The MIMOSA Model for Estimating International Migration in the European Union

James Raymer and Guy AbelFebruary 2008

MIgration MOdelling for Statistical Analyses(Eurostat Project 2006/S 100-106607/EN, LOT 2)

MIMOSA project• Aim of project

– Development and application of statistical modelling techniques for the estimation of missing data on migration flows and foreign population stocks

– Work with National Statistical Agencies to improve their data

• Funded by Eurostat, December 2006-2009– Netherlands Interdisciplinary Demographic Institute

(Coordinator)– Central European Forum for Migration and

Population Research– Southampton Statistical Sciences Research Institute – GéDAP, Université Catholique de Louvain

• Focus of this presentation: Migration flow estimation

Significance• The study of international migration in the

European Union is currently hindered by data availability, quality and consistency

• Harmonization of data collection processes and the data they generate is not even close to being realized, therefore our understanding of population change and migration policy is therefore currently limited

• To overcome these obstacles, we need models to (i) harmonise and correct for inadequacies in the available data and (ii) estimate the missing patterns

Data used in this study• Provided by Eurostat (i.e., data comes

from the Joint Questionnaire on International Migration)

• Immigration and emigration flows by previous / next country of residence (32 by 32 matrix)– 31 European countries: EU plus Iceland,

Liechtenstein, Norway and Switzerland– Rest of world

• Years: 2002, 2003, 2004 and 2005

I = Receiving country’s reported flow; E = sending country’s reported flow;… = no reported data available

Origin BE CZ DK DE EE GR ES FR IE ITBE I 80 587 4291 … … 3037 … … 1959

E … … … … … … … … …CZ I … 232 9258 … … 388 … … 915

E 78 47 950 2 66 70 283 31 197DK I … 65 2693 … … 764 … … 281

E 511 180 2540 133 229 1720 1333 264 782DE I … 1228 3221 … … 13746 … … 12902

E 4623 8909 2712 597 18106 16236 19060 2415 33802EE I … 4 169 947 … 60 … … 103

E … … … … … … … … …GR I … 57 278 12959 … 273 … … 638

E … … … … … … … … …ES I … 103 1665 14647 … … … … 2051

E 647 34 130 2109 4 38 2474 487 801FR I … 462 1488 18133 … … 8847 … 4647

E … … … … … … … … …IE I … 45 306 2046 … … 1649 … 292

E … … … … … … … … …IT I … 274 895 23702 … … 5796 … …

E 1414 20 155 9778 1 211 895 2933 130

Destination

Double-entry matrix for selected countries, 2003

Double-entry matrix for selected countries, 2003

Origin BE CZ DK DE EE GR ES FR IE ITBE I 80 587 4291 … … 3037 … … 1959

E … … … … … … … … …CZ I … 232 9258 … … 388 … … 915

E 78 47 950 2 66 70 283 31 197DK I … 65 2693 … … 764 … … 281

E 511 180 2540 133 229 1720 1333 264 782DE I … 1228 3221 … … 13746 … … 12902

E 4623 8909 2712 597 18106 16236 19060 2415 33802EE I … 4 169 947 … 60 … … 103

E … … … … … … … … …GR I … 57 278 12959 … 273 … … 638

E … … … … … … … … …ES I … 103 1665 14647 … … … … 2051

E 647 34 130 2109 4 38 2474 487 801FR I … 462 1488 18133 … … 8847 … 4647

E … … … … … … … … …IE I … 45 306 2046 … … 1649 … 292

E … … … … … … … … …IT I … 274 895 23702 … … 5796 … …

E 1414 20 155 9778 1 211 895 2933 130

Destination

I = Receiving country’s reported flow; E = sending country’s reported flow;… = no reported data available

