Social Discount Rate for Public Investment Projects for Conservation and Provision of
Ecosystem services: Estimation for Peru1
Cecilia Adrogué2
Tania Lozano3
Stanislao Maldonado4
August 2014
Abstract
The aim of this study is to estimate the appropriate social discount rate for the analysis of public
investment projects for the provision and conservation of ecosystem services through rigorous
systematization of the various methodologies developed for empirical estimation. The novelty of
the case is that traditional cost benefit analysis (CBA) cannot be applied due to the large
proportion of externalities, irreversible effects and the temporal horizon of these services, which
threaten the validity of the basic assumptions underlying the CBA. In particular, due to the
characteristics of the goods involved, additional ethical criteria should be incorporated.
Keywords: social discount rate, ecosystem services, cost benefit analysis
JEL Classification: Q57, D62
Resumen
El objetivo del presente trabajo es estimar una tasa de descuento social adecuada para los
proyectos de inversión pública con fines de conservación y provisión de servicios ecosistémicos
mediante una sistematización rigurosa de las diversas metodologías desarrolladas para su
estimación empírica. La novedad es que no puede aplicarse un análisis costo beneficio (ACB)
tradicional, debido a la gran proporción de externalidades, efectos irreversibles y el horizonte
temporal involucrado, propios de estos servicios, lo cual amenaza la validez de los supuestos
básicos del ACB. En particular, las características peculiares de los bienes en cuestión,
requieren la incorporación de criterios éticos adicionales.
Palabras clave: tasa de descuento social, servicios ecosistémicos, análisis costo beneficio
Clasificación JEL: Q57, D62
1
The authors are very grateful to GIZ, whose support for this project was decisive. The authors also thank
Hans Canicoba and Víctor Huamaní for their assistance.
2
Universidad Austral -Facultad de Ingeniería- y UdeSA-CONICET, Argentina. [email protected]
3
Pontificia Universidad Católica del Perú. [email protected]
4
University of California, Berkeley, USA. [email protected]
1
1. Introduction
Over the past decades, there has been increase concern about the degradation of the
ability of ecosystems to provide Ecosystem Services, these being understood as the social,
economic and cultural benefits arising from their ecological functions. Together with this
concern, there has been a growing interest in promoting their conservation and sustainable use
(del Milenio, 2005). This arises as a response to the recognition of the high dependence
between the social, cultural and political development, and even the survival of the species, and
this type of services; which, additionally, when in "good operating", allow dealing more efficiently
with the doldrums of climate change and provide support for various economic activities (Tyndall
Center, 2003).
In this context, both internationally and within countries various projects have developed
that promote conservation or the provision of Ecosystem Services, posed them under different
schemes and environmental funding mechanisms, including those coming from public funds.
Regarding this last point, Public Investment Projects (PIP) were recently proposed for
Conservation and Ecosystem Services Provision, which are financed by public resources and
evaluated within the National System of Public Investment, which usually include the CostBenefit Analysis (CBA) as a general method for the evaluation. This methodology is based on
the calculation of the social cost of the project, from the comparison of the flows of costs and
social benefits that occur at different points in time and are discounted at a rate that reflects the
opportunity cost of postponing consumption, called Social Discount Rate (SDR).
This leads us to a fundamental question: Will the standard tools of economic theory
designed for general PIP, be appropriate to assess PIP for Conservation and Ecosystem
Services Provision? Throughout the paper we argue that the large proportion of externalities, the
irreversible effects and the time horizon resulting from the nature of the services provided,
threaten the validity of the basic assumptions underlying the CBA. In particular, those supporting
the choice of a SDR according to market prices, because the nature of the effects of such
projects would require the incorporation of additional ethical criteria. It is in this context that it is
imperative a thorough review of the literature and, based on these findings, the introduction of
the necessary changes in the estimation of the CBA in this type of projects (Dasgupta, 2008;
Weitzman, 2009).
Thus, the objective of this study is to estimate a SDR suitable for so-called PIP for
Conservation and Provision of Ecosystem Services. While there are different approaches to
incorporate environmental criteria in the evaluation of projects, we will focus the discussion on
the incorporation of these dimensions through the choice of the SDR, carrying out rigorous
systematization of the various methodologies developed for empirical estimation and conceptual
approaches that support them. A more complex analysis of how to incorporate the valuation of
environmental benefits and costs in the CBA or approximations outside the scope of the
neoclassical paradigm are beyond the scope of this paper (Georgescu-Roegen, 1972; Boulding,
1972).
The report is divided into four sections, besides this introduction. The second section
presents the literature review; the definition of the type of project in question, and its
peculiarities; Ramsey formula is proposed, and a rigorous systematization of empirical
estimation methods used for quantification of SDR internationally is exposed; section 3 details
the data and the methodology used for this study. Section four presents the estimation results
and section five concludes.
2
2. Literature Review
2.1.
Ecosystem Services
In the literature the set of social, economic and cultural benefits (such as recreation and
tourism) that positively affect human well-being, which are derived from the ecological functions
an ecosystem performs are called ecosystem services; here defined as the functional unit in
which dynamically interact plant, animal and micro-organism communities and their non-living
environment (del Milenio, 2005). Thus, such services should be understood as a "theoretical
construct" that links the (intrinsic) value of biodiversity and human well-being; which are usually
exclusive and certain actions that humans execute to increase the supply of one of them, lead to
its degradation.
To illustrate this idea, imagine the case of a forest ecosystem, where agricultural
activities face the regulation for forest conservation. A growing demand for food -by the increase
of the population or its purchasing power- can lead to the intensification of land use in
agricultural activities (expansion of the agricultural frontier) and, therefore, the destruction of
forest. This means the loss of ecosystem services, increased incidence of droughts and floods;
as well as the deterioration of water quality by increasing sediment loads in rivers, among
others. The final choice regarding the use of land will be determined by contrasting the benefits
to be derived from each of the alternatives, choosing, most likely, the most profitable. The agent
does this by taking into consideration the costs and benefits of each process under way from a
private perspective. At this point it is worth considering the rights of each agent to make use of
and benefit from ecosystem services, which in the economic jargon are called property rights.
Within this vast literature, ecosystem services can be classified as public goods because
they share these basic characteristics that define them: non-rival in consumption (consumption
does not affect consumption of other individuals) and non-exclusive (agent´s consumption
cannot be excluded). There are no markets for this type of goods, individuals can enjoy them
without paying for them (existence of "free riders"), and therefore, they do not exhibit a market
price to guide the actions of agents to efficiently allocate towards an optimal consumption. This
ultimately implies that they do not represent a cost to the agent and there is an overuse and
degradation of the environment. Naturally, this impacts on the welfare of others, who did not
participate in the choice made by the agent. These consequences are called in the literature
"externalities." From a wider perspective, as seems predictable, this omission could be extended
in the temporal dimension. For example, decisions of the agent in the present, do not take into
account the effects on the future welfare of others. He will seek returns in the short term at the
expense of long-term, resulting in negative inter-temporal externalities. This overall problem is
alerted by various studies (del Milenio, 2005).
