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



Age patterns are a key dimension to compare migration between countries and over time. Comparative metrics can be reliably computed only if data capture the underlying age distribution of migration. Model schedules, the prevailing smoothing method, fit a composite exponential function, but are sensitive to function selection and initial parameter setting. Although non-parametric alternatives exist, their performance is yet to be established.


We compare cubic splines and kernel regressions against model schedules by assessing which method provides an accurate representation of the age profile and best performs on metrics for comparing aggregate age patterns.


We use full population microdata for Chile to perform 1,000 Monte-Carlo simulations for nine sample sizes and two spatial scales. We use residual and graphic analysis to assess model performance on the age and intensity at which migration peaks and the evolution of migration age patterns.


Model schedules generate a better fit when (1) the expected distribution of the age profile is known a priori, (2) the pre-determined shape of the model schedule adequately describes the true age distribution, and (3) the component curves and initial parameter values can be correctly set. When any of these conditions is not met, kernel regressions and cubic splines offer more reliable alternatives.


Smoothing models should be selected according to research aims, age profile characteristics, and sample size. Kernel regressions and cubic splines enable a precise representation of aggregate migration age profiles for most sample sizes, without requiring parameter setting or imposing a pre-determined distribution, and therefore facilitate objective comparison.

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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. …

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