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The results in this section shed light on four main questions about the labour productivity of Auckland firms:

• How much higher is the productivity of Auckland firms compared with non-Auckland firms?
• How much of the productivity premium is accounted for by the mix of industries in Auckland?
• How does labour productivity vary within Auckland?
• What is the relationship between labour productivity and the density of overall and own-industry employment?

In addressing each of these questions, we focus primarily on the patterns for the most recent year for which we have data – 2006. In addition, we report on patterns of change over the 2000-2006 period.

5.1 Auckland's relative productivity

Average labour productivity in the Auckland cenftral business district (CBD¹⁷) is more than twice as high as average labour productivity outside the Auckland Region. Auckland City as a whole, which accounts for around one sixth of New Zealand's labour input, has a premium of 50 to 80 percent. The broader Auckland Region has a productivity premium of roughly 30 to 50 percent, and accounts for a third of national labour input.¹⁸ The Auckland Urban Area¹⁹ contains the densest areas of the Auckland Region and accounts for most of the Auckland Region's employment and output, showing a productivity premium 5 to 10 percentage points above that of the region as a whole.

For each of the four definitions of Auckland, Table 1 presents the average labour productivity, in nominal dollars, and as a proportion of average labour productivity in the rest of New Zealand (excluding Auckland region). The table shows that the relative size of the productivity premia for the different definitions of Auckland has been maintained throughout the 2000 – 2006 period of the study, despite fluctuation from year to year, and a peak in 2004. In general, productivity in the four areas moves together, suggesting that the fluctuations are due either to changes in areas outside Auckland, or to Auckland-wide movements. The year-to-year changes in the level of value added per worker should be interpreted with caution as they reflect both price and quantity movements. Movements in the relative measures, however, are unaffected by aggregate price changes, although they will incorporate location-specific price and quantity variation.

Similar patterns of relative productivity are evident at various quantiles of the productivity distribution. Median productivity is generally between 70 and 80 percent of average productivity and quantile ratios (e.g.: P90/P50 or P50/P10) are similar across cities, Territorial Authorities (TA) and regions.²⁰

Table 1 The Auckland Productivity Premium 2000-2006

→ Full size version of Table 1 [20 kB GIF]

As suggested by the difference between the Auckland CBD and Auckland Region productivity premia, there is productivity variation between different areas within Auckland. Figure 1 shows, for 2006, the relative performance of the seven different TA areas within Auckland, together with Regional Council Areas including Auckland. Two of the Auckland TAs (Papakura and Franklin) are pooled together, as are some of the RC areas.²¹

Of the areas within Auckland, Auckland and Manukau Cities have the highest relative productivity, of 169% and 139% respectively. In contrast, both Waitakere (88%) and Rodney (84%) have lower average productivity than the non-Auckland average. Auckland region overall is the region with the highest average productivity (144%), followed by Taranaki (134%) and Wellington (134%).

Figure 1 Productivity of Auckland TAs, compared with other Regional Council Areas (2006)

→ Full size version of Figure 1 [30 kB GIF]

An alternative measure of productivity and the productivity premia is also presented in Figure 1 and Table 1, adjusting for differences in industry composition, as discussed in section 4.2. The flatter line in Figure 1 shows the relative productivity profile for 2006, adjusted for differences in industry composition. Part of the reason that Auckland's productivity is high is that Auckland has a relatively high share of industries that have high average productivity nationally. Industry composition is a significant contributor to Taranaki's high average productivity. Taranaki's unadjusted relative productivity of 134 percent is reduced to just 106 percent once adjustment is made for the over-representation of high productivity industries – mainly in the combined Mining and Quarrying / Electricity, Gas and Water groups.

The adjusted figures in Table 1 show that differences in industry composition account for about 45 percent of Auckland's unadjusted productivity premium, although even the adjusted premia are substantial. The 2006 Auckland CBD premium is reduced from 139 percent to 72 percent, and the premium for the Auckland Region is reduced from 44 percent to 25 percent. Auckland Region accounts for 33 percent of national labour input, but has disproportionately large shares of employment in Wholesale Trade (49%), Communication Services (48%), Finance and Insurance (46%), Education (46%), Property and Business Services (42%), and Cultural and Recreational Services (42%). Auckland shares of Agriculture (6%) and Mining/Electricity, Gas and Water (9%) are low. The productivity premium that remains after controlling for industry composition must result from the fact that there is an Auckland productivity premium within at least some industries. An analysis of productivity premia by 2-digit industry is presented in section 5.3.

