Land Leverage and House Prices
Steven C. Bourassa1 Martin Hoesli2 Donato Scognamiglio3 Sumei Zhang4
Abstract
A house is a bundle of land and improvements, with the weights of the twocomponents varying both over time and across locations. We capture the land intensity
or “leverage” of a property by measuring the ratio of land to total value. This isaccomplished using transactions data for single-family homes in Switzerland over theperiod 1978 to 2008. We show how to use hedonic models to develop time series ofland prices and land leverage. Then we estimate error correction models for both house
prices and land leverage. We show the importance of incorporating land leverage whenassessing the determinants of house prices. House price changes are shown to beaffected by changes in land leverage, real GDP per capita, growth of the population
aged 30 to 49, and the term spread, while land leverage changes are a function ofchanges in real GDP per capita, in real construction costs, and in the term spread.
Keywords: land leverage, house price dynamics, land prices, error correction models

1. Introduction
Housing represents a large fraction of wealth in household portfolios and innational economies. A good understanding of housing dynamics and of thedeterminants of house price changes is thus essential. Assessment of the impacts ofchanges in the economy on house prices could potentially benefit by recognizing that ahouse is a combination of a lot and a structure (Bostic et al., 2007; Davis and Heathcote,2007). Indeed, fundamentals affecting the prices of the two components are not thesame, with changes in interest rates, income, population, and land use constraints
driving land values, while building values are related primarily to construction costs. In
fact, a large fraction of house price changes is typically related to land price changes
rather than changes in construction costs.
If the relative value of land and structures were constant over time and locations,disentangling the two components would be of little or no importance. However, land
leverage (that is, the ratio of land value to total property value) will be greater in more
highly populated areas than in rural regions, and also greater at the peak than at thetrough of a housing cycle. Davis and Palumbo (2008), for instance, report a land
leverage of 88.5% for the San Francisco metropolitan area for 2004, but only 23.3% forOklahoma City. Davis and Heathcote (2007) report swings in land leverage in the U.S.
as a whole from less than 30% to above 45%. Moreover, there was an upward trend in1

Department of Urban and Public Affairs, University of Louisville, 426 W. Bloom Street, Louisville, KY
40208, USA, and Bordeaux Management School, France, email: steven.bourassa@louisville.edu(corresponding author).
2
HEC, University of Geneva, boulevard du Pont-d’Arve 40, CH-1211 Geneva 4, Switzerland, Universityof Aberdeen, Scotland, UK, and Bordeaux Management School, France.
3
IAZI/CIFI, Tramstrasse 10, CH-8050 Zurich, Switzerland, and University of Bern, Switzerland.
4
Department of Urban and Public Affairs, University of Louisville, 426 W. Bloom Street, Louisville, KY
40208, USA.

leverage between 1975 and 2006.
It thus seems important to take into account land leverage in analyses of house
price cycles. One approach to this is to consider both components of a property
separately and to analyze the determining factors for each component (Davis andHeathcote, 2007). Research in this area, however, is hampered by the lack of reliable
land price indexes. There are some land price indexes, such as for Japan and someSwiss regions, but these indexes do not control for the “quality” of the land; that is, they
rely on mean or median prices. 1 There have also been some efforts to develop land
value indexes for the United States. Such studies include Case (2007), Davis andPalumbo (2008), and Davis and Heathcote (2007). At a regional level, Been et al. (2009)use teardown values (prices paid for properties purchased for demolition andredevelopment) as a proxy for land values to measure land price changes in New York,
following an approach suggested by Rosenthal and Helsley (1994) and extended by Dye
and McMillen (2007).
This paper makes use of a rich database of house prices for Switzerland covering
the period 1978 through 2008. The database contains a large number of attributes whichenable us to calculate the implied land value for each sale using the depreciated cost
appraisal method. Those values are in turn used to construct a hedonic index of land
prices for Switzerland. We also estimate house price and land leverage hedonic models.
We use those inputs to analyze house price dynamics with error correction
models. We show the importance of including an instrument for land leverage in ahouse price equation. Changes in real house prices appear to be driven by changes inreal GDP per capita, in the term structure of interest rates (the “term spread”), in the
proportion of population aged 30 to 49, and in land leverage. Changes in land leverage
are shown to be affected by changes in real GDP per capita, in real construction costs,
and in the term spread.
The structure of the paper is as follows. The first two sections review theliterature on land leverage and discuss the theory underlying our analysis of thedeterminants of house prices, respectively. We then proceed to discuss our data andmethods. The following section contains a discussion of our results, while a final
section summarizes our conclusions.

2. Recent research on land leverage
Bostic et al. (2007) introduced the term “land leverage” to refer to the ratio ofland value to total property value. Although they do not use the term, Davis andHeathcote (2007) published a paper on land leverage at about the same time. Both setsof authors emphasize the relationship between land leverage and house priceappreciation, a focus that was apparently motivated by a desire to explain the disparities
in house price appreciation rates in different parts of the U.S. during the late 1990s andearly 2000s. Bostic et al.’s empirical study of Wichita, Kansas, demonstrates that land
leverage is positively associated with house price inflation in that city. These authors
estimate land leverage in two ways. The first involves comparing the prices of vacantlots with the prices of the same properties after houses are constructed on them. The
second method simply uses the assessed values for land and improvements determined1

For details on the Japanese and Zurich regional indexes, see http://www.stat.go.jp/english/
data/nenkan/1431-17e.htm and http://www.statistik.zh.ch/bodenpreise/boe.php, respectively.

