OBJETIVOS Objetivos General:

Historically, the proper procedure for discounting future costs and benefits of large public sector investments has been a contentious issue (Boardman et al., 2005). There are two important aspects to the ongoing discounting debate. The first is a focus on ethical norms that should govern social discounting, while the second, aimed more at accounting for the opportunity cost of public investment, is an attempt to make social discounting consistent with individual decisions and the rates of return on private investment observed in the marketplace. The debate on discounting began in the water resources sector in the United States during the 1950s and 60s, later spreading to the energy sector in the late 70s and early 80s (Lind et al., 1982). During the Nixon Administration, the Office of Management and Budget (OMB), in an attempt to standardize discounting across different agencies, issued a directive requiring use of a 10% real rate (U.S. Office of Management and Budget, 1972), which interestingly, did not apply to water projects (Lind et al., 1982).24 This rate has since been revised to 7%, and is said to “approximate the marginal pretax rate of return on an average investment in the private sector in recent years” (US OMB, 1992). It is interesting to note that this OMB rate is far above the social discount rates preferred by the majority of economists (Weitzman, 2001).

In spite of the general consensus among economists that the social discount rate should be lower than the OMB rate, the debate over discounting continues. Today there is a discussion over discounting in the context of climate change, and this issue has attracted the attention of prominent

24

In fact, it was Congress that resisted the move to apply a 10% discount rate to water projects, instead sticking with the formula set forth in Senate Document 97, and later writing into law the formula in Section 80-A of the Water Resources Development Act of 1974 (Public Law 93-251). The Congressional Budget Office (CBO) today uses a 2% discount rate, which is said to approximate the long-term cost of borrowing for the federal government based on a conservative estimate of the long-term real market risk-free interest rate (the Treasury rate).

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theorists (Stern, 2006; Heal, 2007; Nordhaus, 2007; Weitzman, 2007; Dasgupta, 2008; Sterner and Persson, 2008). Of these economists, all but Nordhaus argue that society should make large, immediate investments to reduce climate change. For Cline and Stern, this conclusion stems largely from the use of very low discount rates. For Sterner and Persson, it results from inclusion of

decreasing natural wealth and consumption due to climate change damages. For Weitzman, the imperative to act follows from the effect of uncertainty and the need to avoid even low risks of

catastrophic damages. Finally, for Dasgupta, it comes from a fear that our capacity to mitigate climate change in the future may be lower than we hope.

Summary of key aspects of the debate

The first important dimension of the discounting controversy is the issue of how the

consumption discount rate ρt should be determined, where the subscript refers to time t and allows for

the rate to change over time (perhaps as a hyperbolic discount rate). Some of the recent literature argues that one should look to the long-run real rate of return on capital to calibrate ρt (Nordhaus,

2007; Weitzman, 2007). This approach raises questions about the much lower discount rates used by others such as Stern (2006). The argument holds that using low discount rates will lead to

overinvestment in questionable social policies with very low returns (and possibly too much immediate climate change mitigation), policies that no private agent or firm could logically support.

However, Heal (2007) argues that this line of argument is problematic for two main reasons: a) the equality between the long-run rate of return and the discount rate only holds under very special circumstances, what Dasgupta (2008) calls a “fully optimum economy”, and b) the argument is in fact inverted. For the fully optimum economy assumption to hold, markets must be efficient, agents need to have perfect foresight over all future time, and there must be no external effects, and these cannot be argued to exist in the context of climate change. Many of the same types of arguments can be invoked for long-lived investments in the water resources sector.

To address Heal’s second objection, we need to consider the long-standing theoretical basis for discounting. Based on reasoning that dates back to Ramsey (1928), the consumption discount rate ρt can be written as the sum of two components:

where δ is the pure rate of time preference, η(ct) is the elasticity of the marginal utility of consumption

at time t, and R(ct) is the rate of change of consumption at time t. Heal argues that instead of going

from the long run rate of return on capital to ρt, equation 9 should serve as our starting point, and we

should aim to specify appropriate expressions for η and δ, before deriving the appropriate ρt given ct.

