The potential and cost of increasing forest carbon sequestration in Sweden

Journal of Forest Economics 29 (2017) 78–86

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The potential and cost of increasing forest carbon sequestration in Sweden Jinggang Guo, Peichen Gong ∗ Centre for Environmental and Resource Economics, Department of Forest Economics, Swedish University of Agricultural Sciences, SE-901 83, Umeå, Sweden

a r t i c l e

i n f o

Article history: Received 4 April 2016 Received in revised form 7 June 2017 Accepted 8 September 2017 JEL classification: Q23 Q28 Keywords: Forest sector model Climate change mitigation Carbon sequestration Carbon price Timber supply

a b s t r a c t This paper examines the potential and the cost of promoting forest carbon sequestration through a tax/subsidy to land owners for reducing/increasing carbon storage in their forests. We use a partial equilibrium model based on intertemporal optimization to estimate the impacts of carbon price (the tax/subsidy rate) on timber harvest volume and price in different time periods and on the change of forest carbon stock over time. The results show that a higher carbon price would lead to higher forest carbon stocks. The tax/subsidy induced annual net carbon sequestration is declining over time. The net carbon sequestration during 2015–2050 would increase by 30.2 to 218.3 million tonnes of CO2 , when carbon price increases from 170 SEK to 1428 SEK per tonne of CO2 . The associated cost, in terms of reduced total benefits of timber and other non-timber goods, ranges from 80 SEK to 105.8 SEK per tonne of CO2 . The change in carbon sequestration (as compared with the baseline case) beyond 2050 is small when carbon price is 680 SEK per tonne of CO2 or lower. With a carbon price of 1428 SEK per tonne of CO2 , carbon sequestration will increase by 70 million tonnes of CO2 from the baseline level during 2050-2070, and by 64 million tonnes during 2070–2170. ˚ © 2017 Department of Forest Economics, Swedish University of Agricultural Sciences, Umea. Published by Elsevier GmbH. All rights reserved.

Introduction Using forests to reduce the accumulation of atmospheric CO2 has gained a growing interest in scientific and policy discussions. The world’s forests cover 31% of global land area and store an estimated 296 Gt of carbon in their biomass alone (FAO, 2015). Forests play a significant role in the global carbon cycle, since they act as both major contributors and sinks of atmospheric CO2 . IPCC (2007) assessed that forests could offer an effective way to mitigate climate change through sequestration of carbon. Forests carbon sequestration has the characteristics of a public good, and thus is likely to be under-produced due to the lack of economic incentives for forest managers to take into account the carbon sequestration benefits in their managerial decisions. As pointed out by Sedjo (2001), forest carbon sequestration can be increased by adopting a number of measures, such as creating more forests, reducing the conversion of forests to other land uses, adopting growth enhancing silviculture practices, and reducing the loss of forest biomass caused by nature disasters. Whether or not,

∗ Corresponding author. E-mail address: [email protected] (P. Gong).

and to what extent forest carbon sequestration should be increased depend on the marginal cost of doing so. About 70% of the land area of Sweden is covered by forests, extending to over 28 million hectares, of which 23.2 million hectares are considered productive forestland. Forest growth as well as the standing volume has been steadily increasing since the 1920s when the first national forest inventory was conducted. The current annual growth exceeds 120 million m3 and the total standing volume amounts to over 3 billion m3 (Swedish Forest Agency, 2014). Forest growth in Sweden is expected to maintain the increasing trend in the foreseeable future (Rosvall, 2007; Swedish Forest Agency, 2008, 2014). Compared with the total emission of GHGs in Sweden, which is about 58 Gt CO2 equivalents per year (Eurostat, 2015), the physical potential to use forests in Sweden to sequester carbon is huge. However, timber production is an important objective of forest management in Sweden. To what extent forest owners are willing to use the physical potential of forest carbon sequestration for the purpose of climate change mitigation depends on the benefit and cost of providing this service. The purpose of this paper is to assess the potential and the cost of stimulating forest carbon sequestration through a carbon tax/subsidy scheme. To this end, we will modify a timber market model by including monetary incentive to forest owners for increasing carbon sequestration and use the model to simulate

http://dx.doi.org/10.1016/j.jfe.2017.09.001 ˚ Published by Elsevier GmbH. All rights reserved. 1104-6899/© 2017 Department of Forest Economics, Swedish University of Agricultural Sciences, Umea.

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future timber harvest and forest carbon storage, as well as the benefits of timber and other non-timber goods (such as biodiversity, recreation and so on), associated with different carbon prices (the tax/subsidy rate). This analysis covers most of the productive forestland of the country. The results provide us estimates of the potential and the cost of increasing forest carbon sequestration through a carbon tax/subsidy scheme. The remainder of the paper begins with a review of related previous studies, followed by a brief description of the model we employed. The estimation results are presented and discussed in Section 4. The final section summarizes the main findings and discusses potential extensions of the study.

