John Brandrick and the annuity puzzle

The story of John Brandrick - who's sueing the NHS because he spent his life savings after being misdiagnosed with terminal cancer - highlights a nice economic problem: the annuity puzzle.
In a sense, there are only two economic risks - the risk that we will outlive our wealth (Mr B's fate); or the risk that our wealth will outlive us.
And there is, as Menachem Yaari showed in this classic paper (pdf), a solution: to buy an annuity. This converts your wealth into an income paid as long as you live.
In theory, this would have solved Mr B's problem nicely. He could, in principle, have bought an impaired life annuity which would have paid a huge income on the basis that he would live only a few months. Had he done this, he'd be laughing now.
And this is where the annuity puzzle comes in. Mr B is typical of many people, because demand for voluntary annuities is much weaker than economic theory predicts. Why?
It's not because the average annuity is a bad deal; this paper (pdf) suggests its not - though I suspect Mr B couldn't have gotten as good a rate as his diagnosis would warrant.
Instead, there are several possibilities:
1. Bequest motives. As annuities typically die with us, they leave nothing for our descendants. Many people therefore prefer to keep their wealth.
2. The rainy day factor. If we annuitize all our wealth, we've nothing for emergencies. I suspect this is why Mr B didn't buy an annuity; he regarded all his wealth as emergency cash, to be spent quickly. This is an especially big problem for those with low wealth, who get low annuities.
3. Money illusion. Annuity rates today look worse than they were a few years ago. But this is partly because expected inflation is lower today, so annuitants' income won't be so quickly eroded by rising prices. In failing to see this, some people wrongly regard annuities as a bad deal.
4. Misplaced regret. If you die the day after you've bought an annuity , you'll have got a bad deal. Maybe folks anticipate this, thinking: "if I die, I'll kick myself."
There's much more on annuities in this massive pdf.

Comments

[Chris Williams]

There's another crypto-market in play if he sues: the marginal willingness of doctors to attempt accuracy on the diagnoses that they give to patients and financial institutions will drop precipitously, and we'll all lose out. Thanks a bunch, John.

[jameshigham]

Chris, I can understand a life annuity, especially in these days of extended lifetimes but a fixed period annuity leaves me puzzled. Surely you could invest the money at a better rate?

[dearieme]

If the alternative is your estate paying 40% Inheritance Tax, wouldn't it be wiser to lash out on an annuity and spend the income on loose women and tight strings?

[chris]

James - annuities offer you a higher incomes because folks who die early subsidize them who don't. If you invest for yourself, you don't get this subsidy.
You can, of course, get annuity-style returns in other ways. But all involve extra risk.