رضا افقی

“the effect of risk aversion on the demand for life insurance: the case of iranian life insurance market”

پایان نامه وزارت علوم، تحقیقات و فناوری - دانشگاه علامه طباطبایی - دانشکده اقتصاد 1389
فاطمه صغری بخشی کوهی خیلی غدیر مهدوی

abstract: about 60% of total premium of insurance industry is pertained?to life policies in the world; while the life insurance total premium in iran is less than 6% of total premium in insurance industry in 2008 (sigma, no 3/2009). among the reasons that discourage the life insurance industry is the problem of adverse selection. adverse selection theory describes a situation where the information asymmetry between policy holders and insurers leads the market to a situation that the policy holders claim losses that are higher than the average rate of loss of population used by the insurers to set their premiums (rothschild and stiglitz, 1976).we will examine the existence of adverse selection in iranian life insurance market. following the assessment of the effect of risk aversion on life insurance demand, we discuss the effect of psychological factors as well as economic factors such as the education, occupation, sex, age, income, wealth of household and other factors on life insurance demand. key words: life insurance, risk aversion, advantageous selection, and adverse selection. chapter 1 introduction to risk aversion and adverse selection 1.1. introduction since the seminal work of arrow (1963) and akerlof (1970), the problem of asymmetric information has become a major focus of modern economic research; adverse selection has played an important role in economic theory. in the insurance sector, much theoretical work has shown that the existence of information asymmetry can result in diminished market efficiency or even market failure (see, e.g., rothschild and stiglitz, 1976; wilson, 1979; and relay, 1979). however , the empirical study of asymmetric information in insurance is still rather limited , and the question of how serious this problem is in real-world markets remains unresolved , adverse selection is potentially present in many markets .in this paper we will examine the existence of adverse selection in iranian life insurance market. rothschild and stiglitz’s (1976) research on adverse selection is a seminal article for numerous studies that have augmented or tested their theoretical predictions. their model represents a competitive market for insurance, focusing on health insurance, in which there are two types of individuals: those who are at high risk of being sick and those who are at low risk, the identity of which remains unknown to insurance companies. when consumers are healthy, they pay out premiums to the insurance company and when they are sick, they receive payments from the insurance company. regardless of health status, every consumer’s optimal state of the world would be to have their expected incomes to be equal when they are healthy and when they are sick. an important form of asymmetric information between consumers and insurers is adverse selection. adverse selection occurs when there is an asymmetry of information in the insurance market. this asymmetry of information usually means that buyers have a higher knowledge of their insurance risk than insurance sellers. this difference leads the insurance company to be uncertain of the probability of occurrence of the insured event that any particular customer faces. so, the type of policy will also have significant effect on the extent of adverse selection. for example, we expect higher level of adverse selection in short-term life insurance policy than whole-life insurance. the risk aversion level of individuals has a considerable effect on their demand for life insurance. investigation on buyer’s behavior of life insurance plays a key role on the marketing and promoting the life insurance. the extent of adverse selection is also affected by age, sex, income, wealth, occupation, current health status and the size of policy applied for. it seems that the extent of adverse selection declines over time as people can better guess their health situation for the next year than for many years later. the insurance companies try to calculate the premium on the basis of the expected loss of insured, but usually the insureds have more information about their risk compared to the insurance companies. thus the insurance company cannot distinguish between the risk levels of individuals. consequently, companies offer only one type of contract to all. in this thesis, we will try to collect the data from the insureds (the individuals who bought insurance). these data will be collected through questionnaires. investigating the questionnaires filled out by about 500 insureds (the individuals who bought insurance), and analyzing their characteristics, will result in assessing the existence of adverse selection. 1.2. relevance and importance of the thesis subject: the risk aversion level of individuals has a considerable effect on their demand for life insurance. investigation on buyer’s behavior of life insurance plays a key role on the marketing and promoting the life insurance. the insurance companies try to calculate the premium on the basis of the expected loss of insured, but usually the insureds have more information about their risk compared to the insurance companies. thus the insurance company cannot distinguish between the risk levels of individuals. consequently, companies offer only one type of contract to all. so, if the customers of the insurance companies are low risk individuals ( but, with high level of risk aversion ) , obviously, lower reserves are needed to be held for compensating the losses imposed to the companies , so companies benefit from the situation and normally extra financial resources could be left for investment. as a result, determining the risk aversion level of customers and existence of adverse selection or advantageous selection in the life insurance market leads to the life insurance companies’ insightful considerations regarding their financial circumstances. shortly speaking, in this research we want to examine the effect of risk aversion on the demand for life insurance and show whether adverse selection exists in iranian life insurance market or not. 1.3. theoretical foundation(s) of the thesis: risk aversion means a willingness to pay to eliminate risk. if it is assumed that the low-risk individuals are also sufficiently risk averse, they will value insurance so highly that it will be worthwhile for them to buy it even at a price higher than their actuarial fair rates (mahdavi, 2006). we pursue two main objectives in this research: 1- determining the degree of correlation between risk aversion and the demand for life insurance. 2- examining the existence of adverse selection or advantageous selection in iranian life insurance market. by applying logistic and dummy variable regression models , we estimate the relationship between risk aversion and the parameters of the demand for life insurance . we will examine whether the independent variables of risk aversion parameters (xi) have significant effect on the dependent variable yi (the demand for life insurance). the null hypothesis of h0: ?