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results (Razen et al. 2014 ). As a second extension, we introduce multiplicative
region-specific scaling factors for nonlinear covariates in order to permit spatial
variation in the nonlinear price gradients. This allows highly nonlinear implicit
price functions to vary within a regularized framework, accounting for district-
specific spatial heterogeneity, which can lead to a considerable improvement of
model quality and predictive power (Brunauer et al. 2010 ). We finally describe
publicly available software to estimate the described complex modeling framework
(Umlauf et al. 2012 ).
5.2
Data Description and Model Specification
We have a dataset of owner-occupied single-family homes in Austria at our disposal
which exhibits a quite typical structure for real estate data:
￿
The set of explanatory variables consists of covariates characterizing the house,
namely, the size, age, year of sale, quality, and equipment of the building, which
we call structural attributes/covariates .
￿
Individual observations are linked to municipality codes, which allows as-
sociation with covariates accounting for sociodemographic, economic, and
neighborhood attributes. Following, for example, Can ( 1998 ), we will call these
neighborhood attributes/covariates .
5.2.1
Structural Attributes
The dataset containing dated house prices together with the housing attributes has
been collected in order to estimate the value of the collateral for mortgages by the
UniCredit Bank Austria AG from October 1997 to September 2009. Two slightly
different instructions for data collection have been employed, which is why the
structural covariates affected thereof are encoded accordingly (see Brunauer et al.
( 2013 ) for a detailed description). We use continuous variables measuring the size
and the age as well as the time of sale and categorical variables that describe the
quality of the house. Guided by economic theory on hedonic house prices, we expect
the following directions of the effects:
￿
Continuous covariates/attributes: As we regress the structural covariates on
logged prices per square meter (sq. m.), a decreasing effect of the floor area of the
building due to decreasing marginal returns of additional floor area ( area )andan
increasing effect of the size of the plot it is built on ( area_plot ) can be assumed.
The age of the building ( age ), which is calculated as the difference between the
year of valuation and the year of construction (i.e., the age at the time of sale),
reflects depreciation over time and should therefore have a decreasing effect.
The time index ( time_index , the year of purchase of the house) can be considered
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