Journal of Forest Economics 17 (2011) 127–141
Contents lists available at ScienceDirect
Journal of Forest Economics
journal homepage: www.elsevier.de/jfe
Simulated effects of mandatory versus voluntary
participation in private forest carbon offset
markets in the United States
Gregory Latta a,∗, Darius M. Adams a, Ralph J. Alig b, Eric White a
a
b
Oregon State University, United States
USDA Forest Service, United States
a r t i c l e
i n f o
Article history:
Received 8 July 2010
Accepted 11 February 2011
JEL classification:
C61
L52
Q15
Q23
Q54
Keywords:
Forest carbon markets
Carbon policy simulations
a b s t r a c t
Assumptions regarding landowner participation, whether mandatory or voluntary, are an important determinant in evaluating the
implications of a carbon offset sales program. We modify an existing
intertemporal optimization model of the US forest and agriculture
sectors to allow optional involvement of private forest land in a carbon offset market and compare these results to a case in which all
private land is enrolled. Our analysis of these two cases and various
CO2 e price levels indicate different responses in carbon stock and
flux, forest land area and management, forest product prices, and
forest conditions. The results suggest that the cost of sequestering
carbon in US forests, using either a voluntary or mandatory carbon
offset sales program, may be substantially higher than suggested
by earlier studies.
© 2011 Department of Forest Economics, SLU Umeå, Sweden.
Published by Elsevier GmbH. All rights reserved.
Introduction
Past studies of the costs of sequestering forest carbon in the United States have differed markedly
in terms of the type of model used. In a recent review, Richards and Stokes (2004) categorize these
models and compare their various characteristics in a detailed taxonomy. They find a wide range
∗ Corresponding author at: Department of Forest Engineering, Resources and Management, 280 Peavy Hall, Oregon State
University, Corvallis, OR 97331, United States. Tel.: +1 541 737 6264; fax: +1 541 737 3049.
E-mail address: greg.latta@oregonstate.edu (G. Latta).
1104-6899/$ – see front matter © 2011 Department of Forest Economics, SLU Umeå, Sweden. Published by Elsevier GmbH. All rights reserved.
doi:10.1016/j.jfe.2011.02.006
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G. Latta et al. / Journal of Forest Economics 17 (2011) 127–141
of cost estimates, as do Stavins and Richards (2005) and Dempsey et al. (2010), with a tendency
for “econometric”1 models based on historical land-use data to give somewhat higher estimates of
marginal costs at any given sequestration level than other model types. Looking at this range of modeling studies it is also clear, as we argue below, that they differ in their assumptions about the form of
the carbon “market” or the policy that compensates owners for carbon sequestered. In effect, most past
studies do not examine the same type of forest carbon offset sales policies. As a result, comparisons
of cost estimates would be problematic, even if modeling approaches were identical.
Although forest carbon offset sales programs (COSP) have many dimensions and provisions, one of
the key elements is whether the program includes mandatory (a carbon subsidy/tax system applied
to all eligible lands) or voluntary (forest owners can decide) participation. Prior studies employing
econometric models (e.g., Plantinga et al., 1999; Lubowski et al., 2006) have considered only voluntary carbon markets because their models simulate observed voluntary land market behavior. Analyses
using optimizing models (e.g., Adams et al., 1999; Sohngen and Mendelsohn, 2003), however, have
assumed that all eligible lands are enrolled in the offset sales program mostly as a matter of analytical
simplicity. So-called engineering cost models (e.g., Parks and Hardie, 1995), by virtue of their construction, provide estimates of carbon stock changes only for lands that opt to receive a subsidy. Thus,
past studies have assumed either a voluntary or mandatory participation system and there has been
no attempt, to our knowledge, to compare both options under ceteris paribus conditions.
This paper focuses on the effects of mandatory versus voluntary, or universal versus partial, participation in offset sales markets. We are concerned with the impacts of this difference on: the costs
of forest carbon increments, the mix of increments coming from afforestation versus existing forests,
shifts of land between the forest and agricultural sectors, and the biological condition of the forest in response to mandatory or voluntary participation. To conduct this analysis, we have modified
an existing intertemporal optimization model of the US forest and agriculture sectors, FASOM-GHG
(Adams et al., 1996a; Alig et al., 2010a). Specifically, within the market surplus maximization process
of FASOM-GHG, we allow private forest owners to enroll lands in the offset market to the extent that
this improves their discounted intertemporal producers’ surplus. These results are compared to the
case where all forest lands are assumed to be enrolled in the offset market.
Voluntary versus mandatory subsidies in past studies
In past studies that have employed econometric approaches (Stavins, 1999; Plantinga et al., 1999),
observed land use or land allocation is explained by relative land rents in competing uses and an
array of land and owner characteristics. Although the underlying behavioral model is one of land rent
maximization, it is argued that the model reflects actual behavior of decision makers because of the
use of historical data. Land use decisions respond both to explicit variables (e.g., land rent) included
in the regressions and the complex of omitted variables (implicit factors such as unobservable owner
values for land amenities) that affect real world behavior.2 Thus, land-use decisions projected with the
model may depart from simple land rent maximization because of these unobservable considerations
that are nonetheless reflected in the estimated parameters. Some of these implicit factors would also
be considered when deciding on participation in a carbon sales market.
