Is the choice for insurance driven by adverse selection or propitious selection?

Is the choice for insurance driven by Adverse Selection or Propitious

Selection?

(Using a controlled experiment)

Keywords:

Risky choices, Insurance, Risk-Aversion, Loss-Aversion, Adverse-Selection, Propitious-Selection and Coverage-risk correlation

Student: Ralph Atiya

Student nr: 5909953

Master program: Behavioural Economics and Game Theory University: UvA, Faculty of Economics and Business

Supervisor: Theo Offerman

Preface

The master thesis finalizes my period as a student at the University of Amsterdam and hopefully initiates a new chapter in my continuing academic career. While, the master thesis aims to test the academic skills of a student, performing critical empirical research can be difficult without the opinion and reflection of peers and experts on the topic. Therefore, it only seems fit to thank Theo Offerman for his willingness to supervise the research and his guidance to the project. His belief in the master thesis and expertise in the field of controlled experiments offered a lot of support. In addition, I would like to thank my family for giving me an unforgettable educational experience and supporting me throughout all these years.

Abstract

Within the insurance market there are two possible purchase selections that can emerge, adverse selection and propitious selection. Adverse selection, the more commonly accepted one, causes for a distinction between the higher risk-takers and the more risk-averse individuals because it assumes that higher risk-taking is accompanied with more insurance purchases in order to offset the higher risk. In contrast to the adverse selection model, that strictly uses homogenous risk preferences combined with constant absolute risk aversion within individuals, more recent literature assumes that people’s risk preferences are subject to variability in contexts as well as experiences. Heterogeneous risk preferences give way to the possibility of advantageous selection or also called ‘propitious selection’, which has opposite market effects compared to the adverse selection. Previous studies have tried to capture the selection bias in several insurance markets by looking for the existence of a basic coverage-risk correlation. The present study doesn’t merely focus on the basic coverage-risk correlation rather investigates the interplay between monetary risk-taking and the corresponding personal belief for the necessity of insurance. By excluding moral hazard, underwriting or other variables that influence either insurance purchase or risk-taking after selection, this study presents a clean effect of individual and relative risk perception together with the insurance demand. In an incentivized choice experiment among 42 students at the UVA, this study finds a significant positive relationship between purchasing insurance and risk-averse behavior. This positive relationship was found due to differences in de mean-averages among the insured versus the non-insured participants.

Table of Content

I. Introduction...Pg. 4 II. Related Literature & Theoretical Framework...Pg. 5 a. The Insurance Market...Pg. 6 b. Adverse Selection & Propitious Selection...Pg. 8 c. Risk Preferences...Pg. 13 III. The Experimental design...Pg. 16 IV. Predictions of the Experiment...Pg. 20 V. Empirical Analysis & Results...Pg. 22 VI. Results & Discussion...Pg. 29 VII. Limitations & Future Research...Pg. 30 VIII. Concluding Remarks...Pg. 31 IX. References...Pg. 33 X. Appendix...Pg. 36

I.

Introduction

The possibility of insurance is a highly valued service that provides a well needed sense of security within a society. The interesting game between society and insurance companies is a bit paradoxal. On the one hand society cannot be equally pleasant without the availability of insurance and everybody acknowledges this fact. On the other hand every individual, when aware and willing, can create extra personal gains from the asymmetric information between themselves and the suppliers of insurance. Moral hazard is such an example of individual behavior that is beneficial for the individual but harmful for the insurance supplier and therefore also for the society as a whole. Because of this paradox, insurance policies aimed at achieving a high coverage ratio struggle to set the right prices. This study primarily focuses on the individual’s perception of self-taken risks and its translation into insurance purchase. Do people who knowingly take higher risks also demand higher amounts of insurance? Do people who behave highly risk-averse understand that the insurance policy is less rational for them?

In order to answer these questions it is important to understand the interplay between risk-taking and the demand for insurance. In the context of insurance, risk is associated with the insurance company’s liability due to the sum of the expected claims of the policyholders.

The correlation between risk and insurance demand has two theorized dynamics, adverse selection and propitious selection. Adverse selection describes a situation where an individual's demand for insurance is positively correlated with the individual's risk of loss (higher risk-takers buy more insurance), and the insurer cannot allow for this additional risk in the price of the insurance. Propitious selection describes a situation where an individual’s demand for insurance is negatively correlated with his or her expected loss due to personal heterogeneity in risk-aversity. For example, risk-avoiding behaviour can be positively correlated with the risk-free identity of insurance, which will therefore be more appreciated by low risk-takers. The two selections, which in theory can both be present within an insurance poule, have exactly opposite market implications and must therefore be further investigated in order to adjust future insurance prices and structures accordingly.

The more commonly known correlation between risk and insurance demand is called: the basic coverage risk correlation. This correlation is a handy tool when investigating insurance market stability (see next section) but doesn’t say much about the variability in risk-avoidance within the monetary risk-taking and insurance domain as well as recreational risks. A positive coverage risk correlation is usually associated with adverse selection but is in fact a bigger picture. The risk coverage correlation describes the total sums of the insured population versus that of the not-insured population whereas both selection biases purely describe the interplay between risk preferences in general and the risk-avoidance that comes with insurance selection.

In this thesis I will address the following research question:

Is the choice for insurance driven by adverse selection or propitious selection?

Previously done empirical research is not united in their findings concerning the direction of the risk-coverage correlation. The main focus of previous studies has been the correlation between total insurance claims and individuals in the population that buy insurance. This correlation between insurance claims and insurance purchases is not entirely driven by the two selection biases, propitious- and adverse selection, rather a combination of variables like personal risk assessment, moral hazard and transforming private information into valuable information. This study will investigate the dynamics of insurance selection by conducting a risky choice experiment which, unlike previously done research, excludes factors that can effect the selection or the expected claim other than individual risk perception. This exclusion gives a clean effect of the variable risk-taking / risk-avoidance on insurance coverage demand.

The paper will start with a clean and simplified description of the insurance market and the co-existing models for adverse- and propitious selection in section II.a and II.b respectively. The paper continues by explaining and discussing different measurements of risk in section II.c. In section III, the study presents the experimental design, followed by the results of the experiment in section IV. These results will be discussed in section V along with its implications and limitations in section VI. Finally; the study reports its conclusions in section VII.

