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4.1 Alternative Forms of the Accessibility Analysis

In the initial work undertaken on the analysis of accessibility and agglomeration, accessibility was defined in terms of the total numbers of households or jobs within specified catchment areas. These catchment areas were defined as the zones within 30 minutes of a particular location for trips by private car, and 75 generalised cost minutes for the time related components of trips by public transport (i.e. excluding the fare component). 30 minutes and 75 minutes correspond to the average trip time by the particular mode. Information on the number of households and levels of employment and zone-zone journey times were derived from output from the Auckland Regional Transport Model (ART) for highway times and the Auckland Public Transport (APT) model for public transport times. The estimates of households and employment were common to both models as used in this work.

The initial approach to the assessment of accessibility gives the same weight to all jobs or households within the defined catchment area. Employment or households close to the boundary of the area would therefore have the same impact on accessibility as employment or households closer in. This approach may also produce measures of accessibility which are possibly over-sensitive to changes in travel conditions if there are large numbers of jobs or households just outside the defined catchment area, who switch to being inside the area with small reductions in journey times.

A review of the literature indicated that at least two alternative formulations were possible which might help to reduce these potential problems. These developed more continuous measures in order to measure accessibility for use in the assessment of agglomeration impacts.

4.1.1 Option 1

In the UK, the paper ‘Wider Economic Benefits of Transport Improvements: Link between agglomeration and productivity, Stage 2 Report' develops the concept of "effective density".⁴⁸ This weights all employment on a continuous basis, with effective density (ED) being given broadly by the formula:

ED for zone j = (Employment in zone j/Radius of zone j) +S (Employment)*(1/generalised cost of travel) for all other zones

Separate measures were developed for employment within specific industry groups to give localisation economies, and for other industries to give urbanisation economies.

However, there were significant issues with this since the results depended critically on the radii of the zones themselves and the reliability of the estimated travel times for other short-distance movements. For public transport journeys, these are not well represented in the information for 2001 on which the analysis is based. In addition, the available output of the Auckland transport models is based on journey times rather than the monetary costs of travel, and the derivation of generalised costs involving both time and monetary components could not be readily achieved.

4.1.2 Option 2

Option 2 follows the approach used by the Department for Transport in the UK for defining effective distance, "Measuring Accessibility for the Appraisal of Wider Economic Impacts TAG Unit 3.5.11".⁴⁹ This approach is based on the probability of travel over particular distances, which can be calibrated against local observations and, for computational convenience, can be converted into a number of bands. Using the results for the trip length distribution for the Region (or at least the part of the region for which transport model results are available) as set out in Figures 4.1 and 4.2, the relationships developed are set out in more detail and contrasted with earlier results in Table 4.1.

Figure 4.1: Journeys to Work by Car in the Auckland Region in 2001: Cumulative Proportions with Specified Elapsed Travel Times

→ Full size version of Figure 4.1 [40 kB JPG]

Figure 4.2: Journeys to Work by Public Transport in the Auckland Region in 2001: Cumulative Populations with Specified Generalised Cost Times

→ Full size version of Figure 4.2 [35 kB JPG]

The relationships between accessibility and employment density, using this alternative approach to measuring accessibility, and their comparison with earlier findings are set out in Table 4.1. These relate to an equation of the form:

Log Density = ax+C

where x = accessibility and a and c are coefficients.

Compared to the initial position, the use of a more continuous accessibility measure based on effective density gives an improved fit between accessibility and density for the Region and for all the individual cities. The exception is Manukau City, for which the explanatory power is reduced. The relationship is particularly improved for Auckland City. The use of a continuous relationship avoids some of the problems identified earlier, where there is a defined catchment area. The banding used for this approach is not heavily dependent on forecasts of travel times and generalised costs for relatively short–distance movements. This formulation was therefore adopted for the subsequent analysis.

