1 HOW LONG WILL YOU LIVE: USING LIFE INSURANCE PRICES TO INFER MARKET EXPECTATIONS ABOUT IMPROVEMENTS IN LIFESPAN May 11, 2009 Jimmy Coonan Department of Economics Stanford University Stanford, CA Under the direction of Professor Jay Bhattacharya ABSTRACT Life insurance markets are immensely popular in the United States, helping families to smooth consumption in the event of the death of a primary earner. Insurance firms price these products to reflect the life expectancy of the purchaser. However, life expectancies change over time and steadily lengthened throughout the twentieth century as a result of technological progress in fields like nutrition, sanitation, and healthcare. Given this upward trend in lifespan, I question whether expectations of future increases in life expectancy influence life insurance prices. I build off of research by Alpert, Bhattacharya, and Sood (2004) to construct a theoretical model for insurance prices that excludes any potential expectations effects. By comparing this model to actual life insurance prices from the 1994 Health and Retirement Study (HRS), I observe whether expectations of improvements in medical technology drive life insurance prices downward. After making this comparison, I find no overwhelming evidence that market expectations had a substantial effect on the prices of life insurance products held by HRS respondents. Keywords: market expectation, life expectancy, Health and Retirement Study Acknowledgements: I would like to thank Professor Jay Bhattacharya for his guidance, support, and encouragement through every step of the research and writing process. Without his help the task of writing a thesis would have seemed impossibly difficult. I would also like to thank Professor Geoffrey Rothwell for his indispensable advice guiding how to write and structure an honors thesis.
2 Jimmy Coonan May 11, HOW LONG WILL YOU LIVE: USING LIFE INSURANCE PRICES TO INFER MARKET EXPECTATIONS ABOUT IMPROVEMENTS IN LIFESPAN Table of Contents Introduction.. 2 Literature Review. 5 Model.12 Analysis..19 Conclusions...34 Appendix 37 Reference List 40
3 Jimmy Coonan May 11, Introduction Prices, despite their apparent simplicity, encapsulate a staggering range of information about the products they advertise. These numbers, produced by interactions between supply and demand, reflect costs of labor, machines, transportation, and taxes. Prices reveal consumer trends and tastes, fluctuating across business cycles and regions. Prices for longer-term goods include the influences of market expectations about the future. Consumers are willing to pay more for cars or refrigerators that they expect will last longer or require fewer visits from a repairman. Investors and funds purchase stocks if they expect them to rise in value. Life insurance prices should also contain valuable information about market expectations. Life insurance contracts allow households to make periodic premium payments in exchange for a large transfer upon the death of the purchaser. These products help families to smooth consumption by avoiding a precipitous decline in income following the death of a primary earner. To price life insurance contracts fairly firms must anticipate the life expectancy of buyers. Since they pool many contracts together these firms do not need to accurately pinpoint the future death of each purchaser so long as they predict the average life expectancy within the pool. While determining how to set premiums firms consider factors including age, gender, or whether a person smokes. They integrate this information with knowledge of current life expectancy profiles to create actuarial tables that reflect the probability that someone of a given age will die in a specified year. The value of a life insurance contract should reflect not only knowledge of life expectancy at a given point in time but expectations about future changes in life expectancy. In the United States, life expectancy at birth skyrocketed from 47.3 years in 1900 to 77.8 years in
4 Jimmy Coonan May 11, (National Center for Health Statistics 2007, p.175). This continuous expansion of life expectancy has been driven by increases in nutrition, sanitation, improvements in standards of living, and technological advances in the healthcare industry. Americans may observe these past improvements in life expectancy and extrapolate them into the future, expecting innovative technological breakthroughs to extend their lives. These expectations should drive life insurance prices downward because buyers anticipate that medical advances will increase life spans and delay policy payouts. The purpose of this study is to test whether such expectations of future technology shocks in the healthcare industry influence life insurance prices. First, I develop a framework for considering the influence of expectations on insurance prices and consider how to distinguish expectations effects from insurance market inefficiencies like imperfect competition. In building this model, I rely primarily on research done by Alpert, Bhattacharya, and Sood (2004) focusing on the viatical settlements industry. Viatical settlements markets allow life insurance owners to sell their policies to third parties, and these contracts differ little from life insurance products. I then apply the theory to actual pricing data from the 1994 Health and Retirement Study (HRS). I choose to focus on data from a single year but work to develop a methodology so that future studies can investigate how expectations effects may change over time. I then compare a price model that intentionally excludes expectations effects with the actual pricing information. After adjusting for market inefficiencies, the relationship between the modeled and actual data will allow me to determine whether expectations of improvements in life expectancy influenced the prices of life insurance products held by HRS respondents. Analyzing the influence of market expectations on life insurance prices provides the opportunity to observe the degree of technological advance that markets believe is possible at
