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

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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 lt 90 (since data is truncated at 90)

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Annuity ( Stock) Market Participation

• Annuity market participation 5.9
• Among stockholders 9.6 (sign. diff.)

  2002/ 04 2002 2004  
  A 0 A 1 A 1 Total
S 0 2917 65 31 3013
(Row-) (96.8) (2.2) (1.0) (100.0)
(Total-) (55.7) (1.2) (0.6) (57.6)
S 1 2007 142 71 2220
(Row-) (90.4) (6.4) (3.2) (100.0)
(Total-) (38.4) (2.7) (1.4) (42.4)
Total 4924 207 102 5233
(Total-) (94.1) (4.0) (1.9) (100.0)
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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.

All All A 1 A 1 A 0 A 0
  Mean Median Mean Median Mean Median
Financial wealth 55031 15800 135017 65000 50011 14200
Annual pension 9328 7305 12182 9036 9149 7228
Annual public pension 4796 4732 4945 4940 4787 4723
Annual private pension 4532 1440 7236 3200 4362 1350
Annual annuity income 179 0 3032 984 - -
Stock share percentage 16 0 24 14 16 0
A 1 and S 1 A 1 and S 1 S 1 S 1 S 0 S 0
  Mean Median Mean Median Mean Median
Financial wealth 173619 99300 101937 47586 20470 5000
Annual pension 14142 11660 11523 9132 7711 6315
Annual public pension 4943 4948 4521 4628 4999 4784
Annual private pension 9199 6600 7002 4145 2712 500
Annual annuity income 3656 1200 351 0 53 0
Stock share percentage 35 28 38 32 - -
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Participation over Wealth Distribution
(5, 10, 20, 30, 20, 10, 5) of observations
(2.5, 10, 25, 50, 75, 90, 97.5) wealth
percentiles
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Pension Income Decomposition
(5, 10, 20, 30, 20, 10, 5) of observations
(2.5, 10, 25, 50, 75, 90, 97.5) wealth
percentiles
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Participation by Household Background
Differences in education, health and life
expectancy
  All A 1 A 0
Age / 10 6.93 6.82 6.94
Female 0.53 0.42 0.54
Married 0.56 0.57 0.56
Number of children 2.04 1.98 2.04
Low education 0.59 0.34 0.61
Medium education 0.30 0.41 0.30
High education 0.10 0.25 0.10
Survival probability 0.52 0.57 0.52
Objective GAD probability 0.53 0.56 0.53
Bad health condition 0.19 0.14 0.19
Medium health condition 0.62 0.60 0.63
Good health condition 0.19 0.27 0.18
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Subjective Objective Survival Probs
Underestimation below average sample age (69)
Difference between self-reported and GAD survival
probs.
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Survival Probability, Health Annuities
Difference between self-reported and GAD survival
probs.
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Econometric Analysis Annuity Demand
Voluntary annuity market participation Voluntary annuity market participation Voluntary annuity market participation Voluntary annuity market participation Log annuity demand Log annuity demand
  Probit Probit Marginal effects Marginal effects cond. on participation cond. on participation
Variable estimate t-value estimate t-value estimate t-value
Intercept -2.6844 -5.82 - - 3.7977 2.33
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 -4.49 0.0407 3.61 0.0689 0.36
Number of children 0.0244 1.24 0.0024 1.22 0.0406 0.69
Low education -0.2325 -3.31 -0.0183 -2.98 -0.0144 -0.07
High education 0.1773 2.07 0.0198 1.90 -0.0323 -0.17
Survival probability 0.1896 1.71 0.0182 1.71 0.4047 1.18
Log public pension 0.0171 3.11 0.0016 2.76 0.0154 1.20
Log private pension -0.0038 -0.88 -0.0004 -0.86 -0.0257 -2.32
Log financial wealth 0.1608 5.20 0.0155 4.59 0.3406 2.41
Stockholder (S) -0.8674 -1.88 0.0152 1.78 -2.9970 -1.77
S x log wealth in stocks -0.0569 -1.90 - - -0.2501 -3.07
S x log financial wealth 0.1437 2.66 - - 0.5045 2.74
Number of observations 5233 5233 5233 5233 309 309
Fit of the model Correct predictions 94.10 Correct predictions 94.10 Correct predictions 94.10 Correct predictions 94.10 R-square 27.95 R-square 27.95
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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

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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

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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)

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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

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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

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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
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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
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Simulation Average Consumption
Simulation evaluating policy functions (of
wealth) at the ELSA wealth distribution
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Simulation Annuity Demand (S 0)
If participation increases, the average level
of annuity demand tends to decrease since less
wealthy households join
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Simulation Annuity Demand (S 1)
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• 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.

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Conclusion How Deep is the Puzzle?
Non-Stockholders
        Voluntary Voluntary Share 
Model b ? ? annuity annuity market of wealth
        demand participation annuitized

Estimates 0.2 1.53 0.47 3.95 4.25 20.37

Data       1.65 3.1 36.61
(s.e.) (4.57) (17.57)) (31.57)
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Conclusion How Deep is the Puzzle?
Stockholders
        Voluntary Voluntary Share 
Model b ? ? annuity annuity market of wealth
        demand participation annuitized

Estimates 2.2 0.59 0.10 5.30 10.40 24.00

Data       3.66 9.59 26.27
(s.e.) (9.58) (29.45) (25.77)
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Conclusion How Deep is the Puzzle?

• Maybe not too puzzling, after all
• Thank you.