1# RECORD 17f8f1569fa95f6eb5e22b566b1a1962d7ce1a432# TITLE: OBJECTIVE HOUSING SALES AND RENT PRICES IN REPRESENTATIVE HOUSEHOLD SURVEYS: IMPLICATIONS FOR WEALTH, INEQUALITY, HOUSING MARKET, AND AFFORDABILITY STATISTICS3# YEAR: 2024.0 VENUE: The Review of Income and Wealth DOI: 10.1111/roiw.126924# AUTHORS: M. Naidin; S. Waltl; Michael H. Ziegelmeyer5# PAGES: 75 CANDIDATE TABLE PAGES (1-based): [9, 15, 18, 20, 26, 30, 52, 71, 72, 74]6# 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.789===== PAGE 1 (score 4, numeric-paren 0, table-words 0, var-words 4) =====1011Objective Housing Sales and Rent Prices in12Representative Household Surveys: Implications for13Wealth, Inequality, Housing Market and Affordability14Statistics15M. Denisa Naidin∗a,b, Sofie R. Waltl†c,d, and Michael H. Ziegelmeyer‡e16aLuxembourg Institute of Socio-Economic Research (LISER), Luxembourg17bUniversity of Luxembourg, Department of Geography and Spatial Planning, Luxembourg18cUniversity of Cambridge, Department of Land Economy, United Kingdom19dVienna University of Economics and Business, Department of Economics, Austria20eBanque centrale du Luxembourg (BCL), Luxembourg21Abstract22Many economic analyses require hypothetical but realistic sales and rent prices for23properties representative for the housing stock and reflecting current market conditions.24To achieve this, we replace subjectively reported prices in a representative household25survey in Luxembourg by objectified hedonic imputations informed by observable market26data. Thus, we propose a powerful tool for assessing the health and affordability of housing27markets, compiling housing-related statistics and simulating hypothetical scenarios. This28approach also enables us to test for the reliability of survey responses. When switching to29objectified values, we detect shifts in the wealth distribution, large regional variation in30market indicators and striking affordability concerns: only 18% of Luxembourg’s renters31could theoretically afford purchasing their inhabited dwelling given current market con-32ditions. Further, participants’ tendency to mis-estimate market values strongly correlates33with tenure length and type, dwelling type, income and wealth.34Keywords: Representative Surveys; Housing Sales and Rent Markets; Housing Wealth; Affordability; Housing35Statistics; Measurement Errors36JEL codes: C83; R21; R31.37∗ORCID: 0000-0001-7529-060238†Corresponding author: Sofie R. Waltl; 19 Silver Street, Cambridge, CB3 9EP, UK; sw2123@cam.ac.uk;39www.sofiewaltl.com; ORCID: 0000-0003-2526-383840‡ORCID: 0000-0001-9867-0448414243===== PAGE 9 (score 16, numeric-paren 0, table-words 3, var-words 7) =====4445course, a better unbiased AVM, in the sense of having a lower mean squared error of prediction46across the relevant properties, would still be preferable to a worse (noisier) unbiased AVM, as47it would yield a less noisy aggregate.” In this spirit we perform a wide range of statistical tests48to make our model fit for purpose. These tests are documented in subsection 3.1 and may be49used as guidelines for future research.50We next present the main data used and perform some validation steps before section 3 performs51the actual matching between them.522.253The LU-HFCS54The LU-HFCS is part of the Pan-European HFCS initiative conducting ex-ante harmonised55wealth surveys across Europe.56In the 3rd wave of the LU-HFCS conducted in 2018, 1,61657households have participated (see Chen et al., 2020).58Responses are population-weighted.759Table 1 reports summary statistics.60Table 1 – Summary Statistics: Dwelling Characteristics – HFCS61Surface62Plot sizea63Tenure length64Construction65No. of66Monthly Rentb67Current Valueb68[m2]69[m2]70[years]71Year72Bedrooms73[EUR]74[EUR]75All tenure statuses.76Median77125.0078500.007910.00801985813.00821,50083600,00084Mean85139.48861,028.998715.32881974893.39901,69691642,66092Std. Dev.9380.93947,663.399514.939640.37971.799888599457,772100Owner-occupiers.101Median102146.80103500.0010415.0010519841064.001071,800108652,000109Mean110163.541111,104.3111218.9111319741143.891151,996116747,151117Std. Dev.11881.541198,218.1212015.8112140.191221.73123849124432,997125Renters.126Median12780.00128345.201294.0013019851312.00132950133350,000134Mean13585.93136531.421377.3313819741392.281401,031141410,048142Std. Dev.14346.60144551.831458.3414640.801471.37148531149424,992150Notes: The table reports summary statistics related to the household main residence (HMR). Measures are derived respecting151survey weights.152a The plot size is only available for houses and not for apartments.153b Prices and rents are reported by survey participants.154Source: LU-HFCS, 3rd wave.155The HFCS routinely asks owner-occupiers to estimate their home’s current market price.156Renters, in contrast, report the currently paid monthly rent. While the former reflects subjec-1577The construction of the final population weights of the LU-HFCS follows the principles outlined by the158Household Finance and Consumption Network (HFCN, 2020, section 5).159The precise weighting procedure160applied for the LU-HFCS is described in Chen et al. (2020, section 5.8) and Girshina et al. (2017, section 2.6.4).161With the best available sampling frame in Luxembourg, the Social Security Register, we still miss around 10%162of the population including households exclusively consisting of international civil servants and (standard for163household surveys) collective households such as, for instance, homes for the elderly.1647165166167===== PAGE 10 (score 10, numeric-paren 0, table-words 0, var-words 10) =====168169tive beliefs, the latter could be affected by reporting errors but not subjectivity. It is important170to note that survey participants are, in general, no experts when it comes to real estate markets.171Albeit people interested in buying or selling real estate are likely to gather extra information172by observing the market and gathering expert advise from real estate professionals, such costly173endeavours are very unlikely to be undertaken when preparing for a survey interview. Thus,174responses arguably reflect subjective beliefs and potentially also wishes.175Exclusively, the 3rd wave of the LU-HFCS contains questions about hypothetical prices, as well176as hedonic (physical and locational) characteristics of the main residence. Regarding the for-177mer, owner-occupiers are asked for a hypothetical monthly rent they believe could realistically178charge to a new tenant, and all respondents regardless of their own tenure status are tasked to179estimate a hypothetical current market sales price (see subsection C.2). Regarding the latter,180several physical characteristics have been retrieved during the survey interview or added by181the interviewer