A statistical analysis of the energy effectiveness of building refurbishment

Renewable and Sustainable Energy Reviews 114 (2019) 109297

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A statistical analysis of the energy effectiveness of building refurbishment Tommaso Barbiero, Carlo Grillenzoni

T

∗

Division of Planning, University IUAV of Venice, Santa Croce 1957, 30135, Venice, Italy

ARTICLE INFO

ABSTRACT

Keywords: Beta regression Comfort gain Energy saving Generalized linear models Pearson- cramer statistics Photovoltaic community Spatial analysis

Owing to the rapid urban growth of past decades, the refurbishment of buildings has become a central topic of city development. A key aspect of building renovations deals with energy saving, both for economic and environmental concerns. The present literature mainly focuses on technological solutions for buildings, and the related data are studied with descriptive statistics. Instead, this paper aims to evaluate the energy effectiveness of refurbishment interventions from a global sector viewpoint. This implies building representative datasets, developing a synthetic cost indicator, estimating a proper regression model, evaluating the meaning of results and outline proper support policies. Two relevant case-studies are considered: the first is a published dataset of European service buildings, which contains detailed information on the undertaken interventions. The cost indicator is built by averaging standard costs per square meter; next, a Beta regression model is fitted to the data. This belongs to the class of generalized linear models (GLM) and it is suitable when the dependent variable (the saving rate) has an asymmetrical distribution on the interval [0,1]. The second case study is a survey on the retrofitting decisions of households in an urban area of Venice; the related dataset includes information on the cost of investment, the energy saving, and the comfort improvement. Comfort may be a subjective perception, including physical, psychological and economic wellness; however, it is also a drive for housing renovation and for energy saving itself. Statistical analyses show a significant positive dependence between all variables, confirming the energy saving effectiveness of refurbishment interventions. On the base of these results, proper refurbishment policies, both for public and private actors, are finally proposed.

1. Introduction The rapid urban growth in the postwar period in many countries has produced many buildings with simplified and cheap technologies. Dwellings built before 1970 present low thermal insulation with high transmittance values of the envelope materials, that depends on the thickness and the progressive wear. It follows that EU (European Union) the building sector is responsible for about 40% of the total energy consumption, and for 36% of the total gas emissions [1]. In general, postwar technologies have not ensured suitable energy consumption and human comfort inside dwellings; therefore, refurbishment practices have become increasingly important. These can be distinguished in passive and active interventions, where the first ones decrease energy consumption without modifying heating and cooling systems [2]. Typical examples are the replacement of fixtures and the insulation of walls and roof; whereas, active interventions concern the introduction of more efficient energy systems, such as new boilers and photovoltaic panels. Energetic retrofitting of the building stock aims to decrease the energy consumption by reducing the heat loss; it generally cuts down ∗

the use of fossil fuels, especially natural gas, so that greenhouse gas emissions are also reduced. Insulation interventions improve indoor comfort by preventing summer overheating and heat loss in winter [3]; they render the daily temperature more homogeneous and enhance acoustic insulation. Building renovation policies also sustain economic development, by activating processes of urban regeneration and yielding new jobs in the building industry [4]. The aggregate economic impact of these policies is potentially significant because more than 50% of the existing building stock should be subject to physical interventions [5]. Public refurbishment policies have become increasingly relevant in the last 10 years in the EU. The THINK project of the 7th framework program for research and technological development of the EU Commission stresses “how to refurbish all buildings by 2050” [1]. This program outlines the ambitious goal of renovating the entire building stock from the energy viewpoint by 2050, through an increasing reduction of energy consumption, according to various levels of refurbishment deepness (see Table 1). The deepest level regards the zeroenergy standard, in which buildings should only use the energy available on-site from renewable sources [6]. Instead, a nearly-zero standard

Corresponding author. E-mail address: [email protected] (C. Grillenzoni).

https://doi.org/10.1016/j.rser.2019.109297 Received 21 January 2019; Received in revised form 4 July 2019; Accepted 23 July 2019 Available online 22 August 2019 1364-0321/ © 2019 Elsevier Ltd. All rights reserved.

Renewable and Sustainable Energy Reviews 114 (2019) 109297

T. Barbiero and C. Grillenzoni

Abbreviations ESCO EU GIS GLM

JRC LTV NZEB OLS PVS ZEB

Energy Service Company European Union Geographic Information System Generalized Linear Model

building reaches more than 90% reduction of energy consumption [7]. The Table also shows the desirable shares of buildings in 2050, according to the different deepness levels. A goal of the THINK project is that about 85% of buildings should reach the nearly zero energy building (NZEB) standard or, at least, a deep refurbishment level. The EU Commission program warmly supports the organization of Energy Service Companies (ESCO). These participate in a portion of the profits to the customer's energy savings, so that clients are relieved from the need of finding financial resources for the plants. Finally, the EU commission suggests economic measures to contrast the factors which hinder the refurbishment practices, such as fossil fuel subsidies. In the case of the removal of these subsidies, people are forced to look for alternatives to maintain thermal comfort inside their buildings. Another approach to favor the refurbishment deepness concerns voluntary certifications about energy efficiency evaluations (energy audit). A worldwide audit tool is the Leed Home Certification [8]; this proposes higher standards than those of national regulations, encouraging the construction of more efficient buildings. Further, voluntary certifications are useful to set higher indoor comfort standards, since the early design phases [9]. Most literature on building refurbishment insists on innovative engineering solutions and their technical aspects. A minor, but significant, literature deals with the evaluation of the average performance of common interventions in various classes of buildings. These works also provide data and descriptive statistics on the energy saving and on the decrease in the emission of climate-altering gases [10,11]. However, other authors argue that comfort and aesthetic improvements are fundamental for the decision to renew houses [3,11,12], and show that in cold climate regions energy saving may be compensated by the search for greater thermal comfort [13]. This is evidence of the so-called Jevons' paradox, where money savings allowed by energetic innovations are spent to increase the level of consumption [14]. Articles that analyze data on the performance of common refurbishment interventions refer to both real and potential situations, where the latter is the one in which all houses are renewed. The document

Joint Research Centre Loan-to-Value Nearly-Zero Energy Building Ordinary Least Squares Photovoltaic System Zero Energy Building

“Building Renovation Case Studies” [15] mentions four best practices of refurbished buildings in Austria and in Switzerland. A study [16] supported by the EU provides five examples of refurbishment projects involving social housing. Häkkinen [10] considers a potential scenario, as regards Finland, in which all buildings are equipped with wall insulations, window fixtures, and thermal solar systems. The IEA Annex 56 ASCOT tool file [17] shows a simulation of the energy savings achievable in different locations of Europe. Zachariadis [18] draws a potential scenario of energy saving in the residential sector for Cyprus, assuming analogous interventions of Häkkinen's study. Table 2 summarizes the results and shows that the greatest potential energy saving is in Northern Europe. Furthermore, a significant gap between real and potential situations emerges. Some articles deal with real datasets and are relevant for the present paper. In particular, D'Agostino et al. [19] consider a sample of 977 non-residential buildings involved in the EU Green Building Program, which aims to increase the energy efficiency on a voluntary basis. They describe the various interventions and their effects on primary energy saving. However, the costs of the various interventions are absent, as the members of the Programme were not obliged to provide this information. Instead, Carpino et al. [11] consider a sample of 363 residential buildings in South Italy; then estimate a linear regression model to explain the primary energy for heating (Y). Their explanatory variables (X) regard the age of buildings, the typology of external walls and fixtures, the typology and the age of the heating system, and the presence of renewable energy systems. Some studies develop spatial analyses on the heat loss of buildings, providing maps of urban areas which need substantial interventions. Murshed [20] estimates the buildings heat loss data by using a 3D model and by considering data about the construction age and other information. Another way to collect data on thermal dispersion is by utilizing remote sensing systems, as performed by the Canadian enterprise MyHeat [21]. Finally, many articles compare the cost per square meter of various types of interventions in Europe countries [21–25]. The purpose of this paper is to evaluate the energy-saving impact of

Table 1 Building refurbishment goals in EU until 2050. Refurbishment deepness

Energy Saving

Share of buildings in 2050

Minor Moderate Deep NZEB (nearly zero energy building)

Between 0% and 30% Between 30% and 60% Between 60% and 90% Above 90%

2% 15% 43% 40%

Table 2 Comparison of Energy savings in the residential sector according to different studies. Source

