Property tax in Greece is levied since 1985 not on Market Values but on the “objective value” of the properties as it is defined by the Ministry of Economics. It forms a non-flexible system, with market-irrelevant and unrealistic values, inducing land-policy practices and potential political cost to each periodical update. Furthermore, instead of adjusting taxation levels to the current economic reality, the real estate market is experiencing further burdening through approximately 40 different property taxes and levies, leading to further shrinking and depreciation. The authors believe that a fairer taxation system could significantly assist the property sector in Greece. Thus, through this paper and by studying and analyzing best practices from other countries, they propose models that can be applied with the use of existing data in Greece. This work aims to identify the critical parameters that affecting property values in Thessaloniki to create a Market Value forecasting tool for a fairer taxation system, to highlight the importance of a GIS system for this purpose and to compare the results of MRA with the use of SPSS with those of GWR in ArcGIS environment. For the purposes of this study, the Municipality of Thessaloniki was chosen due to its very well organized portal with significant and well organized geographical data and because authors manage to access some data from the Central Bank of Greece, regarding property valuations.
The property taxation in Greece has been a top issue in the governments’ agenda for many years now, causing confrontation as well as social and economic injustice. The reason for this is that, according to the current government, the various property taxes are being calculated on the Objective Value of a property and not on its Market Value, which is shaped through the equilibrium of demand and supply levels. As stated by Dimopoulos et al.  property tax in Greece is levied since 1985 not on Market Values but on the “objective value” of the properties as it is defined by the Ministry of Economics. The last update of the objective values, which are based on market data, was in 2007 when the property market in Greece was at its peak. Despite the six years of deep recession which resulted in property price drops of c.30-40% on average, objective values have not changed . Apparently, this has lead the actual (market) values of properties to be completely different from the taxable (objective) values. (Note: At this point, it should be mentioned that the objective values have changed while this paper was revised). Furthermore, the update of the objective values is a time-consuming and costly process, which only depicts market conditions at the time of the update without disposing dynamic features. The above issue is the key driver behind the subject study, as it becomes clear that the implementation of a more rational property tax system should be seriously considered by the relevant authorities in Greece. This system should be able to depict as realistically and dynamically as possible the actual value of a property for the relevant taxes would be based on. For the estimate of the actual value of a property, comparable data in its nearby area are being used. Therefore, the geographic position of the property comprises the cornerstone of this system, since a number of spatial data are being taken into consideration. The principles behind such systems are those of mass appraisals and the systems themselves are known as CAMA (Computer Assisted Mass Appraisals).
The subject study will demonstrate that property market values can be effectively predicted through regression analysis and the use of Geographic Information Systems (GIS). Also, the advantages of Geographical Weighted Regression (GWR) method against the traditional method of Ordinary Least Squares (OLS) will be presented. The Municipality of Thessaloniki in North Greece was chosen as a case study, while a total of 2,583 properties (out of an initial sample of 4,435 properties) were used as comparable data for the analysis. The software packages used were ESRI ArcGIS 10.1 and IBM SPSS Statistics Version 22.
Aim of the study
No other study of this sample size, method used (GWR) and application of GIS has taken place in Greece before. Thus, this study can comprise a pilot project for laying the foundations for the complete transformation of the current property tax system into a modern and rational property tax system that would inspire trust to the taxpayers. It should be emphasized that no other study in Greece gives prominence to the use of GIS and the significant advantages that GWR method has against the OLS one.
2 Literature review
2.1 Factors that affect property values
Property values are being affected by a number of qualitative and quantitative factors related to the property itself but also the wider area which is located to. Given that each property is unique, since even two adjacent properties may differ in size, views, quality, etc. there are endless factors that affect their value. According to Kiohos , property values depends on various economic attributes of a property in order to offer a certain level of income or service to its owner. These attributes relate to the usefulness, the rarity defined by the levels of supply and demand as well as the fulfilment of objective and subjective needs. The impact that the usefulness of a property has on its price depends on the property’s features, such its size, location, use, construction quality, building regulations, legal status etc.
Zentelis  divides property values’ impact factors into four spatial levels, and more specifically, on country level, city level, district level and property level. This division has a hierarchical character starting from the more generic country level to the more specific property level, while all country level factors have already affected property value when it is at the property level . In this study, factors related to the Municipality of Thessaloniki in terms of city, district and property levels were assessed.
