Utility, Risk, and Demand for Incomplete Insurance:
Lab Experiments with Guatemalan Cooperatives ∗Craig McIntosh†, Felix Povel‡, Elisabeth Sadoulet§
February 1, 2018

JEL Codes: G22, D81, Q13, O12
Keywords: Risk, Index Insurance, Utility Estimation

Abstract
We play a series of incentivized laboratory games with risk-exposed cooperativized
Guatemalan coffee farmers to understand the demand for index-based rainfall insurance. By eliciting willingness to pay in multiple scenarios featuring partial insurance,
we can estimate an explicit utility curve for every player and hence predict expectedutility demand under counterfactual scenarios. Using these estimates, we are able toprovide a precise money-metric decomposition of the extent to which the low observed
demand for index insurance under multi-peril risk exposure is driven by expected utility
theory, or by behavioral issues arising from a prospect-style utility structure. Exploiting the group structure of the cooperative, we investigate the possibility of using grouploss adjustment to pool the idiosyncratic risks that are not covered by an index. Our results suggest that consumers value probabilistic insurance using a prospect-style utility
function that is concave both in probabilities and in income, and that group insurance
mechanisms are unlikely to solve the issues of low demand that have bedeviled index
insurance markets.
∗

Thanks to Alain de Janvry for extensive discussions, to Eduardo Montoya for research assistance inthe estimation of the utility model, to Rita Motzigkeit for her help with fieldwork, and to Michael Carterand seminar participants at Universite d’Auvergne, PSE, and PACDEV for comments. Funding for thisproject was provided by the United States Agency for International Development. The contents are theresponsibility of the authors and do not necessarily reflect the views of USAID or the US Government†
Corresponding Author, University of California San Diego, ctmcintosh@ucsd.edu, 9500 Gilman Drive,
La Jolla CA, 92093-0519‡
Kreditanstalt fur Wiederaufbau (KfW), Frankfurt, Felix.Povel@kfw.de§
University of California Berkeley, esadoulet@berkeley.edu

1Introduction

Despite the central importance of risk preferences in economics and the potential for insurance to solve risk-driven poverty traps (Brick and Visser, 2015), our understanding of
the drivers of insurance demand remains incomplete. The welfare benefits of insurance appear to be particularly important in agriculture, where weather risk plays a dominant role
(Rosenzweig and Binswanger, 1992). New types of index insurance, in which payouts are
based on a pre-defined index (such as local rainfall), can provide insurance against aggregate shocks without creating moral hazard (Barnett and Mahul, 2007). From a perspective
motivated by the Townsend (1994) model of village-level risk pooling, these products appear
ideal in that they insure precisely the correlated shock that cannot be smoothed by local
risk pooling mechanisms. Yet, when introduced in the field these products have almost universally met with disappointing demand (Cole et al., 2013) and several studies have foundthat interlinking index insurance with credit products actually dampens the demand for
credit (Giné and Yang, 2009; Banerjee, Duflo, and Hornbeck, 2014). Low demand for theseapparently welfare-improving insurance contracts is puzzling, and so a deeper understandingof consumer risk preferences is critical.
A well established feature of index insurance products is the issue of ‘basis risk’, whicharises because the index is only imperfectly correlated with the risk it is meant to protect
against (Barnett, Barrett, and Skees, 2008). Wrapped up in this omnibus term are a numberof distinct components which may have very different effects on demand. Insurance may be
imperfect because it is partial, meaning that payouts fail to cover the full value of losses.
Imperfect insurance can also be probabilistic, meaning that there are important shocks thatare imperfectly correlated with the index. While response to the former type of risk has
typically been found to be easily modelled in an expected utility (EU) framework (Camerer,
2004; Cohen and Einav, 2007; Barseghyan et al., 2013), a large empirical literature hassuggested a prominent role for behavioral drivers in depressing demand for probabilistic
insurance (Kahneman and Tversky, 1979; Tversky and Kahneman, 1992; Wakker, Thaler,
and Tversky, 1997). In particular, numerous experimental studies have suggested that people
over-weight the likelihood of small probabilities, and thus have utility which is concave inprobabilities (Yaari, 1987; Doherty and Eeckhoudt, 1995). Finally, demand is also likely
to interact in complex ways with the nature of complementary institutions such as preexisting informal risk pooling (Mobarak and Rosenzweig, 2014). Understanding the extent
to which the workhorse expected utility model does or does not explain demand for thesenovel insurance products is a matter both of theoretical interest and of substantial policy
importance.

1

In this paper we construct a unique empirical environment that gives us a money-metricquantification of the extent to which insurance demand is driven by expected utility theory. We conducted a set of controlled lab-in-the-field games with a very risk-exposed group:
cooperative-based smallholder coffee farmers in Guatemala. During the course of an incentivized day-long exercise, we presented farmers with a way of visualizing the weather-driven
risks to their farms and recorded their willingness to pay (WTP) for an excess rainfall index insurance product across multiple scenarios.1 These tightly framed games provide astraightforward way of observing how individuals weigh different outcomes in decision making (Harrison and Ng, 2016).2 Truthful revelation of the WTP was incentivized with a
Becker-Degroot-Marschak mechanism, with the selection of one of the scenarios at the endof the day to determine the compensation that each participant received.
An initial set of scenarios measuring WTP for partial insurance are used to estimate autility curve for every player. We can then use these utility curves to predict what WTP
should be in alternate scenarios where the risk and payout structures are more complex. We
utilize this tool to examine two central issues in insurance demand. First, how does demandfor insurance respond when the risk environment is multi-peril? Second, how does demand
respond when the product is provided in a manner intended to induce group risk pooling?
In the benchmark partial insurance game, we present seven scenarios that vary theseverity and the variance of the loss in the insured states of nature. These scenarios effectively
measure the marginal utility of income in a shock state as it becomes more severe, andtherefore provide a straightforward window to the shape of the utility curve across states ofnature. We confirm other studies in finding a low overall demand for index insurance; only
12% of our sample were willing to pay a price above the actuarially fair price in our basescenario. We use a non-linear least squares optimization method to fit a two-parameter utility
function for each player on his stated WTP across these seven scenarios. The estimatedutility curves display an average coefficient of relative risk aversion of 5.8 and a modal utility
function that has very close to constant absolute risk aversion. Once we have a direct modelof utility curves, then we can predict an ‘EU-based’ WTP for an insurance in any otherrisk scenario, assuming that the standard mechanics of concave utility are the only source ofdemand for insurance. This dollar-denominated estimate of EU WTP from the benchmark
partial insurance game gives us a means to decompose the drivers of demand in alternate,
more complex risk scenarios.
1

All probabilities in our games are explicitly defined, meaning that we study risk but not uncertainty(Ellsberg, 1961).
2
Our environment is not informative as to other behavioral features such as ambiguity aversion (Fox andTversky, 1995; Bryan, 2013) or the failure to reduce compound lotteries (Segal, 1990; Elabed and Carter,2015).

2

The first application of our estimated WTP is to the probabilistic insurance game, inwhich we presented a set of scenarios varying the severity and probability of a shock that
occurs with no insurance payout. As predicted by a sizeable behavioral literature, this possibility of contract failure causes a substantial drop in WTP. When we decompose the demand
into the component predicted by expected utility maximization and the ‘behavioral’ residual,
we find that the behavioral dampening in WTP responds strongly both to the probability
and the magnitude of the uninsured shock. Adding a 1 in 21 chance of a small uninsured
loss should have caused a $.43 decrease in WTP under our expected utility estimation but
actually resulted in a decrease of $4.13, implying that almost 90% of the response to a small
uninsured risk is behavioral. Once uninsured shocks become larger or more likely, the EU
drivers of demand dominate and the behavioral component is small. Thus, neither the pureEU model nor the ‘Dual’ model that is linear in utility and non-linear in probabilities are
consistent with our results. Overall this group of Guatemalan coffee farmers appear to behave according to a prospect-style utility function that is concave both in probabilities andin wealth.
This depressive effect of small uncovered risks implies that insurance demand could be
improved if the product was interlinked with local risk-pooling institutions that can smoothsmaller shocks. An obvious candidate for this pairing is the type of informal risk pooling
networks that play a particularly important role in developing-country contexts (de Janvry,
Dequiedt, and Sadoulet, 2014). Given the informational advantages of peers in providing
mutual insurance (Arnott and Stiglitz, 1991), the economies of scale in marketing microfinancial services to groups (Hill, Hoddinott, and Kumar, 2013), and the success of otherinstitutional innovations such as microfinance at inducing mutual insurance (Feigenberg,
Field, and Pande, 2013), it appears attractive to design products that explicitly attempt
to trigger informal risk pooling so as to generate a complementary relationship with formal
insurance (Janssens and Kramer, 2016; Berg et al., 2017). However, it is far from clearthat a formal insurance product attempting to leveraging local group risk pooling is in fact
desirable to consumers. Relying on a group to conduct loss adjustment requires trust in thefairness and transparency of the group (Cassar, Crowley, and Wydick, 2007), and is typicallyenforceable only by a dynamic punishment mechanism that may make cooperation fragile(Coate and Ravallion, 1993; Ligon, Thomas, and Worrall, 2002).3
In the final section of the paper we take our EU-based WTP estimates to the analysis
of demand for a group insurance product. We introduce a product that makes payouts
3