5 Jimmy Coonan May 11, any given moment. Although knowing expectations differs from accurately predicting the future, these expectations provide a unique context for studying the effects of medical advances. As one possible application, Alpert, Bhattacharya, and Sood (2004) suggest that the arrival of radical new HIV/AIDS treatments altered viatical settlements prices as purchasers became more optimistic about the potential for future technological progress. Understanding how expectations influence prices should also provide insight into the market dynamics of an incredibly popular product. According to Retzloff (2005) over 68% of American adults owned life insurance in 2004, a statistic that has remained fairly constant over the past forty years (p.10). Millions of families depend on well functioning life insurance markets to deal with the financial shock of losing a primary stream of income. The presence of expectations effects on insurance prices would indicate a well-functioning market sensitive to consumer sentiments. Life insurance buyers enjoy a wide variety of contract options. Consumers can choose between group and individual policies, with group policies generally packaged through an employer. Although Americans were equally likely to select group or individual coverage in 2004, individual policies tended to have larger face values (Retzloff 2005, p.8). In this study I focus solely on individual policies since insurance companies price these to reflect individual risks rather than the expected mortality of a large pool. Life insurance purchasers also select between term and more flexible insurance products with no defined expiration date (such as universal life or whole life). Term insurance covers the purchaser for a predefined period of time and only pays out if the policyholder dies within that period. These contracts constituted 37% of individual policies in 2004 (Retzloff 2005, p.14). When testing for expectations effects on prices, I use only term insurance policies because their rigid structure allows for more convenient modeling. Life insurance ownership tends to vary across age. People aged thirty-five to sixty-
6 Jimmy Coonan May 11, four are most likely to own any form of life insurance, with men more likely to purchase policies than women (Retzloff 2005, p.17). However, the proportion of women owning life policies has steadily risen as women have integrated themselves into the workforce. Literature Review Although researchers have written relatively little about the effects of expectations of rising life expectancy on life insurance prices, many economists have studied life insurance markets. Much research has focused on testing for market failures due to asymmetric information. Factors like adverse selection, imperfect competition, bankruptcy risk, and expectations could all influence the pricing of life insurance contracts. Understanding the general structure of and potential discrepancies within life insurance markets will help inform the model relating idealized insurance prices to actual data. Cawley and Philipson perform an extensive analysis of the American term life insurance market in their 1999 paper, An Empirical Examination of Information Barriers to Trade in Insurance. Throughout the course of the study the authors examine four distinct data sets including the 1994 HRS to test for adverse selection problems due to informational asymmetries. Many economists have suggested that private information regarding personal health status drives insurance purchasing decisions. In this environment, insurers cannot distinguish between high and low risk individuals so they charge a single price reflecting a society-wide average life expectancy. This single price appears particularly attractive to high risk individuals since they will be underpaying for their life insurance policies. Under the model these high risk individuals purchase more insurance, creating a situation where firms hold an unsustainable number of risky
7 Jimmy Coonan May 11, policies. To compensate, insurers respond to the market failure by charging marginal prices [that] rise with quantity (Cawley and Philipson 1999, p.828). With such a price scheme high risk individuals purchase larger policies but pay higher per unit prices. Insurance firms could then effectively distinguish between high and low risks and continue to operate. This solution only exists if ownership limits prevent buyers from purchasing multiple policies. Otherwise high risk individuals could replicate a low-cost large policy by combining many smaller insurance contracts. Cawley and Philipson (1999) examine data from LIMRA International, the CompuLife price quotation software, the HRS, and the Asset and Health Dynamics Among the Oldest Old (AHEAD, now included in the HRS data) to test for the presence of adverse selection in life insurance markets. The authors perform several regressions of unit-price on quantity of insurance in the four data sets and discover in each case that unit-price appears to be negatively correlated with quantity. This robust evidence of bulk discounting contradicts economic theory indicating that unit-prices should rise with quantity and suggests that adverse selection does not influence the American life insurance market. Cawley and Philipson perform further analysis using the HRS and AHEAD data sets to test for positive covariance between risk and quantity of insurance purchased. Both studies ask respondents to rate self-perceived health, a potential indicator of private information. After comparing both actual and self-assessed mortality risk with quantity, the authors find either insignificant or negative covariance between the two variables. The authors conclude from this evidence that the American life insurance market suffers from no asymmetric information problems. Based on the robustness of their findings and range of data examined, I operate under the assumption that private information does not
