A better look at household income diversity

By Aaron Schiff 14/03/2015


My previous post took a pretty crude look at the local diversity of household incomes in Auckland. The idea was to look at whether each Census area unit in Auckland contains a mix of households with different income levels, or has mostly households with similar income levels.

The major problem with my analysis was the naive comparison of the proportion of households in each income category to 1/6 (there are six household income categories in the Census results). This creates a bias towards finding that lower-income areas are diverse, simply because there are proportionately fewer households in the lowest income categories.

In response, Thomas Lumley made a couple of excellent suggestions on Twitter. First, it’s better to compare the proportion of households in each income bracket to the overall proportion of households in that bracket in the region. This is a more realistic and reasonable benchmark than 1/6. Thomas also suggested that I calculate the income diversity measure as a weighted sum in each CAU of the squared deviations from the regional proportions, where the weights are again the regional proportions of households in the six income categories. Intuitively, if there are not many households in a category overall, we shouldn’t put much weight on that category in the calculation of an income diversity statistic.

These changes significantly improve the analysis, although it’s still not perfect because the Census household income categories are a bit arbitrary, and the top category is open-ended. Nevertheless, here’s the resulting map for 2013. The colours are the deciles of the income diversity measure across Auckland CAUs.

AKL income diversity better

In comparison to my earlier effort the map has changed quite a bit and I think it makes a lot more sense. You can see a lack of household income diversity in both relatively rich areas (eg Herne Bay) and relatively poor areas (eg Otara). There are some interesting variations, for example if you look across the central-western suburbs.

I also made the same map for 2001 for comparison (here the colours are the deciles of the 2001 distribution).

AKL income diversity better 2001

There are definitely quite a few changes but it’s hard to see what’s going on just by comparing the two maps. So here’s a simple two colour map showing areas where household income diversity reduced and increased between 2001 and 2013. Make of this what you will …

AKL income diversity diff

I think local area diversity within cities is quite an interesting topic. Personally I think greater diversity (of all kinds) in a neighbourhood makes it a more interesting place to live, but there are many reasons why that doesn’t always work out.