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*Isidora Barbaccia Real Estate values in Low *∗∗Erika GhiraldoDynamic Markets: proximity effects **Maurizio Festa Translation by Ilene Steingut

Keywords: residential submarkets, real estate prices, cluster analysis, spatial autocorrelation.

Abstract The identification of residential submarkets is of great interest for the correct planning of housing policy. In addition, in recent years increasing demand for more detailed spatial statistical information that requires increasingly specific territorial subsets has emerged. The aim of this paper is to define an aggregation of municipalities characterized by homogeneity in terms of trends and levels of house prices. The empirical analysis is carried out in a first phase using tools of descriptive statistics, global and local econometric spatial indices, and regressive techniques to create a set of useful indicators. In the second phase, a clustering method is applied to define the final groups.

INTRODUCTION The real estate market is characterized by a great degree of complexity that makes housing prices very different in both time and space. Therefore, the market cannot be regarded as a single system but must necessarily be seen as a set of interconnected micro-markets. There is general agreement in the literature regarding the existence of real estate submarkets in the residential market (Goodman and Thibodeau, 2003 and McCluskey et al., 2002). Their identification is of great importance in many fields. The literature identifies two main areas in which knowledge of submarkets can make a significant contribution: • housing policy – in order to understand the location effect of one area with respect to another (Pryce and Evans, 2007) or also to ensure that plans adequately take into account market trends (Bates, 2006); • property taxes - in which the estimation of property values requires the identification of submarkets real estate (Eckert, 1990). Despite the full recognition of their existence and utility, there is no single and coherent definition of submarket (Watkins, 2001). In any case, the origin of submarket studies can be traced to Grigsby’s pioneering work (1963)1. In particular, he proposed the theoretical concept of substitutability2 as the basis for the definition of the submarket. Substitutability is the willingness of the market to replace

1 As shown by Galster (1996) and Megbolugbe et al. (1996). 2 It should be pointed out that the concept of substitutability was derived from Grigsby (1963) from one of the earliest works on submarkets attributable to Rapkin (1953).

* Official in Direzione Centrale Osservatorio Mercato immobiliare e Servizi estimativi - Agenzia del Territorio ([email protected] • erika.ghiraldo @agenziaterritorio.it) ** Office manager of Real Estate Statistics and Studies - Agenzia del Territorio (maurizio.festa@ agenziaterritorio.it) 36 Isidora Barbaccia, Erika Ghiraldo and Maurizio Festa

a dwelling, with all of its attributes, with another one in order to optimize housing needs, while establishing a given constraint on price. When this ability to substitute becomes so weak and does not to produce any recognizable effect on prices, the property can be considered as belonging to a different sub-market. Thus, an area of the real estate market in which all units are linked together in a substitution chain - in the sense that each unit located in an area can be considered as substitute for any other unit - is a submarket. A critical issue regards whether or not the submarket should be defined on a spatial level, or which factors should be applied to the concept of substitutability. According to Watkins (2001), housing submarkets are determined by both spatial and structural factors. In the eyes of empirical fact, among the models used to identify submarkets, undoubtedly the most widespread is the hedonic model (Allen et al., 1996; Goodman, 1981); other studies have used multivariate statistics techniques. Factor analysis is used by Dole-Johnson (1982) and cluster analysis is used for example by Abraham et al. (1994) and Hoesli et al. (1997). In recent years, spatial statistics techniques have been used extensively, as in the work by Basu and Thibodeau (1998) or Peace and Gilley (1997). Starting from Watkins’ consideration (2001) - which had emerged previously (Adair et al., 1996) - on the importance of spatial and structural characteristics, this spatial analysis of the real estate market consists of the identification of groups of homogeneous markets by analyzing spatial and temporal variables relating to market structure through the use of clustering techniques. The article is structured as follows. First the goals of the analysis will be specified, followed by the description of decisive factors. Then we will examine the steps that led to the creation of the set of variables and describe the clustering process. Finally we will present our conclusions and discuss possible future developments.

GOALS OF THE ANALYSIS As mentioned in the introduction, the identification of housing submarkets is of considerable interest from different points of view. In recent years the awareness of the role that the real estate market plays within the overall economy has greatly increased, resulting in a growing demand for more detailed statistical spatial information level requiring increasingly specific territorial subsets. Since 2001, the Agenzia del Territorio’s Real Estate Market Observatory (OMI) has been responsible for the collection, processing and publication of national data regarding real estate values. In about 1,300 municipalities, representing more than 70% of residential real estate transactions, collection of data comes about directly through the compilation of standardized forms throughout the nation resulting in the acquisition of a great deal of information regarding individual dwellings. In the remaining municipalities, especially due to a low dynamic market, data is collected indirectly through comparison methods and through the expertise of the offices working in the appraisal field. In order to improve inference quality, it is necessary to create aggregations of these weak dynamic municipalities in order to obtain groups that are as homogeneous as possible in terms of price levels and trends. In other words, it is a matter of seeking empirical evidence for the hypothesis of the existence of local real estate submarkets that spatially embrace a number of municipalities with the goal of strengthening the procedures for the determination of values. In light of the literature examined, as mentioned in the introduction, the identification of submarkets should omit any reference to administrative boundaries and base the study on information regarding single dwelling units. For the goal of the analysis, in this paper, we have to consider municipal and provincial administrative boundaries because the Agenzia del Territorio is organised at provincial level. This paper will present one way of defining submarkets by taking a number of factors into Real Estate values in Low Dynamic Markets: proximity effects 37 consideration. The method is not intended to have general validity, but rather, it is one possible way of identifying homogeneous price areas, starting from some general factors. The aim of our work, therefore, is to achieve a specific goal that responds, however, to the general need for more detailed information. In particular, this article proposes an experimental analysis of a mid-sized area and make a low complexity due to regional differences. The choice is made to study the 47 municipalities in the Province of Modena3. Although, as pointed out, the province’s real estate market is not particularly diversified, there are particular characteristics that must not be overlooked when we need to divide a region into homogeneous sub-areas. Municipalities in the province of are, in fact, located in plains areas, in foothills and in mountains; some are crisscrossed by two tributaries of the Po, the and the . The importance of industrial area - with the presence of particular districts - cannot be overlooked. The province hosts important food industries (large sausage factories, parmesan production and pork processing), a metalworking and mechanical engineering industry (it is considered the most important center for motor sports manufacturing) as well as ceramics, textiles and biomedical industries. There is no doubt that these characteristics influence the dwelling localization and therefore the determination of house prices. It thus becomes necessary to create a system of variables that can describe - in terms of level and variation - the diversity of residential prices observed in the different municipalities. In other words, we seek to understand, on the one hand, which variables determine the evolution of prices and, on the other, to use these variables to create groupings of municipalities as homogeneous as possible with respect to the selected variables. To this end, clustering techniques will be used.

