WHY IS THE TAKE-UP OF MICROINSURANCE SO LOW? EVIDENCE FROM A HEALTH INSURANCE SCHEME IN INDIA

Authors


  • This research is part of the project “Role of Small-Scale Finance in Rural Development: Rural Finance and Microfinance” undertaken at the Institute of Developing Economies (IDE-JETRO). The authors are grateful to an anonymous referee for useful comments and discussion. The opinions expressed and arguments employed in this paper are the sole responsibility of the authors and do not necessarily reflect those of IDE-JETRO.

Abstract

Insurance for the poor, called microinsurance, has recently drawn the attention of practitioners in developing countries. There are common problems among the various schemes: (1) low take-up rates, (2) high claim rates, and (3) low renewal rates. In the present paper, we investigate take-up decisions using household data collected in Karnataka, India, focusing on prospect theory, hyperbolic preference, and adverse selection. Prospect theory presumes that people behave in a risk-averse way when evaluating gains but in a risk-loving way when evaluating losses. Because insurance covers losses, the risk-loving attitude toward losses might explain the low take-up rates, and we find weak empirical support for this. Households with hyperbolic preference were more likely to purchase insurance, consistent with our theoretical prediction of demand for commitment. We also find some evidence on the existence of adverse selection: households with a higher ratio of sick members were more likely to purchase insurance.

I. INTRODUCTION

Insurance for the poor, called microinsurance, has recently drawn the attention of health-care service practitioners in developing countries. In India, a rapid increase in microinsurance schemes has been observed, due partly to the Insurance Regulation and Development Authority Regulations 2000 (July 14), which made it compulsory for the general insurance companies to allocate 5% of their gross premium income for provision of insurance in the rural and social sectors. The regulations opened up a door for the poor to obtain realistic opportunities to purchase health insurance.

There are, however, problems that are widely shared among health microinsurance practitioners in India: (1) low take-up rates, (2) high claim rates, and (3) low renewal rates. It is often said that the root cause of these symptoms is adverse selection. In the case of (1) and (3), unfamiliarity with insurance is cited as a reason as well. Similarly, in marketing research conducted by microfinance institutions (MFI), it is commonly concluded that programs are not suitably designed to match the demand of the poor households (e.g., relatively large lump sum payments, significant transaction costs, and dependence on relationships with unfamiliar parties), and that the poor are less educated and cannot understand the concept of insurance or risk management, thus justifying the necessity of financial education programs (e.g., Vimo SEWA 2006; International Labour Organization 2007).

Although these are all valid conjectures, their relevance must be assessed empirically. This is particularly true if there are alternative hypotheses that can explain the symptoms. Despite the growing attention toward microinsurance, there is a limited amount of economic research that sheds light on the household's utilization of insurance. In the present paper, we try to understand the mechanism behind low-income households' insurance take-up decisions based on recent empirical insurance literature and on behavioral literature.

In line with the insurance literature that examines the extent of information asymmetry in the insurance markets of developed countries (e.g., Abbring, Chiappori, and Pinquet 2003; Chiappori 2000; Chiappori and Salanié 2000; Chiappori et al. 2006; Cutler, Finkelstein, and McGarry 2008; Finkelstein and McGarry 2006), we test for the presence of adverse selection in microinsurance purchases in a developing country.

In contrast to other studies, we have direct information on health conditions, which can be used as a measure of riskiness. This allows us to use a univariate regression model of purchases on riskiness. In addition, our data ensure that there are no omitted variables that are incorporated in pricing, as suggested by Chiappori and Salanié (2002). The insurer, the state government of Karnataka in our case, applies a universal price and does not price discriminate. The insurance product, at least in theory, is available for sale to everyone. Hence, there cannot be an omitted variable that might be relevant for sales of insurance.

If one regresses purchases on observable covariates, one leaves two important variables in the residual: riskiness and risk preference. As we have a riskiness measure in our data, the consistency of the estimates depends on the orthogonality between riskiness and risk preference heterogeneity. It is not reasonable to assume that they are unorthogonal, so we use an identification strategy similar to that of Finkelstein and McGarry (2006): whereas they use a proxy of risk preference (cautious actions) to control for the preference heterogeneity, we condition on risk preference obtained from the experimental games with substantial monetary rewards. Specifically, conditional on an individual's risk preference, we test for a negative correlation between current health conditions and insurance purchases.

Another novel feature of the present paper is that we test for the preferences underlying prospect theory and hyperbolicity in relation to insurance purchases of poor households. We examine the validity of expected utility theory and prospect theory. In an early contribution, Slovic et al. (1977) conducted a lab experiment in the United States where subjects facing the risk of losses were asked whether they would purchase actuarially fair insurance. They set the probability of losses at 0.1%, 0.5%, 1%, 5%, 10%, and 25%. If subjects were risk-averse, as expected utility theory usually presumes, they should always purchase the insurance and value the insurance more when the loss amount is larger (and, therefore, the probability of losses is lower because of actuarial fairness). They find that when subjects faced a loss risk of 25%, approximately 80% of them purchased the actuarially fair insurance, whereas when they faced a loss risk of 0.1% or 0.5%, only 20% of them purchased the actuarially fair insurance. In addition, 30% of them purchased the insurance against a loss risk of 1%, and 40% of them purchased the insurance against a loss risk of 5%. These findings suggest that individuals tend to underevaluate small-probability losses, which might explain why people do not purchase insurance to the extent that the standard theory predicts.

The most closely related work to ours is Giné, Townsend, and Vickery (2008), who investigate the take-up decisions of rainfall insurance based on a survey in rural Andhra Pradesh, India. Their main findings are that: insurance take-up: (1) decreased with basis risk between insurance payouts and income fluctuations (2) increased with household wealth, (3) was lower among households who faced credit constraints, and (4) was higher among households who were familiar with the insurance vendor (in this case, an MFI) and who participated in a village network. Note that information asymmetry about risks does not play a role in explaining the low take-up, because rainfall shocks and their record are publicly observable. The authors also find that risk-averse households are more likely to purchase insurance among households with previous transactions with the MFI who sells the insurance, but for households without previous transactions, risk-averse households are less likely to purchase insurance. This suggests that households unfamiliar with the insurance vendor seem to regard buying insurance as a risky investment. If this interpretation is correct, it is due to an incomplete contract problem whose solution is simply a matter of trust between an MFI and farmers.

Another related work is Bauer, Chytilová, and Morduch (2008), who analyze household decisions to participate in microcredit using household behavioral data collected in Karnataka, India. They find that individuals with hyperbolic discounting are more likely to participate in a microcredit program, with the reason being that the difficulty in saving makes them more likely to be credit constrained, leading to the demand for microcredit.

A straightforward research strategy based on these preceding works is to examine the relevance of behavioral economics in explaining the low take-up. According to prospect theory (Kahneman and Tversky 1979), individuals are risk-averse toward gains but risk-loving toward losses. Because health insurance covers losses, individuals facing a decision on purchasing health insurance might act as if they are risk-loving. Furthermore, as Slovic et al. (1977) suggest, prospect theory also allows subjective probabilities to be different from objective probabilities. We follow Tanaka, Camerer, and Nguyen (forthcoming) to consider how much such discrepancies, or probability weighting, exist among the sampled individuals. Finally, we hypothesize that hyperbolic discounters are more willing to buy insurance as a commitment device, as long as they acknowledge their weaknesses. Unlike Bauer, Chytilová, and Morduch (2008), who focus on the saving difficulty caused by hyperbolic discounting, we focus on the demand for a commitment device. If individuals know that they tend to save less than they should and, therefore, will not have enough saving in the future, they feel vulnerable to shocks. Having assessed the likeliness of such adversity in the future, they may have an incentive to purchase insurance now to protect themselves in the future from health shocks. This is possibly due to the unique characteristic of this insurance product that is sold to dairy cooperative members whose weekly income may be used for premium payments. To the best of our knowledge, this is the first work that links prospect theory and hyperbolic discounting to household decisions on purchasing insurance using household survey data.

