The demand for insurance under limited credibility: Evidence from Kenya∗ Stefan Dercon,† Jan Willem Gunning,‡ and Andrew Zeitlin† August 2011

Abstract The low demand for microinsurance products observed in recent studies is characterized by two stylized facts: first, demand is negatively correlated with measures of risk aversion, in contrast to simple models; and second, demand is positively associated with measures of trust. In this paper we develop a model of the demand for indemnity insurance that explains both of these stylized facts, based on the idea that individuals have limited trust in the credibility of the insurer’s promise to deliver a payment in the event of an indemnified loss. The model has the further testable implication that, when trust in insurer credibility is heterogeneous across individuals, those with low trust are more sensitive to variation in premium costs. We test and find support for the predictions of this model using data from a randomized, controlled trial of composite health microinsurance product among tea growers in Nyeri, Kenya. To do so we combine experimental variation in prices with measures of risk preferences and trusting behavior from a laboratory experiment conducted in the field at baseline. The results suggest scope for policies that increase insurance purchases by improving potential clients’ confidence in the enforceability of the insurance contract.

∗ We thank Michal Matul (ILO), Ann Kamau and David Ronoh (CIC Kenya), Therese Sandmark (SCC), and Edward Kinyungu and Morris Njagi (Wananchi SACCO) for their support in the design and implementation of the project. Job Harms, Naureen Karachiwalla, and Felix Schmieding provided excellent research assistance. We are grateful to Abigail Barr, Lori Beaman, Gharad Bryan, and Daniel Clarke for helpful comments. Financial support from the ILO Microinsurance Innovation Facility is gratefully acknowledged. † University of Oxford ‡ VU University Amsterdam

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Introduction

Risk, and its mitigation, are widely believed to be an important source of welfare losses in developing countries. Shocks to health and income appear to have long-lasting impacts (Beegle, De Weerdt and Dercon 2008). The mitigation of risk may lead to foregone investment opportunities with substantial expected returns (Rosenzweig and Binswanger 1993, Morduch 1995). High costs of participation in informal insurance networks can restrict resources available for investment in economic activities. Seen in this light, recent empirical evidence of the demand for microinsurance are puzzling. Not only is demand for both indemnity and indexbased insurance products low, but the likelihood of insurance purchases is negatively associated with measures of risk aversion in many contexts (Cole, Gin´e, Tobacman, Topalova, Townsend and Vickrey 2008). Suggestively, in several studies measures of trust are positively associated with insurance demand (Cole et al. 2008, Cai, Chen, Fang and Zhou 2010). In this paper, we develop a model of the demand for indemnity insurance under limited credibility of the insurer to explain these stylized facts, and we test this model using data from a field experiment on health insurance in rural Kenya.1 We define the credibility of the insurer as the potential policyholder’s perceived likelihood that a claim would be paid in the event of a loss. Clearly, limited credibility can reduce the demand for insurance. It can also explain the presence of a negative relationship between risk aversion and insurance demand. Intuitively, a reduction in credibility increases the likelihood of the ‘worst-case’ outcome, in which an insurance premium is paid and a loss is suffered, but no claim is paid; this outcome is particularly threatening to the risk averse. We test the model using data from a randomized, controlled trial of policies affecting demand for ‘Bima ya Jamii’, a composite health insurance product among tea farmers in the district of Nyeri, Kenya. The field experiment was a factorial design, which combined cross-cutting experimental variation in premium costs at the individual level with cluster-randomized treatments of financial literacy training and ‘viral’ marketing. Two laboratorytype experiments were conducted in the field at baseline, a Trust Game (Berg, Dickhaut and McCabe 1995) and a Holt and Laury Gamble-Choice Game (Holt and Laury 2002), to provide measures of trust attitudes and risk preferences respectively. Data from the laboratory experiments allow us to replicate stylized facts in the literature: insurance demand is nega1 The model in this paper is related to Doherty and Schlesinger (Doherty and Schlesinger 1990), who study insurance demand with a possibility of insurer default, and Clarke (2011), who studies the demand for index insurance in the presence of basis risk. In an indemnity (livestock) insurance context, Cai and coauthors (2010) make the related observation that farmers who believe such insurance is unlikely to pay out in the event of a loss are less likely to purchase insurance.

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tively associated with risk aversion as measured in the lab, and positively associated with trusting behavior. Combining these data with experimentally induced variation in premium costs, we find support for the hypothesis that individuals with low trust in insurer credibility are more responsive to price variation, as predicted by the theory. These results suggest that the perceived enforceability of claims for indemnified losses is an important constraint to insurance adoption. Such a finding is potentially important for policy, particularly since a number of studies—including our own—fail to find impacts of financial literacy training on insurance demand, in spite of the widespread view that poor understanding of such financial instruments is a central barrier to their adoption (Karlan and Morduch 2010).2 By contrast, insurers are well positioned to shape perceptions about the likelihood of paying claims; evidence from India suggests that endorsements by trusted authorities may have this effect (Cole et al. 2008). Regulators have tools at their disposal that can improve confidence in these outcomes as well. The remainder of the paper proceeds as follows. Section 2 presents a simple model of indemnity insurance under limited credibility, and derives testable implications. Section 3 describes the field and laboratory experiments, as well as survey data collected. Section 4 presents the main results of the paper, and Section 5 concludes.

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A model of insurance demand under limited credibility

We consider an agent who has to decide whether or not to take indemnity insurance to protect himself against the risk that his wealth, w, is reduced by a fixed amount, c. The probability of this loss is p. Without insurance the agent’s welfare (expected utility) is given by W = (1 − p)u(w) + pu(w − c).

(1)

The agent is risk averse so the utility function u is strictly concave. Under insurance the agent pays a premium, π. If the loss occurs the insurer pays full compensation with probability q and otherwise defaults, 2

A recent paper by Gharad Bryan (2010), on demand for weather-index insurance in an agricultural context, suggests that ambiguity aversion with regard to production technologies may also affect insurance demand. The focus of Bryan’s model is ambiguity with regard to the probability of incurring a loss, rather than with regard to the probability of insurance payouts themselves. This focus is particularly appropriate to settings characterized by uncertainty about new technologies, as considered by Bryan, but seems less appropriate to health, where individuals are likely to have well formed beliefs about their risks of illness.

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paying nothing.3 With insurance the agent’s expected utility is therefore

f = (1 − p)u(w − π) + p[qu(w − π) + (1 − q)u(w − π − c)] W = (1 − pe)u(w − π) + peu(w − π − c)

(2)

where pe = p(1 − q). The probabilities in this compound lottery satisfy 0 < p < 1, 0 < q ≤ 1. f > W. The agent will accept the insurance contract if W The probability q is a measure of the insurer’s credibility. Under full credibility (q = 1) and actuarially fair insurance (π = pc) the probability pe equals 0 and f = u(w − π) = u(w − pc) > (1 − p)u(w) + pu(w − c) = W W by Jensen’s inequality and the concavity of the utility function. This is, of course, the standard result that under full credibility a risk averse agent will prefer insurance. Insurance raises the outcome in the bad case (from w − c to w − pc) and reduces the outcome in the good case (from w to w − pc). When the premium is actuarially fair, this amounts to the opposite of a mean preserving spread and is therefore obviously attractive to a risk averse agent. Limited credibility (q < 1) changes the attractiveness of insurance fundamentally. Insurance now reduces the probability of a loss (from p to pe) but it makes the bad outcome worse: w − π − c instead of w − c. It follows that a very risk averse agent may refuse an insurance contract which a less risk averse agent would accept. The model is similar to that of Doherty and Schlesinger (1990), with one crucial difference. Doherty and Schlesinger assume that the agent can choose the degree of insurance cover. We rule out partial insurance: the loss c is either fully covered by insurance or not at all. In the context of health insurance in developing countries this specification is more realistic: insurance contracts (such as in the Kenyan Bima ya Jamii project) typically offer indemnification for specific risks such as the cost of hospitalisation on an all-or-nothing basis. In that setting limited credibility (q < 1) affects the decision to take up insurance whereas in the Doherty-Schlesinger model it affects the optimal insurance cover. Our model is similar in approach to that of Clarke (2011), who considers the question why a rational agent might refuse index insurance. In this setting the key issue is basis risk: the index is imperfectly correlated 3

This terminology corresponds to a particular interpretation of the model. Nothing would change if the insurer never defaults but the agent is unclear on what is covered by the contract; q is then the subjective probability that a loss is covered.

