The Effects of Auckland’s Metropolitan Urban Limit on Land Prices
Guanyu Zheng^{1}
New Zealand Productivity Commission
Abstract
This paper estimates the impact of Auckland’s Metropolitan Urban Limit (MUL) on land values in the greater Auckland region. The model extends Grimes and Liang (2009) which analysed the effects of the MUL on mean land values across Auckland. This paper, instead, uses quantile regression and focuses on land price deciles. The major advantage of quantile regression is to provide a comprehensive analysis of central tendency (e.g. median) and dispersion (e.g. lower or upper quartile) on the relationship between the variables. The results suggest that the impact of Auckland’s MUL is statistically significant and uneven across land price deciles, with a greater impact on lower decile land prices.
Introduction
The housing boom in the 2000s saw an unprecedented escalation in New Zealand house prices and deteriorating housing affordability. Real house prices almost doubled between 2001 and 2007, an average increase of approximately 12% per year. The steep increase in real house price has decreased the likelihood of households being able to purchase their own home and begin the climb up the property ladder. The Auckland region has 31% and 41% of New Zealand’s housing stock by number and value respectively. During the house price boom, the gap between house prices in Auckland and the rest of the country widened even further. The Auckland region faces the highest housing affordability pressures in the country (New Zealand Productivity Commission 2012).
Section prices have grown more quickly than house prices over the last twenty years suggesting that land supply has become less responsive to increasing demand for housing. Pressure on land prices has been particularly acute in Auckland – land accounts for around 60% of the cost of a new house in Auckland compared to 40% of the cost of building a new house in the rest of New Zealand (Figure 1).
Increasing house prices are indicative of supply side rigidities. Contributing factors include the availability of buildable land. Gyouroko (2009) notes that the strong positive relationship between restrictive land use policies and house prices is wellestablished.
In Auckland, the Metropolitan Urban Limit (MUL) is a zoning restriction that defines “the boundary of the urban area with the rural part of the region”. Grimes and Liang (2009) found that the impact of the MUL was significant. Land prices just inside the MUL were 10 times higher than land just outside MUL. The New Zealand Productivity Commission applied a similar methodology to estimate the impact of the MUL between 1995 and 2010. The Commission found that the value of land just inside the MUL boundary is almost 9 times greater than land just outside the boundary, indicating that the MUL is a binding constraint on land supply. Further, the value of the land price differential has increased since the late 1990s, indicating that the MUL has become increasingly binding as housing demand has intensified in Auckland city.
Figure 1. Housing theme: Auckland region v.s. selected New Zealand cities:
(left) Growth of real land and capital values in 20002007
(right) land value as a share of house value in 2000 and 2007
Source: QVNZ
Figure 2. The impact of the Auckland MUL on land prices
Source: New Zealand Productivity Commission
Note: The price multiple of land 2km within the MUL to land 2km outside the MUL
This paper investigates whether the impact of the MUL is uneven across land price deciles. The Commission’s inquiry into housing affordability generated a particular interest in whether the MUL contributed to higher prices (and declining affordability) of lower quartile and median valued land than more expensive properties. One possible explanation for this difference could be that the demand for lower decile residential properties is higher than more expensive properties at the urban limit.
Method
This section outlines the regression model used to estimate the impact of Auckland’s MUL on land prices in the region. The model extends the modelling work of Grimes and Liang (2009) using quantile regression^{2} and focuses on land price deciles.
Traditional regression analysis (e.g. Ordinary Least Square) is focused on the conditional means. That summarises the relationship between the response variable and predictor variables by describing the mean of the response for each fixed value of the predictors (Hao & Naiman, 2007). However, the conditionalmean framework cannot be extended to noncentral locations (e.g. lower and upper quartiles) that may fail to capture informative trends in the response distribution. Alternatively, quantile regression (Koenker & Bassett, 1978; Koenker, 2005) uses a conditionalquantile framework that is able to provide a comprehensive data analysis on quantiles. It also makes no distributional assumption about the error term in the model. That gives greater flexibility in modelling heterogeneous data.
In this study, the hypothesis is that the impact of Auckland MUL will be uneven across the board. In particular, areas with cheaper than average land values experience a greater impact. Quantile regression is more suitable than ordinary linear regression to test this hypothesis.
In the regression, real median land prices^{3} ($ per hectare) are modelled at the meshblock level across the former seven Auckland territorial authorities – Rodney, North Shore, Waitakere, Auckland city, Manukau, Papakura and Franklin – around 8,000 meshblocks^{4} each year.
