A COMPARISON OF GLOBAL TIMBER MODELS

Transcription

1 Journal of Rural Developmen 34(3): 79~91 79 A COMPARISON OF GLOBAL TIMBER MODELS YOON HYUNG KIM * Keywords global imber model, consan elasiciy of ransformaion, carbon sequesraion cos Absrac This sudy idenifies differences of global imber models in is hree differen versions by comparing marginal abaemen cos. The fores-only model has a relaively linear marginal cos curve; he oher wo models show concave cos curves, indicaing ha he marginal cos for carbon sequesraion increases faser han in he fores-only model. Such basic differences among he models may be caused by he characerisics of he (Consan Elasiciy of Transformaion) model. The differences beween he fores-only model and model are more narrowed when resuls are convered o physical unis. This sudy conribues o he enhancemen of he undersanding of GTM developmen and provides foundaion for fuure sudies o improve global imber modeling. I. Inroducion Foress play radiionally imporan roles in economic life as a source of wood and oher producs. Recenly, heir environmenal usefulness is enjoying he spoligh, as foress can provide a carbon sin via fores carbon sequesraion as a par of reducion in greenhouse gas. This, in urn, should reduce global warming. In paricular, carbon sequesraion using foress increased in policy significance because i presens a mehod for boh a relaively low-cos means * Research Fellow, Korea Rural Economic Insiue, Seoul, Korea

2 80 Journal of Rural Developmen 34(3) of removing carbon dioxide from he amosphere (US Environmenal Proecion Agency, 1995) and long-erm effeciveness for carbon abaemen wih oher policies (Sohngen & Mendelsohn, 2007). In his conex, fores economic models grew ou of radiional supply-demand ones o lin wih various environmenal problems. Given ha greenhouse gas emission from land use change and deforesaion accouned for 17.4% of he oal (IPCC 2007), land-use models for undersanding relaions beween agriculure and fores secors are increasingly imporan in he analysis of environmenal problems. Therefore, here have been various aemps in modeling approaches: Scopes of models of fores economy expanded from wood producs in he pas o soil, land-use changes, and inegraed exising economic models. Such fores models can be roughly divided ino compuable general equilibrium models (CGE) and parial equilibrium models (PEM). Compuable general equilibrium models include general secors of producion and consumpion in economy, and ineracions and feedbac effecs across economic secors can be considered in hese models in cases of various economic environmens and changes in srucures. On he oher hand, parial equilibrium models are for analyzing specific economic secors of concern wihou considering relaions wih oher economic secors. These allow for analysis of concerned secors in he deailed secoral model. Examples of compuable general equilibrium models are GTAPEM (OECD, 2003) and GTAPE-L (Burniaux & Lee, 2003). Boh models are modified versions of he sandard Global Trade Analysis Projec (Herel, 1997) and ofen are used o analyze he impacs of environmenal problems on he enire economy. The Global Timber Model (Sohngen e al., 1999) and he Fores and Agriculural Secor Opimizaion Model (Adams e al., 2005) are examples of parial equilibrium models. Meanwhile, despie he same heoreical bacgrounds (or modeling approaches), here are considerably various models based on scale of model, period of analysis, and saic or dynamic analysis. For insance, opimizaion problems solve for each period in saic models, while dynamic models are for maximizing he ne presen value of welfare defined over he whole period by opimal disribuion of resources over ime hrough ineremporal opimizing wih perfec foresigh. The Timber Assessmen Mare Model (Adams & Haynes, 1980) is an example of a saic model, whereas GTM and FASOM are dynamic models. Also, here are regional models and global modes divided by scale.

