metadata: authors: 0: author: Stein,Daniel Kevin
1: author: Tobacman,Jeremy
count: World
docna: 0: docna: Weather insurance savings accounts
docty: Policy Research Working Paper
subtopic: Taxation & Subsidies,ICT Policy and Strategies,Insurance & Risk Mitigation,Natural Disasters,Financial Sector Policy
teratopic: Finance and Financial Sector Development
abstracts: cdata!: Better insurance against rainfall risk
            could improve the security of hundreds of millions of
            agricultural households around the world. However, customers
            have shown little demand for stand-alone insurance products.
            This paper theoretically and experimentally analyzes an
            innovative financial product called a Weather Insurance
            Savings Account (WISA), which combines savings and rainfall
            insurance. The paper uses a standard model of intertemporal
            insurance demand to study how customers' demand for a
            WISA varies with the amount of insurance offered. A
            laboratory experiment is then used to elicit
            participants' valuations of pure insurance, pure
            savings, and intermediate WISA types. Contrary to the
            standard model, within-subjects comparisons show that many
            participants prefer both pure insurance and pure savings to
            any interior mixture of the two, suggesting that market
            demand for a WISA is likely to be low. Additional
            experimental and observational evidence distinguishes
            between several alternative explanations. One possibility
            that survives the additional tests is diminishing
            sensitivity to losses, as in prospect theory.
repnme: repnme: Weather insurance savings accounts
display_title: Weather insurance savings accounts
listing_relative_url: /research/2015/04/24324721/weather-insurance-savings-accounts
topicv3: Financial Inclusion m1327456 363,Drought m1503313 3162,Monsoon m1503657 3193,Vouchers m1504820 3553,Life Insurance m1505058 3837
publishtoextweb_dt: 2015-04-08T00:00:00Z
historic_topic: Finance and Financial Sector Development
origu: Off of Sr VP Dev Econ/Chief Econ (DECVP)
no_of_pages: 38
author_keys: 0: author_key: 1185883
1: author_key: 688597
model_extractions: 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 security of hundreds of millions of agricultural households around the world. However, customers have shown little demand for stand-alone insurance products. This paper theoretically and experimentally analyzes an innovative financial product called a Weather Insurance Savings Account (WISA), which combines savings and rainfall insurance. The paper uses a standard model of intertemporal insurance demand to study how customers’ demand for a WISA varies with the amount of insurance offered.

A laboratory experiment is then used to elicit participants’ valuations of pure insurance, pure savings, and intermediate WISA types. Contrary to the standard model, within-subjects comparisons show that many participants prefer both pure insurance and pure savings to any interior mixture of the two, suggesting that market demand for a WISA is likely to be low. Additional experimental and observational evidence distinguishes between several alternative explanations. One possibility that survives the additional tests 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<sup>_∗_</sup>

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 Organization 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 excellent 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, Department 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 special concern since it is a covariate risk that cannot be well-insured informally. This paper theoretically motivates and experimentally evaluates an innovation for expanding protection against rainfall risk: linking rainfall index insurance with savings accounts.

Rainfall index insurance was developed to provide risk protection while also remaining 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 government weather stations. Asymmetric information problems are avoided, and claims adjustment is unnecessary, because payouts depend only on measured rainfall. Despite 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, including 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 supplyand 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.<sup>1</sup> In this paper we explore whether bundling rainfall insurance with savings can overcome specific and general barriers to effective risk management (Cole et al.,

> 1See also Tufano et al. (2011) and Cole et al. (2014).

2
2013; Kunreuther et al., 2013).<sup>2</sup> 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 insurance 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.<sup>3</sup> We an insurance model to demand for WISAs as a adapt intertemporal study 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 minimim. 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 insurance to be below demand of both pure products. We then present a laboratory experiment 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 attempt 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

> 2Bundling 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.

> 3If the nominal interest rate on normal savings accounts is _i_ , then nominal losses are possible in a WISA when _γ >_ 1+ _<u>i</u> i_<sup>.</sup>

3
the WISAs were described as a (complicated) combination of insurance and savings, or (simply) an insurance policy with a guaranteed minimum payout. This manipulation 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’ expectation 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 earnings 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 literature, 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 importance 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, insurance 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.<sup>4</sup> Consistent with results in the experimental literature, the private insurance marketplace provides some insurance products that guarantee a positive gross return

> 4In 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 insurance 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 insurance 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; Rosenzweig, 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 insurance 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) offered a savings account where customers received various types of insurance coverage instead of interest on savings (Morduch, 2006). Similarly, many banks and credit unions in economies offer accounts that confer modest auto or developed savings 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 offering “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 will as follows. paper proceed Section 2 introduces a simple insurance demand 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 experimental results, and Section 5 analyzes candidate explanations. We conclude in Section 6.

