WPS6928 Policy Research Working Paper 6928 Confronting the Food-Energy-Environment Trilemma Global Land Use in the Long Run Jevgenijs Steinbuks Thomas W. Hertel The World Bank Development Research Group Environment and Energy Team June 2014 Policy Research Working Paper 6928 Abstract Economic, agronomic, and biophysical drivers affect modest effect on global land use, such shocks combined global land use, so all three influences need to be with rapid growth in energy prices lead to significant considered in evaluating economically optimal allocations deforestation and higher greenhouse gas emissions than of the world’s land resources. A dynamic, forward- in the baseline. Imposition of a global greenhouse gas looking optimization framework applied over the emissions constraint further heightens the competition course of the coming century shows that although some for land, as fertilizer use declines and land-based deforestation is optimal in the near term, in the absence mitigation strategies expand. However, anticipation of the of climate change regulation, the desirability of further constraint largely dilutes its environmental effectiveness, deforestation is eliminated by mid-century. Although as deforestation accelerates prior to imposition of the adverse productivity shocks from climate change have a target. This paper is a product of the Environment and Energy Team, Development Research Group. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The author may be contacted at jsteinbuks@worldbank.org. The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent. Produced by the Research Support Team Confronting the Food-Energy-Environment ∗ Trilemma: Global Land Use in the Long Run Jevgenijs Steinbuks and Thomas W. Hertel JEL Codes: C61, Q15, Q23, Q26, Q40, Q54 Keywords: Biofuels, Climate Change, Deforestation, Energy, Environment, Food, Land Use Sectors: Agriculture, Climate Change, Forestry, Environment ∗ Steinbuks: Development Research Group, The World Bank, jsteinbuks@worldbank.org. Hertel: Center for Global Trade Analysis, Purdue University, hertel@purdue.edu. Acknowl- edgements: We would like to thank Yongyang Cai, Ujjayant Chakravorty, Alla Golub, Kenneth Judd, Todd Munson, Paul Preckel, Brent Sohngen, Farzad Taheripour, Wally Tyner and the participants of the 4th International Workshop on Empirical Methods in Energy Economics, the American Geophysical Union Annual Meetings, the American Economic Association An- nual Meetings, Cowles Summer Conference "Macroeconomics and Climate Change", and re- search seminars at Purdue University and the World Bank for their helpful suggestions and comments. Responsibility for the content of the paper is the authors' alone and does not necessarily reect the views of their institutions, or member countries of the World Bank. We appreciate the nancial support from the National Science Foundation, grant 0951576 "DMUU: Center for Robust Decision Making on Climate and Energy Policy". 1 Introduction The allocation of the world's land resources over the course of the coming cen- tury has become a pressing research question. Continuing population increases, improving, land-intensive diets among the poorest populations in the world, in- creasing production of biofuels and rapid urbanization in developing countries are all competing for land even as the world looks to land resources to supply more environmental services. The latter include biodiversity and natural lands, as well as forests and grasslands devoted to carbon sequestration. And all of this is taking place in the context of faster than expected climate change which is altering the biophysical environment for land-related activities. This com- bination of intense competition for land, coupled with highly uncertain future productivities and valuations of environmental services, gives rise to a signi- cant problem of decision making under uncertainty. The issue is compounded by the inherent irreversibility of many land use decisions. The goal of this paper is to determine the optimal prole for global land use in the context of growing commercial demands for food and forest prod- ucts, increasing non-market demands for ecosystem services, and more stringent greenhouse gas (GHG) mitigation targets. We do so by developing a new model, nick-named FABLE: Forest, Agriculture, and Biofuels in a Land use model with Environmental services. This model determines the optimal allocation of scarce land, both across competing uses as well as across time. While market failures, including ill-dened property rights, poorly developed land markets, lack of in- formation, and credit constraints preclude such a path from being achieved in reality, this optimal path is a useful point of reference for those seeking to inu- ence patterns of global land use. In addition, due to its forward-looking nature, this model can oer important insights regarding the behavior of forward-looking investors under alternative states of the world. As with most new model de- velopments, introducing this intertemporal dimension into the model is costly; as a consequence at this early stage, we are unable to oer the kind of geo- graphic and sectoral (particularly, energy sector) coverage that is usual in the land-based integrated assessment models (Bouwman et al. 2006, Paltsev et al. 2005, Wise and Calvin 2011). 1 1 Because of their complexity most of the integrated assessment models employed to analyze land-use decisions at broad scale are solved recursively rather than as fully inter-temporal forward-looking optimization problems. The forward-looking approach adopted in our paper is uncommon, notwithstanding its better capabilities to address important economic policy issues such as inter-temporal allocation of GHG emission ows from land-use through abatement 2 Our research is related to a number of studies that analyze particular aspects of land-use decisions. The bulk of the literature on agriculture and land use in- vestigates adaptation of agricultural systems to rising food demand stemming from income and population growth in the context of changing productivity (Ianchovichina et al. 2001, Golub et al. 2009, Choi et al. 2011b). The literature on renewable energy and land use focuses heavily on the competition for land be- tween biofuels and food production, and the ensuing implications for land-based GHG emissions (Gurgel et al. 2007, Chakravorty et al. 2008, Gillingham et al. 2008, Searchinger et al. 2008, Chakravorty et al. 2011, Chen et al. 2011). The literature on commercial forestry and land use studies the allocation of land to the commercial forestry sector in the context of timber production and climate mitigation policies (Stavins 1999, Sohngen and Mendelsohn 2003, Richards and Stokes 2004, Sohngen and Mendelsohn 2007, Choi et al. 2011a). The literature on ecosystem services and land use studies optimal natural land conservation de- cisions taking into account irreversibility from loss of biodiversity and signicant option values attached to the future stream of benets from ecosystem services (Conrad 1997, 2000, Bulte et al. 2002, Leroux et al. 2009). 2 Finally, the liter- ature on GHG abatement and land-use explores dierent strategies to manage anthropogenic carbon emissions from terrestrial systems, and their implications for land use (Wise et al. 2009, Burney et al. 2010, Popp et al. 2011). The model we develop seeks to integrate these ve, rather distinct strands of literature into a single, intertemporally consistent, analytical framework on a global scale. FABLE is a long-run, perfect foresight partial equilibrium, dynamic optimization model for the world's land resources over the coming century The optimal path for global land use maximizes the discounted net present value of the services from processed food (including crops and livestock products), liq- uid fuels (including rst- and second generation biofuels), timber, forest carbon and biodiversity. A non-homothetic AIDADS utility function represents model preferences, and, as society becomes wealthier, places greater value on ecosys- tem services, and smaller value on additional consumption of food, energy and timber products. Given the importance of land-based emissions to any GHG mitigation strategy, as well as the potential impacts of climate change itself on policies, eciency implications of carbon taxes and caps, and endogenous depletion of non- renewable land resources. For a detailed discussion on relative pros and cons of recursive versus forward-looking approaches in climate policy analysis, see Babiker et al. (2009). 2 Recent studies by Antoine et al. (2008) and Gurgel et al. (2011) attempted to integrate the demand for recreation services into a broader land-use perspective using recursive-dynamic multi-regional CGE model of the world economy (MIT-EPPA). 3 the productivity of land in agriculture, forestry and ecosystem services, we also characterize the optimal path for the world's land resources in the face of alter- native GHG constraints. The forestry sector is characterized by multiple forest vintages, which add considerable computational complexity in the context of this dynamic forward-looking analysis, but allow us to capture dierential growth rates of harvestable timber and carbon stocks. We solve the model over the 200 year period beginning 2005, focusing analy- sis on the coming century. Our baseline reects developments in global land use over the years that have already transpired, while also incorporating projections of population, income and demand growth from a variety of recognized sources. Though we do not explicitly incorporate uncertainty at the optimization stage of the model, we examine the ways in which global land use responds to changes in factors corresponding to the most important sources of uncertainty associated with this problem. Specically, we consider the comparative dynamic eects of incrementally adding more pressure on the world's land resource base due to lower growth in agricultural productivity from higher temperatures, higher growth in oil prices, as well as global GHG emissions regulations. We show in our model baseline that, even in the absence of climate regula- tion, optimal deforestation associated with cropland expansion, which currently accounts for a large share of land-use GHG emission, should decline in the medium term. Climate impacts have mixed eects on yields - hurting food pro- duction, but beneting biomass yields. The overall impact of climate change is to require additional cropland and encourage additional fertilizer use, both of which contribute to higher GHG emissions. Energy prices and policies have a strong eect on the overall amount of land used in agriculture, since higher prices encourage additional biofuel production, even while making intensica- tion of production more costly. The net eect is even greater GHG emissions. The introduction of a constraint on GHG emissions from land use leads to a signicant long-run reduction in cropland expansion. However, a jump in for- est conversion before the constraint is introduced makes it less eective over the course of the entire century, thereby conrming the `green paradox' (Sinn 2008). Overall, with a `perfect storm' of simultaneous high growth in energy prices, aggressive climate policy, but nonetheless adverse climate change impacts on agriculture, area for cropland is sharply reduced, as is food consumption. This underscores the intensity of the potential food-fuel-environment trade-o which the world faces in the 21st century. 4 2 Model Outline FABLE is a deterministic, discrete dynamic, nite horizon partial equilibrium model. Income, population, wages, oil prices, total factor productivity, and other variable input prices are assumed to be exogenous. There are two natural resources in the model: land and fossil fuels. The supply price of fossil fuels is exogenous, and expected to rise over time. The supply of land is xed and faces competing uses that are determined endogenously by the model. There are nine sectors in the model. The agrochemical sector converts fossil fuels into fertilizers that are used to boost yields in the agricultural sector. The crops sector combines agricultural land and fertilizers to produce intermediate outputs (food and feed crops, and cellulosic feed stocks) that can be used to produce food, animal feed, or biofuels. The livestock sector combines pasture land and animal feed to produce domesticated animals. The food processing sectors convert food crops and livestock into processed food products that are used to satisfy the global food demand. The biofuels sector converts food crops and cellulosic feedstocks into liquid fuels, which substitute for petroleum prod- ucts in nal demand. The energy sector combines petroleum products with the biofuels, and the resulting mix is further combusted to satisfy the demand for energy services. The forestry sector produces an intermediate product, which is sold to the timber processing sector which converts lumber into a nal wood product. The ecosystem services sector provides a public good to society in the form of ecosystem services. The production of other, non-land based goods and services is exogenous. The societal objective function being maximized places value on processed food, energy services, timber products, and eco-system services. Emissions of greenhouse gases (GHGs) are central to the problem at hand. These are treated as a time-varying constraint on the ow of GHGs (emissions target). As the model focuses on the representative agent's behavior, consumption products are expressed in per-capita terms, and multiplied by population in order to obtain global demands. The model's structure, equations, variables, and parameters are summarized in the technical appendix, sections A.1, B.1 and C.1. 5 2.1 Resource Use 2.1.1 Land The total land endowment in the model, L, is xed. The land in the economy at any time t comprises natural forest lands - which are in an undisturbed state (e.g., parts of the Amazon), LN M t , and managed commercial lands, Lt . The land endowment constraint is L = LN M t + Lt . (1) Following the previous literature on natural land use (Antoine et al. 2008, Gurgel et al. 2011) we assume that natural land consists of two types. Institutionally protected land, LR , includes natural parks, biodiversity reserves and other types of protected forests. This land is used to produce ecosystem services for society, and cannot be converted to commercial use. Unmanaged natural land, LU , can be accessed and either converted to commercial land (deforested) or to pro- tected land. Once the natural land is deforested, its potential to yield ecosystem services is diminished and cannot be restored within the (single century) time frame of the analysis. Thus, the conversion of natural lands for commercial use is an irreversible decision. 3 Equations describing allocation of commercial land across time and dierent uses are: LN U R t = Lt + Lt . (2) U,R LU U U U t+1 = Lt − ∆Lt = Lt − ∆Lt − ∆LU,M t , LU 0 > 0, (3) and U,R LR R t+1 = Lt + ∆Lt , LR 0 > 0, (4) Equation (2) shows that the total endowment of natural land is a sum of the hectares of protected and unmanaged natural land. Equation (3) shows that at each period of time the area of unmanaged natural land with initial stock, LU 0, declines by the amounts allocated for conversion to commercial and protected U,M land, ∆LU t = ∆Lt + ∆LU,R t , where the ∆ operator denotes a change in U variables Lt and LR t . Equation (4) shows that at each period of time, the total 3 This point requires additional clarication. The biophysical and ecological literature sug- gests that restoration of forest structure and plant species takes at least 30-40 years and usu- ally many more decades (Chazdon 2008), costs several to ten thousands dollars per hectare (Nesshöver et al. 2009), and is only partially successful in achieving reference conditions (Be- nayas et al. 2009). Modeling restoration of biodiversity under these assumptions introduces greater computational complexity without making signicant changes relative to ndings pre- sented in this study. 