1# RECORD 61571b403ee0b92394b214f7249ffc6c6a95a4dc2# TITLE: Improving housing valuation for taxation: the Norwegian case3# YEAR: 2025.0 VENUE: International Tax and Public Finance DOI: 10.1007/s10797-025-09928-24# AUTHORS: E. E. Bø; O. E. Nygård; Thor O. Thoresen5# PAGES: 21 CANDIDATE TABLE PAGES (1-based): [13, 15]6# ABSTRACT: 7 Several forms of taxation incorporate the market value of housing into their tax base, making accurate and up-to-date property valuations important. However, due to limitations in available information, assessing residential property values poses a significant challenge for tax authorities. This paper presents and examines the simple, inexpensive and transparent methodology currently used in Norway to assign market values to individual dwellings for wealth taxation purposes. The method uses predictions generated through hedonic regression models based on housing transaction data. We present two versions of the method: the current model, introduced in 2010, and a refined version that substantially improves prediction accuracy, through the use of data from smaller geographical units. This latter enhancement incorporates machine learning techniques for geographical clustering.8910===== PAGE 1 (score 3, numeric-paren 0, table-words 0, var-words 3) =====1112POLICY WATCH13International Tax and Public Finance14https://doi.org/10.1007/s10797-025-09928-215Abstract16Several forms of taxation incorporate the market value of housing into their tax 17base, making accurate and up-to-date property valuations important. However, 18due to limitations in available information, assessing residential property values 19poses a significant challenge for tax authorities. This paper presents and examines 20the simple, inexpensive and transparent methodology currently used in Norway 21to assign market values to individual dwellings for wealth taxation purposes. The 22method uses predictions generated through hedonic regression models based on 23housing transaction data. We present two versions of the method: the current model, 24introduced in 2010, and a refined version that substantially improves prediction 25accuracy, through the use of data from smaller geographical units. This latter en26hancement incorporates machine learning techniques for geographical clustering.27Keywords Taxation of housing · Housing valuation · Hedonic regression · 28Machine learning29JEL Classification C51 · D31 · H6130Received: 14 October 2025 / Accepted: 16 October 202531© The Author(s) 202532Improving housing valuation for taxation: the Norwegian 33case34Erlend E. Bø1 · Odd E. Nygård1 · Thor O. Thoresen1,235 36 Erlend E. Bø37eeb@ssb.no38Odd E. Nygård39oen@ssb.no40Thor O. Thoresen41tot@ssb.no421 43Research Department, Statistics Norway, Oslo, Norway442 45Norwegian Fiscal Studies, Department of Economics, University of Oslo, Oslo, Norway461 3474849===== PAGE 13 (score 17, numeric-paren 0, table-words 6, var-words 3) =====5051Improving housing valuation for taxation: the Norwegian case52It is known that the current model does not produce good predictions for the most 53expensive houses.24 To see if the revised model improves these predictions, we next 54look at the most expensive houses in Oslo. Table 2, Panel A, shows measures of 55fit for housing transactions in Oslo with a transaction price of 10 million NOK or 56more.25 The existing model does clearly worse for this subsample, with an R2 of only 570.42—the revised model improves the fit by 40%. The median high-priced house is 58undervalued by 16.7% in the existing model, compared to 7.7% in the revised model.59To visually assess the performance of the prediction models for the most expen60sive houses, Fig. 2 shows transaction prices and predicted prices from the two dif61ferent models for the 369 houses that were sold for more than 20 million NOK over 62the period (2011–2020).26 The predicted prices are almost all below the black circles, 63i.e., below the transaction prices, particularly for the most expensive houses. How64ever, the green crosses of the revised model are generally closer to the transaction 65price than the red triangles of the existing model (as shown by the linear regression 66fit lines).67A common finding from the property taxation literature is that the values of the 68cheapest houses are over-estimated (McMillen & Singh, 2020; Berry, 2021; Amorns69iripanitch, 2022; Avenancio-León & Howard, 2022). To see the extent of overvalu70ation in our setting, we look at results for houses in the lowest 5% of transaction 71prices (sold for 1.3 million NOK or less). The estimates are presented in Table 2, 72Panel B. The existing model overestimates the median price by almost 28%, which is 73almost halved to 14% in the revised model. Also for the other measures of fit, there is 74a clear improvement in the revised model.277524 Such criticism shows up as anecdotal evidence reported in the press, but is also shown in Bø and Nygård 76(2023).7725 Around USD 1.1 million or EUR 1 million (2020); the