
equivalent of safe lottery S for an individual who would have
switched at that point
Pair Risky Lottery (R) Certain ’Lottery’ (D)
Bad outcome Good outcome E(R)-E(D)
1 90,000 320,000 145,000 60,000
2 80,000 320,000 120,000 80,000
3 70,000 320,000 67,800 127,200
4 60,000 320,000 51,000 139,000
5 50,000 320,000 39,000 146,000
6 40,000 320,000 29,300 150,700
7 20,000 320,000 12,600 157,400
8 0 320,000 0 160,000
An expected utility maximizer with α = 1 should switch at the same
pair Serfilippi, Carter & Guirkinger Certainty Preference

16. Lottery Switch Point Results
Main diagonal (in bold) are expected utility maximizers who
switch at same point
Lower triangle (in blue) have a ’certainty preference’ with
α > 1
Also see about 15% are quasi-Gneezy types
’Players types’ (α < 1) in upper triangle
Serfilippi, Carter & Guirkinger Certainty Preference

17. Prevalence of DPC Preferences
Assume that:
Quasi-Gneezy type players are EU types
Strict definition of DPC (anywhere in lower triangle)
Paper shows that results are robust to alternative assumptions
Agent Type Number %
Expected Utility (α = 1) 191 33
Certainty Pref. (α > 1) 168 29
Others (α < 1) 218 38
Given that about one-third of farmers appear to have a strong
preference for certainty, the key question then becomes if these
farmers are sensitive to contract design and framing
Specifically, will these farmers
undervalue conventionally framed insurance relative to
Expected Utility types
respond positively to an insurance contract in which payment
of the premium is uncertain (rebated)
Serfilippi, Carter & Guirkinger Certainty Preference

18. Insurance Game
Game was set up to closely mimic farmer’s reality:
1 hectare of land to use to cultivate cotton
Stochastic yields with 1200 kg of cotton in good year (80%
probability) & 600 kg in bad year.
Cotton price & input costs set at realistic levels
Endowed with a certain savings of 50,000
Good Year Bad Year
Net Revenue 188,000 44,000
Certain Wealth Endowment 50,000 50,000
Family Money 238,000 94,000
0.8w(α50, 000 + 188, 000) + 0.2w(α50, 000 + 44, 000)
Serfilippi, Carter & Guirkinger Certainty Preference

19. Insurance Game
After subjects learned how to farm in this game, were
presented with one of two, randomly chosen, insurance
contracts:
Standard Certain Premium Frame
The amount of your savings is 50.000 CFA. You decide to buy
an insurance before knowing your yield. The insurance price is
20.000 CFA. You pay the insurance with your savings. In case
of bad yield, the insurance gives you 50.000 CFA. In case of
good yield the insurance gives you 0 CFA.
Premium Rebate Frame
The amount of your savings is 50.000 CFA. You decide to buy
an insurance before knowing your yield. The insurance price is
20.000 CFA. You pay the insurance with your savings, BUT
only in case of good yield. In case of bad yield the insurance
gives you 30.000 CFA. In case of good yield the insurance gives
you 0 CFA.
Note that the rebate frame is realistic in context of cotton
production
Serfilippi, Carter & Guirkinger Certainty Preference

20. Insurance Game
Under standard frame, insurance will be purchased if:
0.8w(α(50, 000 − π) + 188, 000) + 0.2w(α(50, 000 − π) + 44, 000 +
> 0.8w(α50, 000 + 188, 000) + 0.2w(α50, 000 + 44, 000)
where π is the premium and IS is the indemnity payment
under the standard frame
Whereas under the premium rebate frame it will be purchased
if:
0.8w(α50, 000 − π + 188, 000) + 0.2w(α50, 000 + 44, 000 + IR)
> 0.8w(α50, 000 + 188, 000) + 0.2w(α50, 000 + 44, 000)
where IR is the indemnity under the rebate frame
For α > 1, insurance purchase will be more likely under the
rebate frame
Note that the actuarially fair price of this insurance under
either frame is 10,000
Serfilippi, Carter & Guirkinger Certainty Preference