6 area of reserved land with initial stock of LR 0 increases by the amount of newly U,R protected land, ∆Lt . Accessing the natural lands comes at per hectare cost, cU t , which derives from road construction and other infrastructure (Golub et al. 2009). In ad- dition, converting natural land to protected land entails per hectare cost, cR t , associated with institutional and physical eort (e.g, passing legislation, creat- ing recreational infrastructure) to create new natural parks. We assume that these costs are continuous, monotonically increasing, and strictly convex func- tions of the share of natural land previously accessed. There are no additional costs of natural land conversion to commercial land, as these costs are assumed to be oset by the revenues from the sale of the forest product. In the technical appendix, section C.1, we discuss specic functional forms and parametariza- tion of these costs. There are no additional costs of natural land conversion to commercial land, as these costs are oset by the revenues from deforestation. Commercially managed lands are fully employed in crops, livestock or forestry sectors (we ignore residential, retail, and industrial uses of land in this partial equilibrium model of agriculture and forestry). Equations describing the allo- cation of commercial land across time and between uses are: LM C P F t = Lt + Lt + Lt . (5) and U,M LM M t+1 = Lt + ∆Lt , LM 0 > 0. (6) Equation (5) shows that total endowment of commercial land, LM , is a sum of the hectares of commercial land dedicated to cropland, LC , pasture land, LP , F and managed forests, L , respectively. Equation (6) shows that at each period of time, the total area of commercial land with initial stock of LM 0 increases by U,M the amount of converted unmanaged natural land, ∆L . 2.1.2 Fossil Fuels Fossil fuels, xf , have two competing uses in our partial equilibrium model of land use. A fraction of fossil fuels, xf,n , is converted to fertilizers that are further used in the agricultural sector. The remaining amount of fossil fuels, xf,e , is combusted to satisfy the demand for energy services. The total demand 7 t for fossil fuels, at time , is thus given by xf f,n t = xt + xf,e t . (7) The per unit cost of fossil fuels, cf t, is predetermined, and reects the expendi- tures on fossil fuels' extraction, transportation and distribution, as well as the costs associated with GHG emissions control (e.g. carbon prices) in the non- land-based economy. In the technical appendix, section C.1, we discuss specic functional forms and parametarization of fossil fuel costs. 2.2 Agrochemical Sector The agrochemical sector consumes fossil fuels, xf,n , and converts them into fertilizers for use in the agricultural sector. The production of fertilizers, xn , can be described by a linear production function: n f,n xn t = θ xt , (8) where θn is the rate of conversion of fossil fuels to fertilizers. We assume that the non-energy cost of conversion of fossil fuels to fertilizers, cn , is constant and scale-invariant. In the technical appendix, section C.1, we discuss parameteri- zation of fertilizers' production technology and costs. 2.3 Crops Sector The crops sector combines agricultural land, LC , and fertilizers, xn , to produce food crops as well as cellulosic feedstocks (but only when it is protable). Food crops, xg,c , are used as inputs to production of food, animal feed, and rst generation biofuels: xg,c c,g l,g b,g t = xt + xt + xt , (9) where xc,g l,g t , xt , and xb,g t respectively denote the amounts of food crops used in food processing, animal feed, and rst generation biofuels. Cellulosic feed stocks, xg,b , can only be converted to second generation biofuels, xb,2 . Agricultural land and fertilizers are imperfect substitutes in the production of agricultural products. The per capita output of agricultural products, xg,i , 8 is thus determined by the constant elasticity of substitution (CES) function: g,i ρg 1 θt ρg ρg xg,i t = αg LC,i t + (1 − αg ) (xn t) , i = b, c, (10) Πt g where Πt is the exogenous population at time t, θt and αg are, respectively, the crop technology (agricultural yield) index and the value share of cropland in production of agricultural product at the benchmark time 0, and LC,i t are hectares of agricultural land allocated for food crops and cellulosic feed stocks. σ g −1 The parameter ρg = σg is a CES function parameter proportional to the g elasticity of substitution of agricultural land for fertilizers, σ . The production of agricultural output is also subject to non-land costs from use of fertilizers and other production factors (such as e.g., labor or capital), cg,i , the prices of which are exogenous. In the technical appendix, section C.1, we discuss parameterization of agricultural yields, technologies and costs. 2.4 Livestock Sector The livestock sector combines pasture land, LP , and animal feed, xl,g , to pro- l duce domesticated animals, x . Pasture land and animal feed are imperfect substitutes in the production of livestock. The per capita output of livestock, xl , is thus determined by the constant elasticity of substitution (CES) function: l 1 θt ρl ρl ρl xl t = αl LP t + 1 − αl Πt xl,g t , (11) Πt l where θt and αl are, respectively, the livestock technology index and the value share of pasture land in production of livestock at the benchmark time 0. The σl −1 parameter ρl =σl is a CES function parameter proportional to the elasticity l of substitution of pasture land for animal feed, σ . The production of livestock is also subject to non-land costs from use of other production factors (such as e.g., labor or capital), cl , the prices of which are exogenous. In the techni- cal appendix, section C.1, we discuss parameterization of livestock production technology and costs. 2.5 Food Processing Sectors The food processing sectors convert food crops, xc,g , and livestock, xl , into pro- g cessed grains, y , and processed animal products (such as meat and dairy), yl , that are further consumed in nal demand. The purpose of these sectors in the 9 model is to capture the eciency gains from technology improvements in food production, which result in lower requirements for agricultural inputs in nal demand. 4 The conversion process is represented by the following production functions: g g,y c,g yt = θt xt , (12) l l,y l yt = θt xt , (13) g,y l,y where θt and θt are technology indices of crop and livestock process- ing, which capture the technological progress in both direct transformation of agricultural products into edible food, and the storage, transportation, and dis- tribution of processed food. We assume that the food processing costs per ton of processed crops, cg,y , and livestock, cl,y , are exogenous and scale-invariant. In the technical appendix, section C.1, we discuss parameterization of food pro- cessing technologies and costs. 2.6 Biofuels Sector The biofuels sector consumes the remaining amount of food crops to produce rst generation biofuels, xb,1 . We assume that a ton of food crops, xb,g , can be b,1 converted to θ tons of oil equivalent (toe s) of rst generation biofuels. The output of rst generation biofuels is thus given by xb, 1 b,1 b,g t = θt x . (14) The biofuels sector also converts cellulosic feedstocks, xg,b , into second genera- b,2 tion biofuels, x , which are expected to take over the market gradually, under a growing energy price scenario. The temporal path of the share of the market controlled by this new technology is expected to follow an S-shaped function (Geroski 2000), reecting gradual penetration in light of capital adjustment costs, scarcity of specialized engineering resources and equipment to install new capacity, and slow regulatory approval processes. In this study, the approach for representing the penetration process is based on McFarland et al. (2004), and 4 For example, technological innovation in food conservation results in fewer losses from spoilage, and, correspondingly, lower amounts of processed food needed to satisfy the com- mercial demand for food. Correspondingly, input requirements for agricultural product also decrease. 10 is similar to that used in the MIT-EPPA integrated assessment model (Paltsev et al. 2005). We explicitly introduce in the production function an additional xed factor specic to the new technology, φ, whose endowment in the economy is limited. As technology penetrates the market, the share of the technology xed factor in the production function declines with the rate of factor-specic φ technological progress, θt (Acemoglu 1998, van Meijl and van Tongeren 1999). Under these assumptions the production of second generation biofuels, xb,2 , is determined by the following CES function 1 φ ρb ρb b θt ρb xb, t 2 =θ b,2 α (φ) + 1−α b xg,b t , (15) b,2 b where θt and α are, respectively, the technology parameter and the value share of xed factor in production of second generation biofuels at the benchmark time σb −1 0. The parameter ρb = σb is a CES function parameter proportional to the elasticity of substitution of technology xed factor for cellulosic feed stocks, σb . The agricultural products' conversion to renewable fuel incurs additional non-food processing costs, cb,i . We assume these costs are constant and scale- 5 invariant. In the technical appendix, section C.1, we discuss parameterization of biofuels' production technologies and costs. 2.7 Energy Sector The energy sector consumes petroleum products, xe , and rst and second gen- b,i eration biofuels, x . First generation biofuels (e.g., corn or sugarcane ethanol) blend with petroleum products in varying proportions, 6 and the resulting mix 7 is further combusted to satisfy the demand for energy services. Following the economic literature on biofuels modeling (Hertel et al. 2010), we assume that rst generation biofuels and petroleum products are imperfect substitutes. Sec- ond generation biofuels (e.g., cellulosic biomass-to-liquid diesel obtained through 5 With introduction of second generation biofuels one would expect these costs to decline, and biofuels conversion rate to increase as the biofuels' production technology improves. We show the model sensitivity to changes in these parameters in section 5 below. 6 Blends of E10 or less are used in more than twenty countries around the world, led by the United States, where ethanol represented 10% percent of the U.S. gasoline fuel supply in 2011. Blends from E20 to E25 have been used in Brazil since the late 1970s. E85 is commonly used in the U.S. and Europe for exible-fuel vehicles. Hydrous ethanol or E100 is used in Brazilian neat ethanol vehicles and ex-fuel light vehicles and in hydrous E15 called hE15 for modern petrol cars in Netherlands. 7 The focus of this model is on services from liquid fuels, which account for about a third of global energy use EIA (2011). 11 Fischer-Tropsch gasication) oer a full `drop-in' fuel alternative. We therefore assume that petroleum products and second generation biofuels are perfect sub- stitutes. Under these assumptions the per capita production of energy services, e yt , is given by the following CES function: 1 ρe ρe ρe xf,e ye e t = θt αe xb, t 1 + (1 − αe ) t + xb, t 2 , (16) Πt where the parameter θe describes the energy technology index, or the eciency of energy production (i.e., the amount of energy services provided by one toe of the energy fuel (Sorrell and Dimitropoulos 2008, p. 639)), αe is the value share of rst-generation biofuels in energy production at the benchmark time σe −1 0, and ρe = σe is a CES function parameter proportional to the elasticity of substitution of petroleum products for rst generation biofuels, σe . The total non-land cost of energy is a sum of the costs of fossil fuels and biofuels net of land-use costs: ce t = cb,i + cf t , i = 1, 2. (17) i In the technical appendix, section C.1, we discuss parameterization of energy production technologies and costs. 2.8 Forestry Sector The forestry sector is characterized by v vintages of trees. At the end of period t each hectare of managed forest land, LF v,t , has an average density of trees of vintage age v, with the initial allocation given and denoted by LF v,0 . Each period of time the managed forest land can be either planted, harvested or simply left to mature. The newly planted trees occupy ∆LF,P hectares of land, and reach the average age of the rst tree vintage next period. The harvested area occu- pies ∆LF,H v hectares of forest land. If the managed forest land is harvested, it w yields θv tons of forest product (raw timber), xw w v , where θv is the merchantable timber yield function, which is monotonically increasing in the average tree den- sity of age v. Forest land becomes eligible for harvest when planted trees reach a minimum age for merchantable timber, v. Managed forest areas with the av- w erage density of oldest trees vmax have the highest yield of θv max . They do not grow further and remain in this vintage until harvested. 12 We assume that the average harvesting costs per ton of forest product, are invariant to scale and are the same across all managed forest areas of dier- ent age. With a continuous growth up to vintage vmax , the average long-run cost of harvesting per hectare of managed forest land, cw , is therefore a de- clining function of timber output. Harvest of managed forests and conversion of harvested forest land to agricultural land is subject to additional short run adjustment costs. The average per hectare planting costs per hectare of newly forest planted, cp , are invariant to scale. The following equations describe the forestry sector: vmax LF t = LF v,t , (18) v =1 F,H LF v +1,t+1 = LF v,t − ∆Lv,t , v < vmax − 1 (19) LF vmax ,t+1 = LF vmax ,t − ∆LF,H vmax ,t + LF vmax −1,t − ∆LF,H vmax −1,t (20) LF 1,t+1 = ∆LF,P t , (21) and vmax w θv,t xw t = ∆LF,H v,t . (22) v =1 Πt Equation (18) describes the composition of managed forest area across forest vintages. Equation (19) illustrates the harvesting dynamics of forest areas with the average ages v and vmax . Equation (21) shows the transition from planted F,P area, ∆Lt , to new forest vintage area. Equation (22) describes the per capita output of forest products. In the technical appendix, section C.1, we discuss parameterization of forest production technologies and costs. 2.9 Timber Processing Sector The timber processing sector converts harvested forest product, xw , into pro- w cessed timber products, y , that are further consumed in nal demand. Similar to food processing, the purpose of this sector in the model is to capture the eciency gains from technology improvements in timber production, which re- sult in lower requirements for forest products in nal demand. 8 The conversion 8 For example, technological innovation in durability of timber products results in their less frequent replacement. Therefore lower amounts of forest product are needed to satisfy the 13 process is represented by a linear production function: w w,y w yt = θt xt , (23) where θw,y is the technology index of timber processing, which captures the technological progress in both direct transformation of forest product into pro- cessed timber, and the quality improvements and durability of timber products. We assume that the timber processing costs per ton of food products, cw,y , are exogenous and scale-invariant. In the technical appendix, section C.1, we discuss parameterization of timber production technologies and costs. 2.10 Ecosystem Services Sector This sector combines dierent types of land to produce terrestrial ecosystem ser- vices. It is well known in both economic and ecological literatures that ecosys- tem services are dicult to dene, and it is therefore challenging to characterize their production processes (National Research Council 2005). This stems in part from the fact that there is signicant heterogeneity in ecosystem services (Costanza et al. 1997, Daily 1997), which include physical products (e.g., subsis- tence food and lumber), environmental services (e.g., pollination and nutrition cycling), and non-use goods which are valued purely for their continued exis- tence (e.g., unobserved biodiversity). In many cases the absence of markets and market prices impedes the translation from quantities of ecosystem goods and services to their production values, and requires the application of non-market and experimental valuation techniques (Bateman et al. 2011). And there are sig- nicant dierences in denitions and modeling approaches in the economic and ecological literatures, which the National Research Council (2005, p.3) refers to as the greatest challenge for successful valuation of ecosystem services. While addressing these limitations is beyond the scope of this study, given their im- portant role in the evolution of the long run demand for land, we incorporate ecosystem services, albeit in a stylized fashion, into the global land use model determining the optimal dynamic path of land use in the coming century. r We assume that the per capita output of ecosystem services, yt , is given by commercial demand for timber products. 