Consumption and Production Profiles
Andrew Mason
Sang-Hyop Lee
Maliki
January 14, 2005
NTA meeting at Berkeley
1
Objectives


2
Identify methodological problems associated
with estimating age profiles
Explain how profiles vary with development,
demography, and institutions
Two Approaches
Indirect
Dependency ratios
Fair and Dominguez
– Direct
Support ratio: Cutler et al
–
3
Advantages of Direct Estimates of Age
Profiles



4
Child and old-age dependency vary with
development, institutions, tastes, etc.
First step to exploring how societies are
reallocating resources across the lifecycle
Essential to understanding the
macroeconomic effects of aging
Production Profiles




5
Y=N*(L/N)*(Y/L)
Entry and departure determine the shape
Effect of aging on earnings at older ages is
not clear because of earlier retirement
For some countries, institutional factors are
important
6
Figure 1-a. Three types of earnings profile
0.04000
0.03000
Japan
0.02000
Brazil
France
0.01000
0.00000
1
12 23 34 45 56 67 78 89 100
Age
7
Figure 1-b. Type I earnings profile
0.04000
0.03000
Taiwan
Brazil
0.02000
Indonesia
Thailand
0.01000
0.00000
1
11
21
31 41
51
Age
8
61 71
81
91 101
Figure 1-c. Type II earnings profile
0.04000
0.03000
Australia
France
0.02000
US
0.01000
0.00000
1 11 21 31 41 51 61 71 81 91 101
Age
9
Observations

Differences among countries are not very
large, but
–
–
–
10
Earnings at young ages more important in low
income countries: age structure and labor force
participation rates
Aging has a muted effect on earnings at older
ages because of earlier retirement
Japan is very distinctive (seniority wage system)
Decomposition of the change in lnY by age,
Taiwan 1978-1998
2.000
1.500
1.000
-0.500
-1.000
-1.500
-2.000
-2.500
11
77
73
69
65
61
57
53
49
45
41
37
33
29
25
dlnN
21
0.000
17
dlnY
13
0.500
dln(L/N)
dln(Y/L)
Methodological Issues



12
Incorporating entrepreneurial income: some
countries have a large informal sector
Seniority based wage: should be spread over
the working life? (funded vs. unfunded)
Using FIES vs. LFS
Consumption Profiles



13
Difficulties in estimating individual profiles
Importance of considering both public and
private consumption
Differences across countries
Methodological Issues (Private)
–
Engel’s Method:


–

14
Child consumption should not be dependent upon
demographic composition.
Probably upward biased estimate of child consumption
Rothbarth Method:

–
y c  e c ( p * q , u )  e( p , u )
y c  e  e a ( p, x a )
Useful for young children, but not for teens or adults
Maybe downward biased.
Both models assume that adults in the household
have same preference irrespective of children
Cost of Children*
Method
Engel
5-9
10-14
114%
144%
Rothbarth
<0
22%
Rothbarth
<0
<0
94%
96%
Ray’s
15
0-4
* Source: Maliki (2004) Reference adults: 30-34
Notes
152%
64% Adult
clothing
38% Adult food
88% Several
goods
Evaluation

Need an alternative method which is
theoretically and empirically sound.
- “Split method” has an empirical advantage
- Assignable goods are important

Can the split method be justified by any
consumer theory?
What are the rule for non-assignable goods?

16
Theory for Split Method:
Collective Bargaining Model


17
Advantage over Engel’s and Rothbarth: the
main result does not depend on household
utility function.
However, whether we can recover the
income sharing rule is the question:
Bourguignon (1999, J Popul Econ) provides
a clue
Collective Bargaining Method


3 people 3 goods: Suppose we have one assignable
good (x3) to a child, one assignable good (x1) to
adult A, and one non-assignable good (x2).
The cost of children is
yc  x3c  y  a  b   F2c  y  a  b   

18
We can directly assign assignable good to children
under this model.
Separate Estimates of Private
Education and Health

Separate estimation on assignable goods
–
–

Considerable variation in education
expenditures
–

19
Education
Health
High in East Asia
Health expenditures concentrated on the
elderly even in lower income countries
Spending/Consumption of
average adult
Private Education Spending, Selected Countries
0.600
0.500
0.400
0.300
0.200
0.100
28
26
24
22
20
18
16
14
12
10
8
6
4
2
0
0.000
Age of recipient
Brazil (1996)
Taiwan (1998)
Japan(1999)
20
France (1995)
Thailand (1996)
Indonesia (2001)
US (2001)
Age Profile for Out-of-Pocket Health Expenditure,
Selected Countries.
3.50
3.00
Brazil (1996)
Density
2.50
France (1995)
Indonesia (1996)
2.00
Taiwan (1998)
Thailand (1996)
1.50
US (2001)
1.00
0.50
0.00
0-4
21
5-19
20-39
40-59
60+
Non-assignable goods

How to allocate non-assignable goods?
yc  x3c  y  a  b   F2c  y  a  b   
–
–
22
Engel’s Method? Problematic. Also there is
measurement error problem.
A priori allocation (0.5 for children, 1 for adult
or any other proportion)?
Indonesia - Susenas 1996
100000
Consumption Allocation
90000
80000
70000
60000
50000
40000
30000
20000
split+engel
engel
10000
a0.5
split+a1
23
95
90
85
80
75
70
65
60
55
50
45
40
35
30
25
20
15
10
5
0
0
24
Importance of Public Consumption


25
Government consumption becomes more
important with development, although with
considerable variation
Government consumption often targets
young and old with important implications for
trends in age profiles
Total Consumption by Age, France 2000
25000
20000
Euros
15000
10000
5000
Age
Private consumption
26
Public consumption
Total consumption
95
90
85
80
75
70
65
60
55
50
45
40
35
30
25
20
15
10
5
0
0
27
28
29
30
The End
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