1# RECORD 36eac2e74fd054fe7faa7ad4134c3aa524d5616d2# TITLE: Mass appraisal for property tax purposes: approach using global and local spatial regression3# YEAR: 2023.0 VENUE: Revista Valorem DOI: 10.29327/2290393.2.2-24# AUTHORS: C. Zilli; Norberto Hochheim5# PAGES: 15 CANDIDATE TABLE PAGES (1-based): [9, 10]6# ABSTRACT: O IPTU é uma fonte de receita essencial para os municípios brasileiros, mas o sistema atual, baseado em valores de avaliação desatualizados, resulta em um tratamento desigual dos contribuintes. Para promovera equidade, são necessárias avaliações regulares de imóveis, especialmente no mercado imobiliário brasileiro, que evolui rapidamente. Um desafio chave neste processo é desenvolver um modelo que trate eficazmente os efeitos espaciais. Este estudo explora aaplicação de modelos de regressão espacial global e local para enfrentar a dependência e heterogeneidade espaciais em avaliações em massa de imóveis, visando garantir uma tributação justado imóvel. Analisando imóveis urbanos, avaliou-seo desempenho do modelo autoregressivo condicional (CAR) como um modelo de regressão global e o modelo de regressãogeograficamente ponderada(GWR) como um modelo de regressão local. As previsões de ambos os modelos são combinadas com a interpolação por krigagem ordinária para gerar uma Planta de Valores Genéricos (PVG)abrangente, representando a área de estudo. Nossos achados demonstram que a modelagem GWR supera o modelo CAR em precisão e sua capacidade de contabilizar a dependência e heterogeneidade espacial. Isso destacao GWR como uma alternativa viável para estabelecer uma base justa e equitativa para o cálculo de impostos sobre imóveis. Esta pesquisa contribui significativamente para o avanço das técnicas de avaliação em massa de imóveis, assegurando que a coleta do IPTU esteja alinhada com a natureza dinâmica do mercado imobiliário brasileiro. As percepções do estudo fornecem orientações valiosas para formuladores de políticas e profissionais na melhoria dos sistemas de tributação de propriedades, beneficiando, em última análise, tanto municípios quanto contribuintes.789===== PAGE 1 (score 9, numeric-paren 0, table-words 0, var-words 9) =====1011VALOREM | REVISTA DA SOCIEDADE BRASILEIRA DE ENGENHARIA DE AVALIAÇÕES | E-ISSN 2764-8532 12 13 Revista Valorem | v. 2 n. 2 (2023) | Página 10 14 15 16Revista da Sociedade Brasileira de Engenharia de Avaliações 17 18 19MASS APPRAISAL FOR PROPERTY TAX PURPOSES: APPROACH 20USING GLOBAL AND LOCAL SPATIAL REGRESSION21 22Avaliação em massa de imóveis para fins de imposto predial: abordagem utilizando 23regressão espacial global e local24 25 26Carlos Augusto Zilli 27http://orcid.org/0000-0002-4926-1186 28Instituto Federal de Santa Catarina (IFSC), 29Florianópolis, Brasil 30carloszilli@gmail.com 31 32Norberto Hochheim 33http://orcid.org/0000-0003-4670-4831 34Universidade Federal de Santa Catarina (UFSC), 35Florianópolis, Brasil 36hochheim@gmail.com 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68Preenchimento dos Editores 69 70INFORMAÇÕES SOBRE O ARTIGO 71Submetido em7218/06/202373Aceito em7422/09/202375Publicado em7625/09/202377 78Comitê Científico Interinstitucional 79Editor-Responsável: Carlos Augusto Zilli 80Avaliado pelo Sistema Double Blind Review 81 82ABSTRACT 83Property tax is a vital revenue source for Brazilian municipalities, but the 84current system based on outdated assessment values results in unequal 85treatment of taxpayers. To promote fairness, regular property appraisals are 86necessary, especially in the rapidly evolving Brazilian real estate market. A 87key challenge in this process is developing a model that effectively 88addresses spatial effects. This study explores the application of global and 89local spatial regression models to tackle spatial dependence and 90heterogeneity in mass property appraisals, aiming to ensure fair property 91taxation. Analyzing urban properties, we evaluate the performance of the 92conditional autoregressive model (CAR) as a global regression model and 93geographically weighted regression (GWR) as a local regression model. 94Predictions from both models are combined with ordinary kriging 95interpolation to generate a comprehensive Property Value Map (PVM) 96representing the study area. Our findings show that the GWR modeling 97surpasses the CAR model in accuracy and its ability to account for spatial 98dependence and heterogeneity. This highlights GWR as a viable alternative 99for establishing a fair and equitable basis for calculating real estate taxes. 