Implementing carbon credits for forests based on green accounting

Ecological Economics 56 (2006) 610 – 621 www.elsevier.com/locate/ecolecon

ANALYSIS

Implementing carbon credits for forests based on green accountingB Robert D. Cairnsa, Pierre Lasserreb,* a Department of Economics, McGill University, Montreál QC, Canada De´partement des Sciences Economiques, Universite´ du Que´bec a Montreál, Montreál QC, Canada

b

Received 14 April 2004; accepted 18 March 2005 Available online 25 May 2005

Abstract This paper presents a carbon-accounting method for forests that is implementable in the sense that it makes use of observable information. The valuation of the effects of carbon dioxide is based on asset values rather than rental values. With minor differences due to the treatment of such accidents as fires and pestilence, the method corresponds to the flow method of the physical carbon-accounting literature. The stock-change method of carbon accounting, however, is incompatible with economic principles. Rather than set carbon values to their optimal levels in the Pigovian tradition we use current societal standards. We also present a discussion of how to implement the scheme in the face of uncertainty. D 2005 Published by Elsevier B.V. Keywords: Carbon credit; Forest; Green accounting; Asset value; Rental value; Afforestation; Deforestation; Wood products; Forest fires; Accidental loss JEL classification: H00; Q280; Q290; Q380; Q390

1. Introduction Considerable quantities of carbon are contained in the world’s forests. As trees grow, they fix (sequester) a quantity of carbon which is proportional to the growth of their biomass. This observation has led many to observe that increasing the area devoted to B

Financial support from the FCAR is gratefully acknowledged. * Corresponding author. E-mail addresses: [email protected] (R.D. Cairns), [email protected] (P. Lasserre). 0921-8009/$ - see front matter D 2005 Published by Elsevier B.V. doi:10.1016/j.ecolecon.2005.03.029

forests, or the stock of timber in existing forests, could be a method to mitigate the increase of atmospheric carbon dioxide (CO2), a greenhouse gas. According to the IPCC (Intergovernmental Panel on Climate Change, 2000), terrestrial ecosystems may have served as a small net sink for CO2 over the last two decades, to the tune of about 200 to 700 million (metric) tonnes per year (Mty 1) of carbon (C). This flow is small when compared with yearly emissions from fossil-fuel consumption of more than 6000 Mty l during the 1990s. There is considerable debate about the potential of afforestation and reforestation or

R.D. Cairns, P. Lasserre / Ecological Economics 56 (2006) 610–621

of improved forestry practices for mitigating climate change. Indeed, the IPCC has attempted to quantify the potential of improved forest management and agroforestry on existing forests, plus the potential of changing land use to agroforestry. It estimates that it is unlikely that the increase in the yearly contribution from forests in 2010 could exceed 586 Mty 1, less than 10% of current emissions from fossil fuels (IPCC, 2000, Tables 2 and 4). The commitment made in Kyoto, however, is for a reduction of total emissions as compared to the 1990 levels, not for their total elimination; several Annex I countries also showed considerable reluctance in committing to such a reduction. Achieving only half of the potential identified by the IPCC would go a long way toward meeting the Kyoto commitment. This is especially true for countries which may rely on forests to meet a portion of their commitments. For example, for Canada, which accounts for 10% of the earth’s forest area and 2.3% of global emissions, the potential contribution of forest and forest products to meeting the Kyoto commitment is very significant. The total store of carbon in forest and related resources (including soil and forest products) was over 225 billion tonnes in the 1990s (Canadian Forest Service, 1999). Of this, very roughly, perhaps 25% is vegetation and may be amenable to human manipulation. The Kyoto commitment of Canada is estimated to imply a reduction of 65 million tonnes per year in C emissions in 2010. In 1990, slash left on forest sites upon harvest to be burnt or allowed to decompose amounted to 16 Mt C. An improvement of 40% in that very particular component of forestry practice would contribute 10% of the Canadian commitment. Similar remarks apply to Scandinavian countries. Quite possibly, if they took advantage of the major possible emission reduction possibilities linked with the forest and forest products, such countries could even find it profitable to participate in meeting part of other countries’ commitments. Whatever the potential contribution of a country’s increasing its forest base, improving its forestry practice, or modifying its forest-products mix to offset CO2 emissions,1 it will fail to materialize unless 1 Soil and litter contain carbon as well, but Schlesinger and Lichter (2001) and Oren et al. (2001) find that rapid turnover of organic carbon and limited other nutrients render them insignificant as long-term sinks.