II. Theoretical Framework & Related Literature a. The Insurance Market

The insurance market can be viewed from different perspectives. An insurance company must remain liable for future claims and individuals all make separate choices whether or not to insure themselves against privately known risks. Some insurance markets have distinctive risk classes while others charge the same price for everyone. For simplicity this study will focus on the situation wherein one price is offered to a total population with individuals that carry different expected claims.

The insurance market can be illustrated graphically with insurance price on the vertical axis and amount of individuals that are insured on the horizontal axis. The demand for insurance is like any normal product decreasing when the price increases, everyone wants more for less. Also, insurance companies normally feel the moral duty or are restricted to insure the biggest part and preferably the entire population against future losses. The most desired insurance quantity in this simplified model is therefore the maximum quantity, Qdesired = Qmax. A graphical description of this simplistic insurance market is given below.

Graphical illustration: Insurance market in textbook scenario

Co-existing with the desire to insure everybody, the insurance price must remain above the average claim of the insured, ACinsured curve, in order to keep the total insurance payouts below the combined insurance income. Also desired is the efficient state in which the insurance price equals the marginal claim of the next individual who opts into the poule, this is point E in the graph. Both desired states Qmax and

Qeff on the graph are out of reach under the assumptions of adverse selection. The

exclusion of these states under adverse selection assumptions is explained in section II.b.

The variable that determines if an insurance company is able to insure the total population is the marginal cost function, MC curve. The curvature of the marginal cost function determines if a population will be efficiently allocated or if the equilibrium insurance quantity will be below the desired states. A decreasing marginal cost function, like the one illustrated above, means that the next individual that chooses for insurance will have a lower expected payout than the infra-marginal buyers (the ones that already bought insurance). This means that the most risky persons will be the most willing to buy insurance at a relatively high price. This implies that the average cost of the insured will be above the MC curve for all insurance quantity distributions. On the other hand, if the marginal cost curve is increasing within the population, the least risky individuals are willing to buy insurance most, and then the average insurance payout will be below the marginal cost for all insurance quantities. Does the insured population have a higher expected average payout than the not-insured population? If this is the case then the ACinsured curve intersects with the demand function before the MC curve does which means an equilibrium price, Peqm, which is higher than the efficiency price, Peff. The efficiency loss described here only happens when the basic coverage-risk correlation is positive.

How a positive basic coverage-risk correlation, a decreasing MC curve, can cause for increasing insurance prices that slowly pushes out the least risky individuals within a population is best illustrated through the dynamics of smoking status and life insurance. It is generally assumed that individuals who do not smoke live longer on average, while individuals who do smoke, on average, die younger. If the life insurance suppliers do not change their prices according to smoking status, life

insurance is, on average, a better buy for smokers than for non-smokers. So smokers would in a rational case be more likely to buy insurance, or buy larger amounts, than non-smokers, thereby raising the average mortality of the combined policyholder group above that of the general population. Now the insurer must raise the price for insurance and as a consequence non-smokers will be even less likely to buy insurance than before. If the population consists of various risk types (smoking more or less), the increase in insurance price may lead the lowest remaining risk types within the insurance poule to cancel or not renew their insurance. This promotes a further increase in price, and again the lowest remaining risks stop their insurance, leading to a further price increase, and so on. Eventually the so called "adverse selection death spiral" might, in theory, lead to the collapse of the insurance market.

Creating a balanced allocation of risk types within an insurance poule has great importance for the insurance company as for the society as a whole. If adverse selection causes for increasing insurance prices it is important to know if there are other underlying variables that interact with the more general basic-coverage risk correlation. In reality we do not see complete under-insurance, ever-increasing insurance prices or suppliers of insurance that go easily bankrupt.

II.b. Adverse Selection & Propitious Selection

Adverse Selection: The term “adverse selection” finds its roots within the context of insurance and the insurance market is used as its main explanatory playground. In the early 70’s and 60’s economists like Arrow (1963), Akerlof (1970), Pauly (1974), Rothschild and Stiglitz (1976) started theorizing about the concept of adverse selection and concluded that it must be active within the insurance market. The general correlation that is associated with adverse selection is the positive risk-coverage correlation in which risk is measured in higher expected insurance payouts due to a larger number of expected claims, a higher expected payout in the event of a claim, or both. The foundation of this correlation is due to an information gap between the policyholder and the insurer that can be used beneficially by the policyholder and can be devastating for the insurer when done by many.

Graphical illustration: Insurance market with Adverse Selection

Source: Selection in Insurance Markets: Theory and Empirics in Pictures, Einav & Finkelstein, 2011 If you drop the assumption of equal pricing, the dynamic of self-selection could, if significantly active, be the solution to identifying different risk types within a population. By offering a menu of contracts Rothschild and Stiglitz theorized that individuals would self-select themselves in their appropriate risk class because humans are strictly rational agents with homogeneous risk preferences. Professor J. Weibull1 cited the following while he was presenting the Nobel Prize to Joseph Stiglitz “a prime example can be found in insurance, where companies usually offer alternative contracts, where higher deductibles may be traded off against lower premiums. In this way, their clients are, by their own choice of contract, effectively divided into distinct risk classes”. Offering different contracts might be effective depending on the basic assumptions of how humans evaluate their own risk. This study primarily focuses on this personal evaluation thereby giving more insights in the effectiveness of the approach Stiglitz and Rothschild proposed in 1976.

                                                                                                                1

Professor Jörgen W. Weibull gave the speech during the 2001 Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel at the Stockholm Concert Hall. A reference to the full text of the

In an important paper ‘Testing for adverse selection in insurance markets’, Alma Cohen and Pieter Siegelman try not to prove either the existence or the absence of the risk-coverage correlation rather they show that it varies across insurance markets and even within the same market. “Adverse selection exists in an insurance market when buyers of insurance have information about their risk that the insurers who underwrite their policies lack and use this information in making their insurance purchases. The policyholder may be better informed about either the probability of a loss, the distribution of the size of the loss in the event that a loss occurs, or both” (A. Cohen & P. Siegelman, 2010). The authors use findings from independently conducted research in automobile insurance, life insurance, long-term care, crop insurance and health insurance markets. The main goal of the studies is identifying the existence of adverse selection. When combining the different findings their conclusion is ambiguous to say the least. Concluding their findings the authors argued for more explanatory additives surrounding the insurance selection problem, there is not one good answer rather several dynamics that interline differently in every market.

