Wei Sun Renmin University, Hanqing Advanced Institute of Economics and Finance and School of Finance Anthony Webb Center for Retirement Research at Boston College Sixth International Longevity Risk and Capital Markets and Solutions Conference Sydney, 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Cumulative survival rate from age 65 – all individuals have population mortality 1 Source: Unpublished Social Security Administration Cohort Life Tables.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Cumulative survival rate from age 65 – all individuals know age of death with certainty 2 Source: Unpublished Social Security Administration Cohort Life Tables.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 “How Should We Insure Longevity Risk in Pensions and Social Security?” Issue in Brief 4. Chestnut Hill, MA: Center for Retirement Research.

Strategy 4 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.

How do people answer? 6 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? 7 Source: Authors’ illustrations. Cumulative Survival Rate Population mortality Optimistic Pessimistic Certain Probability of being alive Age

What kinds of people answer “don’t know” or “refuse”? 8 Estimate probits and ordered probits

9 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 variablesdF/dxStd. err. Age *** Age squared *** Race/ethnicity Caucasian/other Black Hispanic * Education Less than high school High school College/advanced degree ** Math aptitude *** Log total financial wealth *** Log total income Subjective health evaluation * N. obs. (adj.)6528 Log likelihood Pseudo R Obs. P Pred. P