Origin BE CZ DK DE EE GR ES FR IE ITBE I 80 587 4291 … … 3037 … … 1959

E … … … … … … … … …CZ I … 232 9258 … … 388 … … 915

E 78 47 950 2 66 70 283 31 197DK I … 65 2693 … … 764 … … 281

E 511 180 2540 133 229 1720 1333 264 782DE I … 1228 3221 … … 13746 … … 12902

E 4623 8909 2712 597 18106 16236 19060 2415 33802EE I … 4 169 947 … 60 … … 103

E … … … … … … … … …GR I … 57 278 12959 … 273 … … 638

E … … … … … … … … …ES I … 103 1665 14647 … … … … 2051

E 647 34 130 2109 4 38 2474 487 801FR I … 462 1488 18133 … … 8847 … 4647

E … … … … … … … … …IE I … 45 306 2046 … … 1649 … 292

E … … … … … … … … …IT I … 274 895 23702 … … 5796 … …

E 1414 20 155 9778 1 211 895 2933 130

Destination

Double-entry matrix for selected countries, 2003

I = Receiving country’s reported flow; E = sending country’s reported flow;… = no reported data available

DataImmigration Emigration

Timing Other EEA Nationals Other EEA Nationals

Instant DE, IE*, IT*, LU*, ES

BE, EE, FI, DE, IE*, IT*, LV, LU*, ES

EE, DE, IE*, LU*, ES

BE, EE, DE, IE*, LU*, ES

3 months AT*, BE, EE, HU, SI

AT*, HU, SI AT*, BE, HU, SI AT*, HU, SI

6 months DK, IS*, LT, NL, NO

DK, IS*, LT, NL, NO

DK, LV, NO DK, LV, LT, NO

12 months CY, CZ, FI, LV, PT, SE, CH, UK

CY, SE, CH, UK CY, IT*, FI, LT, NL, PT, SE, CH, UK

CY, IT*, FI, NL, PT, SE, CH, UK

Permanent MT*, PL, RO*, SK CZ, MT*, PL, RO*, SK

CZ, MT, PL, RO, SK

CZ, MT, PL, RO, SK

Unknown BG, FR, GR, LI BG, FR, GR, LI, PT

BG, FR, GR, IS*, LI

BG, FR, GR, IS*, LI

•Only partial data exists between 2001 and 2004; •Italics: No data exists between 2001 and 2004

Methodology• Harmonise and clean available data

– Identify base data (DK, FI, SE and NO)– Calculate adjustment ratios and adjust

reported data by using iterative procedure

• Estimate missing data– Immigration and emigration totals for

European matrix– Associations between origins and

destinations

dk nl at fi se no de es cz lu cy lv lt uk si pl ro sk be ee gr fr ie it hu mt pt bg is li ch RW Tdk ** ** ** ** ** ** ** ** ** ** ** ** ** ** **nl ** ** ** ** ** ** ** ** ** ** ** ** ** ** **at ** ** ** ** ** ** ** ** ** ** ** ** ** ** **fi ** ** ** ** ** ** ** ** ** ** ** ** ** ** **se ** ** ** ** ** ** ** ** ** ** ** ** ** ** **no ** ** ** ** ** ** ** ** ** ** ** ** ** ** **de ** ** ** ** ** ** ** ** ** ** ** ** ** ** **es ** ** ** ** ** ** ** ** ** ** ** ** ** ** **cz ** ** ** ** ** ** ** ** ** ** ** ** ** ** **lu ** ** ** ** ** ** ** ** ** ** ** ** ** ** **cy ** ** ** ** ** ** ** ** ** ** ** ** ** ** **lv ** ** ** ** ** ** ** ** ** ** ** ** ** ** **lt ** ** ** ** ** ** ** ** ** ** ** ** ** ** **uk ** ** ** ** ** ** ** ** ** ** ** ** ** ** **si ** ** ** ** ** ** ** ** ** ** ** ** ** ** **pl ** ** ** ** ** ** ** ** ** ** ** ** ** ** **ro ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **sk ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **be ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **ee ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **gr ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **fr ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **ie ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **it ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **hu ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **mt ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **pt ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **bg ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **is ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **li ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **ch ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **RW ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **T ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **

Available data by receiving countries

dk nl at fi se no de es cz lu cy lv lt uk si pl ro sk be ee gr fr ie it hu mt pt bg is li ch RW Tdk ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **nl ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **at ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **fi ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **se ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **no ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **de ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **es ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **cz ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **lu ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **cy ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **lv ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **lt ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **uk ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **si ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **pl ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **roskbeeegrfrieithumtptbgislichRWT