Faced with the problems presented, multiple policy instruments have been established,
transiting from binding environmental agreements at the international level -such as the
Convention on Biological Diversity in 2010- to setting up funding mechanisms for the
conservation at the interior of countries. Within the latter, initiatives involving public resources
are still being explored through proposals for public investment projects (PIP) that provide these
kind of services.
On this last point, several questions arise, mainly because projects involving effects on
ecosystem services have particular properties which hinder the application of standard welfare
analysis, used as the basis for the evaluation of public projects: i) global consequences, ii) longterm and irreversible impacts, iii) uncertainty, iv) not marginal or linear changes; v)
3
intergenerational questions (Kumar, 2010). Public projects are subjected to a complex system of
public investment evaluation, being analyzed in standardized procedures, such as Cost-Benefit
Analysis (CBA), including the discounting of the future.
Such projects have strong ethical issues related to intergenerational equity, ethical
considerations arise from the fact that its effects (benefits or costs) are spread over a wider
period than the corresponding generation; and also because the behavior of resource
depredation or environmental degradation of the existing generation can reduce not only the
welfare of future generations but also their livelihood, having effects on basic ecosystem
services that support life, such as water, natural flood protection and climate regulation. It is here
that the role of the SDR is crucial.
At this point the question arises about whether the rights and preferences of future
generations should be or not to be incorporated into the actual "decision processes", and how
would it be feasible to do so, in a situation where inevitably the present generation preferences
dominate. Because of these concerns, authors such as Stavins (2004) suggest that quantitative
factors should not dominate the qualitative factors in the evaluation of projects and policies;
while Tietenberg & Lewis (2011) recommend that this methodology be used in conjunction with
other available information.
Given the importance of the SDR in the decision process, much of the research agenda
on environmental issues has revolved around this topic (Ramsey, 1928; Feldstein, 1964;
Baumol, 1968; among others). In recent years, the debate gained new impetus due to the
vigorous application of CBA in the economics of climate change (Nordhaus, 1994, 2007, Stern,
2006 and Weitzman, 2007). In this regard, an important milestone was the publication of The
Economics of Climate Change: Stern Review (2006); because it gave rise to a series of
revisions, and criticism regarding the choice of the SDR by Stern. Here, we take advantage of
the ideas presented in the debate on the proper choice of the SDR under the economics of
climate change frame (Nordhaus, 1994, 2007, Stern, 2006; Weitzman, 2007), to be transferable
in many cases, to the economic analysis of ecosystem services, and the estimation of the
appropriate SDR for such projects (Kumar, 2010).
2.2.
Cost Benefit Analysis
The CBA is a fundamental tool in project evaluation and environmental economics. As
anticipated, this methodology is based on the estimation of the net benefit of a project, from the
comparison of the flows of social costs and benefits; that since they occur at different points in
time need to be discounted at a rate that reflects the opportunity cost of postponing
consumption, called Social Discount Rate (SDR). The "principle of compensation" proposed by
Kaldor-Hicks (Hicks, 1939) is used as a normative criterion; thus, a project or policy is
categorized as desirable if it represents a "potential improvement in terms of Pareto." That is, if
there is a change in welfare (or total utility) in which the winners can "potentially" compensate
the losers, no matter how benefits and costs are distributed or if the "potential" compensation
actually takes place (Arrow, 1996).
In practice, the flows of benefits and costs occur at different moments in time. In order to
deal with this matter, project evaluation uses the Net Present Value of Benefits (NPVB) criteria,
which through a discount process allows the evaluation at a certain time, of costs and benefits
that take place at different times, so that the project is desirable when the NPVB is positive.
NPVB formulation is:
4
=∑
{(
−
)(1 +
) }
(1)
Where
are the benefits of the project; are the costs of the project, SDR is the Social
) is known as the discount factor. The SDR converts each
Discount Rate, and (1 +
monetary unit in the future into an equivalent present monetary unit, and, in general, it is
positive. This is because the resources invested today can be transformed through investment in
human or physical capital in more resources in the future and therefore, a positive amount
should be offered to an agent in order to persuade him to postpone current consumption.
If we evaluate the mathematical formulation of this criterion, it appears that small
differences in SDR can mean big differences in the results of the CBA, especially over long
horizons. High discount rates tend to favor projects whose benefits are realized in the short term;
while lower discount rates tend to favor projects with long-term benefits. Therefore, it is not
difficult to see that the SDR is presented as one of the most important parameters in the CBA.5
Although the literature has presented two traditional approaches: the descriptive one,
based on the equilibrium of saving and investment curves in the financial market (current rates);
and the prescriptive one, based on ethical considerations incorporated in the Ramsey formula;
recently, there has been some consensus on some principles that could guide the choice of
SDR for projects regarding environmental concerns (Arrow, Cropper, Gollier, Groom, Heal,
Newell, Nordhaus, Pindyck, Pizer, Portney, Sterner, Tol and Weitzman , 2013).6 Experts have
agreed on the usefulness of the Ramsey formula (base of the prescriptive approach) as a
framework for choosing the SDR for long-term projects; however, there is still certain questioning
about whether it would be feasible to include the SDR in the CBA. These questionings arise
because of the subjective nature of the choice of parameters which can ultimately be based on
purely political considerations (Nordhaus, 2007). This does not invalidate its relevance as an
analytical tool and therefore is proposed as an analytical framework.
Both approaches have different starting point questions that involve positive and
normative issues; however, one of the main points of difference is the way in which they allow
the compensation between generations to take place. While the descriptive approach assumes
there is compensation between generations; the prescriptive one, considers it is limited (Arrow,
1996).7 Additionally, the latter supposes that the market rates represent the equilibrium of a
competitive market, but not taking into account other issues involved, such as inter-temporal
ones. Furthermore, other authors report that this balance reflects only the willingness of agents
to exchange consumption within the temporal horizon of their own life and not between
generations. From this logic, they are different things: individual preferences-those performed on
saving and investing- and collective preferences -more related to public investment or
5
Arrow (1995) mentions that when the very long time is involved, the social choice of a discount rate powerfully
affects the net present value of alternative policies, and thus the policy recommendations that emerge.
6
The descriptive or positive approach postulates that the SDR should be based on the Social Opportunity
Cost of capital (SOC), defined as the value of the best alternative investments in public projects (Baumol,
1968; Harberger, 1973); while the prescriptive or normative approach, states that the SDR should be
based on the Temporal Social Preference Rate (TSPR) and incorporate ethical criteria of intergenerational equity in selecting the rate (Sen, 1961; Feldstein, 1964). The terms SOC and TSPR are
those with which the literature refers to the SDR derived from each approach respectively. Traditional
formulations for discussion of both approaches are presented using as a starting point: i) to the
prescriptive approach, the Ramsey formula, which considers social values as parameters; and ii) for the
descriptive approach, the market equilibrium between savings and investment curves, with some
adjustments to incorporate market imperfections.