2.2 Property Valuations
Kiohos  defines property valuation as the science of value assessment of a movable or immovable asset at a given point of time, according to specific methodology and based on necessary technical information. Labropoulos  states that the value of a property is directly related to the purpose of valuation, such as property purchase/sale, loan acquisition, rental, construction, refurbishment, sale & leaseback, accounting and many others. The five internationally acknowledged valuation methods are the comparative method, the income approach, the depreciated replacement cost method, the profit’s method and the residual method. The former methods are being widely used in mass appraisals, while the comparative method is the preferred one for evaluating residential properties (mainly apartments) if there are sufficient comparable data .
2.3 Mass Appraisals & CAMA systems
Zentelis  notes that the need for a property value system that would offer uniformity, accuracy, effectiveness, cost and time efficiency, but also mass use capabilities, lead to the development of mass appraisals. It is also argued that mass appraisals developed out of the need for consistency and uniformity during ad valorem property tax assessments [5, 7]. Mass appraisals are defined as the systematic assessment of value of a set of homogenous properties, on a given date, by using standardized procedures as well as statistical checks . Mass appraisals are typically applied when a large number of properties need to be valued in a short timeframe and a cost efficient manner as well as for annual property taxation purposes .
Computer Assisted Mass Appraisal (CAMA) systems are automated systems used for information management related to properties, valuations, owners’ notifications and the security of taxation credibility through uniform valuation procedures. CAMA systems, which can operate independently or as part of a broader fiscal system, estimate property values by applying statistical methods (e.g., Multiple Regression Analysis) and controls supported by computers . According to McCluskey et al. , a CAMA system should depict demand and supply levels of the market where one property is located in. CAMA systems should be used when: (a) resources are restricted, (b) completion time of the valuation plays an important role, (c) objectivity and uniformity are sought, and (d) the number of properties is large. Some of the countries that use CAMA systems are Australia, Denmark, Finland, Great Britain, USA, Brazil, Canada, Egypt, Russia, Sweden etc .
|Australia||Department of Lands||MRA|
|Sweden||National Tax Board||MRA|
|North Ireland||Valuation & Lands Agency||MRA, ANN, CSA|
|Tasmania||Valuer General’s Oflce||MRA, AEP|
|New Zealand||Valuation New Zealand||MRA|
|Singapore||Singapore Valuation Department||INDEXATION|
|Hong Kong||Rating & Valuation Department||MRA, INDEXATION|
|USA||Assessment Oflces||MRA, AEP, CSA|
|British Columbia||BC Assessment Authority||MRA|
MRA - Multiple Regression Analysis, ANN - Artificial Neural Networks, CSA - Comparable Sales Analysis, AEP – Adaptive Estimation Procedure
Expert - Expert Systems, Indexation - Indexation of existing assessments
Source: McCluskey and Adair, 1997
CAMA systems are divided into two broad categories; the traditional and the contemporary ones. The former include techniques such as Multiple Regression Analysis, Comparable Sales Analysis, Adaptive Estimation Procedure and Indexation, while the latter include techniques such as Artificial Neural Networks and Expert Systems. Mass appraisals techniques should satisfy a twofold need: (a) achieve a satisfactory level of predictive capability and accuracy and (b) offer sufficient level of explanation and justification of the predicted property values . Eventually, the use of the valuation technique depends on data availability and features, the basis of value and the purpose of valuation [7, 10]. Through the analysis of literature review regarding the use of mass appraisals techniques, two main outcomes are being recorded; (a) the Multiple Regression Analysis (MRA) that is an internationally accepted and widely used valuation technique, and (b) numerous research studies take place towards the development of new techniques as well as the improvement of the existing ones. Table 1 presents the mass appraisals techniques that are being used in various countries.