Table 1 showed the time pattern of relative productivity for Auckland City from 2000 to 2006. In Figure 2, we show the trends for each of the Auckland TAs. The ranking remains stable with the exception of Papakura/ Franklin, which overtook North Shore in 2003. Auckland also appears to have experienced particularly strong growth in relative productivity between 2002 and 2004.

Figure 2 Changes in (adjusted) relative productivity of Auckland TAs 2000-2006

→ Full size version of Figure 2 [20 kB GIF]

Note: Relative productivity has been adjusted for differences in industry composition.

5.2 The geography of Auckland productivity

This section provides a more detailed account of productivity variation within Auckland than is shown in Figure 2. Within each of the TAs shown in Figure 2 there are distinct zones of high and low productivity. The upper panel of Figure 3 is a shaded map (choropleth) of selected area units within the Auckland region, shaded to reflect relative labour productivity levels in 2006.²²

Figure 3 Geographic Variation in Productivity within Auckland (2006)

Auckland City's high labour productivity reflects three high productivity zones – Auckland Central, extending southwest through to Mt Roskill; southern suburbs including Ellerslie, Panmure and Onehunga; and also Avondale. Manukau City's high productivity zones are broadly spread through the central and western parts of the city, including Otahuhu in the north, through Mangere, Wiri and Manurewa. Whitford (Turanga area unit) also shows up on the map as a high-productivity zone, although it has low employment density and only around 500 jobs in any year. The highest productivity areas in North Shore City are in Northcote and Birkenhead – across the Harbour Bridge from Auckland Central, around Albany, and in the low density area of Okura and Long Bay in the north of North Shore City. The remaining TAs within Auckland Region have relatively small zones of high productivity – around central Papakura in Papakura District, around Glenbrook in Franklin District, and around Silverdale in Rodney District.

5.2.1 Productivity and density

One of the key differences between Auckland and the rest of New Zealand, and one that is frequently cited as a likely factor in Auckland's productivity premium is the density of employment. Overall in 2006, New Zealand had 6.7 jobs per square kilometre. Auckland Region had 119 jobs per square kilometre (See Table 2).

Table 2 Employment Density within Auckland 2000-2006 (jobs per square kilometre)

Surprisingly, the TA with the highest employment density is not Auckland City, but North Shore City. This is, however, due to the inclusion of low-employment-density offshore islands in Auckland City. Table 2 presents separate employment density measures for Auckland City including and excluding the offshore islands. If the offshore islands are excluded, Auckland City has the highest employment density, of 1832 jobs. Manukau City had the second highest labour productivity but ranked only third on employment density – partly because over half of Manukau's land area lies in two large low-density area units (Clevedon and Kawakawa-Orere). The exclusion of offshore islands from Auckland City has virtually no impact on average labour productivity, as less than 1 percent of Auckland's employment is offshore.

Productivity and Density variation between Regions

Figure 4 shows a positive cross-sectional relationship between employment density and labour productivity for the Regional Council groupings used in Figure 1, where labour productivity is measured as the log of average labour productivity for the geographic area. The positive relationship is quantified in the first column of Table 3. The coefficient of 0.062 implies that an area with density twice as high as the average will have productivity that is 6.2% higher than average.²³ The relationship is statistically significant and similar in size to the range of estimates summarised by Graham (2005b).

Figure 4 Productivity and Density across Regions and Auckland TAs (2006)

Note: The size of symbols is proportional to average employment levels within each area. Shaded symbols are for Auckland TAs. Other symbols are for Regional Council groupings.

The fixed effects estimate in the second column of Table 3 reflects the relationship between density and labour productivity for a given area over time. The relationship is no longer significant and the coefficient estimate is negative, suggesting a weak tendency of increased density to be associated with lowered productivity. The strong cross-sectional relationship is more closely related to regional differences that were relatively stable over the seven years of our sample, and not to changes over time within areas. It may also be that random fluctuations within the seven years of our sample period mask agglomeration dynamics that operate over longer timeframes.

Table 3 Density and Labour Productivity - Regression estimates across Regional Councils and Auckland Territorial Authorities

Notes: All regressions are weighted by mean area employment. Each observation is for a combination of year and geographic area (Auckland TAs and non-Auckland RCs). Standard errors in parentheses. * significant at 5%; ** significant at 1%.

