Land Value Indices and The Land Leverage Hypothesis in ......and structure of a residential property...

Land Value Indices and The Land Leverage

Hypothesis in Residential Housing⇤

Alicia N. Rambaldi†

School of Economics, The University of Queensland, St Lucia, QLD 4072. Australia

Madeleine S. Tan‡

Department of Treasury and Finance, Victoria. Australia

PREPARED FOR THE INTERNATIONAL CONFERENCE ON

REAL ESTATE STATISTICS. 20-22 FEBRUARY 2019.This version: 28 January, 2019

Abstract

The land leverage hypothesis implies that the value of the land component

grows faster than the value of the structure component, and the predicted prop-

erty price is broadly in line with the median price over time. The value of land

and structure of a residential property is obtained using a new methodology where

a state-space model produces the decomposition of the value of each site into

its land and structure components. The method is applied to unit record level

sales data for all properties that were transacted over 43.5 years between 1975Q1

and 2018Q2, across the state of Victoria (Australia)’s 79 local government areas

(LGAs). The model valuations are used to compute land and structure price

indices for the Inner, Metro and Outer regions of Greater Melbourne. Site values

are provided by the Valuer-General Victoria (VGV) and serve as a benchmark

value of land for every two-year snapshots. The model estimates of the sites sold

in 2014 are priced for 2016 and compared to the 2016 VGV revaluation outcomes.

⇤This project is funded by the Australian Research Council - LP160101518. We thank Corelogic

for supplying the data.†Corresponding author: A.N.Rambaldi (+61(0)7 3365 6576), [email protected]

‡The views and opinions expressed in this article are those of the authors and do not necessarily

reflect the o�cial policy or position of the Department of Treasury and Finance, Victoria Government

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The average di↵erence is 3.27 percentage points. The land value indices com-

puted from the model’s estimates for LGAs within the inner, metro and outer

regions are consistent with the land leverage hypothesis. This is established by

analysing the annual growth rates of each component across the three regions as

well as using a regression of the property price indices on the corresponding land

leverage. We find that the magnitude of the responses vary across the regions

and has a seasonal pattern

Keywords: unit record level sales data; decomposition into land and structure

values; state-space; Fisher indices.

1 Introduction

The unobserved nature of land values poses significant challenges to policy making

and planning especially in urban areas where very few vacant land transactions occur.

Bostic et al (2007) proposed the hypothesis that house price appreciation and house

price volatility are directly related to land leverage which they defined as the ratio of

land value to total value. An increase of 10% in the value of land results in a di↵erent

outcome on the value of the property that has a higher land leverage.

As land tax revenue becomes an increasingly important source of revenue for states,

the uncertainty associated with changes to land values presents a significant risk for

state revenue. Property price transaction data and indicators are widely available,

however properties contain both land and structure components. Changes in the value

of land or structure are not immediately evident from property price indicators alone.

Complicating this further, the structure is a depreciating asset while the land component

is an appreciating one, and both are driven by di↵erent factors more than they are by

common ones.

This paper studies uses a recently developed approach to decomposing the value of

a property into its land and structure components (Rambaldi et al (2016)) to assess

the land leverage hypothesis. Parameter estimates and the indices of the change in the

value of land and the property from settled sales transactions for residential detached

dwellings are used to evaluate the evidence for the land leverage hypothesis using data

from the Greater Melbourne area.

This modelling method maps observed hedonic characteristics of the land and struc-

ture to decouple the value of land and the value of the structure from information

available in the settled sales transactions data such as the sale price and characteristics

of the property at the point of sale. The estimation results are then used to construct

Fisher indices for land, structure and property values to allow for a useful interpretation

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of changes to the value of land and structure over time. Although the main interest is

in extracting the value of land from settled sales property transactions, there are flow-

on advantages in being able to also identify changes in the value of the structure over

time from this same procedure. For example, entities such as local governments require

information on changes to the capital improved value of properties to set council rates.

Section 2 describes the three approaches in the literature that are used to decompose

the value of land and structure from property prices. Section 3 describes the method

used while section 4 summarises the data and estimation process. Section 5 presents es-

timation results, a comparison against past general valuations in the Greater Melbourne

area and the evidence for the land leverage hypothesis. Finally, section 6 concludes with

a summary of findings.