14 the following CES function of dierent land inputs:     ρ1 r r r θ ρr ρr yt =  αi,r Li t + 1 − αi,r  LU t + θR LR t  . (24) Πt i=C,P,F i=C,P,F where the parameter θr describes the technology index of ecosystem services production. 9 The parameters αi,r are the value shares of crop, pasture, and managed forest lands in production of ecosystem services at the benchmark time σ r −1 0. The parameter ρr = σr is a CES function parameter proportional to the elasticity of substitution of dierent types of land in production of ecosystem ser- vices, σr . By characterizing the production process of ecosystem services using equation (24) we assume that agricultural, managed forest, and natural lands substitute imperfectly in production of ecosystem services. Unmanaged and protected natural land produce the same types of ecosystem services (Costanza et al. 1997). However, protected forest lands are more ecient in delivering many ecosystem services and preserving biodiversity, as they have e.g., better management for reducing degradation of biodiversity, and better infrastructure for providing eco-tourism and recreation services (Hocking et al. 2000, Bruner et al. 2001, Rodrigues et al. 2004). The parameter θR captures the relative eectiveness of protected land in delivering eco-system services. We assume that the non-land cost of producing ecosystem services is zero for agricultural and managed forest land, as production of ecosystem services is not their primary function. This cost is also zero for unmanaged natural lands. As regards protected natural lands, we assume that the average non- land cost of producing ecosystem services (e.g., maintenance and infrastructure expenditures) per hectare of reserved natural land, cR t , is exogenous and scale- invariant. In the technical appendix, section C.1, we discuss parameterization of ecosys- tem services production and costs. 2.11 Other Goods and Services o The production of other goods and services, yt , in this model is exogenous. The reason we include it in this partial equilibrium model is to complete the 9 We put the term technology in quotation terms because, as discussed above, character- izing true production process of ecosystem services is beyond the scope of the paper. Here we use the term technology as a scalar that maps ecological assets to ecosystem services in reference period 0. 15 demand system (described in a section below), which determines welfare. As the supply of other goods and services is exogenous, we assume that they grow at the overall rate of total factor productivity (TFP) growth, which is roughly equal to the world economy's TFP growth rate. 10 Because the production of other goods and services does not draw on the land resource, we assume without loss of generality that their cost of production is zero. In the technical appendix, section C.1, we discuss parameterization of other goods and services production. 2.12 GHG Emissions The GHG emissions ows, zt , in the model result from a number of sources: (a) combustion of petroleum products, (b) the conversion of unmanaged and managed forests to agricultural land (deforestation), (c) non-CO2 emissions from use of nitrogen fertilizers in agricultural production, (d) non-CO2 emissions from the livestock sector (which include emissions from enteric fermentation and manure management) and (e) net GHG sequestration through forest sinks (which includes the GHG emissions from harvesting forests). We dierentiate between the emissions resulting from combustion of petroleum products and the emissions resulting from land use, z L , because the price path (and therefore the bulk of the combustion path) for fossil fuels is predetermined, whereas the other sources of GHG emissions are endogenous. We assume that GHG emissions from the rst three sources are linearly related to the use of fossil fuels, and the allocations of commercial lands. A ton of oil equivalent ( toe) of fossil fuel combusted emits µf,e tons of CO2 equivalent (tCO2 e). A ton of oil equivalent (toe) of fossil fuel converted to fertilizer emits µf,n tCO2 e. The conversion of natural forest land to commercial land entails emissions of µL tCO2 e per hectare of land deforested. A ton of fertilizer applied to agricultural land emits µn tCO2 e. The livestock emissions are calculated as a sum of emissions per hectare of pasture land (e.g., due to manure left on pastures), µP , and emissions per ton of livestock produced (e.g., due to enteric fermentation), µl . GHGs can also be reduced by carbon forest sequestration. 11 A hectare of 10 The economy's output has a small fraction of endogenously determined output from land- use. We ignore this complication in this partial-equilibrium model. 11 GHG emissions ows are also sequestered by atmospheric and ocean sinks. We ignore this complication as our model does not provide comprehensive accounting of all GHG emissions ows, and focuses on understanding emissions from land use and related sectors. 16 forest vintage v sequesters µw v tCO2 e. Young forest vintages grow quickly and sequester carbon at a rapid rate. Older vintages grow slowly and eventually cease to sequester carbon. As the unmanaged forest land (both reserved and non-reserved) comprises mainly the older tree vintages, its potential to sequester additional GHGs is small, and may be ignored (Odum 1969). However, the potential for GHG releases when these trees are cut down and burned or left as slash (Fearnside 2000, Houghton 2003) is large. Harvesting managed forests results in emissions of (1 − ϕ)µh tCO2 e per hectare of land harvested, where v h µv is the carbon stock associated with harvested tree vintage v, and ϕ is the share of permanently stored carbon in harvested forest products. We ignore the annual sequestration of carbon by agricultural product, as those crops are harvested and subsequently consumed in the form of food or bioenergy. Based on the above, the equations describing net GHG ows in the economy are zt = µf,e xf,e t +µ f,n f,n L xt + zt , (25) and vmax vmax L zt =µ L ∆LU,M t +µP LP n n l l t + µ xt + µ xt +(1 − ϕ) µh F,H v ∆Lv,t − µw F v Lv,t . (26) v =1 v =1 Equation (25) describes the composition of GHG emissions ows. Equation (26) shows net GHG emissions from deforestation, food and livestock production, and forest sequestration. Finally, we consider institutional control of GHG emissions' ows, which foresees their gradual reduction and the stabilization of atmospheric carbon stocks. Specically, we assume that at any point of time net GHG emissions from deforestation, application of fertilizers, and forest sequestration cannot exceed the emissions' quota, zL. We do not impose the emissions' constraints on GHG emissions from fossil fuels' combustion because they are exogenously determined. Rather we assume that emissions control instruments are reected in exogenous prices of fossil fuels, which aect the demand for fossil fuels. Finally, because biofuels provide a renewable alternative to fossil fuels, we credit the emissions' quota, zL, by the fraction of fossil fuels' emissions displaced by the biofuels. 12 12 This doesn't necessarily mean that biofuels are 'greener' than fossil fuels. That will depend on the emissions associated with agricultural production and natural land conversion. 17 The resulting relationships for emissions control are µb,i L zt ≤ zL z t = θt L zt − 1− xb,i t , i = 1, 2, (27) µx z where global warming intensity, θt is a function determining the evolution of the GHG emissions' quota over time, and µb,1 and µb,2 are non-land-use emissions of rst and second generation biofuels production. Equation (27) describes the constraint on non-fossil fuel emissions in the atmosphere, and shows how this constraint is derived. In the technical appendix, section C.1, we discuss calculation of the GHG emissions parameters. 2.13 Preferences The representative agent's utility, U, is derived from the consumption of food products, energy services, timber products, ecosystem services and other goods and services. The specic functional form for the utility function in this study is based on implicitly directive additive preferences, AIDADS (Rimmer and Powell 1996). Our choice of the utility function based on AIDADS preferences is moti- vated by its several important advantages over other functional forms underpin- ning standard models of consumer demand. 13 First, similar to the well-known AIDS demand system (Deaton and Muellbauer 1980) the AIDADS model is ex- ible in its treatment of Engel eects, as the model allows the marginal budget shares for each good to vary as a function of total real expenditures. Second, AIDADS has global regularity properties, in contrast to the local properties of AIDS. 14 This is essential for solution of the model over a wide range of quanti- ties. In addition, a number of studies (Craneld et al. 2003, Yu et al. 2004) have demonstrated that AIDADS outperforms other popular models of consumer de- mand in projecting global food demand, which makes it especially well-suited for the economic modeling of land use. The utility function for the AIDADS system is the implicitly directly additive 13 The most popular demand systems estimated in recent applied work are the Homothetic Cobb-Douglas System (HCD), the Linear Expenditure System (LES), the Constant Dierence of Elasticities Demand System (CDE), and the Almost Ideal Demand System (AIDS). 14 One of well-known limitations of the AIDS system is that its budget shares fall outside [0, 1] interval. This frequently occurs when AIDS is applied to model the demand for staple food when income growth is large (Yu et al. 2004, p. 102). 18 function (Hanoch 1975): F (y q , u) = 1, (28) q =g,l,e,w,r,o where q = {g, l, e, w, r, o} is the consumption bundle, u is the utility level ob- q tained from the consumption of goods or services y , and F (y q , u) is a twice- direntiable monotonic function that is strictly quasi-concave in yq . Based on q Rimmer and Powell (1996), the functional form for F (y , u) is αq + βq exp(u) yq − γ q F (y q , u) = ln . (29) 1 + exp(u) A exp(u) In equation (29) the parameters αq and βq dene the varying marginal budget q shares of goods and services y in the consumers' total real expenditures. The q parameter γ denes the subsistence level of consumption of goods and services q. The functional form of F (y q , u) implies that the consumption of goods and q services y is always greater than their subsistence levels, γq . The parameter q A aects the curvature of the transformation function F (y , u) . The AIDADS system imposes standard non-negativity and adding-up restrictions based on the economic theory. These restrictions ensure that the consumers' marginal budget shares and minimal consumption level of goods and services γq are greater or equal to zero, and the sum of marginal budget shares in total real expenditures does not exceed one. Rimmer and Powell (1996, p.1615) demonstrate that maximizing the utility function (28) subject to the budget identity constraint (29) yields the following system of inverse demand equations: y− pq y q . αq + βq exp(u) q pq (q ) = , (30) 1 + exp(u) yq − γ q where pq are prices - or in this case, the marginal valuation - of goods and services yq and y is the economy's output per capita. In the technical appendix, section C.1, we discuss the parameter values of the AIDADS utility function. 19 2.14 Welfare The objective of the planner is to maximize the welfare function, Ω, dened as the sum of net aggregate surplus discounted at a constant rate δ > 0, and the bequest value of unmanaged and commercial forest areas. 15 Net surplus is computed by integrating the marginal valuation of each product, less the land access costs and non-land-based costs of producing each good. Thus, for food and timber products, this represents non-land production costs. For energy, these are non-land biofuels costs and fossil fuel costs. For fertilizers, these are non-energy costs. For forestry, these are harvesting and planting costs. And for recreation, these are the costs of maintaining natural parks. The planner allo- cates commercial land for agricultural crops, livestock, and timber production, and the scarce fossil fuels and reserved natural forest land to solve the following problem:  ´ y q∗  0 (pq (y q ) − cq (y q )) dy q T −1  q =g,l,e,w,r,o  δ t  −cU ∆LU,M + ∆LU,R − cR ∆LU,R − cn xn  T max Ω = +δ Γ LU F T , LT  g,l,e,w,r  t t t t t t  t=0 − i cg,i xg,i t − cl − cp ∆LF,P t − c w t (31) s.t. constraints (1)-(30), where Γ is the scrap value function. In the technical appendix, section C.1, we discuss the parameter values of the scrap value function. 3 Baseline Results This section describes the results of simulations of the model baseline. The baseline construction is documented in the technical appendix, section C.1. We solve the model over the period 2005 - 2204, and present the results for the rst 100 years to limit the eect of terminal period conditions on our analysis. Figure 1 depicts the optimal allocation of global land use, consumption of land-based goods and services and associated GHG emissions in the model base- line over the course of the coming century. Beginning with the upper left-hand panel of Figure 1, we see that, in the near term decades, area dedicated to food crops increases by 10 percent compared to 2004, reaching its maximum of 1.55 billion hectares in 2035. Area dedicated to animal feed expands rapidly, adding 15 We do not consider the bequest value of protected forests, as they cannot be scrapped in our model. 20 Figure 1: Model Baseline Allocation of Land Land Based GHG Emissions 6 200 9 8 150 4 Natural Land 7 Protected Forests 100 Conversion 2 Livestock 6 Unmanaged Forests 50 GtCO2e Billion Ha GtCO2e/yr 5 Managed Forests Biofuels' Offsets 0 0 4 Pasture Land Use of Fertlizers Biofuel Crops -50 3 -2 Forest Livestock Feed -100 2 Sequestration Food Crops -4 Net GHG 1 -150 Accumulation 0 -6 -200 2005 2030 2055 2080 2105 2005 2030 2055 2080 2105 Land Based Goods and Services Consumption of Biofuels 600 40% 1800 1600 35% 500 1400 30% Consumption of 2g USD per person 400 Biofuels 1200 Ecosystem Sevices 25% Million toe 1000 Processed Timber Consumption of 1g 300 20% 800 Energy Services Biofuels 600 Processed Livestock 15% 200 Share of Biofuels in 400 Processed Crops 10% Liquid Fuel 200 100 Consumption 5% 0 2005 2030 2055 2080 2105 0 0% Note. Real terms, base year =2004 2005 2030 2055 2080 2105 150 million hectares, whereas pasture land declines, losing 120 million hectares by 2035. Managed and unmanaged forest areas decline by 3 million and 205 million hectares respectively. Changes in areas dedicated to biofuels feedstocks and protected natural forests remain insignicant. By mid-century, slower pop- ulation growth, rising real income, shifting diets, and technology improvements in food processing, storage and transportation result in a decline in demand for food crops. By 2100 area dedicated to food crops falls to 1.25 billion hectares, which is 12 percent lower than in 2004. Improvements in crop technology and agricultural yields result in greater intensication of livestock production. Pas- ture land continues to decline, reaching 2.33 billion hectares, which is 15 percent smaller than 2004. Area dedicated to animal feed increases signicantly to reach 0.73 billion hectares, which is nearly six times greater than 2004. Rising energy prices in the baseline result in signicant growth in the land area dedicated to biofuels, which reaches 0.14 billion hectares by 2100. Managed forest area is lit- tle changed. Rising real incomes, growing demand for ecosystem services, and improvements in management of natural forest lands result in strong growth in protected natural land area, which increases signicantly to 0.68 billion hectares (about three times greater than 2004) in 2100. 