directly. As interviews are usually conducted at the interviewee’s homes and,182thus, the interviewer observes the described dwelling, reporting errors for standard hedonic183characteristics are expected to be rather minor.184The following physical characteristic are retrieved as part of the survey interview: surface,185type of residence, plot size, year of construction, number of bedrooms and the energy class.186The survey interviewer provides an additional assessment of the structure and neighbourhood.187Further, we record the postcode. Luxembourg has a strikingly detailed postcode system: while188small municipalities share one code, in Luxembourg City (almost) every street has a separate189code. Longer streets are even split into several ones. Overall, there are 4,022 regular postcodes190in a country of 2,586 km2 and roughly 600,000 residents.8191This additional information allows us to impute realistic market values retrieved from a hedonic192valuation model for all dwellings described in the survey. We do so for both owner-occupiers193(69%) and renters or households using their residence free of charge (31%).194Some personal characteristics of the interviewee we use for compiling for instance affordability195measures refer – if not stated differently – to the financially most knowledgeable person in the196household who acts as main interview partner (reference person). The LU-HFCS data set is1978See the Luxembourg Data Platform for population sizes per postcode: https://data.public.lu/en/198datasets/population-par-code-postal-population-per-postal-code (last accessed on January 11, 2021).1998200201202===== PAGE 15 (score 14, numeric-paren 0, table-words 4, var-words 4) =====203204Table 3 – Adverts vs. Notary Deeds205Adverts206Notary Deeds207Price per unit [EUR/m2]208Q12094,774.812104,227.05211Median2125,748.912135,188.47214Mean2156,462.812165,550.55217Q32187,506.322196,475.64220IQR2212,731.512222,248.59223Std. Dev.2242,364.862252,024.04226Dwelling surface [m2]227Q122871.0022970.00230Median23187.1623284.66233Mean23491.6523588.46236Q3237106.00238101.35239IQR24035.0024131.35242Std. Dev.24331.6324429.67245Number of Observations2468,3812474,737248Notes: The table reports summary statistics for advertisements and notary deeds for characteristics reported in both sources. The249data refers to flats advertised or sold (registered as for own use) in Luxembourg in 2018. Q1 and Q3 abbreviate quartiles.250Source: Luxembourg’s Housing Observatory.251we pool all adverts appearing during our study period and all deeds recorded at notaries in the252same period.253We perform two tests: First, we check whether relying on adverts would mean a change in the254structure of market data and, second, we measure maximal price differences between advertised255and finally recorded prices by comparing prices per square meter between the two sources.256For checking the first, the two prices are related to each other via (unpaired) Pearson correlation257coefficients. As result, we obtain ρ = 98.38% and, thus, reassuringly document almost perfect258co-movement of prices reported in the two sources.259Concerning the second, we assess prices and dwelling surface (in square meters). Both, the price260and surface distributions are, as a whole, shifted downwards in notary deeds data as compared261to advertisements. Magnitudes are reported in Table 3. While the shifts are significant in262statistical terms14 the differences are minor in economic terms: the median price per square263meter recorded by notary deeds is merely EUR 560 (or roughly 10%) lower.26414According to a one-sided Mood’s median test, the values reported in advertisements are statistically sig-265nificantly higher at the 5% level. Furthermore, a Mann-Whitney U Test is significant at the 1% level indicating266that the two populations are nonidentical level-wise.26713268269270===== PAGE 16 (score 12, numeric-paren 0, table-words 2, var-words 8) =====271272Overall, the price differential appears to be a minor concern here as compared to the other273drawbacks of notary deeds discussed above.2742.5275Comparing Market and Survey Data276Table 1 describes dwelling characteristics as reported in the HFCS and Table 2 reports sum-277mary statistics for advertised units. HFCS statistics are population-representative and thus278a comparison reveals differences between the current residential housing stock and the mix of279dwellings currently on the market. One key insight from this comparison is that the mean and280median age of main residences of renters and owner-occupiers are almost identical.281Looking at differences by tenure status, we find overall similar deviations: dwellings for sale or282already owner-occupied are on average substantially larger than those rented.283While rented properties in the two sets are comparable in size, properties owned/sold appearing284in the pool of advertised properties are noticeably smaller (fewer bedrooms per property and285smaller plot sizes) and are less likely to come with additional private outside space (e.g., a286garden) than existing residences of HFCS respondents.2873288Imputing Market Prices2893.1290Imputation Strategy291In the following, we sketch out our model selection procedure. Appendix A provides compre-292hensive methodological details.293Our imputation model follows a standard hedonic pricing equation and thus we regress sales or294rent prices on physical and locational characteristics. Acknowledging the skewness in the price295distributions, we follow common practise here and use a log-transformation.296Precisely, we estimate separate models for sales and rent data and regress logged sales P S297h ∈Rn298s299or logged monthly rent P R300h301∈Rn302r prices observed during the survey’s fieldwork period for303dwellings h = 1, . . . , n on a set of corresponding characteristics.304Both models follow the same general structure yet refer to either rent or sales data indicated305by the different response variables P tenure306h307, while tenure differentiates between S sales and R30814309310311===== PAGE 18 (score 21, numeric-paren 0, table-words 7, var-words 4) =====312313Table 4 – Hedonic Model Specifications314Main Model315Alt. 1316Alt. 2317Alt. 3318Alt. 4319Physical characteristics320321322323324325Interactions326327328329330331Locality Dummies332333334335336337Distance to Capital338339340341342343Linked Neighbour Spline344345346347348349Notes: Physical characteristics comprise all match-able characteristics specified in Table A.1 except location. Interactions between350dwelling type and surface as well as between construction period and energy class are included in three of the models. Locality351means dummy variables hinting towards the composite geography obtained from combining