=0 states that the risk aversion level of individuals doesn’t have significant effect on the demand for life insurance. we also will examine the existence of adverse selection or advantageous selection in iranian life insurance market. in fact, when the individuals with high level of risk aversion (in other words, low risk individuals) demand more of life insurance services than the individuals with high level of risks, the advantageous selection will occur in insurance market; reversely, when the high risk individuals demand more of life insurance services than the low risk individuals (in other words, individual with higher level of risk aversion), the adverse selection will occur in life insurance market. 1.4. main hypothesis of the thesis: 1- the demand for life insurance has a positive correlation with the level of risk aversion. 2- the iranian life insurance market faces with advantageous selection situation. 1.5. what is the risk aversion? the concept of risk aversion is one of the most important concepts in the theory of decision making under uncertainty. it seems that measuring the risk aversion level has an important role on the demand for life insurance. by simple explanation risk aversion is the inverse of risk tolerance. risk averse is defined as the behavior of a trader to stay away from risky trading practices, even if those have high chances of profits. risk averse traders prefer low risk, often low profitable, products to trade. risk aversion is seen in trading of all products including stocks, bonds, funds, options, futures and currencies. when trading, risk adverse traders often stick to government securities, index funds, low-risk currency pairs, long-term options, and stable price commodities and futures. although seems simple and less followed, risk aversion is the major factor for major market changes. following risk aversion strategy only does not produce any major profit to traders. many successful traders practice risk aversion strategy to trade in difficult market conditions, and as a portfolio diversification method. risk aversion trading strategies are also good for novice traders. in fact a risk adverse investor prefers certainty to risk, and low risk to high risk (emmett g.vaghan, 1997). 1.6. adverse selection theory in insurance market, adverse selection results from the asymmetric information between the insured and insurers. the insureds are heterogeneous with respect to their expected loss and have more information than the insurance company, which is unable to differentiate between risk types. naturally, the high- risk individual has no incentive to reveal his true risk, which is costly to observe by the insurer. adverse selection occurs when there is an asymmetry of information in the insurance market. this asymmetry of information usually means that buyers have a higher knowledge of their insurance risk than insurance sellers. this difference leads the insurance company to be uncertain of the probability of occurrence of the insured event that any particular customer faces.the conventional theory of adverse selection contains the following assumptions: (1) the difference in exposure to risk: people differ in the level of exogenously determined risk exposures. for simplicity, we consider that people are divided into two groups of risk levels, high- and low-risk groups. (2) positive correlation between self-perceived risk level and real risk level: adverse selection occurs when the individuals’ beliefs about their mortality and their true rates are positively correlated. if not, there will not be a systematic difference between policyholders’ and population’s mortality rates and hence no adverse selection occur. (3) no relationship between the level of risk aversion and riskiness: in other words, there’s no way to claim whether high-risk individuals are less risk averse than low-risk individuals and vice versa. (4) customers know more about their riskiness than the insurers and efficiently use their information against the insurers (mahdavi, 2006). 1.7. advantageous selection theory when the individuals with high level of risk aversion (in other words, low risk individuals) demand more of life insurance services than the individuals with high level of risks, the advantageous selection will occur in insurance market. the theory of advantageous selection contains the following assumptions: 1) the difference in exposure to risk. 2) negative correlation between the level of risk aversion and riskiness. 3) effectiveness of precautionary efforts. the remainder of this thesis is organized as follows. chapter 2 delivers the empirical literature. chapter 3 describes the data and variables and logistic model. in chapter 4 we perform the empirical analysis and explain the test in detail. chapter 5 concludes. the definition of the variables, descriptive statistics and tables with estimation coefficients appear in appendix. chapter 2 literature review 2. literature review the concept of risk aversion is one of the most important concepts in the theory of decision making under uncertainty. it seems that measuring the risk aversion level has an important role on the demand for life insurance. an important consequence of asymmetric information between consumers and insurers is adverse selection .there is substantial empirical literature examining adverse selection in insurance markets. however, there is conflicting evidence on the presence of adverse selection; despite this straightforward understanding from the conventional theory of insurance demand under asymmetric information, this theory is not supported by most of the empirical works. there are many empirical evidences that appear to conflict with the standard theory of adverse selection in insurance market. the literature on topic can be categorized as following: 2.1. the literature on the problem of asymmetric information: one prominent source of information asymmetry in an insurance market is weak or nonexistent underwriting, which can lead to severe problems of adverse selection (high vs. low) when there is asymmetric information regarding risk types. also it can arise if information asymmetry leads to problems of moral hazard (arnott and stiglitz, 1988). a positive correlation also can arise if information asymmetry leads to problems of moral hazard (arnott and stiglitz, 1988). these observations motivate the standard “positive-correlation” test for the existence of information asymmetry; that is, to look for positive correlation between the buyer’s levels of risk the amount of insurance purchased (chiappori and salanié, 2000). chiappori and salanié provide a survey of existing empirical studies that have implemented this test for asymmetric information. they show that when observationally identical individuals are offered a choice from the same menu of insurance contracts, higher risk individuals will buy more insurance. the intuition is straightforward. since, at a given price, the marginal utility of insurance is increasing in risk type, higher risk individuals will choose to purchase more insurance than lower risk individuals who face the same set of options. of course, this prediction, and any empirical test based on it, applies conditional on the characteristics