Journal of Housing Economics 21 (2012) 1–15
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Journal of Housing Economics
journal homepage: www.elsevier.com/locate/jhec
Explaining regional variation in equilibrium real estate prices and income
Oliver Bischoff ⇑
Department of Economics, University of Hamburg, Von-Melle-Park 5, 20146 Hamburg, Germany
a r t i c l e i n f o a b s t r a c t
Article history: We combine the real estate model of Potepan (1996) with the spatial equilibrium approach
Received 10 May 2010 of Roback (1982) to prove the interdependency of housing prices, rental prices, building
Available online 6 December 2011 land prices and income via one simultaneous equilibrium analysis. Using unique cross-
sectional data on the majority of German counties and cities for 2005, we estimate the
JEL classiﬁcation: equations in their structural and reduced form. The results show signiﬁcantly positive
C21 interaction effects of income and real estate prices. Moreover, we can conﬁrm model
predictions concerning the majority of exogenous determinants. In particular, expectations
about population development seem to be among the most important determinants of
R31 price and income disparities between regions in the long term.
Ó 2011 Elsevier Inc. All rights reserved.
Regional housing markets
Spatial equilibrium analysis
1. Introduction describing the mechanisms of real estate sectors. It
consists of two sectors: the renter submarket and the
Until now, regional equilibrium analyses of real estate homeowner submarket. The rental market is the sector
markets have been characterized by two qualities. First, for housing services consumed by tenants and owner-
these analyses rely on theoretical approaches that exclu- occupants equally, where the rental price reﬂects the price
sively and explicitly reﬂect the interactions between indi- of housing. In contrast, the homeowner market depicts the
vidual real estate sectors. Steady-state relationships to production side of housing, where the housing price equals
the labor market and possible interdependencies between the amount that landlords and homeowners have to pay
income and several real estate prices, such as, housing, when purchasing habitable living space. The long-term
rental and building prices, have not been examined thus relationship between both sectors is ensured by no arbi-
far. Second, in empirical evaluations, equilibrium analyses trage conditions. Despite the small number of degrees of
of real estate sectors in the US or in Canada have been freedom, they are able to classify the age structure and
examined predominantly. Thus, equilibrium studies inves- land-use restrictions as the most important price determi-
tigating model valuation for European markets, for exam- nants in their reduced-form approach.
ple, are underrepresented. Potepan (1996) introduces an extension of this concept
Initial work on regional housing markets in a steady by including the market for building land in his attempt to
state is presented by Fortura and Kushner (1986), Manning describe the process of providing housing space in more de-
(1989) and Rose (1989), who estimate demand and supply tail. To do so, he decomposes the real estate sector into three
models in their reduced forms. Ozanne and Thibodeau ﬁelds. The ﬁrst sector describes land provision, the second,
(1983) develop the ﬁrst theoretically-based approach for housing production and the third housing consumption.
Using a two-stage least squares procedure, Potepan (1996)
⇑ Fax: +49 (0)40 42838 6251. estimates a three-equation system for the majority of US
E-mail address: email@example.com metropolitan areas. He ﬁnds that infrastructure quality,
1051-1377/$ - see front matter Ó 2011 Elsevier Inc. All rights reserved.
2 O. Bischoff / Journal of Housing Economics 21 (2012) 1–15
property taxes, population size and land-use restrictions the year 2005. In the ﬁrst step, we estimate the four-equa-
matter most in explaining regional price disparities. tion system consisting of housing prices, rental prices,
Although this three-equation system represents a com- building land prices and income via a three stage least
plete model, connections to the labor market remain unex- squares regression to clarify the structural relationships
plored. According to the spatial equilibrium approach of at play. In the second step, we estimate the reduced form
Roback (1982), household living and ﬁrms’ production deci- separately for each equation to detect the total effects of
sions depend fundamentally on the level of local amenities. exogenous price determinants. Thereby, regardless of the
Those amenities determine housing environment and house theoretical setting, which already considers externalities
prices, but they also affect production and income. Because across space, we present additional estimates to account
the supply of amenities is limited, the market process leads for spatial correlation due to the nature of data to make
to adjustments in location decisions of households and ﬁrms our ﬁndings as robust as possible.
given preferences and production strategies. Therefore, di- The remainder of this paper is organized as follows:
rect and indirect effects of amenities, prices and income be- Section 2 presents the theoretical background. Section 3
come capitalized. With regard to empirical evaluation, the describes the data and the empirical methods. Section 4
result is no spatial autocorrelation should exist when the discusses the results, ﬁrst presenting the structural form
market adjustment is completed. In equilibrium, no further estimations, followed by the reduced form estimations.
arbitrage opportunities exist and market agents at the mar- Section 5 concludes the paper.
gin are indifferent across space (Albouy, 2009; Berger et al.,
2008; Ebertz and Buettner, 2009; Glaeser and Gottlieb, 2. Theoretical background
2009; Rappaport, 2008; Winters, 2009).1 However, if compe-
tition for the most productive and highest quality location is This paper begins with the real estate model of Potepan
neglected, the results may be one-sided and biased (Glaeser (1996). That model describes the entire value-added chain
and Gyourko, 2008). of housing from production to consumption to analyze re-
Admittedly, Ozanne and Thibodeau (1983) and Potepan gional disparities in steady states. The setting consists of
(1996) hint at the possible endogeneity of income, but they three subsectors, each delineating one aspect of housing.
do not pursue a deeper investigation of this concept. In- They are sequentially linked by no-arbitrage conditions;
come is generated by the labor market, which is affected therefore, rational agents can equally reﬂect demand and
by location decisions according to the spatial equilibrium supply in consecutive submarkets. Similar to Potepan
approach. Market agents, in turn, orient themselves based (1994), we convert prices, costs and income to real terms
on real estate prices, income and amenities according to using a regional price index to investigate market pro-
their individual strategy. In sum, from a theoretical point cesses in the absence of money illusion or in terms of rel-
of view, the spatial equilibrium model yields a justiﬁcation ative prices.3
for the interdependent relationship between income and Starting at the top of the model, the market for housing
housing prices.2 services depicts the consumption of good housing. In such
Because dominantly US data have been used in the re- a market, tenants and owner-occupants determine the
search conducted so far, applying the model to another housing demand together, where the price for housing ser-
housing market environment provides a method to vali- vices is the rental price. Just as tenants transfer their pay-
date the model. The US market exhibits an owner-occupied ments to landlords during each period, homeowners
rate of approximately 66% (US Census Bureau, 2009). With implicitly do the same for themselves. Thus, there exists
such a high owner-occupant rate, that speciﬁc housing de- one uniﬁed market price for all households. In equilibrium,
mand is automatically reﬂected in the price structure. In under the user-cost of capital approach, households are
contrast, housing markets characterized by a more sym- indifferent regarding the choice between the two options
metric distribution of preferences could provide new in- for tenure choice, renting or owning.
sight into long-term price factors; e.g., in Germany, only The demand function HSD can be generally described as
approximately 42% of all households are owner-occupied follows:
In this paper, we extend the three-equation system of HSD ¼ HSD ðr; inc; am; seniors; t; foreigners; HHsizeÞ;
Potepan (1996) with an additional income equation to cap- ð1Þ
ture interactions between the real estate market and the
labor market in steady state, but also to control for local where:
externalities between regions. For our empirical evalua- @HSD @HSD @HSD @HSD
tion, we use cross-sectional data covering approximately 6 0; P 0; P 0; 6 0;
@r @inc @am @seniors
95% of all independent cities and counties in Germany for D D D
@HS @HS @HS
6 0; 6 0; 6 0:
@t @foreigners @HHsize
Analyses that incorporate migration ﬂows as a key driver to explain If housing is a normal good, the willingness to consume
market processes are shown, e.g., Jeanty et al. (2010) and Vermeulen and housing services will decrease with a higher rental price, r,
van Ommeren (2009), while in Hwang and Quigley (2006) the aspect of
market regulation is stressed.
