Transcript No Slide Title

MicMac
Combining micro and macro approaches
in demographic forecasting
A study commissioned by the European Commission
6th Framework Programme
Call for tenders: FP6-2003-SSP-3
(May 2005 – April 2009)
Introduction to the MicMac project
QMSS2 Immigration and Population Dynamics
Leeds, 2 – 9 July 2009
The project
Aim of MicMac
To develop a methodology that complements
conventional population projections by age and sex
(aggregate projections of cohorts, Mac)
with
projections of the way people live their lives
(projections of individual cohort members, Mic)
Expected outcome of MicMac
A model and software program to generate
detailed demographic projections
that can be used in the context of the development of
sustainable (elderly) health care and pension systems
Participating institutes
• Consortium:
NIDI - Netherlands Interdisciplinary Demographic Institute
VID
- Vienna Institute of Demography
INED - Institut National d’Études Démographiques
BU
- Bocconi University
EMC - Erasmus Medical Centre
MPIDR - Max Planck Institute for Demographic Research
IIASA - International Institute for Applied Systems Analysis
UROS - University of Rostock
• Period:
May 1, 2005 – April 30, 2009
The Work Packages
WP 0
Coordination
NIDI
Expert Meeting on
Assumptions
EMC/UROS
WP 4
Health
NIDI
WP 1
Multi-State Methods
WP 2
Micro Simulation
Education
NIDI/MPIDR
VID
WP 3
Uncertainty
IIAS
A
WP 5
Fertility and living
arrangements
NIDI/MPIDR
WP 6
Dissemination of results
BU/VID/INE
D
The model
MicMac
Biographic forecasting
• A macro-model (MAC)
– Extends the cohort-component model to multistate
populations
– Cohort biographies
• A micro-model (MIC) that models demographic
events at the individual level
– a dynamic micro-simulation model that predicts life
transitions at the individual level
– Individual biographies
– Point of departure: LifePaths (Statistics Canada
The micro-macro link
in demographic projection
The dual approach adopted in the workplan
Trend analysis
Macro by cohort
(transition rates)
Current methodology
Cohort-component method
Individual behaviour
Micro (individual transitions)
Cohort
biographies
Individual
biographies
Macrosimulation
(MACRO)
Microsimulation
(MICRO)
Causal analysis
Life history analysis
Inspired by Coleman (1991) Foundations of social theory. Belknap Press of Harvard
The projection model is
a multistate probability model
• States (attributes)
– At the individual level:
• State probability: probability that an individual has a
given attribute at a given age (is in a given state at a
given age) (state probability)
– At the aggregate (population) level: counts
• State occupancy: expected value of the number of
people of a given age with a given attribute
• Transitions between states
• Transition probability: transitions / risk set
• Transition rate: transitions / exposure time
State variables and covariates
•
•
•
•
•
age
sex
level of educational attainment
living arrangement
health
MicMac is a generic model
Household trajectory
Olivia
Formal workplace trajectory
Olivia
Epros_Lux
State space and transitions
Transition rates
12(t,Z)
state 1
state 2
23(t,Z)
13(t,Z)
state 3
0
 11 (t , Z )
μ(t )   12 (t , Z )
 22 (t , Z )
 13 (t , Z )   23 (t , Z )


0

 33 (t , Z )
11 = 12 + 13 and 22 = 21+ 23
0
State space and transitions
Transition rates
12(x,t)
State 1
Healthy
State 2
Disabled
21(x,t)
13(x,t)
23(x,t)
State 3
Dead
 11 (t )   21 (t )
μ(t )   12 (t )
22 (t )