3 The choice to analyze the came about, of course, prior to the occurrence of the tragic earthquake in May 2012 that affected several municipalities in this province, causing damage and casualties. 38 Isidora Barbaccia, Erika Ghiraldo and Maurizio Festa

Figure 1 Municipalities in the province of Modena4

MIRANDOLA

SAN POSSIDONIO FINALE

CAVEZZO CARPI

MODENA

FORMIGINE

SASSUOLO

MONTEFIORINO

INFLUENTIAL AND DECISIVE FACTORS In the first step we describe the identification of variables to define the subsets of municipalities in the province of Modena. The starting data is provided by real estate quotations database (OMI)5. These values are available on the Agenzia del Territorio website with details for OMI zone and have been published six-month since 2004. A range of market values is generated for each area and for each housing type (luxury, mid- priced, and low cost housing, villas and cottages). By calculating the average of the central values of the intervals of each residential typologies in each OMI zone, an average municipal value can be obtained. This is considered the initial element for the subsequent analysis. The value of the average price, both in absolute terms as well as in relation to other average prices, represents a difference in value of residential real estate located in the municipalities considered. The factors influencing the different price levels are evidently multiple, insofar as they relate to spatial/locational variables that, in turn include building features, the presence of connections but also social and economic elements. In the first models that appeared in the literature, the locational variable is neglected because of the difficulty in obtaining data. These are so-called “location insensitive” models. In recent years, improvements in information technology have facilitated the use of a wide range of indicators that take into account geographical and socio-economic conditions

4 The provincial capital of Modena is hatched. 5 For more details on the process of price formation and the definition of homogeneous areas, see Manuale della banca dati dell’osservatorio del mercato immobiliare (Manual of the database of the observatory of the real estate market) (Agenzia del Territorio, 2008). Real Estate values in Low Dynamic Markets: proximity effects 39

simultaneously (for reference Jackson et al., 2007 or Kestens et al., 2006). In order to obtain a small number of variables is required a careful selection process due to the high number of features. In this study, we try to resolve the high dimensionality problem not by a factorial method, as repeatedly found in the literature (Maclennan and Tu, 1996), but by synthesizing information, that we assign to a factor category, building a single indicator. As we cannot consider all influential variables we set general categories in order to identify a single variable to represent the category. It is important to note that the selected categories, while not exhaustive, do provide a good starting point for further analysis.

DEFINITION OF VARIABLES In the following paragraph, the steps that led to the definition of the variables that constitute the input dataset for the analysis of the groups will be briefly described. As mentioned, starting from an analysis of possible influential factors, six classes of categories are chosen for analysis: • factors regarding the composition of the housing stock in a given zone; • Intensity and dynamics factors in housing market; • pull factors of residential properties; • temporal dynamics factors of house prices; • house prices levels; • Prices’ spatial correlation factors.

Factors regarding the composition of the housing stock in a given zone The classification of a zone as residential rather than industrial or commercial proves, even intuitively, to be an important factor in the formation of average prices in a given area. In fact, it is evident that a greater presence of a certain building typologies modifies the surrounding context with consequences on the values of the residential property located there. It would therefore be appropriate to take into account property types in each municipality through the choice of a suitable variable. To appreciate the differences, it is considered useful to assess the built housing stock6 for each group in terms of units surveyed and cadastral income. For the purposes of constructing the specific variable in this study, real estate stock refers to the number of properties surveyed in the cadastral archives, distinguished by type and income – representing the tax base determined by the Cadastre. In the real estate world, a distinction is usually made between two broad categories of properties: residential and non residential. Analysis of their composition provides information about the types of properties that can qualify an area as residential rather than industrial or commercial. However, a number - understood as the sum of the single units in each type - is not sufficient for providing the information deemed useful. Finding a larger share of residential dwellings in a municipality does not in itself indicate that the municipality can be considered more residential than another. For this reason it is more effective to consider information regarding cadastral income7 and in

particular to calculate the income share of the residential sector, indicated as QRres. In order to set this variable, we consider both the sum of all cadastral income values of residential

properties (Rres) and income values of non-residential properties (Rnres).

6 For a better definition of stock and values, see “STATISTICHE CATASTALI 2010 (CATASTO EDILIZIO URBANO)” “ CADASTRAL STATISTICS 2010” the last of which was published on October 27, 2011 available at www.agenziaterritorio.gov.it 7 Strictly speaking, cadastral income is not the most appropriate indicator for measuring the use of properties in the area. It would be more appropriate to use a parameter that expresses the portion of land occupied by residential properties as compared to other uses. However, we do not have such information so using cadastral income can at least take into account the area of building units according to use. 40 Isidora Barbaccia, Erika Ghiraldo and Maurizio Festa

Rres includes all values of the real estate units surveyed in cadastral category in the group A with

the exception of A10. In Rnres we take into account the cadastral income differing in relation to the permitted use. In the offices sector we consider the urban unit belonging to the A10 (offices) and D5 (banks) cadastral categories. The commercial sector is identified by the C1 and C3 (shops), D8 (commercial buildings) and D2 (hotels) categories. Finally, in the industrial sector we include the D1 and D7 (warehouses) categories.

The QRres variable is then defined as follows:

QRres = Rres / (Rres + Rnres),

and will be added to input matrix for further cluster analysis.

Intensity and dynamics factors in housing market The level of prices and their trends depend on the number of transactions in a given area. In turn, the number of transactions is, in general, a function of the number of urban units in a certain geographical area. To understand a market’s quickness, it is therefore necessary to examine the

number of transactions in the area and the number of homes in the same area simultaneously. As for the number of transactions in each municipality, the number of normalized transactions (NTN)8 per unit traded is taken into account, referring to residential properties or those belonging to the A1 to A11 cadastral categories - excluding A109. For the number of residential units in the municipality, the stock of surveyed units for the same categories used in the NTN is taken into account. To understand the dynamism of the residential sector in each municipality, it is necessary to take into account that the absolute number of transactions depends on the number of urban units (Stock). For this reason, the relationship between NTN and Stock, indicated by IMI, is analyzed. The value of IMI is calculated from 2004 to 2010 for each municipality, as:

IMIit = NTNit / Stockit,

with i as i-th municipality and t as t-th year. IMI therefore expresses the share of dwellings bought and sold in a given year and can be interpreted as the measure of the market’s dynamism in light of the fact that a greater IMI value corresponds to a greater quota of homes bought and sold, net of the effect of the stock’s size. Once the value of IMI is calculated in each municipality in every year, the analysis shows a generally diminishing trend entirely due to the decline in sales identified in all municipalities. To capture the dynamism of the market over time, the difference in IMI between the initial and final periods of observation (2004 and 2010) was taken into account, or more precisely

∆ IMI10-04 = IMI10 – IMI04.

