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Topics 1.FASOM Basics 2.FASOM Equations 3.Analyzing FASOM 4.Modifying FASOM

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I FASOM Basics

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Model Scope Natural Resources Agriculture Forestry Processing Food, Fibre, Timber, Energy Markets

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Purpose and Objectives To study and advice policy makers about the agricultural and forestry sector response to a)Policies b)Environmental change c)Technical change d)Socioeconomic change

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Policy Scope Climate and other environmental policies Research subsidies Agricultural policies Trade policies Simultaneous assessment

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Structural Changes a)Policies b)Environmental change c)Technical change d)Socioeconomic change (population, preferences)

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Methodology Partial Equilibrium Bottom Up Constrained Welfare Maximization Dynamic Optimization Integrated Assessment Mathematical programming GAMS

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Model Structure Resources Land Use Technologies Processing Technologies ProductsMarkets Inputs Limits Supply Functions Limits Demand Functions, Trade Limits Environmental Impacts

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FASOM is a Large Linear Program

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Exogenous Data Resource endowments Technologies (Inputs,Outputs, Costs) Demand functions Environmental Impacts Policies

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Endogenous Data Land use decisions (control variables), Impacts (state variables), Shadow prices of constraints

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Equations Understanding them is to understand FASOM

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Equations Objective Function Resource Restrictions Technological Restrictions Environmental Accounts Others

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Constrained Optimization Maxz = f(X)... objective function s.t. G(X) <= 0... constraints

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FASOM = Large Linear Programs

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Objective Function (Normative Economics) Maximize +Area underneath demand curves -Area underneath supply curves -Costs ±Subsidies / Taxes from policies Maximum equilibrates markets!

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Alternative Objective Function To get „technical potentials“ from land use for alternative objective u, simply use Maximize us.t. all constraints Examples: u = Carbon Sequestration, Wheat production, Mire area

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Is FASOM linear? Input prices increase with increasing input use (scarcity of resources) Output prices decrease with increasing output supply (saturation of demand) Hence, FASOM has non-linear objective function but is solved as Linear Program using linear approximations

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Linear Approximation? For well behaved functions: yes –Concave benefit / convex cost functions –Decreasing marginal utilities –Increasing marginal costs For ill behaved: no, need integer variables –Fixed cost (Investment) –Minimum habitat requirements (Biodiversity)

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PRODUCTBAL_EQU Very important Multi-input, Multi-output Negative coefficients - Inputs Positive coefficients - Outputs

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RESOURCEBAL_EQU Sum resource uses over all technologies, species, farm structures into an accounting variable RESOURCE_VAR(REGION,PERIOD,RESOURCE)

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RESOURCEMAX_EQU Represent resource limits (endowments) RESOURCE_VAR(REGION,PERIOD,RESOURCE) ≤ RESOURCE_DATA (REGION,PERIOD,RESOURCE,”Maximum”)

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LUC_EQU LUC_EQU(REGION,PERIOD,SOILTYPE,SPECIES,CHANGE) $ LUC_TUPLE(REGION,PERIOD,SOILTYPE,SPECIES,CHANGE).. Land use accounting equation Combines individual and aggregated accounting

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LUCLIMIT_EQU LUCLIMIT_EQU(REGION,PERIOD,SOILTYPE,SPECIES,CHANGE) $(LUC_TUPLE(REGION,PERIOD,SOILTYPE,SPECIES,CHANGE) AND LUC_DATA(REGION,PERIOD,SOILTYPE,SPECIES,CHANGE, "MAXIMUM")).. Land use change limits Should be based on land characteristics Currently uses rough assumptions

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FORINVENT_EQU Forest distribution this period depends on forest distribution in last period and harvest activities Note: –Oldest cohort transition –Initial distribution –Harvested forests can immeadiatly be reforested

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INTIALFOREST_EQU Thinning regime cannot be switched Initial thinning distribution unknown Let model decide, which thinning regime to use for initial forests

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REPLANT_EQU Restricts tree species that can be replanted after harvest (can have agricultural break inbetween) Regulated by tuple SPECIESSEQU_MAP(OLDSPECIES,SPECIES) Currently restrictive

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SOILSTATE_EQU To portray important unstable soil properties Carbon sequestration effect depends on soil carbon level Equations are implemented, EPIC data are not yet established SOILSTATE_EQU(REGION,PERIOD,SOILTYPE,SOILSTATE)

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SOILSTATE_EQU To portray important unstable soil properties Carbon sequestration effect depends on soil carbon level Equations are implemented, EPIC data are not yet established

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SOILSTATE_EQU Contains soil state transition probabilities Probability_Data(REGION,SOILTYPE,SOILSTATE,SPECIES, OWNER,COHORT,ALLTECH,POLICY,OLDSTATE) Transition probabilities are calculated from EPIC based carbon functions

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Soil Carbon Transition Probabilities SOC1SOC2SOC3SOC4SOC5SOC6SOC7SOC8 SOC10.810.19 SOC21 SOC30.090.91 SOC40.310.69 SOC50.5 SOC60.740.26 SOC71 SOC80.040.96 No-till Wheat Fallow

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Soil Organic Carbon (tC/ha/20cm) 5 10 15 20 25 30 35 40 45 0 10 20 30 40 50 Time (years) Wheat-Lucerne 3/3 Wheat-Lucerne 6/3 No-till wheat-fallow Tilled wheat-fallow Carbon Functions

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STOCK_EQU STOCK_EQU(REGION,PERIOD,STOCK) $(STOCK_TUPLE(REGION,PERIOD,STOCK) AND STOCK_DATA(REGION,PERIOD,STOCK,"DecompRate")).. Represents dynamics of dead wood (14 types) Linked to emission accounting

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PRODUCTINVENT_EQU PRODUCTINVENT_EQU(REGION,PERIOD,PRODUCT) Represents different product life span of forest products Linked to carbon emissions from forest products

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EMIT_EQU EMIT_EQU(REGION,PERIOD,SUBSTANCE) $ EMIT_TUPLE(REGION,PERIOD,SUBSTANCE).. Accounting equation Contains direct emissions and emissions from stock changes

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Why Large Models? Land use is diverse and globally linked We want both high resolution and large scope More computer power tempts larger models Data availability better

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Large Model Effects Indexed data, variables, and equations Dimensions need to be carefully conditioned More things can go wrong Less intuition in model drivers Causes of misbehavior difficult to guess Higher probability that some errors are not discovered

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Pre-Solution Analysis Generic variable and equation checks About 30 different types Easy in GAMS through use of GAMSCHK, possible with other software

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Example Nonnegative Variable X j occurs only in <= constraints All a ij coefficients are nonnegative All objective function coefficients (c j ) are nonpositive Optimal X j = 0! (Maximization problem)

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More Generic Checks

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Linear Program Duality

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Reduced Cost Shadow prices Technical Coefficients Objective Function Coefficients

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Complementary Slackness Reduced Cost Opt. Variable Level Shadow Price Opt. Slack Variable Level

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Fixing Non-sensible Models Zero/large variables: look at cost and benefits of these variables in individual equations High shadow prices: indicate resource scarcity (check endowments, technical coefficients, units) In general, analyst needs a combination of mathematical and context knowledge

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Conclusions Large mathematical programming models are not necessarily black boxes Drivers for individual results can be traced and understood Generic misspecifications can and should always be corrected Systematic post-optimality analysis is by far better and faster than intuition and guesswork

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