of the individual observed by the insurance company and used in setting insurance prices. they define here their notation. let i = 1, . . . , n denote individuals. the term xi is the set of exogenous variables for individual i (these variables will be constants and dummy variables in their application). also, let wi denote the number of days of 1989 in which individual i was insured. they now define two 0 and 1 endogenous variables: yi =1 if i bought (any form of) comprehensive coverage (a tr contract) ; yi =0 if i bought only the minimum legal coverage (an rc contract); zi =1 if i had at least one accident in which he was judged to be at fault; otherwise (no accident or i not at fault) it is zero. these definitions call for two remarks. first, there are many different comprehensive coverage contracts on offer, with (say) different levels of deductible. ideally, these contracts should be treated separately and not bundled together as we do here. however, this would greatly complicate the model. they separate accidents in which the insured is at fault and those in which he is not. the reason is that if the insured has an accident in which another driver is to blame, any information on his risk type may not be conveyed. also, they do not exploit the further information linked to drivers who had several accidents in 1989; again, there are very few of these cases. they now set up two probit models, one for the choice of coverage and one for the occurrence of an accident. let ?i and ?i be two independent centered normal errors with unit variance. then and they first estimate these two probits independently, weighing each individual by the number of days under insurance wi . then they can easily compute the generalized residuals ?i and ?i . for instance, ?i, is given by where ? and ? denote the density and the cumulative distribution function (cdf) of n(0, 1). now define a test statistic by the general results in gouricroux et al. (1987) imply that under the null of conditional independence cov (?i , ?i) = 0, w is distributed asymptotically as a ?2(1). this provides them with a test of the symmetric information assumption. their main finding is that, although unobserved heterogeneity on risk is probably very important, there is no correlation between unobservable riskiness and contract choice. in other words, when choosing their automobile insurance contracts, individuals behave as though they had no better knowledge of their risk than insurance companies. this interpretation is fully consistent with the view generally shared by french automobile insurers, namely that the information at the companys disposal is extremely rich and that, in most cases, the asymmetry, if any, is in favor of the company. feng gao, michael r. powers, jun wang (2008) in their paper, using data from china’s individual health-insurance market, they studied the problem of information asymmetry. their preliminary results appear to contradict standard-model predictions, showing that higher-risk buyers are more likely to purchase “additional” insurance than lower-risk buyers, but that they also tend to purchase lower limits of “basic” insurance coverage. they therefore develop a theoretical model to capture the effects of buyers’ wealth levels and loss amounts, and show empirically that these effects, in the context of asymmetric information, lead to the coexistence of adverse selection and advantageous selection in china’s health-insurance market. they introduced a simple one-period theoretical model of the health-insurance market. next, they described the data and methods to be used in the present study. for simplicity, let there be two different types of buyers in a health-insurance market type 1 and type 2 each with the same increasing and concave-downward utility function, u (.). furthermore, let wi , ?i ,mi , and li denote, respectively, the initial wealth level, probability of illness, medical loss amount (given that illness occurs), and non-medical loss amount (given that illness occurs) for a buyer of type i . they assumed that these quantities are known to the buyer but unobservable by insurers, and that w 1 >w2, ?1 < ? 2, m 1 > m2 >0 and 0 = l1 < l2. these assumptions correspond to the realistic scenario in which wealthier buyers, as compared to poorer buyer, are less likely to contract illnesses requiring medical treatment; likely to expend greater medical resources once they have contracted illnesses, and likely to expend few (if any) non-medical resources once they have contracted illnesses (because they are afforded sick days and other disability benefits by their employers). given the above formulation, it can be shown that, for certain parameter values, a separating equilibrium exists in which insurers provide two types of policies, x and y, with (per unit) premium rates px and py , coverage limits bx and by of (basic) medical coverage, and coverage limits ax and ay of (additional) non-medical coverage. letting i denote the final wealth level for a buyer of type i, the buyer’s optimization problem is to maximize over j. then, under certain regularity conditions, type 1 buyers will choose a policy x with px = ?1, bx = m1, and ax =0, whereas type 2 buyers will choose a policy y with py = ? 2, by = m2, and ay = l2.this means that high-risk buyers will purchase more insurance – in the sense of additional non-medical coverage – than low-risk buyers, but less insurance – in the sense of a lower medical-coverage policy limit. thus, a buyer’s level of wealth and loss amounts are important factors in determining insurance demand even in the case of cara and so any unobservable heterogeneity of wealth and loss amounts among buyers can lead to both adverse selection and advantageous selection. the existence of asymmetric information has a profound effect on the functioning of insurance markets, especially in developing economies (see chen, powers, and qiu, 2008).however, relying solely on empirical analyses of relationships between risk level and insurance amount does not necessarily lead to correct conclusions. in fact, when significant differences exist among the wealth levels and loss amounts of buyers, lower-risk individuals actually may purchase more insurance exhibiting the phenomenon of advantageous selection because higher loss expenditures, as well as higher risk levels, tend to increase the demand for insurance. their analysis of china’s health-insurance market reveals that the limit of basic insurance purchased by buyers with more ex-post claims is lower, but that these same buyers tend to purchase additional insurance more frequently. this is explained very well by their theoretical model. 