2

by the local property tax assessment office. The two samples yield similar conclusions
about the role of land leverage in house price inflation.
Davis and Heathcote (2007) produce quarterly constant-quality price indexes forresidential land in the U.S. from 1975 through 2006. During this period, the real priceof residential land nearly quadrupled, while the price of structures grew by only onethird. By 2006, land accounted for 46% of aggregate residential property value,compared with 35% in 1975. To construct their land price indexes, a benchmark market
value of housing is calculated for 2000 based on the decennial census and other data.
Various data sources, including Office of Federal Housing Enterprise Oversight (nowthe Federal Housing Finance Agency) price indexes and information about investment
in new residential structures and the replacement cost of residential structures producedby the Bureau of Economic Analysis (BEA), are used to develop land price estimates
for the benchmark date and to extend the series forwards and backwards from thebenchmark date. A somewhat different technique is used to extend the analysis back to1930. According to that series, land leverage was about 15% in 1930 and remained as
low as about 20% in 1970.
Davis and Heathcote also show how taking land leverage into account isimportant when modeling house price dynamics. Their strategy is to regress real house,
land, and structure prices on a set of fundamentals that includes real per capita income,the nominal three-month Treasury Bill rate, and the inflation rate. A second set ofregressions adds three additional variables: population, the percentage of the population
aged 35 to 54 (the primary home-buying category), and the spread between 30-year
fixed mortgage rates and the three-month Treasury Bill rate. The land price regressions
in particular perform better than house price regressions, and the estimates for the house
price regressions appear to be a weighted average of the estimates for the land andstructure price regressions.
In a related paper, Davis and Palumbo (2008) focus on 46 large metropolitan
areas in the US from 1984 to 2004. For these areas, land leverage for single-family
owner-occupied homes increased from an average of 32% in 1984 to 51% in 2004. In
this study, the authors use RS Means construction cost data to price the housing stock ineach area using property characteristics contained in the American Housing Survey(AHS) for a benchmark year. The structures are then depreciated at a rate of 1.5% peryear of age. Land value is the total property value reported in the AHS less thedepreciated value of the structure. The Freddie Mac Conventional Mortgage House
Price Index and other data are then used to develop a time series for each metropolitan
area backwards and forwards from the benchmark date.
Case (2007) estimates land leverage for residential property in the U.S. from1975 through 2005. 2 Using data similar to that employed by Davis and Heathcote(2007), he produces quite different estimates of land leverage: about 14% in 1975 and
38% on 2005. For the three years for which these authors provide comparable data
(1980, 1990, and 2000), Case’s estimates of both total residential property values andstructure values are higher and his estimates of land values are lower than those of
Davis and Heathcote, meaning that his estimates of land leverage are consistently lower.
Among other differences in methods, Davis and Heathcote exclude farmhouses andremove sales commissions from the BEA data, which should account for some of the2

Malpezzi’s (2007) commentary on Case’s paper provides a useful short review of the empiricalliterature on land prices; the most remarkable study is Hoyt’s analysis of land values in Chicago from1830 to 1933 (Hoyt, 1933).

3

discrepancy between Case’s and their results. 3
Bourassa et al. (2009) incorporate a measure of land leverage in models that seek
to explain how individual house prices move relative to the market as a whole in three
New Zealand cities. They measure land leverage using values determined by property
tax assessors. Although the focus of their paper is on the role of atypical housecharacteristics, they also find that houses with greater land leverage are more volatileover the course of the property cycle.
The biggest challenge in studies of land leverage is accurately measuring theratio of land to total property value. One solution, as in Bostic et al. (2007) or Bourassa
et al. (2009) is to rely on separate land and improvement values as assessed for property
tax purposes. This is probably fine for their purposes, which involve the use ofindividual transactions data to test hypotheses about the role of land leverage. It is
generally not suitable for developing indexes of land prices or land leverage over time. 4
As Bell et al. (2009) point out, separate land and improvement assessed values are likely
to be less accurate than the combined assessments. One reason for this is that assessors
typically have no incentive to make the allocation between the two components ofproperty value accurate. In most jurisdictions, property tax rates are the same for land
and improvements and property owners can challenge the total assessment, but not theindividual components. Moreover, assessing land and improvement values is difficult.
The sales comparison approach is hampered by the fact that there are typically few
vacant land sales in developed areas. The replacement cost approach to measuring
structure values depends on what are usually quite rough estimates of depreciation.
Other assessment practices, such as assuming some constant ratio between land andstructure values, are even less accurate. The most accurate assessments rely on hedonic
regression methods that take into account spatial relationships in technicallysophisticated ways.
For the United States, the recognized constant-quality national and regional
house price indexes rely on repeat sales methods. These include the Federal Housing
Finance Agency and S&P Case-Shiller indexes. 5 Because repeat sales indexes are notbased on detailed property characteristics, they do not provide a good basis forconstructing land or land leverage indexes. Consequently, Davis and his co-authors areforced to undertake fairly elaborate procedures in order to construct indexes for the U.S.
In countries with hedonic house price indexes, the task is less convoluted. In
Switzerland, for example, where hedonic house price indexes are well-developed(Bourassa et al., 2008), it is relatively easy to construct hedonic models of land prices
and land leverage. The availability of details about house characteristics makes it
possible to price structures using a depreciated replacement cost method. Then land
values and land leverage ratios can be calculated for individual properties. Indexes canthen be constructed by estimating hedonic models for land prices and land leverage that
3

Both Case (2007) and Davis and Palumbo (2008) provide estimates of land leverage for owner-occupied
properties for the U.S., although Davis and Palumbo’s sample is limited to 46 large metropolitan areas.
Case’s estimate of 33% for 1985 is quite close to Davis and Palumbo’s estimate of 32% for 1984;
however, Case’s estimate of 38% for 2005 is much lower than Davis and Palumbo’s 51% for 2004. It is
likely, however, that land leverage in large cities grew at a much faster rate than in the U.S. as a wholeduring this period.
4
However, Clapp (1990) provides a method for using assessed values to construct vacant land priceindexes.
5
Available at http://www.fhfa.gov and http://www.standardandpoors.com, respectively.

