# RECORD 7b29c36e620db272e042f7b9f343c676a2038678
# TITLE: Interpretable Machine Learning for Real Estate Market Analysis
# YEAR: 2022.0  VENUE: Social Science Research Network  DOI: 10.2139/ssrn.3835931
# AUTHORS: Felix Lorenz; Jonas Willwersch; Marcelo Cajias; F. Fuerst
# PAGES: 31  CANDIDATE TABLE PAGES (1-based): [11]
# ABSTRACT: Machine Learning (ML) excels at most predictive tasks but its complex nonparametric structure renders it less useful for inference and out-of sample predictions. This article aims to elucidate and enhance the analytical capabilities of ML in real estate through Interpretable ML (IML). Specifically, we compare a hedonic ML approach to a set of model-agnostic interpretation meth-ods. Our results suggest that IML methods permit a peek into the black box of algorithmic decision making by showing the web of associative relationships between variables in greater resolution. In our empirical applications, we confirm that size and age are the most important rent drivers. Further analysis reveals that certain bundles of hedonic characteristics, such as large apartments in historic buildings with balconies located in affluent neighborhoods, attract higher rents than adding up the contributions of each hedonic characteristic. Building age is shown to exhibit a U-shaped pattern in that both the youngest and oldest buildings attract the highest rents. Besides revealing valuable distance decay functions for spatial variables, IML methods


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DOI: 10.1111/1540-6229.12397
O R I G I NA L A RT I C L E
Interpretable machine learning for real estate
market analysis
Felix Lorenz1
Jonas Willwersch1
Marcelo Cajias1,2
Franz Fuerst3
1International Real Estate Business
School (IRE|BS), University of
Regensburg, Regensburg, Germany
2PATRIZIA AG, Augsburg, Germany
3Department of Land Economy and
Trinity Hall, University of Cambridge,
Cambridge, UK
Correspondence
Jonas Willwersch, University of
Regensburg, International Real Estate
Business School (IRE|BS),
Universitaetsstrasse 31, 93053 Regensburg,
Germany.
Email:
jonas.willwersch@wiwi.uni-regensburg.de
Abstract
Machine Learning (ML) excels at most predictive tasks
but its complex nonparametric structure renders it less
useful for inference and out-of sample predictions. This
article aims to elucidate and enhance the analytical
capabilities of ML in real estate through Interpretable
ML (IML). Specifically, we compare a hedonic ML
approach to a set of model-agnostic interpretation meth-
ods. Our results suggest that IML methods permit a
peek into the black box of algorithmic decision mak-
ing by showing the web of associative relationships
between variables in greater resolution. In our empiri-
cal applications, we confirm that size and age are the
most important rent drivers. Further analysis reveals
that certain bundles of hedonic characteristics, such as
large apartments in historic buildings with balconies
located in affluent neighborhoods, attract higher rents
than adding up the contributions of each hedonic char-
acteristic. Building age is shown to exhibit a U-shaped
pattern in that both the youngest and oldest buildings
attract the highest rents. Besides revealing valuable dis-
tance decay functions for spatial variables, IML methods
This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits
use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or
adaptations are made.
© 2022 The Authors. Real Estate Economics published by Wiley Periodicals LLC on behalf of American Real Estate and Urban Economics
Association.
Real Estate Econ. 2022;1–31.
wileyonlinelibrary.com/journal/reec
1