7
According to Arrow (1996), the descriptive approach assumes compensation from one generation to another for any
loss of environmental amenities, implicitly leaving unanswered whether compensation is likely to occur.
5
consumption of future generations, also seen as public goods (Sen, 1961; Feldstein, 1964).
Thus, the approach based on current interest rates ignore the fact that individuals have finite
lives and assumes that individual temporal preferences would be equivalent to social temporal
preferences involving a trade-off between the welfare of future generations and present.
The prescriptive approach postulates that the SDR would reflect the way in which society
is willing to exchange consumption between generations, and therefore can be derived from
ethical considerations.8 This approach will guide the interpretation of the results of this study.
The SDR estimated in this way is called Social Time Preference Rate (STPR). The general
formula applied to estimate it is based on the Ramsey formula (1928) and consists of:9
(2)
Where,  is the rate of pure temporal discounting and measures the importance given to the
utility today vs. tomorrow; in the literature, this term is called impatience discount or myopia. The
parameter  is the growth rate of per capita consumption; and is the absolute value of the
elasticity of marginal utility of consumption, which measures the relative effect of a change in
welfare on consumption. Some authors include within this last parameter the relative risk
aversion and the inequality aversion (Gollier, 2002, among others).
Now, although the formula intended to reflect how society values the individuals’
consumption in different points in time; and therefore these parameters represent social or
ethical values associated to a prescriptive approach, the conceptual richness of the Ramsey
formula to capture intergenerational issues has opened the way for it to be widely adopted in
studies of environmental projects (with long-term consequences). The main difference between
both approaches lies in the way they estimate the parameters of interest. The prescriptive
approach bases the estimation of these parameters on i) specific ethical criteria, ii) inferred
criteria from policy decisions or iii) criteria estimated by methods of revealed preferences. While
the descriptive approach base the estimation in the elections or current behaviors revealed in
the financial market.10
8
Dasgupta (2005) performed an extensive discussion of the ethical aspects of the Ramsey formula.
Under a utility function with constant risk aversion (CRRA), the formalization of the problem described is:
U (C) = (C ^ ((1-ε)) -1) / (1-ε). Where C is per capita consumption.
10
Within this line of argument, the main debates have focused around the magnitude of the parameters
used. Some authors propose that the rate of pure temporal discount should be different from zero (   0 )
to incorporate the impatience or myopia of agents. While, from a position known as egalitarian, people
question that this rate should not be positive considering it as "ethically indefensible" (Cline, 1992;
Ramsey, 1928). This position argues that from the social planner´s point of view it should be equal to zero
to reflect the equal weight or value assigned to the current and future generations. Within the prescriptive
perspective, some authors have used ethical arguments to defend parameters policy of  near zero,
which only reflect the possibility of extinction of the human race (Stern, 2006). This approach has been
strongly criticized by incorporating subjectivity and is the focus of the discussion generated around the
Stern Review. A second option has been used to infer the parameters from the choices made by society
through public policies (Groom & Maddison, 2012; Tol, 2010). Finally, other authors base their methods
on revealed preferences; though there is some skepticism about its validity given the abstract nature of
the terms used, such as the rate of pure temporal preference, among others. Within the descriptive
approach, the parameter has been estimated from the observed values in the financial market of the
component of risk aversion. The concerns on this type of approach postulate that the estimated rates
reflect only the preferences of the population related to the financial markets before any trade off between
9
6
2.3.
Types of discounts
There are different methods to estimate the SDR empirically which incorporate ethical
criteria and can be extended to projects for conservation and provision of ecosystem services.
The most used discount rates are the exponential, gamma and hyperbolic.
2.3.1. Exponential discount factor
(4)
The exponential discount allows bringing future flows to present value through a constant
discount rate. It is basically the type of discount which has traditionally been used to calculate
the NPVB presented in equation (1). The fact of using a constant rate in the exponential
discounting implies that the marginal rate of substitution of consumption between two periods
depends only on the distance between the moments considered. This type of discount has the
advantage of being dynamically consistent, i.e., as time passes, the revealed preferences
confirm a priori stated preferences (Frederick, Loewenstein & O'Donoghue, 2002). Since the
presentation of the discount model of utility by Samuelson (1937), this discount type has been
used in various fields. Its simplicity has been very attractive and has contributed to its
dissemination even though there are some limitations, and that in practice rarely, discount rates
are constant over time. It has been used in the evaluation of public projects to weigh costs and
benefits generated by a public project on a given time horizon, with a discount rate, constant and
positive. However, the empirical evidence rejects this type of discount. Thus, applied studies
favor the hypothesis that individuals do not have this pattern of discount, but use a declining
discount rate or a discount with a hyperbolic behavior.
2.3.2. Gamma discount factor
(5)
The Gamma discount type is a generalization of exponential discounting. In other words
we can say that the exponential discounting is a special case of Gamma discount. Within the
literature, the "Gamma Discount" refers to the methodology proposed by Weitzman (2001) to
estimate SDRs, where individuals have discount patterns that are consistent with exponential
discounting, but the aggregation of their subjectivities (discount function) is performed by a
specific function, called Gamma. It hypothesizes that what should be averaged, are discount
functions, not discount rates, and that they should be aggregated via a Gamma probability
distribution. This way of adding the individual rates results in a profile of declining discount rates
over time.
2.3.3. Hyperbolic discount factor
intergenerational consumption. Following this line, Nordhaus (1994, 2007) suggests that 
be chosen so that the SDR approximates the market interest rate.
and 
can
7
(6)
The hyperbolic discounting is a decreasing one, as presented by Dasgupta & Maskin
(2005). The fact that it is decreasing implies that when the realization of the benefit is far away in
time, the individual is willing to wait for a larger reward later; but when the horizon is shorter the
individual becomes impatient and cannot wait. It is based on the empirical observation that
people discount the future in a hyperbolic manner; nearby flows are discounted at higher rates;
and the farthest at lower annual rates (Edwards, 2002). Hyperbolic discounting makes the
penalization of the future to tend asymptotically to zero over time. This is very important when
analyzing projects that have implications over several centuries (Laibson, 1996, Loewenstein &
Prelec, 1992; Sterner, 1994; Henderson & Bateman, 1995; Frederick et al., 2002).
The problem with this type of formulation is that it gives rise to inter-temporal
inconsistencies. If an individual systematically considered a discount rate of, say, 10% for the
first year and 3% for all of the following; when he arrives at the second or third year, he would
have to revise its rate of 3% and raise it to 10%. As Strotz (1956) points out, the time
inconsistency arises at the individual level, when flows are not discounted exponentially.
