Between-Group Adverse Selection: Evidence from Group Critical Illness Insurance. Working Paper. August Abstract. Keywords

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1 a Between-Group Adverse Selection: Evidence from Group Critical Illness Insurance Working Paper August 2014 Martin Eling a *, Ruo Jia a, Yi Yao b Institute of Insurance Economics, School of Finance, University of St. Gallen, St. Gallen, Switzerland. martin.eling@unisg.ch, ruo.jia@unisg.ch b Department of Risk Management and Insurance, School of Economics, Peking University, Beijing, China. yao.yi@pku.edu.cn * Corresponding author. Abstract This paper demonstrates the existence of adverse selection in the group insurance market for policies that allow no individual choice. As a conventional wisdom, grouping mitigates adverse selection, since individual choice is minimized and grouping reduces the variance of risks. We complement this conventional wisdom by analyzing a group insurance scenario in which individual choice is completely excluded, and find that there is still adverse selection (between-group adverse selection). Between-group adverse selection, however, disappears over time if the group renews with the same insurer. Our results thus indicate that the effective way to mitigate adverse selection is not necessarily via group insurance, but through experience rating and underwriting based on the information that insurers learn over time. Keywords Adverse Selection, Information Asymmetry, Learning Over Time, Group Insurance, Critical Illness Insurance 0

2 Introduction Group insurance constitutes a substantial part of global insurance markets and its importance to the life and health insurance is steadily increasing. 1 Administrative efficiency and low volatility of performance are strong motivations for the insurance industry to develop group insurance (Bickelhaupt, 1983). Many policyholders are also in favor of group insurance since it avoids the difficult and anxious task of shopping for insurance (Pauly and Percy, 2000). Managing adverse selection is critical for the success of insurance markets (Akerlof, 1970; Rothshild and Stiglitz, 1976). Therefore, it is worthwhile to take a careful look at adverse selection in group insurance. This paper tests for the existence and, if found, the extent of persistence of adverse selection in a group insurance market with no individual choice. As a conventional wisdom, grouping mitigates adverse selection because (1) the mixture of high and low risks decreases the variance of risks, (2) individual choice is minimized, and (3) individuals do not strategically act on information asymmetry regarding risk types when group insurance is tangential to other factors influencing an employment decision (Browne, 1992; Mayers and Smith Jr., 1981; Smith and Stutzer, 1990). For example, Browne (1992) uses the group insurance market as the benchmark market free of adverse selection and concludes that individual insurance suffers more from adverse selection than group insurance. As a complement to the conventional wisdom, Hanson (2005) argues that the equilibrium in the group insurance market with no individual choice is not materially different from the equilibrium in the individual insurance market. Hanson s (2005) model implies that groups strategically act on their information advantages, if any, in the same way as individuals, which yields group adverse selection. The existence of group adverse selection depends neither on individual choice within a group nor on incomplete pooling, but results from group strategic actions based on the entire group s welfare. The existing empirical evidence on adverse selection in group insurance is highly concentrated in the U.S. health insurance market, where individual choice between competing health insurance plans is an important driver of adverse selection (Cutler and Zeckhauser, 2000). To our knowledge, no empirical literature has tested for the existence or persistence of adverse selection in a group insurance market where no individual choice is allowed. Following Mayers and Smith Jr. (1981), we split the individual choice effect and the group decision effect in group adverse selection by differentiating within- and between-group adverse selection. We present a dataset of group critical illness (CI) insurance. 2 Our findings show that adverse selection may well exist even if individuals within a group are not allowed 1 2 For example, in 2012, the direct written premium of group life and health insurance in U.S. was USD 295 billion, taking 41.9% of the total premium in life and health sector; particularly, group health insurance dominates the health insurance market by taking 53.8% of the total premium in U.S. (Insurance Information Institute, 2013). The portion of group life and health insurance was 36.6% of total life and health premium in 2010 and 36.1% in Critical Illness Insurance covers a limited number of named critical diseases. After a predefined waiting period it pays the insurance amount, if any of the diseases listed in Appendix I are firstly diagnosed during the policy period. The dataset consists of 7,784 valid group policy observations purchased by 3,453 groups, representing more than 2,230,000 individual policies. 1

