Declining Discount Rate Estimate in the Long-Term Economic Evaluation of Environmental Projects

Antonio Nestic`o,Gabriella Maselli

Department of Civil Engineering,University of Salerno,Fisciano(SA),84084,Italy

Keywords Environmental projects Economic evaluation Social discount rate Intergenerational discounting Declining discount rate Economic model

Abstract

1 Introduction

The Environmental Decision-Making is a multidimensional process, for which to make rational choices can become complex for the necessity to integrate in the evaluations both economic and environmental and social aspects(Balasubramaniam and Voulvoulis,2005;Avramenko et al.,2010;De Feo et al.,2014;Molinos-Senante et al., 2016; Nestic`o et al., 2019). This question is of particular theoretical and operational interest when it is necessary to express an economic convenience judgment on environmental projects of public interest,since they are destined to be evaluated over a long time horizon.

There are two critical steps in the economic analyses related to these investment initiatives: 1. the evaluation of non-tangible costs and benefits; 2. the estimate of the Social Discount Rate (SDR). If the evaluation of intangible assets is important to express in quantitative terms the effects that the project is able to generate on the environment and on the community the judgment on the economic feasibility of the project is strongly conditioned by the value of the Social Discount Rate(Fujiwara and Campbell,2011;Shaw and Wlodarz,2013;Muoz Torrecillas and Cruz Rambaud,2017;Del Giudice et al.,2018;Nestic`o et al.,2018). This paper focuses attention on the SDR estimate for inter-generational environmental projects.

Price (1988) defines the SDR as that “discount rate used by society to give relative weight to social consumption or income accruing at different points in time”. Following well-established consolidated theoretical approaches, the SDR can be estimated following the logic of the Social Rate of Time Preference(SRTP)or the economic criterion of the Social Opportunity-Cost of Capital(SOC),depending on whether considerations are made respectively on the consumption (demand) or production (supply) side. The Social Rate of Time Preference is defined as the rate at which the society is willing to postpone a current consumption unit to obtain higher consumption later. The Social Opportunity Cost of Capital corresponds to the marginal rate of return related to a private sector investment(Nestic`o et al.,2015).

Operationally,the Social Discount Rate is that economic parameter that makes financially comparable Cash Flows (CFs) that occur at different time moments, influencing considerably the list of priority of the projects to finance when it is necessary to choose among several investments. Hence, with implications on the entire allocation process of public funds (Nestic`o and Maselli, 2019). This is because as time increases, there is an ever-greater contraction in the current values of cash flows progressively further away than at the time of the evaluation. In other words, as the time horizon with respect to which to carry out the evaluation increases, the risk of underestimating the effects of projects that involve different generations compared to those that supported the project initiative increases.

In general, this applies to those investments which require substantial water and energy consumption and which inevitably entail environmental impacts, especially in the long term. In detail, it is sufficient to think,among others, of the production of thermoelectric power plants, hydraulic works and wastewater treatment plants, interventions for soil protection, reforestation or for the reduction of greenhouse gas emissions. All projects whose benefits are for many decades, while the initial investment costs are concentrated essentially in the first years of life of the works or in the near future(Newell and Pizer,2003;Arrow et al.,2014,Nestic`o and Maselli,2018,2019).

This means that the ability of such projects to pass the benefit-cost test is especially sensitive to the rate at which future benefits are discounted(Arrow et al.,2014).