The selected technique for this study is the MRA, which is a statistical technique used in cases where one variable depends on a number of other variables . The former variable is called dependent variable and the other variables are known as independent variables. In property sector, the dependent variable is usually the property value, whereas independent variables include its size, age, floor, area/location, distance from points of interest ( e.g.sea, transport means, city centre etc) as well as numerous features related to the property and its nearby area. This technique assumes that the variables have a linear relationship which means that the dependent variable can be expressed as a function of the independent ones, where each one of those independent variables has its own coefficient (weight), plus a constant term as shown below:
Y = dependent variable
c = constant term
bn = coefficient of independent variable n
xn = independent variable n
By applying MRA, the independent variables that materially affect property value (dependent variable) are being determined, but also the relevant coefficient factors and constant term are also estimated. For best results, MRA requires a large-size sample whose values are known. MRA is considered as the most important technique used in mass appraisals [7, 12], while it comprises the premier technique taken from the academic to the field level . Greater emphasis towards the use of this method is being put on Guidance Note no.13 of International Valuation Standards (IVS), where it is noted that the development of mass appraisal systems for tax purposes should incorporate acknowledged scientific standards based on statistical applications . For the reasons above, the technique used in this study is the Multiple Regression Analysis (MRA).
2.4 Geographic Information Systems (GIS)
GIS are defined as a set of tools for collection, storage, processing, analysis, management, retrieval and demonstration of groups of spatial real world data, aiming to serve certain needs or support effective decision-making . Liu, Deng & Wang  note that property valuation is a complex procedure that depends on data accuracy, the knowledge and experience of the valuer but also on the technology used by them, as well as the errors that occur during the valuation process. GIS comprise a substantial platform which maximizes accuracy and efficiency for the property sector, since its technology offers large databases, high quality graphic processing and presentation and also strong spatial analysis tools. Zentelis  notes that the use of GIS in real estate is a one-way route and its technologies could be applied by a broad spectrum of property stake-holders, such as constructors, engineers, valuers, owners, consultants, agents and so on.
According to Nawawi, Jenkins and Gronow , computer assisted mass appraisal is a term that describes a software package that in most cases is used by government agencies in valuing real estates for the purposes of ascertaining property tax. The Network of Associations of Local Authorities of South-East Europe  and McCluskey and Anand  state that the mass appraisal method can be used on both single and multiple properties. The development of mass appraisal systems demands continual improvement in order to achieve maximum quality coupled with efficient utilization of available resources . In addition, the quality of property valuation system is also determined by accuracy, uniformity, equity, reliability, as well as a low cost system. The only hindrance to mass valuation is incomplete or obsolete data for accurate valuation performance of the introduction of improvements in mass valuation models .
The basic conditions for the use of the method entail the collection of data regarding the social, physical, economic and geographical conditions in addition to actual property sales. For this method to yield satisfactory results, large amounts of data on property description and costs are analyzed [7, 12]. For accurate and fair results of property value, the computer assisted mass appraisal method is used . According to McCluskey and Borst , the introduction of computers in the appraisal method will enable the combination of cost and geographic data in an operational context and this will facilitate the revaluation and rating of residential properties. Furthermore, the use of computers will facilitate manipulation, analysis and storage of data in a shorter duration of time, thus increasing the value of the appraisal report. For increased usefulness of the available data to assessors, the computer assisted mass appraisals should be able to fully utilize econometric methodology .
For many decades, valuers and appraisers have used CAMA technology in order mass value large numbers of properties at the same time. In addition, the literature on CAMA techniques has long been recognized the fundamental roles of time, space and property characteristics in order to determine the value of the real property. Consequently, the ability to analyze location value has been greatly improved over the last 20 years by the development and integration of GIS and CAMA. This has been observed as a major development that has greatly assisted those who are involved in the mass valuation work. Additionally, large amounts of property attributes data have been assimilated into extensive relational focused database. These databases are potentially the most fundamental sources of information for application within GIS. Therefore, integrating CAMA and GIS technologies is at the core of property tax valuation systems .
Integrating GIS and CAMA is vital because it enables tax assessment functions to be done concurrently with spatial data that is relevant to tax evaluation model. In addition, it supports the creation and maintenance of very accurate land records base map that applies the tool and functions of GIS and also provides descriptive data that support workflow, updates, as well as mass appraisal input. GIS is also important since it adds value to the CAMA systems. For instance, the appraisal model that can place the added value on properties that have a better shape, are adjacent with green areas or have a frontage to a coastline, a lake or a golf course . This integration also supports the maintenance of an accurate single property data repository with respect to the geometry of each land parcel coupled with its descriptive data. This facilitates the calculation of the location impact, provided that a description of the land parcel and the spatial are maintained in a geo-database, where the spatial intelligence of the GIS is employed .