4include time dummy variables. In this paper, we show how to do this and then use theresulting indexes in models of house price dynamics to demonstrate the importance ofcontrolling for land leverage in modeling house price movements.

3. Determinants of house price changes 6
The value of a house is the sum of the structure and land values. In equilibrium,
structure value will equal depreciated replacement cost; if value exceeds cost,developers will construct more houses profitably and if the reverse is true construction
will cease. 7 The construction of new houses will depress prices on existing houses
toward replacement cost, and the lack of construction, in the face of population andincome growth, will eventually raise price to replacement cost. Thus we assume thatstructure value moves with a construction cost index.
The determinants of residential land values are more complex. The economic
might of a metropolitan area or region is the primary determinant of the demand for land.
This can be measured in terms of employment and income per employee or populationand gross domestic product per capita. Real interest rates are also relevant because they
relate expected future land rents to current values. Real mortgage interest rates are an
appropriate measure because they reflect the cost of financing owner-occupied housing.
The term spread may also be a relevant measure in a country such as Switzerland where
all mortgage interest rates are essentially variable (so-called fixed rate mortgages are
fixed for only short periods of time). The difference between short and longer terminterest rates is an indicator of the direction in which financing costs are moving andhence may be more important than the current interest rate.
The demand for urban land is somewhat easier to measure than the supply.
Supply is constrained by topography and land use regulations, both of which can havesubstantial impacts on land values and house prices (Glaeser and Gyourko, 2003;
Glaeser et al., 2005; Quigley and Raphael, 2005; Saiz, 2008). 8 Both are also quite
important in the Swiss context due to the country’s mountainous terrain and relatively
strict land use regulation, although whether the latter constraint changes much over timeis unclear. Nevertheless, they are difficult to measure and, in the Swiss case, measures
do not exist. Consequently, the land variables in our house price model focus on the
demand side of the market.

4. Data and methods
4.1 Data
We use a large database of single-family house transactions provided by the
Informations- und Ausbildungszentrum für Immobilien AG (IAZI) in Zurich. The data
cover the period 1978 to 2008 and include sales price and a large number of structuraland location attributes for each house sold. The data are provided to IAZI mostly bymortgage lenders.
6This section draws from Bourassa et al. (2001) and sources cited therein.
Gyourko and Saiz (2004) demonstrate that this also applies to homeowners’ decisions to invest in
improvements to their homes.
8
However, Ihlanfeldt (2007) finds an inverse relationship between regulatory restrictiveness and land
values in Florida.
75

Approximately 30 variables are used to characterize each structure and lot.
These include attributes such as the year of construction, the condition of the building,the number of bathrooms, the land area, and whether there are any luxury features suchas a swimming pool (a more comprehensive list of variables is provided in Bourassa etal., 2008). In addition, approximately 60 attributes are aggregated into a macrolocational index constructed for small areas within Switzerland, which captures most of
the geographical variation in values. The small areas are either postal codes or smaller
localities within postal codes. The locational characteristics include variables derived
from tax and income statistics, population density and distribution, infrastructure
statistics, and other local geographical and economic factors. These variables comefrom the Swiss Statistical Office, as well as various federal and cantonal tax andstatistical offices.
Around 64,100 transactions of single-family houses in the whole of Switzerland
were available. We excluded atypical properties for which the occupied land area wasless than 5% or more than 30%. When the ratio of building volume (in cubic meters) tothe living area (in square meters) was less than three or more than seven (the typicalvalue of this ratio is four to five), the observation was likewise deleted. Further, if theprice per cubic meter was less than CHF 40 the sale was deleted. 9 Also, properties weredeleted if the calculated land leverage was not between 0% and 100%. These and otherfilters reduced the sample to about 56,300. Of these about 26,000 transactions involved
properties aged 20 years or less since initial construction or major refurbishment. We
further eliminated some house price, land price, and land leverage outliers prior toestimating the hedonic models for each of those variables.
In addition to the data from IAZI, we also use data for the Gross Domestic
Product (GDP), the Consumer Price Index (CPI), and population from the Swiss
Statistical Office. 10 With respect to population, we focus on the primary home buying
age group, 30 to 49. Variable mortgage interest rates, Swiss government 10-year bondyields, and interbank 3-month rates are from the Swiss National Bank. 11 Finally, theconstruction cost index is for Zurich and is available from Baudokumentation. 12 The
Zurich index has the longest history and using it for the entire country does notconstitute a problem as, given the small size of the country, construction costs are by
and large constant across regions. Figure 1 shows nominal construction cost and GDP
indexes as well as the consumer price indexes, while Figure 2 depicts real mortgage
interest rates and the difference between the Swiss government 10-year bond rates andinterbank 3-month interest rates (the term spread) for the period under review. The risein GDP was much more pronounced than that of construction costs during the period.
In fact, construction costs did not rise in real terms. Real interest rates appear to bepositively related (although imperfectly) to the term spread, suggesting that low current
rates pave the way for even lower rates in the future. Figure 3 shows that, while thetotal population grew steadily between 1978 and 2008, the 30 to 49 home buying age
group grew more rapidly than the total population until the mid-1990s and less rapidly
in the 2000s. This provides a rationale for focusing on the 30 to 49 age group rather
than the total population.

