DISCOUNTING COSTS AND BENEFITS IN CARBON SEQUESTRATION PROJECTS Marco Boscolo, Jeffrey R. Vincent, and Theodore Panayotou Environment Discussion Paper No. 41 February 1998 Support for the research reported in this paper was provided by the U.S. Environmental Protection Agency, through a cooperative agreement on "Economic Analysis of International Forestry Issues"; the Smithsonian Tropical Research Institute's Center for Tropical Forest Science, through a grant from the Southern Company; and the Harvard Institute for International Development. Marco Boscolo is a Research Associate at the Harvard Institute for International Development (HIID) and the Center for Tropical Forest Science, Smithsonian Tropical Research Institute. Jeffrey R. Vincent is a Fellow at the Harvard Institute for International Development and Director of HIID's Newly Independent States Environmental Economics and Policy Project. Theodore Panayotou is an Institute Fellow and Director of the International Environment Program at the Harvard Institute for International Development. The views expressed are solely those of the author(s) and do not necessarily represent the views of the U.S. Agency for International Development, the host government or the Harvard Institute for International Development. The boundaries, colors, and other information shown on any map in this volume do not imply any judgment on the legal status of any territory or the endorsement of acceptance of such boundaries. This paper is for discussion purposes and HIID welcomes comments, which will be relayed to the authors. This document should not be quoted without the permission of HIID or the author(s). For additional information please contact: International Environment Program, Harvard Institute for International Development, One Eliot Street, Cambridge, MA 02138. Tel: (617) 496-5176. Fax: (617) 496-8040 1 1. INTRODUCTION Because the effects of higher atmospheric concentrations of carbon dioxide might be felt far into the future, the choice of the discount rate is critical in economic analyses of climate change. Discounting inevitably reduces the weight of future damages, even catastrophic ones, that might result from global climate change. Some economists have proposed using very low discount rates in analyzing carbon- abatement investments (Cline, 1992, 1993; Rothenberg, 1993). Others have argued that "meeting the needs of future generations will only be possible if investible resources are channeled to projects and programs with the highest environmental, social, and economic rates of return [which is not likely] to happen if the discount rate is set significantly lower than the opportunity cost of capital" (Birdsall and Steer, 1993). In short, the choice of the discount rate remains a controversial issue in the climate change literature (cf. Nilsson, 1995; Hoen and Solberg, 1995). This paper addresses the discounting issue in the particular case of carbon sequestration projects. Our concern is to ensure that analyses of different projects are comparable, particularly with respect to the costs of carbon sequestration, and thereby accurately identify the socially most desirable projects. In this sense, our focus is narrower than benefit-cost analysis of global climate change. Our intention is not to advocate or dismiss action to reduce net carbon dioxide emissions. Instead, it is to provide guidelines for selecting an appropriate discount rate, given a desire to sequester carbon from the atmosphere. The paper is organized as follows. First, the basic rationale for using a positive social discount rate in evaluating investment projects is summarized. Second, methods for calculating the social discount rate are reviewed. Although agreement does not yet exist regarding which method is best, significant progress has been made in identifying the economic determinants of the discount rate. Third, arguments for and against the application of discounting to physical units of carbon are summarized. Our conclusion is that physical units should be discounted. Finally, we present an example to clarify the assumptions involved in, and the implications of, selecting a given rate. 2. THE RATIONALE FOR DISCOUNTING Discounting is used to compare benefits and costs that occur at different points in time. The basic argument for using a positive social discount rate is that resources used in both consumption and production have a higher value today than in the future. This is because: (i) consumption today is preferred to consumption tomorrow—the social rate of time preference (SRTP) is positive—and (ii) capital investments enhance production possibilities, and thus consumption possibilities, in the future as well as today—the social return on investment (SRI) is positive. We review these consumption and production aspects of discounting in turn. 2.1 The Social Rate of Time Preference It is useful to think of the SRTP, or consumption rate of interest i, as the sum of two components, a "pure" or "myopic" preference for consuming a good sooner rather than later (r), and a term indicating how changes in consumption affect the marginal utility of consumption: i = r + ?g . (1) ? is the negative of the elasticity of marginal utility with respect to consumption, while g is the expected rate of growth in per capita consumption. Assuming, as is standard, diminishing marginal returns to consumption, ? is positive. 2 The second component in (1) captures the effect that higher interest rates are required to draw forth a given amount of savings when individuals expect consumption to rise in the future, e.g. due to rising income. In that case, society needs to save less in the current period to finance future consumption. The inclusion of this second component indicates that a positive SRTP does not necessarily reflect selfishness on the part of the current generation (r). The SRTP can also be positive because consumption is expected to grow (g > 0). Then, as we will see in a moment, a positive SRTP reflects the balancing, at the margin, of the utility derived from consumption in current and future periods. Markandya and Pearce (1988) provide a particularly lucid derivation of (1). Suppose that the social objective is to allocate consumption between two periods to maximize the discounted sum of utility from consumption: W(Ct) + W(Ct+1)/(1 + i) , (2) subject to the constraint: C = Ct + Ct+1 . (3) That is, a given amount of consumable goods is available for allocation. We have not defined i; indeed, demonstrating that i does not equal zero is the point of the analysis. Solving (3) for Ct+1, substituting the result into (2), and taking the derivative with respect to Ct, we obtain the first-order condition, ?W(Ct)/? Ct = [?W(Ct+1)/? Ct] / (1 + i) . (4) This is the inter-temporal efficiency condition for consumption. Solving it for i yields: t t t C C W C C W C C W i ? ? ? ? ? ? ) ( ) ( ) ( 1 ? = + , (5) or, using more compact notation: ) ( ) ( t C t C C W dt C dW i = . (6) This is the general expression for the SRTP. It indicates that the SRTP equals the proportional change in the marginal utility of consumption from one period to the next. (6) equals the two-component expression given by (1) if the utility function has the following specific functional form: W(Ct) = Ct 1-? * e-rt * (1-?)-1 , (7) Substituting the relevant derivatives of this function into (6), we obtain: 3 i dC dt C r t t = + ? / . (8) dCt/dt / Ct is the rate of growth in consumption, and so (8) is equivalent to (1). i is always positive when consumption is rising. It can be positive even when consumption is falling, as long as r is larger than the absolute value of ?g. The SRTP can be thought of as the supply curve for savings in the economy, with r being the intercept and ?g yielding an upward-sloping relationship between savings (forgone consumption) and the interest rate earned on those savings. This savings function is depicted in Figure 1 by the line S(i). Individuals are willing to postpone consumption (i.e., save) only if they are compensated for their "sacrifice" with a positive return. The higher the return, the more they save. 2.2 The Social Return on Investment The other rationale for discounting stems from the fact that capital is productive, i.e., $1 invested in productive activities instead of consumed will generate additional income, hence additional consumption, in the future. The SRI therefore measures the opportunity cost of investing in, for example, carbon sequestration instead of other productive activities. If Y=F(K,z) is a well-behaved production function, where K is capital and z is a vector of other variables (e.g. labor, technology, etc.), the marginal product of capital, FK, yields the economy's investment demand curve. Assuming that capital exhibits diminishing marginal returns, an incremental unit of capital yields a lower return than the previous unit. Hence, the demand curve slopes downward. We therefore expect that an additional unit of investment will be made only if the additional funds required can be borrowed at a cost lower than the previous unit. The investment function is depicted in Figure 1 by the line I(π), where π is the cost of borrowing funds. 2.3 Market Equilibrium The market interest rate results from the interplay of the supply of savings (positively correlated with the rate of interest) and the demand for investment (negatively correlated with the interest rate). In the absence of distortions (taxes, market imperfections, risk, etc.), supply and demand cross at the market clearing rate i* (see Figure 1). Note that i* = i = π : the market interest rate equals both the SRTP and the SRI. In this situation, there is no ambiguity about the social discount rate. It is simply the market interest rate, which reflects equally consumer and producer rates of time preference. Of course, a distortion-free market is an idealized situation. Taxes and other distortions shift the market supply and demand curves. For example, taxes on interest income cause savers to require compensation of more than i for their postponed consumption. They demand a higher interest rate to save a given amount, because they must share part of their interest income with the government. The upward shift of the savings supply function to S′(i) reflects this reality. Taxation of investment returns introduces similar distortions. Firms that earn π on their productive investments will not be willing to borrow funds at π, as they must use some of the earnings to cover their tax obligations. As a result, the investment demand curve shifts downward to I′(π). The interest rate determined by market interactions is now im, with the associated amount of savings and investment represented by Q0. Note that im does not equal either the SRTP or the SRI. At Q0, im could be much higher than the SRTP and much lower than the SRI. For example, if im is 8% and consumers face a 4 25% income tax and firms face a 50% profit tax, the values of i and π would be 6% and 16%, respectively. Firms return 8% to their investors after paying the profit tax, while investors retain 6% after paying the income tax. What, then, is the social discount rate? Is it π, i, or a combination of the two? 3. METHODS FOR CALCULATING THE SOCIAL DISCOUNT RATE The foregoing discussion indicates that funds made available to finance carbon sequestration projects generally come at the expense of both consumption and investment, but the market interest rate is unlikely to reflect the social opportunity cost of either displaced activity. Four major methods have been proposed to calculate the social discount rate in this situation: the after-tax savings rate, the pre-tax return on investment, the shadow price of capital, and the weighted-average (social opportunity cost of capital) method. We review the particular features of each method in the following sections. 