8 Jimmy Coonan May 11, influence the prices of insurance products held by 1994 HRS respondents. This assumption is reasonable considering I use the same HRS data set as the two authors. Other authors have also tested for market failures due to adverse selection in various markets. Akerlof (1970) introduced much of the initial economic theory guiding analysis of markets with adverse selection problems, applying his framework to the market for used cars. Rothschild and Stiglitz (1976) advanced the field by considering imperfect information within a health insurance context. The authors present a theoretical model of health insurance markets with high and low risk individuals. They display that a competitive separating equilibrium exists in spite of informational asymmetries. Since this study, researchers have performed many empirical tests to apply the economic theory to actual health insurance markets. As an example, Cardon and Hendel (2001) use data from the 1987 National Medical Expenditure Survey to test whether readily observable variables connect healthcare consumption with insurance purchases. The two economists find that such observables almost completely explain insurance purchasing decisions, leaving little role for private information. Chiappori and Salanié (2000) focus only on exclusive insurance contracts where insurers can enforce unit-prices that rise with quantity purchased. They consider a similar model to that employed by Cawley and Philipson (1999), but apply it to the French automobile insurance industry. They find no evidence that buyers take advantage of private information when purchasing insurance. Siegelman (2004) presents a comprehensive overview of papers testing for adverse selection in insurance markets. After reviewing articles focusing on a wide range of markets, the author concludes neither economic theory nor empirical evidence points to adverse selection as the overwhelming, central problem that many courts and scholars describe (p.1274).
9 Jimmy Coonan May 11, Recent study of life insurance markets has focused on the introduction of novel genetic testing procedures. Many countries restrict insurers from using the results of genetic tests to price policies (Hoy and Polborn 2000). These tests confer private information about personal health risks and provide a unique opportunity to evaluate the effects of adverse selection within a life insurance context. Hoy and Polborn (2000) construct a theoretical model linking genetic testing to life insurance purchasing decisions. The authors find that individuals have private incentives to purchase genetic tests when insurers cannot observe the results. However, the authors reach no consensus on the potential social effects of adverse selection. Using their model, they produce examples for a Pareto improvement, a Pareto worsening and for a situation in which those who are tested gain and those who are not lose (p.250). Other literature, such as Armstrong et al. (1999), has applied the theory to actual life insurance markets. Here, the authors consider the introduction of genetic tests for breast and ovarian cancers. They find some evidence of high adverse selection costs in larger policies but conclude that average costs from informational asymmetries remain manageable. Their analysis excludes the potential precautionary benefits from genetic test results. For example, those whose tests indicate high cancer risk may be more proactive about regular medical screening and prevention. Armstrong et al. (2007) update their previous work, studying the influence of the BRCA1/2 genetic test for breast and ovarian cancers on life insurance markets. The researchers estimate changes in insurance demand for twelve cohorts of women with a family history of cancer. They find results consistent with earlier studies, remarking that a ban on the use of genetic screening for insurance pricing generates only limited costs. The authors caution that informational imbalances could prove crippling if future genetic tests become less expensive and have a greater predictive value over a wider spectrum of illnesses.
