Household Life Insurance Demand

Abstract

What types of households own life insurance? Who owns term life and who owns whole life insurance? These are questions of great interest to insurers that operate in a highly competitive market. To answer these questions, we jointly examine household demand of two types of insurance, term and whole life, using data from the Survey of Consumer Finances, a probability sample of the U.S. population. We model both the frequency and the severity of demand for insurance, building on the work of Lin and Grace by using explanatory variables that they developed. For the frequency portion, the household decisions about whether to own term and whole life insurance are modeled simultaneously with a bivariate probit regression model. Given ownership of life insurance by a household, the amounts of insurance are analyzed using generalized linear models with a normal copula. The copula permits the bivariate modeling of insurance amounts for households who own both term and whole life insurance, about 20% of our sample. These models allow analysts to predict who owns life insurance and how much they own, an important input to the marketing process.

Moreover, our findings suggest that household demand for term and whole life insurance is jointly determined. After controlling for explanatory variables, there exists a negative relationship for a household’s decision to own both whole and term life insurance (the frequency part) and a positive relationship for the amount of insurance purchased (the severity part). This indicates that the greater the probability of holding one type, the smaller the probability of holding the other type of life insurance. However, higher demand for both types of insurance exists when a household decides to own both. This mixed effect extends prior work that established a negative relationship, suggesting that term life insurance and whole life insurance are substitutes for one another. In contrast, our findings reveal that the ownership decision involves substitution, but, for households owning both types of insurance, amounts are positively related. Therefore, term and whole life insurance are substitutes in the frequency yet complements in the severity.     

Commitment and Lapse Behavior in Long‐Term Insurance: A Case Study

This article presents a case study of a portfolio of individual long‐term insurance contracts sold by a Spanish mutual company. We describe the risk levels, the rating structure, and the implied cross‐subsidies on a portfolio of policies providing health, life, and long‐term care insurance. We show evidence of reclassification risk through the history of disability spells. We also analyze the lapse behavior and seek to provide a rationale for the portfolio’s dynamics. We discuss the lack of commitment from the policyholders (lapses) and from the mutual company (which took a run‐off decision). Finally, we draw conclusions regarding the design of such contracts.     

Health and Mortality Delta: Assessing the Welfare Cost of Household Insurance Choice

We develop a pair of risk measures, health and mortality delta, for the universe of life and health insurance products. A life‐cycle model of insurance choice simplifies to replicating the optimal health and mortality delta through a portfolio of insurance products. We estimate the model to explain the observed variation in health and mortality delta implied by the ownership of life insurance, annuities including private pensions, and long‐term care insurance in the Health and Retirement Study. For the median household aged 51 to 57, the lifetime welfare cost of market incompleteness and suboptimal choice is 3.2% of total wealth.     

Generalized Life Insurance: Ruin Probabilities

We study ruin probabilities for generalized life insurance programs. These programs include among others whole life and long term care contracts. Clearly, in such programs the claims in successive years are dependent, hence the structure of our problem is different from that of ruin probabilities in general insurance where claims over time are independent. First, we develop algorithms calculating the ruin probabilities for life and LTC insurance programs. Further, upper and lower bounds for these probabilities are derived. These new bounds take into account the joint distribution of claims over time.     

Adverse Selection in Term Life Insurance Purchasing due to the BRCA1/2 Genetic Test and Elastic Demand

Consumer groups fear that the use of genetic testing information in insurance underwriting might lead to the creation of an underclass of individuals who cannot obtain insurance; thus, these groups want to ban insurance companies from accessing genetic test results. Insurers contend that such a ban might lead to adverse selection that could threaten their financial solvency. To investigate the potential effect of adverse selection in a term life insurance market, a discrete‐time, discrete‐state, Markov chain is used to track the evolution of twelve closed cohorts of women, differentiated by family history of breast and ovarian cancer and age at issue of a 20‐year annually renewable term life insurance policy. The insurance demand behavior of these women is tracked, incorporating elastic demand for insurance. During the 20‐year period, women may get tested for BRCA1/2 mutations. Each year, the insurer calculates the expected premiums and expected future benefit payouts which determine the following year's premium schedule. At the end of each policy year, women can change their life insurance benefit, influenced by their testing status and premium changes. Adverse selection could result from (i) differentiated benefits following test results; (ii) differentiated lapse rates according to test results; and (iii) differentiated reactions to price increases. It is concluded that with realistic estimates of behavioral parameters, adverse selection could be a manageable problem for insurers.     