The main contribution of the present paper lies in the well-designed survey that we conducted in Karnataka, India, to understand the nature of purchase decision of households. We collaborated with Biocon Foundation, a nongovernmental organization (NGO), to investigate the underlying problems in the microinsurance market. In this paper, we find some evidence for the existence of adverse selection: households with a higher ratio of sick members are more likely to purchase insurance. Interestingly, we also find that households with sick household heads are less likely to purchase insurance. This might capture the fact that households with sick households have lower incomes and have difficulty in financing the insurance premium. In examining the behavioral explanation for low take-up, we elicit the risk attitudes toward gains and losses and relate them to the actual insurance purchase. We find that an unignorable portion of the surveyed individuals have a preference consistent with prospect theory. The respondents identified as loss-risk-loving were less likely to purchase insurance, although this finding is statistically significant only in some specifications. However, risk aversiveness toward gains does not predict the insurance take-up. We also find that households whose prominent members (respondents) exhibit hyperbolicity are more likely to purchase insurance, consistent with our conjecture.

The next section provides a brief description of the structure of health microinsurance in India and the insurance product we examine in this paper. Section III presents theoretical predictions on purchasing behavior. Section IV summarizes our experimental questions. The survey environment and empirical results are presented in Section V. The final section offers concluding remarks.

II. MICROINSURANCE: YESHASVINI SCHEME

As with microcredit, microsaving, or micro-whatever, there is no agreed upon definition of microinsurance. In the present paper, we use the term to refer to insurance schemes designed, marketed, and operated specifically for the poor.

Insurance is said to be a comparatively more complex concept than saving and credit services, and requires the upfront payment of a premium. Unlike saving and credit, insurance includes nonfinancial services (health-care services) with substantial monetary transactions. This explains why in most microinsurance schemes, there are as many as five parties involved: the insuree, the insurer, the care provider, the third-party administrator (TPA), and the NGO/MFI (See Figure 1). The TPA provides insurance management services, such as policy verification, claim examination, and payment transactions, facilitates cash-free health-care services, which are essential to the cash-constrained poor, and examines the claims from the hospitals. TPA are not unique to India, but are an integral part of providing microinsurance in a large and diverse country like India where one has to design products that are customized at a small scale.

Figure 1.

Typical Microinsurance Contract
Notes: NGO = nongovernment organization; TPA = third-party administrator.

In addition, there are many exceptions to the insurance coverage, mostly specified in tiny print on the back of brochures. These are just a few of the hurdles that practitioners have to struggle with: they have to explain under what conditions indemnity will be paid out, how the policyholders can utilize health-care services, how they can make claims, when to pay the premium, and when they can receive the insurance cards. On top of this, microinsurance providers, mostly MFIs or NGOs, hesitate to impose examinations for preexisting conditions, because, according to a few founders of schemes, their raison-d'être is poverty reduction, not turning down the poors' requests when they have health problems.

All of these seem to lead to the symptoms described earlier: low take-up and renewal rates. Because the poor might not understand the concept fully, they might even think that they have been deceived when they remain healthy and do not utilize insurance because “they have paid the premium but gained nothing.” Medical knowledge is scarce among the poor, and they have difficulty understanding what is and is not covered under the policy. Even when written explicitly, it turns out that, in some cases, the poor go to hospitals only to find out that the procedure for their symptom is not covered, a fact that is then versed as fraud by word of mouth. The inability to prepare cash in a short period of time also plays a role, as microinsurance is usually sold once a year in each region and not everyone is given sufficient time before the marketing day to prepare the cash. These are just issues that are unrelated to information asymmetry. Information asymmetry only complicates things further, by adding the problems of adverse selection, and ex-ante and ex-post moral hazard. Therefore, the MFIs and NGOs who manage the schemes face tough challenges of controlling agency problems while educating and marketing for the poor. This might partly explain why no microinsurance project has ever been successfully scaled up in general.

The insurance product that we examine, Yeshasvini Co-operative Farmers Health Care Scheme (Yeshasvini, hereafter), is the most widespread health microinsurance scheme in Karnataka State. Yeshasvini was initiated on June 1, 2003, with the aim of providing cost-effective quality health care to dairy cooperative farmers and poor people across the state of Karnataka. It is a self-funded scheme that is not tied with any insurance company. It offers a low priced product covering over 1,600 defined surgical procedures to farmers and their family members. The beneficiaries can receive cashless treatment at a network of over 135 hospitals, both public and private, across Karnataka. Yeshasvini is open to all cooperative society members who have been in the cooperative society for at least six months. Ages of the insured range from 0 to 75 years. The policy is valid for one year and the beneficiaries need to pay the premium up-front. The premium is Rs 120 (approximately US$2.4) per year for an adult or a child. For families of five or more members, the premium is discounted by 15%. Notice that the premium does not depend on age, health status, or any other variable. This should, in theory, make the insurance more attractive to less healthy individuals, leading to higher claim rates. This is precisely the adverse selection problem that is often discussed among practitioners in India.

The payout is limited to Rs 200,000 (approximately US$4,000) per year per individual and Rs 100,000 (approximately US$2,000) per surgery per individual. This is enough for almost all surgical treatments at the network hospitals. All procedures are limited to one incidence per year. The policy excludes coverage for prosthesis, implants, joint replacement surgeries, transplants, chemotherapy, cosmetic surgery, burn treatments, dental surgeries, and several other items. Normal delivery is covered. Children born prematurely or with low birth weight who require special care during the first seven days after birth are covered. In addition, the policyholders can receive free outpatient consultation at all participating hospitals, discounted tariffs for investigations and inpatient treatment for non-covered hospitalization.

III. THEORETICAL PREDICTIONS

A. Riskiness

Standard models of adverse selection (e.g., Rothschild and Stiglitz 1976) expect that riskier individuals are more likely to purchase insurance given an equal premium and benefits. In the present paper, we use information on the disease history of household members and current health conditions to examine such predictions.

B. Expected Utility Theory and Prospect Theory

Next, we consider decisions on purchasing insurance based on expected utility theory and its alternative, prospect theory, developed by Kahneman and Tversky (1979).

Expected utility theory usually assumes that individuals are risk-averse and that their utility depends on their levels of consumption or wealth. Risk aversion implies that if the insurance is actuarially fair, individuals should purchase the full coverage. Even if the insurance premium is higher than the expected indemnity payout, individuals will purchase partial coverage if they are sufficiently risk-averse. Given the risk probabilities, individuals with higher risk aversion are more likely to purchase the insurance.

Although expected utility theory assumes that utility depends on consumption or wealth levels, prospect theory focuses on the asymmetric evaluation of gains and losses by individuals. It assumes that people set a reference point and consider lower outcomes as losses and larger ones as gains. The characteristics of prospect theory can be summarized in the shape of its value function, v, which is described in Figure 2.

Figure 2.

Prospect Theory

The value function, v, has three characteristics. First, it does not depend on the wealth level and solely depends on gains and losses relative to the reference point, which corresponds to the origin in Figure 2. Second, v is s-shaped, reflecting “diminishing sensitivity.” This indicates that people attach greater importance to the difference between US$0 and US$100 than to the difference between US$10,000 and US$10,100, regardless of whether they are losses or gains. A final point is that losses have a greater impact than gains, in what is called “loss aversion.”v is kinked at the origin and given any value of x, |v(x)| < |v(−x)|.