A long literature has suggested that in the absence of a formal group dimension to insurance, individual insurance may have a tendency to crowd out informal risk pooling (this has been demonstrated boththeoretically (Attanasio and Rıos-Rull, 2000) as well as shown in empirical work from India (Mobarak andRosenzweig, 2014), China (Lin, Liu, and Meng, 2014), and Ethiopia (Dercon et al., 2014))

3

to the cooperative, thereby providing the group with a chance to loss-adjust the remaining
idiosyncratic losses in the payout state. Because this mechanism addresses only the extent
to which insurance is partial (not probabilistic), it can straightforwardly be compared to thegame on which the WTP model was estimated. Our core question is the extent to which the
WTP for group insurance changes as the degree of loss adjustment conducted by the groupincreases. Because we have already seen the response to risk protection in the context ofindividual insurance, we can use our WTP estimates to cleanly identify the pure preference
for the group risk pooling mechanism. We then examine the drivers of the actual willingness
to pool risk on the part of the group, examining the extent to which issues such as mistrustand dynamic inconsistency may limit risk sharing within the cooperative.
The analysis of group insurance is confirmatory in terms of basic mechanisms, but discouraging in terms of the commercial viability of group insurance as a way to solve basisrisk. We find that individuals recognize and are willing to pay for the ability of the group topool idiosyncratic risk. On the other hand, they only expect their groups to conduct about
a quarter of the degree of risk sharing possible, and there is a secular dislike of the groupmechanism that roughly compensates in terms of WTP for the degree of pooling they expect
to occur. While group insurance is promising in that it holds out some ability to protect
against small uncovered risk, its implementation face many problems, including the threats
posed by dynamic inconsistency and group heterogeneity.
We contribute to the literature on behavior under uncertainty by providing a novel wayof estimating individual-specific utility curves and applying this technique to index insurance
demand in a context of multiperil risks and to group insurance. We find insurance demand
to be low overall, and even in the most straightforward case of partial insurance our results
suggest that a commercial product may not be viable in this context. Introducing evena tiny uninsurable risk leads to a large drop in demand that appears to be driven by theoverweighting of small probabilities posited by prospect-style utility. While group insurance
might seem to be an attractive way of dealing with these small uncovered risks, in our context
the WTP for a group index insurance product is lower, all things equal, and participants are
not optimistic that groups will be successful in conducting risk pooling to any substantial
degree. Seen in a positive light, the large behavioral response to small uncovered risks implies
that apparently minor improvements in the ability of insurance indexes to capture loss events
could lead to large improvements in demand.
The remainder of the paper is organized as follows: Section 2 provides the backgroundand setting for the games, and a detailed description of the exercise. Section 3 uses the partial
insurance game to estimate the best-fit utility function for the data, a control structure thatis then used throughout the paper. Section 4 provides results on the probabilistic insurance
4

game, Section 5 on the group insurance game, and Section 6 concludes.

2

Setting and Game Design

In early 2011 we conducted a cooperative survey of the coffee sector in Guatemala. That
survey attempted a census of every registered first-tier coffee cooperative in the country,
and included data on 120 cooperatives and a sample of their members. Coffee is by far themost important export sector in Guatemala, but yield in the coffee sector is highly variablewith excess rainfall and hurricanes posing the primary source of weather risk exposure.4
For the exercise presented here, we began from this census and then selected from it the
71 cooperatives that reported being vulnerable to excess rainfall risk (the product that thisproject is intended to pilot).
With this group of 71 flood-exposed cooperatives, we conducted a set of lab-in-thefield games to understand the nature of index insurance demand. For each of the selected
cooperatives we attempted to draw in 10 individual members to participate (the actual
number that attended varies between 4 and 13, with 10 as the modal number). Invitations
to attend were sent to a randomly sampled group of cooperative members, but if on the dayof the exercise we did not have 10 members present then we filled in the remaining playerswith any available cooperative members. Comparison of the game participants to the fullcooperative sample from our prior survey shows groups that are well-balanced on basic
demographics, but the game participants are more asset-rich than the average cooperative
member.5 Intensity of coffee production is similar across the two groups. This analysis
suggests that our experimental sample is broadly representative of cooperative membership.

2.1

ProtocolOur experiment consisted of a day of different games conducted with each cooperative,
typically taking place in the cooperative offices. The survey team that ran the games wascomprised of a presenter who ran the sessions and read the scripts, an enumerator who
would sit with the subjects and help them fill in their sheets if they required assistance (25%of the respondents reported never having been to school), and two additional assistants. The
morning was dedicated to introduction and training. The afternoon included an explanation
4

Work by Said, Afzal, and Turner (2015) suggests that risk-exposed groups may be more sensitive to risk
than those who are less exposed.
5
Appendix Table A.2. Given that WTP for insurance is typically found to correlate positively withwealth (Hill, Hoddinott, and Kumar, 2013), our average WTP may be somewhat overestimated relative tothe average cooperative member.

5

of how participants would be compensated as well as the core set of 32 scenarios organized
into three games: on partial insurance, probabilistic insurance, and group insurance demand.
WTP was recorded for each player for every one of the scenarios throughout the day. Finally,
the payments to participants were made for one randomly selected exercise. Participants wereseated apart from each other and not allowed to communicate during the games. See on line
Appendix E for the full set of scripts used during the day’s exercise.
Upon arriving, subjects filled an intake survey asking a set of typical questions abouthousehold composition, wealth, education, risk exposure of the farm, as well as a set of
behavioral questions focusing on risk aversion, ambiguity aversion, discounting, and present
bias. They received 10 Quetzales (Q) for their participation.6
We began the presentation by introducing the principles of an excess rainfall index insurance product. A schematic showing the distribution of historical rainfall events over time wasused to explain the process through which index insurance pays out based on the local rainfall station observation.7 The scripts for this training emphasized the fact that the premiumand payout are uniform within a village despite the fact that losses may be heterogenous,
and are based only on the rainfall totals measured at the nearest monitoring station. We
then introduced the idea of group insurance, whereby participating group members receive
the payout collectively and decide to split the payouts however they want. It was made clearthat the benefit of this arrangement was the ability to share the unequal losses while theproblem is that this process of allocation may be contentious.
After this general introduction, farmers were introduced to the key visualization tool thatwas used throughout the day to represent the frequency and severity of shocks that mightoccur, and whether the shocks would be covered by the insurance. We arrived at this tool
after extensive field testing as the most straightforward way of presenting a visualization ofagricultural income in the different states of nature (no loss, drought loss, or excess rainfall
losses of different amounts) and the probability of each state, relative to the income in stateof normal rainfall (Q10,000). We refer to each of these visualizations as a ‘scenario’, andwe group scenarios together into ‘games’. Figure 1a displays an example of a scenario in
the partial insurance game. There are five possible states of nature: the full income undernormal rainfall is realized with a 17 out of 21 probability, a small uninsurable shock (Q1,000),
and three possible insurable shocks (Q3,000, Q5,000, or Q7,000). For each state we explain
the income the farmer would realize if insured, and if uninsured. The monetary amounts
involved in the scenarios were all framed to be consistent with the real profits and risks faced
6

The exchange rate in 2012 was Q6.30= US$1
The index is based on cumulative rainfall over the fruiting and flowering period for coffee as measured
at the nearest government-administered rainfall station.
7

6

by typical smallholder coffee farmers in the Guatemalan context. All scenarios feature an
excess rainfall index insurance product paying out a given amount (Q1,400) in case of excess
rainfall losses, which always occurred with a 1 in 7 probability. The actuarially fair value ofthe insurance is therefore constant at Q200 across scenarios. Farmers were asked to record
their WTP, i.e. the maximum price at which they would accept to buy the insurance, usinga grid with price increments of Q20, circling the number that most closely approximates
their WTP or writing it in if the number lies outside the range of values provided.
To incentivize truthful revelation of WTP, payouts were based on players’ purchase decisions. The first time participants were shown this visualization, we conducted a trial runof how their WTP would be linked to their purchase decision. Each farmer having recorded
his WTP, the presenter announced a price for the insurance (without disclosure of how it
was chosen for this part of the training), which defined who was insured. A random weather
event was drawn and each participant drew an associated loss from a deck of cards. Eachparticipant could then complete his form and figure out his net income, and comparison
was drawn between those that did and did not purchase the insurance. The exercise wasrepeated with different possible weather cards. These explanations were followed by a shortquiz, with four questions relative to the payout in different cases of rainfall observations
and losses, and two questions on group insurance.8 Results on the basic concept of index
insurance were good, with 59% of subjects having all four answers correct and 84% having
at least three correct. On the group insurance 43% had both answers correct and 86% had
at least one correct answer.
Subjects were then notified that for the remainder of the day’s games, we would record
their WTP for each scenario, and then at the end of the day would randomly choose oneof the day’s scenarios to be the one on which payouts would be made. For this scenario,
we would randomly draw a price and a weather shock, and proceed as just explained. This
framed amount of earnings for the season would then converted to a real payment for the
day equal to 0.7% of the framed financial amount. As an example, an individual who would
8

The questions were as follows: (i) Imagine that you have bought an insurance against excess rainfall.
The meteorological station does not register excess rainfall. Yet, you lost 25% of your harvest due to rain on
your plot. Will you receive a payout from the insurance? (ii) Imagine that two coffee producers, Raul andLucas, purchased the insurance against excess rainfall. The station registers excess rainfall. Raul lost Q2,000
and Lucas lost Q8,000 due to rain. Do you think that Raul will receive more than Lucas, less than Lucas,
or the same as Lucas? (iii) Imagine again that Raul and Lucas have purchased the insurance. The station
does not register excess rainfall. Raul did not loose any income, but Lucas lost Q3,000. How much will Raul
receive: Q0 or Q1,400? (iv) How much will Lucas receive: Q0 or Q1,400? (v) Imagine the company offers agroup insurance. What would be the price each individual would pay relative to the individual insurance:
more, less or the same? (vi) Imagine that you are member of a group of 10 members that purchased thegroup insurance. In case of excess rainfall, the group will receive Q14,000. If there is excess rainfall, howmuch would you receive: Q0, Q1,400, or ‘it depends on the decision of the group’ ?

