Wei SunRenmin University, Hanqing Advanced Institute of Economics and Finance and School of

Finance

Anthony WebbCenter for Retirement Research at Boston College

Sixth International Longevity Risk and Capital Markets and Solutions ConferenceSydney, Australia

September 7-8, 2010

How Do Subjective Mortality Beliefs Affect the Perceived

Value of Longevity Insurance?

Cumulative survival rate from age 65 – all individuals have population mortality

1

Source: Unpublished Social Security Administration Cohort Life Tables.

Population Average Survival Probability for Males Born in 1940

Age

Cumulative survival rate from age 65 – all individuals know age of death with certainty

2

Source: Unpublished Social Security Administration Cohort Life Tables.

Population Average Survival Probability for Males Born in 1940

Age

•Very high – when people believe they have population mortality

•Often less than premium paid – when people know their date of death with certainty

•If annuity is actuarially fair, do not buy unless they anticipate living to age 89.

•If annuity is 85% fair, do not buy unless they anticipate living to age 92.

•Do subjective mortality beliefs explain the lack of demand for

annuitization?

3

Value of annuitization

Source: Jeffrey Brown. 2000. “How Should We Insure Longevity Risk in Pensions and Social Security?” Issue in Brief 4. Chestnut Hill, MA: Center for Retirement Research.

Strategy

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•Exploit newly available Health and Retirement Study (HRS) data on subjective moral beliefs:

•What is the percent chance you will live to age 75 or more?

•What is the percent chance you will live to age 85 or more?

•Problem – how do you interpret responses such as 50%?

In 2008, for the first time, the HRS probes people further.

5

Source: Authors' calculations based on 2008 Health and Retirement Study data.

1. Exact153 Gave #

Answered 0 3. Approximate 65225 71 DK/RF

8/9. DK/RF 63

1.Equally Likely273

Answered 50 ̶ � Q A (LP102) 2.Unsure613 338

8/9. DK/RF2

1. Certain503 Gave #

Total Asked Answered 100 3. Approximate 3405567 866 358 DK/RF

8/9. DK/RF 185

Gave Min Answered mult of 10/25 (incl. 50) 1928 (314)

3237 (542) 1. Exact Number DK/RF Min1029 (175) 257 (47)

3. Approximate Gave Max2185 (361) 1929 (319)

Answered DK/RF 8/9. DK/RF DK/RF Max213 23 (6) 256 (42)

How do people answer?

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•Most people seem to have an idea.

•Most people give sensible answers: P(75) > P(85), etc.

•Previous research shows responses vary appropriately in cross section and time series with known predictors of mortality.

Can you use P(75) and P(85) responses to gauge optimism/pessimism and certainty?

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Source: Authors’ illustrations.

Cumulative Survival Rate

Population mortality

OptimisticPessimisticCertain

Age

What kinds of people answer “don’t know” or “refuse”?

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•Estimate probits and ordered probits

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Probit Regression, Reporting Marginal Effects – Being Unable or Unwilling to Estimate Survival Probability

•Statistically significant at the 10 percent level; ** At the 5 percent level; *** At the 1 percent level Source: Authors' calculations based on Health and Retirement Survey data.

Explanatory variables dF/dx Std. err.Age 0.0215 0.00554***Age squared 0.000137 0.0000378***Race/ethnicity Caucasian/other Black 0.0148 0.0128 Hispanic 0.0299 0.0171*Education Less than high school 0.00617 0.0107 High school College/advanced degree -0.0233 0.00982**Math aptitude -0.0128 0.00490***Log total financial wealth -0.00340 0.000872***Log total income -0.00228 0.00252Subjective health evaluation 0.00676 0.00354*N. obs. (adj.) 6528Log likelihood -1988.395

Pseudo R2 0.0426Obs. P 0.0969Pred. P   0.0883