Place

Mean Energy saving

Scenario

IEA ECBCS Annex 50 [15] D'Agostino [19] Donkelaar [16] This study Häkkinen [10] IEA EBC Annex 56 [17] IEA EBC Annex 56 [17] Zachariadis [18]

Austria and Switzerland Europe Europe Venice (Italy) Finland Copenhagen (Denmark) Nice (France) Cyprus

0.83 0.41 0.40 0.23 0.52 0.65 0.26 0.52

Best practices Good practices Good practices Real Potential Potential Potential Potential

2

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building refurbishment in the residential sector and to propose support policies. The analysis is performed on a statistical basis at a global level (i.e. not on single interventions or edifices), and is articulated in the following points:

energy reduction should be nested into real-estate policies of house renovations, such as granting subsidized loans. Although, individual refurbishment decisions obey to general goals of household wellness, the second case study shows that search for comfort is consistent with energy saving goal. Further, the implementation of collective practices, such as neighborhood PV plants, is able to reduce the energy cost, with parity of the undertaken investment. The plan of the work is as follows: Section 2 investigates the global energy efficacy of refurbishment interventions in the EU dataset of service buildings; Section 3 analyzes a dataset of residential dwellings of a homogeneous urban area; Section 4 describes the main policies for building refurbishment; finally, Section 5 summarizes the conclusions of the work; the Appendices provide technical details and of the Beta regression model and additional estimation results.

1. Get representative datasets with good data quality, and build a synthetic Cost indicator which is insensitive to specific refurbishment interventions or local geographic conditions. 2. Use a regression model which is suitable when the energy saving variable is expressed in percentage and has not Gaussian distribution; then evaluate the meaning of estimates. 3. Define support policies of building refurbishment, both at private and public levels, considering the role of household decisions and collective practices on investments. The first case study deals with the European dataset of service buildings of D'Agostino et al. [19]; it evaluates the cost-effectiveness of refurbishment at a wide spatial scale. Next, a more homogeneous sample of residential dwellings, in an urban area of Venice, is considered. It regards retrofitting decisions of households, including the cost of investment, the rate of energy saving, and the comfort improvement expressed in percentage. Comfort includes thermal, acoustic and aesthetical aspects; hence, it may be a general drive for refurbishment decisions and for energy saving itself. The statistical analysis is performed by estimating Beta-regression models between the total cost indicator ( X ), the energy saving rate (Y ), and the comfort improvement rate (Z ) of interventions. The Beta regression belongs to the class of generalized linear model (GLM) [26–28] and behaves like a non-linear regression scheme. Its use is necessary when the dependent variables (Y , Z ) have an asymmetrical distribution on the interval [0,1]; for instance, when they are expressed in percentage and have a non-Gaussian distribution. Dependence between the variables is also evaluated with non-parametric techniques, such as contingency tables and Pearson-Cramer statistics. Both case studies highlight a significant positive dependence between all variables, in particular among the cost of refurbishment ( X ) and the rate of energy saving (Y ). This suggests that programs for

2. Efficacy of refurbishment in the european context The dataset of D'Agostino et al. [19] regards a large sample (925 units) of European non-residential buildings, providing information on refurbishment techniques, energy consumption and energy savings. The data comes from an authoritative and official source, the Joint Research Centre (JRC) of the European Commission. These data relate to the edifices whose owners voluntarily joined the Green Building Programme between 2006 and 2014 (https://ars.els-cdn.com/content/ image/1-s2.0-S2352340917304201-mmc2.zip). The program, supported by the European Commission, required owners to realize costeffective actions which boost the energy efficiency of their buildings. This dataset represents a suitable basis to study the relationship between refurbishment interventions and energy saving, for the large sample involved. It mainly treats the topic from a technical viewpoint; hence, relevant social aspects such as, cost of interventions and comfort improvement, are neglected. Buildings of JRC database belong to these categories: hotel & accommodation, institutional, logistics & storage, manufacturing & industry, office, restaurant & catering, sport & leisure, transport & infrastructure, and wholesale & retail. The analysis is restricted to offices & hotels, as they are similar to residential dwellings, as regards the

Fig. 1. Spatial location of offices & hotels adhering to the Green Building Program. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) 3

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architectonic structure and the indoor heating. The resulting sample is composed of 211 buildings, of which 90% is located in central and northern Europe (see Fig. 1).

Table 4 Average costs (and ranges) per square meter of refurbishment interventions (and ranges) and their average energy savings (and ranges) in Northern Italy.

2.1. Description of variables To build a global cost indicator, 17 categories of retrofitting interventions are defined: traditional double-glazed fixtures (with typical UW values with transmittance 1.1 m2 K ), recent generation fixtures as triple-

glazed windows (with typical U-values of transmittance 0.7 m2 K ) [29], internal insulation, external insulation, roof insulation, air-air heat pumps, water-air heat pumps, water-water heat pumps, photovoltaic panels, photovoltaic system with accumulation, solar thermal system, geothermal system, boiler replacement, home automation system, onlyair-exchange ventilation system, ventilation system with both air-exchange and heating-cooling functions, and renovation of lighting system using low energy consumption lights (e.g. LED). Furthermore, the energy consumption may also be explained by environmental and physical factors such as the latitude, the year of construction and the dimension (area). The expected signs of the relationships between the energy saving Y and each covariate are commented and summarized in Table 3. Subsequently, a 211x17 matrix D of dummies 0,1 is created (which accounts for the presence or the absence of the interventions in each unit) and a 17x1 vector of relative costs per square meter of the interventions is built. Absolute costs vary from country to country, but the ratios among the various costs are relatively homogeneous within EU. To build the vector , public information is gathered about the average square meter costs and the average percentage of the energy saving for each type of intervention. For example, Paiho et al. [23] investigate the refurbishment costs of residential buildings in Moscow, according to both type and depth of intervention. Similar reviews are made for Vilnius and Västerås (Swe) respectively [24,25]. For south EU, Ferrari and Zagarella [22] study the cost of various kinds of building upgrading in different urban areas (Milan and Palermo) and for different types of buildings. Further, Corrado et al. [30] consider data on the square meter costs of retrofit interventions, concerning an Italian case study. Zachariadis et al. [18] compare the energy saving and the costs of different refurbishment measures, in a sample of residential units in Cyprus. Finally, the Austrian Institute for building and Ecology [9] studies the cost-effectiveness of four variants of refurbishment, illustrating a trade-off between financing costs and energy costs. Finally, the relative price index is obtained by dividing the cost of each intervention by the cost for the standard replacement of fixtures; which is the most common intervention to improve thermal and acoustic comfort. Table 4 shows the square meter costs by refurbishment intervention type in the current building market in Northern Italy, which provides ’ = [1, 1.29, 1.07, …, 0.24]. An indicator of the global cost of refurbishment for each JRC office/ hotel buildings is then obtained by multiplying, rows by columns, the intervention matrix D with the vector : W

Average sq. meter cost [ / m2 ]

Average energy saving [℅]

Type

Traditional fixtures Advanced fixtures Internal insulation External insulation Roof insulation Air-air heat pump Water-air heat pump Water-water heat pump Photovoltaic system Photovoltaic with accumulation Solar thermal system Geothermal system Boiler replacement Home automation system Only air-exchange ventilation Ventilation and heatingcooling Renovation of lighting system

42 (26.5 ÷ 57.5) 54 (33.9 ÷ 74.1) 45 (23.6 ÷ 66.4) 110 (94.0 ÷ 126.0) 140 (93.7 ÷ 186.3) 80 (51.7 ÷ 108.3) 140 (102.9 ÷ 177.1) 140 (116.8 ÷ 163.2) 86 (60,8 ÷ 111.2) 150 (122.9 ÷ 177.1)

9.9 (4.1 ÷ 15.6) 17.6 (14.4 ÷ 20.8) 23.1 (13.7 ÷ 32.5) 30.2 (17.9 ÷ 42.5) 13.8 (10.6 ÷ 16.9) 17.8 (15.0 ÷ 20.7) 19.2 (15.3 ÷ 23.0) 20.2 (17.7 ÷ 22.7) 25.6 (17.8 ÷ 33.3) 44.4 (35.9 ÷ 53)

Passive Passive Passive Passive Passive Active Active Active Active Active

40 (22.1 ÷ 57.9) 200 (144.3 ÷ 255.7) 45 (29.0 ÷ 61.0) 120 (77.3 ÷ 162.7)