An additional benefit is that when GIS is used within a CAMA, there is enhanced visualization capability  that can demonstrate many things such as the impact of the location on the overall value mainly usually with the creation of value maps where range of values are presented as buffer zones. In most cases the results are presented through a map based output that makes it easy to communicate with individuals who lack an appropriate background in mass appraisal and those the mass appraisal affects. Thus, this can assist to make the system more accountable and transparent because it provides the mechanism to communicate more effectively.
Another feature of integrating GIS with CAMA is that it makes easy to improve the analytical capabilities of the methodology used in property appraisal by offering a mechanism to view, query, manage and model spatial information. The advantage of this is that it allows for a number of possibilities that do not exist without the integration. The next possibility is the potential to carry out sub regional analysis very effectively and also to improve the overall management of the spatial data and more importantly the management of the properties upon which the appraisal will be carried out .
Studies into the advantages of different property tax systems also indicate that this integration is vital because the basic idea of a CAMA system is to estimate a price index of a call of property from a representative sample of sold properties, within the entire population. It is this index that is used to relate the sale process with the physical characteristics and the location features of the properties that are sold. Therefore, the integration of CAMA and GIS contributes to the reduction in the amount of data that is necessary from on – site inspections; hence resulting to a considerable cost reduction which leads to the setting up of an accurate fiscal database .
The most significant contribution that GIS technologies have made on mass appraisals field is the incorporation of numerous spatial factors in the valuation process. There are many studies proving that GIS can give very good results in residential mass appraisals, as they combine MRA techniques with spatial analysis techniques, based on which differences between various areas/districts are being depicted . According to Anastasiadou , the key advantage of GIS in statistical analysis is the combined use of a property’s features with information related to its geographic position. McCluskey et al.  argue that GIS significantly enhance quality control during data analysis and properties’ value prediction, due to their spatial analysis capabilities and the visual presentation of results.
Zentelis  summarises the key advantages of GIS technologies on mass appraisals:
GIS combine spatial and visual operations with database operations, which greatly assist valuers to handle thousand properties quickly and efficiently while being able to identify comparable properties in terms of location.
GIS disposes of statistical tools that can be sufficiently applied in mass appraisals. Thus, valuers are able to estimate the impact that location has on property values and assess the weight of various spatial features,e.g. proximity to the sea, the city centre, parks or to other points of interest.
Apart from the traditional OLS method, GIS offer a more advanced statistical method, known as Geographically Weighted Regression (GWR). This method is a local form of linear regression used to model spatially varying relationships. GWR constructs a separate equation for every feature in the dataset incorporating the dependent and explanatory variables of features falling within the bandwidth of each target feature . However, it is recommended that the significant variables for a model should be identified through the OLS method and then use those variables through the GWR method. The advantage of GWR is that it creates different local equations for a set of entities (properties). While the dependent variable is the same for each equation (property value), the independent variables, their respective coefficients (weights) as well as the constant term may differ. At the same time, the results of GWR are visually depicted on a map through the production of thematic maps, which allow for extremely useful conclusions to be extracted. For example, the size of a property may have a high or low positive impact on value in some subareas (of the wider area under evaluation), but a negative impact on value in others. This information alone could offer excellent insight into the dynamics of the property market that could assist stakeholders in the decision-making.
3 Method – Case study of the Municipality of Thessaloniki
The Municipality of Thessaloniki located in North Greece, was selected as case study in this study. The municipality comprises of six Municipal Districts (MD) which are shown in Fig. 1 (a base map of the wider area of Thessaloniki was used as background).
The Municipality of Thessaloniki was selected as case study as it was considered suitable and representative for the following reasons:
It disposes one of the most well-organised GIS portals in Greece (http://gis.thessaloniki.gr/gis2014/) which offers invaluable spatial information used in this study, such as public spaces (parks, squares etc), parking facilities, health facilities, public transport means lines/stations and many more. Most of this information is considered extremely useful when assessing property values since values are directly or indirectly affected by numerous spatial factors.