9

As of December 2009, CHF 1.00 ≈ USD 0.96.
See http://www.bfs.admin.ch.
11
See http://www.snb.ch.
12
See http://www.baudokumentation.ch.
10

6

4.2 Measuring land leverage
For each house in our sample, we calculate the implicit value of the land using
the depreciated cost approach. The method’s economic rationale is that a house buyer
would not be willing to pay more for a property than the construction cost of thestructure net of any depreciation plus the value of the land. As we seek here to estimate
the land value, we subtract from the house price the depreciated cost of the structure at
the time of sale. The method involves calculating the construction cost of each building
as of 2008 by multiplying the house’s volume by a standard construction cost per cubic
meter and backtracking that cost to the time of each transaction using a construction
cost index. We then subtract depreciation to account for physical, functional, andeconomic obsolescence, and obtain land value estimates.
More formally, the procedure is the following. The price paid at time t for asingle-family house ( Pt ) consists of the construction cost of the building ( Ct ) corrected
for depreciation ( Dt ) plus the land value ( Lt ):Pt  Ct  Dt  Lt
(1)
We calculate the construction cost as if new for each building by multiplying thevolume of the building ( Vt ) by the construction cost per cubic meter ( ct ):Ct  Vt  ct 
(2)
The construction costs per cubic meter are based on standard costs for Zurich as of 2008,
which are then backtracked to the year of sale using the Zurich construction cost index.
The standard construction cost per cubic meter as of 2008 is CHF 590 for a house ofgood building quality (see Table 1). A downward (upward) adjustment is made forhouses of poorer (better) quality.
To calculate the appropriate depreciation at time t, we consider the economic ageof the property. The age of the property ( At ) is the minimum of the number of years
since the building was first constructed and the number of years since the last complete
refurbishment of the property. For example, a house constructed in 1800 with acomplete refurbishment in 2000 is considered to be five years old if sold in 2005.
Given the difficulties in estimating depreciation accurately for older properties, wedefine a restricted sample to include only those properties whose age as defined above is
20 years or less at the date of sale. The choice of 20 years is driven by the fact that thefirst substantial renovations of a property (such as the replacement of the kitchen orbathroom) typically occur after 20 years. We also consider the sample containing all
sales.
The annual depreciation rates (d) for various building quality levels are given in
Table 2. The annual geometric depreciation rate for a building in good quality is
assumed to be 1.5%. Higher (lower) depreciation rates are used for buildings of poorer(higher) quality. To test for the robustness of our results, we also use base depreciation
rates of 0.5% and 2.5%. The depreciation of a property at time t is given by:

Dt  Ct  1  1  d  t
A



(3)

Substituting equations (2) and (3) into equation (1):Pt  Vt  ct  1  d  t  Lt
A

(4)

The land value for each transaction is computed as follows:7

Lt  Pt  Vt  ct  1  d  t
A



(5)

To calculate the land leverage ( LLt ) for each property, we divide the land value( Lt ) by the transaction price ( Pt ). We then estimate the following regression equation:
LLt   i  Zi    t  Tt  
i

(6)

t

where: i are the coefficients of the characteristics of the land; Zi are the characteristicsof the land;  t are the coefficients of the time dummy variables; Tt are the time dummy
variables (1 if property sold during year t and 0 otherwise); and  is an error term. A
given transaction was included only if its land leverage was between 0% and 100%. We
use equation (6) to calculate predicted land leverage for each year, LL*t , assuming
median land characteristics.
4.3 Constructing land and house price indexes
No land price index exists at the national level for Switzerland. Some regional
indexes exist (for Zurich and Basel Landschaft, for instance), but they are not constantquality. We opt to calculate a hedonic time dummy index given the availability ofhedonic data and the ability of this method to control for quality changes. We also
calculate a hedonic house price equation.
The land price index is calculated using the following regression:
LPSM t   i  Yi   t  Tt  
i

(7)

t

where: LPSM t is the land price per square meter; i are the coefficients of thecharacteristics of the land; Yi are the characteristics of the land; t are the coefficientsof the time dummy variables, Tt ; and  is an error term. The base year of the index is2008.
For the house price index, the following regression is calculated:
Pt   i Wi   t  Tt  
i

(8)

t

where:  i are the coefficients of the characteristics of the property; Wi are thecharacteristics of the property;  t are the coefficients of the time dummy variables, Tt ;and  is an error term. Again, the base year of the index is 2008.
4.4 Modeling house prices and land leverage
We specify a long-run house price model as follows:

RHPI t   0  1 RCCI t   2 RGDPCt   3 RIRt   4TSt   5 POP3049t   6 LL*t  (9)where: RHPI t is the house price index derived from equation (8) and converted into realterms using the CPI; RCCI t is the real construction cost index; RGDPCt is real GDP
per capita; RIRt is the real mortgage interest rate; TSt is the interest rate spread between
3-month and 10-year securities (defined as the long-term rate minus the short-term rate);8

POP3049t is the growth of population aged 30 to 49; LL*t is the predicted land leveragederived from equation (6); and  is an error term. We use GDP rather thanemployment and wages or household income as a measure of demand due toinconsistencies in measurement in the other data series. A long-run land leverage modelis specified using the same set of independent variables (excluding, of course, land
leverage itself).
Land leverage is likely to be endogenous in a model of house prices because thefactors that influence house prices also influence land and structure values and,
therefore, land leverage. Consequently, we substitute an instrumental variable (IV),
LLIVt , for LL*t in equation (9). In the absence of other practicable alternatives, we usean IV suggested by Durbin (1954) that is defined simply as the rank order of the originalvariable. Thus the smallest land leverage is assigned a value of 1, the next smallest avalue of 2, and so forth. This IV is discussed by Kennedy (2003) and examples ofrecent applications of the technique can be found in Fingleton (2000) and Heckelman(2000).
An error correction model (ECM) represents short-term changes as a function of
the changes (differences) of the right-hand side variables in equation (9), adjusted by anerror correction term that is defined as the deviation of previous observed levels fromlong-run equilibrium levels. The fitted values from equation (9) represent one way to
discover the long-run equilibrium levels. The error correction term, ECt 1 , represents a
disequilibrium in the previous time period and is expected to have a negative effect,
inducing a change in house prices (or land leverage) back toward the equilibrium.
Hence our short-term model is specified as follows:
RHPI t  a0  a1RCCI t  a2 RGDPCt  a3 RIRt  a4 TSt  a5 POP3049t
 a6 LLIVt  a7 ECt 1  (10)Note that LLIVt has been substituted for LL*t as for equation (9). A similar model isestimated with LL*t as the dependent variable (and excluding LLIVt on the right-handside).
There are two commonly used methods to define the error correction term: theregression method (Malpezzi, 1999; Hoesli et al., 2008) and the cointegration method(Engle and Granger, 1987; Greene, 2002). We apply both methods, although we reportresults only for the latter approach. The first method directly uses the error fromequation (9) as an explanatory error correction term in equation (10).
The second method is popular in time series studies and uses cointegration
coefficients to compute the error correction terms. In the case of house prices, the error
correction term is computed as:
ECt 1  RHPI t 1  1' RCCI t 1   2' RGDPCt 1   3' RIRt 1   4' TSt 1   5' POP3049t 1(11)
  6' LLIVt 1
where [1, 1' , …,  6' ] is a cointegration vector that makes ECt 1 a stationary process.
The error correction term for the land leverage equation is computed accordingly.