Productivity and Density variation within Auckland

The relationship between density and labour productivity is somewhat different when we look across different areas within Auckland. Within the denser central areas of Auckland City and Manukau, there is a noticeable correspondence between area units with high relative productivity and those with high employment density. The visual similarity is evident by comparing the two panels of Figure 3. The relationship is shown graphically in Figure 5, which plots the log of area average productivity against the log of area "effective employment density". Effective density is a geographically smoothed measure of density. Smoothing is desirable when examining employment density for area units as it accounts for the influence of nearby dense area units. Specifically, we use the Graham (2005b) effective density measure which is calculated using the following formula:

where E_i is the employment in area unit i; A_i is the land area of area unit i; and d_ij is the distance in km between area units i and j. Panel (a) of Figure 5 shows a clear positive relationship.

To quantify the elasticity of productivity with respect to density across area units, we estimate the relationship between the log of average labour productivity and log effective density, using the same approach as used in Table 3 for cross-regional analysis. The results are reported in Table 4. The first column reports the estimate from weighted least squares estimation (weighting area units by their mean employment level), controlling for year effects. The coefficient of 0.086 implies that an area with employment density that is twice as high as that of another area has value added per worker that is 8.6% higher.

Figure 5 Relationship between Effective Density and Labour productivity

(a) Level of Density and Level of Labour Productivity	(b) Area Fixed Effects relationship (Partial Regression Plot)
(c) Changes in Density and Changes in Labour Productivity

Notes: Each circle represents an area unit within Auckland. The size of the circles is proportional to the level of employment in each area unit.

The relationship is identified both from cross sectional variation (areas with higher productivity also have higher density) and from within-area time variation (when productivity increases in an area, so does density). As noted above, the cross sectional relationship reflects a spatial equilibrium pattern, as well as a possible functional relationship between density and productivity. A tighter test of the link between density and productivity is obtained by examining within-area time variation alone. The second column of Table 4 presents such an estimate, obtained from fixed effects estimation. For a given area unit, productivity and density increase together, with a doubling of density associated with productivity that is 5.4% higher – still a sizeable positive relationship, although the precision of the estimate is considerable smaller, as reflected in the tenfold increase in the standard error. A graphical representation of this fixed effect relationship is shown in panel (b) of Figure 5.

Table 4 Effective Density and Labour Productivity - Regression estimates within Auckland

Notes: All regressions are weighted by mean area employment. Each observation is for a combination of year and Area Unit within Auckland. Standard errors in parentheses. * significant at 5%; ** significant at 1%.

The third column of Table 4 reports estimates of the relationship between year-to-year changes in productivity and year-to-year changes in density. The relationship becomes statistically insignificant, with a coefficient of 0.024. Similarly, changes in density and productivity between the first and last periods of the sample period are not strongly related as shown in the final column of the table. Maps of the six-year changes are shown in Figure 6 and a corresponding graph is shown in panel (c) of Figure 5.

The implication of these patterns is that, within Auckland, firms in denser areas are on average more productive, but that increasing density is not necessarily associated with an increase in productivity. The significant fixed effect estimate is consistent with a positive association between density and productivity, although the lack of a significant relationship in the first difference and six-year difference specifications lessens the support for this inference, and suggests the need for a fuller examination of the dynamics of this relationship.

Figure 6 Geographic Variation in Productivity Change within Auckland (2000 - 2006)

5.3 Localisation and urbanisation

The relationship between density and labour productivity is a coarse summary measure that may mask variation in the importance of density across different industries, and in the nature of agglomeration mechanisms that operate in different industries. To shed light on the size and nature of agglomeration effects for different industries, this section provides a more detailed industry-level examination of the relationship between labour productivity and employment density, distinguishing the relative importance of own-industry employment density (localisation).

Figure 7 plots, for Auckland Region, each industry's relative productivity against an index of the industry's prevalence in Auckland.²⁴ Relative productivity within industries is measured as the difference between the log of average industry productivity in Auckland and that in areas outside Auckland Region. The data are for 2006 although the patterns for other years are very similar.

Relative productivity is highest for the Motion Picture Radio and TV Services industry (P91). This industry in Auckland is more than 3 times as productive as the same industry outside Auckland. Furthermore, Auckland has a disproportionate share of this industry. Other industries that are over-represented in Auckland also tend to have high relative productivity, albeit to a more modest extent. Overall, the upward sloping regression line shows the generally positive relationship between industries' prevalence in Auckland and the size of their Auckland productivity premium, consistent with positive selection of industries – the industries that benefit most from being in Auckland disproportionately locate there.