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with the agent’s outcome variable (e.g. crop yield) so that he may get no compensation after suffering a loss or, conversely, get compensation when in fact he has not suffered a loss. This makes the demand for insurance with basis risk fundamentally different from the case of indemnity insurance (Clarke 2011, pp. 2, 5). Our case is asymmetric: while the agent may fail to be compensated for a loss he will not receive compensation in the absence of a loss. What is similar in the two models is that insurance may be rejected because it makes the worst outcome worse: under index insurance because of imperfect correlation, in our case of indemnity insurance because of limited credibility. f (q). It Insurance will be accepted for q > q ∗ where q ∗ solves W (q) = W follows from (1) and (2) that q∗ = 1 −

u(w − π) − [(1 − p)u(w) + pu(w − c)] . p[u(w − π) − u(w − π − c)]

(3)

Figure 1 plots q ∗ as a function of the degree of relative risk aversion, R for a numerical example with constant relative risk aversion (CRRA) and parameter values p = 0.5, w = 100 and c = 50. The plot is shown for various values of the premium: π = δpc where δ takes the values 1.0 (black), 0.9 (red) or 0.75 (green).4 Note that for δ < 1 the premium is subsidised. For δ = 1 the premium is acturarially fair in the conventional sense (π = pc) but not in the sense of allowing for limited credibility (π = pqc). While π = pqc is obviously the relevant theoretical concept of actuarial fairness it would imply that the insurer lowers the premium to compensate for his own limited credibility; this would seem rather far fetched. We assume that agents are heterogeneous in terms of their perceptions of the probability of default: q is a subjective probability. It follows that an agent is characterised by (q, R) which defines a point in the Figure. Clearly, the agent will accept insurance only if that point lies above the locus. Figure 1 shows that q ∗ is indeed non-monotonic in risk aversion: q ∗ initially decreases with risk aversion, reaches a minimum and then increases. It follows that for agents who differ in risk aversion but not in their perception of the credibility parameter q those with either very low or very high risk aversion will accept insurance while those with an intermediate degree of risk aversion will accept it. This may explain the empirical ‘puzzle’ that more risk averse agents may refuse a contract which less risk averse agents accept. While the numerical example is instructive the result is more general: Proposition 1. For CRRA utility functions and a premium π = δpc the minimum credibility level q ∗ is increasing in the degree of relative risk aversion R at high levels of R (and in case δ < 1 for sufficiently low values of 4

Since π = δpc it follows from (3) that when the utility function is linear (R = 0) q = δ. ∗

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Figure 1: q ∗ locus as a function of price and coefficient of relative risk aversion

Note: Figure plots q ∗ locus for premium with 0% (black), 10% (red) and 25% (green) subsidy.

p). For low risk aversion q ∗ is decreasing in R for low subsidy levels (high δ) but increasing for high subsidy levels and high values of p. f = W: Proof. The q ∗ locus is defined by W (1 − pe)u(w − π) + peu(w − π − c) = (1 − p)u(w) + pu(w − c).

(4)

Note that for δ = 0 (i.e. when the premium is fully subsidised: π = 0) the locus coincides with the horizontal axis since q ∗ = 0 (hence pe = p) then obviously solves (4). The CRRA assumption implies du(x) 1 = u(x)(− ln x + ) = ψ(x). dR 1−R

(5)

Differentiating (4) using pe = p(1 − q ∗ ) and (5) gives dq ∗ A−B = dR p[u(w − π) − u(w − π − c)]

(6)

where A = (1 − p)ψ(w) + pψ(w − c) and B = (1 − pe)ψ(w − π) + peψ(w − π − c). Clearly, the slope of the locus is positive (negative) for A > B (A < B) and changes in the subsidy (δ) affect B (through pe and π) but not A. For high risk aversion (large R) ψ(x) is approximately equal to −u(x) ln x and this function is decreasing and strictly convex. For p = 0 (which implies pe = 0 and π = 0) A = ψ(w) = ψ(w − π) = B so that the slope of the locus is 0. However, evaluating the derivative at p = 0, d(A − B) = [ψ(w − c) − ψ(w)] − δcψ 0 (w) > 0 dp 6

(7)

since ψ is strictly convex and δ ≤ 1. Hence for low positive values of p the slope of the locus is positive. At the other extreme, for p = 1 (hence π = δc and pe = 1 − q ∗ ) A = ψ(w − c) and B = (1 − pe)ψ(w − π) + peψ(w − π − c). It follows that in the absence of a subsidy (δ = 1 hence π = c and from (3) pe = 0) A = B and otherwise A < B. We now have, evaluating the derivative at p = 1: d(A − B) dp

= [ψ(w − c) − ψ(w)] +δc[(1 − pe)ψ 0 (w − δc) + peψ 0 (w − δc − c)] dq ∗ (1 − p )[ψ(w − δc) − ψ(w − δc − c)]. dp

(8) (9)

∗

∗

dq From (4) 0 < dq dp < 1 and therefore a fortiori 0 < p dp < 1. Hence the last term in (8) is negative. Given the convexity of ψ it follows that

d(A − B) <0 dp in a neighbourhood of p = 1. The slope of the q ∗ locus is therefore positive: in the absence of a subsidy for all 0 < p < 1 and in case of a subsidy for sufficiently low values of p.(In our numerical example we chose the value p = 0.5 which apparently is sufficiently low: all loci in Figure 1 have positive slope for large R.) Now consider low values of R. For R → 0 the utility function becomes linear so that (4) reduces to (1 − pe)(w − π) + pe(w − π − c) = (1 − p)(w) + p(w − c).

(10)

For R → 0 u(x) = x and ψ(x) = x(− ln x + 1) < 0 (provided ln x > 1), ∗ ψ 0 (x) = − ln x and dq dδ = 1. Define = x ln x. If the premium is not subsidised (δ = 1) the locus has negative slope. This can be seen by substituting ψ(x) = x − ϕ(x) in the definitions of A and B and using (9): A − B = [(1 − pe)ϕ(w − π) + peϕ(w − π − c)] −[(1 − p)ϕ(w) + pϕ(w − c)] = ϕ(w − pc) − [(1 − p)ϕ(w) + pϕ(w − c)] (since pe = 0 and δ = 1) < 0 (since ϕ(x) is strictly convex). To see how the slope of the locus changes with δ we only need to consider ∗ dB the effect of δ on B. From (8) and using dq dδ = 1 dδ > 0 iff [ψ(w − π) − ψ(w − π − c)] > c[(1 − pe)ψ 0 (w − π) + peψ 0 (w − π − c)] 7

or for ϕ(w − π) − ϕ(w − π − c) < c[(1 − pe)ϕ0 (w − π) + peϕ0 (w − π − c)].