 13 (t )  23 (t )
0
0

0
where 11 = 12 + 13 and 22 = 21+ 23
State 1
Healthy
12(x,t)
14(x,t)
State 2
Disabled
24(x,t)
State 4
Dead
23(x,t)
32(x,t)
State 3
Reactivated
34(x,t)
Pathways to first child
1. Living at
parental home
2. Living alone
(no child)
3. Married
(no child)
5. First child
• States
•Transitions
•Transition rates
4. Cohabiting
(no child)
Living arrangements of women Netherlands,
Retrospective observations, OG98
6000
5000
Censored
Married
4000
Cohabit
Alone
3000
AtHome
2000
1000
0
0
5
10
15
20
25
30
35
40
45
50
6000
5000
Child1
Married
4000
Cohabit
Alone
3000
AtHome
2000
1000
0
0
5
10
15
20
25
30
35
40
Synthetic cohort
biography
Figure 9.4
State occupancies,
Based in OG98women, NL
State occupancies (living arrangements), women, The Netherlands
10000
Number of cohort members
9000
21.1
8000
3.9
Chilld1
7000
Married
6000
Cohabit
5000
Alone
4000
AtHome
3000
2.9
2000
21.2
1000
3.9
0
15
20
25
30
35
Age
40
45
50
45
50
The dynamics of cardiovascular disease
Based on the Framingham Heart Study (1948 - )
Free of CVD (2998)
Free of CVD
2843
hCVD-
1447
hCHD-
hCVD
2382
hAMI
Death
• hCVD = History of (other) CVD
Death
• hCHD = History of coronary heart disease
• hAMI = history of acute myocardial infarction
A. Peeters, A.A. Mamun, F.J. Willekens and L. Bonneux (2002) A cardiovascular
life course. A life course analysis of the original Framingham Heart Study cohort.
European Heart Journal, 23, pp. 458- 466
The effect of covariates or treatment
is incorporated in the model via the
transition intensity (transition rate)
ij (t, Z )  ij (t ) exp1Z1  2 Z2  3Z3 
COX
baseline transition intensity
’s represent influence of covariates
or treatment on transitions between
the states
Survival with and without cardiovascular disease
1.0
Males
Proportion surviving
0.8
hOCVD
0.6
hCHD
0.4
No hCVD
0.2
0.0
50
55
60
65
70
75
80
85
90
95
Age
• hCVD = History of (other) CVD
• hCHD = History of coronary heart disease
• hAMI = history of acute myocardial infarction
State space and transitions
Work Package 5 (D22)
Table 1. Marital status. State space and transitions
From \ to
Never married
First marriage
Never
married
First
marriage
-
TR1
Second
marriage
-
Second
marriage
-
Divorced
TR4
Widowed
TR5
Divorced
Widowed
TR2
TR3
-
State space and transitions
Work Package 5 (D22)
Table 2. Living arrangement. State space and transitions
From \ to
at parental home
(never in union)
Alone/with others
First union
Separated (after 1st
union disruption)
Second union
at parental
home
Alone/with
others
(never in
union)
First union
-
TR7
TR6
-
TR8
-
Separated
(after 1st
union
disruption)
Second
union
TR9
-
TR10
-
State space and transitions
Work Package 5 (D22)
Table 3. Fertility (own children ever born). State space and transitions
childless
1 child
-
TR11
2 children
3 children
4+ children
From \ to
Childless
1 child
2 children
3 children
4+ children
-
TR12
-
TR13
-
TR14
-
State space and transitions
Work Package 5 (D22)
• Covariates
– Sex
• Men
• Women
– Education
• 1. Primary (ISCED0 pre-primary education and ISCED1 first stage of
basic education)
