metadata: authors: 0: author: Hertel,Thomas W.
1: author: Steinbuks,Jevgenijs
count: World
docna: 0: docna: Confronting the food-energy-environment
            trilemma : global land use in the long run
docty: Policy Research Working Paper
subtopic: Climate Change and Agriculture,Crops and Crop Management Systems,Fertilizers,Livestock and Animal Husbandry,Rural and Renewable Energy,Energy Demand,Energy and Environment,Energy and Mining,Renewable Energy
teratopic: Energy,Macroeconomics and Economic Growth,Environment
abstracts: cdata!: Economic, agronomic, and biophysical
            drivers affect global land use, so all three influences need
            to be considered in evaluating economically optimal
            allocations of the world's land resources. A dynamic,
            forward-looking optimization framework applied over the
            course of the coming century shows that although some
            deforestation is optimal in the near term, in the absence of
            climate change regulation, the desirability of further
            deforestation is eliminated by mid-century. Although adverse
            productivity shocks from climate change have a modest effect
            on global land use, such shocks combined with rapid growth
            in energy prices lead to significant deforestation and
            higher greenhouse gas emissions than in the baseline.
            Imposition of a global greenhouse gas emissions constraint
            further heightens the competition for land, as fertilizer
            use declines and land-based mitigation strategies expand.
            However, anticipation of the constraint largely dilutes its
            environmental effectiveness, as deforestation accelerates
            prior to imposition of the target.
repnme: repnme: Confronting the food-energy-environment
            trilemma : global land use in the long run
display_title: Confronting the
            food-energy-environment trilemma : global land use in the
            long run
listing_relative_url: /research/2014/06/19696268/confronting-food-energy-environment-trilemma-global-land-use-long-run
topicv3: Energy and Extractives m1326595 507,Biofuels Energy m1326600 532,Crop Production m1326627 174,Fertilizers m1327354 175,Livestock m1504490 4024
publishtoextweb_dt: 2014-06-01T00:00:00Z
historic_topic: Energy,Macroeconomics and Economic Growth,Environment
no_of_pages: 87
author_keys: 0: author_key: 451732
1: author_key: 666646
model_extractions: 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 global land use, so all three influences need to be considered in evaluating economically optimal allocations of the world’s land resources. A dynamic, forwardlooking optimization framework applied over the course of the coming century shows that although some deforestation is optimal in the near term, in the absence of climate change regulation, the desirability of further deforestation is eliminated by mid-century. Although adverse productivity shocks from climate change have a modest effect on global land use, such shocks combined with rapid growth in energy prices lead to significant deforestation and higher greenhouse gas emissions than in the baseline. Imposition of a global greenhouse gas emissions constraint further heightens the competition for land, as fertilizer use declines and land-based mitigation strategies expand. However, anticipation of the constraint largely dilutes its environmental effectiveness, as deforestation accelerates prior to imposition of the 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<sup>_∗_</sup>

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. Acknowledgements: 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 Annual Meetings, Cowles Summer Conference "Macroeconomics and Climate Change", and research 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 reect 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 century has become a pressing research question. Continuing population increases, improving, land-intensive diets among the poorest populations in the world, increasing 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 combination 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 prole for global land use in the context of growing commercial demands for food and forest products, 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-dened property rights, poorly developed land markets, lack of information, 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 inu- ence patterns of global land use. In addition, due to its forward-looking nature, this model can oer important insights regarding the behavior of forward-looking investors under alternative states of the world. As with most new model developments, introducing this intertemporal dimension into the model is costly; as a consequence at this early stage, we are unable to oer the kind of geographic 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).<sup>1</sup>

> 1Because 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

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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 investigates 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 between 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 decisions taking into account irreversibility from loss of biodiversity and signicant option values attached to the future stream of benets from ecosystem services (Conrad 1997, 2000, Bulte et al. 2002, Leroux et al. 2009).<sup>2</sup> Finally, the literature on GHG abatement and land-use explores dierent 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), liquid 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 ecosystem 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, eciency implications of carbon taxes and caps, and endogenous depletion of nonrenewable 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).

> 2Recent 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).

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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 alternative 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 dierential growth rates of harvestable timber and carbon stocks.

We solve the model over the 200 year period beginning 2005, focusing analysis on the coming century. Our baseline reects 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. Specically, we consider the comparative dynamic eects 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 regulation, 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 eects on yields - hurting food production, but beneting 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 eect on the overall amount of land used in agriculture, since higher prices encourage additional biofuel production, even while making intensication of production more costly. The net eect is even greater GHG emissions. The introduction of a constraint on GHG emissions from land use leads to a signicant long-run reduction in cropland expansion. However, a jump in forest conversion before the constraint is introduced makes it less eective over the course of the entire century, thereby conrming 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.

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# 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 products 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.

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# 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), _L_<sup>_N_</sup> _t_<sup>, and managed commercial lands,</sup><sup>_LM_</sup> _t_<sup>.The land</sup> endowment constraint is 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, _L_<sup>_R_</sup> _,_ 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, _L_<sup>_U_</sup> _,_ can be accessed and either converted to commercial land (deforested) or to protected 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.<sup>3</sup> Equations describing allocation of commercial land across time and dierent uses are: and 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, _L_<sup>_U_</sup> 0<sup>_,_</sup> declines by the amounts allocated for conversion to commercial and protected land, ∆ _L_<sup>_U_</sup> _t_ = ∆ _L_<sup>_U,M_</sup> _t_ + ∆ _L_<sup>_U,R_</sup> _t_ , where the ∆ operator denotes a change in variables _L_<sup>_U_</sup> _t_<sup>and</sup><sup>_LR_</sup> _t_<sup>.Equation(4)showsthatateachperiodoftime,thetotal</sup>

> 3This point requires additional clarication. The biophysical and ecological literature suggests that restoration of forest structure and plant species takes at least 30-40 years and usually 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 (Benayas et al. 2009). Modeling restoration of biodiversity under these assumptions introduces greater computational complexity without making signicant changes relative to ndings presented in this study.

6
area of reserved land with initial stock of _L_<sup>_R_</sup> 0<sup>increasesbytheamountofnewly</sup> protected land, ∆ _L_<sup>_U,R_</sup> _t ._ Accessing the natural lands comes at per hectare cost, _c_<sup>_U_</sup> _t_<sup>_,_whichderives</sup> from road construction and other infrastructure (Golub et al. 2009). In addition, converting natural land to protected land entails per hectare cost, _c_<sup>_R_</sup> _t_<sup>_,_</sup> associated with institutional and physical eort (e.g, passing legislation, creating recreational infrastructure) to create new natural parks. We assume that these costs are continuous, monotonically increasing, and strictly convex functions 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 oset by the revenues from the sale of the forest product. In the technical appendix, section C.1, we discuss specic functional forms and parametarization of these costs. There are no additional costs of natural land conversion to commercial land, as these costs are oset 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 allocation of commercial land across time and between uses are: and Equation (5) shows that total endowment of commercial land, _L_<sup>_M_</sup> _,_ is a sum of the hectares of commercial land dedicated to cropland, _L_<sup>_C_</sup> _,_ pasture land, _L_<sup>_P_</sup> _,_ and managed forests, _L_<sup>_F_</sup> , respectively. Equation (6) shows that at each period of time, the total area of commercial land with initial stock of _L_<sup>_M_</sup> 0 increases by the amount of converted unmanaged natural land, ∆ _L_<sup>_U,M_</sup> _._

# 2.1.2 Fossil Fuels

Fossil fuels, _x_<sup>_f_</sup> _,_ have two competing uses in our partial equilibrium model of land use. A fraction of fossil fuels, _x_<sup>_f,n_</sup> , is converted to fertilizers that are further used in the agricultural sector. The remaining amount of fossil fuels, _x_<sup>_f,e_</sup> _,_ is combusted to satisfy the demand for energy services. The total demand 7
for fossil fuels, at time t, is thus given by The per unit cost of fossil fuels, _c_<sup>_f_</sup> _t_<sup>_,_ispredetermined,andreectstheexpendi-</sup> tures on fossil fuels' extraction, transportation and distribution, as well as the costs associated with GHG emissions control (e.g. carbon prices) in the nonland-based economy. In the technical appendix, section C.1, we discuss specic functional forms and parametarization of fossil fuel costs.

# 2.2 Agrochemical Sector

The agrochemical sector consumes fossil fuels, _x_<sup>_f,n_</sup> , and converts them into fertilizers for use in the agricultural sector. The production of fertilizers, _x_<sup>_n_</sup> _,_ can be described by a linear production function: where _θ_<sup>_n_</sup> is the rate of conversion of fossil fuels to fertilizers. We assume that the non-energy cost of conversion of fossil fuels to fertilizers, _c_<sup>_n_</sup> _,_ is constant and scale-invariant. In the technical appendix, section C.1, we discuss parameterization of fertilizers' production technology and costs.

# 2.3 Crops Sector

The crops sector combines agricultural land, _L_<sup>_C_</sup> , and fertilizers, _x_<sup>_n_</sup> _,_ to produce food crops as well as cellulosic feedstocks (but only when it is protable). Food crops, _x_<sup>_g,c_</sup> _,_ are used as inputs to production of food, animal feed, and rst generation biofuels: where _x_<sup>_c,g_</sup> _t_<sup>_,xl,g_</sup> _t_<sup>,and</sup><sup>_xb,g_</sup> _t_ respectively denote the amounts of food crops used in food processing, animal feed, and rst generation biofuels. Cellulosic feed stocks, _x_<sup>_g,b_</sup> _,_ can only be converted to second generation biofuels, _x_<sup>_b,_2</sup> .