7have lost half of a Q10,000 harvest due to excess rainfall in the selected scenario would be
paid .007*5,000=Q35 for the day (in addition to the participation payment) if WTP did
not exceed the premium price, and .007*(5,000+payout-premium) if WTP did exceed thepremium price. The maximum payment they could receive would be Q70, if there was nobad weather shock and they had not purchased the insurance.
The heart of the day’s exercises was a sequence of three games, each one made up ofa series of scenarios.9 The first game was a set of partial insurance scenarios, where wevary the severity and variance of the shocks occurring in the insured state (e.g., variation
around the scenario in Figure 1a). These scenarios are used to estimate individual-levelutility curves and hence to back out WTP for the other games. The second game presented
a set of probabilistic insurance scenarios, in which we introduced a drought risk that hurt
income but was not covered by the excess rainfall insurance, and we then vary the severity
and likelihood of this drought shock (as in Figure 1b). The third game presented a set ofgroup insurance scenarios (Figures 1c), where the payout was made at the group level andthe cooperative could then choose to conduct some loss adjustment to smooth idiosyncratic
variation.
Our experiment attempted to probe complex and unfamiliar issues in the course of asingle day. Because of this, we decided to design a protocol that is more heavy-handed thanis typical in laboratory experiments (the scripts for the exercise are included in their entirety
in the online Appendix E). Each scenario was prefaced by 3-4 sentences that present how
it differs from the previous scenario, and an explanation that points to a trade-off, given
both an argument while the insurance is valuable (or more valuable than in the previous
scenario), and one argument while it is not valuable (or less valuable than in the previous
scenario). All introductions are structured with ‘On the one hand ... On the other hand’.
In retrospect we feel it may be reasonable to question the balance of the presentation of the
scenarios in two out of the 32 cases presented (I2 and I8), one of which is given in the footnote
below, but overall we made every effort to ensure that the presentation of the changes acrossscenarios was even-handed.10 The objective was to help the participants in their decision
process without introducing bias.
We report in Appendix C the analysis of three features of the games designed to test
the robustness of our results to study effects that might threaten internal validity. One is9

The scenarios will be described in detail as we proceed to analyze them, and a summary table of thestates of nature presented in each scenario is given in Appendix Table A.1
10
The description for I2 reads: ”On the one hand, the insurance continues to pay the standard compensation of Q1,400, even though you suffer greater losses than you did previously in the face of excess rainfall. On
the other hand, the payout from the insurance is more useful in this scenario than the one before, because
it is more difficult to overcome your financial difficulties in years of excess rainfall. Comparing this scenario
to the previous one, what is the maximum price you would be willing to pay to purchase this insurance?”8

that values on the data entry form were randomized to lie between Q40 and Q320 or Q80
and Q360 to test for bracketing effects. Second, we randomized the order of the games andsub-sets of scenarios to the maximum extent possible. And third, we tested for the framing
effect whereby all experiments are presented with monetary values that correspond to coffee
production experiences, but payment at stakes are an order of magnitude different.

2.2

Willingness to Pay

In all scenarios, there are three mutually exclusive states of nature: normal rainfall with noloss, an exogenous set of (excess) rainfall states s ∈ R covered by the insurance, and a set ofstates s ∈ D in which a (heavy rainfall or drought) shock occurs and the index does not trigger, each of which occurs with a given probability.11 Referring to Figure 1, panel a representsa ‘partial’ insurance scenario in which all severe shocks are at least partially covered by the
insurance. In panel b, this ‘probabilistic’ insurance scenario includes a potential insurable
loss of Q5,000 with probability 1/7 due to excess rainfall, a potential uninsurable drought
loss of Q8,000 with probability 1/7, and either normal or heavy rainfall with probability 5/7.
We separately denote the probability of states in which the insurance product will trigger as
πs , and states in which a shock occurs but the insurance does not trigger as ωs . Income isdenoted by K when there is no loss, Rs in state s ∈ R, and Ds in state s ∈ D. An individual
choosing insurance must pay the premium in any state, and if insurance is purchased andthe insured states occur then a payout is received. If c is the cost of insurance and P is thepayout, the payoff in state s ∈ R is Rs if uninsured and Rs − c + P if insured. For the set ofstates s ∈ D payoffs are Ds if uninsured and Ds − c if insured. The state in which no shockPP
occurs and no payout occurs happens with frequency 1 − s∈R πs − s∈D ωs and induces
payoff K if uninsured and K − c if insured.12
Without insurance, an expected utility maximizer will have the following welfare:
EU0 =

X

πs u(Rs ) +s∈RXωs u(Ds ) + (1 −

X

s∈D

s∈R

X

ωs u(Ds − c) + (1 −

πs −

X

ωs )u(K).

(1)

X

(2)

s∈D

With insurance, expected utility is:
EUI =

X
s∈R

πs u(Rs + P − c) +

s∈D

X
s∈R

πs −

ωs )u(K − c).

s∈D

The WTP is the premium payment c that equalizes expected utility across these two options.
1112

The structure of the scenarios is represented in Appendix Figure A.1.
For simplicity, we ignore in this formalization the small loss of $1,000 that may occur with heavy rainfall.

9

While the index insurance literature has typically referred to all variation in income thatis not covered by the index as ‘basis risk’, there are sharply contrasting theoretical predictions surrounding increases in uncovered risk in insured states versus risk in uninsured
states. As the severity of shocks in insured states increases (holding the payout constant), expected utility theory predicts that insurance will become more valuable because its expectedmarginal utility in the insured states rises. Thus, while the insurance product appears worsein the sense that it covers a smaller fraction of the risk, it should in fact yield a higher WTP.
The experimental literature has typically found that demand for partial insurance conforms
relatively well to expected utility theory (Wakker, Thaler, and Tversky, 1997), and hence we
use the partial insurance game to estimate individual-specific utility curves.
Since the other games effectively represent a relabeling and a reweighting of the samestate space used to estimate the utility curves, we can predict what individuals should be
willing to pay in any scenario of the other games if the same function drove risk preferences.
The differences between this EU-predicted WTP and the actual, observed WTP provides
a very clean money-metric measurement of the extent to which demand in more complex
risk environments is ‘behavioral’. Specifically, we can also contrast the expected utility
environment (in which probabilities enter linearly), with prospect-style utility (Kahneman
and Tversky, 1979; Tversky and Kahneman, 1992). In that environment we replace theobjective probabilities πs with decision weights Ω(πs ), which have been found empiricallyto over-emphasize small probabilities and to underweight large probabilities.13 We confirm
that a non-linear weighting of probabilities in our case results in a dramatic over-reaction
to small multi-peril risks, and are able to characterize the magnitude of this response withunusual clarity.
When we turn to group insurance demand, the estimation of expected utility WTP again
provides us with a benchmark that lets us decompose the various candidate explanations
for the demand responses to the collective nature of the group insurance product. We now
discuss in detail how the individual-specific utility curves are estimated.

3

Expected Utility and Demand for Partial Insurance

To estimate individual utility curves, we begin from the seven individual scenarios of thepartial insurance game, which vary the extent to which the insurance fully covers damages.
13

We do not have the ability to test standard versus cumulative prospect theory, and hence do not emphasize the difference between these two theories in our presentation Two other benchmark cases that we will
discuss are the ‘Dual’ model of Yaari (1987), in which the weights Ω are non-linear but the utility functionu(.) is linear, and the rank dependent expected utility theory of Quiggin (1982), in which only unlikely
outcomes that result in extreme changes in utility are overweighted.

10Their structure is similar to that of I6 represented in Figure 1a. Each of the scenario presents
an environment with five possible (mutually exclusive) states of nature: three states of
insurable (excess rainfall) risk with equal probability of occurrence π = 1/21 and incomeRs equal to R, R − σ, and R + σ, respectively, one state with uninsured (heavy rainfall)shock with probability ω = 1/21 and income D = Q9,000, and one state without loss withprobability (1 − 3π − ω) and income K =Q10,000. In the first scenario I1, R = Q7,000
and σ =Q1,000, so that the insurable states correspond to incomes of Q8,000, Q7,000, andQ6,000. In scenarios I2 and I3, we increase the severity of insured shocks (R= Q5,000 andQ3,000, respectively) while keeping their distribution (σ =Q1,000) constant. In scenarios I4
to I7, we keep R = Q5,000 constant, and vary σ in multiple of Q1,000 from 0 to Q3,000.
Panel A of Table 1 reports these values.
Using these partial insurance scenarios, we measure how WTP changes with the severityof the shock in the insured state, and hence provide a simple metric of the desire to moveincome from good states to bad as the bad state gets worse or more frequent. Previous work
has suggested that partial insurance demand conforms relatively well to expected utility
theory (Wakker, Thaler, and Tversky, 1997),14 and so we also use the partial insurance
scenarios to estimate utility functions.

