The age-period cohortproblem: set identificationand point identification
Martin BrowningIan CrawfordMarike Knoef
The Institute for Fiscal StudiesDepartment of Economics, UCL
cemmap working paper CWP02/12
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7)%8(# 92 +8 7-C"@- !(#$"@%$/ S"$"
0 20 40 60 80 1000
0.2
0.4
0.6
0.8
Against age, by cohort
Age
0 20 40 60 80 1000
0.2
0.4
0.6
0.8
Against age, by period
Age
1930 1940 1950 1960 1970 1980 1990 2000 20100
0.2
0.4
0.6
0.8
Against period, by age
Period
110
100
90
80
1930 1940 1950 1960 1970 1980 1990 2000 20100
0.2
0.4
0.6
0.8
Against period, by cohort
Period
1834
1844
18541864 1874 1884 1894 1904
19141924
1850 1900 1950 20000
0.2
0.4
0.6
0.8
Against cohort, by age
Cohort
110
100
90
80 0
1850 1900 1950 20000
0.2
0.4
0.6
0.8
Against cohort, by period
Cohort
1934
1944195419641974
198419942004
aa
7)%8(# ;] 8-$$%&* "*- O$(APQ A-#%(3 OC%33@-PQ B(G(#$ OJ($$(CP -V-B$. $( W-#(
0 20 40 60 80 100-1
-0.5
0
0.5
1
AgeEffects
Age
1930 1940 1950 1960 1970 1980 1990 2000 2010
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
PeriodEffects
Period
1850 1900 1950 2000-0.2
0
0.2
0.4
0.6
0.8
1
1.2
Cohort Effects
Cohort
0 20 40 60 80 100-0.2
0
0.2
0.4
0.6
0.8AgeEffects
Age
1930 1940 1950 1960 1970 1980 1990 2000 2010-1
-0.5
0
0.5
1PeriodEffects
Period
1850 1900 1950 2000-0.02
0
0.02
0.04
0.06
0.08Cohort Effects
Cohort
0 20 40 60 80 1000
0.1
0.2
0.3
0.4
0.5
0.6
0.7AgeEffects
Age
1930 1940 1950 1960 1970 1980 1990 2000 2010-0.03
-0.02
-0.01
0
0.01
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Period
1850 1900 1950 2000-1
-0.5
0
0.5
1Cohort Effects
Cohort
af
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0 20 40 60 80 100-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
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Age
1930 1940 1950 1960 1970 1980 1990 2000 2010-0.08
-0.06
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0
0.02
PeriodEffects
Period
1850 1900 1950 20000
0.05
0.1
0.15
0.2
0.25
Cohort Effects
Cohort
0 20 40 60 80 100-0.2
0
0.2
0.4
0.6
0.8AgeEffects
Age
1930 1940 1950 1960 1970 1980 1990 2000 20100
0.02
0.04
0.06
0.08
0.1
0.12PeriodEffects
Period
1850 1900 1950 2000-0.3
-0.25
-0.2
-0.15
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-0.05
0
0.05Cohort Effects
Cohort
0 20 40 60 80 100-0.2
0
0.2
0.4
0.6
0.8AgeEffects
Age
1930 1940 1950 1960 1970 1980 1990 2000 20100
0.005
0.01
0.015
0.02PeriodEffects
Period
1850 1900 1950 2000-0.02
0
0.02
0.04
0.06
0.08Cohort Effects
Cohort
a[
7)%8(# =] g"&(BG "&3 g(&%*kS-"$(& "&3 l"2.(& &(#C"@%W"$%(&
0 20 40 60 80 100-0.2
0
0.2
0.4
0.6
0.8AgeEffects
Age
1930 1940 1950 1960 1970 1980 1990 2000 2010-0.01
-0.005
0
0.005
0.01PeriodEffects
Period
1850 1900 1950 2000-0.02
0
0.02
0.04
0.06
0.08
0.1Cohort Effects
Cohort
7)%8(# >] MG- 4&$#%&.%B -.$%C"$(#
0 20 40 60 80 100-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
AgeEffects
Age
1930 1940 1950 1960 1970 1980 1990 2000 2010-5
0
5
10
15x 10
-3 PeriodEffects
Period
1850 1900 1950 20000
0.02
0.04
0.06
0.08
0.1
Cohort Effects
Cohort
7)%8(# ?2 !"2%CIC =&$#(A/ =.$%C"$-.