Agricultural land and fertilizers are imperfect substitutes in the production of agricultural products. The per capita output of agricultural products, _x_<sup>_g,i_</sup> _,_ 8
is thus determined by the constant elasticity of substitution (CES) function: where Π _t_ is the exogenous population at time _t_ , _θt_<sup>_g_and</sup><sup>_αg_are,respectively,</sup> the crop technology (agricultural yield) index and the value share of cropland in production of agricultural product at the benchmark time 0 _,_ and _L_<sup>_C,i_</sup> _t_ are hectares of agricultural land allocated for food crops and cellulosic feed stocks. The parameter _ρg_ = _σgσ−g_ 1 is a CES function parameter proportional to the elasticity of substitution of agricultural land for fertilizers, _σ_<sup>_g_</sup> _._ 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), _c_<sup>_g,i_</sup> _,_ 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, _L_<sup>_P_</sup> , and animal feed, _x_<sup>_l,g_</sup> , to produce domesticated animals, _x_<sup>_l_</sup> . Pasture land and animal feed are imperfect substitutes in the production of livestock. The per capita output of livestock, _x_<sup>_l_</sup> _,_ is thus determined by the constant elasticity of substitution (CES) function: where _θt_<sup>_l_and</sup><sup>_αl_are,respectively,thelivestocktechnologyindexandthevalue</sup> share of pasture land in production of livestock at the benchmark time 0 . The parameter _ρl_ =<sup>_<u>σl</u>_</sup> _σ_<sup>_−_</sup> _l_<sup><u>1</u></sup> is a CES function parameter proportional to the elasticity of substitution of pasture land for animal feed, _σ_<sup>_l_</sup> _._ The production of livestock is also subject to non-land costs from use of other production factors (such as e.g., labor or capital), _c_<sup>_l_</sup> _,_ the prices of which are exogenous. In the technical 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, _x_<sup>_c,g_</sup> _,_ and livestock, _x_<sup>_l_</sup> , into processed grains, _y_<sup>_g_</sup> _,_ and processed animal products (such as meat and dairy), _y_<sup>_l_</sup> , that are further consumed in nal demand. The purpose of these sectors in the 9
model is to capture the eciency gains from technology improvements in food production, which result in lower requirements for agricultural inputs in nal demand.<sup>4</sup> The conversion process is represented by the following production functions: where _θt_<sup>_g,y_</sup> and _θt_<sup>_l,y_</sup> are technology indices of crop and livestock processing, which capture the technological progress in both direct transformation of agricultural products into edible food, and the storage, transportation, and distribution of processed food. We assume that the food processing costs per ton of processed crops, _c_<sup>_g,y_</sup> , and livestock, _c_<sup>_l,y_</sup> _,_ are exogenous and scale-invariant. In the technical appendix, section C.1, we discuss parameterization of food processing technologies and costs.

# 2.6 Biofuels Sector

The biofuels sector consumes the remaining amount of food crops to produce rst generation biofuels, _x_<sup>_b,_1</sup> . We assume that a ton of food crops, _x_<sup>_b,g_</sup> , can be converted to _θ_<sup>_b,_1</sup> tons of oil equivalent ( _toe_<sup>_′_</sup> _s_ ) of rst generation biofuels. The output of rst generation biofuels is thus given by The biofuels sector also converts cellulosic feedstocks, _x_<sup>_g,b_</sup> _,_ into second generation biofuels, _x_<sup>_b,_2</sup> , 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), reecting 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

> 4For example, technological innovation in food conservation results in fewer losses from spoilage, and, correspondingly, lower amounts of processed food needed to satisfy the commercial demand for food. Correspondingly, input requirements for agricultural product also decrease.

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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 specic 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-specic technological progress, _θt_<sup>_φ_(Acemoglu1998,vanMeijlandvanTongeren1999).</sup> Under these assumptions the production of second generation biofuels, _x_<sup>_b,_2</sup> _,_ is determined by the following CES function where _θt_<sup>_b,_2</sup> and _α_<sup>_b_</sup> are, respectively, the technology parameter and the value share of xed factor in production of second generation biofuels at the benchmark time 0 . The parameter _ρb_ =<sup>_<u>σb</u>_</sup> _σ_<sup>_−_</sup> _b_<sup><u>1</u></sup> is a CES function parameter proportional to the elasticity of substitution of technology xed factor for cellulosic feed stocks, _σ_<sup>_b_</sup> _._ The agricultural products' conversion to renewable fuel incurs additional non-food processing costs, _c_<sup>_b,i_</sup> _._ We assume these costs are constant and scaleinvariant.<sup>5</sup> 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, _x_<sup>_e_</sup> _,_ and rst and second generation biofuels, _x_<sup>_b,i_</sup> . First generation biofuels (e.g., corn or sugarcane ethanol) blend with petroleum products in varying proportions,<sup>6</sup> and the resulting mix is further combusted to satisfy the demand for energy services.<sup>7</sup> Following the economic literature on biofuels modeling (Hertel et al. 2010), we assume that rst generation biofuels and petroleum products are imperfect substitutes. Second generation biofuels (e.g., cellulosic biomass-to-liquid diesel obtained through

> 5With 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.

> 6Blends 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.

> 7The 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 gasication) oer a full `drop-in' fuel alternative. We therefore assume that petroleum products and second generation biofuels are perfect substitutes. Under these assumptions the per capita production of energy services, _yt_<sup>_e,_isgivenbythefollowingCESfunction:</sup> where the parameter _θ_<sup>_e_</sup> describes the energy technology index, or the eciency of energy production (i.e., the amount of energy services provided by one _toe_ of the energy fuel (Sorrell and Dimitropoulos 2008, p. 639)), _α_<sup>_e_</sup> is the value share of rst-generation biofuels in energy production at the benchmark time 0 _,_ and _ρe_ =<sup>_<u>σe</u>_</sup> _σ_<sup>_−_</sup> _e_<sup><u>1</u></sup> 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: 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, _L_<sup>_F_</sup> _v,t_<sup>_,_hasanaveragedensityoftreesof</sup> vintage age _v,_ with the initial allocation given and denoted by _L_<sup>_F_</sup> _v,_ 0<sup>.Each period</sup> of time the managed forest land can be either planted, harvested or simply left to mature. The newly planted trees occupy ∆ _L_<sup>_F,P_</sup> hectares of land, and reach the average age of the rst tree vintage next period. The harvested area occupies ∆ _L_<sup>_F,H_</sup> _v_ hectares of forest land _._ If the managed forest land is harvested, it yields _θv_<sup>_w_tons of forest product (raw timber),</sup><sup>_xw_</sup> _v_<sup>, where</sup><sup>_θ_</sup> _v_<sup>_w_is the merchantable</sup> timber yield function, which is monotonically increasing in the average tree density of age _v_ . Forest land becomes eligible for harvest when planted trees reach a minimum age for merchantable timber, _<u>v</u>_ ~~.~~ Managed forest areas with the average density of oldest trees _v_ max have the highest yield of _θv_<sup>_w_</sup> max<sup>.Theydonot</sup> grow further and remain in this vintage until harvested.

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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 dierent age. With a continuous growth up to vintage _v_ max , the average long-run cost of harvesting per hectare of managed forest land, _c_<sup>_w_</sup> _,_ is therefore a declining 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, _c_<sup>_p_</sup> _,_ are invariant to scale.

The following equations describe the forestry sector: and 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 _v_ max . Equation (21) shows the transition from planted area, ∆ _L_<sup>_F,P_</sup> _t ,_ 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, _x_<sup>_w_</sup> _,_ into processed timber products, _y_<sup>_w_</sup> _,_ that are further consumed in nal demand. Similar to food processing, the purpose of this sector in the model is to capture the eciency gains from technology improvements in timber production, which result in lower requirements for forest products in nal demand.<sup>8</sup> The conversion

> 8For 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

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process is represented by a linear production function: where _θ_<sup>_w,y_</sup> is the technology index of timber processing, which captures the technological progress in both direct transformation of forest product into processed timber, and the quality improvements and durability of timber products. We assume that the timber processing costs per ton of food products, _c_<sup>_w,y_</sup> _,_ 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 dierent types of land to produce terrestrial ecosystem services. It is well known in both economic and ecological literatures that ecosystem services are dicult to dene, and it is therefore challenging to characterize their production processes (National Research Council 2005). This stems in part from the fact that there is signicant heterogeneity in ecosystem services (Costanza et al. 1997, Daily 1997), which include physical products (e.g., subsistence food and lumber), environmental services (e.g., pollination and nutrition cycling), and non-use goods which are valued purely for their continued existence (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 signicant dierences in denitions 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 important 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.

We assume that the per capita output of ecosystem services, _yt_<sup>_r,_isgivenby</sup> commercial demand for timber products.

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the following CES function of dierent land inputs: where the parameter _θ_<sup>_r_</sup> describes the technology index of ecosystem services production.<sup>9</sup> The parameters _α_<sup>_i,r_</sup> are the value shares of crop, pasture, and managed forest lands in production of ecosystem services at the benchmark time 0 _._ The parameter _ρr_ =<sup>_<u>σr</u>_</sup> _σ_<sup>_−_</sup> _r_<sup><u>1</u></sup> is a CES function parameter proportional to the elasticity of substitution of dierent types of land in production of ecosystem services, _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 ecient 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 _θ_<sup>_R_</sup> captures the relative eectiveness 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 nonland cost of producing ecosystem services (e.g., maintenance and infrastructure expenditures) per hectare of reserved natural land, _c_<sup>_R_</sup> _t_<sup>,isexogenousandscale-</sup> invariant.

In the technical appendix, section C.1, we discuss parameterization of ecosystem services production and costs.

# 2.11 Other Goods and Services

The production of other goods and services, _yt_<sup>_o_,inthismodelisexogenous.</sup> The reason we include it in this partial equilibrium model is to complete the

> 9We put the term technology in quotation terms because, as discussed above, characterizing 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.