In the econometric models, a subsidy/tax or offset sales system is simulated by adding a carbon
value (per unit area) to the estimated net return from forestry and deducting a carbon value from the
net return of a shift out of forestry. This may cause a change in projected land use behavior and hence in
carbon stocks. The changes are representative of voluntary participation, induced by shifts in relative
rents as modified by the unobservable considerations noted above. The total cost of the subsidy and
the net change in carbon stock from a “base” case provide the basis for computing incremental carbon
costs. Carbon changes associated with afforestation and deforestation are considered.3 The effects of
1
The model classifications, “econometric”, “optimization” and “engineering”, derive from the review by Richards and Stokes
(2004) in their Section 5.0.
2
See, for example, the discussion in Lubowski et al. (2006, pp. 136–137).
3
Some studies have also included options to harvest or not harvest timber on afforested lands but the management regimes
and rotation ages were pre-set and not endogenous.
G. Latta et al. / Journal of Forest Economics 17 (2011) 127–141
129
changes in the management of existing stands are not simulated. In models where forest products
prices are endogenous (Lubowski et al., 2006), net land use shifts will reflect these price changes but
forest management, timber harvest, and carbon on lands where use does not change will be unaffected.
In engineering cost studies (Moulton and Richards, 1990; Parks and Hardie, 1995), analysts identify
an array of potential “projects”—uniform areas that may be afforested or whose management may be
modified if already forested. Estimates are developed of the operational costs of afforestation and
changes in management of existing stands plus the opportunity costs required to convince owners
to change behavior (to afforest or shift forest management). The projects are ordered by cumulative
carbon increment and ascending cost per unit of carbon to form a marginal cost relationship. Only
projects with costs at or below a given carbon price (unit carbon subsidy) are “enrolled” in the subsidy
program. Thus, participation is “voluntary”, but this is based on the (rationality) assumption that if
the carbon price exceeds the combined management plus opportunity cost owners will enroll in the
program. Timber product price-induced impacts on participating and non-participating lands have
generally been ignored.
Optimization models (Adams et al., 1999; Sohngen and Mendelsohn, 2003) simulate the functioning
of product and resource markets by setting output and consumption so as to maximize the present
value of the sum of producer and consumer surpluses less production and transport costs plus any
subsidies. Carbon stocks are computed from the forest inventory representation. A carbon offset sales
policy, or subsidy-tax system, is simulated by adding a term to the market surplus objective function
that values the difference in aggregate forest carbon flux (the change in carbon stock) between the
case with a positive carbon price and a “base” case with no carbon price. For example, the addition to
the objective function might appear as:
+
PC [Ct − CtB ](1 + i)
−t
t
where PC is the unit carbon price or subsidy, Ct is the change in carbon stock from period t − 1 to
t in a COSP simulation, CtB is the carbon stock change for the same period in the “base” case, and i
is the discount rate. In this term, it has been customary in past optimization studies to value carbon
increments on all lands being modeled. Thus, the approach assumes mandatory participation in the
offset sales program. If harvest timing and silvicultural investment are endogenous in the model (this
is the case in most past studies), both afforestation and changes in current forest management can
contribute to the carbon stock change. With endogenous forest products prices, a positive carbon price
will generally induce changes in the management of all land classes. In effect, the net carbon impacts of
both these price-induced changes and the subsidy-induced changes are valued in the objective term.
Simulation scenarios in the current study
In this paper we modify the typical treatment in optimization models (as noted above) to differentiate between lands that are participating in the offset sales program and those that are not. Subsidies
are paid, or taxes levied, for carbon stock changes only on the former group. Timber and agricultural
product prices are endogenous in our model, however, so that net changes in total forest carbon across
all owners will reflect both changes on participating lands and product market-induced changes on
non-participating lands.
To provide a specific structure for our voluntary versus mandatory comparisons, we have assumed
that: (i) carbon from both afforestation and existing stands can be counted; (ii) the system is symmetric
and that payments and penalties are charged at the same rate or carbon price; (iii) timber harvesting is
allowed during the contract with carbon reductions subject to penalties; (iv) no reductions in payments
are taken for the risk of losses but (due to the structure of the model) the exact effects of leakage are
recognized in the application of subsidies and penalties; (v) following protocols from the Climate
Action Reserve,4 lands can enroll at any time, but once enrolled in the offset sales system they must
4
See the formal protocol at http://www.climateactionreserve.org/how/protocols/adopted/forest/current/.
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G. Latta et al. / Journal of Forest Economics 17 (2011) 127–141
remain enrolled for 100 years. In addition, given that our model explicitly recognizes land use links
to the agricultural sector, we assume that all agricultural lands are enrolled in an agricultural carbon
offset sales program.
Structure of the FASOM-GHG model
To simulate optional and mandatory participation in a COSP, we have modified the FASOM-GHG5
model of the US forest and agricultural sectors to differentiate between forest lands that are enrolled
in a COSP and those that are not. FASOM-GHG is an intertemporal optimizing sectoral model that
simulates behavior in the markets for agricultural and forestry products and land. Since large areas
of land shift back and forth between forestry and agricultural uses in the US, policy changes in one
sector can readily spill over into the other through impacts on relative land prices. Thus, it is critical
to explicitly represent the land interface between the two sectors.