2 Approaches to decompose the value of land and

structure

A quick survey of the empirical literature on this topic finds that variations of three

methods are used to decompose land and structure values from property prices alone.

They are the vacant land method, the construction cost method and the hedonic re-

gression method. The literature on decomposing the property prices into land and

structure components assumes that the relationship between the value of land (pLL)

and structure (pSS), and the sale price (Pt) looks as follows :

Pt = pstSt + pltLt + ✏t (1)

where, pst is the price of the structure and plt is the price of land, at time t St is the

quantity of the structure (e.g. floor area in square metres) and Lt is the quantity of

land (e.g. lot size in square metres), at time t

A linear and additive relationship as in Equation (1) is used over a log-linearised

or semi-log one. This assumption is required for decomposition of the two components

from the property price as the land and structure components are assumed to be dif-

ferent assets. Land is an appreciating asset while the structure is a depreciating one.

Therefore, a linear and additive relationship assumes that all the three components in

the equation above are orthogonal to each other. Bostic et al (2007) explain that the

land value and structure value each have di↵erent dynamics since land is non-moveable

and its benefits can only be experienced in a specific location, while the structure is

made up of materials and labour that are mobile factors. Land values will generally

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increase in urban areas where population and economic growth increases its price until

economic profit is zero. However, the value of a structure at any given point is made

up of its replacement cost net any accumulated depreciation.

Since the value of the structure is assumed to be made up of its replacement cost

less any accumulated depreciation at a given point in time, the value of improvements

cannot surpass the increase in construction costs. If depreciation is large enough, the

value of improvements could even see a fall, which is less likely to happen with land

value. Decreases in value of improvements is possible since buildings are assets and as

it is with any durable good, use over time reduces the productive capacity. In addition

to this, changes to tastes and technologies also mean that some homes can become

obsolete and less valuable with time.

2.1 Vacant land method

The paper by Clapp (1979) describes the vacant land method, which is often used by tax

assessors and appraisers. From Equation (1), this approach assumes that the sale price,

properties of the structure, and properties of land are known while the price of land pL

can be made known using information on the sales of “comparable” vacant land plots.

Once the value of land is determined, the price of the structure pS can be imputed.

Since urban areas su↵er from the lack of such sales, it is often augmented by the sale

of properties that are sold and the associated structure is immediately demolished.

However, even including these, the data available are still limited. This approach is

used by Thorsnes (1997) and Bostic et al. (2007). However, Clapp (1980) states that

this method is likely not very accurate for the following reasons: as already mentioned,

urban centres are unlikely to have su�cient numbers of vacant land sales, and where

available, the land sales information is unlikely to be comparable due to di↵erences in

location and timing of sales.

2.2 Construction cost method

Essentially, this method takes a similar approach to the vacant land method. However,

instead of the price of land pL that is known, it is the price of the structure, pS that is

made known by ascribing it to be at most equal to its replacement cost, which is essen-

tially the construction cost of the structure. From this, the price of land (pL) related

to the property can be imputed through Equation (1). In Australia, this construction

cost information is available from providers such as Rawlinsons according to type of

building, material and location. This was the approach used by Glaeser and Gyourko

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(2003) and Davis and Palumbo (2008) in the case of residential properties in the US.

Davis and Heathcote (2007) constructs the value of the structure using estimates by the

Bureau of Economic Analysis for the US economy for both the price of the structure

and the quantity of housing.

While the construction cost method is able to account for some locational and timing

di↵erences that the vacant land method is not, it is only an indicative figure. In addition

to this, the value of land and structure components derived are only an approximations

since modelling the nature of depreciation or maintenance cost due to the age of the

structure or other isolated characteristics such as preserving architectural features is

complex at best as illustrated in the analysis in Francke and Minne (2017).

2.3 Hedonic based methods

The upside of hedonic regression modelling is that it is a revealed preference method

that estimates the contribution of each characteristic to the overall price. This approach

in the literature is a response to the vacant land sales method which Clapp (1980)

suggested might not be very accurate for reasons previously mentioned. The hedonic

regression approach assumes that the price of land varies with structural and loca-

tional (access and neighbourhood amenities) characteristics. Generally, this approach

models the property sale price as linearly related to the structural characteristics and

locational characteristics. In the hedonic regression model, the marginal price for each

characteristic of land and structure is determined at every time period through partial

derivatives of the model. These marginal prices are then used to decompose the price

of the property into land and structure components.