(11)

Note that for δ → 1 pe → 0. In that case (10) reduces to ϕ(w − π) − ϕ(w − π − c) < cϕ0 (w − π) and this condition is satisfied since ϕ(x) is strictly convex. Hence dB dδ > 0 for δ = 1. It follows that moving down in the Figure along the vertical axis the slope of the q ∗ locus increases: the locus becomes flatter. In an extreme case (for very high risk and very high subsidy) the slope may even become positive at the point where it intersects the vertical axis (i.e. for R = 0). This may be seen in the limiting case when δ → 0 and p → 1: then π = 0 0 and pe = 1 so that dB dδ < 0 iff ϕ(w) − ϕ(w − c) < cϕ (w − c) and this is true because of the convexity of ϕ(x). A subsidy shifts the q ∗ -locus downwards so that (for a given distribution of agents in (R, q) space) more agents will accept insurance. In particular, a risk neutral agent will now strictly prefer insurance at q = 1 because of the subsidy element. Note from Figure 1 that the minimum shifts to the left: the larger the subsidy the lower the degree of risk aversion beyond which q ∗ is increasing in risk aversion. (Recall that for extreme values of p and δ the minimum does not occur for R > 0: in that case the locus is monotonically increasing. We will ignore this possibility in what follows.) Proposition 1 has two testable implications. First, credibility of the insurer as perceived by the agent should have a positive effect on the probability that insurance is accepted. Secondly, controlling for trust, the probability of insurance purchase should first increase and then decrease in risk aversion. However, empirical tests of Proposition 1 are limited in two ways. First, given the presumptive non-manipulability of risk preferences, there will remain a potential for omitted variables to drive or mask any empirical association between risk preferences and insurance purchase decisions, nonmonotonic or otherwise.5 Second, whether the stated non-monotonicity is observed in any particular application will depend on the support of q and R in the population. Given that our experimental design provides exogenous variation in the price of insurance, we therefore focus on implications of the model for the way in which insurance purchase decisions will covary with price across observable subgroups. This approach allows us to control for these subgroups, 5

Trust in the credibility of the insurer is potentially manipulable, although our experiment did not set out to do so. The results of Cole and coauthors (2008), who use endorsements to enhance credibility, suggest a causal effect of trust as predicted by Proposition 1 and in line with the association observed in our data.

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and test the model’s implications for heterogeneous effects of (randomly assigned) prices for different subgroups. In particular, we consider heterogeneous response along a natural dimension for testing the theory: the perceived credibility of the insurer. To highlight the effects of changes in prices and preferences on insurance demand, we analyze the expected utility differential, taking the difference across states in which the individual is and is not insured. We do so on the grounds that it is a desirable property of a stochastic choice model that the probability of becoming insured should be increasing in this expected utility differential.6 The expected utility differential is decreasing in the price of insurance, trivially; this is what generates a downward-sloping demand curve. We show that strict concavity of the utility function also implies that this expected utility differential is decreasing in price more strongly for individuals who have low trust in the credibility of the insurer (low q). To do so, let us define ˜ − W , the difference in expected the expected utility differential as ∆ ≡ W utility between the insured and uninsured states. Proposition 2 shows that the effect of price on the expected utility gain from adopting insurance is greater among individuals with low trust, q, in the credibility of the insurer. Proposition 2. Let the expected utility differential from insurance adoption be given by ∆, as defined above, and assume that individuals have strictly concave utility, defined over their net wealth. Then ∂∆/∂c < 0, and ∂ 2 ∆/∂π∂q > 0. Proof. Differentiation of ∆ yields
∂2∆ = p u0 (w − π − c) − u0 (w − π) , ∂π∂q where u0 (·) denotes the first derivative of the utility function. By the strict concavity of u(·), this is strictly positive. This is illustrated for the CRRA case in Figure 2, which highlights the effect of applying a discount to the insurance premium π on the resulting expected utility differential, evaluated at alternative (subjective) values of q. Individuals who perceive the insurer to have low credibility are particularly responsive to changes in price. In the context of hospitalization cover, subjective beliefs about the credibility of a particular insurance policy, q, will vary across individuals. These are a composite of several factors, among them: the likelihood of the hospital 6 As Wilcox (2008, 2011) notes, however, the expected utility differential is not always increasing in the degree of risk aversion, even when the distribution in the absence of insurance is a mean-preserving spread of the distribution with insurance. Wilcox suggests a normalization, contextual utility, to address this issue. The propositions that follow can also be shown to hold for the normalized expected utility differential that he employs.

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Figure 2: Differential impact of insurance price on demand, by level of credibility

Notes: Figure shows difference in expected utility with and without insurance for individual with CRRA utility with coefficient of relative risk aversion 2. Initial endowment of w = 100; loss of 60 occurs with probability 0.5. Proportional discount in figure is applied to actuarially fair premium; i.e., cost of insurance is π = pL(1 − d), for discount d.

agreeing to accept the insurance policy; the likelihood of the insurer continuing to be in business and agreeing to pay a claim; and—if the individual is required to make a cash payment at the time of the procedure—the likelihood of reimbursement actually reaching the individual.7 Objective values of q are therefore likely to vary across individuals, who may have variable success in using the policy. Subjective beliefs about one’s own value of q may introduce a further element of subjectivity, as they will depend (among other things) on trust in particular individuals and institutions. To provide an empirical test of Proposition 2, we combine behavior in a laboratory setting with experimental variation in prices, as described in the next section.

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Experimental design and data

We test the model of the preceding section using data from a field experiment conducted in Nyeri District, Kenya. The experiment offered a composite health insurance policy, Bima ya Jamii, to tea farmers belonging to the 7 While the de jure policy is that no up-front payments should be made by Bima ya Jamii policyholders, individuals were in some cases required by hospitals to make such payments in the early stages of implementation (prior to the present study).

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Wananchi Savings and Credit Cooperative Society. The field experiment was a factorial design, in which variation in premium costs of the policy was cross-cut with cluster-randomized marketing and learning interventions, as will be described below. In this paper, we combine baseline data on subjects’ behavior in a series of laboratory experiments conducted in the field with insurance purchase decisions as the basis for our empirical tests. Bima ya Jamii is a composite health insurance product offered by the Cooperative Insurance Company (CIC) of Kenya. This product bundles the in-patient hospitalization cover, provided by the National Hospital Insurance Fund to all public-sector employees, with together with cover for lost work during hospital stays and funeral insurance. There are no exclusions on the basis of prior conditions. At the time of the study, the cost of the policy was KShs 3,650 per year (roughly USD 50 using exchange rates at that time). CIC typically partners with local financial institutions, who act as intermediaries in the delivery of the product. Our study focuses exclusively on their work with Wananchi Savings and Credit Cooperative Society, a cooperative comprised primarily of tea farmers in Nyeri District, Central Province. All Wananchi members hold bank accounts with this SACCO, and payments for their tea harvest is made through these accounts by the Kenya Tea Development Agency. In addition, Wananchi offers a range of loans to its members, though in practice participation in these loans is fairly limited. Wananchi’s members are divided into 162 tea-collection centres, which are grouped in 12 administrative zones. 150 of these centres were selected for inclusion in our study, and these tea-collection centres provide the basis for our cluster-randomized design, as described below. In each centre, we randomly selected 9 farmers at random from Wananchi’s membership roll, together with the elected ‘delegate’ who represents the members in the coop’s meetings, for inclusion in our baseline study. We analyze the decision to purchase insurance among this sample.