The indicator thus calculated represents the variable to be included in the matrix for the cluster analysis.

8 The value of NTN in a given period and for a specific category of property is derived from the Data Base of Real Estate Advertising (former Conservatories). 9 For a breakdown of property within each category see the appendix of the publication “STATISTICS CADASTRAL 2010 (land registry).” Real Estate values in Low Dynamic Markets: proximity effects 41

Pull factors of residential properties In a given area, an important factor in the setting of prices and their dynamics over time is the region’s ability to arouse interest in the purchase of residential properties. The underlying idea is that real estate purchases made by non-residents is a sign of attractiveness of the local market. This interest can be attributed to economic factors relating to the presence of industrial or service activities that provide employment opportunities which encourage the migration and increase housing demand. Other factors can be the proximity to a big city or recreational motivations. Based on these assumptions, pull factors are distinguished mainly in two types: economic and social drivers. Concerning economic factors, reference can be made to information regarding whether or not a municipality lies within an industrial district. This variable - economic factors (Ae) - is therefore based on the industrial specialization of a given area. On the basis of this information, a categorical variable can be defined by assigning the following values to each municipality: • 0 if the municipality does not belong to any district; • 1 if the municipality belongs to an industrial district of the Modena local labor system SLL (urban systems); • 2 if the municipality belongs to the of Carpi SLL industrial district (textiles, leather and clothing); • 3 if the municipality belongs to the SLL industrial district of (other “made in ” systems). The variable relating to social factors (As) is a composite index that takes into account both the combination of the percentage of first homes and the indication of tourist municipalities as indicated

by ISTAT. For each municipality, the percentage of first homes (Q_Abitazp) is calculated as the ratio between the number of homes owned by individuals who claimed to use the property as a first home10 in 2009 and the stock of dwellings in the same year.

On the basis of the values attributed to variable Q_Abitazp, an empirical threshold equal to 40% is

fixed. It is a slight lower value than the first quartile of the distribution of Q_Abitazp of all municipalities equal to about 43%. As for as the subset of municipalities that have a value lower than the threshold are concerned, we take into consideration only the tourist municipalities identified according to the ISTAT definition. In this way we obtained a dummy variable As, whose value is 0 or 1. The variable is equal to zero if the defined condition is not met and the municipality is not attractive; it is equal to one if it is attractive (below the threshold and defined by ISTAT as a tourist municipality). We must note that a low percentage of first homes might also be attributed to a municipality’s depopulation. In the case of the municipalities in question it is believed, however, that the value should be read in a positive sense with the presence of second homes. In fact, many of the selected towns belong to the area, which has the highest altitude in the northern Apennines and in the Emilia- region and is home to a winter ski resort. The Monte Cimone area includes the municipalities of Fiumalbo, Fanano, Riolunato and Sestola which is perhaps the most famous ski resort in Emilia-Romagna. In addition, the municipalities of Pievelago and Fiumalbo border the Pistoia region’s high mountain areas which include some well-known winter and summer mountain resorts, the most well-known of which is probably the town of Abetone. As a simplifying hypothesis, in this study we assume that a small share of first homes in a given municipality, as compared to the rest of the provincial values, can be interpreted as an indication of the ability of a municipality to attract vacation property used for holiday vacations (for rental or direct use).

The variables Ae and As are considered as basic input data for the cluster analysis.

10 For a detailed analysis of the use of the housing stock in Italy see “Gli immobili in Italia. Distribuzione del patrimonio e dei redditi dei proprietari” (“Real estate in Italy. Distribution of assets and income of owners”) available on www.agenziaterritorio.it. 42 Isidora Barbaccia, Erika Ghiraldo and Maurizio Festa

Temporal dynamics factors of house prices It is common knowledge that an ordered sequence of observations over time is a time series whose analysis typically aims at forecasting through the study of the regularities of a phenomenon’s trend. In this case, the regular availability of data for more than ten semesters makes it possible to explore the dynamics of prices recorded over time. On the other hand, the relative brevity of the length of the time series of prices does not allow the application of advanced statistical models, but only a first exploratory examination that is, however, useful for the construction of a variable providing information on the price trends in each municipality. In this sense, the analysis of values over time is carried out in this study with the goal of defining a variable that can indicate the basic price dynamics during the considered period. This variable is defined in two steps: • in the first step the series of prices is analyzed separately for each municipality by applying a temporal regression; • in a second step the coefficients obtained are grouped into categories. Graphical analysis of the series of all the municipalities showed in most cases the presence of a linear trend and sometimes a quadratic trend. Then a regression of prices (Q) is estimated for each municipality with respect to a time variable t and a squared time variable t2. For the single municipality, the regression model estimated was of the following type:

2 Qt = β0 + β1 t + β2 t + ε,

2 β0 is intercept of the model, β1 and β2 are coefficients of the variables t and t respectively, and finallyε is the stochastic component which is assumed to have a normal distribution with mean zero and constant variance, σ2. The estimates of the regression models confirmes what is already evident from the graphical analysis. Essentially there are municipalities characterized by levels of rising prices throughout the period and municipalities that show a downward trend. Once the estimates of the coefficients are obtained for each municipality by ordinary least squares method (details in Appendix A) we defined a variable by assigning:

• null value in the case in which the coefficient β1, linked to the trend and the coefficientβ 2 concerning the squared trend variable are both not significant;

• value 1 in the case in which the coefficients β1 and β2 are both significant; • 2 and 3 both refer to the result in which only the variable t is significant but municipalities are

distinguished in which the coefficientβ 1 assumes a contained value arbitrarily set at less than 10.

These municipalities are assigned a value of 2. When β1 is greater than 10, a value of 3 is assigned. The variable thus defined, which can be indicated by T for the time trend, will be used in the clustering process.