A variant of this hedonic regression method is known as the builder’s approach as

presented in Diewert et al (2015). The method combines the hedonic characteristics of

the property (such as the area of land, area of the structure, age of the structure and

the number of rooms) with an o�cial price index for new construction. Using a non-

linear framework, Diewert et al (2015)’s model interacts the age and size of structure

with an index for the price of new construction. This replaces �t in Equation (2). The

interaction provides an identification of the structure value, which in turn delivers an

identification for the price of land. The basic builder’s model:

Pit = ↵tLit + �t(1� �tAit)Sit + ✏it i = 1, . . . , N(t); t = 1, . . . , T (2)

Pit identifies the sale price for the i � th property at time t, �t the net deprecia-

tion rate at time t, Ait the age of the structure in years, Lit is the size of the land

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and Sit is the size of the structure of property i at time t. �t is defined as the gross

structure depreciation rate less an average renovations appreciation rate. While these

hedonic regressions make sense to decompose the property sale price into the value of

land and structure, this approach shares the same limitations as the construction cost

method so far. Assumptions are required regarding the form of net depreciation making

identification a challenge.

Rambaldi et al (2016) circumvents this by using a state-space model that does not

require the use of an indicator of the price of new construction prices, or the specification

of a depreciation scheme for the structure. The method assumes shocks to prices can

have an asymmetric e↵ect in line with Bostic et al (2007)’s land leverage hypothesis,

where all else equal, properties with higher land leverage will experience stronger price

responses to economic shocks. The decomposition is based on setting up the hedonic

model in a state-space framework where characteristics are uniquely mapped to one

of the unobserved components, land and structure. The variance-covariance of each

unobserved component is a function of a discount factor. This framework follows the

earlier work of West and Harrison (1999). The method is briefly described in further

detail in the next section.

3 Methodology

The basic model from Rambaldi et al (2016) looks as follows:

Pit = Lit + Sit + ✏it; ✏it ⇠ N(0, �2✏ I) (3)

where Pit is the sale price of property i sold in period t

Lit is the value of the land component for the i� th property sold in period t

Sit is the value of the structure component for the i� th property sold in period t

If nt represents the number of observations at time t while kl and ks denote the num-

ber of hedonic characteristics related to the land and structure components respectively,

let XL be an nt ⇥ kl matrix of hedonic characteristics intrinsic to the land component

(e.g. lot size or location) and let XS be an nt ⇥ ks matrix of hedonic characteristics

intrinsic to the structure component (e.g. age of structure, size of the structure, num-

ber of bedrooms or bathrooms). This gives us a model that is in line with the hedonic

regression approach in the literature:

Pit = ↵Lt X

Lit + ↵

St X

Sit + ✏it (4)

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where, ↵ct is the vector of shadow prices capturing the trends for land (L) or structure

(S) at time t; c = L, S; and ✏t ⇠ N(0, Ht).

These shadow prices essentially capture the marginal value of each hedonic charac-

teristic at every time period t. To achieve identification, Rambaldi et al (2016) propose

specifying the law of motion for these shadow prices as being driven by uncorrelated

components’ specific discount factors in the covariance structure.

↵t = [↵Lt ↵

St ]; t = 1, . . . , T (5)

Gt = E(↵t↵0t) (6)

↵0 ⇠ N(a0, G0) is the initial condition (7)

The dynamic discounting literature specifies Gt|t�1 as a discounted Gt�1|t�1 by a

proportion. As the model has two components, there are two discount factors, each

associated with one of the components.

Gt|t�1 = diag��

��1L Gt�1|t�1,[1:kL,1:kL]

�,��1S Gt�1|t�1,[(kL+1):(kL+kS),(kL+1):(kL+kS)]

�

(8)

where Gt|t�1 is a partitioned diagonal matrix with sub-matrices G[a,b] corresponding

to the land and structure components. Each partition is a function of a discount factor,

0 < �L, �S 1, and Gt�1|t�1 associated with the movements in the land or the structure

components in the model in period t� 1. The estimation of the state, ↵t and its MSE

matrix, Gt, follows a modified form of the Kalman filter. It is easy to verify that the

estimates of the state, at|t, for one component are still functions of both the land and

the structure characteristics, XLt and X

St , since the innovation’s covariance, Ft, is a

function of all hedonic characteristics.