3.1

Field experiment

To study insurance adoption and impacts, we adopted a factorial design. First, we randomly assigned tea centres either to control or to one of three treatment arms. Second, we randomly assigned some individuals in each of these three treatment arms to receive vouchers that would reduce the premium cost of the policy, as described below and in Table 1. Sixty of the tea centres in the study were allocated to a control treatment arm, given the eventual interest of the project in studying the impacts of the insurance product on health and economic outcomes. While all Wananchi members were technically eligible to purchase insurance—rendering our experiment an ‘encouragement design’—members of these control centres received no direct information about the product from Wananchi staff, and 11

received no price discounts. In practice takeup of the product was zero in these centres, and they are excluded from the analysis in the remainder of this paper. The remaining 90 tea centres all received a meeting in which basic information about the Bima ya Jamii product was provided by CIC marketing agents, who were accompanied by a representative from Wananchi. These meetings lasted between one and two hours. We refer to the 30 centres that received these meetings but did not receive the educational or the peerreferral treatments described below as the marketing only treatment. In our study circles treatment, a further 30 centres received education in financial literacy, with a focus on insurance. The ‘study circles’ modality used to deliver this educational training is a system practiced in the dissemination of agricultural technologies and other contexts by the Swedish Cooperative Center (SCC), an international NGO that administered this treatment. Its basic idea is to train someone in the community—in this case, the Wananchi Delegate—to lead regular study groups, in which they discuss written materials together with a small group of their peers. SCC developed the curriculum for these study circles together with Microfinance Opportunities, an NGO with extensive experience in financial literacy training. The topics covered were general, in that it did not mention the Bima ya Jamii product by name, though the focus was primarily on indemnity insurance and health-related shocks. The resulting course consisted of 10 modules, which were undertaken on a weekly basis prior to launch of the basic marketing treatment. In order to better position the study to capture any potential impacts of of this treatment, delegates were instructed to include the 9 other sample members in their centre in the first of the study groups they conducted, although they were also encouraged to repeat this curriculum with other members of their centre. The final 30 treatment centres received basic market product information, as in the marketing only treatment, as well as a peer referral incentive. Any Wananchi member belonging to a tea centre in the peer referral treatment arm would receive an incentive equal to 10 percent of the value of the policy (KShs 365) for each member of the same centre whom she brought to Wananchi offices and who signed up for the policy, naming her as a sponsor. The motivation for the inclusion of the peer referral treatment arm in the study was twofold. First, at the time of the study, CIC Kenya was beginning to work in other populations with a marketing agency that was using such a scheme to motivate ‘viral’ or peer-to-peer marketing of the product.8 8

The proposed design of this marketing agent differed markedly from ours, in that it provided payouts to an individual not only if she encouraged others to join the policy, but also when those individuals encouraged a second generation of adopters, and so on. The result was uncomfortably close to a pyramid scheme, and was ultimately overhauled by CIC for this reason, but the potential for peer-to-peer marketing incentives to improve demand and in particular to improve the risk pool for this product, remained an important

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Table 1: Experimental design

Centre-level treatment Control (60) Marketing only (30) Marketing + study circles (30) Marketing + peer referral incentive (30)

Individual premium vouchers No discount 10% discount 20% discount 597 0 0 105 90 102 108 91 100 98 94 103

Notes: Table displays number of survey respondents, by centre-level treatment arm and discount voucher received. Number of tea centres assigned to each centre-level treatment reported in parentheses.

Second, the role of incentives in the diffusion of information about new financial products was a distinct research topic of interest in the study. Such a referral scheme was hypothesized to have two, potentially offsetting effects. On the one hand, it could improve the risk pool, in a setting where it was feared that adverse selection threatened the sustainability of the insurance policy. On the other hand, in a climate in which fears of pyramid schemes were widespread, such a marketing strategy could convey a negative signal about the trustworthiness of the insurer. To foreshadow the results of Section 4, the (detrimental) trust effect appears to have dominated in this case. Wananchi members in centres eligible for the peer referral incentive were significantly less likely to purchase the policy. We suspect that this marketing approach did indeed raise fears of a pyramid scheme among the members of those centres, but we do not have post-intervention survey data that could be used to verify this hypothesis. For this reason, and because the diffusion of information through social networks lies outside the scope of the present paper, we will focus attention on the marketing only and study circles arms in order to test our model of insurance demand under limited credibility. At the individual level, Wananchi members outside of the control centres were randomly allocated vouchers that would reduce the costs of the Wananchi premium by values equivalent to 0, 10, or 20 percent of the original cost. These vouchers were drawn with equal probability during a public lottery conducted during the marketing session common to all treatment arms.9 Since all Wananchi members in treatment centres were invited to these marketing sessions, even members who were not included in the baseone for policymakers. 9 Attendance at these marketing sessions by our sample participants was not universal. In order to ensure that the probability of receiving a voucher was uncorrelated with other possible determinants of insurance demand, we randomly assigned vouchers with the same probabilities to individuals who did not attend this marketing session. Vouchers were delivered to any such individual receiving a non-zero discount by their delegate.

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Table 2: Gamble-choice game: payoffs and probabilities in gain- and lossframed series.

Task 1 2 3 4 5 6

Pr(H) 0.8 0.7 0.6 0.5 0.4 0.3

Gain frame Risky Safe Hr Lr Hs Ls 300 0 100 50 300 0 100 50 300 0 100 50 300 0 100 50 300 0 100 50 300 0 100 50

Loss Risky Hr Lr 0 -300 0 -300 0 -300 0 -300 0 -300 0 -300

frame Safe Hs Ls -200 -250 -200 -250 -200 -250 -200 -250 -200 -250 -200 -250

E[πr − πs ] 150 125 100 75 50 25

Notes: Table shows probability of high payoff, H, in risky and safe lottery choices, together with high and low payoff values, for gain- and loss-frame HL series. E[πr − πs ] denotes difference in expected return from risk versus safe lottery. All payoff values expressed in Kenya Shillings. Subjects endowed with KShs 300 prior to participation in loss-frame series.

line survey were eligible to participate in this lottery. The resulting distribution of vouchers across individuals in the baseline survey is shown, broken down by treatment arm, in Table 1.

3.2

Laboratory experiment

In addition to this field experiment, sampled individuals participated in a pair of laboratory experiments conducted in the field at baseline. These laboratory experiments were employed to provide measures of attitudes toward risk and trust that could be used to test hypotheses about the demand for insurance. 3.2.1

Laboratory measures of risk preferences

To obtain a measure of Wananchi members’ preferences toward risk, we employed a standard gamble-choice game, based on the instrument of Holt and Laury (2002, henceforth HL). Our specific design is adapted from Barr (Barr 2007) to the Kenyan context. This game consists of a series of tasks, in each of which the subject chooses between two binary lotteries, one ‘safe’ lottery and one ‘risky’ lottery. Each lottery consists of a high-payoff outcome (H) and a low-payoff outcome (L). Payoffs from winning and loosing either of these lotteries are constant within the series. In any given task, the probability of the high-payoff outcome is the same in both the risky and safe lotteries; this probability varies across tasks. We played two series of this game, as shown in Table 2: a gain-frame series, and a loss-frame series. In the gain-frame series, subjects began