2.3.4. Estimation methods
The general consensus is that the SDR for projects for conservation and provision of
ecosystem services should be decreasing over time (Arrow et al., 2013). By incorporating this
into the Ramsey formula, Eq. (2); is the estimation (or choice) of the parameters
and
modeling the growth rate of per capita consumption, which will result in decreasing or constant
SDR. The most used way in order to obtain decreasing SDR is through the inclusion of
uncertainty about the temporal structure of the SDR. In the literature, there is a dividing line that
comes from how it is estimated, if necessary, the impact of uncertainty. This distinction agrees
with frontier developments in the empirical literature. Arrow et al. (2013) argues that if the shocks
to consumption growth rate are positively correlated over time, or with unknown mean and
variance, the consideration of uncertainty in the estimate of the SDR leads to declining
estimates over time (Gollier, 2008, 2012).
Arrow et al. (2013) distinguishes, within this section, two approaches to tackle the
estimation exercise in case it leads to decreasing rates over time. On the one hand, the
extended Ramsey formula is used; this explicitly includes a term "caution" to the general
formulation of this expression. While the other approach used is the one of the Expected Net
Present Value (ENPV) developed by Weitzman (2001, 2007), which computes the ENPV with a
"discount rate" effective equivalent decreasing, incorporating the probability distribution of the
discount rate over time. Within this same line; others alternatively employ a reduced form
approach which estimates the discount rate using historical data on interest rates (Newell &
Pizer, 2003; Groom et al., 2007; Hepburn et al., 2006). Recent Developments in Gollier &
Weitzman (2010) seek to reconcile both approaches.
Regarding the empirical estimation, Arrow et al. (2013) indicates that if there are
disagreements between the ethical preferences of individuals -rather than regarding the future of
the economy- it is not appropriate to use these disagreements to set the probabilities of
occurrence of the SDR. Since uncertainty actually reflects the heterogeneity of normative
judgments; an approach such as the one used by Weitzman (2001) could be used to derive
instant discount effective decreasing rates over time.
8
On the contrary, if the uncertainty is defined on the states of the economy with persistent
shocks, a declining discount rate is derived over time. There are two approaches that can be
used to estimate this rate (Arrow et al., 2013): (i) the extended Ramsey formula which involves
choosing the rate of social preference and the elasticity of the marginal utility of consumption,
and modeling, numerically or analytically, the generating process of the growth rate of per capita
consumption, or (ii) reduced form models based on market interest rates.11
On one hand, the use of the extended Ramsey formula implies accepting assumptions
that may not be correlated with reality and be a bad abstraction of it. This formulation has been
recently taken up by Gollier (2002) and is formally expressed as:
(3)
The last term in equation (3) reflects the effect of "caution" that is added to the Ramsey
formula presented in equation (2). This term reduces the SDR, causing the social planner to
save more at present. Intuitively, if shocks are correlated over time, uncertainty would make
future consumption more risky and, therefore, this effect would have a greater impact.
However, this approach assumes that the stochastic nature of consumption growth can
be properly characterized by econometric models based on historical data, which goes against
the widespread literature known as consumption-based asset pricing. Faced with this statement,
Weitzman (2004, 2007) and Gollier (2008) argue that uncertainty about the average growth rate
of consumption is fairly subjective, rather than based on historical data. Therefore, its average
and volatility should be treated as unknown.12 Arrow et al., (2013) finally states that the Ramsey
formula does not easily produce a decreasing pattern over time of these discount rates.
Moreover, the approach of the Expected Net Present Value (ENPV) is considered more
manageable empirically to model uncertainty. Within this approach, there are two different ways
in which uncertainty is modeled; one of them i) on the heterogeneity of value judgments and the
other ii) on the different predictions about reality.
Within the first approximation, the main exponent is Weitzman (2001), which argues that
the different views about the future are only superficial in relation to the different normative
judgments regarding intergenerational justice that may be involved. Thus, the variety of opinions
reflects heterogeneity in preferences rather than uncertainty about the economy; and this is the
basis for declining discount rates. Uncertainty is modeled by the Gamma Discount methodology.
Recently this methodology has been exposed to a series of regional innovation. For example,
Almansa (2006) complements this empirical estimation exercise with the implementation of the
Delphi technique, which allows, through a repetition of surveys or iteration, a feedback of results
11
On the one hand, the extended Ramsey formula mathematically generates discount rates that decrease over time.
Going back to the seminal works of Mankiw (1981), uncertainty in relation to per capita consumption may be
incorporated into the Ramsey formula by adding a term of caution.
One of the most widely used ways to estimate this effect is to model econometrically the growth rate of per capita
consumption in
by a generative process that reproduces an AR (1). In this way,
12
Empirically Weitzman (2004) introduces the Bayesian learning through the addition of a fourth term to the Ramsey
formula, known as the statistic prediction effect. In practice, the planner dissipates the uncertainty regarding
using
the previous observations of .
This assumption derives in effective equivalent discount rates that decrease over time and can even present negative
values.
9
and therefore achieves a lower dispersion of the results, obtained from the opinions of a panel of
experts, in relation to the selection of the SDR.
Within the second approach, Freeman & Groom (2012) argue that it would be
appropriate to combine the responses in order to reduce the prediction error. They find that with
an appropriate method to combine forecasts, discount rates will be more declining than those
estimated by the Gamma approach. Newell & Pizer (2003) used a similar approach in which
discount rate shocks are correlated in time and lead to equivalent effective discount rates also
decreasing.13
2.4.
Gamma discount and Delphi methodology
Projects for conservation and provision of ecosystem services involve important ethical
considerations, about which there are large disagreements based on different ethical
preferences of people. It is therefore that Weitzman (2001) shows rigorous foundation to justify
the use of lower discount rates that decline over time. To model declining discount rates the
alternatives are, to base on the extended Ramsey formula or, on the Expected Net Present
Value (ENPV) approach.
The alternatives, based on the extended Ramsey formula to reproduce declining patterns
over time, although they represent approaches that improve our understanding of the nature of
the problem, the assumptions that support them, as was anticipated, could not be correlated
with reality and could lead to the impossibility to explain widely known phenomena in the
financial markets -as the equity premium puzzle literature-. In particular, assuming that the
stochastic nature of consumption growth can be properly characterized by econometric models
based on historical data seems to be a very strong assumption. In line with this, Arrow et al.
(2013) argues that the Ramsey formula does not easily produce a declining pattern over time for
discount rates, being the ENPV approach easier to address.
Consequently, and following Arrow et al. (2013), it is not appropriate in this scenario to
use disagreements to set the probabilities of occurrence of the SDR. These differences are only
superficial in relation to different normative judgments of intergenerational justice that may be
involved. Thus, the different opinions reflect heterogeneity in preferences rather than uncertainty
about the economy and this is the basis for declining discount rates. Since uncertainty actually
reflects the heterogeneity of normative judgments, it would be appropriate to use an approach
like the one used in Weitzman (2001) to derive declining discount rates over time.
The Delphi methodology in this context allows a greater degree of consensus to be
achieved regarding the appropriate SDR to use for this type of projects. The above methodology
13
Among other approaches are those that not only correct the SDR, but also involve other changes to the
CBA (e.g. estimation of the cost and benefits of the project). For example, some proposed to use different
discount rates for tangible (e.g. manufacturing) and intangible (e.g. ecosystem services) in a single
application of CBA, being lower the fees in the second case than in the first (Almansa, 2006; Almansa and
Calatrava, 2007). Thus, the SDR estimation can be performed by the techniques discussed above.