21 The upper right-hand panel in Figure 1 reports gross land based annual GHG emissions ows and their net accumulation over time. 16 Positive bars in this panel denote emissions, whereas negative bars denote GHG abatement through forest sinks and biofuels osets. Conversion of natural forest lands is a signif- icant driver of land-based GHG emissions in the near term, which amounts to 3.2 GtCO2 e/yr in 2025. By mid-century, increasing access costs of natural land combined with declining demand for food crops, results in a sharp decline in deforestation. GHG emissions from deforestation are eliminated by 2050 along this optimal global path of land use. GHG emissions from application of fer- tilizers remain stable for most of the century, and increase closer to the end of the century along with continued expansion of animal feed. In 2100 annual ows of GHG emissions from the use of fertilizers amount to 0.73 GtCO2 e/yr, which is 40 percent larger than 2004. Continued growth in consumption of meat and dairy products results in a signicant increase in GHG emissions from live- stock. In 2100, annual ows of GHG emissions from livestock amount to 1.84 GtCO2 e/yr, which is 2.2 times larger than 2004. GHG emissions sequestration from managed forests does not change signicantly. In 2100 sequestered GHG emissions amount to 2.1 GtCO2 e/yr, which is about 5 percent smaller than 2004. GHG emissions osets from biofuels are insignicant in the near term. With the arrival of commercial scale production of second generation biofuels, these become a signicant source of land based GHG abatement due to their low emissions intensity relative to petroleum (Dunn et al. 2011). In 2100 annual biofuels osets account for 1.4 GtCO2 e/yr. Overall, accumulation of land based GHG emissions increases in the rst part of this century, reaching its maximum of 80 GtCO2 e around 2040. It then declines in the second part of the century reaching 12 GtCO2 e by 2100. Declining population growth, accompanied by rising agricultural productivity, along with higher oil prices, expansion of bio- fuels, and declining deforestation are the reasons for falling GHG emissions of land based sectors in the second half of the 21st century. The lower left-hand panel in Figure 1 illustrates the results for per-capita consumption of goods and services that draw on land resources. The consump- tion of livestock products, timber products, and biofuels grow in absolute terms. In 2100 the per capita consumption of livestock and land-based energy services is considerably higher compared to their levels in 2004, whereas the increase in timber products consumption is more moderate. The per capita consumption 16 As this study focuses on optimal path of land based GHG emissions, the emissions from combustion of petroleum products are not shown in Figure 1. 22 of processed food crops remains unchanged over the course of this century. The consumption of ecosystem services declines in the near term decades as a result of deforestation. However, the consumption of ecosystem services subsequently increases with greater demand for recreation and continued growth in protected forest areas. Nonetheless, the consumption of ecosystem services in 2100 is still lower than their corresponding levels in 2004  an indication of the intense competition for land-based services in our baseline scenario. The lower right-hand panel of Figure 1 hightlights the results for consump- tion of biofuels. The consumption of rst generation biofuels grows slowly as oil prices and agricultural yields increase. However, along this optimal path, rst generation biofuels do not become a signicant source of energy consumption. In 2100 the consumption of rst generation biofuels is 13 Mtoe, considerably higher than in 2004, but still small in relative terms. Second generation biofuels become competitive around 2035 and rapidly expand reaching 300 million toe in 2050, and 500 million toe in 2100. The share of biofuels in total liquid fuel consumption steadily increases, reaching its maximum of 36 percent in 2075. Further expansion of biofuels is crowded by even greater expansion of animal feed, and the share of biofuels in total liquid fuel consumption declines to about 30 percent in 2100. This is of comparable magnitude to ndings in recent eco- nomic studies on bioenergy and land use (Gurgel et al. 2007, Chakravorty et al. 2011, Popp et al. 2011). 17 4 Counterfactual Scenarios Private and public land allocation decisions must be made despite signicant uncertainty about the future productivity of land in dierent uses, as well as the future valuation of environmental services from this land, including biodiversity and carbon sequestration. This uncertainty is particularly problematic in light of the fact that some of the decisions are irreversible (e.g., cutting down natural forests, extraction and combustion of fossil fuels) and others take considerable time to reverse (e.g., harvesting a mature forest). Though we do not explicitly incorporate uncertainty in the model's optimization stage, we do examine the ways in which global land use responds to changes in factors corresponding to the 17 Direct comparison of model predictions of biofuels penetration is dicult due to consider- able uncertainty in variety of factors, such as, e.g., evolution of biofuels' production technolo- gies, land access costs, yield growth rates, and energy demand projections. We show model sensitivity to these factors in counterfactual simulations below, and in technical appendix, section E.1. 23 most important sources of uncertainty associated with the dynamic allocation of land. These sources include (but are not limited to) variations in agricultural yields, liquid fossil fuels' costs, cf , and the future valuation of GHG abatement, expressed through the stringency of the GHG emissions constraint, zL. To do this, we utilize the model to simulate the eects of the following scenarios, each of which has the potential to put greater pressure on the world's land resources: 18 Scenario A: The permanent decline in potential food crop yields due to ad- verse eects of climate change. The impact of climate change on food crop yields depends critically on their phenological development, which, in turn, depends on the accumulation of heat units, typically measured as growing degree days (GDDs). More rapid accumulation of GDDs as a result of the climate change speeds up phenological development, thereby shortening key growth stages, such as the grain lling stage, hence reducing potential yields (Long 1991). However, raising concentrations of CO2 in the atmosphere results in an increase in po- tential yields due to the  CO2 fertilization eect (Long et al. 2006). When temperature increases are moderate, as we assume in the model baseline, these eects oset each other, and the food crop yields are unaected by the climate change. In scenario A we consider rapid warming, corresponding to Represen- tative Concentration Pathways 8.5 GHG forcing scenario (Moss et al. 2008), so the former eect quickly dominates the latter. We assume that yields of cellus- losic feedstocks do not change under scenario A, as they appear to be relatively insensitive to further temperature increases (Brown et al. 2000). The permanent increase in growth of liquid fossil fuel costs over Scenario E: the medium term. Petroleum and natural gas prices are key factors aecting the competitiveness of biofuels (Hertel et al. 2010, National Research Council 2011) as well as the price of nitrogen fertilizer which is critical for boosting agricultural yields (USGAO 2003). To characterize energy price increases in scenario E in the medium term, we employ the data for the high oil price scenario from Energy Information Administration (EIA) growth projections for 2035 (EIA 2010). 19 We assume that the extent to which the energy prices can grow in the long term is limited by induced innovation (Popp 2002) and available backstop technologies (Nordhaus 1973)], so that it reaches its maximum of $250/bbl at 18 We show the model sensitivity to changes in other important model parameters in tech- nical appendix, section E.1. 19 Of course there are many factors contributing to a potential decline of highly uncertain fossil fuel costs (Pindyck 1999). Our choice of rising fossil fuel costs in this scenario is moti- vated by understanding global land use decisions under greater resource scarcity. 24 the end of the 21st century. Scenario T: The GHG emissions constraint is introduced. The scenario is illustrative of the range of regulatory uncertainty surrounding global GHG emis- sions based on IPCC 4AR projections (IPCC 2007a,b), and recent aspirations of a number of countries to incorporate land based GHG mitigation in their climate policies. 20 In this scenario we introduce a maximum target, amount- ing to a 60% reduction in baseline GHG emissions from petroleum products, crop production and terrestrial carbon uxes by 2100. This corresponds to the upper bound of regulation, aimed at achieving CO2  equivalent concentration (including GHGs and aerosols) at stabilization of 445-490ppm. After the target is introduced in 2025 it rapidly becomes more stringent, reaching the maximum stringency by 2050. We also consider combinations of scenarios A and E (scenario AE) and sce- narios A, E, and T (scenario AET). We assume that all of these alternative scenarios are fully anticipated so that their eect is felt already at the outset in 2005. More detailed information on construction of counterfactual scenarios is provided in the technical appendix, section C.2. 4.1 Results of Counterfactual Scenarios Figures 2, 3, and 4 describe the results of simulations of changes in the optimal allocation of global land-use, GHG emissions, consumption of goods and services that draw on land resources, and consumption of biofuels for scenarios A, AE, and AET. For scenario A, we report changes, which are incremental to the model baseline. For scenario AE, we report incremental changes to scenario A. For scenario AET, we report incremental changes to scenario AE. The results for scenarios E and T alone are available in the technical appendix, tables D.1 and D.2. This section concludes with a comparison of the `perfect storm' (AET) to the baseline in order to understand the combined impact of adverse climate impacts, higher energy prices and stringent climate regulation on land use, and particularly food consumption. 20 In 2008 New Zealand passed legislation to include commercial forestry sector in the emis- sions trading scheme. Regulation of other land-use emissions is expected to take place in 2015 (Source: the New Zealand's Ministry of Agriculture and Forestry website: www.maf.govt.nz). In 2010 the European Commission launched a public consultation on whether emissions and removals of greenhouse gases related to land use, land use change and forestry (LULUCF) should be covered by the EU's target of cutting GHG emissions to 30% below 1990 levels by 2020 (Source: the European Commission's website: http://ec.europa.eu/commission_ 2010-2014/hedegaard/headlines/news/2010-09-10_01_en.htm). 25 4.1.1 Scenario A vs. Baseline: Climate Change Impacts on Agricul- ture Change in Land Use Relative to Baseline Change in GHG Emissions Relative to Baseline 40 200 10 Natural Land 30 Conversion Food Crops 150 8 20 6 Livestock Livestock Feed 100 4 10 Biofuels Crops Biofuels 50 Million Ha MtCO2e/yr 2 Offsets GtCO2e 0 Pasture Land 0 0 Use of -10 Protected Forests -2 Fertilizers -50 Managed Forests -4 Forest -20 -100 -6 Sequestration Unmanaged Forests -30 -150 -8 Net GHG Accumulation -40 -200 -10 2005 2030 2055 2080 2105 2005 2030 2055 2080 2105 Change in Consumption of Land Based Good Change in Consumption of Biofuels Relative to and Services Relative to Baseline Baseline 0 10 6% 8 -10 4% 6 -20 4 Consumption of 2g Million toe Processed Livestock 2% USD Per Person Biofuels 2 -30 Ecosystem Services 0 0% Consumption of 1g Processed Timber -40 Biofuels -2 Energy Services -2% -50 -4 Processed Grains Share of Biofuels in -6 Liquid Fuel -60 -4% -8 Consumption -70 -10 -6% 2005 2030 2055 2080 2105 2005 2030 2055 2080 2105 Figure 2: Scenario A vs. Baseline: Climate Change Impacts on Agriculture Figure 2 describes the results of simulations of changes relative to the model baseline for the counterfactual scenario A, corresponding to a reduction in poten- tial agricultural yields as a consequence of climate change. The upper left-hand panel in Figure 2 shows the results for changes in the allocation of land use relative to the baseline scenario. Declining food crop yields result in greater requirements for cropland and fertilizers to produce agricultural output used in the production of processed food and livestock. However, the expansion of crop- land is relatively small. Compared to the baseline scenario, the areas dedicated to food crops and animal feed increase, respectively, by 9 million and 19 million hectares (0.75 and 2.5 percent) in 2100. The expansion of cropland comes at the expense of reduction in other land areas. Managed, unmanaged and protected forest areas all lose about 5 million hectares by 2100. Area dedicated to biofuels feed stocks declines by 3 million hectares in 2100. Finally, pasture land area declines by an additional 10 million hectares in 2100. As we show below, the reason for the modest increase in use of cropland is the accompanying decline 26 in consumption of processed grains and livestock, as well as an increased use of fertilizers in the wake of climate-induced crop scarcity. The upper right-hand panel in Figure 2 shows the results for changes in annual GHG emissions relative to the baseline scenario. Overall, accumulated GHG emissions change modestly relative to the baseline scenario, increasing by an additional 5 GtCO2 e in 2100. The most signicant eects of declining agricultural productivity on the change in GHG emissions are from additional natural land conversion. Compared to the baseline scenario, the GHG emissions from natural land conversion increase by an additional 150 MtCO2 e/yr by 2045. In the long term, the increases in GHG emissions from increased use of fertilizers, reduced forest sequestration and smaller biofuels osets are largely outweighed by a reduction in GHG emissions from livestock production. The lower left-hand panel in Figure 2 shows the changes in per-capita con- sumption of goods and services that draw on land resources. Compared to the baseline scenario, consumption of all goods and services decreases  indicating declining per capita welfare in the wake of the adverse climate impacts. There is a signicant decline in the consumption of processed food services. In 2100 the real per capita consumption of processed grains and livestock each declines by 10 percent and 6 percent, respectively, relative to the baseline scenario. The re- duction in consumption of services deriving from energy, timber, and ecosystems is less than 1 percent. The lower right-hand panel in Figure 2 shows the results for changes in biofuels. Declining food crop yields depress production of rst generation bio- fuels. In 2100 the total consumption of rst generation biofuels decreases by 2.5 million toe (20 percent) compared to the baseline scenario. Though higher temperatures do not aect yields of cellulosic feedstock, their production also falls in light of increased competition for land used in food crops. However, the decline in second generation biofuels is modest and amounts to less 1 percent compared to the baseline scenario, and therefore the share of biofuels in liquid fuel consumption is little changed, by the adverse climate impacts on crops. 