Previous studies The cost of carbon sequestration has been the subject of numerous studies in the field of forest economics. Richards and Stokes (2004) presented a comprehensive review of the earlier works on this topic. They synthesized the results of various studies and concluded that the cost could range from $10 to $150 per tonne of carbon to fix roughly 2 Gt carbon per year. The markedly varying costs were confirmed by Stavins and Richards (2005) and van Kooten et al. (2009). One factor contributing to the wide range of cost estimates is the different models applied, which can be grouped into three broad categories, namely, bottom-up models, econometric models, and sector optimization models (Sohngen 2010). Analyses using bottom-up models (e.g., Parks and Hardie, 1995) concentrate on measuring the operational costs of and the amount of carbon sequestered by different forestry projects. Effects on the prices of forest products as well as the potential externalities of the projects under examination usually are ignored in such analyses. Econometric models are widely used to identify the preferences of landowners when confronted with alternative land use options. Forest product prices are determined endogenously and used to estimate the relative returns and to assess the probability of land use changes (see, e.g., Lubowski et al., 2006). By using empirical data, econometric approaches could provide reliable predictions of land use changes in response to different policy options. Forest sector optimization models (e.g., Sohngen and Mendelsohn, 2007) attempt to optimize the management of forests under different circumstances and, therefore, are capable of taking into account the behavioral response to changes in a wide range of socioeconomic factors, such as population and income growth. An excellent review of the different types of models can be found in Latta et al. (2013). Another factor accounting for the varying costs is the type of measures used to increase forest carbon sequestration. Much effort in previous studies has been placed on afforestation, reforestation, and avoided deforestation, partly because of the fact that only afforestation and reforestation qualify for carbon sink projects under the Kyoto Protocol (Smith, 2002). For instance, Sohngen and Sedjo (2006) simulated the forest and land use decisions in response to exogenously given carbon price paths at the global level, and found that most carbon sequestration would originate from afforestation and reduced deforestation in tropical and temperate regions. They also stressed that a higher sequestration level can be achieved by implementing rising carbon price policies. Several subsequent studies (e.g., Kindermann et al., 2008; Rose and Sohngen, 2011) provided similar results. In addition to the consideration of land-use change as a possible means of reducing CO2 emissions, many studies focus on the role of changing forest management practices in enhancing carbon uptake. For countries with relatively stable land use patterns and large endowments of forests, this option seems more applicable. Changing rotation age and thinning scheme are two commonly studied methods for managing forests to mitigate climate change.

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For instance, Hoover and Stout (2007) concluded that, by altering the stand structure, thinning could promote timber growth and strengthen the adaptive capacity to withstand disaster risks and subsequently favor carbon sequestration. Liski et al. (2001) found that longer rotations could favor carbon sequestration at the cost of delayed timber revenues. The primary focus of these studies is how forest management practices should be changed in order to increase carbon sequestration (to the optimal level). As such, they generally do not provide estimates of the cost of carbon sequestration. There are exceptions, however. One example is Im et al. (2007). They examined the optimal management intensities and regeneration methods under a range of carbon tax levels. Their results show that the marginal cost of increasing carbon sequestration by private forests in Oregon is comparable with that of afforestation projects in some parts of the United States. Several studies show that increasing forest sequestration can be a cost-effective option to limit CO2 emissions within the EU (see, e.g., Gren et al., 2012; Münnich Vass, 2015). These studies optimize forest carbon sequestration from a social planer’s perspective, assuming that forests shall be used to minimize the total cost to reach a given emission target. A few studies have estimated the potential and the cost of increasing forest carbon sequestration when forest management decisions lie in the hands of landowners. Backéus et al. (2005) used a linear programming model to determine the optimal balance between timber production and carbon sequestration when forest owners get paid for carbon sequestration and pay for CO2 emission resulted from timber harvest. Their results from a case study, which covers 3.2 million ha forests in northern Sweden, show that when carbon price is zero the average annual rate of sequestration (over a period of 100 years) is 1.48 million tonnes of carbon and the net present value (NPV) of timber production is over 40 billion SEK. When carbon price approaches 1000 SEK/tonne of C (273 SEK/tonne of CO2 ), timber harvest in the region reduces to zero, the NPV of timber production diminishes, and the average annual sequestration rate increases to the maximum level of 2.05 million tonnes. In the model of Backéus et al. (2005) timber prices are exogenous. In a large-scale analysis, reduction in timber harvest may lead to significant increases in timber price, which presumably would affect forest owners’ management decisions and hence the effects of carbon tax/subsidy on carbon sequestration. Clearly, one should not generalize the results of Backéus et al. (2005) and predict that a carbon price of 1000 SEK/tonne of C would cause all forest owners in Sweden to stop harvesting. Sjølie et al. (2013) used a partial equilibrium model, which accounts for the impacts of price changes, to assess the increase in forest carbon sequestration in Norway that could result from a carbon tax/subsidy policy with varying carbon prices. Their result shows that a carbon price of D 100 per tonne CO2 would substantially enhance forest management intensity and reduce harvest volume, thereby lead to a significant increase in carbon sequestration. Because forest regeneration investment in Sweden is already very high,1 we expect that a carbon tax/subsidy policy would result in a much lower increase in forest carbon sequestration in Sweden than in Norway. Method The model The model used in this study is an extension of the Swedish Timber Market Model (STIMM) presented in Gong and Löfgren (2003)

