Alternative Measures of
Replacement Rates
Michael D. Hurd
RAND and NBER
Susann Rohwedder
RAND
We gratefully acknowledge research support from the Social Security
Administration via the Michigan Retirement Research Center, and
additional support from the National Institute on Aging.
Adequacy of resources in retirement
Focus of considerable research
Need to put in relationship to resources available during
lifetime.
How to assess those resources?
2
1. Income replacement rate
Pre-retirement income a proxy for lifetime income
Complete replacement of income
Fraction such as 80 percent
But: no systematic accounting of
- taxes
- financing consumption out of savings;
- the time horizon or survival curve of the household;
- returns to scale in consumption: “need” of couple
changes at death of a spouse.
- the changing consumption profile with age;
3
How to assess adequacy?
2. Estimate lifetime income.
Compare accumulated wealth with “optimal”
wealth
Hard to do
3. Can resources at retirement maintain
consumption?
or consumption path…
consumption not necessarily constant
4
Our Method
- Observe someone at 65 consuming at some initial level
- Have theoretically or empirically derived consumption
path
- Ask: can resources support that path?
Examples
5
(Exactly) Affordable Consumption Path
Life-cycle consumption and wealth paths
100
600
90
500
80
70
400
60
50
300
40
200
30
20
100
10
0
65
70
75
80
Consumption
85
90
Annuity
95
100
0
105
wealth
6
Consumption path that leaves excess wealth
Life-cycle consumption and wealth paths
100
600
90
500
80
70
400
60
50
300
40
200
30
20
100
10
0
65
70
75
80
Consumption
85
90
Annuity
95
100
0
105
wealth
7
Consumption Path not Affordable: Under-saving
Life-cycle consumption and wealth paths
100
500
90
450
80
400
70
350
60
300
50
250
40
200
30
150
20
100
10
50
0
65
70
75
80
Consumption
85
90
Annuity
95
100
0
105
wealth
8
Consumption and Activities Mail Survey (CAMS)
October, 2001, CAMS wave 1
5,000 HRS households (random selection)
Couples: one of two spouses at random.
3,866 returned questionnaires:
unit response rate of 77.3 percent.
Low rate of item nonresponse
Spending measure close to spending in Consumer
Expenditure Survey
October, 2003, CAMS wave 1
Sent to same households
Substantially same as CAMS wave 1
Use change in consumption to generate life-cycle paths
9
Real spending (thousands) by singles and percent change
over two years, panel
Age
Wave 1
Wave 2
% change
65-69
25.6
25.5
-0.28
70-74
26.3
27.1
1.48
75-79
24.8
24.5
-0.55
80-84
28.1
22.2
-11.77
85 +
28.3
23.8
-8.66
Age 65 consumption = 100
Age 66 consumption = 100*(1-.0028/2)
Age 67 consumption = (Age 66 cons.)*(1-.0028/2)
10
Comparison of empirical consumption path to model
Simulated consumption path, singles
CAMS actual wealth change similar to model
120
100
80
60
40
20
0
65
75
CAMS
85
95
Model
11
Comparison of empirical consumption path to model
Simulated consumption path,
couples
CAMS has flatter consumption path relative to model;
but not much survival past 85.
140
120
100
80
60
40
20
0
65
75
85
CAMS
Model
95
12
Add data from Health and Retirement Study core
Waves 2000, 2002 & 2004
- work status
- wealth
- Social Security and pension income
13
Choice of sample
Want:
Observe all resources
bequeathable wealth
Social Security
Pension income
(Future earnings)
Singles 66-69, N = 210
Couples 66-69, not working, and spouse 62 or older
N = 282.
14
Initial conditions : Couples 66-69
Couples, thousands 2004$
Total Excess
Percentile Consumption annuity spending Wealth
10%
18.0
12.8
-5.2
14.9
25%
23.6
19.4
-4.2
83.5
50%
33.7
27.9
-5.8 262.8
75%
50.0
42.1
-7.9 669.0
90%
69.3
58.2
-11.1 1154.1
Mean
40.8
32.8
-8.0 525.1
At mean, spending $8,000 more than income,
but $525 thousand in wealth.
15
Initial conditions : Couples 66-69
Couples, thousands 2004$
Total Excess
Percentile Consumption annuity spending Wealth
10%
18.0
12.8
-5.2
14.9
25%
23.6
19.4
-4.2
83.5
50%
33.7
27.9
-5.8 262.8
75%
50.0
42.1
-7.9 669.0
90%
69.3
58.2
-11.1 1154.1
Mean
40.8
32.8
-8.0 525.1
At median spending $6,000 more than income
But $263 thousand in wealth
16
Initial conditions : Singles
Singles, thousands 2004$
ConsumpTotal
Excess
Percentile
tion annuity spending Wealth
10%
10.3
4.7
-5.6
0.0
25%
14.5
7.6
-6.9
4.0
50%
21.6
11.0
-10.5
55.8
75%
29.7
16.9
-12.8
235.6
90%
42.6
25.4
-17.3
568.6
Mean
25.8
14.3
-11.4
183.9
Even at mean wealth barely adequate.
Can support about 15 years of spending.
But not at median.
17
Simulations from initial conditions
Singles
Begin with observed consumption
Follow consumption path of singles
Real annuities (Social Security) and nominal annuities
(pension income)
Random mortality from life-table.
