1. CAPRI CAPRI market model Torbjörn Jansson* Markus Kempen *Corresponding author +49-228-732323 www.agp.uni-bonn.de Department for Economic and Agricultural Policy Bonn University Nussallee 21 53115 Bonn, Germany CAPRI Training Session in Warzaw June 26-30, 2006 CAPRI Common Agricultural Policy Regional Impact

2. CAPRI CAPRI Training Session in Warzaw, June 26-30, 2006 2 Outline About multi-commodity models Principles of the CAPRI market module MultReg step by step –Final demand –Price transmission –Production and processing Iterative solution (Calibration issues)

3. CAPRI CAPRI Training Session in Warzaw, June 26-30, 2006 3 What is a Multi-Commodity Model ? More than one output market, but not general equilibrium System of equations: no objective function Same number of endogenous variables as equations (so called square system, CNS) Many examples: –SWOPSIM (http://usda.mannlib.cornell.edu/data-sets/trade/92012/) –AGLink OECD –FAPRI (http://www.fapri.missouri.edu/) –AgMemod (http://tnet.teagasc.ie/agmemod/public.htm) –WATSIM (http://www.agp.uni-bonn.de/agpo/rsrch/wats_e.htm)

4. CAPRI CAPRI Training Session in Warzaw, June 26-30, 2006 4 Elements of a Multi-Commodity Model Behavioural functions: defining quantities as function of prices, e.g. demand and supply functions Price linkage functions: defining e.g. import prices from border prices and tariffs Market balances

5. CAPRI CAPRI Training Session in Warzaw, June 26-30, 2006 5 Result as an economic equilibrium Marginal willingness to pay = prices paid by consumers (Quantities demanded are on demand function) Marginal costs = prices received by producers (Quantities supply are on supply function) Markets are cleared  “Planned” production equal “Planned demand”

6. CAPRI CAPRI Training Session in Warzaw, June 26-30, 2006 6 Solver World Market Prices Flowchart of a Multi-Commodity Model World Market Balance Regional Prices Pr Supply Sr=f(Pr) Demand Dr=f(Pr) Net Trade NTr=Sr-Dr Regional Prices Pr Supply Sr=f(Pr) Demand Dr=f(Pr) Net Trade NTr=Sr-Dr

7. CAPRI CAPRI Training Session in Warzaw, June 26-30, 2006 7 Components of MultReg Final demand –Generalised Leontief Expenditure (GLE) system –Armington assumption with CES functions Supply of primary and processed products –Normalised quadratic profit functions –Fat and protein balances for dairies Price transmission –Discontinuities (TRQ) solved by fudging functions Market balances

8. CAPRI CAPRI Training Session in Warzaw, June 26-30, 2006 8 Quantity relations in market model Production, change in Intervention Stocks Exports Domestic Sales Demand aggregate (Armington 1) Cakes, Oils, Dairy ProcessingFeed Human Consumption Import aggregate (Armington 2)

9. CAPRI CAPRI Training Session in Warzaw, June 26-30, 2006 9 Price relations in market model Producer Prices (PPri) Average price of quantities consumed (Arm1P) Import Prices (Impp) Average “import” Price from Armington 2 (Arm2P) Price for domestically produced goods (PMrk) PSEs, margin Consumer Prices (CPri) CSEs, margin Processing margins for oilseeds (ProcMarg) Processing yields Processing margins for dairy products (ProcMarg) Prices for milk fat and protein (PFatProt) Import tariffs (Tars,Tarv) Export Subsidies (Expsub) TRQs, safeguards Transport costs (tcost)

10. CAPRI CAPRI Training Session in Warzaw, June 26-30, 2006 10 Parameters and Variables in the Market Module Scenario parametersFixed parametersEndogenous Variables Parameters in behavioural functions: Supply Processing Human consumption Feed Use Technical parameters: Crushing yields Fat & protein content of milk products Prices: Base year price producer Marketing span for final products Parameters in functions determining interventions and subsidized exports Demand shifts: Population growth GDP development Changes in consumption pattern Shifts in behavioural functions Exchange rates Policy instruments: Administrative prices Maximal market interventions Import Tariffs Tariff Rate Quotas Minimal import prices Subsidised exports Commitments Non market PSEs CSEs Quantities: Supply Processing Human consumption Feed Use Intervention sales Bilateral trade flows Price elements: Market prices Producer price Consumer price Processing margins Import prices Export subsidies Tariffs

