3.7 Land consumption

The available data consist of the surface area of consumed land (expressed in hectares), the density of land consumption in relation to the total area of each municipality (expressed in square metres/hectare), and the percentage of consumed land (see Appendices 5 and 6).

Figure 6, derived from the values in Appendix 5, show the trend of land consumption for the entire district of the Land of Fires (Sistema Nazionale per la Protezione dell’Ambiente, 2024).

3.8 Real estate market in the Land of Fires

In temporal analogy with the other indicators, the average values of the residential real estate market (€/sqm) of the municipalities constituting the Land of Fires (Immobiliare.it, 2024) were detected, in the period from 2012 to 2021 (see Appendix 7).

Through the Pareto diagram, it is quicker to identify the municipalities that present the highest trends in average annual property prices, in the time range considered. Figure 7 traces the distribution of the data collected in decreasing order and presents a cumulative line on a secondary axis as a percentage of the total.

It is the municipality of Pozzuoli – followed by Quarto, Pomigliano d’Arco and Caserta – that presents the most significant values in the entire territory of the Land of Fires. Santa Maria La Fossa, Castel Volturno and Francolise are, instead, the municipalities that present the lowest trend.

Instead, by using an average operation of the values relating to all 61 municipalities taken into consideration, the average price is obtained, discriminated for each of the years considered, of residential properties located in the Land of Fires (see Figure 8): the trend appears, in general, decreasing, with a dizzying drop after 2013 and which found substantial completion in 2017 (the year in which the recorded value was the lowest).

4. Methods

4.1 Multiple regression models

Multiple regression models are statistical tools used to analyze the relationship between a dependent variable (or response) and two or more independent variables (or predictors). This methodology is particularly useful for studying complex phenomena where multiple factors influence an observed outcome.

The goal is to estimate the regression coefficients that indicate the contribution of each predictor to explaining the dependent variable, while controlling for the effects of the other predictors.

The general form of the multiple linear regression model is (Simonotti, 1997):

Y = β₀ + β₁X₁ + β₂X₂ + ⋯ + β_pX_p + ε(1)

where:

–Y: dependent variable;

–X₁, X₂, …, X_p: independent variables (predictors);

–β₀: model intercept (expected value of Y when all X values are 0);

–β₁, β₂, …, β_p: regression coefficients (expected change in Y for a one-unit change in X_i, holding other variables constant);

–ε: residual error (the difference between the observed and predicted values).

The coefficients β_i are estimated by minimizing the sum of squared residuals (SSR), which is the difference between the observed (Y_i) and predicted values.

In matrix notation, the model can be expressed as:

Y = Xβ + ε(2)

where:

–Y is the vector of observed values;

–X is the matrix of predictors;

–Β is the vector of coefficients;

–ε is the vector of errors.

The coefficients are estimated as:

$\widehat{\beta }$ = (X^TX)^-1X^TY(3)

Main advantages of using a multiple regression model are: allows simultaneous consideration of multiple predictors, identifies relationships between variables, and provides an interpretable model. On the other hand, the main limitations are constituted by multicollinearity (when predictors are highly correlated, the estimated coefficients can become unstable), strong assumptions (requires linearity, homoscedasticity, and normality of residuals), overfitting (adding too many predictors can make the model overly complex and less generalizable).

4.2 Geoadditive models

Geoadditive models are composed by a semi-parametric additive component to express the relationship between model’s non-linear response and explanatory variables, and a component with linear mixed effects to expresses the spatial correlation of observed values (De Paola et Al., 2019 and 2021; Del Giudice et Al., 2015 and 2021).

In the case of two additive components, if (s_i, t_i, y_i), 1≤ i ≤ n, represent the measurements on two predictors s and t for the response variable y, the additive model is:

$y_i={\beta }_0+f\left(s_i\right)+g\left(t_i\right)+{\epsilon }_i$(4)

where f and g are unspecified smooth functions of s and t respectively. Therefore, if we define u₊ to equal u for u > 0 and 0 otherwise, a penalized spline version of the model (4) involves the following functional form (Del Giudice & De Paola, 2014a and 2014b):

$$\begin{array}{l}{y}_i={\beta }_0+{\beta }_s\cdot s_i+{\sum }_{k=1}^{Ks}{u_k}^s(s_i-{{\kappa }_k}^s)+\\ {\beta }_t\cdot t_i+{\sum }_{k=1}^{Kt}{u_k}^t(t_i-{{\kappa }_k}^t)+{\epsilon }_i\end{array}$$(5)

In equation (5) there is the penalization of the knot coefficients u_k^s and u_k^t, where κ₁^s, …, κ_ks^s and κ₁^t, …, κ_kt^t are knots in the s and t directions respectively. The penalization of the u_k^s and u_k^t is equivalent to treating them as random effects in a mixed model.