3 A Comparison of Global Timber Models 81 Fores Carbon Budge Model (Smih & Healh, 2001), which is he model o esimae carbon in U.S. foress, and he fores carbon flux model FORUG (Verbeec e al., 2006), which was used o analyze NEE (ne ecosysem exchange) for he Hesse Fores in France, are examples of regional models, whereas a GTM is a global model. Recenly, model developers ofen combine or couple exising economic models. Usually, a deailed boom-up model is lined o a comprehensive op-down model. For example, Tavoni e al. (2007) lined he World Induced Technical Change Hybrid Model (WITCH) o a Global Timber Model buil by Sohngen e al. (1999) o invesigae he poenial conribuion of fores managemen o climae sabilizaion. Among hese various fores models, a GTM has several appropriae feaures ha are differeniaed from ohers. Firs, a GTM is a dynamic model. Because foress ae ime o grow and paricipae in a dynamic process affeced by long-erm decision maing, a ime pah should be explicily considered in a model. For insance, accumulaion of carbon in he amosphere resuls in rising carbon prices over ime and consequenly increases incenives, inducing carbon sequesraion using foress. Saic models have a demeri in ha hey rea foress as a seady-sae soc raher han as a dynamic soc and hen fail o explain ineremporal adjusmen in response o changing incenives. However, in a GTM, dynamic opimizaion does accoun for imporan adjusmens in imber invenories, which are composed of rees a various ages, and he dynamics of fores carbon sequesraion are associaed wih ha adjusmen. Second, a GTM is a global model. Regional sudies may be useful in ha relaively elaborae modeling is possible by using deailed daa of a specific region. However, problems such as global warming and changes in land use are no limied o a naional bu worldwide phenomenon, and environmen policies herefore should be conduced on a global basis. In his conex, global models can show significan policy implicaions for environmenal problems. For insance, when a naion imposes carbon ax for carbon sequesraion, i may induce fores owners o release carbon in oher naions. A GTM can presen useful informaion for policymaers boh by considering such leaage and by showing differen reacions of naions on an environmen policy. Or, when inernaional prices of grain increase due o an inernaional shorage of food, foress or pasures of a naion can be convered o compensae for he shorage. Global models are needed o analyze such land conversion and conenion. Finally, a GTM includes fores producs ha are no handled by oher models,

4 82 Journal of Rural Developmen 34(3) indicaing ha i can presen a more accurae analysis of environmenal problems. The purposes of his sudy are o presen and illusrae he curren saus of GTM researches, o compare and conras various models so far, and hen o presen useful informaion for furher sudy. The resuls migh conribue o improvemen of models in he fuure. In his sudy, hree differen versions of global imber models are inroduced. The marginal abaemen cos of each model is compared and analyzed for differences in he models. The paper is organized as follows: A GTM including foress only is inroduced, followed by a GTM including agriculure and livesoc. Models in which he resuls of he GTM including agriculure and livesoc are convered o physical unis are explained, and differences in marginal abaemen coss of he models are described. A conclusion will follow. II. Model and Daa 1. The Global Timber Model (Fores only) The global imber model (fores only) was developed by Sohngen and Mendelson (2003, 2007) o analyze fores carbon sequesraion in a global framewor. The GTM is an opimal conrol model ha solves for he maximum presen value of ne welfare in he fores secor. Ne welfare is defined as he difference beween he imber demand funcion and he coss of producing imber. Annual welfare is given as Q*( ) (1) W = D( Q, Z ) CH ( ) dq( ) 0 j, j, j, j, j, p m G R X j, m ( )( ) j, where = Q H V ( m ) a, a, 0 a In equaion (1), D Q, Z ) is a global demand funcion for indusrial (