95. Results
5.1 Price indexes and land leverage

The following section presents hedonic land and house price indexes as well as
land leverage measures for Switzerland. The regression results for the restricted sample
containing properties whose age is 20 years or younger and the full sample are reported
in Tables 3 and 4, respectively. The R2 statistics are high, in particular for the land priceand house price equations. To respect proprietary features of IAZI’s house price model,
we normalized the building characteristics so that their aggregate effect would lead to an
estimated coefficient of about one.
Figure 4 contains the house and land price indexes and our measure of land
leverage for 1978 through 2008 for both samples of data (the restricted sample and thesample with all transactions). The sample has only a small impact on the land priceindex during the 1990s and early 2000s, when the index for the full sample isconsistently below that for the restricted sample. The index for the restricted sample
rises by 235.2% during the period, compared to 235.4% for the full sample. There is alarger difference between the house price indexes for the two samples. The restricted
sample rises by 126.9%, while the full sample rises by 148.2%. Comparison of the land
price index with the house price index for the full sample suggests that, during theperiod under review, land prices in Switzerland rose more strongly and were morevolatile than house prices. This is particularly true at the end of the 1980s when prices
were rising rapidly. It is commonly accepted that during this period a bubble existed in
the Swiss housing market (Hoesli et al., 1997). As a result, land leverage rose in the
1980s and then declined in the early 1990s as house and land values were declining.
Land leverage then increased again from 1992 to 1994 due to declining construction
costs. The land leverage during this period fluctuates from a low of 30.4% (in 1982) toa high of 48.1% (in 1989) when the restricted sample is used. Land leverage is higher
when all transactions are used, especially after 2003 (from a low of 31.6% in 1982 to ahigh of 53.1% in 2008). These results suggest that the restricted sample is a reasonably
good substitute for the full sample with respect to calculation of land (and house) priceindexes, but not land leverage. As the monocentric model of urban land values would
suggest, younger houses tend to have lower land-to-improvement value ratios because
they are more likely to be in peripheral locations with lower land values (and higher
transportation costs).
Figure 5 shows the distribution of land leverage by commune (local government)
across Switzerland in 2008. This map assumes a medium quality micro location withineach commune. There is a noticeable concentration of high values around several of the
major cities, including Geneva and Lausanne along the edge of Lake Geneva in the west
as well as in the Zurich area in the central north. There are also concentrations around
Basel on the northern border west of Zurich and in the ski resort region in the easternpart of Switzerland.
5.2 House prices and land leverage

The stationarity of our series was tested for both levels and differences, using theAugmented Dickey-Fuller (ADF) and the Phillips-Perron (PP) unit root tests. Both tests
start with an AR(1) model, accommodating some forms of serial correlations, that is,10

previous lagged differences (Greene, 2002). The lags to be included in the model
depend on sample size, and the rule of thumb is 3 n  1 , where n is sample size.
Therefore, lagged differences up to order 3 are allowed for in the model tested. The
tests are conducted under the assumptions that the process has a constant mean or has atrend.
For real house prices, real construction costs, real per capita GDP, the growth of
population aged 30 to 49, and land leverage (for both the restricted and the full samples),the PP tests consistently suggest that the levels are I(1) processes and the differences are
stationary, under the assumption of the existence of a single mean or of a trend. Most of
the tests are significant at the 5% level. The ADF tests reveal similar results, except for
construction costs and GDP, for which the levels are stationary in the trend model when
lagged differences are considered. For the real mortgage interest rate and for the term
spread, which probably are stable over time, the results under the constant mean
assumption may make more sense. Both methods tend to suggest a stationary process
for levels at the 10% significance level. This means that we have a combination of
stationary and I(1) processes in equations (9) and (11) which, while not ideal, is
acceptable. We estimate error correction models using terms calculated with both theregression and cointegration methods, but we report results based on the cointegration
method only. The two methods yield similar results, and both sets of results underscorethe importance of considering land leverage when analyzing house prices.
The regression results based on the sample of houses whose age is less than orequal to 20 years at the time of sale are shown in Table 5, while Table 6 contains theresults when the whole sample is used. Each table gives results for regressions of house
price levels without and with land leverage as an explanatory variable (columns 1 and 2),
for regressions of house price changes with land leverage and an error correction term(column 4), and for regressions of land leverage in levels (column 3) and in changes
with an error correction term (column 5). These error correction models are similar toothers that have been used in the literature on house price dynamics (e.g., Bourassa et al.,2001).
We first discuss the results for house prices and then turn to the results for land
leverage. The results in levels show that the inclusion of land leverage is very importantas it results in a substantial increase in the R2 statistic. Land leverage is also highly
significant. In levels, house prices appear to be driven by real GDP per capita, thechange in the population aged 30 to 49, and land leverage. The results for the restricted
sample also suggest the positive impact of real construction costs. For house pricechanges, we focus on results for a model with land leverage given the poor results forthe levels equations without land leverage. Real house price changes appear to bepositively related to changes in real GDP, changes in growth (i.e., second differences) of
the population aged 30 to 49, and changes in land leverage. As would be expected, thechange in the term spread has a negative effect on house prices. The R2 is high (0.815)
and the error correction term is highly significant. When the sample with all properties
is considered, the R2 is much lower (0.560) and coefficients are less significant. Thechange in GDP per capita, for instance, is only significant at the 10% level. Thishighlights the fact that there may be fewer measurement issues with the restricted
sample. The same conclusion emerges when the alternative depreciation rates (0.5%
and 2.5%) are used in calculation of the land leverage series.
Focusing now on the results for land leverage, we find that the R2 statistics arelower than is the case for house price equations. Real GDP appears to be driving land11

