The Evaluation of Energy Efficiency Policies in the Building Sector: A Regional Analysis Based on the Stochastic Frontier Approach and on the Energy Environmental Kuznets Curve (EKC) and Policy Implications

The Energy Efficiency is seen one of the top priorities of the EU and Member States. The EU energy and climate change package has set goals to cut greenhouse gas (GHG) emission at least 55% (compared to 1990) and to improve energy efficiency at least 32.5% by 2030 to becoming climate neutral by 2050. The European Union (EU) has undertaken numerous initiatives aimed at encouraging the transition process towards cleaner energy sources. 

The increasing attention to energy efficiency from an environmental point of view has led over the years an increasingly role of Energy Efficiency to fight climate change.

The main programmatic EU measures are the European Commission (EC) package "Clean Energy for all Europeans" (EU regulation issued to support the Energy Performance of Buildings Directive (2010/31/EU (EPBD)) and the Energy Efficiency Directive (2012/27/EU), were amended, as part of the “Clean energy for all Europeans package”.)and the Integrated National Energy and Climate Plan (INECP) (To meet the EU’s energy and climate targets for 2030, EU countries need to establish a 10-year integrated national energy and climate plan (INECP) for the period from 2021 to 2030. Introduced under the Regulation on the governance of the energy union and climate action (EU/2018/1999), the rules required the final INECP to be submitted to the Commission by the end of 2019.) sent by each State member to the EC. Energy Efficiency in the current worldwide pandemic scenario with the COVID – 19 crisis remains a key pillar for a EU long term sustainable and climate neutral economy. In the civil sector the EU building stock offers high potential for energy efficiency improvements. Most of the existing buildings are old and rely on fossil fuels for heating and cooling, and use old technologies and wasteful appliances.

Covid 19 offers a unique opportunity to make civil buildings more efficient, comfortable and safety with the financial resources available (Next Generation EU). The role of the building is changing and becoming more central, the homes are often turned on workstation in teleworking and so we are spending more and more time in them.

In the INECP sent by Italy to EU it is highlighted the key role of the civil sector for the reduction of energy consumption with the realization of energy efficiency investments: “The civil sector, along with transport, is identified as the main sector for efficiency improvement measures, with a reduction in energy consumption of approximately 5.7 Mtoe compared with the base scenario for 2030 and a commitment to gradually eliminate oil for heating purposes. In particular, the residential sector contributes to 3.3 Mtoe of this decrease, whereas the tertiary sector reduces the projections for its consumption by 2.4 Mtoe, thanks to structural renovation measures and the installation of heat pumps, as well as a greatly improved efficiency of end-use devices”.

The scope of this paper is to estimate the impact of energy policies instruments on the estimated level of underlying energy efficiency in the Italian building sector. 

The theoretical framework underlying this research is based on the Stochastic Frontier Approach (SFA). Filippini and Hunt [1] have introduced the SFA to define and measure the energy efficiency. Whereas frontier analysis is developed on the estimation of parametric best practice frontier for the use of energy where the level of energy efficiency is computed as the difference between the actual energy use and the predicted energy use. This work, as proposed by Filippini and Hunt [2], uses an econometric approach to estimate the level of energy efficiency at a disaggregated level for the 20 Italian regions in the period 2010-2017.

The paper is organised as follows. Section 2 provides an overview of the main policy in Italy supporting the speed up of energy efficiency investments in the building sector at regional and local level. Section 3 explain the theoretical framework of the Stochastic Frontier used to measure energy efficiency. Section 4 explains regional model to be estimated with the Stochastic Frontier Approach. Section 5 provides the estimation results, while Section 6 sets out the main policy implications.

The approach used in this study is based on the stochastic production frontier model to estimate the frontier energy demand function for the building sector at regional level (Energy Efficiency studies at regional level based on SFA have been carried out by Otsuka and Goto [3]). 

Moreover, econometric specifications of the model give the possibility to analyse the impact of the energy efficiency policy instruments examined at regional level. The analysis is based on the model introduced by Aigner (Aigner, Lovell and Schmidt [4] have used the stochastic frontier function in production theory to measure econometrically the economic performance of production processes at the firm level.) et al. (1976):

${{y}_{i}}=f\left( {{x}_{i}},\beta  \right)+{{\varepsilon }_{i}},i=1,\ldots \ldots ,N,con{{\varepsilon }_{i}}\le 0$             (1)

${{\varepsilon }_{\text{i}}}={{\text{v}}_{\text{i}}},+{{\text{u}}_{\text{i},\text{i}}}=1,\ldots \ldots ,\text{N}$            (2)

The authors specified an error term (2) consisting of two independent parts: a stochastic error (v_it), capturing the effect of noise, and a one-sided non-negative disturbance capturing the effect of inefficiency (u_it). 