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actions to realize it are either imposed or properly rewarded. In this paper, we explore the underlying economic principles that apply to this problem and discuss how carbon credits could be attributed in accord with such principles. We also compare the economic principles with the carbon accounting practices of the IPCC and the UN Food and Agricultural Organization discussed in Winjum et al. (1998). A simple way to accord carbon credits could be to observe the net growth of biomass in the country and to credit the current asset value of carbon fixing to that growth. This value, q(t) per unit at time t, could be determined in various ways such as by fiat, by the value of tradable carbon permits, or by a carbonemissions tax. If df/dt is the growth of biomass, then the credit for biomass changes could be q(t)df/dt. But should not a country that buys or otherwise sets aside land for forestry use receive immediate credit for future carbon fixing? Also, even if the intent is to leave the land as forest forever, forests do not continue to grow forever, but are cut and replanted or else reach a stable state. Pearce (1994) incorporates such considerations into a cost–benefit analysis of afforestation in Scotland. In general, establishing a permanent forest consists, not simply of letting the forest grow at a particular point in time, but of devoting land to this particular use over an indefinite future. Thus, the capacity of the forestland to provide further carbon fixing is affected even as the carbon is fixed. Since the value of the forest to humanity as a sink for carbon is a capital value rather than simply a flow, an internally consistent system of carbon credits would recognize effects on the future ability to absorb carbon as well as the current effect of the growth of trees. Consequently, the credit system is an exercise in green accounting, the attempt to recognize the values of environmental resources as economic assets. In the literature on green accounting, there is a tension between measuring the changes in value through green net national product (NNP) and through changes in market wealth. Although well understood in principle, the methodological issues that we discuss in this paper are of urgent policy relevance and involve delicate theoretical details. Should carbon values be expressed and credited as rental values or can asset values be used? It is well known that wealth and wealth change (here the

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carbon value of a forest and its changes) can be expressed in both ways. However, we show that there are strong practical reasons to use asset values. Should carbon values be set at their optimal level in the Pigovian tradition or using current societal standards? What is the relationship between the methodology used in green accounting on one hand and the methodologies of carbon accounting considered standard in the earth sciences? Are these methodologies compatible? How should the planting of trees be rewarded, by credits based on the current growth of the new trees or by a immediate reward that reflects the total future carbon sequestration to be achieved by the new forest? Although we present what are to us compelling arguments in favor of the former approach, there is confusion in the literature, as underlined by Sohngen and Mendelsohn (2001). Finally, our paper presents a discussion of how to implement the scheme in the face of uncertainty through an institutional prescription for insurance markets that increases the efficiency of the permits by spreading risks faced by smaller units. We characterize the measure of wealth in terms of the ability of a parcel of land to fix carbon. This means the carbon remaining locked in wood products from previous rotations, the carbon being currently fixed and the contributions from future rotations. Our analysis points up some subtle issues that should be addressed in a system of credits for forest growth. Initially we obtain a difficult expression for the credits to be accorded. Fortunately, it turns out that there exists an equivalent system of credits and debits which rely only on current magnitudes. A simple version of this method corresponds to one of two methods of physical carbon accounting currently being used by forest scientists. Therefore, there is common ground among economists and other scientists, at least in the conceptual issues involving the accounting for carbon sequestration. However, the development of appropriate institutions to make the best use of potential resources in an uncertain world indicates that values for the carbon, such as would be determined by economic instruments, are required. Such a system of institutions both puts the accounting of carbon credits on firm conceptual ground and identifies and exploits incentives and the potential for risk sharing. This last consideration implies that, while appropriate ac-

counting for carbon is an essential element of a creditation scheme, implementation of the scheme is more effective under a significant deviation from accounting precepts. The Kyoto agreement has dealt with some of these issues by ruling them out. For example the commitment period is specified to be 2008–2012, and countries are to be credited for average emissions, over this five-year period, below a certain percentage of the 1990 levels, and possibly punished otherwise. Flows cumulated before the beginning of the commitment period will not count, even though changes in forest stocks can be measured. Also, there is no agreement as to what will happen next. This paper lays out, or reminds us of, the principles that would help to improve future choices and addresses some implementation issues.

2. The value of fixing carbon: optima and social norms The bulk of work in economics discussing the issue of carbon fixation has been done in the context of optimal choices. Compare, for example, van Kooten et al. (1995) or Platinga and Birdsey (1994). The former (p. 366) express a faith in implementation of economic incentives, in developed countries at least. The continuing softwood-lumber dispute between Canada and the United States, however, is strong evidence that, even in purely commercial transactions among partners in developed, free-trade areas, interest-group pressures and other sources of non-optimality are rife in policy making with respect to forests. There is no reason to suppose that policy will be optimal for carbon fixation. Similarly, much of the work on green accounting has been done in the context of an optimal economy under conditions of certainty. The fundamental reason for doing green accounting, however, is to obtain information for policy purposes about a non-optimal economy facing uncertainty. Economists may expect that appropriate pricing may nudge the world in the direction of optimality but rarely achieve it. Accounting for credits still needs to be done, and in a practical way. The optimal economy can be viewed as a guide to methodology, suggesting imperfect applications to imperfect economies (Cairns, 2002).