Setting β = (β₀, β_s, β_t)^T, u = (u₁^s, …, u_ks^s, u₁^t, …, u_kt^t)^T, X = (1 s_i t_i) with 1 ≤ i ≤ n, Z = (Z_s|Z_t), with:

Z_s=[(s_i – κ_k^s)₊]_{1 ≤ i ≤ n, 1 ≤ k ≤ Ks} , Z_t=[(t_i – κ_k^t)₊]_{1 ≤ i ≤ n, 1 ≤ k ≤ Kt} (6)

penalized least squares is equivalent to best linear unbiased prediction in the mixed model:

$y=X\beta +Zu+\epsilon$ ; $E\left(\begin{array}{c}u\\ \epsilon \end{array}\right)=0$ ;

$\mathit{cov}\left(\begin{array}{c}u\\ \epsilon \end{array}\right)=\left[\begin{array}{ccc}{{\sigma }^2}_s\cdot I& 0& 0\\ 0& {{\sigma }^2}_x\cdot I& 0\\ 0& 0& {{\sigma }^2}_{\epsilon }\cdot I\end{array}\right]$(7)

Model (7) is a variance components model since the covariance matrix of (u^Tε^T)^T is diagonal. The variance ratio σ_ε²/σ_s² acts as a smoothing parameter in s direction. Penalized spline additive models are based on low rank smoothers, considering that linear terms are easily incorporated into the model through the Xβ component.

At this point we can incorporate a geographical component by expressing kriging as a linear mixed model and merging it with an additive model such as model (7) to obtain a single mixed model (defined as geoadditive model).

Universal kriging model for (x_i, y_i), 1 ≤ i ≤ n (y_i are scalar and x_i represent geographical location included in R² domain) is:

$y_i={\beta }_0+{{\beta }_1}^T{x}_i+S\left(x_i\right)+{\epsilon }_i$(8)

where S(x) is a stationary zero-mean stochastic process and ε_i are assumed to be independent zero-mean random variables with common variance σ_ε² and distributed independently of S. Prediction at an arbitrary location x₀ is done through the following expression:

$y\left(x_0\right)={\beta }_0+{{\beta }_1}^T{x}_0+S\left(x_0\right)$(9)

Then for a known covariance structure of S the resulting equation is:

$y\left(x_0\right)={\beta }_0+{{\beta }_1}^T{x}_0+{c_0}^T{\left(C+{{\sigma }_{\epsilon }}^{2}I\right)}^{-1}\left(y-{\beta }_0-{{\beta }_1}^{T}x\right)$ (10)

where:

$C={\left(\mathit{cov}\left\{S\left(x_i\right),S\left(x_j\right)\right\}\right)}_{1\le i,j\le n}$(11)

${c_0}^T={\left(\mathit{cov}\left\{S\left(x_0\right),S\left(x_i\right)\right\}\right)}_{1\le i\le n}$(12)

For all aspects and matters above reported, a geoadditive model can be described, substantially, as a single linear mixed model as follow:

$y_i={\beta }_0+f\left(s_i\right)+g\left(t_i\right)+{{\beta }^T}_1\cdot x_i+S\left(x_i\right)+{\epsilon }_i$(13)

Or in this further representation:

$y=X\beta +Zu+\epsilon$ (14)

where:

$E\left(\begin{array}{c}{u}^s\\ u^t\\ \tilde{u}\end{array}\right)=0$ ; $\mathit{cov}\left(\begin{array}{c}u\\ \epsilon \end{array}\right)=\left[\begin{array}{cccc}{\sigma }_s^{2}I& 0& 0& 0\\ 0& {\sigma }_t^{2}I& 0& 0\\ 0& 0& {\sigma }_x^{2}I& 0\\ 0& 0& 0& {\sigma }_{\epsilon }^{2}I\end{array}\right]$(15)

5. Case study

Once the useful data relating to the variables considered were collected, to provide a synthetic description of the phenomenon for each municipality, an average operation was chosen to take into account what happens in different years. A comparison was carried out between two types of averages by calculating the standard deviation: simple arithmetic mean (AM) and moving arithmetic mean (MAM). The best average was found to be the AM as it generates a lower standard deviation than the MAM. If the individual municipalities are compared based on the standard deviation, the MA is always better than the MS as the relative normal distribution is much more regular than the one considered as the MAM.