3.1

Evidence of risk aversion and prudence

We first model risk aversion and prudence in our experimental context, examining how thedemand for partial insurance responds to variation in risk. Under the expected utility model,
the WTP is solution of:
EU0 ≡

X

πu(Rs ) + ωu(D) + (1 − 3π − ω)u(K)

(3)

s

=

X

πu(Rs + P − wtp) + ωu(D − wtp) + (1 − 3π − ω)u(K − wtp) ≡ EUIs
14

The authors compare the WTP for three insurance contracts: A standard insurance with no deductible,
a 0.99 partial insurance (which pays 99% of any claim), and a 0.99 probabilistic insurance (which pays thefull claim 99% time). Under expected utility theory, the WTP for the partial and probabilistic insurance
should be approximately 99% of the WTP for the standard insurance. Yet, they find the median ratio of the
WTP for the probabilistic insurance to the standard insurance to be as low as 0.50, while it is 0.95 for thepartial insurance. This leads them to conclude that demand for partial insurance conforms relatively wellwith expected utility, but not the demand for probabilistic insurance.

11

Total differentiation of the solution equation gives:
1 X
dwtp
=
π [u0 (Rs + P − wtp) − u0 (Rs )]dR
EUI0 s

(4)

dwtp
1
=
π [−u0 (R − σ + P − wtp) + u0 (R + σ + P − wtp) + u0 (R − σ) − u0 (R + σ)]
dσ
EUI0
1
≈
π [u00 (R + P − wtp) − u00 (R)] 2σ
EUI0
The first expression confirms that demand falls with the severity of the shock when utility
is concave. From the second expression, dwtp
= 0 if u0 is linear (i.e., u00 is constant). But ifdσ
preferences exhibit prudence (u000 > 0), wtp increases with σ.
Panel A of Table 1 presents the average WTP across the partial insurance scenarios.
Column 1 shows that WTP increases as the severity of the shocks increases across scenarios
I1 to I3, indicating an overall risk aversion among all participants. WTP also increases as
the variance in losses increases across scenarios I4 to I7, suggesting the presence of an overall
prudence in preference. Hence the behavior of participants in the partial insurance game isconsistent with risk aversion and prudence under expected utility theory.
We now proceed to fit an EU demand model for each individual using these partial
insurance scenarios.

3.2

Estimating utility functions under EU

The objective of this section is to estimate a utility function for each player based on revealed
WTP for the incomplete insurance scheme in the seven partial insurance scenarios I1–I7.
This approach is in spirit similar to Currim and Sarin (1989) and Currim and Sarin (1992)
in which the authors calibrate individual behavioral models.
Preferences are represented by the following Power Risk Aversion utility function (Xie,
2000):y 1−β1(5)u(y; k, β) = − e−k 1−βkcharacterized by two parameters (k, β).
We simplify the expressions for EU given in (1) and (2) with a common notation for
all states of nature. Each scenario g presented to the players is characterized by a set ofprobabilities pgx for the states of nature with income x and payout Pxg that the insurance will
pay if the player is insured (this includes 0 for the uninsured shocks). In a given scenario,
the expected utility with and without insurance for an individual with preference parameters12(k, β) are:EU0g (k, β) ≡X

pgx u(x; k, β)x

EUIg (k, β, δ)≡Xpgx u(x + δPxg − c; k, β)xwhere δ ∈ [0, 1] is a trust parameter that the agent places on the insurance payout. The
addition of the parameter δ is prompted by the fact that observed WTP was in most cases
inferior to the actuarially fair price, which is not conceivable with a standard utility function.
Our utility estimates are thus identified from variation between scenarios, but not by theoverall average expected WTP. The willingness to pay is the solution
wtp(g, θ) = (c : EUIg − EU0g = 0)

(6)where θ = (k, β, δ) denotes the vector of parameters of the model.
Despite having only three parameters, this setup is quite flexible. Absolute risk aversion
ARA = β y1 + ky −β decreases with income for (β > 0 and k > −y β−1 ) or (β < 0 and k <−y β−1 ), and increases with income otherwise. It converges to the CRRA function u(y) =− k1 y −k with RRA = k + 1 when β → 1 , and is the CARA exponential utility u = − k1 e−ky
with absolute risk aversion k when β = 0. Absolute risk aversion is an increasing function
0000
000of k and a decreasing function of β, and so are prudence ( uu00 ) and temperance (− uu000 ).15
We proceed now with the estimation of a vector of parameters θ for each individual. We
assume that there is some additive measurement error on the willingness to pay, such thatthe observed willingness to pay by a given individual wtpg is:
wtpg = wtp(g, θ) + g

g = 1, . . . , 7(7)

We also assume the usual regularity conditions on the error g such that our estimatoris consistent and efficient. Let X(θ)G×3 denote the matrix with characteristic element∂wtp(g, θ)/∂θj , j = 1, 2, 3. For each individual, we use a non-linear least squares estimator:θb = arg min
θ∈Θ

G
X

(wtpg − wtp(g, θ))2

(8)

g=1

15

The use of a three-parameter utility function to fit seven WTP data points means that R-squared isvery high, and concerns about mis-specification are further ameliorated by the fact that we never makeout-of-sample predictions because the scenarios in which we predict WTP are conducted over the same state
space as those with which we estimate utility curves.

13implying that θ̂ must satisfy the first order conditions
T−2X(θ̂)wtp − wtp(g, θ̂) = 0

Equation (8) describes a typical non-linear least squares problem, except that in addition
to being nonlinear, the function wtp(g, θ) is only defined implicitly by equation (6). Thus,
the derivatives with respect to θ that define the moment equations, and that are critical toany gradient-based solution algorithm, require application of the implicit function theorem
at each trial value of θ.

3.3

Estimated preferences and predicted WTP

We start by estimating a unique utility function for all 674 players. Results for the parameters, with robust standard errors clustered at the individual level in parentheses, are reported
in Table 2, col. 1. The utility function exhibits risk aversion and prudence, with absoluterisk aversion only slightly decreasing over the range of values of income, from 0.80 to 0.73,
implying that relative risk aversion increases very steeply from 1.6 (for the worst income
equal to 20% of the normal income) to 7.3 when there is no negative shock to income.
We next proceed with the estimation of θ for each individual player. Since we rely on
a very small number of observations for each player (at most 7, and less for the 61 playersthat did not play all 7 scenarios), estimated parameters can take some extreme values.
We therefore report the median and the lowest and highest 5th percentile of the estimatedparameters in Table 2, col. 2-4. We see large variations in estimated parameters acrossindividuals, reflecting heterogeneity in preferences.16
The estimated utility functions are shown in Figure 2. Using these estimated parameters
we can compute for each individual predicted utility and all of its derivatives at any level ofincome, and hence average risk aversion and prudence. Among all participants 76% exhibit
prudence and 10% have an almost quadratic utility function.
b we can compute the predicted WTP, wbdFor each individual with parameter θ,tp(g 0 , θ)that the player ought to have for any scenario g 0 . As above, this is the solution to (6) for
00
that particular scenario characterized by pgx , Pxg . The process converged for 621 players forthe first 3 scenarios and 666 players for all other scenarios.
dSince measures of risk aversion and w
tp will be used as regressors in the analysis of theobserved WTP, we will need some measure of precision on these predicted values to correct
the standard errors in the estimations. This is done by implementing a wild bootstrap
16

The small number of observations imply that standard
are extremely high, and theP7 errors on parameters
2
quality of fit of the estimation, measured by SSR = g=1 (wtpg − wtp(g, θ)) , very good.

14

of the whole procedure using the 6-point distribution proposed by Webb (2013).17 With√√equal probability, the residual for each observation is multipled by ± 0.5, ±1, or ± 1.5.
For each replicate we then re-estimate the parameters, and in turn compute the predicted
b and measure of risk aversion. The wild bootstrap here assumes that errors aredw
tp(g 0 , θ)
independent across observations, but allows them to be heteroskedastic and non-normal.
Notice that because it is computationally intensive to repeat the gradient-based search foreach bootstrap replicate, the bootstrap parameter estimates rely on a grid search method.
The bootstrapped values will be directly used in the estimations that use risk aversion ordw
tp as regressors.