3.1 After-Tax Savings Rate As discussed in section 2.1, the SRTP equals the sum of the pure rate of time preference and the product of the elasticity of the marginal utility of consumption times the expected growth rate of consumption. The few available estimates suggest that the rate of pure time preference ranges from 0 to 2% and the elasticity of marginal utility from 1 to 2 (equaling 1 if utility is strictly proportional to consumption), while income growth differs from country to country (Markandya and Pearce, 1988). This explains why economists generally expect developing countries to have higher discount rates than industrialized ones. The marginal utility of consumption, and its elasticity, are high when people live at a subsistence level and are focused on sheer survival from one period to the next. Moreover, the theory of economic convergence predicts that poor countries will have, on average, higher income growth rates (hence, higher consumption growth rates) than rich countries (Barro and Sala-i-Martin, 1995). If the SRTP is used as the discount rate in carbon sequestration projects, these points suggest that the same project may look very different to developing and developed countries for reasons other than the distribution of benefits and costs. Use of the SRTP in applied studies has not been free of criticism. On the value of r, some have argued that impatience discounting is "irrational" (cf. Pearce and Turner, 1990, for a review). Regarding ?, some economists dispute whether there is a meaningful way to measure the social marginal utility of consumption. The debate centers on the measurability of utility, both across individuals and over time. Finally, projections of future consumption growth are not perfect, and such imprecision makes them relatively easy to criticize. Due to these measurement difficulties, economists often compute the SRTP indirectly by calculating the real, after-tax rate of return on savings. This is typically done by taking the interest rate on long-term, low-risk investments (such as treasury bills) and correcting for inflation and taxes (as in the numerical example in section 2.3). When the SRTP is computed in this way, time-series data covering a long period should be used to avoid short-term fluctuations. Moreover, the SRTP should reflect the marginal, not the average, return on savings. The former is higher than the latter, as can be seen by referring to Figure 1. Boardman et al. (1996) also warn that even if the individual rate of time preference equals the real after-tax savings rate, the social rate may not. Risk in particular is perceived quite differently by individuals and by society at large. The individual risk of death, which is one of the reasons sometimes offered to justify the pure rate of time preference, is higher than the risk of society's disappearance. Based on risk considerations, we might therefore expect the SRTP to be lower than the real, after-tax savings rate that individuals collect. 5 Others have argued that a time-invariant SRTP is inappropriate (Kula, 1992; Rothenberg, 1993). Some of these arguments are based on ethical grounds, while others hinge on the premise (consistent with growth theory and (1)) that future consumption growth will not proceed at rates experienced in the past (Nordhaus, 1994). Because consumption growth is positively correlated with the SRTP due to the ?g term, a reduction over time in the consumption growth rate necessarily leads to a declining SRTP. Cropper et al. (1992) have provided empirical evidence of a diminishing social rate of time preference stemming from (presumably) ethical considerations. In their survey, participants were asked to express their willingness to tradeoff lives saved today with lives saved in the future. The authors found that people were indifferent between a life saved today and two lives saved in five years' time, or 11 lives saved in 50 years' time, or 44 lives saved in 100 years. The implicit rates of time preference were 16.8% for the five-year horizon, 4.8% for the 50-year horizon, and 3.8% for the 100-year horizon. The most fundamental criticism of equating the social discount rate to the SRTP, however, is that the SRTP is purely a measure of the opportunity cost of consumption. The SRTP ignores the opportunity cost of production given by the return on investments. We turn next to a method that computes the social discount rate using the opportunity cost of capital, and then to a method that attempts to rectify this shortcoming of the SRTP. 3.2 Pre-Tax Return on Investment Some economists have suggested that all investment projects, both private and public, should employ a discount rate equivalent to the marginal productivity of capital in the private sector. They argue that, even for public investments, it is in the public interest to sponsor projects that yield the highest return. If the private sector is able to achieve higher returns than prospective public-sector projects, then the government should invest in private rather than public projects. To approximate the marginal productivity of capital, economists often compute the pre-tax rate of return on private investments. This method contains three potential biases (Boardman et al., 1996). First, as in the case of the post-tax savings rate, the relevant rate is the marginal, not the average, productivity of capital. The rate of return is lower on the margin than on average because the "best" deals will be struck first. Hence, additional investments are unlikely to yield as much as the existing ones. Using the average rate of return thus biases the estimated discount rate upward. Second, private rates of return may be distorted by externalities or monopoly pricing. Many economic activities cause some degree of environmental degradation. Thus, additional expenditures on environmental cleanup may be necessary to rectify this degradation and achieve the socially (if not privately) optimal level of environmental quality. These expenditures cause some of the project's output to "evaporate," with the net effect of lowering the marginal social productivity of capital (Weitzman, 1994). Ignoring such negative externalities of investments biases the estimated social discount rate upward, although the bias may be small1 . Similarly, if monopoly power allows firms to increase prices above their socially optimal levels, the private return on investment overestimates the social discount rate. Finally, the private return on investment reflects premia for risk. Since society has wider opportunities to diversify its portfolio than individual investors, social risk premia are probably lower than private risk premia. Hence, again, the social return on investment is likely to be lower than the pre-tax private return. 1 Based on US data, Weitzman (1994) estimated that the bias is likely to range between just 4% and 6% of the discount rate. 6 As with the SRTP, one might expect the social return on investment—computed as the pre-tax private return—to decrease over time (Pearce and Turner, 1990; Weitzman, 1994). There are two main reasons for this. First, capital is usually assumed to exhibit diminishing marginal returns. This argument can be connected to the theory of economic convergence referred to earlier (cf. Barro and Sala-i-Martin, 1995). Second, in a world that is apparently evolving toward an ever-increasing degree of environmental concern, the proportion of expenditures directed toward environmental improvement might also increase. The implication is that the difference between the private rate of return and the social return should decline over time (Weitzman, 1994). The fundamental criticism of the pre-tax investment return method is the mirror image of the one for the post-tax savings rate: it ignores the opportunity cost of savings (Jenkins and Harberger, 1996). From Figure 1, we can see that π may be much higher than i and therby greatly overstate consumers' rate of time preference. 3.3 The Shadow Price of Capital This method applies the SRTP to both consumption and investment flows, after the latter is converted to "consumption equivalents" through the application of a shadow price of capital. This method is associated with contributions by Eckstein (1958), Arrow (1966), Arrow and Kurtz (1970), Feldstein (1972), Bradford (1975), and Lind (1982). The estimation of the shadow price of capital is straightforward if we assume that each dollar invested today yields a perpetual return π that is entirely consumed. In that case, the present value of the annual flow of consumption is given by π/i, where i is the SRTP. This means that π/i can be taken as the shadow price of investments in terms of consumption. Alternative formulas are necessary when less restrictive assumptions are made regarding the proportion of π that is consumed. Bradford (1975) proposed the following formula for the case when investment returns are perpetual but a proportion of the annual return π is re-invested: Shadow price = ( ) 1? ? s i s γ γ , (9) where γ = (1+π)/(1+i), s is the marginal propensity to save, and sγ < 1. The shadow price increases with the fraction of π reinvested. More recently, Cline (1992) suggested a revised formulation of Lind's method (Lind, 1982): Shadow price = + = ∑A i N t t N π , / ( ) 1 1 , (10) where Aπ, N = π/[1-(1+π)-N ]. (11) Aπ, N is the annual payment from an annuity lasting N years and having a present value of $1 when discounted using π. Equations (8) and (9) were used by Cline (1992) in his benefit-cost analysis of mitigation options for global warming. He computed a shadow price of capital of approximately 2 (one unit of capital is worth two units of consumption), consistent with i=0.015, π=0.1, and a 15-year capital 7 life (N). After converting investment flows to consumption equivalents using this shadow price, he then discounted them along with all other benefits and costs using the SRTP. The shadow-price method is conceptually correct. It allows one to use the SRTP as the social discount rate without ignoring the opportunity cost of displaced investment. Hence, it is preferable to either of the first two methods. The main issue with this method has been its practical feasibility. We discuss this issue in the next section. 