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
1
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))
2
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)
3
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
4
– Generate predicted annuity demand and compare with empirical
results
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
5
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)
6
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
2917
65
31
3013
(Row-%)
(96.8)
(2.2)
(1.0)
(100.0)
(Total-%)
(55.7)
(1.2)
(0.6)
(57.6)
2007
142
71
2220
(Row-%)
(90.4)
(6.4)
(3.2)
(100.0)
(Total-%)
(38.4)
(2.7)
(1.4)
(42.4)
4924
207
102
5233
(94.1)
(4.0)
(1.9)
(100.0)
S=0
S=1
Total
(Total-%)
7
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
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
S=1
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
Stock share percentage
35
28
38
32
-
8
0
-
Participation over Wealth Distribution
(5, 10, 20, 30, 20, 10, 5)% of observations
1800
20
1600
18
1400
16
14
1200
12
1000
10
800
8
600
6
400
4
200
2
0
0
0.1
0.7
3.3
15.8
53.3
131.2
% (A = 1); '000 GBP/a (Pension)
Number Observations (All, S = 1)
(2.5, 10, 25, 50, 75, 90, 97.5)% wealth percentiles
348.8
Wealth Distribution ('000 GBP)
All
S=1
A=1
Pension
9
Pension Income Decomposition
(5, 10, 20, 30, 20, 10, 5)% of observations
(2.5, 10, 25, 50, 75, 90, 97.5)% wealth percentiles
21
18
'000 GBP
15
12
9
6
3
0
0.1
0.7
3.3
15.8
53.3
131.2
348.8
Wealth Distribution ('000 GBP)
Public Pension
Private Pension
Voluntary Annuity
10
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
11
Subjective & Objective Survival Probs
Underestimation below average sample age (69)
Difference between self-reported and GAD survival probs.
12
Survival Probability, Health & Annuities
Difference between self-reported and GAD survival probs.
13
Econometric Analysis: Annuity Demand
Voluntary annuity market participation
Probit
Variable
estimate
Log annuity demand
Marginal effects
t-value
estimate
cond. on participation
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
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 children
Number of observations
Fit of the model
5233
309
Correct predictions: 94.10%
R-square: 27.95%
14
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
15
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:
16
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%)
17
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
18
Policy Functions: Annuity Demand
Baseline results:  = 3,  = 1/3 (CRRA), b = 0
Annual Annuity Income (000's £)
18
16
14
12
10
8
6
4
2
0
0
50
100
150
200
250
300
Wealth at Retirement (000's £)
Stockholders
Non-Stockholders
With access to the stock market, a higher level of initial wealth is
required to purchase an annuity
19
Comparative Statics: Non-Stockholders
Annual Annuity's Income (000's £)
Bequest: b = 1; RRA:  = 5; EIS:  = 0.8
18
16
14
12
10
8
6
4
2
0
0
50
100
150
200
250
300
Wealth at Retirement (000's £)
Base
Bequest
RRA
EIS
Increase in bequest motive has negative demand impact, increase
in
20
RRA and EIS positive
Comparative Statics: Stockholders
Annual Annuity Income (000's £)
Bequest: b = 3; RRA:  = 5; EIS:  = 0.8
18
16
14
12
10
8
6
4
2
0
0
50
100
150
200
250
300
Wealth at Retirement (000's £)
Base
Bequest
RRA
EIS
Increase in bequest motive has negative demand impact, increase 21in
RRA and EIS positive
Simulation: Average Consumption
11.0
Consumption (000's £)
10.5
10.0
9.5
9.0
8.5
8.0
7.5
7.0
65
70
75
80
85
90
95
100
Age
Actuarially Fair
Load Factor
Simulation = evaluating policy functions (of wealth) at the ELSA
wealth distribution
22
Simulation: Annuity Demand (S = 0)
If participation increases, the average level of annuity demand
tends to decrease since less wealthy households join
b
γ
2
0
3
5
2
1
3
5
ψ
Voluntary
annuity
demand
Voluntary
annuity market
participation
Share
of wealth
annuitized
Wealth
Equivalence
Measure
0.20
0.30
0.50
0.80
0.20
0.30
0.50
0.80
0.20
0.30
0.50
0.80
5.79
4.57
2.93
2.10
3.62
2.73
2.10
2.09
2.42
2.06
2.09
2.08
6.15
12.80
34.50
66.75
22.10
41.05
66.50
67.10
51.00
66.95
67.10
67.30
34.12
37.73
54.16
92.96
44.30
62.30
93.31
92.49
68.98
89.18
92.53
92.16
99.89
99.76
99.34
97.75
99.75
99.54
99.14
98.64
99.67
99.51
99.38
99.28
0.20
0.30
0.50
0.80
0.20
0.30
0.50
0.80
0.20
0.30
0.50
0.80
3.17
3.39
3.21
0.65
5.15
5.19
5.29
5.55
3.47
3.23
3.03
3.61
3.90
4.00
3.75
1.05
9.25
10.05
10.05
6.95
25.30
29.40
31.75
22.10
15.59
16.73
15.41
2.51
35.35
37.61
38.41
31.94
48.47
50.69
47.90
40.41
99.99
99.99
99.99
99.99
99.89
99.89
99.89
99.95
99.82
99.78
99.78
99.86
23
Simulation: Annuity Demand (S = 1)
b
γ
2
0
3
5
2
1
3
5
ψ
Voluntary
annuity
demand
Voluntary
annuity market
participation
Share
of wealth
annuitized
Wealth
Equivalence
Measure
0.20
0.30
0.50
0.80
0.20
0.30
0.50
0.80
0.20
0.30
0.50
0.80
2.79
3.14
4.71
5.58
4.45
4.68
4.83
5.12
4.92
4.97
4.96
4.96
5.45
7.05
9.85
18.40
17.00
20.60
28.90
40.80
43.25
47.95
57.00
69.25
11.62
13.36
21.10
28.50
23.12
25.94
30.33
38.15
39.04
42.26
47.81
56.53
99.96
99.94
99.84
99.56
99.87
99.81
99.69
99.48
99.69
99.62
99.52
99.36
0.20
0.30
0.50
0.80
0.20
0.30
0.50
0.80
0.20
0.30
0.50
0.80
2.16
2.52
3.37
3.98
4.06
4.34
4.82
5.25
4.89
4.92
4.86
4.92
4.30
4.70
5.30
6.10
13.20
14.25
15.40
12.30
39.25
43.25
49.25
40.80
8.68
10.14
13.54
15.88
19.25
21.00
23.52
23.46
36.57
38.65
40.36
35.83
99.98
99.98
99.96
99.94
99.92
99.90
99.88
99.91
99.74
99.69
99.64
24
99.75
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.
25
Conclusion: How Deep is the Puzzle?
Non-Stockholders
Voluntary
Voluntary
Share
annuity
annuity market
of wealth
demand
participation
annuitized
3.95
4.25
20.37
Data
1.65
3.1
36.61
(s.e.)
(4.57)
(17.57))
(31.57)
Model
Estimate
s
b
0.2
γ
1.53
ψ
0.47
26
Conclusion: How Deep is the Puzzle?
Stockholders
Voluntary
Voluntary
Share
annuity
annuity market
of wealth
demand
participation
annuitized
5.30
10.40
24.00
Data
3.66
9.59
26.27
(s.e.)
(9.58)
(29.45)
(25.77)
Model
Estimate
s
b
2.2
γ
0.59
ψ
0.10
27
Conclusion: How Deep is the Puzzle?
Maybe not too puzzling, after all
…
Thank you.
28