We present results both for our baseline model, Eq. 1, and for the extended model that adds the three social variables, MEDINC1991, POPDENS1991 and NZDEP1991 (as defined in Table 1). Our key focus is a comparison of the estimated coefficients on DMUL2 (ɛ
2) and DMUL4 (ɛ
4) over each of our sample years. To be confident that our model explains spatial urban land values satisfactorily, we expect ɛ
2 ≈ 0, at least for later years when the MUL is likely to have been more binding. If that is the case, and if ɛ
2 > ɛ
4, we can infer that a boundary effect exists with land just inside the MUL being valued more highly than that just outside the MUL after controlling for other factors. (In this situation, we also expect that ɛ
2 > ɛ
3 > ɛ
4, implying that cross meshblocks are valued partially as lying inside, and partially outside, the MUL.)
Results from estimating the baseline model as separate cross-sections for each of 1992, 1995, 1998, 2001 and 2003, using OLS, are presented in Table 4. Meshblocks from all seven TAs are included in each cross-section. We present all coefficients other than those pertaining to the non-CBD nodes.Footnote 17 We have also estimated the same model for five TAs (excluding Papakura and Franklin) through to 2004. The results are very similar to the seven TA case, so we present the results solely for the seven TA specification.
Baseline Model: Non-MUL Terms
Coefficients on the distance functions for both COAST and CBD are such that there is a negative effect of both variables over their relevant ranges.Footnote 18 This occurs even where one of the linear or logarithmic coefficients is positive. To demonstrate this, the impact of distance from the CBD on land values for each year is plotted in Fig. 2.
The impact of distance from the CBD on real land values in Auckland has changed virtually monotonically from 1992 to 2003. In 2003, the impacts of distance from the CBD at 0.25, 5, 25 and 50 km were 1.315, 0.621, 0.247 and 0.102 respectively. Thus land within the CBD was valued at just over twice the rate of land 5 km distant,Footnote 19 five times the rate of land 25 km distant, and almost thirteen times the rate of land 50 km distant. In 1992, by contrast, land values rose slightly over the first 3 km, with ratios of CBD land value to land at 25 and 50 km being 1.7 and 4.4 respectively. Land value has therefore become more concentrated in the area close to the CBD, consistent with increasing agglomeration effects based on the CBD.
Figure 3 graphs the impact of distance from the coast on land values. Unlike the CBD distance effect, the effect of distance from the coast on the real value of land around Auckland has been remarkably stable over time. Furthermore, the (minor) changes have not been consistently in one direction; the 2003 effect is very close to that of 1992. Overall, a coastal location has commanded a premium over locations more distant from the coast over the whole period.
Of the other non-CBD variables, the coefficient on RURAL92 indicates that rural land is consistently cheaper than urban land even after accounting for distance and other effects. The TA dummies show that Auckland City is slightly more expensive than most other TAs, especially in later years.Footnote 20 The R
2 statistic increases throughout the period from 0.729 in 1992 and 1995 to 0.804 in 2003. Overall, the high explanatory power and the sensible coefficients on each of the non-MUL terms give confidence that the MUL boundary effects are estimated within the context of a suitable model for urban and peri-urban land values.
Baseline Model: MUL Boundary Effects
In interpreting the MUL boundary effect, we first examine the behaviour of prices just within the MUL boundary. If the broader model is suitable for modeling land values across the region, we would expect that prices just within the MUL boundary will not be significantly different from those well within the boundary once distance and other controls have been accounted for. The exception would be if there were still major holdings of vacant land within this area.
Meshblocks in this area have DMUL2 = 1. The coefficient on this term for the baseline equation in Table 4 is not significantly different from zero in either 2001 or 2003 implying that in later years the overall model fits the value of land situated just inside the MUL boundary as well as for land that is closer to the CBD. In prior years, this land is slightly under-priced relative to the overall model, with the degree of under-pricing increasing as the sample goes backwards. This finding is in keeping with the hypothesis that a greater portion of this land was rural earlier in the period. Overall, the DMUL2 coefficients imply that the model is valuing land close to the MUL boundary in an appropriate manner.
Land situated just outside the MUL boundary has a sharply decreased price compared with land situated just inside the MUL even with the inclusion of distance and other controls. In 1992, the difference between the coefficients on DMUL2 and DMUL4 was 2.372; since then the difference in coefficients has varied in a tight range between 2.455 and 2.569. Noting that the dependent variable in Eq. 1 is logarithmic, these coefficients indicate that land just inside the MUL boundary is around 12 times more expensive per hectare than is land situated just outside the MUL.Footnote 21
If this figure is caused by an MUL boundary effect, we would expect the cross meshblocks (DMUL3 = 1) to reflect the partial effect of the MUL, as indeed occurs. Each of the DMUL3 coefficients is significantly negative. Consistent with the declining coefficient on DMUL2, the coefficient on DMUL3 has declined over time suggesting that much of the land in these cross meshblocks is now being developed or being priced for future development.