11. CAPRI CAPRI Training Session in Warzaw, June 26-30, 2006 11 Behavioural Functions Supply Side: –Supply of primary products –Supply of selected processed products Demand Side: –Human consumption –Demand for feed use –Demand of the processing industry

12. CAPRI CAPRI Training Session in Warzaw, June 26-30, 2006 12 Processing in the CAPRI Market Model Two classes of processed products –Oils and cakes Sunflower seed, rape seed, soy beans Leontief-Technology assumed Supply depends on the value of output (cakes and oils) minus the value of input (oilseed) –Dairy Submodule Supply driven by the processing margin of the dairy Processing margin: –difference between the retail price and the value of fat and protein Fat and protein balances –ensure that all milk components are used up in the dairy

13. CAPRI CAPRI Training Session in Warzaw, June 26-30, 2006 13 Functional forms Quantity variable (vriable name) Functional form (equation name/names) Driving variables (variable names) Supply (Production) Normalized non- symmetric quadratic (ProdNQ_) Producer prices (PPri) Supply of cakes and oils (Production) Leontief (ProcO_) Processing of oilseeds (Proc), processing yield Supply of dairy products (Production) Normalized non- symmetric quadratic (DairyNQ_,ProcMargM_) Processing margin (ProcMarg) as market price (PPri) minus value of milk fat and protein Feed (FeedUse) Normalized non- symmetric quadratic (FeedNQ_,FeedShift_) Average price domestic/imports (Arm1P) minus feed subsidies Energy shifter (FeedShift, depends on animal production) Processing (Proc) Normalized non- symmetric quadratic (ProcNQ_) Producer prices (Ppri) exemption: processing margin (ProcMarg) for oilseed processing Human consumption (Hcon) Generalised Leontief Expenditure System Consumer prices (Cpri), income, population

14. CAPRI Final demand GLE with Armington

15. CAPRI CAPRI Training Session in Warzaw, June 26-30, 2006 15 Final demand: GLE system Indirect utility function F and G functions, homog. of deg. one in prices P, Y = Income Use Roy’s identity to derive demands X i

16. CAPRI CAPRI Training Session in Warzaw, June 26-30, 2006 16 The Generalised Leontief Expenditure function Expenditure remaining after commitments are covered Value of minimum commitments D i = Consumption independent of prices and income

17. CAPRI CAPRI Training Session in Warzaw, June 26-30, 2006 17 Final demand: GLE and welfare Indirect utility function Invert to expenditure function using U(X) = V(P,Y) Compute: “How much income would be required at the reference prices to let the consumer reach the Utility Level obtained in the simulation?”

18. CAPRI CAPRI Training Session in Warzaw, June 26-30, 2006 18 Why money metric as the utility measurement ? Theoretically consistent Easy to interprete: income equivalent of the utility in the simulation using the prices of the reference situation Can be hence added/compared to costs/revenues/taxes directly to calculate overall welfare (change) Becomes part of the objective function (works as „consumer surplus“)

19. CAPRI CAPRI Training Session in Warzaw, June 26-30, 2006 19 Spatial models Bilateral trade streams included Two standard types: –Transport cost minimisation –“Armington assumption”: Quality differences between origins, let consumers differentiate We want to allow simultaneous export and import of goods.

20. CAPRI CAPRI Training Session in Warzaw, June 26-30, 2006 20 Armington Approach Armington, Paul S. 1969 "A Theory of Demand for Products Distinguished by Place of Production,“ IMF Staff Papers 16, pp. 159-178. CES-Utility aggregator for goods consumed from different origins x i,r Aggregated utility of consuming this product M i,r,s Import streams including domestic sales  shift parameter  share parameter  parameter related to substitution elasticity i product, r importing regions, s exporting regions

21. CAPRI CAPRI Training Session in Warzaw, June 26-30, 2006 21 First order conditions for the Armington First order conditions(FOC) from CES-Utility aggregator ( max {U = CES(M 1,M 2 ): P 1 M 1 +P 2 M 2 = Y } ) Relation between import streams is depending on: –so called “share parameters” –multiplied with the inverse import price relation –exponent the substitution elasticity Imperfect substitution (“sticky” import shares)

22. CAPRI CAPRI Training Session in Warzaw, June 26-30, 2006 22 Flowchart Regional Prices Pr Supply S r =f(P r ) Domestic Sales Imports Regional Prices Pr Supply S r =f(P r ) Domestic Sales Imports GLE demand x i,r = f(P CES ) GLE demand x i,r = f(P CES )

23. CAPRI CAPRI Training Session in Warzaw, June 26-30, 2006 23 Problems of the Armington Approach Few empirical estimations of the parameters => substitution elasticities are set by a “rule-of- thumb” A zero stream in the calibrated points remains zero in all simulation runs The sum of physical streams (domestic sales + imports) is not equal to the utility aggregate in simulations !!! (demand “quantities” are not longer tons, but a utility measurement...)

