11

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 FundingLSE/FMG7-8th June, 2007

22

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))

33

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)

44

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

55

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

66

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)

77

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)

88

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 A = 1 A = 0

  Mean Median Mean Median Mean Median

Financial wealth 55031 15800 135017 650005001

1 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 S = 1 S = 0

  Mean Median Mean Median Mean Median

Financial wealth 173619 99300 101937 475862047

0 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 - -

99

Participation over Wealth Distribution

0

200

400

600

800

1000

1200

1400

1600

1800

0.1 0.7 3.3 15.8 53.3 131.2 348.8

Wealth Distribution ('000 GBP)

Num

ber

Observ

ations (

All,

S =

1)

0

2

4

6

8

10

12

14

16

18

20

% (

A =

1);

'000 G

BP

/a (

Pensio

n)

All S = 1 A = 1 Pension

(5, 10, 20, 30, 20, 10, 5)% of observations

(2.5, 10, 25, 50, 75, 90, 97.5)% wealth percentiles

1010

Pension Income Decomposition

0

3

6

9

12

15

18

21

0.1 0.7 3.3 15.8 53.3 131.2 348.8

Wealth Distribution ('000 GBP)

'00

0 G

BP

Public Pension Private Pension Voluntary Annuity

(5, 10, 20, 30, 20, 10, 5)% of observations

(2.5, 10, 25, 50, 75, 90, 97.5)% wealth percentiles

1111

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

1212

Subjective & Objective Survival Probs

Underestimation below average sample age (69)

Difference between self-reported and GAD survival probs.

1313

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

1414

Econometric Analysis: Annuity DemandVoluntary annuity market participation Log annuity demand

  Probit Marginal effects 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 309

Fit of the model Correct predictions: 94.10% R-square: 27.95%

1515

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

1616

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:

1717

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%)

1818

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

1919

Policy Functions: Annuity Demand

With access to the stock market, a higher level of initial wealth is required to purchase an annuity

0

2

4

6

8

10

12

14

16

18

0 50 100 150 200 250 300

Wealth at Retirement (000's £)

An

nu

al A

nn

uit

y I

nco

me (

00

0's

£)

Stockholders Non-Stockholders

Baseline results: = 3, = 1/3 (CRRA), b = 0

2020

Comparative Statics: Non-Stockholders

0

2

4

6

8

10

12

14

16

18

0 50 100 150 200 250 300

Wealth at Retirement (000's £)

An

nu

al

An

nu

ity

's I

nco

me (

00

0's

£)

Base Bequest RRA EIS

Bequest: b = 1; RRA: = 5; EIS: = 0.8

Increase in bequest motive has negative demand impact, increase in RRA and EIS positive

2121

Comparative Statics: Stockholders

0

2

4

6

8

10

12

14

16

18

0 50 100 150 200 250 300

Wealth at Retirement (000's £)

An

nu

al A

nn

uit

y I

nco

me (

00

0's

£)

Base Bequest RRA EIS

Bequest: b = 3; RRA: = 5; EIS: = 0.8

Increase in bequest motive has negative demand impact, increase in RRA and EIS positive

2222

Simulation: Average Consumption

7.0

7.5

8.0

8.5

9.0

9.5

10.0

10.5

11.0

65 70 75 80 85 90 95 100

Age

Co

nsu

mp

tio

n (

00

0's

£)

Actuarially Fair Load Factor

Simulation = evaluating policy functions (of wealth) at the ELSA wealth distribution

2323

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

Voluntary Voluntary Share Wealth b γ ψ annuity annuity market of wealth Equivalence demand participation annuitized Measure 0.20 5.79 6.15 34.12 99.89 2 0.30 4.57 12.80 37.73 99.76 0.50 2.93 34.50 54.16 99.34 0.80 2.10 66.75 92.96 97.75 0.20 3.62 22.10 44.30 99.75

0 3 0.30 2.73 41.05 62.30 99.54 0.50 2.10 66.50 93.31 99.14 0.80 2.09 67.10 92.49 98.64 0.20 2.42 51.00 68.98 99.67 5 0.30 2.06 66.95 89.18 99.51 0.50 2.09 67.10 92.53 99.38 0.80 2.08 67.30 92.16 99.28 0.20 3.17 3.90 15.59 99.99 2 0.30 3.39 4.00 16.73 99.99 0.50 3.21 3.75 15.41 99.99 0.80 0.65 1.05 2.51 99.99 0.20 5.15 9.25 35.35 99.89

1 3 0.30 5.19 10.05 37.61 99.89 0.50 5.29 10.05 38.41 99.89 0.80 5.55 6.95 31.94 99.95 0.20 3.47 25.30 48.47 99.82 5 0.30 3.23 29.40 50.69 99.78 0.50 3.03 31.75 47.90 99.78 0.80 3.61 22.10 40.41 99.86

2424

Simulation: Annuity Demand (S = 1)

Voluntary Voluntary Share Wealth b γ ψ annuity annuity market of wealth Equivalence demand participation annuitized Measure 0.20 2.79 5.45 11.62 99.96 2 0.30 3.14 7.05 13.36 99.94 0.50 4.71 9.85 21.10 99.84 0.80 5.58 18.40 28.50 99.56 0.20 4.45 17.00 23.12 99.87 0 3 0.30 4.68 20.60 25.94 99.81 0.50 4.83 28.90 30.33 99.69 0.80 5.12 40.80 38.15 99.48 0.20 4.92 43.25 39.04 99.69 5 0.30 4.97 47.95 42.26 99.62 0.50 4.96 57.00 47.81 99.52 0.80 4.96 69.25 56.53 99.36 0.20 2.16 4.30 8.68 99.98 2 0.30 2.52 4.70 10.14 99.98 0.50 3.37 5.30 13.54 99.96 0.80 3.98 6.10 15.88 99.94 0.20 4.06 13.20 19.25 99.92 1 3 0.30 4.34 14.25 21.00 99.90 0.50 4.82 15.40 23.52 99.88 0.80 5.25 12.30 23.46 99.91 0.20 4.89 39.25 36.57 99.74 5 0.30 4.92 43.25 38.65 99.69 0.50 4.86 49.25 40.36 99.64 0.80 4.92 40.80 35.83 99.75

2525

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.

2626

Conclusion: How Deep is the Puzzle?

Non-Stockholders

        Voluntary Voluntary Share 

Model b γ ψ 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)

2727

Conclusion: How Deep is the Puzzle?

Stockholders

        Voluntary Voluntary Share 

Model b γ ψ 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)

2828

Maybe not too puzzling, after all …

Thank you.

Conclusion: How Deep is the Puzzle?