municipalities with the neighbourhood352level for the two largest urban areas in the country. The distance to the capital is retrieved from Glaesener and Caruso (2015).353The linked neighbour spline employs smooth terms linking neighbouring entities of the composite geography.354To check the models’ performance, we assess four dimensions: First, we plot imputed versus355observed market prices. Reassuringly, Figure 2 shows strong correlations. Pearson correlation356coefficients are large and positive, indicating co-movement for both sales (87.19%) and rent357(85.83%) prices. Thus, all our models replicate the original price distribution quite well. Second,358Table 5 reports results of standard goodness-of-fit measures (adjusted R2, AIC and BIC).359The main models outperform the four alternative specifications according to most measures360considered. Third, we assess the models’ predictive power by comparing overall median/mean361Table 5 – Goodness-of-fit Assessment362Adjusted R2363AIC364BIC365Sales models.366S.Main3670.824368-4,962.48369-3,783.79370S.Alt.13710.7033722,282.413732,509.08374S.Alt.23750.819376-4703.96377-4039.10378S.Alt.33790.809380-3,820.68381-2,725.11382S.Alt.43830.5073849,414.073859,550.08386Rent models.387R.Main3880.744389-1,219.10390-164.11391R.Alt.13920.679393307.96394514.81395R.Alt.23960.728397-886.18398-624.54399R.Alt.34000.742401-1,153.16402-174.02403R.Alt.44040.5264053,160.344063,284.46407Notes: The table reports goodness-of-fit measures for all hedonic models considered. AIC means the Akaike information criterion408and BIC the Bayesian information criterion.409Source: Authors’ calculations based on data from the Housing Observatory, on advertisements available between 1 January and 31410December 2018.411absolute errors (MedRE/MAE) and the median/mean relative errors (MedAE/MAE) for sales41216413414415===== PAGE 19 (score 5, numeric-paren 0, table-words 2, var-words 1) =====416417Figure 2 – Correlation Between Imputed and Observed Prices.418Notes: The figure depicts observed and imputed market data for (a) sales and (b) rents prices using the models (S.Main) and419(R.Main).420Source: Authors’ calculations based on data from the Housing Observatory, on advertisements available between 1 January and 31421December 2018.422S or rent R prices:423MAE(S ∨R) = 1424n425n426X427i=1428 ˆP S∨R429i430−P S∨R431i432 and MRE(S ∨R) = 1433n434n435X436i=1437 438ˆP S∨R439i440P S∨R441i442−1443 ,444MedAE(S ∨R) = Median445 ˆP S∨R446i447−P S∨R448i449 and MedRE(S ∨R) = Median450 451ˆP S∨R452i453P S∨R454i455−1456 .457(2)458We assess the models’ predictive power following an out-of-sample (OoS) and within-sample459(WS) procedure: for the first, we re-estimate the hedonic models leaving out 20% (i.e., 4,284)460of all observations based on geographically-stratified random sampling and use the resulting461reduced models to predict sales prices ˆP S and rents ˆP R via plug-in estimators. We compare462the predicted values for these 4,284 units using the full and restricted model, respectively, and463assess the ratio between the two. A MAE close to one and a MRE close to zero suggest that464a respective model works well also for bundles of characteristics not necessarily found in the465original estimation sample. This is important as we use the models for predicting prices for466dwellings that are by definition offthe market and thus not used to train the model.467Table 6 reports the results: OoS and WS MAEs are comparable in size, reflected in ratios468close to one. By construction, OoS errors are expected to be larger than WS errors. This is46917470471472===== PAGE 20 (score 22, numeric-paren 10, table-words 2, var-words 2) =====473474Table 6 – Predictive Power475Out-of-sample (OoS)476Within-sample (WS)477Ratio478Difference479MAE480MRE481MAE482MRE483of absolute484of relative485(MedAE)486(MedRE)487(MedAE)488(MedRE)489errors490errors491S.Main492109,688.74930.1483494108,038.64950.14654961.01524970.0018498(61,288.5)499(0.1063)500(61,256.5)501(0.1055)502(1.0005)503(0.0008)504S.Alt.1505147,367.95060.2062507146,576.85080.20575091.00535100.0004511S.Alt.2512116,955.85130.1596514109,910.55150.14905161.06415170.0105518S.Alt.3519119,256.45200.1587521117,503.15220.15695231.01495240.0018525S.Alt.4526195,999.45270.2726528195,315.85290.27235301.00345310.0002532R.Main533261.655340.1503535252.395360.14415371.03685380.0061539(161.00)540(0.1102)541(154.50)542(0.1083)543(1.0420)544(0.0019)545R.Alt.1546305.645470.1757548298.095490.17105501.02535510.0047552R.Alt.2553272.685540.1570555265.955560.15285571.02535580.0042559R.Alt.3560262.385610.1513562255.415630.14575641.02725650.0055566R.Alt.4567380.335680.2232569376.345700.21985711.01065720.0033573Notes: Out-of-sample (OoS) and Within-sample (WS) mean absolute errors (MAEs) and mean relative errors (MREs) are computed574for units for rent and sale following formula (2). The smaller MRE and MAE, the better the predictive power. We relate the two575measures to each other by computing ratios MAE(OoS)/MAE(WS) for absolute measures and distances MRE(OoS)-MRE(WS) for576relative measures reported in the last two columns. We also include in brackets figures on the median relative errors for the main577models to give a clearer picture of the shape of the error curves.578Source: Authors’ calculations based on data from the Housing Observatory, on advertisements available between 1 January and 31579December 2018.580indeed the case reflected by the ratio of OoS to WS errors being consistently larger than – but581reassuringly very close to – one.582The mean relative prediction error for dwellings excluded from the estimation sample amounts583to roughly 15%. Hence, we must expect an error margin of this size when imputing sales and584rent prices for survey observations. Therefore, we use this margin as a lower bound to identify585over- or under-reported values as detailed in subsection 3.2.586Finally, we examine residuals in detail to detect potential biases.587On average, our models588predict slightly lower sales and slightly higher rent prices than observed ones, however, the589median residual is almost zero (the main model yields an average residual of 0.00259 for sales590prices and of -0.00265 for rent prices). Thus, the models are on average not completely free of591bias, but its expected size is very small and hardly varies across model specifications.592Yet, the models may also be affected by bias in other dimensions.593As, further on, distri-594butional effects will be studied, we check for bias along proxies for the income and wealth595distributions, namely observed sales and rent price distribution. As housing assets are usually596households’ most important single wealth component (see, for instance, Causa et al., 2019),59718598599600===== PAGE 21 (score 4, numeric-paren 0, table-words 0, var-words 4) =====601602Figure 3 – Residuals along the Sales and Rent Price Distribution.603Notes: The figure plots observed market data for (a) sales and (b) rents prices against associated residuals retrieved from models604(S.Main) and (R.Main).605Source: Authors’ calculations based on data from the Housing Observatory, on advertisements available between 1 January and 31606December 2018.607plotting residuals along the sales price distribution comes close to a plot along the wealth608distribution. Similarly, rent payments correlate with income as monthly rent payments are –609generally speaking – restricted by monthly disposable income. For the main models, Figure 3610plots residuals along the observed sales and rent price distributions. Absolute unbiasedness611would mean that residuals perfectly cluster around the horizontal lines.612Throughout large parts of the distributions this is indeed the case. Only at the very bottom613of the distributions prices deviate more. Thus, our predictions are most accurate outside the614lowest price segment.615Furthermore, we assess residuals by the most important price-determining characteristic: loca-616tion. That checks whether imputations systematically deviate in certain areas of the country.617Figure 4 shows residuals per canton retrieved from the main models (S.Main) and (R.Main).618The width of interquartile ranges is quite similar across cantons and consistently overlaps619zero. This holds true even when assessing the much more fine-grained split by our composite620geography roughly corresponding to municipalities as reported in Figure C.1 in Appendix C.621We perform two additional robustness checks: first, we estimate the main specifications as62219623624625===== PAGE 26 (score 117, numeric-paren 84, table-words 5, var-words 8) =====626627Table 8 – Key Estimation Results628Over-reporting629Under-reporting630Response: mis-reported by63110%63215%63310%63415%635Intercept6361.0326370.5216380.9806390.447**640(-0.642)641(-0.323)642(0.310)643(0.147)644Housing status645Owner646(ref. cat.)647Renter6482.571**6492.975**6503.275***6514.434***652(-1.091)653(-1.291)654(0.878)655(1.203)656Education level657Low658(ref. cat.)659Medium6600.9316610.8846620.7966630.714*664(-0.231)665(-0.202)666(0.168)667(0.138)668High6691.0316701.0026711.0006720.868673(-0.288)674(-0.246)675(0.259)676(0.187)677Net income678Q1679(ref. cat.)680Q26810.6306820.7226830.7146840.767685(-0.240)686(-0.343)687(0.229)688(0.265)689Q36900.4366910.3826920.465**6930.413**694(-0.206)695(-0.203)696(0.155)697(0.137)698Q46990.424**7000.455**7010.321***7020.330***703(-0.150)704(-0.167)705(0.096)706(0.098)707Q57080.5187090.5167100.333***7110.311***712(-0.210)713(-0.250)714(0.120)715(0.115)716Net wealth717Q1718(ref. cat.)719Q27201.7697211.4487221.733*7231.569724(-0.845)725(-0.627)726(0.570)727(0.481)728Q37291.2907301.0317310.9937320.914733(-0.611)734(-0.459)735(0.344)736(0.269)737Q47382.0407391.6447400.5767410.510**742(-1.012)743(-0.705)744(0.193)745(0.163)746Q57474.570***7484.133***7490.521*7500.501*751(-2.287)752(-1.942)753(0.201)754(0.181)755Type of HMR756House757(ref. cat.)758Apartment7590.7747600.615**7612.781***7622.558***763(-0.201)764(-0.149)765(0.583)766(0.421)767Surface of HMR7680.9987690.998*7701.003**7711.002***772(-0.002)773(-0.001)774(0.001)775(0.001)776Years since acquisition [log]7771.1707781.261*7791.234**7801.342***781(-0.146)782(-0.162)783(0.107)784(0.119)785Interviewer rating: exterior conditions786mid-range, modest or low-income787(ref. cat.)788luxury or upscale7891.2477901.482**7910.539***7920.588***793(-0.202)794(-0.253)795(0.082)796(0.091)797Interviewer rating: interior conditions798good, fair, poor or not seen799(ref. cat.)800excellent8010.8248020.8698030.475***8040.481***805(-0.195)806(-0.211)807(0.096)808(0.075)809Canton810Countryside811(ref. cat.)812Luxembourg City8130.524***8140.458***8151.970***8161.802***817(-0.124)818(-0.109)819(0.388)820(0.322)821Esch sur Alzette8220.640**8230.668**8240.665**8250.620***826(-0.121)827(-0.118)828(0.112)829(0.100)830Notes: The models regress deviation between reported and imputed prices on dwelling and household characteristics.831Models832(1) −(5) refer to distinct specifications.833We distinguish two response variables describing the deviation between imputed and834observed current values of the HMR. Over-reporting and under-reporting, respectively, means that the reported value diverges by835±10% or ±15% from the imputed one. Q1 to Q5 denote first to fifth quintiles. Models are estimated on the full LU-HFCS data836(1,616 observations). Significance is indicated using standard notation: ∗p-value<0.1; ∗∗p-value<0.05; ∗∗∗p-value<0.01.837Source: LU-HFCS, 3rd wave and authors’ calculations.83824839840841===== PAGE 27 (score 5, numeric-paren 0, table-words 0, var-words 5) =====842843The tenure status, renting versus owner-occupying, turns out to be a prime predictor: Renters844tend to be much more likely to mis-estimate the market value of their home and less likely to845report prices close to the ones suggested by the hedonic model. Households at the top of the846net wealth distribution are more likely to over-report and less likely to under-report relative847to imputed values. Likewise, higher household income is associated with a lower likelihood to848mis-estimate.849In terms of education, we document a lower likelihood to mis-report for persons with medium850or high formal educational attainment. However, the estimated coefficients are only significant851for under-reporting and a medium education level.8524853Implications for Wealth, Inequality, Housing Market and Afford-854ability Statistics8554.1856Net Wealth, Residential Housing Wealth and its Distribution857Switching from reported to imputed values means an adjustment of the measured value of the858current residential housing stock and net wealth at current market prices. These computations859may be particularly helpful for filling gaps in Luxembourg’s canon of official statistics. STATEC860conducts an annual survey to update statistics on the current housing stock. A questionnaire is861sent to every registered owner of newly constructed dwellings. However, only construction costs862are collected, which are usually far from market sales prices.17 In addition, in the non-financial863accounts dwellings (ESA, 2010, code: AN.111) and land underlying buildings and structures864(ESA, 2010, code: AN.2111) are currently not distinguishable between households and non-865profit institutions serving households (NPISHs). There are no reliable estimates of the current866market value of the residential housing stock owned by private households (see also EG-LMM,8672020).868We define net wealth for household h at time t as869Net