In their paper they present four main reasons for adverse-selection to be unidentified: (1) the inability to make the private risk information either available or valuable, (2) good underwriting by the insurer, (3) moral hazard and (4) propitious selection.

Underwriting is a successful method insurance companies use in order to classify the riskiness of insurance purchasers. Underwriting is a very specific question procedure that translates given answers into several risk classes that carry different insurance packages. Underwriting can control for some of the adverse selection but it is safe to say that there are more dynamics contributing to the current stability of insurance companies in general. How people evaluate their own risk when choosing for or against insurance is priority, especially compared to other individuals in the same market. This study primarily focuses on the interplay between risk-taking behaviour (before choosing insurance) and the insurance option while excluding disturbing variables. By doing so it’s possible to test the selection bias solely. The selection bias is two-sided, having propitious selection on the other side.

Propitious Selection: The first person to theorize about another side of the selection bias was David Hemenway. Hemenway presented in 1990 the concept of propitious selection, in his same named paper ‘Propitious Selection’, as a possible counter bias for unfavourable selection as he called it. Propitious selection uses the idea that high-risk individuals might be less risk-averse and people, who don’t like risk, do like insurance even when they don’t take a relative high risk.

The model of adverse selection, used by classical economists like Stiglitz and Rothschild, makes the simplifying and theoretically attractive assumption that all individuals have the same risk preferences and do only vary in their privately known expected claims. As a result, the willingness to pay for insurance is an increasing function of the expected costs. In practice, naturally, individuals may differ not only in their expected cost but also in their risk preferences. The concept of propitious selection compares people with different levels of avoidance or also called risk-aversion. This positive correlation between risk-aversion and the safety option ‘insurance’ together with the negative relation between risk-seeking behavior and the safety identity of insurance can cause for opposite equilibrium results compared to adverse selection. Previously done empirical work has documented substantial heterogeneity in risk preferences within different insurance markets2. In textbook insurance market, as described earlier, heterogeneity in risk preferences could cause for an increasing marginal cost curve that will generate a more efficient insurance allocation, see the graph on the next page.

Consider for example heterogeneity in risk-aversion, in addition to the original heterogeneity in expected cost. Keeping all else equal, the demand for insurance is increasing in aversion and in expected future claims. If heterogeneity in risk-aversion is insignificant, or if those individuals who are high-risk takers are also more risk-averse, the main insights that are being used in textbook analysis remain the same. But if high-risk individuals are less averse and the heterogeneity in risk-aversion is significantly large, propitious selection may emerge creating an upward sloping MC curve with more efficient allocations.

2  _{For  example,  automobile insurance (Cohen and Einav, 2007), reverse mortgages (Davidoff and} Welke, 2007), health insurance (Fang, Keane, and Silverman, 2008) and long-term care insurance (Finkelstein and McGarry, 2006)  

Graphical illustration: Insurance market with Propitious Selection

Source: Selection in Insurance Markets: Theory and Empirics in Pictures, Einav & Finkelstein, 2011 The model of propitious selection as proposed by Hemenway contains six general assumptions3: (1) insurance purchase is voluntary; (2) risks are heterogeneous; (3) heterogeneous risks are lumped together and charged the same price; (4) individuals can take actions that knowingly raise or lower their own risks; (5) potential insurance buyers have different tastes for risk; (6) individuals are (somewhat) consistent in their taste for risk across physical and financial dimensions.

Because in the case of propitious selection, the individuals who are willing to pay the most for insurance are those who are the most risk-averse and also these individuals are associated with the lowest rather than the highest expected cost. It is natural to think that in many situations individuals who value insurance (safety) more may also take action to lower their expected costs: drive more carefully, invest in preventive health care, have an extended hard drive and have a fire alarm installed. DeMeza and Webb (2001) used the same idea to rationalize prevention acts combined with insurance. They show that cautious people put more effort into preventing accidents and are more likely to buy insurance. Most risk-seeking motorists - teen-agers,                                                                                                                

3  _{Interesting to mention is that Hemenway doesn’t reference Stiglitz and Rothschild anywhere.In his} model for both propitious selection and adverse selection he argues for equal pricing. This was exactly the solution Stiglitz and Rothschild presented in their paper in which buyers would self-select

intoxicated drivers, those who follow other cars too closely and who ignore red lights – are among the least likely to buckle up (Baker, O’Neil, and Karpf, 1984).

II.c. Risk preferences

How people perceive personal risk has been a major question in previous economic literature. Homogeneous risk preferences imply that the same individual regardless of previous results or other factors evaluates every risky choice similarly. When overall risk-aversion is assumed, homogeneous risk preferences cause for completely concave utility function. In order for propitious selection to emerge, heterogeneity within risk preferences must be present. The correlation between not liking losses and therefore liking insurance is an example of possible heterogeneity in risk-aversion that could in theory, when significant, lead for propitious selection to undo the risk-coverage correlation.

Expected utility theory is the classical model that analyzes decision-making under uncertainty. This normative and descriptive theory explains that decision makers are rational agents, if they have clearly specified preferences and act as utility maximizers according to an objective function (Friedman and Savage, 1948). The predominant view is that people, on average, are risk-averse. This implies that decision makers are said to be risk-averse only if they prefer sure outcomes to lotteries, when actually the expected value of the lottery is equal to or larger than that of the sure outcome (Pratt, 1962).

If an individual has a concave utility function he or she exhibits homogenous risk preferences. Therefore, an average individual will behave consistently risk-averse regardless of his or her actual utility level or lifetime consumption. Even though, constant absolute risk aversion (CARA) is widely used in economic models, the underlying assumption for this model does not always seem plausible when we observe variability in the risk preferences of decision makers. In fact, individual risk preferences are not always stable when we investigate risk-taking across contexts and scenarios. Also, people’s risk preferences are domain specific, depending on the measure of risk and the context in which risk is being evaluated. Assuming that a decision maker is consistently risk-averse might not be a plausible prediction. The

observed variability in decisions during real-life examples and laboratory experiments require several understandings into how individuals perceive and act on risky choices. The problem of insurance selection is part of this understanding.