17.1 25.9 12.9 16.6

Active Active Active Active

45 (30.3 ÷ 59.7)

0

Active

80 (45.6 ÷ 114.4)

22.2 (17.1 ÷ 27.3)

Active

10 (3.7 ÷ 16.3)

3.6 (1.9 ÷ 5.2)

Active

(11.5 ÷ 22.7) (21.7 ÷ 30.0) (6.6 ÷ 19.2) (9.0 ÷ 24.1)

Y , in order to measure the effectiveness of refurbishing interventions. In the JRC dataset, Y has mean 0.41 and an asymmetric frequency distribution, which can be fitted by a beta probability density f (Y ) , see Fig. 2a. 2.2. Regression analysis Regression analysis is a suitable tool to evaluate the relationship between variables. The linear model k Yi = 0 + j = 1 j Xji + i, i = 1,2, …N usually assumes the Gaussian distribution of the dependent variable Y and of residuals . This condition allows good statistical properties to the parameter estimates and inference on the relationship between Y and Xj . However, in the case of percentage energy saving, the distribution f (Y ) is asymmetrical and has bounded support [0,1]; therefore, the condition of Gaussianity does not hold. Furthermore, one may expect the presence of a non-linear relationship between the variables [31]. For these reasons, the GLM framework [26,27] must be employed in the analysis of the JRC dataset. In this context, the response variable Yi is connected to the linear predictor ‘xi by a proper link function g (.), such as E(Yi |xi ) = µi = g 1 ( ‘xi ). By modelling f (Y ) as the beta-density and choosing the logit as the link function g (µ) = log

( ), one can µ

1

µ

obtain the beta-regression model [26], reviewed in Appendix A. In particular, notice that the logit link implies the exponential relationship

E(Yi |xi ) = µi = g 1 ( ‘xi ) =

(1)

COST = D

Intervention

The indicator (1) must be related to the percentage of energy saving

exp( ‘xi ) 1 = 1 + exp( ‘xi ) 1 + exp(

‘xi )

In the JRC dataset, the histogram of the percentage energy saving,

Table 3 Nomenclature of the explanatory variables for energy the energy saving. Covariate

Expected results

Effect on Y

Latitude (LAT )

The higher latitude the higher should be energy saving because in north Europe deeper interventions are incurred to keep indoor thermal comfort. The lower year of construction the higher should be energy saving because older buildings generally experience a higher heat loss. The greater the area subject to refurbishment, the lower the cost per square meter of the intervention should be, due to economies of scale. Greater energy savings are expected from a relatively high cost of interventions because these, in general, suppose deeper interventions.

+

Year of construction (YEAR _B ) Dimension (DIM ) Cost of intervention (COST )

4

– – +

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Fig. 2. a) Histogram of the variable PERCEN _ SAV and its beta density estimate (with parameters p = 1.5, q = 6.3); b) Histogram of the COST variable of refurbishment interventions; c) Beta regression function of the model “b” in Table 5; d) Plot of actual and fitted energy savings against the observation number, and 95% confidence bands.

Y %, has an asymmetrical distribution, which can be well interpolated by the beta density function (with parameters p = 1.5, q = 6.3). Thus, we may consider the scheme outlined in Table 3:

PERCEN _ SAV = g 1 (

0

+

1 COST

+

2 LAT

+

3 YEARB

+

4 DIM )

relation between the costs of refurbishment and the energy saving, which indicates that as the expenditure increases, the saving gain grows more rapidly. Goodness-of-fit evaluation of GLM models has been developed with pseudo-R2 indices, which have a more general meaning than classic R2 of linear regression, see [67, p.59]. In the literature there are two main approaches: the first is based on second moments and the other is based on model likelihoods (ML), see Appendix A. The pseudo-R2 of Cribari 2 and Ferrari [26,28] RCF belongs to the first group and evaluates the squared correlation between the linear predictor and link-transformed response. More general indicators rely on the likelihood ratio (LR) n = L0 / Ln between the null model, with only the intercept (L0 ),and the full model with all covariates xi ; notice that the transformation 2 log( n ) has a 2 distribution, which enables to test the sign = nificance of n . The basic index of the second group is the likelihood variation PML = (Ln L 0)/Ln = (1 n ) , which has been modified as 2 (2/ n ) RML = [1 ] by Maddala and Cox-Snell, see Ref. [66]. The ration 2 nale is that RML coincides with the classical R2 when the model is linear Gaussian; however, in GLM it under-estimates fitting, see [67, p.61]. In 2 general, RML provides a measure of dependence in probability, rather

+ (2)

By using the beta-regression R package of Cribari-Neto and Zeileis [28], with logit and probit link functions, we obtain the estimates in Table 5. They show that the energy saving mainly depends on refurbishment interventions (as summarized by the cost indicator D ), as the zˆ statistic of its parameter estimate is positive and greater than the critical value 2. Notice that z-statistic is zˆ = ˆ/S , where is the standard error of ˆ . Instead, the physical characteristics (latitude, age, and area of buildings) have not a significant role, despite two minor outliers at rows i = 65, 173 were dropped; hence, these variables can be omitted from the model (2). The beta regression of the energy saving on the indicator cost alone, confirms the significance of the relationship between the two variables. A slight improvement can, instead, be obtained by regressing PERCEN _ SAV on COST 2 , which provides zˆ > 4 , a more significant value. This implies the existence of a non-linear

Table 5 Results of the estimation of beta regression models performed on the European data (z-statistic is zˆ = ˆ/S , where S2 is the variance of ˆ , other indices are explained in Appendix A). Covariates

Coefficient

z-statistic

Coefficient

z-statistic

Coefficient

z-statistic

Intercept

−1.191 2.302e-02

−1.027 3.682

−0.623 0.023

−7.891 3.791

−0.314 .

−9.848 .

−2.074e-03 3.604e-04 −1.597e-06 .

−0.325 0.612 −1.348 .

. . . .

. . . .

. . . 5.305e-04

. . . 4.077

10.6

12.499 0.997 0.065

10.61

12.642 0.998 0.073

10.6

2 RCF (Cribari et al. pseudo R2 )

12.629 0.999 0.074

2 RML (Cox et al. pseudo R2 ) ˆ = 2 log( n )

0.083

0.054

15.81

13.85

15.15

13.28

6.63

6.63

Cost Latitude Year of Construction Dimension 2

Cost Phi PML (% Likelihood variation)

99% 2 critical value Link function

Logit

Logit

5

0.060

Probit

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than linear correlation, and its numerical values are less than 0.5, see Refs. [65,66]. Table 5 provides the estimates of the four indicators for the Beta 2 model fitted on JRC dataset: the pseudo-R2 indices as RC2 and RML have similar and low values, whereas PML and ˆn are 99% significant. It follows that proper evaluation of the goodness-of-fit is probably in the halfway of these indicators. Further, the parameter and its zˆ statistic show the importance of the logit and probit link functions (and so of the GLM specification), with respect to the ordinary linear setting. The regression function of PERCEN _ SAV on COST is displayed in Fig. 2c; the panel (d), shows the actual non-linearity of the beta regression function, especially at the borders. Unfortunately, in the JRC dataset, there are no further explanatory variables that could increase the pseudo-R2 index of the models in Table 5, or factors that could replace the energy saving as a drive for building refurbishments (and their costs). The indoor comfort and the outdoor aesthetic improvements could be suitable variables. Another concern in Table 5 is the difficulty to select the appropriate link function " g " of the beta regression; however, probit and logit are usual choices and provide similar performances.