0 20 40 60 80 100-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
AgeEffects
Age
1930 1940 1950 1960 1970 1980 1990 2000 2010-5
0
5
10
15x 10
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Period
1850 1900 1950 20000
0.02
0.04
0.06
0.08
0.1
Cohort Effects
Cohort
aZ
7)%8(# @2 +; 7-C"@- <"J(# 7(#B- l"#$%B%A"$%(& S"$"
10 20 30 40 50 60 70 800
0.5
1
Against age, by cohort
Age
1974
1959
1944
1929
1914
1899
10 20 30 40 50 60 70 800
0.5
1
Against age, by period
Age
1974
19892004
1970 1975 1980 1985 1990 1995 2000 2005 20100
0.5
1
Against period, by age
Period
1832
46
60
74
1970 1975 1980 1985 1990 1995 2000 2005 20100
0.5
1
Against period, by cohort
Period
1909
1937
1923
1951
1965 1979
1900 1920 1940 1960 19800
0.5
1
Against cohort, by age
Cohort
60
70
20
304050
1900 1920 1940 1960 19800
0.5
1
Against cohort, by period
Cohort
1974 1982 19901998 2006
a_
7)%8(# A2 8-$$%&* "*- O$(APQ A-#%(3 OC%33@-PQ B(G(#$ OJ($$(CP -V-B$. $( W-#(
10 20 30 40 50 60 70 80-1
-0.5
0
0.5
1AgeEffects
Age
1970 1975 1980 1985 1990 1995 2000 2005 2010-0.1
0
0.1
0.2
0.3
0.4PeriodEffects
Period
1900 1920 1940 1960 1980-0.4
-0.2
0
0.2
0.4
0.6
0.8
1Cohort Effects
Cohort
10 20 30 40 50 60 70 80-0.6
-0.4
-0.2
0
0.2
0.4AgeEffects
Age
1970 1975 1980 1985 1990 1995 2000 2005 2010-1
-0.5
0
0.5
1PeriodEffects
Period
1900 1920 1940 1960 19800
0.2
0.4
0.6
0.8Cohort Effects
Cohort
10 20 30 40 50 60 70 800
0.2
0.4
0.6
0.8
1AgeEffects
Age
1970 1975 1980 1985 1990 1995 2000 2005 2010-0.12
-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02PeriodEffects
Period
1900 1920 1940 1960 1980-1
-0.5
0
0.5
1Cohort Effects
Cohort
ac
7)%8(# B2 8-$$%&* "3U"B-&$ "*-. $( J- -^I"@O$(A] eYma`Q C%33@- aYmf`Q J($$(C] fYm[`P
10 20 30 40 50 60 70 800
0.5
1
1.5
2
2.5AgeEffects
Age
1970 1975 1980 1985 1990 1995 2000 2005 2010-0.5
0
0.5
1
1.5PeriodEffects
Period
1900 1920 1940 1960 1980-4
-3
-2
-1
0
1Cohort Effects
Cohort
10 20 30 40 50 60 70 800
0.1
0.2
0.3
0.4
0.5
0.6
0.7AgeEffects
Age
1970 1975 1980 1985 1990 1995 2000 2005 2010-0.1
0
0.1
0.2
0.3
0.4PeriodEffects
Period
1900 1920 1940 1960 1980-0.4
-0.2
0
0.2
0.4
0.6
0.8
1Cohort Effects
Cohort
10 20 30 40 50 60 70 800
2
4
6
8
10AgeEffects
Age
1970 1975 1980 1985 1990 1995 2000 2005 2010-1
0
1
2
3
4
5
6PeriodEffects
Period
1900 1920 1940 1960 1980-20
-15
-10
-5
0
5Cohort Effects
Cohort
aY
7)%8(# 9C2 g"&(BG "&3 g(%&*kS-"$(& "&3 l"2.(& &(#C"@%."$%(&
10 20 30 40 50 60 70 80-0.6
-0.4
-0.2
0
0.2
0.4AgeEffects
Age
1970 1975 1980 1985 1990 1995 2000 2005 2010-0.04
-0.02
0
0.02
0.04
0.06PeriodEffects
Period
1900 1920 1940 1960 1980-0.2
0
0.2
0.4
0.6
0.8Cohort Effects
Cohort
7)%8(# 992 4&$#%&.%B -.$%C"$(#
10 20 30 40 50 60 70 80-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6AgeEffects
Age
1970 1975 1980 1985 1990 1995 2000 2005 2010-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3PeriodEffects
Period
1900 1920 1940 1960 1980-0.2
0
0.2
0.4
0.6
0.8Cohort Effects
Cohort
7)%8(# 9;2 !"2%CIC =&$#(A/ =.$%C"$-.
10 20 30 40 50 60 70 80-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6AgeEffects
Age
1970 1975 1980 1985 1990 1995 2000 2005 2010-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3PeriodEffects
Period
1900 1920 1940 1960 1980-0.2
0
0.2
0.4
0.6
0.8Cohort Effects
Cohort
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