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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.<sup>10</sup> 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-CO 2 emissions from use of nitrogen fertilizers in agricultural production, (d) non-CO 2 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 dierentiate between the emissions resulting from combustion of petroleum products and the emissions resulting from land use, _z_<sup>_L_</sup> _,_ 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 _μ_<sup>_f,e_</sup> tons of CO 2 equivalent (tCO 2 e). A ton of oil equivalent (toe) of fossil fuel converted to fertilizer emits _μ_<sup>_f,n_</sup> tCO 2 e. The conversion of natural forest land to commercial land entails emissions of _μ_<sup>_L_</sup> tCO 2 e per hectare of land deforested. A ton of fertilizer applied to agricultural land emits _μ_<sup>_n_</sup> tCO 2 e.

The livestock emissions are calculated as a sum of emissions per hectare of pasture land (e.g., due to manure left on pastures), _μ_<sup>_P_</sup> , and emissions per ton of livestock produced (e.g., due to enteric fermentation), _μ_<sup>_l_</sup> .

GHGs can also be reduced by carbon forest sequestration.<sup>11</sup> A hectare of

> 10The economy's output has a small fraction of endogenously determined output from landuse. We ignore this complication in this partial-equilibrium model.

> 11GHG 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.

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forest vintage _v_ sequesters _μ_<sup>_w_</sup> _v_<sup>tCO2e.Youngforestvintagesgrowquicklyand</sup> 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_ ) _μ_<sup>_h_</sup> _v_<sup>tCO2eperhectareoflandharvested,where</sup> _μ_<sup>_h_</sup> _v_<sup>isthecarbonstockassociatedwithharvestedtreevintage</sup><sup>_v,_and</sup><sup>_φ_isthe</sup> 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 and 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. Specically, we assume that at any point of time net GHG emissions from deforestation, application of fertilizers, and forest sequestration cannot exceed the emissions' quota, _<u>z</u>_<sup>_~~L~~_</sup> _._ 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 reected in exogenous prices of fossil fuels, which aect the demand for fossil fuels. Finally, because biofuels provide a renewable alternative to fossil fuels, we credit the emissions' quota, _<u>z</u>_<sup>_L_</sup> _,_ by the fraction of fossil fuels' emissions displaced by the biofuels.<sup>12</sup>

> 12This 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.

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The resulting relationships for emissions control are where global warming intensity, _θt_<sup>_z_is a function determining the evolution of the</sup> GHG emissions' quota over time, and _μ_<sup>_b,_1</sup> and _μ_<sup>_b,_2</sup> 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 specic 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 motivated by its several important advantages over other functional forms underpinning standard models of consumer demand.<sup>13</sup> First, similar to the well-known AIDS demand system (Deaton and Muellbauer 1980) the AIDADS model is exible in its treatment of Engel eects, 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.<sup>14</sup> This is essential for solution of the model over a wide range of quantities. In addition, a number of studies (Craneld et al. 2003, Yu et al. 2004) have demonstrated that AIDADS outperforms other popular models of consumer demand 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

> 13The most popular demand systems estimated in recent applied work are the Homothetic Cobb-Douglas System (HCD), the Linear Expenditure System (LES), the Constant Dierence of Elasticities Demand System (CDE), and the Almost Ideal Demand System (AIDS).

> 14One 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).

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function (Hanoch 1975): where _q_ = _{g, l, e, w, r, o}_ is the consumption bundle, _u_ is the utility level obtained from the consumption of goods or services _y_<sup>_q_</sup> , and _F_ ( _y_<sup>_q_</sup> _, u_ ) is a twicedirentiable monotonic function that is strictly quasi-concave in _y_<sup>_q_</sup> . Based on Rimmer and Powell (1996), the functional form for _F_ ( _y_<sup>_q_</sup> _, u_ ) is In equation (29) the parameters _αq_ and _βq_ dene the varying marginal budget shares of goods and services _y_<sup>_q_</sup> in the consumers' total real expenditures. The parameter _γ_<sup>_q_</sup> denes the subsistence level of consumption of goods and services _q._ The functional form of _F_ ( _y_<sup>_q_</sup> _, u_ ) implies that the consumption of goods and services _y_<sup>_q_</sup> is always greater than their subsistence levels, _γ_<sup>_q_</sup> _._ The parameter _A_ aects the curvature of the transformation function _F_ ( _y_<sup>_q_</sup> _, 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 _γ_<sup>_q_</sup> 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: where _pq_ are prices - or in this case, the marginal valuation - of goods and services _y_<sup>_q_</sup> 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.

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## 2.14 Welfare

The objective of the planner is to maximize the welfare function, Ω _,_ dened as the sum of net aggregate surplus discounted at a constant rate _δ >_ 0 _,_ and the bequest value of unmanaged and commercial forest areas.<sup>15</sup> 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 allocates commercial land for agricultural crops, livestock, and timber production, and the scarce fossil fuels and reserved natural forest land to solve the following problem: 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 eect 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 baseline 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

> 15We do not consider the bequest value of protected forests, as they cannot be scrapped in our model.

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Figure 1: Model Baseline <!-- Start of picture text --> Allocation of Land Land Based GHG Emissions<br>6 200<br>9<br>8 4 150 Natural Land<br>7 Protected Forests 100 Conversion<br>6 Unmanaged Forests 2 50 Livestock<br>5 Managed Forests 0 0 Biofuels' Offsets<br>43 Pasture LandBiofuel Crops -2 -50 Use of Fertlizers<br>2 Livestock Feed -100 ForestSequestration<br>1 Food Crops -4 -150 Net GHGAccumulation<br>0 -6 -200<br>2005 2030 2055 2080 2105 2005 2030 2055 2080 2105<br>Land Based Goods and Services Consumption of Biofuels<br>600 40%<br>1800<br>1600 500 35%<br>1400 30% Consumption of 2g<br>1200 Ecosystem Sevices 400 25% Biofuels<br>1000800 Processed TimberEnergy Services 300 20% Consumption of 1gBiofuels<br>600 Processed Livestock 200 15% Share of Biofuels in<br>400 Processed Crops 10% Liquid Fuel<br>200 100 Consumption<br>5%<br>0<br>2005 2030 2055 2080 2105 0 0%<br>Note. Real terms, base year =2004 2005 2030 2055 2080 2105<br>Billion Ha GtCO2e/yr GtCO2e<br>Million toe<br>USD per person<br><!-- End of picture text --> 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 insignicant. By mid-century, slower population 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 intensication of livestock production. Pasture land continues to decline, reaching 2.33 billion hectares, which is 15 percent smaller than 2004. Area dedicated to animal feed increases signicantly to reach 0.73 billion hectares, which is nearly six times greater than 2004. Rising energy prices in the baseline result in signicant growth in the land area dedicated to biofuels, which reaches 0.14 billion hectares by 2100. Managed forest area is little 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 signicantly to 0.68 billion hectares (about three times greater than 2004) in 2100.

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The upper right-hand panel in Figure 1 reports gross land based annual GHG emissions ows and their net accumulation over time.<sup>16</sup> Positive bars in this panel denote emissions, whereas negative bars denote GHG abatement through forest sinks and biofuels osets. Conversion of natural forest lands is a significant driver of land-based GHG emissions in the near term, which amounts to 3.2 GtCO 2 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 fertilizers 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 GtCO 2 e/yr, which is 40 percent larger than 2004. Continued growth in consumption of meat and dairy products results in a signicant increase in GHG emissions from livestock. In 2100, annual ows of GHG emissions from livestock amount to 1.84 GtCO 2 e/yr, which is 2.2 times larger than 2004. GHG emissions sequestration from managed forests does not change signicantly. In 2100 sequestered GHG emissions amount to 2.1 GtCO 2 e/yr, which is about 5 percent smaller than 2004. GHG emissions osets from biofuels are insignicant in the near term. With the arrival of commercial scale production of second generation biofuels, these become a signicant source of land based GHG abatement due to their low emissions intensity relative to petroleum (Dunn et al. 2011). In 2100 annual biofuels osets account for 1.4 GtCO 2 e/yr. Overall, accumulation of land based GHG emissions increases in the rst part of this century, reaching its maximum of 80 GtCO 2 e around 2040. It then declines in the second part of the century reaching 12 GtCO 2 e by 2100. Declining population growth, accompanied by rising agricultural productivity, along with higher oil prices, expansion of biofuels, 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 consumption 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

> 16As 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 consumption 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 signicant 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 economic studies on bioenergy and land use (Gurgel et al. 2007, Chakravorty et al. 2011, Popp et al. 2011).<sup>17</sup>

# 4 Counterfactual Scenarios

Private and public land allocation decisions must be made despite signicant uncertainty about the future productivity of land in dierent 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

> 17Direct comparison of model predictions of biofuels penetration is dicult due to considerable uncertainty in variety of factors, such as, e.g., evolution of biofuels' production technologies, 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, _c_<sup>_f_</sup> _,_ and the future valuation of GHG abatement, expressed through the stringency of the GHG emissions constraint, _<u>z</u>_<sup>_~~L~~_</sup> . To do this, we utilize the model to simulate the eects of the following scenarios, each of which has the potential to put greater pressure on the world's land resources:<sup>18</sup> Scenario A: The permanent decline in potential food crop yields due to adverse eects 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 CO 2 in the atmosphere results in an increase in potential yields due to the CO 2 fertilization eect (Long et al. 2006). When temperature increases are moderate, as we assume in the model baseline, these eects oset each other, and the food crop yields are unaected by the climate change. In scenario A we consider rapid warming, corresponding to Representative Concentration Pathways 8.5 GHG forcing scenario (Moss et al. 2008), so the former eect quickly dominates the latter. We assume that yields of celluslosic feedstocks do not change under scenario A, as they appear to be relatively insensitive to further temperature increases (Brown et al. 2000).

Scenario E: The permanent increase in growth of liquid fossil fuel costs over the medium term. Petroleum and natural gas prices are key factors aecting 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).<sup>19</sup> 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

> 18We show the model sensitivity to changes in other important model parameters in technical appendix, section E.1.