3 to choose their participation and/or coverage; this confirms Henson s (2005) theoretical results. We also find evidence that adverse selection disappears over time if the group renews with the same insurer. With experience and knowledge gained over time, the insurer learns to reject poor risks and adjusts the premium based on each group s claim experience. Therefore, the information advantage of the group insured as a new client diminishes with the renewal process. Kunreuther and Pauly (1985) and Cohen and Siegelman (2010) call this learning over time. Our results imply that group insurance, even without individual choice, cannot be considered as a market free of adverse selection. Insurers should also take measures against adverse selection in group insurance business. In the following, we introduce our hypotheses and theoretical background. Then we present the data and empirical analyses with robustness tests. Finally, we present concluding remarks. Hypotheses and Theoretical Background Adverse selection is the tendency of high risks to be more likely to buy insurance or to buy larger amounts of insurance than low risks (Cummins, Smith, Vance, and VanDerhei, 1983). Adverse selection results from the asymmetric information that favors the insurance buyer over the insurer (Akerlof, 1970; Rothshild and Stiglitz, 1976). In making insurance decisions, 3 insureds self-classify themselves into different risk pools, where low risks suffer a welfare loss because they cannot buy the optimal amount of insurance (Miyazaki, 1977; Rothshild and Stiglitz, 1976; Spence, 1978; Wilson, 1977). The existence of adverse selection has been widely documented in many lines of individual insurance (see Cohen and Siegelman, 2010, for a review). The evidence is extensive obtaining from both real markets (see e.g. Cohen, 2005) and lab experiments (see e.g. Riahi, Levy-Garboua and Montmarquette, 2013), and covering both private competitive markets (see e.g. Cohen, 2005) and public provision of insurance (see e.g. Dumm, Eckles and Halek, 2013). Regarding adverse selection in the group insurance market, Mayers and Smith Jr. (1981) distinguish within-group adverse selection that results from individual choices within a group, from between-group adverse selection that results from group insurance decisions. By differentiating within- from between-group adverse selection, we split the effects of individual choices and group insurance decisions. Adverse selection studies based on U.S. group health insurance argue that the group adverse selection comes from the individual choices within each group, i.e. within-group adverse selection (see Cutler and Zeckhauser, 2000 for a review). Our paper shows the existence and persistence of between-group adverse selection, which results from a pure group decision and from a group strategic action. Table 1 presents the theoretical framework, empirical literature, and contribution of this paper. 3 There are two insurance decisions need to be made by the insurance buyer, which may cause adverse selection. Firstly, the participation decision involves choices whether to buy, to cancel, to renew and/or to switch the insurer for certain insurance policy. Positive participation decision is the necessary condition for the next, insurance coverage decision. The coverage decision involves choices of scope of cover, insurance benefit or amount, deductible and other optional details in the insurance policy. 2

4 Table 1 Three Types of Adverse Selection Types of adverse selection Type I: Individual adverse selection Type II: Within-group adverse selection Type III: Between-group adverse selection Insurance decision on participation and coverage Individual Individual and group: the participation of group members is voluntary and/or coverage choice is allowed within a group. Group: the participation of group members is mandatory and the coverage is identical within a group Literature providing empirical evidence See Cohen and Siegelman (2010) for a review of empirical studies, focusing on the individual insurance market See Cutler and Zeckhauser (2000) for a review of empirical studies, focusing on the U.S. group health insurance market Aim of this paper, not covered by existing literature Classic arguments have been made that collective choice of a group mitigates adverse selection because group risk is an average of individual risks and the variance of group risks is lower than the variance of individual risks (Phelps, 2012; Folland, Goodman, and Stano, 2012). Group insurance is a partial solution to adverse selection problem because it pools heterogeneous risks with identical policies (Smith and Stutzer, 1990) in which individual choice is minimized. On the flip side, Mayers and Smith Jr. (1981) argue that if individuals voluntarily participate or are able to choose benefits, adverse selection may well exist in group insurance. Empirical studies based on U.S. group health insurance confirm Mayers and Smith Jr. s (1981) argument on the relationship between individual choices and within-group adverse selection. Cutler and Zeckhauser (2000) review 14 empirical studies that examine the selection of group health insurance with individual choices, all of which find some type of adverse selection; however, none of them distinguish within-group adverse selection from between-group adverse selection. In summary, there is both theoretical and empirical proof for the existence of within-group adverse selection in the group insurance market when individual choices within a group are allowed. However, whether between-group adverse selection exists and, if so, its extent of persistence, is as yet unknown. There are two competing theoretical predictions about between-group adverse selection. Mayers and Smith Jr. (1981) argue that if the group is formed for other than insurance purposes, the average risk for the group is less likely to deviate from the relevant population average, which solves any between-group adverse selection problem. However, Hanson's (2005) theoretical model yields the opposite result. It compares the equilibria in the individual insurance market with that in the group insurance market with no individual choice. It concludes that a profit-maximizing employer 4 will choose contracts off the same equilibrium contract curve as would a purchaser of individual insurance, which suggests the existence of adverse selection for group insurance. This conclusion is subject to the conditions that (1) the group insured 5 makes all decisions on behalf of group members, (2) there is a uniform group policy, (3) there is no wealth effect, (4) there are no administrative costs, and (5) the group is 4 5 The profit-maximizing employer is defined as the employer who wants to maximize the sum of the benefits its employees get from the group insurance, minus the price paid for the insurance. The group insured is the employer or other types of group purchasing coverage, e.g. the union. 3