Figure 7 Relative Auckland Productivity and Presence in Auckland - within industries (2006)

→ Full size version of Figure 7 [26 kB GIF]

Note: The size of the plotting symbols is proportional to the level of Auckland employment in each industry. The fitted regression line is based on an employment-weighted regression.

Industry prevalence in Auckland is one dimension of industry location patterns but industries also vary in their location patterns within Auckland. We summarise the degree of geographic concentration within Auckland for each industry using a Maurel-Sedillot index (MS) (Maurel and Sedillot (1999)). The MS index is an estimator of the degree of correlation in firms' location decisions and is defined as:

where s_i is the proportion of an industry's employment in area unit i; x_i is the proportion of total employment that is in area unit i; and H is a Herfindahl index of industrial concentration across plants.²⁵ A high value of the index indicates that industry employment is concentrated in particular area units, consistent with localisation.

Figure 8 arranges industries according to their presence in Auckland (LQ) and their concentration within Auckland (MS). Industries have been divided into five groups, reflecting different spatial configurations.²⁶ About 40 percent of employment is in industries that are neither significantly over- nor under-represented in Auckland (LQ of around 1), and are distributed within Auckland roughly in proportion to total employment (MS of around 0). This group of industries is labelled ‘Dispersed' and comprises mainly industries providing local goods and services. There is a "non-Auckland" group of industries that are less prevalent in Auckland than elsewhere, which account for 6% of Auckland's employment. These are industries that are linked to the primary sector.

Figure 8 Presence in Auckland and Concentration within Auckland - by 2-digit industry (2006)

→ Full size version of Figure 8 [36 kB GIF]

Notes: The size of plotting symbols is proportional to employment in each industry. The numbers in brackets show the percent of Auckland's employment accounted for by each group.

Industries that are disproportionately located in Auckland are divided into three groups, reflecting high, medium, and low levels of geographic concentration within Auckland. The first of these groups, labelled "Urbanised" is dispersed throughout Auckland in proportion to overall employment, with a value of MS in the same range as for the "dispersed" group. This group accounts for 6 percent of Auckland employment. The second group, labelled "Localised", accounts for 40 percent of employment and is moderately concentrated within Auckland. The remaining 8 percent of employment is in the "Very Localised" group, for which employment is highly concentrated within Auckland. Transport and storage industries and Finance and Insurance are represented in this group, as is the "Sport and recreation" industry.

Table 5 contains group-level summary statistics on group employment, number of enterprises, group employment, average labour productivity, and the employment weighted averages for the MS and LQ indices. The grouping of industries based on prevalence and concentration is somewhat arbitrary, but serves to separate industries into groups that are potentially affected by different forms of agglomeration effects.

Table 5 Grouped industries – descriptive statistics

Notes: Appendix F contains a version of Table 5 and Table 6 for 2-digit industries. Enterprise and Employment counts have been rounded. Variables are described in the text.

It is plausible, for instance, that the geographic concentration of the "very localised" industries is related to possible within-industry benefits of sharing, matching or learning. In contrast, the "dispersed" industries are located in proportion to overall employment, suggesting no particular advantage to being in Auckland or to being localised.

To investigate how the differing spatial configurations are related to productivity performance, we examine within-industry variation in productivity for each of the groups, comparing Auckland firms to those outside Auckland, and comparing firms in different parts of Auckland. Table 6 presents evidence on the Auckland productivity premium accruing to industries in each group. It also shows the relationship between labour productivity and overall employment density, and between labour productivity and own-industry employment density.

The first column of Table 6 reports the average relative labour productivity premium for industries in each group. These estimates are obtained from a regression as shown in equation (2), where j takes on only two values – Auckland Region, and all other areas. The inclusion of industry dummies absorbs the productivity differences between industries, so the reported estimates show the employment-weighted within-industry premium.

The highest premium (33.3%) is observed for the ‘Very Localised' group, which contains industries that are highly concentrated within Auckland and also over-represented in Auckland. Industries in the ‘Localised' group, which are also concentrated in Auckland, also have a relatively high Auckland premium (28.0%). Urbanised and Dispersed industries have somewhat lower premia of 18% to 23%. The non-Auckland industries, which are relatively highly concentrated within Auckland, have an average premium of 26.5%, although there is a lot of variation across industries, from a low of –61% to a high of 125%.