In accordance with the reference literature,a possibility to give greater weight to Cash Flows over time is to use Declining Discount Rates (DDRs), instead of constant discount rates. Recent political concerns regarding global warming, nuclear waste and, more generally, sustainable development have gradually increased interest in the use of time-declining discount rates in economic evaluations(Evans,2008). This has led in recent decades to the development of new theoretical approaches, following the first important works in this area such as the Modified Discounting Method(Kula,1988)and the Multi-Generational Value Model(Bellinger, 1991). In this regard, the most important contributions to the theory are substantiated in the two main theoretical approaches for estimating the declining discount rate: The Consumption-Based Approach and the Expected Net Present Value Approach. It is precisely on these approaches that the estimates of the States that have decided to adopt Declining Discount Rate for the economic analysis of long-term projects are based. In this regard, France has used the Consumption-Based Approach for the estimation of the DDR (Rapport Leb`egue, 2005), while the United Kingdom has implemented a hybrid approach that takes into account both theories recognized by literature (HM Treasury, 2003). In the United States instead, the Office of Management and Budget (OMB)recommends that “project costs and benefits be discounted at a constant exponential rate (which, other things equal, assigns a lower weight to future benefits and costs than a declining rate), although a lower constant rate may be used for projects that affect future generations” (Arrow et al., 2014). Still the choice of Norway to adopt DDR and,recently,those of Denmark,Sweden and Holland that are examining the possibility of using it,testifies to the effective utility correlated to the use of hyperbolic discounting.

The purpose of this research is to characterize a model for the estimation of the parameters on which the value the declining discount rate depends. The model is structured on probabilistic logic algorithms. In the light of the limits and operational issues to be resolved that emerge from the literature, we therefore intend to establish a tool that is simple to implement,while respecting the mandatory theoretical principles of reference.

The following section 2 provides the theoretical framework of the approaches traditionally used for the estimation of the time-declining rates. In the section 3 a critical examination of the same approaches allows the definition of the logical-operative steps on which the proposed probabilistic model is based. Thus, the model described is implemented in order to estimate the DDRs for the Italian economy. In section 4, the application of the declining discount rates to the economic analysis of an irrigation reconversion project in the Province of Salerno (Italy) allows to test the tool, detecting the “weight” that it attributes to long-term costs and benefits. Finally, section 5 summarizes the implications of the use of hyperbolic discounting on the Environmental Decision-Making,above all the opportunity to allocate financial resources to sustainable projects even for future generations.

2 Literature review

From the public point of view,the investment selection process tends to maximize the utility-or the“happiness”-of the community, or of a representative individual of the same. In agreement with many authors (Feldstein,1972; Bradford, 1975; Lind, 1982; Moore et al., 2013; Kazlauskien˙e, 2015), the utility must be considered from the consumer’s point of view,i.e. it must depend on present and future per capita consumption. Pursuing this ethical objective, the estimate of the social discount rate must take up the SRTP logic, which has as its fundamental principle the maximum increase in the social well-being function. When long periods of analysis are considered,such as those involving initiatives with environmental implications,it is consistent to hypothesize that shocks to the discount rate of consumption, i.e. the rate at which society would trade consumption in year t for consumption in the present, are uncertain but positively correlated. This fundamental basic assumption determines a time-declining structure of the discount rate function(Gollier,2012;Arrow et al.,2014). Based on this principle,in the last few decades two approaches concerning the estimate of the declining discount rate have mainly been established: The Consumption-Based Approach(a)and the Expected Net Present Value Approach(b).

According to the Consumption-Based Approach branch(a)the uncertainty factor is included in the Ramsey formula, specifically in the “consumption growth rate”. Indeed, Ramsey formula (1928) is a function of the following parameters:

where:

· ρ is the time preference rate or rate at which individuals discount future utility;

· η represents the absolute value of the elasticity of marginal utility with regard to consumption,that is the change(percentage)in the well-being derived from a change(percentage)in income(or consumption);

· g is the exchange rate in per capita consumption, generally understood as the expected growth rate of consumption.

The time preference rate or “inter-generational discrimination rate” ρ of (1) reflects the importance that society attributes to the well-being of the current generation with respect to the well-being of the future one. ρ can be estimated through the relation:where l is the discount rate estimated as the average annual mortality rate,given by the ratio between the number of deaths in the country and the total population in the reference year;r is the pure time preference rate,linked to the so-called “myopia”or“irrationality” factor. From the estimates provided by the literature, the value of r between 0 and 0.5%emerges(Kula,1987,2004;Evans,2006;Percoco,2008;Lopez,2008).