3.4 The Weighted-Average Method According to the weighted-average method, the social discount rate is defined as the weighted average of the SRTP (usually computed as the post-tax savings rate) and the SRI (usually computed as the pre-tax investment return). It is associated with contributions by Krutilla and Eckstein (1958), Haveman (1969), Sandmo and Dréze (1971), and Harberger (1976). It is the principal conceptually sound alternative to the shadow-price method. The social discount rate iw is defined as: iw = wc i + (1-wc) π , (12) where wc is the proportion of incremental funds obtained at the expense of current consumption and 1-wc is the proportion obtained at the expense of investment in alternative opportunities. The determination of wc is based on the following reasoning. A new project increases the demand for funds, which causes market interest rates to rise. In turn, this prompts consumers to save more and investors to borrow less for other projects. This displacement of consumption and investment add up to what Jenkins and Harberger call the social opportunity cost of funds. Given a private savings function S(x, im) and a private investment function I(y, im), where x and y are vectors of socio-economic characteristics (including tax rates) and im is the market interest rate, the proportion of incremental funds obtained at the expense of current consumption is: w S i S i I i c m m m = ? ? ? ? ? ? ? . (13) Substituting (13) into (12), we obtain: iw = ? ? i S i I i S i I i m m m m ? ? π ? ? ? ? ? ? . (14) Expressed in elasticity form, (14) is: i i I S I S w s I T T s I T T = ? ? ε πη ε η ( / ) ( / ) , (15) where εs is the elasticity of supply of savings and ηI is the elasticity of demand for funds for private investments with respect to the market interest rate. As an illustrative example, for i = 0.015 and π = 0.1 8 (the same values used by Cline) and values of εs = 0.3, ηI = -1.0 and IT/ST = 0.9 (as suggested by Jenkins and Harberger), we obtain a value of iw of approximately 8%. In theory, the shadow-price method and the weighted-average method should yield equivalent results in terms of the economic desirability of alternative projects (Jenkins and Harberger, 1996:12-7), although they obviously yield different discount rates (with discount rates from the latter method being higher). The weighted-average method, however, has at least one advantage over the shadow-price method, namely that the rate it generates can be applied to different projects. In contrast, rigorous application of the shadow-price method requires the computation of a different shadow price for projects of different lengths. This can be seen from equation (10), which indicates that a different annuity, and thus a different shadow price, is obtained when different time horizons are considered. While maintaining consistency with economic theory, the weighted-average method provides a way to define a discount rate that is independent of project length.2 The choice of which method to use will not necessarily resolve disagreement over the choice of the discount rate, as both methods leave ample room for disagreement about assumptions. In the March 1993 issue of Finance and Development, William Cline's advocacy of a low effective discount rate contrasted sharply with the views of Nancy Birdsall and Andrew Steer of the World Bank. At the heart of the debate was not the method (both accepted the shadow-price method), but rather the assumptions about parameters such as the pure rate of time preference (r), expected growth rate in per capita consumption (g) and the fraction of funds that would come from displaced consumption (wc). Table I summarizes the assumptions made in the debate and the resulting effects on the effective (i.e., weighted-average) discount rate. Divergent assumptions about r and g led to a nearly threefold difference in the SRTP, and this result was accentuated by additional differences in assumptions about displaced consumption. Consequently, the implicit weighted-average discount rate differed by a factor of more than three. 4. DISCOUNTING OF CARBON FLOWS Having reviewed the rationale for using a positive social discount rate and methods to compute the rate, we now come to a potentially tricky question facing analysts of carbon sequestration projects: how should carbon flows be summarized and compared to sequestration costs? Benefit-cost analysis requires monetization of all effects caused by a project. Monetary valuation of the economic benefits of carbon sequestration remains a controversial and difficult matter, and it has been attempted by only a few scholars (Cline, 1992; Nordhaus, 1994; Fankhauser and Pearce, 1994). Furthermore, Mendelsohn et al. (1994) have criticized existing valuation work on the economic damages from climate change, at least with respect to effects on the US agricultural sector. As an alternative to the evaluation of allocative efficiency, which requires expressing benefits as well as costs in monetary terms, most studies have focused instead on evaluating the cost-effectiveness (C-E) of carbon sequestration options. Nordhaus (1991), Richards and Stokes (1995), and Stavins (1996) review these studies. C-E analysis produces a summary statistic such as "dollars spent per ton of sequestered carbon." Although it is silent on the overall economic desirability of carbon sequestration, it permits identification of the options that sequester carbon at the lowest cost. That is, it enables estimation of the supply schedule for carbon sequestration: the marginal cost of sequestration for progressively greater amounts of sequestered carbon (cf. Nordhaus, 1991; Richards and Stokes, 1995; Stavins, 1996; Boscolo et al., 1996). 2 This does not mean that the social discount rate based on the weighted-average method is necessarily constant over time. As discussed earlier, both of its components, the SRTP and SRI, might change over time. 9 The obvious attraction of the C-E approach is that tons of sequestered carbon are easier to quantify than the economic benefits of sequestration. Indeed, documents on most carbon sequestration projects include information on physical flows of carbon (e.g., Faeth et al., 1994; Fundecor, 1994; Barres et al., 1995). Application of the C-E approach demands, however, an answer to the question as to how these flows should be summarized over time and compared to project costs. At least three different methods are used in the literature to account for carbon flows at different points in time. Richards and Stokes (1995) classify them as flow summation, mean carbon storage, and levelization (or discounting). Flow summation measures the total tons of carbon sequestered (in net terms) over the lifetime of a project, regardless of when sequestration occurs. Mean carbon storage is the average amount of carbon stored per year: flow summation divided by the length of the project. Like flow summation, this method assumes indifference between carbon sequestration in the near or distant future. Levelization also converts carbon flows to an annual equivalent, but it then divides this quantity into the annualized present value of project costs. These three methods involve different assumptions about the discount rate. To illustrate, suppose we have a carbon sequestration project lasting T years that involves annual costs of Ct (not necessarily constant) and has annual carbon flows of Xt (again, not necessarily constant). Let p be the unit value of a ton of sequestered carbon (i.e., the avoided damage cost of climate change). Then the net present value of the project is: NPV = ∑ pXt (1+iw)?t ? ∑ Ct (1+iw)?t , (16) where the sums are evaluated over the interval t = 1, …, T. By definition, the break-even price of carbon (pBE) is the unit value that yields a net present value of zero. Setting (16) equal to zero and solving for p (= pBE), we obtain: pBE = ∑ Ct (1+iw)?t / ∑Xt (1+iw)?t . (17) The right-hand side of this expression gives the unit cost of carbon sequestration, consistent with the benefit-cost analysis principles from which (17) is derived. The key finding from this simple exercise is that tons of carbon (the denominator of the expression) are discounted. For this reason, estimates of sequestered carbon calculated using the flow summation and mean carbon storage methods cannot be meaningfully compared to project costs. The levelization method, which involves calculating the annual- equivalent cost value C such that: ∑ C (1+iw)?t = ∑ Ct (1+iw)?t yields estimates of pBE identical to those from (17) as long as the discount rate is also taken into account in calculating the annual-equivalent carbon flow X: ∑ X (1+iw)?t = ∑ Xt (1+iw)?t Discounting treats the amounts of CO2 sequestered from the atmosphere in each period as if it were money3 and yields identical results to levelizing4 (Richards and Stokes, 1995). Table II provides a partial 3 Stated differently, discounting carbon flows yields a break-even value for carbon. 4 As pointed out by Richards (1995) discounting carbon flows like money relies on the assumption of linearity between emissions and damages. Other functional forms may lead to alternative paths. 10 review of alternative methods and discount rates used in empirical studies. It should be noted that, while in the United States most carbon studies have adopted the levelizing/discounting method, similar studies carried out in developing countries have used the flow summation or mean carbon storage methods. It is therefore impossible to undertake a direct comparison of results. In addition, the choice of which method is employed to produce a final summary statistic will significantly affect the results. Here, we discuss an example to illustrate the influence of the summary statistic and the discount rate used on the desirability of a carbon sequestration project measured in terms of "dollars spent per ton of carbon sequestered." In our illustrative example we have derived results for two hypothetical activities: a reforestation and a natural forest management (NFM) activity. The former will take place on private farmland currently used for cattle grazing. The latter will take place on an area under imminent threat of deforestation where we have assumed an annual deforestation rate of 12%. Other basic assumptions are summarized in Table III. Using a discount rate of 6% and flow summation as the summary statistic, reforestation attains carbon sequestration at a unit cost of $4/ton. This compares favorably with the natural forest management activity that achieves sequestration at $7/ton (see Table IV). However, when physical units of carbon are discounted at a rate of 6%, the two activities achieve carbon sequestration with even efficiency: $10/ton (see Table IV). Based on this evidence, we would conclude that the reforestation activity is superior to, or at least as good as, the NFM one. Increase of the discount rate by only one percentage point leads to antithetical results. Under the flow summation statistic, the two activities achieve carbon sequestration at the same unit cost: $7-8/ton. When we discount carbon flows, however, the cost of carbon sequestration through reforestation is $20/ton, twice as high as the cost needed to implement NFM (see Table IV). Under this scenario the NFM activity is superior to, or at least as good as, the reforestation option. This example illustrates three points. First, certain environmentalists' advocacy of a lower discount rate may be counter-productive when the benefits from conservation are to be enjoyed before their costs (as in the case of preventing deforestation as opposed to promoting reforestation). Second, the use of an undefined summary statistic such as "dollars spent per ton of carbon sequestered" may be misleading. Alternative projects or activities will be comparable in their cost-effectiveness only if their carbon accounting is comparable as well. For example, the cost-effectiveness of a project appears more attractive when flow summation is used rather than discounting. Third, the use of a discount rate is fundamentally one of the most serious sources of uncertainty: results will be very sensitive to even small changes in the discount rate, particularly if costs and benefits occur at the beginning and end (or vice-versa) of the project. In these cases sensitivity analyses are strongly encouraged. 