The conventional approach was to set the discount factors to a value, see West and

Harrison(1999), usually in the range between 0.85 and 0.99 for models with components

such as trend, seasonal and cyclical. Rambaldi et al (2016) combine a grid search and

an evaluation of the likelihood function in an iterative procedure.

Based on the arguments made in the literature, land and structure require di↵erent

discount factors that obey the following restriction: �L < �S < 1. Urban land destined

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for residential housing is an appreciating scarce asset, and thus shocks in the market

due to changes in population trends as well as overall macroeconomic conditions are

expected to drive the trend in land prices. The trend in the value of the structure is

expected to be in line with movements in construction costs, which are likely to closely

follow changes in wages and more generally CPI, as well as a more homogeneous evo-

lution across markets (such as major urban cities within a state or country). Individual

structures will be subjected to depreciation which would be a function of the age of

the structure. This point is important as it provides a strong argument for the need to

include a measure of the age of the structure in XSt .

Note that the conventional approach to predicting and explaining property prices is

also based on a decomposition in which there is an overall time trend variable coupled

with a quality adjusted linear combination of hedonic characteristics often in the form of

dummy variables (see Rambaldi and Fletcher (2014) for review). While this is su�cient

for estimating property prices (as a bundle of both land and structure components), it

is not able to di↵erentiate between the dynamics in the price of land or the structure.

The specification in Equation (4) allows for time-varying parameters to capture

changes in the marginal value of each hedonic characteristic over time (which is the

shadow price, ↵ct ; c = S, L). Therefore, this specification facilitates a decomposition

that identifies separate trends in the land and structure components. To achieve iden-

tification, the hedonic characteristics need to be unique to either the structure or land

only, and not both. This is not possible with the use of a common intercept or time

trend variable as per conventional methods.

Estimating this model requires to first estimate �2✏ ,�L,�S which are then used in the

modified Kalman filter algorithm to obtain the estimates of ↵ct ; c = S, L. These are

then used to predict the price of the land, structure and property of each observed sale

at any desired time period allowing the construction of Fisher hedonic imputed price

indices for the property and each component.

In this study the constructed price indices and estimates of the discount factors are

used to assess the empirical evidence for the land leverage hypothesis.

4 Data

CoreLogic’s settled sales data was used. It includes unit record level characteristics

for all properties that were transacted over 43 years between 1975Q1 and 2018Q2,

across Victoria’s 79 local government areas (LGAs). For each property, information is

available on sale price, date of contract and settlement, address, dwelling type, number

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Figure 1: Inner,metro and outer regions of Greater Melbourne

of bedrooms, number of bathrooms, land size, total floor area, land use code and the

year the structure was built.

The dataset used contains only residential detached properties and was grouped into

three regions: inner, metropolitan and outer areas of Melbourne (see Figure 1). As

expected, the outer region of Melbourne contained the most number of transactions

while inner Melbourne had the fewest transactions of residential detached properties.

After the usual data cleaning for outliers, missing data and non-standard transac-

tions, there was a total of 677,460 observations over the period of 1975Q1 – 2018Q2.

There were 362,564 observations in the outer region, 271,628 observations in the metro

region and 43,268 observations in the inner region. The model was estimated sepa-

rately for each of these groups in order to accommodate the di↵erent natures of their

respective property markets.

The majority of detached dwelling transactions occurs in the outer region, which

likely corresponds to having fewer detached dwellings closer to the city centre. Figure

2 plots the number of transactions per quarter for each of the three regions over the

sample period.

It is important to note that this study concentrates on detached housing. The inner

region of Melbourne has much detached housing relative to the other two regions. The

most common housing type in this area is buildings with multiple dwellings (townhouses

9

or units). When a detached housing property is sold in the inner area, it is often the

case that the structure is destined for demolition to make way for multiple dwellings.