5 formed for a purpose other than purchasing insurance. According to Hanson s model, even though the pooling of high and low risks reduces the variance of group risks, this turns out to be irrelevant to the standard equilibrium and thus there is between-group adverse selection in the group insurance market that is independent of individual choices within a group. In other words, individual choice is not a necessary condition for the existence of adverse selection in the group insurance market. The two competing theoretical predictions motivate us to empirically test for the existence, and if found, the persistence of between-group adverse selection in a group insurance market with no individual choice. Hypothesis I: If group insurance does not allow individual choices within each group and if the group is formed for purposes other than purchasing insurance, the group insurance market should have no adverse selection. Under the two conditions in Hypothesis I, two theories explain how adverse selection may still exist. Mayers and Smith Jr. (1981) argue that individual insureds may switch jobs because of the differences in health insurance coverage among similar jobs; therefore, high risks choose jobs that offer more comprehensive health insurance coverage and low risks choose jobs offering less. This explanation is unlikely to apply to our dataset because (1) the frequency of critical diseases is very low in comparison to other health insurance products; in our dataset, on statistical average, the probability of an individual insured having a claim in a particular policy period is 0.069% (see Table 2); and (2) the expected benefit of group critical illness (CI) insurance is relatively small; in our dataset, on statistical average, over 90% of individual insureds have an expected benefit less than CNY 69 (USD 11) per year and over 99% of individual insureds have an expected benefit less than CNY 207 (USD 33) per year. 6 It will not be a solid motivation for the employee to switch jobs because of such a remote event and such small expected benefit. Hanson (2005) provides another explanation for the existence of between-group adverse selection. The profit-maximizing employer will behave the same as the individual insurance buyer when choosing insurance coverage. The employer will choose more comprehensive coverage on behalf of its employees if its employees to be covered are high risks, and vice versa. This explanation requires that the employer, specifically HRs or other responsible department of the employer, possesses an information advantage over the insurer (Akerlof, 1970; Rothshild and Stiglitz, 1976), because, otherwise, the insurer would be able to charge a risk-adequate rate to eliminate adverse selection. Under the condition of group insured/employer making all insurance decisions, the following two theories explain the potential sources of group insured/employer s information advantage over the insurer. Cohen (2005, 2012) argues and provides empirical evidence that the insurer is not able to fully observe a new customer s past claim record and draw inferences about the insured s risk type, because in general the self-reporting of past claims is believed to be incomplete or inaccurate (Insurance Research Council, 1991). Therefore, the insurer can only use risk exposure information and inaccurate risk experience information to make underwriting and pricing decisions for new clients. In other words, an insured is most likely to have the information advantage when he/she is a new customer to the insurer (Cohen,(2005). 6 The expected benefit is calculated by insurance amount, as shown in Table 2, times the average claim frequency of 0.069%. 4

6 This argument applies to both individual and group insurance, therefore applies to our dataset. We will use the sub-portfolio of new policies to test Hypothesis I. Hanson (2005) offers another explanation for the group insured/employer s information advantage. The group insured/employer usually knows the health condition of its employees at the individual level but the insurer only knows this information at the group average level. Our dataset includes the complete information the insurer uses for underwriting decisions and policy pricing. Quite likely, the employer s HR (or other) department has the information on individual employees that the insurer does not, such as whether the employee smokes, or whether the employee himself/herself has a history of heart attacks. In some circumstances, the employer is even aware that some of its employees have certain symptoms of diseases before purchasing insurance. In such a situation, the group insured/employer has an information advantage over the insurer. Finkelstein and McGarry (2006) argue that there are multiple dimensions of private information, not only in regard to insureds risk types but also as to risk attitudes (or risk preferences). They suggest that empirical studies based on a risk-coverage correlation test should control for the insured s risk attitude, since risk-averse insureds often associate with low risk, and this will blur the positive risk-coverage correlation test, because of advantageous selection. However, it is hard to argue that such correlation between risk attitude and risk coverage also applies to group insureds. It has been pointed out that risk aversion is much less of a motivation for corporate insureds to purchase insurance, especially for stock companies, because the stakeholders could instead manage idiosyncratic losses through diversified portfolios (Mayers and Smith Jr., 1982, 1990). In the case of corporate insurance in China, Zhu, Kui, and Fang (2011), based on province-level panel data, find that risk aversion is not a significant factor in insurance demand. In our analysis, since the group insureds are largely corporates and decision makers are usually HRs or other responsible departments in the group, we assume that group insureds risk attitudes are not the major driver of insurance demand and will not distort the risk-coverage correlation. 7 Kunreuther and Pauly (1985) and Watt and Vazquez (1997) emphasize that observing the realization of a policyholder s risks in a given period enables an insurer to update its prior beliefs concerning the risks posed by that policyholder in a future policy period. Kunreuther and Pauly (1985) and Cohen and Siegelman (2010) call this learning over time. Insurer learning over time occurs when the insurer is able to use the observed respective insured s claim experience to adjust the premium and/or reject the renewal. However, this necessary condition does not apply to many individual insurance products. For instance, individual health insurance usually includes the insurer s commitment as a guaranteed renewable clause, which prevents the premium increase and/or the renewal rejection based on the individual s past claim experience with the insurer. Individual life insurance usually involves a long-term commitment from the insurer and, often, policy termination by the insurer or premium rate adjustment are not allowed during the entire policy period. In contrast, an insurer offering 7 In addition, Chiappori and Salanié (2013) provide an alternative explanation. Risk preference alone should have negligible consequences on the positive risk-coverage correlation in competitive markets, because insureds, of all types of risk aversion, prefer full coverage in a competitive market. Group CI insurance in China can be considered as a competitive market with standardized coverage and without rate regulation. 5