经济周期视野下的中国寿险业发展态势探析

运用宏观经济学的研究方法,从经济周期视野对我国寿险业的发展态势进行了探讨。首先,对寿险业发展的宏观脉络进行了分析,认为寿险业的产品特征具有较强的亲周期性,通过HP滤波进行趋势周期分解后证实寿险业的周期性波动幅度比产险业显著。其次,对寿险业发展的当前态势进行了分析,维持了寿险业长期趋势向好的总体判断,但认为经济周期对寿险业的负面冲击效应较大,短期内寿险业难以恢复高增长态势。最后,对寿险业的发展提出了若干政策建议,认为准确定位、改善监管和优化环境是促进寿险业可持续发展的当务之急。     

Household Life Cycle Protection: Life Insurance Holdings, Financial Vulnerability, and Portfolio Implications

Using the Survey of Consumer Finances, we examine the life cycle demand for different types of life insurance. Specifically, we test for the consumer's aversion to income volatility resulting from the death of a household's wage‐earner through the purchase of life insurance. We first develop a financial vulnerability index to control for the risk to the household. We then examine the life cycle demand for life insurance using several definitions of life insurance. We find, in contrast to previous research, that there is a relationship between financial vulnerability and the amount of term life or total life insurance purchased. In addition, we find older consumers use less life insurance to protect a certain level of financial vulnerability than younger consumers. Secondly, our study provides evidence that life insurance demand is jointly determined as part of a household's portfolio. Finally, we consider the impact of family members' nonmonetary contribution on the household's life cycle protection decision. Our results provide some evidence that households take into account the value of nonmonetary contribution in their insurance purchase.     

Can the Life Insurance Market Provide Evidence for a Bequest Motive?

Using U.K. microeconomic data, we analyze the empirical determinants of participation in the life insurance market. We find that term insurance demand is positively correlated with measures of bequest motives like being married, having children, and/or subjective measures of strong bequest motives. We then show that a life‐cycle model of life insurance demand, saving, and portfolio choice can rationalize quantitatively the data in the presence of a bequest motive. These findings provide evidence supporting the presence of a bequest motive.     

FALLACY OF NONLIFE SAVINGS FROM INVESTED DIFFERENCE

Abstract: Usually nonlife savings with term life produce better investment results compared to the cash value in whole life insurance. This paper addressed a potential problem of the former that its balance may decrease during the later years, if the rate of return is relatively low. To fully reveal this declining property to the investors, it is recommended that the investment performance of nonlife savings be disclosed over a 50–year period at 5 and 8 percent returns. Further discussions are delivered regarding similarities and differences between nonlife savings and the cash values under universal and variable life insurance.     

中国寿险市场存在逆向选择吗?——来自CHARLS数据的经验证据

我国寿险市场是否存在逆向选择问题,在理论和实证两个方面缺乏细致的讨论。本文利用CHARLS数据和正相关理论检验了我国定期寿险和终身寿险市场中的逆向选择问题。我们选取了死亡率这一远期指标和健康状况这一近期指标来衡量消费者的死亡风险,从广延边际和集约边际两个方面利用正相关理论进行了深入的研究。实证结论表明,以死亡率和健康状况衡量的死亡风险与寿险消费负相关或者不相关,即我国寿险市场并不存在逆向选择问题。然后,我们讨论了模型的内生性问题,并根据年龄变量检验了结论的稳健性,实证结果表明我们的结论是稳健的。最后,本文利用双变量Probit模型设计了一个机制,并利用该机制验证了利他动机是我国寿险市场不存在逆向选择的原因之一。     

中国寿险市场存在逆向选择吗?——来自CHARLS数据的经验证据

我国寿险市场是否存在逆向选择问题,在理论和实证两个方面缺乏细致的讨论。本文利用CHARLS数据和正相关理论检验了我国定期寿险和终身寿险市场中的逆向选择问题。我们选取了死亡率这一远期指标和健康状况这一近期指标来衡量消费者的死亡风险,从广延边际和集约边际两个方面利用正相关理论进行了深入的研究。实证结论表明,以死亡率和健康状况衡量的死亡风险与寿险消费负相关或者不相关,即我国寿险市场并不存在逆向选择问题。然后,我们讨论了模型的内生性问题,并根据年龄变量检验了结论的稳健性,实证结果表明我们的结论是稳健的。最后,本文利用双变量Probit模型设计了一个机制,并利用该机制验证了利他动机是我国寿险市场不存在逆向选择的原因之一。     

Risk assessment of surplus appropriation schemes in participating life insurance

The aim of this paper is to analyze a life insurance company’s risk exposure with respect to different surplus appropriation schemes in participating life insurance. In this regard, three surplus appropriation schemes are considered, including the bonus system, the interest-bearing accumulation, and the system of shortening the contract term. We further examine an insurance company that offers all three schemes, i.e. each system is used for one third of the policyholders. Focus is laid on the effect of different asset portfolios and shocks to mortality on the insurer’s risk situation with respect to the policyholder’s age level at contract inception.     

German bond markets and US monetary policy

Low interest rates have been a major problem for the European life insurance industry. The implementation of Solvency II certainly has forced European life insurers to improve their risk management procedures and to buy long term bonds in order to handle the interest rate risk inherent to their liabilities. As a consequence, the industry meanwhile more or less seems to be able to cope with the problem of low interest rates. However, now the US central bank has started to hike rates. The Bank of Canada meanwhile has followed its southern neighbor. The changed monetary policy environment in North America might create new challenges for asset managers in the European life insurance industry. This paper provides some additional thoughts and empirical evidence about the linkages between US monetary policy and the European bond market employing techniques of time series analysis.     

