# RECORD 17f8f1569fa95f6eb5e22b566b1a1962d7ce1a43
# TITLE: OBJECTIVE HOUSING SALES AND RENT PRICES IN REPRESENTATIVE HOUSEHOLD SURVEYS: IMPLICATIONS FOR WEALTH, INEQUALITY, HOUSING MARKET, AND AFFORDABILITY STATISTICS
# YEAR: 2024.0  VENUE: The Review of Income and Wealth  DOI: 10.1111/roiw.12692
# AUTHORS: M. Naidin; S. Waltl; Michael H. Ziegelmeyer
# PAGES: 75  CANDIDATE TABLE PAGES (1-based): [9, 15, 18, 20, 26, 30, 52, 71, 72, 74]
# ABSTRACT: Many economic analyses require hypothetical but realistic sales and rent prices for properties representative of the housing stock and reflecting current market conditions. To achieve this, we replace subjectively reported prices in a representative household survey in Luxembourg with objectified hedonic imputations informed by observable market data. Thus, we propose a powerful tool for assessing the health and affordability of housing markets, compiling housing‐related statistics and simulating hypothetical scenarios. This approach also enables us to test for the reliability of survey responses. When switching to objectified values, we detect shifts in the wealth distribution, large regional variation in market indicators, and striking affordability concerns: only 18 percent of Luxembourg's renters could theoretically afford to purchase their inhabited dwellings given current market conditions. Further, participants' tendency to mis‐estimate market values strongly correlates with tenure length and type, dwelling type, income, and wealth.


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Objective Housing Sales and Rent Prices in
Representative Household Surveys: Implications for
Wealth, Inequality, Housing Market and Affordability
Statistics
M. Denisa Naidin∗a,b, Sofie R. Waltl†c,d, and Michael H. Ziegelmeyer‡e
aLuxembourg Institute of Socio-Economic Research (LISER), Luxembourg
bUniversity of Luxembourg, Department of Geography and Spatial Planning, Luxembourg
cUniversity of Cambridge, Department of Land Economy, United Kingdom
dVienna University of Economics and Business, Department of Economics, Austria
eBanque centrale du Luxembourg (BCL), Luxembourg
Abstract
Many economic analyses require hypothetical but realistic sales and rent prices for
properties representative for the housing stock and reflecting current market conditions.
To achieve this, we replace subjectively reported prices in a representative household
survey in Luxembourg by objectified hedonic imputations informed by observable market
data. Thus, we propose a powerful tool for assessing the health and affordability of housing
markets, compiling housing-related statistics and simulating hypothetical scenarios. This
approach also enables us to test for the reliability of survey responses. When switching to
objectified values, we detect shifts in the wealth distribution, large regional variation in
market indicators and striking affordability concerns: only 18% of Luxembourg’s renters
could theoretically afford purchasing their inhabited dwelling given current market con-
ditions. Further, participants’ tendency to mis-estimate market values strongly correlates
with tenure length and type, dwelling type, income and wealth.
Keywords: Representative Surveys; Housing Sales and Rent Markets; Housing Wealth; Affordability; Housing
Statistics; Measurement Errors
JEL codes: C83; R21; R31.
∗ORCID: 0000-0001-7529-0602
†Corresponding author: Sofie R. Waltl; 19 Silver Street, Cambridge, CB3 9EP, UK; sw2123@cam.ac.uk;
www.sofiewaltl.com; ORCID: 0000-0003-2526-3838
‡ORCID: 0000-0001-9867-0448