The elasticity of the marginal utility of the consumption η that appears in(1)is the percentage with which the marginal utility decreases when the consumption increases by 1%(Heal,2009). The literature suggests that η can be estimated through the approach of the“revealed social values”,also called“equal absolute sacrifice”.In this case,η is intended as a parameter of aversion of the social planner,or more generally of the Government,towards income disparity. In accordance with this approach, η is estimated by implementing the formula of Cowell and Gardiner(1999),which is a function of the tax rates both marginal and average T/Y of the country:

For a more detailed analysis of the approaches to estimate the parameter η,refer to the Evans(2004), Kula(2004), Evans et al. (2005), Sheluntsova (2009), Halicioglu and Karatas (2011), Groom and Madison (2013)works.

The growth rate of consumption g in(1)is an indicator of the degree of wealth of the society. In practice,g is generally approximated either by the average annual growth rates of per capita consumption or by the average growth rate of per capita GDP(Percoco,2008;Florio and Sirtori,2013).

Just the uncertainty related to the growth rate of consumption g leads to write the extended Ramsey formula.In particular, if we assume that g is approximated by a sequence of random variables normally, independently and identically distributed with media μ and variance σ2,then(1)becomes:

The (4) shows a function of the discount rate constant over time. However, the term 0,5η2·σ2gsaid “precautionary”, summarizes the uncertainty on the rate of growth of consumption and determines a reduction in the value of the discount rate r compared to what would be obtained from (1). Instead, if the shocks to the growth rate of consumption are positivelycorrelated, then a function of the discount rate decreasing over time is obtained. In this regard,Gollier(2008)suggests a linear self-regressive model AR(1)to predict the possible future values of the DDR.In this case,it is necessary to estimate a correlation parameter of the shocks ρ,whose value significantly influences the result of the forecast.

According to Gollier (2002 a, b; 2008; 2012) it is possible to obtain a declining function of the declining discount rate also by treating the parameters μ and σ of(4)as uncertain. It is then assumed that the consumption register follows a Brownian motion with trend μ(θ)and volatility σ(θ). These values depend on a parameter θ,uncertain at time 0. In this case,(5)and(6)are obtained:

In(5)the average μ of the growth rate of the economy is uncertain,that is μ=μ(θ). In particular ∑qθ=1,with qθprobability that the parameter μ associated with the uncertainty has to occur.

In(6)the volatility σ of the growth rate of the economy is uncertain,i.e. σ =σ(θ). Then ∑qθ=1,where qθis the probability that the parameter σ associated with the uncertainty has to occur.

Instead,following the Expected Net Present Value Approach(b)proposed by Weitzman(1994,1998,2001),the uncertainty concerns the value of the discount rate r. This uncertainty determines a time-declining path of the variable r based on the expected discount factor dtassociated with the distribution of the possible rates that occur at future moments t (Evans,2008). In other words,Weitzman(2001)shows that estimating the Expected Net Present Value(ENPV)of a project with an uncertain but constant discount rate is equivalent to computing the NPV with a certain but decreasing“certainty-equivalent” discount rate until reaching the minimum possible value at the time t =∞. The equation that allows us to estimate the“certainty-equivalent” discount factor dtto the future year t is:

where Liis the probability that the rate rican occur at the generic instant t of the project analysis period.

For each future year t,the value of dtcan be converted into a“certainty-equivalent”discount rate,understood as the exchange rate of the expected discount factor,through the following equation:

Following this approach, long-term government bonds are often used in the literature for the estimation of ri. Authors such as Weitzman (1994, 1998, 2001), Newell and Pizer (2003), Groom et al. (2007), Freeman et al. (2015) believe that past data on government bonds provide information that allows for a reliable forecast of the possible future paths of the rate. In this regard, Newell and Pizer (2003) use the past data of real longterm US government bond rates to forecast future bond rate paths and thus establish a probability function for future discount rates. Then, as regards the prediction of the probability distribution of discount rate, the literature proposes econometric models, such as the linear Auto-Regressive AR (1) based on normal or lognormal distributions of historical data. But also more complex models,such as AR(p)-GARCH(l,m),Regime Switching(RS),State Space model(SS).In these models with the parameters can vary over time and therefore they are able to better approximate the trend of historical data (Weitzman, 1998, 2001; Newell e Pizer, 2003;Groom et al.,2007;Freeman et al.,2015).