Constant relative risk aversion (CRRA) could give a better interpretation of the utility function across different scenarios. This measurement of risk-aversion allows for strengths of preferences amongst alternatives. For example an individual may be more inclined to take on bets for small stakes, due to the outcome of this bet would not dramatically impact his or her utility. In contrast, the same individual might not want to gamble when the stakes are high, since this could significantly change his or her utility. As a result, we can observe utility functions for decision makers who appear to be risk-taking or convex for small bets, but are risk-averse or concave for large bets.

The authors of prospect theory, Tversky and Kahneman (1992), place additional assumptions on subject’s utility functions. Most importantly, it assumes that decision makers are not primarily concerned with final states of utility rather their risk preferences are sensitive to relative changes in utility compared to the status quo or reference point. Prospect theory predicts that decision-makers act differently when confronted with possible gains and losses, because they have asymmetric weighting functions in the loss and gain domains. One the one hand, a decision maker is relatively risk-averse and prefers certainty in the gains domain. On the other hand, a decision maker is keener on taking risk in the loss domain, where apparently decision-makers favor risk-taking in the anticipation to avoid losses over incorporating a sure loss (Tversky and Kahneman, 1992).

In line with prospect theory, March (1988) argues that differences in risk preferences are not only being determined by personality traits, but they are also context dependent. The author suggests that prior histories of greater wealth or performance produce higher aspirations for success and therefore a greater preference for risk if a decision maker perceives that he or she is not doing that well. Cohn et all (2012) find that financial experts who have been primed with financial bursts makes them significantly more risk-averse. Das and Teng (2001) acknowledge that both situational as dispositional factors are important in explaining risky behavior. In their study they present a model where risk-taking depends not only on personality traits and the context in which decision makers face risk, but is also influenced by a specific

time element. Risk-taking differs as it relates to immediate results and postponed results. According to the discounted utility model, the more distant gains and losses will have a lesser significance on a person’s present behavior. The authors argue that situational factors have a greater influence in short-term decision-making, whereas in long term planning horizons dispositional differences can play a more important role, which could explain observed variability in risk preferences over time.

Risk-aversion causes for individuals to demand a risk premium in order to be compensated for the exposure to risk. Loss-aversion could give an explanation why investors typically demand high-risk premiums when investing in risky securities, this is called the equity premium puzzle. In short, historical returns on risky securities exceed returns on relatively risk free investments such as government bonds by far, still people need excessive risk premiums in order to be compensated for being exposed to a higher degree of volatility which could not only be explained by risk aversion (Thaler and Bernartzi, 1995). Loss-aversion refers to people’s tendency to strongly prefer avoiding losses to acquiring gains. Most studies suggest that losses are twice as powerful, psychologically, as gains. Amos Tversky and Daniel Kahneman were the first to introduce the concept of loss-aversion in 1979.

Previously done research concerning risk perception reports that individuals, on average, act consistently risk-averse. In particular, the restrictions that these models place on a person’s objectives and utility function have produced a vast literature on how individual preferences change and differ across contexts, personal characteristics, past experience and temporalities. If this variability in risk preferences will open the door for propitious selection is still unsure but it allows for the possibility. In the next section I will describe the experimental design used for this study that will enable the researcher to analyze the individual and collective risk-taking behavior more easily and gives a clean correlation between this risk and the co-existing insurance coverage demand.

III. Experimental Design

In order to estimate the effects of risk-taking behavior on insurance selection, an observational choice experiment was conducted with 42 participants recruited from around my personal social environment. The variable of interest is whether the participant did or did not choose for the insurance option. The participants could choose between three insurance options, they could insure their entire potential loss/risk, half their potential loss/risk or nothing at all. The second option was presented in order to capture unsure behavior that might affect the results. Only two participants opted for the semi-insurance option showing a significant behavioral desire to either insure everything or nothing. The difference in risk-taking behavior between the two groups, ‘Insured’ versus ‘not Insured’, is the main focus off this study.

All participants were presented with the exact same choice structure and money values. In order to control for the effect starting capital might have on risk-taking, two different endowments4 were handed-out, either 50 € (base-group) or 70 € (shock-group). Each subject participated only once in one of the two treatments. The initial endowments were handed-out in tokens. The use of tokens instead of euros was preferred, since it is argued that with tokens participant’s risk preferences are better elicited for risky choices involving large values compared to small values5. The participants were informed before the start that their initial endowment would suffice for any desired combination of answers. They could only loose their payments. The participants were not told their choice outcome in between their answers, only after all experiments took place the participants were notified their final payout by email6_. The portfolio of answers together with the participant’s initial endowment will determine the final payout, which is simulated by a computer.

Nevertheless, by excluding choice feedback information, the participants make the insurance choice based on their personal risk perception and without factual outcomes. Also because calculating the net expected utility during the experiment is                                                                                                                

4  _{Participants were not randomly selected into the two different starting capital treatments}

rather got divided depending on the grade they received for their selected test. Each

participant could choose between either a Dutch language test or a mathematical calculus test.   5  _{Guiso and Paiella, 2008}  

6  _{According to Das and Teng (2001) postponed information regarding your choices can}

quite hard therefore assessing relative success or success in general is difficult. Without this information participants must decide whether or not to purchase insurance solely by their personal evaluation of their answers and cannot influence the losses/risk afterwards.

The experiment is finalized with five questions derived from the Adventure Quotient test. These answers will be used to test the correlation between monetary risk-aversion (insurance purchase) and non-monetary precautionary behavior in real-life practices. Section I In the appendix provides the instructions for the experiment. All subjects were given an example question with explaining remarks making sure they completely understood the instructions.

In summary, the experiment has 4 parts: part one is the endowment distribution test, part two consists of 4 risky money choices, part three is the insurance option and part four is the questionnaire part.

Table 1: Variables and their Definition.

Variable Definition

Choice Ranges from I to IV, referring to the choices presented in section II of the experiment.

Option Ranges from A to D, referring to the possible answers that can be given in section II and III of the experiment.

Total Payment Ranges from 20 to 40 euro, referring to the possible payment

combination in section II, All four choices require a payment of either 5 or 10 euros.

The amount of money a specific participant starts the game with. Half the participants began the game with 40 € (Base treatment) and the other half with 60 € (Shock Treatment).