The author specified the variable y_i as the maximum output obtainable from xi, a vector of (non-stochastic) inputs, and β as an unknown parameter vector to be estimated. 

The component of the error vi represents a symmetrical disturbance, the vectors {v_i} are independent and symmetrically distributed N (0, σv²). The component {u_i} is distributed independently of vi, satisfies the condition for which u_i ≤ 0. and follows a truncated distribution N⁺(0, σu²).

The non-positive sign of the u_i component implies that the output of each firm production is below or on the stochastic frontier. The u_i component collects the effects due to factors directly controlled by the firms (such as the technology), which allow their different positioning in space and time on the frontier. The random disturbance factor (v_i) can be the result of external and unpredictable events, due for example to climate, topography, machine performance, etc. The Stochastic Frontier approach, previously adopted by Aigner et al. [5] to measure the economic performance of production process, was applied by Filippini et al. [1, 2, 6] (First the stochastic frontier model has been employed by Filippini et al. [1] to estimate in the period 1978-2006 the minimum level of energy needed to produce the energy services of 29 OECD countries, second it has been employed by the author (2012) to estimate in the period 1995-2006 the level of energy efficiency in the residential sector for 48 US states, third it has been employed by the author (2014) to evaluate in the period 1996-2009 the effects of energy efficiency policies on energy demand residential sector for 27 EU Member States.) to estimate the level of energy efficiency of household consumption in the residential sector. 

Filippini et al. refer to the "household production" theory [7] which considers the residential energy demand as a derived demand. In this model, households are considered as firms that produce goods and services not available on the market: i.e. heating their home, cooking a meal, hot water, etc. The production by families of these goods and services could be obtained through the efficient use of the production factors (inputs), such as: energy, available time, accumulated knowledge and capital. 

Heating systems, cooling systems, house thermal insulation, devices for monitoring energy consumption are some examples of the capital could be employed in the household production process. In this scenario it can be understood technology plays a key role in the production process, improvements in technology could reduce the energy consumption necessary for the realization of these goods and services.

This model innovates with respect to previous studies, in which energy intensity, defined as the ratio of energy consumption to GDP, is used as a proxy of energy efficiency. Energy Intensity [8-14] fails to isolate the effects generated by the level of energy efficiency from those attributable to structural changes in the economy. The stochastic frontier model, on the other hand, using parametric models allows to identify the effects on demand due to the level of energy efficiency. In line with Filippini et al. [1, 2, 6] and based on the availability of the data, we have specified in this paper for the period 2010 – 2017 (t = 2010-2017) the aggregate regional energy demand function for the civil sector of the 20 Italian regions (i = 1-20):

$\text{E}{{\text{D}}_{\text{it}}}=\text{E}\left( \begin{align}  & \text{P}{{\text{E}}_{\text{it}}};\text{P}{{\text{G}}_{\text{it}}};\text{Y}{{\text{D}}_{\text{it}}};\text{PO}{{\text{P}}_{\text{it}}}; \\ & \text{HD}{{\text{D}}_{\text{it}}};\text{CD}{{\text{D}}_{\text{it}}};\text{S}{{\text{U}}_{\text{it}}};{{\text{D}}_{\text{t}}};\text{E}{{\text{F}}_{\text{it}}} \\  \end{align} \right)$                               (3)

The dependent variable ED_it represents the final energy consumption in the civil sector, PE_it the price of electricity, PG_it the price of natural gas, YD_it the disposable income per inhabitant, POP_it the regional population, SU_it the average surface area per occupant of the dwellings, HDD_it and CDD_it, respectively, the winter heating degree days and the summer cooling degree days.

The equation estimated in our study is the logarithmic transformation of (3):

$\begin{align}  & \text{e}{{\text{d}}_{\text{it}}}=\text{a}+{{\text{b}}_{1}}\text{p}{{\text{e}}_{\text{it}}}+{{\text{b}}_{2}}\text{p}{{\text{g}}_{\text{it}}}+{{\text{b}}_{3}}{{\text{y}}_{\text{it}}}+{{\text{b}}_{4}}\text{po}{{\text{p}}_{\text{it}}} \\ & +{{\text{b}}_{5}}\text{hd}{{\text{d}}_{\text{it}}}+{{\text{b}}_{6}}\text{cd}{{\text{d}}_{\text{it}}}+\$\${{\text{b}}_{7}}\text{s}{{\text{u}}_{\text{it}}}+{{\text{b}}_{\text{t}}}\text{t}+{{\text{v}}_{\text{it}}}+{{\text{u}}_{\text{it}}}\\\end{align}$                   (4)

where, v_it ~ iid N(0, σ²_v) e u_it ~ N⁺(b_zz_it, σ²_u). The error consists of two independent components: vit, the random disturbance component and u_it, the component that captures the effect of energy inefficiency (EF_it).