2.2. the literature focusing on risk aversion: meza and web (2001) in their paper stated that in addition to precautionary effect that explains the negative correlation between insurance demand and risk level, heterogeneous optimism also supports this negative correlation: high risks are more optimistic about the events to be improbable, so they purchase less insurance. they offer two justifications for the positive correlation between insurance purchase and precautionary activity. the first follows from heterogeneous wealth and lays the foundation for the particular form of heterogeneous tastes that constitutes our second justification. suppose, first, that everyone has the same opportunity to lower the probability of a given financial loss through undertaking preventative effort. in the two-state case, the expected utility of an insured individual i is where wi is the persons wealth, d is the gross loss, y is the insurance premium, and ?y , ? > 0, is the net of premium payout in the event of loss. fi is a binary-choice variable that affects the probability of loss in the same way for all individuals. if fi = 0, the probability of avoiding the loss p (fi) is p0, but if fi = f-, the probability rises to pf . the wealth-dependent part of the utility function exhibits decreasing absolute risk aversion. this standard assumption implies that the marginal rate of substitution between y and ?y falls with wealth. given the magnitude and probability of loss, lower insurance coverage is therefore chosen by wealthier individuals. the increase in expected utility from taking precautions is it follows from decreasing absolute risk aversion that if insurance coverage is partial (d - ?y > y), then ??i / ?wi < 0. according to this formulation, there may be a wealth threshold above which precautions are not taken. moreover, if administrative costs or other reasons lead to high loading factors, wealthy individuals may prefer to be uninsured. now consider a reinterpretation involving differences in preferences. intuitively, more timid types may lower their risk exposure through increased insurance purchase and greater precautionary effort. however, the concept of a pure change in risk aversion is ambiguous; changing the curvature of the utility function alters its height almost everywhere, and the issue is; where should the pivot occur? in general, results are ambiguous, but suppose that the utility function of individual i is ui = u (?i + w) – fi, where ?i is an individual-specific parameter making taste differences formally equivalent to wealth differences. in the relevant range, the utility functions are where ub is linear and ut is strictly concave and w - y > w - d + ?y are the wealth levels in the good and bad states. also they assumed that the bold, though more risk tolerant than the timid types, were nevertheless risk averse, separation may involve both types buying some insurance. administrative costs are then sufficient to generate quality discounts, a conclusion reinforced by a second effect. bold types tend to insure against fewer contingencies and are less inclined to take precautions, so comprehensive policies may be cheaper per dollar of coverage, even net of administrative costs. they argued that heterogeneous risk preference with endogenous precautionary effort could lead to just such a correlation. luigi guiso and monica paiella (2005), in their paper used household survey data to construct a direct measure of absolute risk aversion based on the maximum price a consumer is willing to pay to buy a risky asset. they related this measure to a set of consumers’ decisions that in theory should vary with attitude towards risk. they found that elicited risk aversion has considerable predictive power for a number of key household decisions such as choice of occupation, portfolio selection, moving decisions and exposure to chronic diseases in ways consistent with theory. they also used this indicator to address the importance of self-selection when relating indicators of risk to individual saving decisions. to measure risk aversion they exploit the 1995 wave of the survey of household income and wealth (shiw), which is run every two years by the bank of italy. the 1995 shiw collects data on income, consumption, real and financial wealth and its composition, insurance demand, type of occupation, educational attainment, geographic and occupational mobility, and several demographic variables for a representative sample of 8135 italian households. the respondent could respond in one of three ways: declare the maximum amount he was willing to pay for the asset, which we denote zi; b) answer “don’t know”; c) not answer. notice that the way the hypothetical asset is designed implies that with probability 2/1 the respondent gets 10 million lire and with probability 1/2 he loses zi. so the expected value of the lottery is 2/1(10 ? zi). clearly, zi < 10 million lire, zi = 10, and zi > 10 million lire imply risk aversion, risk neutrality and risk loving, respectively. this characterizes attitudes towards risk qualitatively. within the expected utility framework a measure of the arrow-pratt index of absolute risk aversion can also be obtained for each consumer. let wi denote household is endowment. let ui(•) be its (lifetime) utility function and i be the random return on the security for individual i, taking values 10 million and zi with equal probability. the maximum purchase price is thus given by: where e is the expectations operator; taking a second-order taylor expansion of the right hand side of (1) around wi gives: substituting (2) into (1) and simplifying we obtain: equation (3) uniquely defines the arrow-pratt measure of absolute risk aversion in terms of the parameters of the hypothetical asset of the survey. obviously, for risk-neutral individuals (i.e. those reporting zi = 10), ri(wi) = 0 and for the risk-prone (those with zi > 10), ri(wi) < 0. notice that since the loss zi or the gain from the investment need not be fully borne by or benefit current consumption but may be spread over lifetime consumption, our measure of risk aversion is better interpreted as the risk aversion of the consumer’s lifetime utility. theory of choice under uncertainty implies that preferences for risk should strongly affect individuals’ choices in a variety of contexts. thus, differences in risk attitudes across individuals should be very important in explaining observed differences in behavior. their results show that this measure has strong predictive power on some key consumer decisions including occupational choice, portfolio allocation, investment in education, job change and moving decisions, in ways that are consistent with what theory predicts. in some cases the effects are extremely substantial. their evidence shows strongly that individuals differ markedly in their attitudes towards risk and that these differences lead them to sort themselves out in such a way that the more risk-averse choose lower returns in exchange for lower risk exposure when they invest their assets, choose their occupation, decide to invest in education, migrate or change jobs or to take precautions against illness. 