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Density or Size as an Appropriate Measure of the Intensity of Employment

Linkages with Productivity

Instead of using size as a determinant of average productivity, investigation has been undertaken of the use of size in terms of the numbers employed rather than density as a factor in the determination of earnings and productivity. The results based on size are set out in Figure D.1 below and the equivalent relationships based on density are set out in Figure D.2. Both these measures use the three way breakdown of the data set into areas with less than 800, areas with a high proportion of manufacturing, wholesaling and transport activities and other areas as introduced in Section 6.

Figure D.1: Log Size and Earnings

→ Full size version of Figure D1 [67 kB JPG]

Figure D.2: Log Density and Earnings

→ Full size version of Figure D2 [65 kB JPG]

Compared to the findings from earlier work set out in Figure D.2, Figure D.1 shows that there is a very weak relationship between earnings and size for the small areas, in blue in the graph with an R² of 0.08, a reasonable linkage for the CBD plus big other of an R² of 0.50 and a very strong linkage for industrial areas with an R² of 0.71. This latter represents an interesting result, that earnings are related to size rather than density, although possibly peripheral to the main thrust of the agglomeration work. The disaggregation of the data provides an improved fit for the CBD+ Big Other and Industrial areas compared to the data set as a whole, although the statistical significance of the differences may need testing.

The results using density or size are summarised in the table below.

The relationships estimated using density are very similar to those estimated using size for the "CBD + Big Other" group with an R² of 0.47 instead of 0.50, and are worse for Industry with an R² of 0.56 rather than the very high 0.71. However because of the small size of this component of the data set the differences may not be statistically significant. Density provides better results for the "small" group although for both size and density the R² value is small.

The apparent message from this is that for industrial activities, size and concentration matters, whereas this factor is much less important for service based activities and there is little difference between the two approaches. For the smaller sized areas, the use of density gives a stronger relationship although in both cases the R² is low, and only a limited proportion of the variation is explained.

Size and Accessibility

As well as considering the relationships between productivity and size or density, the relationships between size or density and accessibility have also been examined. The results using size are set out in Figure D.3 below.

Figure D.3: Relationship between Accessibility and Total Size of Employment

→ Full size version of Figure D3 [70 kB JPG]

This can be compared with the relationship using density and this is set out in Figure D.4 below.

Figure D.4: Relationship between Accessibility and Density of Employment

→ Full size version of Figure D4 [76 kB JPG]

The two sets of results are summarised in the table below.

The linkages between accessibility and the total numbers employed are much less robust than those linking accessibility and density. As an example whereas the R² for the CBD + Big Other is about 0.38 when accessibility is related to size, it increases to about 0.56 when accessibility is related to density. There are also similar large differences between the strength of the linkages for the other groups.

Overall Assessment of the Use of Size or Density

In terms of aggregate employment for the main "CBD + Big Other" data set, there is little difference in the relationships between size and earnings and density and earnings. For manufacturing employment the linkage with size is stronger than that with density, but for the "other" smaller zones, the linkage between size and earnings is very weak.

The linkages between accessibility and size are however all weaker than those between accessibility and density.

Overall for the examination of areas other than manufacturing, the explanatory power of the linkages between density and earnings are similar to, or better than, those between size and earnings, and for accessibility, the use of density gives much better results.