Forecasting International Migration in Europe: A Bayesian View

Acknowledgements

Contents

About the Author

About the Contributor

List of Figures

List of Tables

Part I Introduction

1 Introduction and Background

1.1 Migration Forecasting as a Research Problem

1.1.1 Role of International Migration and Its Forecasts

1.1.2 Problems with Errors in Migration Forecasting

1.2 Aim and Structure of the Book

1.2.1 Aim and Scope

1.2.2 Structure of the Book

1.3 Terminology and Symbols

1.3.1 Basic Terms Used in the Study

1.3.2 Mathematical Notation

1.3.3 Bibliographical Notation

2 Preliminaries

2.1 Definitions and Measurement of International Migration

2.1.1 Data Sources and Definitions

2.1.2 Quality and Comparability of Migration Data

2.1.3 Ways of Dealing with Deficient Statistics

2.2 Uncertainty, Subjectivity and Judgement in Population and Migration Forecasting

2.2.1 Uncertainty in Demographic and Migration Forecasting

2.2.2 Subjectivity and Judgement in Population and Migration Predictions

2.3 Bayesian Inference in Statistics: Introductory Notes

2.3.1 The Bayesian Paradigm

2.3.2 Decision-Theory, Empirical and Orthodox Approaches

2.3.3 Bayesian Interval Estimation and Forecasting

2.4 Markov Chain Monte Carlo (MCMC) Simulations

2.4.1 Numerical Solutions to Bayesian Problems: General Remarks

2.4.2 Simulation of Posterior Distributions Using Gibbs Sampling

Part II Explaining and Forecasting Migration

3 Explaining Migration: Brief Overview of Selected Theories

3.1 Different Theoretical Perspectives on Migration Flows

3.1.1 Sociological Theories

3.1.2 Macroeconomic Theories

3.1.3 Microeconomic Theories

3.1.4 Geographical Theories

3.1.5 Unifying Perspectives

3.2 Theory in Migration Forecasting: A Global Outlook

3.2.1 Migration Theories: General Remarks

3.2.2 Use of Theories for Migration Predictions

4 Forecasting Migration: Selected Models and Methods

4.1 Deterministic Methods of Predicting Migration

4.1.1 Judgemental Migration Scenarios

4.1.2 The Delphi Method and Surveys Among Experts

4.1.3 'Migration Potential' Assessment Surveys

4.1.4 Macro-Level Mathematical Models in Demography

4.1.5 Demo-Economic Modelling Attempts

4.2 Probabilistic Migration Forecasts: Assessing Uncertainty

4.2.1 Markovian and Related Models of Aggregate Population Flows

4.2.2 Micro-Level Methods: Event-History Analysis and Ethnosurvey

4.2.3 Selected Attempts to Bridge the Micro and Macro Perspectives

4.2.4 Econometric Forecasts of International Migration

4.2.5 Limitations of Econometric Models

4.2.6 Stochastic Forecasts of Migration Time Series

4.3 Bayesian Approach in Migration Studies and Demography

4.3.1 Bayesian Models and Forecasts of Population Flows

4.3.2 Bayesian Methods in Demography: A Concise Survey

4.4 From Migration Theories to Model-Based Forecasting

4.4.1 Migration Forecasting Methods and Models: State of the Art and Typology

4.4.2 Deterministic Character of Many Existing Predictions

4.4.3 Notes on Including Theory in Population and Migration Forecasts

4.4.4 Implications for the Current and Future Studies

Part III Examples of Bayesian Migration Predictions

5 Bayesian Model Selection and Forecast Averaging

5.1 Selection and Averaging Problems: Simple Stochastic Processes

5.1.1 Methodological Foundations of Bayesian Model Selection

5.1.2 Bayesian Forecast Averaging (Inference Pooling)

5.1.3 Empirical Application: Specification of Forecasting Models

5.1.4 Computations: The Carlin--Chib Algorithm

5.2 Simple Time Series Forecasts: Individual and Averaged

5.2.1 Estimation of the Models and Calculation of Their Posterior Probabilities

5.2.2 Predictions Based on the Formally-Selected and Averaged Stochastic Processes

5.2.3 Interpretation of Forecasts and the Comparison of Ex-Post Errors for 2005--2007

6 Bayesian VAR Modelling x2018;from General to Specificx2019

6.1 VAR Processes and Lindleys Tests for Restrictions

6.1.1 Selection of Predictors in Econometric Models: Rationale for the VAR Modelling

6.1.2 VAR Models and the 'from General to Specific' Approach

6.1.3 Inference on the Impact of Additional Variables on Migration

6.2 Example: Migration Forecasts from General and Reduced VARs

6.2.1 Applying the Reduction Approach: Model Specification, Estimation, and Testing

6.2.2 Results of Forecasts from the General VAR and Marginal AR Models

