1. 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 7-8 th June, 2007

2. 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. 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. 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. 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. 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. 7 Annuity (& Stock) Market Participation Annuity market participation: 5.9% Among stockholders: 9.6% (sign. diff.) 2002/ 0420022004 A = 0A = 1 Total S = 0291765313013 (Row-%)(96.8)(2.2)(1.0)(100.0) (Total-%)(55.7)(1.2)(0.6)(57.6) S = 12007142712220 (Row-%)(90.4)(6.4)(3.2)(100.0) (Total-%)(38.4)(2.7)(1.4)(42.4) Total49242071025233 (Total-%)(94.1)(4.0)(1.9)(100.0)

8. 8 Financial Wealth and Income Financial wealth measured before 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. AllA = 1A = 0 MeanMedianMeanMedianMeanMedian Financial wealth5503115800135017650005001114200 Annual pension9328730512182903691497228 Annual public pension479647324945494047874723 Annual private pension453214407236320043621350 Annual annuity income17903032984-- Stock share percentage1602414160 A = 1 and S = 1S = 1S = 0 MeanMedianMeanMedianMeanMedian Financial wealth1736199930010193747586204705000 Annual pension141421166011523913277116315 Annual public pension494349484521462849994784 Annual private pension91996600700241452712500 Annual annuity income365612003510530 Stock share percentage35283832--

9. 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. 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. 11 Participation by Household Background Differences in education, health and life expectancy AllA = 1A = 0 Age / 106.936.826.94 Female0.530.420.54 Married0.560.570.56 Number of children2.041.982.04 Low education0.590.340.61 Medium education0.300.410.30 High education0.100.250.10 Survival probability0.520.570.52 Objective GAD probability0.530.560.53 Bad health condition0.190.140.19 Medium health condition0.620.600.63 Good health condition0.190.270.18

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

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

14. 14 Econometric Analysis: Annuity Demand Voluntary annuity market participationLog annuity demand ProbitMarginal effectscond. on participation Variableestimatet-valueestimatet-valueestimatet-value Intercept-2.6844-5.82--3.79772.33 Age / 10-0.0637-1.35-0.0061-1.28-0.1720-1.42 Female-0.2189-3.38-0.0175-3.11-0.1609-0.87 Married-0.3240-4.490.04073.610.06890.36 Number of children0.02441.240.00241.220.04060.69 Low education-0.2325-3.31-0.0183-2.98-0.0144-0.07 High education0.17732.070.01981.90-0.0323-0.17 Survival probability0.18961.710.01821.710.40471.18 Log public pension0.01713.110.00162.760.01541.20 Log private pension-0.0038-0.88-0.0004-0.86-0.0257-2.32 Log financial wealth0.16085.200.01554.590.34062.41 Stockholder (S)-0.8674-1.880.01521.78-2.9970-1.77 S x log wealth in stocks-0.0569-1.90---0.2501-3.07 S x log financial wealth0.14372.66--0.50452.74 Number of observations5233309 Fit of the modelCorrect predictions: 94.10%R-square: 27.95%

15. 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. 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. 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. 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. 19 Policy Functions: Annuity Demand With access to the stock market, a higher level of initial wealth is required to purchase an annuity Baseline results:  = 3,  = 1/3 (CRRA), b = 0

20. 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. 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. 22 Simulation: Average Consumption Simulation = evaluating policy functions (of wealth) at the ELSA wealth distribution

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

24. 24 Simulation: Annuity Demand (S = 1)

25. 25 So, how deep is the puzzle? 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.

26. 26 Conclusion: How Deep is the Puzzle? Non-Stockholders Voluntary Share Modelbγψannuityannuity marketof wealth demandparticipationannuitized Estimate s0.21.530.473.954.2520.37 Data 1.653.136.61 (s.e.)(4.57)(17.57))(31.57)

27. 27 Conclusion: How Deep is the Puzzle? Stockholders Voluntary Share Modelbγψannuityannuity marketof wealth demandparticipationannuitized Estimate s2.20.590.105.3010.4024.00 Data 3.669.5926.27 (s.e.)(9.58)(29.45)(25.77)

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