7 group insurance, in almost all lines, is free to adjust the premium rate at renewals or to reject renewals to reflect each group s past claim experience. Therefore, after a few policy periods with the same insurer, the group insured s information advantage over the insurer might disappear. The group insured s information advantage in Hanson (2005) also fails to persist, because high-risk individuals reveal their risk types over time by making claims and the insurer can reject to renew high-risk individuals or adjust the group/individual premium to reflect the experience. The employer s information advantage regarding individual risk type will diminish as high-risk individuals reveal their risk type over time. Eventually, the only possible information advantage the group insured may have pertains to the individual health conditions of its new employees. Mayers and Smith Jr. (1981) summarize that frequent contract renegotiation controls adverse selection as long as the information is revealed over time and the insurer is able to monitor and apply the information in pricing and underwriting accordingly. Since information asymmetry is a necessary condition for the existence and persistence of adverse selection (Akerlof, 1970; Rothshild and Stiglitz, 1976), adverse selection should cease to be a problem as soon as the insurance buyer s information advantage over the insurer disappears. Hypothesis II: The between-group adverse selection in the group insurance market, if any, will disappear if the group renews with the same insurer for a few policy periods. Data and Summary Statistics To test Hypothesis I and II, we use the dataset from a nationwide life and health insurance company in China. The dataset includes the insurer s complete underwriting and claim records for group critical illness (CI) insurance. It covers all group CI policies issued between January 2008 and June 2013, and all claims settled between January 2008 and August 2012 under these group CI policies. 8 The business nature of this insurance portfolio is largely, but not only, employee benefits, including benefits for an employee s family. 9 Critical Illness Insurance is a common type of health insurance innovated in It is a loss occurrence based product with claim trigger as the first diagnose of the critical disease. Usually, there is a 30 to 90 days waiting period for the first time purchaser, and the insurance payment is triggered by insured being firstly diagnosed of critical disease after the waiting period. The claim benefit equals the insurance amount and will be paid to the insured in a lump sum without additional benefit (e.g. medical service). The Insurance Association of China and the Chinese Medical Doctor Association issued guidelines regarding definitions of 25 types of critical diseases in In our case, the insurer followed the guideline strictly. CI insurance serves as a supplement to medical expense insurance. In medical expense insurance, 8 9 The claim information is electronically recorded real time, but only retrieved and organized by the actuarial team once a year. When we obtained our data, the claim information between September 2012 and June 2013 was not yet available. In later analysis, to avoid the potential truncation problem, we identify the claim status for polices expiring after August 2012 as missing values, thus these observations are automatically excluded from our regressions. The group size in our portfolio varies from five people to 28,691 people. 6

8 there are usually co-payment and exclusions for certain treatments, therefore, with an extra layer of protection from CI insurance, insureds are better protected financially. Cochrane (1995) proposed a time consistent health insurance plan, which is providing a lump sum of payment equals to the present value of future health premium increase, so that the insured with long term critical disease could afford the future health insurance coverage. This solution echoes the provision of CI insurance in providing extra funding for insured with critical disease. In 2012, 68 life and health insurers and 62 property and liability insurers operated in China insurance market. Most of them could operate in short term CI insurance line (i.e. are legally eligible to operate the group CI insurance). In 2012, the premium income of CI insurance was CNY 40.6 billion (USD 6.5 billion), accounting for 38.2% of health insurance premium in China. The number of individual insureds in 2012 exceed 90 million (China Insurance Regulatory Committee, 2013; Su, 2013). The original dataset is on individual policy level. For each individual policy entry, the dataset contains (1) policy information including individual policy number, group policy number, insurance amount, premium, policy inception date, policy expiring date, and policy issuance date; (2) individual insured s demographic information including name, age, gender, and occupation category 10 ; and (3) group insured s demographic information including group name, group location area, and group size. The dataset also contains the claim amount and the claim settlement date for those individual policies having claims. 11 We organize the individual policy entries into group policies by referring to the group policy number. Since this paper focuses on between-group adverse selection, where individual choices are not allowed within each group, we select those group policies with identical insurance coverage for each individual insured in the group. 12 This leaves us 7,784 group policy observations purchased by 3,453 groups, representing more than 2,230,000 individual policies. Table 2 summarizes the key features of our insurance portfolio. Our portfolio has low claim frequency, relatively small insurance amount for most policies, and a mixture of different group sizes, occupations, ages, and genders. Since the claim size of CI insurance always equals the insurance amount, the claim severity is also small on average. Table 3 compares the features of new policies to those of renewed policies. Mean difference T-tests are reported. Table 4 further includes the sub-portfolio of policies with two or more consecutive renewals and the sub-portfolio of policies with three or more consecutive The occupation category is based on the tendency of accident of occupations instead of the tendency of illness. We acknowledge that the industry classification reflecting the illness tendency of different occupations is a better indicator to control for the tendency of critical disease than our occupation category; however, it is available neither to the insurer nor to us. We do not have the information on rejected claims, which is a common issue in empirical literature using real market data (see e.g. Cohen and Siegelman, 2010 for a review). However, since what we care is the actual risk type of the insured, it is reasonable to assume that the rejected claims are claims falling outside the policy coverage, thus irrelevant to the actual risk type of the insured. Therefore, rejected claims have minimal impact on our conclusion. In group CI insurance, the only possible coverage difference within a group policy is the insurance amount. No difference in deductible and/or covered critical diseases is allowed. Group policies with identical insurance coverage, i.e. with no individual choice, take more than 75% of all policies. 7