leverage in levels and is also important in explaining changes in land leverage. Landleverage changes are also negatively related to changes in real construction costs aswould be expected. The change in the term spread appears to have a positive impact onland leverage changes. Caution should however be exercised as the significant impact
of term structure vanishes in most instances when other depreciation rates are used.
Interestingly, the results for the full sample do not appear to be of lesser quality thanthose for the restricted sample. In fact, they are even slightly better.
Figures 6 and 7 depict actual house price levels as well as predicted levels basedon the models without and with land leverage for the restricted and full samples,
respectively. The predicted values with land leverage track the actual series moreclosely except during some years at the beginning of the period. For the restricted
sample, the correlation between changes in actual price levels and changes based on
predictions from the model with land leverage is 0.82; for the model without land
leverage, the correlation is 0.52. For the full sample, the correlation coefficients are
0.77 and 0.62, respectively. The difference between the correlation coefficients for thepredicted changes based on the models with land leverage probably reflects thedifficulty in measuring depreciation accurately for older properties.

6. Conclusions
Land in locations desirable for residential use is relatively inelastically supplied.
Consequently, residential land price changes over time are largely the result of changes
in demand factors, such as changes in per capita GDP. In contrast, structures are
relatively elastically supplied, meaning that they are influenced more by changes insupply (replacement) costs than by demand factors. Over the course of a property cycle,
house price changes are largely driven by land price changes. This means that the ratioof land to property value, or land leverage, is an important factor in explaining house
price movements.
It is difficult, however, to measure land prices and land leverage. We show how
to measure land prices and land leverage using transactions data and hedonic models for
Switzerland during the period 1978 to 2008. Structure characteristics combined withconstruction costs and depreciation rates are used to estimate depreciated replacement
costs for single-family homes in the transactions data set. Then land values and land
leverage are calculated for each property as of the transaction date. Hedonic models ofhouse values, land values, and land leverage are then estimated, and the coefficients on
the time dummies from those models are used to construct indexes. As expected, land
prices are more volatile and increase at a more rapid rate than house prices. We also
estimate models using only data for houses aged 20 years or less as a test of ourassumptions about depreciation. We note that the house and land price indexes movesimilarly (although not identically) for the two samples, but that there are somedifferences in the two land leverage series. In particular, land leverage for the fullsample becomes markedly higher than that for the restricted sample after 2004.
Finally, we estimate error correction models of both house prices and land
leverage. We show the importance of including land leverage in an equation of house
prices. Changes in real house prices are driven by changes in real GDP, changes ingrowth in the population aged between 30 and 49, and changes in land leverage.
Changes in land leverage are shown to be affected by changes in real GDP per capita,changes in real construction costs, and changes in the term spread.

12

7. Acknowledgements
The authors appreciate helpful comments provided by Shaun Bond, Dennis
Capozza, John Clapp, John Glascock, Don Haurin, Steve Ross, Tom Thibodeau, Susan
Wachter, Peter Zorn and other participants in a seminar at the Department of Finance,
University of Cincinnati, and at the Weimer School of Advanced Studies in Real Estateand Land Economics.

8. References
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York City, Working Paper, Lincoln Institute of Land Policy, Cambridge, MA.
Bell, M., Bowman, J., and German, J. (2009), The assessment requirements for aseparate tax on land, in: Dye, R., and England, R. (Eds), Land Value Taxation: Theory,
Evidence, and Practice, pp. 171–194, Lincoln Institute of Land Policy, Cambridge, MA.
Bostic, R. , Longhofer, S., and Redfearn, C. (2007), Land leverage: decomposing homeprice dynamics, Real Estate Economics, 35, 183–208.
Bourassa, S., Haurin, D., Haurin, J., Hoesli, M., and Sun, J. (2009), House pricechanges and idiosyncratic risk: the impact of property characteristics, Real Estate
Economics, 37, 259–278.
Bourassa, S., Hendershott, P., and Murphy, J. (2001), Further evidence on the existenceof housing market bubbles, Journal of Property Research, 18, 1–19.
Bourassa, S., Hoesli, M., Scognamiglio, D., and Sormani, P. (2008), Constant-quality
house price indexes for Switzerland, Swiss Journal of Economics and Statistics, 144,
561–575.
Case, K. (2007), The value of land in the United States: 1975-2005, in: Ingram, G., andHong, Y.-H. (Eds), Land Policies and Their Outcomes, pp. 127–147, Lincoln Instituteof Land Policy, Cambridge, MA.
Clapp, J. (1990), A methodology for constructing vacant land price indices, Journal of
the American Real Estate and Urban Economics Association, 18, 274–293.
Davis, M., and Heathcote, J. (2007), The price and quantity of residential land in the
United States, Journal of Monetary Economics, 54, 2595–2620.
Davis, M., and Palumbo, M. (2008), The price of residential land in large U.S. cities,
Journal of Urban Economics, 63, 352–384.
Durbin, J. (1954), Errors in variables, Revue de l’Institut International de Statistique, 22,
23–32.