Another approach, following the suggestions of Krutilla and Fischer (1975), attempts to incorporate the
increased value of environmental goods in time based on its growing scarcity. Examples of this approach
to applied studies are Tol (1994), Rabl (1996), Hasselmann et al. (1997) and Hasselmann (1999).
Finally, another alternative that has been used in the case of intergenerational discounting is applied by
Fearnside (2002), Padilla (2001); Padilla & Pascual (2002) and Sumaila & Walters (2005), which involves
designing different mechanisms to include future generations in the CBA.
10
consists in a repeated survey which allows feedback of results; and often generate greater
consensus among experts about the appropriate rate to be used. Precisely this feature is
formulated as the main advantage, since it also allows the contribution of specialists from
different areas, a key point since the phenomenon under study requires multidimensional
analysis. This type of technique is widely recommended in situations involving ethical and moral
considerations, as well as economic or technical issues (Linstone & Turoff, 2002; and Landeta,
1999).
Regarding the validity of the results, the empirical literature has shown strong evidence in
favor of this type of method. Salazar and Sayadi (2006) show that it provides more accurate
predictions than alternative econometric methods; thus, the subjective judgment of the experts
becomes not only desirable but also important information for forecasting under uncertainty.
Also, applied studies report that the results from groups are more robust than those arising from
individual opinions. In other words, we can say that the Delphi technique provides consensus
information from experts in this area of study to decision makers in the social sciences (Linstone
& Turoff, 2002).
3. Methodology and Data
In this study we adapt the methodology proposed by Weitzman (2001) to estimate, based
on the opinion of experts, the appropriate Social Discount Rate (SDR) to apply in the CBA of
environmental projects. A survey is administered so as to document the experts’ opinion
regarding the different dimensions associated to the election of a SDR.
Following Almansa (2006), we implement the Delphi methodology, which through
successive rounds of surveys and the provision of a feedback of the previous results to the
participants, allows obtaining a greater degree of consensus on the estimation of the SDR.
3.1.
The social discount rate
The model proposed by Weitzman (2001) assumes that each of the economic agents
surveyed discounts the net benefit in time ( ), with an exponential discount rate , fixed in
time but uncertain. In the model, differs naturally among individuals due to their different value
judgments on basic considerations in the interpretation of welfare theory, such as the role of the
government or the ethical foundations of intergenerational discount.
The expected net present value of the net benefits of a project would be equivalent to:
(7)
Where A(t) represents the weight that is used to add the temporal evaluation of agents,
known as discount factor. Z(t) represents the net benefit of year t. The term
is called
“discount factor”, though in this case, it would actually be the expected value of such factor.
Without loss of generality, for the purpose of simplifying calculation, Weitzman (2001)
introduces two key assumptions: i) the individual time-evaluation aggregation weights take the
traditional exponential form and ii) the empirically observed discount rate values are distributed
11
as the realizations of a random variable x, whose probability density function is of the Gamma
form. These assumptions are introduced in the empirical estimation in the following way:
In case we consider the discount factor for a constant discount rate, it can be expressed
in the following way
. Therefore, the aggregated weights of individuals regarding the
temporal evaluation they do could follow the traditional exponential form:
(8)
This approach is coherent with the maximization of utility in the case of a logarithmic
utility function (Gollier & Weitzman, 2010) and implies that individuals choose a constant
discount rate, but the function acquires an exponential form.
The variable xj is a random variable whose probability density function f(x), defined for all
positive x, is of the Gamma form:
(9)
Where
and are positive parameters which should be estimated based on the data
collected through the survey.
Based on these key assumptions, which impose little restrictions and imply almost no
loss of generality, the estimation of the SDR reduces to the estimation of the parameters of a
probability density function. Since the required data is collected through a survey administered
to experts, the problem is relatively easy to grasp. We proceed to present the way in which the
estimation is done:
Since A(t) represents the time evaluation aggregation weights of agents, it can be
expressed as the effective discount function for time t and rewritten as the following:
(10)
In this way, the estimation must be performed on the weighted average of the probability
of distribution of the discount functions, not on the weighted average of the probability of the
discount rates. Therefore, it is not necessary to estimate the distribution of the discount rates,
the information regarding the value judgments is enough. This is really convenient, since the
information needed can be captured through a survey.
The corresponding effective instant discount rate for time t is defined as:
(11)
Considering a stationary probability distribution of ;
time (Weitzman, 2001).
takes a decreasing pattern in
Based on the assumption of the Gamma distribution, presented in equation (9), effective
discount function, presented in equation (10), can be rewritten as:
12
(12)
Or, in a different way:
(13)
The mean and variance in (8) are defined in the usual way:
(14)
(15)
Since the Gamma distribution presents the following formulas for the first two moments of
the distribution:
(16)
(17)
Considering that and
have a direct economic interpretation, while
we invert the equations and obtain the following expressions:
and
do not,
(18)
(19)
Replacing (16) and (17) in (13), the discount function A(t) can be rewritten as:
(20)
From this equation, Weitzman (2001) shows that with the Gamma distribution, if the
uncertainty regarding is described by a Gamma approximation with mean and variance
,
the effective instant discount rate (11) can be expressed in the following way:
(21)
This equation describes an effective discount rate that has the mean value in moment
t=0 and decreases monotonically towards cero as time passes.
The equivalent effective constant discount rate would be:
(22)
13
Substituting the discount function A(t) in (22) we obtain:
(23)
Therefore, based on the mean and the standard deviation
of the experts’ opinions
regarding the SDR, an equivalent effective discount rate can be estimated for each time horizon
and a constant equivalent effective discount rate can also be estimated for the whole
period under study .
3.2.
Data collection
The main source of information for this study was recollected ad-hoc through a Delphi
survey regarding the estimation of the SDR for Public Investment Proyects (PIP) oriented to
preserve and provide ecosystem services. The instrument proposed by Almansa & Calatrava
(2007) was adapted to the Peruvian case, and include key questions which exceed the original
dimensions captured by those proposed by Weitzman (2001), with the aim of improving the way
the preferences are formed.
In addition to asking for the appropriate SDR corresponding to different intervals of time,
certain questions where also included in the instrument, such as i) how relevant the CBA is to
evaluate projects, ii) the implications of the time period when selecting a SDR, iii) the
implications of the characteristics of the environmental service when selecting the SDR and iv)
the use of different SDR for tangible and intangible goods. Interviewers were asked to respond
whether they agree or disagree on a scale from -2 to 2, where -2 means totally disagree and 2
totally agree, and 0 represents a neutral position. The inclusion of these questions provided
evidence regarding the heterogeneity of experts’ judgments, a key assumption in the chosen
methodology.14
To ensure the validity of the results, the methodology requires the instrument to be
applied to a panel or “experts” or “specialist” preserving the heterogeneity of the participants
(Listone & Turoff, 2002). The definition used of “expert” is a wide one –similar to the one applied
in Weitzman (2001) seminal work, and in similar studies in the region (Edwards, 2002 and
Restrepo, 2008)- in which a person is considered “expert” when he has the knowledge or
expertise which allows him to objectify the answers provided in a reasonable and consistent way
(Weitzman, 2001). This type of study has no precedents in Peru therefore there is no list or
registry used before. For its construction, we used as a first criteria, the degree of knowledge of
the subject and as a second criteria, the experience.