Results from estimating the extended model as separate cross-sections for each of 1992, 1995, 1998, 2001 and 2003, using OLS, are presented in Table 5. Meshblocks from all seven TAs are included in each cross-section; again we present all coefficients other than those pertaining to the non-CBD nodes.Footnote 22
The distance effects are very similar to those in the baseline model, with land values becoming more concentrated towards the city centre over time. In 2003 the ratios of land values within the CBD relative to those 5, 25 and 50 km distant are calculated at 2.5, 5.9 and 12.0 respectively. This compares with ratios of 1.0, 1.7 and 3.4 respectively in 1992. As in the baseline model, coastal effects have remained broadly constant over time. Rural and TA effects are similar to the baseline model.
The three social variables are all highly significant with the expected signs. Meshblocks with high population density and high median incomes are valued more highly than other meshblocks, while more deprived areas are associated with low land values. As discussed earlier, the direction of causality in these relationships could run both ways.
Very similar patterns are observed for each of the MUL variables as in the baseline model. The coefficient on DMUL2 (i.e. on meshblocks just inside the MUL boundary) declines monotonically throughout the sample as does the coefficient on the cross meshblocks (DMUL3). The difference between the coefficients on DMUL2 and DMUL4 rises between 1992 and 1998, and stays between 2.25 and 2.35 over 1998–2003. In 2003, land just inside the MUL is valued at 9.5 times that just outside the MUL.
These results control for the effects of population density and also for characteristics of residents that may in turn impact on land prices. One argument previously cited to account for higher values of land inside relative to outside the MUL boundary is that people value highly the rural amenity value of being on the outskirts of the city (i.e. just within the MUL). This would bid up prices for land just inside the MUL boundary, possibly creating an artificial distinction between land values on either side of the boundary. Our results indicate that this is not likely to be part of the explanation for the observed boundary effect for two reasons. First, the estimate for DMUL2 is not significantly different from zero in later years (and is negative in earlier years). Thus the distance variables are adequately capturing the values of land just inside the MUL boundary, implying that there is no extra amenity value placed on this land. Second, even if there were such higher amenity value, it is likely that higher income (and less deprived) households will move into the sought-after area. Our extended model controls for these household characteristics and hence controls for such amenity values.
Both the baseline and extended models have been estimated with OLS. The significance tests employ standard errors that are robust to heteroskedasticity. However, there is still the possibility that spatial autocorrelation will be present which may bias the coefficient estimates and/or make them inefficient (Anselin, 1988).
We test for the presence of spatial autocorrelation in our estimated models using Moran’s I statistic. The null hypothesis is that there is no spatial autocorrelation in the residuals. We are unable to calculate Moran’s I for the complete set of residuals owing to computer memory constraints given the large dataset that we are using. Instead, we test for autocorrelation (using the residuals from the full model) at the level of each TA. We employ tests at different spatial scales: up to 0.25 km, up to 1 km, up to 2 km, up to 5 km and up to 20 km.
The tests cover the two models (baseline and extended), each for 5 years (1992, 1995, 1998, 2001, 2003), each for seven TAs with five spatial scales: a total of 350 test statistics. Rather than presenting each of these results, we summarise the findings. We find significant spatial autocorrelation for virtually all cases over a range of 0–1, 0–2 km and (mostly) over ranges of 0–0.25 and 0–5 km. We do not find spatial autocorrelation over a greater spatial range (0–20 km).
As a result of these tests, we estimate the same underlying relationships using the three additional techniques outlined in “Methodology”, in each case for the seven TA sample in 2001 (results reported in Table 6). The most basic supplement to our approach is to retain OLS as the estimation technique, but to add dummy variables for area units. There are approximately 350 area units across the greater Auckland region compared with 8,800 meshblocks. Area units are akin to suburbs in a metropolitan area and so may capture the impact of shared amenities and desirable locations. The drawback of this approach is that if the area unit boundaries near the city outskirts are similar to the MUL boundaries, the two effects will be highly collinear and so will make it more difficult to detect the MUL boundary effect.
The estimates for the OLS area unit model again show clear, albeit more muted, MUL effects. In the baseline and extended models, the estimated ratio of DMUL2 to DMUL4 land value is 6.3 and 4.9 respectively. For reasons outlined earlier (especially the collinearity between peripheral urban area unit boundaries and the MUL boundary) these estimates are likely to be material underestimates of the MUL boundary effect.
The second approach is to estimate a spatial lag model.Footnote 23 For the baseline model, the implied ratio of land values across the MUL boundary is 13.2; for the extended model, the implied ratio is 10.1. The third approach is to estimate a spatial error model. For the baseline and extended models, the implied ratios of land within DMUL2 relative to DMUL4 are 13.2 and 10.2 respectively. Each of these estimates is similar to the estimates from the OLS model. The only estimates that give a materially different result are those that add the 350 area unit dummies to the OLS equation. These estimates almost certainly provide an under-estimate of the boundary effect. Even here, however, the effect is estimated to be in the order of a factor of 5 (extended model) or 6 (baseline model).