5 A Comparison of Global Timber Models 83 wood producs given he quaniy of wood of wood harvesed depends on H i, j, a, a, 0 Q, and income, Z. The quaniy, he area of land harvesed in he imber ypes in J and, and V ( m ), he yield per hecare of imber in each age class. The yield per hecare depends upon he species, he age of he ree m (a), and he managemen inensiy a he ime of planing ( 0 ). CH ( ) is he cos funcion for harvesing and ransporing logs o mills from each of he imber ypes. Marginal harves coss for emperae and planaion fores ypes are consan, while marginal harves coss for inaccessible foress rise as addiional land is accessed. The coss of planing foress are given as p m G m, where i j G,, is he area of land planed, i j m,, is he managemen inensiy of planing, and p is he per uni cos of a uni of m managemen inensiy. Unis of managemen inensiy enhance yield when he imber is harvesed. The yield funcion has properies ypical of ecological species, e.g., V a > 0 and V aa < 0. In addiion, he following wo condiions hold for rees planed a ime o and harvesed a years laer (a + o ) = ai : dv ( a 0 ) i d dv ( a ) i 0 (2) 0 and 0 dm ( ) dm dm ( ) The GTM Incorporaing Agriculure and Livesoc Secor ( Approach) The model is exended by incorporaing he crop and livesoc secors ino he previous foresry-only model. The model maximizes he ne presen value of consumers plus producers surplus in he foresry, crop, and livesoc mares and uses he consan elasiciy of subsiuion producion (CES) funcion o model he ineracion beween agriculure and foresry. Each daase is aggregaed ino 18 regions wih 18 agro-ecological zones (AEZs). There are many consrains in he model. However, one of he mos imporan consrains is he fores land supply funcion because i capures he ineracion beween agri-

6 84 Journal of Rural Developmen 34(3) culure and foresry. The area of land in each fores ype in each age class is i j given as QF,, and R is he annual renal value of he land. The area of land is he sum of he area of land in each age class. A consan elasiciy of ransformaion () funcion, which conrols he ransformaion beween land uses, is uilized for modeling land supply. The fores supply funcion can be expressed as follows: (3) QF = τ α Cr R 1 τ Cr XE τ + α R Lv i. j. 1 τ Lv α ( F + 6 τ 1 ( α F ) ( R ) = 1 R τ ) τ τ τ 1 (4) XE = ( α X Cr ( τ 1) τ Cr + α X Lv ( τ 1) τ Lv 6 + α = 1 F, X ( τ 1) τ F, ) τ ( τ 1) where X cr, X Lv, and X are AEZ-specific land, and he parameers F α Cr, α Lv, and α F are land shares for supply in crop, livesoc, and foresry. The variables R cr, R Lv are land renal for crop, livesoc. For he purposes of his analysis, i is assumed ha hey are given. The parameer of he supply funcion, τ, can be considered as land supply elasiciy and represens he maximum value on he elasiciy of land supply wih addiional renal paymen (Herel e al., 2009). The parameer is se o based on he economeric wor of Choi e al. (2006). 3. Convering resuls o Physical Unis of Area Wih he, he common assumpion is ha land is imperfecly subsiuable beween differen uses wihin an AEZ. The value of he ransformaion elasiciy deermines he degree of land mobiliy. However, such a non-linear reamen of land in he funcion implies ha land is measured in he value added o he producion raher han physical unis of area. The disadvanage of such reamen of land is ha carbon calculaions based on GTM resuls may no represen realiy. In order o solve his problem, he model was modified by adding several consrains o he GTM. Three equaions are needed o con-

7 A Comparison of Global Timber Models 85 ver hecares o physical ones. Firs, crop hecare is convered o physical ones by using he following equaion: 1 (5) Q1 ( crop) Q0 ( crop) = ( ) ( Q1 ( crop) Q0 ( crop)) 0.66 where Q 0 ( Q 0 ) and Q 1 ( Q 1 ) denoe physical () crop area in he iniial period and in he following period, respecively. I is assumed ha he average produciviy of crop land decreases if fores and livesoc lands are convered o crop land. In his sudy, following Herel e al.(2010), he produciviy parameer is se o 0.66 in his paper, which implies ha approximaely 1.5 (=1/0.66) new physical hecares are required o produce he same amoun of produc ha one hecare of curren crop land produces. Then, an endogenous produciviy adjusmen variable (A) is included o conver fores and livesoc area o physical hecares using he following equaion: (6) Q 1 (foresry or livesoc)= A Q1 * (foresry or livesoc) Addiionally, I is assumed ha he sum of crop, foresry, and livesoc areas is consan over ime. (7) Q 0 ( i) = Q1 ( i) i i (i=crop, foresry and livesoc) Combining he hree equaions above yields he soluion for he produciviy variable (A) using he following equaion: (8) Q 0 ( crop) + Q0 ( foresry ) + Q0 ( livesoc ) = Q1 ( crop) + Q1 ( foresry ) + Q1 ( livesoc ) 1 = Q0 ( crop) + ( ) ( Q1 ( crop) Q0 ( crop)) + A ( Q ( foresry) + Q1 ( livesoc)) Finally, subsiuing A ino equaion (6) yields physical hecares for foresry and livesoc.