Turning to a critical examination of the two main approaches for the estimation of DDRs recognized by the literature,the following considerations apply.

The Consumption-Based Approach is based on the well-known Ramsey formula. This is the methodology most used in Europe for the estimation of the Social Discount Rate, i.e. for the Cash Flows discounting in economic analyses as it is a function of economic, social and demographic indicators. For this reason, it well reflect the socio-economic structure of a nation. On the other hand,the main critiques of the approach are linked to the forecast of the growth rate of consumption g over time. In fact,assuming shocks at the rate of growth of consumption that are persistent over time,the declining function is obtained but it is strongly influenced by the estimate of the parameter ρ of shocks correlation. It follows that its small variations can significantly alter the rapidity with which the DDRs function declines. Instead,assuming that consumption follows a Brownian motion with trend μ(θ) and volatility σ(θ), where θ is the probability that the parameters have to occur (formulas 5 and 6),then the random variable gtis modelled through a normal distribution that is not always the one that best approximates the historical data(Nestic`o and Maselli,2019).

The Expected Net Present Value Approach is open to criticism,as Cropper et al.(2014)argue,for its shortage of link to the theory of benefit-cost analysis. Also because the ENPV Approach estimates the uncertain discount rate based on government bond interest rates. Several authors,in fact,declare that they prefer Ramsey formula to government bonds, since they do not clearly reflect the socio-economic structure of a country. Finally, also in this case,another critical issue concerns the difficulties of econometric models to predict the discount rate ri(see equation 7).

3 Methodology. A probabilistic model to estimate the DDR in economic analysis for environmental projects

3.1 Characterization of the DDR stochastic estimation model

With the aim of overcoming the critical aspects of the approaches described in section 2,a model for the estimation of DDRs to be used in economic analyses of environmental projects, whose effects are inter-generational,is devised. The objective is to define a tool that is rigorous from a theoretical point of view and, at the same time, simple to use for the analyst. This is why we choose to base it on the well-known Ramsey formula, one of the estimating methods of the Social Discount Rate most used in practice. Also chosen by the European Commission (2014), it also makes it possible to estimate the discount rate of consumption by resorting to data easily available from national and international databases. In order to avoid resorting to econometric models that often presuppose stringent preliminary hypotheses, the growth rate of consumption gtthat appears in the formula (1), on which the value of the discount rate rtdepends, is modelled as a stochastic variable. In other words, from the historical trend analysis of gtit is possible to foresee a probability function to be associated with the same parameter. From the probability function thus obtained, then,through the Monte Carlo analysis,a series of probable values is determined to be associated to the gtrate and,consequently,to the unknown rt.

Next, the logical-operational steps on which the probabilistic model for estimating the DDR is based are detailed.

1)Forecast of the discount rate rton a probabilistic basis

Consider Ramsey formula on which the Consumption-Based Approach is based:

The basic assumption is to consider the growth rate of consumption gtas an uncertain and constant variable in the analysis period. This means associating to the uncertain future value of g=gta probability distribution derived from the analysis of the historical trend of gtreferred to a sufficiently long investigation time. In other words once the probable distribution of g-values are expected,the likely values of the consumption discount rate r can be obtained. In fact,the(9)shows that rtis a function of gt,as well as of deterministic variables δ and η,respectively rate of time preference and elasticity of the marginal utility of consumption. In particular, δ and η can be obtained through the formulas(2)e(3). It is evident that such an approach leads to constant probability distributions in the time interval of investigation associated to g,and therefore to r.

2)Estimate of the“certainty-equivalent” discount factor dt

This step allows identifying among the infinite possible values that the probability distribution related to r expresses,which to use in social discounting year by year. Taking up the logic of the ENPV Approach,according to which computing the expected net present value of a project(ENPV)with an uncertain but constant discount rate is equivalent to computing the NPV with a certain but decreasing “certainty-equivalent” discount rate. To this end, it is first necessary to estimate the discount factor dtfor each future instant t, through the following equation:

where:

ri=value of the i-th discount rate,as shown by the probability distribution of r derived from the formula(9)with uncertain variable gt; pi=probability that the i-th value of the rate has to occur;t =temporal variable;m=number of intervals in which the probability function of r is discretized.