4

Demand for Probabilistic InsuranceWith these explicit utility functions in hand we now proceed to the analysis of WTP fora set of six probabilistic insurance scenarios.18 Their structure is similar to that of I13
represented in Figure 1b. Each of the scenario presents an environment with four possible(mutually exclusive) states of nature: a state with a mild uninsurable shock (with Q1,000
loss and probability 1/21), a dominant state of no shock with high probability, a state of
insurable (excess rainfall) shock with probability π = 1/7 and income R = Q5,000, i.e., 50%
of potential income K, and a state of uninsurable ‘drought’ shock. The six scenarios vary theprobability and intensity of this drought risk. They began with a framing of a mild drought
risk, one that was both unlikely to occur (ω = 1/21) and small (loss equal to Q2,000, or 20%
of potential income). The magnitude of the drought-induced loss was then increased acrossscenarios to 40% and 80% of potential income, and then three scenarios were played with theuninsured losses at these same levels but with the probability of this shock being elevated
to 1/7. Panel B of Table 1 reports these values and Figure 1b shows I13, the most extreme
case of both frequent and severe drought risk. Critically, when the uninsured shock rises toa loss of 80%, it will be the case that the purchase of index insurance will make outcomes in
the worst state of nature even worse.
Our goal is to decompose the demand for probabilistic insurance into an EU and a behavioral component, using the precise measure of what the WTP ‘should’ be if agents werestandard expected utility maximizers. This predicted dollar-value WTP under expected util17

With fewer than 10 observations, the 6-point distribution by Webb is recommended over the morecommon 2-point distribution (Cameron, Gelbach, and Miller, 2011).
18
In essence, all insurance that covers specific sources of risk is probabilistic. The labeling of the uninsured
risk as drought was purposefully chosen to highlight this sort of uninsured risk, rather than those unrelated
to weather, or to a risk of non-compliance by the insurance company, which would involve other issues besidethe existence of uninsured states of the world.

15

ity theory is computed for each participant using his/her own estimated vector of parameterθ̂, as described in section 3.3. The difference between this amount and the observed WTP
provides a monetary estimate of the extent to which decreases in demand for probabilistic
insurance are driven by behavioral concerns.

4.1

Comparing the demand for probabilistic and partial insuranceWith partial insurance, payout always occur in states of shocks and hence become evenmore valuable when the severity of the shock increases, as we have shown in section 3.1. In
contrast, when the risk is uninsured the demand for insurance decreases with the severityof the risk because the utility cost of paying premiums in the shock state goes up.19 We
verify these basic relationships in Table 3 by regressing WTP on the standard deviation ofresidual risk after insurance. In order to assess whether there is a behavioral aspect to thedemand for probabilistic insurance, we run the regression for both the observed WTP and
the WTP predicted with the EU model. Column 1 shows that the predicted WTP displays
the expected relationships; a small uninsurable risk leads to a small decrease in predicted
WTP, and more severe shocks in insurable states drives up WTP while more severe shocks in
uninsurable states drive it down. Column 2 shows that, as a result, predicted WTP falls by$3.59 when farmers face a mild drought risk, and by $18.80 when they face a risk so severe
as to make it possible that the worst state of nature is uninsured.
Columns 3 and 4 repeat the previous analysis but using the actual WTP observed acrossscenarios. While the signs of the responses are consistent, the magnitudes display quite adivergent pattern. Actual WTP proves to be very sensitive to small amounts of drought risk,
and then to display little additional sensitivity to the magnitude or likelihood of risk posed bydrought (column 4). This indicates that there is a secular dislike of probabilistic insurance
that manifests itself even when the actual probability of uninsurable risk is minimal. To
understand how actual and predicted WTP relate to each other, Column 5 runs a regression
explaining the former while including the latter as a control variable, and Column 6 uses thesimple difference between the two as dependent variable.
The patterns estimated in Table 3 are represented visually in Figure 3, reporting bothactual and predicted WTP as function of the residual variance in income after payouts would
have occurred. The ‘fitted’ curves are simple quadratic regressions relating the different
actual or predicted WTP for the partial or probabilistic insurance games, separately. The
clear story emerging from these two ways of analyzing the data is that there is a response to19

Since the insurance product is invariant across all scenarios, these two cases correspond to increasing an
uninsurable risk that is positively and negatively correlated with the insurable risk, respectively (Eeckhoudt,
Gollier, and Schlesinger, 1996; Gollier and Pratt, 1996).

16

small uninsurable risk that cannot be squared with our expected utility predictions, and ifanything the surprise in the response to very large uninsurable risk (scenario I13) is that theactual WTP displays less of a decrease than we might expect. Hence, we can conclude veryclearly that there is a behavioral dimension in demand that decreases as the probabilistic
nature of the insurance is magnified.
The literature on probabilistic insurance has compared the demand for insurance when
the payout is probabilistic with the standard case of full insurance (Camerer (2004). In
particular, Wakker, Thaler, and Tversky (1997) show that when the probability of contract
failure is small the WTP under EU should be roughly discounted by the probability of contract failure. We conduct a different but closely related exercise, amplifying the probabilityof an uninsurable loss (and thus shifting the underlying risk profile) while holding the insurance features fixed. We show in Appendix B that under EU the introduction of a small
uninsurable shock induces a reduction in WTP that is approximately proportional to theprobability ω of the shock, that is:[u0 (K) − u0 (K − wtp)] (K − D)
ω<0∆wtp '
πu0 (R − wtp + P ) + (1 − π)u0 (K − wtp)
We can refer again to Table 1 to observe how demand is affected by a small probability
risk. Scenarios I4, I8, and I11 only differ in the drought risk, with no drought in I4, anda small drought loss with probabilities 1/21 in I8 and 1/7 in I11. Column 2 shows thatpredicted WTP falls from its value in I4 by $0.43 in I8, and by $1.24 in I11. Change in
WTP is thus proportional to the probability of uninsured risk as expected from theory whenutility is concave in income and probabilities enter linearly in the EU model. Column 1
shows the actual changes; here by contrast there is a strong response to a very small increasein probability, and then a lower-than-proportional response to increasing the risk further.
WTP falls by $4.13, almost 10 times more than under EU, when the probability of drought
is set at 1/21, but the decrease in WTP only doubles to $8.50 when the probability ofdrought is tripled from here. Increasing the magnitude of loss in uninsured states while
holding probabilities constant leads to a further decrease in WTP for insurance, a fact thatis consistent with concave utility. Consequently, the decision criterion must be concave inincome, but non-linear and concave in probabilities over the state space studied here. This
result is directly inconsistent with the ‘dual’ theory of Yaari (1987), and also with the rank
dependent expected utility theory of Quiggin (1982), since the distortion to decision making(relative to EU) disappears as the magnitude of the low-probability shock increases. It isonly consistent with the prospect theory of Kahneman and Tversky (1979) and Tversky and
Kahneman (1992).
17

4.2

Explaining the behavioral aversion to probabilistic insurance

A major advantage of our cardinal, money-metric measure of the behavioral component of
insurance demand is that we can take this as an outcome and explain the difference between
the predicted and actual WTP in the mild drought scenarios using a set of individual- andfarm-level covariates. The core question we try to answer is the following: is this non-EU
component of demand driven by behavioral attributes of the individual, or does it relate toa real risk exposure in their farming activities that makes drought risk more salient?
To address this question, we bring to bear two sets of covariates. The first are behavioral
attributes of the individual, including risk aversion, ambiguity aversion, and an index oftrust. Ambiguity aversion was measured in the intake survey using four choices between an
urn with increasing known probability of winning and an urn with unknown probability ofwinning. The trust index was built from four questions asking about the extent to which
individuals trust their fellow cooperative members.20 On the other hand risk aversion was not
elicited with typical survey questions but, to be more consistent with this exercise, computedfrom the individual-specific utility function estimated as reported in section 3.3. To explain
actual risk exposure we rely on a set of survey questions as to what are the main risks facing
coffee output on subjects’ farms. We asked about excess rainfall, drought, strong wind, or
disease, and we characterize each risk as being relevant at all or being the dominant sourceof risk for each farmer.
Table 4 presents the results of this analysis. Column 1 shows the simple means of eachright-hand side variable. Column 2 uses only the behavioral attributes, and finds that all
three of these variables have very strong relationships with the behavioral aversion to probabilistic insurance in the direction that we would expect. The risk averse, for whom insurance
is more important overall, are less likely to see large drops in demand as a result of the small
drought risk. Similarly, those with a high trust index are less put off by the presence ofdrought risk and maintain demand. The ambiguity averse, on the other hand show muchlarger drops in demand when faced with the possibility of mild drought. This latter fact
is particularly relevant in that it suggests that the simple survey question eliciting ambiguity aversion does indeed capture relevant information in predicting economically relevant
parameters.21
20

The questions ask whether the cooperative members trust each other, whether the interest of all members are equally considered when decisions are made, whether rules are respected in decision making, andwhether decision making is transparent. For each of these questions, farmers could choose“Strongly disagree”,“Disagree”,“Agree”,“Strongly Agree”, which we coded 1 to 4. The index is the normalized sum of
the 4 scores.
21
To verify that the results are not simply driven by differential understanding of the game, we added
controls for the level of education and the result on the quiz of understanding of the rainfall insurance
administered to the farmers at the end of the training session. The results were essentially unaffected.

18

Columns 3-5 of Table 4 include the actual risk exposure of the farmers to test whether
these can explain the over-reaction to small drought risks. Not only is drought exposure
insignificant in the first two specifications, and not only does a joint F-test of all four measuresof risk exposure prove insignificant both for ‘some’ and for ‘main’ risk, but the point estimateson the behavioral parameters are almost completely unchanged. Even when we dummy out
each level of each risk we find the behavioral determinants of this over-reaction to be very
robust (column 5). Taken together, our results show very clearly that this over-response tosmall risks is driven by the behavioral attributes of the decision-maker and is not driven by
the actual exposure to risk.