It is the second largest municipality in Greece in terms of population (c. 325,000 inhabitants) and the fifth largest in terms of population density (c. 17,000 / sq km). This implies a dynamic property market where property values are being determined by demand and supply levels.
It disposes of features the impact of which on property values are worthwhile to be studied. For example, it has a large frontage on the sea which usually results in higher values for those properties that are closer to it, a historic city centre and is commercially active, which might also command higher values for properties that are close/in it, while it also has low and high-income areas with different features and residents profile.
It was made possible to collect considerable amount of comparable data (c. 4,450 properties) from the Bank of Greece -Real Estate Market Analysis Section, which allows the application of the selected data-hungry statistical methods (OLS & GWR).
It is the home-town of the authors that facilitate the proper interpretation of the results. Given that the spatial features of an area have a key role in the valuation process, good knowledge of the various features and particularities of the subareas was deemed crucial.
It consists of typical urban subareas, thus the results of the study could be applied to and/or compared with other areas of the country that dispose similar features.
For the requirements of this study, the selected reference unit is residential apartments that comprise horizontal divided ownerships in urban environment (Municipality of Thessaloniki). The main reasons for this were [27, 28]: (a) residential properties correspond to 80% of the total building stock in Greece, (b) Greece has among the highest rates of self-occupied residential units in Europe, (c) urban areas are considered more dynamic property markets compared to rural areas, thus property values are being determined by demand and supply levels, (d) apartments (horizontal ownerships) is a type of property with more common and homogenous features compared to other types of properties (e.g. residential villas, offices, retail shops etc), thus the features affecting the values can be much better determined (e.g. floor, age, size, views etc).
4 Data Collection & Processing
4.1 Data sources
The data used in this study have been collected primarily through secondary sources but also, where deemed necessary, primary data were also collected or calculated. The data collected refer to map layers (shapefiles) in ArcGIS, comparable properties database (sample), but also spatial data for each property were used as calculated in ArcGIS. More analytically, the data sources are as follows: Map layers (shapefiles) in ArcGIS: The map layers were provided by the Urban Planning Department (GIS dept.) of the Municipality of Thessaloniki and are as follows:
Public transport means (bus) lines and stops
Public areas, such as parks, sports facilities and squares
Educational units, such as nursery schools, kinder-gardens, primary schools, secondary schools, high schools, universities and others
Hotel units of all categories
Health units, such as hospitals, pharmacies and others
Parking facilities, including public spaces, charge-free spaces, short-term spaces and bicycle spaces
Urban blocks with their respective planning regulations (e.g. minimum frontage and surface, building coefficient, site coverage ration, etc)
Municipal districts of the Municipality of Thessaloniki
Post code areas
All of the above layers are illustrated in Fig. 2 (the whole municipality of Thessaloniki and part of it):
Comparable properties database (sample) : The property sample is perhaps the most important component for the implementation of an effective prediction model based on the selected statistical methods. Data were provided by Bank of Greece -Real Estate Market Analysis Section, though it should be noted that the values of the properties collected refer to estimated market values (by qualified valuers) and not actual transacted prices. However, for the needs of this study these values are deemed very satisfactory. The data that were requested refer to residential apartments within the boundaries of the municipality of Thessaloniki and for the period between January 2010 and June 2014. Despite the fact that the street number was not provided (for confidentiality purposes), the street name and its post code were provided based on which it was made possible to georeference as accurately as possible each property on the map. The sample consists of 4,435 entities (comparable properties) each with the following data:
Type of property
Address (street, post code, district)
Surface (main use areas)
Number and surface of storage and parking space(s)
Other features (excellent construction quality, position/view/environment, recently renovated, depreciated district)
Other secondary data : It was deemed necessary to collect additional secondary data that would facilitate the study. More specifically, the price index of residential properties was collected by Bank of Greece - Real Estate Market Analysis Section, which allowed the econometric analysis of values and their transformation into present values for comparison purposes.
4.2 Initial data processing
It should be noted that the sample provided by Bank of Greece had numerous errors and omissions that had to be corrected. Such errors and omissions were zero values on some parameters and some other incorrect entries. After those transformations, the initial sample of 4,435 was reduced to 2,583 entities. Also, for consistency and comparability purposes, the values of all entities were referenced into Q3 2014 terms as they were referring to the period Q1 2010-Q2 2014. This was achieved by the price index calculated by the Bank of Greece . Furthermore, it was deemed necessary to add further data in the database (such as internal characteristics, state of repair, correct the wrong addresses, etc.).