14

with an initial endowment of zero, and had an opportunity to win either KShs 300 or KShs 0, if they chose the risky lottery, or KShs 100 or KShs 50, if they chose the safe lottery.10 In the loss-frame series, subjects were endowed with KShs 300 prior to play, so that the reduced-form payoffs in each task of the loss-frame series are equivalent to those in the gain-frame series. These were played sequentially, with payoffs made after both series were complete. Monetary payoffs were based on a single task selected at random from across the two series. This payoff mechanism was explained to participants in advance. To the extent that the loss frame changes subjects’ reference point, we may expect that differences in risk preferences manifested in the gain-frame and loss-frame tasks are driven in part by loss aversion. Figure 3 displays population frequencies for the choice of the risky lottery, by task, for both the gain-frame and the loss-frame lotteries. For ease of interpretation, tasks are indexed by the probability of the high-value outcome in that task, which ranges from 0.8 to 0.3. As expected, the fraction of individuals choosing the risky lottery declines as the probability of the high payout decreases. This reflects in part the change in the expected income difference between the risky and safe lotteries, which falls from KShs 150 to KShs 25 as the probability of the high payoff falls from 0.8 to 0.3. A rational, expected-utility maximizing individual, with weakly risk averse preferences should switch from choosing the risky to the safe lottery at most once over the course of the six tasks of the gain-frame series. Assuming that the individual’s preferences over outcomes in this lottery can be represented by a constant relative risk aversion (CRRA) utility function of the form u(x) = x1−R /(1 − R), then for such individuals it is possible to use their observed decisions to place bounds on the CRRA coefficient R. An individual choosing the risky lottery in all tasks must have R ≤ 0.22, whereas an individual choosing the safe lottery in all tasks must have R ≥ 0.82. Those who switch from risky to safe between tasks 1 and 6 will have an R that can be bounded within a strict subset of the interval (0.22, 0.82). In practice, only 53 percent of individuals make decisions in the gainframe series that are can be rationalized as the deterministic choices of an individual with weakly risk averse preferences.11 Such inconsistent behavior is common among decision problems over risky choices in laboratory experiments. For example, Hey (2002) reports that 30 percent of subjects in a laboratory setting make different decisions when faced with the same task twice. To provide an individual-specific measure of risk preferences at the individual level for all individuals, we estimate CRRA parameters by maximum likelihood for each person individually (see, e.g., Harrison et al. 10 The prevailing exchange rate at the time of the laboratory experiment was KShs 75/USD, meaning that the maximum possible payout in this series is USD 4. 11 A comparable number (52 percent) exhibit such consistent preferences in the lossframe series.

15

Figure 3: Decisions in gain-frame and loss-frame lottery-choice experiment

Notes: Figure shows the population frequency of individuals choosing the risky lottery in each task. This is illustrated for all participants in the lottery-choice experiment in treatment villages.

2010).12 To do so, we assume that people place values on each lottery according to expected utility theory, with CRRA utility defined as above. To allow for the possibility of errors, we use the ‘contextual choice’ specification of Wilcox (2008, 2011).13 Defining EU1 (R), EU0 (R) as the expected utility of an agent with CRRA coefficient R in the risky and safe lotteries, respectively, we model agents’ binary decision, D, to choose the risky lottery as   EU1 (R) − EU0 (R) D=1 +e , (12) u(¯ x; R) − u(x; R) where e ∼ (N, σe ), and u(¯ x; R), u(x; R) are utility of highest/lowest payoffs that can occur in either lottery (that is, x ¯ = 300; x = 0). This specification differs from familiar probit models of choice only in that the expected utility differential is scaled by the difference in utility between the highest and lowest outcomes. As Wilcox argues, this specification ensures that an increase in R makes an agent less likely to choose the risky alternative, over 12 For individuals who choose either all risky or all safe lotteries, R cannot be estimated by maximum likelihood. We impose values of R = 0.22, 0.82 in these polar cases. These reflect the highest and lowest values of R, respectively, consistent with observed choices. 13 In the empirical results that follow, we demonstrate that the primary test of the model is robust to alternative parameterizations of risk preferences.

16

Figure 4: Distribution of fitted coefficient of relative risk aversion

all values of R—a desirable property that is not satisfied by linear index models that take the expected utility difference as their index. The resulting distribution of estimated risk preferences is illustrated in Figure 4 for the gain-frame and loss-frame lotteries. The mean value of RG , the CRRA coefficient in the gain-frame lottery, is 0.49 (standard deviation 0.19). As evident in the raw data, behavior in the loss-frame sequence is consistent with a greater degree of risk aversion; the mean estimated coefficient of relative risk averison is 0.55 (0.19) in this series. This puts these estimates in the same range as those found in similar laboratory experiments in the field; for example, Harrison and coauthors (2010), in their EUT model assuming homogeneous preferences, estimate a population parameter of R = 0.54. 3.2.2

Laboratory measures of trust

In the second part of our baseline laboratory experiments, we sought to elicit a measure of trust.To do so we use a variant of the Trust Game, originally designed by Berg, Dickhaut, and McCabe (1995, henceforth BDM). We adapt the design employed in Zimbabwe by Barr (2003) as described below. The basic setup of the Trust Game is as follows. Players are assigned to one of two roles, Sender or Receiver. Both are endowed with KShs 200 at the outset of the game. The Sender can then decide to send a portion of their endowment to the Receiver (from zero to KShs 200, in increments of KShs 50). Any amount that is sent to the Receiver is tripled. The Receiver can 17

then decide to return any portion of this tripled amount—possibly none—to the Sender, at which point the game concludes. We adapt this basic setup in three ways. First, we elicit the decisions of the Receiver by strategy method—that is, we elicit the Receiver’s strategy for each of the possible allocations that they could receive from the Sender.14 Second, since our interest is primarily in Sender behavior, and since we wished to abstract from issues of learning and repeated interaction, we divide the ten participants in each laboratory settings into two groups of five at random. One individual in each group was selected to play the role of the Receiver, while the remaining four individuals played the role of the Sender. The Receiver’s strategy profile determined payoffs for all Senders, while one Sender’s decision was chosen randomly and anonymously to determine the payout of the Receiver.15 Third, we enforce that the Wananchi Delegate was always the Receiver in their group. Since the Delegate represents an authority figure associated with the SACCO and so, potentially, with the credibility of the insurance product being marketed, comparison of trusting behavior of trusting behavior individuals playing with ordinary Wananchi members and those playing with the Delegate may be informative about trust in financial institutions. Sender behavior in the Trust Game is illustrated in Figure 5. Senders in our sample of treatment locations send 65 percent of their endowment, on average, to the Receiver. This is a somewhat greater fraction than observed in some other contexts: Camerer’s (2003) survey finds a typical investment rate of 50 percent in the Trust Game. This high investment rate may stem from a combination of the partially anonymized design and an expectation of greater trustworthiness on the part of the Receiver, whose return to generosity is effectively multiplied by the act of playing with four Senders simultaneously. As in Barr (2003) we observe a substantial fraction of players investing 50 percent of the stake. What is particularly striking in our findings is the strong mode of 100 percent investment (a substantial fraction of individuals are also observed to invest the full stake in the cross-country study of Ashraf et al. 2006). 14

See, inter alia, Ashraf (Ashraf, Bohnet and Piankov 2006), and Barr, Ensminger, and Johnson (2009) for a related uses of the strategy method in the Trust Game. While it is a general concern that use of the strategy method elicits different behavior than sequential play in laboratory experiments, Vyrastekova and Onderstal (2005) provide evidence that the strategy method does not substantially affect Sender behavior, which is the focus of this paper. 15 To the extent that the Receiver has other-regarding preferences, this setup is likely to lead to more generous behavior on her part. Anticipating this, forward-looking Senders may exhibit relatively more trusting behavior then in the standard, two-person Trust Game. Because we are interested not in the comparison of behavior in this game with other implementations of the Trust Game in the literature, but rather in the relationship between variation in behavior in this game to insurance purchase decisions, we do not believe this modification likely to confound our results.

18

Figure 5: Sender investments in trust game

We find that Senders invest less when they have been randomly paired to play with the Delegate in their center. A regression of the share invested on an indicator for whether the Receiver is a Delegate gives a coefficient of -0.05 (standard error 0.03, clustered by tea centre; this difference is significant at the 10 percent level). This difference does not appear to be driven by differences in the trustworthiness of Delegates as compared to ordinary members; if anything, delegates return a slightly higher share of the amount they receive than their counterparts, although this difference is not statistically significant. Caution is required in interpreting this difference as an absence of trust in institutions, since differences in altruism, or distributional preferences over outcomes that include income outside the game, may also drive the difference in observed play. In the analysis of Section 4, we categorize individuals as exhibiting low trust if they invest less than 50 percent of the stake. It should be noted that behavior in the trust game may combine several things, including altruism, attitudes toward risk, expected trustworthiness of the Receiver, and a preference for trusting behavior. A large body of literature has sought to understand the relative contribution of these factors (Barr 2003, Eckel and Wilson 2004, Ashraf et al. 2006). We seek to isolate the contribution of expected trustworthiness by focusing on the predictions of our model for decision to purchase insurance (assuming individuals do not have preferences for exhibiting trust in institutions), by including laboratory measures of risk preferences in all specifications, and by focusing on centres where peer referral incentives were not applied.

