FASOM Hamburg July 1-3, 2008

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

I FASOM Basics

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

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

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

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

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

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

FASOM = Large Linear Programs

Programming Declare and Assign Indexes Exogenous data Endogenous data Equations (endogenous/exogenous) Run Programs and Display Results

Major Indexes (Sets) (decl_basicsets.gms) Regions Periods Altitudes Species Resources Cohorts Farm sizes Farm types Technologies Products Substances

Sets Identify scope Efficient but dangerous and difficult Super sets, Sub sets, Tuples decl_basicsets.gms 2_activesets.gms calc_tuples.gms

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

Exogenous Data Parameters (Tables, Scalars) decl_parameters.gms Data_*.gms

Data Subdirectories EPIC FINDUS FADN+ others OSKAR FAO BIODIV

Endogenous Data Land use decisions (control variables), Impacts (state variables), Shadow prices of constraints Positive and Free Variables (Integer Variabales) 4_eufasom_model.gms

Equations Understanding them is to understand FASOM

Equations Objective Function Resource Restrictions Technological Restrictions Environmental Accounts Others

Major Parameters FOREST_DATA (PERIOD,REGION,SOILTYPE,SOILSTATE,SPECIES,FARM,AGE,ALLTECH,ALLITEM) PEREN_DATA (PERIOD,REGION,SOILTYPE,SOILSTATE,SPECIES,FARM,AGE,ALLTECH,ALLITEM) CROP_DATA (PERIOD,REGION,SOILTYPE,SOILSTATE,SPECIES,FARM,ALLTECH,ALLITEM) ECO_DATA (PERIOD,REGION,SOILTYPE,SOILSTATE,ALLTECH,ALLITEM) LIVE_DATA (PERIOD,REGION,ANIMAL,ALLTECH,ALLITEM) FEED_DATA (PERIOD,REGION,PRODUCT,ALLTECH,ALLITEM) PROCESS_DATA (PERIOD,REGION,ALLTECH,ALLITEM) PRODUCT_DATA (PERIOD,REGION,PRODUCT,ALLITEM) MARKET_DATA (PERIOD,REGION,ALLITEM,SDTYPE,SDITEM) TRADE_DATA (PERIOD,REGION,REGION,PRODUCT,ALLITEM) RESOURCE_DATA (PERIOD,REGION,ALLRESOURCE,SDITEM) STOCK_DATA (PERIOD,REGION,PRODUCT,ALLITEM) LUC_DATA (PERIOD,REGION,SOILTYPE,SPECIES,ALLCHANGE,ALLITEM)

Major Variables RESOURCE_VAR (PERIOD,REGION,RESOURCE) FOREST_VAR (PERIOD,REGION,SOILTYPE,SOILSTATE,SPECIES,OWNER,AGE,FORTECH) PEREN_VAR (PERIOD,REGION,SOILTYPE,SOILSTATE,SPECIES,FARM,AGE,CROPTECH) CROP_VAR (PERIOD,REGION,SOILTYPE,SOILSTATE,SPECIES,FARM,CROPTECH) LIVE_VAR (PERIOD,REGION,ANIMAL,LIVETECH) FEED_VAR (PERIOD,REGION,ANIMAL,PRODUCT,FEEDTECH) ECO_VAR (PERIOD,REGION,SOILTYPE,SOILSTATE,ECOTECH) PROCESS_VAR (PERIOD,REGION,PROCTECH) LUC_VAR (PERIOD,REGION,SOILTYPE,SPECIES,CHANGE) DEMAND_VAR (PERIOD,REGION,PRODUCT) SUPPLY_VAR (PERIOD,REGION,PRODUCT) TRADE_VAR (PERIOD,REGION,REGION,PRODUCT)

Major Equations OBJECTIVE_EQU RESOURCEBAL_EQU (PERIOD,REGION,RESOURCE) RESOURCEMAX_EQU (PERIOD,REGION,RESOURCE) SOILSTATE_EQU (PERIOD,REGION,SOILTYPE,SOILSTATE) FORINVENT_EQU (PERIOD,REGION,SOILTYPE,SOILSTATE,SPECIES,OWNER,AGE,FORTECH) LUC_EQU (PERIOD,REGION,SOILTYPE,SPECIES,CHANGE) LUCLIMIT_EQU (PERIOD,REGION,SOILTYPE,SPECIES,CHANGE) STOCK_EQU (PERIOD,REGION,STOCK) EMIT_EQU (PERIOD,REGION,SUBSTANCE) PRODUCTBAL_EQU (PERIOD,REGION,PRODUCT) MINFEED_EQU (PERIOD,REGION,ANIMAL,NUTRIENT) MAXFEED_EQU (PERIOD,REGION,ANIMAL,NUTRIENT)

Managing the Model Scope 2_active_sets.gms –index elements on/off decl_scope.gms –components on/off

FASOM File Structure Main directory (full access) Data subdirectories (restricted access) –Agriculture (FADN) –Crop environmental impacts (EPIC) –Bioenergy (ENFA) –Nature Reserves (HABITAT) –Forest Stands (OSKAR) –Forest Industry (FINDUS) –FAOSTAT –Dynamics