Dasgupta and Ma¨ler (2000) use a notion of value function which does not rely on an optimizing framework. The resource-allocation mechanism that they call a is not assumed to sustain an optimal economic program, nor even an efficient program. But the accounting prices they have in mind are social shadow values. Arrow et al. (2003) demonstrate in simple models that the appropriate accounting prices may differ substantially from market prices. Actually determining these appropriate prices would be very difficult and would depend on the model used to determine them. The accounting discussed in the present paper requires that there be a spot price at time t, represented by q(t), of sequestering a unit of carbon. This price is an asset price rather than a rental price. We view q(t) as being set in the context of a general determination of the value of a tonne of carbon in the atmosphere, as specified by a carbon tax or, especially, implicitly through an international permits-trading scheme. Any individual forester’s actions will have a negligible effect on the price and so, in practical terms, the forester will be a price taker. The spot price may be meant to be socially optimal as with a Pigovian tax,2 but more generally will arise from a process involving political considerations as well as economics and the sciences of climate change and sequestration. Economists may not view it as a social shadow price. The present analysis relies on there being a price q(t) but does not rely on any specific model of its formation, nor on its optimization of some conception of social welfare, other than that the non-cooperative negotiations can be expected to be a step in the direction of improving welfare (cf. Chander et al., 2002). As proposed by Cairns (2002), we simply use the values of q(t) established by policy. The mathematical expressions we derive bear only a formal resemblance to those used in determining an optimal, Pigovian tax or subsidy. Rather, we propose that contributions from forests be integrated into the economy-wide scheme dealing with carbon, not based on shadow values for forestry. Our method is a direct extension of the national accounts at market prices, the only accounts imaginable at this point for practical use. The account2

Li and Lo¨fgren (2002) and Weitzman (2001), among others, address the question of the correspondence of money values to utility values in an optimal economy.

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ing values have only a pro-forma link with welfare although, given the economic and political context, the spot price q(t) can be likened to a second-best price. Sohngen and Mendelsohn (2001), among others, expect q(t) to rise as the concentration of carbon in the atmosphere increases. Our paper also uses the literature on forestry as a background, but departs from it in an important way. In that literature, an important issue is the determination of the optimal harvest rotation, using generalizations of Faustmann’s formula. Depending on the features the analyst wishes to introduce, the generalizations can be complicated. Indeed, the introduction of carbon credits influences the rotation period (Ariste and Lasserre, 2001; van Kooten et al., 1995), and the choice of species of trees to be grown (cf. Pearce, 1994: Table 17.6). However, we do not assume any particular rule for choosing rotations. Like the carbon values, the rotation decisions depend on a complex environment involving knowledge and various technological and institutional constraints. The rotation period may vary from rotation to rotation as a result of various changes, in particular of changes in q(t). In our model, we do not determine a set of rotation periods, but simply presume that such a set has been or will be determined somehow, be it optimal or not. We recognize that other factors (such as timber values and possibly non-marketed values) than carbon fixing influence the chosen rotation. Our analysis takes as given the choice of rotations as well as the value of carbon. For simplicity we assume that the period of a future rotation is not affected by the timing of its start, as influenced by fires up to the beginning of that rotation. It will be intuitively clear that assuming otherwise would make our derivations more complicated but not affect our conclusions. As there is uncertainty respecting forest fires or pestilence, all of our computations should be understood to be in terms of expected values. We consider that any forest begins with afforestation at a time t 1 which we normalize to 0. Let the time at which the nth rotation begins be t n , and the harvesting age for this rotation be T n . Let us consider a point in time t during the nth rotation, n z 1. If n = 1 and t = t 1 = 0, we are studying afforestation in the sense of the IPCC, that is, dthe establishment of forest on land that has been without forest for a period of time (e.g.,

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20–50 years or more) and was previously under a different land use.T (IPCC, 2000, p. 6). If n N 1 and t = t n , the current action is what the IPCC defines as reforestation, dthe activity of regenerating trees immediately after disturbance or harvestingT. If the forest is old growth or has been set aside as wilderness, we shall say that n = 1 and T 1 = l. Let the quantity of carbon fixed in the biomass of the forest (an even-aged stand) at time tS be f(t t n ). Then the rate of growth is df(t t n ) / dt = f (t t n ). This rate of growth is net of the (expected) damages of pests. (This expected value could easily be expressed in terms of a probability distribution but so expressing it would merely expand notation without increasing the insight sought in this paper.) If the forest survives to age T n , it is cut. A fraction k n is useful and (1 k n ) is waste, immediately being transformed into carbon dioxide (say by burning or rapid decay); this ratio is determined by the choice of inputs (recovery effort) as well as by the production mix (e.g. the proportion of construction products relative to paper in output). The part which is useful is transformed into a mix of wood products, the proportion of each product i being C ni , and its rate of decay c ni (assumed to be constant). For the nth rotation there is a hazard rate, q (which we assume to be constant), of a fire at any instant t b t n + T n . For simplicity of presentation, we assume that fire completely destroys the forest (cf. Reed, 1984). (If destruction is only partial and the remainder of the forest is left to grow, the value of the remainder can be treated similarly to destruction by pests as above; or if some value can be recovered from the burnt forest this can be treated as a special harvest. Such a treatment would complicate the analysis without adding further insight.) Hence, the probability of the nth rotation’s surviving to time t is e q(t t n ). The probability of a fire on the interval (t, t + dt) is qe q(t t n )dt. The proportions k n , C ni and c ni are important elements of the carbon accounting system. In a market economy, they respond to wood product and input prices, as well as the carbon credit, if any. If the value of the carbon credit is increased, one may expect k n to increase and production to be reallocated toward slow-release forest products. For the purpose of green accounting, however, one does not need to analyze how these variables are determined; they just need to be measured.