1 The average regeneration cost in 2012 is about 1000 D /ha (Swedish Forest Agency, 2014).

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and Gong et al. (2013). STIMM is a halfway house between the above-mentioned econometric models and forest-sector optimization models. Like an econometric model, STIMM uses timber supply and demand functions to simulate the market equilibrium harvest volume and price of timber in different time periods. However, STIMM does not use supply functions estimated using empirical data on timber harvest and prices. Rather, the timber supply function associated with each relevant “policy scenario” is optimized by maximizing the sum of discounted total surplus in different periods subject to forest growth and market clearing constraints. The supply function in STIMM may differ among different policy scenarios (Gong et al., 2013), whereas it is exogenously given and policyinvariant in an econometric model. The optimized supply function can be regarded as an “optimal decision rule”, which is used to approximate the optimal harvest volumes in different time periods. Thus, STIMM aims to find the optimal harvest decisions conditional on the initial state and growth of the forest and the relevant policy setting, as the forest-sector optimization models do (see, e.g. Latta et al., 2013), though the optimal decisions are determined indirectly in STIMM. Assume that timber markets in all time periods are perfectly competitive, and that, in the absence of externality, the market equilibrium harvest volumes in different periods are socially optimal. The supply function can then be optimized by maximizing the sum of discounted total surplus of timber production in the current and all future periods (Gong et al., 2013). The extension we made in this paper is that we include forest owners’ private benefits/costs of carbon sequestration/emission and their valuation of other non-timber benefits in the producer surplus. In other words, we consider the case where forest owners manage their forests with the objective of maximizing the NPV of timber production, carbon sequestration, and all other non-timber benefits that have a value to them. In the present analysis, we consider one composite timber assortment (Gong and Löfgren, 2007). The inverse timber demand function in each year t is modelled as: Pt = ˇ1 (Dt )ˇ

2

(1)

where Pt is the price of timber in year t, Dt is the quantity of timber demanded in year t, and ˇ1 and ˇ2 are exogenously given coefficients. We assume that the aggregate supply of timber in each year t, St , depends on the current timber price, Pt , and the standing volume of mature forests (stands which have reached the lowest allowable harvest age), It , in the following manner: St = ˛1 (It )˛2 (Pt )˛3

(2)

where ˛1 is a scale parameter, ˛2 and ˛3 are the inventory and price elasticities of supply, respectively. Eq. (2) is a commonly used functional form for modelling market supply of timber (Buongiorno et al., 2003; Bolkesjø et al., 2010; Lecocq et al., 2011). Assuming that the total area and productivity of forestland as well as the interest rate and management costs are constant, the only factor which may cause the supply curve to shift over time is the standing volume of timber. Hence, the same supply function applies for all time periods. In recursive dynamic models, such as the Global Forest Products Model (Buongiorno et al., 2003) and the French Forest Sector Model (Lecocq et al., 2011), the elasticities of timber supply are exogenously given. In our model, the elasticities are endogenous and may differ among policy scenarios. To be specific, the coefficients of Eq. (2) are optimized in each policy scenario in order to provide the best approximation of the optimal harvests in different time periods. We assume that the time path of optimal harvest leads to maximization of the present value of total (the sum of producer and consumer) surplus (Lyon and Sedjo, 1983). To achieve the best approximation of the optimal harvests, the parameters of

the supply function (2) are determined by maximizing the present value of the total surplus in current and all future periods2 . The present value of the total surplus of timber production is formulated as:

NPVtimber =

⎛ Qs ⎞ t   ⎝ ˇ1 (q)ˇ2 dq − c Xt , Qts ⎠ e−r(t−1) + Rtimber (XT +1 )

T

(3)

t=1 0

Qts

where is the total harvest volume in year t. Qts is determined by the market clearing condition, and thus depends on the supply function coefficients. Xt is the age-class distribution of the forests at  the beginning of year t. c Xt , Qts is the sum of harvest and regeneration costs. r is the discount rate. Rtimber (XT +1 ) is the present value of the forest remaining at the end of the simulation period T. The policy instrument applied in this analysis is a yearly tax/subsidy for increasing/decreasing carbon stock in the forest. In each year, a forest owner will receive a sequestration subsidy if the carbon stock in his or her forest increases, and pay an emission tax if the carbon stock decreases compared with the previous year. The size of the tax/subsidy is proportional to the net change in the carbon stock. The present value of forest owners’ net income from carbon tax/subsidy is: NPVcarbon =

T  t=1



P c × (Vt+1 − Vt ) ×  e−rt + Rcarbon (XT +1 )

(4)

where Pc is carbon price (the rate of carbon tax/subsidy) and Vt is the total standing volume of the forest at time t.  is a biomass expansion and conversion factor (BECF), which is an estimation of the amount (tonne) of CO2 uptake when the standing timber volume increases by 1 m3 . Rcarbon (XT +1 ) is the present value of forest owners’ net income in period T+1 and onwards. Changes in soil carbon are excluded in this study due to lack of empirical models to estimate the effect of forest management activities on soil carbon (Johnson and Curtis, 2001; Nilsen and Strand, 2008). The present value of other non-timber benefits besides carbon sequestration is: NPVother =

T A t=1

a=1

(f (a) Xt,a ) e−rt + Rother (XT +1 )

(5)

where A is the maximum relevant age of a forest stand, f (a) is the per ha value of non-timber benefits of age-class a, Xt,a is the area of age-class a in year t, and Rother (XT +1 ) is the present value of the other non-timber benefits beyond period T. We assume that silviculture program (per unit are regeneration investment, thinning program and so on) is exogenously determined, and harvest volumes in different time periods are the only control variables. The harvest volume in each period is determined indirectly using Eq. (2). Thus, the coefficients of the supply function are the only control variable in our model. With consideration of uncertainty in future demand, we assume that both coefficients of the demand function (1) are normally distributed random variables. The coefficients of the timber supply function are determined by maximizing the expected present value of consumer and producer surplus: max Z = E[NPVtimber + NPVother + NPVcarbon ]

˛1 ,˛2 ,˛3

(6)

s.t It = F (Xt )

2

A.