A long-term relationship between income and house prices using US In our empirical analysis below, we treat all converted variables (prices,
time-series data is presented in Holly et al. (2010), whereas no relationship costs and income) as endogenous. For this reason the instrumental variable
is detected by Gallin (2006). method is used, which should ensure consistent and efﬁcient estimators.
O. Bischoff / Journal of Housing Economics 21 (2012) 1–15 3
but rise with higher income, inc. The same change is ex- number of foreigners, foreigners, which we assume to induce
pected to manifest when local amenities, am, are better. a relatively lower price impact compared to natives, as for-
Potepan (1996) and Ozanne and Thibodeau (1983) also eigners tend to occupy lower quality rental apartments.
include the absolute level of the population as the demand Finally, we use HHsize to consider the declining effect on
factor. In our opinion, the long-term model attempts to ab- demanded living space per square meter with increased
stractly deﬁne rational decisions that depend on economic household size because of the diminishing marginal utility
factors that have been already captured. By applying the of consumption.
spatial equilibrium approach, which internalizes network The supply side comprises landlords and owner-occu-
externalities via population size and includes the funda- pants who provide housing services in the same way. This
mental interdependent relationship between population assumption may appear too strong due to the different
density and productivity in the presence of agglomeration housing quality and types they each offer. However, the
economies (Ciccone and Hall, 1996; Rosenthal and Strange, lower ownership ratio in Germany may balance these dis-
2004; Combes et al., 2011), population, as a further exoge- parities in regard to the total supply effects in the rental
nous demand factor other than (household) income, be- and in the owner-occupied market. The rent-maximum
comes redundant.4 On this account, we keep population strategy, HSS, is modeled as follows:
from becoming an exogenous factor.
We account for population mobility within one district HSS ¼ HSS ðr; p; i; t; expÞ; ð2Þ
using seniors: the number of people over the pensionable
age of 65 in Germany. Because private renters move more where:
often than owner-occupants (Böheim and Taylor, 2002),
older populations exhibit a longer residence duration in @HSS @HSS @HSS @HSS @HSS
rental housing (Deng et al., 2003). In addition, lower P 0; 6 0; 6 0; 6 0; P 0:
@r @p @i @t @exp
household mobility per se lowers the natural vacancy rate
and, thus, lowers the equilibrium rental prices in the long- In observing price effects, the elasticity of housing sup-
term (Gabriel and Nothaft, 2001).5 Thus, a greater number ply is expected to be less than perfectly elastic across dis-
of persons over the age of 65 is assumed to decrease housing tricts due to, for example, restrictions on housing
demand in Germanys’ districts. The price effect of property affordability (Glaeser et al., 2006; Green et al., 2005; Ham-
tax, t, is expected to be negative because the tax burden ilton, 1978).
on landlords, which depends on the price elasticity of de- Rising costs in housing production lead to disincen-
mand, can be transferred to tenants (Tsoodle and Turner, tives to invest; hence, the price of housing capital, p,
2008), inﬂuencing their housing consumption in the end.6 and the mortgage interest rate, i, ought to decrease hous-
To account for differences in population groups according ing services. For Germany, no regional interest data are
to ownership (Borjas, 2002) and especially according to dis- available.8 Nevertheless, because the latter depends almost
crimination (Baldini and Federici, 2011),7 we include the solely on contract length in Germany and on the amount of
equity, it is assumed to be equal across cities and counties
in Germany. Therefore, the interest rate enters in the
Average income or wages are determined by local labor productivity,
which, in turn, is essentially driven by population density and vice versa. The correlation between the property tax rate, t, and
Thus, the effects of population size on housing demand are already the housing service supply is generally expected to be
captured by income implicitly and by productivity explicitly, as presented negative in general. Of course, as we have mentioned
in this paper and discussed below. In addition, Ciccone and Hall (1996),
above, the tax can be imposed on tenants, but only when
Combes et al. (2009) and Glaeser and Gottlieb (2009) doubt that population
is a strongly exogenous variable in regional rathern than in hedonic the contract between tenant and landlord provides for
analyses due to the reciprocal functional chain previously described. To this tax. Otherwise, taxes are costs of housing supply
handle the endogeneity of population empirically they propose to use the costs.
instrumental variable estimation method. Whether positive expectations about future returns on
This causal relationship holds true ceteris paribus even though the
natural rate of vacancy is not considered here. As Wheaton (1990) points
housing capital due to appreciation in housing, exp, are ex-
out, changes in living preferences can occur in the equilibrium state as well, pected to increase the quantity of housing services de-
but, consistent with our approach, this can only happen within the same pends on the agents’ degree of market information.9 As
district. Capozza and Helsley (1989) show in their theoretical long-
Therefore, we implicitly assume no full capitalization of property taxes
term model of urban land conversion, perfect foresight lead
because, after controlling for rental prices, no further inherent effect ought
to appear, particularly when the landlords have the ability to pass the
to the full capitalization of all necessary determinants and
entire tax incidence onto renters. While Yinger et al. (1988) detect thus to an insigniﬁcant effect of population growth. The
capitalization rates of between 16% and 31%, Palmon and Smith (1998) opposite becomes true when urban growth is unexpected
can not reject full capitalization even though their estimates lie between (Capozza and Schwann, 1989).10
62% and 100%.
Gyourko et al. (1999) argue that racial disparities in homeownership
are small with respect to wealth unconstraints but are signiﬁcant for Information by phone, Deutsche Bundesbank, division ‘‘interest statis-
wealth constraints. Painter et al. (2001) and Gabriel and Rosenthal (2005) tics’’, from 25 August 2010.
demonstrate that the probability of black households becoming owners is Appreciation in housing capital or in residential buildings is associated
substantially smaller than it is for white households. Hilber and Liu (2008) with less frequent reinvestments and thus with lower demand for
are able to explain those ethnical differences by referring to personal and construction materials and lower prices.
parental wealth as well as by the degree of urbanization in the place of Dust and Maennig (2008) can empirically prove asymmetric house
residence. price reactions to population shrinkage in Germany.
4 O. Bischoff / Journal of Housing Economics 21 (2012) 1–15
In total, the market equilibrium for housing services re- BLD ¼ HC S ¼ BLD ðp; l; cÞ: ð9Þ
duces to the following:
The land, including natural amenities, is initially owned
r ¼ r ðp; inc; am; i; t; exp; foreigners; seniors; HHsizeÞ by landowners (or, to be more precise, by public authori-
ð3Þ ties) so that the landowners enter as suppliers:
The link to the second subsector, which is the market BLS ¼ BLS ðl; ar; m; arliv ingÞ; ð10Þ
for housing capital, can be found in the equation for the
user-cost of owning. As in any other equilibrium analysis
of housing, all market agents need not have further arbi- @BLS @BLS @BLS @BLS
trage opportunities in changing their tenure choices or in P 0; 6 0; P 0; 6 0:
@l @m @ar @arliv ing
renting or ownership investments (Henderson and Ioan-
nides, 1983; Poterba, 1992): Unlike the two previous studies, we make no further di-
rect price distinction between kinds of land (such as build-
r ¼ ði þ t À expÞ Ã p: ð4Þ ing, rural or agriculture).11 Based on the smaller total land
The market for housing capital ensures the supply of surface and higher population density of Germany compared
housing services. The ‘‘good’’ in this market is the habitable to the US, the conversion of agricultural areas is assumed to
housing stock that is immediately suitable for renting or be less price-intensive.
buying. Landlords or owner-occupants must purchase res- Supply elasticity is assumed to be less than perfectly
idential buildings in advance when offering living space in elastic, so quantity should increase with price, l In turn, legal
the market for housing services. Therefore, they also reﬂect land use restrictions, m, decrease the building land supply.
the demand side of this market, HCD, where the same A larger total surface per district, ar, might offset topograph-
implications for fundamentals apply: ical limitations such as those represented by rock or water
landscapes. However, when the proportion of building land
HC D ¼ HSS ¼ HC D ðr; p; i; t; expÞ: ð5Þ is marginally increased, which creates a larger area already
settled by households and ﬁrms as well as a larger public
Housing capital is produced by housing developers who
thoroughfare, arliving, depicts natural restrictions in new
convert building land and construction materials:
housing construction that diminish the opportunity for
HC S ¼ HC S ðp; l; cÞ; ð6Þ public permission to release building land in the future.