9 renewals. ANOVA mean difference F-tests are reported. We observe no significant difference in claim frequency among these portfolios, which implies that the risk quality of new policy portfolio, renewed policy portfolio and portfolios with more renewal times does not materially differ from each other. Therefore, our conclusions are not influenced by the inherent risk quality difference among portfolios. We find, however, significant trends in most demographic variables and policy features along with the increase of renewal times. The portfolio with more renewal times contains groups with larger size, in richer region, with younger age and with more women. The portfolio with more renewal times has a smaller average insurance amount per person, a lower premium rate and shorter policy duration. The policy duration decreases with the renewal times, because short-term policies renew more times than long-term policy during our observation period. We do not observe a systematic trend on the insured s occupation category along with the renewal times. Considering the observed trends, we will always control the policy features, and control either the insured s demographic features or the premium rate 13, which represents the insurer s projection based on insured s demographic features in later regression analysis. The following two features of our CI insurance portfolio demonstrate its suitability for testing between-group adverse selection. First, the portfolio is a good approximation to the condition of mandatory participation of group members. According to the insurer s underwriting guideline, for small groups of no more than 50 people, the participation ratio has to be 100% in order to issue the group CI policy. For larger groups, the participation ratio can be reduced to a minimum of 75%. The portfolio described in Table 2 satisfies the condition of identical coverage within each group. The dataset eliminates the possibility of within-group adverse selection, therefore, the group adverse selection identified, if any, is between-group adverse selection. Second, the CI insurance is believed to have little moral hazard, because (1) the insured can hardly influence the possibility of being diagnosed with the defined critical diseases after purchasing insurance; (2) considering the very small expected benefit, the insured s incentive to change life style, because of the insurance, is minimal; and (3) the simple claim trigger in CI insurance avoids the over-utilization problem commonly observed in medical expense insurance, because the insurer pays the insurance amount once the defined critical diseases are diagnosed. Similar to our study, Wang, Peng, Sun, and Chang (2011) focus on adverse selection in Taiwan s cancer insurance market. They conclude that purchasing extended cancer insurance would not reduce insureds efforts to prevent cancer. We note the potential issue of claim fraud. However, as in the insurer s claim practice, the insurer always asks the claimant to recheck the disease diagnosis in a second hospital approved by the insurer. The claim payment is subject to the recheck procedure, which significantly reduces the risk of claim fraud. Therefore, the adverse selection in CI insurance is much less disturbed by moral hazard and claim fraud than are medical expense insurance and/or automobile insurance. 13 Premium rate is defined as the policy premium divided by the insurance amount. 8

10 Table 2 Summary Statistics: Insurance Portfolio Overview Variables Descriptions Valid Obs. Mean Min p5 Median p95 Max grpclyn 1 if any claim(s) under the group policy 4,846 c grpclcont Number of claims under the group policy 4,846 c d grpclfreq Average number of claims per insured under the group policy, 4,846 c e i.e. fraction of insureds having a claim amnt Insurance amount per insured in CNY 7,784 61, , , ,000,000 grppoldur Group policy duration in days 7, f actgrpsize Number of individual insureds under the group policy 7, ,691 area a Indicator of relative wealth and insurance market development 7, of the group insured s location sex Fraction of women under the group policy 7, age Group average age 7, h work b Group average level of occupation accident tendency 7, anlpremrate Annualized premium rate per insured 7, N Total number of group policies 7,784 g a. 1 represents the most developed regions in China, 4 represents the least developed areas. The area variable is based on the insurer s branch categories, which considers not only the regional wealth level but also the regional insurance development level. It is a better control variable than pure wealth measurement. b. 1 represents the safest occupations, 6 represents the most dangerous ones. The work variable is measured by the accident tendency of an occupation, e.g. office workers are 1 and coal mine workers are 6. c. The less valid observations are due to time constraints of the dataset. We do not know whether the group policy has a claim if the policy expires after 31 August 2012 and does not settle any claim before 31 August We identify the claim status of such policies as missing values. d. There is only one group policy having 60 claims and only seven policies having more than 20 claims. Our results are robust if excluding these seven policies. e. Small groups may have very high claim frequency in case any insured in the group raises a claim. There are only four group policies with claim frequency higher than 10%. Our results are robust if excluding these four policies. f. Only 19 group policies have policy duration longer than 366 days. They are negotiated conditions for special clients. We recognize that such policies weaken the controlling effectiveness of yearly dummies. However, since they account for only 0.2% of our portfolio and yearly dummies can largely reflect time effects by identifying policy issuance time, we keep time effect controls on yearly basis. Our results are robust if excluding these 19 policies. g. Excluding observations with missing values in various variables, we have 4,734 valid observations with full information. Only observations with full information will be used in later regression analyses. h. The minimum age of zero has only one group, which could be a special group of employee s family with only infants. 9

11 Table 3 Comparison between New Policies and Renewed Policies Variables New Policies Renewed Policies T-Test for Mean Difference Mean Median Valid Obs. Mean Median Valid Obs. Mean Difference T-Value P-Value avgrpclyn a , , avgrpclcont a , , amnt 66, ,000 2,736 65, ,000 3,329 1, grppoldur , , actgrpsize , , area , , sex , , age , , work , , anlpremrate , , N b 2,736 d 3,329 c, d a. av represents the average per insured per day. It scales claim performance indicators to comparable level. b. The total number of new policies and renewed policies, 6,065, is less than the total number of valid group policies, 7,784, because (1) for some policies issued in 2008, we do not know whether they are new or renewed policies as we do not know whether the group insured bought the policy in 2007; (2) some policies are neither renewed nor new but rejoined policies, that the group insured came back to the insurer after a gap period between the previous policy and the rejoined policy. c. The renewed policies are more than new policies because one group insured may have several renewed policies during our observation period but only one new policy with the insurer. d. Excluding observations with missing values in various variables, we have less valid observations with full information than N. Only observations with full information will be used in later regression analyses. 10