Descriptive statistics of the data by region are provided in the Appendix

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Figure 2: Number of Transactions per Quarter (top to bottom:Inner, Metro, Outer)

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5 Results

This section presents estimates of the model, a comparison of the model performance

to the revaluations of the Valuer-General Victoria and provides empirical evidence sup-

porting the land leverage hypothesis.

5.1 Estimated Model and Price Indices

Preliminary hedonic regressions were first run to determine key drivers of the values

of land and structure. Several variables were considered in the modelling. From the

literature, the value of land and the structure is driven by di↵erent factors.

Among the variables considered include:

1. Land size: The plot is measured in square metres

2. Floor area: This measures the size of the structure in square metres

3. Bedrooms: This measures the additional value to the structure of an additional

bedroom. Measured in number of rooms

4. Bathrooms: This measures the additional value to the structure of an additional

bathroom. Measured in number of rooms.

5. Age of structure at time of sale: This is calculated as the di↵erence between the sale

year and the year that the structure was built. Measured in number of years.

6. Number of floors: This can also be thought of as a ratio of the land size to floor

area. This variable suggests that buyers prize an extra square metre of floor space but

only with an equivalent increase in the land size.

Although the number of car spaces variable was also considered, it severely limited

the number of observations as there were more observations that had missing infor-

mation on car spaces than there were on characteristics such as number of bedrooms

and bathrooms. The use of the distance to the Melbourne CBD of each property was

also explored. The rationale behind using this variable was to account for the benefit

of access to amenities and economic opportunities often located in the CBD. However,

it appeared to make more sense to control for location by using postcode dummies as

access to services between the east and west of Melbourne is asymmetric. In addition

to this, controlling for location with postcode dummies better captures for the e↵ect

of access to services, neighbourhood premiums, and other infrastructures available that

would be localised within a particular area only.

The model estimated was

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Pit = ↵Lt X

Lit + ↵

St X

Sit + ✏it (9)

where,

XLit=land size,postcode dummy variables

Xsit =number of bedrooms (splines), number of bathrooms (splines),age of structure,number

of floors

In terms of functional form, both linear and quadratic forms of variables were consid-

ered. The results appear to be robust to the use of either linear or quadratic variables.

The index of land value changes yield similar results.

The models were run at a quarterly frequency for the purpose of this study using

the full sample. However, due the quality of the available data for the period before

the mid 1990s, we only construct the price indices from 1995Q1 onwards.

The first step of the estimation searches over a large set of pairs of discount factors

combinations. Table 1 shows all the possible values used in the estimation. In all cases

both are less than 1 which is required for stability of the method. The smaller the

factor is, the higher the volatility of the component. If the discount factors for the land

and structure component are identical, this would imply a shock to property prices

a↵ects both land and structure components equally. In all three regions the lowest

mean squared prediction errors are given by values of the pairs where the land discount

factor is lower than that of the structure. For the inner and outer regions the pair is

(0.85,0.9), for the metro regions it is (0.8,0.9).

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Table 1: Discount Factors

Land Structure Lowest MSEInner Metro Outer

0.75 0.90.75 0.950.75 0.990.8 0.80.8 0.9 X0.8 0.950.8 0.990.85 0.850.85 0.9 X X0.85 0.950.85 0.990.9 0.90.9 0.990.95 0.950.95 0.99

Figure 3 provides the estimated indices for property, land and structure obtained

for each region. The indices show there are di↵erent trends in prices across the three

regions and the components.

Land prices continue their strong growth in the metro and outer region but appear

to be stabilizing in the inner region. The property price index for detached housing

for the inner region appears to be driven by land prices which is consistent with the

observation that structures in this area are likely to add little value to the land and

could in fact have negative value as they would need to be removed. These plots would

appear to support the land leverage hypothesis for the metro and outer regions. The

land component grows faster than the structure component, and the predicted property

price is broadly in line with the median price over time. We return to the evidence for

the land leverage hypothesis in the Section 5.3.

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Figure 3: Computed Price Indices. Period: 1995Q1 - 2018Q2(1995Q1=1). From the top(Inner,Metro,Outer)

15

Figure 4 presents the estimated land leverage for the period 1995Q1-2018Q2 for the

three regions.

In the next section, the predicted land value changes from the model are evaluated

against site value changes from past biennial revaluations available from the Valuer-

General Victoria (VGV).