5. CONCLUSIONS In order to allow comparison between alternative projects or activities, use of a positive discount rate is fundamental. Four main methods are available to derive the social discount rate. We suggest the use of the weighted-average method, because it is theoretically sound and empirically simple to apply. In order to use this method, approximate values for SRTP and SRI are necessary (keeping in mind potential issues summarized in section 3.1). We have reported some arguments in favor of diminishing SRTP and SRI over time. With respect to the SRTP, these views are consistent with a diminishing income growth (Nordhaus, 1994), or empirical evidence regarding a nonconstant (diminishing) marginal rate of time preference (Loewenstein and Thaler, 1989, Cropper et al., 1992). Our view is that for very long projects a diminishing SRTP may be an appropriate solution. Regarding the SRI we also found arguments in favor of a diminishing rate, given a diminishing "net" marginal productivity of capital (Weitzman, 1994). Capital itself exhibits a diminishing marginal productivity that is further reduced when we account for 11 the fact that many economic activities in the private sector involve environmental externalities. To account for this last effect, however, we suggest that proper valuation of environmental amenities may be a better way to deal with environmental externalities than adjustment of the discount rate. In sum, different methods or assumptions yield different results. However, there are clear guidelines for making informed decisions regarding the selection of the discount rate and for supporting a given decision with arguments grounded in economic theory. Yet, we are probably still far from a time when all will all agree on the most appropriate discount rate for a given project. In the meantime, we suggest that sensitivity analyses should always consider the effects of varying discount rates. Many scholars have criticized the use of the same discount rate for environmental (e.g., carbon sequestration) as opposed to other development projects. However, this argument loses appeal when the issue shifts from questions as to whether an environmental project should be carried out to how a given sequestration goal can be achieved. In this case, discounting project impacts such as carbon sequestration is a fundamental necessity for ensuring comparability. 12 REFERENCES Adams, R. Adams, D. Callaway, J. Chang, C. and McCarl, B. 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(1997) "Simulating Options for Carbon Sequestration in the Management of a Lowland Tropical Rainforest", Environment and Development Economics. Bradford, D. (1975) "Constraints on Government Expenditures and the Choice of the Discount Rate", American Economic Review 60:364-378. Cline, W.R. (1992) The Economics of Global Warming, Institute for International Economics, Washington D.C. Cline, W.R. (1993) "Give Greenhouse Abatement a Fair Chance", Finance and Developement (3):3-5. Cropper, M.L. Aydede, S.K. and Portney, P.R. (1992) "Rates of Time Preference for Saving Lives", American Economic Review: Papers and Proceedings. 82(2):469-472. Dixon, R. Schroeder, P. and Winjum, J. (eds.) (1991) Assessment of promising forest management practices and technologies for enhancing the conservation and sequestration of atmospheric carbon and their costs at the site level. Report of the U.S. Environmental Protection Agency, #EPA/600/3- 91/067. Environmental Research Laboratory, Corvallis, OR. Dixon, R. Winjum, J. Andrasko, K. Lee, J. and Schroeder, P. (1994) "Integrated Land-Use Systems: Assessment of Promising Agroforest and Alternative Land-Use Practices to Enhance Carbon Conservation and Sequestration", Climatic Change 30:1-23. Eckstein, O. (1958) Water Resource Development: The Economics of Project Evaluation, Harvard University Press, Cambridge, MA. Englin, J. and Callaway J.M. (1995) "Environmental Impacts of Sequestering Carbon Through Forestation", Climatic Change 31:67-78. Faeth, P. Cort, C. and Livernash R. (1994) Evaluating the Carbon Sequestration Benefits of Forestry Projects in Developing Countries, World Resources Institute; EPA. Fankhauser, S. and Pearce D. (1994) The Social costs of Greenhouse Gas Emissions. The Economics of Climate Change: Proceedings of an OECD/IEA Conference. OECD. 13 Faris, R. Boscolo, M. and Panayotou T. "Carbon offsets in Costa Rica: A case study", Harvard Institute for International Development, Harvard University, Working paper. 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(1995) "Forest Management Options for Sequestering Carbon in Mexico", Biomass and Bioenergy 8(5):357-367. Markandya, A. and Pearce, D. (1988) "Environmental Considerations and the Choice of the Discount Rate in Developing Countries", World Bank, Environment Department. Working Paper No. 3. Mendelsohn, R. Nordhaus, W.D. and Shaw, D. (1994) "The Impact of Global Warming on Agriculture: A Ricardian Analysis", The American Economic Review, 84(4):753-771. Moulton, R. and Richards, K. (1990) "Costs of sequestering carbon through tree planting and forest management in the United States", General Technical Report WO-58, US Department of Agriculture. Washington D.C. Nilsson, S. (1995) "Valuation of Global Afforestation Programs for Carbon Mitigation: An Editorial Essay", Climatic Change 30: 249-257. Nordhaus, W.D. (1991) "The Cost of Slowing Climate Change: A Survey", The Energy Journal, 12(1):37-65. 14 Nordhaus, W.D. (1994) Managing the Global Commons: The Economics of Climate Change, The MIT Press. Cambridge, MA. Parks, P.J. and Hardie, I.W. (1995) "Least-Cost Forest Carbon Reserves: Cost-Effective Subsidies to Convert Marginal Agricultural Land to Forests", Land Economics 71:122-136. Pearce, D.W. and Turner, R.K. (1990) Economics of Natural Resources and the Environment, Johns Hopkins University Press. Baltimore, MD. Ravindranath, N. and Somashekhar B. (1995) "Potential and Economics of Forestry Options for Carbon Sequestration in India", Biomass and Bioenergy 8(5):323-336. Richards, K.R. Moulton, R. and Birdsey, R. (1993) "Costs of Creating Carbon Sinks in the U.S.", pp. 905-912 in Riemer, P. (ed), Proceedings of the International Energy Agency Carbon Dioxide Disposal Symposium, Pergamon Press, Oxford, U.K. Richards, K.R. (1995) "The Time Value of Carbon in Bottom-up Studies", Pacific Northwest Laboratory. Unpublished manuscript. Richards, K.R. and Stokes, C. (1995) "National, Regional and Global Carbon Sequestration Case Studies: A Review and Critique", Pacific Northwest Laboratory. Washington D.C. Rothenberg, J. (1993) "Economic Perspectives on Time Comparisons: Alternative Approaches to Time Comparisons", in: Choucri (ed.), Global Accord. Environmental Challenges and International Responses, MIT Press. Cambridge, MA. Sandmo, A. and Dréze J.H. (1971) "Discount Rates for Public Investments in Closed and Open Economies", Economica 38:395-412. Stavins, R.N. (1996) "The Costs of Carbon Sequestration: a Revealed-Preference Approach", The RAND Journal of Economics (in press). van Kooten, G. Arthur, L. and Wilson, W. (1992) "Potential to Sequester Carbon in Canadian Forests: some Economic Considerations", Canadian Public Policy XVIII(2):127-138. Wangwacharakul, V. and Bowonwiwat, R. (1995) "Economic Evaluation of CO2 Response Options in the Forestry Sector: the Case of Thailand", Biomass and Bioenergy 8(5):293-307. Weitzman, M. (1994) "On the 'Environmental' Discount Rate", Journal of Environmental Economics and Management, 26:200-209. Xu, D. (1995) "The potential for reducing atmospheric Carbon by large-scale afforestation in China and related Cost/Benefir Analysis", Biomass and Bioenergy 8(5):337-344. 15 Table 1. Same method, different assumptions, different results r ? ? ? ? g i=? ? ? ?g+r (a) vc (b) %c (c) %i (d) discount rate (a*c + a*b*c) Cline 0% 1.5 1% 1.5% 2 0.8 0.2 2% Birdsall and Steer 1% 1.5 2% 4% 2 0.0 1.0 8% vc = shadow price of capital; %c = proportion of investment funds that come from postponed consumption; %i = proportion of investment funds from displaced investments. Source: Based on Cline (1992) and Birdsall and Steer (1993) Table 2. Methods and rates used to discount carbon flows in selected empirical studies Source Methoda discount rateb country Adams et al. (1990) discounting 10% USA Moulton and Richards (1990) discounting 10% (4%-8%) USA Nordhaus (1991) discounting 6% global (forestation option) Dixon, Schroeder and Winjum (1991) MCS - boreal, temperate and tropical Van Kooten et al. (1992) Flow summation - Canada Richards et al. (1993) discounting USA Parks and Hardie (1994) discounting 4% USA Dixon et al. (1994) MCS - S.America, Africa, S.Asia Faeth, Cort and Livernash (1994) Flow summation - Dev. countries Hoen and Solberg (1994) discounting 2%-7% Norway Stavins (1995) discounting 5% (2.5%- 10%) USA Englin and Callaway (1995) discounting 2%-10% USA Fernside (1995) discounting 0%, 1%, 5% Brazil Ismail (1995) discounting 0%, 1%, 3% Malaysia Makundi and Okiting'ati (1995) MCS - Tanzania Masera et al. (1995) MCS - Mexico Ravindranath and Somashekhar (1995) Flow summation - India Wangwacharakul and Bowonwiwat (1995) Flow summationc - Thailand Xu (1995) MCS - China Boscolo, Buongiorno and Panayotou (1996) discounting 6% (10%) Malaysia Notes: a The levelizing method is considered together with discounting; b Includes in parenthesis rates used for sensitivity analyses; c The authors assumed that the value of carbon increases at the rate of interest. This makes their flow summation approach equivalent to discounting. 16 Table 3. Assumptions for hypothetical analysis of reforestation and natural forest management activities REFORESTATION Gross stand growth (commercial assumed 2/3 of gross growth) 0 m3 /ha/yr (years 1-2); 6.9 m3 /ha/yr (years 3-12); 15.5 m3 /ha/yr (years 13-16); 24.2 m3 /ha/yr (years 17-20) Biomass/volume ratio 0.45 tons/m3 Carbon/biomass ratio 0.5 Commercial harvest 10 m3 (at year 12) 142 m3 (at year 20) Price of wood $45/m3 Compensation to farmers(1) $50/ha Plantation and other costs see Faris et al. (1997) NATURAL FOREST MANAGEMENT Standing volume 116 m3 /ha Deforestation rate(1) 12% Volume harvested 20 m3 /ha (in year 1) 10 m3 /ha (in year 11) 10 m3 /ha (in year 20) Stand growth rate 1 m3 /ha Stumpage price $33.84/m3 Compensation to farmers(1) $25/ha Other costs see Faris et al. (1997) Source: Unit management and implementation data have been taken from Faris et al. (1997) who present a case study of the Carfix project (Fundecor, 1994). (1) Our assumptions made for illustrative purposes and which do not correspond to either Faris et al. (1997) or Fundecor (1994). Table 4. Costs ($/ton) of carbon sequestration for two alternative activities Activities Method Reforestation Natural Forest Management r = 6% r = 7% r = 6% r = 7% Flow summation $4/ton $8/ton $7/ton $7/ton Discounting $10/ton $20/ton $10/ton $10/ton 17 Figure 1. Determination of the market interest rate Interest rate and rate of return (%) Quantity of Investment and Savings S(i) savings net of taxes on interest income S(i') rate of return received by savers before paying taxes I(π) return on investment gross of taxes I(π') return on investment net of taxes Q0 i im π i* Source: Adapted from Jenkins and Harberger (1996)