12 Table 4 Comparison between New Policies, Renewed Policies and Policies with More Renewal Times Variables New Policies Renewed Policies (Policies renewed one or more times) Valid Mean Median Obs. Policies renewed two or more times Policies renewed three or more times ANOVA F-Test for Mean Difference Mean Median Valid Valid Valid Mean Median Mean Median Obs. Obs. Obs. F-Value avgrpclyn a , , , avgrpclcont a , , , amnt 66, ,000 2,736 65, ,000 3,329 63, ,000 2,071 60, ,000 1, poldur , , , , actgrpsize , , , , area , , , , sex , , , , age , , , , work , , , , anlpremrate , , , , N 2,736 b 3,329 b 2,071 b 1,368 b a. av represents the average per insured per day. It scales claim performance indicators to comparable level. b. Excluding observations with missing values in various variables, we have less valid observations with full information than N. Only observations with full information will be used in later regression analyses. P-Value 11

13 Empirical Analysis To test Hypothesis I, we use the classical risk-coverage correlation model (see Cohen and Siegelman, 2010) as shown in Equation (1). A positive correlation between risk and coverage shall be a necessary condition of adverse selection, implying that high risks buy more insurance coverage. An insignificant correlation between risk and coverage suggests no adverse selection. Risk = α + βcoverage + γx + ε (1) We measure the actual Risk of a group insured by its ex-post claim performance in group policy i. The claim performance is measured by three claim indicators, which are commonly used in existing literature (see Cohen and Siegelman, 2010 for a review). (1) The claim dummy variable, which equals 1 if there is any claim under group policy i; (2) the total number of claims under group policy i; and (3) the claim frequency, which equals the total number of claims divided by the number of individual insureds under group policy i. We do not use the total claim amount or the claim severity as the claim performance indicator, because the claim severity of CI insurance always equals the insurance amount on individual basis. The total claim amount and/or the claim severity thus add no additional information to the claim frequency. We measure the insurance Coverage for group policy i by the natural logarithm of the insurance amount per insured. The insurance amount per insured under group policy i is identical for every individual insured in the group, since no individual choices are allowed in our portfolio. Our group CI insurance always has a zero deductible and covers the same named critical diseases for all insureds as shown in Appendix 1. X i is a vector of control variables including demographic features and policy features. These features are known to the insurer. They are potentially relevant for classifying the group insured s risk and for the insurance underwriting decision and pricing. In the following regressions, we use the natural logarithm of policy duration and the natural logarithm of actual group size under the group policy to fit the models. We introduce area dummies, area1 to area4, to control the regional differences in wealth level and insurance market development level. We also include year dummies to control the time effects for policies issued in different years. We use the fraction variables of different age ranges to reflect the age mixture within one group, and the fraction variables of occupation categories, work1 to work6, to reflect the mixture of occupations within one group. The fraction variables are better control variables than the group average age or occupation, because they reflect the detailed mixture of different age and occupations within a group. For dummy and fraction control variables, we always omit the largest category from the models to avoid the collinearity. Equation (2) is the detailed form of Equation (1). As noted before, we test Equation (2) in the portfolio of new policies, since new customers are most likely to have the information advantage over the insurer (Cohen, 2005). We use only group policies that do not allow individual choices and that are approximate mandatory participation for group members, we thus exclude the 12

14 possibility of within-group adverse selection. Therefore any adverse selection observed is between-group adverse selection. Claim Performance = α + βlnamount + γ LnPolicyDuration + γ LnGroupSize + γ Area + γ Sex + γ Age + γ Work + δsignyear + ε (2) The results in Table 5 show that the insurance amount positively correlates with claim performance for all three claim indicators. We use the logistic model to fit the dependent variable of claim dummy in Column 1, the negative binomial model to fit the counted dependent variable of total number of claims in Column 2, and the tobit model to fit the zero censored dependent variable of group claim frequency in Column 3. We use cross sectional models because one group usually has only one new policy with the insurer and all these new policies form a cross sectional portfolio. The positive correlation between risk and coverage provides the evidence against Hypothesis I. We exclude the possibility of moral hazard as the reason for such positive correlation in later Discussion section 14. Adverse selection exists in the group insurance market even if the group insurance does not allow individual choices within each group and even if the group is formed for purposes other than purchasing insurance. Such adverse selection is, by definition, betweengroup adverse selection. The results directly support Hanson's (2005) prediction that, in a group insurance market with no individual choice, the group insured behaves the same as the individual insured and self-classifies itself into different coverage categories. Looking into the control variables, we find that there are more claims, if the policy duration is longer, the group size is larger and the average age of group members is older. It is worth to note that the group size remains positively correlated with the claim frequency, which is defined as number of claims divided by group size. It means that large groups have higher claim frequency than small groups. Men are slightly more prone to defined critical diseases than women. The relative wealth and insurance market development level of the group insured s location has a weak but positive correlation with the claim performance. The more developed the region is, the less likely the insured is to have claim. We examined the collinearity, endogeneity and heterogeneity issues of our model in Equation (2). Regarding the collinearity of independent variables, the absolute amount of correlation coefficients between the primary explanatory variable lnamnt, and control variables of area3, age46to60, work3, and work4 are in the range of 20% to 30%. All other coefficients are below 20%, all of which are within the acceptable range. 14 The finding in cross-sectional data that coverage is correlated with risk does not suffice to tell us whether it is caused by adverse selection alone, moral hazard alone, or both (Cohen and Siegelman, 2010). 13