2.3. the literature on concluding the existence of adverse selection in insurance market: georges dionne, christian gouriéroux and charles vanasse (1998) in their paper proposed an empirical analysis of the presence of adverse selection in an insurance market. they first presented a theoretical model of a market with adverse selection and we introduce different issues related to transaction costs, accident costs, risk aversion and moral hazard. they then discussed an econometric modeling based on latent variables and we derive its relationship with specification tests that may be useful to isolate the presence of adverse selection in the portfolio of an insurer. they discussed in detail the relationship between our modeling and that of puelz and snow (1994). finally, they presented some empirical results derived from a different data set. they show that there is no residual adverse selection in the studied portfolio since appropriate risk classification is made by the insurer. consequently, the insurer does not need a self selection mechanism such as the deductible choice to reduce adverse selection. first consider the economy described by rosthschild and stiglitz (1976) (see akerlof, 1970 for an earlier contribution); there are two types of individuals (i = h, l) representing different probabilities of accidents with ph > pl . they assumed that at most one accident may arrive during the period. without insurance their level of welfare is given by: , (1) where: pi is the accident probability of individual type i, i = h , l w is initial wealth c is the cost of an accident u is the von neumann-morgenstern utility function (u(•) > 0, u (•) ? 0) assumed, for the moment, to be the same for the two risk categories (same risk aversion). under public information about the probabilities of accident, a competitive insurer will offer full insurance coverage to each type if there is no proportional transaction cost in the economy. in presence of proportional transaction costs the premium can be of the form p = (1+ k)pili where li is insurance coverage and k is loading factor. with k > 0, less than full insurance is optimal. however an increase in the probability of accident does not necessarily imply a lower deductible if they restrict the form of the optimal contracts to deductibles for reasons that will become evident later on. in fact they show that: proposition 1: in presence of a loading factor (k >0), sufficient conditions to obtain that the optimal level of deductible decreases when the probability of accident increases are constant risk aversion and pi < 1/2 (1+k). under this assumption, it can be shown that a separating equilibrium exists if the proportion of high risk individuals in the market is sufficiently high. otherwise there is no equilibrium. the optimal contract is obtained by maximizing the expected utility of the low risk individual under a zero-profit constraint for the insurer and a binding self-selection constraint for the high risk individual who receive full insurance. they restrict their analysis to contracts with a deductible; the optimal solution for the low risk individual is obtained by maximizing v (pl) with respect to dl under a zero profit constraint and a self-selection constraint: (2) where pl is the insurance premium of the l type, the solution of this problem yields dl* > 0 while dh* = 0 when the loading factor (k) is null. if now they introduce a positive loading fee (k > 0) proportional to the net premium, the total premium for each risk type becomes and they obtain, from the above problem with the appropriate definitions, that which implies that or that so they have as second result: proposition 2: when they introduce a proportional loading factor (k >?) to the basic rothschild-stiglitz model, the optimal separating contracts have the following form: this result indicates that the traditional prediction of rothschild-stiglitz is not affected when the same proportional loading factor applies to the different classes of risk. in order to perform carefully the analysis of adverse selection in this portfolio from a structural model, it is important to design a basic latent model. the discussion presupposes that two deductibles d1 < d2 are available, the latent variables of interest are for the individual i. the ratification variables from the insurer: p1i is the premium for the contract with the deductible d1. p2i is the premium for the contract with the deductible d2. since d1< d2, it is clear that p1i > p2i . their econometric results were derived, however, from a model without different accident costs. they show that individuals who choose the larger deductible have an average frequency of accident lower than the average one of those who chooses the smaller one. however, since the expected numbers of accidents were obtained from observable variables, this result does not mean that there is adverse selection in the portfolio. further analyses show that, in fact, there is no residual adverse selection in the portfolio studied. the insurer is able to control for adverse selection by using an appropriate risk classification procedure. in this portfolio, no other self selection mechanism (as the choice of deductible) is necessary for adverse selection. amy finkelstein and james poterba (2002) in their paper investigated the importance of adverse selection in insurance markets. they used a unique data set, consisting of all annuity policies sold by a large u.k. insurance company since the early 19800s, to analyze mortality differences among individuals who purchased different types of policies. they found systematic relationships between ex-post mortality and annuity policy characteristics, such as whether the annuity will make payments to the estate in the event of an untimely death and whether the payments from the annuity rise over time. these mortality patterns are consistent with the presence of asymmetric information in the annuity market. they found no evidence of substantive mortality differences, however, across annuities of different size, even though models of insurance market equilibrium with asymmetric information would predict such differences. they also find that the pricing of various features of annuity contracts is consistent with the self-selection patterns we find in mortality rates. their results therefore suggest that selection may occur across many specific features of insurance contracts and that the absence of selection on one contract dimension does not preclude its presence on others. this highlights the importance of considering the detailed features of insurance contracts when testing theoretical models of asymmetric information. they estimated mortality differences among different groups of annuitants using the discrete-time, semi-parametric, proportional hazard model used by meyer (1990) and han and hausman (1990). their duration measure is the length of time the annuitant lives after purchasing an annuity. they let ?( t , xi , ? , ?? ) denote the hazard function, the probability that an annuitant with characteristics xi dies t periods after purchasing the annuity, conditional on living until t. the proportional hazard model assumes that ?( t , xi , ? , ?? ) can be decomposed into a baseline hazard ??(t) and a “shift factor” ?(xi ,?) as follows: the baseline hazard ??(t), is the hazard when ?(.) =1. ?(.) represents the proportional shift in the hazard caused by the vector of explanatory variables xi with unknown coefficients ?. the proportional hazard model restricts the effects of the explanatory variables (xi) to be duration-independent. they adopt one of the common functional forms for ?(.), ?