19

There is some precedent for the view that behavior in the Trust Game may correlate with financial decisions. In particular, Karlan (2005) finds that trustworthiness of Receivers in a similar game correlates with microfinance loan repayment rates, but finds no relationship between trusting behavior and loan outcomes. Our focus on trusting behavior reflects the fact that the burden of trust in microinsurance is fundamentally opposite to that in microcredit: in the latter case, it is the microinsurance client who is asked to place their trust in the credibility of the insurer.

3.3

Survey data

In addition to laboratory measures of risk and trust, survey data were collected to measure a range of characteristics potentially affecting insurance purchase choices and impacts. The survey was administered to the same household member who participated in the laboratory exercise. Summary statistics for key variables are presented in Table 3, together with outcomes of the laboratory game. These are disaggregated according to the two dimensions of the experimental design. For each dimension of randomization, we test for equality in means across the treatment arms by regressing the value of each characteristic on a vector of treatment indicators, and testing for equality in these coefficients. In general, the data strongly support the view that these separate dimensions of randomization ‘worked’, in the sense of creating balance along observable characteristics. Only in one of the twenty tests—for risk aversion, with respect to the discount voucher dimension of randomization—are we able to reject the null hypothesis of balance at the ten percent level. Although statistically distinguishable with our sample size, the estimated difference in means is very small. The normalized difference in means between individuals receiving vouchers of zero and 20 percent is only 0.14, well below the critical threshold of one quarter suggested by Imbens and Rubin (Imbens and Rubin Forthcoming, Imbens and Wooldridge 2009).16 Nonetheless, since this variable is of analytical importance, we present results that control both for the level of this variable and its interaction with price, and we explore robustness to flexible and alternative functional forms. Further, we show that the central result of the paper is driven by variation in discounts from zero to ten percent; since risk attitudes (and other characteristics) are balanced between individuals receiving these levels of vouchers, this serves to confirm that results are not driven by imbalance in this characteristic. The target population is poor, though not at the extremes of poverty. Average log household monthly consumption translates to approximately p ¯A − X ¯ B )/ S 2 + S 2 , where for treatment groups A and This is defined as ∆X = (X A B 2 2 ¯ A and SA are the sample mean and variance of characteristic X. X ¯ B and SB B, X are defined analogously. 16

20

21

Marketing only 0.33 ( 0.47) 56.53 ( 15.05) 3.38 ( 1.67) 9.74 ( 1.14) 10.77 ( 1.08) 0.35 ( 0.48) 0.40 ( 0.49) 7.17 ( 2.11) 0.63 ( 0.32) 0.51 ( 0.19)

Marketing treatment Study circles Referral incentive 0.33 0.30 ( 0.47) ( 0.46) 56.39 55.67 ( 14.70) ( 15.01) 3.37 3.58 ( 1.68) ( 1.66) 9.62 9.72 ( 1.12) ( 1.21) 10.70 10.60 ( 1.21) ( 1.08) 0.38 0.37 ( 0.49) ( 0.48) 0.41 0.45 ( 0.49) ( 0.50) 7.03 7.12 ( 2.11) ( 1.66) 0.65 0.67 ( 0.33) ( 0.30) 0.48 0.49 ( 0.19) ( 0.19)

0.38

0.67

0.89

0.48

0.77

0.29

0.53

0.33

0.86

p2 0.65

KShs.

capital. Log medical expenditure is reported for those households reporting strictly positive medical expenditure only. All financial amounts in

treatment assignment. Column (8) presents p-value of test for equality in means across marketing arms. Asset values exclude land and business

associated with F-test of equality in means across voucher levels. Columns (5)–(7) present means and standard deviations by cluster-level marketing

Notes: Columns (1)–(3) present means and standard deviations by individual-level discount voucher assignment. Column (4) presents p-value

coefficient of relative risk aversion

trust game: share sent

ln HH medical expenditure

1[ HH medical expenditure > 0]

1[ HH ever bought insurance ]

ln value HH assets, KShs

ln HH consumption, KShs/month

HH size

age, primary respondent

1[ primary respondent female ]

Discount voucher assignment No discount 10% 20% p1 0.35 0.31 0.30 0.36 ( 0.48) ( 0.46) ( 0.46) 56.74 55.27 56.47 0.39 ( 15.31) ( 15.36) ( 14.09) 3.58 3.33 3.40 0.16 ( 1.76) ( 1.65) ( 1.59) 9.77 9.67 9.62 0.28 ( 1.20) ( 1.16) ( 1.12) 10.67 10.74 10.67 0.75 ( 1.12) ( 1.08) ( 1.17) 0.38 0.37 0.35 0.84 ( 0.49) ( 0.48) ( 0.48) 0.43 0.39 0.43 0.59 ( 0.50) ( 0.49) ( 0.50) 7.20 6.85 7.23 0.32 ( 1.97) ( 1.73) ( 2.10) 0.68 0.63 0.64 0.34 ( 0.32) ( 0.30) ( 0.32) 0.48 0.49 0.52 0.05 ( 0.20) ( 0.19) ( 0.19)

Table 3: Survey characteristics, by discount voucher and marketing treatments

USD 215 using prevailing exchange rates at the time of the baseline survey, or approximately USD 63 per capita. The tea farmers sampled are predominantly male, with average ages in their fifties, and household sizes between three and four individuals. Households in our survey have experienced medical expenses in the past year, though on average these are low, less than a dollar per household per year. Approximately 42 percent of households have experienced a non-zero medical expenditure.17 When it comes to predicting their future medical expenditures, respondents report a similar likelihood of non-zero (hospitalization) expenditure. To obtain an expected value for these hospitalization costs, we follow the approach of Manski and popularized by Delavande et al. (2009) and Attanasio (2009) to elicit subjective probability distributions conditional on nonzero inpatient costs. We compute expected values fitting a triangular distribution to the elicited responses. However, the resulting expected costs greatly exceed historical values, which tempers our view of their usefulness in explaining subsequent insurance decisions. Perhaps most surprisingly, a substantial fraction of households in the survey have purchased insurance in the past. Of the 326 individuals who report their household having ever purchased insurance in the past, 280 report that this cover is still in place. Although we suspect that this may be overreported due to poor baseline levels of understanding of insurance, it should be noted that there is private provision of various forms of insurance in the study area. Health insurance is by far the most common form of insurance with which individuals report experience: 77 percent of those who report a family member having bought insurance of some kind in the past report that this included health insurance. This is followed most closely by life (21 percent), car or motorcycle (6 percent), property (4 percent), and tea insurance (3 percent). This informs the application of the model of Section 2 in this paper, which should be interpreted as highlighting the importance of trust to the introduction of a particular insurer and product.

4

Results

4.1

Reduced-form experimental results

We begin by presenting estimates of the reduced-form effect of our experimental treatments on insurance demand. Given that the model to be estimated consists of a set of binary treatment indicators, we estimate a linear probability model, where the dependent variable is a binary indicator for insurance purchases. The results are presented in Table 4. In the first column of this table, we present results for the basic effects of our treatment arms, without allowing for treatment interactions. Two 17

Figures for realized medical expenditures include outpatient and traditional medicine.