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DISCOUNTING COSTS AND BENEFITS IN CARBON SEQUESTRATION PROJECTS Marco Boscolo, Jeffrey R. Vincent, and Theodore Panayotou Environment Discussion Paper No. 41 February 1998 Support for the research reported in this paper was provided by the U.S. Environmental Protection Agency, through a cooperative agreement on "Economic Analysis of International Forestry Issues"; the Smithsonian Tropical Research Institute's Center for Tropical Forest Science, through a grant from the Southern Company; and the Harvard Institute for International Development. Marco Boscolo is a Research Associate at the Harvard Institute for International Development (HIID) and the Center for Tropical Forest Science, Smithsonian Tropical Research Institute. Jeffrey R. Vincent is a Fellow at the Harvard Institute for International Development and Director of HIID's Newly Independent States Environmental Economics and Policy Project. Theodore Panayotou is an Institute Fellow and Director of the International Environment Program at the Harvard Institute for International Development. The views expressed are solely those of the author(s) and do not necessarily represent the views of the U.S. Agency for International Development, the host government or the Harvard Institute for International Development. The boundaries, colors, and other information shown on any map in this volume do not imply any judgment on the legal status of any territory or the endorsement of acceptance of such boundaries. This paper is for discussion purposes and HIID welcomes comments, which will be relayed to the authors. This document should not be quoted without the permission of HIID or the author(s). For additional information please contact: International Environment Program, Harvard Institute for International Development, One Eliot Street, Cambridge, MA 02138. Tel: (617) 496-5176. Fax: (617) 496-8040 1 1. INTRODUCTION Because the effects of higher atmospheric concentrations of carbon dioxide might be felt far into the future, the choice of the discount rate is critical in economic analyses of climate change. Discounting inevitably reduces the weight of future damages, even catastrophic ones, that might result from global climate change. Some economists have proposed using very low discount rates in analyzing carbon- abatement investments (Cline, 1992, 1993; Rothenberg, 1993). Others have argued that "meeting the needs of future generations will only be possible if investible resources are channeled to projects and programs with the highest environmental, social, and economic rates of return [which is not likely] to happen if the discount rate is set significantly lower than the opportunity cost of capital" (Birdsall and Steer, 1993). In short, the choice of the discount rate remains a controversial issue in the climate change literature (cf. Nilsson, 1995; Hoen and Solberg, 1995). This paper addresses the discounting issue in the particular case of carbon sequestration projects. Our concern is to ensure that analyses of different projects are comparable, particularly with respect to the costs of carbon sequestration, and thereby accurately identify the socially most desirable projects. In this sense, our focus is narrower than benefit-cost analysis of global climate change. Our intention is not to advocate or dismiss action to reduce net carbon dioxide emissions. Instead, it is to provide guidelines for selecting an appropriate discount rate, given a desire to sequester carbon from the atmosphere. The paper is organized as follows. First, the basic rationale for using a positive social discount rate in evaluating investment projects is summarized. Second, methods for calculating the social discount rate are reviewed. Although agreement does not yet exist regarding which method is best, significant progress has been made in identifying the economic determinants of the discount rate. Third, arguments for and against the application of discounting to physical units of carbon are summarized. Our conclusion is that physical units should be discounted. Finally, we present an example to clarify the assumptions involved in, and the implications of, selecting a given rate. 2. THE RATIONALE FOR DISCOUNTING Discounting is used to compare benefits and costs that occur at different points in time. The basic argument for using a positive social discount rate is that resources used in both consumption and production have a higher value today than in the future. This is because: (i) consumption today is preferred to consumption tomorrow—the social rate of time preference (SRTP) is positive—and (ii) capital investments enhance production possibilities, and thus consumption possibilities, in the future as well as today—the social return on investment (SRI) is positive. We review these consumption and production aspects of discounting in turn. 2.1 The Social Rate of Time Preference It is useful to think of the SRTP, or consumption rate of interest i, as the sum of two components, a "pure" or "myopic" preference for consuming a good sooner rather than later (r), and a term indicating how changes in consumption affect the marginal utility of consumption: i = r + ?g . (1) ? is the negative of the elasticity of marginal utility with respect to consumption, while g is the expected rate of growth in per capita consumption. Assuming, as is standard, diminishing marginal returns to consumption, ? is positive. 2 The second component in (1) captures the effect that higher interest rates are required to draw forth a given amount of savings when individuals expect consumption to rise in the future, e.g. due to rising income. In that case, society needs to save less in the current period to finance future consumption. The inclusion of this second component indicates that a positive SRTP does not necessarily reflect selfishness on the part of the current generation (r). The SRTP can also be positive because consumption is expected to grow (g > 0). Then, as we will see in a moment, a positive SRTP reflects the balancing, at the margin, of the utility derived from consumption in current and future periods. Markandya and Pearce (1988) provide a particularly lucid derivation of (1). Suppose that the social objective is to allocate consumption between two periods to maximize the discounted sum of utility from consumption: W(Ct) + W(Ct+1)/(1 + i) , (2) subject to the constraint: C = Ct + Ct+1 . (3) That is, a given amount of consumable goods is available for allocation. We have not defined i; indeed, demonstrating that i does not equal zero is the point of the analysis. Solving (3) for Ct+1, substituting the result into (2), and taking the derivative with respect to Ct, we obtain the first-order condition, ?W(Ct)/? Ct = [?W(Ct+1)/? Ct] / (1 + i) . (4) This is the inter-temporal efficiency condition for consumption. Solving it for i yields: t t t C C W C C W C C W i ? ? ? ? ? ? ) ( ) ( ) ( 1 ? = + , (5) or, using more compact notation: ) ( ) ( t C t C C W dt C dW i = . (6) This is the general expression for the SRTP. It indicates that the SRTP equals the proportional change in the marginal utility of consumption from one period to the next. (6) equals the two-component expression given by (1) if the utility function has the following specific functional form: W(Ct) = Ct 1-? * e-rt * (1-?)-1 , (7) Substituting the relevant derivatives of this function into (6), we obtain: 3 i dC dt C r t t = + ? / . (8) dCt/dt / Ct is the rate of growth in consumption, and so (8) is equivalent to (1). i is always positive when consumption is rising. It can be positive even when consumption is falling, as long as r is larger than the absolute value of ?g. The SRTP can be thought of as the supply curve for savings in the economy, with r being the intercept and ?g yielding an upward-sloping relationship between savings (forgone consumption) and the interest rate earned on those savings. This savings function is depicted in Figure 1 by the line S(i). Individuals are willing to postpone consumption (i.e., save) only if they are compensated for their "sacrifice" with a positive return. The higher the return, the more they save. 2.2 The Social Return on Investment The other rationale for discounting stems from the fact that capital is productive, i.e., $1 invested in productive activities instead of consumed will generate additional income, hence additional consumption, in the future. The SRI therefore measures the opportunity cost of investing in, for example, carbon sequestration instead of other productive activities. If Y=F(K,z) is a well-behaved production function, where K is capital and z is a vector of other variables (e.g. labor, technology, etc.), the marginal product of capital, FK, yields the economy's investment demand curve. Assuming that capital exhibits diminishing marginal returns, an incremental unit of capital yields a lower return than the previous unit. Hence, the demand curve slopes downward. We therefore expect that an additional unit of investment will be made only if the additional funds required can be borrowed at a cost lower than the previous unit. The investment function is depicted in Figure 1 by the line I(π), where π is the cost of borrowing funds. 