In the forestry portion of the model, forest inventory is represented using an age class system of
the “type 2” form as described by Johnson and Scheurman (1977). In addition to age, forest land strata
are differentiated by ownership, region, site quality, forest type, suitability for agriculture, and forest
management intensity (silvicultural regime). Decisions about harvest age, forest type (after harvest),
and forest management intensity are endogenous in the model. Afforestation and deforestation decisions on private land are also endogenous and depend on the relative land rents promised in the two
uses (including any subsidies or taxes). Note that agricultural land can be afforested and not enrolled
in a COSP. Only private timberlands are modeled in detail. Industrial and individually owned private
timberlands are separately represented. Public timber harvests are not determined by market conditions. Public harvest volumes are recognized in the product and log market solutions, but public land
management and carbon stores are calculated outside of FASOM-GHG.
A condensed mathematical description of the FASOM-GHG structure is given in Appendix A by Eqs.
(A1)–(A13). Subscripts (which may number up to a dozen for some variables) are largely ignored in
this description, except where needed to differentiate key concepts. FASOM-GHG includes an array
of explicit foreign trade relationships in both the agricultural and forest sectors, detailed materials
balance relations to aid in tracking residue generation and use at all levels, and a simplified model of
US bio-energy generation. These relations are omitted from the appendix description to focus on the
core model.
The objective function (A1) maximizes the present value of the sum of net producers’ and consumers’ surpluses over the planning horizon (to period T). For the analysis reported here the planning
horizon was 100 years. The discount rate was set at 4%. The first two terms inside the square brackets represent consumers’ surplus and costs of management and production in the forest sector. The
second pair of terms, cF and cA , are the direct costs of shifting land between the two sectors. The next
three terms represent agricultural market surplus. The last term inside the square brackets is the net
subsidy payment for carbon in forestry and agriculture. Only the additional flux on lands enrolled
i − T i ), is subject to subsidy or tax in the objective function. Note that additional
in a COSP, (TC,t
B,t
carbon flux is computed as the change in flux from the base, or no COSP, case. This represents the net
additional carbon sequestered by the COSP.
The final terms in the objective function provide for the valuation of the terminal inventories of
land and timber in the forest and agricultural sectors. They represent the discounted value of projected
steady-state returns after the end of the projection period (see Appendix A for detailed description). In
our evaluation of policy impacts, we focus on the first 50 years of the projection which we believe to be
the policy relevant period. In this period the impact of terminal conditions on the results is minimal.6
Endogenous variables in the model are the areas of existing and regenerated forest including
afforestation (E and R) both enrolled (i) and not enrolled (o) in the COSP, areas transferred between
5
Forest and Agricultural Sector Optimization Model with Greenhouse Gases. Detailed documentation of an earlier version
is given by Adams et al. (1996a) and Alig et al. (1998). Draft documentation of the current version is available as a PDF at
http://agecon2.tamu.edu/people/faculty/mccarl-bruce/papers/1212FASOMGHG doc.pdf, where model structure is described
in chapters 5–9. Copies of the GAMS code and data for FASOMGHG are available from the authors on request.
6
See Adams et al. (1996b) for discussion of sensitivity tests on terminal conditions in a similar model.
G. Latta et al. / Journal of Forest Economics 17 (2011) 127–141
131
forestry and agriculture (AF and FA) where land coming from agriculture into forestry may either be
enrolled in the COSP or not (in the voluntary case), and the allocation of land to crop and livestock
production in agriculture (F).
Timber harvest in forestry (A2) is computed from the areas of existing and regenerated stands
harvested in period t using appropriate yield volumes (via the function h). All existing areas (E) must
be allocated to some harvest regime, including never harvested (A3). In Eqs. (A4) and (A5), lands
regenerated after harvest in period t (both enrolled and not enrolled in the COSP) can be no larger
than the areas harvested in t adjusted for any land exchange with agriculture. In the voluntary case,
land once enrolled in the COSP must remain enrolled for 100 years, effectively precluding shifts in and
out of the COSP during a simulation. Thus we employ separate Eqs. (A4) and (A5) to control regenerated
lands that are in and out of the COSP. The enrollment length requirement in the voluntary case also
V
requires separate treatment of land moving from forest to agriculture (FAM
t , FAt ). In the voluntary
case this land can only come from non-COSP areas (A5), whereas in the mandatory case it can only
come from land in the COSP (since there is not option). Total growing stock inventory is computed in
(A6) using areas of both existing and regenerated stands and appropriate yields per unit area in the
function G.
Eqs. (A7) through (A9) define the agriculture production function, giving consumable products
as functions of basic crop and livestock output, the use of land in basic agricultural output, and the
use of purchased variable cost inputs in production (primarily labor, fertilizer, and water). Eqs. (A10)
and (A11) limit the areas that can shift from forest to agriculture and agriculture to forest based on
biological production capabilities as determined from land inventory data.
The final two sets of Eqs. (A12) and (A13) compute period-to-period carbon flux. Changes on forest lands enrolled in the COSP are included in (A12). As noted in Section “Simulation scenarios in
the current study”, we assume that a COSP is also in place for agricultural lands and that participation is mandatory. Hence, the agricultural carbon flux is also included in (A12). The total flux for
all private lands in and out of the COSP (A13), TC , gives the net effect of the COSP, including leakage effects across owners induced by market changes. This is the carbon mass used in program cost
computations.