21. Willingness to Pay for Insurance
Mimicked the structure of prior games as closely as possible
Started with an initial pair where insurance was priced at
50,000 so that no insurance was the dominant choice
In each subsequent pair, insurance price was dropped (with
prices of 30.000; 25.000; 20.000; 15.000; 10.000; 5000; 0)
Farmer chose whether and when to switch to the ’safer’
insurance option
Under standard expected utility theory, risk averse agent would
be expected to purchase insurance at some price in excess of
10,000 irrespective of frame
Never purchasing insurance was an option
Serfilippi, Carter & Guirkinger Certainty Preference

22. Results
The raw willingness to pay results are:
All Agents DPC Players EUT
Willingness to Pay
15.796 15.271 15.576 16.515
(10.438) (10.677) (9.659) (11.088)
571 166 217 188
Willingness to Pay Std Frame
15.052 13.526 15.631 16.011
(10.356) (10.540) (9.642) (10.875)
287 95 103 89
Willingness to Pay Rebate Frame
16.549 17.605 15.526 16.969
(10.486) (10.483) (9.716) (11.312)
284 71 114 99
t-test (p-value) of frames 0.08 0.01 0.9 0.5
While these results tell story, also examine econometrically
Serfilippi, Carter & Guirkinger Certainty Preference

23. Tobit Estimates & Marginal Impact of Rebate Frame
Tobit Marginal Impacts
Rebate Frame
105 -161
(1418) (1584)
Rebate Frame x DPC
4262* 5374** 3838** 4576**
(2564) (2598) (1862) (1816)
Rebate Frame x EUT
1279 1948 1237 1607
(2158) (2302) (1885) (1896)
Rebate Frame x Player – –
93 -143
(1259) (1404)
DPC Type
-2643 -3073*
(1767) (1830)
EUT Type
-249 -58
(1596) (1709)
Order Effect
3180 3566***
(1183) (1247)
Controls No Yes
Serfilippi, Carter & Guirkinger Certainty Preference

24. Robustness Checks
Paper explores two alternative definitions of those with a
discontinuous preference for certainty:
More restrictive definition of DPC (individual must have
shifted by 2 rows to count as DPC type)
Counting quasi-Gneezy players as DPC
General character of results not changed by these alternative
definitions
Serfilippi, Carter & Guirkinger Certainty Preference

25. Can Prospect Theory Also Explain Results?
Prospect theory has a lot of moving parts (which is one of its
less desirable features in opinion of Andreoni & Sprenger)
Loss aversion & reference points
Preference for degenerate lottery if reference point which
distinguishes gains & losses is between low & high outcomes of
the risky lottery
Similarly, a carefully selected reference point could rationalize a
preference for the rebate frame
Probability weighting function
Problem is that probabilities of good and bad outcomes are
both one half, so no simple or natural interpretation of
probability weighting as the explanation for a Rebate Frame
preference
Show that using standard cumulative prospect theory tools
(Prelec weighting function and rank-dependent utility) can
identify a set of parameters that will explain the choice
However, implies that one 50-50 choice interpreted as 20-80
and vice versa for the other
Serfilippi, Carter & Guirkinger Certainty Preference

26. Welfare Gains from Rebate Frame
Using distribution of agent types and willingness to pay
estimates, we can calculate what percentage of the farmer
population would purchase the insurance if offered with the
rebate as opposed to the standard frame:
If we take the Elabed & Carter insurance impact results from
Mali, then cotton production could be increased by several
percentage points annually by shifting from a standard, certain
premium to a premium rebate frame.
Serfilippi, Carter & Guirkinger Certainty Preference

27. Conclusions
Results provide another example of the predictability of what
appears as irrationalities from the perspective of standard
expected utility theory
While our simple discontinuous preference for certainty model
makes sense of these results, so to can a more convoluted
version of cumulative prospect theory
Irrespective about the interpretation, if this behavior is regular
and predictable, then it does suggest a basis for an alternative
insurance contract design that should meet with bigger
demand and have the potential to pick up some of the money
being left on the table every year by risk avoiding farmers
We hope to be able to test the rebate frame with a real
contract
Serfilippi, Carter & Guirkinger Certainty Preference

28. Appendix: Probability Weighting
Serfilippi, Carter & Guirkinger Certainty Preference