3. Economic evaluation As a guide to incentive effects and accounting, we first present an economic evaluation of current, past and future rotations. Evaluation is in terms of expected values at time t, with the expectations operator suppressed to minimize clutter. To keep the notation simpler, we assume that output is onedimensional: C ni = C = 1 and c ni = c n The value of carbon already in the forest at time t is q(t)f(ttn). We assume that credits for carbon are forwardlooking. The assumption is an important departure from accounting practice, which records realized as opposed to anticipated changes in value. It results in a significant departure of credit implementation from accounting principles. The expected value of the total future contribution of rotation n to carbon fixing is Vtn ¼

Z

tn þTn

eðrþqÞðstÞ qðsÞ f˙ ðs tnÞqf ðs tnÞ ds

t

eðrþqÞðtn þTn tÞ f ðTn Þ½ð1 kn Þqðtn þ Tn Þ eðrþqÞðtn þTn tÞ f ðTn Þ Z l cn eðrþcn Þðstn Tn Þ qðsÞds : kn tn þTn

The first term is the present discounted value of the growth of the forest less the probability of a fire at time s times the quantity of greenhouse gas released in the event of burning. The net expected growth is discounted for interest and for the probability of survival to time s. The second and third terms represent the expected present value of future releases of carbon dioxide from harvested biomass: a fraction 1 k n is released immediately at harvest time; the rest is released in perpetuity at rate c n . For any m b n, the mth rotation also contributes a component of total value. (Recall that t 1 = 0; the rotations begin at the time of afforestation.) This component is negative because it is the value of the decay of what remains of the mth rotation, Z l Vtm ¼ km f ðTm Þ cm qðsÞerðstÞ ecm ðstm Tm Þ ds: t

The factor c m appears in the discount factor e cm (stm Tm ) because of decay of the stored carbon, x, say, giving rise to the differential equation x˙ = c m x. Let d m = 1 if the mth rotation survived to


maturity, and be 0 otherwise. Then the total contribution of harvested rotations is Vtn

¼

n1 X

dm Vtm

m¼1

¼

n1 X m¼1 Z l

dm km f ðTm Þ cm qðsÞerðstÞ ecm ðstm Tm Þ ds:

t

Finally, there are expected contributions by future rotations to value. The mth rotation, m N n, begins at a time which is uncertain, because of the possibilities of fires in rotations n through m 1. The time at which it is planted, then, is stochastic. But the stationarity of our problem allows this randomness to be expressed in terms of the randomness of the beginning of rotation n + 1, in the following way. First, let the expected benefit from the sequence of all future rotations m z n + 1, which begins at time t n + 1, be W n + 1. At time t the starting date of rotation n + 1 is uncertain. We know that the following holds: Prðtnþ1 ¼ Tn þ tn Þ ¼ exp½ qðTn þ tn t Þ; and, for s a (0, T n + t n t), Pr½tnþ1 aðt þ s;t þ s þ dsÞ ¼ qexpð qsÞds: Therefore, the total expected contribution of all future rotations at time t is nþ Vt ¼ Wnþ1 exp½ ðr þ qÞðTn þ tn t Þ Z Tn þtn t rs qs þ e qe ds 0 q r ¼ Wnþ1 þ qþr qþr exp½ ðr þ qÞðTn þ tn t Þ : The total value of the expected contribution at t of maintaining this parcel of land in forest use in perpetuity is Vt ¼ Vtn þ Vtn þ Vtnþ : This value is a capitalized value of all future components of changes of carbon as a result of the project.

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4. The return on the parcel of land The cost of capital, which must be returned by the project, consists of the return on the capital value plus the depreciation. The return on the asset value is included because the carbon in the atmosphere is a stock which produces a flow of costs to society in each time period. Reducing the stock by sequestering it in forest biomass provides a flow of benefits (negative costs). These benefits are the return which society seeks in building up the stock of biomass. Depreciation is the negative of the rate of change of the value V t ; it is positive if the value decreases. Both of these values depend on the realizations of carbon savings over an uncertain future. Determining the return on the capital value is a subtle task. Consider the time derivative of V tn: n V˙ n þ t ¼ rVt

n1 X

dm km f ðTm Þcm qðt Þecm ðttm Tm Þ :

m¼1

ð4:1Þ The rate of change is the interest on the value (which is negative) of previous rotations at time t, plus a second term representing the current contribution. The first term appears because, as time passes, any future event (here, the realization of the decay at future dates) is sooner and is discounted less. We have assumed that the effects of previous rotations are certain, and so the appropriate interest rate is r. For current rotations, V˙ nt ¼ ðr þ qÞVtn qðt Þ f˙ ðt tn Þ qf ðt tn Þ : ð4:2Þ As is common in problems with a Poisson hazard (with hazard rate q), the effective interest rate is r + q, not r, because of the possibility of destruction of the forest by fire. For future rotations, by direct differentiation and substitutions from the equation for V t n+, V˙ nþ t ¼ rWnþ1 exp½ ðq þ rÞðTn þ tn t Þ ¼ ðq þ rÞVtnþ qWnþ1 rþq ¼r Vtnþ : r þ qexp½ðr þ qÞðTn þ tn t Þ ð4:3Þ

