Occasional reflections on Life, the World, and Mathematics

The annuity puzzle


Stanford biodemographer Shripad Tuljapurkar has written a very thoughtful post about the “annuity puzzle”: Why do people generally not choose to purchase annuities that would seem to protect them from a major risk: Being feeble and impoverished 30 or 40 years after retirement? His explanation, which is surely right as far as it goes, is that the shunning of annuities is a rational response to the compensating default risk from the insurance company. You have to live quite a long time to make your nut on an annuity. The “risk” — the probability of living that long — is low, and (he argues, persuasively) one could reasonably conclude that it is outweighed by the likelihood of a financial crash in the interim.

From a behavioural economics perspective, this matches closely one of the standard explanations for discounting: Future returns are drastically uncertain, so we develop the habit of preferring immediate gratification. So this falls in the category of attempts to explain seemingly irrational economic behaviour by showing that it is in fact rational when you take into account limited information or costs of acquiring or analysing information. Of course, any economic theory inevitably struggles to deal with questions of insurance and annuities, where the risk involves the life of the economic agent. The celebrated analysis of this problem by Jack Benny is still relevant.

But while this is a cogent argument for why people shouldn’t buy annuities, I’m skeptical of it as an explanation for why they don’t buy annuities. First, the annuity puzzle is a phenomenon of average people, not savvy investors. I doubt that most people think much about the risk of established financial companies defaulting. One prominent study (based on surveys conducted in 2004) found that 59% of Americans would trade half of their Social Security annuity for an actuarially fair lump sum payment. I’m pretty sure that they are not thinking that they can find a safer investment, with less risk of default, than Social Security.

Second, annuities’ disfavour is not really an isolated phenomenon. We find economists similarly puzzled with regard to index insurance. Economists like Shiller have promoted financial products based on house-price indices, to allow ordinary people to hedge the huge investment they have in their homes. They have found little demand from the general public. Similarly, agricultural index insurance to protect poor farmers from weather shocks have found little support. As Daniel Clarke has shown, a risk-averse individual could reasonably have a preference for zero index insurance.

What is the connection between index insurance and annuities? Classical indemnity insurance reduces risk by lowering the best case (you pay the premium, the house doesn’t burn down) but raising the worst case (paying out more than the premium when the house does burn down). Index insurance, on the other hand, will reduce risk on average, but in the worst case your own crop fails for very local reasons, you pay the premium, but get no relief because the overall harvest in your region was good.

Tuljapurkar’s argument could be put into this context: You could wind up living to 110, paying the cost of the annuity, and still be impoverished because the insurance company bet all the money on currency fluctuations in Kazakhstan. But the risk tradeoff is really more stark than that. The worst case is, you die young and you lose money on the annuity, and that is the most likely outcome. On the other hand, if you’re thinking you will live to 110, well, that sounds great. You might be inclined to skip lightly in your mind over the conditions, financial or medical.

Some other tendencies that might push individuals into this implicit analysis: The bad outcome of buying the annuity is sooner than the bad outcome of not buying the annuity, presumably leading to the latter being discounted relative to the former; there is evidence that personal discount rates increase with subjective approach of mortality. There is also some evidence that risk aversion increases with age after age 65; thus, biases promoted by risk aversion may be exacerbated when the decision involves putting oneself in the position of a very elderly future self.

The annuity puzzle has political implications for the UK, where one of the less-discussed pillars of the Tory electoral strategy — in addition to the twin threats of the barbarians of the north and south, and Ed Miliband’s suspiciously unassimilated eating habits — is direct economic transfer from the young to the old. Thus, child benefit is cut while pensioners keep access to special investment opportunities. The key Conservative priority of withdrawal from the EU would restrict job opportunities for young Britons, one reason why it is decisively popular in the 60+ age group, and has little support among among the under 40s. (I’ve written about this generational warfare more generally here.) One of the more dubious gifts that they rolled out just ahead of the election is the right of workers with private defined-contribution plans to pull out their entire pension pot at age 55 with no tax penalty, rather than be required to convert 75% into an annuity. The pensions minister said last year

If people do get a Lamborghini, and end up on the state pension, the state is much less concerned about that, and that is their choice.

In recognising this as a gift to the older population (one that will, purely coincidentally, bring a temporary boost to tax receipts), they are appealing to the unpopularity of annuities. Thus, the Chancellor of the Exchequer defended the policy by saying “returns from annuities have been much lower over the last 15 years or so,” as though millions of individual pensioners would be able to individually work out plans to preserve their income over their remaining 30 or 40 years with higher returns.

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