100This research significantly contributes to advancing mass appraisal 101techniques, ensuring property tax collection aligns with the dynamic nature 102of the Brazilian real estate market. The study's insights provide valuable 103guidance for policymakers and practitioners in improving property tax 104systems, ultimately benefiting municipalities and taxpayers alike.105Keywords: Mass appraisal of properties; Property tax; Property values 106map; Geographically weighted regression; Spatial econometrics.107RESUMO108O IPTU é uma fonte de receita essencial para os municípios brasileiros, 109mas o sistema atual, baseado em valores de avaliação desatualizados, 110resulta em um tratamento desigual dos contribuintes. Para promover a 111equidade, são necessárias avaliações regulares de imóveis, especialmente 112no mercado imobiliário brasileiro, que evolui rapidamente. Um desafio 113chave neste processo é desenvolver um modelo que trate eficazmente os 114efeitos espaciais. Este estudo explora a aplicação de modelos de regressão 115espacial global e local para enfrentar a dependência e heterogeneidade 116espaciais em avaliações em massa de imóveis, visando garantir uma 117tributação justa do imóvel. Analisando imóveis urbanos, avaliou-se o 118desempenho do modelo autoregressivo condicional (CAR) como um modelo 119de regressão global e o modelo de regressão geograficamente ponderada 120(GWR) como um modelo de regressão local. As previsões de ambos os 121modelos são combinadas com a interpolação por krigagem ordinária para 122gerar uma Planta de Valores Genéricos (PVG) abrangente, representando a 123área de estudo. Nossos achados demonstram que a modelagem GWR 124supera o modelo CAR em precisão e sua capacidade de contabilizar a 125dependência e heterogeneidade espacial. Isso destaca o GWR como uma 126alternativa viável para estabelecer uma base justa e equitativa para o 127cálculo 128de 129impostos 130sobre 131imóveis. 132Esta 133pesquisa 134contribui 135significativamente para o avanço das técnicas de avaliação em massa de 136imóveis, assegurando que a coleta do IPTU esteja alinhada com a natureza 137dinâmica do mercado imobiliário brasileiro. As percepções do estudo 138fornecem 139orientações 140valiosas 141para 142formuladores 143de 144políticas 145e 146profissionais na melhoria dos sistemas de tributação de propriedades, 147beneficiando, em última análise, tanto municípios quanto contribuintes.148Palavras-Chave: Avaliação em massa de imóveis; Imposto predial, Planta 149de valores genéricos; Regressão geograficamente ponderada; Econometria. 150 151 152153154===== PAGE 9 (score 36, numeric-paren 0, table-words 9, var-words 15) =====155156VALOREM | REVISTA DA SOCIEDADE BRASILEIRA DE ENGENHARIA DE AVALIAÇÕES | E-ISSN 2764-8532 157 158 Revista Valorem | v. 2 n. 2 (2023) | Página 18 159In the spatial regression error model, the lambda () represents the term of spatial error autocorrelation 160and is significant at the level of 5.0%. It is also possible to observe that all variables in the spatial regression 161error model were significant at the level of 5.0%, as shown in table 4. 162 163Table 4: Statistics related to the parameters of the CAR model. 164Variable1165Coefficients 166zcalc 167Significance 168Intercepto 16910.6470 17038.1924 1710.00000 172ln (FA) 173– 0.43255 1747.81141 1750.00000 176ln (DA) 177– 0.11770 1785.35113 1790.00000 180NB 1810.05794 1822.76309 1830.00573 184BT 1850.03583 1862.12263 1870.03379 188NG 1890.18520 1908.92755 1910.00000 192SP 1930.09129 1943.47056 1950.00052 196CQ 1970.20171 19812.3279 1990.00000 200 (lâmbda) 2010.56916 2024.57072 2030.00000 2041 Note: FA: floor area; DA: distance to Beira Mar Avenue; NB: number of bedrooms; BT: number of bathrooms; NG: number of 205parking spaces; SP: swimming pool; CQ: construction quality; : term of spatial autocorrelation. 206 207It is possible to observe that all regressors are significant and important for the formation of the model, 208confirmed by the low and close to zero significance. The signs of the regressors of the spatial regression 209error model confirm the expectation of the local real estate market, and are therefore consistent. 210Finally, the Breusch-Pagan test for the residuals of the spatial regression error model indicated that 211there are no problems of heteroscedasticity. With a BP value of 6.57 and a p-value of 0.4740, it can be said, 212at the 5.0% level of significance, that the autoregressive spatial error model is homocedastic. 