This is unfortunately no simple matter. Consider δ, which is exogenous and unchanging in time. This parameter is “the rate at which we discount the welfare of future people just because they are in the future [emphasis in the original]” (Heal, 2007). Many philosophers hold that this normative parameter cannot ethically be anything but zero since discrimination against future people is morally indefensible; increasingly, economists appear to agree as well. Some suggest use of a very small number which reflects the exogenous probability of extinction of the human race in any given year, perhaps 0.001, ignoring the obvious difficulties associated with how one would determine such a probability. In their respective analyses, the authors mentioned above have used δ rates varying from zero or nearly zero to 2 or 3 (Cline, 1992; Stern, 2006; Heal, 2007; Nordhaus, 2007; Dasgupta, 2008; Sterner and Persson, 2008).

The other component of equation 9 is endogenous – it depends on consumption – and is generally thought to be positive. R(ct) is the rate of change of consumption and has to do with the

growth rate of the general economy. η(ct) is the elasticity of the marginal utility of consumption at time

t (positive, and bounded above when greater than or equal to 1). Dasgupta (2008) defines η as “the index of the aversion society ought to display toward consumption inequality among people – be they in the same period or in different periods”.25 All existing studies assume η to be constant (Cline assumes 1.5, Nordhaus, Stern and Sterner and Persson 1, and Weitzman 2), though tractability is the only reason to assume this to be true.26 Dasgupta argues, based on arguments about the

unbelievable savings rate implied by δ = 0 and low values of η, that these values are too low when combined with δ ~ 0, and that η should perhaps instead be around 2-3. He also notes two other problems with assuming that η = 1. First, this implies that the saving rate is independent of the long

η = 1 implies that any increase in one person’s consumption is of equal social worth to a proportionate increase in another person’s consumption, no matter what the consumption level is.

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run return on capital r. Second, η = 1 further implies that the savings rate is not affected by uncertainty about r. Both of these observations make η = 1 implausible.

Some might argue that high values of η also lead to implausible tradeoffs. For example, η = 1 means that a 1% decrease in consumption for a person earning $1000 (i.e. a reduction to $990) leads to an equivalent change in welfare as a 1% decrease in consumption for a person earning $100,000 (i.e. a reduction to $99,000). With η = 2, the consumption of the second person would have to be reduced 50% to $50,000 to represent an equivalent change in welfare as a 1% decrease in consumption for the first. For η = 3, a 93% decrease in the second person’s consumption would be necessary. There is little evidence that the world’s societies would look favorably on such massive income redistribution. However, Dasgupta (2008) points out that this is at least partly because we think of η within the context of a single generation. Because of this, the η that can be derived from society’s redistribution choices is contaminated by peoples’ concerns over moral hazard and adverse selection. Such concerns have less relevance when thinking of the intergenerational context.

Nonetheless, the inability to calibrate η based on observed behavior presents a problem, because we have little intuition to guide us in thinking about the curvature of individuals’ utility functions. Nor do we have any basis for exploring what form η(ct) might take if it is not constant.

Next, consider R(ct), the long-term growth rate of consumption in the economy. We expect

based on recent economic history that this is increasing, thus η(ct)·R(ct) is positive and the discount

rate should be greater than the pure rate of time preference. This squares well with the long-standing argument in welfare economics that discounting future generations’ benefits is justified based on the fact that they will be richer than present generations (we need not appeal to δ to achieve this).