Initial Capital

Expected Net Payout The variable measures the expected final payout by subtracting the total payments from the total expected outcome.

Possible Loss The variable measures the losing possibility for the given answers by possible loss times the probability of them occurring.

Answer variance Variable gives the standard deviation of the outcome distribution for a specific answer for example; answer A at choice I (C1.A). The variable ranges from 0,59 to 7,07 in C1.A and C2.D respectively. Portfolio variance Variable gives the average standard deviation for a specific participant

given his portfolio of answers. Ranging from 1,77 to 4,85. Variable takes on the terms Insured, semi-Insured or not-Insured. Meaning that the participant is 100% insured, 50% insured or 0% insured respectively. In this study there were 20 fully insured

individuals, 2 semi-insured individuals and 20 not-insured individuals. Insurance coverage

A short description of the game used in the experiment:

Each participant is asked to answer 4 choices; each choice presents 4 possible options that differ in payment amount, outcome distribution and monetary outcome possibilities. The choices and possible outcomes are denoted as I, II, III and IV, the options are denoted as A, B, C and D. All participants were presented with the same order of choices. As an illustration, choice I as presented to the participants is shown below.

Choice I

Given the probability distribution and outcomes described in the table below, which option do you choose?

Choice I Outcome I II III IV Option Payment Distribution (%) 2% 28% 35% 35% A 1 blue token € 50 € 5 € 2,50 € 0 B 2 blue _token € 120 € 10 € 5,00 € 0 Distribution (%) 2% 28% 70% C 1 blue _token € 80 € 5 € 0 D 2 blue token € 170 € 10 € 0

So, if a participant would choose option C for example he or she can win 80 € with 2%, 5 € with 28% and nothing with 70%. Option C requires a payment of 5 € (1 blue token), the outcome – the payment = net utility.

Each choice has the same structure. The answers within each choice differ in three aspects: (1) answers A and C always require a payment of 5 € (one blue token) and answers B and D always require a 10 € payment (two blue tokens); (2) answers A and B always have an extra outcome possibility that changes the outcome distribution in such a way that it lowers the expected loss compared to answers C and D respectively

and (3) the monetary outcome values differ for all choices therewith creating different decision-making environments in each choice. Choice I has an overall negative expected net outcome (losing domain), choice II has an expected net outcome of zero (indifferent domain) for all answers and choices III and IV both have positive expected net outcomes (gain domain). In other words, answers A & C are always cheaper than options B & D and answers A & B are always safer than C & D respectively. Choice 1 is the least secure environment and choices 3 and 4 are the

most secure environments.

Table 2: Risk Category per Answer

Choice 1 Choice 2 Choice 3 Choice 4

Very Risky D D Risky B C D Rational C A & B D B Safe A C C Very Safe A A Irrational B

Table 2 shows an overview of all the possible answers and their relative riskiness compared to one another.

After answering all four choices the participant must have a certain feeling of security considering his or her answers. The foundation of this security is tested with an insurance option. The same insurance prices are offered to all participants, which is mandatory in both the adverse and the propitious selection model as proposed by D. Hemenway. Semi-insurance carries a payment of 4 € (4 black tokens) and full-insurance costs 7 € (1 blue token and 2 black tokens).

Risk and net utility is not perfectly positively correlated in the game. Choosing option D in every choice does not give the highest net utility, the highest net utility answer distribution for the game is (A (B) D (B)). The required total payment for this allocation is 35 € and the net expected utility is 3,40 €. The combination of answers with the lowest expected net utility is (D (D) A A), this combination has an expected net utility of -1,80 € making the insurance option an overall irrational proposal.

IV. Predictions of the Experiment

From the experiment it is possible to investigate several measurements of risk. For the purpose of this study the main focus will be identifying risk-averse behavior and measuring its correlation with insurance purchase. Besides the expected claim difference between the insured and the not insured there are more revealing variables that can show either risk-taking and/or risk-averse behavior. For example, spending more money is very heuristically correlated with higher risk-taking and therefore a good indicator of relative risk perceptions. The obvious risk-taking associated with spending more money (sum of payments) must, if something, be positively correlated to insurance purchase. Also, choice I represents an environment that is very similar to a lottery with very low chances of winning a large amount, making it a very obvious risk.

Hypothesis (1) : Subjects with a more expensive investment-portfolio will tend to choose the insurance policy more than subjects with a less expensive investment-portfolio. (Adverse-selection)

Hypothesis (2) : Subjects who opted for answer D at choice I will, on average, choose the insurance policy more often than the other subjects. (Self-selection)

On the side of risk-averse behavior the experiment gives several interesting variables. For example in choice II the participant can choose either a fifty/fifty percent chance of doubling/losing his payment or a forty/forty percent chance of doubling/losing his payment and a twenty percent chance of getting the payment back making it an obvious safer choice. It is widely assumed that more volatility, a larger standard deviation of the net outcomes, is accompanied with a higher risk premium (Pratt, 1962). At choice II no extra risk premium is presented for the extra risk presented in options C & D making them unlikely answers by the dynamics of risk-aversion. At choices III & IV higher payments are in fact rational decisions therefore avoiding these opportunities makes the individual even more risk-averse.

Hypotheses (3) : Subjects who choose, on average, for options with smaller variance will tend to select for the insurance option more than the subjects who choose for options with higher variance. (Propitious-selection)

Hypothesis (4) : Subjects who opted for A at choices III & IV will, on average, choose the insurance policy more often than the other subjects. (Propitious-selection)

Hypotheses (5) : Subjects will, on average, prefer to select for option A & B at choice I due to the absence of a risk-premium. (Theory of risk-aversion)

Participants were unaware of their test scores and were not told about the different treatment groups. Also, answering all four choices is mandatory and no feeling of loss is induced during the game, therefore the endowed starting capital shouldn’t have much influence on the answers. But because a significant difference in payments between the treatments can imply that starting capital is actually interfering with the game it is important to control for this variable.

Hypotheses (6) : Subjects in the base group do not have different average payments compared to subjects in the shock group

In line with DeMeza and Webb (2001) I think this study will show a positive correlation between risk-avoiding behaviors across several domains.