The diminishing sensitivity or s-shaped value function implies that individuals are risk-averse toward gains but risk-loving toward losses. Because health insurance only covers losses, individuals facing a decision on purchasing health insurance might act as if they are risk-loving. We should note that prospect theory has been used to explain “over-insurance” instead of “under-insurance.”Cutler and Zeckhauser (2004) argue that loss aversion can explain why, in developed countries, people often buy insurance for newly purchased cars or electronic items whose premium is substantially more expensive than what the probability of failure might justify. This “over-insurance” is caused by the fact that decisions on purchasing insurance are made when they buy the cars or electronic items. In this case, the reference point is the point before they buy the cars or electronic items. Because they obtain gains from buying these items (this is why they buy them), we are looking over the positive (gains) region, and risk aversiveness leads to “over-insurance.”Cutler and Zeckhauser (2004) actually note that “over-insurance” is not observed when people buy insurance for cars that they already own. Therefore, “over-insurance” for newly purchased items and “under-insurance” for health insurance can be explained under the same framework of prospect theory. By directly surveying risk attitudes toward gains and losses and relating the response to insurance take-up, we examine whether loss-risk lovingness can explain “under-insurance.” It should also be noted that expected utility theory allows risk-lovingness, and Friedman and Savage (1948) point out the possibility of non-concavity of the utility function to explain the observation that people often buy insurance and lottery tickets at the same time. It is possible, by chance, that the utility function is convex for “gains” and for “losses.” However, this possibility is low because the standard utility theory depends on consumption or wealth levels but not on a reference point. To account for our results with the standard expected utility theory, in the relevant range, each respondent's utility must be convex from below and concave from above exactly at the points of the respondent's wealth level at the time of our experiment. Therefore, if we observe that a substantial portion of individuals respond risk-aversely to gains and risk-lovingly to losses, and that they are less likely to purchase insurance, we can safely postulate that the loss-risk lovingness of prospect theory explains “under-insurance” in the microinsurance market.

In addition, prospect theory allows the subjective probabilities to be different from the objective probabilities. This can be captured by a probability weighting function, w(p). It is often argued that people tend to overvalue gains from low probability events, but undervalue gains from medium-probability and high-probability events (Kahneman and Tversky 1979). In contrast, Slovic et al. (1977) find that individuals tend to undervalue losses with low probability, which might explain why they do not purchase insurance covering large but infrequent losses as much as expected utility theory predicts.

C. Self-control Problem

We also focus on another behavioral economics issue, the self-control problem. There are several models for self-control. Laibson (1997) uses hyperbolic discounting models to show that individuals without perfect commitment technology will consume excessively in the current period. From a set of axioms, Gul and Pesendorfer (2001, 2004) derive temptation models consisting of a usual utility function and a temptation cost function that depends on the set of potential consumption. Fudenberg and Levine (2006) develop a dual self model, which provides simpler analytical solutions to the self-control problem than hyperbolic discounting models. Most of the predictions, however, are similar across these models. Individuals with a self-control problem expect that they will be tempted to consume and have difficulty saving. These individuals have a demand for any commitment device if available. Ashraf, Karlan, and Yin (2006) find in the Philippines that individuals who are identified as time-inconsistent are more likely to participate in commitment saving in which they are restricted from withdrawing money from their account. In the context of insurance, individuals aware of self-control problems expect that they will be tempted to consume excessively, and that they will not have enough money for treatments when they do get sick. Therefore, they have higher incentives to purchase insurance to ensure access to medical treatment in the future.

IV. EXPERIMENTAL QUESTIONS

In forming the experimental questions, we aimed to identify the various preference characteristics: attitude toward risks in the positive region, risks in the negative region, hyperbolicity, probability weighting, and self-control. We also asked about other important entitlement characteristics of households; namely, about credit entitlement.

In an effort to identify households with credit constraints, we asked a series of questions regarding whether they had tried to, if they had, and if they could borrow as much money as needed. If the answers to these questions were negative, we asked the reasons. With this information, we identify households with credit constraints. Concretely, we use the strong version of the definition of credit constrainedness described in Attanasio, Goldberg, and Kyriazidou (2008).1 We define a household as being credit constrained if one of the following conditions is true:

  • The household did not try to borrow because of anticipation of being rejected, not being familiar with the process, or feeling intimidated, or reasons other than “no need for credit.”
  • The household tried to borrow but did not obtain loans or did not get as much as wanted under the proposed conditions.

Controlling for the credit constrainedness is necessary as it may make the premium costlier. We expect this variable to be negatively correlated with the take-up decision, because constrained individuals may not buy while people just above the constrainedness may purchase in anticipation of possible future income shocks.

In the experimental questions, our main interest is on the risk preference parameters. The set of questions we used for eliciting risk preference parameters is presented in Table 1. First consider question QX3, where respondents can gain a certain amount of money by choosing a lottery. Notice that lottery B is most attractive in case 1 and becomes gradually less attractive. In the last row, B is definitely a worse option than A. Therefore, a respondent will choose lottery B in case 1 and switch to lottery A at some point, or choose A in all cases. There will be no double switches if respondents are logically coherent. Following Tanaka, Camerer, and Nguyen (forthcoming), we assume a constant relative risk aversion (CRRA) value function v(y) = yα, α > 0, where y denotes the gains from lottery. α < 1 implies risk averseness, α = 1 risk neutrality, and α > 1 risk lovingness. We denote lottery A by LA = (35, 40; 0.5, 0.5), expressing that the outcome of gaining 35 occurs with probability 0.5 and outcome of gaining 40 occurs with probably 0.5. Lottery B can be written as LB = (B, 10; 0.5, 0.5), where we vary the amount of gain in the first outcome, B. Because the probabilities of better outcomes and bad outcomes are equal, we ignore the probability weighting here. Therefore, when E[v(LA)] = E[v(LB)], we have:

Table 1. 
Questions for Eliciting Risk Preference
QX3 Now consider the following draws. This time one of the following rows will be randomly selected and you actually gain the amount of the money described according to your choice (A or B) and your draw. Note that B is most attractive in case 1 and gets gradually less attractive. In the last row, B is definitely a worse option than A.
GainABChoiceDifference in Expected ValuesOpen Interval of α if Subject Switches to Lottery b
Note 1Note 2Note 1Note 2
 1403515010A/B−42.5 
 2403513010A/B−32.5(0, 0.045)
 3403512010A/B−27.5(0.045, 0.100)
 4403511010A/B−22.5(0.100, 0.169)
 5403510010A/B−17.5(0.169, 0.258)
 640359010A/B−12.5(0.258, 0.378)
 740358010A/B−7.5(0.378, 0.547)
 840357010A/B−2.5(0.547, 0.808)
 940356010A/B2.5(0.808, 1.267)
1040355010A/B7.5(1.267, 2.357)
1140354010A/B12.5 
QX4 This time you have to choose an unlucky draw from one of the two bags. Which bag do you choose? One of the following rows in QX4 to QX6 will be randomly selected and you actually have to pay the amount of money described according to your choice and your draw. Note that B is least attractive in case 1 and gets gradually more attractive. In the last row, B is definitely a better option than A.
LossABChoiceDifference in Expected Values
Note 1Note 2Note 1Note 2
 1−40−35−150−10A/B42.5
 2−40−35−130−10A/B32.5
 3−40−35−120−10A/B27.5
 4−40−35−110−10A/B22.5
 5−40−35−100−10A/B17.5
 6−40−35−90−10A/B12.5
 7−40−35−80−10A/B7.5
 8−40−35−70−10A/B2.5
 9−40−35−60−10A/B−2.5
10−40−35−50−10A/B−7.5
11−40−35−40−10A/B−12.5
QX5 As in QX4, you have to choose an unlucky draw from one of the two bags. Which bag do you choose? As stated in QX4, one of the rows in QX4–QX6 will be randomly selected and you actually have to pay the amount of money described according to your choice and your draw. Note that B is least attractive in case 1 and gets gradually more attractive. In the last row, B is definitely a better option than A.
LossABChoiceDifference in Expected Values
All 10 Notes1 Note9 Notes
12−10−2000A/B10
13−10−1750A/B7.5
14−10−1500A/B5
15−10−1250A/B2.5
16−10−1000A/B0
17−10−750A/B−2.5
18−10−500A/B−5
19−10−250A/B−7.5
20−10−100A/B−9
QX6 As in QX4, you have to choose an unlucky draw from one of the two bags. Which bag do you choose? As stated in QX4, one of the rows in QX4 to QX6 will be randomly selected and you actually have to pay the amount of money described according to your choice and your draw. Note that B is least attractive in case 1 and gets gradually more attractive. In the last row, B is definitely a better option than A.
LossABChoiceDifference in Expected Values
All 50 Notes1 Note49 Notes
21−2−2000A/B2
22−2−1750A/B1.5
23−2−1500A/B1
24−2−1250A/B0.5
25−2−1000A/B0
26−2−750A/B−0.5
27−2−500A/B−1
28−2−250A/B−1.5
29−2−100A/B−1.8
30−2−20A/B−1.96
image

