20
40
60
80
Age
0.7
40
60
Age
y
80
0.5
0.6
20
0.4
Republican Vote
0.3
2000
2004
2008
2012
2000
2004
2008
2012
0.3
0.6
0.4
0.5
Republican Vote
0.6
0.5
0.4
0.3
Republican Vote
2008 McCain Vote
Lining up by Birth Year
0.7
Non−Monotonicity in Other Elections
0.7
Non−Monotonic Age Curve in 2008
1990
1970
1950
Birth Year
1930
1940
1950
1960
1970
1980
1990
2000
2010
0
Obama
Bush II
Clinton
Bush I
Reagan
Carter
Ford
Nixon
Johnson
Kennedy
Eisenhower
Truman
Roosevelt
25
50
75
Gallup Presidential Approval
Approve / (Approve + Disapprove)
100
T = {1960, 1961, . . . , 2012}
g∈G={
}
{1937, 1938, . . . , 1994}
c
∈
C
=
t ∈
θj
y
j
yj ∼
T
(nj , θj ) ,
θj
j
1990
1985
1980
1975
1970
1965
1960
1955
1950
1945
1940
2012
2008
2004
2000
1996
1992
1988
1984
1980
1976
1972
1968
1964
1960
0
0
10,000
2,000
20,000
40,000
4,000
30,000
6,000
50,000
Number of Survey Responses Included in Analysis
Sample Size by Election Year
Sample Size by Birth Year
J
yj
nj
j xj,i
i ∈ I = {1, 2, . . . , 70}
wi ∼
(wi−1 , 1) ,
w1
−1
β
w
g[j]
y=1
β
xj,1 = +21
w
σ=1
w
xj,2 = −1 × (88 − 50) = −38
x
αt,g ∼
t
g
γj = βg[j]
70
!
period
α
(0, σα )
wi xj,i ,
i=1
λg[j ]
wi
i
Aj
βg[j]
j
Aj = αt[j],g[j] + λg[j] wi[j] αt[j],g[j]
"
#
= 1 + λg[j] wi[j] αt[j],g[j] .
w
λ
w
λ∼
(0, σλ )
x
θj = γj + Aj
t
j
g
j
R̂
w
w1
The Formative Years
Formative Years Not As
Important for Minorities
0.02
●●
●
●
●
●
●
●●
●
●● ●● ●
●
●
●● ● ● ●
●
●
●
●
●
●● ●
●●
●
●● ●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
● ●
0.1
0.01
0.00
0.4
●
0.3
●
●
Posterior Density
0.03
●●
●●
● ● ●● ●
●
●
●
Non−Southern White
Southern White
Minority
0.2
0.04
Posterior Mean
50% C.I.
95% C.I.
0.0
−0.01
Age−Specific Weights (w)
0.5
18
10
20
30
40
50
60
70
0
5
10
Estimate of βg
Age
β
βg
x
15
20
Are Period Effects Stronger
During Formative Years?
Non−Southern White
Southern White
Minority
●
●
●
●
●
●
●
●
●
0
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
10
−2
●
5
●
●
●
Posterior Density
2
15
Non−Southern White
Southern White
Minority
●
1960
0
−4
Model Coefficient (αt, g)
4
Period Effects
by Race/Region
1970
1980
1990
2000
2010
Election
1.00
1.25
1.50
1.75
2.00
Effect Size Ratio, (Age 18 / Age 70)
λ
λ
β
β
R2
R2
53%
56%
57%
58%
Period/Group
Effects Model
Full Model
50%
Full Model
75%
100%
Non−Southern
White
Period/Group
Effects Model
Full Model
50%
Overall
Period/Group
Effects Model
25%
89%
Full Model
Period/Group
Effects Model
0%
Percent of Variance Explained
How Well Does the Model Explain Macro−Level Vote Choice?
Southern
White
Minority
92%
71%
x
w
N = 1242
N = 8162