Motivation
Model
Data
Result
Education and Health: The Role of Cognitive
Ability
Govert Bijwaard1
1 Netherlands
2 Erasmus
Hans van Kippersluis2
Interdisciplinary Demographic Institute (NIDI)
University Rotterdam, Erasmus School of Economics
Tinbergen Institute Rotterdam
Netspar, Tilburg, The Netherlands
Health, Education and Retirement over the Prolonged Life
Cycle, Nov. 27-29, 2013, Vienna
Conclusion
Motivation
Model
Data
Result
Conclusion
Motivation
Differences in health and life expectancy across educational
groups are striking and pervasive.
Recent results deriving from natural experiments in education
suggest that causal effect of education on health is small or
even absent (e.g. Lleras-Muney, 2005; Van Kippersluis et al.
2011; Meghir et al. 2012; Clark and Royer, 2013)
Suggest an important role for confounding factors, such as
discount rates, cognitive and non-cognitive skills (Murasko,
2007; Carneiro et al. 2007)
Motivation
Model
Data
Result
Conclusion
Motivation (2)
Established that cognitive ability and some non-cognitive
factors such as self-esteem are associated with health
outcomes at ages 30-40 (Elias, 2004; Auld and Sidhu, 2005;
Murasko, 2007; Carneiro et al. 2007; Kaestner and Collison,
2011)
Nonetheless, hardly anything is known about how much of the
association between education and health is explained by
these cognitive and non-cognitive abilities.
Motivation
Model
Data
Result
Conclusion
Motivation (3)
One notable exception: series of papers by Conti and Heckman
(2010), Conti et al. (2010; 2011), and Heckman et al. (2011) in
which they:
estimate a structural equation model modeling the
interdependence between education, health, and latent factors
capturing cognitive and non-cognitive abilities.
use the British Cohort Study with self-reported health
outcomes measured around age 30
show that around half of the association is due to the causal
effect of education on health outcomes, other half is selection
Motivation
Model
Data
Result
Conclusion
Our contribution
Disentangle the effects of education and cognitive ability on health
outcomes, using a multistate structural equation model
Contribution is twofold:
1
We observe mortality and hospitalization between ages 55 and
75 as objective health indicators
2
Extend structural equation model by Conti et al. (2010) to
allow for duration dependent variables (multistate);
time to death, time to hospitalization and time till discharge
from hospital
Motivation
Model
Data
Result
Basic model: educational choice
Assume a probit model for educational choice:
Let Di = 1 if the individual enters secondary education, and 0
otherwise.
(
1 if Di∗ ≥ 0
Di =
0 otherwise
Underlying latent utility for education depends on observed
characteristics X D and latent cognitive ability θ.
Di∗ = γXiD + αD θ + υD
with υD independent of XiD and θ
Conclusion
Motivation
Model
Data
Result
Conclusion
Basic model: potential outcomes
Two potential outcomes Yi 1 and Yi 0 depending on educational
choice, with observed outcome Yi
Yi = Di Yi 1 + (1 − Di )Yi 0
Where both Yi 1 and Yi 0 depend on exogenous characteristics X Y
and on latent cognitive ability θ.
Yi 0 = β0 XiY + α0 θ + υ0
Yi 1 = β1 XiY + α1 θ + υ1
with (υ0 , υ1 ) are independent of X Y and ability θ.
Motivation
Model
Data
Result
Basic model: measurements
Measurements for the ability
Mi ,1 = δ1 XiM + α1,M θ + υ1,M
..
.
Mi ,N
= δN XiM + αN,M θ + υN,M
2 )
with υM independent of XiM and θ and υM ∼ N (0, σM
θ is assumed to be discrete (3 level)-ability with Pr(θl ) = pl
For identification: α1,M = 1 and E(θ) = 0
Conclusion
Basic model: graphical representation
✯
M
θ
✲
D
❫
❄
Y0 , Y1
✙
D∗
Motivation
Model
Data
Result
Conclusion
Multistate
Multistate model
In our case, the outcome (mortality, time to discharge/admission)
is a duration, and we have 8 potential hazards λ(1) and λ(0) , with
(for each transition) the observed hazard:
λ(ti ) = λ(1) (ti 1 )Di · λ(0) (ti 0 )1−Di
with ti 1 is the duration for an individual with high education
(Di = 1) and ti 0 is the duration for an individual with low
education (Di = 0).
Multistate model: Y0 , Y1 transition rates
Healthy
λIH (τ )
✛
Illness
✲
λHI (t)
λID (τ )
λHD (t)
✎
❘
Death
Motivation
Model
Data
Result
Conclusion
Multistate
Hazards Multistate model
Assume Gompertz proportional hazard from the healthy state:
(k)
λHI (ti |X , θ) = e βkHI 0 +akHI ti exp βkHI Xi + αkHI θ
(k)
λHD (ti |X , θ) = e βkHD0 +akHD ti exp βkHD Xi + αkHD θ
and exponential: piecewise constant hazard from the illness
state
P
(k)
λIH (τi |X , ti , θ) = e βkIH0 + j akIH,j Ij (τ ) exp βkIH Xi + αkIH θ
P
(k)
λID (τi |X , ti , θ) = e βkID0 + j akID,j Ij (τ ) exp βkID Xi + αkID θ
for k = 0, 1 (education), t is age and τ is time in hospital (in days)
Motivation
Model
Data
Result
Conclusion
Multistate
Gains from changing school level
Use estimated model to derive effects of changing education:
ATE (t) =
ATET (t) =
ATEU(t) =
Z Z
ZZ
ZZ
E Y1 (t) − Y0 (t)|X = x, θ dFX ,θ (x, f )
E Y1 (t) − Y0 (t)|X = x, θ, D = 1 dFX ,θ|D=1(x, f )
E Y1 (t) − Y0 (t)|X = x, θ, D = 0 dFX ,θ|D=0 (x, f )
with Y1 (t), Y0 (t) many desired outcomes,
e.g. survival, life-expectancy, # of hospitalizations, probability ever
in hospital.