Available data by sending countries

Step 1 of iterative adjustment procedure: Identify and adjust base

data

Origin DK FI SE NO NL DE 7 8 9 10

DK

FI Very reliable sending country (E) data

SE (adjusted)

NO

NL

DE Very reliable receiving

7 country data

8 (not adjusted)

9

10

Destination

Note, procedure applied to 2002-2005 data pooled over time

Step 2 of iterative adjustment procedure: Calculate adjustment

ratios

Origin DK FI SE NO NL DE 7 8 9 10

DK Divide the sum of the

FI corresponding flows

SE from base by the sum of

NO these flows

NL

DE

7 Divide the sum of the

8 corresponding flows

9 from base by the sum of

10 these flows

Destination

Note, procedure applied to 2002-2005 data pooled over time

Step 3 of iterative adjustment procedure: Add adjusted flows to base

data

Origin DK FI SE NO NL DE 7 8 9 10

DK

FI Very reliable sending country (E) data

SE (adjusted)

NO

NL

DE Very reliable receiving

7 country data Adjusted emigration

8 (not adjusted) data

9 Adjusted

10 immigration data

Destination

Note, procedure applied to 2002-2005 data pooled over time

Adjustment factors for receiving country (I) and sending country (E) migration data, 2002-2005

Country I E Country I E

Denmark 1.000 1.081 Latvia 6.990 7.433

Finland 1.000 0.994 Lithuania 3.624 3.314

Sweden 1.000 1.055 United Kingdom 1.059 1.048

Norway 1.000 1.122 Slovenia 0.779 0.816

Netherlands 0.960 0.795 Italy 2.027 2.523

Germany 0.758 0.792 Luxembourg 1.256 1.218

Czech Republic 4.464 6.700 Austria 0.804 1.095

Spain 0.821 2.839 Iceland 0.947 0.976

Cyprus 0.738 2.883

Final adjusted matrixdk nl at fi se no de es cz lu cy lv lt uk si pl ro sk be ee gr fr ie it hu mt pt bg is li ch RW T

dk ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **nl ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **at ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **fi ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **se ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **no ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **de ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **es ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **cz ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **lu ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **cy ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **lv ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **lt ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **uk ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **si ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **pl ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **ro ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **sk ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **be ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **ee ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **gr ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **fr ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **ie ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **it ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **hu ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **mt ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **pt ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **bg ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **is ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **li ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **ch ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **RW ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **T ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **

Estimated coefficients for regressions on natural logarithms of available immigration and emigration flows from / to EU matrix and rest of world (n = 59)