Hypotheses (7) : Subjects who do choose for the insurance policy take more precautionary matters in order to prevent undesirable outcomes in real life when looking at non-monetary risk taking behavior. (Propitious-selection)

V. Empirical Analysis & Results

This study focuses on the correlation between risk behavior and the personal believe in the necessity of insurance. Adverse selection prescribes that individuals who knowingly take more risk will select a higher coverage when choosing an insurance policy than the more risk-averse individuals. Opposite to this assumption, propitious selection hypothesizes that risk-averse individuals will be so more frequently and in different domains, in this case the participant’s dislike for risk is also correlated with the liking of insurance.

In total, 42 participants took part in the experiment. The majority of the participants were Dutch and they all had previous experience with buying insurance. In addition, the sample consisted out of 17 female participants and 25 males who were allocated into two different treatment groups after grading their test. The experiment took place during four sessions, counting ten participants on average, which lasted each for about 30 minutes. The two participants, who opted for the semi-coverage option, were omitted from the insurance analyses because the focus of this study lies in the difference between the insured and the not-insured group.

Before analyzing the differences between the insured and the not-insured groups it is important to control for portfolio differences between the two treatments. Even though the participants are told that their starting capital will suffice for every possible combination of answers it is important to check if the starting capital influenced their respective choices. Participants in the base and shock treatments were equally divided, counting 21 participants each. In order to test for mean differences between the two unrelated groups an independent sample t-test is used. The results are shown below.

Table 3, Mean group differences in payments and possible loss between the shock and base treatments

IV

treatment

N Mean Std. Deviation Std. Error Mean

DV Payments 0 21 30,95 7,003 1,528

1 21 30,71 6,381 1,392

DV Possible Loss 0 21 -13,0319 4,31434 ,941

1 21 -13,2333 3,20491 ,699

The dependent variables payments and possible loss are measured separately in each independent treatment (0=base & 1=shock) having on first sight very similar outcomes.

Note here that the average amount of payments in the base and shock treatment is 30,95 € and 30,71 € respectively. Also the average possible loss within the shock treatment is not much different than the average for the base treatment, respectively -13,23 € and -13,03 €.

Table 4, Independent Samples Test: Payments and Possible Loss in the base and shock treatment

Levene's Test for Equality of

Variances

t-test for Equality of Means

F Sig. t df Sig. (2-tailed) Mean Differen ce Std. Error Differen ce 95% Confidence Interval of the Difference Lower Upper DV payments Equal variances assumed ,681 ,414 ,115 40 ,909 ,238 2,067 -3,940 4,417 Equal variances not assumed ,115 39,65 ,909 ,238 2,067 -3,942 4,418

DV Expected Possible Loss

Equal variances assumed 4,586 ,038 ,172 40 ,865 ,20143 1,17281 -2,16890 2,57176 Equal variances not assumed ,172 36,92 ,865 ,20143 1,17281 -2,17508 2,57793

This table shows the outcome for the Levene’s test for equality of variances and the independent t-test for equality of means between the base and shock group.

The mean differences between the base and shock treatment are not significant, see column (Sig 2-tailed), for both payments and possible loss, which is in line with the sixth hypotheses. So, it is safe to assume that the allocation of starting capital will therefore not interfere with the participant’s insurance coverage demand. Given that a higher initial endowment will not result in higher payments or higher possible losses it is possible to compare the means of the insured versus the not-insured without controlling for heterogeneity within the treatment groups.

So how did the insured population behave compared to the not insured population? The variables of risk used for analyses are: payments, net utility, average choice variance and possible loss. In order to investigate mean and variance differences within each variable independently, again an independent sample test is used. As shown on the next page, the variables payments and average choice variance have significant differences in means. The insured population had a total individual payment that, on average, was 6 € lower than the participants who did not choose for the insurance option, this is not in line with the first

hypotheses. Payments as well as possible losses and average choice variance are all significantly different between the insured and the not insured groups. The results show differences, favoring the dynamics of propitious selection because lower risk-takers opted for insurance more often than the high risk-takers. In line with the fact that calculating net utility is difficult and not perfectly correlated with extra risk, no significant mean difference is found here. The participants do not use the variable net utility as a measurement in order to change their risk-perception.

Table 5, Group Statistics: Insured versus not Insured group

Insurance N Mean Std. Deviation Std. Error Mean

Payments 1 20 28,00 5,477 1,225 0 20 34,00 6,609 1,478 Net Payout 1 20 ,8440 1,00149 ,22394 0 20 ,7155 1,06010 ,23705 Possible Loss 1 20 -11,0965 2,59807 ,58095 0 20 -15,1070 3,84046 ,85875 Av. variance 1 20 2,7740 ,61409 ,13732 0 20 3,7570 ,90776 ,20298

The dependent variables payments, net utility, average choice variance and possible loss are measured separately in each group (0=not insured & 1=insured).

Table 6, Independent Samples Test: Payments, Net Utility, Average variance and Possible Loss.

Levene's Test for Equality of

Variances

t-test for Equality of Means

F Sig. t df Sig. (2-tailed) Mean Difference Std. Error Difference 95% Confidence Interval of the Difference Lower Upper Payments Equal variances assumed 2,191 ,147 -3,126 38 ,003 -6,000 1,919 -9,886 -2,114 Equal variances not assumed -3,126 36,73 ,003 -6,000 1,919 -9,890 -2,110 Net Payout Equal variances assumed ,000 ,989 ,394 38 ,696 ,12850 ,32610 -,53165 ,78865 Equal variances not assumed ,394 37,87 ,696 ,12850 ,32610 -,53172 ,78872 Possible Loss Equal variances assumed 10,113 ,003 3,868 38 ,000 4,01050 1,03680 1,91160 6,10940 Equal variances not assumed 3,868 33,37 ,000 4,01050 1,03680 1,90202 6,11898 Av. variance Equal variances assumed 7,948 ,008 -4,011 38 ,000 -,98300 ,24506 -1,47911 -,48689 Equal variances not assumed -4,011 33,37 ,000 -,98300 ,24506 -1,48137 -,48463

This table gives the outcome for the Levene’s test for equality of variances and the independent t-test for equality of means between the insured and the not insured group. The mean differences for Payments, Possible Loss and Av. Variance are all significantly different on a 0.001 percent scale.