8 86 Journal of Rural Developmen 34(3) 4. Daa Fores invenories by region, he produciviy of foress, he coss of exracing and ransporing imber o mills daa are obained from Sohngen e al. (2009). This analysis is based on a definiion for agro-ecological zones ha builds on he wor of he FAO and IIASA (2000), and is described in Monfreda e al. (2009) and Lee e al. (2009). The Food and Agriculure Organizaion of he Unied Naions and he Inernaional Insiue for Applied Sysems Analysis have developed he Agro-ecological Zones (AEZ) mehodology. The agro-ecological zones differ by growing period (6 caegories of 60-day growing period inervals) and climaic zone (ropical, emperae and boreal). The lengh of growing period depends on emperaure, precipiaion, soil characerisics and opography, and he suiabiliy of each agro-ecological zone for producion of alernaive crops and livesoc is based on currenly observed pracices. In each region of his model, here are up o 18 agro-ecological zones and here are up o 6 imber ypes in each AEZ. Daa on land rens and land areas in each agro-ecological zone are obained from Lee e al. (2009). To mae projecions in he foresry secor, I uilize a demand funcion of he form (9) Q = A ( P ) e Y N h where Y is global gross domesic produc, N is global populaion, P is he global price of imber, h is income elasiciy, and e is he price elasiciy. Gross domesic produc per capia Y is assumed o grow a 2.3% per N year. Income elasiciy for foresry producs is calculaed from he AIDADS (An Implicily Direcly Addiive Demand Sysem) modeling sysem developed by Rimmer and Powell (1996) and esimaed by Yu e al (2002). Iniially, i is 0.87, and i rises o 0.93 over he cenury.

9 A Comparison of Global Timber Models 87 III. Resuls and Conclusion 1. A Comparison of Carbon Sequesraion Cos The carbon sequesraion cos curves of each model explained above are compared by inroducing carbon prices ino he model. Carbon gains are measured as he difference beween baseline carbon emissions and emissions in each price scenario, and hen carbon credis are obained by convering he ne presen value of carbon over differen periods. The parameer, which conrols he ransformaion beween each of he land uses, is se o in his simulaion. Table 1 presens carbon gains worldwide in each model relaive o baseline by 2055, 2075 and For example, he ne presen value of carbon over a 70-year period shows ha for $11.01 per Mg C, around 8 Pg of addiional carbon is sored in he fores-only model, while 3 Pg and 12 Pg of addiional carbon is sored in he GTM including agriculure and livesoc and he GTM wih physical hecares, respecively. For $55.05 per Mg C, around 31 Pg of addiional carbon is sored in he fores-only model, while 15 Pg and 34 Pg of addiional carbon is sored in he GTM including agriculure and livesoc and he GTM wih physical hecares, respecively. For $110.1 per Mg C, around 44 Pg of addiional carbon is sored in he fores-only model, while 24 Pg and 42 Pg of addiional carbon is sored in he GTM including agriculure and livesoc and he GTM wih physical hecares, respecively. Since he resul of he fores-only model is given in erms of physical unis, comparing he resul and physical uni resul wih ha of he fores-only model is ineresing. For purposes of comparison, I is assumed ha he resul of he fores-only model is he rue quaniy and calculae he relaive errors from his value. The relaive error for he physical uni resul is approximaely 56% of ha of he fores-only model a $11.01 per Mg C, decreasing o 4% a $110.1 per Mg C, and he differences beween he fores-only and he fores model wih agriculure and livesoc are narrower when he resul is convered o physical unis. However, he relaive error for he resul is 59% of ha of he fores-only model a $11.01 per Mg C. The resul remains comparaively high (45%) a $110.1 per Mg C. This resul is consisen over differen periods.