Wealthht = Real Assetsht + Financial Assetsht −Liabilitiesht.870(5)87117 For details see http://www.statistiques.public.lu/stat/TableViewer/document.aspx?ReportId=87213442&IF_Language=eng&MainTheme=4&FldrName=4&RFPath=35 (Last accessed October 21, 2021).87325874875876===== PAGE 30 (score 16, numeric-paren 0, table-words 4, var-words 5) =====877878distributions is squeezed.879Table 10 – Changes in Net Wealth Distribution880Imputed881Q1882Q2883Q3884Q4885Q5886Total887Reported888Q188919.658900.428910.008920.008930.0089420.07895Q28960.4189716.008982.978990.589000.0890120.04902Q39030.009043.4190512.449063.869070.2390819.94909Q49100.009110.119124.3291312.849142.7591520.02916Q59170.009180.029190.299202.7292116.9192219.94923Total92420.0692519.9792620.0192720.0092819.96929100.00930Notes: For the complete sample (owners and renters), the table reports the percent of observations changing quintile in the net931wealth distribution due to the imputation. Figure C.4 presents these results graphically.932These quite significant changes indicate that an objective evaluation does not simply shift the933entire distribution but reveals differential effects along several dimensions. This can lead to934changes in wealth decompositions such as, e.g., distributional national accounts (see EG-LMM,9352020; Waltl and Chakraborty, 2022; Waltl, 2022). The impact is likely larger for countries with936a significant share of owner-occupiers. For purely illustrative purposes, applying the shifts along937the wealth and income distribution identified in Luxembourg to other countries participating938in the HFCS provides an indication of how important reporting issues could be.939For this hypothetical analysis of other countries, we take country-specific total residential hous-940ing wealth and owner-occupation rate, and apply Luxembourg’s measured mis-reporting rates941per wealth and income18 quintile to owner-occupiers in other countries. To obtain a full wealth942measure, we then subtract reported residential housing wealth from total wealth and plug in943the adjusted equivalent. Appendix B describes the compilation steps applied.944Results are compiled by first adjusting quintile-specific wealth for owner-occupiers. The pro-945portion of owner-occupiers varies widely across countries in the European HFCS (ranging from94643.9% in Germany to 88.8% in Slovakia in 2018). Indeed, the relation between owner-occupation947rate and the change in net wealth is statistically significant as reported in Table 11.948Therefore, we select four HFCS countries that represent different realities in this regard. This949includes the countries with the lowest (Germany) and the highest (Slovakia) proportion of95018The harmonised HFCS core questionnaire only asks for gross household income. For Luxembourg, the951Pearson correlation coefficient between gross and net household income is ρ ≈0.8.95228953954955===== PAGE 31 (score 16, numeric-paren 0, table-words 6, var-words 4) =====956957owner-occupiers, as well as two with intermediate shares (France and Italy). We expect changes958to be larger for countries with a larger share of owner-occupiers.959Table 11 – As-if analysis960Germany961France962Luxembourg963Italy964Slovakia965Owner-occupation Rate [%]96643.996757.996869.096968.597088.8971Change in Net Wealth [%]9723.289733.499743.569753.899764.20977ρ97893.76% (p-value: 0.0185)979Notes: The table reports changes in measured total net wealth for four European countries increasingly ordered by the change980in net wealth when applying mis-reporting shares found for Luxembourg. ρ measures the Pearson correlation between changes981in measured total net wealth and the owner-occupation rate across countries. The p-value reports results of a Pearson’s product-982moment correlation test for H0 : ρ = 0 rejected at the 5% level. See Appendix B for computational details.983Source: HFCS, 3rd wave.984Table B.2 in the appendix reports full results. In general, the adjustment factors computed for985Luxembourg lead to a small decrease in inequality and a large increase in overall wealth. As986reported in Table 11, total net wealth is most affected in Slovakia, which also had the largest987share of owner-occupiers. At the other extreme, total net wealth is least affected in Germany,988which had the lowest share of owner-occupiers. This finding suggests that wealth distributions989may be poorly measured in countries with large shares of owner-occupiers or large shares of990residential housing in overall wealth. Given the very large amounts at play even small shifts –991whenever found to be systematic – imply large aggregate impacts.9924.2993Housing Market Indicators994Common housing market measures include the price-to-rent (PR) ratio, price-to-income (PI)995ratio, and the rent-to-income (RI) ratio. PI and RI ratios are widely used affordability measures:996A high RI ratio implies households spend a large share of monthly earnings on rent payments.997A high PI ratio suggests low affordability. The PR ratio is considered a measure of investment998potential and the sustainability of the housing market: a high ratio suggests that sales prices are999high compared to potential returns, i.e., rents. This implies high expected future house prices1000according to the user cost model for durable goods (Hicks, 1975).1001For residential housing,1002Himmelberg et al. (2005) show that in equilibrium the cost of buying and using a housing unit1003for a period (the sales price Pt multiplied by the per-dollar user cost ut) should equal the total1004rent for the same period (Rt): Rt = ut · Pt, where ut includes the interest rate, maintenance1005and average transaction costs, the depreciation rate for housing, a risk premium for owning as100629100710081009===== PAGE 52 (score 384, numeric-paren 320, table-words 10, var-words 9) =====10101011A.31012Imputation Models1013We estimate the hedonic model (1) relying on all linkable predictors (re-)coded as described1014in Table A.1. The model’s performance is slightly improved (increase in adjusted R2 by one1015percentage point) when excluding five influential statistical outliers from the sales data set1016identified via Cook’s distance (see Cook, 1977). Table A.2 reports estimation results.1017Table A.2 – Hedonic Regression Results1018log(P S)1019log(P R)1020(S.Main)1021(S.Alt.1)1022(S.Alt.2)1023(S.Alt.3)1024(S.Alt.4)1025(R.Main)1026(R.Alt.1)1027(R.Alt.2)1028(R.Alt.3)1029(R.Alt.4)1030Intercept103112.104***103212.469***103312.25***103412.347***103512.446***10366.276***10376.834***103812.252***10396.456***10406.684***1041(0.037)1042(0.020)1043(0.016)1044(0.037)1045(0.019)1046(0.160)1047(0.038)1048(0.016)1049(0.158)1050(0.032)1051Dwelling characteristics.1052Type of