The variable possible loss uses the chosen payment amounts together with their probability of losing, therefore the average portfolio variance and payments are somehow incorporated in this variable. In the table below, the correlations between all variables are presented. Average variance and possible loss as well as payments and possible loss are both significantly correlated at a 0.01 percent level. Together with the fact that all three variables are extremely negatively correlated with the insurance option, this experiment shows strong significant dynamics away from the adverse selection predictions. Whether propitious selection is active must be further tested.

Table 7, Correlations for all variables

Insurance Payments Net Payout Poss. Loss Av. variance

Insurance Pearson Correlation 1 -,452** _{,064 ,532}** _-,545** Sig. (2-tailed) ,003 ,696 ,000 ,000 N 40 40 40 40 40 Payments Pearson Correlation -,452** _{1 -,164 -,860}** _,847** Sig. (2-tailed) ,003 ,312 ,000 ,000 N 40 40 40 40 40 Net Payout Pearson Correlation ,064 -,164 1 ,221 -,147 Sig. (2-tailed) ,696 ,312 ,171 ,365 N 40 40 40 40 40 Possible Loss Pearson Correlation ,532** _-,860** _{,221 1 -,937}** Sig. (2-tailed) ,000 ,000 ,171 ,000 N 40 40 40 40 40 Av. variance Pearson Correlation -,545** _,847** _{-,147 -,937}** ₁ Sig. (2-tailed) ,000 ,000 ,365 ,000 N 40 40 40 40 40

**. Correlation is significant at the 0.01 level (2-tailed).

Propitious selection uses the idea of heterogeneous risk preferences, which could lead to a positive correlation between risk-aversity and insurance. In order to see choice pattern differences, especially patterns that prove high risk-aversion, between the insured and the not insured group have a look at the three tables on the next page. The first table gives the answer distribution for the population as a whole, the second gives the answer distribution for the insured population and the third gives the distribution for the not-insured population.

Table 8, Answer distribution total population

Total

Population Choice I Choice II Choice III Choice IV % total Total

Option A 13 9 5 15 26% 42

Option B 9 21 12 8 31% 50

Option C 6 3 9 12 19% 30

Option D 12 7 14 5 24% 38

Sum 40 40 40 40 100% 160

The table shows that for the population as a whole option B is chosen most and option C is chosen least. Option B at choice II is the most favored answer counting 21 times.

Table 9, Answer distribution insured population

Insured

Population Choice I Choice II Choice III Choice IV % total Total

Option A 11 7 4 11 41% 33

Option B 4 10 8 4 33% 26

Option C 3 3 4 5 19% 15

Option D 2 0 4 0 8% 6

Sum 20 20 20 20 100% 80

The table shows that the insured population opted for option A most and option D least. Option A, at choices I & IV, were most favored by the insured counting 11 times.

Table 10, Answer distribution not insured population

Not-Insured

Population Choice I Choice II Choice III Choice IV % total Total

Option A 2 2 1 4 11% 9

Option B 5 11 4 4 30% 24

Option C 3 0 5 7 19% 15

Option D 10 7 10 5 40% 32

Sum 20 20 20 20 100% 80

The table shows that the not insured population opted for option D most and options A least, exactly opposite to the insured population. Also option B, at choice II, is most favored by the not insured population counting 11 times.

In line with previous results, that favor propitious selection, it is clear from the tables that option A is consistently preferred in the insured group and option D is consistently preferred by the not insured group. To be more precise, the insured group opted for option A 33 times while the not insured group opted for A only nine times. The not insured group opted for option D 32 times while the insured group only opted for D six times.

Choosing option D at choice I is an obvious high risk that should be accompanied with higher tendencies to insure. In practice this was not the case, only two participants out of the twelve that opted for the risky option D at choice I decided to insure their portfolio. Clear from this study is that individuals who indeed become more risk-taking within the loss domain (as expected by prospect theory) are also those individuals who do not see the necessity for insurance. This is not in line with the second hypotheses.

The assumption that humans, on average, are risk-averse is visible within the second choice. In choice II there is a clear preference for the 40/40 options in both groups compared to the 50/50 options, this is in line with the fifth hypotheses. To be precise, thirty participants out of forty choose for options A or B at choice II while ten opted for either options C or D. This bias towards safety is more significant within the insured group than in the not insured group.

Choice III & IV are both in the gain domain therefore making especially option A a risk-averse possibility. In both choices the results show that the insured population was much more likely to choose for option A than the not insured population, again favoring the dynamics of propitious selection.

Also, participants who opted for option D more then three times during the game were obviously taking high relative risks. In the insured group zero participants had a choice portfolio that consisted out of three or more D answers while seven participants in the not-insured group had a portfolio with three or more D answers.

From the previous analysis it is clear that the more risk-averse individuals that took part in the experiment opted for the insurance option more. A bit similar but different; the more risk seeking individuals in the experiment opted for the no-insurance option more. Both these findings confirm the existence of propitious selection in this study. Interesting to add is that the participants did not use the payment amount as an indicator for risk, the average total payment amount in the insured group is lower than that of the not-insured group. Not a kind of rationality rather only personal emotions and risk perception were used when choosing for or against insurance coverage.

Another aspect of propitious selection is the heterogeneity in risk preferences across several domains. In order to investigate real-life risk attitudes compared to the insurance demand regarding monetary risks, this study uses four questions derived form the Adventure Quotient test. The distribution of answers is shown, separately, for both groups in table 11.

Table 11, Answers of the Questionnaire part

Insured Not-Insured Answer Question 1 A 16 10 B 4 10 Question 2 A 5 5 B 15 15 Question 3 A 10 4 B 10 16 Question 4 A 15 10 B 3 8 C 2 2 Distribution 4 × A 2 0 3 × A 7 0 2 × A 4 7

In short, seven participants opted for the safe answer A more than three times in the questionnaire while zero participants had the same answer distribution in the not-insured group. Even more so, two participants in the insured group answered all questions with the safety option A. These results show a consistent bias towards the safe options within the insured population proving strong heterogeneity in risk-aversion between monetary risk insurance and risk-avoiding behavior in non-monetary situations.