10 88 Journal of Rural Developmen 34(3) Table 1. World carbon gains from carbon price scenarios Carbon price($ per Mg C) $11.01 $25.69 $55.05 $110.1 $220.2 $440.4 $917.5 Fores-only C gain over 50 years C gain over 50 years Relaive Error 60.2% 52.4% 52.3% 44.1% 40.8% 47.1% 57.9% Physical C gain over 50 years Relaive Error 57.3% 44.7% 8.9% 4.6% 12.5% 30.2% 46.5% Carbon price($ per Mg C) $11.01 $25.69 $55.05 $110.1 $220.2 $440.4 $917.5 Fores-only C gain over 70 years C gain over 70 years Relaive Error 59.0% 52.4% 52.3% 45.2% 42.4% 49.4% 58.8% Physical C gain over 70 years Relaive Error 56.4% 40.6% 10.5% 4.2% 12.1% 29.7% 46.2% Carbon price($ per Mg C) $11.01 $25.69 $55.05 $110.1 $220.2 $440.4 $917.5 Fores-only C gain over 90 years C gain over 90 years Relaive Error 60.3% 53.7% 53.2% 46.7% 44.5% 51.8% 61.4% Physical C gain over 90 years Relaive Error 55.3% 37.7% 9.2% 4.3% 12.2% 30.1% 46.4% Since he carbon sequesraion cos curve is he locus of carbon gains in each carbon price scenario, he carbon abaemen cos curve can be presened, rendering he differences beween he model and fores-only model clearer. Figure 1 presens he world abaemen cos curve for each model. The fores-only model has a relaively linear marginal cos curve, while he oher wo models show concave cos curves, indicaing ha he marginal cos for carbon sequesraion increases faser han in he fores-only model. Such basic differences among he models may be caused by he characerisics of he model. The model is based on incomplee subsiuion relaions among land use, and he parameers of he funcions deermine he degrees of mobiliy for each land use. The differences beween he wo models are narrower when he resul is convered o physical unis.

11 A Comparison of Global Timber Models 89 FIGURE 1. World carbon abaemen cos curves (C gain over 70 years) 2. Conclusion Global imber model is a dynamic opimizaion model and has been used for examining global land-use and climae change miigaion policies including carbon prices. The GTM model used in his sudy has been developed over a number of years. The objecive of his sudy is o presen he curren saus of GTM researches and illusrae he differences among models so far. One concern wih using a approach o model land supply is ha land areas calculaed by he funcion are given in value added erms raher han physical erms. Therefore, special aenion was given o conver resuls o physical uni ones because he fores-only model considered jus he fores (he resuls of he model do no need o be convered o physical unis). On he oher hand, he fores model wih agriculure and livesoc uses he funcion; hus, is resuls should be convered o physical unis. This is because incomplee land subsiuion relaions among agriculure, livesoc, and fores are esablished in he model. In order o solve he problem, he model was adjused by adding several consrain equaions o i. In his sudy, differences in he given models are presened by describing a GTM in is hree differen versions and comparing marginal abaemen cos. Based on he comparison of marginal cos curves, he fores-only model