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The effective interest rate for future rotations varies with the point in the rotation period. The equations for V˙ tn, V˙ tn and V˙ tn+ are examples of the fundamental asset–market-equilibrium equation, which equates the total return on an asset to the sum of a dividend and a capital gain. Society invests in the forest in such a way as to be compensated for the opportunity cost of the resources invested, and the compensation must take into account the possibility of destruction of the current and future rotations by fire. As noted above, the compensation is for the return on and the depreciation of the asset value. The change in value, for t a (t n , t n + T n ), is

involves the imputation and capitalization of future flows over an uncertain future and their rates of change. As has been pointed out by scholars studying the green accounts (e.g. Aronsson and Lo¨fgren, 1998), calculating the stock values would be a formidable task. Fortunately, there is a way to express the credit proposed in Eq. (4.4) in a way which involves only current flows of value, and not the imputation and capitalization of future flows over an uncertain future represented by V tn, V tn , and their rates of change. Rearranging Eq. (4.4) using Eqs. (4.1), (4.2) and (4.3) yields, for t a (t n , t n + T n ) (for times strictly between planned harvests),

˙ n ˙ nþ V˙ t ¼ V˙ n t þVt þVt :

(

If V˙ t is positive, there is an appreciation of value, and if V˙ t is negative, there is a depreciation. The upshot is that, at times strictly between planned harvests, we can express the credit for sequestration C t in terms of the asset values of the forest: the net contribution of the forest to society, and hence its credit, at time t, is the sum of the return on the asset value and the depreciation, Ct ¼ rVtn þ ðr þ qÞVtn rþq V nþ V˙t þr r þ qexp½ðr þ qÞðTn þ tn t Þ t ¼ rV n þ ðr þ qÞV n V˙ n V˙ n : ð4:4Þ t

t

t

t

In Eq. (4.4), the terms involving future rotations m N n exactly cancel out. To that extent the calculations are simplified. The formula carries an important message: in the attribution of credits for carbon sequestration, no current consideration should be given to the contribution of future rotations. Rather, future rotations should be credited when realized.

5. A current measure Some authors have proposed that credits for carbon be accorded as a type of rental payment on the full stock of carbon fixed in the forest, as prescribed by Eq. (4.4). This method, however, employs risk-adjusted discount factors and the expected depreciation of the stock value in the forest and in previously produced forest products. It

C t ¼ qð t Þ

n1 X

˙f ðt tn Þ qf ðt tn Þ

)

dm km f ðTm Þcm e

cm ðttm Tm Þ

:

ð5:1Þ

m¼1

The credit involves only physical changes occurring at the current instant, all evaluated at the current price q(t), as determined by the current price of carbon permits, for example.3 In comparing our scheme with rental-price schemes, we observe that the price q(t) of carbon credits represents a capitalized value of the damages caused by a unit of carbon. It may be established in the market for exchangeable permits, if such a market exists, or implicitly valued, in a carbon tax for example. Any unit of carbon fixed is credited with the full capitalized value when it is fixed. But that unit is charged the (future) capitalized value at the time it is released back to the atmosphere. Use of current asset values as we propose is equivalent to methods based on rentals of carbon accorded in each time period, except that our method is easier to administer: it uses the directly observed, current

3

A fixed amount might be added or subtracted from the above credit in circumstances such as the Kyoto agreement where the emission target might be translated into a similar reduction objective at the forestry and forest products level. Such a fixed term, whose value would normally reflect q(t), would raise important distributional and implementation issues but would not affect the marginal properties of the proposed scheme.


changes in carbon fixation and the directly observed (or set) current asset price of (or tax on) carbon, rather than relying on the imputation of rental prices, most of which cannot yet be observed or set because they are too far in the future. If socially optimal, the asset price of a carbon credit q(t) represents the capitalized value of the social damages caused by a unit of carbon at t; in general it represents the value implicitly or explicitly given to such damages given current institutions and information. In any case an agent who fixed more carbon at t than allowed by the prescribed benchmark would not bank or sell a quantity of carbon but the corresponding dollar value; if q was increasing and the credit was intended to be used at a later time, banking the credit would allow the release of a lower quantity of carbon in the future. This is a major difference with schemes based on quantities, for they effectively assume a constant carbon value. At harvest times, when t = t n + T n , there is a discrete jump in the value V t n because the fraction (1 k n ) of the harvest is wasted immediately, and so the change in value is (1 k n )f(T n )q(t n + T n ). In case of a fire occurring at time s a (t n , t n + T n ), there is also a discrete jump in V t n . However, the formula remains valid, with appropriate changes in n and t n : a new rotation starts right after the fire, so that n is incremented to n + 1 and the beginning of the new rotation is set at t n + 1 = s. Thus the credit C t experiences a discrete jump at s, but the formula to apply is unchanged. This method of evaluation suggests the following policy for distribution of carbon credits, to nations and through them to local decision-making units: Carbon credit implementation scheme 1. At dates t strictly between planned harvests, when the age of the stand is t t n , impute a credit of the value of carbon fixing through forest growth, q(t) f˙(t t n ), with a deduction of qq(t)f(t t n ). This deduction may be interpreted as an insurance premium against fire (and pest or weather related) damages, and justifies that no carbon debit be imputed in case of accidental damage to the forest. 2. At dates t when a fire (or weather, or pest related, damages) occurs, do not impose any debit; only