All properties were imported in ArcGIS at their exact geographical position through the process of geocoding (by using MS Office Excel ’07 add-on application called ‘Terra Excel Geocoder’). The results of this process are demonstrated in Fig. 3.
4.4 Spatial data calculation
Using the literature and professional experience, the main spatial factors that may affect property values were selected. Each of those factors is treated as an independent variable in the regression models in an attempt to determine and measure their impact on property values. These factors were divided into two broad categories; (a) Points of Interest (POIs), and (b) Spatial Features (SF), as shown in the Table 2.
|POIs||Educ200||Number of educational units||Within a 200m zone from the property|
|POIs||BusStat200||Number of bus stations||Within a 200m zone from the property|
|POIs||BusLine50||Number of bus lines||Within a 200m zone from the property|
|POIs||Health100||Number of health units||Within a 200m zone from the property|
|POIs||Parking||Distance from nearest parking facility||In meters (from the property)|
|POIs||Parks200||Public spaces (parks, squares, sports facilities)||Within a 200m zone from public space 0=falls outside, 1=falls within|
|SF||Seafront||Sea frontage||0=without frontage, 1=with frontage|
|POIs||MRoad50_01||Main road axis||Within a 200m zone from public space 0=falls outside, 1=falls within|
|SF||CBD_01||Central Business District (CBD)||0=falls outside, 1=falls within|
|POIs||CityCentre||Distance from City Centre||In meters (from the property)|
As regards spatial features, they are polygons where every property that falls within it takes the value 1 and all others the value 0. The two SF factors are the ‘Seafront’ and ‘CBD_01’; properties with a sea frontage usually show high values due to the unobstructed sea views and, similarly, properties located in the CBD show higher values due to their convenient location, easy access to shops, public authorities etc. and proximity to the commercial activity of the city. Figure 4 demonstrates the respective polygons as well as the properties that fall within each polygon (green color).
|Valid N (listwise)||2583|
Regarding points of interest, these are point features and various tools from ArcToolbox were used in order to measure distances, buffer zones etc. from the sample properties. Despite the fact that no drivetimes polygons were calculated (through network analysis) due to lack of necessary layers, measurements were still deemed satisfactory. The following factors/variables were calculated through ArcGIS:
Number of educational units within a range of 200m from each property. Proximity to schools or universities usually has a positive impact on property values due to easy access for students.
Number of public transport (bus) stops within a range of 200m from each property. Again, the higher this number the higher the value, as it implies convenient access.
Number of public transport (bus) lines within a range of 50m from each property. It is expected that the higher this number, the lower the value, since it may have negative impact due to increased traffic, noise, environmental pollution and parking difficulties.
Number of health units (pharmacies, hospitals etc) within a range of 100m from each property. It is expected that the higher this number, the lower the price, since it would imply high population density (in order to serve their needs), thus low quality of the built environment and life as well as parking difficulties.
Distance of each property from the nearest parking space. Proximity to such a space might have a positive impact on property values, since it can save valuable time from searching for street parking.
Properties that fall within a range of 200m from a public space (e.g. park or square) get the value of 1, while properties outside this zone get the value of 0. It is expected that proximity to a park or square might have a positive impact on property values.
Properties that fall within a range of 50m from main road axis. It is expected that the values of those properties might be either negatively affected, due to increased traffic, noise, environmental pollution and parking difficulties, or positively affected, due to easy accessibility.
Distance of each property from the city center. Proximity to the city center might have a positive impact on property values, due to longer drive times to the commercial area, public authorities etc, but also the fact that the use of car seems inevitable.
Figure 5 demonstrates extracts from ArcGIS during the calculation process of the aforementioned factors/variables.
5 Results and discussion
As discussed, data were initially analysed in SPSS in order to determine the variables that are significant for the prediction of property values. Table 3 presents the descriptive statistics for all variables. An explanation of the variables contained in this table is given in the Appendix.