This can be solved numerically for α using a root finding algorithm. If a respondent who faces a series of lottery choices switches his or her choice from B to A in the seventh question, for example, then we can deduce that the respondent's α lies between α and inline image, where α satisfies 35α + 40α = 10α + 90α and inline image satisfies inline image. The rightmost column presents the range of α that justify a switch in the choice of lottery from B to A.2 According to the CRRA value function, a lack of nonzero values of α justifies the choice of lottery A in the first row (B = 150). Therefore, if the CRRA value function is reliable, few respondents will choose A in all cases.

As discussed in the previous section, we want to examine whether respondents are risk-averse or risk-loving when they face the risk of loss. As in the above, we assume a CRRA value function, inline image, inline image, where y < 0 is the losses from the lottery. Notice that inline image implies risk lovingness here. If α < 1 and inline image, it is consistent with prospect theory. We expect that households with inline image are less likely to purchase the insurance. We elicit inline image by question QX4, which is analogous to QX3. Notice that lottery B is least attractive in case 1 and becomes gradually more attractive. In the last row, lottery B is definitely a better option than A. inline image can be elicited in the same way as α, by using information on the point at which a respondent switched his or her choice. Because the probability of better outcomes and poorer outcomes is fifty–fifty, we ignore the probability weighting in eliciting inline image.

In addition, we investigate whether undervaluation of tragic but infrequent events is suppressing the “rational” demand for health insurance. This can be expressed as a low probability being deflated while a high probability is inflated, or probability weighting. Following Tanaka, Camerer, and Nguyen (forthcoming), we assume the subjective probability q to have a one-parameter form of Prelec's (1998) axiomatically derived weighting function:

image

Note that undervaluation of low probability events occurs if b > 1 as qp is an inverse-U-shaped function.

We set LA = (−A; 1) and LB = (−B, 0; 0.1, 0.9) in QX5, and LA = (−A; 1) and LB = (−B, 0; 0.02, 0.98) in QX6. If E[v(LA)] = E[v(LB)], we can solve for b using:

image

The last equality follows as v(0) = 0. Then, with the imputed value of inline image from QX4, we can obtain b:

image

In Tables 2 and 3, we present the median of the imputed ranges of b from QX5 and QX6, respectively.

Table 2. 
Probability Weights Derived from QX5
 Loss Switch
121314151617181920
Risk Switch         
 2−1.85−1.90−1.97−2.05−2.17−2.33−2.59−3.27−∞
 3−1.10−1.16−1.23−1.31−1.42−1.58−1.85−2.52−∞
 4−0.55−0.61−0.67−0.75−0.87−1.03−1.30−1.97−∞
 5−0.08−0.13−0.20−0.28−0.39−0.55−0.82−1.50−∞
 60.370.320.250.170.05−0.11−0.38−1.05−∞
 70.820.770.700.620.500.340.08−0.60−∞
 81.321.261.191.111.000.840.57−0.10−∞
 91.931.871.811.721.611.451.180.51−∞
 102.962.902.832.752.642.482.211.53−∞
Table 3. 
Probability Weights Derived from QX6
 Loss Switch
21222324252627282930
Risk Switch          
 2−1.33−1.37−1.41−1.46−1.53−1.62−1.76−2.05−2.59−∞
 3−0.59−0.62−0.67−0.72−0.78−0.88−1.02−1.31−1.85−∞
 4−0.03−0.07−0.11−0.16−0.23−0.32−0.46−0.75−1.30−∞
 50.440.400.360.310.240.150.01−0.28−0.82−∞
 60.890.850.810.760.690.600.460.17−0.38−∞
 71.341.301.261.211.141.050.910.620.08−∞
 81.831.801.751.701.641.541.401.110.57−∞
 92.452.412.372.322.252.162.021.721.18−∞
 103.473.443.393.343.273.183.042.752.21−∞

As described later, the respondents have shown very few switches in QX3. The majority stuck with the initial choice, and it is only after we repeatedly explained that, in the last question of QX3, LA is strictly less attractive for “everyone except one who enjoys the prospect of losing a larger amount of money without possible gains to cancel the loss out,” that some switched to LB on the last question. However, only 10% of the respondents switched, and the rest stayed with LA. In addition, there are irrational responses showing multiple switches on QX3, QX4, QX5, and QX6. Our enumerators tried to eliminate multiple switches by going back to the earlier questions at which the respondents switched, but some respondents chose to have multiple switches. We define them as irrational and assign them “NAs” (not applicable) in the respective dummy variables.

We have difficulty in reasoning with such results. We tried several variations in QX3 in the pretesting stage by wiggling the amounts of LA and LB, or by inflating or deflating the amounts, or by changing the difference of B between ith and (i + 1)th questions, or by going from the last question to the first, or by asking the same questions again on the other page of the questionnaire. We used visual tools by showing cards with the rupee amounts written and two boxes with the labels A and B. We took time to explain what the questions were asking by giving respondents training questions in QX1 and QX2, and explained the notion of choosing a box from which they could draw one card.

However, the results were consistently at odds with our expectations. One should also note that we were providing an incentive, as Tanaka, Camerer, and Nguyen (forthcoming) did in Vietnam, for respondents to be truthful to their own preference by explaining to the respondents before the questions that they would actually play the lottery that they chose. Our results are as perplexing as Bauer, Chytilová, and Morduch's (2008) successfully observed the switches in the majority of respondents. One of Bauer, Chytilová, and Morduch's (2008) surveys was conducted in a proximate location of peripheral Bangalore, and employed exactly the same format with a smaller range between max{B} and min{B}, making the chance of observing a switch smaller, and they randomly picked only few respondents to actually play the lotteries, which gave weaker incentives to be truthful than ours, as we let all the respondents play the lottery.

Nonetheless, we can identify the attitudes, if not the actual parameter values, toward risks. We define an individual as being risk-averse if LA ≥ LB where LB is the mean preserving spread of LA, and conversely, as risk-loving if LA ≤ LB. More specifically, in QX3, a risk neutral individual must switch from LB to LA at the ninth question from the top in which respondents were. Therefore, if the switch happens before question 9, we identify the person as risk-averse in the positive region. A similar definition is used for the loss risks in QX4, QX5, and QX6. There are some respondents who switched in reverse: from LA to LB. This goes against any classical notion of risk attitudes, as this implies that the individual favors lower mean returns and higher risks. Note that even risk lovers would not choose an inferior lottery when given the chance to choose higher mean returns. Hence, these reverse switchers are defined as “irrational” and are assigned NAs in their risk attitudes. In the estimation, we use QX4 and QX6 but not QX5 because QX5 and QX6 are similar in mean and highly correlated, and QX6 has fewer missing values.