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course, a better unbiased AVM, in the sense of having a lower mean squared error of prediction
across the relevant properties, would still be preferable to a worse (noisier) unbiased AVM, as
it would yield a less noisy aggregate.” In this spirit we perform a wide range of statistical tests
to make our model fit for purpose. These tests are documented in subsection 3.1 and may be
used as guidelines for future research.
We next present the main data used and perform some validation steps before section 3 performs
the actual matching between them.
2.2
The LU-HFCS
The LU-HFCS is part of the Pan-European HFCS initiative conducting ex-ante harmonised
wealth surveys across Europe.
In the 3rd wave of the LU-HFCS conducted in 2018, 1,616
households have participated (see Chen et al., 2020).
Responses are population-weighted.7
Table 1 reports summary statistics.
Table 1 – Summary Statistics: Dwelling Characteristics – HFCS
Surface
Plot sizea
Tenure length
Construction
No. of
Monthly Rentb
Current Valueb
[m2]
[m2]
[years]
Year
Bedrooms
[EUR]
[EUR]
All tenure statuses.
Median
125.00
500.00
10.00
1985
3.00
1,500
600,000
Mean
139.48
1,028.99
15.32
1974
3.39
1,696
642,660
Std. Dev.
80.93
7,663.39
14.93
40.37
1.79
885
457,772
Owner-occupiers.
Median
146.80
500.00
15.00
1984
4.00
1,800
652,000
Mean
163.54
1,104.31
18.91
1974
3.89
1,996
747,151
Std. Dev.
81.54
8,218.12
15.81
40.19
1.73
849
432,997
Renters.
Median
80.00
345.20
4.00
1985
2.00
950
350,000
Mean
85.93
531.42
7.33
1974
2.28
1,031
410,048
Std. Dev.
46.60
551.83
8.34
40.80
1.37
531
424,992
Notes: The table reports summary statistics related to the household main residence (HMR). Measures are derived respecting
survey weights.
a The plot size is only available for houses and not for apartments.
b Prices and rents are reported by survey participants.
Source: LU-HFCS, 3rd wave.
The HFCS routinely asks owner-occupiers to estimate their home’s current market price.
Renters, in contrast, report the currently paid monthly rent. While the former reflects subjec-
7The construction of the final population weights of the LU-HFCS follows the principles outlined by the
Household Finance and Consumption Network (HFCN, 2020, section 5).
The precise weighting procedure
applied for the LU-HFCS is described in Chen et al. (2020, section 5.8) and Girshina et al. (2017, section 2.6.4).
With the best available sampling frame in Luxembourg, the Social Security Register, we still miss around 10%
of the population including households exclusively consisting of international civil servants and (standard for
household surveys) collective households such as, for instance, homes for the elderly.
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tive beliefs, the latter could be affected by reporting errors but not subjectivity. It is important
to note that survey participants are, in general, no experts when it comes to real estate markets.
Albeit people interested in buying or selling real estate are likely to gather extra information
by observing the market and gathering expert advise from real estate professionals, such costly
endeavours are very unlikely to be undertaken when preparing for a survey interview. Thus,
responses arguably reflect subjective beliefs and potentially also wishes.
Exclusively, the 3rd wave of the LU-HFCS contains questions about hypothetical prices, as well
as hedonic (physical and locational) characteristics of the main residence. Regarding the for-
mer, owner-occupiers are asked for a hypothetical monthly rent they believe could realistically
charge to a new tenant, and all respondents regardless of their own tenure status are tasked to
estimate a hypothetical current market sales price (see subsection C.2). Regarding the latter,
several physical characteristics have been retrieved during the survey interview or added by
the interviewer directly. As interviews are usually conducted at the interviewee’s homes and,
thus, the interviewer observes the described dwelling, reporting errors for standard hedonic
characteristics are expected to be rather minor.
The following physical characteristic are retrieved as part of the survey interview: surface,
type of residence, plot size, year of construction, number of bedrooms and the energy class.
The survey interviewer provides an additional assessment of the structure and neighbourhood.
Further, we record the postcode. Luxembourg has a strikingly detailed postcode system: while
small municipalities share one code, in Luxembourg City (almost) every street has a separate
code. Longer streets are even split into several ones. Overall, there are 4,022 regular postcodes
in a country of 2,586 km2 and roughly 600,000 residents.8
This additional information allows us to impute realistic market values retrieved from a hedonic
valuation model for all dwellings described in the survey. We do so for both owner-occupiers
(69%) and renters or households using their residence free of charge (31%).
Some personal characteristics of the interviewee we use for compiling for instance affordability
measures refer – if not stated differently – to the financially most knowledgeable person in the
household who acts as main interview partner (reference person). The LU-HFCS data set is
8See the Luxembourg Data Platform for population sizes per postcode: https://data.public.lu/en/
datasets/population-par-code-postal-population-per-postal-code (last accessed on January 11, 2021).
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Table 3 – Adverts vs. Notary Deeds
Adverts
Notary Deeds
Price per unit [EUR/m2]
Q1
4,774.81
4,227.05
Median
5,748.91
5,188.47
Mean
6,462.81
5,550.55
Q3
7,506.32
6,475.64
IQR
2,731.51
2,248.59
Std. Dev.
2,364.86
2,024.04
Dwelling surface [m2]
Q1
71.00
70.00
Median
87.16
84.66
Mean
91.65
88.46
Q3
106.00
101.35
IQR
35.00
31.35
Std. Dev.
31.63
29.67
Number of Observations
8,381
4,737
Notes: The table reports summary statistics for advertisements and notary deeds for characteristics reported in both sources. The
data refers to flats advertised or sold (registered as for own use) in Luxembourg in 2018. Q1 and Q3 abbreviate quartiles.
Source: Luxembourg’s Housing Observatory.
we pool all adverts appearing during our study period and all deeds recorded at notaries in the
same period.
We perform two tests: First, we check whether relying on adverts would mean a change in the
structure of market data and, second, we measure maximal price differences between advertised
and finally recorded prices by comparing prices per square meter between the two sources.
For checking the first, the two prices are related to each other via (unpaired) Pearson correlation
coefficients. As result, we obtain ρ = 98.38% and, thus, reassuringly document almost perfect
co-movement of prices reported in the two sources.
Concerning the second, we assess prices and dwelling surface (in square meters). Both, the price
and surface distributions are, as a whole, shifted downwards in notary deeds data as compared
to advertisements. Magnitudes are reported in Table 3. While the shifts are significant in
statistical terms14 the differences are minor in economic terms: the median price per square
meter recorded by notary deeds is merely EUR 560 (or roughly 10%) lower.
14According to a one-sided Mood’s median test, the values reported in advertisements are statistically sig-
nificantly higher at the 5% level. Furthermore, a Mann-Whitney U Test is significant at the 1% level indicating
that the two populations are nonidentical level-wise.
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Overall, the price differential appears to be a minor concern here as compared to the other
drawbacks of notary deeds discussed above.
2.5
Comparing Market and Survey Data
Table 1 describes dwelling characteristics as reported in the HFCS and Table 2 reports sum-
mary statistics for advertised units. HFCS statistics are population-representative and thus
a comparison reveals differences between the current residential housing stock and the mix of
dwellings currently on the market. One key insight from this comparison is that the mean and
median age of main residences of renters and owner-occupiers are almost identical.
Looking at differences by tenure status, we find overall similar deviations: dwellings for sale or
already owner-occupied are on average substantially larger than those rented.
While rented properties in the two sets are comparable in size, properties owned/sold appearing
in the pool of advertised properties are noticeably smaller (fewer bedrooms per property and
smaller plot sizes) and are less likely to come with additional private outside space (e.g., a
garden) than existing residences of HFCS respondents.
3
Imputing Market Prices
3.1
Imputation Strategy
In the following, we sketch out our model selection procedure. Appendix A provides compre-
hensive methodological details.
Our imputation model follows a standard hedonic pricing equation and thus we regress sales or
rent prices on physical and locational characteristics. Acknowledging the skewness in the price
distributions, we follow common practise here and use a log-transformation.
Precisely, we estimate separate models for sales and rent data and regress logged sales P S
h ∈Rn
s
or logged monthly rent P R
h
∈Rn
r prices observed during the survey’s fieldwork period for
dwellings h = 1, . . . , n on a set of corresponding characteristics.
Both models follow the same general structure yet refer to either rent or sales data indicated
by the different response variables P tenure
h
, while tenure differentiates between S sales and R
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Table 4 – Hedonic Model Specifications
Main Model
Alt. 1
Alt. 2
Alt. 3
Alt. 4
Physical characteristics