To simulate the case of mandatory participation in a COSP, variables with o subscripts in the
appendix equations would be eliminated—all lands are required to be in the COSP. Eq. (A5) would
be dropped, together with its FAVt term. Eq. (A13) would not be needed, because all carbon changes
would be subject to a subsidy/tax and only total carbon change for all lands would appear in the objective function. Lastly, only the FAM
t terms would be active in Eqs. (A8), (A10) and (A11) and the AFO,t
terms would be dropped (because all land is “in” the COSP).
With appropriate linearizations of portions of the objective function, the model is formulated as a
linear program and solved using the CPLEX algorithm in the GAMS programming language (Rosenthal,
2008).
Results
We expect that not all landowners will be interested in voluntarily participating in a COSP.
Forest owners with older stands will realize limited returns from subsidy payments associated
with carbon-related benefits and would be subject to a large near-term cost for the carbon reduction at time of harvest. The 100-year commitment in our COSP contract (see Section “Simulation
scenarios in the current study”) limits flexibility for owners who may wish to move land out
of the program at some future point. Agricultural owners may be less interested in afforestation
for this same reason if they wish to shift land back into agriculture after a single forest rotation. As a result, we anticipate smaller forest carbon increments under a voluntary program as
compared to a mandatory program, with reduced impacts on harvest and forest sector prices,
and smaller increments in forest inventory. Smaller carbon increments are expected to shift the
marginal cost curve to the left, leading to higher marginal costs for sequestering a given level
of additional carbon under voluntary participation than would be projected assuming mandatory
participation.
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G. Latta et al. / Journal of Forest Economics 17 (2011) 127–141
0.8
0.6
Billion tonnes CO2(e)
0.4
0.2
0
2000
-0.2
Base
$5 Mandatory
$15 Mandatory
$5 Voluntary
$15 Voluntary
2010
2020
2030
2040
2050
2060
2070
-0.4
-0.6
-0.8
-1
-1.2
-1.4
Fig. 1. US forest carbon flux for base, and two carbon prices ($5 and $15 per tonne CO2 e) under voluntary and mandatory COSPs.
Flux does not include soil carbon or wood products.
Carbon flux and stock
Excluding changes in the carbon in products removed from the forest, US private forest carbon
stocks are expected to decline in the base (no COSP) case over the next five decades. This reduction
reflects both the loss of forested land to other uses and a gradual shift in the species composition
of private forests away from hardwoods and toward softwoods. Land losses to agriculture alone are
expected to reach nearly 2.8 million hectares over the 2010–2030 period, with an additional 5.2 million
hectares shifting into urban/suburban uses (Alig et al., 2010b). A change in the species mix of private
forests is significant because softwoods are less carbon dense than hardwoods, i.e., they contain less
carbon per unit volume. Thus, even though the total cubic volume stock of private forests is not
expected to change markedly over the next 50 years, the proportion that is hardwood will fall and
with it the net carbon stock.
Carbon offset sales programs act to raise the net private carbon flux over time, as illustrated in
Fig. 1. The effects are reduced under a voluntary participation system. In our simulations, a $15 per
tonne CO2 e price would be required under a voluntary system to yield roughly the same net increase
in carbon flux as a $5 per tonne price under a mandatory system.7
Afforestation versus management changes in existing forests
Although afforestation often receives the greatest attention as a vehicle for expanding forest carbon,
changes in the management of existing forests appears to hold a larger physical potential. In our
analysis, forest management can be modified to add carbon by extending rotation age, shifting species
composition in regeneration after harvest, and employing different regimes of silvicultural treatments
over time. Fig. 2 shows the FASOM-GHG projections under a $5 per tonne CO2 e price and mandatory
and voluntary COSPs. Regardless of the form of the COSP, changes in existing forest management
account for more than 80% of the average carbon stock increase from the base case over the next 50
years. Existing forests become less important, relative to afforestation, as carbon price rises, however,
with their share of the average stock increment dropping to about 75% at a $30 per tonne CO2 e price.
The mandatory COSP produces a larger increment in forest carbon stocks at all prices examined,
but the extent of the difference declines markedly as the CO2 e price rises. At a $5 per tonne price,
the carbon stock increment for a mandatory COSP is 6 times larger than the voluntary for changes in
management but only 3 times larger for the contributions from afforestation. At a $30 per tonne CO2 e
7
In FASOMGHG some non-CO2 GHG’s are tracked in the agricultural sector and in the forest sector there are some non-CO2
GHGs emitted in bioenergy generation. As a result we use CO2 equivalents, CO2 e, rather than just CO2 .
G. Latta et al. / Journal of Forest Economics 17 (2011) 127–141
133
3.5
$5 Mandatory Afforest
$5 Voluntary Afforest
$5 Mandatory Exist
$5 Voluntary Exist
Billion tonnes CO2(e)
3
2.5
2
1.5
1
0.5
0
1990
2000
2010
2020
2030
2040
2050
2060
2070
Fig. 2. Change in US private forest carbon stock from the base for existing forests and afforested land at a $5/tonne CO2 e carbon
price for voluntary and mandatory COSPs.
price, however, a mandatory COSP produces about 2.6 times as much additional carbon from forest
management changes as a voluntary system and about 2.4 times as much from afforestation.
