MicMacCombining micro and macro approaches in demographic
forecasting
A study commissioned by the European Commission6th Framework Programme
Call for tenders: FP6-2003-SSP-3(May 2005 – April 2009)
Introduction to the MicMac project
QMSS2 Immigration and Population DynamicsLeeds, 2 – 9 July 2009
The project
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)
Aim 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
Expected outcome of MicMac
• Consortium:NIDI - Netherlands Interdisciplinary Demographic InstituteVID - Vienna Institute of DemographyINED - Institut National d’Études DémographiquesBU - Bocconi University EMC - Erasmus Medical CentreMPIDR - Max Planck Institute for Demographic ResearchIIASA - International Institute for Applied Systems AnalysisUROS - University of Rostock
• Period: May 1, 2005 – April 30, 2009
Participating institutes
Expert Meeting on Assumptions
WP 2Micro
Simulation
WP 3Uncertain
ty
WP 4Health
WP 5Fertility and living
arrangements
WP 6Dissemination of
results
WP 0Coordinatio
n
WP 1Multi-State
Methods
Education
NIDI
VID
NIDI
BU/VID/INED
NIDI/MPIDR
NIDI/MPIDR
The Work Packages
EMC/UROS
IIASA
The model
MicMacBiographic 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
Macro
Micro
Trend analysis by cohort (transition rates)
Individual behaviour (individual transitions) Individual
biographies
Current methodology Cohort-component method
Causal analysis Life history analysis
Macro-simulation (MACRO)
Micro-simulation (MICRO)
Cohort biographies
The micro-macro linkin demographic projection
The dual approach adopted in the workplan
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
Olivia
Formal workplace trajectory
Household trajectory
Olivia
Epros_Lux
State space and transitionsTransition rates
state 1
state 3
state 2
13(t,Z) 23(t,Z)
),( ),(),(
0),( ),(
00),(
)(
332313
2212
11
ZtZtZt
ZtZt
Zt
t
μ
11 = 12 + 13 and 22 = 21+ 23
12(t,Z)
State space and transitionsTransition rates
State 1Healthy
State 2Disabled
State 3Dead
12(x,t)
21(x,t)
23(x,t)13(x,t)
0 )()(
0)( )(
0)()(
)(
2313
2212
2111
tt
tt
tt
t
μ
where 11 = 12 + 13 and 22 = 21+ 23
State 1Healthy
State 2Disabled
State 3Reactivated
State 4Dead
12(x,t) 23(x,t)
34(x,t)
32(x,t)
24(x,t)14(x,t)
1. Living at parental home
5. First child
3. Married (no child)
4. Cohabiting
(no child)
2. Living alone
(no child)
Pathways to first child
• States•Transitions•Transition rates
Living arrangements of women Netherlands, Retrospective observations,
OG98
0
1000
2000
3000
4000
5000
6000
0 5 10 15 20 25 30 35 40 45 50
Censored
Married
Cohabit
Alone
AtHome
F igu re 9 .4
S ta te o cc u p a n c ie s ( liv in g a rra n gem en ts ) , w o m en , T h e N e th e rla n d s B ased in O G 9 8
0
1 0 0 0
2 0 0 0
3 0 0 0
4 0 0 0
5 0 0 0
6 0 0 0
7 0 0 0
8 0 0 0
9 0 0 0
1 0 0 0 0
1 5 2 0 2 5 3 0 3 5 4 0 4 5 5 0
A g e
Num
ber o
f coh
ort m
embe
rs
C h illd 1
M a rrie d
C o h a b it
A lo n e
A tH o m e
`
2 1 .1
3 .9
2 .9
3 .9
2 1 .2
Synthetic cohort biographyState occupancies, women, NL
0
1000
2000
3000
4000
5000
6000
0 5 10 15 20 25 30 35 40 45 50
Child1
Married
Cohabit
Alone
AtHome
Free of CVD (2998)
Death
hCVD
Free of CVD
Death
hAMI
hCVD- hCHD-
The dynamics of cardiovascular diseaseBased on the Framingham Heart Study (1948 - )
• hCVD = History of (other) CVD• hCHD = History of coronary heart disease• hAMI = history of acute myocardial infarction
1447
2382
2843
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
332211exp)(),( ZZZtZt ijij
baseline transition intensity
’s represent influence of covariates or treatment on transitions between the states
The effect of covariates or treatment is incorporated in the model via the transition intensity (transition rate)
COX
0.0
0.2
0.4
0.6
0.8
1.0
50 55 60 65 70 75 80 85 90 95
Age
Pro
po
rtio
n s
urv
ivin
g
hOCVD
Survival with and without cardiovascular disease
No hCVD
hCHD
• hCVD = History of (other) CVD• hCHD = History of coronary heart disease• hAMI = history of acute myocardial infarction
Males
Table 1. Marital status. State space and transitions
From \ toNever
marriedFirst
marriageSecond
marriageDivorced Widowed
Never married - TR1
First marriage - TR2 TR3
Second marriage
-
Divorced TR4 -
Widowed TR5 -
State space and transitionsWork Package 5 (D22)
Table 2. Living arrangement. State space and transitions
From \ toat parental
homeAlone/with
others (never in union)
First union Separated (after 1st
union disruption)
Second union
at parental home (never in union)
- TR7 TR6
Alone/with others - TR8
First union-
TR9
Separated (after 1st union disruption)
- TR10
Second union -
State space and transitionsWork Package 5 (D22)
Table 3. Fertility (own children ever born). State space and transitions
From \ tochildless 1 child 2 children 3 children 4+ children
Childless - TR11
1 child - TR12
2 children - TR13
3 children - TR14
4+ children -
State space and transitionsWork Package 5 (D22)
State space and transitionsWork 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
TRANSITIONAllowed covariates
TR1 never-married married (1st marriage) 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
* “Own children ever born” is always coded in only two categories: “childless/with children”.