4.2 Disaggregation of Zones by Sectoral Composition

In order to assist in the more detailed examination of the relationships between accessibility and employment and employment and productivity, an analysis has been undertaken looking at the effects of breaking down the CAUs by type and then looking at the relationships which apply. The CAUs have been broken down as follows:

• Small zones with less than 800 employees – no further breakdown has been applied (Type 3).
• Large zones with a high proportion of manufacturing or distribution activities. These were defined as all large zones which had more than 40 per cent of employment in the sectors of Manufacturing, Wholesale Trade and Transport and Storage (Type 2).
• Other zones. For presentation purposes these have been divided into two groups although since there are only a small number of zones defined as Type 1a, the two have been combined in developing the regression relationships:
  • Those which have more than 40% of employment in Communication Services, Finance and Insurance, and Property and Business services, which are primarily located in the CBD plus Newmarket, Ellerslie South and Balmoral (Type 1a).
  • Other areas with employment over 800 and not included in the Manufacturing/ Distribution group (Type 1b).

The distribution of these zones is set out in Figure 4.3.

Figure 4.3: Disaggregation of Zones by Sectoral Composition

→ Full size version of Figuer 4.3 [87 kB JPG]

Type 1b activities are mainly located in the CBD fringes and along the main transport corridors particularly the Southern Motorway corridor to the south, along the Northwestern Motorway, and along Manukau Road and Mount Albert Road. Individual centres such as Blockhouse Bay and Mission Bay are also included in this group.

The relationships each of these groups were defined initially for the linkages between accessibility and density (measured here in natural logs). These are set out in Figure 4.4 and in more detail in Table 4.2.

Figure 4.4: Auckland City 2001: Accessibility and Density with Zonal Disaggregation

→ Full size version of Figure 4.4 [63 kB JPG]

Note: dependent variable equals ln density
Note: independent variable equals accessibility

The different zone types show different relationships between accessibility and density. For the Type 1 zones, the areas with high levels of business services, the relationship is sensitive and reasonably robust with an R² value of about 0.55 and significant t-stats for the regression coefficients. The CBD zones are mainly at the top right of the graph.

For other area types, accessibility is a less important determinant of density, with lower sensitivity to accessibility changes and a less robust statistical relationship. This implies that other factors may play a more important role in the determination of employment density. Our accessibility measures are primarily based on access to the potential workforce and jobs by motorised modes. For the smaller zones, with a higher level of activities serving more local markets, local pedestrian and car access may play a more important role. For the industrial areas, it is possible that the accessibility for freight movements focussed on the highway network that is more important. As an example, the Rosebank area has relatively poor accessibility for workers but very good accessibility for the movement of goods given its proximity to the motorway network in the north.

The relationship between density and earnings/average productivity is set out in Figure 4.5. Following our earlier analysis, the relationships displayed here are not corrected for sectoral effects, since these may make significant differences to the patterns observed. In Section 4.3 of this report we do, however, report on measures that attempt to develop more comprehensive regression equations to incorporate density, sectoral and educational effects on a common city-wide basis.

Figure 4.5: Auckland City 2001: Density and Earnings with Zonal Disaggregation

→ Full size version of Figure 4.5 [64 kB JPG]

Note: dependent variable equals average earnings
Note: independent variable equals ln density

For density and earnings, the different area types largely lie on the same straight line suggesting that similar factors affect all three types of area in a broadly continuous fashion. The relationships are strong for the Type 1 and Type 2 zones with high R² terms and t-statistics for the regression coefficients, indicating the importance of density in supporting high levels of productivity. The relationship is, however, less clear for the smaller and more mixed Type 3 zones where the much lower R² term indicates that other factors may be more important.

4.3 Multiple Linear Regression Analysis: The Components of Average Earnings

4.3.1 Purpose

In the analysis set out above, we used simple linear regression to explore the relationship between average earnings and log density. The analysis had been performed using unadjusted average income data, as well as data adjusted for sectoral composition and educational attainment. While this provided useful insight into the relationship between average earnings and employment density, we also wanted to explore the combined interrelationships between average earnings in Census Area Units, and measures of sectoral composition, education and employment density. Of particular interest was the relative importance of the three independent variables in explaining variations in average earnings.

4.3.2 Methodology and Data

To attempt to explore this interaction, multiple linear regression was used to explore these relationships. In addition to identifying the relationships themselves the opportunity was taken to explore some of the underlying measures of statistical significance.

