WPS7235
Policy Research Working Paper 7235
Weather Insurance Savings Accounts
Daniel Stein
Jeremy Tobacman
Development Research Group
Impact Evaluation Team
April 2015
Policy Research Working Paper 7235
Abstract
Better insurance against rainfall risk could improve the A laboratory experiment is then used to elicit participants’
security of hundreds of millions of agricultural house- valuations of pure insurance, pure savings, and intermediate
holds around the world. However, customers have shown WISA types. Contrary to the standard model, within-sub-
little demand for stand-alone insurance products. This jects comparisons show that many participants prefer both
paper theoretically and experimentally analyzes an innova- pure insurance and pure savings to any interior mixture
tive financial product called a Weather Insurance Savings of the two, suggesting that market demand for a WISA is
Account (WISA), which combines savings and rainfall likely to be low. Additional experimental and observational
insurance. The paper uses a standard model of intertem- evidence distinguishes between several alternative expla-
poral insurance demand to study how customers’ demand nations. One possibility that survives the additional tests
for a WISA varies with the amount of insurance offered. is diminishing sensitivity to losses, as in prospect theory.
This paper is a product of the Impact Evaluation Team, Development Research Group. It is part of a larger effort by the
World Bank to provide open access to its research and make a contribution to development policy discussions around the
world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The authors may be
contacted at dstein@worldbank.org.
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development
issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the
names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those
of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and
its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent.
Produced by the Research Support Team
Weather Insurance Savings Accounts
Daniel Stein and Jeremy Tobacman∗
JEL Codes: G22 (Insurance), D81 (Decision-Making Under Uncertainty), D03 (Behavioral
Economics). Keywords: Index insurance, Prospect theory, WISA, Agricultural risk, Rainfall,
Microsavings, Microinsurance
∗ We would like to thank the Microinsurance Innovation Facility of the International Labour Orga-
nization for ﬁnancial support, and Shawn Cole and the Centre for Microﬁnance at IFMR for sharing
resources during the laboratory experiment. Risha Asokan and Maulik Chauhan provided excel-
lent research assistance. We are grateful to Tim Besley, Shawn Cole, Greg Fischer, Daniel Gottlieb,
Howard Kunreuther for valuable feedback. All remaining errors are our own. Contact details: Stein,
Development Economics Research Group, World Bank, dstein@worldbank.org; Tobacman, Depart-
ment of Business Economics and Public Policy, Wharton School at the University of Pennsylvania,
tobacman@wharton.upenn.edu.
1 Introduction
Although poor households can be especially vulnerable to risk, many are not well
served by formal insurance markets (Morduch, 1994, 2006). Rainfall risk is of spe-
cial concern since it is a covariate risk that cannot be well-insured informally. This
paper theoretically motivates and experimentally evaluates an innovation for ex-
panding protection against rainfall risk: linking rainfall index insurance with sav-
ings accounts.
Rainfall index insurance was developed to provide risk protection while also re-
maining affordable and accessible (Hess, 2004; Skees et al., 2001). A typical policy
covers drought risk during the early and middle phases of the growing season and
ﬂood risk during the late and harvest phases, underwritten using data from govern-
ment weather stations. Asymmetric information problems are avoided, and claims
adjustment is unnecessary, because payouts depend only on measured rainfall. De-
spite high theoretical beneﬁts (Cole et al., 2011, 2013), early trials have shown limited
demand at market premiums (Giné and Yang, 2009; Karlan et al., 2010a; Giné et al.,
2008; Cole et al., 2011, 2013).
By contrast, saving is ubiquitous among the poor. According to the World Bank’s
Global Financial Inclusion Database (Demirgüç-Kunt and Klapper, 2012), in 2010
over half of adults worldwide had an account at a formal ﬁnancial institution, in-
cluding 41% in developing economies and 24% even in countries with per capita
income of $1005 or less. Informal saving and durable goods investment bring total
savings participation rates higher still.
More pointedly, savings accounts with stochastic returns have shown promise in
a number of contexts. Guillén and Tschoegl (2002) report in detail on the supply-
and demand-side success of lottery-linked deposit accounts offered in Argentina,
and Kearney et al. (2011) argue that positive skew in prize-linked savings account
returns may effectively mobilize saving by low-income households.1
In this paper we explore whether bundling rainfall insurance with savings can
overcome speciﬁc and general barriers to effective risk management (Cole et al.,
1 See also Tufano et al. (2011) and Cole et al. (2014).
2
2013; Kunreuther et al., 2013).2 We introduce a Weather Insurance Savings Account
(WISA), which combines features of a savings account with rainfall index insurance
by indexing the return on savings to rainfall realizations. To ﬁx ideas, denote the in-
surance share of the WISA by γ ∈ [0, 1]. Then γ = 0 implies pure savings, with
a standard (non-rainfall-dependent) interest rate on savings, and γ = 1 implies
pure insurance. Intermediate values of γ would provide returns equal to a linearly
weighted average of the insurance payout and the regular interest earnings.3
We adapt an intertemporal insurance model to study demand for WISAs as a
function of γ. The most important prediction from the model is that under the
standard regularity conditions, demand as a function of γ cannot have a local min-
imim. Practically, this means that demand for a mixture of savings and insurance
(0 < γ < 1) must be higher than demand for pure insurance (γ = 1), pure savings
(γ = 0), or both. The model does not allow demand for a mixture of saving and in-
surance to be below demand of both pure products. We then present a laboratory ex-
periment that tests this key prediction. As the experiment uses real products offered
to real farmers, it also serves as a pilot for the WISA concept. Preferences for WISAs
with a range of γ’s were elicited using a Becker-DeGroot-Marschak (BDM) incentive
compatible mechanism. We also measured risk and time preferences. Contrary to
the model’s central prediction, our within-subject design reveals many participants
value both pure savings and pure insurance more highly than any interior mixture
of the two. This preference for pure products is stronger for those with higher risk
aversion.
We then evaluate three candidate alternatives to the standard model in an at-
tempt to account for participants’ puzzling preferences for both pure products over
interior mixtures of them. First, farmers may value mixtures less because they are
harder to understand than pure products. Experimentally, we manipulated whether
2 Bundling rainfall insurance with loans has previously been attempted. The Weather Based Crop
Insurance Scheme (WBCIS) of The Agriculture Insurance Company of India (AICI) saw substantial
rainfall index insurance coverage when it was a compulsory add-on to agricultural loans. Similarly,
the NGO Microensure provides weather insurance exclusively tied to loans. In experiments by Giné
and Yang (2009), requiring insurance as a loan add-on decreased demand for the loan.
3 If the nominal interest rate on normal savings accounts is i, then nominal losses are possible in a
i
WISA when γ > 1+ i.
3
the WISAs were described as a (complicated) combination of insurance and savings,
or (simply) an insurance policy with a guaranteed minimum payout. This manip-
ulation made no difference, casting doubt on lack of understanding as a driver of
the results. Second, we tested whether the results could be driven by farmers’ ex-
pectation that they would be less likely to collect small payouts, which could make
the savings/insurance mixtures less attractive. After the monsoon, we observed that
farmers with higher payouts were not more likely to collect their experimental earn-
ings than farmers with smaller payouts, making this explanation unlikely. Third, we
consider the possibility that participants’ choices over insurance are better explained
by behavioral models (Richter et al., 2014; Ganderton et al., 2000). Prospect theoretic
diminshing sensitivity (Kahneman and Tversky, 1979) implies consumers may not
value small insurance payouts, as they view them as an insigniﬁcant contribution
to a large loss. Therefore they would value savings/insurance mixtures less, as they
provide insigniﬁcant amounts of insurance coverage. Our results are consistent with
this extension to the baseline model.
The idea to combine insurance and savings is inspired by a few strands of litera-
ture, as well by observing various insurance markets. Slovic et al’s (1997) insight that
many people view insurance as a form of investment is supported by observations in
the life insurance market (Gottlieb, 2013). Johnson et al. (1993) show that participants
in a lab experiment prefer insurance with a rebate to that with a deductible. Anagol
et al. (2013) advance the hypothesis that since customers underappreciate the im-
portance of compounding returns, they may view insurance products that provide
savings as offering higher returns than they actually do. As market-priced insurance
generally gives a negative (risk-unadjusted) return on the invested premium, insur-
ance is clearly a poor investment, and consumers who ignore the state-dependence
of insurance payouts will tend to be dissatisﬁed with standard insurance products.
