The Insurability of Risk in the Micro Health Insurance Market

Bachelor Thesis, 2013

36 Pages, Grade: 1,7



1 Relevance of Micro Health Insurance

2 Health Insurance Economics
2.1 The principles of Insurance
2.2 Adverse Selection
2.3 Moral Hazard
2.4 Micro Health Insurance

3 Risk and Insurability
3.1 The Concept of Risk
3.2 The Concept of Insurability

4 Insurability in Micro Health Insurance
4.1 Adaptation of Berliner’s Criteria .
4.2 Actuarial Criteria
4.3 Market Criteria
4.4 Societal Criteria

5 Discussion and the way forward

6 References

7 Appendix

List of Tables

1 Berliner’s Criteria

2 Berliner’s Criteria according to Biener and Eling

3 Adapted Criteria of Insurability

List of Figures

1 Basic Model with one Risk Type

2 Basic Model with two Risk Types

3 Non-existence of a pooling equilibrium with asymmetric information

4 Separating Equilibrium with Asymmetric Information

5 Geometric Model

A.1 Publication Overview


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1 Relevance of Micro Health Insurance

Microfinance has been on the rise ever since Muhammad Yunus received the Nobel Peace Prize in 2006. While the focus used to be on microcredit, the perception of microfinance has broadened now including microsavings as well as microinsurance. It has been recognized that microcredits often are not the most adequate tool to combat a specific problem. Hence, the tools of microsavings and microinsurance have been introduced, in order to improve targeting and thus alleviating poverty more effectively.

The health sector plays a key role in microfinance, due to different aspects. A major concern was (somehow still is) that six out of ten microcredits defaults are due to sickness of the credit taker or a member of the family (Stojanovska & Winter 19.30.2012). Since the aim is to reduce defaulting it seemed appropriate to come up with insurance products which would cover sickness expenses or would cover instalments of the credit. Another issue is that health/social security systems in developing countries are often underdeveloped1 which leads to out-of-pocket payments. The out-of-pocket payments often have devastating effects on the poorer members of society. Since they usually do not have the money at their disposal they are forced to borrow the money. Sickness has several effects on the economic status, the first being that the sick person is not able to work, therefore losing money as it is. On top of this, the out-of-pocket payment has to be made in order to get access to treatment. If the poor household does not have the money, which is likely, the most common action is borrowing money, which is usually accompanied by extremely high interest rates. This is termed ’medical poverty trap’ and can be combated with micro health insurance (Di McIntyre & Thiede 2008: 81 & 84). Another problem with out-of-pocket spending refers to ’catastrophic medical spending’. Two possible definitions exist, one being that medical spending accounts for more than 40 per cent of household consumption, the other one being ”health spending that drives families below the poverty level” (Kruk et al. 2009: 1057). It should be evident that out-of-pocket spending affects disproportionally the poorest part of society. Hence, microinsurance seems to be an adequate tool (savings not so much as health costs can be very high and it would thus take a long time in order to built up a cash stock which would suffice) to lighten the burden.

The desirability of micro health insurance is usually beyond doubt but the sustainable provision is a different matter. Even traditional insurance economics have issues which complicate the adequate coverage of risks but the problems in the microinsurance environment are even more difficult to handle. When looking for an approach on how to analyse risks in micro health insurance and how to insure them one will fail to find one. So far, data is very rare. Usually it is only possible to find a small amount of data extracted out of small scale studies/evaluations. The microinsurance database of the World Bank is an attempt to collect all kinds of relevant data concerning microinsurance but so far, there is only some basic data for six countries2.

Recently there has been the attempt to start an analytical framework on how to assess insurability of risk in microinsurance. Biener and Eling provide a starting point by adjusting the insurability criteria of Berliner to a microinsurance environment. This paper will continue the work in the area of micro health insurance and suggests a further criterion to be used when assessing the insurability of risk.