[Standing volume of mature forestin year t]

(7)

A brief explanation of the principle of the method is presented in the Appendix

J. Guo, P. Gong / Journal of Forest Economics 29 (2017) 78–86

Qts = ˛1 (It )˛2 (Pt )˛3



Pt = ˇ1 Qtd Qts = Qtd

ˇ 2





[Aggregate supply of timber in year t]

[Inverse timber demand function in year t]

Market clearing condition

 s

Xt+1 = G Xt , Qt



[Growth function of the forest]

X 1 = X 0 [Initialforestconditionisgiven]

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(8) (9) (10) (11) (12)

For each set of values of the supply function coefficients (˛1 , ˛2 , ˛3 ), the value of the objective function (6) is estimated through Monte Carlo simulation. First, we generate a random demand scenario (i.e., a set of T timber demand functions, one for each year t = 1. . .T) from the probability distributions of the demand function parameters ˇ1 and ˇ2 . Next, the different types of benefits in each year t = 1. . .T are determined. Starting from t = 1 and X1 = X0 , the volume of mature timber stock is calculated. Then, we solve Eqs. (8)–(10) to determine the market equilibrium timber supply Qts and price Pt in year t. The total harvest volume Qts is allocated to different ageclasses to determine the final harvest area in each age-class and the total management cost in year t.3 Thereby the consumer and producer surplus of timber harvest in year t is calculated (see Eq. (3)). Using the final harvest area in each age-class we update the ageclass distribution, calculate the carbon tax/subsidy and the value of other non-timber benefits realized in year t, and then move on to year t+1. To calculate the present value of the forest remaining at the end of the simulation period, Rtimber (XT +1 ), we assume that, starting from year T+1, forest owners will convert the forest to a steady state with a uniform age-class distribution in the most rapid approach and maintain this state to infinity4 . Then, the harvest volume, regeneration area, and XT+1 evolvement of the age-class distribution for t = T+1. . . are uniquely determined by XT+1 . Timber price in each year t ≥ T + 1 is determined using the expected demand function. Rother (XT +1 ) and Rcarbon (XT +1 ) are calculated based on the same management rule. The sum of the discounted benefits during year 1 to T and Rtimber (XT +1 ), Rother (XT +1 ), and Rcarbon (XT +1 ) gives the present value of the total surplus associated with the current demand scenario. The process is repeated N times, and the mean value of the present values of the total surplus is taken as the expected present value. Data The analysis is conducted at the national level and includes 85% of the productive forestland in Sweden5 . There are three major tree species managed for timber production in Sweden: Norway spruce, Scots pine and birch. The total area of birch forest is negligible. Most of the birch trees are mixed in Norway spruce and/or Scots pine dominated stands, and are not managed separately from Norway spruce and/or Scots pine. Norway spruce differs from Scots pine in growth and optimal harvest age. However, the impact of tree species is relatively small compared with the effect of site quality. Moreover, tree-species specific timber demand functions for

3 Timber harvest consists of final harvest and thinning. Thinning removal is determined based on the age-class distribution of the forest and a predetermined thinning program (i.e. ages and intensities of thinning). The remaining amount (the difference between Qts and thinning removal) is produced through final harvest, which is carried out following “the oldest age-class first” principle. We assume that regeneration takes place immediately after a final harvest. 4 The oldest age-class in the steady state is equal to an optimal rotation age determined using the average timber price in the first T years. Note that the average price during the first T years, and thus the optimal rotation age may differ among different carbon price scenarios. 5 Forests in national parks, nature reserves, and other nature protection area, as well as forests older than 120 years are excluded.

Fig. 1. Initial age-class distribution of the forest covered in the analysis, grouped by high- and low-productivity sites. (Data Source: Swedish Forest Agency, 2014).

Table 1 Means and standard deviations of the demand function coefficients. Coefficient

Mean

Standard deviation

ˇ1 ˇ2

574150 -1.67

28707.5 0.0835

Sweden are not available. For these reasons, we choose to disregard tree species composition and distinguish forestland between two different site productivities6 . Fig. 1 shows the initial age-class distributions. The lowest allowable harvest age in our model is set at 60 years, which is also the stand age used when calculating the mature timber volume. The maximum stand age is 120 years (we assume that stand growth beyond this age is zero). The mean value of ˇ2 in the demand function is adopted from previous research (Brännlund et al., 1985). The mean value of ˇ1 is determined based on the average annual harvest level and price during the past five years and the mean value of ˇ2 . For both parameters, the standard deviation is assumed to be 5% of their mean values (Table 1). Regeneration cost in the low- and high-productivity land is 7000 and 9000 SEK/ha, respectively. The harvest cost is 160 SEK/m3 for thinning and 90 SEK/m3 for final felling (Swedish Forest Agency, 2014). We assume that thinning shall be conducted each year in 5% of the forests in age-classes 40-60. Thinning removal is 40 m3 /ha for forests on low-productivity sites and 80 m3 /ha for high-productivity land. According to the estimates by Petersson et al. (2012), the BECF for increment of standing volume in Sweden in different periods during 1990–2005 varies between 0.85 and 1.22 tonnes of CO2 per m3 . The variation is likely due to a combination of sampling errors and real changes in BECF over time. In this paper, we set  equal to 1 tonne CO2 /m3 . IPCC (2006) suggests that an effective carbon price signal within the range of 20–80 USD per tonne of CO2 could bring sufficient economic incentives for producers to adopt many mitigation measures. We tested 5 different carbon prices in the range 170–1428 SEK (20–168 USD) per tonne of CO2 to assess the potential impacts of providing economic incentives for forest carbon sequestration. The price of 1428 SEK/tonne of CO2 is equal to the Swedish carbon tax on fossil fuels7 . The baseline scenario (with zero carbon price)