Fig.1 Logical-operative steps of the model.

3)Estimate of the“certainty-equivalent” discount rate

The formula(8)already introduced in section 2 is used:is therefore the rate of progression from t to t+1 or even marginal discount rate. It is declining over time.Figure 1 summarizes the logical-operative steps described above on which the model is based.

3.2 Estimation of the DDR for Italy

Based on the proposed model,summarized in Figure 1,the estimate of the DDRs for Italy is now conducted. In section 4,this estimate of the DDR is useful for the economic analysis of an unlawful reconversion intervention,the effects of which concern several generations.

3.2.1 Forecast of the discount rate rt on a probabilistic basis

a. Estimation of constant parameters δ and η. The time preference rate δ is given by the sum of two contributions: discount rate l based on mortality and the pure time preference rate r. In fact,returning to(2):

l is the ratio between the number of deaths in the year of reference and the average number of residents. Assuming that the average mortality rate in the last generation of births remains constant in the future, then we consider the data of the last thirty year(1989-2018), although reporting that the mortality rate undergoes small variations with the variation of the time interval. For Italy l=0.99%(sources: ISTAT and World Bank). This result is in line with that obtained by Percoco(2008)according to which l is equal to 0.98%and 1.00%. These values correspond to the probability of survival in Italy respectively in the years 2001 and 2002. This estimate is also close with that of Florio and Sirtori(2013),which suggest l=0.98%based on the mortality rate for Italy in 2011.

The pure time preference rate r is positive and reflects the irrational behavior of individuals in their choices about the distribution of resources over time. In order not to create excessive disparity of treatment between the current and future generations, it is estimated r=0.3%, according to literature data (Evans et al. 2009).Definitely: δ =0.99%+0.3%=1.3%.

This estimate is consistent with the literature values concerning countries with advanced economies, for which ρ is close to 1%(Evans et al.,2005;Evans,2006;Lopez 2008;Evans and Kula,2009).

The elasticity η of the marginal utility of consumption is estimated by implementing the formula Cowell and Gardiner(1999)formula,as expressed by the(3):

where t is the marginal tax rate; T/Y is the average tax rate, the ratio between the total amount of income taxes and the taxable income before taxes. Based on data from the Organization for Economic Cooperation and Development Countries (OECD)that provides the marginal rates and those average T/Y of individual income tax for multiple multiples(67%,100%,133%,167%)of the average salary,the final value of η is equal to 1.334.

This result is in line with the known values of the literature where the government behavior revealed approach leads to 1 ＜η ＜2(Azar,2007;Florio and Sirtori,2013).

b. Analysis of the historical series of consumption growth rate gt. According to Percoco(2008) and Florio and Sirtori(2013),gtis estimated based on the GDP per capita growth rate. The study on the trend of the growth rate of GDP per capita induces to select the data of the last forty years, i.e. those relating to the period 1979-2018. This is because GDP growth rates linked to historical-economic scenarios that are not comparable with current ones and probably not even with future ones are not consistent. In other words, the GDP growth rates recorded,for example,in the historical period of the Unification of Italy or even during the two World Wars,are the reflection of situations no longer referable to the economic,social and cultural context of the Country.

c. Identification of the probability distribution that best approximates historical data. This distribution is identified with the help of the Oracle Crystall Ball software. Specifically, the Anderson-Darling test finds that the best approximation of historical data is given by the logistic curve.

d. Monte-Carlo analysis to estimate the probable values of gt. The distribution of the probable values of the GDP growth rate is expected through the Monte Carlo analysis,based on the probability distribution established in point c. Implementing the Monte-Carlo analysis, 10, 000 random extractions to predict the unknown parameter are performed.

e. Estimate of the probability distribution of the discount rate r. Starting from the probability distribution of the growth rate of consumption g,applying Ramsey formula(1)yields the distribution of the discount rate r.Table 1 shows an excerpt of the elaborations carried out.