Importance: don’t need resources to last forever
Example…
18
Overspending if live until 83, but might die before 83.
Life-cycle consumption and wealth paths
100
500
90
450
80
400
70
350
60
300
50
250
40
200
30
150
20
100
10
50
0
65
70
75
80
Consumption
85
90
Annuity
95
wealth
100
0
105
19
We measure “Excess” Wealth
By how much did initial bequeathable wealth exceed
necessary wealth?
Necessary wealth: amount needed to follow CAMS
consumption path
- Simulate 10 consumption paths for each person.
- Find probability of outliving resources
- Find “excess” wealth
Same as present value of end-of-life wealth
20
Singles, thousands 2004$
Mean Median
Initial wealth
Present value annuities
Total resources
Present value consumption
Excess wealth
183.9
159.4
343.3
279.8
63.5
55.8
127.3
205.8
224.0
5.7
Mean
40-60 pctl.
56.0
120.6
176.6
167.6
9.1
At mean singles can afford consumption path.
Also at median.
21
Singles, thousands 2004$
Mean Median
Initial wealth
Present value annuities
Total resources
Present value consumption
Excess wealth
183.9
159.4
343.3
279.8
63.5
55.8
127.3
205.8
224.0
5.7
Mean
40-60 pctl.
56.0
120.6
176.6
167.6
9.1
Mean among those in 40-60th percentile of excess wealth
Consumption $9,000 less than resources
But those in lower part of distribution cannot afford path.
22
Couples
Begin with observed consumption by a couple.
Follow consumption path of couples as long as both alive
At widowing
Reduce consumption according to returns to scale
Reduce annuities by 1/3 (as is typical with Social
Security )
Then follow singles’ path
Example. Returns-to-scale: poverty line. Single needs
0.79 of consumption by couple
23
(Exactly) Affordable Path
100
600
80
500
400
60
300
40
200
20
Wealth
consumption
Widowing at 80
100
0
0
65
70
75
80
Consumption
85
Annuity
90
95
100
Wealth
24
Consumption Path not Affordable: Under-saving
100
500
80
400
60
300
40
200
20
100
0
Wealth
consumption
Widowing at 80
0
65
70
75
80
Consumption
85
Annuity
90
95
100
Wealth
25
Couples, thousands 2004$
Mean Median Mean 40-60
Initial wealth
530.1
262.8
291.5
Present value annuities
312.9
268.6
308.6
Total resources
843.0
631.6
600.1
Present value consumption 408.2
326.8
351.5
Excess wealth
434.8
244.3
248.7
At mean and median substantial excess wealth.
26
Summary so far:
At population level (mean or median) couples have
adequate resources; also singles (barely).
What about distribution?
Problem of measurement error in income, wealth and
consumption.
With classical measurement error
Negative observation error on wealth and/or income;
Positive observation error on consumption
Either or both => Under-saving (possibly falsely)
27
Group by characteristics such as education
28
Singles. Thousands of 2004$
Present value
N
wealth annuities Cons’n
Less than high school 58
40.1
107.5
225.1
High school
83
170.0
158.2
267.7
Some college
45
285.3
169.8
303.0
College +
24
388.9
269.7
410.2
All
210
183.9
159.4
279.8
Less educated begin with much less wealth;
lower annuities and lower consumption
29
Singles. Excess wealth (2004$ thousands) and percent
with positive
N % positive Mean Median
Less than highschool
58
37.6 -77.5
-29.6
High-school
83
52.2
60.5
6.1
Some college
45
60.9 152.1
45.9
College +
24
68.8 248.4
80.2
All
210
51.9
63.5
15.0
Sharp variation by education level.
Less educated will have to reduce consumption
Systematic variation despite measurement error
30
Couples. Thousands of 2004$
Present value
N wealth annuities Cons’n
Less than high school
61
296.0
208.1
305.9
High school
118
416.5
320.4
384.2
Some college
47
531.8
349.2
436.4
College and above
56 1022.9
381.0
546.6
All
282
530.1
312.9
408.2
Less educated begin with much less wealth;
lower annuities and lower consumption
31
Couples. Excess wealth (2004$ thousands) and percent
with positive
N % positive
mean median
Less than highschool
61
67.5 198.3
77.4
High-school
118
81.3 352.7 240.7
Some college
47
79.1 444.6 289.5
College and above
56
83.2 857.3 519.8
All
282
78.3 434.8 244.3
But even among least educated, mean and median excess
wealth positive.
College and above “over-saved.”
32
Still to be done
Differential mortality:
Poor tend to die earlier than well-to-do.
Will reduce difference between least educated and most
educated
Wider sample
Better treatment of housing wealth
33
Conclusions
Preparation for retirement adequate at population level.
Some have under-saved but with measurement error;
hard to say how many.
But less educated have under-saved on average
Have used observed spending levels and age-patterns:
a good guide to future?
Obvious question: future out-of-pocket health care costs.
So far not a big problem
34
Percent of budget spent on health care by age band
(Consumer Expenditure Survey)
20
15
10
5
0
1989
1992
1995
1998
All
1999
65-74
2000
2001
2002
2003
2004
75 or over
Flat since 1992 among those 62-74
Possible upward movement among those 75+, but not dramatic.
35
Next Steps
36