If consumers do view insurance as an investment, then it may make sense to design
insurance products that provide a positive payment in most states of the world.4
Consistent with results in the experimental literature, the private insurance mar-
ketplace provides some insurance products that guarantee a positive gross return
4 In lab settings, Connor (1996) ﬁnds evidence that consumers view insurance as an investment,
while Schoemaker and Kunreuther (1979) document the opposite.
4
on the premium through policies that offer “no-claim refunds.” With this type of
insurance, policy holders receive part (or all) of their premium refunded to them if
they do not make an insurance claim. One example common in developed countries
is “whole life insurance,” in which customers pay monthly premiums for life insur-
ance but receive a lump sum of all the nominal premiums paid if they are still alive
at a certain age. Customers pay extra for this service, and insurance companies earn
returns on loadings and investment of the held premiums.
If people choose “no-claim refunds” policies, they show a preference for using in-
surance as a vehicle for savings. Similarly, many studies support the importance of
the precautionary motive as a primary driver of saving (Karlan et al., 2010a; Rosen-
zweig, 2001; Fafchamps and Pender, 1997; Carroll and Samwick, 1997; Lusardi, 1998;
Guiso et al., 1992). Despite the frequent usage of savings to protect against shocks,
the rural poor are generally underinsured against large aggregate shocks such as
droughts (Townsend, 1994). In a survey of farmers participating in a rainfall insur-
ance pilot in Andhra Pradesh, 88% listed drought as the greatest risk they faced (Giné
et al., 2008). If people are saving primarily to protect against shocks yet these savings
are not enough to buffer against the most important risk they face, they might ﬁnd a
savings account with an insurance component especially attractive.
While to our knowledge there are no existing commercial products combining
weather insurance with savings accounts, savings accounts offering other types of
insurance do exist. In the 1990s the China Peoples’ Insurance Company (CPIC) of-
fered a savings account where customers received various types of insurance cover-
age instead of interest on savings (Morduch, 2006). Similarly, many banks and credit
unions in developed economies offer savings accounts that confer modest auto or
renters insurance as beneﬁts. Savings accounts that offer some insurance in lieu of
interest (such as the one offered by CPIC described above), and insurance policies of-
fering “no-claim refunds” can be seen as lying along a spectrum between insurance
and savings. The CPIC savings accounts are mostly savings, while the “no-claim
refunds” policies are mostly insurance. Seemingly there would be scope for these
mixtures in many insurance markets, including the nascent market for rainfall risk in
developing countries. This paper’s theory and experimental evidence suggest some
caution: diminishing sensitivity in the loss domain may mean consumers prefer to
5
segregate decisions about savings from decisions about insurance.
This paper will proceed as follows. Section 2 introduces a simple insurance de-
mand model to explain how people choose between savings and insurance, and
to motivate the WISA concept. Section 3 outlines the experimental procedure and
provides summary statistics about the participants. Section 4 presents the main ex-
perimental results, and Section 5 analyzes candidate explanations. We conclude in
Section 6.
2 Optimal WISA Theory
In this section we introduce a simple model to study consumer decision-making
about WISAs with varying insurance shares. In particular, to concentrate on the
consumer’s valuation of different WISA types, and to align with the experimen-
tal implementation discussed in the next section, we consider a scenario where a
consumer receives a gift of a ﬁxed amount of money invested in a WISA. We then
analyze how the certainty equivalent of this gift varies with the WISA’s insurance
share and with the consumer’s risk and time preferences. The model assumes plau-
sibly that the consumer has access to savings but not rainfall insurance outside of
the experiment.
2.1 Model Setup
We consider the two-period problem of a consumer who faces an uncertain negative
shock x˜ in the second period. A standard savings instrument is available, in which
an investment of s in the ﬁrst period pays gross return R > 1. WISA investments
consist of a mix of savings and insurance. The structure of the WISA is determined
by γ ∈ [0, 1], which parameterizes the share of the WISA allocated to insurance.
An investment of w in a WISA results in savings of (1 − γ) w (with the same gross
interest rate R as standard savings) and γw allocated to insurance. The insurance
is standard proportional coinsurance as in Schlesinger (2000), where the premium
is equal to the expected payout times 1 + λ, with λ > 0 the loading factor. This
6
means that for each rupee allocated to insurance, the customer receives a payout of
˜
x
˜)
(1+ λ ) E ( x
˜.
in the event of income shock x
Next, deﬁne the payout from the WISA as
˜
x
˜ , γ) = (1 − γ) wR + γw
g ( w, x (1)
˜)
(1 + λ ) E ( x
Full insurance is achieved when γw = (1 + λ) E ( x ˜ ). Since γ is bounded above by 1,
if w < (1 + λ) E ( x˜ ) there is no WISA which provides full insurance. As described
further below, our lab setup ﬁxes w to isolate the effects of varying γ.
We assume that the consumer is endowed in the ﬁrst period with income Y1 and
a WISA with insurance share γ and current face value of w. Savings s is chosen,
Y1 − s is consumed, and ﬁrst period utility is realized. In period 2, the shock arrives
and the consumer receives Y2 − x ˜ . Savings and the WISA yield Rs and g (w, x ˜ , γ ),
respectively. All resources are consumed, and second period utility is realized.
We assume that utility U is time-separable, with period utility u globally continu-
ous, thrice differentiable, and concave. Let the discount factor be β. Expected utility
over the two periods is:
EU = u (Y1 − s) + β E [u (Y2 − x ˜ , γ))]
˜ + Rs + g (w, x (2)
The customer chooses savings s to maximize this expression. Indirect expected util-
ity V , as a function of the endowments and the WISA payment function g (w, x˜ , γ ),
is deﬁned as:
max
˜ , γ)) =
V (Y1 , g (w, x {u (Y1 − s) + β E [u (Y2 − x ˜ , γ))]}
˜ + Rs + g (w, x (3)
s
Note that s is left unconstrained, but all predictions of the model are robust to credit
constraints where 0 ≤ s ≤ Y1 . Denote the optimal value of s as s∗ (γ) . For simplicity
deﬁne:
c1 = Y1 − s∗ (γ)
7
˜ + Rs∗ (γ) + g (w, x
c2 = Y2 − x ˜ , γ)
The following ﬁrst order condition, a standard Euler equation, holds for s∗ (γ):
dU
= −u (c1 ) + β RE u (c2 ) = 0 (4)
ds s=s∗ (γ)
We are interested in understanding how valuations of a WISA vary with γ. To do
this, we deﬁne the willingness to accept (WTA) A (γ), which makes a customer indif-
ferent between receiving a monetary payment of A (γ) or receiving an endowment
of a WISA with parameter γ:
˜ , γ))
V (Y1 + A (γ) , 0) = V (Y1 , g (w, x (5)
2.2 WISA Valuation
Differentiating Equation (5) with respect to γ and rearranging, while holding s con-
stant, we can write:
˜ ,γ )
dg(w,x
dA (γ) βE dγ u ( c2 ) βw 1 1
= = −R +
E u ( c2 ) ˜
Cov u (c2 ) , x
dγ u ( c1 ) 1+λ
u ( c1 ) ˜)
(1 + λ ) E ( x
(6)
1
This expression reveals two effects.5 Since 1+ λ < R, the ﬁrst term represents the
loss from substituting away from savings. The second term represents the gain from
dA(γ)
acquiring more insurance. Thus dγ is of ambiguous sign, and its sign can change
over the range of γ.
However, some properties of A (γ) can be determined. From the extreme value
theorem, we know there must be a γ∗ ∈ [0, 1] which maximizes A (γ). More in-
terestingly, we can show that A (γ) weakly decreases as one moves away from this
optimum γ: there are no other local maxima. This is most usefully formalized as
5 Continuity and differentiability of the utility function guarantee that dA(γ) is deﬁned everywhere,
dγ
and therefore A (γ) is globally continuous and differentiable.
8
follows.
Proposition 1. A (γ) has no interior local minima.
Proof. We will show this in two steps:
2
1. Prove that if dd
γ2
˜ , γ)) < 0 , A (γ) has no interior local minima.
V (Y1 , g (w, x
d2
2. Prove that d γ2
V ˜ , γ)) < 0.