Almost all industries are more productive in Auckland than elsewhere. Only 3 industries are more productive outside Auckland – ‘Agriculture', ‘Mining and Quarrying', and ‘Petrol Coal Chemical & Assoc Prod Mfg'. Almost 80 percent of Auckland employment is in industries with a premium greater than 15 percent, with 40 percent in the 15% to 25% range. The widespread nature of productivity premia within Auckland is consistent both with urbanisation and with Auckland-wide price effects. It is not clear from the observed patterns the extent to which an industry's presence in Auckland raises technical efficiency, or to which the productivity advantage reflects allocative efficiency.

Table 6 Grouped industries – Auckland Premium and Density elasticities (2006)

Notes: **: 5% significance. *: 10% significance. Each row contains estimates from three separate regressions. The dependent variable in each is the log of VAPW. Appendix F contains a version of Table 5 and Table 6 for 2-digit industries.

To gauge the evidence for density-related explanations of the high relative productivity of Auckland firms, we examine whether labour productivity is higher for firms in denser parts of Auckland, compared with less dense parts of Auckland. Specifically, we run the following regression

where VAPW_gk is the average labour productivity of workers in industry k working in area unit g. Effective density is as defined in equation (3). Own-industry effective density is calculated using the same method but using only own-industry employment. The log specification means that β₁ and β₂ can be interpreted as the elasticities of average local productivity for an industry with respect to effective density and own-industry effective density respectively. The inclusion of industry intercepts ensures that these elasticities are identified from spatial variation within industries, and do not reflect between-industry differences.

The means of the density measures are shown in Table 5. Firms in "Very localised" industries have the highest average effective employment density. Urbanised and Localised industries have similar effective densities, implying that they are exposed to a similar degree of urbanisation. The higher MS measure for the Localised industries indicates that they tend to be more concentrated within Auckland and are thus exposed to a greater degree of localisation. Differences in own-industry effective densities are more difficult to interpret, as they reflect relative industry size as well as different patterns of localisation. The MS measure provides a more interpretable indication of localisation. However, variation in own-industry effective density measures across firms in the same industry provides an indication of exposure to potential localisation effects.

The second column of Table 6 shows estimates of equation (5), estimated separately for each group of industries, and with β₂ constrained to be zero. The relationship between effective density and labour productivity differs markedly across the five industry groups. The Very Localised industries have the highest effective density elasticity of 0.66, followed by the Localised industries with an elasticity of 0.51. The elasticity for the Urbanised industries is lower, at 0.16. The dispersed industries, although not geographically concentrated within Auckland, nevertheless have higher productivity in more dense areas, with an elasticity of 0.24.

The two columns labelled (3) in Table 6 contain estimates of β₁ and β₂ from equation (5), allowing for overall effective density and own-industry effective density to have different relationships with productivity. Consistent with the effects of localisation, the productivity of Localised and Very Localised industries has a particularly strong link with own-industry density. In contrast, for Dispersed and Urbanised industries, overall effective density has a stronger link with productivity, consistent with these industries benefiting from urbanisation effects. Productivity in the non-Auckland industries is positively related to both overall and own-industry density.

It is significant that the elasticity of productivity with respect to own-industry density is stronger than the overall-density elasticity. This suggests that localisation effects are generally more pronounced than the urbanisation effects of density per se. The exception is the ‘urbanised' group, for which the two elasticities are relatively close. Even the dispersed industries, which tend to provide local services, benefit most from localisation, despite the effects of competition that would favour dispersion.

These patterns are certainly suggestive of different types of agglomeration effects operating in different industries. They are, however, consistent with a range of explanations. Clearly, any explanation of the Auckland productivity premium must include a link with employment density, given the prevalence of positive density elasticities across a range of industries. Density-related productivity advantages could, however, include technical and/or allocative efficiency benefits. As outlined earlier, technical efficiency benefits may include advantages of matching, sharing, and learning, all of which are arguably greater in dense areas. Allocative efficiency may arise if output prices are higher in dense areas, as may occur in higher land rent areas.

The existence of positive own-industry density elasticities suggests that interactions with other firms in the same industry are advantageous. It is not possible, however, to distinguish the contributions of shared inputs (such as transport infrastructure for the highly concentrated Transport and Storage industries) from the possible contributions of intra-industry knowledge transfers or matching with a common set of suppliers or customers. Finally, the patterns in Table 6 are based on cross-sectional variation. The analysis of the link between area density and average area labour productivity that was presented in Table 4 and Figure 5 demonstrated that cross-sectional patterns are not necessarily reflected in time series variation.