Variable B t Sig. Adj. R 2B t Sig. Adj. R 2

A. EU matrix

(Constant) -4.9000 -1.6802 0.0990 0.9119 9.5455 4.1967 0.0001 0.9355

ln of Population (in 1000) 0.7448 11.9010 0.0000 0.6998 14.3387 0.0000

65+ / 20-64 years -0.0415 -1.4781 0.1455 -0.0582 -2.6547 0.0106

life expectancy (females) 0.0848 2.2626 0.0280 -0.0867 -2.9651 0.0046

GDP (relative) 0.0062 3.1971 0.0024 0.0063 4.1116 0.0001

% refugees of foreign-born -0.0467 -3.7380 0.0005 -0.0377 -3.8666 0.0003

% urban 0.0273 3.7797 0.0004 0.0333 5.9243 0.0000

ln of % foreign-born 0.0499 0.4114 0.6825 -0.1320 -1.3958 0.1688

Dummy variable for DE 0.7422 2.8628 0.0061 1.1528 5.7011 0.0000

B. Rest of world

(Constant) -8.4355 -1.9840 0.0526 0.9636 28.3149 5.0110 0.0000 0.9113

ln of Population (in 1000) 1.0910 22.7613 0.0000 0.9424 14.7935 0.0000

65+ / 20-64 years -0.0574 -2.3774 0.0212 -0.0891 -2.7779 0.0076

life expectancy (females) 0.1179 2.3527 0.0225 -0.3052 -4.5827 0.0000

GDP (relative) -0.0087 -5.1765 0.0000 -0.0127 -5.7010 0.0000

% refugees of foreign-born -0.0040 -0.3504 0.7275 -0.0298 -1.9415 0.0577

% urban 0.0188 2.9673 0.0046 0.0036 0.4257 0.6721

ln of % foreign-born 0.1726 1.7728 0.0822 0.6918 5.3451 0.0000

Dummy variable for EAST -0.3584 -1.4596 0.1505 -1.9921 -6.1042 0.0000

EmigrationImmigration

Multiplicative components

where

Origin by destination migration flow table

1 2 3 Total

1 0 n12 n13 n1+

2 n21 0 n23 n2+

3 n31 n32 0 n3+

Total n+1 n+2 n+3 n++

Region of

Origin

Region of Destination

1 2 3 Total

1 0 OD12 OD13 O1

2 OD21 0 OD23 O2

3 OD31 OD32 0 O3

Total D1 D2 D3 T

Region of

Origin

Region of Destination

Multiplicative component model

))()()(( ijjiij ODDOTn

)])()(/[(

/

/

jiijij

jj

ii

DOTnOD

TnD

TnO

nT

Estimating the ODij assocations• ODij = reported to expected flows

• Expected flows obtained using iterative proportional fitting (IPF) and estimated margins from EU matrix

• Two sets of ODij

– Available data– Missing data: ...)ln( 2211 ijijij XXOD

Estimated coefficients for regression on available origin-destination associations within the EU matrix (n=2540)

Variable B t Sig. Adj. R 2

(Constant) 0.4697 1.5630 0.1182 0.4073

contiguity 0.3398 4.0653 0.0000

new accession countries 0.7157 3.7117 0.0002

language family 0.4348 4.9863 0.0000

after 2003 0.1340 3.2068 0.0014

ln of GNI PPP ratios 0.1088 5.5536 0.0000

ln of distance -0.1097 -2.6194 0.0089

ln of foreign-born OD associations 0.2262 14.4113 0.0000

ln of trade OD assocations 0.2950 11.9247 0.0000

Estimated migration totals, 2002-2005: within the EU matrix and from / to rest of world

Within From To Net GainEU Rest of Rest of Rest of

Year Matrix World World Total World

2002 1,267 2,201 1,118 4,587 1,0832003 1,437 2,247 1,130 4,814 1,1172004 1,534 2,290 1,110 4,934 1,1802005 1,577 2,200 1,091 4,867 1,108

Top 20 estimated immigration and emigration countries (in thousands), 2002-2005

0 200 400 600

2002 ES2002 UK2003 UK2005 DE2002 IT

2002 FR2003 FR2004 IT2005 IT

2004 DE2005 UK2003 DE2004 FR2005 FR2004 UK2003 ES2003 IT

2004 ES2005 ES2002 DE

0 200 400 600

2005 FR2003 PL2004 FR2004 ES2005 ES2002 FR2004 PL2003 FR2005 PL2005 RO2004 RO2003 RO2002 UK2003 UK2004 UK2005 UK2002 DE2003 DE2005 DE2004 DE

Immigration Emigration

Estimated emigration flows from Poland, 2002-2005

0

20,000

40,000

60,000

80,000

100,000

120,000

DK FI SE NO NL DE CZ ES CY LV LT UK SI IT LU AT IS RO SK PL BE EE GR FR IE HU MT PT BG LI CHRW

Destination

2002

2003

2004

2005

Estimated emigration flows from France, 2002-2005

0

20,000

40,000

60,000

80,000

100,000

120,000

DK FI SE NO NL DE CZ ES CY LV LT UK SI IT LU AT IS RO SK PL BE EE GR FR IE HU MT PT BG LI CHRW

Destination

2002

2003

2004

2005

Summary• To produce an overall picture of EU

migration, one has to address issues concerning the availability, quality and consistency of migration data– Harmonisation and cleaning of

reported data– Estimation of missing data (marginal

totals and origin-destination associations) based on patterns found in available data and covariates

Next steps• Much research still needed

– Integration– EM and Bayesian methods– Standard errors of estimates

• MIMOSA project– Flows by age, sex and citizenship– Flows to be linked to population

estimates and change