(Y1 , g (w, x
d2
Step 1: Show that if d γ2
V ˜ , γ)) < 0, A (γ) has no interior local minima.
(Y1 , g (w, x
˜ , γ)) from Equation 5 and applying the enve-
Using the deﬁnition of V (Y1 , g (w, x
lope theorem:
˜ , γ))
dV (Y1 , g (w, x dV (Y1 + A (γ) , 0) dA (γ)
= = u (Y1 + A (γ) + s∗ (γ)) (7)
dγ dγ dγ
d2 V (Y1 , g (w, x
˜ , γ)) d2 A ( γ )
2
= 2
u (Y1 + A (γ) + s∗ (γ)) +
dγ dγ
dA (γ) dA (γ) ds∗ (γ)
+ u (Y1 + A (γ) + s∗ (γ)) (8)
dγ dγ dγ
In general, the sign of the second term in Equation 8 is unclear. Since A (γ) is
dA(γ)
continuous and differentiable, at any local extrema dγ = 0 and the second term
goes to zero. Also at any extrema we have,
d2 A ( γ ) d2 V (Y1 , g (w, x
˜ , γ)) 1
=
d γ2 d γ2 u (Y1 + A (γ) + s∗ (γ))
d 2 V (Y , g ( w , x
1 ˜ ,γ)) d2 A ( γ )
When d γ2
< 0, dγ2 will be less than zero because u > 0. This means
that any local extremum must be a maximum, and therefore no interior local mini-
mum can exist. Note that Equation 7 also shows that the γ which locally maximizes
˜ , γ)) will also locally maximize A (γ).
V (Y1 , g (w, x
d2
Step 2: Show that d γ2
V ˜ , γ)) < 0.
(Y1 , g (w, x
Using the envelope theorem,
9
d ˜ , γ)
dg (w, x
˜ , γ)) = β E
V (Y1 , g (w, x u ( c2 ) (9)
dγ dγ
2
d2 ˜ , γ)
dg (w, x ˜ , γ) ds∗ (γ)
dg (w, x
˜ , γ)) = β E
V (Y1 , g (w, x u (c2 ) + β RE u ( c2 )
d γ2 dγ dγ dγ
(10)
The ﬁrst term is negative, but the second is of ambiguous sign. In order to sign the
expression, we can leverage the ﬁrst order condition for s. Differentiating Equation
ds∗ (γ)
4, we get the following expression for dγ :
∂ dU ˜ ,γ )
dg(w,x
ds∗ (γ) ∂γ ds
β RE dγ u ( c2 )
=− =− (11)
dγ ∂ dU
∂s∗ (γ) ds
u (c1 ) + β R2 Eu (c2 )
ds∗ (γ)
Rearranging terms and multiplying both sides by dγ yields the following equa-
tion.
2 2
ds∗ (γ) ds∗ (γ) ds∗ (γ) dg (w, x
˜ , γ)
u ( c1 ) + β E R u ( c2 ) + β E R u ( c2 ) = 0
dγ dγ dγ dγ
As the above expression is equal to zero, we can add it to the right hand side of
Equation 10:
2
d2 ˜ , γ)
dg (w, x ˜ , γ) ds∗ (γ)
dg (w, x
˜ , γ)) = β E
V (Y1 , g (w, x u (c2 ) + β RE u ( c2 ) +
d γ2 dγ dγ dγ
2 2
ds∗ (γ) ds∗ (γ) ds∗ (γ) dg (w, x
˜ , γ)
u ( c1 ) + β E R u (c2 ) + β RE u ( c2 )
dγ dγ dγ dγ
Collecting and factoring the terms inside the expectation operator,
10
2 2
d2 ds∗ (γ) ˜ , γ)
dg (w, x ds∗ (γ)
˜ , γ)) =
V (Y1 , g (w, x u ( c1 ) + β E +R u ( c2 )
d γ2 dγ dγ dγ
(12)
Both terms are negative due to the concavity of the utility function. Therefore,
d2
d γ2
˜ , γ)) < 0. Combined with Step 1, this allows us to conclude that
V (Y1 , g (w, x
A (γ) cannot have any interior local minima.
The intuition for Proposition 1 resembles that of Mossin (1968)’s theorem. A risk
averse consumer would fully insure in the absence of loading but only partially in-
sure when the available insurance carries a load. Our theoretical and experimental
context involves positive loading, so only partial insurance is optimal.
2.3 Risk and Time Preferences
In this subsection we analyze A (γ) as a function of risk and time preferences. We
seek to solve a general model of demand without making overly restrictive assump-
tions on functional form; hence the model does not always yield unambiguous pre-
dictions. Therefore some of the discussion is reserved to the emprical section.
Classical insurance demand models (such as Schlesinger (2000)) predict insur-
ance demand increases in risk aversion. In this paper’s model, this is not necessar-
ily the case, as intertemporal smoothing also plays a role. To see how argmax
γ A (γ)
changes with risk aversion, consider the γ∗ and s∗ which jointly maximize expected
utility U .
argmax
γ∗ , s∗ ≡ u (c1 ) + β Eu (c2 ) s.t. 0 ≤ γ ≤ 1 (13)
γ, s
Assuming that the optimal γ is not at a boundary6 , the following ﬁrst order con-
ditions will hold.
∂U ˜ , γ∗ )
dg (w, x
= 0 = βE u ( c2 ) (14)
∂γ dγ
6 If argmax
γ∗ is at a boundary, a marginal change in risk or time preferences will not affect γ A ( γ ).
11
Deﬁne a function v (c) which is globally more risk averse (Pratt, 1964) than the
original utility function u (c). We would like to to understand how A (γ) will differ
for a person with utility function v (c) compared with someone with utility func-
tion u (c) . The following exposition closely follows the proof of Proposition 3 in
Schlesinger (2000), which shows (without permitting external savings) that an in-
crease in risk aversion increases insurance demand.
Pratt (1964) guarantees the existence of a function h such that v (c) = h (u (c)),
h > 0, and h < 0. Substituting h into the expected utility function, we have the
following expression, which represents a person with utility function v who has se-
lected γ∗ and s∗ (which are the optimal choices for someone with utility function
u):
U = h (u (c1 )) + β Eh (u (c2 )) (15)
For someone with utility function v, we must examine how the choice of γ∗ com-
pares to their optimal γ. Taking the derivative of Equation 15, utility changes as
follows when we increase γ above γ∗ :
dU ds∗ ˜ , γ∗ )
dg (w, x
= −h (u (c1 )) u (c1 ) + β RE h (u (c2 )) u (c2 ) + β E h (u (c2 )) u (c2 )
dγ γ=γ∗ dγ dγ
(16)
Since U is concave in γ (shown in Proposition 1), if dU
> 0 then
dγ γ∗
lies above
the new γ which maximizes U . This means that an increase in risk aversion would
increase argmax
γ A (γ). However, the sign of dUdγ γ=γ∗ is not immediately apparent.
Substituting u (c1 ) from Equation 14 and rearranging,
dU dg (w, x˜ , γ∗ ) ds∗
= βE h (u (c2 )) u (c2 ) + β RE u (c2 ) h (u (c2 )) − h (u (c1 ))
dγ γ=γ∗ dγ dγ
(17)
The ﬁrst term in this expression represents the beneﬁts of insurance in the second
period and is greater than zero (Schlesinger, 2000). The second term represents the
intertemporal smoothing effects of the WISA and is of ambiguous sign. As studied
12
in Kimball (1990), demand for precautionary savings is governed by the prudence of
the utility function, which depends on the third derivative. Therefore, argmax
γ A (γ)
will unambiguously increase with risk aversion only if prudence is also weakly de-
creasing. Under CRRA preferences, relative risk aversion and relative prudence are
positively correlated, meaning that under CRRA an increase in risk aversion has
ambiguous effects on argmax
γ A ( γ ).
The model also does not provide a clear indication of how argmaxγ A (γ) changes
with the discount factor. As β increases, consumers would show increasing appetite
for savings and insurance, but the net effect on argmax
γ A (γ) is ambiguous. The ex-
plicit insurance coverage through the WISA and self-insurance through (loading-
free) savings could be substitutes. The experimental analysis below measures com-
parative statics with respect to risk and time preferences, among other objectives, to
provide insight where the theory is not conclusive.