(xi ;?) =exp(x?i?). they found evidence of annuitant self-selection with respect to the time profile of annuity payouts, and with respect to whether the annuity may make any payments to the annuitants estate. all else equal, annuitants who are longer lived select annuities with back-loaded payment streams. similarly, annuitants who are shorter lived select annuities that make payments to the annuitant’s estate in the event of an early death. they also found evidence that back loaded annuities are priced higher, and annuities with payments to the estate are priced lower, than other annuities. this is consistent with our findings that longer-lived annuitants buy back loaded policies, while the shorter-lived purchase estate protection. their findings on the differential mortality experience of annuitants who purchase different types of policies are consistent with individuals having private information about their mortality experience, and acting on this information in their insurance purchases. daifeng he (2008) in their paper found evidence for the presence of adverse selection in the life insurance market, a conclusion contrasting with the existing literature. in particular, he found a significant and positive correlation between the decision to purchase life insurance and subsequent mortality, conditional on risk classification. individuals who died within a 12-year time window after a base year were 19 percent more likely to have taken up life insurance in that base year than were those who survived the time window. moreover, they found that individuals are most likely to obtain life insurance four to six years before death. methodologically, he addresses sample-selection and omitted-variables issues overlooked in the previous literature. they used the health and retirement study (hrs) dataset. hrs is a nationally representative longitudinal survey of the elderly and near-elderly in the united states. it contains rich information on health status, insurance coverage, financial measures, demographics, and family structure as well as some data on individuals’ expectations. their analysis uses the hrs cohort, which consists of individuals born between 1931and 1941. this cohort has been interviewed biennially since 1992. their sample ends in 2004. they obtained data on life insurance coverage from two early waves, 1992 and 1994, in order to simplify comparison with the previous literature. the 1992 and 1994 waves also are the only ones in which the hrs survey explicitly asked whether a respondent held individual term life insurance. they found, contrary to the earlier literature, evidence for adverse selection in the life insurance market. after supply or pricing factors are carefully taken into account, individuals with higher mortality risk are 19% to 48% more likely to buy individual term life insurance than are those with lower risk, depending on the length of the time window in which mortality risk is defined. moreover, buyers appear to employ this informational advantage by seeking to take up insurance four to six years before death. these results provide an alternative view of the informational content of life insurance markets, calling into question the widely held notion that life insurance is free of adverse selection. furthermore, the failure of the life insurance industry’s comparatively stringent underwriting practices to eliminate strategic purchasing suggests that informational asymmetry might be even more prevalent in other insurance markets. 2.4. the literature resulting advantageous selection in life insurance market: mahdavi and rinaz (june 2005) in their paper "when effort rimes with advantageous selection: a new approach to life insurance pricing" investigated the demand for and pricing of life insurance when insureds risk aversion is correlated with their precautionary effort. they assumed that the population is divided into two groups: (i) very risk-averse individuals who have a low probability of death (pod)1 because of the precautionary effort they undertake and (ii) less risk-averse individuals who undertake less effort and thus have a higher pod. after computing the pooling equilibrium price under perfect competition for a class of crra2 utility and bequest functions, they computed the level of demand for life insurance by the two groups. under the assumption of negative correlation between risk aversion and risk exposure, lower-risk individuals still buy insurance even if the price offered is higher than the fair price corresponding to their group. this is because low risks are assumed to be more risk averse, valuing insurance so highly that they can tolerate higher than fair prices. they also present some cases when low-risk individuals purchase more than their high-risk neighbors even though they realize them subsidizing the high risks. in such cases, the insurers gain the advantage of facing a pod which is smaller than the rate they normally expect. is smaller than the rate they normally expect. this fact contradicts the so-called adverse selection hypothesis. they will denote by ei, i ? {l, h} the effort made by each group, and by ui and vi, i ? {l, h}, the utility and bequest functions of each group. when we need an explicit expression for these two functions, we will assume that for each i ? {l, h}, ui and vi are identical crra utility functions with parameter ?i ? [0, 1]. 1. probability of death 2. constant relative risk aversion effort levels are assumed to be a characteristic of individuals and cannot be adjusted. for simplicity here we consider only two groups, but we may want to consider in a more general way that the probability of death p = p(e) is a decreasing function of the effort e and that the risk aversion parameter ? = ? (e) is an increasing function of the effort e. they sum up all constraints relative to the parameters they just introduced. they have: of course, insurance companies are assumed to be unable to sort customers between the two groups and consequently will only offer one type of contract to all. the contract may be purchased in quantities subject to constraints relative to wealth and income. they are interested in computing the demand levels xi (q), i ? {l, h}, for the two groups of people depending on the price q of one contract unit. each group of individuals will maximize its own expected utility, and thus will solve the following problem: subject to the constraints where wi and yi, i ? {l, h} are respectively the initial wealth and expected income of the corresponding group. they predicted that increasing processing cost alters the regime from advantageous selection; science low-risk individuals who are more risk averse, can tolerate higher deductibles and prices and keep buying insurance in the market , while less risk averse high-risk individuals can tolerate lower levels of deductibles and prices and drop out of the markets. so the market ends up with relatively more risk-averse low risk individuals, which means switching the regime to a situation of advantageous selection. ghadir mahdavi (2006), in his paper " advantageous selection versus adverse selection in life insurance market " proved that under certain circumstances when the individuals are sufficiently risk averse, the probability of death is smaller than its critical value, and the processing cost is sufficiently large the selection effect will be advantageous to the market. he also showed that when individuals are not sufficiently risk