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update the age of the stand for application of item 1 the following year. 3. At all dates, for each past harvest m b n impute (estimate) a debit for the value of the current decay of forest products, f(T m )k m c m q(t)e cm (ttm Tm ). Making this imputation would be very difficult. Consistency, however, requires that some attempt be made. 4. Make no imputation for future harvests, m N n. Future harvests are not evaluated until they are actually planted. 5. At the time of harvest, impute a discrete debit for the value of waste, (1 k n )f(T n )q(t n + T n ). In this scheme, the value of waste (carbon released into the atmosphere) at harvest, (1 k n )f(T n )q (t n + T n ), could be levied as a charge against profits or royalties realized at harvest. Similarly, although it is not related to current forest management activities, the charge for current decay of forest products could be levied against the credit for current growth in the same fashion as the insurance premium qq(t)f(t t n ). Alternatively, since the charge for current forest-products decay would be fairly regular and predictable, it could be levied as any conventional tax. Whether made discretely at harvest or continuously, levies for decay of wood products raise serious incentive issues, briefly discussed in the next section. As an alternative to the above scheme, the deduction for insurance against accidental damage in Item 1 could be replaced with full payment when the damage occurred. By the same token, an attempt could be made to evaluate realized, rather than expected, rates of decay. This policy would be consistent with the green accounts, as they would record changes in values as realized. However, imposing a sudden, discrete cash outflow may imply hardships for some countries or firms. If these countries or firms are risk averse, they would have a reduced incentive to invest in forests to sequester carbon in this way. But one can imagine that insurance markets could develop to share these risks, in which case the scheme would differ from the above one only by its institutional implementation. Therefore, the green accounts provide an essential basis for evaluation, but the economic analysis suggests a departure from accounting practice when there is uncertainty.

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6. Discussion and conclusion A number of important issues remain: How does green accounting compare with existing carbon accounting systems? What are the informational requirements for implementation of the carbon-credit scheme? What are the incentive effects of introducing such a system and what precautions do they suggest? There is a parallel literature on carbon accounting. Carbon accounting is widely used by scientists in various disciplines, and is a standard tool for the IPCC. As far as forests and wood products are concerned, Winjum et al. (1998) identify two main methodologies, atmospheric flow and stock change. Except for the focus on physical units instead of values, stock change evokes formula (4.4), giving the change in the carbon value of a parcel. This method, however, involves the integral of physical magnitudes rather than values. Physical magnitudes at different dates cannot be integrated in this way. There has to be some method of comparing changes in physical magnitudes at different dates (making them commensurable), and this method requires pres-

ent-value prices (prices multiplied by appropriate discount factors). Stock change is not consistent with economic principles. This fact may not be obvious to scientists in view of earlier economic studies that assumed the price of carbon to be constant through time, so that the price could be factored outside the integral, leaving an integrand expressed in physical magnitudes. Sohngen and Mendelsohn (2001) point out that bcarbon prices rise over time, but most forest sequestration studies assume static prices.Q Moreover, discounting is of fundamental importance to appropriate intertemporal trade-offs. Let us, then, focus on the atmospheric-flow method, which Winjum et al. summarize in their Fig. 1, reproduced below. The general equation for the atmospheric-flow method is: dnet C [carbon] flux to the atmosphere equals C fluxes to the atmosphere associated with harvesting and use of wood minus C uptake during regrowth of harvested forests.T (p. 273). Step 1 (roundwood harvest) corresponds to the measurement of f(T n ), the current harvest, but involves a conversion from volume units in which harvest data are usually

Fig. 1. (reproduced from one Winjum et al., 1998). Diagram of steps used in the atmospheric-flow method for computing estimates of a country’s annual carbon emissions to the atmosphere from forest harvests and use of wood products. C= consumption, P = production, I = imports, and E = exports. The arrows to the box labeled carbon emissions to the atmosphere represent the C fluxes due to A — decomposition of slash, B — oxidation or decay of long-term wood products (N5 year) from the past use (inherited emissions), C — oxidation of wood products with short-term (b5 year) uses, D — oxidation of waste (burning or decaying) from the production of commodities, and F — burning of fuelwood and charcoal. The shaded boxes are those used in calculations for the stock-change method.