3. Analysis of refurbishment interventions in a homogeneous context The data used in the previous section belong to different geographic contexts and pertain to offices & hotels buildings, which approach residential dwellings as architectonic structure and heating system. Moreover, information on costs of refurbishment and comfort improvement are absent. The comfort may influence the energy consumption. Indeed, the indoor temperature could be raised by subjective regulation of the boiler. However, we show that refurbishment interventions, to improve indoor wellness, are consistent with energy saving goals (see Table 7). For these reasons, a homogeneous urban zone is now considered, to evaluate the main drivers and the effectiveness of retrofitting, net to the effect of different latitude, legislation, and energy use behavior. The focus is on a suburb of Venice mainland, on a sample of about 200 households, interviewed about the type of refurbishment, the related costs, the resulting economic saving and the comfort enhancement. A more specific question concerns the citizens’ willingness to build up a neighborhood solar community (see Subsection 4.3). 3.1. The study area

2.3. Frequency table analysis

The area is a suburb in the western side of the non-insular part of Venice municipality. Its surface is about 1 square Km with a population is 5848 inhabitants [32]; there are 977 residential buildings, with mean 5.99 people per building. The GIS shapefile with the geometrical characteristics is available from Regione del Veneto [33]. This area includes a significant part of detached and semi-detached houses, including 47.7% of total buildings and 33.3% of the total population. Fig. 4 provides the frequency distributions of houses by size, and the shares of the population living in; the first is decreasing, whereas the latter is nearly uniform. The area has a recent urban development, as the share of houses built since 1990 is 52.1%. We obtain the buildings age from the historical maps dated back to 1965, 1984 and 2005 (sources: Italian Geographic Military Institute and Veneto Region Technical Maps). From the energy viewpoint, the portion of houses with photovoltaic systems is 7,6% (74 plant on 977 buildings), available from the geoportal Atlaimpianti [34]. To represent the building stock from the energetic viewpoint, we construct a heat loss map of the zone, expressed in kWh/m2 year . Thermal maps are often used by refurbishment market agents to signal the buildings needing for deeper retrofit [1], and by policymakers to evaluate the sustainability of urban development projects [20]. Various examples of heat loss maps are provided by MyHeat [21], which

Given the parametric limitations of the regression analysis, we perform a Pearson test between refurbishment costs X and energy savings Y, to evaluate their dependence in probability. This test compares the observed joint frequencies nij with the theoretical ones nij*, ni nj computed under the condition of independence as nij* = n , where ni , nj are the marginal frequencies and n = 211 is the sample size. The Pearson statistic is given by

ˆn = W

H

K

i=1 j =1

(nij

nij*)2 nij*

(3)

where H , K are the number of rows and columns of the joint frequency table. As is known, this test is non-parametric (does not assume a specific model) and accounts for all forms of dependence (linear and nonlinear); thus, it is more general than correlation and regression which only deal with the linear dependence. Under the hypotheses of independence, the distribution of Pearson statistic is Chi-square as ˆ n ~ 2 [(H 1)(K 1)]. The decision rule is to reject the condition of W ˆ n > 2 , where 2 is the independence if the statistic is high, i.e. if W 0.05 0.05 tabulated 5%. Finally, to have an idea of the strength of the relationship, one may consider the Cramér index Vˆn , which is the square root of ˆ n and its maximum value. Hence, a further analysis between the ratio W Costs and Savings is performed by dividing their range into six equalwidth classes, obtaining the bivariate histogram in Fig. 3. The calcuˆ n= 79.3 and Vˆn= 0.275. The Pearson statistic lations provide the value W is 99% significant, meaning a strong dependence between the two variables. These results confirm, and strengthen, those of the beta regression in Table 5. These estimates provide good statistical evidence of the relationship between refurbishment costs and percentage energy savings of the offices & hotels buildings accounted. This relationship, however, is of non-linear type, as shown by the beta regression and Chi-square tests. In addition, other physical factors, such as age, dimension, and location of buildings do not affect the energy effectiveness of retrofitting interventions, probably because building typology and refurbishment techniques are relatively homogeneous in the EU countries. Specifically, the correlation between the percentage energy saving and the latitude is negligible (−0.08), meaning that the latitude does not influence the relative energy saving, although different climate conditions may influence the amount of energy consumptions and thus the absolute energy savings.

Fig. 3. Bivariate histogram of absolute frequencies of energy saving and refurbishment costs. 6

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Table 6 Correlations between thermal dispersion and building characteristics. Build. Age

Roof type

Economic class

Sun exposition

Ratio ext. area/vol

Ratio vol./inhabitants

−0.871

−0.719

−0.272

−0.187

−0.033

0.109

Table 7 Estimates of beta regression models on Venice data. Dependent variables

Energy Saving Y

Covariate Intercept Refurbishment costs X Comfort Z Phi PML (% Likelihood variation)

2 RCF (Cribari et al. pseudo R2 )

Coefficient −1.767 1.679e-05 . 10.909 0.981 0.198

2 RML (Cox et al. pseudo R2 ) ˆ = 2 log( n )

0.286

0.398

0.051

52.26

71.49

7.64

6.63 Logit

6.63 Logit

6.63 Logit

99% critical value Link function

Comfort Enhancement Z z-statistic −19.187 6.928 . 8.29

Coefficient 1.380e-01 2.843e-05 . 9.929 0.998 0.341

collects data from remote sensing and processes them with sophisticated numerical algorithms. In our case study, the map is obtained by combining several layers of GIS shapefiles and point data. These concern the age of buildings, the material of roofs, the real-estate value, the sun exposition, the ratio external surface/volume, the ratio volume/ tenants per building, etc. Technical details of the heat loss estimation are discussed in Appendix B. Finally, the various data are combined in a 3D model with the use of ArcMap software. The thermal dispersion of the entire zone is shown in Fig. 5(a and b). Dark red buildings have dispersion 280 kWh/m2 year , while dark blue units have the lowest heat loss, around 20 kWh/m2 year . The average dispersion is 148.11 and regards the buildings in the inner part of the area. Fig. 5b provides a dichotomic version of 5a, where the units in red are those which exceed the threshold 100. This value represents the present standard for Italian good-insulated upgraded buildings. Nowadays, the target of heat dispersion for passive houses is around 15–20 kWh/m2 year [9], but the costs to achieve this performance are not affordable by most citizens. In the considered zone, only 185 out of 977 units (18.9%) have thermal lower than the threshold 100, in which 1528 people live (26.1% out of the total population), see Fig. 5b. The difference between the two percentages is explained by the recent development of areas densely populated, with good energy saving performance. Indeed, a large part of these buildings is equipped with 3-panes windows and wall-roof insulation systems. On the other side, many detached-houses, mostly built in the 60s and 70s, are not yet involved in retrofitting interventions. By analyzing the data with descriptive statistics, we compute the correlation between the thermal dispersion and the building features. Table 6 shows that major correlations are those with the age and the roof type.

Energy Saving Y z-statistic 1.782 11.443 . 8.644

Coefficient −1.805 . 0.789 11.51 0.980 0.049

z-statistic −9.801 . 3.004 8.721

3.2. The survey A sample of n= 204 households, potentially interested in house refurbishment, was interviewed about energy saving (Y ), comfort enhancement (Z ) and refurbishment expense ( X ) of their interventions. Both variables Y and Z are expressed in percentage with respect to the previous level of comfort as perceived by households, and with respect to the previous energy expense, that includes the energy used for heating and electricity. The comfort improvement Z ranges from 0 (poor), to 1 (excellent). Instead, the expense, X , is in thousands of euros. The variable Z includes direct physical aspects, such as the improvement of acoustic and thermal indoor comfort, and the reduction of humidity damages [9]. In some cases, physical interventions are just necessary to counteract building wear. However, comfort also regards subjective and psychological aspects; for example, aesthetic interventions can improve the mood of tenants, as may be regarded as signs of status symbol. Thermal insulation also improves acoustic comfort, and so the perception of privacy; in addition, modern metal fixtures improve the perception of security. Comfort also deals with real estate aspects; one may refurbish in order to sell the house (short-term period) or to extend the house life span on behalf of descendants (long-term period). Fig. 6 synthesizes the variables involved and the meanings of comfort mentioned. In any event, many of these comfort aspects are consistent with physical energy saving. For instance, the replacement of fixtures and the introduction of insulation systems optimize physical, subjective and real estate aspects, improving the energy performances of buildings. The sole case where thermal comfort is in contrast with energy saving,

Fig. 4. Frequency distribution of buildings and population by building size: 1 = detached and semi-detached house, 2 = up-to-6-flats buildings; 3 = larger buildings. 7

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Fig. 5. a): Heat loss map. b): Heat loss binary map. Blue buildings have heat loss lower than 100 kWh/m2 per year. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

interventions to obtain an immediate enhancement of comfort, with a relatively low expense. This is proven by the stronger relevance of comfort in driving the interventions, in comparison to energy saving. Further details are given in Appendix C.