House prices levels The analysis of price divergence that can be found in different areas is of such great interest that the topic stands on its own due to the number of studies devoted to it. In general, it can be assumed that price differences among municipalities is representative of the amenities within an area in consideration of a wide range of factors. In this sense, it might be useful to analyze these differences in order to define a variable that can measure the differences in price levels. Straightforwardly, to highlight the differences between price levels we take into account the relationship between the price in each municipality and a price considered particularly important as benchmark. The latter can be represented by a maximum value, a minimum, or by the average or a Real Estate values in Low Dynamic Markets: proximity effects 43

value selected from a municipality that plays a role of interest in the analysis. The above-mentioned ratio, that can be called differential, provides information on the distance between the average price in a municipality and the benchmark municipality. In this analysis, the differential (Diff) is calculated for each semester as the ratio between the price

in each municipality (Qi) and the Modena quotation (QM), which is considered representative of the price since it is both the provincial capital and also represents the maximum price for almost all semesters. This variable is given by:

Diffit = Qit / QMt,

with i as the indicator of the municipality and t the indicator of the semester. Fifteen values for the differentials in each municipality are obtained (from the first half of 2004 to the first half of 2011). The dynamic of differential is analyzed through the distribution of the frequency of the differentials observed throughout the period establishing a single size of the classes11 for each municipality. In this way, it is observed that the differentials for each municipality are fairly stable over time. Most of the municipalities show a substantial permanence of the differential value in the same class for

the entire period. Thus we decided to use the average of the differentials from the period, Diffi., as a variable to express the differences in values among the municipalities.

Prices’ spatial correlation factors Many authors have shown that geographic location, and, more generally, the spatial dimension, play a central role in the analysis of the determinants of house prices (Smith et al., 1988). Real estate values have, in fact, peculiar geographic features. The factors of spatial dynamics are expressed through the set of a variable based on a spatial correlation indicator. The concept of spatial correlation based on quantitative geography is that what happens nearby is more important than what happens in more distant places. More precisely, in the analysis of a spatial phenomenon, it is expected that the correlation between two variables observed in two locations at a distance x decreases when x increases. Therefore, it is necessary to analyse this phenomenon of “distance decay” through a weights matrix that shows the correlation between variables observed at various distances. In empirical analysis, spatial linkages are usually taken into account through the construction of a spatial weights matrix, W12. The choice of the distance matrix is, in some cases, not neutral. Indeed, as

11 Five classes were established: 0 -|0,5; 0,5 -| 0,7; 0,7 -| 0,9; 0,9 -| 1; 1-|1,1. 12 With regard to the construction of such a matrix, in the literature there are two approaches: a first standard approach based on contiguity and on measures based on distance; another recent approach consists of a series of measurement attempts, among which we mention the Bayesian method that searches for the “best fit,” non-parametric techniques, spatial correlation, iterative techniques, etc. In this sense, Bhattacharjee and Jensen-Butler (2006) point out that the choice of weights is frequently arbitrary and that there is substantial uncertainty about the choice of the matrix (W); results of the studies vary considerably as a function of the choice of spatial weights. The choice of W should be lead to a good and parsimonious result but the risk of an erroneous specification always exists. In the standard approach, the choice of this matrix is a priori, and it is always assumed that

the elements wi,i of the diagonal of the matrix W are zero to avoid falling directly into problems of endogeneity. Among the most common matrices there are:

• Matrices of contiguity, in which the generic element wi,j of W is equal to one if areas i and j share a border, or zero otherwise • Matrices with distance bands in which the generic element wi,j is one if the locations i and j are located at a distance of di,j less than a predetermined threshold d, or zero otherwise;

• Functional matrices in which the generic element wi,j assumes a value equal to a function of their distance, di,j. However, the same distance is not a simple concept; it can also be referred to a economic distance between the regions, eg. proximity technology. 44 Isidora Barbaccia, Erika Ghiraldo and Maurizio Festa

shown by Anselin (1988); different matrices can lead to different conclusions regarding the strength and geographic extension of spatial correlation. However, there is no generally valid rule and the choice of the matrix depends on the nature of the phenomenon that we want to analyse. When there is no precise idea of the nature of the underlying spatial process more neutral choices are represented by either contiguity or distance matrices. A peculiarity of these matrices is that, unlike functional ones, more than one can be used in the same analysis. For example, contiguity matrices can be set to understand the spatial correlation between zero and fifty kilometres, fifty and one hundred, one hundred and one hundred and fifty, and so on. Then they can all be used together to verify at what distance evidence of correlation can be found. Rosenthal and Strange (2003) make use of this technique, for example, to see at what distance Marshallian externalities affect the establishment of new businesses. Among the many possible choices, the most coherent with the municipalities is the distance matrix. In particular, it is decided to adopt the K-nearest neighbour rule. In fact the geographic extent of the area is, in most cases, very narrow so it would seem logical to consider correlation matrices in which not only what is directly contiguous has a direct effect, but the influence also extends to “neighbours of neighbours.”

According to this rule, two municipalities Si and Sj can be defined as neighbours if the distance between them is less than a predetermined threshold. Given the particular irregular form of administrative borders, a number of five neighbouring municipalities is chosen, meaning that the five closest towns were considered to be contiguous (the shortest distance between the centroids of the polygons of the municipalities). Thus, starting from the assumption that house prices are not only affected by the characteristies the area in which the property is located, but that they are also influenced by the features of proximal economic, social and physical areas, it is assumed that the determinants of real estate prices have a broader range than the municipal boundaries in which a property is located. Thus, a variable representing the set of factors of spatial dynamics is proposed; it seeks to capture that part of the price that escapes traditional statistical measurements that do not take the spatial dimension into account. It should be noted, however, that the analysis is limited - for obvious reasons of simplicity - to the administrative boundaries of the province and therefore does not take into account any influences from neighbouring towns in other provinces. In order to calculate the Spatial Indicator variable (Is), the concept of spatial correlation should be explained. In fact, depending on the phenomenon to be analyzed, once the most suitable matrix has been chosen, spatial correlation can be measured. To verify the statistical significance spatial autocorrelation between house prices we calculate13 the Moran index for each semester. The Moran test shows the existence of significant spatial dependence between house prices in all semesters.

