How robust is Courgeau’s K index in cross-national comparisons of internal migration?

Martin Bell, University of Queensland
Tom Wilson, University of Queensland
Salahudin S. Muhidin, Macquarie University

A key challenge in making meaningful comparisons of internal migration between countries is to account for differences in the statistical geography used to collect the data. As with other forms of spatial data, migration statistics are prejudiced by differences in the number and shape of geographic zones; this is commonly recognised as the Modifiable Areal Unit Problem. One of the most promising attempts to tackle this issue was made by Daniel Courgeau (1973), who proposed an index, K, which approximately standardises for the number of statistical areas in a country. He defined K as the slope of the straight line when plotting the Crude Migration Intensity (CMI) from two or more sets of geographies against the logarithm of the number of areas in each geography. In a recent assessment of Courgeau’s K for 27 countries, Bell and Muhidin (2009) found qualified support for Courgeau's index as a means of discriminating mobility levels but identified limitations due to the small number of data points available in standard statistics. This paper addresses these issues by asking: how robust is Courgeau’s K to changes in statistical geography, both in terms of the number and shape of the areas comprising each geography? Is the relationship of the CMI against the logarithm of the number of areas a linear one or would an alternative function be more appropriate? How many data points are required to obtain a robust estimate of K? We tackle these questions by randomly generating thousands of different geographies for ten case study countries: Australia, Brazil, Canada, Chile, China, Indonesia, Malaysia, Portugal, South Africa, and the USA. The results demonstrate how the CMI is related to the number of areas in each geography, and the extent to which it varies as a result of the shape of areas comprising each geography.