is when active energy systems are used to increase the internal temperature deliberately. An example is when the boiler is replaced with a more efficient one, but the money saved by the greater efficiency is spent to increase the internal temperature; this is an example of the socalled Jevons’ paradox [14]. The spatial distribution of sampled households is given in Fig. 7, showing adequate spatial coverage. Very recent buildings are not involved, since they may not need refurbishment interventions yet. Finally, the survey accounts only for property houses, as owners can autonomously undertake refurbishment interventions. Globally, 75% of the sample have incurred at least one intervention of refurbishment. Concerning the 153 retrofitted dwellings, many interviewees (85%) have adopted passive measures, such as fixtures replacement and insulation. The share of retrofitted households that have carried out active interventions is almost the same, 86.3%. Nevertheless, this percentage decreases to 62.1%, when excluding the interventions of substitution of the heating boiler. Apart from this necessary and cheap intervention, people tend to adopt basic passive

3.3. Regression analysis As in Section 2, to evaluate the effectiveness of interventions, the beta regression framework is employed. Thus, the models Y = g 1 ( 1 + 1 X ) and Z = g 1 ( 2 + 2 X ) are estimated, and the z-statistics of the parameter are evaluated. Estimation results are in Table 7 and show a strong relationship between cost and comfort, with zˆ = +11.443; while that between cost and saving is smaller zˆ = +6.930, but still significant. These results indicate that an increase in spending leads to an improvement both in comfort and in energy saving. We also evaluate the models is with the pseudo-R2 indexes; that of Cribari et al. [26,28] provides 0.391 for the comfort and 0.198 for the 2 other. The RML of Cox and Maddala is slightly better and the ˆn statistics 8

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Fig. 6. Scheme of the variables involved in survey data analysis.

are uniformly greater than their 99% critical values, confirming the validity of all models. These estimates are performed after excluding 9 outliers, which represent households who have realized only active energy interventions. For example, PV plants have high initial cost, but do not improve the perceived comfort. The complete analysis of residuals of the models in Table 7 is provided in Appendix D; instead, their regression functions are displayed in Fig. 8. They exhibit a marked non-linearity; in particular, the first is concave and the other is convex. Fig. 8a shows the presence of decreasing rate of return on investment, meaning that a relevant improvement of comfort can be achieved with cheap and low-innovative interventions. Nevertheless, the Italian refurbishment sector persists in employing relatively simple technologies. In fact, the share of Research & Development expenditures in the construction sector, compared to gross value added, was just 0.05% in 2015

[35]. Then, building sector needs technological innovation to reach growing wellness inside dwellings. Also, a comfort variation is considered as a return of the individual investment, just as the energy saving. Indeed, the enhancement of comfort implies an increase in the utility and in the perceived wellness. Oppositely to the case of the comfort, the convex regression function in Fig. 8b shows an increasing rate of return of energy saving with respect to expense. Thus, a low expense provides a marginal energy saving; further, significant savings can only be attained by consistent investments and innovation on energy plants. The importance of indoor comfort in the household decision for refurbishment is also confirmed by Cramér and Pearson statistics, see Eq. (3). Owing to the asymmetric distribution of the costs of interventions, the variable X is changed to logarithm form; next, three equalwidth classes are defined for each variable. The Cramér index Vˆn

Fig. 7. Spatial distribution of sampled households. 9

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Fig. 8. a) Beta regression functions between Comfort enhancement and Expense for refurbishment; b) Beta regression functions between Economic energy saving and Cost of refurbishment.

ˆ n is 33.85 (which is between (Z , X ) is 0.30, while the Pearson statistic W 99.9% significant); for the couple (Y , X ) the indexes are smaller, but still significant: 0.25 Cramér and 25.76 Pearson. These results confirm the existence of a significant non-linear relationship between the comfort achieved and the refurbishment spending. Similarly, one may evaluate the direct influence of the comfort achievement on energy saving, as Z may be the determinant of refurbishment decisions. The results of the beta regression are in the last two columns of Table 7 and the graphical results are in Fig. 9. The z-statistic of is significant (3.004), the concavity of the regression function is not much pronounced, but noticeable, and the residuals are acceptable. These results confirm that comfort is a driver for refurbishment expense, which, Y is in turn, enables energy saving. The strength of the relationship Z also supported by the 99% significant statistic ˆn (see Table 7).

important explanatory factors for energy saving. In particular, one may argue that refurbishment interventions are determined by the willingness to enhance house comfort in general. Therefore, the variable Z is a driver for the renovations, specifically for Z is the the expenses X ; indeed, in Table 8 the relationship X Y is positive and still strongest one, and the additional estimate Z statistically significant. It follows that the causal chain of the pheX Y . For example, insulation nomenon may be summarized as Z interventions are motivated by the need for better indoor livability and lead to non-negligible energy savings. It follows that energetic policies should be nested into building activity programs, which pursue comfort, aesthetic and real estate goals in general. Below, the three main approaches to stimulate building refurbishment are presented. The first concerns law regulation tools, the second is about financial incentives and the last deals with collective practices.

4. Energy policies and building refurbishment

4.1. Law regulation approach

Sections 2 and 3 have tested the relationships between the cost of refurbishment (X), the implied energy saving (Y) and the comfort improvement (Z). The results show a significant positive dependence between all variables; in particular, the zˆ statistics of Beta regression ˆ n of frequency models, the ˆn statistics, and the Chi-square statistics W tables are all greater than their respective 99% critical values (2.33 and 13.28), see Table 8. It follows that refurbishment deepness (as expressed by the expenditure level) and comfort improvements are

In specific countries, a mandatory legislative approach has proven to be successful in stimulating energy renewals. In Italy, the Law 30/4/1976, n.373 [36] reduces the limits of the thermal dispersion of buildings, promoting the use of materials with lower transmittance values; further, since 2013, the Energy Performance Certificate must accompany any new construction or renovation [37]. Moreover, the Law 9/1/1991, n.10 states that the local administrations are obliged to control the heating efficiency

Fig. 9. a) Beta regression functions of Energy Saving on Comfort Enhancement; b) Residuals of Beta regression model of Saving on Comfort Enhancement. 10

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Table 8 Main dependence statistics of the case studies of Sections 2 and 3. Relation

zˆ - Beta regression

X Y X Z Z Y 99% Limits

EU +3.79 . . 2.34

ˆ n - Frequency tables W

ˆ n - Likelihood ratio Italy +6.93 +11.44 +3.004 2.34

EU 13.85 . . 6.63

of the boilers, as a specific measure to limit air pollution [38]. Furthermore, a European directive makes mandatory the employment of condensing boilers, when substituting building furnaces [39]. Other municipality instruments are the SEAPs (Sustainable Energy Actions Plans). These tools are important for raising funds from the EU. The aims of these plans are to abate CO2 emissions, to increase the share of renewable energies, and to reduce the energy needs [40]. The access to the funds depends on the adhesion to an EU project named Covenant of Mayors, whose objective is to increase energy efficiency and sustainability. Another effective tool is the 50% deductions on the personal income tax for house renovations and for energy-efficiency interventions, according to the Ministerial Decree 5/7/2012 [41]. In addition, the Feed-in tariff programs support energy production by renewable sources; the incentive consists of a financial contribution per kWh of produced energy [42]. These instruments can directly trigger the diffusion of energy-saving technologies, which, however, are not affordable by low-income people; therefore, the validity of these measures is confined to developed areas.

Italy 52.26 71.49 7.64 6.63

EU 15.31 . . 13.28

Italy 25.76 33.85 14.32 13.28

of a loan to the asset value. This index decidedly decreased during the recent real-estate crisis, from 72% in 2011 to 55% in 2013 [44]; thus, investments became unsuitable. In 2017, the credit pressure relaxed, so that the LTV ratio recovered to about 60%. Hence, the average value of the granted loans increased by +7.61%, compared to 2016 [45]. However, in this period the investments for building renewal just increased by +0.5%, keeping the refurbishment investments afloat [46]. Retrofit interventions also influence economic activity in general, just starting from the value of housing asset benefits. In 2016 in Italy, the average price of a restructured dwelling was 299000 €; instead, the mean price of a non-refurbished house was just 233000 € [47]. However, the refurbishment sector is more relevant for real economic activity, whose industry may increase employment rate and city development. For example, in Switzerland, 12.7 jobs were created per every million-€ directly invested in the sector or in satellite activities [4]. In addition, the renovation of the exterior facades can activate processes of urban regeneration. In Italy, the potential market of dwellings requiring retrofits amounts to 6.7 billion € [48]. Hence, the size of this market would guarantee important socio-economic benefits. However, the effectiveness of this approach depends on the general economic situation that influences the access to bank credit.