2.3 Market Equilibrium The market interest rate results from the interplay of the supply of savings (positively correlated with the rate of interest) and the demand for investment (negatively correlated with the interest rate). In the absence of distortions (taxes, market imperfections, risk, etc.), supply and demand cross at the market clearing rate i* (see Figure 1). Note that i* = i = π : the market interest rate equals both the SRTP and the SRI. In this situation, there is no ambiguity about the social discount rate. It is simply the market interest rate, which reflects equally consumer and producer rates of time preference. Of course, a distortion-free market is an idealized situation. Taxes and other distortions shift the market supply and demand curves. For example, taxes on interest income cause savers to require compensation of more than i for their postponed consumption. They demand a higher interest rate to save a given amount, because they must share part of their interest income with the government. The upward shift of the savings supply function to S′(i) reflects this reality. Taxation of investment returns introduces similar distortions. Firms that earn π on their productive investments will not be willing to borrow funds at π, as they must use some of the earnings to cover their tax obligations. As a result, the investment demand curve shifts downward to I′(π). The interest rate determined by market interactions is now im, with the associated amount of savings and investment represented by Q0. Note that im does not equal either the SRTP or the SRI. At Q0, im could be much higher than the SRTP and much lower than the SRI. For example, if im is 8% and consumers face a 4 25% income tax and firms face a 50% profit tax, the values of i and π would be 6% and 16%, respectively. Firms return 8% to their investors after paying the profit tax, while investors retain 6% after paying the income tax. What, then, is the social discount rate? Is it π, i, or a combination of the two? 3. METHODS FOR CALCULATING THE SOCIAL DISCOUNT RATE The foregoing discussion indicates that funds made available to finance carbon sequestration projects generally come at the expense of both consumption and investment, but the market interest rate is unlikely to reflect the social opportunity cost of either displaced activity. Four major methods have been proposed to calculate the social discount rate in this situation: the after-tax savings rate, the pre-tax return on investment, the shadow price of capital, and the weighted-average (social opportunity cost of capital) method. We review the particular features of each method in the following sections. 3.1 After-Tax Savings Rate As discussed in section 2.1, the SRTP equals the sum of the pure rate of time preference and the product of the elasticity of the marginal utility of consumption times the expected growth rate of consumption. The few available estimates suggest that the rate of pure time preference ranges from 0 to 2% and the elasticity of marginal utility from 1 to 2 (equaling 1 if utility is strictly proportional to consumption), while income growth differs from country to country (Markandya and Pearce, 1988). This explains why economists generally expect developing countries to have higher discount rates than industrialized ones. The marginal utility of consumption, and its elasticity, are high when people live at a subsistence level and are focused on sheer survival from one period to the next. Moreover, the theory of economic convergence predicts that poor countries will have, on average, higher income growth rates (hence, higher consumption growth rates) than rich countries (Barro and Sala-i-Martin, 1995). If the SRTP is used as the discount rate in carbon sequestration projects, these points suggest that the same project may look very different to developing and developed countries for reasons other than the distribution of benefits and costs. Use of the SRTP in applied studies has not been free of criticism. On the value of r, some have argued that impatience discounting is "irrational" (cf. Pearce and Turner, 1990, for a review). Regarding ?, some economists dispute whether there is a meaningful way to measure the social marginal utility of consumption. The debate centers on the measurability of utility, both across individuals and over time. Finally, projections of future consumption growth are not perfect, and such imprecision makes them relatively easy to criticize. Due to these measurement difficulties, economists often compute the SRTP indirectly by calculating the real, after-tax rate of return on savings. This is typically done by taking the interest rate on long-term, low-risk investments (such as treasury bills) and correcting for inflation and taxes (as in the numerical example in section 2.3). When the SRTP is computed in this way, time-series data covering a long period should be used to avoid short-term fluctuations. Moreover, the SRTP should reflect the marginal, not the average, return on savings. The former is higher than the latter, as can be seen by referring to Figure 1. Boardman et al. (1996) also warn that even if the individual rate of time preference equals the real after-tax savings rate, the social rate may not. Risk in particular is perceived quite differently by individuals and by society at large. The individual risk of death, which is one of the reasons sometimes offered to justify the pure rate of time preference, is higher than the risk of society's disappearance. Based on risk considerations, we might therefore expect the SRTP to be lower than the real, after-tax savings rate that individuals collect. 5 Others have argued that a time-invariant SRTP is inappropriate (Kula, 1992; Rothenberg, 1993). Some of these arguments are based on ethical grounds, while others hinge on the premise (consistent with growth theory and (1)) that future consumption growth will not proceed at rates experienced in the past (Nordhaus, 1994). Because consumption growth is positively correlated with the SRTP due to the ?g term, a reduction over time in the consumption growth rate necessarily leads to a declining SRTP. Cropper et al. (1992) have provided empirical evidence of a diminishing social rate of time preference stemming from (presumably) ethical considerations. In their survey, participants were asked to express their willingness to tradeoff lives saved today with lives saved in the future. The authors found that people were indifferent between a life saved today and two lives saved in five years' time, or 11 lives saved in 50 years' time, or 44 lives saved in 100 years. The implicit rates of time preference were 16.8% for the five-year horizon, 4.8% for the 50-year horizon, and 3.8% for the 100-year horizon. The most fundamental criticism of equating the social discount rate to the SRTP, however, is that the SRTP is purely a measure of the opportunity cost of consumption. The SRTP ignores the opportunity cost of production given by the return on investments. We turn next to a method that computes the social discount rate using the opportunity cost of capital, and then to a method that attempts to rectify this shortcoming of the SRTP. 3.2 Pre-Tax Return on Investment Some economists have suggested that all investment projects, both private and public, should employ a discount rate equivalent to the marginal productivity of capital in the private sector. They argue that, even for public investments, it is in the public interest to sponsor projects that yield the highest return. If the private sector is able to achieve higher returns than prospective public-sector projects, then the government should invest in private rather than public projects. To approximate the marginal productivity of capital, economists often compute the pre-tax rate of return on private investments. This method contains three potential biases (Boardman et al., 1996). First, as in the case of the post-tax savings rate, the relevant rate is the marginal, not the average, productivity of capital. The rate of return is lower on the margin than on average because the "best" deals will be struck first. Hence, additional investments are unlikely to yield as much as the existing ones. Using the average rate of return thus biases the estimated discount rate upward. Second, private rates of return may be distorted by externalities or monopoly pricing. Many economic activities cause some degree of environmental degradation. Thus, additional expenditures on environmental cleanup may be necessary to rectify this degradation and achieve the socially (if not privately) optimal level of environmental quality. These expenditures cause some of the project's output to "evaporate," with the net effect of lowering the marginal social productivity of capital (Weitzman, 1994). Ignoring such negative externalities of investments biases the estimated social discount rate upward, although the bias may be small1 . Similarly, if monopoly power allows firms to increase prices above their socially optimal levels, the private return on investment overestimates the social discount rate. Finally, the private return on investment reflects premia for risk. Since society has wider opportunities to diversify its portfolio than individual investors, social risk premia are probably lower than private risk premia. Hence, again, the social return on investment is likely to be lower than the pre-tax private return. 1 Based on US data, Weitzman (1994) estimated that the bias is likely to range between just 4% and 6% of the discount rate. 6 As with the SRTP, one might expect the social return on investment—computed as the pre-tax private return—to decrease over time (Pearce and Turner, 1990; Weitzman, 1994). There are two main reasons for this. First, capital is usually assumed to exhibit diminishing marginal returns. This argument can be connected to the theory of economic convergence referred to earlier (cf. Barro and Sala-i-Martin, 1995). Second, in a world that is apparently evolving toward an ever-increasing degree of environmental concern, the proportion of expenditures directed toward environmental improvement might also increase. The implication is that the difference between the private rate of return and the social return should decline over time (Weitzman, 1994). The fundamental criticism of the pre-tax investment return method is the mirror image of the one for the post-tax savings rate: it ignores the opportunity cost of savings (Jenkins and Harberger, 1996). From Figure 1, we can see that π may be much higher than i and therby greatly overstate consumers' rate of time preference. 