The following data was used for this regression analysis.

Dependent variable: Average income across all employees in the relevant census area unit (Y).

Independent variables: Proportion of total employees with higher educational attainment⁵⁰ in the relevant census area unit (EDU).

Proportion of employees classified as working in the advanced business services sector in the relevant census area unit (ABS).

Employment density in employees per hectare in the relevant census area unit (DENS).

All the variables were transformed into natural logarithms, as this avoided some of the heteroscedasticity problems experienced when regressing average income in dollars against logs of the independent variables.

4.3.3 Summary of Results

All multiple regression analyses were undertaken using natural logs of both the dependent and independent variables as regressions of average income on natural logs of the independent variables were in some instances by heteroscedasticity. While reducing the heteroscedasticity issue, the use of natural logs to measure the income term did result in some loss of explanatory power of the of the relationships defined and this may be an area where further more detailed investigation may be desirable in the future.

The results of these three regressions are outlined in the summary table below.

We also conducted tests for collinearity between the independent variables and found some collinearity between ABS and DENS and this linkage has been supported by other analysis. Therefore, the only regression with neither heteroscedasticity nor multicollinearity is the Regression 3 (Y on EDU and DENS). We concentrate on this regression in our interpretation of the results.

4.3.4 Interpretation

Regression 3 (Y on EDU and DENS) is the only regression without heteroscedasticity and without multicollinearity.

For this regression, the coefficient for educational attainment indicates that a 1% increase in the proportion of the workforce having higher educational attainment would tend to increase average incomes in that census area unit by 0.161 percent. Similarly, a 1% increase in employment density would tend to increase average incomes in that census area unit by 0.099%.

A 100% increase in employment density would therefore increase average income in a census area unit by 9.9%. This figure is broadly consistent with the agglomeration literature where the elasticities of average income with respect to a 100% increase in employment density range from 3-12%.

While we can be confident that heteroscedasticity and multicollinearity are not of concern, a geographical plot of residuals (contained in Appendix C) suggests that spatial autocorrelation (SA) may be present. The presence of SA (meaning that locations close to each other exhibit more similar values than those further apart) may result in biased parameter estimates and can increase type I errors. That is, we may falsely reject the null hypotheses of zero effect. Thus, these results should be interpreted as preliminary. Further work, perhaps in a panel data (cross-sectional data across time) context, would be useful to examine these preliminary results further.

From the test for multicollinearity, it appears that educational attainment and employment density are not closely related. This is an interesting result considering that theory suggests that human capital is an important driver of productivity. We would therefore expect a strong relationship to exist between human capital and density.

One possible reason for this unexpected result is that our measure of educational attainment does not reflect human capital well in that we simply measure the proportion of the workforce that has either an advanced vocational qualification or a degree. In reality, and as widely noted in the literature, human capital is likely to be driven by a much wider range of personal attributes. Le, Gibson & Oxley's literature review provides a good summary of the many challenges facing researchers when developing measures for human capital.⁵¹

In addition, the relative size of the coefficients is of interest because of their practical implications for policy makers. It would be desirable to investigate the empirical relationships more thoroughly, possibly with analysis of time series and through investigating the cost and effectiveness of alternative interventions. Given the coefficients obtained from the regression analysis, it appears possible that both courses of action would potentially contribute to improvements in productivity. However, while we have not examined this issue in detail, the intervention that would be required to increase productivity significantly through increasing the proportion of the current workforce with higher educational attainment is likely to be significant, time consuming and costly. Its potential role particularly in relation to measures to improve accessibility needs further investigation.

4.4 Other Analytical Approaches

4.4.1 Size or Density

One issue that emerged in the course of the Phase 2 work was the choice of an appropriate measure of intensity of employment and whether density or size was a better measure. This was explored using the zonal disaggregation introduced at the beginning of this section to determine whether there were particular differences between the different types of areas. This issue is explored in more detail in Appendix D, but the general conclusion was that, 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 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. For accessibility, the use of density provides much better results.