In equilibrium, the price function that implies all mar-
where ginal effects of (9) and (10) mentioned above is as follows:
@HC S @HC S @HC S L ¼ l ðp; c; ar; m; arliv ingÞ: ð11Þ
P 0; 6 0; 6 0;
@p @l @c
This is the limit of model Potepan’s (1996) model, but
As in the market for housing services, supply is ex- there is room for further extension. Further embedding in
pected not to be perfectly elastic. Incentives to supply a regional framework is possible. For example, according
should emerge with higher returns, p, but disincentives to Rosen (1979) and Roback (1982), spatial equilibrium
should occur with higher building land prices, l. Similarly, arises when households and ﬁrms have no further incen-
housing capital supply should decline with higher con- tive to move. The economic intuition behind this model
struction costs c because it is unlikely that developers will is relatively simple but noteworthy. Assuming a market
be able to impose the entire cost burden on homeowners environment characterized by perfect factor mobility and
and landlords. no moving costs, households and ﬁrms compete for a lim-
The steady-state relationship in the market for housing ited supply of land and amenities because these natural re-
capital, including the relationships described in (5) and (6), sources can fundamentally inﬂuence living quality and
results in the following: production; the effects become visible in housing prices
P ¼ p ðr; i; t; exp; l; cÞ: ð7Þ and wages or, in our case, in the price for housing services
and in income. A steady state is achieved when direct and
The connection between the market for housing capital indirect (externalities) effects over time and, in particular,
and the third sector, the market for building land, is given across space are fully capitalized into local prices and
in equation (8). The average return of housing capital, p, wages. If and only if this circumstance holds true, market
must be equal to the space unit cost of the production of agents do not have incentives to change their location
housing capital separated into construction costs c and decisions.
building land costs, l: Following Glaeser et al. (2006), the spatial equilibrium
p ¼ ðc þ lÞ: ð8Þ condition can be stated as:
The market for building land is related to the space U þ r ¼ w þ I þ am: ð12Þ
available for construction. Unlike agricultural land, build- Substituting labor income w and non-labor income I
ing land is already connected to the public infrastructure with household income inc and treating individual utility
Housing developers take on the position of demand, so 11
Building land represents undeveloped parcels that exhibit an ample
that their payment reserve equals its calculation in (6) public infrastructure provision and are released for construction by local
with identical outcomes: public authorities.
O. Bischoff / Journal of Housing Economics 21 (2012) 1–15 5
U as uniform, the spatial equilibrium model is part of the 3. Data & empirical strategy
housing services model and vice versa. Because a long-
term interaction exists between income and housing In our paper, we use a comprehensive data set for inde-
prices, equation (12) acts as an equilibrium bridge like pendent cities and counties in Germany for the year 2005.
the other two conditions, (4) and (8). As Fig 1 shows, we cover the majority of districts, corre-
To model an income equation, we specify the labor mar- sponding to approximately 95% of all districts or 418 sam-
ket as simply as possible. We expect that income is pre- ple units; the district boundaries were dated on 12/31/
dominantly generated by labor:12 2006.14
Data for residential rents per square meter of living
LD ¼ LD ðinc; productiv ityÞ; ð13Þ
space, r, are provided by the Federal Ofﬁce for Building
where: and Regional Planning (BBR),15 which records basic, freely
ﬁnanced supply rents offered in daily newspapers and via
@LD @LD popular internet platforms. They were compiled only for
6 0; P 0:
@inc @productiv ity multi-apartment houses with at least three dwelling units.
Firms will naturally hire more workers when the costs Thus, no information about single-family houses is available,
of labor, inc, are lower. Amenities, am, can make the pro- but this limitation has a negligible impact within our
duction process more efﬁcient, so that the marginal prod- framework.
uct of capital increases, while the marginal product of We also receive housing supply prices, p, from the BBR.
labor simultaneously decreases ceteris paribus. However, The BBR exclusively analyzes data for single-family houses
those effects are already captured in the productivity vari- that feature living space between 100 and 150 m2. The
able, so amenities are redundant for explaining income.13 associated lot size for properties in large cities amounts to
Regardless, a higher level of labor productivity increases 200 to 650 m2; in surrounding areas, the span extends from
recruitment by the non-perfectly inelastic labor supply. 250 to 700 m2, and in rural districts it runs from 300 to
Labor supply is depicted as follows: 850 m2. Nevertheless, data only exist in absolute terms.
To convert this data into information on relative prices,
LS ¼ LS ðinc; r; children; amÞ; ð14Þ we assign each district a respective average value in accor-
where: dance with the classiﬁcation established by the BBR.16
One limitation must be noted. Because there were few
@LS @LS @LS @LS offers in some districts, relevant data for 2005 and 2006
P 0; 6 0; 6 0; P 0:
@inc @r @children @am are bundled.
Once again, market supply is assumed to be less than A similar restriction also holds for building land prices,
perfectly elastic but still positive in regard to returns, inc. l, published by the BBR. The average purchase prices per
In contrast, higher prices for housing services, r, force indi- m2 for building land are only presented for 2003–2005
viduals to move and hence reduce the region-speciﬁc labor and are available in the published data set INKAR 2007.
supply. Moreover, population size per se does not reveal We use the same source to receive the majority of ame-
the entire potential of one districts’ labor force because la- nities, am. To measure some sort of public amenities, but
bor supply depends on its population being within the also the geographic location of one district, we include
appropriate working age, starting as a rule at the age of commuting time, which measures the average travel time
18. A higher population number under the age of 18, chil- in minutes by public trains to the three nearest agglomer-
dren, who exist outside of that range ought to lead to a (rel- ation centers.17
atively) lower labor supply. Despite controlling for the
prices of housing services and income, the inﬂuence of 14
For descriptive statistics, including sources, see Table 1.
the amenity level on labor supply is positive because 15
The BBR has separated housing data by district for Brandenburg,
otherwise households would not settle in that district distinguishing between narrow and broad-integration areas. For a more
and thus would not supply labor as the spatial equilibrium appropriate comparison, we use data for broad areas. For rental prices see
condition implies. http://www.bbr.bund.de/cln_015/nn_23744/BBSR/DE/Raumbeobachtung/
Combining labor demand (13) and supply (14), the
and for house prices see http://www.bbr.bund.de/cln_015/nn_23744/
equilibrium in the labor market becomes the following: SharedDocs/GlossarEntry/P/PreisStandardhaus.html.
The BBR divides the regions into four so-called WIM-district types
inc ¼ incðproductiv ity; r; am; childrenÞ: ð15Þ
(metropolitan districts, large city districts, surrounding districts, and rural
districts) to account for different patterns of development in real estate
markets. For metropolitan and large-city districts, the assigned average is
425 m2; for surrounding districts, the average is 475 m2; and for rural
We ignore income from ﬁnancial capital investments, so the differences areas, the average is 575 m2. A map of classiﬁcation is available on the BBR
between income and wages are due to net tax excess or to social transfer homepage: http://www.bbr.bund.de/nn_499850/BBSR/DE/WohnenImmo-
Following Roback (1982), an example of a negative (‘‘unproductive’’) pen/WIMKreistypen.html.
impact of a natural amenity on ﬁrms’ production efﬁciency is clean air The following agglomeration centers within and around of Germany
because production factors have to be spent to comply with regulations are considered: Berlin, Bremen, Dresden, Essen, Frankfurt, Hamburg,
concerning the production process and pollution. A positive (‘‘productive’’) Hannover, Köln, Leipzig, Mannheim, München, Nürnberg, Stuttgart,
impact could be the lack of ‘‘acts of god’’ such as earthquakes, ﬂoods or Amsterdam, Antwerpen, Basel, Brüssel, Den Haag, Eindhoven, Genf,
snow storms because they are responsible for greater production uncer- Kopenhagen, Liège, Lille, Lodz, Lyon, Mailand, Paris, Prag, Rotterdam,
tainty and loss. Stettin, Straßburg, Turin, Utrecht, Venedig, Wien and Zürich.