213 2143.3. LOCAL SPATIAL REGRESSION RESULTS (GWR) 215 216The GWR model was adjusted with the same transformations and the same 190 market data used in 217the spatial regression of the error. To choose the best weighting function, whether fixed or variable, and the 218optimal bandwidth, the software GWR4 by Fotheringham et al. (2005) was employed, as described in the 219Methodology. Multiple simulations were conducted, which were separated according to selection criteria 220defined by the user in the GWR4 software interface. 221The type of weighting function was evaluated between fixed or variable Gaussian and fixed or variable 222bi-squared. The software also allows you to choose the stopping criterion and check the automatic checkbox 223for the best bandwidth. It then generates several models for different bandwidths, based on the selected 224weighting function and finally presents the one with the lowest value for the selected criterion (AIC, AICc and 225CV). 226Twelve models were generated and the chosen one would be the one that provided the lowest value in 227the Akaike information criterion (AIC), a parameter that will be used to make the comparison between the 228models generated in this study. The model that generated the lowest value in the AIC criterion was the fixed 229Gaussian weighting function with bandwidth = 278.42 m. 230As seen, there is still the possibility that, among the seven explanatory variables considered in this 231study, one of them presents spatial stationarity, that is, it does not have a relevant spatial variability along the 232geographic plane. 233In general, the geographic variability for each coefficient can be tested by comparing models. To test 234the geographical variability of the k-th variable coefficient, a model comparison is performed between the 235adjusted GWR and a test model in which only the k-th coefficient is fixed, while other coefficients are 236maintained as in the geographically weighted adjusted model. 237In this case, if the adjusted GWR is better than the test GWR model, using the AICc as a comparison 238criterion, we can conclude that the k-th coefficient certainly varies in space. This test routine repeats this 239comparison between models for each geographically variable coefficient. 240For this test, as described by Leung et al. (2000), a positive DIFF Criterion, especially greater than 2.0, 241suggests that the local variable can be assumed as global. In the test, only the pool variable (PS) showed a 242positive result and greater than 2.0. In this study, this variable will be considered as global. The model, 243containing average coefficients for the local variables, and fixed coefficient for the pool variable, is in (9): 244 245ln (UV) = 0 + 1 ln (FA) + 2 ln (DA) + 3 (NB) + 4 (BT) + 5 (NG) + 6 (SP) + 7 (CQ) 246(9) 247248249===== PAGE 10 (score 29, numeric-paren 0, table-words 12, var-words 2) =====250251VALOREM | REVISTA DA SOCIEDADE BRASILEIRA DE ENGENHARIA DE AVALIAÇÕES | E-ISSN 2764-8532 252 253 Revista Valorem | v. 2 n. 2 (2023) | Página 19 254In the GWR model, the transformations adopted in the CAR model remained. It is noteworthy that the 255average coefficients were used because the GWR modeling, being a local regression, generates a 256regression equation for each sample point, weighted by the distance from its neighbors. The GWR model 257generated a report containing 190 regressions with the parameter estimates, the calculation of the t statistics 258and the standard error for each variable, as well as the predicted value, the local determination coefficient, 259the Cook distance and the influence, for each observation of the sample. Table 5 shows the statistics of the 260GWR model: 261 262Table 5: Statistics related to the parameters of the GWR model. 263Variable264Average Coefficients 265Median Coefficients 266DIFF Criterion 267Type 268Intercepto 26910.73166 27010.73542 271– 681.00 272Local 273ln (FA) 274– 0.51700 275– 0.50740 276– 490.75 277Local 278ln (DA) 279– 0.08873 280– 0.10434 281– 685.68 282Local 283NB 2840.06497 2850.06628 286– 6.0723 287Local 288BT 2890.06173 2900.06011 291– 8.8288 292Local 293NG 2940.19071 2950.19394 296– 8.5496 297Local 298SP 2990.09732 3000.09732 3012.2167 302Global 303CQ 3040.20735 3050.22325 306– 13.272 307Local 308 309The signs of the regressors of the geographically weighted regression model (GWR) were the same as 310the signs of the spatial error model (CAR) and confirm the expectation of the local real estate market, being, 311therefore, coherent. 312 3133.4. GOODNESS OF FIT AND PERFORMANCE 314 315In this study, the quality of the fit of the models was analyzed using the Akaike (AIC), Bayesian (BIC) 316and Loglikelihood (LIK) information criteria, the determination coefficient (R²) and the standard error of the 317regression. Table 6 shows the indicators. 