4.1.2 Scenario AE vs. A: Climate Change Impacts on Agriculture and Rising Fossil Fuel Costs Figure 3 describes the results of simulations of changes for the counterfactual scenario AE relative to scenario A. This adds the eect of permanent increase in the rate of growth in liquid fossil fuel costs over the medium term to the eect 27 Change in Land Use Relative to Scenario A Change in GHG Emissions Relative to Scenario A 150 1000 20 Food Crops 800 100 15 Natural Land Livestock Feed 600 Conversion 10 Livestock 50 Biofuels Crops 400 5 MtCO2e/yr Million Ha 200 Biofuels GtCO2e Pasture Land 0 Offsets 0 0 Use of Protected Forests -200 Fertilizers -50 Managed Forests -5 Forest -400 Sequestration Unmanaged Forests -10 -600 Net GHG -100 Accumulation -800 -15 -150 -1000 -20 2005 2030 2055 2080 2105 2005 2030 2055 2080 2105 Change in Consumption of Land Based Good Change in Consumption of Biofuels Relative to and Services Relative to Scenario A Scenario A 300 40% 40 30 30% 200 20 20% Consumption of 2g 10 Processed Livestock 100 Biofuels USD Per Person 10% Million toe 0 Ecosystem Services 0 0% Consumption of 1g -10 Processed Timber Biofuels -20 -10% Energy Services -100 -30 -20% Share of Biofuels in Processed Grains Liquid Fuel -40 -200 -30% Consumption -50 -300 -40% -60 2005 2030 2055 2080 2105 2005 2030 2055 2080 2105 Figure 3: Scenario AE vs. A: Climate Change Impacts on Agriculture and Rising Fossil Fuel Costs 28 of a permanent decline in potential food crop yields. The upper left-hand panel in Figure 3 shows the results for changes in allocation of land use relative to scenario A. Rising oil and natural gas prices increase the costs of fertilizers and petroleum consumption. As biofuels substitute for fossil fuels in demand for energy services, the demand for biofuels increases. This, in turn, increases the demand for cropland needed to produce the feedstock. Cropland requirements also rise due to the increased cost of fertilizer - a key ingredient in the intensi- cation of agricultural production. Compared to scenario A, agricultural areas dedicated to biofuels feedstocks expand signicantly, adding 95 million hectares by 2035. The expansion of biofuels feedstock comes mainly at the expense of non-biofuel crops. Areas dedicated to food crops and animal feed decline by 65 and 11 million hectares. Pasture land and managed forest areas each decline by 5 million hectares, and unmanaged and protected forest areas decline, respec- tively, by 10 million and 2.5 million hectares. In the long term, as energy prices become closer to baseline, their impact on land use becomes less pronounced. In 2100 combined cropland areas increase relative to scenario A, cumulatively adding 24 million hectares, whereas other land areas decline by a comparable amount. The upper right-hand panel in Figure 3 shows the results for changes in annual GHG emissions. In near decades the increase in GHG emissions comes mainly from deforestation, caused by conversion of natural and managed forest areas to cropland. In 2025 the GHG emissions from natural land conversion increase by 275 MtCO2 e/yr (10 percent) compared to scenario A, and continue to be signicant by mid-century. In the medium term, GHG emissions also decline as biofuels expand and higher costs drive fertilizer consumption down. In 2035, GHG emissions abatement from biofuels osets and the decline in fertilizers' use grow by 700 and 95 MtCO2 e/yr compared to scenario A. In the long term, the impact of energy prices on GHG emissions diminishes, as natural land conversion ceases and expansion of biofuels declines. Overall, compared to scenario A accumulated GHG emissions increase in the near decades, reaching their maximum of 2 GtCO2 e in 2025, and decline thereafter to a level 15 GtCO2 e lower than scenario A by 2100. The lower left-hand panel in Figure 3 shows the results for changes in per- capita consumption of goods and services that draw on land resources. The expansion of the biofuels sector results in an increase in consumption of bio- energy services. Compared to scenario A their real per capita consumption is 13 times higher in 2035 and 11 percent larger in 2100. The consumption of all 29 other land-based goods and services decreases. The most signicant decline is in consumption of services from processed grain and livestock products. Compared to scenario A their real per capita consumption declines by 11 percent and 8 percent in 2035, and by 2.5 percent and 1.5 percent, repectively, in 2100. The lower right-hand panel in Figure 3 shows the results for changes in biofuels. Higher oil prices increase the demand for biofuels, and facilitate faster commercial scale use of second generation biofuels, which become competitive in 2025 - 10 years earlier compared to scenario A. By 2035 the consumption of second generation biofuels increases by additional 275 million toe compared to scenario A. Combined with a decline in consumption of petroleum products (see Table D.2 in the technical appendix) this results in a signicant increase in the share of biofuels in total liquid fuel consumption, which accounts for 40 percent in 2035. In the longer term, as energy prices become closer to the baseline, the amount of biofuels produced, and their share in liquid fuel production returns nearly to the baseline levels. 4.1.3 Scenario AET vs. AE: Climate Change Impacts on Agriculture and Rising Fossil Fuel Costs and Land-Use Emissions Target Figure 4 describes the results of simulations of changes relative to scenario AE for the counterfactual scenario AET. This gure illustrates the eect of adding the land-use GHG emissions constraint starting in 2025 to the eects of a permanent increase in the rate of growth in liquid fossil fuel costs in mid- century and permanent decline in the potential food crop yield. The upper left-hand panel in Figure 4 shows the results for changes in allocation of land use relative to scenario AE. Introduction of a land-use GHG emissions constraint has an intertemporal eect on the allocation of global land use. In anticipation of the implementation of a GHG emissions target, a fraction of natural forest land is converted to newly planted managed forests, which, as explained in section 2.12, are very eective in land based climate abatement. Compared to scenario AE, the managed forest area expands by an additional 15 million hectares in 2025. As the GHG emissions target becomes more stringent, there is an increase in managed forest area used for GHG sequestration. Compared to scenario AE, the managed forest area expands further by 40 million hectares in 2050 and by 160 million hectares in 2100. There is also an expansion in the area dedicated to biofuels feedstocks. Compared to scenario AE this area increases by 16 million hectares in 2050 and 27 million hectares in 2100. Introduction 30 Change in Land Use Relative to Scenario AE Change in GHG Emissions Relative to Scenario AE 300 3 40 Natural Land Food Crops Conversion 200 30 Livestock Feed 2 Livestock 20 100 Biofuels Crops 1 Biofuels 10 Million Ha GtCO2e/yr Pasture Land Offsets GtCO2e 0 0 0 Protected Forests Use of Fertilizers -10 -100 Managed Forests -1 Forest -20 Sequestration Unmanaged Forests -200 -2 -30 Net GHG Accumulation -300 -3 -40 2005 2030 2055 2080 2105 2005 2030 2055 2080 2105 Change in Consumption of Land Based Good Change in Consumption of Biofuels Relative to and Services Relative to Scenario AE Scenario AE 20 40 20% 10 30 15% 0 20 10% -10 Consumption of 2g Processed Livestock Biofuels USD Per Person -20 10 5% Million toe -30 Ecosystem Services 0 0% Consumption of 1g -40 Processed Timber Biofuels -10 -5% -50 Energy Services -60 Processed Grains -20 -10% Share of Biofuels in Liquid Fuel -70 -30 -15% Consumption -80 -40 -20% -90 2005 2030 2055 2080 2105 2005 2030 2055 2080 2105 Figure 4: Scenario AET vs. AE: Climate Change Impacts on Agriculture and Rising Fossil Fuel Costs and Land-Use Emissions Target 31 of the GHG constraint puts signicant pressure on cropland and pasture land areas. Compared to scenario AE, cropland areas dedicated to food crops and livestock feed decline by 18 million and 92 million hectares, respectively, in 2100. Pasture land declines by 112 million hectares. As natural land conversion stops, unmanaged natural forest areas increase after the target is introduced. Compared to scenario AE, unmanaged natural forest area increases by 47 million hectares in 2100. The upper right-hand panel in Figure 4 shows the results for changes in an- nual gross GHG emissions. Preceding the introduction of the GHG emissions constraint, there is a large increase in GHG emissions, which in turn increases the GHG emissions stock and signicantly reduces the eectiveness of the target. Two factors contribute to this increase. First, there is an increased conversion of natural forest lands. Second, GHG sequestration by managed forests declines, driven by the change in the vintage structure of managed forests. In 2025 the GHG emissions from natural land conversion and reduced forest sequestration increase by 0.7 and 1.2 GtCO2 e/yr compared to scenario AE. After introduction of the GHG emissions constraint, the GHG emissions from land use decline. By mid-century, the main source of reduction in GHG emissions is due to the decline in natural land conversion, which amounts to 2.8 GtCO2 e/yr, immediately after the target is introduced. In the long term, greater GHG sequestration by man- aged forests is the main factor contributing to the reduction in GHG emissions. Compared to scenario AE, the reduction in GHG emissions due to increased forest sequestration amounts to 0.7 GtCO2 e in 2100. Introduction of the GHG target also results in a small increase in GHG abatement from additional use of second generation biofuels. In 2100 the land based GHG mitigation from biofuels osets is 5 MtCO2 e/yr larger compared to scenario AE. Finally, the emissions from fertilizer and livestock farming and management both decline after the GHG target is introduced. Compared to scenario AE, GHG mitiga- tion from fertilizers use and livestock farming and management decline by 112 MtCO2 e/yr and 200 MtCO2 e/yr, respectively. Overall, in the presence of intertemporal substitution, the land based GHG emissions target appears to be rather ineective over the 100 year time hori- zon. Preceding the introduction of the constraint, cumulative GHG emissions increase by 97 GtCO2 e. After the introduction of the constraint, the GHG emissions from land use cumulatively decline by 114 GtCO2 e. The resulting intertemporal leakage (the ratio of cumulative increase in GHG emissions pre- ceding the GHG target to cumulative decline after the GHG target) is 85 per- 32 cent. 21 The lower left-hand panel in Figure 4 shows the results for changes in per- capita consumption of goods and services that draw on land resources. In- troduction of the GHG emissions constraint lowers the consumption of GHG intensive services from processed food and livestock. Compared to scenario AE real per capita consumption of services from processed grains and livestock de- clines by 7 percent and 13 percent, repectively. The consumption of bio-energy and ecosystem services expands with the increase in biofuels consumption and the decline in deforestation. Compared to scenario AE, real per capita consump- tion of bioenergy and ecosystem services increases by 3 percent and 1 percent, repectively, in 2100. The lower right-hand panel in Figure 4 shows the results for changes in bio- fuels. Introduction of the GHG emissions constraint favors the displacement of petroleum products by biofuels. However, the expansion of second genera- tion biofuels is limited as the GHG emissions constraint hinders expansion in agricultural area. In 2100 the consumption of biofuels is just 17 million toe larger compared to scenario AE. The biofuels share in liquid fuel consumption increases signicantly as petroleum consumption further declines after the GHG target is introduced, accounting for 46 percent in 2100. 4.1.4 Scenario AET vs. Baseline: Assessing the Impacts of a Perfect Storm Thus far, we have analyzed the impacts of each scenario individually and in- crementally, however, it is also relevant to consider their combined eect. In a sense, this represents a type of `perfect storm' in global land use in which climate change slows productivity growth, high energy prices intensify the food- fuel tradeo as well as raising the cost of intensication, and nally, climate regulations places increased value on leaving land in forests. Figure 5 reports changes in the optimal allocation of global land use, GHG emissions, consump- tion of goods and services that draw on land resources, and consumption of biofuels for this scenario (AET), which are incremental to the model baseline. As shown in the upper left-hand panel in Figure 5, the combined eect of higher energy prices and climate regulations induces a signicant expansion of land dedicated to biofuels crops as well as forested lands. Compared to the baseline scenario, managed and unmanaged forest areas increase by 150 million 21 The size of intertemporal leakage is reduced to 37 percent over the period of 200 years. 33 Change in Land Use Relative to Baseline Change in GHG Emissions Relative to Baseline 300 4 40 Natural Land Food Crops Conversion 200 3 30 Livestock Feed Livestock 2 20 100 Biofuels Crops Biofuels GtCO2e 1 10 Million Ha GtCO2e/yr Pasture Land Offsets 0 0 0 Protected Forests Use of -1 -10 Fertilizers -100 Managed Forests Forest Unmanaged Forests -2 -20 Sequestration -200 -3 -30 Net GHG Accumulation -300 -4 -40 2005 2030 2055 2080 2105 2005 2030 2055 2080 2105 Change in Consumption of Land Based Good Change in Consumption of Biofuels Relative to and Services Relative to Baseline Baseline 50 300 50% 40% 200 0 30% 20% Consumption of 2g Processed Livestock 100 USD Per Person Biofuels -50 Million toe 10% Ecosystem Services 0 0% Consumption of 1g Processed Timber -100 -10% Biofuels Energy Services -100 -20% Processed Grains Share of Biofuels in -150 -30% Liquid Fuel -200 -40% Consumption -200 -300 -50% 2005 2030 2055 2080 2105 2005 2030 2055 2080 2105 Figure 5: Scenario AET vs. Baseline: Assessing the Impacts of a Perfect Storm and 30 million hectares, respectively, and the area dedicated to biofuels feed- stocks increases by 35 million hectares in 2100. The second-generation biofuels are deployed much earlier now, in 2023 (lower right-hand panel in Figure 5). Their deployment is rapid and accounts for a signicant share of liquid fuel con- sumption (60 percent by late in the 21st century), as petroleum consumption is squeezed by the combined eect of higher oil prices and stringent climate reg- ulations. The expansion of biofuels and commercial forestry sectors, and GHG abatement-based forest management strategies result in a signicant decline in land based GHG emissions in the long term (upper right-hand panel in Fig- ure 5). However, the eectiveness of GHG climate regulations is distorted by accelerated deforestation and shifts in forest management strategies before the emissions target is introduced. The resulting intertemporal leakage for scenario AET as compared to the model baseline is 56 percent. As a consequence, even though adverse climate impacts on crop yields sug- gests the need for additional cropland, such expansion does not happen in this `perfect storm' scenario, as higher energy prices and climate regulations force crop land to contract. Compared to the baseline scenario, areas dedicated to 34 food crops and animal feed decline respectively by 5 million and 67 million hectares (0.5 and 9.5 percent) in 2100. Pasture land also declines by an addi- tional 128 million hectares (5.5 percent) in 2100. The combined eect of adverse climate impacts on crop yields, higher energy prices and climate regulations thus results in a signicant decline in services from processed food and livestock, which decline sharply, relative to the model baseline (lower left-hand panel in Figure 5). Compared to the baseline scenario, the consumption of processed grains declines by 18 percent, whereas the consumption of processed livestock declines by 19 percent by 2100. This underscores the food-fuel-environment tradeo which the world may face over the coming century. 5 Discussion and Limitations One of the most important questions for this intertemporal investigation of land use competition over the 21st century is the sensitivity of the path of optimal land use to model parameters. Therefore, we have undertaken a series of alternative baseline simulations in which key parameters are perturbed and we investigate the impact on model results. These are reported in the technical appendix, section E. These sensitivity analyses indicate that the most important parameter governing baseline land use is the discount rate. Raising our discount rate from 1.5% to 2.25% (i.e. boosting it by half ) results in a signicant shift away from unmanaged and protected lands (150 Mha less by 2100), towards commercial use in food, timber and biofuel production. As a consequence, future ecosystem services, which only acquire strong demand later in the century, are signicantly reduced in favor of commercial services from land. The next most important parameter for setting the optimal prole of land use over the 21st century is the elasticity of substitution between fertilizer and land which governs the ease of intensication. When this is increased, land devoted to food crops and livestock feed production increases over the baseline due to the rising cost of fertilizer which reduces fertilizer use in the baseline. This is followed by the short run marginal cost of land conversion. Not surprisingly, reducing this cost results in more land conversion  about 60 Mha by 2100. However, these parameter changes are generally found to have a small eect on the deviations from the baseline due to our three scenarios: A, AE and AET. 22 In other words, while they do make a dierence in the baseline, they have little 22 The only exception is the interplay of GHG emissions target and higher discount rate, where the decline in natural land conversion is larger compared to the model baseline. 