TRANSITION Episode starts atEvents that cause
transitionsEvents that cause
censoringDates required(1)
TR1never-married married (1st marriage)
respondent’s birth 1st marriage interview (ymarr,mmarr)
TR2married (1st marriage)divorced
1st marriage divorcedeath of spouse,
interview
(ymarr,mmarr)(ydiv,mdiv)
(yved, mved)
TR3married (1st marriage) widowed
1st marriage death of spouse divorce, interview(ymarr,mmarr)
(ydiv,mdiv)(yved, mved)
TR4divorcedmarried (2nd marriage)
divorce 2nd marriagedeath of spouse,
interview
(ymarr,mmarr)(ydiv,mdiv)(yved,mved)
(ymarr2,mmarr2)
TR5widowedmarried (2nd marriage)
death of spouse 2nd marriage interview
(ymarr,mmarr)(ydiv,mdiv)(yved,mved)
(ymarr2,mmarr2)
TR6at parental home (never in union) first union
date of birthexit from parental home for union
exit from parental home for other
reasons ,interview
(ypartn,mpartn()yexit,mexit)
TR7at parental home alone/with others (never in union)
date of birthexit from parental
home for other reasons
exit from parental home for union,
interview
(ypartn,mpartn)(yexit,mexit)
TR11childless 1 child
respondent’s birth 1st child’s birth interview (ych1,mch1)
TR121 child 2 children
1st child’s birth+ 9 months
2st child’s birth interview(ych2,mch2)(ych1,mch1)
State space and transitionsWork Package 5 (D22)
Episodes and dates required for each transition
State space and transitionsWork 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
ik
kikii
i XageftimeExp
Events
)(
.ln 0
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 educationon the transition TR1, Italy
Smoothed curves
15 20 25 30 35 40 45 50
0.0
00.
05
0.1
00.
15
TR1 (never married->1st marriage) - MEN
Age
Tra
nsiti
on r
ate
15 20 25 30 35 40 45 50
0.0
00.
05
0.1
00.
15
by Education - MEN
Age
Tra
nsiti
on r
ate
primlowsecuppsectert
15 20 25 30 35 40 45 50
0.0
00.
05
0.1
00.
15
by Children Ever Born - MEN
Age
Tra
nsiti
on r
ate
noch1+ch
15 20 25 30 35 40 45 50
0.0
00.
05
0.1
00.
15
by Living Arrangement - MEN
Age
Tra
nsiti
on r
ate
par_homno_partpartner
Age-specific rates of transition TR1, Italy (smooth)
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)
0 3 6 9 12 16 20 24 28 32 36 40 44 48
Age
Co
un
t
02
00
04
00
06
00
08
00
01
00
00
01234+
Number of children, Females, Netherlands (MAPLE and OG2003)
35.55 5.19
6.90
1.890.38
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
State space, several domains of life
TOPALSA TOol for Projecting Age profiles
using Linear Splines
Joop de BeerNicole van der Gaag
(NIDI)
TOPALS is a relationale method: describes deviations from a standard schedule by linear splines
Age specific fertility, 2005
0.00
0.02
0.04
0.06
0.08
0.10
0.12
16
18
20
22
24
26
28
30
32
34
36
38
40
42
44
46
48
Europe2005 IT2005
Italy and average of Europe
TFR (Europe2005): 1.46
TFR (IT2005): 1.32
• 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
TOPALS relational model
Relative risks
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
Age groups and relative risks
*,
,x
xixi q
qr
is the rate at age x according to the standard age schedule
*xq
xiq , transition rate at age x in country i
age
rela
tive
ris
k
fertility, females IT2005
16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48
0.8
0.9
21
.04
1.1
61
.28
1.4
Linear spline through relative risks
0.00
0.02
0.04
0.06
0.08
0.10
0.12
16
18
20
22
24
26
28
30
32
34
36
38
40
42
44
46
48
Europe2005 IT2005 Brass TOPALS
Age specific fertility, 2005
TOPALS fit
TFR (Europe2005): 1.46
TFR (IT2005): 1.32
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
• 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
MicMac: Processor
Thank you
www.micmac-projections.org
www.demogr.mpg.de/go/micmac