6 The priority of harvesting different age-classes with different site productivities is determined in the order of decreasing cost of delaying the harvest by 1 year. 7 Readers interested in the carbon tax in Sweden are referred to Åkerfeldt and Hammar (2015).

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Fig. 3. Projected time paths of timber price in different scenarios. Fig. 2. Projected annual timber harvest in different scenarios. Table 2 Effects of carbon tax/subsidy on timber harvest in 2015. Carbon price (SEK/tonne)

Total harvest volume (million m3 )

0 170 340 510 680 1428

85.13 84.33 83.48 81.11 80.31 78.23

Change in harvest volume from baseline case (million m3 )

(%)

0 -0.81 -1.66 -4.02 -4.83 -6.91

0 -0.95 -1.95 -4.73 -5.67 -8.11

serves as a benchmark against which each hypothetical scenario is compared. The per ha value of the other non-timber benefits of age-class a is estimated using the following function (Gong and Guo, 2017): f (a) =

1000 1 + exp

 60−a  15

The discount rate used in the analysis is 3%. The model is implemented in Matlab and solved using the LGO global search solver in TOMLAB (Pintér et al., 2006). When optimizing the supply function coefficients, 100 randomly generated demand scenarios over 100 years are used in estimating the objective function value. After the supply function has been determined, we redo the simulation for 1000 demand scenarios. The average results of the 1000 replications are reported below. Results In our model, carbon tax/subsidy alters forest owners’ harvest decisions and thereby changes net carbon sequestration as well as the magnitudes of other benefits and management costs. Fig. 2 shows that implementation of the carbon tax/subsidy policy would initially cause the harvest level to decrease. A higher carbon price leads to a larger decrease in the total harvest volume. With a carbon price of 1428 SEK/tonne of CO2 , the total harvest volume in 2015, the time when the hypothetical carbon tax/subsidy is introduced, would decrease by 6.91 million m3 , or by 8% compared with the base case. However, the decline resulting from a marginal increase in carbon price is small when carbon price is low as well as when it is very high. It appears that the harvest volume is most sensitive to changes in carbon price between 340 and 510 SEK/tonne of CO2 (see Table 2). Fig. 2 also shows that the differences in harvest levels between different scenarios decreases over time, implying that the effect of carbon tax/subsidy on the harvest level decreases with time. A

Fig. 4. Accumulative net CO2 sequestration with different carbon prices.

decrease in the harvest volume in one year will result in a larger standing volume in the next year, which will cause the supply curve to shift downwards. As time goes, the inventory effect accumulates, and will offset an increasingly larger part of the negative effect of carbon tax/subsidy on timber harvest. By 2050, the difference among different scenarios in total harvest volume is less than 2.0 million m3 , or 1.4% of the baseline level. In year 2100, the difference further decreases to less than 0.3 million m3 . Simulations beyond 2115 show that the carbon tax/subsidy leads to a higher harvest level than in the baseline scenario after 2140, but the effect is fairly small. With a carbon price of 1428 SEK/tonne of CO2 , the optimal harvest level exceeds the baseline level by 0.7–1.59 million m3 during 2014–2210. The effect is even smaller with a lower carbon price. Given that we have a fairly stable downward sloping demand curve, carbon price affects the harvest level and timber price just in the opposite direction (Fig. 3). The price in 2015 is between 344 and 396 SEK/m3 and gradually decreases to 302–310 SEK/m3 by 2075. Fig. 4 presents the cumulative net carbon sequestration during 2015-2115. The difference between the baseline case and each of the other curves shows the increase in net carbon sequestration induced by the carbon tax/subsidy policy with different carbon prices. Recall that net sequestration in each year is proportional to the current annual increment in the total standing volume. Thus, the cumulative net carbon sequestration in each year t > 2015 is proportional to the difference in the total standing volume between year t and 2015. In the baseline scenario, the total standing volume decreases until 2020. Thereafter, it increases steadily and will reach the initial level in 2030. Accordingly, the net sequestration is negative before 2020 and will be positive thereafter. The accumulative net sequestration by 2050 is 153 million tonnes CO2 . It will increase

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Fig. 5. Changes in annual CO2 sequestration induced by the tax/subsidy policy with different carbon prices.