It should be noted that the sample was divided into two parts: (a) 90% of the properties (2,337 entities), also called ‘Input Group’, that would be used for the creation of the models, and (b) the rest 10% of the properties (246 entities), called ‘Control Group’, is not used in the model formation but in its verification and statistical check.
5.1 OLS method
After a thorough statistical analysis on SPSS by using the MRA method, a prediction model that satisfied all statistical checks (significance of independent variables, independency of entities, multicollinearity, Homoscedasticity, normality and linearity) was created. It should be noted that a number of outliers and influential points (116 entities) were removed from the sample in order to improve its credibility and prediction power (indeed, the coefficient of determination was significantly improved from R2 = 61.2% to R2 = 75.9%). Also, the results were exactly the same by using the OLS method in ArcGIS. Table 4 displays the position of the ‘Control Group’ entities (246 properties), those entities that were removed from the sample as outliers or influential points (116 properties) and the ‘Input Group’ entities (2,221 properties).
The final prediction model is presented below:
The model above shows a very satisfactory coefficient of determination R2 = 75.9% and the Akaike’s Information Criterion (AICc), which will be used for comparison with the GWR model, is 51,450 (models with low AICc value are preferred). The results of the OLS method are summarized in Table 4.
Having estimated a satisfactory prediction model, its prediction accuracy should be controlled. To achieve this, the model is being applied on the ‘Control group’ of entities which correspond to 10% of the whole sample (which consist of those entities were not included in the model formation in order to not affect it). This control takes place in SPSS by calculating the Pearson Correlation factor between the actual property values and the predicted ones. This factor equals 0.87 which is considered very satisfactory as the value of 1.0 means 100% prediction accuracy of the model. The very good fit of the model is depicted in Fig. 7 showing the correlation between the actual and predicted values.
5.2 GWR method
As previously mentioned, GWR is a local regression method which highlights spatial differences instead of spatial similarities between entities in a given area. This means that independent variables which have spatial concentration should not be included in the model ( e.g.properties that fall within the CBD or seafront zone), as they create multicollinearity problem. After many trial-and-error efforts, the four variables Health100, Seafront, CBD_01, CityCentre and Poor_Qual were excluded from the model, which remains with five independent variables (Age, Floor, Area/Surface, Number of storages, Number of superior features). Given that GWR creates one equation for each property based on nearby properties, any spatial features affecting property values will be taken into consideration.
Again, the created GWR model satisfies all statistical checks. The coefficient of determination (R2 = 83.3%) is much higher than that of OLS method and its Akaike’s Information Criterion (AICc) (51,224) is lower than that of OLS method (lower AICc values are preferred). These two parameters demonstrate that the GWR model is superior compared to the OLS one. The report table of statistical results of GWR method is presented as Table 6.
The significant advantage of the GWR method, and ArcGIS accordingly, is the creation of a series of thematic maps (raster layers) of the variables’ coefficients and the constant term. This allows for identification of spatial differentiations within the study area, which can assist in effective decision-making. Through these maps, it is possible to obtain excellent insight into the key parameters that affect property value in a certain area. For example, the age of a property may have a significant negative impact on its value in a newly developed area where the majority of properties are brand new, while it may have a positive impact in the city centre where older buildings dispose of extreme architectural features and historic significance.
To shed more light on this, the results of ‘Age’ coefficient will be presented. As can be seen in Fig. 8, its values present a relative variation with of most of them being negative while there are also some positive values. As someone would expect, in the majority of cases, age is inversely proportional to property value, since the older the property the lower its value due to obsolescence, deterioration and depreciation. However, in some parts of the study area, property values are directly proportional to age for the aforementioned reasons. More specifically, coefficient values range between c. −[Euro.osf]1,800 and +[Euro.osf]280, the average is c.−[Euro.osf]730 and the standard deviation [Euro.osf]370.
Interestingly, as noticed in Fig. 9, positive values of the coefficient are concentrated in the historic city centre of Thessaloniki where there are many neoclassic listed building. On those buildings, age is not usually a negative factor due to their rarity and character. On the other hand, the highest negative values of the variable’s coefficient are concentrated in the a uent south-east suburbs of the city, where brand new properties are sought after by buyers; demand is low for old properties, thus age have a negative impact on property values.