For each indicator, and in correspondence with each municipality, the average annual increase for the period 2012-2021 was developed (see Appendix 8).

In the case of interest, we referred to a regression model without an intercept, in order to ignore other possible variables on the average percentage variation of the price.

Any outliers were eliminated from the sample, namely: some small municipalities adjacent to large municipalities, as they may be affected by the influence of the phenomena of the adjacent municipality in addition to those of their own; some municipalities in the coastal area characterized by a strong phenomenon of irregular migration, such that the variable relating to the presence of foreigners would have had a preponderant aspect compared to the other independent variables.

Starting from the exploratory analysis of the regression model, the determination coefficient R² is equal to 0.85, denoting an acceptable value in order to hypothesize a good adaptation of the regression plan to the observed points. The value of the corrected R² is equal to 0.80, while the multiple R is equal to 0.92, returning an acceptable degree of relationship between observed and predicted values, and the relationship between the set of independent variables defined and the dependent variable is sufficiently adequate. The standard error, on the other hand, corresponds to 0.014: being close to zero, it guarantees that the regression model is accurate.

The confirmatory analysis of the model is the process of testing against a null hypothesis. In regression analysis, the null hypothesis consists in the absence of a linear relationship between the dependent variable and the explanatory variables. Since in our case p-value is associated with the F statistic < 0.05 we can affirm that there is an effective linear relationship between the independent variables and the dependent variable and that the model is not a mere theoretical construction: the relationships in the model actually exist and are not random, therefore there is evidence that at least one variable X_i significantly influences the price variable Y.

The equation of the regression model is the following:

∆_price = – 0,392∙∆_mortality–0,217∙∆_{multi-ethnic groups}–0,090∙∆_{land reclamation}+0,062∙∆_landfills+0,00008∙∆_{toxic fires}–0,791∙∆_{land consumption}(16)

Using the regression coefficients and the mean value of the individual independent variables, it is possible to determine the influence of the individual “weighted” variable for the dependent variable; the information obtained from the Weighted Average Coefficient (WAC) is, in fact, more complete as an information set. To define the WAC, both the sign of the mean value inherent to the individual variable and the sign inherent to the “weight” deriving from the results of the regression model must be considered. A summary is provided in Table 4 where the impact of the single variable following a unitary change in price. However, if we consider the average of the price changes in the municipalities of the selected sample, we can see how much the single variable impacts the real average change ($\stackrel{-}{∆}$ _price = -0.031).

We can define the RWAC (Relative Weighted Average Coefficient):

${CMPR}_i=\frac{{CMP}_i}{{\stackrel{-}{\Delta }}_{valore}}=\frac{{CP}_i* {\stackrel{-}{\Delta }}_i}{{\stackrel{-}{\Delta }}_{valore}}$(17)

Through the RWAC it is found that an average change in real estate prices of -3.1% is correlated with a change of:

- +46,77% in mortality rate;

- +29.35% in the multi-ethnic groups;

- -0.581% in the unreclaimed land;

- +2.516% in the presence of landfills;

- -0.645% in toxic fires;

- +15.29% in land consumption.

It follows that: the mortality rate is the factor that most influences the collapse of real estate prices, followed by the rate of multi-ethnic groups and land consumption. The same qualitative information is obtained from the WAC: observing the absolute value, the ranking of the variables that affect the cost is the same.

Considering the average variation of a phenomenon has allowed us to examine phenomena of temporal evolution in a stationary manner: the results we obtained must therefore always be read in terms of variation in a “horizontal” manner.

There is an inverse relationship between the mortality rate and the variation in prices, the same one present with the rate of multi-ethnic groups, unreclaimed land and land consumption; this implies that as one of the above-mentioned rates increases, there is a decrease in the increase, over time, of real estate prices. The distrust resulting from the poor liveability of a generally unhealthy urban context, such as that of the Land of Fires, is tangible from the high values of all four of the above-mentioned variables; life in a territory that presents: a higher mortality rate than the national average (the causes of which are strongly linked to the low urban quality of the place), a high rate of multi-ethnic groups, tending to increase, generally overshadowed by the possibility of an “easy life” offered by organized crime (just think of the migrant settlements – located in unauthorized or abusive areas – that turn into a real business for eco-mafias), high levels of unreclaimed land and particularly the land consumed by artificial casings, cannot but translate into a disadvantage, which also affects property prices, in which the distrust deriving from the dangerousness of the place is poured, without remedy, onto the real estate market discouraging the value of the assets pertaining to it. However, in the analysis conducted, there are two rates that, by increasing, generate positive variations in prices, they are the presence of landfills and that of toxic fires.