In summary, the main prediction of the theoretical model is that for any individ-
ual, demand for a mixture of savings and insurance (0 < γ < 1) should be greater
than demand for pure savings, pure insurance, or both. The model does not allow
demand for a mixture to be less than demand for both pure savings and both insur-
ance. However, the effect of risk and time preferences on the relative demand for
savings and insurance are ambiguous.
3 Experimental Design
3.1 Procedures
To learn more about savings and insurance decision-making, and to pilot WISA fea-
tures, we recruited 322 male farmers from rural areas surrounding Ahmedabad, In-
dia, for a laboratory experiment in April-May 2010. Sessions were conducted in the
Ahmedabad ofﬁce of the Centre for Microﬁnance. During the computer-based ses-
sions implemented using Qualtrics software, subjects participated in tasks designed
to elicit preferences about risk, time, savings, and insurance. The savings and insur-
ance products used in the exercise were real, and participants had the opportunity to
leave the session with rainfall insurance policies or vouchers for delayed payments
13
in the future. Since many of the participants had little prior experience using com-
puters, they were paired with enumerators, one per subject, who read the questions
out loud from the screen as necessary and helped enter subjects’ answers into the
computer. The lab contained 12 workstations, but the interviews were conducted
with no more than 4 subjects in the room at a time, in order to allow the participants
to spread out and not hear or be inﬂuenced by answers of others. Partitions between
computers blocked views of other participants’ screens, and participants were in-
structed not to speak to each other during the exercise. Summary statistics on the
experimental population are presented in Table 1.
The experimental tasks began with standard time preference elicitation, using
hypothetical smaller-sooner vs larger-later questions. Farmers were asked whether
they would prefer Rs 80 now or Rs 60, 80, 100, ..., 280, roughly six months later, when
insurance payouts were to be determined.78 Risk preferences were measured next,
with a real-money task. Subjects were asked to pick from a menu of lotteries where
the payout would be determined by a (virtual) coin ﬂip. At the end of the session
(after all other experimental tasks were complete) the coin ﬂip was performed, and
subjects were paid according to the result. The maximum payout from this risk pref-
erence task was Rs 200, corresponding to the wages of 2-3 days of agricultural labor
(Ministry of Labour and Employment 2010). Additional implementation details for
these and all experimental tasks, along with the complete text of the instructions, are
included in the Appendix.
The main part of the experiment came next. Using a Becker-DeGroot-Marschak
(BDM) incentive-compatible mechanism (Becker et al., 1964), we established each
2 1
participant’s WTA for each of four WISAs. The WISAs had γ’s of 1, 3 , 3 , 0 . These
products were described, respectively, as a large insurance policy with maximum
sum insured of Rs 1500; a medium insurance policy with maximum sum insured of
7 The exchange rate on May 1, 2010, was $1 = Rs. 44.
8 To be clear, throughout the paper we do not regard the intertemporal choices studied here as suf-
ﬁcient to identify the discount function. For example, marginal utility may fall unobservably from the
pre-planting time of the experimental sessions to the post-harvest period. Additionally, the discount
placed to money received in the future may reﬂect a lack of trust that the money will actually be
received. Instead, we seek to add some intertemporal insight into an important insurance decision-
making context.
14
Rs 1000 plus a guaranteed payment of Rs 60; a small insurance policy with maximum
sum insured of Rs 500 plus a guaranteed payment of Rs 120; and a guaranteed pay-
ment of Rs 180 after the monsoon.9 The market price of Rs 500 of insurance coverage
was Rs 66, making all the bundles of comparable monetary value.10
WTA values were elicited in two ways for the ﬁrst three γ’s (the ones containing
some insurance). Speciﬁcally, the subjects were also asked to give their WTA under
the circumstance that the money paid to give up the WISA would be paid on the day
of the experiment, or post-monsoon. These questions allowed us to obtain additional
(incentivized) evidence about time preferences. 11
Choices were recorded by asking subjects to enter bids for each into the computer,
by selecting from a multiple-choice menu of Rs 0 to Rs 250 in intervals of Rs 10, with
an additional option to choose a WTA of “Greater than 250.”12 Subjects were told
that after giving their minimum WTA for each of these 3x2+1 WISA WTA tasks,13 the
computer would randomly select one to be given to the subject, for which a random
“offer price” (ranging from 0-250) would be drawn. If the offer price was above
the bid for that γ, the participant would sell the WISA back to the experimenter
and instead receive the amount of the offer in cash at the end of the experimental
session or at the end of the monsoon. If the offer was less than the bid, the subject
9 As an example, in the case of γ = 1, the English version of the question text read as follows: “Con-
sider receiving a gift of one large rainfall insurance policy. This policy can ordinarily be purchased
for Rs 180 and pays out a maximum of Rs 1500 in the event of bad rainfall. What is the minimum
amount of immediate payment you would require to give up the insurance policy? Our offer to pur-
chase this policy from you will be between Rs 10 and Rs 250. You would receive the payment at
the end of today’s session.” All policies were underwritten by ICICI/Lombard, the largest private,
general insurance company in India.
10 We rounded down slightly (i) to make comparisons between bundles easier, and (ii) because the
small insured amount caused the loading on this policy to fall toward the upper end of loadings we
have observed in the market.
11 Withγ = 0, the WISA would be equivalent to the post-monsoon cash, so there was no need to
repeat the elicitation in that case.
12 In most of the analysis below, a stated WTA of “Greater than Rs 250” is conservatively coded as
Rs 260. When we run Tobit speciﬁcations that formally take into account the censoring, our results
are almost identical.
13 Allsubjects entered WTA’s in descending order, 1, 2 1
3 , 3 , 0 , alternating between present and fu-
ture payments. Subjects were permitted to go back and change earlier reported valuations, but did
not do so.
15
would keep the WISA. Subjects who retained their WISAs got coupons at the end
of the experiment that could be brought back to the lab at the end of the monsoon
season to claim the proceeds of the WISA. Since all farmers reported WTA’s for all
γ’s, within-subjects comparisons of valuations can be performed.
In addtion, between subjects, we manipulated an aspect of the way that the
WISAs were described. One-quarter of participants were randomly assigned to
the “Bundle Frame,” where the WISAs are described as an insurance policy plus
a voucher for guaranteed money. One-quarter were shown the “Insurance Frame,”
in which the WISAs were presented as an insurance policy with a minimum payout
equal to γ ∗ Rs(180). This frame was designed to mimic “no claim refund” insurance
policies. The rest of the participants were shown the “ICICI Bundle Frame,” which
is the same as the “Bundle Frame” except that it adds that the farmer could purchase
the policy directly from ICICI-Lombard. This frame was designed to test if associat-
ing products with a well-known brand would increase WTA.14 A given farmer faced
the same frame throughout the WISA WTA task, so analysis of framing effects will
be between-participant. The full text used for these framing manipulations may be
found with the rest of the experimental instructions in the Appendix.
To increase the realism of the lab experiments we offered real ﬁnancial prod-
ucts that paid out money after the monsoon. Delayed payouts (which proxied for
savings) were guaranteed by a voucher, which could be redeemed for cash in the
Ahmedabad laboratory. Participants had two months after the end of the monsoon
to come to Ahmedabad to redeem their vouchers,15 and also had the option of send-
ing the voucher with someone else who was designated to collect their funds.
The monsoon was normal in Gujarat (and most of India) in 2010, so the insurance
portions of the WISA did not pay out.
14 Trustin the insurer was emphasized by Cole et al. (2013) as a signiﬁcant factor in rainfall insur-
ance adoption.
15 Speciﬁcally, they were told that they could redeem their vouchers after the Hindu holiday of
Dashera, which corresponded roughly with the end of both the monsoon season and the insurance
policy.
16
4 Experimental Results
4.1 Insurance and Savings Preferences
Our main empirical result is that most farmers prefer both pure savings and pure
insurance to any interior mixture of the two.16 Figure 1 displays the average valu-
ation versus γ, the insurance share of the WISA. Participants reported the highest
average valuations of pure savings and pure insurance, with these bids statistically
indistinguishable. Valuations for both interior mixtures of savings and insurance
were signiﬁcantly lower than those for pure products. Our ﬁnding of an interior lo-
cal WTA minimum in the percentage of insurance is inconsistent with the standard
intertemporal insurance model and Proposition 1.
