Sunk Costs and Screening: Two -Part Tariffs in Life Insurance

1. SunkCosts and Screening: Two-Part Tariffs in Life Insurance James M. Carson, University of Georgia Cameron M. Ellis, TempleUniversity Robert E. Hoyt, University of Georgia Krzysztof Ostaszewski, Illinois State University May 22, 2019

2. Life insurance backdating • Life insurance backdating occurs when an insurance contract bears a policy date that is prior to the application date. • From the applicant’s perspective, the primary motivation for backdating is the reduction in premium that occurs because the price is based on an age that is less than the applicant’s age at the time of application. • The obvious disadvantage of backdating is the necessity of paying a premium for time that already has elapsed and for which no insurance coverage existed. • Carson (1994) shows that the present value of backdating can be positive after relatively short periods of time. The actuarial present value of backdating also generally is positive (Carson and Ostaszewski, 2004).

3. Backdating incentives to all parties • Backdating ultimately is a zero-sum game, but immediate and potential benefits of backdating lead insurers, agents, and consumers to participate (Carson, Clark, and Ostaszewski, 2012). • Because first-year expenses often exceed first-year premiums for a life insurance contract, insurers (and agents) strive for high persistency rates: A lapse in the first year (or longer) is costly for the insurer without any hope of recovery of such costs in later policy years. Backdating effectively shortens the first policy year, thus lowering the expected cost of early lapse.

4. Backdating incentives • Backdating has the same effect as a front-end load on the policy, which the consumer cannot recover. In case of lapse, this payment may be viewed as a phantom surrender charge (see Carson et al., 2012). Having made such a payment, the consumer is less likely to lapse, largely because the front-end load / phantom surrender charge of the initial payment encourages the consumer to keep the policy in force, similar to having paid “points” on a mortgage in order to obtain a reduced interest rate. Also, the consumer who purchased a backdated policy will experience lower premium cost only by persisting in owning the policy and paying the premium. The front-end load is recouped only in the form of lower future premiums.

5. Backdating incentives • Backdating therefore appears to be a very natural mechanism for helping a life insurer achieve a key goals: attracting consumers who will persist, and thus help the insurer achieve profitability. • Note that life insurers have used other mechanisms, such as dividends and persistency bonuses, and backdating would appear to be a further mechanism for encouraging life insurance persistency and controlling adverse selection. Of course, for those other mechanisms, if consumers hold their life insurance "too long" and life insurers' assumptions about lapse rates prove incorrect (too high), then the persistency benefit becomes a problem (in so called lapse supported products).

6. Price discrimination • Price discrimination in economics refers to the situation when identical or largely similar goods or services are transacted at different prices for different consumers, or products with differing costs are transacted at the same price, or, most generally, different consumers face different relationship of price paid to the cost of the good/service sold. • First-degree price discrimination: Every consumer pays his/her reservation price. • Second-degree price discrimination: Price per unit depends of volume, package size, or other incentives. • Third-degree price discrimination: Different prices in different submarkets.

7. Other forms of price discrimination (special cases of second-degree price discrimination) • Two part tariff: A consumer pays an entry fee and then pays a price per unit. • Buffet pricing: Fixed price with “all you can eat.” Two-part tariff with zero price per unit.

8. Misperceptions of price discrimination • Robinson-Patman Act influenced by the misperception that price discrimination equals harmful predatory pricing. • In reality (Nahata, Ostaszewski, Sahoo, 1990) third-degree price discrimination can lead to lower prices in all sub-markets (can be shown in real life), or higher prices in all sub-markets (the only real-life example is prohibition of backdating, the law in six states, a sub-optimal solution).

9. Backdating as a two-part tariff and relevance to lapse rates • In this paper, we develop a model of life insurance pricing under heterogeneous lapse behavior with asymmetric information about lapse likelihood. • Lapse rates in life insurance are substantial. Between 1991 and 2010, $29.7 trillion of new individual life insurance coverage was issued in the United States. During this same time period, $24 trillion of coverage lapsed. • Eighty-eight percent of whole life insurance policies never pay a death benefit. • There are several theories on why consumers lapse on their polices: • preference shocks, • income shocks, • policy replacement, and • non-expected utility explanations.

10. Asymmetric information • Even though asymmetric information on lapse risk may appear different than asymmetric information on loss probability, the same intuition applies. • Life insurance incurs a front-loading of underwriting-related costs both through direct underwriting costs and agent commission. It is expected that the costs of underwriting will be recovered by the insurer over the long life of the contract. When a consumer lapses, the insurer is unable to recoup that cost. Thus, consumers with higher likelihood of lapsing have higher (expected) average cost per year because the fixed cost is spread over a shorter period. • If the policy lapses after less than a year, part or all of the commission the agent receives is typically refunded to the insurer.