4.2. Financial incentives approach An indirect way to promote refurbishment interventions is to facilitate access to bank credit. The availability of subsidized loans encourages the renewal of dwellings. Otherwise, the activity of the building industry becomes contracted [43]. Indeed, from 2007 to 2014 in Italy, the total loans disbursed for the residential sector decreased by −70% [44]. Furthermore, in 2007, about 30% of the funding was addressed to the building sector, whereas this percentage dropped to 14% in 2014. The availability of bank credit depends on the loan-to-value (LTV) ratio, which is the ratio

4.3. Collective practice approach Collective practices consist of organized initiatives of groups of citizens concerning their consumption and investment decisions. With respect to energy saving, they span from condominium decisions on building interventions, up to investments in medium scale

Fig. 10. Actual PV plants and public-schools roofs areas for potential solar community plants. 11

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photovoltaic plants (solar community). At the same expense level, the collective community is preferable to the aggregation of domestic individual PV plants, for four reasons. First, larger plants present a lower cost per kW installed, compared to that of small individual installations [49,50], because of scale economy in the production. Second, system losses in great plants are contained. Third, the project of a solar community would be an occasion to optimize the position of panels, maximizing the energy producible. Fourth, the plants of the solar community may also be identity objects as they are directly visible by the neighborhood. Given these reasons, many interviewees (85) of the Venice survey would support the constitution of this community. Furthermore, the large majority (86%) of the supporters are favorable to the installation of the plants over the public buildings of the suburb. According to the data and the methodology of calculation presented in Appendix E, the investment in the solar community project is 2.4 times more effective in producing energy, compared to the employment of individual installations. This result sounds because the cost per m2 of large plants is roughly half of that of individual PV systems [50]. Further, the community plants result 20% more efficient from the energy viewpoint, because of the efficiency of components (such as the inverter) and because of its optimized sun exposition. Ultimately, in the suburb, an expense of 700000 € annually produce 383 MWh of electric energy; whereas, the same expense would yield an annual production of 908 MWh (see Appendix E) in the case of the solar community. Then, at the same level of energy needed, the community allows greater private savings, reducing the payback period. This economic evaluation is inserted in the context of lack of incentives for the sellers of energy from PV systems. Unfortunately, a consistent program of incentives for photovoltaics in Italy is missing since 2013, when funds from the EU Feed-in tariff programs ran out. Actually, this tool does not apply to new PV systems, reducing the economic convenience of energy selling. Concerning the solar community, a possible way to raise the profitability of PV plants is the adoption of accumulation systems, avoiding the necessity to purchase energy during nights. Nevertheless, they may be expensive for large plants. Thus, a more appropriate tool is to provide an incentive per each kWh sold to the electric network. This incentive should cover the difference between the general cost of electricity, 0.21 /kWh [51], and the selling price of household energy, 0.07 /kWh [52]. An important condition for the realization of the solar community is the coordination of public authorities. The local government would guide citizen initiatives and would declare the public interest to the project, through a Municipal Plan. Further, the Italian Ministry of Economy and Finance would define incentives. Fig. 10 shows the map of existing PV plants [34] and the possible location of the solar community, placed on large public buildings. It is possible to exploit the flat roofs of 8 public schools whose aggregate area is 20376 m2 .

refurbishment, and advanced refurbishment. A cost of 120000 € is supposed [53] for a conventional 100 m2 new house. The cost of a new house reconstructed is assumed to be 200000 €, in view of the costs shown in Table 4. The demolition expenses are added to the costs mentioned [54]. For the advanced reconstruction case, the cost includes the adoption of low transmittance insulation systems, heat pumps, a PV system equipped with energy accumulation, and a solar thermal system. On the other hand, conventional refurbishment includes interventions on fixtures and thermal insulation. Instead, advanced refurbishment also encompasses the interventions of the advanced reconstruction case. Costs related to conventional and advanced refurbishment are supposed respectively 25000 € and 75000 €, according to the information provided by Table 4. Further, the values of energy saving related to the four hypotheses (Table 9), are obtained by considering the report in Ref. [55] and the information provided by the Venice data set. Additionally, it is assumed that the energy performances of advanced reconstructions correspond to NZEB standards [1]. It is considered the hypothesis that banks grant loans for the interventions. Examples of loans about the Italian real estate market are provided in Ref. [56]. Passive interests are calculated by applicating an amortization with constant shares of capital. The 50% rate of deduction on personal income tax is also accounted for, remembering that the maximum deductible amount is 96000 € [42]. The Gross Costs presented in Table 9 encompasses both interests and deductions, whose hypothesis are presented in Appendix F. The annual energy savings are calculated with reference to an average expense of 2500 €, considering heating and electricity expenses. The results of the four scenarios are summarized in Table 9. Clearly, fully reconstructed buildings guarantee higher energy savings (52.4%) compared to renovated houses (21.5%). These results are obtained by weighting the shares of buildings [55], according to the outlined levels of refurbishment and reconstruction. However, refurbishment is cheaper and more cost-effective than complete reconstruction (see Table 9). Deciding to invest now, by 2050 the 48.8% of costs would be recovered in case of refurbishment; whereas, the quote is just 21.8% in the case of rebuilding. These values are obtained by considering the respective percentages of both conventional and advanced cases. This analysis confirms that building interventions are usually not undertaken for a mere purpose of energy saving; instead, people decide to incur relevant expenses mainly for reasons of indoor livability. This is even more true for building reconstruction, in which expenses are hardly recoverable within the edifice life span or the human life expectancy. 5. Conclusions This article evaluates the effectiveness of refurbishment interventions in enhancing energy saving and indoor comfort. Two real case studies are examined. The first considers a dataset of European service buildings [19] and deals with energy saving. The second concerns a statistical survey in the homogenous context of a Venice suburb, that also investigates the search for indoor wellness; that is a general concept including several physical, psychological and decisional aspects. Both case studies show a significant positive dependence between the cost of refurbishment ( X ) and the rate of energy saving (Y ). However, the empirical analysis of Venice data shows that the statistical relationship between the comfort enhancement Z and the cost X of retrofitting is stronger than the one between the savings Y and the expense

4.4. Refurbishment vs reconstruction A further remark concerns the evaluation of the cost-effectiveness of building refurbishment compared to that of complete reconstruction. This analysis considers four hypotheses of building interventions: conventional reconstruction, advanced reconstruction, conventional Table 9 Percentage of energy saving for scenarios of building renovation. Scenario

Build. Stock

Gross Costs [€]

Econ. Saving

Annual sav. [€]

Sav. by 2050 [€]

Saving Cost

Convent. Recontruct. Advanced Recontruct. Convent. Refurbishm. Advanced Refurbishm.

9.5% 4.4% 58.0% 11.5%

143000 228140 21438 92719

35% 90% 14% 59%

875 2250 353 1483

26250 67500 10575 44475

0.18 0.30 0.49 0.48

12

2050

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X . Indeed, z-statistics of the beta-regression coefficients are respectively 11.968 and 6.926, and the nonparametric analysis of frequency ˆ n Pearson Index). The tables agree (respectively 33.85 versus 25.76 for W Z sounds also because 66.7% of interviewees declare to relation X have renovated for a desire/necessity to improve indoor wellness. Further, the search for indoor comfort positively influences the energy saving achieved. Indeed, the z-statistic of the coefficient of the beta regression Energy Saving Comfort Enhancement is +3.004. It follows that the causal chain of the phenomenon may be summarX Y . For instance, interventions that improve indoor inized as Z sulation satisfy the need for comfort. Nevertheless, they also improve house energy saving performances. Thus, generally, the mentioned aspects of comfort agree with energy saving, with the only exception of the deliberated increase of indoor temperature, through the regulation of boiler. The consequence is that energy policies should be nested into building activity programs, which pursue comfort, aesthetic and real estate goals in general. Reversely, refurbishment policies are valid from both economic and environmental viewpoints. The framework discussed is also robust against different conditions of climate, law, and incentives. Indeed, it is consistent with general real-estate dynamics (e.g. refurbishment is driven by the search for the increase of real estate values). Further evidence is that the cited interventions guarantee savings even in hot climates, in particular, the thermal insulation prevents overheating. Section 4 gives information on how it is possible to stimulate refurbishment, in order to raise levels of comfort and energy saving. Facilitating access to bank credit would encourage building renovations.