This approach is in line with Battese and Coelli [15] (BC95 hereafter) that defined a stochastic frontier production function for panel data on firms, in which the non-negative technical inefficiency effects (u_it) are assumed to be a function of firm-specific variables and time. The authors assumed the inefficiency effects to be independently distributed as truncations of normal distributions with constant variance, but with means which are a linear function of observable variables. (In Bottese and Coelli [15] the stochastic frontier model in terms of the original production value is explained by:

y_it =f(x_it β + v_it - u_it) i = 1,……,N)

Y_it denotes the production at the t-th observation (t = 1, 2 ..... T) for the i-th firm (i = 1, 2 .... , N); xit is a (1 x k) vector of values of known functions of inputs of production and other explanatory variables associated with the i-th firm at the t-th observation; β is a (k x 1) vector of unknown parameters to be estimated; the vit are assumed to be iid N(0, σ²v) random errors, independently distributed of the uit; the uit are non-negative random variables, associated with technical inefficiency of production, which are assumed to be independently distributed, such that uit is obtained by truncation (at zero) of the normal distribution with mean, zitδ, and variance, σ²; zit is a (1 x m) vector of explanatory variables associated with technical inefficiency of production of firms over time; and δ is an (m x 1) vector of unknown coefficients.

The technical inefficiency effect, uit could be specified in equation:

u_it = z_itδ + W_it (2), where the random variable, Wit, is defined by the truncation of the normal distribution with zero mean and variance, σ2, such that the point of truncation is - z_itδ, i.e., W_it > - z_itδ.)

Filippini et al. [2] following BC95 model considered the techincal part of the error term (u_it) as a one-sided non-negative disturbance capturing the effect of inefficiency, as an indicator of the inefficient use of energy. 

In this paper as in Filippini et al. [2] the inefficiency term u_it in Eq. (4) is modified to have a systematic component associated with a vector of policy measures (zit) and a random component (e_it):

${{u}_{it}}={{b}_{z}}{{z}_{it}}+{{e}_{it}}$         (5)

The energy efficiency policies considered within the control variable z can be of different nature: fiscal, voluntary, regulatory, as already specified in Table 1. In the econometric model analysed the energy efficiency policy variables have been represented by the indicators summarized in Table 2. Policy instruments efficacy in promoting energy efficiency have been analysed in several studies [16]. 

Table 2. Energy Efficiency policy indicators control variables

In this paper we focus on the effects of energy policy measures on the level of energy efficiency at regional level. We have identified the panel data model proposed by Battese and Coelli for the estimation of Eq. (4) through the stochastic frontier model (SFM). Following Filippini et al. [2] BC95 panel data model it is a suitable approach because allow to estimate the level of energy efficiency to vary over time and to depend on a set of variables (i.e. the presence of subsidies, fiscal deduction for building renovation expenses, energy efficiency voluntary measures adoption, utilization of European Funds available for energy efficiency).

The estimated energy-efficiency level could be identified in terms of efficiency score: 

$\text{E}{{\text{F}}_{\text{it}}}=\text{E}{{\text{F}}_{\text{it}}}/{{\text{E}}_{\text{it}}}\exp \left( -{{\mu }^{\widehat{\text{it}}}} \right)\$,$          (6)

where, EDit is the observed final energy demand and EDFit is the respective frontier demand of the i th italian region in time t.

Our theoretical framework is also based on the Environmental Kuznets Curve (The the environmental Kuznets curve (EKC) was coined by U. Panayotou [17] and the relatioship between the evolution of the distribution of per capita income and the trend of environmental pressure was confirmed by the independent empirical studies by Grossman and Krueger (1991), Shafik and Bandyopadhyay (1992) and Panayotou (1993).) (EKC). EKC shows an inverted U relationship, as in the Kuznets [18] (Kuznets [18] observed in the first stage of a country development, as per capita income increases, the level of inequality within the population increases, as those who earn a higher per capita income tend to invest a greater share of it, increasing the gap with the poorer population. The point that leads to a progressive decrease in the level of inequality is due to the introduction by the government taxation mechanisms penalizing the part of population with greater availability of capital and income.) original curve, between the evolution of the distribution of per capita income and the trend of environmental pressure. The assumptions underlying this trend can be traced back to the fact that in the early stages of the development of an economic system, the population does not have adequate awareness of environmental issues and the negative effects that could arise from uncontrolled economic growth. Such growth in per capita income could lead to a resource wasting rate higher than its regeneration rate and to a significant increase in the level of pollution.