13 The Moran index is given by the following expression:

N w (x -x−) (x -x−) (N/S0) ∑ ij i j i,j=l

I = N (x -x−)2 ∑ i i=l

Where N is the total number of areas; in xi represents the variable property prices in the municipality i, xj is the variable property prices in the municipality j and wij are the weights of the matrix W and n w S0 = ∑ ij i,j=l is the sum of all the elements of the matrix in which according to the distance between points contiguity between the areas is defined. This indicator measures the correlation of a variable with itself through space, and has a variation range between -1 and 1. Real Estate values in Low Dynamic Markets: proximity effects 45

In order to classify submarkets based on the house prices, given the significant global autocorrelation, besides the global Moran index, the corresponding local indicator of spatial association, LISA, was also calculated. This indicator measures the degree of autocorrelation for each territorial unit. Autocorrelation exists if some localization pattern of a variable can be identified. In particular, if nearby areas are more similar than distant ones, then there is positive autocorrelation. If neighbour areas are more different than distant ones, then the autocorrelation is negative. If the patterns are random, there is no correlation. The local Moran meets two criteria. The first is that the LISA for each observation should give information about the significance of spatial clustering of similar values around an observation. Secondly the sum of the LISA indicators for all observations should be proportional to the global indicator of spatial association. The local version of Moran’s I statistic for each observation i can be written as:

z I i w z i = 2 ∑ ij j z j j∊Ji N Σ −− i=l N where zi is the value corresponding to the municipality i of the already normalized variable, j is the set of municipalities near i. The null hypothesis is the absence of spatial autocorrelation so if the test, which is distributed as a standard normal, gives significantly positive values, there is a cluster of regions with similar characteristics. Conversely, significant negative values indicate a cluster of diverse regions. In other words, for each unit, it will be possible to indicate the type of correlation (positive or negative) and its level of significance. The LISA of real estate prices allows us to verify the membership of each municipality in a cluster that can only be of four types: 0, not significant, 1 high high (H - H), 2 low low (L - L) , 3 Low High (L - H), 4 high-low (H - L). The results are reported in detail in Appendix B. The LISA analysis for each semester shows the existence of two areas with positive autocorrelation of the L - L type (the first in the northern part of the province of Modena and surrounding towns, including the towns of Concordia sul Secchia, , , Mirandola, San Felice sul Panaro, Medolla and Camposanto; the second in the south-west of the province, includes the municipalities of Frassinoro, , Lama Mocogno and Polinago). In particular, we can note the presence of an area, near the capital with positive autocorrelation of the H – H type, that comprises the municipalities of Modena, Campogalliano, , Fiorano Modenese, Maranello, Castelvetro di Modena, Vignola, Spilamberto and Castelfranco Emilia. In addition there is the “atypical” San Cesareo sul Panaro municipality with low real estate values, but surrounded by shopping centres with values higher than the provincial average (L - H). In order to create a single variable to represent the results obtained by LISA, the membership of each municipality in a cluster is compared for each semester in question. If the municipality remaines in the cluster of the specified type for a certain number of times (even if not consecutive) exceeding a threshold, we assume that the municipality belongs to the cluster. The threshold is equal to 6 semesters out of a total of 22 semesters analysed, corresponding to 3 years. 46 Isidora Barbaccia, Erika Ghiraldo and Maurizio Festa

At this point, an ordinal variable is built which we defined as the spatial indicator, Is, taking on values 0, 1, 2, 3 and 4 as follows: • 0 if the municipality has not been shown to belong to any cluster for at least 6 semesters; • 1 if the municipality is located in a cluster of municipalities in which there are high prices and these influence each other (H - H) for at least 6 semesters; • 2 if the municipality is located within a cluster of municipalities where there are low prices with a positive correlation between them (L - L) for at least 6 semesters; • 3 and 4 if the municipality is located in an area where the municipal prices have a negative correlation between them of type 3 low-high or 4 high-low for at least 6 semesters. This variable represents the indicator of spatial correlation Is.

MUNICIPALITIES CLUSTERING Methods for aggregating spatial units in order to divide a larger-sized area are based mainly on cluster analysis procedures. It is also a useful technique when we want to create new homogeneous areas - in terms of grouping various municipalities - with respect to a set of variables for which it could be interesting to publish periodical information from administrative sources. Cluster analysis is a technique widely used in applied sciences and is supported by an extensive literature that in recent years has made available a large number of new methods as well as in-depth analyses and improvements on existing tools. As pointed out in one of the latest review by Jain et al. (1999), such a wide availability of clustering algorithms can easily confuse a researcher in the selection of the appropriate algorithm to resolve an applied problem. Despite this vast literature, many questions are still open and the solution is most often left to the user’s experience. Therefore the following paragraphs briefly illustrate the steps followed to define the final clustering. Before proceeding with clustering, an initial exploratory analysis is performed on the data matrix. For the 47 municipalities in the province of Modena, seven variables are created, each of which synthesize

a larger number of factors. Of the 7 variables, 3 are continuous (QRres, ∆ IMI11-04 e Diffi.) even if they take on values in the interval [0, 1] and 4 are categorical (As, Ae, T and Is). Table 1 shows the descriptive statistics of the 3 quantitative variables while Figures 2 and 3 display the maps for each variable. It is clear that the share of cadastral income that can be attributed to the residential sector is greater in municipalities in the south of the province with respect to the remaining area examined. In particular, the municipalities in which the weight of the residential sector is significantly higher than the offices, commercial and industrial sectors are located south of Modena. Real Estate values in Low Dynamic Markets: proximity effects 47

Regarding the difference in IMI between 2004 and 2010, the map shows a general decrease in market dynamics due to diminishing transactions. The municipalities located to the east of Modena suffer the biggest loss. An analysis of house price divergence shows that, within the province, there are significant differences in values between the different municipalities. Similar values can be noted in municipalities around the capital, which show a value of the differential in the class between 0,7 and 1. The exceptions are Sestola and Vignola which, while having values similar to Modena’s, are located in the south of the province. Values that are distant from Modena’s reference values are found equally in the south and in the north of the provincial capital. About half of the municipalities do not belong to any manufacturing district and are located almost exclusively in the south of the capital with the exception of Camposanto and Medolla which have no features of economic attractiveness. The other municipalities in the province are part of three districts. In particular, 13 municipalities, mainly located in the capital belt, belong to the Modena urban system. Carpi, Modena Novi and Soliera form Carpi’s industrial textiles, leather and clothing industry district. Finally, the 7 municipalities in the northeast belong to the Made in Italy district. Note that the Ae variable confirms what is observed in the analysis of the QRres variable showing a less number of non-residential activities in the area to the south of Modena. With regard to the As variable, shown in the second map of Figure 3, most of the municipalities in the province have characteristics typical of first homes. The southeastern part shows attractiveness as a location for second homes. Regarding trends, unlike the other variables, the municipalities do not manifest a particular geographic structure, showing a fairly diversified evolution of prices over time within the province. The map referring to the Is variable shows that twenty-two municipalities in the province of Modena do not belong to any cluster. Nine municipalities around the province of Modena are part of a cluster in which high prices in the various municipalities positively influence one another. The largest cluster - in terms of number of municipalities - is characterized by positive correlation between low real estate values and includes twelve municipalities. These municipalities are located in two clearly defined areas in the southwest and in the north of the province. Campogalliano, San Cesareo sul Panaro and Savignano sul Panaro are outliers with low real estate prices, despite being located in an area characterized by high housing prices. The town of Mirandola is also an outlier with high prices in an area with prevalently low prices.