The structure of the following work is divided into three main parts. First, an extensive introduction into health insurance economics will be given in order to provide the necessary background regarding the calculation of premiums and possible market failures in particular. The second part discusses the concepts of risk and insurability. Deviating from the standard analytical assessment of risk the aspect of perceived risk will be stressed. Insurability will be defined according to Berliner and his nine criteria will be introduced. The third section will discuss the application of Berliner’s criteria to micro health insurance. The adaptation of the criteria according to Biener and Eling will be taken over. Yet, these do not seem to suffice in order to analyse insurability. Therefore, an additional criterion ’culture’ will be suggested as it will become apparent that micro health insurance is highly sensitive to local conditions.

2 Health Insurance Economics

When considering health as an economic commodity it becomes apparent that health differs from other goods since the demand for health cannot be satisfied directly. Rather, the demand for health can only be satisfied via a demand for health care. According to Hurley, health care has four distinctive features which allow for market failures. The first, as mentioned, the demand for health care is an indirect demand for health, the second is the existence of externalities, the third lies in the information asymmetry between provider and patient and the last characteristic is the uncertainty of the amount of health care needed as well as the quality of the health care (Hurley 2000: 67). Health insurance provides an answer to the problem of uncertainty.

2.1 The principles of Insurance

”Insurance is a device for the reduction of uncertainty of one party, called the insured, through the transfer of particular risks to another party, called the insurer, who offers a restoration, at least in part, of economic losses suffered by the insured” (Pfeffer and Klock in Müller 1981: 64). How exactly this is done is going to be discussed in the following section.

Risk Preferences Before discussing the principles of insurance it is necessary to clarify which individual demands insurance. Individuals can be characterized according to their preference for risk. There are three possibilities: risk-averse, risk-neutral and risk-loving. A risk-averse individual is prepared to pay in order to avoid risk (e.g. insurance), a risk-loving individual buys risk (e.g. a lottery ticket) and a risk-neutral is indifferent (Rosner 2003: 34

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The left side of the above equation represents an risk-averse individual and the right side a risk-loving one. The insurance industry is based on risk-averse individuals who are willing to spend money on risk reduction. The utility function used is a von-Neumann-Morgenstern utility function. This utility function expresses risk aversion trough strict convexity. Therefore, u′ (y) > 0 and u′′ (y) < 0 expresses risk aversion in an individual (Breyer & Buchholz 2007: 24 & 94). Insurance companies are risk-neutral since they are profit maximisers. Every outcome yields a certain profit which is the utility. Therefore, expected utility equals expected profits. EU (X) = EX · Π =

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In order to make profits the companies are accepting risks (Rosner 2003: 34 & 35). To sum up, in the insurance market the individuals are risk-averse and the companies risk-neutral.

Basic Model In the basic model of health insurance the probability for an individual to fall sick is π and the probability to stay healthy is 1 − π with (0 < π < 1). It is assumed that in case of illness medical treatment is received which restores health completely. M is the cost of this treatment. The insurance consists of the premium P and the insurance benefit I. The premium always has to be paid and the insurance benefit is received when ill (0 ≤ I ≤ M). The gross income of the individual is Y, the disposable income is y and the utility is u (y). Since the individual is risk-averse, u′ (y) > 0 and u′′ (y) < 0. The disposable income in case the individual is healthy is yh and in case of sickness ys.

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Assume the expected insurance benefit πI equals the premium P (which defines an actuarially fair contract3 ) then the expected utility of an individual can be written as

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Given the actuarially fair contract yh and yh can be written as

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Plugging these into the expected utility function yields

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The optimal cover of insurance is determined via the first-order condition.

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The optimal coverage in case of an actuarially fair contract is full coverage and the individual has an income of yh = ys = Y − πM. All contracts offering full insurance cover are located on the bisecting line (see figure 1). The actuarially fair premium depends on the slope of the budget line. The budget line b can be retrieved by solving yh for I and substituting I into ys.

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The individual’s indifference curves have a slope of:

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On the certainty line (ys = yh) the slope of the indifference curve is therefore reduced to [Abbildung in dieser Leseprobe nicht enthalten]. Thus, the point C in figure 1 represents the optimum since the slope of the budget line equals the slope of the indifference curve. The budget line shows that the certainty income is Y − πM (Zweifel et al. 2009: 163-166).