35 eect on the insights obtained from our counterfactual analyses. An important limitation of our study is our assumption that the incentive to expand biofuel production is driven solely by oil prices. Government mandates have played an important role in biofuel expansion in the US and the EU, in particular. However, in the long run, the fate of biofuels will be largely deter- mined by oil prices. Recent evidence for the US suggests that biofuel mandates were either not binding (e.g., for corn ethanol see Meyer et al. 2011) or unlikely to be met (e.g., for US-RFS2 mandate for cellulosic biofuels, see National Re- search Council 2011). More generally, we expect that budgetary pressures will limit the extent to which governments will be willing to subsidize biofuels in the coming decades. However, even if these mandates were implemented, when oil prices are rising steadily (as in our baseline) the global biofuels mandates do not play are large role in our framework, since there is a market incentive to expand in any case (Steinbuks and Timilsina 2014). It is the case, however, that rather than forcing second generation biofuels into the mix over the next decade, the model suggests that, under current technology and the baseline oil price trajectory, these biofuels will not enter a socially optimal land use path until after 2030. A more serious limitation to this study is our omission of the potential demand for biomass in power generation. Under some scenarios, authors have shown this to be an important source of feedstock demand by mid-century (Rose et al. 2012). However, absent a full representation of the electric power sector, our framework is ill-suited to addressing this issue. Nonetheless, we nd that energy prices and GHG mitigation strategies do have a signicant impact on land use. While our numbers seem large, they are not inconsistent with the ndings of other studies. For example, the results of simulations based on the MIT EPPA model (Gurgel et al. 2007) suggest cropland expansion around 420-470 million Ha for bioenergy production by 2050 in their reference case. Similarly, a study by Chakravorty et al. (2011) predicts biofuels feedstock area of about 150 Mha in the medium-income countries (per the World Bank's classication) by 2025 in their reference case scenario. 6 Conclusions We analyze the optimal allocation of the world's land resources over the course of the coming century within a unied economic framework, which integrates 36 ve rather distinct strands of literature into a single, intertemporally consis- tent, analytical model on a global scale. This long-run, forward-looking, partial equilibrium model covers key sectors drawing on the world's land resources, and incorporates growing demands for food, renewable energy, and forest products, and increasing non-market demands for ecosystem services. We also consider alternative GHG constraints, as well as the potential impacts of climate change itself on the productivity of land in agriculture, forestry and ecosystem services. Our baseline reects developments in global land use over the 10 years that have already transpired, while also incorporating long-run projections of popu- lation, income and demand growth from a variety of international agencies. The model baseline suggests that, even in the absence of GHG regulations, deforesta- tion rates associated with cropland expansion decline along the optimal land-use trajectory in the medium term. This is important, since deforestation accounts for a large share of current global GHG emissions. In the long term there is a signicant expansion of the livestock sector, driven by increasing per capita incomes, and this is fueled by increasingly intensive production practices. The area of protected natural lands, which deliver valuable ecosystem services, also increases strongly in the long run. However, this nding is sensitive to the choice of social discount rate. A higher rate of discount results in a sacrice of forest cover and ecosystem services in favor of more immediate delivery of services from food and energy consumption. Along the baseline, the consumption of biofuels increases rapidly after second generation biofuels become commercially viable in 2035, and provides for about a third of total liquid fuel consumption by the end of this century, along the optimal path under our baseline scenario. We consider three counterfactual scenarios aimed at capturing the most im- portant sources of uncertainty associated with this long run trajectory for global land use. These include: climate impacts on agriculture, energy prices, and global GHG emissions regulations. Adverse climate impacts on crop yields cur- tail food production, requiring additional cropland and encouraging additional fertilizer use, thereby leading to higher GHG emissions. Energy prices aect the optimal deforestation rate as well as the overall amount of land used in agri- culture. By mid-century, cropland area increases sharply under higher energy prices, due to the incentive for increased biofuel production as well as higher fertilizer prices which raise the cost of intensication. Substantially more defor- estation occurs under this scenario and the increased GHG emissions from land use change outweigh the emissions fall from displacement of petroleum consump- tion by biofuels and declining fertilizer use. When we also require the world's 37 land base to deliver land-based GHG abatement, the pressure on global natural land resources becomes even more signicant. While the introduction of the land based GHG emissions constraint leads to a signicant reduction in GHG emission ows over the 21st century, its eectiveness is eroded by a substantial increase in GHG emissions after the policy is announced, but before the policy is actually implemented. This mimics the `green paradox' (Sinn 2008, Eichner and Pethig 2011) found in other areas of environmental regulation. Since such pre-announcement seems inevitable from a political-economic perspective, it is an issue which deserves greater attention. Indeed, we nd a leakage rate of 56 percent, which is very high and threatens to undo most of the GHG mitigation benets of such a policy. When all three `scenarios' are simultaneously realized, the world's land re- sources face a `perfect storm' in which the cost of agricultural intensication is higher, biofuels expand their area, additional cropland is needed to oset the adverse impacts of climate change, and climate regulation also places new pressures on land availability for food. In this case the optimal path of food consumption is signicantly lower, highlighting the potential for intense com- petition for land in the production of the world's food, fuel and environmental services over the 21st century. 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Yu, W., Hertel, T., Preckel, P. and Eales, J.: 2004, Projecting World Food Demand Using Alternative Demand Systems, Economic Modelling 21(1), 99 129. 45 Welfare GHG Emissions Other Goods Processed Energy Processed Livestock and Services Food Services Timber Technical Appendix Livestock 1st Gen. 2nd Gen. 1 Feed Biofuels Biofuels Timber Ecosystem Food Cellulosic Services Crops Feedstocks Figure A.1: Structure of the Economy Forest Land (Multiple Pasture Agricultural Fertilizers Vintages) Land Land Protected Unmanaged Commercial Forests Forests Land Land Fossil Fuels B.1 FABLE Model Equations, Variables and Pa- rameters Equations Land Use L = LN M t + Lt , (B.1) LN U R t = Lt + Lt , (B.2) U,M LU U U U t+1 = Lt − ∆Lt = Lt − ∆Lt − ∆LU,R t , LU 0 > 0, (B.3) U,R LR R t+1 = Lt + ∆Lt , LR 0 > 0, (B.4) 2 LN t+1 ∆LU,M t + ∆LU,R t cU t+1 = cu t − u ξ1 ln + u ξ2 , (B.5) LN0 LN t U,R cR R R t = ξ0 + ξ1 ∆Lt , (B.6) LM C P F t = Lt + Lt + Lt , (B.7) U,M LM M t+1 = Lt + ∆Lt , LM 0 > 0, (B.8) Fossil Fuels xf f,n t = xt + xf,e t , (B.9) cf f κf t T c0 e cf t = , cf 0 > 0, (B.10) cf f T + c0 (e κf t − 1) Agrochemical Sector n f,n xn t = θ xt , (B.11) Agricultural Sector xg,c c,g l,g b,g t = xt + xt + xt , (B.12) g,i ρg 1 θt ρg ρg xg,i t = αg LC,i t + (1 − αg ) (xn t) , i = b, c, (B.13) Πt σg σg xg,i αg 1−σg 1−σg 1−σg LC,i t = t g,i α σg cC,i t g σg + (1 − α ) cf t , (B.14) θt cC,i t 1 1 1−σg,i 1−σg 1−σg g σg cg,i t = g,i (α ) cC,i t + (1 − α ) g σg cf t , (B.15) θt 2 g,c g,c κg,c t g,c θT θ0 e θt = g,c , (B.16) θT + θ0 (eκg,c t − 1) g,b g,b g,b θt +1 = θt + κg,b , θ0 > 0, (B.17) Livestock Farming Sector l 1 θt ρl ρl ρl xl t = αl LP t + 1 − αl Πt xl,g t , (B.18) Πt 2 cl l l l P t = c0 xt + ξ0 ∆Lt , (B.19) Food Processing Sector g g,y c,g yt = θt xt , (B.20) l l,y l yt = θt xt , (B.21) i,y i,y i,y θt+1 = κi,y θt , θ0 > 0, i = g, l, (B.22) Biofuels Sector xb, 1 b,1 b,g t = θt x (B.23) 1 φ θt ρb ρb ρb xb,2 t =θ b,2 αb (φ) + 1 − αb xg,b t (B.24) φ φ φ θt+1 = κφ θt , θ0 > 0 (B.25) Energy Sector 1 ρe ρe ρe xf,e ye t = e θt α e xb, t 1 + (1 − α ) e t + xb, t 2 , (B.26) Πt e e e θt +1 = κe θt , θ0 > 0 (B.27) ce t = cb,i + cf t , i = 1, 2. (B.28) i Forestry Sector vmax LF t = LF v,t , (B.29) v =1 3 F,H LF v +1,t+1 = LF v,t − ∆Lv,t , v < vmax − 1, (B.30) LF vmax ,t+1 = LF vmax ,t − ∆LF,H vmax ,t + LF vmax −1,t − ∆LF,H vmax −1,t , (B.31) LF 1,t+1 = ∆LF,P t , (B.32) vmax w θv,t xw t = ∆LF,H v,t , (B.33) v =1 Πt w w w w θv,t+1 = θv,t + κv , θv,0 > 0 (B.34) 2 cw t = w ξ0 w θv, F.H w 0 ∆Lv,t + ξ1 ∆LF,H F,H v,t − ∆Lv,t−1 (B.35) v v 2 w F,P +ξ2 ∆LF.H v,t − ∆Lt , v Timber Processing Sector w w,y w yt = θt xt , (B.36) w,y w,y w,y θt+1 = κw,y θt , θ0 > 0, (B.37) Ecosystem Services Sector     ρ1 r r r θ ρr ρr yt =  αi,r Li t + 1 − αi,r  LU t + θR LR t  (B.38) Πt i=C,P,F i=C,P,F cR 0, cR t = R t c0 > 0 (B.39) (1 + κR ) Other Goods and Services Sector o o o θt +1 = κo θt , θ0 > 0 (B.40) GHG Emissions zt = µf,e xf,e t +µ f,n f,n L xt + zt , (B.41) vmax vmax L zt = µL ∆LU,M t + µP LP n n l l t + µ xt + µ xt + (1 − ϕ) µh F,H v ∆Lv,t − µw F v Lv,t . v =1 v =1 (B.42) 4 µb,i L zt ≤ zL z t = θt L zt − 1− xb,i t , i = 1, 2 (B.43) µx Preferences y− pq y q . αq + βq exp(u) q pq (q ) = , 0 ≤ αq , βq ≤ 1 (B.44) 1 + exp(u) yq − γ q αq + βq exp(u) yq − γ q F (y q , u) = ln , 0≤q 0, (C.4) cf T + cf 0 (eκf t − 1) where the parameters cf 0, and cf T, reect the oil prices in the beginning and in the end of this century, and κf is the growth rate in costs of liquid fossil fuels. We obtain the value of the oil price in 2004 from the EIA, and calibrate the values of terminal oil price and the growth rate to match projections of the U.S. Energy Information Administration reference case scenario for 2035 (EIA 2010a, p. 86, Table 10). C.1.3 Agrochemical Sector There are three types of fertilizer used in agricultural production: nitrogen fer- tilizers, phosphate fertilizers, and potash fertilizers. In our model we focus on nitrogen fertilizers. These fertilizers are particularly important in the climate policy debate, because their production is the most energy- and GHG- inten- sive. They are also critical to boosting yields in response to scarcity of land. 1 2 We use the FAOSTAT database to obtain the global production of nitrogen fertilizers in 2004. For fertilizers' production costs and conversion rates we con- sider anhydrous ammonia (NH3 ), which is one of the most common nitrogen fertilizers. We use USDA ERS fertilizer use and price dataset 3 to obtain the fertilizers' price. We then subtract the fossil fuels' price from the fertilizers' 1 Note that by von Liebig's Law of the Minimum (yield is proportional to the amount of the most limiting nutrient, whichever nutrient it may be) the production of other two types of fertilizers will follow the path of nitrogen fertilizers. 2 Thorough description of the FAOSTAT database is available from the following website: http://faostat.fao.org/. 3 Thorough description of the dataset is available from the following website: http://www. ers.usda.gov/Data/FertilizerUse/. 15 price to obtain non-energy cost of fertilizers' production. This cost does not vary much across time because fossil fuels' and nitrogen fertilizers' prices are highly correlated and follow the same trend (USGAO 2003). C.1.4 Crops Sector The initial amount of food crops (measured as the global physical production of agricultural crops) and global expenditures on food crops in 2004 come from the FAOSTAT database. We set the production of cellulosic feedstocks close to zero, as the production of second generation biofuels was practically non existent in 2004. The elasticity of substitution of nitrogen fertilizers for agricultural land is based on Hertel et al. (1996) estimates for the US corn production over the 1976-1990 period. We obtain the economic rent of global cropland from GTAP v.7 database. The crop technology index and value shares of agricultural land and fertiliz- ers in 2004 are calibrated from known values of agricultural output, fertilizers, and the agricultural land as described in Rutherford (2002). Based on the agro- nomic literature (Cassman 1999, Cassman et al. 2010) we assume that crop technology index, θg,c is a logistic function with declining growth over time: g,c g,c κg,c t g,c θT θ0 e θt = g,c , (C.5) θT + θ0 (eκg,c t − 1) g,c g,c where θ0 is the initial value of crop technology index, θT is crop yield potential, i.e., the yield an adapted crop cultivar can achieve when crop man- agement alleviates all abiotic and biotic stresses through optimal crop and soil management (Evans and Fischer 1999), and κg,c is the logistic growth rate. In a comprehensive study Lobell et al. (2009) report a signicant variation in the ratios of actual to potential yields for major food crops across the world, ranging from 0.16 for tropical lowland maize in Sub-Saharan Africa to 0.95 for wheat in Haryana, India. Following global estimates of Licker et al. (2010) we assume the average ratio of 0.53. We calibrate the value of the logistic growth rate κg,c to match recent crop yield dynamics, and allow for yield plateau when g,c they reach 7080% of the potential yield, θT . As regards the cellulosic feedstocks, we assume that their yield grows linearly across time, adding a constant amount of technology gain per annum g,b g,b g,b θt +1 = θt + κg,b , θ0 > 0, (C.6) 16 g,i where the parameters θ0 and κg,i corresponds to the initial level and growth rate in agricultural yield of cellulosic feedstocks. We obtain the agricultural yield growth rate based on production-weighted average of econometric estimates of Cassman et al. (2010) for major grain yields using global data over 1966 - 2009 period. We obtain the yield data for cellulosic feedstocks ( miscanthus giganteus) from Taheripour and Tyner (2011). We also account for the potential impact of climate change on the growth rate of agricultural yields. In the baseline we assume moderate temperature increase by the end of the century following Representative Concentration Pathways (RCP) 2.6 GHG forcing scenario (Moss et al. 2008). We assume that potential crop yields remain unchanged by the end of the century, as a decline in yields due to moderate increase in temperature is likely to be oset by CO2 fertil- ization eect (Long et al. 2006). In contrast, second generation biofuels feed stocks benet from higher temperatures and yields increase strongly (Brown et al. 2000). Based on the simulation results for switchgrass yields in the upper Midwest of the United States (Brown et al. 2000), agricultural yield growth for cellulosic feedstocks is expected to increase by 50% in 2100. We annualize the growth by assuming that agricultural yield growth rate of cellulosic feed stocks relative to 2005 increases by 10% every twenty years until 2100. It can be shown (see, e.g., Rutherford (2002) for complete derivation) that non-land costs per ton of agricultural product, cg,i , are given by 1 1 1−σg,i 1−σg 1−σg σg cg,i t = g,i (αg ) cC,i t + (1 − αg )σg cf t , (C.7) θt where cC,i t are endogenous shadow prices (rents) of agricultural lands dedicated to food crops and cellulosic feedstocks. These prices are determined from a conditional input demand function for agricultural lands: σg σg xg,i αg 1−σg 1−σg 1−σg LC,i t = t g,i α σg cC,i t g σg + (1 − α ) cf t . (C.8) θt cC,i t C.1.5 Livestock Sector The initial output of livestock products (measured as the global physical pro- duction of meat, diary and eggs) in 2004 come from the FAOSTAT database. 17 We obtain the economic rent of global pasture land and the expenditures on animal feed, from GTAP v.7 database. The initial amount of animal feed comes from the USDA FAS PSD database. 