15 We consider the potential endogeneity of the primary explanatory variable lnamnt and perform instrumental variable (IV) endogenous tests. The IV selected is the natural logarithm of annualized premium rate, lnanlpremrate, which significantly and negatively correlates with our primary explanatory variable, lnamnt. The insurance price (premium rate) inversely correlates with the demand quantity (insurance amount). Moreover, the insurance price does not relate to error terms, because we control all pricing factors in the regressions. The Wald tests of endogeneity 15 are conducted for nonlinear models with claim dummy and claim frequency as dependent variables, which yield p-values of 0.85 and 0.68 respectively. The Durbin-Wu- Hausman (DWH) test of endogeneity is conducted using Two-Stage Least Square model with total number of claims as the dependent variable. The DWH test yields the p-value of All tests suggest we accept the null hypothesis of exogenous lnamnt. 16 As suggested by Chiappori and Salanié (2000), the use of simple, linear functional forms, such as logit or probit, should be restricted to homogeneous populations. We find our dataset approximates the homogeneity, because (1) the business nature of our portfolio is largely similar, as employee benefits; (2) the insurer sources its business nationwide in China; and (3) we are able to control the potential heterogeneities among different group insureds, e.g. the relative wealth level and insurance market development level, the group occupation difference, etc See Wooldridge (2002), pp , for a detailed discussion of Wald Test. We use Probit model to perform Wald endogenous test with claim dummy as the dependent variable, since the error term of Logit model is not normally distributed, which significantly increases the difficulty of such test. We use 2SLS model to perform DWH endogenous test with total number of claims as the dependent variable, since the counted number of claims approximates to continuous variable, thus standard DWH test for linear models can apply. 14

16 Table 5 Risk-Coverage Correlation: New Policies MODELS Logistic a,c Negative Binomial a,c Tobit with Lower Limit at 0 c VARIABLES grpclyn grpclcont grpclfreq (scaled up by 1,000) lnamnt *** *** 3.783*** ( ) ( ) (1.430) lngrppoldur ** ** 17.07** (0.0158) (0.0185) (7.599) lnactgrpsize *** *** 10.01*** ( ) ( ) (1.387) area ( ) ( ) (3.638) area (0.0108) ( ) (4.525) area * (0.0368) (0.0183) (6.816) sex * * (0.0126) (0.0107) (6.783) age0to (0.0346) (0.0193) (28.12) age31to *** *** 23.16** (0.0146) (0.0128) (9.995) age46to *** *** 42.11*** (0.0173) (0.0161) (13.78) age61over e 0.107*** e (0.0611) (0.0408) (29.36) work ( ) ( ) (5.479) work ( ) ( ) (3.551) work (0.0110) ( ) (5.969) work5 b (0.0301) (0.0220) (14.83) signyear (0.0132) ( ) (8.504) signyear ( ) ( ) (3.400) signyear ( ) ( ) (3.901) signyear12 b * (0.0779) (0.0395) (10.13) Pseudo R N. A Observations d 1,597 1,597 1,597 *** p<0.01, ** p<0.05, * p<0.1 Robust standard errors clustered by groups are in parentheses a. Marginal effects at the means of independent variables are reported. b. Work6 and Signyear13 are omitted due to too few valid observations in this sub-dataset. c. Intercepts are included in models but not reported. d. The dataset using here is the same as the new policy portfolio shown in Column 1, Table 4. The smaller number of observations is due to missing values of respective variables. e. Only 0.7% of individual insureds are older than 60 in this regression portfolio, thus the coefficients become less significant and unstable in some models. 15

17 To analyze the robustness of our conclusion regarding Hypothesis I, we conduct the following five additional tests. The results of the robustness tests can be found in the appendices. First, we present the reduced-form analysis introduced by Chiappori and Salanié (1997) as shown in Equations (3.1) and (3.2). It is more robust than the structural approach in Equation (2) since it does not allow for a complete identification of the underlying model structure, thus it is compatible with nonparametric techniques (Chiappori and Salanié, 1997). The variables used for Risk, Coverage and X are the same as in Equation (2). Table 6 shows that the correlation coefficients between the residuals ε in Equation (3.1) and ω in Equation (3.2) are significantly positive, which means, conditional on observables, the coverage choice and the occurrence of claims are not independent phenomena. The choice with higher amount of coverage predicts a larger tendency of claims. Risk = g(x ) + ε (3.1) Coverage = f(x ) + ω (3.2) Table 6 Correlation between Residuals of Claim Performance and Residuals of Coverage Correlation Coefficients Residual of OLS Model on Lnamnt Pearson Residual of Logistic Model on Group Claim Dummy (0.0046) Pearson Residual of Negative Binomial Model on Total Number of Claims (0.0091) Generalized Residual of Tobit Model on Group Claim Frequency (0.0087) Observations 1,597 P values are in parentheses Second, we use other econometric models to fit Equation (2). Appendix 2 shows the results from Probit model on the group claim dummy, Poisson, Zero-Inflated Poisson, and Zero-Inflated Negative Binomial models on the total number of claims, and OLS model on the group claim frequency. All alternative models yield similar results to the results in Table 5, with the only exception on the reducing significance level for OLS on the group claim frequency. Third, we consider the potential nonlinear effect in the linear model of Equation (2). Dionne, Gouriéroux, and Vanasse (2001) argue that the significant correlation between claim performance and coverage may disappear after adding the projected primary explanatory variable to the classic model. We mirror their methodology by (1) regressing Lnamnt on all demographic and policy information, (2) predicting the projected lnamnt from the step 1 regression, and (3) adding the projected Lnamnt as an additional independent variable to Equation (2). Appendix 3 shows that 16

