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
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1 How Deep is the Annuity Market Participation Puzzle? Joachim Inkmann, Tilburg University, CentER and Netspar Paula Lopes, London School of Economics.
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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)
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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
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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.”
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
(**: 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:
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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
With access to the stock market, a higher level of initial wealth is required to purchase an annuity
0
2
4
6
8
10
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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
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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