4 The elasticity of substitution of animal feed for pasture land is taken from Golub et al. (2009). The livestock technology index and value shares of agricultural land and fertilizers in 2004 are calibrated from known values of livestock output, animal feed, and the pasture land as described in Rutherford (2002). Non land livestock farming costs are given by 2 cl l l l P t = c0 xt + ξ0 ∆Lt . (C.9) where cl 0 captures the non-land cost per ton of livestock, and l ξ0 captures the adjustment costs of pasture land conversion. We obtain the non-land cost of livestock farming from GTAP v.7 database, and calibrate the adjustment cost parameter to match recent trends in grain and livestock production (Taheripour et al. 2013). C.1.6 Food Processing Sectors The growth of technology indices in food processing sectors is described by the following equation: i,y i,y i,y θt+1 = κi,y θt , θ0 > 0, i = g, l, (C.10) i,y where the parameters θ0 and κi,y reect the initial level and annual growth rate in technologies of the food processing sector. We calculate the level of technology index of the grain and livestock processing in 2004 using GTAP v.7 database. For grains, we dividing the output of processed grains and crops (GTAP sectors 21, 23-25) by the output of grains and cereals (GTAP sectors 1-8). For livestock, we dividing the output of processed livestock and diary (GTAP sectors 19-20, 22) by the output of livestock products (GTAP sectors 9-11). We set the growth rate of the technology in the food processing sector equal to the economy's TFP. We obtain the non-land food processing costs from GTAP v.7 database. 4 see http://www.fas.usda.gov/psdonline, last accessed in August 2013. 18 C.1.7 Biofuels Sector In the model baseline we dene the rst-generation biofuels as a grain-based ethanol and the second generation biofuels as cellulosic biomass-to-liquid diesel obtained through Fischer-Tropsch gasication. The values for biofuels con- version rate and cost for ethanol and biomass-to-liquid diesel are taken from Taheripour and Tyner (2011). Following Winston (2009) we adjust the quan- tity of rst generation biofuels produced by 0.7 to match the energy content of liquid fossil fuels. The elasticity of substitution of second generation biofuels feedstocks for xed factor technology and their value shares in CES function (B.24) are calculated based on MIT-EPPA model (Paltsev et al. 2005, Tables 12 and 13, p.40 ). The change in factor-specic technological progress is described by the fol- lowing equation: φ φ φ θt+1 = κφ θt , θ0 > 0. (C.11) The rate of factor-specic technological change, κφ , is highly uncertain and is an important contribution to the uncertainty in projected deployment in second generation biofuels (Creutzig et al. 2012). Following the economic literature on biofuels modeling (Popp et al. 2011, Wise and Calvin 2011) we set the rate to 0.5 percent. In section E.1 we perform a sensitivity analysis with respect to a higher value of the rate of factor-specic technological change. C.1.8 Energy Sector We obtain the initial values for total consumption of liquid fossil fuels and rst generation biofuels from EIA (2010b, p. 24, Table 3). We set the initial consumption of second generation biofuels close to zero. The elasticity of sub- stitution of fossil fuels for rst generation biofuels is based on Hertel, Tyner and Birur (2010) econometric estimates for the US biofuel industry over the 2001-2008 period. The technology of energy production, and the value shares of biofuels and fossil fuels in energy production in 2004 are calibrated as described in Rutherford (2002). The growth in the energy eciency is described by the following equation: e e e θt +1 = κe θt , θ0 > 0, (C.12) e where the parameters θ0 and κe reect the initial level and annual growth 19 rate in the energy eciency. We set the energy eciency in 2004 equal to one, and obtain the growth rate in the energy eciency from World Energy Council (2008). C.1.9 Forestry Sector We set the number of forest tree vintages to 100 and assume that average den- sities of managed forest land corresponding to dierent tree ages are uniformly distributed. Following the literature on the economic analysis of managed forests (Sohngen and Mendelsohn 2007, Sohngen et al. 2009b) we assume that the mer- chantable timber yield function is given by the following equation: w ψ2 θv = exp ψ1 − , if v > v (C.13) v−v w θv = 0, if v ≤ v. In equation (C.13),the parameters ψ1 and ψ2 are growth parameters deter- mining the support and the slope of the timber yield function, and v is a min- imum age for merchantable timber. The yield function (C.13) parameters, the minimum age for merchantable timber, and the average planting and harvest- ing costs come from GTAP Global Forestry Data Base (Sohngen et al. 2009b). Similar to the agricultural sector, we assume that the merchantable timber yield per hectare of forest land with the average tree age v grows linearly across time, adding a constant amount of technology gain per annum: w w w w θv,t+1 = θv,t + κv , θv,0 > 0, (C.14) w where the parameters θv,0 and κw v correspond to the initial levels and tech- nology gains to the merchantable timber yield of vintage v. We obtain the data for yield growth in the commercial forestry sector by annualizing the dierence in the average yields from global forest studies of Sedjo (1983) and Cubbage et al. (2010). Forest harvesting costs are given by 2 cw t = w ξ0 w θv, F.H w 0 ∆Lv,t + ξ1 ∆LF,H F,H v,t − ∆Lv,t−1 (C.15) v v 2 w F,P +ξ2 ∆LF.H v,t − ∆Lt , v 20 w w w where the parameters ξ0 , ξ1 , and ξ2 correspond to long-run forest har- vesting costs and short-run adjustment costs of harvesting and harvested land conversion to agricultural land. We calibrate short-run adjustment costs of har- vesting and conversion of harvested forest land to agricultural land to match recent dynamics in commercial land-use. C.1.10 Timber Processing Sector The growth of TFP in the timber processing sector is described by the following equation: w,y w,y w,y θt+1 = κw,y θt , θ0 > 0, (C.16) w,y where the parameters θ0 and κw,y reect the initial level and annual growth rate in the technology of the timber processing sector. We calculate the tech- nology index of the timber processing sector in 2004 using GTAP v.7 data, by dividing the output of timber products (GTAP sectors 30-31) by the output of commercial forestry sector (GTAP sector 13). We set the growth rate of the technology in the timber processing sector equal to growth rate of the economy's TFP. We obtain the timber processing costs from GTAP v.7 database. C.1.11 Ecosystem Services Sector The parameters for production of ecosystem services in production function B.38 are based on the estimates of Costanza et al. (1997), who estimated values for 17 ecosystem services from 16 ecosystem types at global scale. 5 We exclude the services from the production of food and timber, as well as from based cli- mate abatement, as those are determined endogenously in the model. We also exclude the production of ecosystem services from ecosystems not represented in the model (e.g., marine, grasslands and deserts). We use agroecological zone (AEZ) representation of GTAP land use database to dierentiate between trop- ical and temperate/boreal forest land. Based on ecological literature (Ehrlich and Mooney 1983) we assume that there is a limited substitution between dif- ferent land types in production of ecosystem services. Because eectiveness of protected land areas is very dicult to quantify (Chape et al. 2005), we set the parameter θR large enough to make sure new protected areas are established. 5 We are familiar with multiple criticisms of this approach National Research Council (2005, p. 188-189). However, there have been very few attempts to evaluate production of ecosystem services at global scale, and the work of Costanza et al. (1997) still remains most inuential. 21 We measure the non-land costs of managing protected natural areas based on GTAP v.7 database as public expenditures on outdoor recreation services per hectare of protected land. 6 We assume that the non-land cost of managing protected natural areas declines over time with technological improvements in non-land inputs. We characterize the change in non-land costs of managing protected natural areas by the following equation: cR 0, cR t = R t c0 > 0, (C.17) (1 + κR ) where the parameters κR reect the annual rate of decline in the non-land cost of managing protected natural areas. C.1.12 Other Goods and Services The growth of TFP is described by the following equation: o o θt +1 = κo θt , θ > 0, (C.18) o where the parameters θ0 and κo reect the initial level and annual growth rate in the TFP of the economy. The initial values for the production of other goods and services and economy's output per capita are based on the value of output at agents' prices from GTAP v.7 database. The production of other goods and services is obtained from GTAP v.7 sectors 12, 14-15, 18, 26-29, 33-42, 45, 47-54 and 56-57. We set total factor productivity growth rate using Jorgenson and Vu (2010) projections based on econometric estimates for 122 economies over the 1990 - 2008 period. C.1.13 GHG Emissions The value of the GHG emission coecient from combustion of liquid fossil fuels comes from the US Energy Information Administration (EIA) website . 7 The GHG emission coecient from production of ammonia from fossil fuels comes from IPCC (2006a) Tier 1 estimates. We compute GHG emissions per ton of anhydrous ammonia applied to crop lands as follows. First, we calculate the 6 Following Antoine et al. (2008), we dene outdoor recreation services sector based on GTAP v.7 database. This sector comprises of hunting and shing, wildlife viewing in reserves, and other wildlife viewing activities. 7 See http://www.eia.doe.gov/oiaf/1605/coefficients.html, last checked in August, 2013. 22 17 nitrogen equivalent mass of anhydrous ammonia using conversion factor of 28 . We then use IPCC (2006b) Tier 1 estimates to compute the amount of nitrogen released to the atmosphere from ammonia application. We then convert the amount of nitrogen released to the atmosphere to nitrogen dioxide (NO2 ) using 44 conversion factor of 28 . Finally, we nd the carbon dioxide equivalent of the nitrogen dioxide using global warming potential of NO2 . The GHG emissions coecients from livestock are taken from FAOSTAT database. These include the emissions from enteric fermentation, and manure management (per ton of livestock) and the manure left on pasture land (per hectare of land). The GHG emissions factor per hectare of converted non- reserved natural land is based on the estimates of Hertel, Golub, Jones, O'Hare, Plevin and Kammen (2010) using methodology from Searchinger et al. (2008). The non-land-use emissions of biofuels' production are taken from GREET life- cycle model (Searchinger et al. 2008, Dunn et al. 2011). We do not impose any regulation for land-use emissions in the baseline scenario, and consider it in the following sections of this study. Following the literature on forest carbon sequestration in economic analysis of land-use (Sohngen and Mendelsohn 2007, Sohngen et al. 2009a) the carbon stock per hectare of harvested forest vintage v , µh v, is given by: ψ2 µh w v = µ exp ψ1 − . (C.19) v In equation (C.19) the parameter µw is the carbon conversion factor, that accounts for the stocking density of specic timber types, whole tree factors, and forest oor carbon, and ψ1 and ψ2 are the parameters dening merchantable timber yield function from equation (C.13). 8 Then the amount of GHG se- questered by a hectare of forest land of tree vintage v is µw h h v = µv − µv −1 . (C.20) We obtain the carbon conversion factor and yield function (C.13) parameters from GTAP Global Forestry Data Base (Sohngen et al. 2009b). The share of permanently stored carbon in harvested forest products is from Sohngen and Mendelsohn (2007). 8 Note that the minimum age parameter, v , is not included in equation (C.20). This is because at young ages, stands may have substantial carbon, but little merchantable timber Sohngen et al. (2009b). 23 C.1.14 Preferences and Welfare The parameters αq and βq dening the varying marginal budget shares of goods and services q in the consumers' total real expenditures in equation (B.45) are estimated by maximum likelihood as described in Craneld et al. (2003) and Yu et al. (2004). The parameters q dene the subsistence level of consumption of goods and services q were calibrated to match the initial allocation of land resources. The social discount rate is the same as in the Dynamic Integrated model of Climate and the Economy (DICE), version 2007. 9 We parameterize the scrap value function as vmax LF v,T Γ LU F T , LT = U 1 LT + 2 , ( 1 > 0, 2 > 0), (C.21) v =1 δ T −v where the parameters 1 and 2 denote the scrap prices of unmanaged and commercial forests at the beginning of period T. We calibrate the values of 1 and 2 , so that forest replanting rates are stable over time and unmanaged natural lands are not depleted over 50 percent of their initial amount during the time horizon of the problem. 10 C.2 Construction of Counterfactual Scenarios The values of the model parameters corresponding to the three counterfactual scenarios are summarized in Table C.1 and Figure C.2. To quantify the impact of climate change impact on potential crop yields we follow Steinbuks and Hertel (2013), who obtained results from runs of the Decision Support System for Agrotechnology Transfer (DSSAT) crop simulation ◦ model (Jones et al. 2003), run globally on a 0.5 grid and weighted by agricultural output of four major food crops (maize, soybeans, wheat and rice) under most optimistic (RCP2.6) and pessimistic (RCP8.5) Representative Concentration Pathways GHG forcing scenarios (Moss et al. 2008) and alternate assumptions on CO2 fertilization eects over the period between 1971 and 2099. For scenario A, we calculate the change in potential agricultural yield for food crops assume the pessimistic RCP8.5 without CO2 fertilization eect. 9 For a detailed description of the DICE model see Nordhaus (2008). DICE 2007 model parameters can be accessed at the following website: http://nordhaus.econ.yale.edu/ DICE2007.htm 10 We have tried setting dierent values of 1 , and the optimal path of natural land con- version was not signicantly aected over the rst 100 years. 24 For scenario E, the steeper growth rate of liquid fossil fuels costs is taken from the U.S. Energy Information Administration High Oil Price case scenario for 2035 projections EIA (2010a, p. 86, Table 10). We calibrate the value of the logistic oil price growth rate, κf , so that most of the additional increase in prices take place by mid-century (see Figure C.2). For scenario scenario, T we set the land-use emissions' target in 2100 to 60% less compared to 2004. The global warming intensity, θzt (zτ , t) dening the land-use GHG emissions' target is a logistic function: z zT zτ eκµ t θt = , (C.22) zT + zτ (eκµ t − 1) where zτ are GHG emissions in 2025, zT are the GHG emissions cap in 2104, and κµ is the targeted rate of decline in land-use GHG emissions. We calibrate the targeted rate of decline so that the target's stringency increases rapidly after it is introduced, with larger GHG emissions' reductions taking place by 2050. Figure C.2: Projections of Exogenous Variables, 2005-2104 10 300 9 250 8 Oil price, $/bbl Crop Yield, t/Ha 7 200 6 5 150 4 100 3 2 50 1 0 0 2005 2030 2055 2080 2105 2005 2030 2055 2080 2105 Baseline Scenario A Baseline Scenario E 120% 4.00 3.50 GHG Shadow Price Index, 2025 = 1 100% GHG Emissions as % of Baseline 3.00 80% 2.50 60% 2.00 1.50 40% 1.00 20% 0.50 0.00 0% 2025 2050 2075 2100 2025 2050 2075 2100 Scenario T Scenario T 25 Table C.1: Parameters for Counterfactual Scenarios Parameter Description Units Value Scenario A (Declining Growth of Agricultural Yield) g,c θT Food Crop Yield in time T tons / Ha 8.05 Scenario E (Rising Fossil Fuel Costs) κf Logistic Oil Price Growth Rate 0.075 Scenario T (Land-Use Emissions Target) zτ GHG Emissions in 2025 GtCO2 e zT GHG Emissions in 2104 GtCO2 e 0.4zτ κµ Logistic Rate of Decline in Land-Use Emissions 0.04 E.1 Model Sensitivity to Parameter Values This section explores the model sensitivity to the values of several important parameters used in the empirical analysis. These include the conversion cost of natural lands, substitutability between agricultural lands and fertilizers in pro- duction of agricultural output, the costs and eciency of biofuels' production, energy eciency, and the demand for energy services. We show model baseline sensitivities with respect to the following changes 11 : • a 50% decline in short-term adjustment costs of natural land conversion; • a 50% increase in elasticity of substitution between agricultural land and fertilizers, • a 50% improvement in second generation biofuels' production technology, • a 50% increase in xed factor specic technological change, • a 50% decline in energy eciency growth rate, and 11 Becauseof a lack of space, we are unable to show sensitivity results across all parameters and scenarios. In this section we concentrate on the parameters subject to largest uncertain- ties. The additional results are available from authors upon request. 