Interactions





Locality Dummies





Distance to Capital





Linked Neighbour Spline





Notes: Physical characteristics comprise all match-able characteristics specified in Table A.1 except location. Interactions between
dwelling type and surface as well as between construction period and energy class are included in three of the models. Locality
means dummy variables hinting towards the composite geography obtained from combining municipalities with the neighbourhood
level for the two largest urban areas in the country. The distance to the capital is retrieved from Glaesener and Caruso (2015).
The linked neighbour spline employs smooth terms linking neighbouring entities of the composite geography.
To check the models’ performance, we assess four dimensions: First, we plot imputed versus
observed market prices. Reassuringly, Figure 2 shows strong correlations. Pearson correlation
coefficients are large and positive, indicating co-movement for both sales (87.19%) and rent
(85.83%) prices. Thus, all our models replicate the original price distribution quite well. Second,
Table 5 reports results of standard goodness-of-fit measures (adjusted R2, AIC and BIC).
The main models outperform the four alternative specifications according to most measures
considered. Third, we assess the models’ predictive power by comparing overall median/mean
Table 5 – Goodness-of-fit Assessment
Adjusted R2
AIC
BIC
Sales models.
S.Main
0.824
-4,962.48
-3,783.79
S.Alt.1
0.703
2,282.41
2,509.08
S.Alt.2
0.819
-4703.96
-4039.10
S.Alt.3
0.809
-3,820.68
-2,725.11
S.Alt.4
0.507
9,414.07
9,550.08
Rent models.
R.Main
0.744
-1,219.10
-164.11
R.Alt.1
0.679
307.96
514.81
R.Alt.2
0.728
-886.18
-624.54
R.Alt.3
0.742
-1,153.16
-174.02
R.Alt.4
0.526
3,160.34
3,284.46
Notes: The table reports goodness-of-fit measures for all hedonic models considered. AIC means the Akaike information criterion
and BIC the Bayesian information criterion.
Source: Authors’ calculations based on data from the Housing Observatory, on advertisements available between 1 January and 31
December 2018.
absolute errors (MedRE/MAE) and the median/mean relative errors (MedAE/MAE) for sales
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Figure 2 – Correlation Between Imputed and Observed Prices.
Notes: The figure depicts observed and imputed market data for (a) sales and (b) rents prices using the models (S.Main) and
(R.Main).
Source: Authors’ calculations based on data from the Housing Observatory, on advertisements available between 1 January and 31
December 2018.
S or rent R prices:
MAE(S ∨R) = 1
n
n
X
i=1
 ˆP S∨R
i
−P S∨R
i
 and MRE(S ∨R) = 1
n
n
X
i=1

ˆP S∨R
i
P S∨R
i
−1
 ,
MedAE(S ∨R) = Median
 ˆP S∨R
i
−P S∨R
i
 and MedRE(S ∨R) = Median

