Academic journal article Journal of Risk and Insurance

Life Insurance Demand under Health Shock Risk

Academic journal article Journal of Risk and Insurance

Life Insurance Demand under Health Shock Risk

Article excerpt


For most households, labor income is the essential source to finance lifetime consumption. Therefore, a potential income loss following an early death of the wage earner is a crucial risk. Consequently, a life insurance is of special importance to hedge future consumption of the remaining family members. Following Richard (1975), most studies simplify the insurance decision by including an instantaneous term insurance contract. However, in practice buying life insurance usually involves a long-term commitment and later changes are costly. Furthermore, health checks prevent agents from contracting an insurance if they already have a critical illness. As a benchmark scenario, we thus study a life-cycle problem where a family has access to long-term life insurance that can only be bought or sold at realistic lump-sum costs. (1) In a second step, we demonstrate that our results also hold if we add annuities or short-term life insurance contracts.

Our model involves several relevant features: the family receives unspanned labor income earned by the head of the household and faces short-sale constraints that bind its stock demand, especially at young ages. Furthermore, the wage earner faces the risk of suffering from a health shock that we interpret as critical illness. After such a health shock the family has no access to the insurance market any more, that is, cannot buy new insurance or change/extend existing contracts. Additionally, the wage earner's probability of dying increases significantly. We calibrate the health shock and mortality process to cancer and mortality data.

The combination of these features (long-term insurance contracts, transaction costs, unspanned labor income, short-sale constraints, health shocks) distinguishes our model from the related literature discussed in the "Related Literature" section. This combination generates interesting qualitative effects that are important for the optimal decisions of the family over the life cycle: the long-term nature of the insurance contract amplifies the effect of negative labor income shocks, since in the undesired case of a negative labor income shock a premature termination of the contract or a reduction of the insurance sum leads to additional losses. In an already bad state, the family might be worse off due to the stickiness of the insurance contract. Therefore, families with higher income uncertainty have significantly lower insurance demands.

Most importantly, we find that younger families (head of household less than 30 years old) optimally stay away from long-term life insurance markets. Therefore, an unexpected death in younger years can lead to severe problems for the family. Our findings significantly differ from the results in frameworks that model life insurance decisions via an instantaneous contract instead of a long-term contract as in the benchmark case of our article. In these frameworks, the theoretically optimal participation rates are typically higher. We address this point by also considering a situation where families have access to short-term life insurance contracts as well (see the "Extending the Insurance Market" section). In this case, families buy short-term contracts at young ages. However, the demand for long-term contracts is essentially unaffected, which shows the robustness of our benchmark results. Consequently, young families leave the risk uninsured that the head of the household suffers from a health shock so that the short-term contract cannot be extended.

Furthermore, we find that it is optimal for families to increase long-term insurance protection over the life cycle. This is because the long-term contract design becomes less relevant as agents get older, since the contract duration and the uncertainty about human wealth goes down. Therefore, if an older wage earner suddenly dies, the accumulated financial wealth and existing insurance contracts ensure that surviving family members can maintain their standard of living, although consumption growth must be reduced. …

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