5.2 Evaluation of model results (Incomplete)

Site values are provided by the Valuer-General Victoria (VGV) and are used as the

benchmark value of land for every two-year snapshot. The biennial growth rate from

the land value index is compared against the land value growth, using the revaluation

outcome data from the VGV. The VGV has made available the revaluation outcomes

for each LGA in Victoria on their website1 since 20142. This data contains the total site

value (in $ amounts) for each LGA at a point in time i.e. the 2018 revaluation outcome

determines the site value of properties as at 1 January 2018. The LGA site values were

aggregated up to match the definition of inner, metro and outer in the model. From

there, the biennial growth rate was calculated in line with that generated from the land

value index e.g. (Site V alue inner 2018/SiteV alue inner 2016� 1)⇥ 100% compared

against (LV I 2018/LV I 2016� 1)⇥ 100%.

Table 2 summarises the estimated revaluation outcome from the model and the

benchmark revaluation outcome that is calculated as the percentage change between

total site values for the inner, metro and outer LGAs relative to the same figure, two

years before.

The results are very encouraging with the model giving very similar growth rates

as that available from the VGV. In the past, revaluations from VGV were run every

two years and were part of the general valuation which also determines council rates.

So, the valuation approach may di↵er from LGA to LGA depending on the respective

valuers’ judgement. However, from 2019 onwards, revaluations will be run on an annual

basis and the process is centralised through the VGV. Where previously, the VGV only

had oversight, these changes will centralise the actual valuations across Victoria, finally

standardising the drivers of changes to land values. Coupled to this, the move to annual

valuations from biennial valuations might create more volatility in land values.

Vacant land sales have not been included in the modelling presented in this study.

These can be used to evaluate the performance of the land price index. Appendix Table

8 provides some descriptive statistics of what is available. The next version of the

1https://www.propertyandlandtitles.vic.gov.au/valuation/council-valuations22018, 2016 and 2014 revaluation rounds

16

Figure 4: Estimated Land Leverage (top to bottom: Inner,Metro, Outer)

17

Table 2: Comparison of VGV revaluation outcome versus modelestimates

Region Revaluation year Benchmark Model Di↵erence Absolute di↵erenceInner

2018 TBA2016 30.90% 25.30% 5.60% 5.60%

Metro2018 TBA2016 34.40% 30.97% 3.43% 3.43%

Outer2018 TBA2016 18.70% 19.48% -0.78% 0.78%

manuscript will provide some comparison based on the model and the observed prices

of vacant land.

5.3 The Land Leverage Hypothesis

In this section we provide some statistics to evaluate the land leverage hypothesis. The

first is based on the performance of the model and the resulting estimates of the discount

factors. The estimated discount factors (see Table 1) indicate the data supports an

asymmetric e↵ect of shocks in prices on the land and structure component. The lower

land discount factor is evidence that land absorbs a larger proportion of the shocks

which is consistent with the land leverage hypothesis.

The second set of empirical evidence is based on the computed annualised average

growth rate of the estimated components obtained from the hedonic imputed price

indices. Table 3 presents these for the three regions. These results provide evidence in

favour of the land leverage hypothesis as the growth rates of the land component are

larger than those of the structure components in all three regions and the growth rate

of property prices is between that of the two components.

Table 3: Annualised Growth in Components (1995-2017)

Land Structure PropertyInner 29.9 25.8 28.9Metro 33.7 24.3 28.3Outer 27.2 19.8 23.3

The third empirical test is based on a regression of the year-on-year price change

for each quarter on intercept land leverage (see Figure 4). These regressions show the

18

heterogeneity across quarters as well as regions. The results are presented in Table 4.

Bostic et al (2007) indicate the land leverage hypothesis holds if the coe�cient of the

land leverage is positive.

Table 4: Regressions of Year-on-Year Chained Indices on inter-cept and land leverage - Coe�cient of Land Leverage

Inner Metro Outer

Q1 90.781 67.528 44.360Q2 88.319 71.891 54.721Q3 106.297 73.244 42.456Q4 69.576 71.785 41.487

The annual changes for each quarter presented in Table 4 show very strong evidence

for the leverage hypothesis with all estimates being positive. The relative magnitudes

of these coe�cients are also consistent with expectations as the largest are those for the

Inner region and lowest those for the Outer region.