26 Table D.1: Model Simulation Results, 2050 Variable / Scenario Baseline Scenario A Scenario E Scenario T Scenario AE Scenario AET (Level) (Deviation from Baseline) (∆A) (∆AE) Land Cropland Area, MHa 1951 16.9 29.9 -39.4 30.0 -38.7 - Food Crops, MHa 1459 11.0 -27.0 -27.0 -25.0 -20.0 - Animal Feed, MHa 399 8.7 -2.7 -41.8 -3.4 -34.7 - Biofuels Crops, MHa 93 -2.8 59.6 29.4 58.4 16.0 Pasture Land Area, MHa 2547 -4.9 -8.0 -41.0 -8.0 -39.2 Commercial Forest Area, MHa 1587 -3.0 -6.0 53.0 -6.0 40.0 Unmanaged Natural Land Area, MHa 2183 -7.0 -11.0 22.0 -11.0 29.0 Protected Natural Land Area, MHa 291 -2.4 -4.7 5.2 -4.7 8.7 Intermediate Products Agricultural Product, Mton 4407 -242.2 -437.9 -260.9 -419.2 -167.7 Livestock, Mton 890 -29.7 -60.9 -87.2 -60.3 -63.0 Fertilizers, Mton 128 6.5 -26.2 -10.6 -27.8 -6.5 Petroleum, Mtoe 773 0.0 -400.6 -270.2 -400.6 -111.8 27 Biofuels, Mtoe 314 -2.7 55.7 36.0 56.4 10.1 Timber Products, Mton 2515 0.0 0.0 0.0 0.0 0.0 Final Consumption Processed Food Services per capita, 2004 USD 263 -15 -27 -11 -25 -7 Processed Livestock Services per capita, 2004 USD 291 -10 -20 -28 -20 -21 Bioenergy Services per capita, 2004 USD 33 0 26 4 26 2 Processed Timber Services per capita, 2004 USD 271 0 0 0 0 0 Ecosystem Services per capita, 2004 USD 259 -1 -2 4 -2 5 GHG Emissions Natural Land Conversion, MtCO2 e 0 0 0 0 0 0 Fertilizers' Use, MtCO2 e 519 26 -106 -43 -113 -27 Biofuels Combustion, MtCO2 e 195 -2 35 22 35 6 Livestock Farming ans Management, MtCO2 e 1241 -28 -58 -87 -57 -64 Net Forest Sequstration, MtCO2 e -2029 12 28 -246 29 -76 Petroleum Combustion, MtCO2 e 2240 2 -1161 -790 -1162 -319 GHG Emissions from Land Use, MtCO e 2 -74 7 -101 -355 -106 -161 Accumulated GHG Emissions from Land Use, GtCO e 2 67.9 5.1 -8.2 5.4 -8.4 12.4 Table D.2: Model Simulation Results, 2100 Variable / Scenario Baseline Scenario A Scenario E Scenario T Scenario AE Scenario AET (Level) (Deviation from Baseline) (∆A) (∆AE) Land Cropland Area, MHa 2139 24.1 25.0 -83.5 25.0 -84.5 - Food Crops, MHa 1261 8.0 7.0 -16.0 7.0 -19.0 - Animal Feed, MHa 735 19.3 5.8 -96.7 6.0 -92.9 - Biofuels Crops, MHa 143 -3.2 12.2 29.2 12.0 27.4 Pasture Land Area, MHa 2330 -9.8 -6.7 -114.3 -6.8 -111.7 Commercial Forest Area, MHa 1616 -5.0 -2.0 171.0 -2.0 157.0 Unmanaged Natural Land Area, MHa 1795 -5.0 -11.0 39.0 -10.0 47.0 Protected Natural Land Area, MHa 678 -4.3 -4.9 -11.9 -4.9 -9.1 Intermediate Products Agricultural Product, Mton 6188 -629.8 -140.0 -659.8 -120.0 -549.8 Livestock, Mton 1577 -96.0 -23.1 -214.2 -21.8 -186.4 Fertilizers, Mton 179 5.7 -11.4 -31.1 -11.4 -27.8 Petroleum, Mtoe 1170 -10.0 -150.0 -469.9 -140.0 -399.9 28 Biofuels, Mtoe 507 -3.5 8.3 19.8 8.3 16.8 Timber Products, Mton 3399 0.0 0.0 0.0 0.0 0.0 Final Consumption Processed Food Services per capita, 2004 USD 275 -29 -7 -18 -6 -15 Processed Livestock Services per capita, 2004 USD 480 -29 -7 -65 -7 -57 Bioenergy Services per capita, 2004 USD 85 -1 9 3 9 3 Processed Timber Services per capita, 2004 USD 344 0 0 0 0 0 Ecosystem Services per capita, 2004 USD 329 -1 -2 4 -2 4 GHG Emissions Natural Land Conversion, MtCO2 e 0 0 0 0 0 0 Fertilizers' Use, MtCO2 e 727 25 -46 -124 -48 -112 Biofuels Combustion, MtCO2 e 322 -5 6 10 6 9 Livestock Farming ans Management, MtCO2 e 1844 -101 -25 -234 -24 -202 Net Forest Sequstration, MtCO2 e -2075 28 18 -768 19 -697 Petroleum Combustion, MtCO2 e 3382 -22 -417 -1346 -415 -1144 GHG Emissions from Land Use, MtCO e 2 817 -53 -47 -1115 -47 -1002 Accumulated GHG Emissions from Land Use, GtCO e 2 11.8 4.8 -15.4 -34.2 -15.7 -18.2 • a 50% increase in AIDADS marginal budget shares for energy services. Table E.1 summarizes the changes in parameters values under consideration. 12 Change in Land Use Relative to Baseline Change in GHG Emissions Relative to Baseline 80 0.8 40 Natural Land 60 Food Crops Conversion 0.6 30 Livestock Feed Livestock 40 0.4 20 Biofuels Crops 20 0.2 10 Biofuels GtCO2e Million Ha GtCO2e/yr Pasture Land Offsets 0 0 0 Protected Forests Use of -20 -0.2 -10 Fertilizers Managed Forests Forest -40 -0.4 -20 Sequestration Unmanaged Forests -60 -0.6 -30 Net GHG Accumulation -80 -0.8 -40 2005 2030 2055 2080 2105 2005 2030 2055 2080 2105 Change in Consumption of Land Based Good Change in Consumption of Biofuels Relative to and Services Relative to Baseline Baseline 7 10% 10 8% 5 8 6% 3 Consumption of 2g 6 Processed Livestock 4% Biofuels USD Per Person Million toe 1 2% 4 Recreation Services 0% Consumption of 1g 2 Processed Timber -1 Biofuels -2% Energy Services -4% 0 -3 Share of Biofuels in Processed Grains -6% Liquid Fuel -2 -5 -8% Consumption -4 -7 -10% 2005 2030 2055 2080 2105 2005 2030 2055 2080 2105 Figure E.1: Sensitivity Analysis: 50% Decline in Short Term Adjustment Costs of Natural Land Conversion Figure E.1 shows the eects of a 50% decline in short-term adjustment costs of natural land conversion (all of the gures in this section report changes, relative to the baseline). Greater ease of natural land conversion results in a decline in unmanaged forest land, which decreases further by 65 million Ha in 2100. Agricultural land dedicated to food crops and animal feed expands in near decades and the medium term. In the long term, there is also an increase in managed and protected forest areas and the area dedicated to biofuels feed- stocks. The additional conversion of natural lands results in increased GHG ows, and net GHG accumulation increases by 25 GtCO2 e in mid-century, and remains constant thereafter. The consumption of ecosystem services declines 12 The magnitudes of parameter changes in model sensitivity analysis are not based on pro- jections from other studies. Rather these magnitudes represent a simple attempt to construct condence intervals for baseline predictions. 29 in the mid term as a result of additional deforestation, but increases thereafter with the increase in protected lands. The consumption of all other land-based goods and services, and biofuels increase modestly in the long term. Change in Land Use Relative to Baseline Change in GHG Emissions Relative to Baseline 200 1.5 40 Natural Land 150 Food Crops Conversion 30 1 Livestock Livestock Feed 100 20 Biofuels Crops 0.5 50 10 Biofuels GtCO2e Million Ha GtCO2e/yr Pasture Land Offsets 0 0 0 Protected Forests Use of -50 -10 Fertilizers Managed Forests -0.5 Forest -100 -20 Sequestration Unmanaged Forests -1 -150 -30 Net GHG Accumulation -200 -1.5 -40 2005 2030 2055 2080 2105 2005 2030 2055 2080 2105 Change in Consumption of Land Based Good Change in Consumption of Biofuels Relative to and Services Relative to Baseline Baseline 0 40 10% 30 8% -10 6% 20 Consumption of 2g 4% -20 Processed Livestock Biofuels USD Per Person Million toe 10 2% Ecosystem Services -30 0 0% Consumption of 1g Processed Timber Biofuels -10 -2% -40 Energy Services -4% -20 Share of Biofuels in Processed Grains -6% Liquid Fuel -50 -30 Consumption -8% -40 -10% -60 2005 2030 2055 2080 2105 2005 2030 2055 2080 2105 Figure E.2: Sensitivity Analysis: 50% Increase in Elasticity of Substitution between Agricultural Land and Fertilizers Figure E.2 shows the eects of a 50% increase in elasticity of substitution between agricultural land and fertilizers. Given the increase in fertilizers' costs in baseline scenario, better substitution between agricultural land and fertilizers implies additional demand for agricultural land, which increases by about 150 million Ha in 2100. All forest areas decline. GHG ows increase with the addi- tional conversion of natural lands. However, the decline in fertilizers' use results in smaller GHG ows. The former eect dominates, and net GHG accumulation increases by 30 GtCO2 e in 2100. The consumption of all land based goods and services declines. There is also a small decrease in the consumption of biofuels. Figure E.3 shows the eects of a 50% improvement in second generation biofuels production technology. This improvement makes second generation biofuels a more competitive alternative to petroleum products, and they enter 30 Change in Land Use Relative to Baseline Change in GHG Emissions Relative to Baseline 40 1.5 50 Natural Land 30 Food Crops 40 Conversion 1 Livestock Livestock Feed 30 20 Biofuels Crops 20 10 0.5 Biofuels GtCO2e Million Ha Pasture Land GtCO2e/yr 10 Offsets 0 0 0 Protected Forests Use of -10 -10 Fertilizers Managed Forests -0.5 -20 Forest -20 Sequestration Unmanaged Forests -30 -1 -30 -40 Net GHG Accumulation -40 -1.5 -50 2005 2030 2055 2080 2105 2005 2030 2055 2080 2105 Change in Consumption of Land Based Good Change in Consumption of Biofuels Relative to and Services Relative to Baseline Baseline 350 30% 60 250 20% 50 150 Consumption of 2g 40 10% Processed Livestock Biofuels USD Per Person Million toe 30 Ecosystem Services 50 0% Consumption of 1g 20 Processed Timber -50 Biofuels Energy Services -10% 10 -150 Processed Grains Share of Biofuels in -20% Liquid Fuel 0 -250 Consumption -10 -350 -30% 2005 2030 2055 2080 2105 2005 2030 2055 2080 2105 Figure E.3: Sensitivity Analysis: 50% Increase in Biofuels' Conversion Rate 31 large scale commercial production considerably earlier. After arrival of second generation biofuels, their production increases by 300 million toe, and the biofu- els share in liquid fuel production increases to reach 47% in 2100. Agricultural area dedicated to cellulosic feedstocks increases by additional 30 million Ha in 2100, whereas areas dedicated to food crops, animal feed and natural forests de- cline. GHG ows increase with the additional conversion of natural lands, and later decline with biofuels' osets. The latter eect dominates in the long run, and net GHG accumulation declines by 40 GtCO2 e in 2100. The consumption of energy services increases, and the consumption of other land based goods and services declines. Change in Land Use Relative to Baseline Change in GHG Emissions Relative to Baseline 50 1.5 20 Natural Land 40 Food Crops Conversion 15 30 1 Livestock Livestock Feed 20 10 Biofuels Crops 0.5 5 Biofuels GtCO2e 10 Million Ha GtCO2e/yr Pasture Land Offsets 0 0 0 Protected Forests Use of -10 Fertilizers -5 Managed Forests -0.5 -20 Forest -10 Sequestration -30 Unmanaged Forests -1 -15 Net GHG -40 Accumulation -50 -1.5 -20 2005 2030 2055 2080 2105 2005 2030 2055 2080 2105 Change in Consumption of Land Based Good Change in Consumption of Biofuels Relative to and Services Relative to Baseline Baseline 250 20% 30 200 15% 25 150 20 10% Consumption of 2g 100 Processed Livestock Biofuels USD Per Person Million toe 15 50 5% Ecosystem Services 10 0 0% Consumption of 1g Processed Timber Biofuels -50 -5% 5 Energy Services -100 0 -10% Share of Biofuels in Processed Grains -150 Liquid Fuel -5 -200 -15% Consumption -10 -250 -20% 2005 2030 2055 2080 2105 2005 2030 2055 2080 2105 Figure E.4: Sensitivity Analysis: 50% Increase in Fixed Factor Specic Techno- logical Change Figure E.4 shows the eects of a 50% increase in xed factor specic techno- logical change. Similar to the improvements in biofuels' production technology, faster technological progress in biofuels penetration make biofuels a more com- petitive alternative to petroleum products. Biofuels production increases by 150 million toe, and the biofuels share in liquid fuel production increases to reach 32 39% in 2100. Agricultural area dedicated to cellulosic feedstocks increases by additional 36 million Ha in 2100. All other areas decline. GHG ows increase because of additional conversion of natural lands, and decline due to greater biofuels' osets. The latter eect dominates in the long run, and net GHG ac- cumulation declines by 10 GtCO2 e in 2100. The consumption of energy services increases, and the consumption of other land based goods and services declines. Change in Land Use Relative to Baseline Change in GHG Emissions Relative to Baseline 40 1.5 10 Natural Land 30 Food Crops Conversion 8 Livestock Feed 1 Livestock 20 6 Biofuels Crops 4 10 0.5 Biofuels Million Ha GtCO2e/yr Pasture Land 2 Offsets GtCO2e 0 0 0 Protected Forests Use of -10 -2 Fertilizers Managed Forests -0.5 -4 Forest -20 Unmanaged Forests -6 Sequestration -1 -30 -8 Net GHG Accumulation -40 -1.5 -10 2005 2030 2055 2080 2105 2005 2030 2055 2080 2105 Change in Consumption of Land Based Good Change in Consumption of Biofuels Relative to and Services Relative to Baseline Baseline 2 10 6% 0 8 4% 6 -2 4 Consumption of 2g Processed Livestock 2% USD Per Person Biofuels Million toe -4 2 Ecosystem Services -6 0 0% Consumption of 1g Processed Timber -2 Biofuels -8 Energy Services -2% -4 -10 Processed Grains Share of Biofuels in -6 Liquid Fuel -4% -12 -8 Consumption -14 -10 -6% 2005 2030 2055 2080 2105 2005 2030 2055 2080 2105 Figure E.5: Sensitivity Analysis: 50% Decline in Energy Eciency Growth Rate per annum Figure E.5 shows the eects a 50% decline in energy eciency growth rate. Smaller energy eciency implies increased requirements for energy fuels (here petroleum products and biofuels) to satisfy the demand for energy services. The increased consumption of petroleum and biofuels results in a greater demand for agricultural land. Areas dedicated to biofuels feedstocks add 3 million Ha. All other areas dedicated to commercial land decline in response to demand reduc- tion for land based goods and services due to higher energy prices. Unmanaged forest lands increase by additional 26 million Ha in 2100. The GHG emissions ows from land use decline slightly in the medium term because of avoided de- 33 forestation. The consumption of biofuels increase by a small amount, although their share in liquid fuel consumption modestly declines because of even greater increase in demand for petroleum products. The income eect of increased re- quirements for petroleum products propagates into decline in consumption of all land based goods and services, except for energy services. Change in Land Use Relative to Baseline Change in GHG Emissions Relative to Baseline 200 5 200 Natural Land 150 Food Crops 4 Conversion 150 Livestock Feed 3 Livestock 100 100 Biofuels Crops 2 50 50 Biofuels GtCO2e Million Ha GtCO2e/yr 1 Pasture Land Offsets 0 0 0 Protected Forests Use of -50 -1 -50 Fertilizers Managed Forests -2 Forest -100 -100 Sequestration Unmanaged Forests -3 -150 -4 -150 Net GHG Accumulation -200 -5 -200 2005 2030 2055 2080 2105 2005 2030 2055 2080 2105 Change in Consumption of Land Based Good Change in Consumption of Biofuels Relative to and Services Relative to Baseline Baseline 10 10% 15 10 8 8% 5 6 6% 0 4 4% Consumption of 2g Processed Livestock USD Per Person -5 Biofuels Million toe 2 2% -10 Ecosystem Services 0 0% Consumption of 1g -15 Processed Timber -2 -2% Biofuels -20 Energy Services -25 -4 -4% Processed Grains Share of Biofuels in -30 -6 -6% Liquid Fuel -35 -8 -8% Consumption -40 -10 -10% 2005 2030 2055 2080 2105 2005 2030 2055 2080 2105 Figure E.6: Sensitivity Analysis: 50% Increase in Social Discount Rate Figure E.6 shows the eects of a 50% increase in social discount rate. This results in a substitution of ecosystem services, which have relatively greater im- portance in more distant future, for all other land based goods and services. The conversion of unmanaged natural land increases substantially by mid-century, and protected forests decline by 150 million hectares in 2100. All other land areas expand. Areas dedicated to food crops and animal feed grow by additional 20 add 7 million Ha, pasture and managed forest areas gain additional 100 and 10 million Ha in 2100. Changes in social discount rate thus result in increase in the GHG emissions ows from land use because of increased deforestation. Net GHG accumulation increases by nearly 75 GtCO2 e in 2100. The conversion of natural forest land result in a signicant decline in consumption of ecosystem 34 services. The consumption of biofuels and their share in liquid fuel consumption increases by a small amount. 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