ˆP S∨R
i
P S∨R
i
−1
 .
(2)
We assess the models’ predictive power following an out-of-sample (OoS) and within-sample
(WS) procedure: for the first, we re-estimate the hedonic models leaving out 20% (i.e., 4,284)
of all observations based on geographically-stratified random sampling and use the resulting
reduced models to predict sales prices ˆP S and rents ˆP R via plug-in estimators. We compare
the predicted values for these 4,284 units using the full and restricted model, respectively, and
assess the ratio between the two. A MAE close to one and a MRE close to zero suggest that
a respective model works well also for bundles of characteristics not necessarily found in the
original estimation sample. This is important as we use the models for predicting prices for
dwellings that are by definition offthe market and thus not used to train the model.
Table 6 reports the results: OoS and WS MAEs are comparable in size, reflected in ratios
close to one. By construction, OoS errors are expected to be larger than WS errors. This is
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Table 6 – Predictive Power
Out-of-sample (OoS)
Within-sample (WS)
Ratio
Difference
MAE
MRE
MAE
MRE
of absolute
of relative
(MedAE)
(MedRE)
(MedAE)
(MedRE)
errors
errors
S.Main
109,688.7
0.1483
108,038.6
0.1465
1.0152
0.0018
(61,288.5)
(0.1063)
(61,256.5)
(0.1055)
(1.0005)
(0.0008)
S.Alt.1
147,367.9
0.2062
146,576.8
0.2057
1.0053
0.0004
S.Alt.2
116,955.8
0.1596
109,910.5
0.1490
1.0641
0.0105
S.Alt.3
119,256.4
0.1587
117,503.1
0.1569
1.0149
0.0018
S.Alt.4
195,999.4
0.2726
195,315.8
0.2723
1.0034
0.0002
R.Main
261.65
0.1503
252.39
0.1441
1.0368
0.0061
(161.00)
(0.1102)
(154.50)
(0.1083)
(1.0420)
(0.0019)
R.Alt.1
305.64
0.1757
298.09
0.1710
1.0253
0.0047
R.Alt.2
272.68
0.1570
265.95
0.1528
1.0253
0.0042
R.Alt.3
262.38
0.1513
255.41
0.1457
1.0272
0.0055
R.Alt.4
380.33
0.2232
376.34
0.2198
1.0106
0.0033
Notes: Out-of-sample (OoS) and Within-sample (WS) mean absolute errors (MAEs) and mean relative errors (MREs) are computed
for units for rent and sale following formula (2). The smaller MRE and MAE, the better the predictive power. We relate the two
measures to each other by computing ratios MAE(OoS)/MAE(WS) for absolute measures and distances MRE(OoS)-MRE(WS) for
relative measures reported in the last two columns. We also include in brackets figures on the median relative errors for the main
models to give a clearer picture of the shape of the error curves.
Source: Authors’ calculations based on data from the Housing Observatory, on advertisements available between 1 January and 31
December 2018.
indeed the case reflected by the ratio of OoS to WS errors being consistently larger than – but
reassuringly very close to – one.
The mean relative prediction error for dwellings excluded from the estimation sample amounts
to roughly 15%. Hence, we must expect an error margin of this size when imputing sales and
rent prices for survey observations. Therefore, we use this margin as a lower bound to identify
over- or under-reported values as detailed in subsection 3.2.
Finally, we examine residuals in detail to detect potential biases.
On average, our models
predict slightly lower sales and slightly higher rent prices than observed ones, however, the
median residual is almost zero (the main model yields an average residual of 0.00259 for sales
prices and of -0.00265 for rent prices). Thus, the models are on average not completely free of
bias, but its expected size is very small and hardly varies across model specifications.
Yet, the models may also be affected by bias in other dimensions.
As, further on, distri-
butional effects will be studied, we check for bias along proxies for the income and wealth
distributions, namely observed sales and rent price distribution. As housing assets are usually
households’ most important single wealth component (see, for instance, Causa et al., 2019),
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Figure 3 – Residuals along the Sales and Rent Price Distribution.
Notes: The figure plots observed market data for (a) sales and (b) rents prices against associated residuals retrieved from models
(S.Main) and (R.Main).
Source: Authors’ calculations based on data from the Housing Observatory, on advertisements available between 1 January and 31
December 2018.
plotting residuals along the sales price distribution comes close to a plot along the wealth
distribution. Similarly, rent payments correlate with income as monthly rent payments are –
generally speaking – restricted by monthly disposable income. For the main models, Figure 3
plots residuals along the observed sales and rent price distributions. Absolute unbiasedness
would mean that residuals perfectly cluster around the horizontal lines.
Throughout large parts of the distributions this is indeed the case. Only at the very bottom
of the distributions prices deviate more. Thus, our predictions are most accurate outside the
lowest price segment.
Furthermore, we assess residuals by the most important price-determining characteristic: loca-
tion. That checks whether imputations systematically deviate in certain areas of the country.
Figure 4 shows residuals per canton retrieved from the main models (S.Main) and (R.Main).
The width of interquartile ranges is quite similar across cantons and consistently overlaps
zero. This holds true even when assessing the much more fine-grained split by our composite
geography roughly corresponding to municipalities as reported in Figure C.1 in Appendix C.
We perform two additional robustness checks: first, we estimate the main specifications as
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Table 8 – Key Estimation Results
Over-reporting
Under-reporting
Response: mis-reported by
10%
15%
10%
15%
Intercept
1.032
0.521
0.980
0.447**
(-0.642)
(-0.323)
(0.310)
(0.147)
Housing status
Owner
(ref. cat.)
Renter
2.571**
2.975**
3.275***
4.434***
(-1.091)
(-1.291)
(0.878)
(1.203)
Education level
Low
(ref. cat.)
Medium
0.931
0.884
0.796
0.714*
(-0.231)
(-0.202)
(0.168)
(0.138)
High
1.031
1.002
1.000
0.868
(-0.288)
(-0.246)
(0.259)
(0.187)
Net income
Q1
(ref. cat.)
Q2
0.630
0.722
0.714
0.767
(-0.240)
(-0.343)
(0.229)
(0.265)
Q3
0.436
0.382
0.465**
0.413**
(-0.206)
(-0.203)
(0.155)
(0.137)
Q4
0.424**
0.455**
0.321***
0.330***
(-0.150)
(-0.167)
(0.096)
(0.098)
Q5
0.518
0.516
0.333***
0.311***
(-0.210)
(-0.250)
(0.120)
(0.115)
Net wealth
Q1
(ref. cat.)
Q2
1.769
1.448
1.733*
1.569
(-0.845)
(-0.627)
(0.570)
(0.481)
Q3
1.290
1.031
0.993
0.914
(-0.611)
(-0.459)
(0.344)
(0.269)
Q4
2.040
1.644
0.576
0.510**
(-1.012)
(-0.705)
(0.193)
(0.163)
Q5
4.570***
4.133***
0.521*
0.501*
(-2.287)
(-1.942)
(0.201)
(0.181)
Type of HMR
House
(ref. cat.)
Apartment
0.774
0.615**
2.781***
2.558***
(-0.201)
(-0.149)
(0.583)
(0.421)
Surface of HMR
0.998
0.998*
1.003**
1.002***
(-0.002)
(-0.001)
(0.001)
(0.001)
Years since acquisition [log]
1.170
1.261*
1.234**
1.342***
(-0.146)
(-0.162)
(0.107)
(0.119)
Interviewer rating: exterior conditions
mid-range, modest or low-income
(ref. cat.)
luxury or upscale
1.247
1.482**
0.539***
0.588***
(-0.202)
(-0.253)
(0.082)
(0.091)
Interviewer rating: interior conditions
good, fair, poor or not seen
(ref. cat.)
excellent
0.824
0.869
0.475***
0.481***
(-0.195)
(-0.211)
(0.096)
(0.075)
Canton
Countryside
(ref. cat.)
Luxembourg City
0.524***
0.458***
1.970***
1.802***
(-0.124)
(-0.109)
(0.388)
(0.322)
Esch sur Alzette
0.640**
0.668**
0.665**
0.620***
(-0.121)
(-0.118)
(0.112)
(0.100)
Notes: The models regress deviation between reported and imputed prices on dwelling and household characteristics.
Models
(1) −(5) refer to distinct specifications.
We distinguish two response variables describing the deviation between imputed and
observed current values of the HMR. Over-reporting and under-reporting, respectively, means that the reported value diverges by
±10% or ±15% from the imputed one. Q1 to Q5 denote first to fifth quintiles. Models are estimated on the full LU-HFCS data
(1,616 observations). Significance is indicated using standard notation: ∗p-value<0.1; ∗∗p-value<0.05; ∗∗∗p-value<0.01.
Source: LU-HFCS, 3rd wave and authors’ calculations.
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The tenure status, renting versus owner-occupying, turns out to be a prime predictor: Renters
tend to be much more likely to mis-estimate the market value of their home and less likely to
report prices close to the ones suggested by the hedonic model. Households at the top of the
net wealth distribution are more likely to over-report and less likely to under-report relative
to imputed values. Likewise, higher household income is associated with a lower likelihood to
mis-estimate.
In terms of education, we document a lower likelihood to mis-report for persons with medium
or high formal educational attainment. However, the estimated coefficients are only significant
for under-reporting and a medium education level.
4
Implications for Wealth, Inequality, Housing Market and Afford-
ability Statistics
4.1
Net Wealth, Residential Housing Wealth and its Distribution
Switching from reported to imputed values means an adjustment of the measured value of the
current residential housing stock and net wealth at current market prices. These computations
may be particularly helpful for filling gaps in Luxembourg’s canon of official statistics. STATEC
conducts an annual survey to update statistics on the current housing stock. A questionnaire is
sent to every registered owner of newly constructed dwellings. However, only construction costs
are collected, which are usually far from market sales prices.17 In addition, in the non-financial
accounts dwellings (ESA, 2010, code: AN.111) and land underlying buildings and structures
(ESA, 2010, code: AN.2111) are currently not distinguishable between households and non-
profit institutions serving households (NPISHs). There are no reliable estimates of the current
market value of the residential housing stock owned by private households (see also EG-LMM,
2020).
We define net wealth for household h at time t as
Net Wealthht = Real Assetsht + Financial Assetsht −Liabilitiesht.
(5)
17 For details see http://www.statistiques.public.lu/stat/TableViewer/document.aspx?ReportId=
13442&IF_Language=eng&MainTheme=4&FldrName=4&RFPath=35 (Last accessed October 21, 2021).
25