3.3 The Shadow Price of Capital This method applies the SRTP to both consumption and investment flows, after the latter is converted to "consumption equivalents" through the application of a shadow price of capital. This method is associated with contributions by Eckstein (1958), Arrow (1966), Arrow and Kurtz (1970), Feldstein (1972), Bradford (1975), and Lind (1982). The estimation of the shadow price of capital is straightforward if we assume that each dollar invested today yields a perpetual return π that is entirely consumed. In that case, the present value of the annual flow of consumption is given by π/i, where i is the SRTP. This means that π/i can be taken as the shadow price of investments in terms of consumption. Alternative formulas are necessary when less restrictive assumptions are made regarding the proportion of π that is consumed. Bradford (1975) proposed the following formula for the case when investment returns are perpetual but a proportion of the annual return π is re-invested: Shadow price = ( ) 1? ? s i s γ γ , (9) where γ = (1+π)/(1+i), s is the marginal propensity to save, and sγ < 1. The shadow price increases with the fraction of π reinvested. More recently, Cline (1992) suggested a revised formulation of Lind's method (Lind, 1982): Shadow price = + = ∑A i N t t N π , / ( ) 1 1 , (10) where Aπ, N = π/[1-(1+π)-N ]. (11) Aπ, N is the annual payment from an annuity lasting N years and having a present value of $1 when discounted using π. Equations (8) and (9) were used by Cline (1992) in his benefit-cost analysis of mitigation options for global warming. He computed a shadow price of capital of approximately 2 (one unit of capital is worth two units of consumption), consistent with i=0.015, π=0.1, and a 15-year capital 7 life (N). After converting investment flows to consumption equivalents using this shadow price, he then discounted them along with all other benefits and costs using the SRTP. The shadow-price method is conceptually correct. It allows one to use the SRTP as the social discount rate without ignoring the opportunity cost of displaced investment. Hence, it is preferable to either of the first two methods. The main issue with this method has been its practical feasibility. We discuss this issue in the next section. 3.4 The Weighted-Average Method According to the weighted-average method, the social discount rate is defined as the weighted average of the SRTP (usually computed as the post-tax savings rate) and the SRI (usually computed as the pre-tax investment return). It is associated with contributions by Krutilla and Eckstein (1958), Haveman (1969), Sandmo and Dréze (1971), and Harberger (1976). It is the principal conceptually sound alternative to the shadow-price method. The social discount rate iw is defined as: iw = wc i + (1-wc) π , (12) where wc is the proportion of incremental funds obtained at the expense of current consumption and 1-wc is the proportion obtained at the expense of investment in alternative opportunities. The determination of wc is based on the following reasoning. A new project increases the demand for funds, which causes market interest rates to rise. In turn, this prompts consumers to save more and investors to borrow less for other projects. This displacement of consumption and investment add up to what Jenkins and Harberger call the social opportunity cost of funds. Given a private savings function S(x, im) and a private investment function I(y, im), where x and y are vectors of socio-economic characteristics (including tax rates) and im is the market interest rate, the proportion of incremental funds obtained at the expense of current consumption is: w S i S i I i c m m m = ? ? ? ? ? ? ? . (13) Substituting (13) into (12), we obtain: iw = ? ? i S i I i S i I i m m m m ? ? π ? ? ? ? ? ? . (14) Expressed in elasticity form, (14) is: i i I S I S w s I T T s I T T = ? ? ε πη ε η ( / ) ( / ) , (15) where εs is the elasticity of supply of savings and ηI is the elasticity of demand for funds for private investments with respect to the market interest rate. As an illustrative example, for i = 0.015 and π = 0.1 8 (the same values used by Cline) and values of εs = 0.3, ηI = -1.0 and IT/ST = 0.9 (as suggested by Jenkins and Harberger), we obtain a value of iw of approximately 8%. In theory, the shadow-price method and the weighted-average method should yield equivalent results in terms of the economic desirability of alternative projects (Jenkins and Harberger, 1996:12-7), although they obviously yield different discount rates (with discount rates from the latter method being higher). The weighted-average method, however, has at least one advantage over the shadow-price method, namely that the rate it generates can be applied to different projects. In contrast, rigorous application of the shadow-price method requires the computation of a different shadow price for projects of different lengths. This can be seen from equation (10), which indicates that a different annuity, and thus a different shadow price, is obtained when different time horizons are considered. While maintaining consistency with economic theory, the weighted-average method provides a way to define a discount rate that is independent of project length.2 The choice of which method to use will not necessarily resolve disagreement over the choice of the discount rate, as both methods leave ample room for disagreement about assumptions. In the March 1993 issue of Finance and Development, William Cline's advocacy of a low effective discount rate contrasted sharply with the views of Nancy Birdsall and Andrew Steer of the World Bank. At the heart of the debate was not the method (both accepted the shadow-price method), but rather the assumptions about parameters such as the pure rate of time preference (r), expected growth rate in per capita consumption (g) and the fraction of funds that would come from displaced consumption (wc). Table I summarizes the assumptions made in the debate and the resulting effects on the effective (i.e., weighted-average) discount rate. Divergent assumptions about r and g led to a nearly threefold difference in the SRTP, and this result was accentuated by additional differences in assumptions about displaced consumption. Consequently, the implicit weighted-average discount rate differed by a factor of more than three. 4. DISCOUNTING OF CARBON FLOWS Having reviewed the rationale for using a positive social discount rate and methods to compute the rate, we now come to a potentially tricky question facing analysts of carbon sequestration projects: how should carbon flows be summarized and compared to sequestration costs? Benefit-cost analysis requires monetization of all effects caused by a project. Monetary valuation of the economic benefits of carbon sequestration remains a controversial and difficult matter, and it has been attempted by only a few scholars (Cline, 1992; Nordhaus, 1994; Fankhauser and Pearce, 1994). Furthermore, Mendelsohn et al. (1994) have criticized existing valuation work on the economic damages from climate change, at least with respect to effects on the US agricultural sector. As an alternative to the evaluation of allocative efficiency, which requires expressing benefits as well as costs in monetary terms, most studies have focused instead on evaluating the cost-effectiveness (C-E) of carbon sequestration options. Nordhaus (1991), Richards and Stokes (1995), and Stavins (1996) review these studies. C-E analysis produces a summary statistic such as "dollars spent per ton of sequestered carbon." Although it is silent on the overall economic desirability of carbon sequestration, it permits identification of the options that sequester carbon at the lowest cost. That is, it enables estimation of the supply schedule for carbon sequestration: the marginal cost of sequestration for progressively greater amounts of sequestered carbon (cf. Nordhaus, 1991; Richards and Stokes, 1995; Stavins, 1996; Boscolo et al., 1996). 2 This does not mean that the social discount rate based on the weighted-average method is necessarily constant over time. As discussed earlier, both of its components, the SRTP and SRI, might change over time. 9 The obvious attraction of the C-E approach is that tons of sequestered carbon are easier to quantify than the economic benefits of sequestration. Indeed, documents on most carbon sequestration projects include information on physical flows of carbon (e.g., Faeth et al., 1994; Fundecor, 1994; Barres et al., 1995). Application of the C-E approach demands, however, an answer to the question as to how these flows should be summarized over time and compared to project costs. At least three different methods are used in the literature to account for carbon flows at different points in time. Richards and Stokes (1995) classify them as flow summation, mean carbon storage, and levelization (or discounting). Flow summation measures the total tons of carbon sequestered (in net terms) over the lifetime of a project, regardless of when sequestration occurs. Mean carbon storage is the average amount of carbon stored per year: flow summation divided by the length of the project. Like flow summation, this method assumes indifference between carbon sequestration in the near or distant future. Levelization also converts carbon flows to an annual equivalent, but it then divides this quantity into the annualized present value of project costs. These three methods involve different assumptions about the discount rate. To illustrate, suppose we have a carbon sequestration project lasting T years that involves annual costs of Ct (not necessarily constant) and has annual carbon flows of Xt (again, not necessarily constant). Let p be the unit value of a ton of sequestered carbon (i.e., the avoided damage cost of climate change). Then the net present value of the project is: NPV = ∑ pXt (1+iw)?t ? ∑ Ct (1+iw)?t , (16) where the sums are evaluated over the interval t = 1, …, T. By definition, the break-even price of carbon (pBE) is the unit value that yields a net present value of zero. Setting (16) equal to zero and solving for p (= pBE), we obtain: pBE = ∑ Ct (1+iw)?t / ∑Xt (1+iw)?t . (17) The right-hand side of this expression gives the unit cost of carbon sequestration, consistent with the benefit-cost analysis principles from which (17) is derived. The key finding from this simple exercise is that tons of carbon (the denominator of the expression) are discounted. For this reason, estimates of sequestered carbon calculated using the flow summation and mean carbon storage methods cannot be meaningfully compared to project costs. The levelization method, which involves calculating the annual- equivalent cost value C such that: ∑ C (1+iw)?t = ∑ Ct (1+iw)?t yields estimates of pBE identical to those from (17) as long as the discount rate is also taken into account in calculating the annual-equivalent carbon flow X: ∑ X (1+iw)?t = ∑ Xt (1+iw)?t Discounting treats the amounts of CO2 sequestered from the atmosphere in each period as if it were money3 and yields identical results to levelizing4 (Richards and Stokes, 1995). Table II provides a partial 3 Stated differently, discounting carbon flows yields a break-even value for carbon. 4 As pointed out by Richards (1995) discounting carbon flows like money relies on the assumption of linearity between emissions and damages. Other functional forms may lead to alternative paths. 