The IMEM model for estimating international migration flows in the European Union

1. The IMEM model for estimating international migration flows in the European Union Peter W. F. Smith Southampton Statistical Sciences Research Institute (S3RI), University of Southampton, p.w.smith@soton.ac.uk Presentation prepared for the Joint UNECE/Eurostat Work Session on Migration Statistics (Geneva, 14-16 April 2010)

2. Background • Recent major investments in improving migration data in Europe: • THESIM, Poulain et al. (2006), documented the differences in migration data collection methods across European countries • New European Parliament (2007) regulation on harmonised migration statistics: ‘As part of the statistics process, scientifically based and well documented statistical estimation methods may be used.’

3. Background (cont.) • MIMOSA, funded by Eurostat, 2007-09 produced the first set of consistent and complete migration flow estimates for flows between EU and EEA countries • NORFACE, representing 13 countries, gathered 26 million Euros to study migration

4. Objective • To provide a general framework for modelling migration flows between countries in the world in the context of inconsistent, inadequate and missing data • Focus is on recent international migration flows between countries in the European Union, using primarily publicly available sources, as well as qualitative information from experts

5. The IMEM Team • S3RI, Southampton • James Raymer • Jonathan J. Forster • Jakub Bijak • Arkadiusz Wiśniowski • Guy J. Abel • Netherlands Interdisciplinary Demographic Institute, The Hague • Rob van der Erf • University of Oslo • Nico Keilman • Solveig Christiansen

6. Double-entry matrix for selected countries, 2003 I = Receiving country’s reported flow; E = sending country’s reported flow; … = no reported data available

7. Double-entry matrix for selected countries, 2003 I = Receiving country’s reported flow; E = sending country’s reported flow; … = no reported data available

8. Double-entry matrix for selected countries, 2003 I = Receiving country’s reported flow; E = sending country’s reported flow; … = no reported data available

9. Double-entry matrix for selected countries, 2003 I = Receiving country’s reported flow; E = sending country’s reported flow; … = no reported data available

10. Solutions • To overcome the various obstacles, we propose a Bayesian model for harmonising and correcting the inadequacies in the available data and for estimating the completely missing flows • The methodology is integrated and capable of providing a synthetic data base with measures of uncertainty for international migration flows and other model parameters

11. Advantages of Bayesian approach • A coherent and probabilistic mechanism for describing various sources of uncertainty contained in the various levels of modelling, i.e., migration processes, models and model parameters • Facilitates the combination of multiple data sources, with differing levels of error • Provides a formal mechanism for the inclusion of expert judgement to supplement the deficient migration data • Provides a single prediction with an associated measure of uncertainty

12. Methodology • There are two key design aspects of our methodology • The development of the underlying statistical framework • The specification and elicitation of relevant expert prior information

13. The statistical modelling framework Model of migration (gravity-type) • Definition used in the sending country • Duration • Coverage • Definition used in the receiving country • Duration • Coverage True flows (unobserved) Accuracy of data collection mechanism Accuracy of data collection mechanism Flows reported by the receiving country Flows reported by the sending country Undercount of emigration

14. Data model

15. Measurement model

16. Migration model

17. Bayesian estimation Prior distributions of parameters q p(q) (*) p(q|x) = p(q)p(x|q) / p(q)p(x|q)dx Posterior distribution p(q | x) Bayes’ Theorem (*) (1763) Likelihood of data x p(x | q)

18. Elicitation • Experts will be asked to rate the credibility of different types of data collection mechanisms and to share their beliefs with respect to model parameters • The totality of expert opinions will be combined into a single set of distributions, allowing for the introduction of yet another source of uncertainty (heterogeneity of experts) • A two-stage Delphi survey will be used for the elicitation of expert judgement, whereby the expert opinions are allowed to converge towards a consensus

19. Testing the model framework

20. Example outputs (9 country model) Modelling differences in duration

21. Migration between Czech Republic, Germany, Denmark and Finland Destination Czech Rep. Germany Origin Denmark Finland

22. Posterior distributions for the Austria-Sweden, Czech Republic-Denmark and Finland-Netherlands flows

23. Conclusion • The focus of this presentation has been on the initial model framework of the IMEM project • Prototype testing has been undertaken on a subset of countries and it appears to be a promising approach • The models are being programmed in both R and WinBUGS (dedicated software for Bayesian computations)

24. Next steps • Continue developing the model • Borrowing of strength over time • Include varying accuracies • Refine migration model • Extensions to include age and sex • Elicit expert information on the definition, coverage and accuracy aspects of the model