6 O. Bischoff / Journal of Housing Economics 21 (2012) 1–15
Fig. 1. Sample units – 2005. Source: This image was made by Gabriel Ahlfeldt. Notes: Shaded districts display independent cities, grey districts display
counties and black districts display units that are not included. The district boundary is dated on 12/31/2006.
The average number of persons per household is dis- reﬂects a relative scale (given that Bonn is set as the refer-
played via HHsize, while the number of registered doctors ence category).
per 1000 capita is used to describe the health care of one The other major data source that we make use of is the
region. In contrast to Ozanne and Thibodeau (1983) and free online database provided by the statistical ofﬁces of
Potepan (1996), who use recent population growth as a the German federal government and the German states.
predictor of expected future returns in housing capital, This data source is used to calculate proxies of economic
exp, we use the calculated forecast value for population activity.
growth between 2004 and 2020. This indicator relies on To create income, inc, we use disposable income per
past information about natural population changes and person in an average household, which incorporates the
movements. salaries of employees and the net excess of social pay-
Using the same source, the total area of settlement and ments and taxes.
public thoroughfare, arliving, is provided in a relative scale Deﬁning labor productivity, productivity, we calculate
per capita, which we recalculate for our analysis in abso- the ratio according to the gross-domestic product and the
lute terms. volume of work expressed according to the working hours
To deﬂate prices, costs, productivity and income, we of the entire labor force. In addition, because labor produc-
pull a regional price level index from the online platform tivity depends on the degree of human capital which in
for the Federal Institute for Research on Building, Urban turn essentially depends on agglomeration effects and thus
Affairs and Spatial Development (BBSR).18 It measures on factors eventually being not included in our model, we
disparities in cost of living for the year 2009, whereby it circumvent the problem of omitted variable bias by speci-
fying it as endogenous. We take the female population, wo-
men, as an instrumental variable because of the different
http://www.bbr.bund.de/nn_335560/BBSR/DE/Aktuell/Medieninfos/ supply elasticities of gender (Abe, 2011; Hirsch et al.,
2009/Ablage__Medieninfos/PM__Berichte30.html (click on « Preisindex 2010) and the different sum of man-years affecting wo-
aller Kreisregionen Deutschlands ») or see BBSR (Ed.): Regionaler Preisin- men’s productivity.
dex. Bonn 2009. = Berichte, Bd. 30, Anhang 3.
O. Bischoff / Journal of Housing Economics 21 (2012) 1–15 7
Variable Scale Source Mean Std. dev. Min Max
Real rental price, r €/m2 BBR 5.91 0.80 4.50 9.19
Real housing price, p €/m2 BBR 445.55 135.86 223.75 881.19
Real building land price, l €/m2 INKAR 2007 128.95 100.14 12.79 657.77
Real income, inc €/Person (in average household) vgrdl.de; bbr.de 18912.1 1998.1 14,656 27,584
Population forecast, exp Relative change, 2004–2020 INKAR 2007 -0.013 0.079 -0.302 0.219
Population À18, children Total regionalstatistik.de 4325.22 4545.0 794 74,834
Population +65, seniors Total regionalstatistik.de 36478.18 38977.4 7538 585,313
Regional price index Relative scale to Bonn bbsr.bund.de 0.9089 0.0486 0.83 1.14
Time to centers, Commuting time In minutes INKAR 2007 101.20 36.22 24 228
Number of beds, Tourism Total regionalstatistik.de 6064.90 8036.7 230 81,779
Health care, doctors Per 1000 capita INKAR 2007 1.539 0.515 0.69 3.71
Child care, nursery Total regionalstatistik.de 7464.28 8475.4 1180 126,168
Foreign population, foreigners Total regionalstatistik.de 16849.2 34547. 572 466,518
Property tax, t In 100% regionalstatistik.de 3.5996 0.6200 2.37 6.6
Real construction costs, c €/h https://www- 82.30 10.56 56.33 124.63
Independent city, m Dummy Own calculation 0.263 0.441 0 1
Area surface, ar km2 regionalstatistik.de 824.86 596.91 35.7 3058.1
Area of settlement, arliving km2 INKAR 2007, own conversion 106.52 73.31 12.97 880.73
Real productivity €/h vgrdl.de 41.58 5.68 27.81 70.75
Land ﬁlls Total regionalstatistik.de 4.6 7.4 0 67
Female population, women Total regionalstatistik.de 97010.1 111,884 18,105 17,31,180
Household HHsize Persons per household INKAR 2007 2.17 0.175 1.74 2.74
Construction ﬁrms Total regionalstatistik.de 855.6 899.8 39 13,931
Source: Based on data described in 3.
Notes: Data are shown in their original form. Data for income and productivity were retrieved on 08/08/2008 before data according to the restructuring in
Saxony in 2008 has been published.
The aforementioned administrative bodies also provide errors in variables, we specify construction costs as an
data on the population number below the age of 18, chil- endogenous variable instrumentalized by the number of
dren, above the age of 65, seniors, the female population, construction ﬁrms available for each district for the year
women, foreigners, total area size, ar, and the property 2006. To ensure orthogonality to white noise, we assume a
tax, t. Legal land use restrictions, m, are proxied by a dum- perfectly competitive market environment in which each
my variable that is one if the district is an independent city. ﬁrm makes zero proﬁt, as the spatial equilibrium model al-
While in German independent cities there is one superior ready suggests that ﬁrms in and outside the market are
public administrative body, in German counties, public equally well off.
decisions are predominantly made in the municipality. This completes our set of variables used in this paper. In
To consider the negative externalities of landﬁlls on res- sum, our aggregate data comes overwhelmingly from ofﬁ-
idential property values following Reichert et al. (1992), cial resources and not from household surveys. Therefore,
we incorporate the number of landﬁlls. household-based information about individual housing
The two additional amenity variables, nursery and tour- characteristics are not available. So, contrary to Potepan
ism, are the total number of places in day nurseries for chil- (1996) but similar to Roback (1982), we do not use hedon-
dren under the age of 14 and the number of beds in tourist ically measured rental and housing prices, which arise
accommodations. By including nursery, we attempt to cap- from the implicit prices of the housing attributes evaluated
ture the ability of the publicly provided child care system by households according to their living preferences (Rosen,
to provide households with the ﬂexibility to participate in 1974). By treating individual utility as uniform, the price
the labor market (Doiron and Kalb, 2005). The variable tour- data discrepancy might be mitigated.
ism acts as a rough proxy for districts’ opportunities for pri- To examine the structural approach combining (3), (7),
vate activities including cultural events, sports, shopping (11), and (15), ensuring consistent and efﬁcient estimators,
etc., proceeding from the assumption that tourism services we choose the three-stage least squares method (Zellner
are predominantly offered in areas characterized by a rela- and Theil, 1962). The system of equations can be simply for-
tively high quality and quantity of local (private) amenities. mulated as follows when assuming linear market functions:
Construction data, c, are very scarce in Germany and do
not exist on the county level. However, the German Federal YA þ XB ¼ E with i ¼ 1; . . . ; n observations ð16Þ
Ofﬁce of Statistics documents total revenue and working
hours in the residential construction sector for each month where Y T ¼ ½ri pi li inci is a 4 Â n vector of endogenous vari-
and each state. Thus, we calculate the average ratio and as- ables, X is a n Â k matrix of the corresponding exogenous
sume an uniform cost distribution for each state. Material covariates k and the error vector E has the dimension
costs are omitted, but a more suitable indicator of cost dif- n Â 4. In this speciﬁcation, errors have a zero conditional
ferences is not available. To avoid misspeciﬁcation through mean and are conditionally homoskedastic but are
8 O. Bischoff / Journal of Housing Economics 21 (2012) 1–15
cross-correlated. The ﬁrst diagonal parameter matrix A is an explanation power in the range of 59% and 83%. One
4 Â 4 and depicts the interdependencies among all four reason for the relatively higher white noise in our study
endogenous variables, while the second parameter matrix could be that we use supply rather than hedonic prices.