Dwelling1053Flat1054(ref. cat.)1055House10560.493***10570.543***10580.488***10590.031***1060-0.103***10610.265***10620.310***10630.488***10640.239***10650.082***1066(0.014)1067(0.018)1068(0.014)1069(0.006)1070(0.009)1071(0.025)1072(0.027)1073(0.014)1074(0.012)1075(0.016)1076Surface10770.006***10780.007***10790.006***10800.003***10810.003***10820.004***10830.004***10840.006***10850.004***10860.004***1087(0.000)1088(0.000)1089(0.000)1090(0.000)1091(0.000)1092(0.000)1093(0.000)1094(0.000)1095(0.000)1096(0.000)1097Plot size10980.00010990.00011000.00011010.00011020.00011030.00011040.00011050.00011060.00011070.0001108(0.000)1109(0.000)1110(0.000)1111(0.000)1112(0.000)1113(0.000)1114(0.000)1115(0.000)1116(0.000)1117(0.000)1118Construction year1119pre 19501120(ref. cat.)11211950-196911220.089***11230.134***11240.093***11250.066***11260.051**11270.228***11280.120**11290.093***11300.042 .1131-0.0201132(0.014)1133(0.018)1134(0.014)1135(0.010)1136(0.016)1137(0.036)1138(0.037)1139(0.014)1140(0.022)1141(0.029)11421970-198911430.118***11440.229***11450.119***11460.078***11470.223***11480.2035***11490.1091*11500.119***11510.0281152-0.0641*1153(0.022)1154(0.028)1155(0.022)1156(0.012)1157(0.018)1158(0.043)1159(0.045)1160(0.022)1161(0.024)1162(0.031)11631990-199911640.162***11650.192***11660.164***11670.118***11680.088***11690.266**11700.038011710.164***11720.0371173-0.145***1174(0.038)1175(0.049)1176(0.038)1177(0.013)1178(0.020)1179(0.099)1180(0.107)1181(0.038)1182(0.026)1183(0.034)11842000-200911850.146*11860.196*11870.140 .11880.113***11890.102***11900.292*11910.15511920.140 .11930.054*1194-0.111***1195(0.073)1196(0.094)1197(0.073)1198(0.012)1199(0.019)1200(0.119)1201(0.128)1202(0.073)1203(0.024)1204(0.031)12052010-202012060.21612070.33012080.20512090.040***12100.02812110.296**12120.288*12130.20512140.078**1215-0.0241216(0.203)1217(0.262)1218(0.204)1219(0.011)1220(0.018)1221(0.105)1222(0.116)1223(0.204)1224(0.024)1225(0.032)1226Number of bedrooms122711228(ref. cat.)1229212300.143***12310.100***12320.143***12330.242***12340.181***12350.119***12360.112***12370.143***12380.120***12390.092***1240(0.006)1241(0.008)1242(0.006)1243(0.005)1244(0.009)1245(0.006)1246(0.007)1247(0.006)1248(0.006)1249(0.008)1250312510.182***12520.122***12530.183***12540.375***12550.320***12560.165***12570.146***12580.183***12590.166***12600.154***1261(0.008)1262(0.011)1263(0.008)1264(0.006)1265(0.010)1266(0.010)1267(0.011)1268(0.008)1269(0.009)1270(0.013)12714+12720.226***12730.150***12740.224***12750.419***12760.372***1277-0.137***1278-0.135***12790.224***1280-0.145***1281-0.109***1282(0.010)1283(0.013)1284(0.010)1285(0.008)1286(0.013)1287(0.009)1288(0.010)1289(0.010)1290(0.009)1291(0.012)1292Energy Efficiency Class1293low (H-I)1294(ref. cat.)1295medium (E-G)12960.063***12970.083***12980.068***12990.032***13000.155***13010.317***13020.250***13030.068***13040.032**13050.243***1306(0.019)1307(0.024)1308(0.018)1309(0.006)1310(0.010)1311(0.045)1312(0.048)1313(0.018)1314(0.010)1315(0.012)1316high (A-D)13170.157*13180.268***13190.141*13200.132***13210.217***13220.358***13230.285*13240.141*13250.123***13260.290***1327(0.061)1328(0.077)1329(0.060)1330(0.007)1331(0.011)1332(0.106)1333(0.116)1334(0.060)1335(0.013)1336(0.016)1337Dwelling State1338planned1339(ref. cat.)1340new-build13410.0091342-0.043*13430.00313440.0161345-0.0211346-0.0061347-0.0291348-0.00513490.00413500.0031351(0.014)1352(0.018)1353(0.014)1354(0.015)1355(0.024)1356(0.019)1357(0.022)1358(0.014)1359(0.020)1360(0.026)1361good1362-0.032***1363-0.085***1364-0.038***1365-0.044***1366-0.065***1367-0.033**1368-0.020 .1369-0.038***1370-0.039***13710.040**1372(0.007)1373(0.009)1374(0.007)1375(0.007)1376(0.011)1377(0.010)1378(0.011)1379(0.007)1380(0.010)1381(0.013)1382average1383-0.054***1384-0.078***1385-0.059***1386-0.058***1387-0.073***1388-0.059***1389-0.052***1390-0.059***1391-0.063***1392-0.038***1393(0.005)1394(0.006)1395(0.005)1396(0.005)1397(0.008)1398(0.008)1399(0.009)1400(0.005)1401(0.008)1402(0.011)1403Interactions1404Dwelling Type × Surface1405-0.003***1406-0.004***1407-0.003***1408140914100.00014110.0001412-0.003***141314141415(0.000)1416(0.000)1417(0.000)1418(0.000)1419(0.000)1420(0.000)1421Construction Year × Energy Class14221423142414251426142714281429143014311432Geographical characteristics.1433Locality Dummies1434143514361437143814391440144114421443Distance to Capital14441445-0.014***14461447144814491450-0.013***1451145214531454(0.000)1455(0.000)1456Linked neighbour Spline14571458145914601461146214631464146514661467Notes: P S and P R denotes the advertised sales or monthly rent price, respectively. Coefficients for single localities are left out.1468We indicate in- and exclusion of a (set) of variables by and , respectively. Significance is indicated using standard notation: .1469p-value<0.1; ∗p-value<0.05; ∗∗p-value<0.01; ∗∗∗p-value<0.001.1470Source: Authors’ calculations based on data from the Housing Observatory, on advertisements available between 1 January and 311471December 2018.14726147314741475===== PAGE 53 (score 16, numeric-paren 0, table-words 2, var-words 12) =====14761477As we impute prices for dwellings per construction not part of the training sample, we estimate1478the potential imputation error from an OoS prediction check. Therefore, we leave out randomly1479selected 20% of the data used for validation applying geographically stratified random sampling.1480The selected hedonic model is subsequently used to impute sales and rent prices for each1481dwelling described in the HFCS survey. For this article, we added several questions describing1482the physical features of the main residence as well as a question about its location. For questions1483where the respondents refused to answer, five multiply imputed implicates are introduced. For1484apartments no plot size is reported. The following physical dwelling characteristics elicited in1485the HFCSA.8 are used to impute prices, after ensuring that they are transformed into the same1486scales/categories used for the Housing Observatory model: dwelling type (hlb0100), dwelling1487surface (hb0100), plot surface (hlb0200x), year of construction (hlb0210), number of bedrooms1488(hlb0310), energy score (hlb0410) and dwelling status (sc0400). See Table A.1 for details.1489As locational measure, we elicit a postcodes (hl0100) in the course of the LU-HFCS survey in-1490terview. Luxembourg features an exceptionally fine grained postcode system: There are 4,0221491postcodes, with a maximum population per postcode of 1,500. On average, there are only1492158 persons per code.A.9 Yet, the codes have the distinct disadvantage of occasionally crossing1493administrative boundaries at neighbourhood and municipal levels. We therefore convert the1494post codes into our composite geography by applying a juxtaposition strategy in QGIS: the1495geographical centroids of postcodes are superimposed to the boundaries of our composite ge-1496ography. For postcodes that fall across municipal lines, the centroids cover municipal sections1497of the shared postcode; consequently, the resulting enhanced attribute table allocates multiple1498municipalities to single postcodes that cover residences in different administrative units.1499This non-unique allocation is acknowledged by using the five implicates of the HFCS dataset.1500The dwelling is allocated randomly between the neighbourhoods or municipalities across these1501five implicates so that the uncertainty is properly reflected in our estimates.1502A.8Item codes follow the EU-wide harmonised coding scheme whenever applicable; and Luxembourg-specific1503codes for amended questions. See Household Finance and Consumption Network (2020).1504A.9See https://data.public.lu/en/datasets/population-par-code-postal-population-per-postal-code/1505(Last accessed November 9, 2021)15067150715081509===== PAGE 71 (score 191, numeric-paren 158, table-words 1, var-words 7) =====15101511Table C.4 – The Source of Deviations between Reported and Imputed Values.1512Over-reporting1513(1)1514(2)1515(3)1516(4)1517(5)1518Response: reported > imputed by151910%152015%152110%152215%152310%152415%152510%152615%152710%152815%1529Intercept15301.09115310.642***15320.72115330.376*15340.489**15350.238***15361.354***15370.806**15381.03215390.5211540(0.092)1541(0.051)1542(0.398)1543(0.197)1544(0.177)1545(0.087)1546(0.143)1547(0.084)1548(0.642)1549(0.323)1550Housing status1551Owner1552(ref. cat.)1553Renter15541.01715550.89315561.713*15571.53315582.577***15593.043***15601.06415610.94815622.571**15632.975**1564(0.212)1565(0.192)1566(0.542)1567(0.471)1568(0.883)1569(1.064)1570(0.227)1571(0.208)1572(1.091)1573(1.291)1574Education level1575Low (ISCED ∈{0, 1, 2})1576(ref. cat.)1577Medium (ISCED ∈{3, 4})15780.90315790.85515800.93115810.8841582(0.219)1583(0.194)1584(0.231)1585(0.202)1586High (ISCED ∈{5 −8})15870.90815880.85115891.03115901.0021591(0.248)1592(0.203)1593(0.288)1594(0.246)1595Net income1596Q11597(ref. cat.)1598Q215990.65016000.73216010.63016020.7221603(0.240)1604(0.332)1605(0.240)1606(0.343)1607Q316080.443*16090.389*16100.43616110.3821612(0.196)1613(0.196)1614(0.206)1615(0.203)1616Q416170.440**16180.484**16190.424**16200.455**1621(0.146)1622(0.168)1623(0.150)1624(0.167)1625Q516260.52816270.53416280.51816290.5161630(0.202)1631(0.248)1632(0.210)1633(0.250)1634Net wealth1635Q11636(ref. cat.)1637Q216381.60816391.28616401.76916411.4481642(0.746)1643(0.532)1644(0.845)1645(0.627)1646Q316471.15516480.92916491.29016501.0311651(0.538)1652(0.400)1653(0.611)1654(0.459)1655Q416561.85216571.56516582.04016591.6441660(0.894)1661(0.644)1662(1.012)1663(0.705)1664Q516653.753***16663.532***16674.570***16684.133***1669(1.770)1670(1.561)1671(2.287)1672(1.942)1673Type of HMR1674House1675(ref. cat.)1676Apartment16770.78916780.617**16790.77416800.615**1681(0.190)1682(0.142)1683(0.201)1684(0.149)1685Surface of HMR16861.00116871.00016880.99816890.998*1690(0.001)1691(0.001)1692(0.002)1693(0.001)1694Years since acquisition [log]16951.337***16961.418***16971.17016981.261*1699(0.134)1700(0.148)1701(0.146)1702(0.162)1703Interviewer Rating: exterior conditions1704mid-range, modest or low-income1705(ref. cat.)1706luxury or upscale17071.25417081.507***17091.24717101.482**1711(0.195)1712(0.239)1713(0.202)1714(0.253)1715Interviewer Rating: interior conditions1716good, fair, poor or not seen1717(ref. cat.)1718excellent17190.84717200.88217210.82417220.8691723(0.188)1724(0.200)1725(0.195)1726(0.211)1727Canton1728Countryside1729(ref. cat.)1730Luxembourg City17310.682*17320.599**17330.524***17340.458***1735(0.150)1736(0.124)1737(0.124)1738(0.109)1739Esch sur Alzette17400.614***17410.647***17420.640**17430.668**1744(0.107)1745(0.107)1746(0.121)1747(0.118)1748Sex1749Male1750(ref. cat.)1751Female17521.02817531.07817541.05317551.1001756(0.179)1757(0.189)1758(0.191)1759(0.199)1760Age176116-341762(ref. cat.)176335-4417640.87617651.35517660.85317671.2941768(0.240)1769(0.414)1770(0.240)1771(0.413)177245-5417730.89617741.22217750.80617761.0331777(0.252)1778(0.367)1779(0.239)1780(0.329)178155-6417820.96817831.26617840.80117850.9611786(0.282)1787(0.411)1788(0.252)1789(0.341)179065+17911.06617921.25817930.83717940.8571795(0.338)1796(0.410)1797(0.306)1798(0.316)1799Household size18001.06418011.02518021.05418030.9951804(0.072)1805(0.071)1806(0.077)1807(0.075)1808Country of birth1809Other1810(ref. cat.)1811Luxembourg18121.32518131.518**18141.18518151.2621816(0.237)1817(0.276)1818(0.229)1819(0.248)1820Mode of acquisition (HMR)1821purchased or own construction1822(ref. cat.)1823inherited or gifted18241.19018251.68918261.05418271.4631828(0.468)1829(0.639)1830(0.453)1831(0.592)183225183318341835===== PAGE 72 (score 226, numeric-paren 190, table-words 2, var-words 7) =====18361837Table C.4 – The Source of Deviations between Reported and Imputed Values (cont’d).1838Under-reporting1839(1)1840(2)1841(3)1842(4)1843(5)1844Response: reported < imputed by184510%184615%184710%184815%184910%185015%185110%185215%185310%185415%1855Intercept18561.505***18570.865*18584.349***18592.843**18600.98018610.447**18621.480***18630.87318641.35718650.6561866(0.121)1867(0.068)1868(1.943)1869(1.165)1870(0.310)1871(0.147)1872(0.162)1873(0.086)1874(0.734)1875(0.345)1876Housing status1877Owner1878(ref. cat.)1879Renter18803.273***18813.385***18821.719**18831.670**18843.275***18854.434***18863.155***18873.301***18882.422***18893.649***1890(0.562)1891(0.518)1892(0.434)1893(0.398)1894(0.878)1895(1.203)1896(0.545)1897(0.513)1898(0.817)1899(1.213)1900Education level1901Low (ISCED ∈{0, 1, 2})1902(ref. cat.)1903Medium (ISCED ∈{3, 4})19040.79619050.714*19060.78319070.707*1908(0.168)1909(0.138)1910(0.170)1911(0.144)1912High (ISCED ∈{5 −8})19131.00019140.86819150.84919160.7561917(0.259)1918(0.187)1919(0.237)1920(0.174)1921Net income1922Q11923(ref. cat.)1924Q219250.71419260.76719270.82219280.9141929(0.229)1930(0.265)1931(0.277)1932(0.331)1933Q319340.465**19350.413**19360.56219370.500*1938(0.155)1939(0.137)1940(0.196)1941(0.170)1942Q419430.321***19440.330***19450.383***19460.391***1947(0.096)1948(0.098)1949(0.124)1950(0.128)1951Q519520.333***19530.311***19540.367**19550.344**1956(0.120)1957(0.115)1958(0.140)1959(0.134)1960Net wealth1961Q11962(ref. cat.)1963Q219641.733*19651.56919661.63419671.4731968(0.570)1969(0.481)1970(0.549)1971(0.494)1972Q319730.99319740.91419750.91619760.7991977(0.344)1978(0.269)1979(0.328)1980(0.257)1981Q419820.57619830.510**19840.426**19850.333***1986(0.193)1987(0.163)1988(0.155)1989(0.125)1990Q519910.521*19920.501*19930.253***19940.208***1995(0.201)1996(0.181)1997(0.112)1998(0.090)1999Type of