===== PAGE 30 (score 16, numeric-paren 0, table-words 4, var-words 5) =====

distributions is squeezed.
Table 10 – Changes in Net Wealth Distribution
Imputed
Q1
Q2
Q3
Q4
Q5
Total
Reported
Q1
19.65
0.42
0.00
0.00
0.00
20.07
Q2
0.41
16.00
2.97
0.58
0.08
20.04
Q3
0.00
3.41
12.44
3.86
0.23
19.94
Q4
0.00
0.11
4.32
12.84
2.75
20.02
Q5
0.00
0.02
0.29
2.72
16.91
19.94
Total
20.06
19.97
20.01
20.00
19.96
100.00
Notes: For the complete sample (owners and renters), the table reports the percent of observations changing quintile in the net
wealth distribution due to the imputation. Figure C.4 presents these results graphically.
These quite significant changes indicate that an objective evaluation does not simply shift the
entire distribution but reveals differential effects along several dimensions. This can lead to
changes in wealth decompositions such as, e.g., distributional national accounts (see EG-LMM,
2020; Waltl and Chakraborty, 2022; Waltl, 2022). The impact is likely larger for countries with
a significant share of owner-occupiers. For purely illustrative purposes, applying the shifts along
the wealth and income distribution identified in Luxembourg to other countries participating
in the HFCS provides an indication of how important reporting issues could be.
For this hypothetical analysis of other countries, we take country-specific total residential hous-
ing wealth and owner-occupation rate, and apply Luxembourg’s measured mis-reporting rates
per wealth and income18 quintile to owner-occupiers in other countries. To obtain a full wealth
measure, we then subtract reported residential housing wealth from total wealth and plug in
the adjusted equivalent. Appendix B describes the compilation steps applied.
Results are compiled by first adjusting quintile-specific wealth for owner-occupiers. The pro-
portion of owner-occupiers varies widely across countries in the European HFCS (ranging from
43.9% in Germany to 88.8% in Slovakia in 2018). Indeed, the relation between owner-occupation
rate and the change in net wealth is statistically significant as reported in Table 11.
Therefore, we select four HFCS countries that represent different realities in this regard. This
includes the countries with the lowest (Germany) and the highest (Slovakia) proportion of
18The harmonised HFCS core questionnaire only asks for gross household income. For Luxembourg, the
Pearson correlation coefficient between gross and net household income is ρ ≈0.8.
28


===== PAGE 31 (score 16, numeric-paren 0, table-words 6, var-words 4) =====

owner-occupiers, as well as two with intermediate shares (France and Italy). We expect changes
to be larger for countries with a larger share of owner-occupiers.
Table 11 – As-if analysis
Germany
France
Luxembourg
Italy
Slovakia
Owner-occupation Rate [%]
43.9
57.9
69.0
68.5
88.8
Change in Net Wealth [%]
3.28
3.49
3.56
3.89
4.20
ρ
93.76% (p-value: 0.0185)
Notes: The table reports changes in measured total net wealth for four European countries increasingly ordered by the change
in net wealth when applying mis-reporting shares found for Luxembourg. ρ measures the Pearson correlation between changes
in measured total net wealth and the owner-occupation rate across countries. The p-value reports results of a Pearson’s product-
moment correlation test for H0 : ρ = 0 rejected at the 5% level. See Appendix B for computational details.
Source: HFCS, 3rd wave.
Table B.2 in the appendix reports full results. In general, the adjustment factors computed for
Luxembourg lead to a small decrease in inequality and a large increase in overall wealth. As
reported in Table 11, total net wealth is most affected in Slovakia, which also had the largest
share of owner-occupiers. At the other extreme, total net wealth is least affected in Germany,
which had the lowest share of owner-occupiers. This finding suggests that wealth distributions
may be poorly measured in countries with large shares of owner-occupiers or large shares of
residential housing in overall wealth. Given the very large amounts at play even small shifts –
whenever found to be systematic – imply large aggregate impacts.
4.2
Housing Market Indicators
Common housing market measures include the price-to-rent (PR) ratio, price-to-income (PI)
ratio, and the rent-to-income (RI) ratio. PI and RI ratios are widely used affordability measures:
A high RI ratio implies households spend a large share of monthly earnings on rent payments.
A high PI ratio suggests low affordability. The PR ratio is considered a measure of investment
potential and the sustainability of the housing market: a high ratio suggests that sales prices are
high compared to potential returns, i.e., rents. This implies high expected future house prices
according to the user cost model for durable goods (Hicks, 1975).
For residential housing,
Himmelberg et al. (2005) show that in equilibrium the cost of buying and using a housing unit
for a period (the sales price Pt multiplied by the per-dollar user cost ut) should equal the total
rent for the same period (Rt): Rt = ut · Pt, where ut includes the interest rate, maintenance
and average transaction costs, the depreciation rate for housing, a risk premium for owning as
29