The gradual increase in awareness of environmental issues, even in the presence of sustained levels of economic growth, instead favors the definition of specific environmental laws and regulations, greater investments in research and development in favor of new, more efficient and less polluted technologies and the creation of greater civitenship within the community to which they belong.

The specification of the cubic standard model of the EKC is expressed in the following formula:

${{\text{E}}_{\text{it}}}={{\text{A}}_{\text{i}}}+{{\beta }_{1}}{{\text{Y}}_{\text{it}}}+{{\beta }_{2}}\text{Y}_{\text{it}}^{2}+{{\beta }_{3}}\text{Y}_{\text{it}}^{3}+{{Z}_{\text{it}}}+{{\text{e}}_{\text{it}}}$                    (7)

where, E is the indicator of per capita energy consumption expressed in logarithmic form, Y is per capita income, also expressed in logarithmic form, A is the set of time variables, Z represents a series of control variables that could impact energy consumption, e represents a random error component.

In the Energy Environmental Kuznets Curve the energy consumption is a key indicator for the environmental pressure. Luzzati et al. [19-24] have already analyzed and confermed in their work a strong relationship between income and energy consumption which shows an inverted U relationship.

In Romero et al. [20] it has been analysed whether the municipalities of Andalusia that have joined the "Covenant of Mayors" have reduced the level of energy consumption and climate-altering emissions. Consumption has also been divided within the civil sector between the Public Administration and residential buildings. Control variables Z were defined in Romero et al. [20], as follows:

${{Z}_{it}}={{\beta }_{4}}\text{C}{{\text{M}}_{it}}+{{\beta }_{5}}A{{D}_{it}}+{{\beta }_{6}}S{{E}_{it}}$              (8)

where, CM (Covenant of Mayors) is a dummy which takes value 1 if the municipality has joined or 0 if not, the variables D and SE indicate, respectively, the population density and the area of the municipality. The existence of an inverted U relationship implies that for the relations between energy consumption and income β1>0, β2<0 and β3≤0. The results of the econometric estimates reveal differences in consumption between the Andalusian municipalities that have joined the Covenant of Mayors compared to those that have not joined. 

Following the approach introduced by Romero et al. and based on the availibility of data we have specified the relationship between income and energy consumption in the period 2010 – 2017 (t = 2010-2017) for the civil sector of the 20 Italian regions (i = 1-20):

${{\text{E}}_{\text{it}}}=\text{E}\left( {{\underline{\text{YD}}}_{\text{it}}};{{\underline{\text{YD}}}^{2}}\text{it};{{\underline{\text{YD}}}^{3}}\text{it};{{\text{Z}}_{\text{it};}}\text{DPO}{{\text{P}}_{\text{it};}}{{\text{S}}_{-}}\text{K}{{\text{M}}^{2}}\text{it} \right)$                    (9)

The dependent variable Eit represents the final energy consumption in the civil sector, YD_it geometrical mean of the disposable income per inhabitant, DPOP_it; the population density and S_KM²_it the regional surface.

5.1 Estimated energy demand model for the building sector

The BC95 SFA model estimation results (Table 4) of the relationship (4) between the building energy sector demand and the other variables, that include as usual time dummies (btt), expressed in logarithms form (10) prove to have the expected signs and are generally statistically significant:

$\begin{align}  & {{\text{e}}_{\text{it}}}=\alpha +{{\text{b}}_{1}}\text{p}{{\text{e}}_{\text{it}}}+{{\text{b}}_{2}}\text{p}{{\text{g}}_{\text{it}}}+{{\text{b}}_{3}}\text{y}{{\text{d}}_{\text{it}}}+{{\text{b}}_{4}}\text{po}{{\text{p}}_{\text{it}}}+{{\text{b}}_{5}}\text{hd}{{\text{d}}_{\text{it}}} \\ & +{{\text{b}}_{6}}\text{cd}{{\text{d}}_{\text{it}}}+{{\text{b}}_{7}}\text{s}{{\text{u}}_{\text{it}}}+{{\text{b}}_{8}}{{\text{Z}}_{\text{it}}}+{{\text{b}}_{\text{t}}}\text{t}+{{\text{v}}_{\text{it}}}+{{\text{u}}_{\text{it},}} \\  \end{align}$                        (10)

Since energy consumption and the regressors relating to the variables examined are in logarithms the estimated coefficients are directly interpretable as demand elasticities. where, i is the th Italian region and t is the th time and we assume that v_it ~ iid N(0, σ²_v) e uit ~ N⁺(b_zz_it, σ²_u).