# **2 Optimal WISA Theory**

In this section we introduce a model to consumer simple study 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 experimental 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 plausibly 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 (1+ _λx_ ̃) _E_ ( ̃ _x_ )<sup>in the event of income shock</sup><sup>_x_ ̃.</sup> Next, define the payout from the WISA as 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 _Y_ 1 and a WISA with insurance share _γ_ and current face value of _w_ . Savings _s_ is chosen, _Y_ 1 _− s_ is consumed, and first period utility is realized. In period 2, the shock arrives and the consumer receives _Y_ 2 _− 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 continuous, thrice differentiable, and concave. Let the discount factor be _β_ . Expected utility over the two periods is: The customer chooses savings _s_ to maximize this expression. Indirect expected utility _V_ , as a function of the endowments and the WISA payment function _g_ ( _w_ , _x_ ̃, _γ_ ), Note that _s_ is left unconstrained, but all predictions of the model are robust to credit constraints where 0 _≤ s ≤ Y_ 1. Denote the optimal value of _s_ as _s_<sup>_∗_</sup> ( _γ_ ) . For simplicity 7
The following first order condition, a standard Euler equation, holds for _s_<sup>_∗_</sup> ( _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 indifferent between receiving a monetary payment of _A_ ( _γ_ ) or receiving an endowment of a WISA with parameter _γ_ :

# **2.2 WISA Valuation**

Differentiating Equation (5) with respect to _γ_ and rearranging, while holding _s_ constant, we can write: This expression reveals two effects.<sup>5</sup> Since 1+1 _λ_<sup>_<R_,thefirsttermrepresentsthe</sup> loss from substituting away from savings. The second term represents the gain from acquiring more insurance. Thus<sup>_dA_</sup> _d_<sup><u>(</u></sup> _γ_<sup>_<u>γ</u>_</sup><sup><u>)</u></sup> 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_<sup>_∗_</sup> _∈_ [0, 1] which maximizes _A_ ( _γ_ ). More interestingly, 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 5Continuity and differentiability of the utility function guarantee that<sup>_dA_</sup> _d_<sup><u>(</u></sup> _γ_<sup>_<u>γ</u>_</sup><sup><u>)</u></sup> is defined everywhere, 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:

1. Prove that if<sup>_<u>d</u>_2</sup><sup>_x_ ̃,</sup><sup>_γ_))</sup><sup>_<_0 ,</sup><sup>_A_(</sup><sup>_γ_) has no interior local minima.</sup> _dγ_<sup>2</sup><sup>_V_(</sup><sup>_Y_1,</sup><sup>_g_(</sup><sup>_w_,</sup> 2. Prove that<sup>_<u>d</u>_2</sup><sup>_x_ ̃,</sup><sup>_γ_))</sup><sup>_<_0.</sup> _dγ_<sup>2</sup><sup>_V_(</sup><sup>_Y_1,</sup><sup>_g_(</sup><sup>_w_,</sup> **Step 1** : Show that if _d_<sup>_<u>d</u>_</sup> _γ_<sup>22</sup><sup>_V_(</sup><sup>_Y_1,</sup><sup>_g_(</sup><sup>_w_,</sup><sup>_x_ ̃,</sup><sup>_γ_))</sup><sup>_<_0,</sup><sup>_A_(</sup><sup>_γ_) has no interior local minima.</sup>

Using the definition of _V_ ( _Y_ 1, _g_ ( _w_ , _x_ ̃, _γ_ )) from Equation 5 and applying the envelope theorem: In general, the sign of the second term in Equation 8 is unclear. Since _A_ ( _γ_ ) is continuous and differentiable, at any local extrema<sup>_dA_</sup> _d_<sup><u>(</u></sup> _γ_<sup>_<u>γ</u>_</sup><sup><u>)</u></sup> = 0 and the second term goes to zero. Also at any extrema we have, When<sup>_d_2</sup><sup>_V_</sup><sup><u>(</u></sup><sup>_Y_</sup><sup><u>1,</u></sup><sup>_<u>g</u>_</sup><sup><u>(</u></sup><sup>_w_</sup><sup><u>, ̃</u></sup><sup>_x_</sup><sup><u>,</u></sup><sup>_<u>γ</u>_</sup><sup><u>))</u></sup> _<_ 0,<sup>_d_2</sup><sup>_A_</sup><sup><u>(</u></sup><sup>_<u>γ</u>_</sup><sup><u>)</u></sup> will be less than zero because _u_<sup>_′_</sup> _>_ 0. This means _dγ_<sup>2</sup> _dγ_<sup>2</sup> that any local extremum must be a maximum, and therefore no interior local minimum can exist. Note that Equation 7 also shows that the _γ_ which locally maximizes _V_ ( _Y_ 1, _g_ ( _w_ , _x_ ̃, _γ_ )) will also locally maximize _A_ ( _γ_ ).