12 90 Journal of Rural Developmen 34(3) has a relaively linear marginal cos curve, whereas he oher wo models show concave cos curves, indicaing ha he marginal cos for carbon sequesraion increases faser han in he fores-only model. Such basic differences among he models may be caused by he characerisics of he model. The model is based on incomplee subsiuion relaions among land use, and he parameers of funcions deermine he degrees of mobiliy of each land use. The differences beween he wo models are more narrowed when resuls are convered o physical unis. This sudy conribues o he enhancemen of he undersanding of GTM developmen and provides foundaion for fuure sudies o improve global imber modeling. REFERENCES Adams, D.M. and R.W. Haynes The 1980 imber asse mare model: Srucure, projecions, and policy simulaions. For. Science 26(3): Monogr. 22. Adams, D. e al FASOMGHG Concepual Srucure, and Specificaion. Burniaux, J.-M., Lee, H.-L Modelling Land Use Changes in GTAP. Cho S. e al Land use change in he Midwesern U.S. Deparmen of Agriculural, Environmenal, and Developmen Economics, Ohio Sae Universiy. Herel T. W Global Trade Analysis: Modeling and Applicaions. Cambridge Universiy Press. Herel, T. W., Lee, H., Rose, S. & Sohngen, B Modeling land-use relaed greenhouse gas sources and sins and heir miigaion poenial. In T. Herel, S. Rose, & R. Tol (Eds.), Economic analysis of land use in global climae change policy (chaper 6). New Yor: Rouledge Press. Herel, T. W., Tyner, W. E., & Birir, D. K The global impacs of biofuels mandaes. The Energy Journal 31(1): Food and Agriculure Organizaion (FAO) of he Unied Naions & Inernaional Insiue for Applied Sysems Analysis (IIASA) Global agro-ecological zones Rome, Ialy, and Laxenburg, Ausria. Inergovernmenal Panel on Climae Change Climae Change 2007-Synhesis Repor Lee, H.-L. e al An inegraed global land use daa base for CGE analysis of climae change policy opions. In T. Herel, S. Rose, & R. Tol (Eds.), Economic analysis of land use in global climae change policy (Chaper 4). New Yor: Rouledge Press.

13 A Comparison of Global Timber Models 91 Monfreda, C., Ramanuy, N., & Herel, T. W Global agriculural land use daa for climae change analysis. In T. Herel, S. Rose, & R. Tol (Eds.), Economic analysis of land use in global climae change policy (Chaper 2). New Yor: Rouledge. OECD PEM Technical Documen Draf. OECD, Paris. Rimmer, M. T. & Powell, A.A An implicily addiive demand sysem. Applied Economics 28: Sohngen, B., R. Mendelsohn, R. Sedjo Fores Managemen, Conservaion, and Global Timber Mares. American Journal of Agriculural Economics 81(1): Sohngen, B., R. Mendelsohn An opimal conrol model of fores carbon sequesraion. American Journal of Agriculural Economics 85(2): Sohngen, B. & Mendelsohn, R A sensiiviy analysis of carbon sequesraion. In M. Schlesinger (Ed.), Human-Induced Climae Change: An Inerdisciplinary Assessmen. Cambridge: Cambridge Universiy Press. Sohngen, B. e al Global foresry daa for he economic modeling of land use. In T. Herel, S. Rose, & R. Tol (Eds.), Economic analysis of land use in global climae policy (Chaper 3). New Yor: Rouledge Press. Smih, J.E. and Heah, L.S Idenifying influences on model uncerainy: an applicaion using a fores carbon budge model." Environmenal Managemen 27: Tavon M., B. Sohngen and V. Bosei Foresry and he Carbon Mare Response o Sabilize Climae. Energy Policy. 35(11): US Environmenal Proecion Agency Climae Change Miigaion Sraegies in he Fores and Agriculure Secors, EPA 230-R Verbeec, H. e al Parameer sensiiviy and uncerainy of he fores carbon flux model FORUG: a Mone Carlo analysis. Tree Physiol 26: Yu, W. e al Projecing World Food Demand using Alernaive Demand Sysems. Economic Modeling 21: Dae Submied: June 30, 2011 Period of Review: July 6~July 19, 2011