Changes in forest land area
As noted above, the base case anticipates a continued decline in private forest area over the next
two decades. A COSP of either form would impact the shift of forest to agriculture, as noted in Table 1,
with higher CO2 e prices slowing or even reversing the trend. A voluntary system is projected to be
less effective than a mandatory one at any CO2 e price.
Table 1 also shows land use responses at the regional level. The North and South have large areas
of land suitable for both agriculture and forestry while the West does not. Any form of COSP would
bring a reversal of the flow of forest land to agriculture in the West. There are also notable differences
in the responsiveness of the North and South both to the form of the COSP and the level of the CO2 e
price, with particular differences under the mandatory system.
Marginal costs of forest carbon sequestration
For each form of COSP, we compute the marginal cost schedule using the annualization approach
described by Richards and Stokes (2004) and illustrated in Im et al. (2007). Quantities are computed
as annualized increments in forest carbon flux relative to the base case as carbon price rises from zero.
Incremental costs are computed as the differences in annualized net carbon payments divided by the
Table 1
Net shift of forest land to agriculture over the 2010–2030 period (<0 means a loss to agriculture) with two carbon prices, under
voluntary and mandatory COSPs.
COSP policy
Scenario
North
South
West
US total
Thousand hectares
None
Mandatory
Mandatory
Voluntary
Voluntary
Base
$5/tonne
$15/tonne
$5/tonne
$15/tonne
−1157
−561
1272
−1066
−705
−1593
−1240
1200
−1600
−723
−6
917
917
355
925
−2755
−884
3390
−2311
−503
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G. Latta et al. / Journal of Forest Economics 17 (2011) 127–141
60
$US per tonne CO2(e)
50
40
30
Mandatory Total
Voluntary Total
20
Mandatory Existing
Voluntary Existing
10
Mandatory Afforest
Voluntary Afforest
0
0
50
100
150
200
250
300
350
Million tonnes CO2(e) per year
Fig. 3. Marginal costs of forest carbon sequestration for afforestation, management of existing forests, and total under voluntary
and mandatory COSPs.
increments in annualized carbon quantities for each carbon price increment.8 For comparability with
past studies, the costs recognized here might be termed “program” costs, since they are net subsidy
payments. Welfare changes of producers and consumers, as discussed in Im et al. (2007), are not
included.
Results of this analysis are shown in Fig. 3, disaggregated into the cost contributions of afforestation
and management of existing forests. As anticipated, the voluntary system has a higher marginal cost
relation. In both forms of the COSP, afforestation is the most costly component. This latter finding
may explain in part the consistent difference found between marginal cost estimates of econometric
and other types of cost analysis in past studies. Shifting land out of agriculture into an effectively
permanent forest use requires greater inducements for the landowner than simply postponing rotation
or changing species mix during planting of harvested timberland areas. At the same time, these forest
management changes, though modest on a single tract, appear to be capable of producing substantial
carbon increments when practiced across the full private forest base.
The mandatory COSP system forces forest land owners to optimize their behavior within a constrained sphere of options. The result is a reduction in producer surpluses for traditional products
relative to the case of an unconstrained operational environment. Similarly, consumers of traditional
forest products consume less at higher prices. In the shift from voluntary to mandatory COSP, the
consumer and producer welfare losses in product markets exceed the producer welfare gains in the
carbon market. These latter gains are indicated by the area differences between the marginal cost
curves at any specific CO2 e price in Fig. 3.
Impacts on forest conditions
To partially characterize the impacts of the COSPs on forest conditions, we compute the proportion
of area in the total private timberland base by age class. From biological studies we know that shifts
in the age structure of the forest impact habitat for wildlife species, with older areas often preferred
habitat for rare species. Forest age structure may also impact the quality of certain types of recreational activities, visual and amenity values, water yields and water quality, and forage production for
domestic livestock. We would expect that as the CO2 e price rises, we would see more area in older
age classes, particularly as rotation ages are lengthened and the total forest inventory rises. Results
are shown in Fig. 4, for the base (no carbon sales) and mandatory and voluntary COSPs at a $15 per
tonne CO2 e price, all in a snapshot at year 2030.
8
This is just the slope of the “total” carbon flux curve: change in annualized cost/change in annualized output (flux).
G. Latta et al. / Journal of Forest Economics 17 (2011) 127–141
135
Fig. 4. Proportions of area by age class at start of year 2030 for base, mandatory and voluntary COSP cases at $15 per tonne
CO2 (e). Voluntary case shows distribution of lands IN and OUT of the program.
G. Latta et al. / Journal of Forest Economics 17 (2011) 127–141
450
Million cubic meters
600
425
500
HARVEST
400
400
300
375
200
PRICE
100
350
BASE HARVEST
15 HARVEST MANDATORY
15 HARVEST VOLUNTARY
BASE PRICE
15 PRICE MANDATORY
0
1990
2000
2010
2020
325
$US per thousand board feet
136
15 PRICE VOLUNTARY
2030
2040
2050
2060
300
2070
Fig. 5. US private timber harvest (all species) and softwood lumber price, base (♦ and ), $15 CO2 e price with voluntary COSP
( and ) and $15 CO2 e price with mandatory COSP ( and ).
In the graphs it is difficult to discern much difference between the base and $15 mandatory case.