**Step 2** : Show that _d_<sup>_<u>d</u>_</sup> _γ_<sup>22</sup><sup>_V_(</sup><sup>_Y_1,</sup><sup>_g_(</sup><sup>_w_,</sup><sup>_x_ ̃,</sup><sup>_γ_))</sup><sup>_<_0.</sup> Using the envelope theorem,

9
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Both terms are negative due to the concavity of the utility function. Therefore, _<u>d</u>_<sup>2</sup><sup>_x_ ̃,</sup><sup>_γ_))</sup><sup>_<_0.CombinedwithStep1,thisallowsustoconcludethat</sup> _dγ_<sup>2</sup><sup>_V_(</sup><sup>_Y_1,</sup><sup>_g_(</sup><sup>_w_,</sup> _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 insure 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 assumptions on functional form; hence the model does not always yield unambiguous predictions. Therefore some of the discussion is reserved to the emprical section.

Classical insurance demand models (such as Schlesinger (2000)) predict insurance demand increases in risk aversion. In this paper’s model, this is not necessarily the case, as intertemporal smoothing also plays a role. To see how<sup>_argmax_</sup> _γ A_ ( _γ_ ) changes with risk aversion, consider the _γ_<sup>_∗_</sup> and _s_<sup>_∗_</sup> which jointly maximize expected utility _U_ .

Assuming that the optimal _γ_ is not at a boundary<sup>6</sup> , the following first order conditions will hold.

6 If _γ∗_ is at a boundary, a marginal change in risk or time preferences will not affect<sup>_argmax_</sup> _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 function _u_ ( _c_ ) . The following exposition closely follows the proof of Proposition 3 in Schlesinger (2000), which shows (without permitting external savings) that an increase in risk aversion increases insurance demand.

Pratt (1964) guarantees the existence of a function _h_ such that _v_ ( _c_ ) = _h_ ( _u_ ( _c_ )), _h_<sup>_′_</sup> _>_ 0, and _h_<sup>_′′_</sup> _<_ 0. Substituting _h_ into the expected utility function, we have the following expression, which represents a person with utility function _v_ who has selected _γ_<sup>_∗_</sup> and _s_<sup>_∗_</sup> (which are the optimal choices for someone with utility function _u_ ): For someone with utility function _v_ , we must examine how the choice of _γ_<sup>_∗_</sup> compares to their optimal _γ_ . Taking the derivative of Equation 15, utility changes as follows when we increase _γ_ above _γ_<sup>_∗_</sup> : Since U is concave in _γ_ (shown in Proposition 1), if<sup>_<u>dU</u>_</sup> _dγ_<sup>_>_0then</sup><sup>_γ∗_liesabove</sup> the new _γ_ which maximizes _U_ . This means that an increase in risk aversion would increase<sup>_argmax_</sup> _γ A_ ( _γ_ ). However, the sign of<sup>_<u>dU</u>_</sup> _dγ_ �� _γ_ = _γ_<sup>_∗_isnotimmediatelyapparent.</sup> Substituting _u_<sup>_′_</sup> ( _c_ 1) from Equation 14 and rearranging, 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,<sup>_argmax_</sup> _γ A_ ( _γ_ ) will unambiguously increase with risk aversion only if prudence is also weakly decreasing. 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<sup>_argmax_</sup> _γ A_ ( _γ_ ).

The model also does not provide a clear indication of how<sup>_argmax_</sup> _γ A_ ( _γ_ ) changes with the discount factor. As _β_ increases, consumers would show increasing appetite for savings and insurance, but the net effect on<sup>_argmax_</sup> _γ A_ ( _γ_ ) is ambiguous. The explicit insurance coverage through the WISA and self-insurance through (loadingfree) savings could be substitutes. The experimental analysis below measures comparative 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 individual, 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 insurance. 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 features, we recruited 322 male farmers from rural areas surrounding Ahmedabad, India, for a laboratory experiment in April-May 2010. Sessions were conducted in the Ahmedabad office of the Centre for Microfinance. During the computer-based sessions implemented using Qualtrics software, subjects participated in tasks designed to elicit preferences about risk, time, savings, and insurance. The savings and insurance 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 computers, 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 instructed 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.<sup>78</sup> 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 preference 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 participant’s WTA for each of four WISAs. The WISAs had _γ_ ’s of 1, 3<sup><u>2,1</u></sup> 3<sup>, 0</sup> . 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

> 7The exchange rate on May 1, 2010, was $1 = Rs. 44.

