Hedonic House Price ModelingBased on Multilevel Structured Additive Regression - Computational Approaches for Urban Environments - page 94

5.1 Introduction

The Basel II and III frameworks strictly define the conditions under which financial
institutions are authorized to accept real estate as collateral in order to decrease
their credit risk, including the evaluation of the properties on a regular basis by
means of statistical methods. A widely used concept here is the hedonic pricing
model (Rosen 1974 ). It assumes that the price of a property can be decomposed into
implicit prices of its attributes, which are estimated in a regression analysis of price
against attributes. Reviews of hedonic price theory in a real estate context can be
found, for example, in Follain and Jimenez ( 1985 ), Sheppard ( 1999 ) or Malpezzi
( 2003 ).
The bundle of attributes characterizing a property involves not only individual
attributes of the building itself but also locational attributes of the region where the
building is located in. Thus, the real estate market intrinsically is spatial; why there
is a vast literature on spatial house price modeling, see, for example, Banerjee et al.
( 2004 ), Cohen and Coughlin ( 2008 ) or Helbich et al. ( 2014 ). Typically, residential
properties belong to several levels of spatial (administrative) units, which turns the
hedonic model into a multilevel or hierarchical regression problem (Gelman and
Hill 2006 ). For instance, in our case study, house selling prices with associated
individual attributes (the elementary level-1) are grouped in municipalities (level-2),
which form districts (level-3), which are themselves nested in counties (level-
4). Available neighborhood covariates on either of these spatial resolutions that
might be important for predicting house prices should be accounted for, and it is
furthermore reasonable to assume that unmeasured neighborhood characteristics
such as local policy and infrastructure affect individual house prices. Another major
problem in hedonic price modeling is that economic theory does not provide clear
guidance concerning the functional form of the dependence of price on character-
istics, which suggests that hedonic pricing models should allow for nonlinearity in
the price functions.
A particularly broad and rich framework for nonlinear and spatial modeling is
provided by generalized structured additive regression (STAR) models, described,
for example, in Fahrmeir et al. ( 2013 ). In STAR models, continuous covariates are
modeled as P(enalized)-splines. Furthermore, random effects for spatial indexes,
smooth functions of two-dimensional surfaces, and (spatially) varying coefficient
terms may also be estimated using this methodology.
The purpose of this chapter is to review recent developments in hedonic modeling
of house prices based on STAR models. More specifically, we describe multilevel
versions of STAR models (Lang et al. 2014 ; Brunauer et al. 2013 ) as our basic
modeling framework and develop a number of extensions. With respect to value-
at-risk concepts, financial institutions are often not only interested in the expected
value but also in different quantiles of the distribution of real estate prices. To meet
these requirements, we apply multilevel STAR models for location scale and shape
(GAMLSS type regression, Klein et al. 2013 ; Rigby and Stasinopoulos 2005 )anda
Bayesian version of quantile regression (Waldmann et al. 2013 ) and compare the