However, there are two additional complications to consider: 1) this term could become negative if the impacts of climate change are strongly negative and lead to decreasing aggregate consumption (Stern, 2006; Heal, 2007), and b) the consumption of certain goods (for example ecosystem services) may very well decrease in a climate-damaged world, even as aggregate consumption continues to rise (Sterner and Persson, 2008). If ecosystem services and general consumption are complementary goods, this decrease could turn ρt negative. This can be seen by looking at equation 10, which is an

ρi,t = δ + ηii(ct)·R(ci,t) + ∑j≠iηij(ct)·R(cj,t), (10) Equation 10 says that the discount rate ρi,t for consumption of good i (perhaps general

consumption of non-ecosystem services) could be greater or less than the pure rate of time preference δ depending on the signs of R(cj,t ) (the growth rate of consumption of good(s) j, which

might be ecosystem services) and ηij(ct) (the elasticity of marginal utility of good i with respect to

consumption of good(s) j), and the relative magnitudes of terms 2 and 3.27 If goods i and j are

complements, which may be the case for environmental and non-environmental goods, then ηij(ct) will

be negative and rising consumption of good(s) j will result in a lower consumption discount rate for good i via the effect of term 3.

Another issue raised in the literature on discounting under climate change is that posed by uncertainty. Weitzman (2007) argues based on a survey of economists that the true value of ρ is uncertain (the survey responses follow a gamma distribution28). He shows that incorporating

uncertainty about the discount rate naturally leads to hyperbolic discounting. Hyperbolic discounting, though, is considered problematic because it allows for preference reversals (or time inconsistency). Dasgupta and Maskin (2005) however find that uncertainty makes preference reversals possible, using a simple theoretical model. They argue that there is no time inconsistency in this, since the nature of uncertainty changes over time as payoffs become nearer.

Another dimension of uncertainty comes from the difficulty in predicting long term economic growth R(ct). This is especially relevant when applying Ramsey’s normative framework for evaluating

long-lived investments. If there is variability in the growth forecast for the economy, the risk-free consumption discount rate ρ must be adjusted downwards (Dasgupta, 2008):

ρt = δ + η(ct)·E[R(ct)] – [η(ct)] 2

·var[R(ct)]/2. (11)

This last point is important, because it means that higher values of η combined with growth in consumption may not be sufficient to increase the risk-free rate ρ. We note that ρ will be constant if and only if η(ct) is constant, since δ, E[R(ct)] and var[R(ct)] are all constant. Variability in future growth

decreases the risk-free rate (on the basis of risk aversion and the precautionary motive), which is the

27

Here we assume that R(ci,t) > 0.

28

More precisely, non negative responses followed a gamma distribution; out of 2,160 respondents to the questionnaire, 46 respondents gave zero as their best estimate, and 3 indicated negative discount rates.

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rate that a social planner should use in evaluation of social investments. Therefore, returning to equation 9, we note that it suggests that the discount rate ρt will not be constant unless one very

special condition holds, namely that R(ct) = 0, or that consumption is unchanging over time, which

seems unlikely.29 This provides some justification for considering non-constant discount rates discussed in the literature, such as hyperbolic discounting.

There are thus many reasons why the social discount rate ρt is unlikely to be the same as the

rate of return on capital r observed from today’s marketplace. In a real, non-optimum economy, where capital investment and consumption change at different rates, r is not generally equal to the social rate of return on investment. Given the fact that climate change imposes externalities on consumption across generations, there is good reason to believe that the discount rate should be considerably lower than the r observed from market interest rates and/or other measures derived from consumer behaviors.30 But this also implies that capital investment itself needs to be revalued. Dasgupta (2008) shows that the shadow value of capital in the imperfect economy grows as the wedge between r and ρ increases; this should reassure those who argue that use of a low value for ρ will lead to over- investment in low-yield capital investments.

Implications for cost-benefit analysis of large water resources projects

The current theoretical debate on discounting is useful for highlighting its ethical dimensions, but the practical implications of this debate for project evaluation are unclear. It remains difficult to appropriately specify Equation 9 for two primary reasons: 1) the lack of consensus on what η(ct)

should be, and 2) the fact that uncertainty about the true social rate of discount, similarly to uncertainty of the consequences of climate change, does not readily lend itself to probability distributions. For the major part of this research, a simplified approach is taken to deal with these difficulties. We first consider the different parameters that have been used by the aforementioned authors, and determine the discount rates implied by these parameter values in combination with Stern’s 1.3%/yr growth projection for the business-as-usual scenario (Table 9). As shown, the implied

29

A frequently-cited point estimate of consumption growth under business as usual is R(ct) = 1.3% (Stern, 2006).

