How Deep is the Annuity Market Participation Puzzle?

1. How Deep is the Annuity Market Participation Puzzle? Joachim Inkmann, Tilburg University, CentER and Netspar Paula Lopes, London School of Economics and FMG Alexander Michaelides, London School of Economics, CEPR and FMG The Future of Pension Plan Funding LSE/FMG 7-8th June, 2007

2. The Annuity Market Participation Puzzle • Life annuities offer protection against mortality risk • Theoretical results indicate that consumers should annuitize all their wealth under certain conditions • Yaari (1965): risk aversion • Davidoff et al (2005): complete markets • Empirical evidence suggests that voluntary annuity demand is very small. This is the puzzle! • increasing life expectancy • a trend towards occupational pension arrangements which do not require (full) annuitization of pension wealth at retirement age (DC plans like 401(k))

3. Possible Explanations for the Puzzle: • A number of theoretical explanations have been given which may contribute to solving the puzzle • Lack of actuarial fair pricing (Mitchell et al, 1999) • Bequest motives (Friedman and Warshawsky, 1990) • Habit formation (Davidoff et al, 2005) • Compulsory annuitization in the public and private pension system (Bernheim, 1991, Brown et al, 2001) • Minimum purchase requirements (Lopes, 2006) • Lack of flexibility (Milevsky and Young, 2002)

4. Contribution of this Paper • We start from data to get the benchmark right • Which households demand voluntary annuities? • Conditional on participation, how much annuities? • Surprisingly, such a detailed empirical analysis of annuitization still seems missing in the literature • We then built a simple life-cycle model • Captures the sign. empirical causes of annuitization • Saving, portfolio choice and annuitization • Finally, we can quantify the depth of the puzzle • Feed wealth distribution from data into model • Generate predicted annuity demand and compare with empirical results

5. Findings of this Paper • Factors which significantly affect voluntary annuity demand in the data • Education • Life expectancy • Compulsory annuitization • Possible bequest motive for surviving spouse • Financial wealth • Stock market participation • These factors also appear relevant in the life-cycle model • Model replicates all factors except education • The puzzle might not be as deep as previously thought • For reasonable preference parameters we can generate theoretical predictions, which resemble data

6. Empirical Analysis • Data: English Longitudinal Study of Ageing (ELSA) • First two waves: 2002/03 and 2004/05 • Individuals aged 50 and over • Information on public pensions, private (personal or occupational) pensions and voluntary annuitization • “Annuity income is when you make a lump sum payment to a financial institution and in return they give you a regular income for the rest of your life.” • Sample selection • Households with at least one retired person • Financial unit level (N = 5,233) • Age < 90 (since data is truncated at 90)

7. Annuity (& Stock) Market Participation • Annuity market participation: 5.9% • Among stockholders: 9.6% (sign. diff.)

8. Financial Wealth and Income • Financial wealth measuredbefore annuitization • Annuity market participants much more wealthy than non-participants: mean diff = 85,000 GBP • Conditional on annuity market participation, stock market participants demand higher annuities.

9. Participation over Wealth Distribution (5, 10, 20, 30, 20, 10, 5)% of observations (2.5, 10, 25, 50, 75, 90, 97.5)% wealth percentiles

10. Pension Income Decomposition (5, 10, 20, 30, 20, 10, 5)% of observations (2.5, 10, 25, 50, 75, 90, 97.5)% wealth percentiles

11. Participation by Household Background Differences in education, health and life expectancy

12. Subjective & Objective Survival Probs Underestimation below average sample age (69) Difference between self-reported and GAD survival probs.

13. Survival Probability, Health & Annuities Difference between self-reported and GAD survival probs.

14. Econometric Analysis: Annuity Demand

15. Summary of Empirical Findings • Variables affecting voluntary annuity market participation: + Education** + Life expectancy* - Possible bequest motive for surviving spouse** + Financial wealth** + Stock market participation* • Variables affecting conditional voluntary annuity demand: - Compulsory annuitization** + Financial wealth** + Stock market participation** (**: significant at 5% level, *: significant at 10% level) • This is the benchmark for any theory of annuitization

16. Implications of a Life-Cyle Model • Life-cycle model of savings and portfolio choice • Starts at retirement age 65 (t = 1); max. age = 100 (T = 35) • Mortality risk reflected by cond. survival probabilities p • Available assets: • real annuity that can be purchased at t = 1 • stocks (equity premium 4%, std.dev. 18%) • risk-free asset • Household already receives pension L (mandatory annuity) • Every period household decides on optimal consumption C and (for stockholders) the share  of savings to invest in stocks subject to a budget constraint for cash-on-hand X:

17. Annuity Pricing • At time t = 1 household decides to buy an annuity that makes an annual payment A • EPDV = Expected Present Discounted Value • P = Load factor (Mitchell et al (1999): 8%-20%)

18. Preferences and Data Input • The household has Epstein-Zin preferences • with : coefficient of relative risk aversion : elasticity of inter-temporal substitution b: strength of the bequest motive • We take the following inputs from the data • Wealth distribution (described by 20 percentiles) by stock market participation status • Median pension level (sum of public and private) by stock market participation status • GAD survival probabilities for ELSA gender mix

19. Policy Functions: Annuity Demand Baseline results:  = 3,  = 1/3 (CRRA), b = 0 With access to the stock market, a higher level of initial wealth is required to purchase an annuity

20. Comparative Statics: Non-Stockholders Bequest: b = 1; RRA:  = 5; EIS:  = 0.8 Increase in bequest motive has negative demand impact, increase in RRA and EIS positive

21. Comparative Statics: Stockholders Bequest: b = 3; RRA:  = 5; EIS:  = 0.8 Increase in bequest motive has negative demand impact, increase in RRA and EIS positive

22. Simulation: Average Consumption Simulation = evaluating policy functions (of wealth) at the ELSA wealth distribution

23. Simulation: Annuity Demand (S = 0) If participation increases, the average level of annuity demand tends to decrease since less wealthy households join

24. Simulation: Annuity Demand (S = 1)

25. Perform Method of Simulated Moments to select parameters: • : coefficient of relative risk aversion; • : elasticity of inter-temporal substitution; • b: strength of the bequest motive; • To match selected moments in the data with model: • Annuity market participation; • Amount of annuity demand (conditional on participation); • Share of wealth annuitized. So, how deep is the puzzle?

26. Conclusion: How Deep is the Puzzle? Non-Stockholders

27. Conclusion: How Deep is the Puzzle? Stockholders

28. Conclusion: How Deep is the Puzzle? Maybe not too puzzling, after all … Thank you.