Academic journal article Journal of Risk and Insurance

Uncertain Bequest Needs and Long-Term Insurance Contracts

Academic journal article Journal of Risk and Insurance

Uncertain Bequest Needs and Long-Term Insurance Contracts

Article excerpt


People 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.

In the life insurance market, most contracts extend many years into the future. Such prevalence of long-term contracts is largely explained in the literature as a way to protect against the "insurability risk." More specifically, a person's health status may deteriorate with consequences on the affordability of short-term life insurance in the future. In the extreme, one's health could deteriorate to such an extent that life insurance is unavailable. A long-term insurance contract with a front-loaded premium schedule can provide insurance against this reclassification or renewability risk. (1)

Although it may be advantageous from an insurability standpoint to arrange for life insurance early, the need for life insurance many years later depends on the future demographic structure of the household, as well as the financial condition of family members and their preferences, and may not be known in advance (see Lewis, 1989). Absent any insurability risk, it would therefore appear to be optimal to purchase life insurance contracts later in life, when bequest needs are better known. Another possibility is to purchase short-term contracts and to adjust the insurance level as needed at a later date.

In this article, we show that a short-term purchasing strategy for life insurance is not optimal, even without the insurability risk. Intuitively, although delaying the purchase of life insurance can help individuals to determine the appropriate level of insurance, in concordance with their known bequest demand, one must still pay the extra insurance premium if one's demand turns out to be high. That is, one must plan for the possibility of needing to spend more on insurance premia in the future. Note that this form of "premium risk" has nothing to do with the insurability risk. Here the risk is on the budget required to finance the required amount of life insurance, not on whether or not the premium rate is higher.

We consider the design of a long-term life insurance contract that can help to partially insure the risk of possibly having a high bequest need in the future. Our model setup is similar to that of Polborn, Hoy, and Sadanand (2006), except that we first analyze a situation without insurability risk. When there is only a risk of demand type, the insurance premium per unit of coverage should not change for short-term contracts. Hence, one can always buy more life insurance later at the same price. Polborn, Hoy, and Sadanand (2006) also mention this case of pure demand type risk, but conclude that there is no benefit to purchasing insurance earlier. The conclusion follows from their requirement of zero-profit insurance pricing within each period.

However, long-term contracts are not subject to this constraint; that is, the zero-profit condition can be implemented over the duration of the contract rather than within each time period. As a result, long-term contracts can allow individuals to partially hedge their future preference risk by effectively transferring some wealth from future states where their bequest needs are low to states for which bequest needs are higher. Although some family changes are observable, such as a change in the number of children, others are not. Our focus in this article is this type of unverifiable shift in bequest demand. When bequest needs are not verifiable, the contract cannot just pay a transfer to anyone who claims to have high bequests needs. …

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