Bayesian model averaging in forecasting international migration

Jakub Bijak, Central European Forum for Migration Research

The paper is devoted to the development of Bayesian methodology for international migration forecasting. The aim of the study is to present a Bayesian framework for formal selection of a forecasting model, as well as for producing averaged forecasts based on various models. The essence of Bayesian inference is a formal transformation of the subjective prior beliefs of the researcher about the parameters of the models to the posterior knowledge by incorporating the information provided by the sample of observations. The Bayesian model averaging allows for combining information from different models, weighted by their posterior probabilities conditional on the observed data. The main expected benefit of averaging forecasts yielded by different models is the reduction of forecast error, resulting from the decrease of uncertainty of model specification. The Bayesian framework ensures the formal status of applied statistical tools in addressing the uncertainty issue, allowing at the same time for an explicit incorporation of subjective expert opinions in the model. The theoretical discussion is supported by an empirical example of a forecast of migration between Poland, Germany, Italy and Switzerland for 2004–2010, based on the aggregate data from the population registers. The analysis is restricted to forecasting models based on simple stochastic processes. The paper comprises of four parts. Firstly, a brief discussion of the issues of subjectivity and judgement in migration forecasting is presented, in order to provide justification for the application of Bayesian methods. The second part contains a description of the methodology of Bayesian model averaging, which is illustrated with the empirical example in the third part of the paper. The last section of the paper summarises the main conclusions and suggests possibilities of further research in this area.