4.3

Risk aversion and demand for insurance against severe risk

We now focus on the response to the ‘worst state’ drought risk. These are scenarios I10
and I13, where the Q8,000 loss suffered in case of drought is more severe than the Q5,000
loss that would be inflicted by excess rainfall, implying that the worst state of nature is notcovered by the insurance, and is even made worse by the fact the the premium has to be paidin this state. The literature on demand for index insurance has paid particular attention tothis specific type of contract non-performance as a candidate explanation for low demandfor index insurance. As shown by Clarke (2016), using an EU model, the possibility of theworst state being uninsured can introduce non-monotonicity into the relationship between
risk aversion and insurance demand. The drop in WTP for insurance that features this worst
possibility should be particularly pronounced among those with high risk aversion. Similarly,
the Maximin Expected Utility framework used by Gilboa and Schmeidler (1989) and Bryan(2013) evokes a pessimism in which decision-makers fixate on the worst thing that could
possibly happen in making insurance purchase decisions, another context in which the effectof these extreme tail risks would be accentuated. Having established that our subjects do
not behave according to EU theory in the context of a probabilistic insurance, we revisit thisrelationship between risk aversion and WTP in our game.
To investigate this, we use data from all the drought scenarios (I8 to I13) and I4, thepartial insurance scenario with the same insurable risk (but no drought), distinguishing
between the severe drought (I10 and I13) and mild drought for the other cases. We interact
dummies for mild drought and severe drought with the measure of risk aversion to study theextent to which WTP drops differentially with the risk of severe drought for the most risk
averse.
Consistent with the argument in Clarke (2016), Column 1 of Table 5 shows that while
mild drought risk leads to differentially higher EU-based predicted WTP among the more19

risk averse, this relationship flips over with the severe drought, leading to a substantial
and differentially lower demand WTP among the more risk averse. In sharp contrast tothis, Column 2 illustrates that actual WTP does not differentially decrease in the most
severe drought scenarios for the most risk averse (the point estimate is even positive but notsignificant), even though the premium must be paid in this state. Thus the non-monotonicity
in demand over risk aversion as the severity of uninsurable risk increases predicted in the
EU model is not observed in actual WTP.
In conclusion, while the overall aversion to insurance featuring large uninsurable risk islargely in line with expected utility theory (Table 3), the mechanism of high risk aversion
leading to large drops in WTP does not appear to be the operative one.

5

Demand for Group Insurance

The premise of insuring groups (rather than individuals) is that superior information heldby group members allows payouts to be adjusted to reflect the actual losses experienced.
Because the smoothing opportunity in group index insurance only occurs in the context ofa payout, we only model this scenario in our game and study the way in which the groupmechanism can make index insurance less partial. In principle this can permit superiorsmoothing, and index insurance for aggregate risk can be thought of as complementary togroup insurance for idiosyncratic risk (Dercon et al., 2014). Despite this potential, there areimportant factors that work against group insurance. The group negotiation process is notfrictionless, and thus distrust or social costs may make group negotiation an unattractive
way to provide smoothing. Even groups that have the capacity to pool risk may fail to do so,and the informality of the typical risk sharing contract means that issues of contract enforcement and dynamic consistency will be important. Groups may struggle to maintain pooling
if the members’ risk exposures are too dissimilar. We now present the results of several
experimental scenarios intended to isolate the relative importance of these mechanisms.
The group game presents risk scenarios that are similar to those of the partial insurance
scenarios I5 to I7, where excess rainfall experienced at the group level may lead to threepossible levels of idiosyncratic losses leading to income of R, R − σ and R + σ, where R =Q5,000 now represents the average income in the group. Take the example of G4 represented
in Figure 1.c, with σ = Q1,000: should there be excess rainfall, individuals within the samegroup may experience losses of Q4,000, Q5,000 or Q6,000. Hence at the individual level,
the risk profile is the same as the individual scenario I5. However, in the group game,should the group be insured, the group will receive an aggregate payout of Q1,400 times thenumber of insured members. This aggregate payout can then be either equally shared among20

members, or attributed according to experienced losses. In a first set of scenarios, the degreeof sharing is pre-specified. In scenario G4-a, there is no sharing and each individual receives
Q1,400. In scenario G4-b, there is partial sharing and individuals who lost less (more)
receive somewhat less (more) than Q1,400, and in scenario G4-c, there is full sharing andall individuals have after compensation the same average net loss of Q3,600. Similar groupscenarios with σ = Q2,000 (G5) and Q3,000 (G6) were also played. Notice that the ability
to loss adjust is capped by the size of the payout, so that ‘complete sharing’ is replaced by‘maximum possible degree of loss adjustment’ in G5-c and G6-c; when insurance is partial
then the ability to loss adjust is similarly incomplete.
The group insurance game is played individually. The subject is asked what would be
his WTP for such an insurance. The game does not require any coordination with the otherparticipants, although it was clearly framed as a potential group insurance for the membersof the cooperative to which they all belong, meaning that whatever trust or reservation they
have with regard to their cooperative could influence their decision in the game.
The concept of the group insurance was extensively presented in the training session,
where we facilitated a discussion in which we explicitly presented the potential for grouploss adjustment through unequal sharing of the group payout. A short review preceded thegroup game exercise.

5.1

The demand for group sharing and the role of trust

We begin our analysis of WTP with the results from these tightly framed scenarios in which
the within group loss adjustment was specified (scenarios G4-G6) The benchmark case inwhich no loss adjustment is conducted is exactly comparable to the individual scenarios I5-I7,
meaning that the difference in WTP comes from a ‘pure’ preference for the group modality
itself. We again use the individual utility curves estimated from the partial insurance gameto compute predicted WTP.
Column 1 of Table 6 shows the predicted WTP for group insurance under the threepotential levels of risk pooling, as compared to the baseline individual insurance scenario,
for the scenarios of low variance (I5 and G4, with σ = Q1,000). By construction, thepredicted WTP in the ‘no loss adjustment’ scenario is identical to the individual scenario.
The third row of Column 1 shows that the maximal possible risk pooling achievable by thegroup ought to increase WTP by $7.19. Column 2 shows the same estimation for actual
WTP, and provides three fundamental insights into the demand for group risk pooling. The
first row illustrates that when farmers are presented with a group index insurance product(G4-a) that is precisely comparable to an individual equivalent (I5), WTP is $5.21 lower.

21

This provides the pure preference for group insurance, demonstrating that all things equal
there is a dislike of the group modality and farmers would prefer to be insured individually.
We can also compare the changes in the WTP coefficients across the rows of Columns 1 and
2, and here we see that the increase in actual WTP for group insurance as loss adjustment
increases to its maximum is $6.07 (.86+5.21), while the predicted WTP increases by slightly
more than a dollar more than this. Hence, risk protection that arises from group loss
adjustment is slightly less attractive than risk protection that is provided by the insurancecompany. Finally, while the group becomes more attractive as its degree of loss adjustment
increases, the secular dislike of the group mechanism is sufficiently strong that farmers arebasically indifferent between even the maximally risk pooling group insurance mechanism
and individual insurance. Column 3 pools all scenarios with low, medium, and high variancesin risk, and shows that this result is very stable even when we increase the degree of variancein losses.
What is the origin of this dislike of group insurance? One obvious explanation is that
farmers simply do not understand the group game. To test this, we use the score that eachindividual obtained on two questions relative to group insurance in the quiz taken at the endof the training session. In Column 4 of Table 6, we interact this test score with a dummy forthe group scenarios. While individuals with better understanding of group insurance have ahigher (though not statistically significant) WTP, even those with the maximum test scoreof 2 have a reduction in WTP of $4.65 (highly significant with a standard error of 0.67).
The next possible interpretation is that farmers do not trust their groups. To test this, we
exploit our trust index (described in footnote 20). In Column 5 of Table 6, we interact thistrust index with a dummy for the group scenarios. While high-trust individuals do indeed
have significantly higher demand for group insurance, the magnitude of this effect is small(93 cents) and hence it would appear that distrust can account for at most about one fifth of
the secular dislike of the group mechanism. Column 6 shows that trust does not alter WTP
for the group modality as the level of environmental risk increases. Hence, while trust is notinconsequential, it does not appear to explain the magnitude of the preference for individual
insurance.

5.2

How much risk will groups actually choose to share?

