1# RECORD c30509d1b7dff13ef9c6d68570be3618b239e0cd2# TITLE: An Assessment Methodology for the Evaluation of the Impacts of the COVID-19 Pandemic on the Italian Housing Market Demand3# YEAR: 2021.0 VENUE: Buildings DOI: 10.3390/buildings111205924# AUTHORS: F. Tajani; F. Di Liddo; M. Guarini; Rossana Ranieri; D. Anelli5# PAGES: 28 CANDIDATE TABLE PAGES (1-based): [6, 14, 16, 17]6# ABSTRACT: Due to the forced changes that the COVID-19 pandemic has had in many aspects of ordinary life (working, social life, training and learning in schools etc.), the characteristics of domestic spaces have significantly modified buying, selling and renting decisions in the real estate market. The aim of this research was to structure a methodology, articulated into four steps, to assess the variation that has occurred in residential market demand as a result of COVID-19 anti-contagion measures, with regard to six metropolitan Italian cities. We considered two samples of properties for each city, the first referencing the pre-COVID-19 pandemic spread and the second collected in the current situation. Consequently, we were able to determine variations in residential market appreciations through the application of a regressive econometric technique. The obtained results highlighted the relevance assumed by indoor acoustic and thermal comfort property factors, compared with the pre-COVID-19 condition. The proposed methodology could be useful to support the public and private entities involved in urban investment decision-making processes, allowing us to identify the most appreciated factors of the residential real estate market demand, in order to improve the conditions of existing and future assets and reduce the related risk levels.789===== PAGE 1 (score 14, numeric-paren 0, table-words 0, var-words 14) =====1011 12 13 14 15Buildings 2021, 11, 592. https://doi.org/10.3390/buildings11120592 16www.mdpi.com/journal/buildings 17Article 18An Assessment Methodology for the Evaluation of the Impacts 19of the COVID-19 Pandemic on the Italian Housing 20Market Demand 21Francesco Tajani 1,*, Felicia Di Liddo 2, Maria Rosaria Guarini 1, Rossana Ranieri 1 and Debora Anelli 2 221 Department of Architecture and Design, Sapienza University of Rome, Via Flaminia 359, 00196 Rome, Italy; 23mariarosaria.guarini@uniroma1.it (M.R.G.); rossana.ranieri@uniroma1.it (R.R.) 242 Department of Civil, Environmental, Land, Building Engineering and Chemistry (DICATECh), Polytechnic 25University of Bari, Via Orabona 4, 70125 Bari, Italy; felicia.diliddo@poliba.it (F.D.L.); 26debora.anelli@uniroma1.it (D.A.) 27* Correspondence: francesco.tajani@uniroma1.it 28Abstract: Due to the forced changes that the COVID-19 pandemic has had in many aspects of or-29dinary life (working, social life, training and learning in schools etc.), the characteristics of domestic 30spaces have significantly modified buying, selling and renting decisions in the real estate market. 31The aim of this research was to structure a methodology, articulated into four steps, to assess the 32variation that has occurred in residential market demand as a result of COVID-19 anti-contagion 33measures, with regard to six metropolitan Italian cities. We considered two samples of properties 34for each city, the first referencing the pre-COVID-19 pandemic spread and the second collected in 35the current situation. Consequently, we were able to determine variations in residential market 36appreciations through the application of a regressive econometric technique. The obtained results 37highlighted the relevance assumed by indoor acoustic and thermal comfort property factors, 38compared with the pre-COVID-19 condition. The proposed methodology could be useful to sup-39port the public and private entities involved in urban investment decision-making processes, al-40lowing us to identify the most appreciated factors of the residential real estate market demand, in 41order to improve the conditions of existing and future assets and reduce the related risk levels. 42Keywords: COVID-19 pandemic; housing market; property prices; genetic algorithm; housing 43demand 44 451. Introduction 46Starting in the first half of 2019, the COVID-19 pandemic has spread rapidly 47worldwide and, in order to minimize contagion, governments have applied many of 48measures that, most of all, have forced people to stay at home. This has changed the 49shape of ordinary lives, requiring people to continue some activities in the domestic 50space [1–3]. In this way, rooms such as the living room, the bedrooms and the kitchen 51have had to accommodate functions for which they may not have been equipped: in 52many cases they have been transformed into working spaces, gyms, and meeting rooms. 