Making sense of insurance
Posted April 7, 2008on:
I recently mentioned that prospect theory tells us that most people are risk seeking in losses. CPW commented that this seems to be at odds with the fact that people buy insurance. After all, if people like risky losses, why would they pay money to avoid them by purchasing insurance? According to John Nyman the answer lies in a straightforward reframing of the choice consumers face when they buy insurance.
Rather than thinking of insurance as a choice between a certain loss and an uncertain loss, think of it as a choice between two contracts, each containing uncertainty. Suppose that full insurance against a loss of $1,000 costs $100:
- If you don’t buy insurance then you have $100 extra to spend on stuff relative to the uninsured case. Note that there is uncertainty in this outcome because you still might lose $1.000.
- If you do buy insurance then you pay $40 in order to receive $1,000 if loss occurs. Again, there is uncertainty because you may or may not receive the $1,000.
In each case the probability of a loss and the amount lost can be treated as exogenous and constant. This reframing of the problem as a choice between two expected utilities avoids the problem of risk seeking behaviour by changing the frame of reference of the problem. Insurance can still be attractive within the framework of prospect theory if it is thought of in this way.
The obvious objection is that Nyman is solving the problem by arbitrarily changing the reference point from the status quo to the situation where loss has occurred. It seems like a semantic distinction that gets around the problem by using clever wording rather than providing any insight. Nyman has two, rather convincing, answers: first, there is no reason to prefer the conventional loss formulation when it’s based on a demonstrably incorrect idea about how people make choices across uncertain outcomes.
Secondly, and most importantly, he examines survey evidence of insurance choices and concludes that insurance gambles only become attractive to people when they’re phrased in terms of gains rather than losses. So, while it may appear a semantic distinction, humans do respond strongly to the way choices are framed. Changing the framing of the problem may seem mathematically irrelevant, but it is hugely important to the actual decisions people make. Reframing the insurance decision allows us to understand it in a fashion consistent with the best available empirical evidence on consumer choice.