averse and consequently their probability of death is not sufficiently small, the necessary condition for having advantageous selection regime is the processing cost to be smaller than its critical value. he supposed that all individuals have the same opportunity to lower the probability of death by preventive efforts. each individual i faces the probability of death p (ei) where ei indicates the precautionary efforts and is assumed to affect the probability of death in the same way for all the individuals. he assumed p? < ? which emphasizes that precautionary activity improves the survival rate and has negative effect on the probability of death. letting the function u (0) represent utility in the life state and v(0) utility for surviving members of the household in the death state, the expected utility of a policyholder i is the variable q is the insurance unit premium, wi is the individual’s wealth, yi is the income and, xi(ei) refers to the demand for life insurance which is defined as the total coverage in the event of death. this model suggests that the agents invest in both of precautionary effort for reducing the probability of death and, life insurance for handling the remaining risk. obviously, the amount of insurance demand should be nonnegative, xi(ei) ? ?. they determine the demand level for two groups of more risk-averse low-risk individuals and less risk-averse high-risk individuals to check if advantageous selection occurs in this setting. they assume the utility and bequest functions are of a class of crra. the problem will be to maximize the expected utility function the classical theory of demand for insurance under asymmetric information results in insufficient provision of policies and adverse selection. these conclusions seem to contradict most of the empirical works in the field. he try to resolve this contradiction by introducing the effect of precautionary activities which improves the survival rates, and assuming a negative correlation between risk aversion and risk exposure. under these two assumptions, the so-called adverse selection regime can be substituted with a favorable situation which is called advantageous selection. he could also show that under certain circumstances when the probability of loss is smaller than its critical value, the policy holders are sufficiently risk averse and the processing cost is sufficiently large, the selection effect will be advantageous to the market and the so-called adverse selection regime prevails no longer. he could also show graphically the cases that good risks are better off with pooling equilibrium rather than drop out of the insurance pool. as a result of negative correlation between risk aversion and risk exposure, the low-risk individuals prefer to purchase life insurance policy even though the price is not fair to them and they are actually subsidizing the high-risk policyholders. if the individuals are not sufficiently risk averse and have higher probability of death, then the necessary condition for having advantageous selection regime will be facing a low level of processing cost smaller than its critical value. as mentioned above in insurance market, these papers discussed about risk aversion level of individuals on the demand for insurance and the existence of adverse selection or advantageous selection in insurance market. we will apply the logistic and dummy variables models in this thesis. our goal is to estimate the correlation between the risk aversion (the characteristics of insured) and the demand for life insurance and examine the existence of adverse selection in iranian life insurance market. chapter 3 methodology qualitative or categorical variables can be very useful as predictor variables in regression analysis. qualitative variables such as sex, marital status or job can be represented by indicator or dummy variables. these variables take only two values, usually 0 and 1. the two values signify that the observation belongs to one of two possible categories. the numerical values of indicator variables are not intended to reflect a qualitative ordering of the categories, but only serve to identify category or class membership. regression analysis is a conceptually simple method for investigating functional relationships among variables. we examine whether the demand for life insurance is related to various psychological and demographic variables such as: age, marital status, education, income and the wealth of household. the relationship is expressed in the form of an equation or a model connecting the dependent variable and explanatory or predictor variables. we denote the dependent variable by y and the set of predictor variables by x1, x2, … , xp where p denotes the member of predictor variables. the true relationship between y and x1, x2, …, xp can be approximated by the regression model where ? is assumed to be a random error representing the discrepancy in the approximation .the function f(x1,x2, … ,xp ) describes the relationship between y and x1,x2, … ,xp . an example is the linear regression model where ?0 , ?1 , … , ?p called the regression parameters or coefficients , are unknown constants to be determined (estimated)from the data (samprit chatterjee, ali s.hadi, bertram price;1999). we will apply logistic regression model and dummy variable regression model to estimate the effect of variables on the demand for life insurance. 3.1. logistic model we will apply logistic model to examine the existence of adverse selection in life insurance market. logistic model is often used when the object of the study is to model the probability of an event. logistic regression is a form of regression which is used when the dependent variable is dichotomous, discrete, or categorical and the explanatory variables are of any kind. using the logit transformation, logistic regression predicts always the probability of group membership in relation to several variables independent of their distribution. the logistic regression analysis is based on calculating the odds of the outcome as the ratio of the probability of having the outcome divided by the probability of not having it. logistic regression is the linear regression analysis to conduct when the dependent variable is dichotomous (binary). data will be collected via questionnaire. since there are qualitative data (sex, marital status, occupation, education, and etc.), so the logistic model will be an appropriate method for estimating our parameters (1) the model defines a relationship between the dependent variable and the characteristics of individuals (xi); such as age, occupation, sex, etc. yi is a dependent variable and shows the function of independent variables such as sex, marital status, occupation, education, and etc. the logistic model can be generalized directly to the situation where we have several predictor variables. so, we have; we let ; (2) yi shows the demand for life insurance. yi can take two amounts: yi is 1; if the individuals demand life insurance (pi = ?(x)). yi is 0; if the individuals don’t demand life insurance (pi = 1- ?(x)). i : denotes the individuals (insured) ( i = 1,2, …, n ) . n: is the number of insureds . ?