53The impossibility of conducting outdoor activities, on the other hand, has meant that 54balconies, terraces or condominium green outdoor spaces have become the only way out 55of the house, and they too have been transformed into gyms, places of leisure, relaxation 56or work, and meeting areas. In other words, domestic spaces that previously performed a 57certain number of functions, strictly related to the ordinary daily activities of people be-58fore the restrictive measures of COVID-19, had to welcome new ones, often proving to be 59inadequate. Moreover, spaces such as balconies or terraces, not always present in all 60types of residential buildings, have been found to be essential for many reasons—from 61Citation: Tajani, F.; Di Liddo, F.; 62Guarini, M.R.; Ranieri, R.; Anelli, D. 63An Assessment Methodology for the 64Evaluation of the Impacts of the 65COVID-19 Pandemic on the Italian 66Housing Market Demand. Buildings 672021, 11, 592. https://doi.org/10.3390/ 68buildings11120592 69Academic Editor: Dirk H. R. 70Spennemann 71Received: 25 October 2021 72Accepted: 24 November 2021 73Published: 28 November 2021 74Publisher’s Note: MDPI stays neu-75tral with regard to jurisdictional 76claims in published maps and insti-77tutional affiliations. 78 79Copyright: © 2021 by the authors. 80Licensee MDPI, Basel, Switzerland. 81This article is an open access article 82distributed under the terms and 83conditions of the Creative Commons 84Attribution 85(CC 86BY) 87license 88(http://creativecommons.org/licenses89/by/4.0/). 909192===== PAGE 6 (score 11, numeric-paren 0, table-words 2, var-words 5) =====9394Buildings 2021, 11, 592 956 of 28 96 97In the second step (Step II) a study sample related to residential properties sold in 98the period prior to the anomalous event was collected for the investigation of the “ordi-99nary” market mechanism. Therefore, with reference to the present analysis, a sample of 100165 housing properties for each city sold in the second half of 2019 (Phase I: 101“pre-COVID-19 pandemic”) was detected. For each data set, some preliminary correla-102tion analysis and descriptive statistic examinations were carried out for the monitoring of 103data samples statistical robustness. (Tables S1–S24 in the Supplementary files, respec-104tively). Then, an econometric technique was implemented in order to obtain a function 105for each city able to identify the main relationships between the factor selected and the 106selling prices. 107The third step (Step III) refers to the same logical approach carried out in the second 108step with reference to the Phase I, by detecting data related to the period following the 109occurrence of the phenomenon. In the specific case, the study samples were related to the 110six Italian cities selected for the analysis, with reference to the first half of 2021 (Phase II: 111“COVID-19 pandemic in progress”). 112In the fourth step (Step IV) the comparison of the outputs obtained in the two stages 113(Phases I and II) is performed. Thus, the synthesis of the results was developed in order 114to (i) identify the variations in the residential market demand deriving from the 115COVID-19 pandemic arising and (ii) to provide a framework for orienting the planning 116and design decisions. 117In Figure 1, a summary of the main steps for the implementation of the methodology 118proposed is reported. 119 120Figure 1. Summary of the main steps of the methodology for the assessment of the effects of anomalous events on hous-121ing market. 1224. Case Study 1234.1. Implementing Step I of the Methodology 1244.1.1. The Study Samples 125In order to assess the changes occurred in the Italian residential market, the six 126largest Italian metropolitan cities were selected: Milan and Turin for Northern Italy, 127Rome and Florence for Central Italy, and Naples and Catania for Southern Italy and the 128Islands. For each city, the main social, urban, economic and demographic factors were 129investigated in order to understand the context of reference for each city. In Table 1, a 130summary of the distinctive features for each city is reported [67]. 