There is in fact a very small shift of area proportions in the mandatory distribution toward the oldest
classes (95 years and older). With all forest and agricultural lands participating in the COSP, there
is no motivation to markedly adjust the age distribution. And, with fewer forest hectares shifting to
agriculture (and increments in afforestation), it is still possible to expand carbon flux relative to the
base case. The voluntary case shows a markedly different picture. Lands that are not enrolled in the
COSP are harvested more heavily than in the base case as forest products prices rise above base levels.
Areas in the youngest age groups rise markedly on these lands and areas in the middle age groups
(35–70 years) shrink. On lands enrolled in the COSP, in contrast, there is a major expansion of area in
the middle ages and reduction in the younger ages.
Markets for traditional forest products
Forest owner behavior under a COSP leads to reduced timber harvest. This is illustrated in Fig. 5
for the $15 per tonne CO2 e carbon price under both voluntary and mandatory systems. Because the
voluntary system induces a smaller response from land owners, the harvest impact is also reduced. As
this change in timber supply works its way through the market chain, production of traditional products such as sawnwood and paper are also reduced. The price impacts of these changes are illustrated
60
Stavins (1999)
Lubowski et al. (2006)
$US per tonne CO2(e)
50
Mandatory Total
Voluntary Total
40
30
20
10
0
0
200
400
600
800
1000
1200
Million tonnes CO2(e) per year
Fig. 6. Comparison of marginal forest carbon sequestration costs from FASOM-GHG with results from two econometric studies.
G. Latta et al. / Journal of Forest Economics 17 (2011) 127–141
137
in Fig. 5 for the case of softwood lumber. Because consumer demands for virtually all wood products
in the US are inelastic, the price changes are larger in percentage terms.
Over time, total harvest and product prices under both COSP systems gradually converge to base
case levels. This happens in part because the incremental returns derived from carbon sales decline as
the private forest carbon stock rises at a decreasing rate. When the value of an additional unit of timber
harvested rises above its carbon-related value stored for an additional period, owners increase harvest
of traditional products to take advantage of higher prices in those timber-related markets. Payments
under COSPs act to extend rotations and raise timber inventories. Early periods of lower harvests (and
rising inventories) to capture carbon income can be followed in later periods by increased harvests,
relative to the base case, while still maintaining higher carbon flux and stocks.
Conclusions
Regardless of the COSP system employed, we find that modifications in the management of existing
forests could provide the largest part of carbon flux gains from the US private forest sector. Although
demonstrating the additionality of carbon increments from these sources is difficult, we believe that
past studies have given inadequate attention to their potential. Our analysis also suggests that carbon
increments from existing forest management are possible in many cases at a substantially lower cost
than from traditional afforestation. In addition, changes in existing forests allow significant near-term
(5–10 years) increments in flux, while afforestation gains gradually accumulate as plantations mature
(as illustrated in Fig. 2). As a result, comparison of carbon costs from past studies that involve different
mixes of options for afforestation and management of existing stands will be difficult.
We find large differences in the efficacy and costs of voluntary versus mandatory COSPs. Our voluntary system produced smaller carbon increments at all CO2 e prices—about one-third the carbon
mass of a mandatory system for the range of prices we examined. Based on considerations of land
value maximization alone (in our model), a substantial area of forested land would not be enrolled in
a voluntary COSP. At a $5 per tonne CO2 e price, roughly two-thirds of private land is out of the COSP,
while at $30 the proportion is close to half. The decision not to enroll is made if the discounted costs
of carbon penalties at harvest outweigh the discounted values of prior subsidy payments (considering
any adjustments in rotation or silviculture). Since the COSP requires a 100-year enrollment period,
this comparison must be made over the full projection period. Lands not enrolled in the COSP provide
a larger portion of the timber harvest response to higher prices of traditional products. Their future
age class distributions would be more heavily concentrated in the younger age classes as a result, with
associated implications for supplies of ecosystem services from these lands.
The 100-year commitment period in our voluntary COSP simulation (drawn from the existing
Climate Action Reserve program) likely acts to increase the costs of carbon sequestered in the analysis.
Shorter periods, allowing forest owners more flexibility to opt in and out during the course of a 100year projection may lead to lower program costs. However, some minimum enrollment commitment
would almost surely be required as a way of ensuring permanence to the purchaser of offsets. Varying
levels of commitment in a COSP would most likely lead to differing carbon prices (lower prices for
short term instruments and higher prices for long term carbon instruments) as well as adjustment
in the discount factors applied in various COSP protocols to address the risk of reversal. A systematic
evaluation of the effects of the length of commitment period and associated changes in the discounting
terms of carbon contracts would be a valuable topic for future research.
Past studies employing econometric land use models have generally found higher marginal costs
for forest carbon sequestration in the US than studies using other approaches. It has been argued that
this arises because non-econometric models fail to recognize an array of unobservable determinants
of land use decisions. In this regard Stavins (1999, p. 1003) notes that these omissions, “. . .would
tend to lead ‘engineering’ or ‘least-cost’ analyses to underestimate sequestration costs.” Both Stavins
(1999) and Lubowski et al. (2006) present graphical comparisons of econometric and other studies
that support this conclusion.