top 3.5% of dwellings in Oslo.7826 The set of housing transactions exceeding 10 million NOK, shown in Table 2, is too large to serve as the 79basis for an effective visualization in this manner.8027 For the specific purpose of the Norwegian wealth tax, the overvaluation is not that problematic, as 81people owning the cheapest houses are rarely in a wealth tax position. Primary housing is assessed at 25% 82of its predicted value, meaning that an estimated value of 1.3 million NOK corresponds to a tax valuation 83(A) Expensive84(B) Cheap85Model86Existing Revised Existing Revised87Average absolute error (%)8817.498912.879040.659126.1692Median absolute error (%)9315.449410.509528.079616.0997Median error (%)98−16.6899−7.7010027.8510114.33102Standard deviation10318.2210415.3810544.9110634.52107R21080.4151090.5901100.0961110.217112Panel A describes model performance for expensive housing in the 113Oslo-area (transaction price of 10 million NOK or more) by five 114different measures, comparing predicted prices to realized prices 115from transaction data. Panel B describes the same measures for all 116housing with low transaction prices (transaction price of 1.3 million 117NOK or less)118Table 2 Model performance of 119the existing and revised models. 120Expensive and cheap houses121 1221 3123124125===== PAGE 14 (score 17, numeric-paren 0, table-words 4, var-words 9) =====126127E. E. Bø et al.128As mentioned in Sect. 4, the available transaction data includes more informa129tion on properties than what is currently exploited in the model. Using more of that 130information could possibly reduce omitted variable bias. We thus test the inclusion of 131some extra variables in the new model, specifically the number of bedrooms and plot 132size for single-family houses and semi-detached houses, and the number of bedrooms 133and the floor for apartments.28 With reference to the indicators reported in Table 1341, including these variables increases R2 by approximately 1%, whereas the other 135three measures yield an improvement of around 6% (see Table A.2 in the Online 136appendix). This indicates that some improvements could be made by adding further 137explanatory variables to the hedonic model.29 However, there is a trade-off between 138fit and implementation cost, as adding variables would involve the collection of these 139variables for all housing units by the tax administration.1405.2 Out-of-sample estimates141In machine learning models, there is a risk of overfitting to the observed data (Mul142lainathan & Spiess, 2017). To assess whether that is the case, it is common to split 143the sample of observations in two: one set to estimate the model (the training set) and 144of 0.325 million NOK. The minimum deduction per person in the wealth tax was 1.5 million NOK in 2020. 145For the municipal property tax, however, overvaluation of cheap houses is a larger concern.14628 These additions only change the hedonic model. The clustering of calculation groups is not affected.14729 Another approach worth considering is replacing the year dummies in the model with a Fourier expan148sion, as suggested by Ihlanfeldt (2004)149Fig. 2 Predicted prices for expensive houses. Comparison of predictions from the existing model (red 150triangles) and the revised model (green crosses) to transaction prices (black circles) for expensive 151houses (sold for more than 20 million NOK over the period 2011–2020). Fitted lines obtained by linear 152regression153 1541 3155156157===== PAGE 15 (score 19, numeric-paren 0, table-words 7, var-words 3) =====158159Improving housing valuation for taxation: the Norwegian case160one to test the model (the test set). Although overfitting is not expected to pose a sig161nificant issue in this context, since machine learning is used solely to group BSUs by 162geography and square meter price, it remains useful to apply this approach to assess 163robustness.30164We estimate the results on a random 90% estimation sample, testing on the remain165ing 10%. In this setting, the minimum number of required observations is reduced by 16610%, from 500 to 450, to retain roughly the same number of calculation groups. For 167comparison, we also do an out-of-sample test for the existing method, even though 168there is little reason to assume that overfitting should be a problem in a hedonic 169regression model with many observations and few parameters.170The results, shown in Table 3, confirm these expectations. The performance of the 171revised model is a little worse on the test set, for all four measures (the training results 172are very similar to the full sample results). For the existing model, the full sample, 173test and training data give almost indistinguishable results. We note that even for 174the test data set, the revised model represents a clear improvement over the existing 175model.1765.3 Revenue and distributional effects177The new valuation system would have implications for both wealth tax revenue and 178distributional effects