micmac combining micro and macro approaches in demographic forecasting a study commissioned by the...

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 -


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 -



• 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)


Episodes and dates required for each transition


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)

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

http://www.micmac-projections.org/

http://www.demogr.mpg.de/go/micmac

micmac combining micro and macro approaches in demographic forecasting a study commissioned by the...

Documents