131Table 1. Main distinctive features for each Italian city considered in the analysis. 132Factor 133Turin 134Milan 135Florence 136Rome 137Naples 138Catania 139Number of inhabitants (n.) 140870,952 1411,396,059 142372,038 1432,837,332 144962,589 145311,402 146Surface (km2) 147130.01 148181.67 149102.32 1501,287.36 151119.02 152182.90 153Population density (inhabitant/km2) 1546,699.12 1557,684.59 1563,636.02 1572,203.99 1588,087.62 1591,702.58 160Old age index 161204.10 162196.30 163220.40 164162.60 165114.40 166139.60 167Square meters per occupant in occupied 16841.00 16941.50 17041.40 17129.40 17231.70 17337.10 174175176===== PAGE 7 (score 5, numeric-paren 0, table-words 0, var-words 5) =====177178Buildings 2021, 11, 592 1797 of 28 180 181residential units (m2) 182Number of residential buildings (n.) 18336,158 18442,980 18531,070 186137,021 18740,755 18828,988 189Empty residential properties (n.) 19036,779 19137,073 1925164 193118,531 19414,140 19528,567 196Per capita income (€) 19725,015 19834,046 19926,503 20028,241 20122,434 20220,179 203Source: elaborations of the authors on ISTAT database. 204As can be seen in Figures 2 and 3, for each city two study samples consisting of 165 205housing properties were detected. The first concerned 165 residential units sold in the 206second half of 2019 (Phase I), whereas the second related to 165 residential units sold in 207the first of 2021 (Phase II). In Figure 2, the locations of the properties (green points) col-208lected for the cities in the pre-COVID-19 spread are represented, and it is possible to note 209their heterogeneous distribution throughout the urbanized territory. The entire sample 210was detected in order to take into account all municipal trade areas provided by the Real 211Estate Market Observatory (OMI) of the Italian Revenue Agency, i.e., the “portion of the 212territorial band that reflects a homogeneous part of the local real estate market, in which 213there is a substantial uniformity of appreciation for economic and socio-environmental 214conditions is observed” [68] or, the central, semi-central, peripheral and suburban por-215tion of urbanized territory that synthetized the features of the neighborhood. The same 216considerations were carried out for Figure 3, pertaining to the locations of the properties 217(red points) that refer to the sample of Phase II. 218 219 220City of Turin 221City of Milan 222 223 224City of Florence 225City of Rome 226227228===== PAGE 14 (score 23, numeric-paren 0, table-words 4, var-words 7) =====229230Buildings 2021, 11, 592 23114 of 28 232 233Iteration 4 2342.329 2353.120 2362.789 2372.789 2382.329 2392.329 2402.329 2412.329 2422.015 2432.015 2442.997 2453.102 246Iteration 5 2472.279 2483.089 2493.256 2503.256 2512.279 2522.279 2533.345 2543.345 2552.058 2562.058 2572.279 2582.279 259Iteration 6 2602.228 2613.310 2623.658 2633.658 2642.228 2652.228 2662.228 2672.228 2682.987 2692.987 2702.228 2712.228 272Iteration 7 2733.123 2743.531 2753.987 2763.987 2773.123 2783.123 2793.004 2803.004 2812.753 2822.753 2833.123 2843.123 285Iteration 8 2862.127 2872.178 2883.854 2893.854 2902.127 2912.127 2922.127 2932.127 2942.861 2952.861 2962.127 2972.127 298Iteration 9 2993.404 3003.650 3013.145 3023.145 3033.404 3043.404 3052.767 3062.767 3072.001 3082.001 3093.404 3103.404 311Iteration 10 3122.026 3132.077 3143.521 3153.521 3162.026 3172.026 3182.026 3192.198 3203.021 3213.021 3222.026 3232.026 324In Table 5 a summary of the variables selected in each model is shown to conven-325iently compare the most influencing factors among those analyzed. 326Table 5. Variables selected by the models generated by EPR-MOGA for each study sample of Phase 327I. 328No. 329City 330N. Variables 331Si 332Sg 333Sb 334Se 335L 336B 337Yc 338C 339Sc 340P 341Mg 342Me 343Vm 3441 345Turin 3469 347✓ 348 349✓ 350 351 352✓ 353✓ 354 355✓ 356✓ 357✓ 358✓ 359✓ 3602 361Milan 3627 363✓ 364 365✓ 366✓ 367 368✓ 369✓ 370 371 372 373✓ 374 375✓ 3763 Florence 3779 378✓ 379✓ 380✓ 381 382✓ 383✓ 384✓ 385 386 387✓ 388 389✓ 390✓ 3914 392Rome 39310 394✓ 395✓ 396✓ 397 398✓ 399✓ 400✓ 401✓ 402 403 404✓ 405✓ 406✓ 4075 408Naples 4099 410✓ 411 412 413 414✓ 415✓ 416✓ 417 418✓ 419✓ 420✓ 421✓ 422✓ 4236 424Catania 42510 426✓ 427 428✓ 429✓ 430✓ 431✓ 432✓ 433✓ 434✓ 435 436 437✓ 438✓ 439It should be noted that the variables referring to the internal area (Si), the number of 440bathrooms in the property (B), the building construction year (Yc) and the average mar-441ket value (Vm) were present in all six equations, with a non-zero multiplicative coeffi-442cient. Furthermore, no variable was excluded by the models and all factors analyzed 443were included in at least two models. 