HMR2000House2001(ref. cat.)2002Apartment20032.781***20042.558***20052.519***20062.362***2007(0.583)2008(0.421)2009(0.611)2010(0.430)2011Surface of HMR20121.003**20131.002***20141.006***20151.006***2016(0.001)2017(0.001)2018(0.001)2019(0.001)2020Years since acquisition [log]20211.234**20221.342***20231.400***20241.686***2025(0.107)2026(0.119)2027(0.167)2028(0.210)2029Interviewer Rating: dwelling (exterior)2030mid-range, modest or low-income2031(ref. cat.)2032luxury or upscale20330.539***20340.588***20350.641***20360.726*2037(0.082)2038(0.091)2039(0.107)2040(0.120)2041Interviewer Rating: interior conditions2042good, fair, poor or not seen2043(ref. cat.)2044excellent20450.475***20460.481***20470.540***20480.563***2049(0.096)2050(0.075)2051(0.116)2052(0.098)2053Canton2054Countryside2055(ref. cat.)2056Luxembourg City20571.399**20581.26220591.970***20601.802***2061(0.234)2062(0.185)2063(0.388)2064(0.322)2065Esch sur Alzette20660.78020670.767*20680.665**20690.620***2070(0.120)2071(0.110)2072(0.112)2073(0.100)2074Sex2075Male2076(ref. cat.)2077Female20780.98320791.01020800.92320810.9432082(0.162)2083(0.154)2084(0.158)2085(0.151)2086Age208716-342088(ref. cat.)208935-4420901.04220911.27920921.05620931.2692094(0.251)2095(0.282)2096(0.268)2097(0.295)209845-5420991.44521001.626**21011.47621021.539*2103(0.351)2104(0.342)2105(0.387)2106(0.348)210755-6421081.36521091.539*21101.21621111.2082112(0.348)2113(0.353)2114(0.337)2115(0.304)211665+21171.817**21181.806**21191.40521201.1132121(0.507)2122(0.448)2123(0.449)2124(0.320)2125Household size21261.01121270.99721281.00021290.9722130(0.062)2131(0.055)2132(0.068)2133(0.061)2134Country of birth2135Other2136(ref. cat.)2137Luxembourg21380.76921390.744*21400.75921410.657**2142(0.127)2143(0.118)2144(0.140)2145(0.122)2146Mode of acquisition (HMR)2147purchased or own construction2148(ref. cat.)2149inherited or gifted21501.14821511.63221521.22421531.8162154(0.421)2155(0.600)2156(0.482)2157(0.721)2158McFadden (1974) Pseudo-R221590.02921600.03421610.10121620.11221630.07421640.08221650.03921660.04221670.15421680.1692169AIC21703,28921713,33821723,11621733,13821743,16121753,19521763,26521773,31721782,96721792,9742180BIC21813,31121823,35921833,32021843,34321853,24821863,28121873,30821883,36021893,25721903,265219126219221932194===== PAGE 73 (score 5, numeric-paren 0, table-words 1, var-words 2) =====21952196Table C.5 – Prices versus Rents versus Income2197Quantile Level – ϑ2198102199252200502201752202902203All tenure statuses.2204Price-to-Rent Ratio (PR)220524.7220627.6220732.0220837.1220942.62210Price-to-Income Ratio (PI)22116.422128.4221312.0221418.7221531.32216Rent-to-Income Ratio (RI)22170.1922180.2622190.3822200.5922210.962222Owner-occupier.2223Price-to-Rent Ratio (PR)222424.9222528.0222632.8222737.8222843.92229Price-to-Income Ratio (PI)22306.322318.1223211.4223317.5223430.62235Rent-to-Income Ratio (RI)22360.1822370.2422380.3522390.5322400.942241Renter.2242Price-to-Rent Ratio (PR)224324.3224426.7224530.5224634.9224739.32248Price-to-Income Ratio (PI)22496.822509.4225113.5225221.3225332.02254Rent-to-Income Ratio (RI)22550.2322560.3222570.4522580.6822591.002260Notes: Numbers based on imputed objective prices and rents. Ratios are computed respecting survey weights. The median is2261represented by ϑ = 0.5.2262Source: Authors’ calculations using data from the LU-HFCS, 3rd wave and the Luxembourg Observatoire de l’Habitat.226327226422652266===== PAGE 74 (score 86, numeric-paren 79, table-words 2, var-words 3) =====22672268Table C.6 – Affordability for Selected Household Categories2269PA ∩RA2270PA2271RA2272[%]2273[pp]2274[%]2275[pp]2276[%]2277[pp]2278Total227918.12280(2.2)228130.62282(3.0)228337.02284(2.7)2285Age228616-34228729.32288(5.3)228935.42290(5.5)229161.12292(5.9)229335-44229422.82295(5.0)229629.72297(6.8)229851.72299(6.0)230045-54230117.52302(4.6)230337.42304(6.8)230532.52306(5.8)230755-6423084.92309(2.4)231017.92311(5.1)23125.72313(2.7)231465+23151.42316(1.6)231731.82318(11.6)23191.42320(1.6)2321Net Liquid Assets2322Q123230.02324–23250.02326–232723.02328(4.3)2329Q2233010.52331(4.4)233215.52333(6.0)233437.92335(5.8)2336Q3233723.22338(6.9)233944.92340(9.2)234137.32342(7.6)2343Q4234444.82345(8.7)234673.72347(8.1)234854.92349(8.4)2350Q5235158.92352(10.1)235398.62354(2.9)235558.92356(10.1)2357Net Income2358Q123593.92360(3.0)236114.62362(5.8)236310.62364(3.4)2365Q2236617.92367(5.6)236837.72369(8.5)237030.72371(6.0)2372Q3237325.22374(5.9)237534.62376(6.5)237759.72378(6.9)2379Q4238033.62381(9.0)238244.52383(9.7)238476.52385(6.2)2386Q5238745.22388(9.2)238951.72390(9.4)239171.82392(8.2)2393Canton2394Luxembourg239515.82396(3.3)239724.82398(4.2)239935.32400(4.4)2401Other240219.72403(3.1)240434.42405(4.0)240638.12407(3.5)2408Household size24091241015.52411(3.4)241229.02413(4.4)241424.12415(4.0)24162241721.32418(4.8)241936.52420(6.4)242140.32422(5.6)24233242422.22425(6.7)242635.22427(7.2)242855.22429(6.9)24304243124.52432(6.8)243325.22434(6.8)243561.12436(8.2)24375+24386.92439(4.2)244021.52441(10.1)244237.62443(10.6)2444Gift or inheritance received2445Yes244622.22447(7.1)244841.82449(9.3)245036.12451(7.9)2452No245317.62454(2.3)245529.12456(2.9)245737.12458(2.9)2459Gift or inheritance expected2460Yes246134.02462(5.8)246343.62464(6.6)246551.82466(6.0)2467No246813.02469(2.2)247026.42471(3.3)247232.22473(3.1)2474Notes: The table reports the share of renting households simultaneously fulfilling purchase affordability and repayment affordability,2475or fulfilling each criteria separately. Standard errors are reported in parentheses. Selected household characteristics represent some2476of the main ingredients for the construction of the affordability measures. Q1 to Q5 denote quintiles.247728247824792480===== PAGE 75 (score 2, numeric-paren 0, table-words 0, var-words 2) =====24812482References2483Chen, Y., Math¨a, T. Y., Pulina, G., Schuster, B., and Ziegelmeyer, M. (2020). The Luxembourg2484Household Finance and Consumption Survey: Results from the third wave. BCL Working2485Papers, No. 142.2486Cook, R. D. (1977). Detection of influential observation in linear regression. Technometrics,248719(1):15–18.2488Glaesener, M.-L. and Caruso, G. (2015). Neighborhood green and services diversity effects on2489land prices: Evidence from a multilevel hedonic analysis in Luxembourg. Landscape and2490Urban Planning, 143:100–111.2491Hill, R. J., Steurer, M., and Waltl, S. R. (2023). Owner-occupied housing, inflation and mone-2492tary policy. Journal of Money, Credit and Banking, https://doi.org/10.1111/jmcb.13059.2493Hill, R. J. and Syed, I. A. (2016). Hedonic price-rent ratios, user cost, and departures from2494equilibrium in the housing market. Regional Science and Urban Economics, 56:60–72.2495Household Finance and Consumption Network (2020). HFCS user database: Documentation2496core and derived variables. HFCS, March-2020.2497292498