Explaining regional variation in equilibrium real estate prices and income

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					                                                     Journal of Housing Economics 21 (2012) 1–15

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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
Simultaneous equation

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:                              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:
(ECB, 2005).
    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.
  2                                                                                  3
    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.                                                       
   Combining labor demand (13) and supply (14), the
                                                                                   and for house prices see
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:
payments.                                                                          bilien/Wohnungsmarkt/MethodenWerkzeuge/Fachbeitraege/WIMKreisty-
    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
 18               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

Table 1
Data overview.

  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);                    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                                   4325.22    4545.0      794      74,834
  Population +65, seniors             Total                                   36478.18   38977.4     7538     585,313
  Regional price index                Relative scale to Bonn                          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                                   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                                   7464.28    8475.4      1180     126,168
  Foreign population, foreigners      Total                                   16849.2    34547.      572      466,518
  Property tax, t                     In 100%                                 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                                     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                                                 41.58      5.68        27.81    70.75
  Land fills                           Total                                   4.6        7.4         0        67
  Female population, women            Total                                   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                                   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 Š is a 4  n vector of endogenous vari-
and each state. Thus, we calculate the average ratio and as-                     ables, X is a n  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  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  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.
Table 2
Structural form.

                              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.
Table 3
Reduced form.

                                            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.
Table 4
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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Description: We combine the real estate model of Potepan (1996) with the spatial equilibrium approach of Roback (1982) to prove the interdependency of housing prices, rental prices, building land prices and income via one simultaneous equilibrium analysis. Using unique crosssectional data on the majority of German counties and cities for 2005, we estimate the equations in their structural and reduced form. The results show significantly positive 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 price and income disparities between regions in the long term.