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Dye, R., and McMillen, D. (2007), Teardowns and land values in the Chicago
Metropolitan Area, Journal of Urban Economics, 61, 45–63.
Engle, R., and Granger, C. (1987), Co-integration and error correction: representation,
estimation, and testing, Econometrica, 55, 251–276.
Fingleton, B. (2000), Spatial econometrics, economic geography, dynamics andequilibirum: a ‘third way’? Environment and Planning A, 32, 1481–1498.
Glaeser, E., and Gyourko, J. (2003), The impact of building restrictions on housing
affordability, Economic Policy Review, 9, 21–39.
Glaeser, E., Gyourko, J., and Saks, R. (2005), Why have housing prices gone up?
American Economic Review, 95, 329–333.
Greene, W. (2002), Econometric Analysis, 5th ed., Prentice Hall, Upper Saddle River,
NJ.
Gyourko, J., and Saiz, A. (2004), Reinvestment in the housing stock: the role ofconstruction costs and the supply side, Journal of Urban Economics, 55, 238–256.
Heckelman, J. (2000), Consistent estimates of the impact of special interest groups on
economic growth, Public Choice, 104, 219–327.
Hoesli, M., Lizieri, C., and MacGregor, B. (2008), The inflation hedging characteristics
of U.S. and U.K. investments: a multi-factor error correction approach, Journal of Real
Estate Finance and Economics, 36, 183–206.
Hoesli, M., Giaccotto, C., and Favarger, P. (1997), Three new real estate price indicesfor Geneva, Switzerland, Journal of Real Estate Finance and Economics, 15, 93–109.
Hoyt, H. (1933), One Hundred Years of Land Values in Chicago: The Relationship of
the Growth of Chicago to the Rise of Its Land Values, 1830-1933, The University of
Chicago Press, Chicago.
Ihlanfeldt, K. (2007), The effect of land use regulation on housing and land prices,
Journal of Urban Economics, 61, 420–435.
Kennedy, P. (2003), A Guide to Econometrics, 5th ed., Massachusetts Institute ofTechnology Press, Cambridge, MA.
Malpezzi, S. (1999), A simple error correction model of house prices, Journal of
Housing Economics, 8, 27–62.
Malpezzi, S. (2007), Commentary on K. E. Case, The value of land in the United States:
1975-2005, in: Ingram, G., and Hong, Y.-H. (Eds), Land Policies and Their Outcomes,
pp. 148–156, Lincoln Institute of Land Policy, Cambridge, MA.

14

Quigley, J., and Raphael, S. (2005), Regulation and the high cost of housing in
California, American Economic Review, 95, 323–328.
Rosenthal, S., and Helsley, R. (1994), Redevelopment and the urban land price gradient,
Journal of Urban Economics, 35, 182–200.
Saiz, A. (2008), On local housing supply elasticity, http://ssrn.com/abstract =1193422,
last accessed April 21, 2010.

15

350

300

250

200

150

100

50
1978

1980

1982

1984

1986

1988

Gross domestic product

1990

1992

1994

1996

Construction cost index

1998

2000

2002

2004

2006

2008

Consumer price index

Figure 1. Nominal construction costs, gross domestic product, and inflation,
1978-2008

16

5%

4%

3%

2%

1%

0%

-1%

-2%

-3%

-4%

-5%
1978

1980

1982

1984

1986

1988

1990

1992

Real interest rate

1994

1996

1998

2000

2002

2004

2006

2008

Term spread

Figure 2. Real mortgage interest rates and term spread, 1978-2008

17

8,000

31%

7,000

30%

6,000

29%

5,000

28%

4,000

27%

3,000

26%

25%

2,000
1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008
Population (1,000s)

Population aged 30 to 49 (%)

Figure 3. Population and percentage of population aged 30 to 49, 1978-2008

18

500

54%

450

48%

400

42%

350

36%

300

30%

250

24%

200

18%

150

12%

100

6%

0%

50
1978

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

2004

House price index (<= 20 years)

House price index (all transactions)Land price index (<= 20 years)

Land price index (all transactions)Land leverage (<= 20 years)

Land leverage (all transactions)

2006

2008

Figure 4. Nominal house and land price indexes, and land leverage, 1978-2008

19

G3s09.shp

relativeland value 2008
G3g09.shp
0.1 - 0.2
0.2 - 0.3
0.3 - 0.4
0.4 - 0.5
0.5 - 0.6
>0.6

Figure 5. Land leverage for Swiss communes, 2008

20

145
140
135
130
125
120
115
110
105
100

1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008

95

Actua lPredicted (wi th LL)

Predi cted (wi thout LL)

Figure 6. Actual and predicted real house price levels: properties 20 years old or
younger

21

155

145

135

125

115

105

1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008

95

ActualPredi cted (wi th LL)

Predi cted (wi thout LL)

Figure 7. Actual and predicted real house price levels: all properties

22

Table 1. Construction costs, 2008
Building quality

Luxuryproperty

Construction costcorrection (%)

Construction costs (CHF
per m3)

Poor

No

-10

531

Average

No

-5

561

Good

No

0

590

Very good

No

+5

620

Very good

Yes

+10

649

23

Table 2. Depreciation rates (geometric)
Condition of thebuilding

Depreciation rate
correction factor

Annual depreciation rate
(%)

Poor

1.50

2.25

Average

1.25

1.88

Good

1.00

1.50

Very good

0.75

1.13

24

Table 3. Hedonic regression results: properties 20 years or younger
VariableIntercept
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
1986
1985
1984
1983
1982
1981
1980
1979
1978
Land area (ln)Floor area ratio
Micro location index
Macro location index
Building characteristics
R2
Sample size