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A.3
Imputation Models
We estimate the hedonic model (1) relying on all linkable predictors (re-)coded as described
in Table A.1. The model’s performance is slightly improved (increase in adjusted R2 by one
percentage point) when excluding five influential statistical outliers from the sales data set
identified via Cook’s distance (see Cook, 1977). Table A.2 reports estimation results.
Table A.2 – Hedonic Regression Results
log(P S)
log(P R)
(S.Main)
(S.Alt.1)
(S.Alt.2)
(S.Alt.3)
(S.Alt.4)
(R.Main)
(R.Alt.1)
(R.Alt.2)
(R.Alt.3)
(R.Alt.4)
Intercept
12.104***
12.469***
12.25***
12.347***
12.446***
6.276***
6.834***
12.252***
6.456***
6.684***
(0.037)
(0.020)
(0.016)
(0.037)
(0.019)
(0.160)
(0.038)
(0.016)
(0.158)
(0.032)
Dwelling characteristics.
Type of Dwelling
Flat
(ref. cat.)
House
0.493***
0.543***
0.488***
0.031***
-0.103***
0.265***
0.310***
0.488***
0.239***
0.082***
(0.014)
(0.018)
(0.014)
(0.006)
(0.009)
(0.025)
(0.027)
(0.014)
(0.012)
(0.016)
Surface
0.006***
0.007***
0.006***
0.003***
0.003***
0.004***
0.004***
0.006***
0.004***
0.004***
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
Plot size
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
Construction year
pre 1950
(ref. cat.)
1950-1969
0.089***
0.134***
0.093***
0.066***
0.051**
0.228***
0.120**
0.093***
0.042 .
-0.020
(0.014)
(0.018)
(0.014)
(0.010)
(0.016)
(0.036)
(0.037)
(0.014)
(0.022)
(0.029)
1970-1989
0.118***
0.229***
0.119***
0.078***
0.223***
0.2035***
0.1091*
0.119***
0.028
-0.0641*
(0.022)
(0.028)
(0.022)
(0.012)
(0.018)
(0.043)
(0.045)
(0.022)
(0.024)
(0.031)
1990-1999
0.162***
0.192***
0.164***
0.118***
0.088***
0.266**
0.0380
0.164***
0.037
-0.145***
(0.038)
(0.049)
(0.038)
(0.013)
(0.020)
(0.099)
(0.107)
(0.038)
(0.026)
(0.034)
2000-2009
0.146*
0.196*
0.140 .
0.113***
0.102***
0.292*
0.155
0.140 .
0.054*
-0.111***
(0.073)
(0.094)
(0.073)
(0.012)
(0.019)
(0.119)
(0.128)
(0.073)
(0.024)
(0.031)
2010-2020
0.216
0.330
0.205
0.040***
0.028
0.296**
0.288*
0.205
0.078**
-0.024
(0.203)
(0.262)
(0.204)
(0.011)
(0.018)
(0.105)
(0.116)
(0.204)
(0.024)
(0.032)
Number of bedrooms
1
(ref. cat.)
2
0.143***
0.100***
0.143***
0.242***
0.181***
0.119***
0.112***
0.143***
0.120***
0.092***
(0.006)
(0.008)
(0.006)
(0.005)
(0.009)
(0.006)
(0.007)
(0.006)
(0.006)
(0.008)
3
0.182***
0.122***
0.183***
0.375***
0.320***
0.165***
0.146***
0.183***
0.166***
0.154***
(0.008)
(0.011)
(0.008)
(0.006)
(0.010)
(0.010)
(0.011)
(0.008)
(0.009)
(0.013)
4+
0.226***
0.150***
0.224***
0.419***
0.372***
-0.137***
-0.135***
0.224***
-0.145***
-0.109***
(0.010)
(0.013)
(0.010)
(0.008)
(0.013)
(0.009)
(0.010)
(0.010)
(0.009)
(0.012)
Energy Efficiency Class
low (H-I)
(ref. cat.)
medium (E-G)
0.063***
0.083***
0.068***
0.032***
0.155***
0.317***
0.250***
0.068***
0.032**
0.243***
(0.019)
(0.024)
(0.018)
(0.006)
(0.010)
(0.045)
(0.048)
(0.018)
(0.010)
(0.012)
high (A-D)
0.157*
0.268***
0.141*
0.132***
0.217***
0.358***
0.285*
0.141*
0.123***
0.290***
(0.061)
(0.077)
(0.060)
(0.007)
(0.011)
(0.106)
(0.116)
(0.060)
(0.013)
(0.016)
Dwelling State
planned
(ref. cat.)
new-build
0.009
-0.043*
0.003
0.016
-0.021
-0.006
-0.029
-0.005
0.004
0.003
(0.014)
(0.018)
(0.014)
(0.015)
(0.024)
(0.019)
(0.022)
(0.014)
(0.020)
(0.026)
good
-0.032***
-0.085***
-0.038***
-0.044***
-0.065***
-0.033**
-0.020 .
-0.038***
-0.039***
0.040**
(0.007)
(0.009)
(0.007)
(0.007)
(0.011)
(0.010)
(0.011)
(0.007)
(0.010)
(0.013)
average
-0.054***
-0.078***
-0.059***
-0.058***
-0.073***
-0.059***
-0.052***
-0.059***
-0.063***
-0.038***
(0.005)
(0.006)
(0.005)
(0.005)
(0.008)
(0.008)
(0.009)
(0.005)
(0.008)
(0.011)
Interactions
Dwelling Type × Surface
-0.003***
-0.004***
-0.003***


0.000
0.000
-0.003***


(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
Construction Year × Energy Class










Geographical characteristics.
Locality Dummies









Distance to Capital

-0.014***




-0.013***



(0.000)
(0.000)
Linked neighbour Spline










Notes: P S and P R denotes the advertised sales or monthly rent price, respectively. Coefficients for single localities are left out.
We indicate in- and exclusion of a (set) of variables by and , respectively. Significance is indicated using standard notation: .
p-value<0.1; ∗p-value<0.05; ∗∗p-value<0.01; ∗∗∗p-value<0.001.
Source: Authors’ calculations based on data from the Housing Observatory, on advertisements available between 1 January and 31
December 2018.
6


===== PAGE 53 (score 16, numeric-paren 0, table-words 2, var-words 12) =====

As we impute prices for dwellings per construction not part of the training sample, we estimate
the potential imputation error from an OoS prediction check. Therefore, we leave out randomly
selected 20% of the data used for validation applying geographically stratified random sampling.
The selected hedonic model is subsequently used to impute sales and rent prices for each
dwelling described in the HFCS survey. For this article, we added several questions describing
the physical features of the main residence as well as a question about its location. For questions
where the respondents refused to answer, five multiply imputed implicates are introduced. For
apartments no plot size is reported. The following physical dwelling characteristics elicited in
the HFCSA.8 are used to impute prices, after ensuring that they are transformed into the same
scales/categories used for the Housing Observatory model: dwelling type (hlb0100), dwelling
surface (hb0100), plot surface (hlb0200x), year of construction (hlb0210), number of bedrooms
(hlb0310), energy score (hlb0410) and dwelling status (sc0400). See Table A.1 for details.
As locational measure, we elicit a postcodes (hl0100) in the course of the LU-HFCS survey in-
terview. Luxembourg features an exceptionally fine grained postcode system: There are 4,022
postcodes, with a maximum population per postcode of 1,500. On average, there are only
158 persons per code.A.9 Yet, the codes have the distinct disadvantage of occasionally crossing
administrative boundaries at neighbourhood and municipal levels. We therefore convert the
post codes into our composite geography by applying a juxtaposition strategy in QGIS: the
geographical centroids of postcodes are superimposed to the boundaries of our composite ge-
ography. For postcodes that fall across municipal lines, the centroids cover municipal sections
of the shared postcode; consequently, the resulting enhanced attribute table allocates multiple
municipalities to single postcodes that cover residences in different administrative units.
This non-unique allocation is acknowledged by using the five implicates of the HFCS dataset.
The dwelling is allocated randomly between the neighbourhoods or municipalities across these
five implicates so that the uncertainty is properly reflected in our estimates.
A.8Item codes follow the EU-wide harmonised coding scheme whenever applicable; and Luxembourg-specific
codes for amended questions. See Household Finance and Consumption Network (2020).
A.9See https://data.public.lu/en/datasets/population-par-code-postal-population-per-postal-code/
(Last accessed November 9, 2021)
7