> 19Of 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 motivated 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 emissions 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.<sup>20</sup> In this scenario we introduce a maximum target, amounting 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 scenarios A, E, and T (scenario AET). We assume that all of these alternative scenarios are fully anticipated so that their eect 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.

> 20In 2008 New Zealand passed legislation to include commercial forestry sector in the emissions 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 Agriculture <!-- Start of picture text --> Change in Land Use Relative to Baseline Change in GHG Emissions Relative to Baseline<br>40<br>200 10 Natural Land<br>30 Food Crops 150 8 Conversion<br>20 Livestock Feed 100 6 Livestock<br>10 Biofuels Crops 50 42 BiofuelsOffsets<br>0 Pasture Land 0 0 Use of<br>-10 Protected Forests -50 -2 Fertilizers<br>-20 Managed ForestsUnmanaged Forests -100 -4-6 ForestSequestration<br>-30 -150 -8 Net GHG<br>Accumulation<br>-40 -200 -10<br>2005 2030 2055 2080 2105 2005 2030 2055 2080 2105<br>Change in Consumption of Land Based Good Change in Consumption of Biofuels Relative to<br>and Services Relative to Baseline Baseline<br>0 10 6%<br>8<br>-10 6 4%<br>-20 Processed Livestock 4 2% Consumption of 2gBiofuels<br>-30 Ecosystem Services 2<br>-40 Processed Timber -20 0% Consumption of 1gBiofuels<br>-50 Energy ServicesProcessed Grains -4 -2% Share of Biofuels in<br>-60 -6-8 -4% Liquid FuelConsumption<br>-70 -10 -6%<br>2005 2030 2055 2080 2105 2005 2030 2055 2080 2105<br>Million Ha MtCO2e/yr GtCO2e<br>USD Per Person Million toe<br><!-- End of picture text --> 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 potential 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 cropland 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 GtCO 2 e in 2100. The most signicant eects 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 MtCO 2 e/yr by 2045. In the long term, the increases in GHG emissions from increased use of fertilizers, reduced forest sequestration and smaller biofuels osets 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 consumption 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 signicant 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 reduction 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 biofuels. 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 aect 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 eect of permanent increase in the rate of growth in liquid fossil fuel costs over the medium term to the eect 27
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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 intensication of agricultural production. Compared to scenario A, agricultural areas dedicated to biofuels feedstocks expand signicantly, 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, respectively, 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 MtCO 2 e/yr (10 percent) compared to scenario A, and continue to be signicant 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 osets and the decline in fertilizers' use grow by 700 and 95 MtCO 2 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 GtCO 2 e in 2025, and decline thereafter to a level 15 GtCO 2 e lower than scenario A by 2100.

The lower left-hand panel in Figure 3 shows the results for changes in percapita consumption of goods and services that draw on land resources. The expansion of the biofuels sector results in an increase in consumption of bioenergy 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 signicant 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 signicant 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 eect of adding the land-use GHG emissions constraint starting in 2025 to the eects of a permanent increase in the rate of growth in liquid fossil fuel costs in midcentury 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 eect 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 eective 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
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of the GHG constraint puts signicant 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 annual 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 signicantly reduces the eectiveness 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 GtCO 2 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 GtCO 2 e/yr, immediately after the target is introduced. In the long term, greater GHG sequestration by managed 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 GtCO 2 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 osets is 5 MtCO 2 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 mitigation from fertilizers use and livestock farming and management decline by 112 MtCO 2 e/yr and 200 MtCO 2 e/yr, respectively.

Overall, in the presence of intertemporal substitution, the land based GHG emissions target appears to be rather ineective over the 100 year time horizon. Preceding the introduction of the constraint, cumulative GHG emissions increase by 97 GtCO 2 e. After the introduction of the constraint, the GHG emissions from land use cumulatively decline by 114 GtCO 2 e. The resulting intertemporal leakage (the ratio of cumulative increase in GHG emissions preceding the GHG target to cumulative decline after the GHG target) is 85 per32
# cent.<sup>21</sup>

The lower left-hand panel in Figure 4 shows the results for changes in percapita consumption of goods and services that draw on land resources. Introduction 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 declines 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 consumption 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 biofuels. Introduction of the GHG emissions constraint favors the displacement of petroleum products by biofuels. However, the expansion of second generation 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 signicantly 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 incrementally, however, it is also relevant to consider their combined eect. 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 foodfuel tradeo as well as raising the cost of intensication, 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, consumption 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 eect of higher energy prices and climate regulations induces a signicant 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

> 21The size of intertemporal leakage is reduced to 37 percent over the period of 200 years.

33
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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 additional 128 million hectares (5.5 percent) in 2100. The combined eect of adverse climate impacts on crop yields, higher energy prices and climate regulations thus results in a signicant 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 signicant 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 signicantly reduced in favor of commercial services from land.

The next most important parameter for setting the optimal prole of land use over the 21st century is the elasticity of substitution between fertilizer and land which governs the ease of intensication. 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 eect on the deviations from the baseline due to our three scenarios: A, AE and AET.<sup>22</sup> In other words, while they do make a dierence in the baseline, they have little

> 22The 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
eect 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 determined 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 Research 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 signicant 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 classication) 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 unied economic framework, which integrates 36
ve rather distinct strands of literature into a single, intertemporally consistent, 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 reects developments in global land use over the 10 years that have already transpired, while also incorporating long-run projections of population, income and demand growth from a variety of international agencies. The model baseline suggests that, even in the absence of GHG regulations, deforestation 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 signicant 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 sacrice 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 important 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 curtail food production, requiring additional cropland and encouraging additional fertilizer use, thereby leading to higher GHG emissions. Energy prices aect the optimal deforestation rate as well as the overall amount of land used in agriculture. 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 intensication. Substantially more deforestation occurs under this scenario and the increased GHG emissions from land use change outweigh the emissions fall from displacement of petroleum consumption 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 signicant. While the introduction of the land based GHG emissions constraint leads to a signicant reduction in GHG emission ows over the 21st century, its eectiveness 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 benets of such a policy.

When all three `scenarios' are simultaneously realized, the world's land resources face a `perfect storm' in which the cost of agricultural intensication is higher, biofuels expand their area, additional cropland is needed to oset 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 signicantly lower, highlighting the potential for intense competition for land in the production of the world's food, fuel and environmental services over the 21st century.

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45
# Technical Appendix

<!-- Start of picture text --> Gen. Fertilizers<br>nd<br>2 Biofuels<br>Energy Services Cellulosic Fossil Fuels<br>Feedstocks<br> Gen.<br>st<br>1 Biofuels Land<br>Food<br>Agricultural<br>Processed<br>Food Crops<br>Land<br>GHG Emissions Livestock Feed Commercial<br>Welfare Livestock Pasture Land<br>(Multiple Vintages) Land<br>Timber Timber Forest Land<br>Processed Forests<br>Unmanaged<br>Forests<br>Services Protected<br>Ecosystem<br>Other Goods and Services<br><!-- End of picture text --> Figure A.1: Structure of the Economy 1
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~~“~~ EO© OC ~~7~~ () () tC)|