10 Jimmy Coonan May 11, Although few economists have linked expectations of life expectancy gains with life insurance markets research has examined the dynamics of subjective life expectancy. Savings and consumption decisions in life-cycle welfare models depend on an individual s expected lifespan. Hamermesh (1985) notes the importance of subjective life expectancy to life-cycle models and questions whether increases in life expectancy that may motivate theoretical interest are incorporated in individuals expectations (p.390). The author analyzes the results of a questionnaire sent to a group of 650 economists and 975 other individuals randomly selected from a Midwestern city. By comparing subjective life expectancy with actuarial tables in both samples, Hamermesh finds that people take past improvements in life expectancy into account when projecting their own longevity. He also observes that projections tend to be overly optimistic and that individuals rely heavily on the life expectancies of close relatives when formulating their own expectations. This result suggests that individuals do react to increases in life expectancy and that life insurance prices should include such expectations effects. Other authors have examined the relationship between subjective life expectancy and improvements in lifespan using data from the HRS. Hurd and McGarry (1995) use responses to questions about life expectancy in the 1990 HRS to test if expected lifespan differs significantly from life tables from the same period. The authors found that expectations closely resembled the life tables, possibly meaning that past improvements in expectancy do not determine expected lifespan. If this finding is accurate perhaps expectations do not substantially influence life insurance pricing. However, expectations can vary across time and people may be more or less optimistic about life expectancy in different periods. The authors may have selected a time period when markets were pessimistic about the possibility of future medical advances. Smith (2008) investigates this possibility by analyzing changing expected longevity over time. The
11 Jimmy Coonan May 11, author studies the period before and after Hurricane Andrew in 1992, following a group of Florida residents most affected by the disaster. Smith regresses changes in subjective life expectancy on a set of dummy variables indicating those affected by the hurricane and concludes that the hurricane had a significant negative influence on expected lifespan. These findings suggest that people adjust subjective life expectancies in response to new information, which could include improvements in actual life expectancy over time or specific technology shocks. Alpert, Bhattacharya, and Sood (2004) provide the ideological and procedural foundation that I rely upon to study the connection between life insurance prices and market expectation of improvements in lifespan. The authors analyze the rapid expansion and decline of the viatical settlements industry in the late 1980s and 1990s, an industry that created a secondary market for life insurance contracts. Viatical settlements allow individuals to sell their insurance contracts back to the underwriting company or to another third party. The third party then makes all future premium payments on the policy and collects the face value when the original policyholder dies. These contracts proved especially popular among patients diagnosed with HIV/AIDS because many such patients purchased life insurance before contracting the virus. When these people tested positive for the disease their mortality risk jumped sharply, building value into their life insurance policies. This increase in value provides incentives for individuals to viaticate their insurance contracts to help pay the enormous medical costs initially associated with treating HIV/AIDS. The viatical settlements industry abruptly contracted following the dissemination of a new class of drug in 1996 known as HAART that drastically extended the lives of patients with HIV/AIDS. While analyzing price dynamics in the viatical settlements industry, Alpert, Bhattacharya, and Sood (2004) observe that contract prices fell relatively more for policyholders with longer
12 Jimmy Coonan May 11, life expectancies after the introduction of HAART therapies. They suggest that the technological shock of the more effective drug treatments boosted the market s expectation of future innovation in HIV/AIDS medication, which would have an inordinate effect on the contracts of those with longer life expectancies. Individuals with short life expectancies would likely not survive long enough to benefit substantially from future innovation. Those expected to live longer have a better chance of benefiting from future technological advances. As a result, the prices of viatical settlements faced by patients with longer life expectancies should drop by more in response to strong market expectation of innovation. The authors model this hypothesized change in expectation as an increase in the cost of capital that firms require to purchase an insurance policy from the original policyholder. Cost of capital serves as a useful way to quantify this expectation since it has a multiplying effect over time, just as individuals expected to live longer will be more likely to have their lives extended by a technological shock. The market reaction described by Alpert, Bhattachary, and Sood (2004) in response to a specific technological shock displays that insurance markets can react to expectations of increases in life expectancy. This kind of event study would prove difficult in broader life insurance markets where no single technological advance is likely to influence all policyholders. However, if viatical settlements markets respond to specific technological shocks, perhaps life insurance markets react to past trends in life expectancy. This connection seems reasonable considering steady technological advance across many fields of research drives society-wide trends in mortality. Life insurance markets may actually be more likely integrate expectations into pricing considering these markets are larger and more established than that for viatical settlements. Before constructing an empirical test to evaluate whether expectations influence life insurance prices I develop a model to consider how these two variables interact.