Table 1 Descriptive statistics of the quantitative variables

Statistics QRres ∆ IMI10-04 Diffi.

Minimum 0.174 -0.036 0.384

First quartile 0.418 -0.018 0.499

Median 0.474 -0.013 0.588

Average 0.518 -0.014 0.609

Third quartile 0.656 -0.010 0.705

Maximum 0.839 0.002 1.000 48 Isidora Barbaccia, Erika Ghiraldo and Maurizio Festa

Figure 2 Maps of the quantitative variables

Share of residential cadastral income, QR Res Difference in residential IMI, ∆ IMI10-04 n 66% - 84% (12) n - 0,01 - 0,003 (12) n 52% - 66% (7) n - 0,014 - 0,01 (15) n 42% - 52% (15) n - 0,018 - 0,014 (7) n 0 - 42% (13) n -0,036 - 0,018 (13)

Average Differential, Diffi.

n 0,71 - 1 (11) n 0,61 - 0,71 (9) n 0,5 - 0,61 (15) n 0 - 0,50 (12)) Real Estate values in Low Dynamic Markets: proximity effects 49

Figure 3 Maps of the categorical variables

Economic attractiveness, Ae

n 0 (24) n 1 (13) n 2 (3) n 3 (7)

Social attractiveness, As

n 0 (37) n 1 (10)

Difference in residential IMI, ∆ IMI10-04 n - 0,01 - 0,003 (12) n - 0,014 - 0,01 (15) n - 0,018 - 0,014 (7) n -0,036 - 0,018 (13)

Trend, T

n 0 (16) n 1 (8) n 2 (15) Spatial indicator, I n 3 (8) s n 0 (22) n 1 (9) n 2 (12) n 3 (3) n 4 (1) 50 Isidora Barbaccia, Erika Ghiraldo and Maurizio Festa

Based on the results obtained with the selection of variables, whose details are described in the previous sections, in the next step we apply the clustering procedure. We decide to standardize the variables to avoid any problems of scale and since there is no particular reason to keep it. In terms of the choice of algorithm, the study takes into account the fact that the non-hierarchical techniques are more efficient when seeking groups characterized by high internal homogeneity and thus we choose the K-means algorithm. The K-means method, developed for the first time by MacQueen in 1967, belongs to the so-called partitioning methods, in contrast to hierarchical methods. Through an iterative procedure, the K-means method allows the division of n units into k partitions so that each unit belongs to a single group. The steps14 of the algorithm can be summarized as follows: • choose the number k of clusters; • randomly choose data from the input matrix which are the initial centroids of the clusters; • assign the remaining data to the centres of the closest clusters using a criterion function (usually a function that minimizes the sum of the squares of the differences between the units and the centroids); • use the data in each cluster to calculate a new average for each cluster; • If the new averages are identical to those previously calculated, the process has reached convergence and can be terminated. Otherwise, use the new averages as cluster centres and repeat steps 3 - 5. As mentioned for this type of technique, the first step is the choice of the fixed number of groups. To make this choice, we use a model-based technique15 which returns 5 as the optimal number of groups present in the data base. Among the several algorithms available for processing the data matrix, the algorithm proposed by Hartigan and Wong (1979) is implemented by the software R through which the partition is obtained. Then, by establishing 5 as the number of groups, the partition of the municipalities displayed in the map in Figure 4 is obtained. The map shows the clusters obtained with k-means.

14 Reference may be made, among others, to Jain et al. (1999). 15 In particular we used the Mclust function of the mclust Package. It is available for the software R. The package mclust version 3 for R is described in MCLUST Version 3 for R: Normal Mixture Modeling and Model-Based Clustering, Technical Report no. 504, Department of Statistics, University of Washington, September 2006. Real Estate values in Low Dynamic Markets: proximity effects 51

Figure 4 Map of the cluster obtained with the K-Means

n 1 (10) n 2 (9) n 3 (9) n 4 (8) n 5 (11)

To check for the robustness of the partition, a fuzzy technique is applied to the same data matrix, setting 5 groups. In fuzzy set theory (whose origin can be traced back to Zadeh’s work in 1965) a unit can belong to a cluster with a degree of membership that takes on a value in the range [0, 1]. Then each unit, or each municipality in this case, can belong to several groups simultaneously with the constraint that the sum of memberships is equal to 1. Once the probability of belonging16 to each group has been obtained for each municipality, units are assigned using subjective thresholds. Municipalities are assigned to groups with a high probability of belonging, > 0.6 or a good probability of belonging in the range [0.4 and 0.6). Table 2 shows bar charts for each municipality illustrating the distribution of the probability of belonging to each group. The map in Figure 5 shows the groupings by assigning the municipalities that follow to the described rule. Essentially two kinds of municipalities can be distinguished: those showing good probability of belonging to a group and those for which belonging to one group is not clear. For the first category, fuzzy clustering returns results that were entirely identical to those obtained with the K-means also highlighting the robustness of the previously obtained subdivisions. On the other hand, a problem of overlapping emerged for municipalities with characteristics of similarity with more than one group. However, these municipalities generally have greater probability of belonging to two groups and low probability for the rest of the groups. Thus the divisions obtained by using K-means can be accepted. Further, to check the clustering results, K-means is carried out by applying an ANOVA test on the values.

16 To obtain the fuzzy distribution we used the package e1071 available for the R software by setting 5 as the optime number of groups and using the fuzzy method of partition C-Means introduced by Bezdek (1981). 52 Isidora Barbaccia, Erika Ghiraldo and Maurizio Festa

As we do not want consider a single period value we calculate the average value for each municipality

from the first half of 2004 to the first half of 2011 (indicated generically byi Q ).

To verify the null hypothesis of average prices equality in each group Cj against the alternative

hypothesis H1 otherwise we apply a test. We assume the following model:

Qij = Cj + εij

where Qij indicates the average price of the i-th municipality, which proved to belong to the j-th

cluster, Cj is the average price of the j-th cluster and finallyε ij are the errors for hypotheses normally distributed with zero means and constant variance σ2. The value obtained for the F-statistic is equal

to of 12,54 which leads to rejection of H0. It can be argued that the average prices of each cluster are not equal.