FASOM File Naming (Main Dir) Data files (data_*.gms) Declaration files (decl_*.gms) Input calculation files (calc_*.gms) Program files (#_*.gms) GAMSCHK files (*.gck), Solver option files (*.opt) Report files (rep_*.gms) Special program files (z#_*.gms) *= description #=1,2,...,k

FASOM Sub Directories Store original data files in provider format Convert data to FASOM format (names, resolution, unit consistency) Automated programs, slow, infrequent use Protect main FASOM directory from information floods Confidentiality (FADN), IPR

FASOM Execution 1_load_data.gms (primary data files) 2_active_sets.gms (determine model size) 3_precompute.gms (calculation files) 4_eufasom_model.gms (equations) 5_base_report.gms (base solution report) 6_scenario.gms (repeated solves) 7_results.gms (scenario differences)

Save / Restart When using GAMSIDE, each program segment must restart from previous one and save for the next 1_load_data.gms (save.\t\a1) 2_active_sets.gms (restart.\t\a1 save.\t\a2) 3_precompute.gms (restart.\t\a2 save.\t\a3) 4_eufasom_model.gms (restart.\t\a3 save.\t\a4) 5_base_report.gms (restart.\t\a3 save.\t\a4)...

1_load_data.gms * Indexes $include decl_basicsets.gms $include decl_foresttuple.gms $offlisting * Load Data $include data_crop2000.gms $include data_faowood.gms $include data_faocrop.gms $include data_faoworldcrop2002.gms $include data_oatsprice.gms $include data_feed.gms $include data_land.gms $include data_cropsupply.gms $include data_averagecropemission.gms $include data_euepic.gms $include data_euluc.gms $include data_uscrops.gms $include data_peat.gms $include data_forprocess.gms $include data_forproduct.gms $include data_formarket.gms $include data_treelog.gms $include data_rotlength.gms $include data_forestrent.gms $include data_forest_set.gms $include data_forest_nor.gms $include data_forest_lrg.gms $include data_forest_sml.gms

2_active_sets.gms Define active set elements Region Period Product Cohort Can limit model scope to 1 Region, 1 Period, 1 Product

3_precompute.gms Assumptions and Definitions (Discounting) Deal with Data Gaps Calculations (Data, Tuples) Checks Calibrations (Zero Marginal Profits!) Experiments Check whether statements can be moved to subdirectory

4_eufasom_model.gms Variable declarations Equation declarations On/off switches for some equations FASOM equations (see part II) First solve statement 4_eufasom_model.gck

5_base_report.gms Declaration of report indexes and parameters Display of FASOM base solution –Current period (?=? observation) –Future periods (?=? econometric forecast)

6_scenario_loop.gms Define scenarios –Number (Set) –Assumptions (Parameters) –Declare report Loop over scenario set –Restore all parameters to original values –Implement scenario assumptions –Solve –Save solution

7_scenario_report.gms Display scenario results Comparison between base line solution and scenario solution

8_scenario_graphs.gms Display scenario results graphically Need gnupltxy installed

II FASOM Equations 4_eufasom_model.gms

Understanding FASOM Equations a)GAMS code (indexed equation block) b)DISPLAYCR output (individual equations) c)Display equation components

Condition(al)s Restrict cases (very important, many indexes) Use GAMSCHK to check PRODUCTBAL_EQU(REGION,PERIOD,PRODUCT) $ PRODUCT_TUPLE(REGION,PERIOD,PRODUCT).. calc_tuples.gms

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

FASOM = Large Linear Programs

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

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

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

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)

Linear Approximation in FASOM Use step variables (x i )... with i steps Convexity Restriction Sum(i, x i ) = 1 Identity Restriction Sum(i, a i x i ) = x DEMAND_VAR(REGION,PERIOD,PRODUCT) DEMAND_STEP(REGION,PERIOD,PRODUCT,STEP) DEMAND_CONVEXITY(REGION,PERIOD,PRODUCT) DEMAND_IDENTITY(REGION,PERIOD,PRODUCT) How many steps?

Correct Convex Combination? Model will automatically choose closest neighbor points

Constraints

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

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

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

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

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

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

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

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

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)

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 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

Soil Carbon Transition Probabilities SOC1SOC2SOC3SOC4SOC5SOC6SOC7SOC8 SOC SOC21 SOC SOC SOC50.5 SOC SOC71 SOC No-till Wheat Fallow

Soil Organic Carbon (tC/ha/20cm) Time (years) Wheat-Lucerne 3/3 Wheat-Lucerne 6/3 No-till wheat-fallow Tilled wheat-fallow Carbon Functions