Fair valuation of cliquet-style return guarantees in (homogeneous and) heterogeneous life insurance portfolios

Participating life insurance contracts allow the policyholder to participate in the annual return of a reference portfolio. Additionally, they are often equipped with an annual (cliquet-style) return guarantee. The current low interest rate environment has again refreshed the discussion on risk management and fair valuation of such embedded options. While this problem is typically discussed from the viewpoint of a single contract or a homogeneous* insurance portfolio, contracts are, in practice, managed within a heterogeneous insurance portfolio. Their valuation must then – unlike the case of asset portfolios – take account of portfolio effects: Their premiums are invested in the same reference portfolio; the contracts interact by a joint reserve, individual surrender options and joint default risk of the policy sponsor. Here, we discuss the impact of portfolio effects on the fair valuation of insurance contracts jointly managed in (homogeneous and) heterogeneous life insurance portfolios. First, in a rather general setting, including stochastic interest rates, we consider the case that otherwise homogeneous contracts interact due to the default risk of the policy sponsor. Second, and more importantly, we then also consider the case when policies are allowed to differ in further aspects like the guaranteed rate or time to maturity. We also provide an extensive numerical example for further analysis.     

Optimal life insurance with no-borrowing constraints: duality approach and example

We solve an optimal portfolio choice problem under a no-borrowing assumption. A duality approach is applied to study a family’s optimal consumption, optimal portfolio choice, and optimal life insurance purchase when the family receives labor income that may be terminated due to the wage earner’s premature death or retirement. We establish the existence of an optimal solution to the optimization problem theoretically by the duality approach and we provide an explicitly solved example with numerical illustration. Our results illustrate that the no-borrowing constraints do not always impact the family’s optimal decisions on consumption, portfolio choice, and life insurance. When the constraints are binding, there must exist a wealth depletion time (WDT) prior to the retirement date, and the constraints indeed reduce the optimal consumption and the life insurance purchase at the beginning of time. However, the optimal consumption under the constraints will become larger than that without the constraints at some time later than the WDT.     

VEBAs--ordinary and necessary expenses--deductions and constructive dividends. Neonatology Associates, P.A. v. Commissioner of Internal Revenue

Contributions made by professional medical corporations into voluntary employee benefit program plans (VEBAs), which were well in excess of the cost of the term life insurance provided to the participants, were not ordinary and necessary business expenses, and the distributions of surplus cash to owner physicians upon conversion to individual policies constituted constructive dividends taxable to the individual taxpayers.     

How does the insurer's mobile application sales strategy perform?

While the impact of an Internet-based sales strategy on sales performance has been well studied, there is little academic research that examines the impact of a mobile application (MA) sales strategy on the sales performance of insurers. Using a unique data set for term life insurance policies from a Chinese life insurer, we study the impact of implementing this strategy on insurance purchases. We find a significant growth in the insurance purchase quantity and somewhat lower growth in premiums received from new policies. This paper determines that this is due to improved channel accessibility and the cost reduction of the MA channel. Although sales of traditional distribution channels are cannibalized in the short term by the MA distribution strategy, this substitution effect does not persist in the long run. In addition, we find that this strategy reduces impulsive purchases.     

Portfolio Choice and Life Insurance: The CRRA Case

We solve a portfolio choice problem that includes life insurance and labor income under constant relative risk aversion (CRRA) preferences. We focus on the correlation between the dynamics of human capital and financial capital and model the utility of the family as opposed to separating consumption and bequest. We simplify the underlying Hamilton–Jacobi–Bellman equation using a similarity reduction technique that leads to an efficient numerical solution. Households for whom shocks to human capital are negatively correlated with shocks to financial capital should own more life insurance with greater equity/stock exposure. Life insurance hedges human capital and is insensitive to the family's risk aversion, consistent with practitioner guidance.     

城镇企业养老保险个人账户给付期测算研究——基于预期寿命的视角

养老保险个人账户给付期的科学设计是养老保险个人账户制度持续、稳定运行的关键.本文从预期寿命的角度构建了城镇企业职工养老保险个人账户给付期的测算模型,并从分性别和分地区预期寿命角度对养老保险个人账户给付期进行了测算,测算表明我国法定养老保险个人账户给付期设计与预期寿命变化不协调,并导致个人账户超支月数越来越大.可通过适当延长养老保险个人账户给付期、推迟退休年龄提高我国养老保险个人账户制度的运行效率.     

The Impact of Disability Insurance on a Portfolio of Life Insurances

The aim of this article is to study the impact of disability insurance on an insurer's risk situation for a portfolio that also consists of annuity and term life contracts. We provide a model framework using discrete time nonhomogeneous bivariate Markov renewal processes and in a simulation study focus on diversification benefits as well as potential natural hedging effects (risk-minimizing or risk-immunizing portfolio compositions) that may arise within the portfolio because of the different types of biometric risks. Our analyses emphasize that disability insurances are a less efficient tool to hedge shocks to mortality and that their high sensitivity toward shocks to disability risks cannot be easily counterbalanced by other life insurance products. However, the addition of disability insurance can still considerably lower the overall company risk.