Table 2 Probability of belonging to each group obtained through a fuzzy clustering procedure Probability Probability Probability Municipality Municipality of belonging Municipality of belonging of belonging P>0,6 0,4<= P<0,6 P<0,4

Castelfranco Emilia Modena Campogalliano

Cavezzo Bastiglia Fiorano Modenese

Finale Emilia Bomporto Guiglia

Fiumalbo Camposanto Serramazzoni

Formigine Carpi Novi di Modena

Castelnuovo Montefiorino Pavullo nel Frignano Rangone Castelvetro Montese Polinago di Modena Concordia sulla Prignano sulla Nonantola Secchia Secchia

Riolunato Fanano Ravarino

San Felice San Cesareo Frassinoro sul Panaro sul Panaro

San Possidonio Lama Mocogno San Prospero

Savignano Maranello sul Panaro

Spilanberto Marano sul Panaro Sestola

Zocca Medolla Vignola

Mirandola

Montecreto

Palagano

Pievepelago

Soliera Real Estate values in Low Dynamic Markets: proximity effects 53

Figure 5 Map of clusters obtained using fuzzy clustering

n 1 (5) n 2 (6) n 3 (8) n 4 (9) n 5 (5)

CONCLUSIONS AND DEVELOPMENTS The empirical study analyses extensive categories of factors through the use of simple descriptive statistical tools, global and local econometric spatial indicators and regressive techniques. This led to define a set of variables that, when used together to group municipalities with the multidimensional clustering technique, is useful for the identification of groups of municipalities whose house prices seem to be homogeneous. Thus the empirical idea of the existence of real estate submarkets and their homogeneity seems to be confirmed. The homogeneity found through the analysis of spatial, temporal, social, economic and real estate variables makes it possible to detect the values in some of the municipalities in the identified cluster. This procedure seems to be able to capture both effects of spatial factors relating to the geographic, territorial and structural features of the residential market. However, as seen, the application of the fuzzy technique shows the existence of an overlapping problem or the probability of a municipality to belong to multiple groups. Some elements, therefore, still render the analysis not entirely objective insofar as it is influenced by the analysts’ choices. Despite this fact, it is believed that the result is a good starting point for subsequent explorations that can take into account the fact that, in addition to showing high spatial variability, over time house prices can be very different due to changes in the locational context of reference, for example. In this sense, also for submarkets, which undergo mutual influences and influences from neighbouring territories, evaluations will become necessary to verify the validity. Furthermore, even with its limitations, this exercise utilizes readily-available variables that are easily reproducible in other studies. 54 Isidora Barbaccia, Erika Ghiraldo and Maurizio Festa

In terms of new developments, two further paths can be pursued. One natural extension is the application of the study to other areas to assign whether the methodology used in this pilot study is valid in other regions. In particular, the limitations posed by the provinces’ administrative borders can be overcome by applying the method to larger and therefore more complex territorial areas. The study of the differences in values between the different submarkets identified may be of particular interest. However, at this level of analysis we may conclude that the results obtained, in combination with the specific knowledge of experts, can be useful for improving knowledge of the connections among real estate submarkets in a given geographical area therefore helping to improve the quality of the inference about municipalities that were not directly surveyed.

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APPENDIX A Details on the estimates of the trend The table 3 shows the results obtained from the regression model, in particular, for each municipality: estimates of the coefficients, values of the t statistics, level of significance (where *** indicates α=0,01, ** indicates α=0,05 and * indicates α =0,1).

Table 3 Estimates of coefficients, t statistics and significance of the time series analysis

Municipality ß0 ß1 ß2 Municipality ß0 ß1 ß2 Municipality ß0 ß1 ß2

1.430,14 62,15 -2,90 1.128,26 14,60 -0,32 1.000,43 16,41 -0,16 Modena -47,23 7,14 -5,47 Fanano 102,79 4,83 -1,73 Bomporto 35,27 2,48 -0,41 *** *** *** *** *** *** **

1.046,36 13,06 -0,96 773,97 60,03 -1,24 Castelfranco 1.122,83 15,74 0,29 Guiglia 44,89 1,95 -2,37 Fiumalbo 8,05 2,42 -0,83 Emilia 49,35 2,51 075 *** * ** *** ** *** **

Marano 1.062,40 18,98 -0,82 Lama 753,15 9,65 0,18 988,18 33,19 -0,65 sul 54,85 3,41 -2,43 Mocogno 40,18 1,87 0,59 Nonantola 32,30 3,90 -1,26 Panaro *** *** ** *** * *** ***

765,42 8,29 0,03 762,54 22,92 -0,79 850,52 15,19 -0,55 Montese 53,51 2,02 0,12 Serramazzoni 57,26 7,32 -4,66 Ravarino 76,19 5,21 -3,13 *** * *** *** *** *** *** ***

740,27 9,81 -0,06 739,58 10,71 0,30 San Cesario 799,86 9,59 0,16 Zocca 49,70 2,29 -0,21 Montecreto 36,39 1,83 0,83 sul 52,40 2,33 0,62 *** ** *** * Panaro *** **

613,92 7,90 0,17 Pavullo 939,55 16,87 -0,04 914,44 20,98 -0,78 Frassinoro 33,53 1,50 0,52 nel 49,69 3,15 -0,12 Campogalliano 100,49 9,58 -5,96 *** Frignano *** *** *** *** ***

848,23 11,69 -0,55 849,65 14,09 0,31 1.241,16 40,59 -1,93 Montefiorino 78,05 3,90 -3,02 Pievepelago 27,29 1,60 0,59 Carpi 54,31 6,90 -5,43 *** *** ** *** *** *** ***

530,97 8,10 0,64 718,90 9,56 0,08 Novi 692,45 7,27 0,09 Palagano 14,73 0,78 1,01 Riolunato 47,40 2,29 0,32 di Modena 75,21 2,93 0,58 *** *** ** *** **

625,33 8,19 0,35 1.256,07 39,09 -0,62 913,66 14,46 -0,26 Polinago 27,33 1,30 0,92 Sestola 32,12 3,52 -0,92 Soliera 65,57 3,70 -1,08 *** *** *** *** ***

Prignano 697,78 36,69 -1,77 Castelnuovo 1.486,62 4,45 -0,40 682,18 36,86 -1,09 sulla 31,97 6,43 -5,17 Rangone 50,04 0,53 -0,77 17,31 3,58 -1,76 Secchia *** *** *** *** *** ***