From the estimated coefficients it emerges that as the price electricity decreases (pe) energy consumption in the building sector (ed) increases, in line with the decarbonisation objectives of the INECP, for example by replacing gas boilers with heat pumps, it is also possible to provide summer cooling, which is especially important in Southern Italy. Consumption does not seem to be affected by changes in gas prices (pg), because is necessary a minimum energy requirements to heat homes (the variable pg is not elastic to changes in gas prices). From the estimates of the coefficients it can be deduced, in line with expectations, that an increase in population (pop), in the average area occupied (su), in disposable income (yd), in heating (hdd) and cooling degrees days (cdd) determines an increase in energy demand in the building sector (ed). 

The estimates confirms the effectiveness of policy instruments examined such as Ecobonus (fis) and the Thermal Account (fis_ct) in reducing energy consumption in the building sector. 

There is also some evidence that Covenant of Mayors (sind) contribute to the improved technical efficiency. 

Although some results of the estimates show the effectiveness of the Covenant of Mayors initiative on reducing consumption, this level of effectiveness is not always confirmed. The partial effectiveness in reducing consumption can be attributed to the nature of the Covenant of Mayors, which is on a voluntary basis. The adherence by the municipalities to the Covenant should lead to a series of actions within two years of signing (SECAP, inventory of emissions, periodic monitoring, etc.) that are not always implemented. 

In fact, in the ten years of life of the initiative, despite Italy is the country with the highest number of adhesions, the participation of the municipalities in the initiative was limited in most cases to a "formal adhesion". 

The other policy instruments examined such as Energy Efficiency Projects financed by Cohesion Funds (prgee) and Environmental Energy Regional Plans (pear) do not seem to have an influence on reducing energy consumption in the building sector. As can be seen from Table 4, the fis, fis_ct and sind indicators are significant and effective in reducing regional energy consumption in the building sector (ed). 

The introduction of a t-1 time lag in the SFA model (11), that include as usual time dummies (btt), is justified by the delayed effect of the policies promoting energy efficiency analysed in the model:

$\begin{align}  & \text{e}{{\text{d}}_{\text{it}}}=\alpha +{{\text{b}}_{1}}\text{p}{{\text{e}}_{\text{it}-1}}+{{\text{b}}_{2}}\text{p}{{\text{g}}_{\text{it}-1}}+{{\text{b}}_{3}}\text{y}{{\text{d}}_{\text{it}-1}}+{{\text{b}}_{4}}\text{po}{{\text{p}}_{\text{it}-1}}+{{\text{b}}_{5}}\text{hd}{{\text{d}}_{\text{it}-1}} \\ & +{{\text{b}}_{6}}\text{cd}{{\text{d}}_{\text{it}-1}}+{{\text{b}}_{7}}\text{s}{{\text{u}}_{\text{it}-1}}+{{\text{b}}_{8}}{{\text{Z}}_{\text{it}-1}}+{{\text{b}}_{\text{t}}}\text{t}+{{\text{z}}_{\text{it}-1}}+{{\text{v}}_{\text{it}-1}}+{{\text{u}}_{\text{it}-1}}, \\   \end{align}$                      (11)

where, i is the th Italian region and t is the th period and we assume that v_it ~ iid N(0, σ²_v) e u_it ~ N+(b_zz_it, σ²_u).

The building renovation investment produce their effect generally one year later than when the expenses were incurred.

The estimates by introducing a t-1 delay (Table 5) for all variables confirm the effectiveness of the fiscal and economic incentives (fis, fis_ct). 

The estimates were repeated by evaluating in the SFA model the joint effect of the policy variables fis_ct, sind, prgee, pear:

$\begin{align}  & e{{d}_{it}}=\alpha +{{b}_{1}}p{{e}_{it}}+{{b}_{2}}p{{g}_{it}}+{{b}_{3}}y{{d}_{it}}+{{b}_{4}}po{{p}_{it}}+{{b}_{5}}hd{{d}_{it}}+{{b}_{6}}cd{{d}_{it}}+{{b}_{7}}s{{u}_{it}} \\ & +{{b}_{8}}{{f}_{1t}}{{s}_{t}}{{t}_{it}}+{{b}_{9}}sin{{d}_{it}}+{{b}_{10}}prge{{e}_{it}}+{{b}_{11}}pea{{r}_{it}}+{{b}_{t}}t+{{v}_{it}}+{{u}_{it}} \\   \end{align}$                         (12)

where, i is the th Italian region and t is the th period and we assume that v_it ~ iid N(0, σ²_v) e u_it ~ N+(b_zz_it, σ²_u).

Table 4. Estimated Energy demand for building sector

* p-value = 0.10, ** p-value = 0.05, *** p-value = 0.001

Table 5. Estimated Energy demand for building sector with a t-1 delay

* p-value = 0.10, ** p-value = 0.05, *** p-value = 0.001

The results (Table 6) highlight the significance and the negative sign of fis_ct, sind and prgee so the estimates suggest a positive impact of the energy policy mix compared to the single policy. 