The first group includes: (i) Peruvian people with postgraduate studies or teachers of the
subject in a Peruvian university or at a foreign country and (ii) those that perform environmental
research at prestigious research centers. Peruvian universities were recorded using the
University Directory 2013 of the National Assembly of Rectors (ANR); filtering by those
institutions that incorporate masters, doctoral or related institutions belonging to the economics
of natural resources or environmental issues. The official web sites were thoroughly examined to
access listings of students and teachers specialized in the subject. In the case of foreign
universities, due to the difficulties to find experts, we used a type of non-probability sampling
called “snowball sampling”, on the assumption that experts have at least one ‘social network’ in
14
The instruments are available upon request to the authors.
14
which is possible to contact them, key experts (doctoral students who had just returned to Peru)
were asked to nominate other people in the population that would have the same probability of
being selected (Goodman, 1961). Finally, to contact researchers, we used as a framework a list
of researchers affiliated to official websites of the institutions associated to the Consortium for
Economic and Social Research (CIES).
The second group includes: (i) government officials and multilateral agencies involved in
environmental issues and (ii) specialized consulting staff. For public officials, Specialist, Senior
Staff and Directors of the Ministry of Environment (MINAM) related to the topic were included.
Additionally the National Environmental Fund (FONAM) and Supervisor Organisms
(OSINERGMIN OSIPTEL) were included. Additionally, within the international organizations
included were the Food and Agriculture Organization of the United Nations (FAO) and the
Friends of Nature Foundation. Regarding the specialized consultant agencies, the Registry or
Authorized Agencies to perform environmental impact studies by the Ministry of Energy and
Mines (see Ministerial Resolution No. 580-98-EM/VMM); however, the lists of experts were not
possible to obtain in many cases.
As a final product of this first stage, a list with information of 253 people who could
potentially be included as experts was constructed. The distribution by category can be seen in
the first column of table 1, where university students and teachers represent almost 70% of the
total. As the information was obtained in official sites at a certain moment in time, some
students, teachers, specialist or researchers could have changed their contact information by
the time the interview took place. This problem is even worse when the e-mail provided was the
institutional one. Once the first interview was performed, 54 registries were eliminated from the
list, because of the problem described, (42), because they were on a trip (7) and because the
rejected to participate (6). As can be observed, the main cause was the impossibility to reach the
person, mainly in the university category, 30 of 42 cases. After a depuration, registries for 199
specialists were obtained and classified by degree of knowledge and expertise, higher or lower
(university students); obtaining a list of 114 specialist of the first group.
The process of collecting information for the first round of the Delphi survey had two
stages; the first one was executed between November 26 and December 15, 2013; while the
second one between January 15 and February 25. For filling out of the survey, the Survey
Monkey platform was applied, creating a custom link by specialist. While this brought a number
of minor issues, such as more than one answer per link; in the first round there were three cases
and in the second one, 7. The survey was introduced in a presentation e-mail, accompanied by
a Letter of Introduction on behalf of the General Directorate of Investment Policy (DGPI) of the
MEF and an Information Booklet that elaborates on the specifics of the PIP for Conservation and
Provision of Ecosystem Services (specifically, those related to afforestation and reforestation)
and exposes the debate over the choice of an appropriate SDR for them. The latter is presented
as a key instrument in these types of studies; in which the subject can be a bit dark, even for
connoisseurs. Thus, we sought to standardize the concepts and interpretations.
The second step was done with the aim of improving the answer rate, which up to that
moment was around 20%, below the usual answer rate for this type of studies; that varies
between 38% and 45% (Edwards, 2002; Restrepo, 2008). Thus, follow-ups were conducted to
reinforce the invitation to participate of the study through a phone call or, forwarding the
invitation electronically to those who had not filled the information yet. This process was
repeated at least three times. Finally the answer rate rose to 35% for all the specialists and to
39% for the senior specialists, equivalent to 70 and 45 responses respectively, which was
15
considered appropriate, since the introduction of the Delphi methodology reduced the sample
size requirement considerably.
Table 1: Number of specialists and senior specialists by category
University
181
Research Centers
39
Governmental Agencies 19
Consulting Agencies
14
Total
253
Source: Own estimation
2
2
2
1
7
30
6
2
3
42
3
2
1
0
6
N
146
29
14
10
199
N
Responds
Doesn’t
respond
Answer
rate
N
2° List (higher)
Responds
Doesn’t
respond
Answer
rate
Category
2° List
Absent
Unreacha
ble
Rejection
1° List
47 99 32%
13 16 45%
7
7 50%
3
7 30%
70 129 35%
61
29
14
10
114
22 39 36%
13 16 45%
7 7 50%
3 7 30%
45 69 39%
Note: Since categories can overlap, the first source is taken into account, and no
information is duplicated.
Aimed at the second round of the Delphi survey, a question regarding the disposition to
participate in the second process was included. Of the 70 specialist that completed the
information in the first round, 7 showed their rejection to participate in the second round, while 4
did not answer. Finally, of the 63 surveys sent, 34 were returned (54% answer rate).This amount
is in line with the recommendations for this type of methodologies, and similar to the figure
obtained by Almansa (2006).15
Regarding the degree of knowledge we observed and average of auto-reported
knowledge of about 7 points, with a lower level for research centers. This finding, though contra
intuitive, could be related to the fact that senior researchers are also teachers, and may be
considered in the latter category.
Table 2: Number of answers – 2nd round
15
Category
N
Answer
rate
Evaluatio
n
Climate
chante
Evaluatio
n
Climate
Change
Do Answer
No
Total
Yes
Response
University
Research Centers
Governmental Agencies
Consulting Agencies
42
12
6
3
21
8
3
2
21
4
3
1
50%
67%
50%
67%
7.48
5.55
5.43
6.67
8.00
4.14
6.33
7.50
7.85
5.29
7.33
9.00
Total
63
Source: Own estimation.
34
29
54%
6.89 6.97
7.18
5.82
6.86
8.33
6.97 7.31
Research samples recommended are over 17 observations (Dalkey, 1969).
16
4. Results
In this section we present the estimation of the SDR to be used for the PIP. The
approach used for the estimation is called Gamma. Additionally, to contextualize, the opinion of
experts regarding the environmental discount are presented.
Before turning to the results of the survey, we analyzed whether the effort of performing a
second round has had results to make it worth it. Indicators regarding the degree of consensus
and stability that follow will provide the answer to this question.
4.1.
