Framing-Proof Complete Insurance Markets Under (Narrow) Framing and Loss Aversion

Abstract

Framing effect is one of the behavioral biases, in which economic agents’ decisions are affected by the way the problems are presented. For example, a person may or may not buy annuities depending on whether annuities are described as a risky investment (i.e., risky investment frame) or as a valuable hedging instrument against longevity risk (i.e., insurance frame). This paper revisits the notion of complete markets when consumers are subject to framing effect. It, then, proposes the notion of framing-proof complete markets. The concept of framing-proof completeness is as follows. If consumers’ choices are affected by frames (i.e., the way the choice set is described) and if a choice within a certain frame attains the maximum utility (hereafter, the u-max frame), then markets where u-max frames are provided are better markets. As consumers’ preferences are heterogeneous, the u-max frame differs from person to person. Hence, in order for many consumers to attain the utility maximization, many frames are needed. A framing-proof complete market is defined by the markets where complete set of frames are provided for every choice set.

This paper also provides empirical evidence that the uptake of life insurance is affected by framing effect: loss aversion plays a critical role in the uptake of term-life insurance, which is often framed as a risky investment because it doesn’t pay out anything if an accident doesn’t occur within the pre-specified term. Loss aversion, however, plays little role in the uptake of whole-life insurance, which is often perceived as a safe saving because it guarantees death benefits.

This paper, then, specifies the concept of framing-proof complete insurance market using return-of-premium insurance. It notes that there are two opposite effects of the return of a premium. As the amount of return increases, the insurance policy looks less risky (savings frame increases), hence, consumers are more likely to accept the insurance offer. However, in that case, consumers buy a lower amount of insurance. As a result, a larger amount of future consumption is at risk. These scenarios lead to the idea of optimal savings frame (or optimal ratio of the return of the premium), the frame which maximizes the consumer’s life time utility. Depending on individual’s preference, the optimal savings frame differs. For example, for consumer i, guaranteeing a return of 30% premium (i.e., 30% savings frame) could be the best for him, for consumer j, guaranteeing a return of 50% premium (i.e., 50% savings frame) could be the best for him. Framing-proof complete insurance market is the market where 0-100 percent continuum return-of-premium insurance is provided for every possible state. Hence, for the insurance market to be a framing-proof complete market, contingent claims should be provided completely not only in the dimension of states, but also in the dimension of frames.

Keywords: Narrow framing, Loss Aversion, Term-life insurance, Whole-life insurance, Complete market

JEL Classification: D03, D81, G22