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> > ( )] (> )

~~~~~ y () yoo ~~)~~ y y
~~C~~ C ~~)~~ ) ~~—— (—)~~ <u>-</u> > CO ()
Table B.2: Model Endogenous Variables

|Parameter|Description|Units|
|---|---|---|
|_L_<sup>_C,i_</sup><br>_t_<br>|Agricultural Land Area of Crop _i_|GHa|
|_L_<sup>_P_</sup><br>_t_<br>|Pasture Land Area|GHa|
|_L_<sup>_F_</sup><br>_t_|Commercial Forest Land Area|GHa|
|_L_<sup>_U_</sup><br>_t_<br>|Unmanaged Natural Lands|GHa|
|∆_L_<sup>_U,M_</sup><br>_t_|Flow of Deforested Natural Lands per annum|GHa|
|_L_<sup>_R_</sup><br>_t_<br>|Protected Natural Lands|GHa|
|∆_L_<sup>_U,R_</sup><br>_t_<br>|Flow of Protected Natural Lands per annum|GHa|
|∆_L_<sup>_F,P_</sup><br>_t_|Replanted Forest Land Area|GHa|
|∆_L_<sup>_F,H_</sup><br>_v,t_<br>|Harvested Forest Land Area of Vintage _v_|GHa|
|_c_<sup>_C,i_</sup><br>_t_<br>|Shadow Prices of Agricultural Areas|GHa|
|_x_<sup>_f_</sup><br>_t_<br>|Fossil Fuels|Gtoe|
|_x_<sup>_f,e_</sup><br>_t_<br>|Petroleum Combusted|Gtoe|
|_x_<sup>_f,n_</sup><br>_t_|Fossil Fuels Allocated to Fertilizers|Gtoe|
|_x_<sup>_n_</sup><br>_t_<br>|Fertilizers Produced|Gton|
|_x_<sup>_g,i_</sup><br>_t_<br>|Agricultural Output of Crop _i_|Gton|
|_x_<sup>_l,g_</sup><br>_t_<br>|Animal Feed|Gton|
|_x_<sup>_l_</sup><br>_t_<br>|Livestock Product|Gton|
|_y_<sup>_f_</sup><br>_t_|Services from Processed Grains||
|_y_<sup>_l_</sup><br>_t_<br>|Services from Processed Livestock||
|_x_<sup>_b,i_</sup><br>_t_|First (_i_= 1) and Second (_i_= 2) Generation Biofuels|Gtoe|
|_y_<sup>_e_</sup><br>_t_|Energy Services||
|_x_<sup>_w_</sup><br>_t_|Forest Product|Gton|
|_y_<sup>_w_</sup><br>_t_|Services from Processed Timber||
|_y_<sup>_r_</sup><br>_t_|Eco-system Services||
|_z_<sup>_L_</sup><br>_t_|GHG Emissions from Land Use|GtCO2e|
|_zt_|GHG Emissions|GtCO2e|

6
# C.1 Empirical Implementation of FABLE

The model baseline extends for a period of 200 years, with an emphasis on the rst century, and the starting point being the world economy in 2004. It is consistent with the IPCC (2000) A1B climate change scenario's storyline that describes a future world of strong economic growth, global population that grows quickly until mid-century and slows thereafter, the rapid introduction of new and more ecient technologies, and balanced energy use across all sources. It also foresees that, as the economy grows, its economic structure changes toward a service economy, including the expansion of ecosystem services sector. The majority of model's baseline parameters are based on the Global Trade Analysis Project (GTAP) v.7 data base (Hertel 1997, Narayanan and Walmsley 2008) and its satellite data for land use and global climate change policy (Hertel et al. 2009). The values of other model parameters come from variety of the international or government agencies (United Nations, FAO, U.S. Energy Information Administration) and economic, agronomic and environmental science literatures. The values of baseline parameters are summarized in Table B.3 and Figure C.1.

## C.1.1 Population

We assume that the population, Π _t,_ follows logistic (Verhulst) model with declining growth rates over time: where Π0 is level of population in 2004 _,_ Π _T_ is the limiting population in 2104 _,_ and _π_ is the population growth rate. Compared to standard exponential growth assumption the logistic model provides a better t to demographic projections, and has been recently adapted in the economic literature (Guerrini 2006, Bucci and Guerrini 2009, Guerrini 2010). Data on population in 2004 are from GTAP v.7 database. The estimate of limiting population is from United Nations Department of Economic and Social Aairs Population Division (2011). The logistic growth rate of population is calibrated to match United Nations Department of Economic and Social Aairs Population Division (2011) demographic projections.

7
||Table B.3: Baseline Parameters|||
|---|---|---|---|
|Parameter|Description|Units|Value|
|Population||||
|Π0|Population in 2004|Billion People|6.39|
|Π_T_|Population in time T<br>|Billion People|10.1|
|_π_|Logistic Population Growth Rate||0.042|
|Land Use||||
|_L_<br>|Total Land Area|Billion Ha|5.83|
|_L_<sup>_C,_1</sup><br>0|Area of Agricultural Land in 2004|Billion Ha|1.533|
|_L_<sup>_C,_2</sup><br>0|Area of Cellulosic Feedstocks in 2004|Billion Ha|0.0001|
|_L_<sup>_P_</sup><br>0<br>|Area of Pasture Land in 2004|Billion Ha|2.73|
|_L_<sup>_F_</sup><br>0|Area of Commercial Forest Land in 2004|Billion Ha|1.62|
|_L_<sup>_U_</sup><br>0|Area of Unmanaged Natural Land in 2004|Billion Ha|2.47|
|_L_<sup>_R_</sup><br>0|Area of Protected Natural Land in 2004|Billion Ha|0.207|
|_ξ_<sup>_u_</sup><br>1|Natural Land Access Cost Function Parameter||0.264|
|_ξ_<sup>_u_</sup><br>2|Natural Land Access Cost Function Parameter||42,000|
|_ξ_<sup>_R_</sup><br>0|Protection Cost Function Parameter||5|
|_ξ_<sup>_R_</sup><br>1|Protection Cost Function Parameter||300|
|Fossil Fuels<br>||||
|_c_<sup>_f_</sup><br>0<br>|Oil Price in 2004|1000USD/toe|0.242|
|_c_<sup>_f_</sup><br>_T_|Oil Price in time T|1000USD/toe|1.84|
|_κ_|LoisticOilPriceGrowthRate||0045|
|_f_|g||.|
|Agrochemica|l Sector|||
|_c_<sup>_n_</sup>|Non-Energy Fertilizer Costs|1000USD/ton|0.137|
|_x_<sup>_n_</sup><br>0|Fertilizers' Consumption in 2004|Billion ton|0.937|
|_θ_<sup>_n_</sup><br>_t_|Fertilizer's Conversion rate|ton/toe|1.07|
|Agricultural <br>|Sector|||
|_θ_<sup>_g,c_</sup><br>0|Food Crop Yield in 2004|tons / Ha|4.89|
|_θ_<sup>_g,c_</sup><br>_T_|Food Crop Yield in time T|tons / Ha|9.29|
|_κg,c_|Logistic Food Crop Yield Growth Rate||0.025|
|_θ_<sup>_g,b_</sup><br>0|Cellulosic Feedstocks Yield in 2004|tons / Ha|21.4|
|_κg,b_<br>|Cellulosic Feedstocks Yield Growth Rate p.a.||0.115|
|_c_<sup>_g,b_</sup>|Non Land Cost of Cellulosic Feedstocks|1000USD/ton|0.161|

8
Table A.3: Baseline Parameters (continued)

|Parameter|Description|Units|Value|
|---|---|---|---|
|_a_<sup>_g_</sup>|Share of Agricultural Land in CES function||0.55|
|_ρg_|CES Parameter for Agricultural Land and Fer-<br>tilizers||0.123|
|Livestock F|arming Sector|||
|_θ_<sup>_l_</sup>|Livestock Technology Index||0.69|
|_a_<sup>_l_</sup>|Share of Pasture Land in CES function||0.35|
|_ρl_|CES Parameter for Pasture Land and Animal||-0.33|
||Feed|||
|_c_<sup>_l_</sup><br>0|Livestock Processing Cost|1000USD/ton|0.21|
|_ξ_<sup>_l_</sup><br>0|Adjustment Cost Function Parameter||300|
|Food Proce|ssing Sector|||
|_θ_<sup>_g,y_</sup><br>0|Crop Processing Technology Index in 2004||1.5|
|_κg,y_|Crop Processing Technology Growth Rate p.a.||0.022|
|_c_<sup>_g,y_</sup>|Crop Processing Cost|1000USD/ton|0.081|
|_θ_<sup>_l,y_</sup><br>0|Livestock Processing Technology Index in 2004||1.7|
|_κl,y_|Livestock Processing Technology Growth Rate||0.022|
|_c_<sup>_l,y_</sup>|Livestock Processing Cost|1000USD/ton|0.27|
|Biofuels Se<br>|ctor<br>|||
|_θ_<sup>_b,_1</sup>|1G Biofuels' Conversion Rate|toe/ton|0.283|
|_c_<sup>_b,_1</sup>|Non Land Cost of 1G Biofuels|1000USD/ton|0.442|
|_θ_<sup>_b,_2</sup>|2G Biofuels' CES Production Technology||0.467|
|_c_<sup>_b,_2</sup>|Non Land Cost of 2G Biofuels|1000USD/ton|0.577|
|_a_<sup>_b_</sup>|Share of Fixed Factor in CES function||0.4|
|_ρb_|CES Parameter for Cellulosic Feedstocks and<br>||-1.5|
||Fixed Factor|||
|_φ_0|Fixed Factor Endowment in 2004||0.05|
|_κ_<sup>_φ_</sup>|Growth of Factor Specic Tech. Change p.a.||1.005|
|Energy Sec|tor|||
|_ρe_|CES Parameter for Drop-in Fuels and 1G Biofu-<br>els||0.5|
|_α_<sup>_e_</sup>|Share of 1G Biofuels in CES Function||0.09|
|_θ_<sup>_e_</sup><br>0|Energy Eciency Index in 2004||1.195|
|_κe_|Energy Eciency Growth Rate p.a.||0.016|

9
Table A.3: Baseline Parameters (continued)

|Parameter<br>Description|Units|Value|
|---|---|---|
|Forestry Sector|||
|_ξ_<sup>_w_</sup><br>0<br>Forest Harvesting Cost|1000USD/ton|0.019|
|_ξ_<sup>_w_</sup><br>1<br>Forest Harvesting Adjustment Cost|1000USD/Ha|150,000|
|_ξ_<sup>_w_</sup><br>2<br>Forest Conversion Adjustment Cost|1000USD/Ha|300|
|_c_<sup>_p_</sup><br>Forest Regeneration Cost|1000USD/Ha|0.036|
|_κ_<sup>_w_</sup><br>_v_<br>Yield Gains per annum of Vintage v|Share of Yield 0|0.011|
|_ψ_1<br>Merchantable Timber Yield Parameter 1||5.75|
|_ψ_2<br>Merchantable Timber Yield Parameter 2||75|
|_v_<br>Minimum Age for Merchantable Timber|Years|11|
|Timber Processing Sector|||
|_θ_<sup>_w,y_</sup><br>0<br>Timber Processing Technology Index in 2004||15.2|
|_κw,y_<br>Timber Processing Technology Growth Rate p.a.||0.022|
|_c_<sup>_w,y_</sup><br>Timber Processing Cost|1000USD/ton|1.74|
|Ecosystem Services Sector|||
|_ρe_<br>CES Parameter for Ecosystem Services||0.123|
|_θ_<sup>_r_</sup><br>Technology Parameter for Ecosystem Services||0.64|
|_α_<sup>_C,r_</sup><br>Share of Agricultural Lands in CES Function||0.02|
|_α_<sup>_P,r_</sup><br>Share of Pasture Lands in CES Function||0.14|
|_α_<sup>_F,r_</sup><br>Share of Managed Forest Lands in CES Function||0.26|
|_θ_<sup>_R_</sup><br>Eectiveness of Protected Lands||10|
|_κR_<br>Decline in Costs of Managing Protected Lands||0.022|
|p.a.|||
|_c_<sup>_R_</sup><br>0<br>Cost of Managing Protected Land in 2004|1000USD/Ha|0.175|