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LORENZ et al.
11
TA B L E 2
Results of the OLS, GAM, and SAR estimation
Dependent variable: log Rent per month
OLS
GAM
SAR
log size in sq.m.
0.939***
(0.002)
0.900***
0.928 ***
(0,008)
Floors
0.002***
(0.0004)
0.003***
(0.0003)
0.003 ***
(0,002)
Age (relative to 2017)
−0.0002***
(0.00003)
s 8.000***
−0.000 ***
(0,0001)
Bathtub
−0.032***
(0.002)
−0.016***
(0.001)
−0.032 ***
(0,006)
Refurbished
−0.015***
(0.002)
0.005***
(0.002)
−0.013 ***
(0,007)
Built-in kitchen
0.084***
(0.002)
0.077***
(0.002)
0.077 ***
(0,007)
Balcony
0.011***
(0.002)
0.025***
(0.002)
0.012 ***
(0,007)
Parking
0.053***
(0.002)
0.032***
(0.002)
0.048 ***
(0,008)
Elevator
0.053***
(0.002)
0.020***
(0.002)
0.048 ***
(0,009)
Terrace
0.041***
(0.002)
0.020***
(0.002)
0.041 ***
(0,009)
log Purchasing Power
0.406***
(0.011)
0.069***
(0.002)
0.313 ***
(0,040)
CBD_distance
−0.019***
(0.001)
s 8.692***
−0.014 ***
(0,002)
Bar_distance
−0.031***
(0.002)
s 8.579***
−0.024 ***
(0,008)
Beergarden_distance
−0.020***
(0.002)
s 8.631***
−0.015 ***
(0,005)
Cafe_distance
−0.014***
(0.003)
s 8.700***
−0.011 ***
(0,010)
Bakery_distance
−0.011***
(0.003)
s 8.842***
−0.016 ***
(0,009)
Convenience store_distance
−0.036***
(0.002)
s 8.144***
−0.035 ***
(0,007)
Department store_distance
−0.006***
(0.001)
s 8.580***
−0.008 ***
(0,005)
Supermarket_distance
−0.018***
(0.006)
s 6.487***
−0.029 ***
(0,020)
Bus station_distance
−0.028***
(0.001)
s 8.794***
−0.017 ***
(0,004)
Railway station_distance
−0.020***
(0.002)
s 8.757***
−0.020 ***
(0,007)
Traffic signals_distance
0.086***
(0.007)
s 8.243***
0.075 ***
(0,024)
Car wash_distance
0.012***
(0.002)
s 8.763***
0.007***
(0.006)
Park_distance
−0.024***
(0.006)
s 8.343***
−0.019***
(0.020)
School_distance
−0.003***
(0.005)
s 8.412***
0.008 ***
(0,006)
Constant
−34.043***
(3.087)
2.405***
(0.100)
−22.860***
(11,359)
rho
0.131***
Time controls
Yes
Yes
Yes
Locational controls
Yes
Yes
Yes
Observations
52,966
52,966
52,966
R2
0.880
0.885
adjusted R2
0.880
0.898
UBRE
0.028
Note: *p < 0.1; **p < 0.05; ***p < 0.01, standard errors are displayed in parentheses. The GAM column reports the estimated
degrees of freedom of the smooth terms (s) as well as their joint significance. Time controls (year and month) as well as location
controls (apartment coordinates) are included in all models.
shows the results of the OLS, GAM, and spatial autoregressive regression (SAR) models. OLS and
SAR display similar coefficients for all variables.
Variables that exhibit nonlinear behavior are included as splines in the GAM with the esti-
mated degrees of freedom of smoothing terms being provided (denoted with “s”). Regarding the
goodness of fit, OLS shows an adjusted R2 of 0.880 and the SAR a R2 of 0.885. The GAM has a


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12
LORENZ et al.
F I G U R E 2
Hyperparameter tuning and model accuracy
Note: The figure displays the root mean square error (RMSE) decline per iteration step. The stacked bars represent boxplots with
the black line indicating the median RMSE value.
Source: Own depiction.
marginally better fit of 0.898, which is likely due to its capability of handling nonlinear relation-
ships. The structural hedonic variables, such as size, floor, and age, are highly significant and
show expected signs. Similar findings are reported by Dumm et al. (2016, 2018) and Seo (2018) for
property prices. The same holds true for the binary variables (kitchen, balcony, parking, elevator,
and terrace). Gröbel and Thomschke (2018) or Stamou et al. (2017) provide analogous results for
rents and prices, respectively. The location variables are also highly significant and show mostly
negative signs, indicating that the smaller the distance to a certain amenity, the higher the rent.
Only distance to car wash facilities and distance to traffic signals are positive, with greater distance
resulting in higher rental values confirming that negative externalities associated with these fea-
tures such as noise and air pollution result in a desire to not live in their immediate vicinity. In
summary, the results presented in Table 2 show that the hedonic approach seems to work, and
thus, justifies a more in-depth ML analysis.
5.2
Nonparametric models and machine learning
To set up a functional ML framework, we first train the XGB algorithm on our dataset of rental
prices described in the data section. We apply random cross-validation with five folds and five rep-
etitions. Appendix B provides additional information on parameter tuning. The final XGB model