B has dimension k Â 4, containing the marginal effects of Another reason could be the different kinds of amenities
all exogenous covariates. that both studies include. Nevertheless, the covariates in
Afterwards, we obtain the reduced form for each equa- our study are always jointly signiﬁcant, as the chi statistic
tion that can be individually estimated by ordinary least clearly indicates.
squares: Concerning the endogenous variables for each equation,
price elasticity of housing services, r, with respect to hous-
Y ¼ XBAÀ1 þ EAÀ1 ¼ X P þ V ð17Þ ing capital, p, is positive and statistically signiﬁcant. This
or in our case to circumvent misleading calculations, result conﬁrms the hypothesis that homeowners or land-
according to Aigner et al. (1984), by two- stage least lords reduce their housing service supply when faced with
squares: higher investment costs for housing capital. In comparison,
the price elasticity value of approximately 0.37% is below
ZY ¼ ZX P þ ZV ð18Þ the 0.49% detected in the U.S. market. The lower degree
of price sensitivity in Germany might be due to the lower
where Z denotes the instrumental matrix.
(real) central bank discount rate in 2005, which reduced
The differences between equations (16) and (17) are lar-
the opportunity costs of housing capital, e.g., by increasing
gely theoretical. In general, the reduced form results from
incentives for capital net exports.
the solution for endogenous interactions and is appropriate
The opposite is true for income, inc. Income has a posi-
whenever the total impact of the exogenous variables is of
tive and signiﬁcant inﬂuence of 0.33% on German housing
main interest. By contrast, estimating structural or simulta-
demand and reﬂects a relatively higher level of preference
neous equation models makes it possible to consider the
regarding housing services than the 0.20% for U.S. house-
interdependencies in its entirety. These calculations are
holds. Comparing the extended model to the baseline mod-
generally closer to theoretical and causal predictions.
el, where income is speciﬁed as exogenous, the elasticity is
signiﬁcantly negative, meaning that housing is an inferior
4. Results good. That outcome clearly indicates misspeciﬁcation in
the baseline model, at least when it is applied to the Ger-
4.1. Structural form estimation man case. Omissions of relevant determinants for income,
as the spatial equilibrium model suggests, automatically
The estimation results for the system equations, consist- lead to inconsistencies and inefﬁciencies in the estima-
ing of our proposed four-equation setting called ‘‘extended tions. By contrast, the same argument can not be adopted
model’’ and of the three-equation setting according to Pote- to explain the diametrical sign in our baseline model com-
pan (1996) called ‘‘baseline model’’, are shown in Table 2. In pared to Potepan’s (1996) result. Again, both studies use
principle, our further comparisons refer to Potepan’s (1996) different types of price data. Because we are not able to
study even when no explicit remark is made to that effect. further control for housing quality and location within
Moreover, because almost all variables are transformed into each district, and only partially for apartment size in the
their natural logarithms (with the exception of population price variables, there is very likely room for an upward bias
forecasts, property tax, and landﬁlls), we can interpret the in the income effect. As a consequence, a pure comparison
coefﬁcients as price or income elasticities and, thus, as rela- concerning income in all three equation settings should be
tive effects, as is typically the case for those log–log made cautiously. Nevertheless, assumptions of initial exo-
models.19 geneity on the district level, as seen in Mayo (1981), might
First, we ﬁnd empirical evidence for the interdependence be not applicable to the entire structure of local economic
of real estate prices and income. They exhibit a signiﬁcant interrelations.
effect associated with their expected sign. As the reference In the market for housing capital, we can conﬁrm almost all
setting shows, without an endogenization of household in- model predictions for the endogenous variables. Although
come, remarkable changes in the coefﬁcient magnitudes higher returns in the housing services market, as depicted by
and signiﬁcances in the housing services equation become higher rental prices, coincide with an increase in the home-
obvious concerning both the income and the population owners’ and landlords’ incentives to enlarge the supply by
forecasts. approximately 0.02%, that ﬁnding is not signiﬁcant at any con-
Because this analysis focuses on Germany, the results ventional level. However, this lack of signiﬁcance may be due
lend additional support to the underlying framework; the to the fewer degrees of freedom and the complex estimation
analysis does not work exclusively for the U.S. market. method at play.
For all four equations, the model explains between 27% However, housing capital supply is determined by
and 51% of the variance, even if Potepan (1996) obtains housing developers, who use the price of land, l, to deter-
mine their course of action. The larger the expenditures re-
We do not take the logarithm of these three variables because quired to secure suitable land, the lower the available
population forecasts and property tax are already in relative scale and no market quantity should be. This effect is why the price of
landﬁlls are located in approximately 20% of all districts. However, the
interpretation of non-logarithmized variables in relative terms and loga-
building land exhibits a positive and highly statistically
rithmized variables in absolute terms is similar to the explanation of a signiﬁcant coefﬁcient of approximately 0.40, which is
logarithmized dependent variable. roughly close to the ﬁgure of 0.32 for the U.S. sector.
Extended model Baseline model
3SLS Housing services Housing capital Building land Labor market Housing services Housing capital Building land
Rental price Housing price Land price Income Rental price Housing price Land price
Rental price – 0.016 (0.13) – 0.3266⁄⁄⁄ (4.34) – À0.0431 (À0.38) –
Housing price 0.3208⁄⁄⁄ (4.35) – 3.1593⁄⁄⁄ (25.17) – 0.4239⁄⁄⁄ (6.85) – 3.1889⁄⁄⁄ (24.81)
Land price – 0.2959⁄⁄⁄ (10.64) – – – 0.3029⁄⁄⁄ (11.45) –
Income 0.3318⁄⁄ (2.39) – – – À0.178⁄⁄⁄ (À3.60) – –
Nursery 0.1567⁄⁄⁄ (6.87) – – –0.092⁄⁄⁄ (À3.43) 0.1184⁄⁄⁄ (7.25) – –
O. Bischoff / Journal of Housing Economics 21 (2012) 1–15
Population forecast 0.1021 (1.29) 0.0430 (0.61) – – 0.1557⁄⁄ (2.19) 0.0580 (0.87) –
HHSize À0.2329⁄⁄ (-2.59) – – – À0.1819⁄⁄ (À2.17) – –
Property tax À0.038⁄⁄⁄ (À4.06) À0.009 (À1.01) – – À0.056⁄⁄⁄ (À6.89) À0.0149⁄ (À1.78) –
Construction costs – 0.3988⁄⁄⁄ (3.43) À1.140⁄⁄⁄ (À3.44) – – 0.3679⁄⁄⁄ (3.22) À1.166⁄⁄⁄ (À3.49)
Independent cities – – 0.0137 (0.26) – – – 0.0582 (1.27)
Area surface – – À0.083⁄⁄ (À2.27) – – – À0.064⁄ (À1.91)
Area of settlement – – 0.1000⁄⁄⁄ (2.72) – – – 0.0920⁄⁄⁄ (2.64)
Productivity – – – 0.5499⁄⁄⁄ (9.22) – – –
Children – – – 0.0713⁄⁄⁄ (2.61) – – –
Seniors À0.077⁄⁄⁄ (À3.13) – – – À0.061⁄⁄⁄ (À2.77) – –
Landﬁlls À0.003⁄⁄⁄ (À4.86) – – 0.0010 (1.41) À0.002⁄⁄⁄ (À3.48) – –
Foreigners À0.053⁄⁄⁄ (À3.91) – – – À0.0297⁄⁄ (À2.11) – –
Commuting time À0.0270⁄⁄ (À2.01) – – 0.0100 (0.60) À0.0260⁄⁄ (À2.03) – –
Tourism 0.0243⁄⁄⁄ (4.37) – – À0.0006 (À0.10) 0.0185⁄⁄⁄ (3.51) – –
Doctors 0.1059⁄⁄⁄ (4.40) – – À0.0414⁄⁄ (À2.17) 0.1005⁄⁄⁄ (4.25) – –
Intercept À3.594⁄⁄⁄ (À2.98) 2.951⁄⁄⁄ (5.14) À9.461⁄⁄⁄ (À7.21) 7.404⁄⁄⁄ (29.15) 1.1082⁄⁄ (2.27) 3.180⁄⁄⁄ (5.74) À9.621⁄⁄⁄ (À7.34)
N 418 418 418 418 418 418 418
R2 0.2817 0.5136 0.2699 0.3415 0.2545 0.5152 0.2584
Chi2-statistic 468.94⁄⁄⁄ 848.19⁄⁄⁄ 726.61⁄⁄⁄ 291.29⁄⁄⁄ 466.62⁄⁄⁄ 846.21⁄⁄⁄ 712.79⁄⁄⁄
Notes: All variables are converted into the natural logarithm except property tax, landﬁlls and population forecast. The endogenous variables are rental price, housing price, building land price, productivity and
construction costs. In addition to the exogenous variables, female population and the number of construction ﬁrms are used as further instrumental variables in the extended version, while for the baseline model,
the female population is neglected. Estimations are made using the three-stage least squares method. Z-statistics are in parentheses; the asterisks ⁄⁄⁄, ⁄⁄ and ⁄ denote signiﬁcance at the one percent, ﬁve percent
and ten percent levels.