gradually to 365 million tonnes in 2070 and then decreases to 163 million tonnes CO2 by 2115. The gap in the accumulative net sequestration between each scenario with a positive carbon price and the baseline scenario is widening with time in the initial phase of the simulation (Fig. 4). It means that an introduction of the carbon tax/subsidy policy would initially increase the annual net sequestration. The effect is decreasing as time goes, however. Fig. 5 shows that, with a carbon price of 170-680 SEK/tonne of CO2 , the carbon tax/subsidy policy would lead to a lower net sequestration than in the baseline case during 2070–2100. Given enough time, the net annual sequestration will approach zero and the carbon stock in the forests will stabilize, though a higher carbon price will result in a larger steady-state carbon stock. Fig. 6 presents a set of carbon “supply curves”, which more clearly show the effect of carbon price on net carbon sequestration during different time periods. The vertical axis is the price paid per tonne of CO2 sequestered and the horizontal axis is the increase (as compared with the baseline scenario) in the net amount of carbon sequestered by 2020, 2030, 2040, and 2050, respectively. For example, the leftmost curve shows that a carbon tax/subsidy of 340 SEK per tonne of CO2 would increase the net carbon sequestration during 2015–2020 by 8.7 million tonnes CO2 . The increase in net carbon sequestration during this period would be 20.5 million tonnes when carbon price increases to 510 SEK/tonne of CO2 . The average cost of increasing carbon sequestration does not increase monotonously, as one would have expected. The irregular change in the average cost of increasing carbon sequestration is due to the difference in productivity of forestland, and to the fact that the cost of increasing carbon sequestration was estimated using the change in total surplus within a limited time period. The marginal effect on carbon sequestration of reducing timber harvest increases when land productivity increases, but decreases with the age of the forest to be saved, because higher land productivity or lower forest age implies faster growth of the timber retained. On the other hand, land productivity and forest age have little effect on the instantaneous welfare loss caused by a marginal reduction in timber harvest. Tables 3 and 4 describe the effects of increasing carbon sequestration on the NPV of different components of the total surplus during 2015–2030 and 2105–2050, respectively. Consumer surplus and producer surplus of timber harvest move in opposite direction after the introduction of the carbon tax/subsidy policy. Note that the producer surplus in here (in Tables 3 and 4) refers to forest owners’ profits from timber production (the NPV of timber revenues net of the NPV of management costs), whereas the income from carbon tax/subsidy is excluded. It may appear strange that carbon

Fig. 6. Forest carbon supply curves for different time periods during 2015–2050.

tax/subsidy would increase forest owners’ profits from timber production, as it causes the harvest level to decrease. The result is due to the fairly inelastic demand curve. The carbon tax/subsidy policy leads to a relatively small decrease in total harvest volume, but causes a sufficiently large increase in timber price so that the profit becomes larger. Similar results have been reported in Lecocq et al. (2011) and Caurla et al. (2013). The non-timber benefits increase with carbon price as well. In our model, the non-timber benefits are positively related to the age of the standing timber stock. A high carbon price causes a larger reduction in harvest level, which means that the area of older forest stands increases and so does the non-timber benefits. Lower harvest level and higher timber price would cause the surplus of “timber consumers” to decrease. Tables 3 and 4 show that the loss in consumer surplus is greater than the gain in producer surplus and non-timber benefits and, therefore, the NPV of the total surplus decreases when carbon price increases. In terms of the reduction in total surplus, the cost of increasing net sequestration through the carbon tax/subsidy policy with a carbon price of 170–1428 SEK/tonne CO2 is 142.1–179.7 SEK/tonne CO2 for the period 2015–2030 and 80.0–105.8 SEK/tonne CO2 for 2015–20508 . When considering the welfare change within a short time period, the marginal cost of increasing carbon sequestration decreases when land productivity increases, and increases when forest age increases. When carbon price is low, the carbon tax/subsidy induced timber harvest reduction takes place mainly on land with low productivity. An increase in carbon price causes the harvest age on the low-productivity land to increase, with small effect on the harvest on high-productivity land. Thus, the marginal cost of increasing carbon sequestration increases. As carbon price increases, an increasingly larger share of the timber harvest reduction takes place on land with high productivity, which causes the average cost of carbon sequestration to decrease. Increasing carbon price from 680 SEK/tonne CO2 leads to further reduction of timber harvest on both types of land. The harvest age increases on both the high- and low-productivity land, implying that the marginal cost of increasing carbon sequestration increases. Finally, Table 5 presents the coefficients of the timber supply function in the absence and in the presence of a carbon tax/subsidy policy with varying carbon prices. The result shows that the supply

8 The average cost presented in Tables 3 and 4 was calculated by dividing the reduction in the NPV of the total surplus during 2015-2030 and 2015-2050, respectively, by the increased amount of CO2 sequestration during the same period.

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Table 3 Effects of carbon price on the NPVs of consumer surplus, producer surplus, and other non-timber benefits, and on the accumulative carbon sequestration during 2015–2030. CO2 price (SEK/tonne)

Consumer surplus

Producer surplus

Non-timber benefits

Total surplus

CO2 sequestration (million tonne)

Social cost of sequestration (SEK/tonne)

243.0 246.0 249.6 259.4 262.2 270.6

88.4 88.5 88.7 89.3 89.5 89.9

903.9 901.9 899.7 893.2 891.3 885.6

5.6 19.7 31.9 65.9 79.0 107.7

– 142.1 161.7 177.1 171.2 179.7

Billion SEK 0 170 340 510 680 1428

572.6 567.4 561.4 544.5 539.7 525.1

Table 4 Effects of carbon price on the NPVs of consumer surplus, producer surplus, and other non-timber benefits, and on the accumulative carbon sequestration during 2015–2050. CO2 price (SEK/tonne)