of the wealth tax. We use the tax-benefit model LOTTE (Jia et 179al., 2024) to obtain information on effects of going from the existing system to the 180new system.181We find that the revenue from the wealth tax increases by 1.6% (NOK 281 mil182lion), which is caused by higher valuation of expensive houses. While the average 183predicted housing value is equal in both models, expensive houses get higher values, 184and they are to a large extent owned by people who pay wealth taxes. Houses that get 185lower valuations, often cheap housing in rural areas, affect tax revenue less, as their 186owners often do not pay any wealth tax. A switch to the revised model would increase 187the wealth tax for 300,000 persons, while 225,000 persons get a decrease.18830 Another useful validation approach is illustrated in Ihlanfeldt (2004), where model predictions are com189pared with subsequent (post-assessment) sales. The model is made to predict valuation at the end of the 190training data period, but uses data for 10 years. The suggested method would be a good test of the model’s 191predictive accuracy at the prediction time. We do however lack sales from after 2020 in the available data 192set.193Table 3 Model performance of the existing and revised models, training and test194Model195Existing196Revised197Full198Training199Test200Full201Training202Test203Average absolute error (percent)20415.5820515.5820615.5420711.2920811.2520912.00210Median absolute error (percent)21111.4821211.4821311.472148.112158.082168.53217Standard deviation21822.4421922.4622022.3222116.7222216.6422318.19224R22250.8332260.8332270.8322280.9052290.9062300.890231The table describes model performance by four different measures, comparing predicted prices to 232realized prices from transaction data. The columns marked Full shows the results from Table 1, while 233training and test shows results the 90% training sample and the 10% test sample, respectively2341 3235236237===== PAGE 16 (score 15, numeric-paren 0, table-words 6, var-words 1) =====238239E. E. Bø et al.240To evaluate the distributional effects of applying the revised model, we first focus 241on individuals directly affected by the changes—those whose wealth tax liabilities 242are influenced by the new model. In Table 4, these individuals are ranked by gross 243income, and we estimate the change in tax payments for each income decile using 244the tax-benefit model. Overall, the increases in tax payments are relatively modest, 245reaching 1,224 NOK for decile 10 and averaging 532 NOK across all deciles. When 246we express the change in tax payments as a percentage of gross income, the new 247model appears to make the wealth tax slightly more regressive for these individuals. 248The most notable effect is observed in decile 1, where the change in tax payments is 249the highest relative to income. This is partly attributable to the presence of wealthy 250individuals in the first decile who report low or negative incomes, either due to sub251stantial capital losses or life-cycle-related low earnings.252When examining the effects on the entire population, the overall picture changes, 253see Table 5. Now, the introduction of the revised model no longer makes the wealth 254tax more regressive. The relative impact on individuals in higher income deciles 255increases, while it decreases in low income deciles. This is because few people with 256Decile257Gross income258Change in tax 259payments260As share 261of income 262(%)263126441,994265142660.0342672268187,269269212700.0112713272270,464273232740.0092754276333,858277332780.0102795280399,554281462820.0122836284467,034285462860.0102877288539,054289492900.0092918292623,770293572940.0092959296759,918297882980.012299103001,442,3343012693020.019303All304506,525305653060.013307Table 5 Existing versus revised 308model for 2020. All individuals 309ranked by gross income310Estimates are averages in NOK 311obtained by the use of the tax-312benefit model LOTTE-Skatt. 313Change as percentage share 314of income is calculated as the 315average of change divided by 316the average of income. The 317table includes all individuals 17 318years and older319 320Decile321Gross income322Change in tax 323payments324As share 325of income 326(%)3271328188,6393293713300.1973312332304,6343332643340.0873353336369,5893373033380.0823394340430,9953413773420.0873435344501,3063454083460.0813476348588,0173494733500.0803517352695,0563535173540.0743558356851,4733576343580.07435993601,134,6753617453620.066363103643,024,47436512243660.040367All368808,8863695323700.066371Table 4 Existing versus revised 372model for 2020. Individuals 373experiencing change in tax pay374ments ranked by gross income375Estimates are averages in NOK 376obtained by the use of the tax-377benefit model LOTTE-Skatt. 378Change as percentage share 379of income is calculated as the 380average of change divided by 381the average of income. The 382table includes individuals 17 383years and older experiencing 384change in tax payments385 3861 3387