Land prices
Estimate
9.145 ***
-0.034 ***-0.085 ***-0.147 ***-0.158 ***-0.251 ***-0.275 ***-0.302 ***-0.346 ***-0.335 ***-0.256 ***-0.243 ***-0.173 ***-0.029-0.0290.012-0.068-0.225 ***-0.036-0.016-0.282 ***-0.445 ***-0.488 ***-0.583 ***-0.671 ***-0.844 ***-1.124 ***-0.771 ***-0.965 ***-1.255 ***-1.210 ***-0.582 ***0.196 ***
0.230 ***
3.741 ***—
0.728
25,364

House prices
Estimate
8.546 ***
-0.036 ***-0.089 ***-0.124 ***-0.138 ***-0.167 ***-0.162 ***-0.161 ***-0.205 ***-0.218 ***-0.187 ***-0.174 ***-0.116 ***-0.079 ***-0.083 ***-0.046 ***-0.074 ***-0.074 ***-0.056 ***-0.104 ***-0.264 ***-0.357 ***-0.374 ***-0.436 ***-0.465 ***-0.543 ***-0.558 ***-0.632 ***-0.708 ***-0.822 ***-0.819 ***——0.088 ***
1.631 ***
1.000 ***

Land leverage
Estimate
0.231 ***
0.000
0.000
-0.009 ***-0.013 ***-0.035 ***-0.049 ***-0.052 ***-0.043 ***-0.040 ***-0.019 ***-0.014 ***-0.0020.015 *
0.027 ***
0.018 *
-0.024 *-0.040 ***0.006
0.047 ***
0.002
-0.030 **-0.021-0.049 ***-0.055 ***-0.057 ***-0.130 ***-0.078 ***-0.092 ***-0.098 ***-0.117 ***——0.046 ***
0.798 ***—

0.872
24,6850.495
25,718

Note: *, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively.

25

Table 4. Hedonic regression results: all properties
VariableIntercept
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
1986
1985
1984
1983
1982
1981
1980
1979
1978
Land area (ln)Floor area ratio
Micro location index
Macro location index
Building characteristics
R2
Sample size

Land prices
Estimate
8.516 ***
-0.042 ***-0.101 ***-0.170 ***-0.216 ***-0.354 ***-0.338 ***-0.364 ***-0.418 ***-0.399 ***-0.338 ***-0.344 ***-0.287 ***-0.106 ***-0.065 **-0.041-0.113 **-0.199 ***-0.032-0.039-0.271 ***-0.436 ***-0.478 ***-0.597 ***-0.637 ***-0.853 ***-1.120 ***-0.797 ***-0.931 ***-1.238 ***-1.213 ***-0.494 ***0.564 ***
0.224 ***
3.662 ***—
0.730
54,480House prices
Estimate
8.829 ***
-0.040 ***-0.107 ***-0.142 ***-0.167 ***-0.202 ***-0.194 ***-0.194 ***-0.245 ***-0.260 ***-0.252 ***-0.230 ***-0.171 ***-0.118 ***-0.113 ***-0.079 ***-0.142 ***-0.051 ***-0.080 ***-0.129 ***-0.303 ***-0.402 ***-0.414 ***-0.458 ***-0.543 ***-0.562 ***-0.587 ***-0.737 ***-0.754 ***-0.883 ***-0.909 ***——0.119 ***
1.860 ***
0.947 ***

Land leverage
Estimate
0.384 ***
0.000
-0.001-0.022 ***-0.054 ***-0.112 ***-0.118 ***-0.114 ***-0.110 ***-0.107 ***-0.093 ***-0.087 ***-0.081 ***-0.063 ***-0.051 ***-0.056 ***-0.092 ***-0.127 ***-0.073 ***-0.038 **-0.087 ***-0.112 ***-0.069 ***-0.101 ***-0.141 ***-0.157 ***-0.215 ***-0.170 ***-0.140 ***-0.184 ***-0.200 ***——0.026 ***
0.832 ***—

0.878
49,6180.420
53,213

Note: *, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively.

26

Table 5. House price and land leverage regression results: properties 20 years old or younger
House prices (without
land leverage)

Variables
Intercept-47.59LevelsHouse prices (withland leverage)

Land leverage

ChangesHouse prices (withland leverage)
Land leverage

-9.42

0.08

-2.76***-0.01*

Real construction cost index

0.65

0.76***-0.0004-0.35-0.004*

Real GDP per capita (CHF
1,000s)2.69***

0.86**

0.01***

6.60***

0.03***

Real interest rate

225.37107.370.91-52.19-0.46

Term spread

7.68-33.320.56-74.87**0.81***

Change in population aged 30 to49

0.53***

0.36***

0.001

0.22**-0.0002

Land leverage (instrument)—

0.78***—

0.35***—

Error correction term

—

—

—

-0.80***-0.03**
29

Sample size
2

Adjusted R

30

30

30

29

0.754

0.937

0.585

0.815

0.459

Note: *, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively.

27

Table 6. House price and land leverage regression results: all properties
House prices (without
land leverage)

Variables
Intercept

LevelsHouse prices (withland leverage)

Land leverage

ChangesHouse prices (withland leverage)
Land leverage-70.08-13.26

-0.16

-3.06

0.006

Real construction cost index

0.63

0.51

0.0009-0.29-0.009***Real GDP per capita (CHF
1,000s)3.67***

1.84***

0.02***

4.04*

0.04***

Real interest rate

188.01

46.64

0.89

-110.35-0.16

Term spread-23.39-24.350.21

5.36

0.85**

Change in population aged 30 to49

0.62***

0.69***-0.0004

0.68***

0.0006

Land leverage (instrument)—

0.78***—

0.52**—

Error correction term

—

—

—

-0.30*-0.13***
29

Sample size
2

Adjusted R

30

30

30

29

0.776

0.901

0.620

0.560

0.491

Note: *, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively.

28