444For all the equations obtained for Phase I, their algebraic structure did not allow an 445immediate interpretation of the functional relationships among the variables, as each 446additive term was a combination of different variables that occurred several times in the 447same model. Therefore, in order to verify the empirical consistence of the functional links 448between the independent explanatory variables selected by each model, and the values of 449the dependent variable of total selling prices, a simplified exogenous approach that con-450sidered the other variable values equal to the average values of the starting database 451(value “1” or “0” if the factor was a dummy variable) was used. This approach deter-452mined the marginal price of the generic variable through the changes in value of the as-453sessed variations of selling prices, in correspondence with each i-th variable in the ad-454missible range of its corresponding sample collected. In particular, for each Italian city, 455with reference to the Phase I (second half of 2019 “pre-COVID-19 pandemic”) Figures 456S1–S6 in the Supplementary Materials show the functional correlations detected for each 457explanatory variable selected by the six models. 458The marginal influence on selling prices, in terms of the average percentage varia-459tion obtained in correspondence with the passage from one level to the next, or from the 460absence to the presence of a specific factor, was reported for each variable. The analysis of 461the functional correlations between independent explanatory variables, selected by the 462models and housing prices, verified the empirical evidence of the coefficient signs for all 463the cities, as the consistency of the links with the expected phenomena was confirmed. 464According to the aim of the research, some interest can be accomplished for the in-465trinsic factors analyzed, connected with the domestic spaces and their related accessory 466surfaces: 467i. 468A direct link between the internal surface and housing prices was detected for the six 469cities considered (+26% for the city of Turin, +37% for the city of Milan, +20% for the 470city of Florence, +38% for the city of Naples, +25% for the city of Rome, and + 6% for 471the city of Catania, considering an average variation of 40 m2). 472473474===== PAGE 15 (score 13, numeric-paren 0, table-words 0, var-words 13) =====475476Buildings 2021, 11, 592 47715 of 28 478 479ii. 480Variables related to direct and private accessory surfaces, i.e., balconies or terraces and 481gardens, had different influences; for example, for the city of Turin the presence of 482balconies was strongly appreciated up to a surface of 9.50 m2 (+22%), beyond which 483the contribution on the prices progressively decreased (an average +5%). The marginal 484contribution on selling prices provided by the biggest balconies or terraces and gar-485dens surfaces was confirmed by the microeconomics principle, for which the rele-486vance of a good was strongly associated with the need of it (known as law of de-487creasing marginal utility). Moreover, the variable was also directly linked to the sell-488ing prices in the city of Milan, for which the variation between the absence and the 489presence of balconies was higher (+14%), compared with the subsequent balconies 490area (+4%). The model selected for the city of Florence proved a growth of the resi-491dential values in correspondence with the presence of balconies (+31% compared with 492its absence), and a progressive attenuation in prices increase for larger balcony surface 493areas (+17%). Similarly, for the city of Catania, a direct correlation between the varia-494ble related to the surface of balconies Sb and housing prices was found, with a relevant 495initial variation equal to +19% between the properties without balconies and those 496characterized by the balcony presence. Then, the percentage variation decreased, and 497was equal on average to +4%. The presence of private gardens was not included in the 498models of the