Degree of consensus
In order to study whether the second round achieved the basic objective followed, such
as an increase in the consensus in the answers of experts, we proceed to analyze the variability
of each question in each of the rounds, in such a way that if the variability decreased, we will
have reached a greater consensus. To analyze this aspect, only the answers of those that
participated in both rounds were taken into account. In concrete, if the standard deviation of a
question is lower in the second round (σ2) than in the first round (σ1), the [(σ1)- (σ2)] would be
positive and would suggest a greater consensus has been achieved. The results are presented
in Table 3.
Table 3. Variability in the degree of dispersion
Standard
Changes in
Standard
Deviation
dispersion
Deviation1/
(σ1) - (σ2)
1a
2°
1a
2°
Round
Round
Round
Round
(σ1)
(σ2)
(σ1)
(σ2)
SDR intangible
1.293
0.826
0.467
1.362
0.826
SDR variable
0.974
0.899
0.075
1.182
0.899
SDR type of good
0.673
0.511
0.162
0.748
0.511
SDR horizon
1.227
0.961
0.266
1.278
0.961
SDR minor
1.060
0.925
0.135
1.198
0.925
SDR few decades
0.985
0.849
0.137
1.040
0.849
CBA appropriate
1.218
1.300
-0.082
1.442
1.300
Inter1-3
1.148
1.248
-0.100
1.324
1.248
Inter3-5
1.399
1.479
-0.080
1.336
1.479
SDR 25-50
1.499
1.416
0.083
1.198
1.416
SDR 50-75
1.485
1.175
0.310
1.699
1.175
SDR more than
2.108
1.262
0.846
2.686
1.262
75
Average
1.256
1.071
0.185
1.374
1.071
Note: 1/ Only considering those who answered the second round.
Changes in
dispersion
(σ1) - (σ2)*
0.536
0.283
0.237
0.317
0.273
0.191
0.142
0.076
-0.143
-0.219
0.524
1.424
0.303
It can easily be seen that 9 out of twelve answers have gained greater consensus, and
only in three it has decreased. If the whole pane is analyzed, the dispersion reduces
considerably, from 1.256 to 1.071, which represents an increase of the consensus of
approximately 14.46%.
4.2.
Stability
17
In this section, the stability of the answers provided by the experts is addressed by
studying the individual absolute stability, that is, the percentage of experts who have not
modified any of their answers in the second round, and the average number of responses
modified by the panelist. In this methodology, it is desirable that the stability condition is not very
high, as a way to show the effectiveness of the feedback between rounds, proper of the method.
The results obtained in this direction showed all the experts, the 34 who responded the
second round, modified their answers. This yields a low stability index, 0%, indicating that the
panelists reflected as a result of getting the answers for the first round. Thus, of the 12 items
presented in the panel, each panelist, amended in average 4.94 of the responses.
In summary, the second round provided an increase in the consensus and a decrease in
stability, both desirable characteristics for any Delphi study, justifying its application thereof.
4.3.
Qualitative results
Most of the experts surveyed consider that the CBA is appropriate for the evaluation of
public projects, including the PIP. Though this acceptance is not unconditional, as manifested in
their responses consistently, this methodology should ideally be subjected to some modifications
to ensure its relevance and validity. In this line, 88% of the experts believe it is appropriate that
the general SDR would be reconsidered when the temporal horizon of the project encompasses
more than a few decades and 85% of the experts consider the time horizon of the project should
be taken into account for the estimation of the SDR.
In relation to these premises, according to 91% of the respondents, the SDR should use
a variable discount factor instead of a constant one; this would entail a decreasing SDR. And
97% of the experts answered that the SDR should be decreasing and lower than the one for
investment projects in general. This result is associated with the incorporation of sustainability
criteria to the CBA by giving greater weights to the cost and benefits that occur in the long run.
This shows a tendency towards a reconsideration of focus of the discount within the CBA when
the context has intergenerational implications, in line with what academics believe.
Another important point in the statements provided by the specialists is the need to
consider the characteristics of the environmental good or service involved in the project when
estimating the SDR; expressed by 91% of the experts. And even 70% of those interviewed state
that if the impacts of the project fall on goods of different features, different SDR be incorporated
into a single evaluation; different SDR for tangible and intangible goods and services. As to the
first attempts to estimate a single SDR, experts do not seem to distinguish between rates that
are in a range from 1% to 3% or 3% to 5%, although the former has greater approval with 77%
versus 60% in the second.
In summary, the answers are in line with the need for adequacy of the framework of CBA,
that although perceived as appropriate, deserves certain adaptations to include in the estimation
of the SDR the time horizon of the project and the characteristics of the goods or services
impacted; allowing the possibility of incorporating different SDR for tangible and intangibles in
the same CBA. As a first approximation towards a point estimate of the SDR, it would have
some inclination towards rates between 1 to 3%.
4.4.
Quantitative results
18
Regarding the quantitative information provided by the specialists, the average discount
rate given by the panel of experts for a time horizon of 25-50 years for the case of PIP for the
provision and conservation of ecosystem services –in particular those provided by forest
ecosystems in reforestation and afforestation projects- is 2.98%. In the case of a time horizon of
50-75 years the mean value is 2.48%. Finally, for a time horizon of more than 75 years the
proposed value has a mean value of 2.12%.
Table 4: SDR for PIP for the provision and conservation of ecosystem Services (%):
Specialists
25- 50 years: 50- 75 years: More than 75years: All the periods
0,030

0,014

(R t)
3,02%
Source: Own estimation.
0,025
0,012
2,39%
0,021
0,012
1,22%
0,026
0,014
1,69%
The observations recollected were aggregated using a Gamma distribution and give as
results values of 3.02%, 2.39% and 1.22% for the SDR for analysis of projects from 25 to 50
years, 50-75 years and over 75 years respectively.
In the case of the senior specialists, the average estimates for the different horizons are
lower. Thus, in the range from 25-50 years, the average value is 3.4%, in the range from 50-75
years the average value is 2.5% and for more than 75 years, 1.9%. Aggregated with a Gamma
distribution, the SDR for the intervals of 25-50 years, 50-75 years and more than 75 years are
3.02%, 2.39% and 1.74%, respectively.
Table 5: SDR for PIP for the provision and conservation of ecosystem services (%):
Senior Specialists
25- 50 years: 50- 75years: More than 75 years: All periods
0,034

0,014

(R t)
3,02%
Source: Own estimation
0,025
0,012
2,39%
0,019
0,012
1,22%
0,028
0,015
1,74%
We have also obtained the results by category: universities, research centers and
agencies (consulting agencies were not considered as only 1 person answered the questions
related to the estimation of SDR). As can be seen in Table 6, the differences in terms of average
SDR are not very large; additionally, estimates of the SDR by the Gamma method differ only in
the case of universities, being similar in the case of research centers and agencies. Thus, for the
evaluation of projects with horizons from 25 to 50 years, 50-75 years and over 75 years,
universities report a SDR of 2.67%, 1.82% and 1.46%; while research centers, 3.19%, 2.06%
and 1.31%; agencies, 3.58%, 2.46% and 1.37% and consultant agencies, 3.37%, 4.26% and
4.15% respectively for all cases.