22

Table 4: Demand for insurance by experimental treatment

voucher, 10% voucher, 20% peer referral incentive study circles voucher, 10% × referral voucher, 10% × study circles voucher, 20% × referral voucher, 20% × study circles Constant Obs H1 : p-value H2 : p-value

(1) 0.0666** 0.109*** -0.0742** -0.0179

0.132*** 928 0.620

(0.03) (0.03) (0.04) (0.04)

(0.03)

(2) 0.0622 0.127** -0.0636 -0.0141 -0.00756 0.0205 -0.0244 -0.0296 0.127*** 928

(0.05) (0.06) (0.04) (0.05) (0.06) (0.07) (0.07) (0.07) (0.04)

0.961

Notes: Linear probability model. Dependent variable = 1 if respondent completed application. Robust standard errors, clustered by tea-collection center. Test statistics for hypotheses that (H1 ) coefficient on voucher of 20 percent is twice coefficient on voucher of 10 percent; and (H2 ) interaction effects are jointly insignificant.

results are notable here. First, the ‘study circles’ financial literacy intervention had no measurable effect on demand. This may of course be attributable to a failure of the usefulness or execution of this particular curriculum. However, insofar as the curriculum should have improved members’ ability to form beliefs over insurance payouts, this finding provides prima facie evidence against the policy-manipulability of ambiguity aversion in insurance demand in this context. Second, the peer referral incentive has a negative, significant effect on the probability of insurance purchase. This is difficult to reconcile with assumptions of perfect information and free disposal, since no one was required to take advantage of this extra incentive. Instead, we conjecture that the peer referral incentive acted as a negative shock to Wananchi members’ trust in the policy, by cueing fears of a pyramid scheme. This may have been interpreted as a negative signal of the credibility of the insurer. Several high-profile pyramid schemes had been exposed around the time of the intervention, and public service messages often warned against these.18 In our own sample, we find that the deterrent effect of the peer referral incentive is negative and significant only for those individuals with high measured 18 See for example, BBC News, July 13 2007 (http://news.bbc.co.uk/2/hi/ africa/6288618.stm); Kenya Office of Public Communications, June 28 2007 (http://www.communication.go.ke/media.asp?id=411); Republic of Kenya, Report of the Taskforce on Pyramid Schemes 2009 (http://www.slideshare.net/guestd260ae/ report-of-the-taskforce-on-pyramid-schemes).

23

trust in the laboratory experiment. These individuals, it appears, may have had more faith to lose. Because this gives strong reason to believe that the pre-intervention trust measures were severely disrupted by the referral incentive, we exclude this treatment arm from the analysis of trust and its interaction with price that follows. We test the hypothesis that the probability of purchase is linear in the amount of the discount voucher offered, and we comfortably accept this null hypothesis. In column (2), we estimate a fully saturated model, allowing for interactions between vouchers and the cluster-level treatments. We are able to accept the null that these interactions are all equal to zero (hypothesis H2 ). In testing interactions with laboratory preference measures, we will restrict the model to a linear price effect with no treatment interactions, which improves power and simplifies exposition.19

4.2

Risk, trust, and price in the demand for insurance

Here we present evidence that decisions to purchase insurance depend on the credibility as suggested by the model of Section 2. We show that the probability of purchasing insurance is decreasing in measured risk aversion and increasing in a proxy for the perceived credibility of the insurer. These findings provided the motivation for our theory and replicate similar findings in other contexts (Cole et al. 2008, Cai et al. 2010). We further test the hypothesis (Proposition 2) that the impact of price reductions should be greater on those with low trust, and find this to be the case. To do so we use behavior in the Trust Game as a proxy for individuals’ subjective perceptions of the credibility of the insurer. Undoubtedly, this is an imperfect proxy for our theoretical measure, q. We hypothesize that sender behavior in the Trust Game is related to faith in the credibility of the insurer, but we recognize that this is at best only one factor contributing to subjective values of q. Accordingly, failure to reject a null hypothesis that trust game behavior—or its interaction with price—were uncorrelated with insurance purchase decisions should not be taken as strong evidence against the theory of insurance demand under limited credibility. On the other hand, rejection of such a null hypothesis does provide empirical support for the theory.20 19

More precisely, we estimate a probit model in which the index is linear in price, and the effect of cluster-level treatments is enters additively; the probit functional form introduces nonlinearities in the predicted probabilities. The main results are shown to go through for a model that relaxes the first of these assumptions. 20 It is well understood in the literature that sender behavior in the Trust Game depends not only on beliefs about the trustworthiness of the recipient, but also on risk attitudes and altruism vis-a-vis the respondent. The former of these confounds is addressed empirically by the inclusion of controls for risk preferences from the gamble-choice game, and their interaction with prices, as discussed below. The latter is less of a concern to the extent that we do not expect altruism (in regard to a randomly matched member of the community)

24

We report coefficients from a probit model of the decision to purchase insurance in Table 5. Randomly assigned premium prices are expressed in units that correspond to shares of the full price. RG is the estimated coefficient of relative risk aversion from the gain-frame Holt and Laury gamblechoice game. Cluster-randomized assignment to a tea center where financial literacy training was conducted via ‘study circles’ is denoted by the variable study circles. Controls for zone are included in all specifications, though their omission does not substantially alter the results. Table 5: Risk, trust, and price in insurance demand

submitted complete application price

RG

(1)

(2)

(3)

-3.083*** (0.93)

-3.069*** (0.92)

-2.542** (1.06)

-0.598 (2.64)

-0.960** (0.39)

-1.037** (0.42)

-0.962** (0.39)

-1.368** (0.66)

-0.866*** (0.24)

-1.018*** (0.27)

-3.419* (1.91)

-4.127** (1.93)

2 RG

low trust

-2.140 (2.12) -0.437** (0.19)

-0.441** (0.19)

price × low trust

price ×RG

study circles

(4)

-3.872 (5.12) -0.110 (0.17)

-0.117 (0.17)

-0.105 (0.17)

-0.0971 (0.17)

Individual characteristics

No

No

No

Yes

Zone controls Observations

Yes 457

Yes 457

Yes 457

Yes 448

Notes: Probit coefficients reported. Dependent variable equals unity if respondent purchased Bima ya Jamii insurance policy. Robust standard errors reported, clustered at tea-centre level. Controls for individual characteristics include logs of household asset values, household size, and respondent age, as well as indicators for the gender of the respondent and whether any household member has post-primary education.

Column (1) reports the basic findings of the experiment, with measures to be correlated with the demand for a household health insurance policy in the way predicted by the model. In particular we have no prediction for the interaction between altruism and price; however, in the absence of direct measures of altruism, we cannot exclude the possibility of such an alternative mechanism.

25

of risk preferences and trusting behavior. This reproduces the basic stylized facts, observed across various contexts, that motivate our model (Cole et al. 2008, Cai et al. 2010). Demand is increasing in the amount of the discount, decreasing in measured risk aversion, and increasing in measured trust. In column (2) we test for a nonlinear association between risk aversion and demand, as suggested by Proposition 1. To do so we include the square of the measure of risk aversion, less its mean of 0.5 in the estimating sample. Although we cannot reject equality of the coefficient on this quadratic term with zero, the resulting point estimates are consistent with Proposition 1. For risk-neutral individuals (R = 0), the implied marginal effect of an increase in R is positive (point estimate 0.27; standard error 0.41), whereas for risk-averse individuals with a CRRA coefficient of unity, the implied marginal effect of an increase in R is negative (point estimate -3.17; standard error 2.29). Column (3) provides the central test of our theory: namely, the prediction (Proposition 2) that price variation should have a stronger effect on those who hold low values of q, as proxied by low-trust behavior in the trust game. This is supported in the data. The result is strengthened in column (4) by the inclusion of controls for a range of potentially confounding variables: natural logarithms of household asset values, household size, and respondent age, as well as indicators for the gender of the respondent and whether any household member has post-primary education. Estimated coefficients imply substantial differences in the marginal effect of price on the probability of insurance purchase. For a high-trust individual with the characteristics of the mean individual in the sample, the marginal effect of a change in price is -0.76 (with standard error 0.36), starting from a base value of 0.8 times the full price. This implies that an increase to 0.9 times the full price would reduce demand by 7.6 percentage points. By contrast, the estimated marginal effect for a low-trust individual is much larger, at -1.72 (0.70). Not only is the low-trust individual less likely to purchase insurance at this initial price, but a further increase in price to 0.9 times the full price is estimated to cause a 17 percentage point reduction in the probability of insurance purchase. To summarize, we find empirical results that are broadly consistent with the model outlined in Section 2. Demand is increasing in the laboratory measure of trust and decreasing in the laboratory measure of risk aversion. In line with Proposition 1, we find modest evidence of non-monotonicity of demand in the measure of risk aversion.

