Under-Annuitization
The annuity puzzle is the empirical fact that retirees almost never annuitize their wealth, even though Yaari (1965) showed that under standard assumptions a rational agent should annuitize of her wealth at retirement. An annuity converts a lump sum of wealth into a series of guaranteed periodic payments that continue until death, hedging the mortality risk of outliving one’s assets. The Yaari result is one of the most extreme predictions in microeconomics: in a frictionless world with actuarially fair annuities and no bequest motive, full annuitization strictly dominates any strategy that holds non-annuitized wealth into retirement, because the surviving annuitants effectively earn the “mortality credit” — the share of premium pool returned to those still alive — which exceeds any safe-asset return.
Empirically. Voluntary annuitization rates in the U.S. are below of retirees, and even among those with substantial defined-contribution wealth, the figure barely changes. The U.K., where annuitization was once mandatory for personal-pension wealth, shifted to voluntary in and saw demand collapse. Across countries and across product variants, the same picture holds: when households are not forced or strongly nudged into annuities, they reject them.
Rational explanations include bequest motives (households want to leave wealth to heirs), high actuarially-unfair loads (insurance company markups, – in many markets), correlated medical expenditure risk (the household may need a lump sum to pay for end-of-life care), and Social Security crowd-out (the U.S. household already has a substantial real annuity through Social Security and may not want more). These are real but quantitatively cannot explain rejection rates above .
Behavioral explanations include framing effects (annuities are presented as a gamble — “you might die early and lose” — rather than as insurance against living too long), loss aversion combined with the mental accounting of converting a large visible lump sum into a sequence of small payments, mental accounting separating “wealth I see” from “wealth I receive,” ambiguity aversion about the insurance company’s solvency, and complexity aversion. Brown, Kling, Mullainathan & Wrobel (2008) show experimentally that the same product framed as “consumption insurance” is much more popular than the same product framed as “investment with mortality risk” — clear evidence that framing dominates rational comparison.
Intuition
A retiree with $ at age faces an open-ended planning problem: she does not know how long she will live. If she spends as if she will live to but lives to , she spends her last decade in poverty. If she spends as if she will live to but dies at , she leaves $ on the table that could have funded a more comfortable retirement. The mathematically clean solution is to convert the wealth into a lifetime annuity that pays the right amount each year, contingent on still being alive. The annuity provider pools mortality risk across thousands of clients, so the survivors receive higher payments than they could earn in any individual asset — this is the “mortality credit,” typically worth – percentage points of effective return on top of the underlying portfolio return.
Real retirees do not see it this way. They look at the annuity contract and think: “I am giving the insurance company $, and if I die next year they keep it.” The framing is one of gambling — the household perceives itself as betting against its own longevity — rather than insurance against the risk of living too long. The same household happily buys homeowners insurance, where the same logic (“I pay the premium and if my house doesn’t burn down I get nothing back”) feels like prudent protection. The asymmetry comes from the fact that homeowners insurance protects against a vivid, scary outcome (your house burns down), while annuities protect against an outcome that does not feel scary in the present (living a long time). Loss aversion attaches to the visible lump sum the household is “losing” by buying the annuity, not to the much larger expected loss the household is avoiding through the annuity.
Properties
(Yaari Benchmark) Full annuitization is optimal in the standard model.
Yaari (1965) considers a retiree with no bequest motive, additive lifetime utility, and access to actuarially fair annuities. He proves that any non-annuitized portfolio is strictly dominated by full annuitization. The intuition: annuitizing trades the unrealized return on wealth that survives to a state in which the annuitant is dead (where the marginal utility of consumption is zero) for higher payments in states where she is alive (where marginal utility is positive). The exchange has no rational downside in the absence of a bequest motive. Davidoff, Brown & Diamond (2005) show that even with realistic departures (incomplete markets, bequest motives, fee loads up to about ), at least partial annuitization remains optimal for the vast majority of households — yet voluntary annuitization rates remain near zero.
(Mortality Credit) Annuitants earn an extra – effective return.