These prices were based on the land value portion of Quotable Value residential property valuations. The median land values are weighted medians for two main types of properties – residential dwellings and lifestyle dwellings. These properties usually have detached or semidetached dwellings on clearly defined sections and make up over 70% of the total number and value of dwellings in the Auckland region. For other types of dwellings, land is usually crossleased or not clearly defined. In these cases, assessments of land area are difficult to measure because there is no legally assigned portion to the land parcel, like a flat or apartment. These dwellings were therefore excluded from the analysis.
The key variables of interest in the model are the MUL dummy variables. The dummy variables were constructed on the basis of meshblock distance from the MUL boundaries. Specifically, each meshblock was assigned into one of four categories depending on its distance to the MUL. The categories are: greater than 2km inside the MUL, 2km within the MUL, 2km outside the MUL, and greater than 2km outside the MUL. If a meshblock was dissected by the MUL, it was randomly assigned to either just inside or outside MUL by a uniform distribution^{5}. This study used the 2009 MUL boundary^{6} and assumed that it remained constant over time. Although this is not the case in reality, changes of MUL over the last 15 years have been relatively minor (Appendix 1).
The regression includes a set of locational factors which removed largescale variations in land values associated with geographical locations. These locational factors are territorial authority (TA) dummies, urban area dummies and latitudelongitude. TA dummies consist of Rodney, North Shore, Waitakere, Manukau, Papakura and Franklin. Urban area dummies were derived from rural and urban profiles from the 2006 Census (Statistics New Zealand). Rural areas were defined as rural areas with high, moderate or low urban influence. The local centric nodes include a set of high business centres that recognise a polycentric Auckland region^{7}. Quadratic terms of latitude and longitude, including the interaction term, were used to capture the distributional effect of land values associated with location^{8}.
The following regression was estimated:
such that
Y and X are dependent and independent variables. is a function of quantile regression with regard to specific quantile q.
(1)
Where,
Ln(RLV) is log real median land value per hectare in meshblock i at 1995 price.
MUL is MUL dummies. MUL2, MUL3 and MUL4 represent meshblocks just inside MUL within 2km, just outside MUL within 2km and greater 2km outside MUL. MUL1, well inside MUL, is set to be a baseline.
TA is TA dummies. TA4, TA5, TA6, TA8, TA9 and TA10 represent Rodney, North Shore, Waikakere, Manukau, Papakura, Franklin. Auckland city, TA7, is set to a baseline.
URBAN is an urban dummy. It is defined by Census classification in 2006.
NOD is local centric node dummy variable. NOD=1 when a meshblock is no more than 5km away from the centric node. Otherwise, NOD=0.
LAT and LON represent latitudes and longitudes of central meshblock. They have linear, quadratic and interaction terms.
is the intercept
is residuals that are assumed to be independently distributed.
Data
Historic land value data from 1995 to 2010 was sourced by Quotable Value New Zealand (QVNZ). The valuation data in the QVNZ series provides capital, land and improvement values as well as land area and type. However, these values are only updated when revaluations are carried out. That normally occurs in a threeyear cycle, and dates varied slightly different across the territorial authorities. Linear interpolation was applied to obtain estimated land prices between valuation cycles. Interpolation required another QVNZ dataset – sales data^{9} – to indicate price movement. There are two main assumptions for interpolation: 1) land prices are strictly correlated with sale prices and 2) movements of land prices at meshblocks within the same territorial authority are identical. The first assumption was made to match movement of land prices with sales prices. And the second assumption was made as sales price at meshblock level was unavailable.
The method of linear interpolation is done in the following equation (2).
(2)
Scripts L and S are land prices and sales price index. Subscripts t and c represent the first year of valuation and the length of cycle (e.g. 2, 3 or 4). Subscript i represents the time period of interpolation, that falls between t and t + c.
Under the equation, interpolated land prices () are calculated in two parts. The first part is the observed land price at the beginning of the valuation year (). The second part calculate value growth between valuation years. That discounts the observed increment between cycles by the proportion of incremental change of sale price index over the same period .
Since the valuation data is obtained triennially, data and results from modelling are reported for every third year: 1995, 1998, 2001, 2004, 2007 and 2010. Real land prices are calculated on the basis of 1995 constant prices using New Zealand’s CPI.
The following tables (table 1 – 3) provide summary statistics on real land prices by quantiles and MUL groups and reveal a number of key results:

Land prices decline from MUL1 to MUL4, that is, from well inside the MUL to well outside (more than 2km) the MUL. This is partially associated with distances to the Auckland CBD.

Step price changes are associated with the MUL boundary for lowerquantile and median priced land. In 19952010, relative price differences between MUL2 (within 2km inside the MUL) and MUL3 (within 2 km just outside the MUL) were 7 for lower quartile and 3.5 for median priced land (Figure 4).

Lowerquartile and median priced land in MUL2 (within 2km inside the MUL) experienced the highest growth rates. In comparison, price growth for land in MUL3 (within 2km outside the MUL) is the lowest. This suggests that the land price impact of the MUL has been increasing and concentrated on cheaper land located around the boundaries.
Table 1: Real lowerquartile land price per hectare (based on 1995 price) by MUL
LowerQuartile

1995

1998

2001

2004

2007

2010

Count

%change
95  10

MUL1

612,006

599,128

867,115

1,193,720

2,164,494

2,531,960

5,416

314%

MUL2

405,205

375,952

462,086

765,334

1,379,914

1,726,659

2,294

326%

MUL3

47,766

58,149

72,782

89,907

144,313

184,590

2,22

286%

MUL4

24,507

30,712

38,161

51,623

85,604

98,995

879

304%

Table 2: Real median land price per hectare (based on 1995 price) by MUL
Median

1995

1998

2001

2004

2007

2010

Count

%change
9510

MUL1

956,702

1,039,128

1,461,094

2,035,915

3,470,675

3,534,351

5,416

269%

MUL2

492,288

476,459

637,069

965,015

1,868,390

2,077,143

2,294

322%

MUL3

109,866

120,873

169,622

214,852

370,284

380,311

222

246%

MUL4

52,182

65,504

80,624

109,121

197,555

215,803

879

314%

Table 3: Real upperquartile land price per hectare (based on 1995 price) by MUL
UpperQuartile

1995

1998

2001

2004

2007

2010

Count

%change
9510

MUL1

1,520,958

1,815,876

2,491,920

3,615,172

5,511,004

5,392,102

5,416

255%

MUL2

689,022

818,923

1,060,365

1,485,820

2,836,567

2,896,644

2,294

320%

MUL3

386,102

412,105

578,933

780,399

1,161,163

1,649,450

222

327%

MUL4

234,466

270,333

326,978

563,465

1,064,863

1,183,199

879

405%

Figure 3. Relative price difference on MUL, 19952010
Note: MUL1 – land well inside MUL
MUL2 – land just inside MUL (within 2km)
MUL3 – land just outside MUL (within 2km)
MUL4 – land 2km outside MUL
Results
This section details regression results (OLS and quantile regressions) on the effects of the MUL boundary on real land prices from 19952010. Some detailed regression estimates are presented in appendix 2.
The results suggest that spatial correlation is statistically significant. The presence of spatial correlation may either bias coefficient estimates or make inefficient estimates (Anselin, 1988). Bootstrapping was undertaken on both OLS and quantile regressions suggesting the latter problem i.e. coefficient estimates remain unbiased, but are less efficient on standard errors (Appendix 3).
The impact of the MUL is assessed by comparing the value of land situated just inside the MUL relative to land situated just outside the MUL, as measured by the difference^{10} between the coefficient on MUL2 and MUL3. Both OLS and quantile regression show similar impact of MUL on mean and median, around 56 times (see figure 4 and 5). Figure 5 also reveals the impact of the MUL is uneven with land in lower decile range experiencing the highest impact. On average, the price difference in the lowest decile is around 10 which is 1.8 and 6.9 times greater than for land in the median and highest deciles.
Over the time period, the impact of the MUL on the lowest decile land and median land increased. In 1995, the impact on the lowest decile and median were 8.1 and 4.3 respectively. In 2010, both increased to 9.7 and 5.6, up 20% and 30%. Conversely, the impact on the highest decile remained relatively flat, just 1.3. This indicates that most of the binding constraint from the MUL falls on the lowest to median valued land. Consequently, price gaps between less and more expensive land have widened (Figure 6).
Figure 4. Relative price differences between MUL2 and MUL3 from OLS regressions
Figure 5. Relative price differences between MUL2 and MUL3 from quantile regressions
Figure 6. Growth gaps from quantile regressions
For land situated in urban and rural areas^{11}, price differences are relative minor and stable through the period (figure 6 and figure 7). Particularly in urban areas, price differences are around 1. This implies that urban and rural land prices grow at similar rates and the MUL does not intensify price pressures onto inner urban and remote rural areas.
Figure 7. Relative price differences between MUL1 and MUL2
Figure 8. Relative price differences between MUL3 and MUL4
Conclusion
The containment of Auckland city through the Metropolitan Urban Limit is a supply side rigidity that puts pressure on residential land prices, in particular around the MUL boundaries.
The MUL is a binding constraint on land supply. The value of the land price differential has increased since the late 1990s, indicating that the MUL has become increasingly binding as housing demand has intensified in Auckland region.
This study shows that the impact of the MUL is uneven. The impact on the lowerquartile land price range is the highest, suggesting that the MUL has a profound effect on housing affordability for those at the lower end of the housing market.
References
Anselin, L. (1988) Spatial Econometrics: Methods and Models, Dordrecht: Kluwer Academic
Cliff, A. D., Ord, J. K. 1981 Spatial processes, Pion
Efron, B. (1979). "Bootstrap Methods: Another Look at the Jackknife". The Annals of Statistics
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