In any event nowadays, access to bank credit is not generalized, then simple and more economical solutions are often adopted. These interventions are useful to provide immediate comfort enhancement; nevertheless, their application just marginally reduces energy consumption. Technologies such as PV plants can considerably reduce the amount of energy used; however, their initial costs are too high for most of the population. Collective practices exploiting large PV systems would reduce the cost of energy production, compared to the case of individual plants. Therefore, PV technology would become affordable for many more people. It would follow an important increase in private economic saving and environmental benefits. Further development could consist in extending the analysis to other building sectors and to different territorial contexts, aiming to confirm the validity of the results obtained. At a local level, the ways to implement the solar community should be deepened. For example, an appropriate public or private organizational form could be hypothesized, involving citizens and public authorities. A final idea is the progressive extendibility of the community, according to additional adhesions. Acknowledgments We thank the Reviewers and the Editors for useful suggestions which have substantially improved the exposition and the content of the paper. The final version is the result of joint work of the two authors.

Appendix A. (Section 2.2): The beta-regression model In a regression model, when the dependent variable Y is expressed in percentage and has an asymmetrical distribution, the linear Gaussian model cannot be used. As the beta-density may represent a wide range of frequency distributions (symmetrical and asymmetrical) on the support [0,1], the beta-regression model could be implemented [26]. This approach is similar to logit and probit regression models, where the dependent variable is strictly binary (0 or 1) and the distribution is binomial. All these models belong to the class of generalized linear model (GLM) [67], in which the k response variable Yi is connected to the regression surface ‘xi = 0 + j = 1 j Xij by a proper link function g (.), as E(Yi ) = µi = g 1 ( ‘xi ) . The expression g (µ) = ‘xi is also called linear predictor and g = 1 in the classical linear Gaussian model. The generalized linear model based on Beta density function is treated in Chapter 6.2 of the book “Generalized Linear Models for Categorical and Continuous Limited Dependent Variables” written by Smithsons M. and Merkle E.C [27]. In particular, the beta regression usually adopts the logit link function, where g (µ) = log

( ), which implies µ

1

µ

exp( ‘xi ) 1 g 1 ( ‘xi ) = = 1 + exp( ‘x i ) 1 + exp(

‘xi )

In the beta regression the dependent variable has a beta density function as

f (Y , p , q ) = where

(p + q) p Y (p) (q)

1 (1

Y )q

1,

(A.1)

(.) is the gamma function, and p , q are shape parameters. Ferrari et al. [26] use the parameterization, µ =

E (Y ) = µ , which enables to rewrite the function (A.1) as

f (Y , µ,

)=

(µ )

( ) ((1

µ) )

Yµ

1 (1

Y ) (1

µ)

1

p p+q

and

= p + q , where

(A.2) µ (1 µ) 1+

where the parameter affects the variance of Y. In fact, Var (Y ) = so that high values of yield small variability; this is the reason why is called precision parameter. Given a sample of N observations, the vector of regression parameters is estimated by maximum likelihood (ML) method [57]. For the betaregression model, based on the beta density at Eq. (A.2), the log-likelihood function lN ( , µ, |{xi}) is the sum of individual terms:

log

( )

log

(µ )

log

[(1

µ ) ] + (µ

1)log(Yi ) + [(1

µ)

1]log(1

Yi )

Differentiating the resulting functional with respect to the regression parameters obtain the system of non-linear equations:

lN ( , ) =

T

l =

lN ( , )

=0

l =

lN ( , )

=0

and

(which has the meaning of residual variance), one may

These equations cannot be solved analytically, and it is necessary to use numerical methods, such as the Newton-Raphson algorithm. Letting = ( 0, ..., k , ) , the k –th iteration is given by

13

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ˆk + 1 = ˆk

2l ( ˆ ) N k T

1

lN ( ˆk )

,

which may be initialized with OLS estimates of the linearized model, as regards the vector . The matrix of second derivatives is also known as the Hessian matrix and is used to compute the standard errors (and therefore the z-statistics) of the estimates ˆ . Evaluation of the goodness-of-fit of Beta regression models is based on the likelihood ratio (LR) statistic n = (L 0 /Ln ) [0,1], where L0 is the value of the likelihood function (LF) of the model without covariates, and Ln is the value of the LF of the full model, estimated with ML. It is well known that under IID sampling, the Wilk's transformation n = 2log( n ) has an asymptotic 2 (k ) distribution, where k is the number of covariates; this enables to test the significance of n . 2 2 The definition of a relative index of fitting for GLM has received various solutions, see [67, p.59]. As the classical R2 = (1 e / y ) measures the P = (1 L / L ) = (1 ) quote of variance reduction, the likelihood increment is given by ML 0 n n . However, a more referred index, usually ascribed to 2 (2/ n) = [1 ]. Its rationale is that it coincides with the classical R2 when the GLM model is linear and Gaussian. Maddala and Cox-Snell [67], is RML n 2 As other likelihood-based measures, the RML index detects the dependence in probability (not just the correlation, as R2 ); therefore, it usually assumes moderate values, less than 0.5, see Refs. [65,66]. The betareg package of Cribari et al. [28] proposes a specific measure of goodness-of-fit given by squared correlation between the linear predictor ‘xi and the link-transformed response log[Yi /(1 Yi )]. However, in our applications its 2 values are close to those of RML . Appendix B. (Section 3.1): Data and method for the heat loss maps This Appendix concerns the computation of heat loss values of the buildings, displayed in Fig. 5a and b. In particular, the first part provides an explanation of how these data are found. Then, the method of the estimation of heat loss values is described. Data considered The age of the buildings. The higher age of buildings should imply greater heat losses because of the gradual improvement of energy performances over time, see Table B1. The material of the house roofs. The value assigned to a building having clay roofs is “1”, whereas the value related to concrete roofs is “2”. A layer of concrete tiles has a thermal conductibility of 1 W /(m K ) ; whereas, this value for clay tiles is 1.5 W /(m K ) [58]. Indeed, the thermal energy saving achievable through concrete tiles may reach 25–30%, in comparison to the use of clay tiles [59]. The economic value of the dwellings. Values “1″ are assigned to popular houses, whereas “3″ are assigned to dwellings owned by people of upper social class. The hypothesis is that richer people can afford interventions with high energy savings, thus limiting heat loss. The energy saving performances of these buildings are comparable to the average saving of the buildings in D'Agostino's data set [19]. Hence, these buildings feature a 40% lower heat loss with respect to popular buildings. The sun exposure. Values “1″ are attributed to buildings whose sun exposure encounters obstacles affecting most of the external walls. On the opposite case, values “4″ concern buildings with optimal sun exposure. Buildings, with good sun exposure, are characterized by relatively higher outdoor temperatures. This implies a lower difference between indoor and outdoor temperatures, hence a lower heat loss. According to a subjective assessment, buildings with optimal exposure may have a 20% lower heat loss than buildings that are poorly exposed. The ratio external surface area of the building/volume. The lower is the ratio, the more compact is the building. Indeed, the dispersion surfaces of buildings are relatively small compared to the volume. In fact, according to this study [60], large and multi-story buildings present a thermal energy saving of around 10%, compared to less compact constructions, at the same level of other features. The ratio volume/resident population per building: The higher is the ratio, the lower should be the thermal dispersion. Indeed, people having a large availability of indoor space, do not occupy all parts of the house. In this case, some rooms are not permanently heated, and thus, heat transfer from the building to the outside is reduced. Hence, low-populated buildings present a relatively low heat loss (see Table B2), at the same level of the other variables mentioned. The population per building is calculated, by considering the population and number of buildings of each census section [61]. Method of estimation The method of estimation of the heat loss is composed of two steps. The first is to estimate a regression model of the thermal dispersion on the year of construction, considering the data in Table B1 [62]. This provides preliminary predictions of heat loss values for any building in the area. Table B.1

Heat loss in buildings in Italy, according to year of construction Year

Heat loss [kWh/m2]

Before 1950 1960 1970 1980 1990 2000 2010

250 235 224 200 160 105 63

The second step is to correct the obtained estimates of the heat loss, by introducing the other variables mentioned before. The process of correction of the first step estimates is fulfilled by progressive application of percentages, in agreement with the algorithm described in Table B2.