===== PAGE 71 (score 191, numeric-paren 158, table-words 1, var-words 7) =====

Table C.4 – The Source of Deviations between Reported and Imputed Values.
Over-reporting
(1)
(2)
(3)
(4)
(5)
Response: reported > imputed by
10%
15%
10%
15%
10%
15%
10%
15%
10%
15%
Intercept
1.091
0.642***
0.721
0.376*
0.489**
0.238***
1.354***
0.806**
1.032
0.521
(0.092)
(0.051)
(0.398)
(0.197)
(0.177)
(0.087)
(0.143)
(0.084)
(0.642)
(0.323)
Housing status
Owner
(ref. cat.)
Renter
1.017
0.893
1.713*
1.533
2.577***
3.043***
1.064
0.948
2.571**
2.975**
(0.212)
(0.192)
(0.542)
(0.471)
(0.883)
(1.064)
(0.227)
(0.208)
(1.091)
(1.291)
Education level
Low (ISCED ∈{0, 1, 2})
(ref. cat.)
Medium (ISCED ∈{3, 4})
0.903
0.855
0.931
0.884
(0.219)
(0.194)
(0.231)
(0.202)
High (ISCED ∈{5 −8})
0.908
0.851
1.031
1.002
(0.248)
(0.203)
(0.288)
(0.246)
Net income
Q1
(ref. cat.)
Q2
0.650
0.732
0.630
0.722
(0.240)
(0.332)
(0.240)
(0.343)
Q3
0.443*
0.389*
0.436
0.382
(0.196)
(0.196)
(0.206)
(0.203)
Q4
0.440**
0.484**
0.424**
0.455**
(0.146)
(0.168)
(0.150)
(0.167)
Q5
0.528
0.534
0.518
0.516
(0.202)
(0.248)
(0.210)
(0.250)
Net wealth
Q1
(ref. cat.)
Q2
1.608
1.286
1.769
1.448
(0.746)
(0.532)
(0.845)
(0.627)
Q3
1.155
0.929
1.290
1.031
(0.538)
(0.400)
(0.611)
(0.459)
Q4
1.852
1.565
2.040
1.644
(0.894)
(0.644)
(1.012)
(0.705)
Q5
3.753***
3.532***
4.570***
4.133***
(1.770)
(1.561)
(2.287)
(1.942)
Type of HMR
House
(ref. cat.)
Apartment
0.789
0.617**
0.774
0.615**
(0.190)
(0.142)
(0.201)
(0.149)
Surface of HMR
1.001
1.000
0.998
0.998*
(0.001)
(0.001)
(0.002)
(0.001)
Years since acquisition [log]
1.337***
1.418***
1.170
1.261*
(0.134)
(0.148)
(0.146)
(0.162)
Interviewer Rating: exterior conditions
mid-range, modest or low-income
(ref. cat.)
luxury or upscale
1.254
1.507***
1.247
1.482**
(0.195)
(0.239)
(0.202)
(0.253)
Interviewer Rating: interior conditions
good, fair, poor or not seen
(ref. cat.)
excellent
0.847
0.882
0.824
0.869
(0.188)
(0.200)
(0.195)
(0.211)
Canton
Countryside
(ref. cat.)
Luxembourg City
0.682*
0.599**
0.524***
0.458***
(0.150)
(0.124)
(0.124)
(0.109)
Esch sur Alzette
0.614***
0.647***
0.640**
0.668**
(0.107)
(0.107)
(0.121)
(0.118)
Sex
Male
(ref. cat.)
Female
1.028
1.078
1.053
1.100
(0.179)
(0.189)
(0.191)
(0.199)
Age
16-34
(ref. cat.)
35-44
0.876
1.355
0.853
1.294
(0.240)
(0.414)
(0.240)
(0.413)
45-54
0.896
1.222
0.806
1.033
(0.252)
(0.367)
(0.239)
(0.329)
55-64
0.968
1.266
0.801
0.961
(0.282)
(0.411)
(0.252)
(0.341)
65+
1.066
1.258
0.837
0.857
(0.338)
(0.410)
(0.306)
(0.316)
Household size
1.064
1.025
1.054
0.995
(0.072)
(0.071)
(0.077)
(0.075)
Country of birth
Other
(ref. cat.)
Luxembourg
1.325
1.518**
1.185
1.262
(0.237)
(0.276)
(0.229)
(0.248)
Mode of acquisition (HMR)
purchased or own construction
(ref. cat.)
inherited or gifted
1.190
1.689
1.054
1.463
(0.468)
(0.639)
(0.453)
(0.592)
25


===== PAGE 72 (score 226, numeric-paren 190, table-words 2, var-words 7) =====

Table C.4 – The Source of Deviations between Reported and Imputed Values (cont’d).
Under-reporting
(1)
(2)
(3)
(4)
(5)
Response: reported < imputed by
10%
15%
10%
15%
10%
15%
10%
15%
10%
15%
Intercept
1.505***
0.865*
4.349***
2.843**
0.980
0.447**
1.480***
0.873
1.357
0.656
(0.121)
(0.068)
(1.943)
(1.165)
(0.310)
(0.147)
(0.162)
(0.086)
(0.734)
(0.345)
Housing status
Owner
(ref. cat.)
Renter
3.273***
3.385***
1.719**
1.670**
3.275***
4.434***
3.155***
3.301***
2.422***
3.649***
(0.562)
(0.518)
(0.434)
(0.398)
(0.878)
(1.203)
(0.545)
(0.513)
(0.817)
(1.213)
Education level
Low (ISCED ∈{0, 1, 2})
(ref. cat.)
Medium (ISCED ∈{3, 4})
0.796
0.714*
0.783
0.707*
(0.168)
(0.138)
(0.170)
(0.144)
High (ISCED ∈{5 −8})
1.000
0.868
0.849
0.756
(0.259)
(0.187)
(0.237)
(0.174)
Net income
Q1
(ref. cat.)
Q2
0.714
0.767
0.822
0.914
(0.229)
(0.265)
(0.277)
(0.331)
Q3
0.465**
0.413**
0.562
0.500*
(0.155)
(0.137)
(0.196)
(0.170)
Q4
0.321***
0.330***
0.383***
0.391***
(0.096)
(0.098)
(0.124)
(0.128)
Q5
0.333***
0.311***
0.367**
0.344**
(0.120)
(0.115)
(0.140)
(0.134)
Net wealth
Q1
(ref. cat.)
Q2
1.733*
1.569
1.634
1.473
(0.570)
(0.481)
(0.549)
(0.494)
Q3
0.993
0.914
0.916
0.799
(0.344)
(0.269)
(0.328)
(0.257)
Q4
0.576
0.510**
0.426**
0.333***
(0.193)
(0.163)
(0.155)
(0.125)
Q5
0.521*
0.501*
0.253***
0.208***
(0.201)
(0.181)
(0.112)
(0.090)
Type of HMR
House
(ref. cat.)
Apartment
2.781***
2.558***
2.519***
2.362***
(0.583)
(0.421)
(0.611)
(0.430)
Surface of HMR
1.003**
1.002***
1.006***
1.006***
(0.001)
(0.001)
(0.001)
(0.001)
Years since acquisition [log]
1.234**
1.342***
1.400***
1.686***
(0.107)
(0.119)
(0.167)
(0.210)
Interviewer Rating: dwelling (exterior)
mid-range, modest or low-income
(ref. cat.)
luxury or upscale
0.539***
0.588***
0.641***
0.726*
(0.082)
(0.091)
(0.107)
(0.120)
Interviewer Rating: interior conditions
good, fair, poor or not seen
(ref. cat.)
excellent
0.475***
0.481***
0.540***
0.563***
(0.096)
(0.075)
(0.116)
(0.098)
Canton
Countryside
(ref. cat.)
Luxembourg City
1.399**
1.262
1.970***
1.802***
(0.234)
(0.185)
(0.388)
(0.322)
Esch sur Alzette
0.780
0.767*
0.665**
0.620***
(0.120)
(0.110)
(0.112)
(0.100)
Sex
Male
(ref. cat.)
Female
0.983
1.010
0.923
0.943
(0.162)
(0.154)
(0.158)
(0.151)
Age
16-34
(ref. cat.)
35-44
1.042
1.279
1.056
1.269
(0.251)
(0.282)
(0.268)
(0.295)
45-54
1.445
1.626**
1.476
1.539*
(0.351)
(0.342)
(0.387)
(0.348)
55-64
1.365
1.539*
1.216
1.208
(0.348)
(0.353)
(0.337)
(0.304)
65+
1.817**
1.806**
1.405
1.113
(0.507)
(0.448)
(0.449)
(0.320)
Household size
1.011
0.997
1.000
0.972
(0.062)
(0.055)
(0.068)
(0.061)
Country of birth
Other
(ref. cat.)
Luxembourg
0.769
0.744*
0.759
0.657**
(0.127)
(0.118)
(0.140)
(0.122)
Mode of acquisition (HMR)
purchased or own construction
(ref. cat.)
inherited or gifted
1.148
1.632
1.224
1.816
(0.421)
(0.600)
(0.482)
(0.721)
McFadden (1974) Pseudo-R2
0.029
0.034
0.101
0.112
0.074
0.082
0.039
0.042
0.154
0.169
AIC
3,289
3,338
3,116
3,138
3,161
3,195
3,265
3,317
2,967
2,974
BIC
3,311
3,359
3,320
3,343
3,248
3,281
3,308
3,360
3,257
3,265
26