11. Adverse selection in life insurance? • This is discussed from all perspectives in literature. • Advantageous selection may in fact exist in life insurance: Potential insureds who are less risky also tend to be more risk-averse, and thus more likely to purchase coverage. On the other hand, internal mortality studies in life insurance tend to indicate that their insured populations have worse mortality than the general population. How does one from initial advantageous selection to ultimate adverse selection? Through lapses. • Two-part tariff addresses the problem: Consumers who choose to pay the higher up-front fee and lower recurring premiums are signaling their intention to persist.

12. Backdating to “save age” • Policy is backdated so that it is issued at a lower age (the extent depends on whether it is priced based on age last birthday, or age nearest birthday). • Consumer pays for coverage from the backdates policy issue date till now without any opportunity of going back in time and dying before today, and then enjoys lower price in the future. • Carson and Ostaszewski (2004) show that the actuarial present value of backdating is generally positive.

13. Why would backdated policies persist? • Self-selection: Consumers who expect not to lapse are more likely to choose a backdated policy. • Behavioral finance: Sunk cost fallacy (I already paid so much, might as well keep the policy).

14. How do consumers choose to backdate? • Self-selection, but also • Random effect of distance from the date in the past that lowers age at issue.

15. Hard to separate self-selection from sunk-cost fallacy … • Our evidence for sunk cost fallacy requires that we are properly controlling for the differences in premiums. This is difficult. There is no reason to believe adding a linear control is sufficient. To fully account for this, we turned to the machine learning literature for a non-linear model selection technique and use the Lasso technique. Using it, we are able to control for non-linear effects in premiums on lapse rates up to the third polynomial and all possible interactions in all control variables (over 900 variables) while maintaining the linearity in coefficients necessary for our control function identification approach. • The Lasso (least absolute shrinkage and selection operator) is a model selection technique originally developed by Tibshirani (1996) as an improvement on step-wise regression and adapted to Cox hazard models by Tibshirani et al. (1997). The technique is currently popular in the machine learning literature and has recently entered the econometrics literature.

16. Model

17. Results • The initial regression results are congruent with our theoretical predictions. Policy owners who choose to back- date their life insurance contracts (effectively paying a two-part tariff) signal their lower likelihood for lapsing by their willingness to pay for time that already has elapsed that only results in net saving if the policy is held for a relatively long period of time. However, this coefficient does not fully identify the selection effect that we seek. Potentially, consumers who backdate may have no additional knowledge of their propensity for lapsing and are instead exhibiting sunk cost fallacy.

18. Results • To identify these separate effects, we exploit inherent randomness in the time of year, relative to the consumer’s birthday, that the consumer applies for life insurance. This allows us to perform a pseudo-random experiment exploiting variation in the initial tariff consumers have to pay while holding constant the reduction in future premiums. Our instrument is strong and loads in the predicted manner – people who have to pay a higher initial tariff, ceteris paribus, are less likely to choose to backdate.

19. Self-selection or sunk-cost fallacy? • The Lasso procedure indicates that the sunk cost effect of backdating reduces the per-period hazard rate of lapsing by 14.2%.

20. How significant is the lapse reduction? • Backdating reduces lapse rates predominantly in the first several years of the policy, and that the difference in lapse rates between backdated and non-backdated policies converges over time. • Interestingly, backdating may lead to three potentially interacting effects: a shortened period for recovering underwriting and policy issuance expenses, a further time period during which the backdated policies are still profitable, and then a further time period during which some of the remaining policies may become unprofitable for the insurer (if there is some lapse-supported policy feature). Insurers are better off during the first two time periods, and worse off for the policyholders who still remain during the third time period.

21. We have computers now, why are annual mortality table still around? • Our research provides key insight into why insurers do not use continuous (with regards to age) pricing despite the computational ease of doing so – the value of the screening provided by offering the optional two-part tariff outweighs any actuarial downside caused by discreteness in years.

22. Two-part tariff pricing for life insurance • Thus backdating seems to do a lot of things both the insurers and the insureds want. • But backdating is a form of imposed two-part tariff, not necessarily an optimal two-part tariff. • Would you be willing to just pay your life insurance full underwriting costs upfront and have the policy continue more or less “at cost” after that?

23. Some literature (more in the paper) • Carson, J. M. 1994. “Backdating of Life Insurance Contracts: An Examination,” Journal of Insurance Regulation, 13: 185-200. • Carson, J., and K. Ostaszewski, 2004. “The Actuarial Value of Life Insurance Backdating,” Journal of Actuarial Practice, 11: 63-77. • Carson, J., C. Clark, and K. Ostaszewski, 2012, “The Incentives and Welfare Economics of Life Insurance Backdating,” Journal of Insurance Regulation, 31: 91-103. • BabuNahata, Krzysztof Ostaszewski, and P.K. Sahoo, "Direction of price changes in third-degree price discrimination", American Economic Review, 80(1990), pp. 1254-1258.