These policies mix contributes to the reduction of energy consumption and to a greater value of technical efficiency thanks to greater energy efficiency investments. Probably this behaviour could be due to potential synergy between different policy instruments, i.e. the economic measure could be favoured by normative and voluntary measures.

Descriptive statistics of the level of energy efficiency are reported in Table 7. The estimated average energy efficiency resulting from the BC95 model is 86.8% in the case control variable z is equal to fis_ct and is 87% in the case the control variable z is equal to fis.

Table 6. Estimated Energy demand for building sector with the joint effect of the control variables

* p-value = 0.10, ** p-value = 0.05, *** p-value = 0.001

Table 7. Technical Efficiency for Fiscal and Economic Incentive Policies (The analysis is carried out for the more effective energy efficiency policies studied in the econometric models analysed.)

5.2 Estimated energy demand model for the building sector with geographical and regional dummies

The introduction of the geographical dummy (b_gg) North, Centre and South (Table 8) in the estimated model, that include as usual time dummies (bt_t) and geographical dummies (b_gg), shows greater effectiveness of fis, fis_ct and sind for the areas of Northern Italy:

$\begin{align}  & \text{e}{{\text{d}}_{\text{it}}}=\alpha +{{\text{b}}_{1}}\text{p}{{\text{e}}_{\text{it}}}+{{\text{b}}_{2}}\text{p}{{\text{g}}_{\text{it}}}+{{\text{b}}_{3}}\text{y}{{\text{d}}_{\text{it}}}+{{\text{b}}_{4}}\text{po}{{\text{p}}_{\text{it}}}+{{\text{b}}_{5}}\text{hd}{{\text{d}}_{\text{it}}} \\ & +{{\text{b}}_{6}}\text{cd}{{\text{d}}_{\text{it}}}+{{\text{b}}_{7~\text{s}}}{{\text{u}}_{\text{it}}}+{{\text{b}}_{8}}\text{zit}+{{\text{b}}_{\text{t}}}\text{t}+\text{bg}+{{\text{v}}_{\text{it}}}+{{\text{u}}_{\text{it},}} \\   \end{align}$                              (13)

where, i is the th Italian region and t is the th period and we assume that v_it ~ iid N(0, σ²_v) e u_it ~ N⁺(b_zz_it, σ²_u). By introducing a t-1 delay for all the variables (Table 9) in the model, that include as usual time dummies (bt_t) and geographical dummies (b_gg), the policy indicators fis and fis_ct are significant, of negative sign:

$\begin{align}  & \text{e}{{\text{d}}_{\text{it}}}=\alpha +{{\text{b}}_{1}}\text{p}{{\text{e}}_{\text{it}-1}}+{{\text{b}}_{2}}\text{p}{{\text{g}}_{\text{it}-1}}+{{\text{b}}_{3}}\text{y}{{\text{d}}_{\text{it}-1}}+{{\text{b}}_{4}}\text{po}{{\text{p}}_{\text{it}-1}}+{{\text{b}}_{5}}\text{hd}{{\text{d}}_{\text{it}-1}} \\ & +{{\text{b}}_{6}}\text{cd}{{\text{d}}_{\text{it}-1}}+{{\text{b}}_{7}}\text{s}{{\text{u}}_{\text{it}-1}}+{{\text{b}}_{8}}{{z}_{\text{it}-1}}+{{\text{b}}_{\text{t}}}\text{t}+{{\text{b}}_{\text{gg}}}+{{\text{v}}_{\text{it}-1}}+{{\text{u}}_{\text{it}-1}} \\ \end{align}$                              (14)

where, i is the th Italian region and t is the th period and we assume that v_it~ iid N(0, σ²_v) e u_it~ N⁺(b_zz_it, σ²_u).This tendency is confirmed by the data monitored annually (by ENEA), which show a greater concentration of investments in Northern Italy.

Table 8. Estimated Energy demand for building sector with the geographical dummy

* p-value = 0.10, ** p-value = 0.05, *** p-value = 0.001

Table 9. Estimated Energy demand for building sector with geographical dummy introducing a t-1 delay

* p-value = 0.10, ** p-value = 0.05, *** p-value = 0.001

Table 10. Estimated Energy demand for building sector with regional dummy

* p-value = 0.10, ** p-value = 0.05, *** p-value = 0.001

Table 11. Estimated Energy demand for building sector with regional dummy introducing a t-1 delay

* p-value = 0.10, ** p-value = 0.05, *** p-value = 0.001

The renovation interventions promoted with ECOBONUS and Thermal Account mechanisms are more effective in the North area of Italy because they are mainly dedicated to the reduction of heat requirements (i.e. replacement of doors and windows and the winter heating system). All the estimates, that include as usual time dummies (bt_t), have been repeated by introducing in the SFA model regional dummies (b_rr) for each Italian region: 