expressed into carbon content. Step 2 (slash) corresponds to establishing k n , where waste must include waste upon harvest and at the production stage. Step 3 (commodity) corresponds to establishing the breakdown of production into various products. As we mentioned earlier, c n is in fact a vector, each wood product having in theory its own decay rate. Winjum et al. distinguish two types of product: products whose life exceeds five years and other products; other studies have used finer breakdowns (Obersteiner, 1999; Haripriya, 2001). In fact, decay rates and product breakdown are used in step 4 (inherited), which corresponds to Item 3 in our scheme. Our brief review indicates that there is a clear correspondence between our economic mechanism and one of the physical carbon accounting methods, atmospheric flow. The required data are basically the same and, by using only current values, the atmospheric flow method avoids the inconsistency of integrating non-commensurables inherent in the stockchange method. Obtaining values from the physical units is obtained simply by multiplying by q(t). Consistently with green accounting, physical carbon-accounting methods would not impose a deduction qq(t)f(t t n ) for fire risk, but impose a debit q(t)f(t t n ) at the time t when a fire occurred. Both accounting methods suggest imposing debits when fires (and weather or pest related damages) occur. Realized values may differ from expected ones. Given that the social costs depend on realized values of carbon emissions, this divergence from expected values is desirable. Besides being less demanding in information and directly tracking realized social costs, that treatment would also provide sound incentives. Forest decision-makers would benefit fully from their attempts to reduce fire or infestation hazards. It is obviously more difficult to obtain data on the risk of fire than data on fire: estimating the parameter q requires regional time series on the incidence of fires, while simply deducting losses from fires requires only current data. Indeed, contrary to our assumption, q is unlikely to be constant. It may depend on global warming, and hence on the success of efforts to reduce global warming. The reason that our implementation scheme departs from the green accounting on which it depends is that discrete, random charges imply sudden needs for individual decision-making units (firms or small countries) to go into

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the market for permits or to use financial markets. We have already alluded to the possibility that insurance markets may develop and cover those needs. If fires on the planet are not correlated, insurance markets can develop. Of course, the estimation problems remain. There has also been some question concerning the estimation of the amount of carbon a forest can absorb. But insurance companies with a financial interest would have as much incentive as any disinterested governmental or international institution to determine more accurate values for these parameters, as well as to anticipate the future values of carbon in the atmosphere, q(t). We stress that, if no such insurance opportunity was available, risk averse countries or firms could be reluctant to participate in increasing their forested areas. Improving the estimates of the various parameters — and also of q(t) if there are tradable emissions permits — would improve the functioning of the scheme. The use of insurance markets in implementation moves the analysis slightly back toward the evaluation of capitalized values, as in Eq. (4.4), rather than the strictly current values inherent in the atmosphericflow method. For this reason, good and improving estimates are required for the scheme, and enlisting the self-interest of insurance companies is an aid to the scheme beyond the insuring of risk. Any method of carbon credits would work best in an institutional framework in which values were determined using economic instruments, such as a carbon tax or quantity restrictions accompanied by transferable quotas. Therefore, economic analysis has much common ground with scientific measures, but there are subtle differences in the implementation of any mechanism for carbon credits. Applying our scheme at the production stage (not explicitly modeled above) would also provide sound incentives toward choosing the right product mix. Although the prices of wood products do not appear in our scheme, and although there is no provision for, say, subsidies favoring long-lived wood products over short-lived ones, forward looking producers, if they expected high future values q(t), would have an incentive to adopt a product mix favoring slowly decaying products (low c) in order to reduce future debits associated with wood products decay (Item 3). Clearly, such a beneficial effect would not occur unless the payments associated with Item 3 were truly linked

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with producers’ own product mix, e.g. through prices faced by consumers. (By the same type of argument, incentives toward recycling or avoiding consumer waste would have to be handled using additional instruments.) Incentives would be appropriate for choices of current and future rotation periods T m , m z n,4 forestry practices, waste rates k n , etc. One of the benefits of our proposal is that the two economic instruments, tradable permits and insurance markets for risk, reinforce each other. Better estimates of insurance risk require and lead to better estimates of the value of permits, and a more efficient market for permits leads to better estimates of the costs and value of insurance. Incentives are aligned more effectively. By reinforcing each other, the two institutions help to integrate markets internationally as well, thereby increasing efficiency. As more countries join the general carbon-abatement protocol determining q(t), efficiency is further enhanced. Involving private, transnational insurance companies in the mechanism would require a high degree of transparency of the scheme at the outset. Once the companies were confident enough to participate, their presence and actions would increase transparency and likely improve enforcement and stability of the mechanism. A problem is that, as in any insurance market, there is moral hazard: the very existence of insurance would reduce the power of the incentive to manage forests optimally. In this mechanism, however, there is a mitigating feature. Since the discussion is of a uniform global problem, of CO2 concentrations in the atmosphere, logically insurance should not be limited to afforestation and improvements in forest management. This amounts to a different perspective on the use of forests in climate control, for discussion to date tends to be limited to afforestation and not continuing forestation. If an ancient forested area, such as the New Forest in England or the Black Forest in Germany, suffered damage due to pest or to fire, it should also be charged for the additional emissions. This would imply, in principle, bringing all forests in the world into the insurance scheme, even if not into the permits scheme. Such a requirement would provide 4 Analytically, maximizing the value of fixing carbon in a forest is similar to maximizing commercial values of timber or pulp, as summarized by, for example, Hanley et al. (1997: 352–353). A complete optimizing model would combine all values.