• 2. Lower secondary (ISCED2 second stage of basic education)
• 3. Upper secondary (ISCED3 upper secondary education and ISCED4
post secondary non-tertiary education)
• 4. Tertiary (ISCED5 first stage of tertiary education and ISCED6 second
stage of tertiary education)
Allowed covariates for each transition
TRANSITION
TR1 never-married  married (1st marriage)
* “Own children ever born” is
always coded in only two
categories: “childless/with
children”.
Allowed covariates
EDU, LIV, CHI
TR2 married (1st marriage) divorced
EDU,CHI
TR3 married (1st marriage) widowed
EDU,CHI
TR4 divorced married (2nd marriage)
EDU, CHI
TR5 widowed married (2nd marriage)
EDU, CHI
TR6 at parental home (never in union)  first union
EDU, CHI*
TR7 at parental home alone/with others (never in
union)
EDU, CHI*
TR8 alone/ with others (never in union)  first union
EDU, CHI*
TR9 first union separated (after 1st union
disruption)
EDU, MAR, CHI,
TR10 alone or with other persons (after the 1st union
disruption) with a partner (2nd union)
EDU, MAR,CHI
TR11 childless  child
EDU, MAR, LIV
TR12 1 child 2 children
EDU, MAR, LIV
TR13 2 children  3 children
EDU, MAR, LIV
TR14 3 children  4 children
EDU, MAR, LIV
State space and transitions
Work Package 5 (D22)
Episodes and dates required for each transition
TRANSITION
Episode starts at
Events that cause
transitions
Events that cause
censoring
TR1
never-married 
married (1st marriage)
respondent’s birth
1st marriage
interview
TR2
married (1st marriage)
divorced
1st marriage
divorce
death of spouse,
interview
(ymarr,mmarr)
(ydiv,mdiv)
(yved, mved)
TR3
married (1st marriage)
widowed
1st marriage
death of spouse
divorce, interview
(ymarr,mmarr)
(ydiv,mdiv)
(yved, mved)
death of spouse,
interview
(ymarr,mmarr)
(ydiv,mdiv)
(yved,mved)
(ymarr2,mmarr2)
(ymarr,mmarr)
(ydiv,mdiv)
(yved,mved)
(ymarr2,mmarr2)
TR4
divorced
married (2nd marriage)
TR5
widowed
married (2nd marriage)
divorce
2nd
marriage
Dates required(1)
(ymarr,mmarr)
death of spouse
2nd marriage
interview
TR6
at parental home (never in
union)  first union
date of birth
exit from parental
home for union
exit from parental
home for other
reasons ,interview
(ypartn,mpartn
()yexit,mexit)
TR7
at parental home
alone/with others (never
in union)
date of birth
exit from parental
home for other
reasons
exit from parental
home for union,
interview
(ypartn,mpartn)
(yexit,mexit)
TR11
childless 
1 child
respondent’s birth
1st child’s birth
interview
TR12
1 child 
2 children
1st child’s birth+ 9
months
2st child’s birth
interview
(ych1,mch1)
(ych2,mch2)
(ych1,mch1)
State space and transitions
Work Package 5 (D22)
Age-specific transition rates are estimated using
Generalized Additive Models (GAM)
Hastie and Tibshirani (1990)
http://en.wikipedia.org/wiki/Generalized_additive_model
http://www.statsoft.com/textbook/stgam.html
Purpose of generalized additive models: maximize the quality of
prediction of a dependent variable Y from various distributions of the
predictor variables. Predictor variables are "connected" to the dependent
variable via a link function.
GAMs combine GLMs and linear models
 Eventsi
ln
 Exp.tim ei