To account for hyperbolic preference, one must choose the extent of the distant future, n days from now, to construct the discount rates between two dates that are separated by k days. Let us denote the discount rate β ? [0,1] between today (0 day from now) and k days later as β(0, k), and between n days from now and n + k days from now as β(n, n + k). Then, an individual is said to be hyperbolic if:

image

There can be four possibilities if we can compute the discount rates β(0, k), β(nn + k). In the classification shown in Table 4, an individual choosing earlier dates on both occasions is called impatient, whereas one choosing the later dates on both occasions is called patient. Hyperbolicity is identified by the lower left quadrant of the table where the individual chooses the earlier date for the present and the later date for n days after. The upper right quadrant has no name so we just call it “inconsistent.” As with the risk preference question of QX3, we tried a variety of configurations and have observed that one should not use the immediate future for k, such as k = 1, 2, and that one should set at least a few months time for n. Therefore, we set k = 7 or one week, and n = 180 or six months, as presented in Table 5.

Table 4. 
Hyperbolicity
 Todayk Days Later
n days laterImpatient“Inconsistent”
n + k days laterHyperbolicPatient
Table 5. 
Questions for Eliciting Risk Preference : QX1 You will be given a prize on one of below dates. If you choose later, a trustful agent will deliver the prize. Which date do you choose?
 Now+6 Months
Now1 Week Later6 Months Later6 Months + 1 Week
1Rs 200Rs 320Rs 200Rs 320
2Rs 200Rs 300Rs 200Rs 300
3Rs 200Rs 280Rs 200Rs 280
4Rs 200Rs 260Rs 200Rs 260
5Rs 200Rs 240Rs 200Rs 240
6Rs 200Rs 220Rs 200Rs 220
7Rs 200Rs 200Rs 200Rs 200

Regardless of whether the respondent was hyperbolic or not, we asked in QX7 whether the respondents prefer periodic installments or a lump-sum payment at the end of the period. In a series of questions contrasting periodic installments and a lump-sum including interest payments, we define a respondent as “sophisticated” when he or she chooses the periodic installments for all choices. In the argument of hyperbolic discounting, it is important to see whether an individual is “naïve” or “sophisticated.” Sophisticated individuals know that they are tempted to overvalue current consumption. They are willing to utilize commitment devices, if available (Ashraf, Karlan, and Yin 2006). It is not yet clear how these sophisticated individuals reply to questions like QX1. If they are quite sophisticated, they might choose larger gains in the future as a measure of commitment and there might be no difference in the elicited discount rates of β(0, k) and β(n, n + k), even if they are sophisticated hyperbolic discounters. Fernández-Villaverde and Mukherji (2002) propose to directly detect the preference for commitment by asking whether respondents prefer: (a) 180 minutes of access to a videogame for three days with a constraint on time allocation (60 minutes a day), or (b) 180 minutes of access to a videogame for three days without any constraint on time allocation. Along the same line, we use questions asking whether the respondents prefer periodic installments or a lump-sum payment at the end of a period, to detect the preference for commitment.

V. EMPIRICAL RESULTS

To investigate take-up decisions of Yeshasvini, 209 households were randomly selected from three villages in rural Bangalore, Karnataka in September 2008. The villages are characterized as being mostly semi-urban and are under rapid development due to surrounding factory outlets. Villages are within a half-hour distance of both private and public hospitals, including a clinic run by the insurer. As is customary in the state of Karnataka, households engaging in dairy production have been exposed to Yeshasvini, or a state-funded surgical insurance scheme. Villages were purposefully selected to study the areas without significant commercial medical insurance penetration while being availed of an array of health-care providers.

The interviewers visited the selected households and distributed invitations to the survey to be conducted in the village halls. Household members were assigned one-hour intervals from 9 a.m. to 3 p.m. to show up in the hall. The questionnaire consisted of two parts, one on household background information and perceptions on insurance, and another on results from experiments.

Table 6 provides the descriptive statistics for the data we obtained. The variables can be categorized into three groups: household level (Table 7), individual level,3 and experimental (Table 8). Household level information provides the standard household background information, including roster and members' education levels. Individual-level information provides information about the respondents, including self-reported health conditions. Experimental information includes the responses to our experimental questions. As seen in Table 8, 22% of our respondents are from below-poverty-line households, although they have relatively high values of land assets, reflecting the fact that our site is near Bangalore. Still, only 66% have a latrine or a toilet, and only 26% have a water tap on their premises.

Table 6. 
Description of Variables
VariablesDescription
Household-level variables 
 bpl1 if household is below poverty line, 0 otherwise
 landvalValue of land assets in Rs 10,000
 nonlandvalValue of nonland assets in Rs 10,000
 tap1 if household has piped water access, 0 otherwise
 osew1 if household has open sewerage, 0 otherwise
 csew1 if household has covered sewerage, 0 otherwise
 toilet1 if household has a toilet, 0 otherwise
 barn1 if household has a barn, 0 otherwise
 anycc11 if household is credit constrained to at least one lender
 bank.cc11 if household is credit constrained to a bank
 HHsizeHousehold size
 adultfemrNumber of adult female members divided by household size
 kidsrNumber of child members divided by household size
 elderlyrNumber of elder members divided by household size
 hdageHead age
 hdmarageHead age at marriage
 hdedu1 if head's education level is above 5th standard
 hdtopincrank1 if head is ranked as first in income earning
 sickrNumber of sick members divided by household size
 headill1 if household head is ill 0 otherwise
 illfor6Number of members who have been sick for more than six months
 illmonrHousehold total months of illness divided by household size
 havey1 if has Yeshasvini, 0 otherwise
 havehi1 if has health insurance, 0 otherwise
 numdiaNumber of members with diarrhea in last 30 days
 numrespNumber of members with upper respiratory infection in last 30 days
 village1Village dummy variable for village 1
 village2Village dummy variable for village 2
Experimental variables 
 hyperbolic1 if hyperbolic, 0 otherwise
 sophisticated1 if prefers periodic installments in all 6 choices, 0 otherwise
 posriskaverse1 if risk-averse in positive region of QX3, 0 otherwise
 lossrisklove11 if risk-loving in negative region of QX4, 0 otherwise
 lossrisklove21 if risk-loving in negative region of QX5, 0 otherwise
 lossrisklove31 if risk-loving in negative region of QX6, 0 otherwise
Table 7. 
Household Information
 Minimum25%Median75%MaximumMeanStandard Deviation0sNAsNumber of Observations
  • † 

    Number of observations whose values are 0.

HHsize2456104.821.5800209
kidsr000010.260.21600209
elderlyr000010.090.161440209
adultfemr000010.360.1420209
bpl000010.220.4115511209
landval (Rs10,000)0241002522,000203.10305.090137209
nonlandval (Rs10,000)06184450336.9259.3340209
tap000110.260.441514209
osew000110.320.471394209
csew000110.360.481324209
toilet001110.610.49804209
lat001110.660.48704209
barn000010.210.411624209
anycc1000110.350.481350209
hdage03240509043.1314.6430209
hdmarage122225285224.914.6404209
hdedu001110.620.49800209
hdtopincrank011110.830.38360209
headill000110.250.441560209
sickr000010.160.211070209
illfor6000110.480.501090209
havey000110.320.471394209
havehi000130.480.711304209
numdia000130.610.707759209
numresp011161.250.992259209
Table 8. 
Results of Experiments
 Minimum25%Median75%Maximum
HH152104155209
hyperbolic00001
posriskaverse00111
lossrisklove101111
lossrisklove201111
lossrisklove301111
 MeanStandard Deviation0sNAsNumber of Observations
  • Note: NA = Not applicable.

  • † 

    Number of observations whose values are 0.