Concerning the first factor, the data show that, from 2017 to 2021, there was a reduction in the quantity of active landfills in the territory, consequently generating an increase in decommissioned plants (a landfill that does not comply with European directives is a danger during the work phase as well as during closure, since the resulting leachate penetrates the subsoil causing irreparable and profound pollution); this increase, while on the one hand it may seem like a potentially positive effect and generate an increase in changes in real estate prices, in reality it hides serious negative implications. The last rate discussed is that relating to fires; the harmful fires for which we have information are those collected by official monitoring that uses actual video surveillance booths. It is a variable with a very low weight – in the order of 10^-5 – whose positive influence on price changes deserves careful attention; the positive variation in the number of fires recorded is seen to correspond to a positive variation in prices, the impact of which is very small, being a phenomenon characterized by a negative prerogative and extremely monitored and opposed. Despite the actions implemented regarding monitoring, knowledge and prevention, it remains a disadvantageous factor in terms of the liveability of the place.

Synthesizing, in short, what has been exposed, it is clearly noted that the majority of environmental and social phenomena, considered in the analysis, lead to a negative variation in property prices; this is indicative of a real estate market that receives an increasingly smaller number of consents and that appears vigorously stigmatized by the indelible mark that pollution has placed on the territory (the stigma effect, in fact, is not only linked to the dangerousness of the phenomenon but also, and above all, to the perception that one has of it). The situation worsens if we consider that phenomena such as the setting of fires, dumping activities, and the presence of illegal landfills dedicated to the disposal of illicit waste, appear to be out of control, taking on a greater gravity in the eyes of those who perceive it.

Of the 61 municipalities that are part of the Land of Fires, the municipalities of Acerra, Nola and Marigliano, due to their geographical positioning and the high mortality linked to the onset of tumors, have been defined as “the triangle of death”.

The high mortality rate in these municipalities appears to be mainly linked to pollution caused by the illegal dumping of toxic substances in the environment managed by the Camorra, which operates an illegal waste traffic throughout the country, transporting industrial waste produced by industries in northern Italy to the Campania region. The illegal dumping of waste occurs in illegal landfills but often also in legal landfills, all accompanied by the phenomenon of fires that already devastate the entire area of the Land of Fires.

To describe the real estate market of this territory in spatial terms, n. 384 residential properties, chosen in such a way as to homogeneously cover the territory of the 3 municipalities, were detected during the year 2021 (Immobiliare.it, 2024). The real estate market remained stationary until 2024. To take into account the different locations, the data were “homogenized” through specific market ratios drawn up based on data from the Real Estate Market Observatory of the Italian Revenue Agency (Osservatorio del Mercato Immobiliare, Agenzia delle Entrate, 2024).

For each property the real estate market price and the amounts of some real estate characteristics are known, as shown in Table 5 and Table 6.

Based on real estate data, the following geoadditive model has been implemented:

UPRICE = FLOOR + MAIN + CAR + f(XCOORD, YCOORD)(18)

Results and main indices of model verification are presented in tables and graphics that follow. The determination of knots for the spatial component and its geographical coordinates are identified by the space filling algorithm, implemented in default.knots.2D function library of R Software Wand et Al., 2005). The geoadditive model was therefore estimated by the Re.M.L. method using the spm library of R software.

A preliminary multiple regression analysis conducted on the data relating to the individual municipalities, to verify the reliability of the data used in the geoadditive model, is provided in Table 7.

The estimates of effects in the non-linear model have been significant by values of freedom degrees (df) and smoothing parameters (spar). The values of obtained predictions are consistent with observed data, also analysis of residuals has not shown any abnormality in its structure. In examined area, the spatial distribution of real estate unitary prices clearly shows how the geographical component affects the prices of sampled properties.

The main result of the interpolation is a thematic map depicting the real estate unitary values in the urban context considered, in which blue and red colors represent unitary values, respectively, lowest and highest values (see Figure 9).

From Figure 9 it can be observed that unit prices increase from the municipality of Acerra (high vertex of the triangle, with lower prices) to that of Nola (low vertex of the triangle, with higher prices).

Unit sales prices cover a range from € 1220/sqm to € 1340/sqm and fall within the range of values provided by the Real Estate Market Observatory of the Italian Revenue Agency for the areas analysed.