3.2.2 Estimate of the“certainty-equivalent” discount factor dt

Table 1 shows an excerpt of the series of values of the discount rate r and the relative probability that each of them has to occur. From these data and using formula(10),we estimate the certainty-equivalent discount factor.Table 2 shows the certainty-equivalent discount factors over time for Italy.

3.2.3 Estimate of the“certainty-equivalent” discount rate

Finally, the implementation of (8) leads to the estimate of the certainty-equivalent discount rate of which, as evidenced by the elaborations summarized in tables 3 and 4,is declining over time.

Table 3 shows how the declining discount rate for Italy starts from an initial value of 3.65% to settle at2.68%after 30 years,2.18%after 50 and 0.49%after 300 years. The estimate provides a discount rate value that in three hundred years declines by about 2.5%, with a more marked decrease in the first eighty years and less appreciable with the progression of the time horizon. Table 4 shows the average rates for seven time intervals and shows how the rate for the first thirty years is 3.3%,a result that does not differ much from that suggested by the European Commission(2014)for the economic analyses that,for the 2014-2020 period,it is 3.0%. Figure 2 represents the function at intervals(dotted line)that approximates the continuous function of the declining test.

Table 1 Probability distribution of r deriving from the Monte-Carlo simulation.

Table 2 Certainty-equivalent discount factor.

Table 3 Values of the certainty-equivalent discount rate.

Table 4 Values of the certainty-equivalent discount rate for time intervals.

Fig.2 Term structure of DDR for Italy.

4 Based DDR-economic analysis for an irrigation reconversion intervention. Results and discussions

The DDR for Italy, deriving from the estimate conducted in section 3, is used for the economic analysis of an irrigation reconversion intervention in the Province of Salerno(Italy). The aim is to show how the discounting of cash flows generated by interventions with long-term environmental effects leads to markedly different results if time-declining or, on the contrary, time-invariant discount rates are used. In other words, it is intended to determine to what extent the choice of discount rate involves the attribution of a different weight to costs and benefits that are progressively more distant over time,influencing the investment choices of the decision-makers.To this end, the economic evaluation of the irrigation network restructuring operation is then conducted over a 60-year analysis period with different discount rates:

a) constant discount rate of 3.0%, that is the one proposed by the European Commission (2014) in the Guide to Cost-Benefit Analysis for economic analysis concerning investment initiatives for the 2014-2020 proprogramming period;

b) declining discount rates, deriving from the implementation of the proposed model, according to three times intervals. In particular,a rate of 3.3%for the years 1-20,a rate of 2.7%for the years 21-40,a rate of 2.1%for the range of 41-60 years.

4.1 Project description

The intervention consists in replacing the current“gravity”irrigation distribution system with an improved technology, i.e. under pressure, both to reduce water dispersion along the network and to ensure a better quality of the water resource. The installation of instruments for detecting the flow rates provided to individual users and the introduction of a new contribution system mean that each farmer is induced to withdraw what is strictly necessary, thus favouring the preservation of groundwater levels. This in order to offer a sustainable and economically advantageous irrigation service to the greatest number of users.

From the estimate of the reduction both of the localized losses connected to the state of degradation of the current water network and of those distributed by surface runoff and evaporation, there is a reduction in water waste of about 50%. Specifically, with reference to the currently most widely used crop, i.e. that of maize, it is estimated that the actual requirement is approximately 4,000 m3of water for each hectare cultivated, while at present the requirement is satisfied through a supply of 7, 000 m3. The resource savings resulting from the modernization intervention can be redistributed towards more profitable products, incompatible with the preintervention condition. It is assumed to increase the water supply up to 5, 000 m3/ha, thus making it possible to cultivate vegetable plants such as cauliflower, fennel, lettuce, tomato, courgette, which are added to those already practiced, that is artichoke, alfalfa, corn,aubergine, apple,pepper. This determines, with respect to the current situation,increase in Gross Saleable Production(GSP)and decrease in water consumption.

