# RECORD 61571b403ee0b92394b214f7249ffc6c6a95a4dc # TITLE: Improving housing valuation for taxation: the Norwegian case # YEAR: 2025.0 VENUE: International Tax and Public Finance DOI: 10.1007/s10797-025-09928-2 # AUTHORS: E. E. Bø; O. E. Nygård; Thor O. Thoresen # PAGES: 21 CANDIDATE TABLE PAGES (1-based): [13, 15] # ABSTRACT: 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. ===== PAGE 1 (score 3, numeric-paren 0, table-words 0, var-words 3) ===== POLICY WATCH International Tax and Public Finance https://doi.org/10.1007/s10797-025-09928-2 Abstract 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 en­ hancement incorporates machine learning techniques for geographical clustering. Keywords  Taxation of housing · Housing valuation · Hedonic regression · Machine learning JEL Classification  C51 · D31 · H61 Received: 14 October 2025 / Accepted: 16 October 2025 © The Author(s) 2025 Improving housing valuation for taxation: the Norwegian case Erlend E. Bø1 · Odd E. Nygård1 · Thor O. Thoresen1,2 Erlend E. Bø eeb@ssb.no Odd E. Nygård oen@ssb.no Thor O. Thoresen tot@ssb.no 1 Research Department, Statistics Norway, Oslo, Norway 2 Norwegian Fiscal Studies, Department of Economics, University of Oslo, Oslo, Norway 1 3 ===== PAGE 13 (score 17, numeric-paren 0, table-words 6, var-words 3) ===== Improving housing valuation for taxation: the Norwegian case It is known that the current model does not produce good predictions for the most expensive houses.24 To see if the revised model improves these predictions, we next look at the most expensive houses in Oslo. Table 2, Panel A, shows measures of fit for housing transactions in Oslo with a transaction price of 10 million NOK or more.25 The existing model does clearly worse for this subsample, with an R2 of only 0.42—the revised model improves the fit by 40%. The median high-priced house is undervalued by 16.7% in the existing model, compared to 7.7% in the revised model. To visually assess the performance of the prediction models for the most expen­ sive houses, Fig. 2 shows transaction prices and predicted prices from the two dif­ ferent models for the 369 houses that were sold for more than 20 million NOK over the period (2011–2020).26 The predicted prices are almost all below the black circles, i.e., below the transaction prices, particularly for the most expensive houses. How­ ever, the green crosses of the revised model are generally closer to the transaction price than the red triangles of the existing model (as shown by the linear regression fit lines). A common finding from the property taxation literature is that the values of the cheapest houses are over-estimated (McMillen & Singh, 2020; Berry, 2021; Amorns­ iripanitch, 2022; Avenancio-León & Howard, 2022). To see the extent of overvalu­ ation in our setting, we look at results for houses in the lowest 5% of transaction prices (sold for 1.3 million NOK or less). The estimates are presented in Table 2, Panel B. The existing model overestimates the median price by almost 28%, which is almost halved to 14% in the revised model. Also for the other measures of fit, there is a clear improvement in the revised model.27 24 Such criticism shows up as anecdotal evidence reported in the press, but is also shown in Bø and Nygård (2023). 25 Around USD 1.1 million or EUR 1 million (2020); the top 3.5% of dwellings in Oslo. 26 The set of housing transactions exceeding 10 million NOK, shown in Table 2, is too large to serve as the basis for an effective visualization in this manner. 27 For the specific purpose of the Norwegian wealth tax, the overvaluation is not that problematic, as people owning the cheapest houses are rarely in a wealth tax position. Primary housing is assessed at 25% of its predicted value, meaning that an estimated value of 1.3 million NOK corresponds to a tax valuation (A) Expensive (B) Cheap Model Existing Revised Existing Revised Average absolute error (%) 17.49 12.87 40.65 26.16 Median absolute error (%) 15.44 10.50 28.07 16.09 Median error (%) −16.68 −7.70 27.85 14.33 Standard deviation 18.22 15.38 44.91 34.52 R2 0.415 0.590 0.096 0.217 Panel A describes model performance for expensive housing in the Oslo-area (transaction price of 10 million NOK or more) by five different measures, comparing predicted prices to realized prices from transaction data. Panel B describes the same measures for all housing with low transaction prices (transaction price of 1.3 million NOK or less) Table 2  Model performance of the existing and revised models. Expensive and cheap houses 1 3 ===== PAGE 14 (score 17, numeric-paren 0, table-words 4, var-words 9) ===== E. E. Bø et al. As mentioned in Sect. 4, the available transaction data includes more informa­ tion on properties than what is currently exploited in the model. Using more of that information could possibly reduce omitted variable bias. We thus test the inclusion of some extra variables in the new model, specifically the number of bedrooms and plot size for single-family houses and semi-detached houses, and the number of bedrooms and the floor for apartments.28 With reference to the indicators reported in Table 1, including these variables increases R2 by approximately 1%, whereas the other three measures yield an improvement of around 6% (see Table A.2 in the Online appendix). This indicates that some improvements could be made by adding further explanatory variables to the hedonic model.29 However, there is a trade-off between fit and implementation cost, as adding variables would involve the collection of these variables for all housing units by the tax administration. 5.2  Out-of-sample estimates In machine learning models, there is a risk of overfitting to the observed data (Mul­ lainathan & Spiess, 2017). To assess whether that is the case, it is common to split the sample of observations in two: one set to estimate the model (the training set) and of 0.325 million NOK. The minimum deduction per person in the wealth tax was 1.5 million NOK in 2020. For the municipal property tax, however, overvaluation of cheap houses is a larger concern. 28 These additions only change the hedonic model. The clustering of calculation groups is not affected. 