10 review of alternative methods and discount rates used in empirical studies. It should be noted that, while in the United States most carbon studies have adopted the levelizing/discounting method, similar studies carried out in developing countries have used the flow summation or mean carbon storage methods. It is therefore impossible to undertake a direct comparison of results. In addition, the choice of which method is employed to produce a final summary statistic will significantly affect the results. Here, we discuss an example to illustrate the influence of the summary statistic and the discount rate used on the desirability of a carbon sequestration project measured in terms of "dollars spent per ton of carbon sequestered." In our illustrative example we have derived results for two hypothetical activities: a reforestation and a natural forest management (NFM) activity. The former will take place on private farmland currently used for cattle grazing. The latter will take place on an area under imminent threat of deforestation where we have assumed an annual deforestation rate of 12%. Other basic assumptions are summarized in Table III. Using a discount rate of 6% and flow summation as the summary statistic, reforestation attains carbon sequestration at a unit cost of $4/ton. This compares favorably with the natural forest management activity that achieves sequestration at $7/ton (see Table IV). However, when physical units of carbon are discounted at a rate of 6%, the two activities achieve carbon sequestration with even efficiency: $10/ton (see Table IV). Based on this evidence, we would conclude that the reforestation activity is superior to, or at least as good as, the NFM one. Increase of the discount rate by only one percentage point leads to antithetical results. Under the flow summation statistic, the two activities achieve carbon sequestration at the same unit cost: $7-8/ton. When we discount carbon flows, however, the cost of carbon sequestration through reforestation is $20/ton, twice as high as the cost needed to implement NFM (see Table IV). Under this scenario the NFM activity is superior to, or at least as good as, the reforestation option. This example illustrates three points. First, certain environmentalists' advocacy of a lower discount rate may be counter-productive when the benefits from conservation are to be enjoyed before their costs (as in the case of preventing deforestation as opposed to promoting reforestation). Second, the use of an undefined summary statistic such as "dollars spent per ton of carbon sequestered" may be misleading. Alternative projects or activities will be comparable in their cost-effectiveness only if their carbon accounting is comparable as well. For example, the cost-effectiveness of a project appears more attractive when flow summation is used rather than discounting. Third, the use of a discount rate is fundamentally one of the most serious sources of uncertainty: results will be very sensitive to even small changes in the discount rate, particularly if costs and benefits occur at the beginning and end (or vice-versa) of the project. In these cases sensitivity analyses are strongly encouraged. 5. CONCLUSIONS In order to allow comparison between alternative projects or activities, use of a positive discount rate is fundamental. Four main methods are available to derive the social discount rate. We suggest the use of the weighted-average method, because it is theoretically sound and empirically simple to apply. In order to use this method, approximate values for SRTP and SRI are necessary (keeping in mind potential issues summarized in section 3.1). We have reported some arguments in favor of diminishing SRTP and SRI over time. With respect to the SRTP, these views are consistent with a diminishing income growth (Nordhaus, 1994), or empirical evidence regarding a nonconstant (diminishing) marginal rate of time preference (Loewenstein and Thaler, 1989, Cropper et al., 1992). Our view is that for very long projects a diminishing SRTP may be an appropriate solution. Regarding the SRI we also found arguments in favor of a diminishing rate, given a diminishing "net" marginal productivity of capital (Weitzman, 1994). Capital itself exhibits a diminishing marginal productivity that is further reduced when we account for 11 the fact that many economic activities in the private sector involve environmental externalities. To account for this last effect, however, we suggest that proper valuation of environmental amenities may be a better way to deal with environmental externalities than adjustment of the discount rate. In sum, different methods or assumptions yield different results. However, there are clear guidelines for making informed decisions regarding the selection of the discount rate and for supporting a given decision with arguments grounded in economic theory. Yet, we are probably still far from a time when all will all agree on the most appropriate discount rate for a given project. In the meantime, we suggest that sensitivity analyses should always consider the effects of varying discount rates. Many scholars have criticized the use of the same discount rate for environmental (e.g., carbon sequestration) as opposed to other development projects. However, this argument loses appeal when the issue shifts from questions as to whether an environmental project should be carried out to how a given sequestration goal can be achieved. In this case, discounting project impacts such as carbon sequestration is a fundamental necessity for ensuring comparability. 12 REFERENCES Adams, R. Adams, D. Callaway, J. Chang, C. and McCarl, B. 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(1994) Managing the Global Commons: The Economics of Climate Change, The MIT Press. Cambridge, MA. Parks, P.J. and Hardie, I.W. (1995) "Least-Cost Forest Carbon Reserves: Cost-Effective Subsidies to Convert Marginal Agricultural Land to Forests", Land Economics 71:122-136. Pearce, D.W. and Turner, R.K. (1990) Economics of Natural Resources and the Environment, Johns Hopkins University Press. Baltimore, MD. Ravindranath, N. and Somashekhar B. (1995) "Potential and Economics of Forestry Options for Carbon Sequestration in India", Biomass and Bioenergy 8(5):323-336. Richards, K.R. Moulton, R. and Birdsey, R. (1993) "Costs of Creating Carbon Sinks in the U.S.", pp. 905-912 in Riemer, P. (ed), Proceedings of the International Energy Agency Carbon Dioxide Disposal Symposium, Pergamon Press, Oxford, U.K. Richards, K.R. (1995) "The Time Value of Carbon in Bottom-up Studies", Pacific Northwest Laboratory. Unpublished manuscript. Richards, K.R. and Stokes, C. (1995) "National, Regional and Global Carbon Sequestration Case Studies: A Review and Critique", Pacific Northwest Laboratory. Washington D.C. Rothenberg, J. (1993) "Economic Perspectives on Time Comparisons: Alternative Approaches to Time Comparisons", in: Choucri (ed.), Global Accord. Environmental Challenges and International Responses, MIT Press. Cambridge, MA. Sandmo, A. and Dréze J.H. (1971) "Discount Rates for Public Investments in Closed and Open Economies", Economica 38:395-412. Stavins, R.N. (1996) "The Costs of Carbon Sequestration: a Revealed-Preference Approach", The RAND Journal of Economics (in press). van Kooten, G. Arthur, L. and Wilson, W. (1992) "Potential to Sequester Carbon in Canadian Forests: some Economic Considerations", Canadian Public Policy XVIII(2):127-138. Wangwacharakul, V. and Bowonwiwat, R. (1995) "Economic Evaluation of CO2 Response Options in the Forestry Sector: the Case of Thailand", Biomass and Bioenergy 8(5):293-307. Weitzman, M. (1994) "On the 'Environmental' Discount Rate", Journal of Environmental Economics and Management, 26:200-209. Xu, D. (1995) "The potential for reducing atmospheric Carbon by large-scale afforestation in China and related Cost/Benefir Analysis", Biomass and Bioenergy 8(5):337-344. 15 Table 1. Same method, different assumptions, different results r ? ? ? ? g i=? ? ? ?g+r (a) vc (b) %c (c) %i (d) discount rate (a*c + a*b*c) Cline 0% 1.5 1% 1.5% 2 0.8 0.2 2% Birdsall and Steer 1% 1.5 2% 4% 2 0.0 1.0 8% vc = shadow price of capital; %c = proportion of investment funds that come from postponed consumption; %i = proportion of investment funds from displaced investments. Source: Based on Cline (1992) and Birdsall and Steer (1993) Table 2. Methods and rates used to discount carbon flows in selected empirical studies Source Methoda discount rateb country Adams et al. (1990) discounting 10% USA Moulton and Richards (1990) discounting 10% (4%-8%) USA Nordhaus (1991) discounting 6% global (forestation option) Dixon, Schroeder and Winjum (1991) MCS - boreal, temperate and tropical Van Kooten et al. (1992) Flow summation - Canada Richards et al. (1993) discounting USA Parks and Hardie (1994) discounting 4% USA Dixon et al. (1994) MCS - S.America, Africa, S.Asia Faeth, Cort and Livernash (1994) Flow summation - Dev. countries Hoen and Solberg (1994) discounting 2%-7% Norway Stavins (1995) discounting 5% (2.5%- 10%) USA Englin and Callaway (1995) discounting 2%-10% USA Fernside (1995) discounting 0%, 1%, 5% Brazil Ismail (1995) discounting 0%, 1%, 3% Malaysia Makundi and Okiting'ati (1995) MCS - Tanzania Masera et al. (1995) MCS - Mexico Ravindranath and Somashekhar (1995) Flow summation - India Wangwacharakul and Bowonwiwat (1995) Flow summationc - Thailand Xu (1995) MCS - China Boscolo, Buongiorno and Panayotou (1996) discounting 6% (10%) Malaysia Notes: a The levelizing method is considered together with discounting; b Includes in parenthesis rates used for sensitivity analyses; c The authors assumed that the value of carbon increases at the rate of interest. This makes their flow summation approach equivalent to discounting. 16 Table 3. Assumptions for hypothetical analysis of reforestation and natural forest management activities REFORESTATION Gross stand growth (commercial assumed 2/3 of gross growth) 0 m3 /ha/yr (years 1-2); 6.9 m3 /ha/yr (years 3-12); 15.5 m3 /ha/yr (years 13-16); 24.2 m3 /ha/yr (years 17-20) Biomass/volume ratio 0.45 tons/m3 Carbon/biomass ratio 0.5 Commercial harvest 10 m3 (at year 12) 142 m3 (at year 20) Price of wood $45/m3 Compensation to farmers(1) $50/ha Plantation and other costs see Faris et al. (1997) NATURAL FOREST MANAGEMENT Standing volume 116 m3 /ha Deforestation rate(1) 12% Volume harvested 20 m3 /ha (in year 1) 10 m3 /ha (in year 11) 10 m3 /ha (in year 20) Stand growth rate 1 m3 /ha Stumpage price $33.84/m3 Compensation to farmers(1) $25/ha Other costs see Faris et al. (1997) Source: Unit management and implementation data have been taken from Faris et al. (1997) who present a case study of the Carfix project (Fundecor, 1994). (1) Our assumptions made for illustrative purposes and which do not correspond to either Faris et al. (1997) or Fundecor (1994). Table 4. Costs ($/ton) of carbon sequestration for two alternative activities Activities Method Reforestation Natural Forest Management r = 6% r = 7% r = 6% r = 7% Flow summation $4/ton $8/ton $7/ton $7/ton Discounting $10/ton $20/ton $10/ton $10/ton 17 Figure 1. Determination of the market interest rate Interest rate and rate of return (%) Quantity of Investment and Savings S(i) savings net of taxes on interest income S(i') rate of return received by savers before paying taxes I(π) return on investment gross of taxes I(π') return on investment net of taxes Q0 i im π i* Source: Adapted from Jenkins and Harberger (1996)