Consumer surplus

Producer surplus

Non-timber benefits

Total surplus

CO2 sequestration (million tonne)

Social cost of sequestration (SEK/tonne)

419.2 424.0 429.2 443.4 447.1 460.2

157.1 157.7 158.4 160.3 160.8 162.3

1567.0 1564.5 1561.7 1553.9 1551.8 1544.1

153.8 184.0 210.0 276.9 301.4 372.0

– 80.0 94.4 105.8 102.5 104.7

Billion SEK 0 170 340 510 680 1428

990.7 982.8 974.0 950.2 943.9 921.6

Table 5 Coefficients of the timber supply function in the baseline case and in the presence of carbon tax/subsidy with different carbon prices (SEK/tonne CO2 ). Scenario Baseline CO2 price = 170 CO2 price = 340 CO2 price = 510 CO2 price = 680 CO2 price = 1428

˛1 −17.859

e e−4.8524 e−8.0741 e−14.955 e−2.6037 e−9.0199

˛2

˛3

1.3619 0.7337 0.9438 1.5055 0.7258 1.0907

2.0846 0.6546 0.9335 1.3778 0.2687 0.8814

function would change in response to the implementation of the carbon tax/subsidy policy. The inventory elasticity of supply varies between 0.73 and 1.51, and the price elasticity is between 0.27 and 2.08. Even though the elasticities appear very large in some cases, they are comparable with the empirically estimated elasticities (Buongiorno et al., 2003; Turner et al., 2006). We would like to emphasize that we used the value of mature timber stock as an argument in the supply function, which means that the inventory elasticity would be higher than when the total standing volume of timber is used. Moreover, only a small section of the supply curve in each period is effective. In other words, when determining the supply function coefficients, we evaluated the performance of only a small section of the supply curve. Therefore, the price elasticity should be interpreted with caution. Summary and discussion This paper examines the potential and cost of increasing forest carbon sequestration in Sweden by providing forest owners a yearly tax/subsidy in proportion to the net increase in the carbon stock in their forests. The analysis covers about 85% of the productive forestland in Sweden. Carbon prices (the tax/subsidy rate) examined range from 170 to 1428 SEK/tonne of CO2 . For each carbon price, we used a forest sector model STIMM to determine the optimal timber supply function and then use the obtained supply function to simulate the market equilibrium harvest level and timber price as well as the net change in forest carbon stock during 2015–2115. In the simulation, we also calculated the consumer surplus, forest owners’ profits from timber production, and the other non-timber

benefits in addition to carbon sequestration. Simulation results for different carbon prices are compared with the baseline case (when carbon price is zero) to assess the effects of the carbon tax/subsidy policy. The main results are summarized as follows. 1. In the baseline scenario, the net annual sequestration is negative during the first years, is positive during 2020-2070, and becomes negative again thereafter. The accumulative net sequestration reaches the highest level (about 265 million tonnes CO2 ) in 2070, and then declines to 163 million tonnes of CO2 by 2115. 2. Carbon tax/subsidy reduces timber harvest and increases net sequestration within the short to medium term. The effect is negligible when carbon price is below 340 SEK per tonne of CO2 . A higher carbon price leads to a larger increase in net sequestration. However, the marginal effect of increasing carbon price is small when price is above 680 SEK per tonne of CO2 . For all the tested carbon prices, the effect on carbon sequestration decreases with time. 3. With a carbon price of 1428 SEK per tonne of CO2 , the tax/subsidy policy can increase the average annual net sequestration during 2015-2030 by 6.8 million tonnes of CO2 . The increase in average annual net sequestration during 2015–2050 is 6.2 million tonnes of CO2 . 4. Implementing the carbon tax/subsidy policy would reduce the surplus of “timber consumers”, but increase the profits of timber harvest and the non-timber benefits other than carbon sequestration. In terms of the reduction in total surplus, the cost of increasing net sequestration through the tax/subsidy scheme with a carbon price of 170–1428 SEK/tonne CO2 is 142.1–179.7 SEK/tonne CO2 for the period 2015–2030 and 80.0–105.8 SEK/tonne CO2 for 2015–2050. These results suggest that paying forest owners for increasing forest carbon sequestration is, from a social economic point of view, a cost-effective option to increase Sweden’s contribution to climate change mitigation. However, the potential increase in carbon sequestration is relatively small. Moreover, implementing such a policy would require transactions of large amounts of public funds to forest owners. If carbon price is 680 SEK/tonne CO2 , for example, the average annual net sequestration during 2015–2030 increases

J. Guo, P. Gong / Journal of Forest Economics 29 (2017) 78–86

from 0.38 to 5.27 million tonnes, which means a total subsidy of (680 × 5.27=) 3.58 billion SEK per year. The focus of this paper is the effect of a tax/subsidy policy on forest carbon sequestration and on other benefits of forest management. In the analysis, we implicitly assume that carbon removed from the forest is released to the atmosphere instantly at the time of harvesting. This assumption leads to an overestimation of the potential increase in forest carbon stock. Although timber harvest reduces the carbon stock in forests, it does not increase the total emission by an equivalent amount. A considerable share of the carbon removed from forests will be stored in wood products. Production of wood products also reduces the demand for energyintensive materials such as concrete and steel. Use of forest biomass in energy production would reduce the emission from fossil fuels. The analysis should be extended to include the carbon stock in wood products and the substitution effects in order to assess the full potential of using forests to mitigate climate change.