29 Another approach worth considering is replacing the year dummies in the model with a Fourier expan­ sion, as suggested by Ihlanfeldt (2004) Fig. 2  Predicted prices for expensive houses. Comparison of predictions from the existing model (red triangles) and the revised model (green crosses) to transaction prices (black circles) for expensive houses (sold for more than 20 million NOK over the period 2011–2020). Fitted lines obtained by linear regression 1 3 ===== PAGE 15 (score 19, numeric-paren 0, table-words 7, var-words 3) ===== Improving housing valuation for taxation: the Norwegian case one to test the model (the test set). Although overfitting is not expected to pose a sig­ nificant issue in this context, since machine learning is used solely to group BSUs by geography and square meter price, it remains useful to apply this approach to assess robustness.30 We estimate the results on a random 90% estimation sample, testing on the remain­ ing 10%. In this setting, the minimum number of required observations is reduced by 10%, from 500 to 450, to retain roughly the same number of calculation groups. For comparison, we also do an out-of-sample test for the existing method, even though there is little reason to assume that overfitting should be a problem in a hedonic regression model with many observations and few parameters. The results, shown in Table 3, confirm these expectations. The performance of the revised model is a little worse on the test set, for all four measures (the training results are very similar to the full sample results). For the existing model, the full sample, test and training data give almost indistinguishable results. We note that even for the test data set, the revised model represents a clear improvement over the existing model. 5.3  Revenue and distributional effects The new valuation system would have implications for both wealth tax revenue and distributional effects of the wealth tax. We use the tax-benefit model LOTTE (Jia et al., 2024) to obtain information on effects of going from the existing system to the new system. We find that the revenue from the wealth tax increases by 1.6% (NOK 281 mil­ lion), which is caused by higher valuation of expensive houses. While the average predicted housing value is equal in both models, expensive houses get higher values, and they are to a large extent owned by people who pay wealth taxes. Houses that get lower valuations, often cheap housing in rural areas, affect tax revenue less, as their owners often do not pay any wealth tax. A switch to the revised model would increase the wealth tax for 300,000 persons, while 225,000 persons get a decrease. 30 Another useful validation approach is illustrated in Ihlanfeldt (2004), where model predictions are com­ pared with subsequent (post-assessment) sales. The model is made to predict valuation at the end of the training data period, but uses data for 10 years. The suggested method would be a good test of the model’s predictive accuracy at the prediction time. We do however lack sales from after 2020 in the available data set. Table 3  Model performance of the existing and revised models, training and test Model Existing Revised Full Training Test Full Training Test Average absolute error (percent) 15.58 15.58 15.54 11.29 11.25 12.00 Median absolute error (percent) 11.48 11.48 11.47 8.11 8.08 8.53 Standard deviation 22.44 22.46 22.32 16.72 16.64 18.19 R2 0.833 0.833 0.832 0.905 0.906 0.890 The table describes model performance by four different measures, comparing predicted prices to realized prices from transaction data. The columns marked Full shows the results from Table 1, while training and test shows results the 90% training sample and the 10% test sample, respectively 1 3 ===== PAGE 16 (score 15, numeric-paren 0, table-words 6, var-words 1) ===== E. E. Bø et al. To evaluate the distributional effects of applying the revised model, we first focus on individuals directly affected by the changes—those whose wealth tax liabilities are influenced by the new model. In Table 4, these individuals are ranked by gross income, and we estimate the change in tax payments for each income decile using the tax-benefit model. Overall, the increases in tax payments are relatively modest, reaching 1,224 NOK for decile 10 and averaging 532 NOK across all deciles. When we express the change in tax payments as a percentage of gross income, the new model appears to make the wealth tax slightly more regressive for these individuals. The most notable effect is observed in decile 1, where the change in tax payments is the highest relative to income. This is partly attributable to the presence of wealthy individuals in the first decile who report low or negative incomes, either due to sub­ stantial capital losses or life-cycle-related low earnings. When examining the effects on the entire population, the overall picture changes, see Table 5. Now, the introduction of the revised model no longer makes the wealth tax more regressive. The relative impact on individuals in higher income deciles increases, while it decreases in low income deciles. This is because few people with Decile Gross income Change in tax payments As share of income (%) 1 41,994 14 0.034 2 187,269 21 0.011 3 270,464 23 0.009 4 333,858 33 0.010 5 399,554 46 0.012 6 467,034 46 0.010 7 539,054 49 0.009 8 623,770 57 0.009 9 759,918 88 0.012 10 1,442,334 269 0.019 All 506,525 65 0.013 Table 5  Existing versus revised model for 2020. All individuals ranked by gross income Estimates are averages in NOK obtained by the use of the tax- benefit model LOTTE-Skatt. Change as percentage share of income is calculated as the average of change divided by the average of income. The table includes all individuals 17 years and older Decile Gross income Change in tax payments As share of income (%) 1 188,639 371 0.197 2 304,634 264 0.087 3 369,589 303 0.082 4 430,995 377 0.087 5 501,306 408 0.081 6 588,017 473 0.080 7 695,056 517 0.074 8 851,473 634 0.074 9 1,134,675 745 0.066 10 3,024,474 1224 0.040 All 808,886 532 0.066 Table 4  Existing versus revised model for 2020. Individuals experiencing change in tax pay­ ments ranked by gross income Estimates are averages in NOK obtained by the use of the tax- benefit model LOTTE-Skatt. Change as percentage share of income is calculated as the average of change divided by the average of income. The table includes individuals 17 years and older experiencing change in tax payments 1 3