Figure 1 shows within-subject differences in average valuations as a function of
γ. In addition, we group the subjects according to various patterns of the bids, which
indicate distinct preferences over insurance or savings. These groups are shown in
Table 2. Eighteen percent of respondents were indifferent, which means they had
the same valuation for each product. Seven percent preferred savings, i.e., their
bids were weakly decreasing in the percentage of insurance contained in the prod-
uct. Thirteen percent showed a preference for insurance, meaning their bids were
weakly increasing in the percentage of insurance contained in the product. Eleven
percent preferred an interior mix, which means they had the highest bid for one of
the mixture products, with the bids weakly decreasing as one moves away from the
highest bid. A strong plurality of 39 percent of the subjects had preferences that
corresponded to the average, meaning they showed a preference for both pure in-
surance and pure savings over any of the mixtures. Twelve percent of subjects did
not express clear preferences, meaning that their bids changed directions twice as γ
increased.
Regressions of WTA on a quadratic in γ and various controls support these de-
scriptive patterns. Results are shown in Table 3. Column 1 contains only the linear
16 Exceptwhere speciﬁed to the contrary, in this Section for simplicity all analysis we report in-
volves the elicited same-day WTA. For the qualitatively-similar results using the post-monsoon WTA
elicitations, see the Appendix. In addition, this Section pools across the between-subjects framing
manipulations, to which we return in Section 5.
17
term of the fraction of insurance, and we ﬁnd it enters positively and signiﬁcantly.
In Column 2 we add the squared term, and now the linear term is negative while
the squared term is positive, which is consistent with the U-shape seen in Figure 1.
In Column 3 we run a Tobit (as some values of WTA are censored from above), and
ﬁnd results very close to the OLS speciﬁcation in Column 2. As the Tobit speciﬁca-
tion has little effect on the results, we focus hereafter on OLS speciﬁcations for ease
of interpretation.
4.2 Risk and Time Preferences
Since the previous subsection showed that most people do not have an interior most-
preferred insurance share in a WISA, the comparative statics of the optimum with
respect to risk or time preferences cannot achieve the interpretation envisioned in
subsection 2.3. Nevertheless, the empirical average relationships between WTA and
risk and time preferences are of interest and we present them in Table 4.
Recall that we have two methods of calculating discount factors: a set of ques-
tions involving hypothetical choices (“Hyp Discount Factor”), and a comparison of
WTA for WISAs when the payout from the BDM exercise happens directly after the
session versus in the future (“BDM Discount Factor”). Details of the two discount
factor calculations are given in the Appendix.
We ﬁrst look at the correlations between WTA and risk and time preferences for
all WISAs. Columns 1 and 2 of Table 4 show that people with higher discount factors
have higher WTA, and those who are more risk averse have lower WTA. The partial
correlation with the BDM Discount Factor is an order of magnitude larger than the
partial correlation with the Hyp Discount Factor. In Columns 3 and 4 we interact the
risk and discounting parameters with γ, and ﬁnd that the interaction terms on the
discount factors are not signiﬁcantly different from zero, while people with higher
risk aversion have a preference for pure products (γ ∈ {0, 1}) over interior mixtures
(γ ∈ 1 2
3, 3 ) .
18
5 Interpretation of Findings
Section 2’s model predicted that participants’ WTA would not have an interior local
minimum inγ. However, within-subjects experimental comparisons implied that
most people preferred pure savings and pure insurance to any interior mixture of
the two. Looking at the heterogeneity of preferences in Table 2, we see that only 49%
of the respondents gave results compatible with standard insurance theory. This
section analyzes possible explanations.
5.1 Simplicity Preference
Our results could have arisen if respondents were simply confused about the interior
WISA mixtures, as they might be more difﬁcult to understand than the pure prod-
ucts. If this were true, a preference for simplicity (or, equivalently here, a suspicion
of complexity) could cause people to value pure products over mixtures.
Our between-subjects framing manipulation allows a direct test of this hypothe-
sis. As explained earlier, participants were introduced to the WISAs using the Bun-
dle Frame, the Insurance Frame, or the ICICI Bundle Frame. While the Bundle Frame
and ICICI Bundle Frame explained WISAs as an insurance product plus a savings
voucher, the Insurance Frame explained WISAs as an insurance policy with a guar-
anteed minimum payout. Arguably, the Insurance Frame is simpler to understand,
as it presents the farmers with just one product to contemplate instead of two. If
simplicity preference is operative, we would expect the preference for pure products
to be greater for participants shown the Bundle Frames as opposed to the Insurance
Frame.
In Table 5, we test this hypothesis directly. Column 1 introduces dummies for
the frames to see how they affected subjects’ average bids (the simpler Insurance
Frame is the omitted category). Compared to the Insurance Frame, the other two
frames do not cause signiﬁcantly different average bids. However, the ICICI Bun-
dle Frame does show bids higher than the normal Bundle Frame, indicating that
including the ICICI-Lombard brand increases particpants’ WTA. Column 2 interacts
dummies for both complex (Bundle) frames with a quadratic in the insurance shareγ
19
to test whether the complexity of the frame varies the relative valuation of savings
versus insurance. None of the interaction terms are signiﬁcant.
Column 3 is the main speciﬁcation, which pools both complex frames and inter-
acts them with the insurance share γ. The interaction terms are again both economi-
cally small and not signiﬁcantly different than zero, indicating that the general shape
of A(γ) is unaffected by a more complicated presentation of the products.
More precisely, the coefﬁcients in Column 3 imply the following. For the simpler
dA(γ)
Insurance Frame, at γ = 2 3 , dγ = 40.1 (95% conﬁdence interval [20.3,59.9]), while
dA(γ)
for people with either of the more complex frames dγ = 34.4 (95% conﬁdence
interval [21.6,47.3]). Therefore at γ = 2 3 the marginal effects of γ on WTA are not
signiﬁcantly affected by the complexity of the frame. This pattern is consistent across
the range of γ.
Finally, rainfall index insurance itself is a confusing product compared to a simple
savings voucher. If a preference for simplicity was driving the results, the WTA
for pure insurance might be lower than that for pure savings. However, the mean
WTAs for these two products are not statistically distinguishable. While we do not
have explicit tests for whether a preference for simplicity caused subjects to value
the WISAs less than pure products, the available evidence suggests that this is not
the case.
5.2 Anticipated Voucher Redemption
Another conceivable explanation for participants’ lower valuation of mixed WISAs
than pure products concerns their expectations about redeeming their vouchers post-
monsoon. In the experiment, 197 participants (61%) received a voucher that could
be redeemed for certain cash after the monsoon. Once the vouchers were ready to be
redeemed, we repeatedly called all voucher holders who had given us a phone num-
ber to remind them that they had money to pick up, and we reminded them how to
redeem the voucher. Despite these attempts, only 83 of these people (42%) eventu-
ally redeemed their vouchers. Any insurance payouts would have been available
for pickup at the same time and location, but recall that the monsoon was normal
so insurance payouts did not occur. If during the experiments the farmers took into
20
account the possibility that they might not redeem their vouchers, this could have
decreased demand for mixed WISAs.
For example, suppose a farmer has a ﬁxed cost of Rs 130 for redeeming the
voucher. As the WISAs with interior mixtures (γ ∈ 1 2
3 , 3 ) implied guaranteed
payments of less than Rs 130, the participant would anticipate not redeeming the
voucher in the event the insurance did not pay out, making these bundles relatively
unattractive.
However, at least ﬁve reasons suggest this mechanism is not driving Section 4’s
ﬁndings. First, as described above, vouchers could be redeemed at any point dur-
ing an extended period of time, reducing the marginal cost of redemption. Second,
voucher redemption could be delegated, so that any ﬁxed costs could be spread
across all the participants in a village.
Third, if customers expected their probability of receiving delayed payments to
be increasing in the size of those payments (due to ﬁxed costs of voucher redemp-
tion), we might expect that the WISA with the smallest guaranteed voucher to have
the lowest valuation. This is the 1/3 Savings + 2/3 Insurance product, which has
a voucher of only Rs 60. However, the bids for the 2/3 Savings + 1/3 Insurance
bundle (which has a voucher of Rs 120) were signiﬁcantly lower even though the
voucher size was larger. Fourth, in the WTA elicitation tasks with post-monsoon
offer amounts, described further in the Appendix, respondents’ bids were similar to
the same-day bids.
