Uncertain Bequest Needs and Long‐Term Insurance Contracts

Abstract

We examine how long-term life insurance contracts can be designed to incorporate uncertain future bequest needs. An individual who buys a life insurance contract early in life is often uncertain about the future financial needs of his or her family, in the event of an untimely death. Ideally, the individual would like to insure the risk of having high future bequest needs, but since bequest motives are typically unverifiable, a contract directly insuring these needs is not feasible. We derive a long-term life insurance contract that is incentive compatible and achieves a higher welfare level than the naïve strategy of delaying the purchase of insurance until after one's bequest needs are known. We also examine the welfare effects of our contract and we show how third-party financial products, although beneficial to the individual in the short run, can be detrimental to one's ex ante utility. IntroductionPeople purchase life insurance to protect their dependents against financial losses caused by their deaths. Bernheim (1991) shows that there is a demand by breadwinners to hold part of their assets in a solely bequeathable form, as opposed to a form that could also be used for current consumption if one is alive. A similar result falls out of intertemporal equilibrium models, such as Farhi and Werning (2007), who show how it is desirable in an overlapping-generations context for parents to insure their children against the financial risks of their family.

Guaranteed renewable life insurance under demand uncertainty

“…We demonstrate through the use of simulations that, as in Fei et al (2013), GR insurance can be effective in smoothing consumption across demand types and so can improve welfare even if there is no reclassification risk (i.e., individuals are of homogeneous risk type). The source of the welfare improvement is that first‐period purchases of GR with favorable (“subsidized”) renewal terms allows for shifting second‐period death state consumption toward those with higher marginal utility of consumption (i.e., toward high‐demand types).…”

“…However, as noted above, in the presence of both demand and risk type it may be that the optimal GR contact involves a renewal price above the actuarially fair price for low‐risk types who allow their policies to lapse and purchase their second‐period insurance needs from the spot market. In this scenario, which is not considered in Fei et al (2013), high‐demand types who are also low‐risk types are excluded from the benefits of the “subsidy.” Although Polborn et al (2006) consider a two‐period model with both demand and risk type uncertainty, they do not model insurance needs in the first period. Therefore, as with Fei et al (2013), they do not capture the importance of the interaction of these characteristics with the possibility of increasing demand over time which creates an additional obstacle for GR or long‐term insurance to improve welfare.…”

Guaranteed Renewable Life Insurance Under Demand Uncertainty

“…We demonstrate through the use of simulations that, as in Fei et al (2013), GR insurance can be effective in smoothing consumption across demand types and so can improve welfare even if there is no reclassification risk (i.e., individuals are of homogeneous risk type). The source of the welfare improvement is that first-period purchases of GR with favorable ("subsidized") renewal terms allows for shifting second-period death state consumption toward those with higher marginal utility of consumption (i.e., toward high-demand types).…”

“…However, as noted above, in the presence of both demand and risk type it may be that the optimal GR contact involves a renewal price above the actuarially fair price for low-risk types who allow their policies to lapse and purchase their second-period insurance needs from the spot market. In this scenario, which is not considered in Fei et al (2013), high-demand types who are also low-risk types are excluded from the benefits of the "subsidy." Although Polborn et al (2006) consider a two-period model with both demand and risk type uncertainty, they do not model insurance needs in the first period.…”

“…In a similar environment but without differential demand types, Peter, Richter, and Steinorth (2015) consider the implications of individuals learning imperfectly about their risk type over time with this information being private. Fei, Fluet, and Schlesinger (2013) also use a model that features demand uncertainty but that does not include risk type uncertainty nor any dynamic features of insurance demand present in our model of GR insurance.…”