10 O. Bischoff / Journal of Housing Economics 21 (2012) 1–15
Similarities also appear in the market for building land. obtain a signiﬁcantly positive impact on housing prices
In relation to housing capital, building land prices are elas- and a negative impact on building land prices, which is
tic. A one-percent increase in housing capital revenue in- in line with the theoretical framework.
creases demand by developers and ultimately leads to an Subject to the spatial equilibrium approach in equation
average increase in building land price of almost 3.16% (12), amenities, am, that increases living quality raise the
compared to the 2.33% in the U.S. case. Thus, the price in- value of housing services and simultaneously decrease
crease suggests indirectly that there are comparatively production output. Therefore, all (dis-)amenities appear
large proﬁt margins for housing developers and land own- in the housing services and in the labor market equally.
ers across the markets of various nations. For almost all amenity variables, which reﬂect the qual-
The fourth equation presents the market for labor and ity of public services, geographical location, leisure oppor-
earnings. The highly signiﬁcant coefﬁcient of the housing tunities and health care, the results provide individual
services price variable in the amount of 0.33% supports evidence for each according to model predictions.
our conjecture about income endogeneity because house- In addition to amenities, housing services demand also
hold location choices (or, equivalently, household labor depends on housing stock heterogeneity and on the com-
supply) are signiﬁcantly inﬂuenced by the price of housing position of its demanders. By foreigners, which exerts a dis-
services as well. tinctly negative effect on the average price for housing
Turning toward the exogenous determinants, as equa- services, we can sustain the thesis about disparities in
tion four suggests, property tax expenses, t, indicate higher housing among ethnic groups. We also detect that house-
costs for housing capital followed by lower demand for hold mobility or apartment changes within districts are
housing capital and, ﬁnally, by a lower price for housing remarkable even in equilibrium because seniors is signiﬁ-
capital. The shortage of housing capital simultaneously re- cantly negative. Moreover, the results also conﬁrm the
duces the supply of habitable dwellings in the market for negative relationship between the demand for living space
housing services, inducing a rental price increase. While and average household size for the German housing mar-
Potepan (1996) obtains signiﬁcant coefﬁcients along theo- ket by the negative outcome of size.
retical suggestions, we estimate that taxes will have a sig- When considering the labor market, productivity reﬂect-
niﬁcantly negative impact on rental prices and a negative, ing labor efﬁciency and children presenting a factor that af-
but insigniﬁcant, impact on housing prices. Contrary to fects labor quantity are included. By comparison, an
Potepan (1996), we highlight the importance of property increase of children, as per the assumption, reduces labor
taxes as a key factor inﬂuencing market agents’ housing supply and thus increases wages or income relatively; in
consumption. Thus, two antagonistic inﬂuences-lower de- our case, by approximately 0.07% holding all other factors
mand and lower supply-affect the rental price at the same constant, while productivity, increases earnings by 0.55%.
time. As our estimates show, the demand for housing ser- For the German labor market, one can therefore conclude
vices is more elastic than the supply with regard to prop- that quality effects outweigh quantity effects. This ﬁnding
erty taxes. German households seem to be faced with is in line with Suedekum (2008) or Arntz (2010), who de-
high opportunity costs concerning investments in non- tect regional convergence for human capital, especially
tradable goods, as, e.g., high (expected) returns for invest- for well-educated people in Germany, and is in contrast
ments in other ﬁnancial assets or tradable goods. Compar- to Berry and Glaeser (2005) for the US Given the equal dis-
ing our tax estimates in the housing capital equation for tribution of education level in a steady state, income dis-
both model types, the coefﬁcient becomes insigniﬁcant parities mainly emerge in terms of differences in labor
when income is speciﬁed as endogenous. The high estima- efﬁciency.
tion uncertainty, which leads to the insigniﬁcance after Finally, with regard to the building land market, dispar-
controlling for income determinants, probably comes from ities between our observation units, independent cities and
the assumption of an identically assumed interest rate counties declared by m, are not present. Instead, larger area
across space, even though the parameter sign is steadily size, ar, signiﬁcantly lowers the value of building land by
in line with the model prediction. approximately 0.08%. Conversely, the larger the housing
Referring to condition (4) again, and bearing in mind sprawl, arliving, the larger the shortage of new building
that there are no ﬁnancial barriers across space in Ger- land and the more expensive is its relative price; in our
many, expectations about future returns on housing capital case, 0.10%. Nevertheless, both outcomes points to an
are also important to investments and consumption choice inelastic reaction indicating that there is still sufﬁcient
decisions. Thus, higher rates of expected future population building land for new construction in the average German
growth, exp, should raise demand for housing capital while district.
increasing housing services supply. In each case, the esti-
mates are insigniﬁcant for both sectors, so the results con- 4.2. Reduced form estimation
ﬁrm the certainty model of Capozza and Helsley (1989), at
least for the structural form. Now we turn to the reduced form elasticities of all
Following equation (8), construction costs determine exogenous price drivers. A prior analysis of the structural
developers’ investment strategy in the market for housing form is difﬁcult because interactions between the endoge-
capital and building land in a fundamental way. As men- nous variables obscure the issue. In addition to presenting
tioned above, developers reduce their demand for building the results using two stages least squares (2SLS) methods,
land and their supply of housing capital when construction thereby specifying construction costs and productivity as
costs, c, are higher. In contrast to Potepan (1996), we endogenous, calculations controlling for error terms and
O. Bischoff / Journal of Housing Economics 21 (2012) 1–15 11
omitted variables that might be correlated across space Third, all variables that are signiﬁcant in the 2SLS models
Anselin (1988) and that are addressed by spatial autore- are also relevant in the spatial 2SLS models. Thus, there
gressive models (SAR) are also shown.20 Despite using the are similarities in the ﬁndings that follow the theoretical
spatial equilibrium model, which captures spatial correla- and empirical lines, especially for housing capital and the
tion from a theoretical perspective, we ensure robustness labor market. Therefore, we will now focus on the param-
using a various set of empirical outcomes. Tables 3 and 4 eters in Table 3, which are signiﬁcant at the 10% level at
present the results for the reduced forms with or without least.
modeling household income interdependencies with real es- Beginning with the housing service market, on average,
tate prices in addition to spatial correlations. those districts with the best health care systems, doctors,
Referring to the tests of Durbin (1954), of Wu (1974), of and the highest expected population trends, exp induce rel-
Hausman (1978) and of Wooldridge (1995), all of which ative price increases by 0.29% and 0.57%, respectively. The
determine whether variables are indeed endogenous as positive sign of the latter might be counterintuitive in re-
speciﬁed, except for the housing capital sector, they clearly gard to the user cost of capital approach in Eq. (4). How-
support our presumption of the joint endogeneity of pro- ever, under the structural estimates, the impact of
ductivity and construction costs due to omitted variable bias housing capital on housing services is larger than the re-
and to errors in variables. Even at the 1% signiﬁcance level, verse effect, so the ﬁrst outweighs the second.