Fifth, Table 6 reports regressions showing that the probability of redeeming a
given voucher is not correlated with the voucher’s size. Further elaboration on this
table and other evidence is provided in the online appendix. Together, these consid-
erations make us skeptical that anticipated redemption probabilities drove the main
pattern of elicited valuations, in which pure products are valued more than interior
mixtures of savings and insurance.
5.3 Diminishing Sensitivity
The key assumption for Proposition 1’s result that A (γ) cannot have an interior local
minimum is the concavity of the utility function. If we relax this assumption, then
21
the theory would allow an interior local minimum for A (γ). While the assumption
of risk averse agents is common, prospect theory (Kahneman and Tversky, 1979)
developed partly from evidence that consumers have diminishing sensitivity to both
gains and losses, possibly resulting in risk-seeking behavior in the loss domain. For
a consumer with diminishing sensitivity, given reference point r, the prospect theory
value function v satisﬁes:
v (c) < 0 if c > r
v (c) > 0 if c < r
If people exhibited diminishing sensitivity around a reference point, this means
that their utility function is convex for losses below a reference point, and Proposi-
tion 1 fails to hold. In order to see this, let’s take a look again at the central result of
Proposition 1. Deﬁne the reference level of consumption in each period to be r1 and
r2 respectively. Assuming that people calculate their WTA based on the prospect
theory value function17 , Equation 12 now becomes:
2 2
d2 ds∗ (γ) ˜ , γ)
dg (w, x ds∗ (γ)
˜ , γ)) =
V (Y1 , g (w, x v ( c1 − r1 ) + β E +R v ( c2 − r2 )
d γ2 dγ dγ dγ
(18)
For a consumer with diminishing sensitivity, v (c) is no longer everywhere less
than zero, so the above expression is not necessarily negative. Instead, the sign will
be determined by the speciﬁc shape of the utility function and the choice of the ref-
erence point.
In the ﬁrst period, we can consider the reference point r1 to be the amount of
ﬁrst period consumption in a world where the consumer has not recieved a gift of
a WISA. If the gift of a WISA causes the consumer to increase (decrease) savings,
then c1 − r1 will be less than (greater than) zero. Unfortunately, the model does not
17 Inmodels of prospect theory, total utility is taken to be a weighted sum of “consumption utility,”
which follows standard assumptions of expected utility theory, and the prospect theory value func-
tion. In most circumstances, subjects evaluate individual lotteries according to the value function.
(For instance, this setup is deﬁned formally in Gottlieb (2013)) Since stating a WTA is analogous to
evaluating a lottery, we assume that WTA would be determined using the value function.
22
contain clear predictions about how the gift of the WISA will change savings, and
therefore the ﬁrst term has ambiguous sign.
In the second period, the choice of the reference point is less clear. One reason-
able choice would be the level of consumption if was no gift of a WISA and when
x˜ = E (x˜ ) (Köszegi and Rabin, 2006). In this case, second period consumption can
be above or below the reference point, and therefore the value function is neither
globally convex or concave, making the second term also ambiguous in sign.
We can resolve this ambiguity with a few simplifying assumptions. Assume that
savings is ﬁxed and that the second period reference point is the level of consump-
tion when x ˜ = 0. In farming situations, this reference point is not unrealistic, as
losses may come during rare catastrophic events while most seasons bring good har-
vests. In this scenario, we can drop the ﬁrst term of Equation 18 as ﬁrst period utility
is always equal to reference utility. The second term is positive, as c2 − r2 is always
either zero or negative.18 In this scenario, A (γ) can have an interior local minimum.
In general, the necessary conditions for A (γ) to have an interior local minimum
are that there is a γ over the range of 0 < γ < 1 that solves the ﬁrst order condition
for γ (found in Equation 9), and also satisﬁes the following second order condition :
2 2
ds∗ (γ) ˜ , γ)
dg (w, x ds∗ (γ)
v ( c1 − r1 ) + β E +R v ( c2 − r2 ) > 0
dγ dγ dγ
The intuition behind this effect is as follows. When people have diminishing
sensitivity to losses, partial insurance is especially unattractive because the marginal
utility of wealth is very low after a large loss. Therefore, the low amount of insurance
offered as part of a WISA with a low γ is unattractive, making the WISA unattractive
overall compared to the pure products.
Our experiment does not shed light on whether the above necessary conditions
are satisiﬁed for people who showed a local minimum in A (γ). However, results of
18 Note that v ( c − r ) is technically undeﬁned when c = r. However, we can ﬁnesse this issue by
assuming that in a world where savings does not adjust, ﬁrst period utility will always be zero and
should therefore be removed from the indirect utility function altogether. For the second term, we
simply consider the expectation for all situations where c2 = r2 .
23
our experiment are consistent with predictions of a model with agents who exhibit
diminishing sensitivity around a reference point. This would be an interesting topic
for further research.
6 Conclusion
Achieving adequate management of rainfall risk is a serious, consequential chal-
lenge for farmers around the world. We sought to understand whether and how
a savings account with rainfall-indexed returns, a Weather Insurance Savings Ac-
count, might help. Contrary to standard theory, most farmers preferred both pure
savings and pure insurance to an interior mixture of the two. Alternative explana-
tions like simplicity preference do not appear to account for this fact. Instead, lower
valuation of mixed products seems consistent with a model where participants ex-
perience diminishing sensitivity to wealth changes around a reference point. Di-
minishing sensitivity to losses can imply a preference for full insurance over partial
insurance. This suggests some WISAs, if offered commercially by ﬁnancial institu-
tions, may face low adoption rates.
One potential alternative formulation for mixing savings and weather insurance
would follow the example of whole life insurance. “Whole weather” policies might
entail multi-year coverage, with premiums due each year and insurance coverage for
each monsoon. If at the end of the term cumulative premiums exceeded cumulative
payouts, the (nominal) difference would be returned to policyholders. A variety of
distortions are present in whole life markets (for pointed recent evidence in India,
see Anagol et al., 2013), but the substantial market demand for whole life suggests
whole weather might also experience widespread adoption.
More promsingly still, recent years have seen considerable successful innova-
tion in the design of microsavings products (Ashraf et al. (2006); Brune et al. (2011);
Karlan et al. (2010b)). Our experiments found limited demand for WISAs with
γ∈ 1 2
3 , 3 . WISAs with a smaller insurance share, for example guaranteeing a non-
negative net return (like a one-year whole weather policy), might be attractive as a
savings product while providing meaningful risk protection in some environments.
24
References
Anagol, Santosh, Shawn Cole, and Shayak Sarkar, “Understanding the Advice of
Commissions-Motivated Agents: Evidence from the Indian Life Insurance Mar-
ket,” 2013. Working paper, 2013.
Ashraf, Nava, Dean Karlan, and Wesley Yin, “Tying Odysseus to the mast: Evi-
dence from a commitment savings product in the Philippines,” The Quarterly Jour-
nal of Economics, 2006, 121 (2), 635–672.
Becker, G. M., M. H. DeGroot, and J. Marschak, “Measuring utility by a single-
response sequential method.,” Behav Sci, July 1964, 9 (3), 226–232.
Brune, Lasse, Xavier Giné, Jessica Goldberg, and Dean Yang, “Commitments to
save: A ﬁeld experiment in rural Malawi,” World Bank Policy Research Working
Paper Series, Vol, 2011.
Carroll, Christopher D. and Andrew A. Samwick, “The nature of precautionary
wealth,” Journal of Monetary Economics, 1997, 40 (1), 41 – 71.
Cole, Shawn A., Xavier Giné, Jeremy Tobacman, Petia Topalova, Robert
Townsend, and James Vickery, “Barriers to Household Risk Management: Evi-
dence from India,” American Economic Journal: Applied Economics, Jan 2013, 5 (1),
104–35.
Cole, Shawn Allen, Benjamin Charles Iverson, and Peter Tufano, “Can Gambling
Increase Savings? Empirical Evidence on Prize-Linked Savings Accounts,” 2014.
Working paper.
Cole, Shawn, Daniel Stein, and Jeremy Tobacman, “What’s Rainfall Insurance
Worth? A Comparison of Valuation Techniques,” 2011.
Connor, Robert A., “More than risk reduction: The investment appeal of insurance,”
Journal of Economic Psychology, 1996, 17 (1), 39 – 54.
