Academic journal article Demographic Research

Smoothing Internal Migration Age Profiles for Comparative Research

Academic journal article Demographic Research

Smoothing Internal Migration Age Profiles for Comparative Research

Article excerpt

(ProQuest: ... denotes formulae omitted.)

1. Introduction

Internal migration is an age-selective process, with young adults being the most mobile group. Migration intensities typically decrease from birth to the teenage years before peaking at young adult ages. They then decline steadily with increasing age, sometimes rising again around the age of retirement. Rogers and Castro (1981) have demonstrated that this broad age profile is replicated across a number of countries and at various spatial scales. Subsequent analysts have proposed summary indicators of the age profile that can be used to make comparisons across countries and over time (Bell et al. 2002; Bernard et al. 2014a) and to examine the association of the migration age profiles with other demographic processes such as life-course age patterns (Bernard et al. 2014b).

Since its introduction by Rogers et al. (1978), the model migration schedule has been widely adopted as the main method to smooth migration age profiles. As a composite exponential function, the model schedule constrains migration to follow a prototypical shape founded on the theoretical link between migration and life-course transitions. While model schedules are based on accumulated evidence primarily from contemporary Europe and the United States, they constrain migration age patterns to follow a standard predicted shape that may not describe migration age patterns accurately in other regions or in historical populations. Furthermore, model schedules face limitations related to their estimation (Bernard et al. 2014a), including the difficulty of selecting an optimal set of component curves specific to each age profile (Rees et al. 2000), the instability of parameter estimates (Congdon 1993), and the sensitivity of estimates to initial parameter values (Rogers et al. 2005). Researchers have therefore to employ a trial-and-error approach to decide on the set of component curves and initial parameter values that will yield the best fit, which directly influences the shape of the estimated curve and the value of the estimated parameters. This, in turn, undermines the reliability of these parameters for comparative analysis.

Demographers have recourse to a range of other statistical methods for data smoothing, including non-parametric models such as cubic splines and kernel regressions, which have been widely used to smooth fertility (Moguerza et al. 2010) and mortality age profiles (Peristera and Kostaki 2005). Non-parametric models have the advantage of avoiding the imposition of a pre-determined shape (Pagan and Ullah 1999) and are also easier to implement using automated processes free of sensitivity to subjective assumptions (Wand and Jones 1995). As a result of the widespread adoption of model schedules, there appears to have been no previous attempt to systematically assess the different methods available to smooth migration age profiles.

The age and intensity at which migration peaks have widely been used to characterise and compare migration age patterns across countries, either alongside other metrics (Rogers and Castro 1981) or as the main or sole summary measures (Bell et al. 2002; Bell and Muhidin 2009; Bernard et al. 2014a; Bracken and Bates 1983; Rees et al. 2000). The choice of a particular model and its specification affect the shape of the fitted curve, which in turn influences estimates of the age and intensity at peak. Inappropriate model selection or incorrect model misspecifications are therefore likely to result in incorrect inferences when comparing countries on these measures or when examining the evolution of migration age patterns within a country. Comparative analysis of migration calls for smoothing methods that preserve the overall distribution shape of the age profile and retain discriminating features.

This paper seeks to evaluate and compare the strengths and limitations of cubic splines, kernel regressions, and model schedules for smoothing migration age profiles at a range of sample sizes. …

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