Use simulation based on estimated coefficients.
Motivation
Model
Data
Result
Conclusion
”Brabant” Data and mortality and hospitalization
Survey in 1952 among pupils of the sixth grade of primary schools
in the Dutch province of Noord-Brabant.
Detailed info on individual intelligence, social background and
school achievement (N = 5, 823)
Follow-up surveys in 1957, 1983 and 1993 providing labour
market behaviour (N = 2, 998)
Linkage to administrative records (Stat NL) municipality-,
cause of death- and hospital discharge register
Providing mortality and demographics (1995-2010) and
admission and discharge of hospitals, whether it was acute
(1995-2005) (N = 2579)
Motivation
Model
Data
Result
Conclusion
Descriptive statistics
Low-educated
48%
High-educated
52 %
16%
23%
12%
18%
2.4
25%
4.3
1.8
25%
4.8
95.2
57%
37%
107.6
59 %
18%
Mortality
died
% died in hospital
Hospitalization
# hospital stays
emergency
length of stay (days)
Intelligence
IQ
Male
Child works
0.90
0.85
0.80
0.75
Primary
Above primary
0.70
survival probability
0.95
1.00
Kaplan-Meier survival, by education level
55
60
65
age
70
75
Primary
Above primary
1.5
1.0
0.5
0.0
number of hospitalizations
2.0
2.5
Cumulative Number of hospital visits, by education level
56
58
60
62
age
64
66
0.04
Primary
Above primary
0.03
Primary
Above primary
0.01
0.02
cumulative incidence
0.6
0.4
0.00
0.2
0.0
cumulative incidence
0.8
1.0
Cumulative incidence from Healthy, by education level
56
58
60
62
64
age
Hospital admission
66
56
58
60
62
age
Death
64
66
0.015
Cumulative incidence from Hospital, by education level
Primary
Above primary
0.010
cumulative incidence
0.000
0.005
0.4
0.2
0.0
cumulative incidence
0.6
Primary
Above primary
0
5
10
15
20
days in hospital
Hospital discharge
25
30
0
5
10
15
days in hospital
Death
20
25
30
Parameter estimates (selection)
Education
Hazards
from healthy
(0)
λHI
(1)
λHI
(0)
λHD
(1)
λHD
from ill
(0)
λIH
(1)
λIH
(0)
λID
(1)
λID
Measurement
α
−1.33∗
male
0.04
workchild
−0.21∗
brank5
−0.11
Prot.
0.49∗
acute
−
−6.47∗
−5.65∗
−4.62∗
−4.48∗
0.40∗
0.37∗
1.05∗
0.59∗
−0.19∗
−0.08
0.28
−0.02
0.53∗
−0.24∗
0.20
−0.83∗
−
−
−
−
−
−
−
−
−0.12
0.77∗
−0.56
−0.63
1
0.02
−0.03
0.48
0.23
−0.92
−0.21∗
0.11
−0.19
−0.39
−3.81∗
0.04
−0.15
−0.02
−0.30
−3.03∗
−
−
−
−
5.18∗
−0.83∗
−0.67∗
2.05∗
1.01∗
−
ATE
ATET
ATEU
0.10
0.05
0.00
difference in survival
0.15
0.20
Survival gain for high educated
60
70
80
age
90
100
0.10
Decomposition
0.00
0.02
0.04
0.06
0.08
Treatment Effect
Selection Effect
55
57
59
61
63
65
67
69
71
73
age
Decomposition of observed difference in Kaplan-Meier survival
function in treatment effect and selection effect
Treatment Effect
Selection Effect
0.0
−0.5
−1.0
−0.5
−1.0
ATE
ATET
ATEU
56
−2.0
−2.0
−1.5
−1.5
difference in # hospitalizations
0.5
0.0
1.0
Gain in number of hospital visits
58
60
62
64
66
age
Estimated gain in # visits
55
56
57
58
59
60
61
62
63
age
Decomposition
64
65
66
67
0.00
−0.05
0.05
Treatment Effect
Selection Effect
−0.05
−0.10
−0.10
−0.15
ATE
ATET
ATEU
56
−0.15
−0.20
difference in probability ever in hospital
0.00
0.10
Gain ever in hospital
58
60
62
64
age
Estimated gain in
probability
66
55
56
57
58
59
60
61
62
63
age
Decomposition
64
65
66
67
Motivation
Model
Data
Result
Conclusion
Gain of education
High educated live longer and are less frequent in hospital
Latent (cognitive) skills (selection)
Survival
Positive selection, explains up to 50%
Ever in hospital/number of hospitalizations
Negative selection, increases education gain
Conclusion