(x): is the probability of demand for life insurance. xi: is an independent variables and shows the characteristics of individuals who demand life insurance; such as: age, occupation, sex, marital status, etc. ? denotes the intercept of the equation. ?: is the coefficient of independent variables xi ;it shows the degree of correlation between the characteristics of individuals who demand life insurance ( xi) (or risk aversion criteria of individuals ) and the demands for life insurance (yi). equation (2) is non-linear in the parameters ?0, ?1, ?2, … , ?n . however, it will change to linear form by the logarithmic transformation; we obtain the equation (3); (3) 3.1.1. maximum likelihood (ml) analysis: since our data follow a binomial distribution (because the individuals either demand life insurance or not), we apply maximum likelihood analysis using the binomial likelihood with mean value given by an appropriate function of predictors. it can be written as: (a) we examine whether the independent variables (xi) have significant effect on the dependent variable (yi) or not. h0: ?=0 states that the yi (is independent of xi ( independent variable) or the demand for life insurance doesn’t have correlation with the characteristics of individuals who demand for life insurance ; such as : age, occupation, sex,… ) . we use wald test method for performing significance test of hypothesis h0: ?= 0 about parameters in glms (general linear models).the simplest uses the large-sample normality of ml estimates. the test statistic * has an approximate standard normal distribution when ?= 0 . one refers to the standard normal table to get one-sided or two-sided. equivalently, for the two-sided alternative, (z2) has a chi-squared (?2) distribution with df=1; the p-value is then the right chi-squared probability above the observed value. this type of statistic, which divides a parameter estimate by its standard error and then squares it, is called a wald statistic. the wald can be used to test the true value of the parameter based on the sample estimate. then the wald test can be used to test whether the characteristics of individuals have significant effect on the demand for life insurance. we used the wald test to examine the statistical significance of each coefficient in the model. the value of this statistic is obtained from multinomial logit results. to test the null hypothesis, the amount of wald test which show that whether these variables (age, occupation, sex …) have significant effect on the demand for life insurance 0.05 level of significance. 3.1.2. likelihood-ratio (lr) test we also use the statistical test; likelihood-ratio for determining the * ase: adjusted standard error effectiveness specifically. the likelihood-ratio test statistic equals (b) where; l0: is the maximum over the possible parameters values that assume the null hypothesis (h0: ?= 0). l1: is the maximum over the larger set of possible parameters values for the full model, permitting the null or the alternative (h1: ?0 ? ?). this transformation of l0 and l1 yields a chi-squared statistic. under h0: ?= 0, it also has a large sample chi-squared statistic with df =1. the obtained statistic is compared to the ?2 distribution. we examine the effect of these variables on the demand for life insurance by using the amount of the likelihood-ratio test statistic (?2) for each characteristic (such as age, occupation, sex…). 3.1.3. graphical methods the relationship (1) is called logistic response function and has the shape shown in figure 3.4.1. • 3.1.the logistic curve g (the cumulative normal distribution) • x since the response function in relation (2) (section 3.1) is non-linear in the parameters ?0, ?1, ?2, … , ?n . we can work with transformed variables will having no constant variance; then we must use the weighted least squares methods for fitting the transformed data. the logistic model can be generalized directly to the situation where we have several predictor variables. if ?(x) is the probability of an event happing, the ratio (?(x)/1-?(x)) is called the odds ratio for the event. this amount is equal to (c) the logarithm of the odds ratio is called the logit. it can be seen from (3) that the logit transformation produces a linear function of the parameters ?0, ?1, ?2, … , ?n . note also that while the range of values of ?(x) in (c) is between 0 and 1, the range of values is between –? and +?, which makes the log (?(x)/1-?(x)) (the logarithm of the odds ratio) more appropriate for linear regression fitting. modeling the response probabilities by the logistic distribution and estimating the parameters of the model given in (3) constitutes fitting a logistic regression. the parameter ? determines the rate of increase or decrease of the curve. when ?>0, ?(x) increase as x increase. when ?<0, ?(x) decrease as x increase .the magnitude of determines how fast the curve increase or decrease. 3.2. dummy variable regression since our data consist of the numerical variables (sex, marital status, occupation, education, and etc.) and dummy variable regression model defines a relationship between the dependent variable and numerical variables, so the dummy variable regression model can be an appropriate model for estimating our parameters. one of the limitations of multiple-regression analysis is that it accommodates only quantitative explanatory variables. dummy-variable regression can be used to incorporate qualitative explanatory variables into a linear model, substantially expanding the range of application of regression analysis. the model defines a relationship between the dependent variable and the characteristics of individuals (xi); such as age, occupation, sex, etc. we are interested in the effect of a qualitative independent variable on the demand for life insurance. if we assume that variable affect on intercept in this model, then this effect can be incorporated into a model. the resulting regression model is the dummy variable di is a regressor, representing the explanatory variable such as gender, education, employment, risk aversion, health and etc. pre is a dependent variable and shows the premium of insureds. the quantitative explanatory variable income is only quantitative independent variable and is shown by xi. for example, in this case the regression functions for the premium of insureds in the two genders are: if di = regressor for gender so, we have: if di = regressor for education if di = regressor for employment if di = regressor for marital status if di = regressor for risk averse if di = regressor for warden if di = regressor for health if di = regressor for worry about family future if di = regressor for premium value if di = regressor for respect to laws ?i is a standard error with normal distribution (n(0,1)). in this case, we test h0: ? = 0against h1: ? > 0, since we expect the effect to be positive. by applying dummy-variable regression, we estimate the relationship between risk aversion and the parameters of the demand for life insurance .we will examine whether various psychological and independent variables of risk aversion parameters (such as: age, marital status, education, income and the wealth of household) have significant effect on the dependent variable (demand for life insurance) or not.

نام پژوهشگر: رضا افقی