Technical Appendix to. The Global Impacts of Biofuel Mandates. Forthcoming in The Energy Journal

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1 Tehnial Appendix to The Global Impats of Biofuel Mandates Forthoming in The Energy Journal by Thomas W. Hertel*, Wallae E. Tyner and Dileep K. Birur Center for Global Trade Analysis Department of Agriultural Eonomis, Purdue University *Corresponding author: T.W. Hertel. Exeutive Diretor, Center for Global Trade Analysis, Purdue University, West Lafayette, IN 47907, USA. The authors gratefully aknowledge researh support from the US Environmental Protetion Ageny, the US Department of Energy, and Argonne National Labs.

2 In this appendix, we supply supplementary materials on the model and additional results. We begin by outlining the partial equilibrium model used in the paper and then provide global maps of land over hanges, by AEZ. Finally, additional information on the Systemati Sensitivity Analysis is provided. A Partial Equilibrium Model of the Ethanol Market Consider an ethanol industry selling into two domesti market segments: in the first market, ethanol is used as a gasoline additive ( QI ), in strit proportion to total gasoline prodution. As disussed in the paper, legal developments in the additive market were an important omponent of the US ethanol boom between 200 and The seond market is the market for ethanol as an energy substitute ( QE ). In ontrast to the additive market, the demand in this market is prie sensitive, with ethanol s market share depending on its prie, relative to refined petroleum. For ease of exposition, and to be onsistent with the general equilibrium model, we will think of the additive demand as a derived demand by the petroleum refinery setor, and the energy substitution as being undertaken by onsumers. Market learing, in the absene of exports, may then be written as: QO = QI + QE () or, in perentage hange form, where lower ase denotes the perentage hange in the upper ase variable: qo = ( α ) qi+ αqe (2) where α = QE / QO, is the share of total ethanol output (Q O ) going to the prie sensitive side of the market. 2

3 Now we formally haraterize the behavior of eah soure of demand for ethanol as follows (again, lower ase variables denote perentage hanges in their upper ase ounterparts): qi = ai + qp (3) where AI = QI / QP is the ethanol input output oeffiient in the Leontief prodution funtion for petroleum produts, so that when MTBE s are banned, for example, AI inreases, thereby boosting intermediate input demand. For final demand we have: qe = q σ( pe p) (4) Where Q is the aggregate demand for household liquid fuel onsumption and σ is the onstant elastiity of substitution ( CES) amongst energy produts onsumed by the household. The prie ratio PE / P refers to the prie of ethanol relative to a omposite prie index of all energy produts onsumed by the household. The perentage hange in this ratio is given by the differene in the two perentage hanges: ( pe p ). When pre-multiplied by σ, this determines the prie-sensitive omponent of households hange in demand for ethanol. Substituting (3) and (4) into (2), we obtain a new expression for ethanol market learing: qo = ( α)( ai + qp) + α[ q σ( pe p)] (5) On the supply side, we assume onstant returns to sale in ethanol prodution, whih, along with entry/exit, gives zero pure profits in the medium run: po= θ pf (6) Where po is the perentage hange in the produer prie for ethanol, pf is the perentage hange in prie of input, used in biofuel prodution, and θ is the ost share of that input. Assuming that orn is the only input in less than perfetly elasti supply, and that it is used in 3

4 fixed proportion to ethanol output (fixed QF / QO ), we an omplete the supply side speifiations with the following equations: qf = qo (7) qf = ν pf (8) where ν is the supply elastiity of orn to the ethanol setor. With pf = 0, we an solve (6) for pf = po. Plugging this and (7) into (8) gives the market supply of ethanol: θ qo = νθ po (9) We omplete the model by allowing for ethanol subsidies. These are typially provided in the form of blenders subsidies (U.S.) or tax abatements (EU). We write them here as the power of an ad valorem equivalent subsidy: S= PO/PE, i.e. the ratio of produer to user pries for ethanol. Totally differentiating and onverting to perentage hange form, we have the final equation in the partial equilibrium model: po= pe+ s (0) Now, in solving this model, we will make the additional assumptions that: (a) the aggregate prie of of liquid fuels is fixed ( p = 0 ), and (b) aggregate household demand for liquid fuels is fixed ( q = 0). All of these assumptions are relaxed in the empirial setion of the model. Using (0) to eliminate pe from (6) and equating supply (9) and demand (6), we an solve for the equilibrium produer prie of ethanol: po* = [( α) ai + ασ ( p + s)]/ ν θ ασ () [ ] Where ασ= ε is the aggregate prie elastiity of demand for ethanol, and ν θ d = ε is the s prie elastiity of supply for ethanol. To determine the equilibrium output, multiply both sides 4