   0  f (agei )    k X ki   i
k

Cubic spline
Effect of covariates for
each age interval
delimited by 2 knots
Proportional effects of education
on the transition TR1, Italy
Baseline = grand mean for whole same (deviation coding); report p. 24
Proportional effects of education
on the transition TR1, Italy
Smoothed curves
Age-specific rates of transition TR1, Italy (smooth)
by Education - MEN
0.15
0.10
0.00
25
30
35
40
45
50
15
20
25
30
35
40
Age
Age
by Children Ever Born - MEN
by Living Arrangement - MEN
50
0.15
par_hom
no_part
partner
0.00
0.00
0.05
0.10
Transition rate
0.15
noch
1+ch
45
0.10
20
0.05
15
Transition rate
prim
lowsec
uppsec
tert
0.05
Transition rate
0.10
0.05
0.00
Transition rate
0.15
TR1 (never married->1st marriage) - MEN
15
20
25
30
35
Age
40
45
50
15
20
25
30
35
Age
40
45
50
Age-specific rates of transition TR2, Italy (smooth)
Age-specific rates of transition TR2, Italy (smooth)
Age-specific rates of transition TR11, Italy (smooth)
Transitions that can be analyzed with FFS-NL
TR1 never-married  married (1st marriage)
TR2 married (1st marriage) divorced
TR3 married (1st marriage) widowed
TR4 divorced married (2nd marriage)
TR5 widowed married (2nd marriage)
TR6 at parental home (never in union)  first union
TR7 at parental home alone/with others (never in union)
TR8 alone/ with others (never in union)  first union
TR9 first union separated (after 1st union disruption)
TR10 alone or with other persons (after the 1st union disruption) with a
partner (2nd union)
TR11 childless  child (only women)
TR12 1 child 2 children (only women)
TR13 2 children  3 children (only women)
TR14 3 children  4 children (only women)
Age-specific rates of transition TR1, NL (smooth)
10000
Number of children, Females, Netherlands (M APLE and OG2003)
0.38
8000
1.89
Count
6000
6.90
35.55
5.19
0
2000
4000
0
1
2
3
4+
0
3
6
9
12
16
20
24
Age
28
32
36
40
44
48
State space, several domains of life
M
males
F
females
nS
never smoker
dS
daily smoker
pS
past daily smoker
I02
low level education
I34
middle level education
I56
high level education
nD
non disabled
D
disabled
TOPALS
A TOol for Projecting Age profiles using
Linear Splines
Joop de Beer
Nicole van der Gaag
(NIDI)
TOPALS is a relationale method: describes deviations
from a standard schedule by linear splines
Age specific fertility, 2005
Italy and average of Europe
0.12
0.10
0.08
0.06
0.04
0.02
Europe2005
IT2005
TFR (Europe2005): 1.46
TFR (IT2005):
1.32
48
46
44
42
40
38
36
34
32
30
28
26
24
22
20
18
16
0.00
TOPALS relational model
• Assume a standard age schedule
– European average / Model schedule (Hadwiger)
• Model deviations using relative risks (RR)
– RRs for limited number of knots
– RR is average value for age interval
• Describe age pattern of RRs by linear splines
– A piecewise linear curve
• Calculate transition rates
– Multiply standard age schedule by RRs
Age groups and relative risks
Relative risks
qi , x
ri , x  *
qx
q*x
qi , x
Age
IT2005 vs
Europe 2005
Knots
16-21
0.48
19
22-26
0.65
24
27-29
0.78
28
30-32
0.96
31
33-40
1.90
36
41+
1.50
44
is the rate at age x according to the standard age schedule
transition rate at age x in country i
1.16
1.04
0.92
0.8
relative risk
1.28
1.4
females IT2005
Linear splinefertility,
through
relative risks
16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48
age
Age specific fertility, 2005
TOPALS fit
0.12
0.10
0.08
0.06
0.04
0.02
Europe2005
IT2005
Brass
TFR (Europe2005): 1.46
TFR (IT2005):
1.32
TOPALS
48
46
44
42
40
38
36
34
32
30
28
26
24
22
20
18
16
0.00
Assumptions for MicMac scenarios
•
Future values of transition rates
•
General procedure:
- specify model curve describing age pattern
choose age schedule that captures general pattern
- specify assumptions on future values of the parameters
of the model curve
model deviations from the general pattern
using relative risks
The software
MicMac: Processor
• Pre-processor: estimates the transition
rates
• Processor:
– Produces population projections
– Produces cohort and individual biographies
– Sequence of states
– Sojourn times
• Postprocessor
– Processes the results
– Tabulations
– Graphics
– Analysis
Thank you
www.micmac-projections.org
www.demogr.mpg.de/go/micmac