$\begin{align}  & \text{e}{{\text{d}}_{\text{it}}}=\alpha +{{\text{b}}_{1}}\text{p}{{\text{e}}_{\text{it}}}+{{\text{b}}_{2}}\text{p}{{\text{g}}_{\text{it}}}+{{\text{b}}_{3}}\text{y}{{\text{d}}_{\text{it}}}+{{\text{b}}_{4}}\text{po}{{\text{p}}_{\text{it}}}+{{\text{b}}_{5}}\text{hd}{{\text{d}}_{\text{it}}} \\ & +{{\text{b}}_{6}}\text{cd}{{\text{d}}_{\text{it}}}+{{\text{b}}_{7~\text{s}{{\text{u}}_{\text{it}}}}}+{{\text{b}}_{8}}{{\text{Z}}_{\text{it}}}+{{\text{b}}_{\text{t}}}\text{t}+{{\text{b}}_{\text{r}}}\text{r}+{{\text{v}}_{\text{it}}}+{{\text{u}}_{\text{it}}} \\ \end{align}$                                (15)

where, i is the th Italian region and t is the th period and we assume that v_it~ iid N(0, σ²_v) e u_it~ N⁺(b_zz_it, σ²_u). The results (Table 10) confirm the negative sign and the significance of the policy indicators fis, fis_ct and sind. The estimates of the model (17), including as usual time dummies (bt_t) and regional dummies (b_rr), have been repeated by introducing a delay t-1 (Table 11) confirming the negative sign and the significance of the financial variables fis and fis_ct: 

$\begin{align}  & \text{e}{{\text{d}}_{\text{it}}}=\alpha +{{\text{b}}_{1}}\text{p}{{\text{e}}_{\text{it}-1}}+{{\text{b}}_{2}}\text{p}{{\text{g}}_{\text{it}-1}}+{{\text{b}}_{3}}\text{y}{{\text{d}}_{\text{it}-1}}+{{\text{b}}_{4}}\text{po}{{\text{p}}_{\text{it}-1}}+{{\text{b}}_{5}}\text{hd}{{\text{d}}_{\text{it}-1}} \\ & +{{b}_{6}}cd{{d}_{it-1}}+{{b}_{7}}s{{u}_{it-1}}+{{b}_{8}}{{z}_{it-1}}+{{b}_{t}}t+{{b}_{r}}r+{{v}_{it-1}}+{{u}_{it-1}} \\     \end{align}$                  (16)

where, i is the th Italian region and t is the th period and we assume that v_it~ iid N(0, σ²_v) e u_it~ N⁺(b_zz_it, σ²_u). Econometric evidence are consistent with Ecobonus, the greater building renovation mechanism pursued by the Italian government for more than a decade. Since 2011 over 2.6 million interventions have been carried out and over 3.6 million since the start of the Ecobonus mechanism (2007).

The classification of the top ten Italian regions based on the estimated level of average energy efficiency is reported in Table 12.

Table 12. Classification of top 10 Italian region based on technical efficiency for fiscal and economic incentive policies

Most of the Italian municipalities of the top ten regions belongs to climate zones (The six climatic zones that characterize the Italian territory are distinguished within the D.P.R. n. 412 of 26 August 1993. The criterion underlying the zoning is based on degree days, that is the sum of the difference (only the positive one) between the internal indoor temperature (fixed by convention at 20℃) and the average external temperature daily. Obviously, higher this number is, colder it will be in that particular Municipality. So, the municipalities will fall into the following intervals: A. municipalities with degree-days below 600℃; B. municipalities with degree-days between 600 and 900℃; C. municipalities with degree-days between 901 and 1400℃; D. municipalities with degree-days between 1401 and 2100℃. E. municipalities with degree-days between 2101 and 3000℃. F. municipalities with degree-days above 3000℃.) characterized by low external average temperature values compared to internal indoor temperature (fixed by convention at 20℃). For example, in Abruzzo the main town Aquila belongs to climatic zone E, in Lombardia the municipalities of Milano, Bergamo, Brescia, Como, Cremona, Lecco, Pavia, Varese belong to climate zone E, in Calabria the town of Vibo Valentia to climate zone E, in Liguria the capital Genova and La Spezia to climate zone D, Perugia the capital of Umbria to climate zone E, in Piemonte the municipalities of Torino, Alessandria, Asti, Lodi, Novara, Sondrio, Pavia, Vercelli to climate zone E and the municipality of Cuneo to climate zone F, in Veneto the municipalities of Padova, Vicenza and Venezia to climate zone F, in Campania Avellino to climate zone E, in Toscana Arezzo to climate zone F and Firenze, Luca, Pia, Pistoia, Prato, Siena to climate zone E, in Lazio Rieti to climate zone F and Viterbo and Roma to climate zone E.