13 Jimmy Coonan May 11, Model To measure the effect of expectations of improving lifespan on life insurance prices I first construct an idealized price model that allows for the exclusion of any expectations effects. By comparing this model to actual life insurance data I can evaluate whether expectations significantly alter pricing. I begin with a model almost identical to that used by Alpert, Bhattacharya, and Sood in their 2004 analysis of the viatical settlements industry. In their model, a consumer purchases a life insurance policy in period τ with term length T, face value F, and per period premium π. This premium is not the per period payment in dollar terms, but rather the periodic payment as a fraction of the policy s face value, which allows for the comparison of premiums between policies of varying sizes. I use the term premium interchangeably with price and convert all premiums into annual values to arrive at a normalized price. β τ is the market discount rate for life insurance products at time τ, while D(t) refers to the probability of dying in period t and S(t) is the probability of surviving at least until period t + 1. By inserting values for D(t) and S(t) from a static life expectancy profile in period τ, I can ensure that this component of the model ignores the potential effects of expectation of future technology shocks. Within this framework, the present value of a life insurance product purchased at time τ will be: TT tt PPVV ττ = (SS(tt)BB ττ ππππ DD(tt)ββ tt ττ FF) (1). tt=1 Intuitively, Equation 1 states that the value of a life insurance contract is the expected cost to the firm subtracted from the expected benefit evaluated over the life of the product. The probability that the purchaser survives period t reflects the probability that the company will
14 Jimmy Coonan May 11, t receive the annual premium that period, making the expected benefit S(t)β τ πf. Similarly, the probability of dying in a given period is the probability that the company will have to pay the t face value of the contract, producing the expected cost D(t)β τ F. I assume the buyer purchases the contract in t = 0, but does not make the first payment until the beginning of the next period. Alpert, Bhattacharya, and Sood (2004) use a nearly identical model to value viatical settlements contracts although they reverse the expected cost and benefit portions of the equation. With viatical settlements the purchasing firm pays the regular premiums and receives the face value of t the policy upon the death of the original policyholder, meaning D(t)β τ F represents the expected benefit at time t. Before I consider the role of expectations in the model, I must first arrive at an expression for the life insurance premium π. In a perfectly competitive environment the premium should be set such that the present value of the contract equals zero at time τ. To see why consider the situation where an insurance company sets π such that the present value is greater than zero. In a competitive environment another firm could offer a slightly cheaper contract to attract customers while still earning positive profits. This process would continue until the premium is set so that the present value converges to zero and no firm earns positive profits. With this assumption the above expression simplifies to: TT tt 0 = (SS(tt)BB ττ ππππ DD(tt)ββ tt ττ FF) tt=1 TT TT tt tt ππ = (DD(tt)BB ττ )/ (SS(tt)BB ττ ) (2). tt=1 tt=1
15 Jimmy Coonan May 11, By rearranging the equation, I arrive at an expression that relates the price of an insurance contract with the term length, the discount factor, and the survival and mortality probabilities. Notice that the face value F disappears from the equation, which makes sense considering the dollar value of the policy is irrelevant given the ratio between the periodic premium payments and the face value. This assumes that unit-prices of life insurance do not change with quantity purchased. Equation 2 also relies on the assumption of perfect competition although actual life insurance markets likely do not have such a stylized structure. Insurance companies may have administrative costs and loading fees associated with creating new policies, possibly the result of imperfect competition. Given the popularity of life insurance any imperfect competition would derive from a limited number of firms offering policies as opposed to a lack of buyers in any particular age demographic. Imperfect competition of this type would cause a proportional upward shift in insurance prices across buyers of all ages. Such a shift could be easily distinguished from any expectations effect, which should drive prices down and have a varying influence on prices of insurance policies for buyers of different ages. Expectations of increases in life expectancy should affect premiums differently as the age of the policyholder varies. Elderly individuals with low life expectancies will be unlikely to survive long enough to benefit significantly from the arrival of a radical new treatment. As a result, they should only see a miniscule dip in premium payments due to expectations. Similarly, younger people already have such low probabilities of dying that the policy term will likely expire before a new technology could perceptibly alter their mortality rates. These buyers should also not see a large decline in prices from any expectations effect. Those in middle or latemiddle age should be the most affected by the possibility of future treatments improving mortality rates within the term of the insurance product. The most common length of term
16 Jimmy Coonan May 11, insurance is twenty years (Durham, Isenberg and Terry 2005), so a purchaser aged fifty would be seventy by expiration. Near the end of this period the probability of dying should begin to rise at an accelerating rate providing both the time and opportunity for new healthcare technologies to tangibly increase the value of the policy. The most natural way to model this variable expectations effect is through the discount rate β τ. Alpert, Bhattacharya, and Sood (2004) decompose this rate as ββ ττ = 1 1+rr ττ +δδ ττ, where r τ represents the risk-free rate in period τ and δ τ is the risk premium charged to a firm purchasing a viatical settlement. In a life insurance context this risk premium should include both the possibility that the originating firm goes bankrupt and fails to honor the policy and the possibility of future technology improving life expectancy. Although both effects should decrease premium payments, the bankruptcy risk component is constant across all policies written by the same firm and should be relatively homogenous between firms. Rather than represent δ τ as a static value faced by all individuals, I use the function δ τ (e) where the risk premium adjusts with a buyer s life expectancy. For the purposes of this study I use age a proxy for life expectancy. This substitution would not work if my life insurance ownership sample consisted mostly of individuals suffering from deadly illnesses like HIV/AIDS where expected lifespan may be uncorrelated with age. Among a large population sample, however, age should serve as a viable proxy for life expectancy. As an individual ages, δ τ (e) should rise, peak, and eventually decline once the person reaches old age. Using Equation 2 I construct a price model that excludes expectations effects by setting δ τ (e) = 0. I can then compare the idealized prices to real world pricing data, which may include effects due to expectations of increases in lifespan. By observing how the difference between the