5 by ε s to get the following (where we have used the definitions of supply and demand elastiities given above): qo* = ε s[( α) ai εd( p + s)]/[ εs ε D] (2) From (2), we an see a number of important things. First of all, the ontribution of hanges in the additive requirements of gasoline to total ethanol output depend on the hange in the input-output ratio (ai) as well as the initial share of total sales going to this market segment. The prie sensitive portion of the market depends on what happens to the prie of liquid fuels in general (p) and the power of the ad valorem subsidy (s), whih are additive in the solution of the model. Their signifiane depends on the share of the total market for ethanol that is prie sensitive (α ) and the ease of substitution between ethanol and other fuels ( σ ). We also see from (2) that supply response is important. If the total availability of feedstok (orn) is fixed ( ν = 0 ), then qo * = 0. Furthermore, as the supply response of orn rises ( ν >> 0 )and the share of orn in overall ethanol osts falls ( θ 0 ), ν θ = ε rises, s thereby boosting supply and dampening the equilibrium prie hange. Equation (2) is ritial when it omes to deomposing the ontribution of the three main drivers of ethanol prodution over the period. 5

6 -27.0 (minimum) (median) (maximum) Perent hange in Harvested Coarse Grains Area: Coarse Grains: (2006-5) USA Canada EU Brazil Perent hange Change in million ares Figure. Change in Land Area under Coarse Grains aross AEZs ( ) 0.88 (minimum) (median) (maximum) Perent hange in Harvested Oilseeds Area: Oilseeds: (2006-5) USA Canada EU Brazil Perent hange Change in million ares Figure 2. Change in Land Area under Oilseeds aross AEZs ( ) 6

7 -.3 (minimum) (median) (maximum) Perent hange in physial land over under Pasture: Pasture over: (2006-5) USA Canada EU Brazil Perent hange Change in million ares Figure 3. Change in Land Area under Pasture land aross AEZs ( ) (minimum) (median) (maximum) Perent hange in physial land over under Forest : Forest over: (2006-5) USA Canada EU Brazil Perent hange Change in million ares Figure 4. Change in Land Area under Forest aross AEZs ( ). 7

8 Table A. Systemati Sensitivity Analysis (SSA) of US and EU Biofuel Mandates Amount of Variation of Key Parameters 2 3 Parameters Yield elastiity (YDE_Target) Lower bound Mean Upper bound Standard Deviation Amount of Variation: SD*(6^0.5) Elastiity of transformation of land supply (ETRAE-2) 2 Elastiity. of transformation for rop land (ETRAE-) 3 4 Armington CES elastiity of substitution for domesti and imported (ESUBD) 4 : a. Coarse Grains b. Other Grains Oilseeds d. Sugarane e. Other Agri Soures: Keeney and Hertel (2008); 2 Ahmed, Hertel and Lubowski (2009); 3 FAPRI (2004); 4 Hertel et al. (2007) 8

9 Table A2. Sensitivity Analysis of US and EU Biofuel Mandates for Variation in Key Parameters Land Cover Change (%) Parameter values No hange in parameters Varying Armington Elastiity Varying Yield elastiity Cropland Cover elastiity Harvested area elastiity Lower Upper Lower Upper Lower Upper Lower Upper Base parameters Vary by rop USA Crops Forest Pasture EU Crops Forest Pasture Brazil Crops Forest Pasture Note: Refers to the mean values of all the four parameters presented in Table A. 2 The lower and upper bound values respetively, for all the rops were inluded together. The lower and upper bound values of ESUBD for five rops onsidered were also analyzed when onsidered individually and the results are presented in Table A3. 9

10 Table A3. Sensitivity Analysis of Biofuel Mandates to Variation in Armington Elast. of Substitution for Crops (% Change) Harvested area Coarse Grains Oilseeds Sugar-rops Other Grains Other Agri All Crops & land over type Lower Upper Lower Upper Lower Upper Lower Upper Lower Upper Parameter Base Values values USA CrGrains area Oilseeds area Sugarane area OthGrains area OthAgri area Crops over Forest over Pasture over EU CrGrains area Oilseeds area Sugarane area OthGrains area OthAgri area Crops over Forest over Pasture over Brazil CrGrains area Oilseeds area Sugarane area OthGrains area OthAgri area Crops over Forest over Pasture over Note: Base values refer to the mean values of all the four parameters presented in Table A. 0