Because annuity payments to survivors are funded partly by the wealth of pool members who have died, surviving annuitants effectively earn the underlying portfolio return plus the mortality credit — the dollar amount transferred from non-survivors. At age the credit is about per year of effective return; by age it has grown to roughly per year. The mortality credit is the central reason annuities offer a risk-return profile that no individual asset can match. A household that rejects annuities is therefore not just rejecting a hedge — it is rejecting a return premium that grows with age.
(Voluntary Take-Up Below 5%) The puzzle is enormous in magnitude.
In the U.S., voluntary annuitization rates among retirees with at least $ in retirement assets are below . Among those with employer-sponsored defined-benefit pensions (which are themselves annuities), most retirees who are offered a lump-sum buyout take the lump sum — converting an existing annuity into non-annuitized wealth, exactly the wrong direction under Yaari. The U.K., where annuitization was historically mandatory for personal-pension drawdown, made it voluntary in ; voluntary annuity sales fell by more than within a year. The cross-jurisdictional uniformity of the puzzle rules out narrowly local explanations.
(Bequest Motives Cannot Explain It) Even households with no heirs reject annuities.
A natural rational explanation is that households want to leave wealth to children and therefore avoid annuitizing. This explains some of the rejection but not the rest: childless households reject annuities at nearly the same rates as households with heirs, and households with heirs typically leave bequests in forms (real estate, savings) other than the annuity-vs-non-annuity decision. The bequest explanation is real but a small part of the picture.
(Framing Dominates Comparison) Brown et al. show “consumption frame” outperforms “investment frame.”
Brown, Kling, Mullainathan & Wrobel (2008) randomly assign survey respondents to evaluate the same annuity product under two different framings. In the consumption framing, the annuity is described as “guaranteeing a certain spending level for the rest of your life.” In the investment framing, the same product is described as “an investment that pays returns conditional on you still being alive.” Respondents in the consumption frame chose the annuity at substantially higher rates ( vs. in some cuts) than respondents in the investment frame, holding the underlying product fixed. The fact that the same product can be acceptable or unacceptable depending on words alone is hard to reconcile with any rational evaluation; it is the cleanest direct evidence that framing, not preferences, drives the puzzle.
(Implications for Policy) Default options matter as much as for (k) participation.
Just as (k) participation rose dramatically when auto-enrollment became standard, annuity uptake rises dramatically when annuitization is the default option in retirement plans. The U.K.’s mandatory-annuitization era produced near-universal coverage; its voluntary era produced near-universal rejection — with the same households making opposite choices depending on the default. Policy proposals to require defined-contribution plans to offer (or default to) lifetime income options are motivated by exactly this evidence.
Examples
A 65-year-old retiree facing the annuitization decision
A retiree with $ in a (k), no bequest motive, and average life expectancy of more years compares two strategies. Strategy A (no annuity): invest in a - stock-bond portfolio and draw down per year ($). Under historical returns this lasts about years on average but has a – chance of running out before age . Strategy B (annuity): buy an immediate fixed annuity at age for $, receive about $ per year for life. Strategy B pays more per year and never runs out. The retiree picks Strategy A — because the $ is visible and the annuity payments are not, because Strategy A “preserves the principal” (an irrelevant accounting fact under additive utility), and because the framing of “if I die early they keep it” feels worse than the much larger expected loss of running out of money in old age.
The Brown-Kling-Mullainathan-Wrobel framing experiment
Brown et al. (2008) ran a survey experiment on U.S. households. Each respondent was shown the same lifetime-annuity product but with one of two framings randomly assigned:
- Investment frame: “For an investment of $, Mr. Red will get \650$400$ each month, but if he dies, his money goes back to his heirs…”
- Consumption frame: “Mr. Red can spend \650$400$ per month for as long as he lives plus an additional sum if he dies early…”
Under the investment frame, only of respondents preferred the annuity. Under the consumption frame, preferred it. The product is identical; the framing dictates whether it appears as a risk to take or as protection to accept. The result is one of the cleanest tests of frame dependence in adult financial decision-making and the basis for arguing that the annuity puzzle is fundamentally a behavioral phenomenon.
See Also
- 8.10. Behavioral Household Finance — parent hub.
- 8.5.1. Prospect Theory — the loss-aversion microfoundation for the framing effect.
- 8.10.5. Household Liabilities Puzzles — sibling: another set of household-finance puzzles where rational benchmarks fail.