|Other Goods and Services|||
|_o_0<br>Output of Other Goods and Services in 2004|10000USD|0.95|
|_θ_<sup>_o_</sup><br>0<br>TFP in 2004||1|
|TFPh||0022|
|_κo_<br> growt rate per annum||.|
|GHG Emissions<br><br>|||
|_μ_<sup>_L_</sup><br>GHG Emissions from Natural Land Conversion|tCO2e per Ha|515|
|_μ_<sup>_g_</sup><br>GHG Emissions from Fertilizers|tCO2e per ton|4.066|

10
Table A.3: Baseline Parameters (continued)

|Parameter|Description|Units|Value|
|---|---|---|---|
|_μ_<sup>_b,_1</sup>|GHG Emissions from Combustion of 1G Biofuels|tCO2e per toe|1.729|
|_μ_<sup>_b,_2</sup>|GHG Emissions from Combustion of 2G Biofuels|tCO2e per toe|0.609|
|_μ_<sup>_x_</sup><br>|GHG Emissions from Petroleum Combustion|tCO2e per toe|2.902|
|_μ_<sup>_P_</sup>|GHG Emissions from Manure on Pasture Land|tCO2e per Ha|0.208|
|_μ_<sup>_l_</sup>|GHG Emissions from Livestock|tCO2e per ton|4.641|
|_μ_<sup>_~~w~~_</sup>|Forest Carbon Stocking Density|MgC per _m_<sup>3</sup>|1.1|
|_φ_|Share of Stored Carbon in Harvested Forest<br>Products||0.3|
|Preferences|and Welfare Parameters|||
|_αg_|AIDADS Marginal Budget Share at Subsistence<br>Income for Processed Grain Products||0.21|
|_αl_|AIDADS Marginal Budget Share at Subsistence<br>Income for Processed Livestock Products||0.14|
|_αe_|AIDADS Marginal Budget Share at Subsistence<br>Income for Energy Services||0.11|
|_αw_|AIDADS Marginal Budget Share at Subsistence<br>Income for Processed Timber Products||0.03|
|_αr_|AIDADS Marginal Budget Share at Subsistence<br>Income for Ecosystem Services||0.02|
|_αo_|AIDADS Marginal Budget Share at Subsistence<br>Income for Other Goods and Services||0.49|
|_βg_|AIDADS Marginal Budget Share at High Income<br>for Processed Grain Products||0.03|
|_βl_|AIDADS Marginal Budget Share at High Income<br>for Processed Livestock Products||0.04|
|_βe_|AIDADS Marginal Budget Share at High Income<br>for Energy Services||0.05|
|_βw_|AIDADS Marginal Budget Share at High Income<br>for Processed Timber Products||0.02|
|_βr_|AIDADS Marginal Budget Share at High Income<br>for Ecosystem Services||0.05|
|_βo_|AIDADS Marginal Budget Share at High Income<br>for Other Goods and Services||0.81|

11
Table A.3: Baseline Parameters (continued)

|Parameter|Description|Units|Value|
|---|---|---|---|
|_γ_<sup>_g_</sup>|AIDADS Subsistence Parameter for Processed<br>Grain Products||0.33|
|_γ_<sup>_l_</sup>|AIDADS Subsistence Parameter for Processed<br>Livestock Products||0.003|
|_γ_<sup>_e_</sup>|AIDADS Subsistence Parameter for Energy Ser-<br>vices||0.03|
|_γ_<sup>_w_</sup>|AIDADS Subsistence Parameter for Processed<br>Timber Products||0.03|
|_γ_<sup>_r_</sup>|AIDADS Subsistence Parameter for Ecosystem<br>Services||0.03|
|_γ_<sup>_o_</sup>|AIDADS<br>Subsistence<br>Parameter<br>For<br>Other<br>Goods and Services||0.35|
|_A_|AIDADS Utility Function parameter||1|
|_δ_|Social Discount Rate||0.015|
|_π_1|Scrap Price of Unmanaged Forests||50|
|_π_2|Scrap Price of Commercial Forests||10|
|_δ_|Social Discount Rate||0.015|

12
<!-- Start of picture text --> The<br>a<br><!-- End of picture text -->
# C.1.2 Resource Use

## C.1.2.1 Land

The data for the total land and commercial land endowments come from the GTAP Integrated Global Land Use Data Base (Lee et al. 2009) and GTAP Global Forestry Data Base (Sohngen et al. 2009b). We dene the initial amount of commercial land as the sum of crop land, pasture land, and managed (accessible) forest land areas. The initial amount of natural land is dened as the area of unmanaged (inaccessible) forest land. Other land areas, such as builtup lands, grasslands, savannah, shrublands, desserts, and barren lands, are not included in the current version of the model. The data for initial allocation of natural lands come from Antoine et al. (2008, p.8, Table 3).

Following past literature on land access modelling (Gouel and Hertel 2006, Golub et al. 2009) we assume that marginal natural land access cost per hectare is given by: In equation (C.2), the variable _c_<sup>_u_</sup> _t_<sup>referstothemarginalaccesscost,im-</sup> plied by the marginal valuation of non-reserved natural land. The parameter _ξ_ 1<sup>_N_determinesthelong-runelasticityofnaturallandaccesscostswithrespect</sup> to cumulatively accessed hectares, which eventually becomes innite as the remaining non-reserved natural land is exhausted. The parameter _ξ_ 2<sup>_N_governs the</sup> size of the short-term adjustment costs. We assume that additional costs per hectare of converting natural land to protected land are given by In equation (C.3), the parameter _ξ_ 0<sup>_R_referstothelong-runtime-invariant</sup> costs of protecting land. The parameter _ξ_ 1<sup>_R_governsthesizeoftheshort-term</sup> adjustment costs. We set the value of the marginal access cost, _c_<sup>_u_</sup> _t_<sup>_,_equalto</sup> the shadow price of agricultural lands dedicated to food crops (see equation C.8 below). The parameter values dening natural land access cost function (C.2), and natural land protection cost function (C.3) are calibrated based on FAO (2010) data to match deforestation rates in 2004 and ensure stable rates of natural land access and protection.

14
## C.1.2.2 Fossil Fuels

The primary fossil fuels linked to the economic analysis of land use are petroleum products and natural gas. Biofuels substitute for petroleum products and, to lesser extent, natural gas, in energy demand for transportation services. The natural gas is also the key input in nitrogen fertilizers' production. As petroleum products' and natural gas prices are closely related in the long run (Hartley et al. 2008), we use the crude oil price as a reference cost of fossil fuels. Following the U.S. Energy Information Administration (EIA) projections (EIA 2010a)we assume that the cost of fossil fuels is logistic function with declining growth over time: where the parameters _c_<sup>_f_</sup> 0<sup>,and</sup><sup>_cf_</sup> _T_<sup>,reecttheoilpricesinthebeginningand</sup> 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 fertilizers, 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- intensive. They are also critical to boosting yields in response to scarcity of land.<sup>1</sup> We use the FAOSTAT database<sup>2</sup> to obtain the global production of nitrogen fertilizers in 2004. For fertilizers' production costs and conversion rates we consider anhydrous ammonia (NH 3 ), which is one of the most common nitrogen fertilizers. We use USDA ERS fertilizer use and price dataset<sup>3</sup> to obtain the fertilizers' price. We then subtract the fossil fuels' price from the fertilizers'

> 1Note 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.

> 2Thorough description of the FAOSTAT database is available from the following website: http://faostat.fao.org/.

> 3Thorough 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 fertilizers in 2004 are calibrated from known values of agricultural output, fertilizers, and the agricultural land as described in Rutherford (2002). Based on the agronomic literature (Cassman 1999, Cassman et al. 2010) we assume that crop technology index, _θ_<sup>_g,c_</sup> is a logistic function with declining growth over time: where _θ_ 0<sup>_g,c_</sup> is the initial value of crop technology index, _θT_<sup>_g,c_</sup> is crop yield potential, i.e., the yield an adapted crop cultivar can achieve when crop management 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 signicant 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 they reach 7080% of the potential yield, _θT_<sup>_g,c_.</sup> As regards the cellulosic feedstocks, we assume that their yield grows linearly across time, adding a constant amount of technology gain per annum 16
where the parameters _θ_ 0<sup>_g,i_</sup> 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 oset by CO 2 fertilization eect (Long et al. 2006). In contrast, second generation biofuels feed stocks benet 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, _c_<sup>_g,i_</sup> _,_ are given by where _c_<sup>_C,i_</sup> _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:

# C.1.5 Livestock Sector

The initial output of livestock products (measured as the global physical production 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.<sup>4</sup> 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 where _c_<sup>_l_</sup> 0<sup>captures the non-land cost per ton of livestock, and</sup><sup>_ξ_</sup> 0<sup>_l_captures the</sup> 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: where the parameters _θ_ 0<sup>_i,y_</sup> and _κi,y_ reect 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.

> 4see http://www.fas.usda.gov/psdonline, last accessed in August 2013.

18
# C.1.7 Biofuels Sector

In the model baseline we dene the rst-generation biofuels as a grain-based ethanol and the second generation biofuels as cellulosic biomass-to-liquid diesel obtained through Fischer-Tropsch gasication. The values for biofuels conversion rate and cost for ethanol and biomass-to-liquid diesel are taken from Taheripour and Tyner (2011). Following Winston (2009) we adjust the quantity 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-specic technological progress is described by the following equation: The rate of factor-specic 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-specic 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 substitution 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 eciency is described by the following equation: where the parameters _θ_ 0<sup>_e_and</sup><sup>_κe_reecttheinitiallevelandannualgrowth</sup> 19