HH104.0360.1100205
hyperbolic0.050.231904205
posriskaverse0.620.49757205
lossrisklove10.780.42454205
lossrisklove20.850.362910205
lossrisklove30.860.35291205

Table 8 summarizes the results of the experimental questions. It shows that among all non-NA respondents, 62% are risk-averse in the positive region (gain-risk averters), whereas approximately 80% are risk-loving in the negative region (or loss-risk lovers). There are variations in the ratio of loss-risk lovers depending on which lottery table one looks at, but the variation is not so large, hovering around 80%. This is striking, because the sole purpose of insurance is to cover the prospect of loss, while the results show that the people welcome such a prospect. The two column segments in Table 9 cross-tabulate the distribution of gain-risk aversion and loss-risk aversion. It turns out that a substantial number of respondents behave in a way consistent with prospect theory: risk-averse in the positive region and risk-loving in the negative region. Fisher exact tests are performed to see if gain-risk averters and lovers differ significantly in their loss-risk attitudes.4 The result from the table for QX4 is not significant, whereas that for QX6 is. This indicates that one should control both gain-risk attitudes and loss-risk attitudes to better explain insurance purchase decisions.

Table 9. 
Risk Attitudes
 QX3 and QX4QX3 and QX6
LossLoss
AverseLovingAverseLoving
Gain    
 Averse0.1170.4830.0590.537
 Loving0.1020.2490.0830.283
Fisher testp = 0.159p = 0.021

We identified only 5% of our respondents as hyperbolic, as shown in Table 8. This is too small a variation to be used as a dummy variable with efficiency. This might be due to the fact that we subsequently asked the respondents to make a choice between the present and one week later, and, immediately after that, a question on a choice between six months later and six months and one week later, causing people to take the same choice. Whatever the underlying reason for the low hyperbolic population, we need to be careful when interpreting the results on this variable as it has large standard errors. Sophistication associated with preference toward periodic installments is found in 85% of respondents. Table 10 shows that the majority of hyperbolic respondents are sophisticated, although the Fisher test shows that non-hyperbolic individuals also show a similar preference.

Table 10. 
Hyperbolicity and Sophistication
 Sophisticated
YesNo
Hyperboic  
 Yes0.1480.794
 No0.0050.053
Fisher testp = 0.999

Using probit model, we estimate purchases of Yeshasvini in Tables 11 and 12, and general health insurance, including Yeshasvini in Tables 13 and 14. A comparison of the tables reveals that the estimated results from Tables 11 and 12 show a similarity with those of Tables 13 and 14.

Table 11. 
Probit Estimation Results of Yeshasvini, Part 1
 (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)
  • Notes: 1. Probit estimation with robust standard errors.

  • 2. Asset values are in Rs10 million.

  • ***, **, and * 

    represent statistical significance at the 1%, 5%, and 10% level, respectively.

(Intercept)−0.284***−0.250−0.204−0.715**−0.610*−0.225−0.083−0.5040.3570.335
(0.103)(0.443)(0.456)(0.425)(0.418)(0.467)(0.413)(0.450)(0.583)(0.625)
headill−0.833***−0.907***−0.993***−1.041***−1.015***−0.988***−0.964***−0.957***−0.952***−0.927***
(0.241)(0.238)(0.226)(0.212)(0.211)(0.232)(0.235)(0.231)(0.234)(0.241)
hdage 0.009*0.009*0.014**0.013**0.009*0.009*0.014**0.0080.010*
 (0.007)(0.007)(0.007)(0.007)(0.007)(0.007)(0.006)(0.007)(0.006)
hdmarage 0.0020.0040.0010.0010.0030.0010.006*0.0040.002
 (0.004)(0.004)(0.004)(0.004)(0.004)(0.004)(0.004)(0.003)(0.004)
hdedu 0.062−0.024−0.030−0.041−0.019−0.0470.046−0.057−0.006
 (0.226)(0.224)(0.238)(0.253)(0.231)(0.218)(0.216)(0.227)(0.216)
village1 −1.394***−1.469***−1.415***−1.419***−1.447***−1.586***−1.530***−1.538***−1.695***
 (0.249)(0.247)(0.250)(0.267)(0.243)(0.259)(0.268)(0.273)(0.305)
village2 −0.354*−0.287−0.131−0.149−0.287−0.288−0.242−0.320−0.287
 (0.238)(0.250)(0.260)(0.256)(0.259)(0.253)(0.251)(0.256)(0.263)
landval  −0.335−0.654−0.613−0.332−0.288−0.290−0.292−0.187
  (0.520)(0.590)(0.576)(0.524)(0.593)(0.482)(0.527)(0.570)
nonlandval  1.6361.0251.0771.6751.1231.4101.6000.967
  (2.155)(1.998)(2.020)(2.173)(1.900)(2.023)(2.101)(1.902)
bpl  −0.186−0.190−0.214−0.172−0.228−0.186−0.137−0.221
  (0.211)(0.220)(0.220)(0.215)(0.222)(0.212)(0.224)(0.234)
tap   0.0990.057     
   (0.273)(0.267)     
toilet   0.1960.237     
   (0.194)(0.192)     
csew   0.1540.128     
   (0.220)(0.252)     
osew   0.0680.073     
   (0.223)(0.220)     
barn   0.528**0.502**     
   (0.265)(0.260)     
bank.cc1    −0.245    −0.384*
    (0.344)    (0.270)
numdiarh     −0.085    
     (0.176)    
numresp     0.056    
     (0.092)    
hyperbolic      0.979**  0.995**
      (0.485)  (0.594)
posriskaverse       −0.027 0.004
       (0.206) (0.216)
lossrisklove1        −0.104−0.076
        (0.263)(0.261)
lossrisklove3        −0.461*−0.455*
        (0.303)(0.326)
Table 12. 
Probit Estimation Results of Yeshasvini, Part 2
 (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)
  • Notes: 1. Probit estimation with robust standard errors.

  • 2. Asset values are in Rs10 million.

  • ***, **, and * 

    represent statistical significance at the 1%, 5%, and 10% level, respectively.

