The Welfare Effects of Long-Term Health Insurance Contracts

Abstract

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Long-Term Health Insurance: Theory Meets Evidence

“…We start by formalizing the calculation of GLTHI premiums over the lifecycle. Then we compare them to the lifecycle premium profile of the optimal dynamic contract as derived by Ghili et al (2019) (GHHW). Let P t (ξ t ) be the premium offered when signing a GLTHI contract in period t. P t (ξ t ) depends on the individual's health risk in year t, ξ t , as GLTHI contracts are individually underwritten at inception (see Section 2).…”

“…In contrast, Ghili et al (2019) study the optimal dynamic health insurance contract that maximizes consumer welfare, subject to break-even, no lapsation, and no borrowing constraints, in an environment where individuals have time-separable and risk averse preferences subject to stochastic health expenditure shocks. Ghili et al (2019) show that the optimal dynamic insurance contract provides a consumption guaranteec t (ξ t , y T t ) that is a function of enrollees' current health risk as well as the vector of current and future income y T t ≡ {y t , y t+1 , ....y T }. The optimal dynamic insurance contract establishes that the individual will start consumingc 1 (ξ 1 , y T 1 ).…”

“…After an initial risk-rating, the policies are guaranteed renewable until death (without an expiration date or enrollment period) and future premium changes have to be community rated; that is, premium changes over the lifecycle are independent of changes in the policyholder's health status. 1 The simple design of the German long-term health insurance contract (henceforth GLTHI) differs substantially from the welfare-maximizing contract derived by Ghili et al (2019) (henceforth GHHW). The German contract foresees the payment of constant real premiums over the lifecycle, regardless of the evolution of an individual's income and health status.…”

“…Similarly, Cochrane (1995) proposes a scheme of severance payments, made after the realization of health shocks, which provides full insurance against reclassification risks. Hendel and Lizzeri (2003) and Ghili et al (2019) show that the optimal contract only partially insures reclassification risk, because fully eliminating reclassification risks requires large frontloaded payments, preventing consumption smoothing over the lifecycle. These results are mostly theoretical, and the proposed contracts typically have complex designs that have high informational requirements to implement.…”

“…The rest of the paper is organized as follows. In Section 2, we provide the institutional details of the GLTHI market; in Section 3, we derive the theoretical life-cycle premiums under the GLTHI framework and contrasts them with the premiums of the optimal contract as derived in Ghili et al (2019); in Section 4, we describe our data sets and provide summary statistics; in Section 5, we model the health risk and income dynamics over the lifecycle. In Section 6, we make use of the theoretical and the empirical inputs to simulate the economy quantify various welfare under different contracts, and present implications of our findings on the U.S. health reform; in Section 7, we discuss the robustness of our main results to different values of risk aversion, and to Epstein and Zin (1989)'s recursive preferences; finally, in Section 8, we conclude.…”