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Figure 1: Basic Model with one Risk Type

Source: Zweifel et al. 2009: 165

The basic insurance model assumes that the risk of sickness is constant for all individuals. The premium is fair, meaning it is equal to the expected benefit. The optimal insurance coverage with an actuarially fair contract is full coverage. The actuarially fair health insurance premium implies that the risk can be insured at no costs which does not hold in practice since there are costs involved (e.g. administrative costs).

Basic Model with two risk types The probability to get sick is not constant among all individuals. Therefore the model is expanded to allow for two groups of risk types which are coded as H for high risk and L for low risk types. The probabilities to get sick are respectively πH and πL with πL < πH. Further the distribution in society needs to be distinguished with λ being the share of low risk individuals in the population and (1 − λ) being the share of high risk individuals in the population. The income is now defined as yi k with [Abbildung in dieser Leseprobe nicht enthalten]. Thus, expected utility is given by

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Assuming that there is no asymmetric information the insurer as well as the insured can observe the risk type (the probability to get sick πi). Under the assumption of actuarially fair contracts the premium is Pi = πiIi. Obviously, the premiums differ depending on the risk type, being higher for high risk individuals than for low risk individuals. Symmetric information leads to a separating equilibrium where the high risk individuals will be offered a

contract to their actuarially fair premium and the low risk individuals get their own actuarially fair premium (see figure 2). Both types of individuals will get a contract that fully insures them. The budget lines are given as

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and the budget line slopes are

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The budget line of the low risk type is steeper than the budget line of the high risk type since πH > πL. The two equilibria are in CH and CL (Zweifel et al. 2009: 171 & 172).

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Figure 2: Basic Model with two Risk Types

Source: Zweifel et al. 2009: 172

The question at stake is what happens in case of asymmetric information? The following sections will deal with this market failure. The first problem to be discussed is adverse selection followed by the issue of moral hazard.

2.2 Adverse Selection

Asymmetric information ”occurs when one party to a transaction has more information pertinent to the transaction than does the other party, which may allow the better-informed party to exploit the less-informed party” (Hurley 2000: 73). Adverse selection is a version of asymmetric information and leads to risk selection in insurance markets. In the following it is assumed that only the individual knows its risk type but not the insurer. The insurer only knows the distribution of low risk types in the population (λ). Further assumptions are that the insurer offers contracts with a fixed reimbursement level I and a premium P and these contracts are within the (yh, ys) space. In this case the insurer determines the price and the quantity offered which is plausible in health insurance markets. Further it is assumed that each individual can only buy one contract (Rothschild & Stiglitz 1976: 632 & 633).

Under asymmetric information different definitions for an equilibrium exist. A commonly employed concept is the definition used by Rothschild and Stiglitz.

”A Rothschild-Stiglitz (RS) equilibrium in the health insurance market consists of a set of contracts with the following properties,

(i) all individuals choose the contract which maximizes their expected utility;
(ii) each contract leads to nonnegative expected profits for insurers;
(iii) no contract outside the set of equilibrium contracts yields nonnegative expected profits” (Zweifel et al. 2009: 173).

Pooling Equilibrium The separation equilibrium achieved under symmetric information is not viable under adverse selection since high and low risk types are risk-averse agents who want to achieve full risk coverage. As the insurer is not able to differentiate between high and low risk individuals the high risk types will opt for CL (in figure 2) since they get full coverage for a lower premium. Thus, this contract cannot sustain and this is not an equilibrium. Since this separating equilibrium does not hold, one needs to check for a pooling equilibrium.

A pooling equilibrium in the case of two risk types would have to be on the combined budget line for both (p) with the slope [Abbildung in dieser Leseprobe nicht enthalten] (see figure 3) (Zweifel et al. 2009: 174).