(Intercept)−0.396***0.1410.3670.256−1.079−1.069−0.863−1.547*−0.546−0.845
(0.141)(0.209)(0.477)(0.605)(0.954)(0.942)(0.961)(0.994)(1.008)(1.059)
headill−0.906***−0.919***−1.094***−1.259***−1.317***−1.315***−1.379***−1.359***−1.270***−1.376***
(0.288)(0.261)(0.308)(0.242)(0.269)(0.267)(0.278)(0.268)(0.278)(0.315)
illfor6−0.086−0.195−0.227−0.341−0.332−0.318−0.425*−0.283−0.265−0.262
(0.255)(0.249)(0.303)(0.282)(0.263)(0.257)(0.260)(0.292)(0.261)(0.285)
illmonr−0.007−0.001−0.0020.000−0.001−0.0010.0040.001−0.0010.004
(0.010)(0.015)(0.024)(0.020)(0.016)(0.016)(0.014)(0.018)(0.012)(0.013)
sickr1.292***1.251***1.340***1.266***1.441***1.442***1.544***1.514***1.459***1.573***
(0.508)(0.432)(0.435)(0.476)(0.462)(0.462)(0.459)(0.447)(0.468)(0.451)
village1 −1.383***−1.349***−1.387***−1.346***−1.346***−1.514***−1.421***−1.452***−1.591***
 (0.266)(0.268)(0.268)(0.248)(0.259)(0.251)(0.244)(0.278)(0.289)
village2 −0.423**−0.415**−0.282−0.203−0.204−0.134−0.162−0.263−0.164
 (0.230)(0.239)(0.317)(0.278)(0.278)(0.310)(0.275)(0.281)(0.309)
kidsr  −0.0460.1510.5920.5940.5160.5200.6510.591
  (0.504)(0.605)(0.735)(0.744)(0.771)(0.735)(0.679)(0.731)
elderlyr  0.6480.6370.1100.1090.485−0.138−0.0770.200
  (0.708)(0.980)(0.962)(0.960)(1.070)(0.932)(0.944)(1.022)
adultfemr  0.8061.156*1.347**1.342**1.141*1.353**1.366**1.323**
  (0.775)(0.730)(0.742)(0.751)(0.765)(0.743)(0.743)(0.789)
HHsize  −0.114**−0.160***−0.153**−0.151**−0.126**−0.151**−0.166**−0.133**
  (0.068)(0.063)(0.069)(0.077)(0.065)(0.069)(0.077)(0.074)
landval   −0.589−0.661*−0.646*−0.554−0.676*−0.584−0.474
   (0.521)(0.483)(0.492)(0.552)(0.462)(0.479)(0.536)
nonlandval   1.2831.3851.3880.3241.0311.6190.606
   (2.221)(1.899)(1.917)(1.951)(1.777)(1.689)(1.697)
bpl   −0.241−0.236−0.243−0.264−0.231−0.192−0.262
   (0.220)(0.233)(0.235)(0.239)(0.232)(0.246)(0.241)
tap   0.0830.0440.0310.0920.099−0.102−0.075
   (0.370)(0.310)(0.303)(0.320)(0.303)(0.259)(0.266)
toilet   0.0180.1150.1250.0060.1330.1900.167
   (0.215)(0.221)(0.221)(0.218)(0.212)(0.219)(0.222)
csew   0.0970.1410.1350.2220.0620.0720.054
   (0.225)(0.222)(0.225)(0.216)(0.216)(0.232)(0.234)
osew   0.0980.1050.1050.1720.1450.1210.202
   (0.264)(0.249)(0.249)(0.263)(0.253)(0.234)(0.248)
barn   0.699***0.679***0.669**0.672***0.730***0.709**0.702**
   (0.284)(0.284)(0.288)(0.282)(0.283)(0.307)(0.318)
hdage    0.018**0.018**0.015*0.026***0.018**0.020**
    (0.011)(0.011)(0.011)(0.010)(0.011)(0.011)
hdmarage    0.0050.0050.0020.0060.006*0.006*
    (0.005)(0.005)(0.005)(0.005)(0.005)(0.005)
hdedu    0.0480.0440.0350.168−0.0030.089
    (0.284)(0.287)(0.280)(0.254)(0.265)(0.250)
hdtopincrank    0.1380.1360.0370.1960.1990.144
    (0.367)(0.364)(0.378)(0.357)(0.296)(0.297)
bank.cc1     −0.062   −0.222
     (0.351)   (0.268)
hyperbolic      1.182***  1.006***
      (0.370)  (0.427)
posriskaverse       −0.094 −0.034
       (0.200) (0.206)
lossrisklove1        −0.299−0.262
        (0.252)(0.258)
lossrisklove3        −0.383−0.378
        (0.387)(0.378)
Table 13. 
Probit Estimation Results of Any Health Insurance, Part 1
 (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)
  • Notes: 1. Probit estimation with robust standard errors.

  • 2. Any health insurance including Yeshasvini.

  • 3. Asset values are in Rs10 million.

  • ***, **, and * 

    represent statistical significance at the 1%, 5%, and 10% level, respectively.

(Intercept)−0.149*−0.0050.018−0.243−0.1000.1650.187−0.3440.5360.494
(0.102)(0.408)(0.435)(0.442)(0.434)(0.473)(0.434)(0.468)(0.591)(0.630)
headill−0.883***−0.886***−0.969***−0.978***−0.953***−0.933***−0.938***−0.925***−0.921***−0.898***
(0.234)(0.221)(0.211)(0.202)(0.200)(0.219)(0.219)(0.218)(0.217)(0.236)
hdage 0.0020.0010.0020.001−0.001−0.0010.004−0.000−0.000
 (0.007)(0.007)(0.008)(0.007)(0.008)(0.008)(0.007)(0.007)(0.008)
hdmarage 0.006*0.011***0.008**0.007**0.009***0.006**0.014***0.010***0.007**
 (0.003)(0.003)(0.004)(0.004)(0.004)(0.004)(0.003)(0.003)(0.004)
hdedu 0.010−0.056−0.069−0.075−0.030−0.064−0.000−0.089−0.031
 (0.197)(0.200)(0.206)(0.211)(0.203)(0.205)(0.204)(0.203)(0.216)
village1 −0.941***−1.011***−0.956***−0.968***−1.010***−1.080***−0.977***−1.084***−1.123***
 (0.238)(0.251)(0.261)(0.268)(0.244)(0.274)(0.262)(0.264)(0.288)
village2 −0.292−0.198−0.111−0.132−0.239−0.207−0.131−0.225−0.161
 (0.234)(0.248)(0.259)(0.256)(0.262)(0.255)(0.249)(0.253)(0.263)
landval  0.4360.2660.3360.3890.5330.5120.5100.718*
  (0.404)(0.493)(0.487)(0.402)(0.450)(0.402)(0.419)(0.497)
nonlandval  1.0140.7480.8030.9840.4500.7430.9800.174
  (2.086)(2.086)(2.116)(2.001)(1.952)(1.968)(2.017)(2.061)
bpl  −0.255−0.236−0.273−0.232−0.284−0.255−0.231−0.321
  (0.240)(0.256)(0.260)(0.244)(0.261)(0.244)(0.243)(0.273)
tap   0.0540.001     
   (0.248)(0.245)     
toilet   0.0880.145     
   (0.209)(0.211)     
csew   0.1030.065     
   (0.223)(0.235)     
osew   0.1500.151     
   (0.214)(0.212)     
barn   0.2980.265     
   (0.263)(0.258)     
bank.cc1    −0.348    −0.478**
    (0.272)    (0.283)
numdiarh     −0.206    
     (0.176)    
numresp     0.028    
     (0.096)    
hyperbolic      0.962**  1.127*
      (0.498)  (0.797)
posriskaverse       0.093 0.151
       (0.200) (0.212)
lossrisklove1        −0.188−0.173
        (0.251)(0.268)
lossrisklove3        −0.341−0.318
        (0.299)(0.319)
Table 14. 
Probit Estimation Results of Any Health Insurance, Part 2
 (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)
  • Notes: 1. Probit estimation with robust standard errors.

  • 2. Any health insurance including Yeshasvini.

  • 3. Asset values are in Rs10 million.

  • ***, **, and * 

    represent statistical significance at the 1%, 5%, and 10% level, respectively.