they allow us to reject the null hypothesis of exogeneity. In the market for housing capital, expectations about
As the results of the Wald test and the Lagrange multi- future population development also matter likewise. Con-
plier test for the spatial autoregressive parameter show, at trary to the ﬁndings above, we detect a signiﬁcant impact
least from an empirical perspective, it might be preferable that reveals partial information uncertainty among market
to control for further spatial externalities. From a theoret- agents. Nevertheless, this diametrality in evidence clearly
ical perspective, the model is expected to be fully speciﬁed reveals the necessity to present structural and reduced
and to account for spatial externalities by deﬁnition; a con- forms, especially when the information set is limited and
tradiction therefore emerges between theoretical and the equation system is complex. In sum, the ﬁndings for
empirical predictions. Two possible and opposed explana- Germany rather supports the results of Capozza and Schw-
tions exist: ﬁrst, that the empirical spatial outcomes are ann (1989). The positive causality between seniors and the
spurious and second, that the model speciﬁcation is not price for housing capital seems to be a further contradic-
sufﬁcient. While either explanation could be generally tion to the structural estimates. Bearing in mind that a lar-
valid, the problem of omitted variables correlated across ger proportion of population above the age of 65 can reﬂect
space can empirically exist without leading to inconsistent average household wealth as well, as far as income deter-
and inefﬁcient estimations, assuming that those neglected minants are insigniﬁcant due to collinearity, in this case,
effects are uncorrelated to our model parameters (as stated that effect can be also interpreted as an indirect signal
earlier in Section 3). Because our degrees of freedom corre- for higher returns in the market for housing services. To
spond to 400, the estimates can also be interpreted in explain the negative coefﬁcient of area settlement, arliving,
asymptotical terms. Closely linked, even though the major- and the positive of area size, ar, one have to consider the
ity of determinants in Table 3 are accounted as insigniﬁ- interrelations of markets again. A shortage of free building
cant due to multicollinearity, they predominantly exhibit land given total area size pushes up the price, reduces the
the expected sign and as the Wald Chi2-statistic respec- incentive for housing developers to invest and thus de-
tively shows, the joint explanation power of all determi- creases capital production. Moreover, housing capital is
nants matters. signiﬁcantly more expensive in independent cites than in
Comparing Tables 3 and 4, three general facts become counties, as the parameter for m shows. The higher price
obvious. First, more variables are signiﬁcant under the may be due to the administrative structure, under which
spatial 2SLS method than in the pure 2SLS. Second, the planning decisions in large cities are made centrally and
majority of coefﬁcient disparities between both methods are probably more restrictive than in counties due to the
are relatively small when estimation uncertainty is small. stronger limitations on available land.
Concerning the market for building land, only
expectations about future population development are
To choose the appropriate spatial pattern, we obtain the robust Lag important according to the pure 2SLS, while almost all
range multiplier test for the spatial lag and the spatial error model determinants are highly signiﬁcant when following the
following Anselin and Bera (1996). While for each reduced form equation
for the spatial error approach the robust Lag range multiplier test conﬁrms
spatial 2SLS approach. The remarkable price response
our model assumption of no misspeciﬁcation due to spatial correlation at conﬁrms the value of expectations for agents’ decisions
the one percent signiﬁcance level, for the spatial lag approach the same test in the housing market. Similar to the causality line high-
reveals the opposite. Therefore, we only present results for the spatial lag lighted for the other signiﬁcant determinants above, this
approach. Using Eq. (18), the model becomes to: ZY = pWZY + ZXP + ZV with
outcome can be explained via the positive real estate price
q denoting the spatial autoregressive parameter rho, W denoting the spatial
weights matrix and Z the instrumental matrix including the number of interdependencies.
construction ﬁrms and female population as two additional exogenous To say something about the ﬁnding in the labor market
covariates. As Kelejian and Prucha (1998) prove, the pure 2SLS procedure, is quite more difﬁcult. The positive impact of household
which we apply in this paper, is consistent, but not fully efﬁcient compared size might be due to its correlation to children, which is
to their suggestion of a generalized spatial two-stage least squares (GS2SLS)
procedure. Because we focus our interpretation on variables that are
supposed to have a positive inﬂuence on income. Because
signiﬁcant at least at the ﬁve percent level, this asymmetry in standard the latter is highly insigniﬁcant, size may capture a large
errors can be mitigated asymptotically. proportion of children’s effectiveness.
Extended model Baseline model
2SLS Housing services Housing capital Building land Labor market Housing services Housing capital Building land
Rental price Housing price Land price Income Rental price Housing price Land price
Nursery À0.026 (À0.13) 0.013 (0.08) À0.220 (À0.21) À0.034 (À0.20) À0.027 (À0.41) À0.176 (À1.14) À0.020 (À0.73)
Population forecast 0.566⁄⁄ (1.99) 0.518⁄⁄ (2.23) 3.558⁄⁄⁄ (2.63) 0.380 (1.59) 0.394⁄⁄⁄ (3.80) 0.295 (1.54) 2.579⁄⁄⁄ (7.15)
HHSize À0.116 (À0.24) 0.266 (0.57) À0.735 (À0.30) 1.087⁄⁄ (2.42) 0.151 (0.78) 0.459 (0.98) 0.918 (1.11)
Property tax 0.047 (0.50) 0.010 (0.12) 0.302 (0.60) 0.065 (0.78) À0.028⁄ (À1.83) À0.014 (À0.47) À0.066 (À1.08)
Construction costs À0.918 (À0.83) À0.064 (À0.06) À1.889 (À0.33) À0.322 (À0.34) À0.986⁄⁄ (À2.17) À0.969 (À1.01) À2.749 (À1.55)
O. Bischoff / Journal of Housing Economics 21 (2012) 1–15
Independent cities À0.0109 (À0.12) 0.167⁄⁄ (2.01) 0.407 (0.90) À0.047 (À0.60) À0.079⁄ (À1.85) 0.111 (1.30) 0.813 (0.50)
Area surface 0.130 (1.26) 0.161⁄ (1.88) 0.624 (1.23) 0.113 (1.28) À0.020 (À0.49) 0.025 (À0.31) À0.163 (À1.15)
Area of settlement À0.281 (À1.41) À0.407⁄⁄ (À2.38) À1.690 (À1.57) À0.251 (À1.43) À0.002 (À0.03) À0.066 (À0.46) À0.206 (À0.88)
Productivity 2.380 (1.14) 0.919 (0.50) 12.02 (1.10) 2.193 (1.18) – – –
Children 0.322 (0.95) À0.088 (À0.30) 1.807 (1.00) 0.151 (0.49) – – –
Income – – – – 0.279⁄ (1.72) 0.467 (1.44) 1.857⁄⁄⁄ (2.95)
Seniors À0.069 (À0.70) 0.232⁄⁄ (2.71) À0.036 (À0.07) 0.101 (1.14) À0.085⁄⁄ (À2.09) 0.035 (0.53) À0.049 (À0.36)
Landﬁlls À0.005 (À1.33) 0.005 (1.38) À0.026 (À1.41) À0.004 (À1.12) 0.002 (1.14) 0.008⁄⁄ (2.57) 0.008 (1.32)
Foreigners À0.069 (À0.70) 0.099 (0.69) À0.710 (À0.83) À0.121 (À0.81) 0.104⁄⁄⁄ (3.50) 0.186⁄⁄⁄ (3.17) 0.519⁄⁄⁄ (4.75)
Commuting time À0.055 (À1.06) À0.002 (À0.05) À0.310 (À1.24) À0.033 (À0.72) À0.017 (À0.70) 0.006 (0.12) À0.076 (À0.91)
Tourism 0.079 (1.35) À0.012 (À0.23) 0.314 (1.01) 0.044 (0.85) 0.032⁄⁄⁄ (2.84) À0.012 (À0.58) 0.086⁄ (1.86)
Doctors 0.287⁄ (1.88) À0.007 (À0.05) 0.770 (1.00) 0.199 (1.48) 0.183⁄⁄⁄ (5.14) À0.034 (À0.39) 0.235 (1.55)
Intercept À3.626 (À0.71) 0.866 (0.19) À36.18 (À1.40) 1.966 (0.44) 3.430⁄⁄⁄ (3.27) À25.8⁄⁄⁄ (À6.34) À3.02 (À0.78)
Wald Chi2-statistic 89.3⁄⁄⁄ 581.1⁄⁄⁄ 172.8⁄⁄⁄ 288.2⁄⁄⁄ 609.3⁄⁄⁄ 684.9⁄⁄⁄ 1734⁄⁄⁄
Durbin Robust Chi2-statistic 18.79⁄⁄⁄ 0.32 29.63⁄⁄⁄ 4.96⁄ 4.04⁄⁄ 0.06 2.91⁄
Wu-Hausman Robust F-statistic 9.39⁄⁄⁄ 0.15 15.22⁄⁄⁄ 2.39⁄ 3.92⁄⁄ 0.06 2.82⁄
Wooldridge Robust F-statistic 7.64⁄⁄⁄ 0.15 13.66⁄⁄⁄ 2.75⁄ 3.27⁄ 0.07 2.20
Notes: All variables are converted into natural logarithm except property tax, landﬁlls and population forecast. The endogenous variables are rental price, housing price, building land price, productivity and
construction costs. Besides the exogenous variables, female population and the number of construction ﬁrms are used as further instrumental variables in the extended version, while for the baseline model female
population is neglected. Estimations are made using the 2SLS method with heteroskedasticity robust standard errors. Z-statistics are in parentheses, the asterisks ⁄⁄⁄, ⁄⁄ and ⁄ denote signiﬁcance at the one percent,
ﬁve percent and ten percent levels, respectively.