Having understood how much the groups are willing to pay for loss adjustment, we undertooka number of additional experiments to try to unpack some of the most obvious threats
to successful group risk sharing, namely 1) how much loss adjustment they believe thegroup would in fact conduct, 2) the vulnerability of risk pooling arrangements to ex-post22renegotiation, and 3) the influence that heterogeneity within the group has on the ability topool risk. In other words, not how much loss adjustment they want, but now much do they
expect?
To measure the expected degree of loss adjustment, we presented participants with three
scenarios G1-G3, in which we asked WTP for a group insurance with exactly the same risk
context as G4-G6, but the degree of loss-adjustment left unstipulated. These scenarios wereplayed before any group scenario with stipulated sharing rules. Results are reported in Table
6. In column 7, we consider the scenarios with small variance in losses (I5, G1 and G4a-c
with σ = Q1,000). By comparing WTP in the G1 scenario to the G4 scenarios in which lossadjustment was stipulated, we can measure expectations over pooling in a very exact way.
The coefficient on this unstipulated scenario is -$3.62, relative to a coefficient of -$2.23 for agroup insurance with moderate pooling and of -$5.20 with no pooling. The implication is thatthe cooperative members expect that their groups would conduct a fraction of the possible
degree of loss adjustment of idiosyncratic risk (corresponding to approximately a quarter ofthe idiosyncratic risk). Column 8 extends the analysis to all three variance scenarios andarrives at very similar conclusions. Finally, we can ask whether a lack of group trust effects
the extent of pooling that the members expect from the group. This is accomplished inColumn 9 by interacting group trust with a dummy for the scenario in which the sharing
rule was not stipulated; here we see an insignificant effect suggesting that trust is not thedriver of expected loss adjustment.
A second issue with group risk pooling is that the contract is not formalized and hence
pooling will only occur if those who have the capacity to pay do not seek to re-negotiate thecontract after shocks have been realized. To try to simulate this possibility in a laboratory
context, we conducted a sequenced ‘group deliberation exercise’ described in more detailin Appendix D. We first asked players as individuals what degree of loss adjustment theywould prefer (1 = none, 2 = moderate, 3 = as much as possible) if they were obtaining
group insurance. We then asked them to discuss and decide upon this issue as a group, andrecorded the outcome. Finally, we attempted to mimic the incentive to renege on group risk
sharing by asking each individual to draw an actual rainfall shock (and thus a level of income)and to vote again on the group risk pooling decision. On average, the participants reportwanting ‘moderate’ risk sharing (50% of potential), both before and after the weather draw,
individually and in group.22 Yet, even in this contrived environment in which individuals
are ask to state their preference twice over a very short period of time and with only asmall sum of money at stake, we find evidence that the ex-post incentive incompatibilityof risk pooling will prove problematic. Individuals who draw large negative shocks pivot to
22

See Appendix Table D.1

23desire greater pooling, and those who draw small shocks desire less pooling. The magnitudeof the change in behavior provides some evidence for the extent to which the inability towriting binding contracts will pose a constraint on pooling agreements that must be ex-post
incentive compatible.
Finally, we examined the issue that heterogeneity in expected risk exposure introduces
a redistributive element into group risk pooling contracts, since certain individuals can be
expected to be systematically making larger claims on the group than others. Our groupheterogeneity analysis, presented in Appendix Table D.2, finds that this is indeed a concern.
Simply framing the group as made up of heterogeneous agents causes WTP to drop by$6.54, more than the overall drop from group relative to individual insurance. While WTPchanges in the expected direction depending on whether the farmer would on net be making
or receiving transfers through the group mechanism, the magnitudes we estimate suggestthat when pooling would induce transfers to other group members, WTP falls by only about
half as much as it would if the transfer were to the insurance company.
These results provide a mostly negative picture of the demand for group insurance. While
farmers do have a strong WTP for loss adjustment via the group mechanism and reportwanting to share idiosyncratic risk at 50% of potential, they only expect their groups to loss
adjust one quarter of the potential idiosyncratic variation. Given our evidence that both the
dynamic consistency of risk sharing and the heterogeneity of group members is a problem inpractice, the expectation that actual risk pooling will come in below the level desired may
be well justified.

6

Conclusion and Discussion

Using an artefactual field experiment, we investigate the demand for index insurance among
coffee farmers in Guatemala. Willingness to pay is in general lower than the actuarially fairrate, which is an initial piece of evidence that partial insurance products do not generate thekind of demand that we would expect from risk-averse agents if offered perfect insurance.
We use the lab context to decompose the potential reasons that insurance products may
meet with limited demand and to investigate one promising modality to stimulate demand:cooperative-level loss adjustment combined with index insurance to the group.
Our study provides several novel perspectives on how people respond to risk. First,
we can explicitly estimate utility functions from the demand for risk reduction that we
believe is well explained by EU theory. This permits us to harness the EU model to predict
WTP in a wide variety of counterfactual scenarios, and provides an unusually direct way of
decomposing insurance demand. We confirm the very strong role that uninsurable sources24

of risk play in undermining WTP, and find the drivers of this response to be complex. Whenthe magnitude of uninsurable losses is high, EU responds strongly to the risk and behavioral
explanations appear to play very little role in driving the drop in demand. In contrast, evenvery small and low-probability uninsurable risks have strong effects on WTP. In these cases
the EU model would predict only very modest shifts in WTP, and so we find that roughly
90% of the response to small uninsurable risk is behavioral. A prospect-style utility function
where the decision criterion is concave in both wealth and probabilities is consistent withthese results.
We verify the mechanisms underlying group insurance, but fail to provide much hope thatsuch products will prove commercially viable. Farmers understand the risk pooling benefitsof loss adjustment, and indeed they expect their cooperatives would provide about a quarterof the possible degree of risk pooling. Despite this, there is a secular dislike of the groupmechanisms, increasing in the degree of distrust of the cooperative, that makes even a fully
loss-adjusted group insurance product only just equal to individual insurance. Given the
expected degree of loss adjustment, the average individual would prefer individual insurance
to group. Hence, while we verify that the underlying mechanisms that make group insurance
potentially attractive are indeed at play, in the end in this context they are insufficient tocompensate for the overall dislike of the group mechanism.
Taken together, these results suggest that micro-insurance suppliers bear a substantial
burden in terms of creating desirable insurance products and marketing them effectively. Index insurers will struggle to generate demand in environments with multiple risks, and groupinsurance does not appear to be an attractive way to overcome this hurdle. While insurance
demand would rise if climate change caused more severe or more variable shocks in the dimension captured by the index, even a very small increase in risks not covered by the index
prove highly detrimental to demand. As uninsured shocks become larger and more likely behavioral explanations become less important, but only because even Expected Utility models
predict such large decreases in WTP in these scenarios. This study therefore reinforces theneed to push index insurance products to cover multi-peril risks, as can be achieved withmore sophisticated indexes, or to find ways of directly indemnifying agricultural losses.

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28

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29

Tables and Figures
Table 1: Summary Statistics on WTP by Game
Scenarios
Description
Panel A: Partial Insurance Game
I1
Partial, small shock
I2
Partial, medium shock
I3
Partial, large shock
I4
Partial, base (no variability)
I5
Partial, some variability
I6
Partial, med variability
I7
Partial, large variability

R (in Q)
7,000
5,000
3,000
5,000
5,000
5,000
5,000

σ (in Q)
1,000
1,000
1,000
0
1,000
2,000
3,000

Drought risk
ω
Panel B: Probabilistic Insurance GameD (in Q)I4
No drought
0
I8
Drought, rare & small
1/21
8,000
I9
Drought, rare & med
1/21
6,000
I10
Drought, rare & worst
1/21
2,000
I11
Drought, freq & small
1/7
8,000
I12
Drought, freq & med
1/7
6,000
I13
Drought, freq & worst
1/7
2,000
WTP are in US$. The exchange rate in 2012 was Q6.30= US$1

ActualWillingness to Pay
(1)
24.38
29.51
33.87
25.72
29.10
32.31
35.58

Predicted EU
Willingness to Pay
(2)
22.73
29.92
35.02
28.49
29.41
31.42
33.40

25.72
21.59
18.71
15.58
17.22
14.26
11.72

28.49
28.05
26.48
12.36
27.24
23.50
9.86

Table 2: Estimated Parameters of Utility Functions
Overall utility
Parameters
Coeff. (se)b
β0.042 (0.120)bk0.801 (0.194)bδ
0.156 (0.004)

Individual utilities
Median Lowest 5% Highest 5%
.720
-.959
3.64
.849
-4.03350.500.217.0737
1.034730

Table 3: Willingness to Pay in the Probabilistic Game
Dependent Variable:
WTP, US$Any Drought
Residual SD of Income
in Probabilistic Game
Residual SD of Income
in Partial Game

Predicted WTP(1)-7.71***(0.2240)

Actual WTP

(2)

(3)
-14.03***(0.4160)

(4)

(5)

(6)

-3.59***(0.11)-12.02***(0.38)-10.03***(0.35)-8.44***(0.34)-18.80***(0.60)-16.31***(0.45)-5.87***(0.62)

2.48***(0.58)-79.33***(2.6280)-31.10***(1.14)

62.32***(2.1190)55.41***(2.05)

Mild Drought
Drought Inducing the
Worst Possible State
Predicted WTP
Constant

Difference
Actual WTP- Predicted WTP

0.56***(0.03)
31.91***(0.17)

30.00***(0.12)

31.73***(0.23)

30.03***(0.19)

13.36***(0.79)

0.05(0.17)

Observations
8,523
8,523
8,547
8,547
8,517
8,517
R-squared
0.795
0.771
0.74
0.704
0.775
0.41
*** p<0.01, ** p<0.05, * p<0.1. Regressions are estimated using scenarios I1-I13. There are fixed effects at theindividual level, and standard errors are clustered at the individual level. In column (5), standard errors bootstrappedfrom 300 iterations in each of which risk aversion is re-calculated to account for the prediction error of the estimatedright-hand side variable.