The structural interventions connected to the construction of the work consist of: restructuring and monitoring of the intake structure;restructuring and remote control of the lifting system;improvement of the abduction and distribution network; construction of a storage tank and of the plant for the production of energy from Renewable Energy Sources(RES).This last intervention uses the flow rate derived from the Sele River exceeding that necessary for the irrigation supply of the consortium district in the non-irrigated months. This flow rate is then returned to the river by means of a special existing discharge procedure. The system is able to cover a rate equal to 57%of the energy costs necessary for the operation of the adjacent lifting system.

Auxiliary works are also envisaged such as:positioning of a bridge crane for the installation and maintenance of the aforementioned equipment; arrangement of the access road to the plant through road paving and curbs;consolidation of masonry work;installation of a video surveillance system;installation of a shielded fibre optic cable,for direct connection between the lifting system and the accumulation tank,for the remote control of the pumps serving the irrigation utilities.

4.2 Economic analysis

The economic analysis is developed from the point of view of the community,with the aim of evaluating the main benefits that the water system modernization project is able to generate in the area affected by the intervention.It is assumed that:

· the analysis period is 60 years,as it is a water resource management optimization project,therefore with significant environmental implications to be evaluated over a sufficiently long time interval;

· the construction costs are entirely incurred by the Ministry of Agriculture;

· the construction phase is 2 years. In this period, as the existing plant continues to operate, the costs and revenues of the current condition are calculated.

Going into the details of the items that contribute to defining the economic plan, the construction costs of the works amount to C12,459,722.41 and it is assumed that they will be distributed equally over the 2 years of the construction phase.

Revenues,on the other hand,include:

a) the increase in tax taking related to the increase in Gross Saleable Production. This increase is estimated in percentage terms with respect to profit. The latter,in turn,is supposed to be equal to 25%of farm incomes,as can be seen from paragraph 1094 of the art. 1 of the 2007 financial law no. 296 of 27 December 2006.Agronomic and financial studies relating to the reference benchmark lead to estimate the GSP equal to C4,064,575.98 deriving from the totality of the crops envisaged and considering a vintage with average rainfall;

b) the monetary quantization of water savings deriving from the modernization of the network, according to the shadow price. In fact, the main purpose of the modernization of the irrigation network concerns the optimization of water resource management. In this regard,the United Nations Environment Program report UNEP(2010) notes that agriculture, together with forestry, fishing and aquaculture, is among the most important drivers of environmental pressures. Since agriculture in Italy has a particularly significant impact on the entire national territory, in recent years, it has increasingly focused on initiatives to integrate agricultural dynamics and environmental sustainability, tending to favour a more rational and responsible use of natural resources. Moreover,the problem of water resource management is made even more relevant and topical by recent theories on global climate change, which envisage future scenarios characterized by less and less water availability(Khalkhali et al.,2018,Mehzabeen et al.,2018). In order to consider the aforementioned issues in the Cost-Benefit Analysis,we estimate the shadow price of water for irrigation. Shadow price means the value attributed to the resource by the community in the context offree market bargaining, different from the administered tariff at which the asset is ordinarily exchanged.The evaluation procedure that follows is that of the Water Framework Directive 2000/60 EC,which specifies how the water good should be considered a natural resource to be protected and not a commercial good from which to profit. Processing on agronomic data allows us to estimate the shadow price of water at C0.042/m3;

Table 5 Estimation of costs and benefits for economic analysis.