city of Turin, Naples, Catania and Milan, due to the most common res-499idential typology sold in those markets, i.e., residential units located in apartment 500buildings. A decrease in housing prices was found for the city of Florence model 501(−11%), in correspondence with properties with private gardens. With reference to the 502study sample collected, only 6% of the total individuals included were characterized 503by this domestic space, and all were localized in the higher hydrogeological risk areas 504of the city. Furthermore, a significant influence of private green area was detected for 505the city of Rome, especially due to the position of the sample residential units, in par-506ticular, valued urban zones (in the proximity of the Appia Antica Regional Park). 507iii. 508The models selected showed a lack of appreciation for the presence of condominium 509areas, in the second half of 2019, in the cites of Naples, Turin, Florence and Rome. On 510the other hand, the price functions generated by the EPR-MOGA technique for the 511cities of Catania and Milan denoted a relevant contribution—positive for the first city, 512negative for the second—deriving from the presence of these spaces on selling prices. 513In particular, for the city of Catania, it should be outlined that most properties col-514lected in the study sample were located in prestigious residential complexes, in which 515the shared gardens were in excellent conservative conditions, and were for the exclu-516sive use of inhabitants. On the other hand, for the city of Milan, most residential units 517in the study samples considered for the external condominium area (41% of the total 518sample individuals) were constituted by economic buildings, for which other factors 519could negatively influence the selling prices. 520iv. 521The floor level on which each residential property was located influenced the housing 522dynamics in the cities of Florence, Rome, Naples and Catania. The model selected for 523the city of Naples indicated an average variation on selling prices equal to +7%, and a 524higher significance in correspondence with the passage from the ground floor to the 525first floor (+25%), and an attenuation for the highest floors, from level eight upward 526(+5%). For the city of Catania, a direct functional correlation was found on average 527equal to +2%, and a relevant appreciation for the ground floor was detected, if the 528properties were characterized by condominium areas, compared with the higher 529floors. The same positive link typology was revealed with regards to the study sample 530collected for the city of Rome, for which the highest floor levels were those most ap-531preciated, compared with the lowest ones. In addition, in the central trade area, the 532location on the highest floors allowed panoramic views that implied a strong influ-533ence on housing values. A moderate contribution on selling prices was observed for 534the city of Florence, with a marginal price equal to 4%. 535536537===== PAGE 16 (score 16, numeric-paren 0, table-words 4, var-words 3) =====538539Buildings 2021, 11, 592 54016 of 28 541 542v. 543The central municipal trade area variable was included in the models selected for the 544cities of Rome and Catania; the semi-central areas appeared in the models of the cities 545of Turin, Catania and Naples, and the peripheral area factor was also present in the 546price functions of Turin, Florence and Naples. It should be outlined that the 547semi-central municipal trade area was particularly appreciated in the context of the 548city of Naples (+25%) and in the city of Catania (+52%), whereas a negative influence 549was given by the position of housing properties in the semi-central trade area and pe-550ripheral area of the city of Turin (−33% and −38%, respectively). In the city of Florence, 551the selling price variation determined by the localization of the property in the pe-552ripheral area was equal to –18%, whereas for the city of Naples a decrease in housing 553prices equal to –20% was recorded for the peripheral trade area. The location of 554properties in the central municipal trade area of the city of Rome determined an in-555crease in selling price equal to +13%, whereas this was equal to +5% in the central area 556of Catania. 