31

Table 4: Deviation from EU Behavior when Facing Small Uninsured Risk

Behavioral Characteristics
Risk Aversion
Ambiguity Aversion
Trust Index

Perceived Risk Exposure
Excess Rainfall
Drought
Strong Wind
Crop Disease

Mean
(sd)
(1)

Reduction in WTP under Mild Drought Risk
Mean value of (Predicted WTP - Actual WTP) in US$
(2)
(3)
(4)
(5)

5.76
(0.80)
2.2(1.17)-0.01(1.00)-0.88***(0.36)
0.83***(0.30)-1.00***(0.30)-0.81**(0.37)
0.85***(0.30)-0.95***(0.31)-0.86**(0.37)
0.82***(0.30)-0.95***(0.30)

11.65***(2.47)(Some Risk)-0.10(1.15)-0.04(0.89)
1.52*(0.79)-0.94(0.71)
11.50***(2.68)(Main Risk)
0.41(1.90)
2.20(2.48)
3.66(2.91)
0.71(2.29)
11.02***(3.08)

644
0.047
1.737

644
0.041
0.782

(Some Risk)
0.91(0.29)
0.17(0.38)
0.24(0.43)
0.60(0.49)

Constant

Observations
644
R-squared
F_stat. for exposure to risk variables

644
0.036

-0.87**(0.38)
0.87***(0.32)-0.88***(0.31)

Dummy
variablesfor each
levelof eachrisk

16.14**(7.14)
644
0.064
1.089

*** p<0.01, ** p<0.05, * p<0.1. Risk aversion is the estimated average risk aversion based on the individualspecific utility model. Ambiguity aversion is an indicator from 1 to 5 based on the answers to choices between an
urn with increasing known probability of winning and an urn with unknown probability of winning. Trust index is anormalized index of four questions related to trust in the coop. The risk variables are constructed from responses tothe question: Does (Excess rainfall / Drought / Strong Wind / Diseases) represent a risk to your coffee production?
Potential answers are: the highest risk, 2nd highest risk, 3rd highest risk, 4th highest risk, no risk. In columns 1 and3, the risk variable is set to 0 if answer is no risk, 1 otherwise. In column 4 the risk is set to 1 if it is the highest
risk. In column 5, there is one variable per type of risk and rank. Standard errors on behavioral characteristics
bootstrapped from 300 iterations in each of which risk aversion is re-calculated to account for the prediction errorof the estimated right-hand side variable.

32

Table 5: Willingness to Pay and Risk Aversion
Dependent Variable:
Willingness to Pay, US$
Risk aversion * Mild Drought
Risk aversion * Severe Drought
Risk Aversion
Mild Drought
Severe Drought
Constant

Observations
R-squared

Predicted WTP

Actual WTP

(1)
0.15*
(0.10)-6.83***(0.93)
0.99(0.67)-3.01***(0.58)
21.95***(5.46)
22.80***(3.90)(2)
0.33(0.54)
0.7(0.61)
1.73**(0.70)-9.69***(3.20)-16.12***(3.61)
15.75***(3.85)

4662
0.319

4686
0.142

*** p<0.01, ** p<0.05, * p<0.1. Regressions are estimated using scenarios I4 and I8-I13.
Standard errors bootstrapped from 300 iterations in each of which risk aversion is re-calculated
to account for the prediction error of the estimated right-hand side variable.

33

Table 6: Willingness to Pay for Group Insurance
Dependent Variable:
Willingness to Pay, US$

Group with No Loss Adjustment
Group with Moderate Loss Adjustment
Group with Maximal Loss Adjustment

Amount of Loss Adjustment Conducted by Group
Predicted
WTP(1)
0(0.00)
2.11***(0.10)
7.19***(0.35)

ActualWTP(2)-5.21***(0.52)-2.25***(0.53)
0.86(0.56)

Medium Variance (σ=2,000) in Loss
High Variance (σ=3,000) in Loss

ActualWTP(3)-5.45***(0.47)-2.17***(0.48)
0.06(0.49)
2.85***(0.16)
5.84***(0.23)

Test Score * Group Game

Understanding ofGroup Insurance
ActualWTP(4)-6.95***(1.12)-3.68***(1.11)-1.45(1.12)
2.85***(0.16)
5.84***(0.23)
1.15(0.75)

Trust in Group * Group Game

Trust in Group

34

ActualWTP(5)-5.52***(0.47)-2.25***(0.49)-0.05(0.49)
2.81***(0.16)
5.91***(0.23)

ActualWTP(6)-5.52***(0.47)-2.25***(0.49)-0.05(0.49)
2.82***(0.16)
5.91***(0.23)

0.93*(0.51)

0.90*(0.52)
0.1(0.22)
0.02(0.32)

Trust * Group * Moderate Loss Adjustment
Trust * Group * Maximal Loss Adjustment
Sharing Rule Not Stipulated

Amount of Loss Adjustment Expected from Group
ActualWTP(7)-5.20***(0.50)-2.23***(0.51)
0.87(0.54)

ActualWTP(8)-5.20***(0.46)-2.15***(0.48)
0.07(0.48)
3.10***(0.16)
6.32***(0.24)

ActualWTP(9)-5.27***(0.46)-2.24***(0.48)-0.04(0.48)
3.07***(0.16)
6.38***(0.25)

0.93*(0.50)-3.62**(1.42)-2.89*(1.53)

29.62***(0.11)

29.27***(0.38)

29.50***(0.34)

29.56***(0.34)

29.43***(0.35)

29.43***(0.35)

29.22***(0.44)

29.21***(0.50)-2.92*(1.55)-0.72(1.16)
29.18***(0.52)

Observations
R-squared

2664
0.954

2646
0.744

6610
0.695

6594
0.695

6463
0.685

6463
0.685

3306
0.417

8590
0.392

8413
0.386

Scenarios used

I5, G4abc

I5, G4abc

I5-I7, G4-G6

I5-I7, G4-G6

I5-I7, G4-G6

I5-I7, G4-G6

I5, G1, G4abc

I5-I7, G1-G6

I5-I7, G1-G6

Trust * Group * Sharing Not Stipulated
Constant

low variance
low variance
all variances
all variances
all variances
all variances
low variance
all variances
all variances*** p<0.01, ** p<0.05, * p<0.1. Regressions include fixed effects at the individual level, and standard errors are clustered at the individual level.
Note: Scenarios G1, G2, and G3 present the same risk profiles as I5, I6, and I7, respectively, as do G4, G5, and G6. All scenarios have the same expected revenue R=Q5,000 but varying variance in loss
(σ=1,000 in I5, G1, and G4; σ=2,000 in I6, G2, and G5, σ=3,000 in I6, G3, and G6). In G1-G3, the rule of allocation of the group payout is not specified. In G4, G5, and G6, the rule of allocation is specified
with no loss adjustment (a), partial loss adjustment (b), or maximum loss adjustment (c) in the group. Columns 1-2 only use the scenarios with low variance in loss, columns 3-6 use all three levels of loss
variance. Columns 7-9 also include the three scenarios G1-G3 in which the rule of allocation is not specified. The test score variable is equal to the number of correct answers on the two questions ofunderstanding of group insurance.

Figure 1: Examples of Representations Used in Games
a. ‘Partial’ Game (I6)
uninsured

10,00010,000-1,000-premium - premiumb. ‘Probabilistic’ Game (I13)
uninsuredinsured

10,000- 3,000- premium+1,40010,000- 5,000- premium+1,400insured

10,00010,000-1,000- premium - premium

10,000- 7,000- premium+1,40010,000- 5,000- premium+1,40010,000- 8,000- premiumc. ‘Group’ Game (G4)
uninsured

10,000- premiuminsured

10,000-1,000- premium

10,000- 4,000- premium

10,000- 5,000- premium

10,000- 6,000- premium+ 1,400+ 1,400+ 1,400

no sharing

par;al sharing+ 1,120+ 1,400+ 1,680

par;al sharing

full sharing+ 400+ 1,400+ 2,400

full sharing

no sharing

Note: Columns represent different states of nature. On the left, the state of nature with no loss shows an
income of Q10,000, while the other columns represent states with losses ranging from Q1,000 to Q8,000.
Circles indicate frequencies, with 4 circles representing an event with probability of 1/21. The pictogram(rain gauge or sun) and the color of the circles indicate weather events: white circle represent normal rainfall,yellow circles heavy rainfall below the threshold for insurance payout, red circles excess rainfall covered by
the insurance, and grey circles incidence of drought. Panel a represents a scenario in which normal rainfall
occurs with probability 5/7, heavy rainfall with either no loss or Q1,000 loss with probability 1/7, andexcessive rainfall with losses of Q3,000, Q5,000, or Q7,000, each with probability of 1/21. In panel b, thescenario includes a potential loss of Q5,000 with probability 1/7 due to excess rainfall, a potential drought
loss of Q8,000 with probability 1/7, and either normal or heavy rainfall with probability 5/7. Panel c shows agroup game scenario, with alternative rules of risk sharing. If the individual is insured, payment of premium
occurs in all states of nature, and the payout of Q1,400 occurs in states of excess rainfall in individual games
and of the indicated amount for the group risk pooling scenarios.

35

0

.2

.4

Utility.6.8

1

Figure 2: Estimated Individual Utility Functions

1

2

3

4

5
6
Income (1000 Q)

7

8

9

10

Note: Utility curves are shown for the different deciles of their distribution, when individuals are ranked
according to their risk aversion at the mid-point of the income range. The thick curve is the estimatedaggregate utility curve.

Figure 3: Actual versus Estimated WTP in Partial and Probabilistic Insurance Games
35

I7
I3

WTP, US$
20
25

30

I6
I2
I4
I1
I8
I9

worst

I11

worst

15

I10
I12

10

I13

100

200

300
400
SD of Income if Insured in GameActual WTP, Partial
Predicted WTP, Partial
Fitted Actual, Partial
Fitted Predicted, Partial

36

500

Actual WTP, Probabilistic
Predicted WTP, Probabilistic
Fitted Actual, Probabilistic
Fitted Predicted, Probabilistic