18 the positive correlation between claim performance and insurance amount remains significant after considering the potential nonlinear effect. Fourth, we test whether between-group adverse selection is robust for large groups, since the smaller the group is, the more private information the group has and can use compared to the insurer. Large groups may not have or may fail to act on such private information simply because the group is too large. As shown in Table 2, our dataset contains both small groups and large groups. We further regress Equation (2) on the sub-portfolios of policies with more than 500 people and those with 500 or less people. The results, shown in Appendix 4, confirm that our conclusion holds across large and small groups. Finally, we use the insurer s actuarial prediction to control the risk classification (Finkelstein and McGarry, 2006). We use the average annualized premium rate per person as the insurer s best estimate for the risk of each group. We assume that the standardized premium rate has incorporated the information of all demographic features and yearly effects, therefore, should replace all of them as shown in Equation (4) below. Claim Performance = α + βlnamount + γ LnPolicyDuration + γ LnGroupSize + γ StandardizedPremiumRate + ε (4) The results in Column 1 of Table 7 confirm the positive correlation between claim performance and coverage. The premium rate positively correlates with the claim performance, since it incorporates risk demographic information of the group insured. This method is important for both of our hypotheses. It controls all the information that the insurer knows and applies to insurance pricing. It suggests that the remaining positive correlation between risk and coverage come from the private information processed by the group insured. To test Hypothesis II on the extent of persistence (or lack thereof) of adverse selection for repeat customers, we monitor adverse selection in the three layered sub-portfolios of renewed policies respectively: (1) all renewed policies, (2) policies renewed two or more times, and (3) policies renewed three or more times. Hypothesis II predicts that the positive correlation between risk and coverage shall disappear along with increasing renewal times. Table 7 shows the results of Equation (4). We use the standardized premium rate as the control variable instead of the insured s demographic information, because the premium rate not only incorporates all demographics and yearly effects but also reflects the insurer s reaction to the respective group insured s past claim experience. For the renewed portfolio, the premium rate, as the best predictor from the insurer, is the preferred control variable for risk classification (for a detailed discussion, see Finkelstein and McGarry, 2006). In other words, we assume that the insurer uses mainly the exposure rating for new clients but uses both exposure rating and experience rating for repeat clients. The results in Table 7 show that for policies renewed two or more times, the positive riskcoverage correlation disappears. We conduct additional Chow tests and Z-statistic tests to 17

19 compare the claim-coverage coefficient of the new policy portfolio (Column 1) with the claimcoverage coefficient of the renewed policy portfolio (Column 2). We find that two coefficients are not statistically different from each other, although the claim-coverage coefficients for the renewed portfolio become smaller. The results suggest that there is between-group adverse selection in the new policies and that it might continue to exist in first-time renewed policies but does not persist in policies renewed two or more times. Since the risk-coverage correlation is a necessary condition of adverse selection 17 (Chiappori and Salanie, 2000), we conclude that between-group adverse selection disappears over time as the group insured renews with the same insurer. The evidence directly supports Hypothesis II. This finding echoes the effect of learning over time in the insurance market (noted above), that is, the insurer s efforts in underwriting and pricing based on respective group s claim experience mitigate the group insured s information advantage, and thus mitigate between-group adverse selection. 17 Finkelstein and McGarry (2006) argue that the positive correlation between insurance coverage and risk may be neither a necessary nor a sufficient condition for the presence of asymmetric information about risk type, by introducing the private information of risk preference. However, as noted before, risk preference or risk attitude is not a primary driver for group insurance decisions in group insurance. 18

20 Table 7 Risk-Coverage Correlation: New Policies and Layered Sub-Portfolios of Renewed Policies Sub-Portfolios New Policies Renewed Policies (Policies renewed one or more times) Policies Renewed Two or More Times Policies Renewed Three or More Times Panel A Logistic on grpclyn a,c lnamnt ** ** ( ) ( ) ( ) ( ) lngrppoldur *** *** *** ** (0.0228) ( ) ( ) ( ) lnactgrpsize *** *** ** ** ( ) ( ) ( ) ( ) anlpremrate 1.529** (0.633) (0.737) (0.446) (0.361) Observations d 1,690 1,850 1, Panel B Negative Binomial on grpclcont a,c lnamnt *** ** ( ) ( ) ( ) ( ) lngrppoldur *** *** *** ** (0.0227) ( ) ( ) ( ) lnactgrpsize *** *** ** ** ( ) ( ) ( ) ( ) anlpremrate 1.515** 1.407* (0.608) (0.772) (0.565) (0.442) Observations d 1,690 1,850 1, Panel C Tobit with Lower Limit of 0 on grpclfreq (scaled up by 1,000) c lnamnt 2.076* e (1.169) (0.689) (0.786) (1.818) lngrppoldur 29.30*** 11.39*** 8.826*** 9.115*** (10.82) (2.336) (1.872) (2.619) lnactgrpsize 9.893*** 4.915*** 4.053*** 4.594*** (1.257) (0.506) (0.583) (0.997) anlpremrate (358.8) (308.1) (370.6) (590.4) Observations d 1,690 1,850 1, *** p<0.01, ** p<0.05, * p<0.1, robust standard errors clustered by groups are in parentheses a. Marginal effects at the means of independent variables are reported. c. Intercepts are included in models but not reported. d. The dataset used here is the same as the portfolios shown in Table 4. The smaller number of observations is due to missing values of respective variables. e. p-value equals