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

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

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

Resource Balance * Resource Equations LUC_EQU(REGION,PERIOD,SOILTYPE,SPECIES,CHANGE) Land Use Change Equation LUCLIMIT_EQU(REGION,PERIOD,SOILTYPE,SPECIES,CHANGE) Land Use Change Limits * Environmental Externality Accounts * POPULATION_EQU(REGION,PERIOD,ECOSYSTEM,ANIMAL) Wildlife Population Accounting Equation * HABITAT0_EQU(REGION,PERIOD,ECOSYSTEM,ANIMAL) Habitat Requirement Equation * HABITAT1_EQU(REGION,PERIOD,ECOSYSTEM,ANIMAL) Habitat Requirement Equation * Production Equations: Jointly model agricultural and forestry products HARVESTINERTIA_EQU(REGION,PERIOD) Harvest Inertia Equation MINFEED_EQU(REGION,PERIOD,ANIMAL,MINNUTRIENT) Minimum Feed Intake MAXFEED_EQU(REGION,PERIOD,ANIMAL,MAXNUTRIENT) Maximum Feed Intake CROPMIX_EQU(REGION,PERIOD,SPECIES) Crop Mix Restrictions TOTALCROPMIX_EQU(REGION,PERIOD) Crop Mix Identity PRODUCTMIX_EQU(REGION,PERIOD,ALLPRODUCT) Product Mix Restrictions ANIMALMIX_EQU(REGION,PERIOD,SPECIES) Animal Mix Restrictions * PLANTCAP_EQU(REGION,PERIOD,COHORT,PROCTECH)

III Analyzing FASOM

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

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

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

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)

More Generic Checks

Generic Errors Caused by: Missing/misspecified data Missing/misspecified conditions Missing/misspecified equations Correction (rule of thumb): All individual variables need the same condition in all individual equations

Generic Checks Large models frequently reveal unchecked generic errors Errors may or may not impact optimal solution Correction always increases model speed Detection and correction of generic errors also applicable to non-linear models

Post-Solution Analysis of “Misbehaving” Solutions Infeasible equations  empty solution Unbounded variables  objective reaches infinity Non-sensible solutions

Infeasibility Very easy to detect Easy to fix Use artificial variables Analyze equations with non-zero artificial variables Look for constraints with high shadow prices

Unbounded Solution Very easy to detect Easy to fix Add artificial bounds Look for high variable levels Examine equations coefficients of unbounded variables

Non-sensible solution values Detection requires context knowledge Problem analysis more challenging Large deviations easier Must employ post optimality checks Start at the symptom Go backwards alternating between variables and equations

Linear Program Duality

Reduced Cost Shadow prices Technical Coefficients Objective Function Coefficients

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

Reduced Cost Equality Links variables with individual equations Positive a ij *U i  costs (Maximization) Negative a ij *U i  benefits (Maximization)

## CROP_VAR(Alabama,Corn,DryLand,BASE,W3-8Land,Vent,NONE,ND,Nbase) SOLUTION VALUE UPPER BOUND E+10 EQN Aij Ui Aij*Ui OBJT ProductBal(Corn,Southeast) MAXLAND(Alabama,W3-8Land) LABOR(Southeast) MIXREG(Corn,Alabama,All) MIXREGTOT(Alabama,All) EMITACCT(Southeast,FuelCarbon) E EMITACCT(Southeast,DrygCarbon) E EMITACCT(Southeast,FertCarbon) E EMITACCT(Southeast,PestCarbon) E EMITACCT(Southeast,SoilCarbon) E EMITACCT(Southeast,N2ODeNit) E EMITACCT(Southeast,N2OFert) E TRUE REDUCED COST ## CROP_VAR(Alabama,Corn,DryLand,BASE,W3-8Land,Vent,NONE,ND,Nbase) SOLUTION VALUE UPPER BOUND E+10 EQN Aij Ui Aij*Ui OBJT ProductBal(Corn,Southeast) MAXLAND(Alabama,W3-8Land) LABOR(Southeast) MIXREG(Corn,Alabama,All) MIXREGTOT(Alabama,All) EMITACCT(Southeast,FuelCarbon) E EMITACCT(Southeast,DrygCarbon) E EMITACCT(Southeast,FertCarbon) E EMITACCT(Southeast,PestCarbon) E EMITACCT(Southeast,SoilCarbon) E EMITACCT(Southeast,N2ODeNit) E EMITACCT(Southeast,N2OFert) E TRUE REDUCED COST Ex: Reduced Cost Computation

## FEEDINGBAL_EQU(Pacific,turkeypro0) VAR Aij Xj Aij*Xj LVSTBUDGET(CaliforniN,turkey,0,BASE) E E LVSTBUDGET(CaliforniS,turkey,0,BASE) E LVSTBUDGET(Oregon,turkey,0,BASE) E REGPROCESS(Pacific,trkpromix4) =L= =L= RHS COEFF SLACK EQUALS SHADOW PRICE ## FEEDINGBAL_EQU(Pacific,turkeypro0) VAR Aij Xj Aij*Xj LVSTBUDGET(CaliforniN,turkey,0,BASE) E E LVSTBUDGET(CaliforniS,turkey,0,BASE) E LVSTBUDGET(Oregon,turkey,0,BASE) E REGPROCESS(Pacific,trkpromix4) =L= =L= RHS COEFF SLACK EQUALS SHADOW PRICE Row Summing

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

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

IV Modifying FASOM

Watch out Unit consistency (5 year) Documentation