5574.3. Implementating Step III of the Methodology 558Application of the Technique to Phase II: “COVID-19 Pandemic in Progress” 559By recalling the aim of the present research, the identification of the changes in res-560idential market demand caused by the COVID-19 pandemic in six Italian metropolitan 561cities, Step III of the analysis concerns the same operative logic carried out as in the pre-562vious Step II. Therefore, six study samples, each consisting of 165 housing properties sold 563in the first half of 2021 (one for each city) were collected. For each residential unit, the 564same factors detected for Phase I were investigated in order to determine the most in-565fluential factors on selling prices, and to study the functional correlation between the 566explanatory independent variables and price. Thus, the same stages developed in Phase I 567(second half of 2019) were replicated in Phase II (first half of 2021). 568The implementation of the EPR-MOGA technique was iteratively carried out for all 569the samples. The dependent variable of total selling price was constituted by its natural 570logarithm (Y = ln(Q)). The application of EPR-MOGA generated several models able to 571describe the residential market dynamics, and those chosen for the analysis of the func-572tional link between influential factors and housing prices are reported in Table 6. 573Table 6. Models generated by the EPR-MOGA implementation for each Italian city analyzed for the Phase II. 574City 575Model 576CoD (%) 577Turin 578Y = + 2.434 Vm0.5 + 0.3733 Me0.5 + 0.99371 Sb0.5 B0.5 Vm0.5 – 579+ 4.4136 Sb0.5 B0.5 Yc0.5 P0.5 Me0.5 + 7.617 Si0.5 − 4.1752 Si Vm0.5 + 580+ 7.4833 58185.53 582Milan 583Y = + 0.49351 C0.5 Vm − 0.88769 Yc0.5 P − 0.56312 L0.5 B0.5 Mg + 584+ 24.1533 Sg0.5 Se2 L + 1.2286 Sg Vm + 8.1673 Si0.5 − 4.1711 Si + 585+ 2.8284 Si L B0.5 + 10.7489 58696.04 587Florence 588Y = + 23.2683 Vm0.5 − 13.2187 Vm + 0.61728 B0.5 Me 0.5 Vm2 + 589+ 1.8377 Sb2 + 5.8364 Si0.5 + 170.3596 Si0.5 Sb2 L Yc – 590+ 2.2608 Si + 0.18337 59193.00 592Rome 593Y = + 2.3773 Vm0.5 + 0.27166 Me – 0.66914 Yc0.5 Me2 + 594+ 9.5008 Se Yc2 P2 + 1.7449 Sb L0.5 B + 3.0846 Si0.5 + 595+ 2.5818 Si0.5 L0.5 Yc2 Me2 + 9.402 59689.84 597Naples 598Y = + 4.3382 Vm − 2.0486 Vm2 + 0.98283 L Yc0.5 Me2 + 0.75291 Sb0.5 B0.5 599 Me0.5 + 9.3479 Si0.5 − 4.2403 Si + 7.4542 60093.72 601Catania 602Y = + 1.9795 Vm0.5 + 0.38123 Me2 + 1.0016 B0.5 + 13.2376 L0.5 B2 Yc2 Mg + 603+ 2.5865 Sb0.5 Se2 B Yc C Me2 + 2.1141 Sg2 Yc0.5 Vm2 + 2.762 Si0.5 + 604+ 8.1768 60584.73 606For each polynomial equation, the CoD was specified; in particular, a high statistical 607accuracy level was associated with them (+85.53% for the city of Turin, +96.04% for Milan, 608609610===== PAGE 17 (score 31, numeric-paren 0, table-words 5, var-words 8) =====611612Buildings 2021, 11, 592 61317 of 28 614 615+93.00% for Florence, +89.84% for the city of Rome, +93.72% for Naples, +84.73% for Ca-616tania). 617Moreover, in this analysis the main statistical indicators (RMSE, MAPE and 618MaxAPE) were calculated, and a ten-fold cross-validation was carried out. With reference 619to the statistical indicator the lowest RMSE was concerned with the city of Milan (3.21%) 620and the highest referred to the city Turin (3.98%). Furthermore, the lowest MAPE was 621calculated for the Milan study sample (2.80%), and the highest MAPE was calculated for 622the city of Catania (3.78%). Moreover, the city of Catania presented the highest MaxAPE 623(9.21%), and the lowest MaxAPE was verified for the Florence case study (8.12%). Table 7 624reports the output of the ten-fold cross-validation. These analyses confirmed that the se-625lected samples were stable and statistically performing. 626Table 7. Average percentage errors (%) obtained through a ten-fold cross-validation for Phase II. 627No. Itera-628tion 629Turin 630Milan 631Florence 632Rome 633Naples 634Catania 635 636Training 637Set 638Validation 639Set 640Training 641Set 642Validation 643Set 644Training 645Set 646Validation 647Set 648Training 649Set 650Validation 651Set 652Training 653Set 654Validation 655Set 656Training 657Set 658Validation 659Set 660Iteration 1 6612.217 6622.351 6632.551 6642.614 6652.292 6662.434 6672.227 6682.237 6692.125 6702.136 6712.660 6722.667 673Iteration 2 6742.872 6752.889 6762.121 6772.179 6782.880 6792.887 6802.917 6812.938 6822.884 6832.894 6843.201 6853.212 686Iteration 3 6872.091 6882.078 6892.889 6902.985 6913.210 6923.221 6932.156 6942.208 6952.485 6962.506 