6.2.3 'From General to Specific' Modelling: Discussion of the Outcomes

7 Selected Approaches to Discontinuities in Trends

7.1 From Deterministic Analogies to Stochastic Volatility

7.1.1 The Simplest Options: Dummy Variables and Forecasting by Analogy

7.1.2 Models with Changing Conditional Variance ARCH, GARCH, Stochastic Volatility

7.2 Example: Forecasts from Models with Discontinuities

7.2.1 Application to Polish-German Flows: Models with Analogy to Iberian Migration

7.2.2 Models with Changing Conditional Variance: Model Selection for AR(1) Extensions

7.2.3 Predictions Prepared with Models Acknowledging Discontinuity in Trends

8 Evaluation of Presented Forecasts of European Migration

8.1 Robustness of Forecasts Against Certain Changes In Priors

8.1.1 Role of Sensitivity Analysis in the Bayesian Approach: Basic Remarks

8.1.2 Robustness of Forecasts Yielded by Selected Models

8.1.3 Discussion and Tentative Conclusions

8.2 Comparison of Selected Bayesian and Frequentist Forecasts

8.2.1 General Remarks on Ex-Ante and Ex-Post Prediction Errors

8.2.2 Likelihood-Based Estimation and Model Selection Framework

8.2.3 Selected Bayesian and Frequentist Migration Forecasts for 2000--2007

8.2.4 Comparison of Ex-Ante and Ex-Post Errors for Various Predictions

9 Bayesian Computing in Practice

9.1 A Short Survey of Available Bayesian Software

9.1.1 R programming Language

9.1.2 Octave

9.1.3 BUGS

9.2 Bayesian Computation in WinBUGS

9.2.1 Model and Data Specification

9.2.2 Model Compilation, Initialisation and Updating

9.2.3 Convergence Diagnostics and Inference

9.3 Example of Bayesian Computation in R Language

9.3.1 Forecasting Migration Using R

9.3.2 The Model of Immigration Flows

9.3.3 Sampling

9.3.4 Carlin--Chib Model Selection Procedure

9.4 Conclusions

Part IV Perspectives of Forecast Makers and Users

10 Extensions and Limitations of Migration Forecasts

10.1 Data, Theories and Judgement: Towards a Synthesis?

10.1.1 Theory in an Atheoretical Setting: Prior Distributions in Multivariate Models

10.1.2 Data Versus Judgement: Elicitation of Expert Knowledge

10.2 Controlling Plausibility of Outcomes in Demographic Models

10.2.1 Combining Deterministic Population Models with Stochastic Forecasts

10.2.2 The Bayesian Melding Approach: Outline and Discussion

10.3 Imperfect Knowledge Forecasting of Migration and Population

10.3.1 Micro-level Foundations in Macro-level Forecasting

10.3.2 The Imperfect Knowledge Paradigm: Quantitative Versus Qualitative Predictions

10.4 Implications for Forecast-Makers and Future Research Agenda

10.4.1 Limitations of Predictability and Plausible Horizon of Non-stationary Forecasts

10.4.2 Forecasting Migration and Population: Proposal for a Research Agenda

11 Dealing with Uncertain Forecasts: A Policy Perspective

11.1 Preliminaries of the Decision Analysis: A Bayesian Perspective

11.1.1 Background: Selected Insights into Decisions and Attitudes Towards Uncertainty

11.1.2 Estimation and Prediction in the Bayesian Decision Framework

11.1.3 Bayesian Decision Analysis: Some Stylised Examples

11.1.4 Possible Extensions of the Decision Framework

11.2 Limitations of Uses of Migration and Population Predictions

11.2.1 Alternatives to the Use of Optimal Forecasts

11.2.2 Which Questions Can the Forecasts Answer?

11.2.3 Towards Interactive Demographic Forecasting?

Part V Conclusion

12 Summary and Conclusion: Beyond Migration Forecasting

12.1 Summary of the Key Findings

12.1.1 Bayesian Model Selection and Forecast Averaging

12.1.2 Vector Autoregression Models and Their Reduction

12.1.3 Models Acknowledging Discontinuity in Trends

12.1.4 Sensitivity of the Results to Changes in Priors

12.1.5 Ex-ante and Ex-post Comparison of Forecasts: Implications for Users

12.1.6 General Conclusions

12.2 Bayesian Forecasts in the Population Forecasting Debates

12.2.1 Bayesian Methods in Perspective: Uncertainty, Judgement and Occam's Razor

12.2.2 Migration Forecasting as a Continuous Process

12.2.3 From Point Predictions to Decision Support: In Need of a Paradigm Shift?

12.3 A Possible Future of Migration and Its Forecasts

Annex A Empirical Illustrations: Data Sources and Preparation

Migration Flows

Population Stocks

Economic Variables

Annex B WinBUGS Code Used in the Forecasting Examples

Annex C Selected Results of Presented Migration Forecasts

References

Author Index

Subject Index