The analysis of the geo-additive model appears to be in line with a series of phenomena related to the urban quality of the municipal contexts considered. To explain the phenomenon of the variability of unit prices between these three municipalities, in the municipality of Acerra there are 137 industries, in that of Marigliano 322 and in that of Nola 484: the number of industries increases from municipality to municipality and with it, the perception of the potential for growth and economic development increases and in accordance with this it is easy to think that a greater prospect of a better environment from a socio-economic point of view is linked to a greater real estate value. If we take into account the fact that in Nola there is the Campania interport, which is an international logistics platform connected to the main world hubs, we realize that the higher sale price, demonstrated by the geo-additive model, of the properties in this area is largely justified. If we consider the percentage of consumed land as an indicator of urbanization (how much artificial has been built on the territory), we see that, for increasing values of the percentage of consumed land, the municipal ranking we obtain is: Acerra, Marigliano, Nola. Therefore, Acerra appears to be the least urbanized municipality while Marigliano is the medium urbanized one while Nola is the most urbanized one. For this reason, it can be assumed that, since the price of a property is directly linked to the urban context and the services that a certain place offers, it increases with the increase in the degree of urbanization since the increase in the latter also increases the services that the city can offer to its residents. The fact that the lowest selling prices refer to the municipality of Acerra, the highest ones to the municipality of Nola and the intermediate ones to the municipality of Marigliano, can also be linked to other factors that are also linked to the perception of healthiness of the area. If we consider that moving from the municipality of Acerra to that of Nola there is a reduction in polluted surfaces of 10%, we can understand how an urban context of better environmental quality is certainly associated with a higher price of properties since environmental quality is an asset that impacts the quality of life of residents who are therefore willing to pay more to live in an urban context that is considered better as it is home to a lower polluting impact.

When talking about remediation and soil pollution, it is good to remember that the chemical, physical and biological alteration of the soil is linked to anthropic phenomena and human activities that can compromise it, even irreversibly. In this regard, it can be considered that among the most disastrous causes is the incorrect disposal of waste, which often occurs without regulations and in a completely abusive manner. The municipalities considered are part, as we know, of the broader context of the Land of Fires characterized by the presence of abusive fires that are triggered to burn waste that is sometimes even toxic and dangerous. Following this, we realize that going to live in a context where there is a greater ignition of toxic fires is certainly less inviting than going to live in places where phenomena of this type do not occur. If we move from the municipality of Nola to that of Acerra, the data on the ignition of fires (obviously we are talking about those registered but the real number is much higher as the phenomenon appears to be uncontrolled), an increase in fires, on average per year, of 60% is recorded, therefore it is easy to understand that prices in correspondence with this notable increase undergo a notable decrease as the perception, and the actual, dangerousness of the phenomenon discourages buyers from living in these areas.

6. Conclusions

This work was aimed at verifying how environmental and social externalities influence the market prices of residential buildings in the Land of Fires.

The results obtained make it clear that the problems strongly related to environmental pollution strongly influence the real estate market, even if their consequences appear, only theoretically, less worthy of consideration than those generated by the elements concerning the mortality risk and those relating to social risks, specific to the territory taken into consideration.

The clear sign of a real estate market that admits a number of consents that is gradually declining is visible in the reduction of property values in the selected municipalities, guilty of being located on a land affected by an indelible stigma, related not only to environmental pollution – due to the scattered and massive toxic fires and harmful elements discernible from abandoned industrial and waste disposal sites – but also to an ever-increasing trend in mortality (which sees the development of tumor diseases as the main cause) and multi-ethnic groups subjugated by the presence of criminal organizations, capable of actively establishing themselves in social reasoning.

Through data processing tools, it has been concluded that positional characteristics have effects on the formation of market prices, but how can this information be put to good use? Rather than implementing future estimates regarding the trend of costs, it would be of fundamental and primary importance to make changes to the sick matrix of the “Land of Fires”, not only from the point of view of environmental remediation which, only marginally, is already underway – through innovative soil phytoremediation technologies, which allow the restoration of the original conditions, replacing those physical-chemical steps that return totally infertile soils – but also by determining more precise comparison frameworks, in particular for the municipalities not included in the final analysis and through continuous monitoring of those factors that generate the greatest critical issues, drawing inspiration from the operations already implemented regarding the “fire issue”. The crisis of the Land of Fires serves as a harsh reminder of the complex interaction between industrialization, lax regulation and environmental degradation and highlights the need for proactive measures to prevent similar crises from emerging elsewhere. It is clear that by learning from the mistakes made on this soil, governments, industries and civil societies can work together to create a more sustainable future, characterised by responsible waste management, strong regulatory frameworks and a commitment to preserving the health of the planet and its inhabitants.

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