6972.998 6983.008 699Iteration 4 7002.373 7012.348 7022.789 7032.843 7042.384 7052.394 7062.385 7072.448 7082.444 7092.496 7102.581 7112.602 712Iteration 5 7132.299 7142.364 7153.256 7163.258 7172.309 7182.330 7193.345 7203.403 7212.252 7222.315 7232.411 7242.463 725Iteration 6 7262.247 7272.231 7282.543 7292.653 7302.268 7312.320 7322.273 7332.369 7342.987 7353.045 7363.012 7373.075 738Iteration 7 7393.208 7403.138 7412.852 7422.985 7433.260 7443.323 7453.004 7463.058 7472.101 7482.197 7492.589 7502.647 751Iteration 8 7522.130 7532.129 7542.998 7552.895 7562.193 7572.251 7582.184 7592.186 7602.001 7612.055 7622.875 7632.971 764Iteration 9 7653.201 7663.321 7673.145 7683.145 7693.259 7703.355 7712.767 7722.782 7732.589 7742.591 7753.001 7763.055 777Iteration 10 7782.028 7792.080 7803.521 7813.521 7822.124 7832.178 7842.049 7852.198 7863.021 7873.036 7882.498 7892.500 790In Table 8, a summary of the variables selected in each model is reported. All equa-791tions included a large number of influential factors among those considered in the anal-792ysis (seven for the cities of Turin, Florence and Naples, ten for Milan, nine for the city of 793Rome, and eleven for the study sample of Catania). 794Table 8. Variables selected by the models generated by EPR-MOGA for each study sample for 795Phase II. 796No. 797City 798N. Variables 799Si 800Sg 801Sb 802Se 803L 804B 805Yc 806C 807Sc 808P 809Mg 810Me 811Vm 8121 813Turin 8147 815✓ 816 817✓ 818 819 820✓ 821✓ 822 823 824✓ 825 826✓ 827✓ 8282 829Milan 83010 831✓ 832✓ 833 834✓ 835✓ 836✓ 837✓ 838✓ 839 840✓ 841✓ 842 843✓ 8443 845Florence 8467 847✓ 848 849✓ 850 851✓ 852✓ 853✓ 854 855 856 857 858✓ 859✓ 8604 861Rome 8629 863✓ 864 865✓ 866✓ 867✓ 868✓ 869✓ 870 871 872✓ 873 874✓ 875✓ 8765 877Naples 8787 879✓ 880 881✓ 882 883✓ 884✓ 885✓ 886 887 888 889 890✓ 891✓ 8926 893Catania 89411 895✓ 896✓ 897✓ 898✓ 899✓ 900✓ 901✓ 902✓ 903 904 905✓ 906✓ 907✓ 908First of all, it should be noted that the internal surface (Si), the number of bathrooms 909(B), the building construction year (Yc) and the average market value (Vm) represented 910significant factors in selling price formation, as they were in all six models with a multi-911plicative coefficient greater than zero. Furthermore, only the variable related to the loca-912tion of the properties in the semi-central trade area (Sc) was excluded. 913For all price functions obtained for Phase II, the polynomial form of the equations 914did not allow an immediate analysis of the functional correlations among the explanatory 915variables and selling prices. Therefore, the same simplified exogenous approach imple-916mented in Phase I was used for the verification of the empirical coherence of the func-917tional links. In Figures S7–S12 in the Supplementary Materials, for each Italian city with 918reference to Phase II (first half of 2021 “COVID-19 pandemic in progress”), the functional 919correlations between the independent variables selected by the six models and the 920921922===== PAGE 18 (score 6, numeric-paren 0, table-words 1, var-words 4) =====923924Buildings 2021, 11, 592 92518 of 28 926 927housing prices are reported. Moreover, the average percentage of selling price variations 928detected was specified. 929For all study samples collected and the variables selected, the empirical evidence of 930the equation’s coefficient signs, i.e., the consistency of the relationships with the expected 931market phenomena, was verified. 932For the variables for which a direct functional correlation was detected, their influ-933ence (represented by their average marginal contribution) on selling prices is reported in 934the graphs in Figure 5. In particular, for the quantitative continuous factors related to 935surfaces (Si), (Sg) and (Sb), the average marginal contribution was analyzed by taking 936into account specific ranges (<10 m2, 10–30 m2, 31–70 m2, >71 m2 for the surface of a pri-937vate garden, < 70 m2, 71–100 m2, 101–130 m2, >131 m2 for the internal surface, < 6 m2, 7–20 938m2, 21–50 m2, >51 m2 for the surface of balconies or terraces). For the dummy variables 939(Se), (Me), (C), the marginal contribution was determined considering the variations that 940occurred with the absence or the presence of this property characteristic, whereas for the 941quantitative discrete variables (L) and (B), the marginal price related to each increase of 942the factor was determined. 943