===== PAGE 73 (score 5, numeric-paren 0, table-words 1, var-words 2) =====

Table C.5 – Prices versus Rents versus Income
Quantile Level – ϑ
10
25
50
75
90
All tenure statuses.
Price-to-Rent Ratio (PR)
24.7
27.6
32.0
37.1
42.6
Price-to-Income Ratio (PI)
6.4
8.4
12.0
18.7
31.3
Rent-to-Income Ratio (RI)
0.19
0.26
0.38
0.59
0.96
Owner-occupier.
Price-to-Rent Ratio (PR)
24.9
28.0
32.8
37.8
43.9
Price-to-Income Ratio (PI)
6.3
8.1
11.4
17.5
30.6
Rent-to-Income Ratio (RI)
0.18
0.24
0.35
0.53
0.94
Renter.
Price-to-Rent Ratio (PR)
24.3
26.7
30.5
34.9
39.3
Price-to-Income Ratio (PI)
6.8
9.4
13.5
21.3
32.0
Rent-to-Income Ratio (RI)
0.23
0.32
0.45
0.68
1.00
Notes: Numbers based on imputed objective prices and rents. Ratios are computed respecting survey weights. The median is
represented by ϑ = 0.5.
Source: Authors’ calculations using data from the LU-HFCS, 3rd wave and the Luxembourg Observatoire de l’Habitat.
27


===== PAGE 74 (score 86, numeric-paren 79, table-words 2, var-words 3) =====

Table C.6 – Affordability for Selected Household Categories
PA ∩RA
PA
RA
[%]
[pp]
[%]
[pp]
[%]
[pp]
Total
18.1
(2.2)
30.6
(3.0)
37.0
(2.7)
Age
16-34
29.3
(5.3)
35.4
(5.5)
61.1
(5.9)
35-44
22.8
(5.0)
29.7
(6.8)
51.7
(6.0)
45-54
17.5
(4.6)
37.4
(6.8)
32.5
(5.8)
55-64
4.9
(2.4)
17.9
(5.1)
5.7
(2.7)
65+
1.4
(1.6)
31.8
(11.6)
1.4
(1.6)
Net Liquid Assets
Q1
0.0
–
0.0
–
23.0
(4.3)
Q2
10.5
(4.4)
15.5
(6.0)
37.9
(5.8)
Q3
23.2
(6.9)
44.9
(9.2)
37.3
(7.6)
Q4
44.8
(8.7)
73.7
(8.1)
54.9
(8.4)
Q5
58.9
(10.1)
98.6
(2.9)
58.9
(10.1)
Net Income
Q1
3.9
(3.0)
14.6
(5.8)
10.6
(3.4)
Q2
17.9
(5.6)
37.7
(8.5)
30.7
(6.0)
Q3
25.2
(5.9)
34.6
(6.5)
59.7
(6.9)
Q4
33.6
(9.0)
44.5
(9.7)
76.5
(6.2)
Q5
45.2
(9.2)
51.7
(9.4)
71.8
(8.2)
Canton
Luxembourg
15.8
(3.3)
24.8
(4.2)
35.3
(4.4)
Other
19.7
(3.1)
34.4
(4.0)
38.1
(3.5)
Household size
1
15.5
(3.4)
29.0
(4.4)
24.1
(4.0)
2
21.3
(4.8)
36.5
(6.4)
40.3
(5.6)
3
22.2
(6.7)
35.2
(7.2)
55.2
(6.9)
4
24.5
(6.8)
25.2
(6.8)
61.1
(8.2)
5+
6.9
(4.2)
21.5
(10.1)
37.6
(10.6)
Gift or inheritance received
Yes
22.2
(7.1)
41.8
(9.3)
36.1
(7.9)
No
17.6
(2.3)
29.1
(2.9)
37.1
(2.9)
Gift or inheritance expected
Yes
34.0
(5.8)
43.6
(6.6)
51.8
(6.0)
No
13.0
(2.2)
26.4
(3.3)
32.2
(3.1)
Notes: The table reports the share of renting households simultaneously fulfilling purchase affordability and repayment affordability,
or fulfilling each criteria separately. Standard errors are reported in parentheses. Selected household characteristics represent some
of the main ingredients for the construction of the affordability measures. Q1 to Q5 denote quintiles.
28


===== PAGE 75 (score 2, numeric-paren 0, table-words 0, var-words 2) =====

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