6 Conclusions

The paper explores the land leverage hypothesis which proposes that the land compo-

nent of property prices grows faster than that of the structure component, and that the

predicted property price is broadly in line with the median price over time. The value

of land and structure of residential property are obtained using a new methodology

where a state-space model produces the decomposition of the value of each site into its

land and structure components. The method is applied to unit record level sales data

for all detached properties that were transacted over 43.5 years between 1975Q1 and

2018Q2, across the state of Victoria (Australia)’s 79 local government areas (LGAs).

The model valuations are used to compute land and structure price indices for the

Inner, Metro and Outer regions of Greater Melbourne. Two parameters in the model

determine the degree of asymmetric behaviour of the land and structure components.

The lowest mean squared errors are found with models that are consistent with asym-

metric behaviour of the components where the land absorbs the largest portion of the

shocks that impact property prices. Site values are provided by the Valuer-General

Victoria (VGV) and serve as a benchmark value of land for every two-year snapshot to

compare with the model’s predicted land value. The model estimates are compared to

the 2016 VGV valuation outcomes (revaluation from 2014) and the di↵erences are 5.6%

for the Inner, 3.43% for the Metro and 0.78% for the Outer. The land value indices

19

are computed from the model’s estimates for LGAs within the inner, metro and outer

regions and are consistent with the land leverage hypothesis. This is established by

analysing the annual growth rates of each component across the three regions as well

as by a regression of the property price indices on the corresponding land leverage. We

find the magnitude of the responses vary across the regions and quarters.

References

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Table 5: Descriptive Statistics - Inner Region

INNER Min Max Mean Median StDev

salequarter 1.0000 4.0000 2.5849 3.0000 1.1137vacant 0.0000 0.0000 0.0000 0.0000 0.0000PRICE 1500.0000 12000000.0000 703484.9657 437450.0000 821528.6334BED 0.0000 6.0000 2.9484 3.0000 0.8871BATH 0.0000 4.0000 1.6054 1.0000 0.6953HOUSE 13.0000 2000.0000 158.6338 137.0000 82.2028AGE 0.0000 213.0000 85.7465 92.0000 32.0331

FLOOR 0.0201 2.0000 0.6218 0.5695 0.2656AREA 40.0000 1496.0000 307.5594 220.0000 222.7128Sample 43268 0 0 0 0

Table 6: Descriptive Statistics - Metro Region

METRO Min Max Mean Median StDev


FLOOR 0.0134 1.9926 0.3202 0.2845 0.1510AREA 54.0000 1500.0000 592.0773 602.0000 191.8056AGE2 0.0000 46225.0000 2906.9526 1764.0000 3233.9845Sample 271628 0 0 0 0

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Table 7: Descriptive Statistics - OUTER Region

OUTER Min Max Mean Median StDev


FLOOR 0.010 1.996 0.254 0.224 0.138AREA 91.000 1500.000 683.273 649.000 198.903Sample 362564 0 0 0 0AREA 40 1496 307.559351 220 222.7128173Sample 43268 0 0 0 0

Table 8: Number and Share of Transactions of Vacant Land1995-2017

LGA Vacant # Total # LGA share Region

PORT PHILLIP 360 128816 0.30% InnerSTONNINGTON 634 119778 0.50% InnerMELBOURNE 818 146348 0.60% InnerBOROONDARA 988 148396 0.70% MetroBAYSIDE 600 88092 0.70% MetroGLEN EIRA 800 117213 0.70% MetroYARRA 670 88418 0.80% InnerMORELAND 2762 125725 2.20% MetroWHITEHORSE 3091 133342 2.30% MetroDAREBIN 3148 112114 2.80% MetroMARIBYRNONG 2402 72686 3.30% MetroMONASH 4556 133407 3.40% MetroMOONEE VALLEY 3605 94643 3.80% MetroBANYULE 4218 95440 4.40% MetroKINGSTON 6134 138505 4.40% MetroGREATER DANDENONG 6276 117837 5.30% OuterMAROONDAH 5758 103148 5.60% OuterMANNINGHAM 6093 97231 6.30% MetroFRANKSTON 10954 142209 7.70% OuterHOBSONS BAY 5744 72808 7.90% Metro

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