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Table B.2 Percentage correction factors assumed, involving the other variables Variable

Modality

Numeric. Modality

Correction factor of heat loss value

Roof type

Clay Concrete Low Medium High Scarce Medium Good Optimal Highest Mean Lowest Lowest Mean Highest

1 2 1 2 3 1 2 3 4 0.79 0.52 0.28 66 180 550

0% −25% +20% 0% −20% +5% 0% −5% −10% +5% 0 −5% +5% 0% −10%

Economic class Sun Exposition

Ext. area/volume [m2/m3] Vol./inhabitants [m3/resid]

Appendix C. (Section 3.2): Descriptive statistics of the Venice Sample The following tables provide insights into the outcomes of the Venice case-study. Table C1 and C2 concern the diffusion of refurbishment interventions. Instead, Table C3 illustrates the driving motivations declared by the households for the interventions. The main results from these tables are discussed in Part 3.2. Table C.1

Proportions of households by interventions Refurbishment interventions

System Type

Absolute frequency

Proportion of refurbished houses

Substitution of internal fixtures Substitution of external fixtures Interior thermal insulation Exterior thermal insulation Roof thermal insulation Solar thermal interventions Air-air heat pump Air-water heat pump Substitution heat boiler Home automation interventions Solar photovoltaic system Ventilation system interventions Fireplace heating interventions Underfloor heating system

Passive Passive Passive Passive Passive Active Active Active Active Active Active Active Active Active

68 63 19 48 65 29 56 8 90 20 32 1 6 3

0.444 0.412 0.124 0.314 0.425 0.190 0.366 0.052 0.588 0.131 0.209 0.006 0.039 0.020

Table C.2

Proportions of households having realized refurbishment interventions

Total households With refurbishment interventions With refurbishment no heat boiler Passive refurbishment intervent. Active refurbishment intervent. Active refurb., no heat boiler Passive refurbishment only Active refurbishment only Both passive-active refurb.

Absolute freq.

Proportion of total

Proportion of refurbished houses

204 153 142 131 132 95 21 22 110

1 0.750 0.696 0.642 0.647 0.466 0.103 0.108 0.539

n.a. 1 0.928 0.856 0.863 0.621 0.137 0.144 0.719

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Table C.3

Households' motivations declared to refurbish

Total households having refurbished Comfort motivation declared Energy Saving motivation declared Investment motivation declared Only Comfort motivation declared Only Energy Saving motivation Only Investment motivation

Absolute frequency

Proportion of refurbished houses

153 102 74 26 52 28 18

1 0.667 0.484 0.170 0.339 0.183 0.118

Appendix D. (Section 3.3): Residual analysis of Beta Regression model This appendix performs the analysis of residuals of Beta regression models, estimating of Venice data. A critical point is the detection of the outliers, which make coefficient estimates biased and, therefore, the inference of the model unreliable. A preliminary step is the analysis of the distribution of the dependent variables Z and Y (energy saving and comfort improvement). The appropriate model is the Beta density (A.1). For variable Z the values of these parameters are 4.9 and 2.2, whereas for the variable Y the parameters p and q are respectively 3.75 and 16. Fig. D1 shows the distributions of Z and Y .

Fig. D.1. a) Histogram of variable Z , and its beta density estimate. b) Histogram of variable Y , and its beta density estimate.

The residuals are the difference between the observed values of the dependent variable and the fitted ones obtained by the Beta regression model adopted. The interval of residuals is not [0,1], however their ranges never exceed one. Therefore, residuals, from the Beta regression models estimated, may follow translated Beta distributions having zero mean. Residuals of Beta regression of Z on X follow a Beta distribution with p = 7 and q = 3.2; whereas, the values of the parameters for the residuals of the regression of Y on X are 6 and 25, see Fig. D2.

Fig. D.2. a) Histogram of the residuals of the variable Z on the variable X , and its beta density estimate. b) Histogram of the residuals of the variable Y on X , and its beta density estimate.

The outliers are the 2.5% lowest and to the 2.5% highest values of Beta functions. Once dropped them, it is possible to estimate the Beta regressions of Z on X and of Y on X , discussed in Section 3.3. Panels c) and d) of Fig. D3 represent the residuals of these regressions.

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Fig. D.3. a) Residuals of Beta regression functions of Comfort Enhancement Z on Expense X with 95% confidence bands; b) Residuals of Beta regression functions of Saving Y on Expense X with 95% confidence bands.

The estimates of regression coefficients are reliable since there are no more outliers, with a slight exception in Panel d) of Fig. D3. The 95% confidence bands (Table D1) are obtained by interpolating the residuals shown in Fig. D3 through Beta density functions ( p = 12 , q = 6.5 for the model Z on X , and with p = 25, q = 32 for the model of Y on X ). Table D.1

95% confidence bands for residuals displayed in Fig D3 Model

X X

Z Expense Y Expense

Comfort Enh Saving

Lower 95% limit

Upper 95% limit

−0.3625 (−2.75 ) −0.2254 (−2.4 )

0.2636 (+2 ) 0.2817 (+3 )

Appendix E. (Section 4.3): Cost-effectiveness of the solar community In the case study area, the aggregate installed power of 343.27 kW [34] involves 74 PV systems. The annual irradiation of the area is 1689.95 kWh/m2 [63]. It is also hypothesized a conversion efficiency of PV systems of = 14.4% . Then, the annual energy production per square meter is assumed to be 243.4 kWh/m2 , without energy losses. According to an analysis based on Google Maps [64], the total surface of the plants is 2310 m2 . So, the surface necessary to install a power of 1 kW is 6.73 m2 . Energy losses are of two types: the first is related to system and the second concerns the position. System losses are subdivided into losses attributable to the performance of the components (e.g. inverter), and into other losses (e.g. from overheating). Positional losses arise from the non-optimal position of the panels. The simulator [63] shows a percentage of loss due to components of 14% and a total system loss of 24.3%, concerning domestic installations. Instead, for a solar community, it is assumed a 7% loss due to components, with a total system loss of 17.3%. Further, a positional loss of 10% is attributable to the non-optimal position of the individual plants. Oppositely, the position of the solar community plants is optimized. Table E1 summarizes and compares the loss mentioned, for both the aggregate individual installations and the solar community plants. Table E.1

Losses and energy performances of current domestic plants and the solar community

Energy production per sqm without losses System percentage losses [%] Positional percentage losses [%]

[kWh/m2]

Current Domestic plants

Solar Community plants

243.35

243.35

1

1.21

−24.3% −10% 165.79

Actual energy production per sqm [kWh/m2] Production - effectiveness ratio

−17.3% 0% 201.25

The cost per m2 of home installations is 304.6 /m2 which corresponds to 2050 /kW [49,50]. Accounting for the total surface of PV systems (2310 m2 ), the total fixed cost for home installations amounts to around 700000 €. Instead, the cost per m2 of large installations is 156 /m2 equivalent to 1050 /kW [49]. It is interesting what a solar community investment of 700000€ would produce in terms of plants size and producible energy. The size is obtained by dividing this investment by the cost per square meter of the photovoltaic modules. The annual electric energy produced is calculated by multiplying the surface of the plants by the energy produced per square meter. As shown in Table E2, the surface of panels in the solar community almost doubles, compared to the aggregation of the current domestic plants; but, the key outcome is that the solar community would be able to produce 2.37 times, the energy produced by households, at the same level of expense.

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Table E.2

Performances of current domestic plants and the solar community, with parity of expense

Number of plants

Total energy produced per m2 [kWh/m2]

Current Domestic plants

Solar Community plants

74 165.79

3 201.25

703.7 2310

703.7 4511

304.6

Cost per m2 [ /m2] Total installed cost [k ]

Total surface of the plants [m2] Annual electr. energy produced [MWh] Cost-effectiveness ratio

156

383.0 1

907.8 2.37

Appendix F. (Section 4.4): Calculations of the Gross costs of the scenarios This Appendix clarifies the way the gross costs of refurbishment and reconstruction interventions are obtained, with reference to Subsection 4.4 and Table 9. Gross costs encompass both passive interests and the 50% rate of deduction on personal income tax deduction. Notice that the maximum deductible amount is 96000 € [42]. Table F1 shows details of the loans and the resulting passive interests. Table F.1

Details of the calculations of the Gross costs related to the reconstruction and refurbishment scenarios of Part 4.4 Scenario

Net Costs [€]

Loan [€] Loan Span [yr]

Passive int. rate

Passive Int. [€]

Deduct. [€]

Gross costs. [€]

Convent. Recontruct. Advanced Recontruct. Convent. Refurbishm. Advanced Refurbishm.

129000

100000

30

4%

62000

−48000

143000

214140

100000

30

4%

62000

−48000

228140

25000

25000

10

6.5%

8938

−12500

21438

75000

75000

30

4.75%

55219

−37500

92719

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