30

In addition, it is plausible that the real social rates of return on many investments – perhaps those that generate high emissions of greenhouse gases – are negative, as their external costs have not been accounted for.

discount rates range from 2 to 5%, with several authors suggesting use of rates close to the standard 4% long-run return on capital. These rates can be supplemented with those used by the US

government (2 and 7% for the CBO and OMB, respectively). The bulk of the economic calculations in this dissertation (Chapters 5 through 9) will rely on a similar range of discount rates, centered on 4% with a 2-6% range. This analysis can thus be considered to apply to a single state of the world which is characterized by similar global long-run economic growth as that experienced since the onset of the Industrial Revolution.

Table 9. Discounting assumptions of different authors in their assessments of climate change, assuming R(ct) = 1.3%/yr.

Cline Nordhaus Stern Sterner &

Persson Weitzman Dasgupta Jeuland δ = pure rate of time

preference 0 3 ~0.1 3 2 0 N/A η = elasticity of marginal utility with respect to consumption 1.5 1 1 1 2 3 to 4 N/A ρt = social discount rate (%) 1.95 4.3 1.4 4.3 4.6 3.9 to 5.2 2 to 6

In Chapter 10, however, a different approach is used to demonstrate the importance this discounting debate has on project appraisal. For the purposes of illustration, equation 9 will be parameterized for three plausible states of the world with different economic growth rates, using an illustrative η(ct) function that seems consistent with the arguments presented by Dasgupta. These

different growth trajectories and the shape of η(ct) will be shown to have a profound influence on how

we would think about the social welfare implications of large public investments such as Blue Nile dams. Though the specification of η(ct) is arbitrary, the analysis will be useful in highlighting the extent

of the differences of opinion that arise among people on the various ends of this discounting debate. To conclude this section, we discuss two other important questions related to the larger discounting debate for the cost-benefit of water resources projects:

1. What is the real opportunity cost of the capital being allocated?

2. What should be assumed about the role of the project (relative to its displaced alternative) in the beneficiary economy?

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Including the true opportunity cost of capital. Even if the relation between the social discount rate and the marginal productivity of capital (i.e. the rate of return on capital) is unclear at best, the opportunity cost of capital is directly influenced by this marginal productivity, and should be considered carefully when evaluating large public infrastructure projects. Dasgupta (2008) puts forward the argument that capital ought to be revalued in a world affected by climate change. The idea that capital has a shadow value different from 1, however, goes much further back (Marglin, 1963; Dasgupta et al., 1972). In highly capital constrained economies, there are limited public resources for large projects. Investing several billion dollars in dam construction would appear to have a high opportunity cost, as it displaces the best alternative project(s), which may also have very high returns.

If we assume that the shadow value of capital is equal to one, conventional procedures used in project appraisal apply, such that costs can be debited directly from the project benefits weighted by the discount factor for the point in time at which they occur. This procedure is only appropriate if the economy sacrifices an equivalent amount of consumption in the same year as that in which the capital outlay occurs. If instead the capital expense incurred displaces alternative investment, the consumption that is sacrificed is actually deferred in time, such that the shadow value of capital will be different from one. This shadow value will depend on several key parameters that describe the economy, including the social rate of discount, the marginal productivity of capital, and the rate of reinvestment of returns from capital.

In the context of the JMP projects, however, it appears likely that the capital would come from donor monies devoted specifically to the JMP. These resources do not have obvious alternative uses in capital investment, and it is plausible that they would otherwise be absorbed into general world consumption. This argument seems appropriate since sponsors are uniquely interested in supporting cooperative ventures among Nile Basin countries, and would probably not spend this money on other development projects if the JMP projects were to fall through. Thus, because this analysis only includes the subset of alternative anchor JMP projects being considered by these donor agencies, we use a shadow value of capital of 1. I emphasize, however, that this rate may not be appropriate if the