19
Table 6: SDR for PIP for the provision and conservation of ecosystem services (%):
Categories
25- 50
years:


(Rt)
50- 75
years:
Universities
0,035
0,024
0,017
0,011
2,84%
1,85%
25- 50
years:
0,036
0,005
3,58%
(Rt)
Source: Own estimation


50- 75
years:
More
than 75
years:
0,017
0,008
1,27%
More
than 75
years:
Agencies
0,033
0,033
0,015
0,025
2,46%
1,37%
More
than 75
years:
Research Centers
0,032
0,021
0,015
0,004
0,003
0,005
3,19%
2,06%
1,31%
25- 50
years:
50- 75
years:
More
than 75
years:
Consulting Agencies
0,035
0,045
0,045
0,007
0,007
0,007
3,37%
4,26%
4,15%
25- 50
years:
50- 75
years:
Table 7: SDR for PIP for the provision and conservation of ecosystem services (%):
Categories - Experts
25- 50
years:


(Rt)
50- 75
years:
Universities
0,038
0,027
0,026
0,016
2,67%
1,82%
25- 50
years:
50- 75
years:
More
than 75
years:
0,018
0,008
1,46%
More
than 75
years:
Agencies
0,036
0,033
0,033

0,005
0,015
0,025

3,58%
2,46%
1,37%
(Rt)
Source: Own estimation
More
than 75
years:
Research Centers
0,032
0,021
0,015
0,004
0,003
0,005
3,19%
2,06% 1,31%
25- 50
years:
50- 75
years:
More
than 75
years:
Consulting Agencies
0,035
0,045
0,045
0,007
0,007
0,007
3,37%
4,26% 4,15%
25- 50
years:
50- 75
years:
Table 8 also shows the estimation of the SDR but by profession types. Since there were
multiple types of them, aggregation was done in the most important ones, and calculations with
the 40 responses were redone. The table shows that the 3 answers given by those skilled in
projects, on average, exceed by more than double those given by the other professions. Without
considering the specialization in projects, in terms of average, the results are not very different,
20
and the main reason for the different estimated rates derives by different standard deviations
within samples. Because of this, one should keep in mind that a sample of just a few answers is
not the most convenient to apply the Gamma methodology (projects, ecology) therefore, for
them the results are merely indicative.
Table 8: SDR for PIP for the provision and conservation of Ecosystem Services:
Profession 1/
25- 50
años:
μ
σ
(Rt)
50- 75
años:
Más de 75
años:
Environmental Economics
0,034
0,024
0,015
0,186
0,012
0,009
2,73%
1,85%
1,10%
25- 50
años:
50- 75
años:
Más de 75
años:
Economics
μ
0,036
0,025
0,018
0,01
0,008
0,007
σ
3,41%
2,19%
1,48%
(Rt)
1/
Senior professionals were considered.
25- 50
años:
50- 75
años:
Más de 75
años:
0,036
0,009
3,42%
Ecology
0,027
0,012
2,11%
0,025
0,016
1,41%
25- 50
años:
50- 75
años:
Más de 75
años:
0,03
0,014
2,57%
Project
0,027
0,017
1,79%
0,025
0,02
1,08%
Source: Own estimation.
The above results are compared with the international experience of using declining
discount rates. Table 9 shows three examples. In the case of UK rates fall from 3.5% set for 30
years up to 1% for a horizon of 300 years or more. France also shows a reduction, but faster,
since all projects that have a skyline evaluation over 30 years, will be assessed at a rate of 2%.
United States, in addition to recommending lower rates for projects with a large horizon,
establishes a SDR of 1.1% when they exceed 30 years.
Table 9: SDR for PIP in other countries (%)
Years
United Kingdom
France 1/
United States
0-30
3,5
4
Real SDR of 1.1%
31-75
3
2
for policies exceeding 30 years
16-125
2,5
2
201-300
1,5
2
300- a más
1
2
1/
In the case of France, it is proposed that from a 30 years horizon, the rate
decreases to a minimum of 2%.Source:
Own estimation
21
5. Conclusion
The ecosystem services are defined as the social, economic and cultural benefits that
arise from the ecological functions of ecosystems. From an economic perspective, these
services are classified as public goods therefore the market by itself does not provide the
appropriate price for them. As a consequence, there is an overuse of them which degrades them
and as a consequence, is detrimental for their conservation.
In Peru, the Public Investment Projects (PIP) to preserve and provide ecosystem
services emerge as a response to the concern regarding their degradation, and specifically, to
reforest and afforest. In particular, in this study, we intended to shed light on the election of the
SDR, the parameter used in the CBA to discount the cost and benefits that take place in the
future and therefore, one which has a critical role in the determination of the profitability of the
project. The election of the discount rate for projects in general is done following the Harberger
(1973) method, based on market prices. However, through this document we have discussed
that ethical concerns are predominant in these situations and should be taken into account
rather than letting the market alone. The latter approach is known as the descriptive approach,
and the prior, as the prescriptive approach. In line with the statement, we propose a prescriptive
approach based on the Ramsey formula.
For the estimation of the SDR there are several methodologies that derive from the
Ramsey formula. To model declining discount rates one can either use the extended Ramsey
formula or the Expected Net Present Value (ENPV) approach. The first one is based on
assumptions that may not have correlation with reality and therefore, it is not prepared to provide
an explanation for widely known phenomena in the financial market such as the equity premium
puzzle; consequently the ENPV appears as the most easily approachable. Within it, we have
chosen the Gamma methodology which employs lower and declining discount rates in which
uncertainty reflects the heterogeneity of normative judgments.
We have adapted the methodology proposed by Weitzman (2001) in order to estimate
the SDR based on the preferences of an expert panel. Following Almansa (2006), we have
introduced the Delphi methodology, which implies that the experts are surveyed twice or more,
and they get a feedback of the responses obtained in the previous rounds. In this way, the
Gamma discount allows to estimate the SDR taking into account the opinion of experts, while
the Delphi methodology permits to obtain a greater degree of consensus regarding the
appropriate SDR to apply in this type of projects.
The responses obtained are in line with the need of adequacy of the CBA, which is
perceived as appropriate, in case the temporal horizon associated to the project exceeds one
generation, or the goods or services affected are, what we call in economics, public goods. In
addition, they mention the possibility to apply different SDR for intangible goods within the same
CBA. A first approach to a punctual estimation of the SDR would be between 2 and 3%, and
2.98%, 2.48% and 2.12% for the SDR corresponding to the horizons of 25-50 years, 50-75
years and more than 75 years respectively. Taking into account the responses provided by the
senior specialists, the results are slightly different, the punctual estimation is between 2 and 3%,
and for the same intervals, the SDR assumes the values 3.4%, 2.5% and 1.9%.
22
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