Abstract
AbstractGuaranteed renewability (GR) is a prominent feature in many health and life insurance markets. We develop a model that includes unpredictable (and unobservable) fluctuations in demand for life insurance as well as changes in risk type (observable) over individuals' lifetimes. The presence of demand type heterogeneity leads to the possibility that optimal GR contracts may have a renewal price that is either above or below the actuarially fair price of the lowest risk type in the population. Individuals whose type turns out to be high risk but low demand renew more of their GR insurance than is efficient due to the attractive renewal price. This results in imperfect insurance against reclassification risk. Although a first‐best efficient contract is not possible in the presence of demand type heterogeneity, the presence of GR contracts nonetheless improves welfare relative to an environment with only spot markets.
Highlights
Guaranteed renewability, which is a prominent feature in health and life insurance markets, provides an opportunity for individuals to insure against reclassification risk
We allow for spot markets in each period as well as guaranteed renewable that can be purchased in the first period
As in Pauly et al (1995) and other previous work, we find that when individuals face only future risk type uncertainty, Guaranteed renewable (GR) may allow individuals to fully insure against reclassification risk and achieve a first best efficient allocation
Summary
Guaranteed renewability, which is a prominent feature in health and life insurance markets, provides an opportunity for individuals to insure against reclassification risk. Individuals have homogeneous preferences in period 1 with their felicity in the life state being u1(·) and that in the death state being v1(·), the latter of which is meant to reflect the insurance purchaser’s perspective on the survivor family’s future utility (including prospects for period 2 and beyond).. Following Hendel and Lizzeri (2003) we assume that individuals cannot commit to long-term contracts They may opt out of their GR contracts and purchase spot insurance (L2ij) at the risk type specific price (πi2 = pi). The fact that Ci2jD > Ci2jN even though the survivor family has fewer individuals can be accounted for by imagining that in a third period (and beyond) the main breadwinner earns income at the beginning of that period which accommodates for higher consumption for the whole family than would be available for the survivor family This can readily be captured by the state contingent felicities v2(·; θj) and u2(·). It seems reasonable to leave these issues aside as explicitly including additional periods would unduly complicate the model
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