Demirgüç-Kunt, Asli and Leora Klapper, “Measuring Financial Inclusion: The
Global Findex Database,” 2012. World Bank Policy Research Working Paper 6025.
25
Fafchamps, Marcel and John Pender, “Precautionary Saving, Credit Constraints,
and Irreversible Investment: Theory and Evidence from Semiarid India,” Journal
of Business And Economic Statistics, 1997, 15 (2), pp. 180–194.
Ganderton, PhilipT., DavidS. Brookshire, Michael McKee, Steve Stewart, and
Hale Thurston, “Buying Insurance for Disaster-Type Risks: Experimental Evi-
dence,” Journal of Risk and Uncertainty, 2000, 20 (3), 271–289.
Giné, Xavier and Dean Yang, “Insurance, credit, and technology adoption: Field
experimental evidencefrom Malawi,” Journal of Development Economics, 2009, 89
(1), 1 – 11.
, Robert Townsend, and James Vickery, “Patterns of Rainfall Insurance Participa-
tion in Rural India,” World Bank Economic Review, October 2008, 22 (3), 539–566.
Gottlieb, Daniel, “Prospect Theory, Life Insurance, and Annuities,” 2013.
Guillén, Mauro and Adrian Tschoegl, “Banking on Gambling: Banks and Lottery-
Linked Deposit Accounts,” Journal of Financial Services Research, June 2002, 21 (3),
219–231.
Guiso, Luigi, Tullio Jappelli, and Daniele Terlizzese, “Earnings Uncertainty and
Precautionary Saving,” CEPR Discussion Papers 699, C.E.P.R. Discussion Papers
June 1992.
Hess, Ulrich, “Innovative ﬁnancial services for India, monsoon indexed lending and
insurance for smallholders,” ARD Working Paper, 2004, 09.
Johnson, Eric, John Hershey, Jacqueline Meszaros, and Howard Kunreuther,
“Framing, probability distortions, and insurance decisions,” Journal of Risk and Un-
certainty, 1993, 7 (1), 35–51.
Kahneman, Daniel and Amos Tversky, “Prospect Theory: An Analysis of Decision
under Risk,” Econometrica, 1979, 47 (2), pp. 263–292.
26
Karlan, Dean, Issac Osei-Akoto, Robert Osie, and Chris Udry, “Examining Under-
investment in Agriculture: Returns to Capital and Insurance in Ghana,” Novem-
ber 2010. Presentation given at the 6th Annual Microinsurance Conference in
Manila, Philippines.
, Margaret McConnell, Sendhil Mullainathan, and Jonathan Zinman, “Getting
to the top of mind: How reminders increase saving,” Technical Report, National
Bureau of Economic Research 2010.
Kearney, Melissa, Peter Tufano, Erik Hurst, and Jonathan Guryan, “Making Sav-
ings Fun: An Overview of Prize-Linked Savings,” in Olivia Mitchell and Amma-
maria Lusardi, eds., Financial Literacy: Implications for Retirement Security and the
Financial Marketplace, Oxford, 2011.
Kimball, Miles S., “Precautionary Saving in the Small and in the Large,” Economet-
rica, 1990, 58 (1), pp. 53–73.
Köszegi, Botond and Matthew Rabin, “A Model of Reference-Dependent Prefer-
ences,” Quarterly Journal of Economics, 2006, 121 (4), 1133–1165.
Kunreuther, Howard, Mark Pauly, and Stacey McMorrow, Insurance and Behavioral
Economics: Improving Decisions in the Most Misunderstood Industry, Cambridge Uni-
versity Press, 2013.
Lusardi, Annamaria, “On the Importance of the Precautionary Saving Motive,” The
American Economic Review, 1998, 88 (2), pp. 449–453.
Ministry of Labour and Employment, Government of India, “Wage Rates in Rural
India (2009-2010),” Technical Report 2010.
Morduch, Jonathan, “Poverty and vulnerability,” The American Economic Review,
1994, 84 (2), 221–225.
, “Micro-Insurance: The Next Revolution?,” in Dilip Mookherjee Abhijit Banerjee,
Roland Benabou, ed., What Have We Learned About Poverty?, Oxford University
Press, 2006.
27
Mossin, Jan, “Aspects of Rational Insurance Purchasing,” Journal of Political Econ-
omy, 1968, 76 (4), pp. 553–568.
Pratt, John W., “Risk Aversion in the Small and in the Large,” Econometrica, 1964, 32
(1/2), pp. 122–136.
Richter, Andreas, Jörg Schiller, and Harris Schlesinger, “Behavioral insurance:
Theory and experiments,” Journal of Risk and Uncertainty, 2014, 48 (2), 85–96.
Rosenzweig, MR, “Savings behaviour in low-income countries,” Oxford Review of
Economic Policy, 2001, 17 (1), 40–54.
Schlesinger, Harris, “The Theory of Insurance Demand,” in Dani Rodrik and Mark
Rosenzweig, eds., The Handbook of Insurance, Boston: Kluwer Academic Publishers,
2000, chapter 5.
Schoemaker, Paul J. H. and Howard C. Kunreuther, “An Experimental Study of
Insurance Decisions,” The Journal of Risk and Insurance, 1979, 46 (4), pp. 603–618.
Skees, Jerry, Stephanie Gober, Panos Varangis, Rodney Lester, and Vijay
Kalavakonda, “Developing rainfall-based index insurance in Morocco,” Policy
Research Working Paper Series 2577, The World Bank April 2001.
Slovic, Paul, Baruch Fischhoff, Sarah Lichtenstein, Bernard Corrigan, and Barbara
Combs, “Preference for Insuring against Probable Small Losses: Insurance Impli-
cations,” The Journal of Risk and Insurance, 1977, 44 (2), pp. 237–258.
Townsend, Robert M., “Risk and Insurance in Village India,” Econometrica, 1994, 62
(3), pp. 539–591.
Tufano, Peter, Jan-Emmanuel De Neve, and Nick Maynard, “US consumer demand
for prize-linked savings: New evidence on a new product,” Economics Letters, 2011,
111 (2), 116–118.
28
Appendix
Appendix available online at:
https://www.dropbox.com/s/voknbwgzwgfwgxq/WISA%20Appendix%2020150311.pdf
29
Figure 1: Average Willingness to Accept for All Products
200
Average WTA (Rs)
190
180
170
160
100% Savings 1/3 Insurance + 2/3 Insurance + 100% Insurance
(γ=0) 2/3 Savings 1/3 Savings (γ=1)
(γ=1/3) (γ=2/3)
WISA Type
Notes: This figure shows the average valuation of participants for the four WISA products studied. Valuation is
calculated as the WTA from a BDM elicitation done as part of the lab experiment. The fraction of insurance γ takes
discrete values of 0, 1/3, 2/3, and 1 for each individual. The experiment elicits a WTA for each product, so each
individual provides a data point for each γ. Error bars indicate two-standard-deviation bands.
Table 1: Summary Statistics
Personal Characteristics
Age 43.14
(13.48)
Land owner 86.65%
(0.34)
Village distance from Ahmedabad (Km) 23.20
(3.12)
Have a telephone 43.17%
(0.50)
Decision Parameters
Discount factor between experiment and post-ponsoon 0.78
(0.65)
Estimate of coefficient of partial risk aversion 2.23
(3.07)
Rainfall Risk Exposure
If there was a severe drought during the upcoming monsoon season,
would the income of you or your family be affected?
Yes, A Lot 82.92%
Yes, A Little 16.46%
No 0.31%
Have government crop insurance 12.73%
Roughly how much money could you gain from drawing on savings
and selling assets if there was an emergency? (Rs.) 7574.34
(3366.06)
Roughly how much money could you borrow if there was an
emergency? (Rs.) 5559.78
(3654.97)
If there was a serious drought in the upcoming monsoon, how would
you and your family cope?
Draw upon cash savings 36.65%
Sell assets such as gold, jewlery, animals 40.68%
Rely on help from friends and family 49.38%
The government would step in to help 52.80%
Take a loan 44.10%
Number of Respondents 322
Notes: Summary statistics are from participants in the WISA lab experiment, which took
place in the Centre for Microfinance computer lab in Ahmedabad, India, from March-May,
2010. Data were gathered using a computer-based survey, with enumerators assisting
respondents with data entry into the computers. Standard deviations are in parentheses.