8To be clear, throughout the paper we do not regard the intertemporal choices studied here as sufficient 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 decisionmaking context.

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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 payment of Rs 180 after the monsoon.<sup>9</sup> The market price of Rs 500 of insurance coverage was Rs 66, making all the bundles of comparable monetary value.<sup>10</sup> 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.<sup>11</sup> 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.”<sup>12</sup> Subjects were told that after giving their minimum WTA for each of these 3x2+1 WISA WTA tasks,<sup>13</sup> 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: “Consider 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 purchase 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.

10We 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.

> 11With _γ_ = 0, the WISA would be equivalent to the post-monsoon cash, so there was no need to repeat the elicitation in that case.

12In 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.

13All subjects entered WTA’s in descending order,�1,<sup><u>2</u></sup> 3<sup>,</sup><sup><u>1</u></sup> 3<sup>, 0</sup> �, alternating between present and future payments. Subjects were permitted to go back and change earlier reported valuations, but did not do so.

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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 associating products with a well-known brand would increase WTA.<sup>14</sup> 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 products 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,<sup>15</sup> and also had the option of sending 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.

14Trust in the insurer was emphasized by Cole et al. (2013) as a significant factor in rainfall insurance adoption.

> 15Specifically, 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.

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# **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 interior mixture of the two.<sup>16</sup> 1 the valu- any Figure displays average 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 local 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 product. 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 insurance and over of the mixtures. Twelve did pure savings any percent of subjects 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 descriptive patterns. Results are shown in Table 3. Column 1 contains only the linear

> 16Except where specified to the contrary, in this Section for simplicity all analysis we report involves 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.

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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 specification 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 mostpreferred 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 discount factors: a set of calculating questions 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 ∈_ 31<sup>,</sup><sup><u>2</u></sup> 3 ) . � � 18
# **5 Interpretation of Findings**

Section 2’s model predicted that participants’ WTA would not have an interior local minimum in _γ_ . 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 products. 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 hypothesis. As explained earlier, participants were introduced to the WISAs using the Bundle 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 guaranteed 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 Bundle 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 share _γ_ 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 interacts them with the insurance share _γ_ . The interaction terms are again both economically 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 Insurance Frame, at _γ_ =<sup><u>2</u></sup> 3<sup>,</sup><sup>_dA_</sup> _d_<sup><u>(</u></sup> _γ_<sup>_<u>γ</u>_</sup><sup><u>)</u></sup> = 40.1 (95% confidence interval [20.3,59.9]), while for people with either of the more complex frames<sup>_dA_</sup> _d_<sup><u>(</u></sup> _γ_<sup>_<u>γ</u>_</sup><sup><u>)</u></sup> = 34.4 (95% confidence interval [21.6,47.3]). Therefore at _γ_ = 3<sup><u>2</u>themarginaleffectsof</sup><sup>_γ_onWTAarenot</sup> 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 postmonsoon. 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 number 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%) eventually 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 ∈_ <u>13</u><sup>,</sup><sup><u>2</u></sup> 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 during 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 redemption), 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 considerations 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_ If people exhibited diminishing sensitivity around a reference point, this means that their utility function is convex for losses below a reference point, and Proposition 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 _r_ 1and _r_ 2 respectively. Assuming that people calculate their WTA based on the prospect theory value function<sup>17</sup> , Equation 12 now becomes: _v_<sup>_′′_</sup> _c_ For a consumer with diminishing sensitivity, ( ) 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 reference point.

In the first period, we can consider the reference point _r_ 1 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 _c_ 1 _− r_ 1 will be less than (greater than) zero. Unfortunately, the model does not 17In models 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 function. 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.

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contain clear predictions about how the gift of the WISA will change savings, and therefore the first term has ambiguous sign.

In the second the choice of the reference is less clear. One reason- period, point 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 harvests. 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 _c_ 2 _− r_ 2 is always either zero or negative.<sup>18</sup> 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 : 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

> 18Note 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 _c_ 2 = _r_ 2.

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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 challenge for farmers around the world. We sought to understand whether and how a savings account with rainfall-indexed returns, a Weather Insurance Savings Account, might help. Contrary to standard theory, most farmers preferred both pure and insurance to an interior mixture of the two. Alternative savings pure explanations like simplicity preference do not appear to account for this fact. Instead, lower valuation of mixed seems consistent with a model where ex- products participants perience diminishing sensitivity to wealth changes around a reference point. Diminishing sensitivity to losses can imply a preference for full insurance over partial insurance. This suggests some WISAs, if offered commercially by financial institutions, 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 innovation 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 ∈_ 31<sup>,</sup><sup><u>2</u></sup> 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.

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