improved incentives to managers of existing forests, as well as thicken the insurance market. It would reduce adverse selection. Any investment in forests as a carbon sink may not continue to provide large net credits forever (Schimel et al., 2001). Eventually the fixing of carbon from new growth will be offset by debits from decay or fire and mortality, so that net credits will pinch out. Similarly changes in the management and utilization of current forests will result in transitional net sequestration that will eventually stabilize or even turn downward. Moreover, some forests may be taken out of forestry into other uses. However, the observation that benefit flows eventually pinch out and in some cases decline is no more reason to neglect the potential contribution of forests than the observation that the total supply of a non-renewable resource is limited and will decline is reason not to utilize the resource. Any afforestation or any change in the management of current forests results in a change in the stock of carbon stored in the form of standing trees and wood products, and the transition involves significant flows over periods that can be compared with the duration of the transition from fossil sources of energy to non-fossil energy. Neglecting the potential contribution from forests and wood products to carbon sequestration on the grounds that it will eventually stabilize is logically flawed. Furthermore, the analysis in terms of present values points out that a relatively cheap current solution, even if temporary, can successfully be adopted in order to postpone the need to adopt costlier ones. As in the case of non-renewable resources, this observation is even more important if society anticipates that technological change may lower the cost of alternatives over time. References Ariste, R., Lasserre, P., 2001. La Gestion Optimale d’une Foreˆt Exploiteé pour la Valeur Stochastique de son bois et son Potentiel de Diminution des Gaz a` Effet de Serre. Actualite´ Ećonomique 77 (1), 27 – 52. Aronsson, T., Lo¨fgren, K.-G., 1998. Green accounting in imperfect market economies: a summary of recent research. Environmental and Resource Economics 11 (3–4), 273 – 287. Arrow, K., Dasgupta, P., Ma¨ler, K.-G., 2003. Evaluating Projects and Assessing Sustainable Development in Imperfect Economies. Environmental and Resource Economics 26 (4), 647 – 685.

R.D. Cairns, P. Lasserre / Ecological Economics 56 (2006) 610–621 Cairns, R.D., 2002. Green accounting using imperfect, current prices. Environment and Development Economics 7, 207 – 214. Canadian Forest Service, 1999. bClimate Change and ForestsQ mimeo, Natural Resources Canada, Ottawa. Chander, P., Tulkens, H., Ypersele, J.-P.v., Willems, S., 2002. The Kyoto protocol: an economic and game-theoretic interpretation. In: Kristro¨m, B., Dasgupta, P., Lo¨fgren, K.-G. (Eds.), Economic Theory for the Environment: Essays in Honour of Karl-Goran Ma¨ler. Edward Elgar, Cheltenham UK, pp. 98 – 117. Dasgupta, P., Ma¨ler, K.-G., 2000. Net national product, wealth, and social well-being. Environment and Development Economics 5 (1&2), 69 – 94. Hanley, N., Shogren, J.F., White, B., 1997. Environmental Economics in Theory and Practice. Oxford University Press, Oxford. Haripriya, G., 2001. A framework for assessing carbon flow in Indian wood products. Environment, Development and Sustainability 3, 229 – 251. Intergovernmental Panel on Climate Change, 2000. Land Use, Land-Use Change, and Forestry. Cambridge University Press, Cambridge. Li, C.-Z., Lo¨fgren, K.-G., 2002. On the Choice of Metrics in Dynamic Welfare Analysis: Utility versus Monetary Measures, www.econ.umu.se/ues/ues590.pdf. Obersteiner, M., 1999. bCarbon Budget of the Forest Industry of the Russian Federation: 1928–2012Q, IIASA Interim Report IR-99033, Laxenburg, Austria; internet: www.iiasa.ac.at. Oren, R., Ellsworth, D.S., Johnsen, K.H., Phillips, N., Ewers, B.E., Maler, C., et al., 2001. Soil fertility limits carbon sequestration by forest ecosystems in a CO2-enriched atmosphere. Nature 411, 469 – 471 (May).

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Pearce, D.W., 1994. Assessing the social rate of return from investment in temperate-zone forestry. In: Layard, R., Glaister, S. (Eds.), Cost–Benefit Analysis, Second edition. Cambridge University Press. Platinga, A.J., Birdsey, R.A., 1994. Optimal forest stand management when benefits are derived from carbon. Natural Resource Modeling 8 (4), 373 – 387. Reed, W., 1984. The effects of the risk of fire on the optimal rotation of a forest. Journal of Environmental Economics and Management 11, 180 – 190. Schimel, D.S., House, J.I., Hibbard, K.A., Bousquet, P., Ciais, P., Peylin, P., et al., 2001. Recent patterns and mechanisms of carbon exchange by terrestrial ecosystems. Nature 4–14, 169 – 172 (Nov.). Schlesinger, W.H., Lichter, J., 2001. Limited carbon storage in soil and litter of experimental forest plots under increased atmospheric CO2. Nature 411, 466 – 469 (May). Sohngen, B., Mendelsohn, R., 2001. bOptimal forest carbon sequestrationQ, Working Paper AEDE-WP-0009-01, Ohio State University. van Kooten, G.C., Binkley, C.S., Delcourt, G., 1995. Effect of carbon taxes and subsidies on optimal forest rotation age and supply of carbon services. American Journal of Agricultural Economics 77, 365 – 374 (May). Weitzman, M., 2001. A contribution to the theory of welfare accounting. Scandinavian Journal of Economics 103, 1 – 24. Winjum, J.K., Brown, S., Schlamadinger, B., 1998. Forest harvests and wood products: sources and sinks or atmospheric carbon dioxide. Forest Science 44 (2), 272 – 284.