Having estimated a satisfactory prediction model through GWR method, its prediction accuracy should be controlled. ArcGIS has automatically calculated predicted values for the 10% of entities (‘Control Group’). Table 6 presents the results of this process showing that each property (or groups of properties) gets different local R2, predicted values and coefficients’ values.
As a next step, prediction accuracy of the created GWR model is performed in SPSS by calculating the Pearson Correlation factor between the actual property values and the predicted ones. This factor equals 0.84 which is considered very satisfactory despite the fact that it is slightly lower than that of OLS method. The very good fit of the model is depicted in Fig.10 depicting the correlation between the actual and predicted values.
|Coeflcient of determination R2||75.8%||83.3%|
|Akaike Information Criterion (corrected)||51,450||51,224|
|Prediction accuracy (Rearson correl.)||0.870||0.840|
|Number of independent variables||10||5|
|Type of input data||Property & Spatial data||Property data|
|Coeflcient per variable||One||Many|
6 Concluding remarks
Two prediction models have been created by applying the OLS and the GWR methods in ESRI ArcGIS 10.1. Both models show very good fit to the input data, pass all statistical checks and have excellent prediction accuracy. However, as shown through the analysis, GWR method has a number of advantages compared to the OLS one. Table7 shows a comparison between the two methods in order to extract useful conclusions.
More specifically, GWR method has a much higher coefficient of determination R2 which means that the created model(s) fit much better in the data. The higher percentage shows that the dependent variable (property value) is better explained (by 83.3%) from the selected independent variables, while this percentage is lower in the OLS method (75.8%), though still high. The AICc value of GWR model is lower compared to that of OLS (51,224 versus 51,450 respectively). According to theory, the absolute value of AICc does not mean anything, though models with lower AICc are preferred. As regards the predictive accuracy, both models have a very high Pearson correlation factor (OLS: 0.87, GWR: 0.84) which demonstrate their very good prediction accuracy.
Perhaps the most significant advantages of the GWR method are the three last points, which relate to the ability of this method to create different local equation(s) for each entity or for a set of entities in the nearby area. This ability allows the removal of any variable with spatial concentration, as it creates multicollinearity problem. In this study, the GWR method uses only 5 independent variables compared to OLS method which uses 10 variables. It is not only the fact that more variables do not necessarily lead to better results, but also a more practical difficulty. The calculation of each of the 5 variables’ values, that were removed from GWR model, is both a time-consuming process and requires good knowledge of GIS. Additionally, the type of input data that the GWR method requires is solely property data (i.e. information like floor, age, size etc), while OLS method requires spatial data as well (i.e. information like distance from sea/city centre/public transport etc). The calculation of spatial data is again a time-consuming process, but most importantly, requires a number of layers that are not always available (e.g. layers of bus stops/lines, educational & health units etc). Last, the ability of GWR to create thematic maps with the variables’ coefficients is a key advantage that greatly assists decision-making and extraction of invaluable conclusions.
For all the reasons above, it should be stressed that the GWR method can lead to superior prediction models compared to the traditional OLS method, while it becomes clear that the use of GIS can have great positive impact on mass appraisals field through the application of advanced statistical and spatial analysis techniques.
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|Age||Years since it was built|
|Floor||Level that the property is located|
|Area_Main||Surface of property (sq m)|
|Storages||Number of storages that belong to the property|
|ParkSpaces||Number of parking spaces that belong to the property|
|Poor_Qual||Poor quality in terms of location, area, construction quality, state of repair (Y/N)|
|Good_Point||Number of superior features (e.g. excellent views, renovated and privileged location)|
|Educ200||Number of educational units within a 200m range range from each property|
|BusStat200||Number of bus stops within a 200m range from each property|
|BusLine50||Number of bus lines within a 200m range from each property|
|Health100||Number of health units within a 100m range from each property|
|Parking||Distance from nearest parking facility from each property|
|Parks200||Properties that lie within a 200m range from public space (e.g. park, square etc) (0/1)|
|Seafront||Properties that lie in the seafront zone (0/1)|
|MRoad50_01||Properties that lie within a 50m range from main road axis (0/1)|
|CBD_01||Properties that lie within the City Business District (CBD) (0/1)|
|CityCentre||Distance of each property to the city centre|
© 2016 T. Dimopoulos and A. Moulas
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