rate in the energy eciency. We set the energy eciency in 2004 equal to one, and obtain the growth rate in the energy eciency from World Energy Council (2008).

# C.1.9 Forestry Sector

We set the number of forest tree vintages to 100 and assume that average densities of managed forest land corresponding to dierent 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 merchantable timber yield function is given by the following equation: In equation (C.13),the parameters _ψ_ 1 and _ψ_ 2 are growth parameters determining the support and the slope of the timber yield function, and _<u>v</u>_ is a minimum age for merchantable timber. The yield function (C.13) parameters, the minimum age for merchantable timber, and the average planting and harvesting 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: where the parameters _θv,_<sup>_w_</sup> 0<sup>and</sup><sup>_κw_</sup> _v_<sup>correspondtotheinitiallevelsandtech-</sup> 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 dierence in the average yields from global forest studies of Sedjo (1983) and Cubbage et al. (2010).

Forest harvesting costs are given by 20
where the parameters _ξ_ 0<sup>_w_,</sup><sup>_ξ_</sup> 1<sup>_w,_and</sup><sup>_ξ_</sup> 2<sup>_w_correspondtolong-runforesthar-</sup> vesting costs and short-run adjustment costs of harvesting and harvested land conversion to agricultural land. We calibrate short-run adjustment costs of harvesting 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: where the parameters _θ_ 0<sup>_w,y_</sup> and _κw,y_ reect the initial level and annual growth rate in the technology of the timber processing sector. We calculate the technology 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.<sup>5</sup> We exclude the services from the production of food and timber, as well as from based climate 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 dierentiate between tropical and temperate/boreal forest land. Based on ecological literature (Ehrlich and Mooney 1983) we assume that there is a limited substitution between different land types in production of ecosystem services. Because eectiveness of protected land areas is very dicult to quantify (Chape et al. 2005), we set the parameter _θ_<sup>_R_</sup> large enough to make sure new protected areas are established.

> 5We 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 inuential.

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.<sup>6</sup> 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: where the parameters _κR_ reect 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: where the parameters _θ_ 0<sup>_o_and</sup><sup>_κo_reecttheinitiallevelandannualgrowth</sup> 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 coecient from combustion of liquid fossil fuels comes from the US Energy Information Administration (EIA) website<sup>7</sup> . The GHG emission coecient 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

> 6Following Antoine et al. (2008), we dene 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.

> 7See http://www.eia.doe.gov/oiaf/1605/coefficients.html, last checked in August, 2013.

22
nitrogen equivalent mass of anhydrous ammonia using conversion factor of<sup><u>17</u></sup> 28<sup>_._</sup> 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 (NO 2 ) using conversion factor of<sup><u>44</u>Finally,wendthecarbondioxideequivalentofthe</sup> 28<sup>_._</sup> nitrogen dioxide using global warming potential of NO 2 _._ The GHG emissions coecients 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 nonreserved 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 lifecycle 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_ , _μ_<sup>_h_</sup> _v_<sup>,isgivenby:</sup> In equation (C.19) the parameter _<u>μ</u>_<sup>_~~w~~_</sup> is the carbon conversion factor, that accounts for the stocking density of specic timber types, whole tree factors, and forest oor carbon, and _ψ_ 1 and _ψ_ 2 are the parameters dening merchantable timber yield function from equation (C.13).<sup>8</sup> Then the amount of GHG sequestered by a hectare of forest land of tree vintage _v_ is 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).

> 8Note that the minimum age parameter, _<u>v</u>_ , 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_ dening 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 Craneld et al. (2003) and Yu et al. (2004). The parameters _<u>q</u>_ dene 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.<sup>9</sup> We parameterize the scrap value function as where the parameters _π_ 1 and _π_ 2 denote the scrap prices of unmanaged and commercial forests at the beginning of period _T_ . We calibrate the values of _π_ 1 and _π_ 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.<sup>10</sup>

# 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<sup>_◦_</sup> 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 CO 2 fertilization eects 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 CO 2 fertilization eect.

> 9For 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

> 10We have tried setting dierent values of _π_ 1 _,_ and the optimal path of natural land conversion was not signicantly aected 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_ ) dening the land-use GHG emissions' target is a logistic function: 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 <!-- Start of picture text --> 10 300<br>9<br>250<br>8<br>7<br>200<br>6<br>5 150<br>4<br>100<br>3<br>2<br>50<br>1<br>0 0<br>2005 2030 2055 2080 2105 2005 2030 2055 2080 2105<br>Baseline Scenario A Baseline Scenario E<br>120% 4.00<br>3.50<br>100%<br>3.00<br>80% 2.50<br>60% 2.00<br>1.50<br>40%<br>1.00<br>20% 0.50<br>0.00<br>0%<br>2025 2050 2075 2100<br>2025 2050 2075 2100<br>Scenario T Scenario T<br>Crop Yield, t/Ha Oil price, $/bbl<br>GHG Emissions as % of Baseline GHG Shadow Price Index, 2025 = 1<br><!-- End of picture text --> 25
Table C.1: Parameters for Counterfactual Scenarios

|Parameter|Description|Units|Value|
|---|---|---|---|
|Scenario A|(Declining Growth of Agricultural Yield)|||
|_θ_<sup>_g,c_</sup><br>_T_|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|GtCO2e||
|_zT_|GHG Emissions in 2104|GtCO2e|0.4_zτ_|
|_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 production of agricultural output, the costs and eciency of biofuels' production, energy eciency, and the demand for energy services. We show model baseline sensitivities with respect to the following changes<sup>11</sup> :

- 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 specic technological change,

- a 50% decline in energy eciency growth rate, and

> 11Because of 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 uncertainties. The additional results are available from authors upon request.

26
|AE<br>Scenario AET<br>(∆AE)<br>-38.7<br>-20.0<br>-34.7<br>16.0<br>-39.2<br>40.0<br>29.0<br>8.7<br>-167.7<br>-63.0<br>-6.5<br>-111.8<br>10.1<br>0.0<br>-7<br>-21<br>2<br>0<br>5<br>0<br>-27<br>6<br>-64<br>-76<br>-319<br>-161<br>12.4|
|---|
|T<br>Scenario<br>(∆A)<br>30.0<br>-25.0<br>-3.4<br>58.4<br>-8.0<br>-6.0<br>-11.0<br>-4.7<br>-419.2<br>-60.3<br>-27.8<br>-400.6<br>56.4<br>0.0<br>-25<br>-20<br>26<br>0<br>-2<br>0<br>-113<br>35<br>-57<br>29<br>-1162<br>-106<br>-8.4|
|Scenario <br>e)<br>-39.4<br>-27.0<br>-41.8<br>29.4<br>-41.0<br>53.0<br>22.0<br>5.2<br>-260.9<br>-87.2<br>-10.6<br>-270.2<br>36.0<br>0.0<br>-11<br>-28<br>4<br>0<br>4<br>0<br>-43<br>22<br>-87<br>-246<br>-790<br>-355<br>5.4|
|, 2050<br> A<br>Scenario E<br>on from Baselin<br>29.9<br>-27.0<br>-2.7<br>59.6<br>-8.0<br>-6.0<br>-11.0<br>-4.7<br>-437.9<br>-60.9<br>-26.2<br>-400.6<br>55.7<br>0.0<br>-27<br>-20<br>26<br>0<br>-2<br>0<br>-106<br>35<br>-58<br>28<br>-1161<br>-101<br>-8.2|
|ation Results<br>e<br>Scenario <br><br>(Deviati<br>16.9<br>11.0<br>8.7<br>-2.8<br>-4.9<br>-3.0<br>-7.0<br>-2.4<br>-242.2<br>-29.7<br>6.5<br>0.0<br>-2.7<br>0.0<br>-15<br>-10<br>0<br>0<br>-1<br>0<br>26<br>-2<br>-28<br>12<br>2<br>7<br>5.1|
|del Simul<br>Baselin<br>(Level)<br>1951<br>1459<br>399<br>93<br>2547<br>1587<br>2183<br>291<br>4407<br>890<br>128<br>773<br>314<br>2515<br>263<br>291<br>33<br>271<br>259<br>0<br>519<br>195<br>1241<br>-2029<br>2240<br>-74<br><br>67.9|