In fact, most of the studies summarized in these comparisons were engineering studies. To our
knowledge there have been no direct comparisons of marginal forest carbon cost curves derived from
FASOM-GHG with those from other approaches. To help resolve this issue, we developed Fig. 6 which
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G. Latta et al. / Journal of Forest Economics 17 (2011) 127–141
compares forest carbon costs from two national econometric land use studies with ours for voluntary
and mandatory COSPs. Clearly our costs are substantially higher than estimates from the land-use
models. This results despite the fact that our analysis includes both land use change and changes in
management of existing forests. Further, based on previous discussion, it is appropriate to compare
only the even more costly voluntary FASOM-GHG results with the land-use models.
There are several reasons for these results. In fact, the Stavins (1999) analysis was developed by
scaling up estimates derived from a small set of county land use data in the US South. There is no
reason why these cost results should relate to the entire US. The Lubowski et al. (2006) model does
cover the contiguous 48 states but specifically allows land to change from rangeland to forest use.
Their figure 2 (page 146) suggests that the largest part of the projected expansion in forest area over
the first 50 years of their forecast at a $247 per hectare subsidy comes from a rangeland to forest
shift. Although the definition of rangeland is problematic in some regions of the US, we believe that
relatively little rangeland could biologically sustain such a shift. As a result we currently exclude such
a shift in FASOM-GHG, potentially raising our costs for afforestation by restricting the pool of eligible
lands. Another reason for potentially higher cost estimates with the FASOM-GHG model is that it
considers the trade-offs between land values to sequester forest carbon versus its value for producing
timber products, as contrasted to consideration of forest carbon values only in most land use models.
Finally, there has been an array of energy-related policy developments enacted in the years since the
completion of the Lubowski et al. study that impact agricultural lands (and are not reflected in their
analysis). Most significant among these are subsidies for ethanol production and a renewable fuels
standard that have acted to raise values of land for agricultural production making land use shifts
more costly.
Our overall findings indicate that the cost of sequestering carbon in US forests, using either a
voluntary or mandatory COSP, may be substantially higher than suggested by earlier studies. In their
review of past estimates, Stavins and Richards (2005) concluded that carbon prices between $8 and
$23 per tonne CO2 e could yield additional forest carbon sequestration of roughly 1100 million tonnes
CO2 e per year. In our analysis, prices in excess of $25 per tonne CO2 e would be required to yield just
300 million tonnes CO2 e per year in the mandatory case and prices would have to be well over $30
per tonne to obtain 300 million annual tonnes in the voluntary case.
Appendix A. Mathematical representation of the FASOM-GHG model
A simplified mathematical description of the FASOM-GHG model as modified for the analysis
reported in this paper is given below (see Adams et al., 1996a; Alig et al., 1998 for more details on
model components). Most subscripts are ignored except as needed to emphasize key aspects of the
model. See text in Section “Structure of the FASOM-GHG model” for discussion.
In this description, the key model decision activities in the forest sector are the variables Eit , Rit , Eot ,
and Rot , which represent allocation of existing forest areas (E) to specific harvest dates (t) and newly
regenerated areas (R) in each period to a future harvest date (t). The activities E and R correspond
to Johnson and Scheurman’s (1977) model 2 activities for “existing” and “regenerated” stands (ones
created since the start of the simulation). For the voluntary COSP case, the model must also allocate
lands within E and R between participation in the COSP (subscript i) and non-participation (subscript o).
Areas allocated to participate in the COSP are eligible for carbon payments and subject to taxes through
i − T i ) in the objective function, while non-participating areas
the carbon valuation term, PC (TC,t
B,t
are not. In the mandatory COSP case, all lands are automatically enrolled in the COSP and the variables
with subscript o are not used.
Eqs. (A3)–(A5) are the basic linear dynamics of the model 2 structure. Land shifting from agriculture
to forestry (AF) can either be enrolled in the COSP or not. Land moving from forestry to agriculture must
come from the forest land not enrolled in the COSP, since we assume a minimum COSP enrollment
period of 100 years, consistent with several existing forest carbon sales protocols. Harvest and growing
stock inventory are computed in (A2) and (A6). Eqs. (A7)–(A9) define agricultural sector production
and uses of land. (A10) and (A11) place limits on the amount of land that can move from forestry to
agriculture (based on inventories of land qualities, not all forest land is suitable for agriculture) and
G. Latta et al. / Journal of Forest Economics 17 (2011) 127–141
139
from agriculture to forestry (not all agricultural land can support forestry).
The final two constraints (A12) and (A13), define the forest carbon flux that is subject to carbon
payments/taxes in the voluntary program and the total carbon flux on all forests (A13). Under the
mandatory program, only (A12) is used since all lands must be enrolled in the program.