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Figure 3: Non-existence of a pooling equilibrium with asymmetric information

Source: Zweifel et al. 2009: 174

One example for such a contract could be Z. It is placed on the budget line p which takes into account the average probability of loss π consequently the contract breaks even. Further, the indifference curves of both types intersect the budget line. Since the premium based on π is higher than the premium for low risk individuals the contract in Z is not actuarially fair to low-risk types. Hence, it is plausible to assume they would opt for less than full insurance in order to reduce the cost in a pooling contract. Since the indifference curve of the high risk type is flatter than the indifference curve of the low risk type the two curves are intersecting each other thus producing the shaded area between bL, EUH and EUL. If Z was an equilibrium than there must not be a contract that would produce positive profits. The contract Q lies in the shaded area. If a company would offer this contract it would attract low risk individuals since this contract yields a higher utility (and the premium would be lower). This contract would produce positive profits since only low risk individuals would demand this contract and Q lies below the budget line for low risk types bL. Respectively, Z would produce negative profits since only high risk individuals are left and Z is placed above the budget line bH which means that their premiums are not sufficient to cover the expenses. Hence, this is no RS-equilibrium since there can be contracts offered which do produce expected profits (Zweifel et al. 2009: 173 & 174 and Rosner 2003: 44 & 45).

Since every pooling contract under adverse selection produces an area between bL, EUH and EUL there cannot be a pooling equilibrium.

Separating Equilibrium It has been shown that neither a separating equilibrium with actuarially fair contracts for both types nor a pooling equilibrium exist under adverse selection. Thus, Rothschild and Stiglitz propose a self-selection mechanism which forces individuals to reveal their risk type and makes them choose the contract the insurer would like them to take if the risk type was publicly known (Rothschild & Stiglitz 1976: 632). Part of a separating equilibrium has to be the contract CH (in figure 4). If an insurer offers full coverage for a high premium the only individuals purchasing this contract will be high risk types since it is their actuarially fair premium. Hence, CH is the first part of the separating equilibrium. The contract offered to low risk individuals has to be on the budget line bL and it must not be on the certainty line yis = yih 4. This implies that low risk types will only be offered partial insurance coverage for an actuarially fair premium as this is the only way to reach a point that is undesirable to low-risk individuals. This point has to be C′L which marks the intersection of bL and EUH in order to ensure that the contract offered to low risk individuals does not yield a higher expected utility for high risk individuals than they would achieve in CH (Rothschild & Stiglitz 1976: 635 & 636 and Zweifel et al. 2009: 174 & 175). If a separating equilibrium exists in a market with adverse selection it consists of the contracts CH and C′L.

This equilibrium does not have to exist it’s existence rather depends on the distribution of high (1 − λ) and low risk (λ) types in the population. If λ is sufficiently large the combined budget line p runs pretty steep and is close to the bL. Figure 4 shows a possible contract in point T which would make both risk types better off since it yields higher utility levels. T itself cannot be an equilibrium as it has been shown before that a pooling equilibrium under adverse selection does not exist in a RS equilibrium5 (Zweifel et al. 2009: 176). ”This establishes that a competitive insurance market may have no equilibrium” (Rothschild & Stiglitz 1976: 637).


1 There is usually no social health insurance system and if there it is chronically underfunded (according to the World Health Organisation (WHO) only Mongolia, Pakistan, Sudan, Vietnam and Senegal spend more than 15 per cent of government expenditure on the social health insurance system) (Bennett et al. 2008: 160).

2 Bangladesh, Colombia, India, Mexico, Peru, and the Philippines (World Bank Group 29.10.2009).

3 If the premium charged covers exactly the risk the premium is fair and the contract is called ’actuarially fair’.

4 If it was, the contracts offered would be the same like in the separating equilibrium without adverse selection (figure 2).

5 This problem has been addressed. In the case of a high share of low-risk individuals a Wilson equilibrium or a Wilson-Miyazaki-Spence (WMS) equilibrium exists, see Zweifel et al. 2009: 175 & 176.

Excerpt out of 36 pages


The Insurability of Risk in the Micro Health Insurance Market
University of Trier
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Risk, Insurance, micro, health, insurability, economics
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B.A., B.Sc. Esther Schuch (Author), 2013, The Insurability of Risk in the Micro Health Insurance Market, Munich, GRIN Verlag,


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