c) the monetization of the reduction of carbon dioxide emissions into the atmosphere. The replacement of the gravity system with pressure network involves the centralization of the water lifting and the consequent interruption of the operation of the motor pumps by individual farmers. This leads to less use of fossil fuels, with reduced carbon emissions in the form of CO2and pollutants from the combustion of hydrocarbons,such as PM10particulates,HC hydrocarbons,NOx nitrogen oxides,SO2sulphur dioxides.The analysis of the literature and the study of the climatic and podiatric conditions of the area allow us to estimate: a) a reduction in CO2emissions deriving from the modernization of the network of around 0.9 t/ha per year; b) an economic damage of $ 220, about C198, caused by a ton of CO2released into the atmosphere. For the project under examination, a benefit of C44, 544.42/year is estimated for the reduction of CO2emissions;

d) the residual value Vrof the works at the end of the analysis period. Having foreseen extraordinary maintenance interventions that allow the works and plants to maintain full efficiency during the entire analysis period,Vris equal to the initial construction cost.Table 5 details the costs and revenues that contribute to the preparation of the economic plan. Tables 6 and 7 provide the results of the calculations,i.e. they return the economic plans drawn up respectively with a constant discount rate and declining discount rates. Tables 6 and 7 also show the values of economic performance indicators,specifically the Net Present Value(NPV)and the Internal Rate of Return(IRR).

The economic analyses carried out show the economic sustainability of the investment in both cases, i.e.both in the valuation with constant discount rate (table 6) and in the valuation with declining discount rates(table 7). In detail:

· the Internal Rate of Return(IRR)is equal to 4.3%,thus exceeding the 3%discount rate(case a)and the 3.3%rate corresponding to the highest of the declining rates used(case b);

Table 6 Economic plan(case a,with time-invariant discount rate).

It should be highlighted that the estimated NPV with declining rates is about twice as much compared to the one deduced with constant discounting. Thus,the elaborations show that traditional economic feasibility studies,based on time-invariant discount rate,greatly underestimate the effects that the investment project generates on the territory.

5 Conclusions

Recent political concerns regarding climate change,global warming and,more broadly,sustainable development have progressively increased attention to the optimal use of resources with the aim of minimizing environmental impacts (Mehzabeen et al., 2018). To this end, it is important to provide decision makers with a complete profile of knowledge of the effects,both financial and extra-financial,that the projects are able to produce. This information framework can be obtained by implementing economic studies that correctly evaluate the set of costs and benefits that the investments determine even in the long term (Nestic`o and Maselli, 2018, 2019). In cost-benefit analyses this can be done by giving due weight to long-term externalities through careful selection of the social discount rate(SDR).An economic parameter that makes it possible to compare financially the Cash Flows (CFs) that occur at different time points, the SDR strongly influences the result of a cost-benefit test.Generally, the social discounting operation carried out for public projects takes place at a constant rate. In this way,however, there is the risk of excessively contracting the most distant financial terms over time. These are almost always very substantial financial terms for investments with environmental implications.

The aim of the work is first to demonstrate how to resort to hyperbolic discount namely, to time-declining discount rates is important for the purpose of a correct economic evaluation of the benefits deriving from projects with environmental implications. These are evaluations conducted from the point of view of the public operator over long time horizons,where recourse to a constant discount rate in the CBA produces excessive contractionhence undervaluation -of the effects that in the long term the project for environmental sustainability is in able to determine.

In the perspective outlined,a further purpose of the paper is to characterize a probabilistic estimation model of the declining discount rate,able to overcome the limits of the approaches recognized in literature. The implementation of the model to the Italian economy and the application of the DDRs thus estimated to the economic feasibility study of an irrigation reconversion intervention,on the one hand,allows testing the evaluation protocol. On the other hand,it shows that the NPV estimated through time-declining discount rates(6,208,876.27)is roughly double that obtained with time-invariant discount rates (3, 586, 922.42). This result explains that applying a constant discount rate, an investment with economic returns concentrated at the beginning of the analysis period rather than another with high initial costs and long-term benefits would be preferred. In other words,the long-term positive externalities that characterize sustainable development interventions would end up being underestimated.

In conclusion, the probabilistic approach proposed for the estimation of the DDR is based on theoretical references widely consolidated in the literature and is easy to use. It can therefore encourage decision-makers to choose time-declining discount rates in the cost-benefit analysis of projects with inter-generational effects. It emerges that the adoption of hyperbolic discounting in economic evaluations allows increasing the reliability of performance estimates. This with significant repercussions on the selection of the investments to be financed and therefore on the entire allocation process of resources to be assign to projects with effects on the environment.