318 319Table 6: Quality indicators of the modeling performed. 320Statistics 321CAR Model 322GWR Model 323Determination Coefficient (R2) 3240.8169 3250.9239 326Log Likelihood (LIK) 32797.348 328182.005 329Schwarz Criterion (BIC) 330– 152.80 331– 187.12 332Akaike Criterion (AIC) 333– 178.70 334– 209.78 335Standard Error of Regression (Se) 3360.1425 3370.1303 338 339It is possible to notice that the GWR model proved to be superior to the CAR model in all the fit quality 340indicators in table 6. 341It was also verified how the absolute relative errors of the values predicted by the models were 342dispersed. Then, linear interpolation was performed to generate the surface of gradients, containing the 343absolute relative errors estimated for each modeling. These interpolations can be seen in figures 4a and 4b. 344 345 346Figure 4: Surface of relative absolute errors for 4a) CAR model and 4b) GWR model. 347 348Figures 4a and 4b show that the surface of relative errors for the GWR modeling was more uniform, 349with errors of lesser magnitude, evidenced by the dominance of the blue color. 350351352===== PAGE 11 (score 18, numeric-paren 0, table-words 8, var-words 1) =====353354VALOREM | REVISTA DA SOCIEDADE BRASILEIRA DE ENGENHARIA DE AVALIAÇÕES | E-ISSN 2764-8532 355 356 Revista Valorem | v. 2 n. 2 (2023) | Página 20 357As a way of visualizing the predictive power of the models, a dispersion graph of the observed versus 358adjusted values was constructed for each of the models, according to figures 5a and 5b. 359 360 361 362Figure 5: Dispersion diagram for 8a) CAR model and 8b) GWR model. 363 364It is possible to notice that the GWR model was more adjusted, with less dispersed points, indicating 365that it is an adjustment with greater predictive power of unit values than the CAR model. To analyze the 366performance of the modeling, we used the metrics established by the IAAO (2013). The limits established by 367the standard for the properties under study are shown in table 2. 368The data from the validation partition contained 17 properties in the Centro neighborhood, 6 properties 369in the Agronômica neighborhood and 12 properties in the Trindade neighborhood, as shown in table 1. The 370validation partition was analyzed to verify the presence of some discrepant data that could impair the results. 371It was found that the data AV_14, whose unit value of the property is R$ 17,500.00, is an outlier and, for this 372reason, was not used in the calculations. 373To calculate the performance of the geographically weighted regression, the prediction of the unit 374values of the validation partition was performed directly in the GWR4 software. The GWR4 software 375provides, for each of the validation partitions, based on the selected kernel and bandwidth, a prediction 376equation, with the respective t-statistic, standard error and local R² values. 377The results of the three indicators recommended by the IAAO (International Association of Assessing 378Officers) are shown in table 7. 379 380Table 7: Performance indicators of the modeling performed. 381Statistics 382CAR Model 383GWR Model 384Median of the Assessment Ratios (RATIO) 3850.968 3860.957 387Coefficient of Dispersion of the Median (COD) 38812.22% 38910.57% 390Price Related Differential (PRD) 3911.017 3921.015 393 394It can be observed that the two models presented values within the limits recommended by the 395standard. However, the GWR modeling proved to be superior, indicating greater uniformity in the 396assessment, as evidenced by the lower value in the COD. As for the PRD, the results indicate that there was 397no progressivity or regressivity in the predictions. Nevertheless, the GWR model exhibited slightly superior 398performance in this indicator. 399In addition, the square root of the mean square error (RMSE) was also calculated for the unit values 400predicted by the validation partition. The results are shown in table 8. 401 402Table 8: Root mean squared error (RMSE) for the validation partition. 403Statistics 404CAR Model 405GWR Model 406RMSE VALIDATION PARTITION 4071,412.27 4081,321.25 409Notes: The currency exchange rate in 05/2023 is US$ 1.00 = R$ 5.05 410 411In this case, the GWR modeling, which is a local spatial regression, again presented lower values for 412the RMSE. This phenomenon corroborates the idea that the value of a given property is strongly affected by 413the value of the properties in its surroundings. 414