We would like to thank two anonymous referees and the associate editor for valuable and constructive comments on an earlier version of the paper. Appendix A. Intertemporal optimization of timber harvest based on timber supply function The model we applied in this paper optimizes timber harvest in different time periods through optimization of the coefficients of a short-run timber supply function. The method was documented in Gong (1994) and Gong and Löfgren (2003). In what follows we provide a brief explanation of the principle of this method. To focus on the method, we use the growing stock of timber to describe the state of the forest, and ignore all non-timber benefits. Let Xt denote the timber stock at the beginning of period t, Yt the harvest in period t (assume that harvest in each period takes place at the end of the period), and F(Xt ) the net growth (total growth net of natural mortality) during period t. First, let us consider the optimal decision at firm-level. Assume that the forest owner is a price taker with the objective of maximizing the NPV of timber production. The harvest decision problem can be modelled as:

 ∞

{Yt }

˘=

t (Xt , Yt , Pt )

t=1

subject toXt+1 = Xt + F(Xt ) − Yt for t ≥ 1

(A1)

X1 = X0 > 0 given where Pt is timber price in period t, (Xt , Yt , Pt ) is the profit in period t, ␳ is the discounting factor, and X0 is the initial timber stock. Denote by{Yt∗ } the optimal solution of problem (A1). Define the following function Y t = S(˛,X t ,P t ),

(A2)

where ˛ is a set of coefficients of the function. For the moment, we can regard (A2) as a decision rule − a specific way to determine the harvest level conditional on timber stock and price. The harvest level determined using (A2) depends on both the functional form of S(˛, Xt , Pt ) and the values of ˛. Given a functional form of S(˛, Xt , Pt ), one can change the harvest level indirectly by calculating {Yt } using (A2) with different values of ˛. This implies that we can reformulate (A1) as a problem of optimizing the values of ˛. Consider, for example, the following specification of (A2). Yt = ˛1 (Xt )˛2 (Pt )˛3

By imposing this decision rule, problem (A1) can be reformulated as: ˘=

max

˛1 ,˛2 ,˛3

∞ 

t (Xt , Yt , Pt )

t=1

subject to Yt = ˛1 (Xt )˛2 (Pt )˛3

(A4)

Xt+1 = Xt + F(Xt ) − Yt for t ≥ 1 X1 = X0 > 0 given Note that the decision variables in (A4) are {˛1 , ˛2 , ˛3 }, whereas {Yt } are treated as intermediate variables, which are functions of {˛1 , ˛2 , ˛3 }. Denote the optimal solution of (A4) by {˛ ˆ 1, ˛ ˆ 2, ˛ ˆ 3} and {Yˆ t }. Suppose that the optimal harvest determined by (A1) can be described exactly by a function of the form (A3), i.e. Yt∗ = ˛∗1 (Xt∗ )

˛∗

2

(Pt )

˛∗

(A5)

3

Xt∗

Acknowledgments

max

85

(A3)

where is the growing stock of timber in period t following the time path of optimal harvest {Yt∗ }. In this case, it is quite obvious that ˆ i = ˛∗i (fori = 1, 2, 3) and Yˆ t = Yt∗ for the optimal solution of (A4) is ˛ all t ≥ 1. If the relationship between Yt∗ and the timber stock and price in period t has a different form than (A5), the decision rule optimized through (A4) will leads to a time path of harvest which is as close to {Yt∗ } as possible, provided that a larger deviation of {Yt } from {Yt∗ } leads to a lower NPV of future profits. By definition, (A5) is the short-run timber supply function of the forest owner. Thus, we can think of the decision rule (A3) as an approximation of the short-run supply function. Problem (A4) aims to find the best approximation of the short-run timber supply function, in order make the best estimates of the optimal harvest in different periods (i.e. the optimal solution of problem (A1)). In a partial equilibrium framework, the intertemporal harvest optimization problem can be modelled as: max {Yt }

˘=

∞ 



Yt

t [

D(y)dy − C(Xt , Yt )] 0

t=1

subject to Xt+1 = Xt + F(Xt ) − Yt for t ≥ 1

(A7)

X1 = X0 > 0 given where D(y) is the inverse demand function, and C(Xt , Yt ) is the management and harvest costs in period t. As in the case where timber prices are exogenous, we can use a short-run supply function as a decision rule to determine the harvest level in each period based on the prevailing state of the forest and timber price. After the functional form of the short-run supply function has been determined, we need to find the values of the coefficients of the function so that the resulting supply function provides the best estimation of the optimal harvest levels. In other words, we can reformulate the intertemporal optimization problem (A7) as: max ˛

˘=

∞ 

 t [

t=1

Yt

D(y)dy − C(Xt , Yt )] 0

subject to Yt = S(˛, Xt , Pt ) Pt = D(Yt )

(A8)

Xt+1 = Xt + F(Xt ) − Yt for t ≥ 1 X1 = X0 > 0 given The first two constraints in (A8), i.e. the supply and demand functions, together determine the market equilibrium harvest level and timber price in each period. The main benefits of using the short-run supply function to approximate the intertemporal optimization problem, as described

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