VI. Summary of the Results & Discussion

In this study, opposite to textbook theory, adverse selection is not the prevailing bias when choosing an insurance coverage rather a consistent and significant propitious selection bias is found. Note that in this study the adverse selection does not necessarily imply higher expected net utility rather a combination of higher risk measurements like payments, possible losses and average choice variance. In order for propitious selection to be active the correlation between risk-aversion and the liking of insurance must be present in the study. The difference in risk-averse behavior is further investigated by looking at the choices separately. Given the exclusion of moral hazard, underwriting, outcome feedback and difficult private information any differences between the two insurance groups must be due to the selection bias. In table 12 below again the means per variable is listed for every group separately. The mean differences between the insured and not insured groups are significantly different on 0.001 percent scale favoring the dynamics of propitious selection.

As mentioned before all insurance options were irrational choices for any given participant, for the simple fact that no answer combination had an expected net result below seven euros. Making the insurance option an even more risk-averse choice, than originally intended, might trigger only the true risk-avoiders who are also more constantly cautious in real-life situations, as presented in the results. Nevertheless, half the participants opted for the insurance option instead of a much smaller part of the participant as can be expected due to the choice context. This also shows a tendency for humans to tackle the insurance problem irrationally giving

Table 12: summary of average variables per group

Group Partici- pants Payment Net Payout Possible Loss variance Av.

(1) 100% Insured 20 € 28,00 € 0,844 € 11,09- 2,77 (2) 0% Insured 20 € 34,00 € 0,715 € 15,11- 3,75 (3) 70 Euro (Shock) 21 € 30,71 € 0,72 € 13,23- 3,33 (4) 50 Euro (Base) 21 € 30,95 € 0,52 € 13,03- 3,24

much way for emotional responses. Not numbers rather a personal evaluation of confidence emerges when the possibility of insurance is presented making rational calculations useless.

Also, the self-selection method Rothschild and Stiglitz propose which could effectively divide the individuals into their appropriate risk-class by presenting a basket of insurance options would not stand given the results of this study. Even extremely high-risk takers don’t always decide to insure their risk. When excessive risk-taking is observed like choosing option D at choices I & II, a strong preference for not insuring is usually followed.

VII. Limitations & Further Research

First it is important to state that this research does not focus on the dynamics of the insurance market as a whole rather shows how individual risk perception translates into insurance coverage. The direction of this translation will be the main driver of the marginal cost curve but other factors like underwriting and moral hazard can influence the insurance payout independent of the selection. The insurance choice is done only with the personal belief about the outcomes without a constant risk comparison measurement. It is found, that the participants use no rational measurement, of any sort, when the insurance option is presented. Therefore it is interesting to investigate further how the participants experienced the experiment. Did they think their answers were risky or that the portfolio of choices in general was risky? If you scale the personal risk perception of the game in general and the individual’s risk perception given the answers after the experiment took place it is possible to correlate this belief with the actual answers and the co-existing insurance coverage. This will give more detailed insight into how the insurance option is selected.

A point of critique could be whether participants would have reacted differently if actual losses would have been incorporated instead of a reduction of endowed earnings. Unfortunately, it’s difficult to test this alternative approach in choice experiments. To overcome this problem, typically experimental studies use hypothetical scenarios in which they induce fake feelings of loss through framing. Although, Tversky and Kahneman (1992) claim that this is a legitimate procedure for investigating behavior in choice experiments, it is debatable whether participants

behavior is consistent in these hypothetical scenarios compared to actual behavior in real-life scenarios (Laury and Holt, 2008). Especially when investigating the dynamics of insurance, incurring a real loss is highly preferable. Nevertheless, the experimental design that is used in this study can be used in order to test risk attitude within several domains while being able to strictly correlate that attitude with insurance coverage. The exclusion of exact utility and risk calculations during the experiment, moral hazard, outcome feedback, underwriting and difficult private information gives way for a simple and precise measurement of the correlation between monetary risk preferences and the overall insurance choice. Just from a behavioral point of view, are people continuously aware of their relative risk and do they see the necessity of this insurance when this risk exceeds that of the average population? The personal belief of someone’s risk perception relative to that of the population for sure depends on how that same individual evaluates his own risky outcomes, personal confidence can be a very important assessment variable. Further research investigating these answers can be very helpful when asymmetric information can cause for unfavorable selection.

The game used in this study can only highlight some environmental choices. By focusing on different environments, therewith creating different levels of rational importance concerning the insurance option it is possible to see changes in insurance demand while keeping relative choice distributions constant. In this thesis I choose to make the calculations extra difficult thereby excluding them from the decision leaving only easy variables and personal perception. It can also be interesting to see what individuals do when the calculations are easy, how do they deviate from easy rational choices?

VIII. Concluding Remarks

This study is motivated by inconclusive findings concerning the existence of adverse selection. Using the idea of constant absolute risk-aversion together with basic insurance market philosophy gives a theoretically unwanted price increase that slowly pushes out the least risky individuals within a population. This has been the main assumption in general textbook scenarios and is explained as the positive coverage-risk correlation. Hemenway was the first to mention a possible counter bias that when significantly active could erase the adverse market implications, calling it advantageous selection or ‘propitious selection’. As a consequence many further research was conducted in order to investigate the selection bias more thoroughly. A major problem when doing so is the many different interfering variables that make clean measurements of risk impossible. In this study a new model that excludes the interfering variables and only measures relative group differences and personal risk attitudes in combination with the possibility of insurance is used. The risk measurement is completely independent of informational feedback and therefore also free from a relative sense of success.

The results of this study show significant dynamics in favor of propitious selection. By closely looking at the safe option A, the study shows a consistent and often significant preference for this option in the insured group, implying that the insured group liked to minimize their losses more than the not-insured group. Also group measurements like average choice variance, payments and possible losses showed significant results implying that low risk-takers were more likely to opt for insurance than the high risk-takers.

Research concerning the interplay between risk-taking and insurance coverage is still very active but remains inconclusive. In line with Alma Cohen and Pieter Siegelman this might imply that there truly are different dynamics that interline differently in every market. Nevertheless, it is safe to assume that risk preferences are heterogeneous and that individuals are, on average, risk-averse. Concluding this study it is safe to assume that there is a positive correlation between different safety options, not only did the insured participants choose for the safety identity of A more they did also take more precautionary actions in non-monetary real-life scenarios. Also, high risk-takers do not always act on this fact when it comes to insurance making self-selection an undesired approach.