Reduced form – spatial lag approach.
Extended model Baseline model
2SLS spatial lag Housing services Housing capital Building land Labor market Housing services Housing capital Building land
Rental price Housing price Land price Income Rental price Housing price Land price
Nursery 0.003 (0.71) À0.012 (À0.09) À0.030 (À0.12) À0.050 (À1.26) 0.069⁄⁄ (2.33) À0.002 (À0.02) 0.262⁄ (1.68)
Population forecast 0.319⁄⁄⁄ (3.96) 0.442⁄⁄ (2.23) 2.722⁄⁄⁄ (7.93) 0.153⁄⁄ (2.13) 0.203⁄⁄⁄ (2.85) 0.445⁄⁄ (2.20) 1.920⁄⁄⁄ (5.58)
HHSize À0.230⁄⁄ (À1.97) 0.113 (0.29) À1.157⁄⁄ (À2.04) 0.226⁄ (1.68) À0.087 (À0.81) À0.151 (À0.44) À0.331 (À0.61)
Property tax 0.023 (0.73) 0.012 (0.13) 0.211 (1.22) 0.051 (1.64) À0.025⁄ (À1.72) À0.042 (À0.98) À0.098 (À1.32)
Construction costs À0.243 (À0.51) À0.235 (À0.15) À0.076 (À0.03) À0.406 (À0.99) À0.135 (À0.31) 0.503 (0.39) 0.568 (0.24)
O. Bischoff / Journal of Housing Economics 21 (2012) 1–15
Independent cities 0.013 (0.45) 0.182⁄⁄ (2.15) 0.431⁄⁄⁄ (3.56) À0.063⁄⁄ (À2.14) À0.025 (À0.93) 0.192⁄⁄ (2.43) 0.235⁄ (1.89)
Area surface 0.100⁄⁄⁄ (2.62) 0.136 (1.35) 0.566⁄⁄⁄ (3.40) 0.040 (1.01) 0.010 (0.57) 0.100⁄ (1.73) À0.015 (À0.17)
Area of settlement À0.205⁄⁄⁄ (À2.70) À0.320⁄ (À1.77) À1.42⁄⁄⁄ (À4.18) À0.111⁄ (-1.69) À0.042 (À1.42) À0.25⁄⁄⁄ (À2.82) À0.343⁄⁄ (À2.31)
Productivity 1.598⁄⁄ (2.22) 1.001 (0.50) 10.45⁄⁄⁄ (2.96) 1.260⁄ (1.81) – – –
Children 0.240⁄⁄ (2.10) À0.034 (À0.12) 1.565⁄⁄⁄ (3.09) 0.047 (0.46) – – –
Income – – – – 0.026 (0.31) 0.148 (0.59) 0.676 (1.48)
Seniors À0.052 (À1.57) 0.203⁄⁄⁄ (2.67) À0.055 (À0.46) 0.110⁄⁄⁄ (3.20) À0.032 (À1.31) 0.105⁄ (1.75) 0.041 (0.40)
Landﬁlls À0.004⁄⁄⁄ (À2.95) 0.004 (0.97) À0.03⁄⁄⁄ (À4.10) À0.002 (À1.08) À0.001 (À1.05) 0.005⁄⁄ (2.39) À0.001 (À0.41)
Foreigners À0.125⁄⁄⁄ (À2.28) 0.044 (0.30) À0.74⁄⁄⁄ (À2.98) À0.077 (À1.45) 0.010 (0.78) 0.099⁄⁄⁄ (2.75) 0.114⁄ (1.83)
Commuting time À0.053⁄⁄⁄ (À3.06) 0.006 (0.12) À0.27⁄⁄⁄ (À3.24) À0.016 (À0.82) À0.021⁄⁄ (À1.96) 0.003 (0.09) À0.054 (À1.15)
Tourism 0.045⁄⁄ (2.49) À0.008 (À0.15) 0.238⁄⁄ (2.47) 0.021 (1.26) 0.013⁄ (1.84) À0.031 (À1.52) 0.035 (0.96)
Doctors 0.214⁄⁄⁄ (6.06) 0.086 (0.07) 0.789⁄⁄⁄ (4.62) 0.113⁄⁄⁄ (2.75) 0.146⁄⁄⁄ (6.72) À0.045 (À0.59) 0.310⁄⁄⁄ (2.99)
Rho 0.656⁄⁄⁄ (17.24) 0.327⁄⁄⁄ (5.83) 0.483⁄⁄⁄ (10.93) 0.454⁄⁄⁄ (7.39) 0.655⁄⁄⁄ (16.87) 0.339⁄⁄⁄ (6.05) 0.492⁄⁄⁄ (11.68)
Intercept À4.187⁄⁄ (À2.17) À0.277 (À0.05) À31.7⁄⁄⁄ (À3.65) 1.528 (0.85) 0.406 (0.96) 0.900 (0.66) À6.697⁄ (À3.36)
N 418 418 418 418 418 418 418
Pseudo R2 0.782 0.591 0.878 0.574 0.777 0.589 0.877
Wald Chi2-test (rho = 0) 297.17⁄⁄⁄ 33.96⁄⁄⁄ 119.48⁄⁄⁄ 54.65⁄⁄⁄ 284.52⁄⁄⁄ 36.63⁄⁄⁄ 136.33⁄⁄⁄
LM Chi2-test (rho = 0) 190.32⁄⁄⁄ 34.69⁄⁄⁄ 142.74⁄⁄⁄ 43.82⁄⁄⁄ 185.91⁄⁄⁄ 38.04⁄⁄⁄ 148.74⁄⁄⁄
Notes: All variables are converted into the natural logarithm except property tax, landﬁlls and population forecast. The endogenous variables are rental price, housing price, building land price, productivity and
construction costs. In addition to the exogenous variables, the female population and the number of construction ﬁrms are used as further instrumental variables in the extended version, while for the baseline
model female population is neglected. Estimations are made using the 2SLS method for spatial lag models with heteroskedasticity robust standard errors. The elements of the spatial weights matrix are 1 if two
districts have the same border, otherwise the elements are 0. Z-statistics are in parentheses, the asterisks ⁄⁄⁄, ⁄⁄ and ⁄ denote signiﬁcance at the one percent, ﬁve percent and ten percent levels, respectively.
14 O. Bischoff / Journal of Housing Economics 21 (2012) 1–15
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