Models for Migration Age Schedules: A Bayesian Perspective with an Application to Flows between Scotland and England

Abstract

Listen

Translate article

This chapter will consider alternative models for migration age schedules, using as an example data on migration from Scotland to England. Migration exchanges between Scotland and England exhibit features of international migration ‡ows such as young adult labour migration to England and retirement age return migration to Scotland (Gordon, 1982). A comparison is made between alternative models under a fully Bayesian inference and estimation approach. The data consists of ve year age group migration ‡ows but the models are for individual age rates, allowing imputation of the missing single year of age migration data. One model considered is the multiexponential scheme, as in Rogers and Castro (1981). An alternative parametric regression approach retains the Rogers-Castro parameterisation but with gamma mixing on the model rates. The gamma mixing is often necessary to model overdispersion. A contrasting approach is by nonparametric regression involving an unknown smooth function. Inclusion of random e¤ects under either nonparametric or parametric approaches facilitates the pooling of inference strength in joint estimation for similar migration schedules (e.g. when male and female migration rate schedules from the same origin region are likely to be similarly shaped) as opposed to separate estimation of models for each schedule. How the di¤erent model schemes perform in terms of t and model complexity is based on a Bayesian version of the AIC, that adjusts t to take account of model complexity. A model check based on predictive sampling is also used. 1. Introduction Schedules of migration rates tend to show regular features such as a peak in the young adult ages and declining migration propensities in old age, though there may be elevated migration around retirement age. These features characterise ‡ows between countries when the young adult ‡ow is associated with labour migration but return migration in later life may re‡ect enduring cultural or familial a¢ liations. One way to capture these regularities, whether present in internal or international migration, involves nonlinear regression whereby the rate of migration is represented by a sum of exponential or shifted exponential terms; this is known as the multi-exponential migration schedule (Rogers & Castro, 1981). This paper considers a Bayesian modelling approach to migration schedules, starting with a purely parametric model but considering also a model that avoids a nonlinear regression speci cation but instead uses a dynamic general linear