Smoothing internal migration age profiles for comparative research

Aude Bernard; Martin Bell

doi:10.4054/DemRes.2015.32.33

Volume 32 - Article 33 | Pages 915–948

Smoothing internal migration age profiles for comparative research

By Aude Bernard, Martin Bell

Date received:

11 Jun 2013

Date published:

12 May 2015

Word count:

6169

Keywords:

cross-national comparison, cubic spline, kernel regression, migration age profile, model migration schedule, smoothing

DOI:

10.4054/DemRes.2015.32.33

Replicable Material:

demographic-research.32-33 (zip file, 229 kB)
readme.32-33 (text file, 1 kB)

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Abstract

Background: 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.

Objective: 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.

Methods: 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.

Results: 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.

Conclusions: 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.