845,02 17,19 -0,60 Castelvetro 1.126,01 3,59 0,37 652,82 8,11 1,06 Camposanto 56,33 4,16 -2,41 di Modena 47,12 0,58 0,98 Medolla 13,41 0,60 1,30 *** *** ** *** ***

767,19 7,39 0,27 Fiorano 1.123,80 17,62 -0,45 712,42 42,13 -1,06 Cavezzo 61,55 2,11 1,28 Modenese 74,81 4,33 -1,78 Mirandola 17,68 3,92 -1,62 *** * *** *** *** ***

Concordia 697,78 36,69 -1,77 1.153,51 21,91 -0,89 San Felice 561,54 27,51 -0,34 sulla 31,97 6,43 -5,17 Formigine 44,98 3,19 -2,12 sul 16,28 2,99 -0,60 Secchia *** *** *** *** *** * Panaro *** **

1.057,78 14,10 -0,53 1.024,76 32,85 -1,36 533,35 22,83 -0,12 Spilamberto 100,97 4,89 -3,04 Maranello 36,08 4,09 -2,78 San Possidonio 15,23 2,36 -0,20 *** *** ** *** *** ** *** **

1.257,38 14,19 -0,13 1.183,18 16,63 -0,41 742,55 9,20 -0,12 Vignola 109,05 4,18 -0,61 Sassuolo 102,40 5,09 -2,05 San Prospero 57,36 2,53 -0,20 *** *** *** *** * ***

1.028,05 24,86 -0,72 Savignano 908,07 13,21 -0,33 Bastiglia 103,75 8,98 -4,26 sul 84,64 4,71 -1,96 *** *** *** Panaro *** *** * 56 Isidora Barbaccia, Erika Ghiraldo and Maurizio Festa

APPENDIX B Details of spatial autocorrelation For each semester, the table below shows values of Moran’s I statistic, expected value, standard deviation and p-value. In particular, the inference for Moran’s I statistic is obtained by using non parametric techniques based on the permutations of the observations.

Table 4 Results of the I-Moran index

Semester I-Moran E (I) Sd (I) p-value

I 2001 0.42 -0.02 0.07 0.01 **

II 2001 0.45 -0.02 0.08 0.01 ***

I 2002 0.39 -0.02 0.09 0.01 **

II 2002 0.39 -0.02 0.09 0.01 **

I 2003 0.39 -0.02 0.08 0.01 **

II 2003 0.40 -0.02 0.08 0.01 **

I 2004 0.42 -0.02 0.08 0.01 **

II 2004 0.41 -0.02 0.08 0.01 **

I 2005 0.40 -0.02 0.08 0.01 **

II 2005 0.39 -0.02 0.08 0.01 **

I 2006 0.39 -0.02 0.09 0.01 **

II 2006 0.38 -0.02 0.08 0.01 **

I 2007 0.36 -0.02 0.08 0.01 **

II 2007 0.31 -0.02 0.08 0.01 **

I 2008 0.31 -0.02 0.09 0.01 **

II 2008 0.25 -0.02 0.08 0.01 **

I 2009 0.25 -0.02 0.08 0.01 **

II 2009 0.27 -0.02 0.08 0.01 **

I 2010 0.27 -0.02 0.09 0.02 **

II 2010 0.27 -0.02 0.08 0.01 **

I 2011 0.27 -0.02 0.08 0.01 **

II 2011 0.30 -0.02 0.09 0.01 ** Real Estate values in Low Dynamic Markets: proximity effects 57

The maps below show the results of the spatial indicator LISA applied to the variable Q for each semester. In red, the municipalities for which the LISA returns a significant positive correlation (H – H); blue signifies a significant negative correlation (L – L); purple and pink are associated outliers that indicate a significant negative correlation near positive values (L – H) and a significant positive correlation near negative values (H – L).

Figure 6 Maps of the Local Indicator Spatial Association (LISA)

Q I sem 2001 Q II sem 2001

n H - H (9) n H - H (10) n L - L (7) n L - L (9) n L - H (1) n L - H (1) n H - L (1) n H - L (1) n Not significant (29) n Not significant (26)

Q I sem 2002 Q II sem 2002

n H - H (8) n H - H (9) n L - L (8) n L - L (7) n L - H (3) n L - H (3) n H - L (1) n H - L (1) n Not significant (27) n Not significant (27) 58 Isidora Barbaccia, Erika Ghiraldo and Maurizio Festa

Q I sem 2003 Q II sem 2003

n H - H (8) n H - H (8) n L - L (8) n L - L (8) n L - H (3) n L - H (3) n H - L (1) n H - L (1) n Not significant (27) n Not significant (27)

Q I sem 2004 Q II sem 2004

n H - H (10) n H - H (8) n L - L (12) n L - L (12) n L - H (2) n L - H (2) n Not significant (27) n Not significant (25) Real Estate values in Low Dynamic Markets: proximity effects 59

Q I sem 2005 Q II sem 2005 n H - H (8) n H - H (8) n L - L (12) n L - L (12) n L - H (2) n L - H (1) n Not significant (25) n Not significant (26)

Q I sem 2006 Q II sem 2006 n H - H (7) n H - H (7) n L - L (12) n L - L (11) n L - H (1) n L - H (1) n Not significant (27) n Not significant (28) 60 Isidora Barbaccia, Erika Ghiraldo and Maurizio Festa

Q I sem 2007 Q II sem 2007

n H - H (7) n H - H (5) n L - L (12) n L - L (10) n L - H (1) n L - H (1) n Not significant (27) n Not significant (31)

Q I sem 2008 Q II sem 2008

n H - H (5) n H - H (4) n L - L (10) n L - L (10) n L - H (1) n L - H (2) n Not significant (31) n H - L (1) n Not significant (30) Real Estate values in Low Dynamic Markets: proximity effects 61

Q I sem 2009 Q II sem 2009 n H - H (4) n H - H (4) n L - L (10) n L - L (9) n L - H (2) n L - H (2) n H - L (1) n H - L (1) n Not significant (30) n Not significant (31)

Q I sem 2010 Q II sem 2010 n H - H (4) n H - H (4) n L - L (10) n L - L (8) n L - H (2) n L - H (2) n H - L (1) n H - L (1) n Not significant (30) n Not significant (32) 62 Isidora Barbaccia, Erika Ghiraldo and Maurizio Festa

Q I sem 2011

n H - H (4) n L - L (9) n L - H (2) n H - L (1) n Not significant (31)

Q II sem 2011

n H - H (5) n L - L (9) n L - H (1) n Not significant (32)