Table 2: Patterns of Preferences
As a Function of the WISA's Insurance/Saving Mix
Preference over γ Percentage of Respondents
Indifferent 18%
Prefer Savings 7%
Prefer Insurance 13%
Prefer Interior Mix 11%
Prefer Pure Product 39%
Other 12%
Notes: This table classifies subjects by their expressed
preferences. Participants are coded as "Indifferent" if their WTA is
constant across all products, "Prefer Savings" if their WTA always
declines in γ, "Prefer Insurance" if their WTA always increases in γ,
"Prefer Mix" if they have an internal maximum in γ, and "Prefer
Pure Product" if they have an internal minimum in γ. Participants
are coded as "Other" if their bids changed directions twice.
Table 3: Share Insurance and Willingness to Accept
Dependent Var is WTA Bid (Rs)
(1) (2) (3)
OLS FE OLS FE Tobit
Fraction of Insurance (γ) 8.059*** -79.22*** -72.21***
(3.006) (13.79) (20.33)
Fraction of Insurance Squared (γ2) 87.27*** 82.19***
(13.68) (20.27)
Constant 178.9*** 188.6*** 197.5***
(1.503) (2.061) (3.68)
Observations 1,288 1,288 1,288
R-squared 0.695 0.718
Notes: This table estimates how participants' valuations for WISAs varies with the fraction of
insurance (γ) in the product. Valuation is calculated as the WTA from a BDM elicitation done
as part of the lab experiment. γ takes discrete values of 0, 1/3, 2/3, and 1 for each individual,
so there are four observations for each of 322 individuals, resulting in a total of 1288
observations. The dependent variable for each regression is the WTA bid, in Indian Rupees.
Columns 1 and 2 are OLS regressions including individual fixed effects. Column 3 is a Tobit,
taking into account censored values of WTA. Robust standard errors are in parentheses. In
columns 1 and 2 standard errors are clustered at the individual level. ***
p<0.01, ** p<0.05, * p<0.1
Table 4: Risk and Time Preferences
Dependent Variable is Willingness to Accept
(1) (2) (3) (4) (5)
Fraction of Insurance (γ) -84.86*** -84.86*** -84.86*** -47.21 -169.4
(13.55) (13.56) (13.56) (34.39) (110.4)
2
Fraction of Insurance Squared (γ ) 93.69*** 93.69*** 93.69*** 68.08** 188.3*
(13.36) (13.37) (13.37) (34.44) (111.5)
Frac. Ins. (γ) X Risk Aversion -10.75** -10.49**
(5.213) (5.172)
Frac. Insurance Sq (γ2) X Risk Aversion 9.489* 9.561*
(5.191) (5.130)
Frac. Ins (γ) X Hypothetical Discount Factor -15.87
(33.17)
2
Frac. Insurance Squared (γ ) 5.153
(33.47)
Frac. Insurance (γ) X BDM Discount Factor 112.6
(110.0)
-120.9
Frac. Insurance Sq (γ2) X BDM Discount Factor
(112.2)
Risk Aversion -1.873* -3.009***
(1.009) (0.914)
Hypothetical Discount Factor 23.67***
(5.937)
BDM Discount Factor 235.6***
(26.81)
Constant 189.4*** 173.2*** -29.84 189.4*** 189.4***
(2.953) (6.389) (25.79) (2.314) (2.323)
Individual Fixed Effects NO NO NO YES YES
Observations 1248 1248 1248 1248 1248
R-squared 0.030 0.082 0.303 0.717 0.717
Notes: This table shows the relationship between WISA valuation and the fraction of insurance γ, and how this relationship varies with
risk and discount parameters. Valuation is calculated as the WTA from a BDM elicitation done as part of the lab experiment. γ takes
discrete values of 0, 1/3, 2/3, and 1 for each individual. The sample in all columns is restricted to the 312 participants (out of 322 total)
who had risk preferences from the Binswanger lottery that were not inefficient, and discount factors that were calculable from the
hypothetical elicitation exercise. There are four observations for each of the 312 individuals, resulting in 1248 observations. There are
two discount factors calculated: one using hypothetical questions, entitled "Hypothetical Discount Rate", and one using the BDM
procedure, entitled "BDM Discount Rate". Robust standard errors are in parentheses. All errors are clustered at the individual level.
*** p<0.01, ** p<0.05, * p<0.1
Table 5: Framing
Dependent Variable is Willingness to Accept
(1) (2) (3)
Fraction Insurance (γ) -79.22*** -73.06*** -73.06***
(11.96) (23.99) (23.96)
Fraction of Insurance Squared (γ2) 87.27*** 85.70*** 85.70***
(11.85) (23.76) (23.74)
(Complex) Bundle Frame -8.904
(7.646)
(Complex) ICICI Bundle Frame 3.578
(7.076)
Either Complex Frame X Fraction Insurance
-8.505
(γ)
(29.23)
Either Complex Frame X Fraction of
2.173
Insurance Squared (γ2)
(28.97)
(Complex) Bundle Frame X Fraction Insurance
-28.03
(γ)
(37.86)
(Complex) Bundle Frame X Fraction of
26.80
Insurance Squared (γ2)
(37.91)
(Complex) ICICI Bundle Frame X Fraction
4.232
Insurance (γ)
(31.19)
(Complex) ICICI Bundle Frame X Fraction
-13.89
of Insurance Squared (γ2)
(30.68)
Constant 189.6*** 188.4*** 188.6***
(5.380) (2.04) (2.06)
Individual Fixed Effects NO YES YES
Observations 1,288 1,288 1288
R-squared 0.033 0.718 0.719
Notes: This table shows the effect of a complexity vs simplicity framing manipulation on the relationship between
WISA valuation and the fraction of insurance γ. Valuation is calculated as the WTA from a BDM elicitation done as
part of the lab experiment. γ takes discrete values of 0, 1/3, 2/3, and 1 for each individual. There are four
observations for each of the 322 individuals, resulting in a total of 1288 observations. The dependent variable for
each regression is the WTA bid, in Indian Rupees. In all columns, the (simpler) "Insurance Frame" is the omitted
category. All columns present OLS regressions, and standard errors are clustered at the individual level. ***
p<0.01, ** p<0.05, * p<0.1.
Table 6: Voucher Size and Picking Up Payouts
Voucher is Picked Voucher is Picked Up Before Voucher is Picked Up After
Dependent Variable: Up Second Phone Call the Second Phone Call
(1) (2) (3) (4) (5) (6)
Log Amount of Individual Voucher -0.0989 -0.101 0.0436 0.0505 -0.143** -0.147*
(0.0789) (0.0843) (0.0329) (0.0309) (0.0660) (0.0839)
Log of Total Vouchers in Village 0.0618 0.0292
(0.122) (0.0903)
Village Distance from Ahmedabad (km) -0.0281 -0.0119 -0.0262
(0.0228) (0.0150) (0.0249)
Have Phone Number 0.0828 0.136 0.0324 -0.00294 0.0504 0.155
(0.0704) (0.0879) (0.0603) (0.0433) (0.0676) (0.0993)
Log of Total Village Vouchers Remaining
After Second Phone Call 0.0733
(0.146)
Constant 0.853** 1.066 -0.0881 -0.0312 0.942*** 1.077
(0.377) (1.223) (0.151) (0.718) (0.314) (1.216)
Village Fixed Effects YES NO YES NO YES NO
Observations 197 197 197 197 197 171
R-squared 0.528 0.072 0.372 0.024 0.561 0.083
Notes: This table shows the relationship between the amount of vouchers received and the probability they were redeemed for
cash. The sample frame in columns 1-5 is the set of people who received vouchers (redeemable roughly three months later) as
part of the experiement. The sample frame in column 6 is restricted to those people who both had received vouchers and lived in
a village where there were some vouchers remaining to be redeemed after the second reminder phone call to the village. In
columns 1-2, the dependent variable is a dummy taking a value of 1 if the voucher was ever redeemed. In columns 3-4 the
dependent variable is a dummy taking a value of 1 if the voucher was redeemed before the second reminder phone call. In
columns 5-6 the dependent variable is a dummy taking a value of 1 if the voucher was redeemed after the second reminder
phone call. There is one observation per individual. All columns report OLS regressions. Standard errors are clustered at the
village level. *** p<0.01, ** p<0.05, * p<0.1