(Intercept)−0.177*0.2430.697*0.560−0.095−0.0810.251−0.4850.3470.264
(0.136)(0.204)(0.454)(0.551)(0.844)(0.834)(0.824)(0.870)(0.950)(0.974)
headill−0.873***−0.861***−0.990***−1.148***−1.144***−1.144***−1.199***−1.129***−1.083***−1.142***
(0.278)(0.253)(0.276)(0.235)(0.240)(0.236)(0.244)(0.239)(0.248)(0.272)
illfor6−0.233−0.315*−0.293−0.374*−0.397*−0.377*−0.494**−0.384*−0.356*−0.400*
(0.248)(0.239)(0.275)(0.270)(0.261)(0.257)(0.259)(0.281)(0.253)(0.282)
illmonr−0.008−0.004−0.006−0.004−0.004−0.0040.001−0.003−0.0040.002
(0.010)(0.012)(0.019)(0.018)(0.015)(0.014)(0.013)(0.015)(0.013)(0.012)
sickr1.141**1.075***1.068***1.016**1.095***1.098***1.176***1.119***1.102***1.152***
(0.505)(0.455)(0.458)(0.455)(0.450)(0.446)(0.463)(0.457)(0.446)(0.470)
village1 −0.943***−0.885***−0.913***−0.878***−0.879***−1.008***−0.816***−0.966***−0.956***
 (0.242)(0.234)(0.257)(0.251)(0.258)(0.268)(0.261)(0.273)(0.302)
village2 −0.337*−0.324*−0.158−0.122−0.123−0.073−0.067−0.175−0.059
 (0.235)(0.240)(0.288)(0.273)(0.273)(0.300)(0.272)(0.277)(0.311)
kidsr  0.1980.5740.847*0.844*0.7400.7750.902*0.780
  (0.498)(0.524)(0.632)(0.630)(0.648)(0.656)(0.629)(0.693)
elderlyr  0.7560.8280.6460.6491.0180.4400.4920.810
  (0.667)(0.879)(0.933)(0.933)(1.012)(0.931)(0.941)(1.032)
adultfemr  0.1610.4430.5900.5780.3340.5620.6270.482
  (0.789)(0.791)(0.835)(0.839)(0.824)(0.854)(0.841)(0.886)
HHsize  −0.131***−0.182***−0.176***−0.172***−0.160***−0.182***−0.185***−0.173***
  (0.056)(0.053)(0.065)(0.069)(0.062)(0.064)(0.074)(0.072)
landval   0.4490.4800.5080.5910.5190.5950.775*
   (0.585)(0.554)(0.553)(0.590)(0.547)(0.554)(0.601)
nonlandval   0.9191.0121.016−0.0220.7441.1280.037
   (2.077)(1.970)(1.993)(1.994)(1.877)(1.815)(1.879)
bpl   −0.298−0.291−0.304−0.308−0.277−0.274−0.330
   (0.244)(0.256)(0.262)(0.264)(0.272)(0.255)(0.274)
tap   0.1000.0750.0540.1210.097−0.015−0.014
   (0.276)(0.263)(0.254)(0.266)(0.270)(0.250)(0.262)
toilet   0.0000.0720.090−0.0560.0990.1430.108
   (0.214)(0.220)(0.225)(0.218)(0.231)(0.219)(0.230)
csew   0.0540.0640.0530.145−0.0170.004−0.012
   (0.223)(0.225)(0.223)(0.219)(0.236)(0.217)(0.228)
osew   0.1910.1740.1740.2470.2010.1820.271
   (0.233)(0.230)(0.229)(0.238)(0.232)(0.226)(0.240)
barn   0.508**0.463*0.447*0.468**0.476**0.480**0.472*
   (0.280)(0.282)(0.285)(0.280)(0.280)(0.290)(0.301)
hdage    0.0070.0070.0030.012*0.0070.006
    (0.009)(0.009)(0.009)(0.009)(0.009)(0.010)
hdmarage    0.0050.0050.0020.008*0.007*0.007*
    (0.005)(0.005)(0.005)(0.005)(0.005)(0.005)
hdedu    −0.011−0.015−0.0080.087−0.0590.045
    (0.250)(0.253)(0.253)(0.234)(0.237)(0.240)
hdtopincrank    0.0370.034−0.0600.0660.072−0.028
    (0.290)(0.286)(0.285)(0.280)(0.285)(0.275)
bank.cc1     −0.110   −0.245
     (0.302)   (0.314)
hyperbolic      1.202***  1.180**
      (0.379)  (0.538)
posriskaverse       0.079 0.163
       (0.202) (0.207)
lossrisklove1        −0.287−0.275
        (0.254)(0.257)
lossrisklove3        −0.258−0.247
        (0.365)(0.364)

In both Tables 12 and 14, households with healthy head members are more likely to purchase the policies, as indicated by the negative estimates on headill. This is surprising as Yeshasvini is losing money and is considered to be afflicted with adverse selection. However, the ratio of sick members contributes positively to the purchase, implying the existence of adverse selection. Although this is cross-sectional data and one cannot directly identify the causation, it is unlikely that reverse causation or any other omitted variable will negate adverse selection. One explanation is that households with a sick household head had less income flow (our data set do not include information on income flow) and had difficulty in financing the insurance premium. The negative coefficient of household size (Tables 12 and 14) might also capture the higher income of smaller households. Negative estimates on land values for Yeshasvini in Table 12 might have captured the fact that dairy cooperative members have smaller plots of land.

One village dummy (village1) is significantly negative because that village does not have dairy cooperatives, whereas the other two do. Households owning barns (barn) are also more likely to purchase policies, a fact that simply depicts the reality that Yeshasvini is a dairy cooperative-based insurance scheme.

As for risk attitude, estimates on risk aversion in the domain of gain change the sign, and none are statistically significant. Combined with the fact that many of the respondents show a pattern of choice that is consistent with the prospect theory, this seems to suggest that risk attitude toward gains is not useful for predicting the insurance take-up decision. The coefficient of loss-risk lover dummies is always negative, although only the loss-risk–loving attitude identified from QX6 is statistically significant at the 10% level in (9) and (10) of Table 11, partly due to our small sample size.

The hyperbolicity coefficient is positive and statistically significant. Although we need to exercise caution in interpreting this result because we see few variations in this variable, this positive sign is consistent with the theoretical prediction that households with hyperbolic discounting are more likely to buy insurance as a measure of commitment. However, the sophistication dummy has positive signs for Yeshasvini purchases but negative signs for all health insurance, and it is difficult to interpret the results.

Estimates on credit constraints are generally negative (but not significant) in all tables, consistent with the results of Giné, Townsend, and Vickery (2008) who investigate the take-up decision of rainfall insurance in India. The negative coefficient implies that credit constrained households are cash constrained in buying insurance, and/or that near-constrained households are forward looking enough to buy insurance.

VI. CONCLUSION

Following the rapid expansion of microcredit, microinsurance has drawn the attention of practitioners and academics. However, take-up rates of microinsurance have been low despite its perceived need and the enthusiasm of microfinance practitioners. In this paper, we focused on the take-up decision of health microinsurance in India, using originally collected household data.

We find some evidence that people behave in a risk-loving way when facing the risk of losses, which is consistent with prospect theory. Because insurance covers losses, we suspect that these people are less likely to take up insurance and we find some evidence supporting this view. We also find that hyperbolic discounters are more likely to purchase insurance, a fact that can be explained by the demand for commitment among sophisticated hyperbolic discounters. However, this result should be interpreted with caution because of the small size of our sample. We also find some evidence for the existence for adverse selection: households with a higher ratio of sick members are more likely to purchase insurance. Interestingly, we also find that households with a sick household head are less likely to purchase insurance. This might capture the fact that households with a sick household head have less income flow and have difficulty in financing the insurance premium.

Understanding the take-up decision is only a part of the efforts being made toward making microinsurance more popular among the poor. Identifying the means for increasing take-up rates and decreasing dropout rates while keeping the policy financially sustainable is equally important. We leave this task for our ongoing project and future works.

Footnotes

  • 1

    Attanasio, Goldberg, and Kyriazidou (2008) note that there are two notions of credit constrainedness, strong and weak. The strong version is more widely used and implies that the person could not borrow as much as she wanted under the given conditions. The weak version defines a person as credit constrained if the borrowing and lending rates differ. We take the strong version of the definition because the weaker version may apply to almost everyone in the sample.

  • 2

    The columns titled “Difference in expected values” and “Open interval of α if subject switches to lottery B” were not shown to the respondents.

  • 3

    The descriptive statistics for this group are not shown as they are only used for relating the respondents to other household members.

  • 4

    A Fisher exact test examines, in a 2 × 2 table, if the row (column) ratios are significantly different. In our context, it tests if the ratios of loss-risk averters between gain-risk averters and lovers differ significantly. A small p-value indicates occurrence of a rare event, or two groups coming from two different populations.

Ancillary