5.3 Estimated energy demand model for the building sector with geographical dummies and interactions between variables

Table 13. Estimated Energy demand for building sector with geographical dummies and with and without a t-1 delay

* p-value = 0.10, ** p-value = 0.05, *** p-value = 0.001

The estimates (Relationship between the aggregate energy demand of the building sector and the other variables for the i-th Italian region in the t-th period, with temporal dummies (btt) and geographical dummies (bgg) and the iteration between fiscal policy and the Dummy North (n_fis_ct), Dummy Centre (c_fis_ct) and Dummy South (s_fis_ct).), that include as usual time dummies (btt), were repeated by introducing the interaction between North, Centre, South dummies and the fiscal policies to analyse the relationship between regional disposable income and the efficacy of the fiscal policy promoting the energy efficiency investments:

$\begin{align}  & ed{{\$}_{\text{it}}}=\alpha+{{b}_{1}}p{{e}_{it}}+{{b}_{2}}p{{g}_{\text{it}}}+{{b}_{3}}y{{d}_{\text{it}}}+{{b}_{4}}po{{p}_{\text{it}}}+{{b}_{5}}hd{{d}_{\text{it}}}+{{b}_{6}}cd{{d}_{\text{it}}}+{{b}_{7}}s{{u}_{it}}\\&+{{b}_{8}}fisc{{t}_{\text{it}}}+{{b}_{9}}{{W}_{1it}}+{{b}_{10}}{{W}_{2it}}+{{b}_{11}}{{W}_{3it}}+{{b}_{t}}t+{{b}_{g}}g+{{v}_{it}}+{{u}_{it}}\\\end{align}$         (17)       

with: w1it = n_fis_ct, w2it = c_fis_ct, w3it = s_fis_ct, where i is the th Italian region and t is the th period and we assume that v_it~ iid N(0, σ²_v) e u_it~ N⁺(b_zz_it, σ²_u). The results in Table 13 confirm the greater effectiveness of fiscal policies in Northern Italy because the mechanism is based on the expectation of future margin income necessary to deduct the expenditure incurred. In other words, a higher (expected) annual income favours the use of the tax incentive: notoriously, the Northern regions show higher average per capita income values than those of the Central and South regions.

5.4 Estimated energy demand model for the building sector an application of Energy Environmental Kuznets Curve (EKC)

Energy EKC has been applied to understand the relationship between per capita income and energy consumption. 

The equation estimated in the study is the logarithmic transformation of (9) which identifies the relationship between the aggregate energy demand of the buildings sector and the other variables indicated for the i-th Italian region for the t-th period:

$\begin{align}  & {{\text{e}}_{\text{it}}}={{\text{A}}_{\text{it}}}+{{\beta }_{1}}{{\text{y}}_{\text{it}}}+{{\beta }_{2}}\text{y}_{\text{it}}^{2}+{{\beta }_{3}}{{\text{y}}^{3}}\text{it}+{{\beta }_{4}}\text{Zit} \\ & +{{\beta }_{5}}dpo{{p}_{\text{it}}}+{{\beta }_{6}}~{{\text{S}}_{-}}\text{k}{{\text{m}}^{2}}\text{it}. \\   \end{align}$       (18)                 

The estimation results of the energy demand model for the building sector applying the Energy EKC framework with the Stochastic Frontier Approach and the Generalized List Squares are shown in Table 14. 

Table 14. Energy ECK - relationship between income and energy consumption

* p-value = 0.10, ** p-value = 0.05, *** p-value = 0.001

For estimates carried out with Generalized Least Squares method can be observed that, since the estimated coefficient (β4) relating to adhesion to the Covenant (sind) is negative, the actions undertaken by the joining municipalities produce positive results in terms of reducing electricity consumption. 

It can be observed an inverted U trend from the estimates of the coefficients (β1, β2 and β3) related to the geometric mean of disposable income (Yd). 

In the first phase, as disposable income increases, energy consumption increases, while beyond a specific threshold, as disposable income increases, there is a decrease in energy consumption. This effect, in the first phase of growth, can be traced back to the need to ensure an adequate level of heating and cooling of buildings. 

The European Commission reports that around 34 million Europeans are unable to afford keeping their home adequately heated. The share of families in energy poverty condition is approximately 8% of the total, with an increasing trend in recent years (reaching in 2016 a value of approximately 8.6%, equal to 2.2 million families, this value would be more or less confirmed in 2017). In the descending phase, the phenomenon can be attributed to the greater awareness of citizens and the entire community (partly due to the adhesion to the Covenant of Mayors initiative), to environmental issues and specifically to measures relating to energy efficiency (i.e. buildings renovation).