|Table D.1: Mo<br>Variable / Scenario<br>Land<br>Cropland Area, MHa<br>- Food Crops, MHa<br>- Animal Feed, MHa<br>- Biofuels Crops, MHa<br>Pasture Land Area, MHa<br>Commercial Forest Area, MHa<br>Unmanaged Natural Land Area, MHa<br>Protected Natural Land Area, MHa<br>Intermediate Products<br>Agricultural Product, Mton<br>Livestock, Mton<br>Fertilizers, Mton<br>Petroleum, Mtoe<br>Biofuels, Mtoe<br>Timber Products, Mton<br>Final Consumption<br>Processed Food Services per capita, 2004 USD<br>Processed Livestock Services per capita, 2004 USD<br>Bioenergy Services per capita, 2004 USD<br>Processed Timber Services per capita, 2004 USD<br>Ecosystem Services per capita, 2004 USD<br>GHG Emissions<br>Natural Land Conversion, MtCO2e<br>Fertilizers' Use, MtCO2e<br>Biofuels Combustion, MtCO2e<br>Livestock Farming ans Management, MtCO2e<br>Net Forest Sequstration, MtCO2e<br>Petroleum Combustion, MtCO2e<br>GHG Emissions from Land Use, MtCO2e<br>Accumulated GHG Emissions from Land Use, GtCO2e|

27
|AE<br>Scenario AET<br>(∆AE)<br>-84.5<br>-19.0<br>-92.9<br>27.4<br>-111.7<br>157.0<br>47.0<br>-9.1<br>-549.8<br>-186.4<br>-27.8<br>-399.9<br>16.8<br>0.0<br>-15<br>-57<br>3<br>0<br>4<br>0<br>-112<br>9<br>-202<br>-697<br>-1144<br>-1002<br>-18.2|
|---|
|T<br>Scenario<br>(∆A)<br>25.0<br>7.0<br>6.0<br>12.0<br>-6.8<br>-2.0<br>-10.0<br>-4.9<br>-120.0<br>-21.8<br>-11.4<br>-140.0<br>8.3<br>0.0<br>-6<br>-7<br>9<br>0<br>-2<br>0<br>-48<br>6<br>-24<br>19<br>-415<br>-47<br>-15.7|
|E<br>Scenario <br>ne)<br>-83.5<br>-16.0<br>-96.7<br>29.2<br>-114.3<br>171.0<br>39.0<br>-11.9<br>-659.8<br>-214.2<br>-31.1<br>-469.9<br>19.8<br>0.0<br>-18<br>-65<br>3<br>0<br>4<br>0<br>-124<br>10<br>-234<br>-768<br>-1346<br>-1115<br>-34.2|
|, 2100<br> A<br>Scenario <br>on from Baseli<br>25.0<br>7.0<br>5.8<br>12.2<br>-6.7<br>-2.0<br>-11.0<br>-4.9<br>-140.0<br>-23.1<br>-11.4<br>-150.0<br>8.3<br>0.0<br>-7<br>-7<br>9<br>0<br>-2<br>0<br>-46<br>6<br>-25<br>18<br>-417<br>-47<br>-15.4|
|ation Results<br>e<br>Scenario <br><br>(Deviati<br>24.1<br>8.0<br>19.3<br>-3.2<br>-9.8<br>-5.0<br>-5.0<br>-4.3<br>-629.8<br>-96.0<br>5.7<br>-10.0<br>-3.5<br>0.0<br>-29<br>-29<br>-1<br>0<br>-1<br>0<br>25<br>-5<br>-101<br>28<br>-22<br>-53<br>4.8|
|del Simul<br>Baselin<br>(Level)<br>2139<br>1261<br>735<br>143<br>2330<br>1616<br>1795<br>678<br>6188<br>1577<br>179<br>1170<br>507<br>3399<br>275<br>480<br>85<br>344<br>329<br>0<br>727<br>322<br>1844<br>-2075<br>3382<br>817<br><br>11.8|
|Table D.2: Mo<br>Variable / Scenario<br>Land<br>Cropland Area, MHa<br>- Food Crops, MHa<br>- Animal Feed, MHa<br>- Biofuels Crops, MHa<br>Pasture Land Area, MHa<br>Commercial Forest Area, MHa<br>Unmanaged Natural Land Area, MHa<br>Protected Natural Land Area, MHa<br>Intermediate Products<br>Agricultural Product, Mton<br>Livestock, Mton<br>Fertilizers, Mton<br>Petroleum, Mtoe<br>Biofuels, Mtoe<br>Timber Products, Mton<br>Final Consumption<br>Processed Food Services per capita, 2004 USD<br>Processed Livestock Services per capita, 2004 USD<br>Bioenergy Services per capita, 2004 USD<br>Processed Timber Services per capita, 2004 USD<br>Ecosystem Services per capita, 2004 USD<br>GHG Emissions<br>Natural Land Conversion, MtCO2e<br>Fertilizers' Use, MtCO2e<br>Biofuels Combustion, MtCO2e<br>Livestock Farming ans Management, MtCO2e<br>Net Forest Sequstration, MtCO2e<br>Petroleum Combustion, MtCO2e<br>GHG Emissions from Land Use, MtCO2e<br>Accumulated GHG Emissions from Land Use, GtCO2e|

28
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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.

<!-- Start of picture text --> Change in Land Use Relative to Baseline Change in GHG Emissions Relative to Baseline<br>200 1.5 40 Natural Land<br>150 Food Crops 30 Conversion<br>100 Livestock Feed 1 20 Livestock<br>50 Biofuels Crops 0.5 10 Biofuels<br>Pasture Land Offsets<br>0 Protected Forests 0 0 Use of<br>-50 -10 Fertilizers<br>Managed Forests -0.5 Forest<br>-100 Unmanaged Forests -20 Sequestration<br>-1<br>-150 -30 Net GHG<br>Accumulation<br>-200 -1.5 -40<br>2005 2030 2055 2080 2105 2005 2030 2055 2080 2105<br>Change in Consumption of Land Based Good Change in Consumption of Biofuels Relative to<br>and Services Relative to Baseline Baseline<br>0 40 10%<br>30 8%<br>-10 6%<br>-20 Processed Livestock 2010 4%2% Consumption of 2gBiofuels<br>Ecosystem Services<br>-30 0 0% Consumption of 1g<br>Processed Timber -10 -2% Biofuels<br>-40 Energy Services -4%<br>-50 Processed Grains -20-30 -6%-8% Share of Biofuels inLiquid FuelConsumption<br>-60 -40 -10%<br>2005 2030 2055 2080 2105 2005 2030 2055 2080 2105<br>Million Ha GtCO2e/yr GtCO2e<br>USD Per Person Million toe<br><!-- End of picture text --> Figure E.2: Sensitivity Analysis: 50% Increase in Elasticity of Substitution between Agricultural Land and Fertilizers Figure E.2 shows the eects 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 additional conversion of natural lands. However, the decline in fertilizers' use results in smaller GHG ows. The former eect dominates, and net GHG accumulation increases by 30 GtCO 2 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 eects 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
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large scale commercial production considerably earlier. After arrival of second generation biofuels, their production increases by 300 million toe, and the biofuels 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 decline. GHG ows increase with the additional conversion of natural lands, and later decline with biofuels' osets. The latter eect dominates in the long run, and net GHG accumulation declines by 40 GtCO 2 e in 2100. The consumption of energy services increases, and the consumption of other land based goods and services declines.

<!-- Start of picture text --> Change in Land Use Relative to Baseline Change in GHG Emissions Relative to Baseline<br>50<br>1.5 20 Natural Land<br>40 Food Crops 15 Conversion<br>30 Livestock Feed 1 Livestock<br>20 10<br>10 Biofuels Crops 0.5 5 Biofuels<br>Pasture Land Offsets<br>0 Protected Forests 0 0 Use of<br>-10 -5 Fertilizers<br>-20 Managed Forests -0.5 Forest<br>-30 Unmanaged Forests -1 -10 Sequestration<br>-40 -15 Net GHG<br>Accumulation<br>-50 -1.5 -20<br>2005 2030 2055 2080 2105 2005 2030 2055 2080 2105<br>Change in Consumption of Land Based Good Change in Consumption of Biofuels Relative to<br>and Services Relative to Baseline Baseline<br>30 250 20%<br>25 200 15%<br>150<br>2015 Processed Livestock 10050 10%5% Consumption of 2gBiofuels<br>Ecosystem Services<br>10 0 0% Consumption of 1g<br>5 Processed TimberEnergy Services -100-50 -5% Biofuels<br>0 Processed Grains -150 -10% Share of Biofuels inLiquid Fuel<br>-5 -200 -15% Consumption<br>-10 -250 -20%<br>2005 2030 2055 2080 2105 2005 2030 2055 2080 2105<br>Million Ha GtCO2e/yr GtCO2e<br>USD Per Person Million toe<br><!-- End of picture text --> Figure E.4: Sensitivity Analysis: 50% Increase in Fixed Factor Specic Technological Change Figure E.4 shows the eects of a 50% increase in xed factor specic technological change. Similar to the improvements in biofuels' production technology, faster technological progress in biofuels penetration make biofuels a more competitive 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' osets. The latter eect dominates in the long run, and net GHG accumulation declines by 10 GtCO 2 e in 2100. The consumption of energy services increases, and the consumption of other land based goods and services declines.

<!-- Start of picture text --> Change in Land Use Relative to Baseline Change in GHG Emissions Relative to Baseline<br>40<br>1.5 10 Natural Land<br>30 Food Crops 8 Conversion<br>20 Livestock Feed 1 6 Livestock<br>10 Biofuels Crops 0.5 4 Biofuels<br>Pasture Land 2 Offsets<br>0 Protected Forests 0 0 Use of<br>-10 -2 Fertilizers<br>Managed Forests -0.5 -4 Forest<br>-20 Unmanaged Forests -1 -6 Sequestration<br>-30 -8 Net GHG<br>Accumulation<br>-40 -1.5 -10<br>2005 2030 2055 2080 2105 2005 2030 2055 2080 2105<br>Change in Consumption of Land Based Good Change in Consumption of Biofuels Relative to<br>and Services Relative to Baseline Baseline<br>2 10 6%<br>0 8<br>6 4%<br>-2-4 Processed Livestock 42 2% Consumption of 2gBiofuels<br>Ecosystem Services<br>-6 Processed Timber 0 0% Consumption of 1g<br>-8 Energy Services -2-4 -2% Biofuels<br>-10 Processed Grains Share of Biofuels in<br>-6 -4% Liquid Fuel<br>-12 -8 Consumption<br>-14 -10 -6%<br>2005 2030 2055 2080 2105 2005 2030 2055 2080 2105<br>Million Ha GtCO2e/yr GtCO2e<br>USD Per Person Million toe<br><!-- End of picture text --> Figure E.5: Sensitivity Analysis: 50% Decline in Energy Eciency Growth Rate per annum Figure E.5 shows the eects a 50% decline in energy eciency growth rate. Smaller energy eciency 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 reduction 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 de33
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services. The consumption of biofuels and their share in liquid fuel consumption increases by a small amount.

Table E.1: Parameter Changes in Model Sensitivity Analysis

|Parameter|Description|Baseline<br>Value|New<br>Value|
|---|---|---|---|
|_ξ_<sup>_u_</sup><br>2|Natural Land Access Cost Function Parameter|42,000|28,000|
|_σg_|Elasticity of Substitution between Land and Fer-<br>tilizers|1.14|1.71|
|_θ_<sup>_b,_2</sup>|2G Biofuels' Conversion Technology|0.467|0.71|
|_κφ_|Factor Specic Tech. Change Growth p.a.|1.005|1.0075|
|_κe_|Energy Eciency Growth Rate p.a.|0.016|0.011|
|_δ_|Social Discount Rate|0.015|0.0225|

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