T −1 Max
[
PF (Ht )dH −
t=0
PA (At )dA − O(Ft ) −
+
V
M({Ec,j }j≥t , {Rc,j }j≥t ) − cF (FAM
t + FAt ) − cA (AFi,t + AFo,t )
c
i
i
− TB,t
)](1 + r)−t + [TCF(GST , PF,T )
SL (Wt )dW + Pc (TC,t
+ TCA(FT , PA,T )](1 + r)−T
Ht −
o
h(Ec,t , Rc,t ) ≤ 0 for t < T
(A1)
(A2)
c=i
t
Ec,t ≤ LF
(A3)
c
Ri,j − Ri,t − Ei,t + FAM
t − AFi,t ≤ 0 for t < T
(A4)
Ro,j − Ro,t − Eo,t + FAVt − AFo,t ≤ 0 for t < T
(A5)
j>t
j>t
GSt −
o
G({Ec,j }j>t , {Rc,j }j>t ) = 0 for all t
(A6)
c=i
At − y(Ft ) ≤ 0 for all t
(A7)
V
−FAM
t − FAt + AFo,t + l(Ft ) ≤ LA for all t
(A8)
w(Ft ) − Wt ≤ 0 for all t
(A9)
V
FAM
t + FAt − AFi,t − AFo,t ≤ FAMAX for all t
(A10)
V
−FAM
t − FAt + AFi,t + AFo,t ≤ AFMAX for all t
(A11)
i
= 0 for all t
CFi (Hi,t , {Ei,j }j>t , {Ri,j }j>t ) + CA (At , Ft , Wt ) − TC,t
(A12)
i
CFo (Ho,t , {Eo,j }j>t , {Ro,j }j>t ) + TC,t
= TC,t for all t
(A13)
where
c = i, o: subscripts denote that a vector or matrix will have elements that are, or are derived from,
lands with areas in (i) and/or out (o) of the COSP,
j, t, T: subscripts for time and the terminal period of the projection,
At : production of agricultural products,
l(Ft ): land used in crop/livestock production,
LF ,LA : initial areas of forest and agricultural land,
AFi,t , AFo,t : land moved from agriculture to forestry (and either enrolled in a COSP or not),
V
M
FAM
t , FAt : land moved from forestry to agriculture (FAt is non-zero only in the mandatory COSP,
140
G. Latta et al. / Journal of Forest Economics 17 (2011) 127–141
because all land is enrolled in the COSP in this case. FAVt is non-zero only in the voluntary COSP, and
land shifting to agriculture must come from outside the COSP),
Ht : production in the forest sector,
h(Ec,t ,Rc,t ): production of forest products determined as a function, h, of existing and replanted stands,
in and out of COSP (c = i,o); this function represents the product of areas harvested times the yield
volume per unit area,
cF (FAt ): conversion costs for moving forest land to agricultural use and agricultural land,
cA (AFi,t + AFo,t ): to forest (either enrolled in a COSP or not),
GSt , G: total growing stock inventory at the start of period t, and inventory computation function (G),
which is the product of areas times the yield volumes per unit area summed across all strata,
Ei,t , Eo,t : the areas of forest stands existing at the start of the projection in and out of COSP, that will
be harvested in period t,
Ri,t , Ro,t : forest stands regenerated or afforested during the simulation, for land in and out of the COSP,
and harvested in period t,
{Ec,j }j>t : represent the sets of all areas of existing and regenerated forests with harvest,
{Rc,j }j>t : periods later than t when j > t, or the same as or later than t when j ≥ t,
{Ec,j }j≥t : these are used in computing inventories of growing stock and carbon and costs,
{Rc,j }j≥t : when the entire standing inventory is considered; c represents areas in and out of the COSP
and may be i or o or both depending on the context,
Ft : crop and livestock production (used to produce consumable agricultural products, At ),
FAMAX : maximum areas of land in forestry suitable for agriculture and land in AFMAX : agriculture
suitable for forestry, respectively,
r: discount rate,
Wt : price-sensitive inputs used in crop and livestock production as a function. w, of crop/livestock
output (Ft ),
M(Ei,t ,Ri,t ,Eo,t ,Ro,t ): costs of maintenance, harvest, planting and product shipment for lands in and out
of COSP,
O(Ft ): costs of producing, processing and shipping agricultural products dependent on crop/livestock
and secondary product output, PA (·): price dependent demand function for agricultural products,
PC : price of carbon, set in policy simulations,
PF (·): price dependent demand function for products from the forest sector,
SL (Wt ): supplies of price-sensitive inputs used in crop and livestock production (irrigation water,
labor, and other inputs),
y(Ft ): yield of agricultural products from crops and livestock,
i : carbon flux from lands in COSP,
Tc,t
Tc,t : total carbon flux from all private forests and agriculture,
i : carbon flux in the base case on the lands enrolled in the COSP (the basis for assessing addiTB,t
tionality),
CFi (·): changes in carbon inventory (carbon flux) on forest lands in and out CFo (·): of the COSP, as
functions of the inventories of existing and regenerated stands CA : and harvests, and the change in
carbon stocks on agricultural lands.
Note on terminal conditions:
TCF(GST ,PF,T ) and TCA(FT ,PA,T ) are the terminal conditions for the forest (F) and agriculture (A) sectors, respectively, representing the discounted values at time T of infinite future series of periodic
returns. For the forest sector, the terminal private forest inventory, GST , aggregated by forest type,
owner, region, and disposition with respect to the COSP, is assumed to be fully regulated on rotations
equivalent to the average of those observed in the last three periods of the solution. The periodic (5year) harvest volume from this regulated inventory is then computed using von Mantel’s formula (see
Davis and Johnson, 1987, p. 558) and valued using the forestry demand functions PF and appropriate management costs. The discounted value of an infinite series of these periodic net harvest values
is then computed. For the agricultural sector, average outputs during the last period of the solution
(T − 1) are valued using the agricultural product demand functions PA and appropriate costs and the
discounted value of an infinite periodic series computed.
G. Latta et al. / Journal of Forest Economics 17 (2011) 127–141
141
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