4.3

Risk confound and alternative interpretations of the laboratory trust measure

Behavior in the BDM trust game is interpreted above as proxying for an element trust in the insurance product. However, sender behavior in the 26

Table 6: Are trusting and risk aversion correlated?

Rgain Rloss

Low trust 0.48 ( 0.19) 0.55 ( 0.19)

High trust 0.50 ( 0.20) 0.56 ( 0.19)

p-value 0.16 0.87

Notes: Table reports means and standard deviations for alternative measures of behavior in Holt and Laury gamble-choice game, by level of trust. Rgain , Rloss give fitted coefficient of relative risk aversion from gain- and loss-frame gamble-choice tasks, respectively. pvalues from test of equality in means, with standard errors clustered by experimental session.

trust game is potentially confounded by risk attitudes. The potential importance of risk attitudes in determining behavior in the trust game has been widely discussed in the literature. As Ben-Ner and Putterman (2001) note, for a given belief in the trustworthiness of the receiver, an individual with a higher level of risk aversion should desire to send a smaller amount. The empirical support for this intuitive view is mixed. Eckel and Wilson (2004) fail to find a correlation between trusting and a range of survey-based and incentivized of risk measures. Karlan (2005) interprets relatively high microfinance default rates among high-trust individuals as evidence that they are more prone to take risks. Ashraf and coauthors (2006) are unable to detect a statistically significant relationship between sender decisions in a trust game and decisions in a gamble-choice game. Given that measured risk attitudes explain very little of the variation in trusting behavior they observe, Ashraf show that expected trustworthiness is quantitatively most important in determining trusting behavior. Schechter (2007) uses a measure of risk attitudes derived from a risky investment game explicitly designed to mimick the structure of the trust game, and finds decisions in this risk game to significantly predict trusting behavior for men, but not for women. Schechter argues for the importance of controlling for risk attitudes when interpreting trust game decisions as trust. Empirically, we can address the possibility that failure to adequately control for risk aversion can confound the price-trust interaction in several ways, provided that risk attitudes are well measured by behavior in the Holt and Laury (HL) laboratory game. In Table 6, we confirm that trust game behavior and risk attitudes are only weakly correlated in our sample. We also note that in the main results of Table 5, the point estimate and statistical significance of the interaction between price and trust behavior were unaffected by the inclusion not only of a control for the level of risk aversion, but also the interaction between risk aversion and price. 27

In Table 7, we show that this is robust to inclusion of controls for alternative measures of risk aversion that can be constructed from HL game decisions. We employ flexible functional forms for these measures and their interactions with price: in each column of Table 7, we control for a fourthorder polynomial in a measure of risk aversion, R, and its interaction with price. Columns (1)–(3) employ as measures of risk aversion, respectively, the fitted coefficient of relative risk aversion from the gain-frame lottery task; the the fitted coefficient of relative risk aversion from the loss-frame task; and the fraction of safe lotteries chosen in the gain-frame task. The interaction term in the probit model is always statistically significant at the five percent level. We separately compute marginal effects of a price change for low- and high-trust types, for mean characteristics and a base price corresponding to a ten percent discount, to illustrate the greater price elasticity of low-trust individuals. To investigate whether imbalance in levels of risk aversion across discount voucher assignments could be causing our results, we restrict attention in column (4) to the zero and ten percent voucher individuals, who are statistically indistinguishable in this respect. To do so, we repeat the specification of column (1). If anything, the results are much stronger for this subset of individuals. This suggests that a risk-price confound arising from the specific allocation of vouchers is unlikely to be driving the results. It remains possible that a component of risk aversion is not well measured by either of the HL series, and that this component of risk aversion is correlated with trust game behavior. However, the robustness of the findings to alternative risk measures, coupled with the fact that the price-risk aversion interaction will in fact have the opposite sign under some choice models, provides support for the view that the observed trust-price interaction is not driven by confounding risk attitudes.

5

Conclusions

This paper has provided evidence for a model of demand for indemnity insurance when the insurer has limited credibility. Individuals are assumed to form subjective beliefs about the probability that they will receive a payout in the event that they suffer a loss. These beliefs are hypothesized to depend—among other factors—on a generalized form of trust, which is partly captured by behavior in a laboratory game. The model is capable of reproducing two emergent stylized facts of the demand for insurance: that demand for insurance can be decreasing in measures of risk aversion, and that demand for insurance is increasing in measures of trust. We take two further predictions of the model to experimental data from Kenya, and find results consistent with the model. These findings lend support to the view that limited trust in the credibility of insurers

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Table 7: Probit coefficients and marginal effects, with alternative controls for risk and risk-price interactions

price low trust price× low trust high trust: ∂E[Y ]/∂π low trust: ∂E[Y ]/∂π Measure of risk aversion Sample N

(1) 0.38 ( 1.79) -1.10 ( 0.29) -5.21 ( 2.02) 0.09 ( 0.44) -0.66 ( 0.30) Rgain all 448

(2) -2.15 ( 1.88) -1.04 ( 0.26) -4.39 ( 1.85) -0.55 ( 0.48) -0.88 ( 0.34) Rloss all 448

(3) -0.58 ( 1.59) -1.05 ( 0.29) -4.39 ( 2.06) -0.14 ( 0.39) -0.66 ( 0.32) Fgain all 448

(4) -0.69 ( 5.42) -4.50 ( 0.22) -44.00 ( 4.57) -0.16 ( 1.32) -9.62 ( 3.73) Rgain π > 0.8 295

Notes: Dependent variable equals unity if individual purchased insurance. Probit coefficients and standard errors reported in first three rows. Marginal effects of a change in price, π, on the probability of insurance purchase are reported in fourth and fifth rows, for a high- and low-trust individual, respectively. Marginal effects computed for discount level of 10%, at mean of remaining characteristics. Robust standard errors in parentheses, clustered at tea-center level. All specifications include controls for zones, marketing treatment, and individual characteristics as in Table 5. Each column controls for a fourthorder polynomial in a measure of risk aversion, and its interaction with price. These are the fitted coefficient of relative risk aversion from the gain-frame (columns 1 and 4) and loss-frame (column 2) HL series, and the fraction of safe lotteries chosen in the gain-frame HL series (column 3). Column (4) restricts the sample to individuals assigned vouchers of zero or ten percent.

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constrains the adoption of indemnity insurance. If trust in insurer credibility is a barrier to the use of formal insurance by the poor and risk averse, this raises the policy question of whether trust can be improved. Other papers have suggested that trust may indeed be affected by policy, either through endorsements by trusted third parties (Cole et al. 2008), or through direct observation of insurance payouts (Cai et al. 2010), but direct evidence of the policy-manipulability of trust remains scarce. Similarly, a byproduct of one of the marketing treatments that was piloted in this context appears to have been the undermining of trust, a result that underscores the need for caution in the promotion of insurance products when trust is fragile. On the other hand, there would appear to be substantial scope for government to improve trust in such schemes by strengthening regulations that affect the enforceability of insurance contracts.

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