24. CAPRI CAPRI Training Session in Warzaw, June 26-30, 2006 24 CES function: Iso-utility lines (M1,M2)(M1,M2) (M1*,M2*)(M1*,M2*) Enforced in calibration by choice of 

25. CAPRI Supply of primary and processed products Normalised quadratic profit function

26. CAPRI CAPRI Training Session in Warzaw, June 26-30, 2006 26 Reminder – Micro Theory Production in implicit form: Maximizing Profit: Optimal Supply: Input Demand: Normalized Quadratic Profit Function:

27. CAPRI CAPRI Training Session in Warzaw, June 26-30, 2006 27 Processing industry Normalised quadratic profit function plus –Fixed processing yield for oilseed crushing –Protein and fat balances for dairies

28. CAPRI Price Transmission Smoothing out corners with fudging functions

29. CAPRI CAPRI Training Session in Warzaw, June 26-30, 2006 29 Motivation Import price is foreign price minus subsidies plus transport costs and tariffs S= export subsidied of exporting country C= transportation cost Ta= ad-valorem tariff Ts= specific tariff D= variable import levy to emulate entry price system Discontinuities: -If TRQ is filled, MFN tariff is applied, otherwise tariff is lower -If import price is higher than the min. border price, tariff is lower than MFN -If import price is higher than the entry price, tariff is also lower than MFN

30. CAPRI CAPRI Training Session in Warzaw, June 26-30, 2006 30 Handling functions with corners f = max (0, x) and g = min (x, y) are very difficult for solver because the derivative in the corner is not defined/unique. Common approximations: (try x = 10, x = -10) f*= ½(x +  (x 2 +  ) –  ) g*= ½(x + y –  ((x – y) 2 +  ) –  ) h(x) = {l if x ≤ C, u if x > C} can be approximated using logistic function, cumulative normal distribution function or GAMS internal sigmoid() to obtain S-shaped curve.

31. CAPRI CAPRI Training Session in Warzaw, June 26-30, 2006 31 Illustration TRQ TRQ = Tariff Rate Quota If import volume is below quota, tariff < MFN tariff Bilateral or global Modelled by GAMS-function “sigmoid”, represented by f() T = T pref + (T mfn -T pref )f(M – TRQ) TRQImport T pref T mfn Tariff True function Sigmoid function

32. CAPRI CAPRI Training Session in Warzaw, June 26-30, 2006 32 Illustration minimum border price If P cif is below the minimum border price, a variable levy is added to reach the border price The additional levy is limited by the MFN rate D true = min (max (0,P cif +T mfn - P min ),T mfn ) D = ½(F + T mfn -  ((F- T mfn ) 2 +  2 ) -  ) F = ½(P cif +T mfn -P min +  ((P cif +T mfn -P min ) 2 +  2 ) -  ) T mfn P cif P imp True function Sigmoid function D P min

33. CAPRI Iterative solution

34. CAPRI CAPRI Training Session in Warzaw, June 26-30, 2006 34 Supply Supply Regional optimisation models Perennial sub-module Markets Markets Multi-commodity spatial market model Prices Reminder – General Model Layout Quantities Iterations Comparative Static Equilibrium Young animal trade Direct payment model

35. CAPRI CAPRI Training Session in Warzaw, June 26-30, 2006 35 On convergence d s q p p0p0 p0p0 q p s d s

36. CAPRI CAPRI Training Session in Warzaw, June 26-30, 2006 36 Conclusions If “demand elasticity” > “supply elasticity”, it will converge, otherwise not CAPRI has to be solved iteratively Elasticities are chosen bases on economic criteria not to obtain convergence  We will likely need some mechanism promote convergence in CAPRI

37. CAPRI CAPRI Training Session in Warzaw, June 26-30, 2006 37 Different ways of promoting convergence Adjustment cost: Additional production cost for deviating from the supply in the previous step Price expectation: Supply uses weighted average of prices in several previous step. Used in CAPRI Partial adjustment: Supply only moves a fraction of the way towards the optimum in each step Approximate supply functions used in market instead of fixed supply. Used in CAPRI

38. CAPRI CAPRI Training Session in Warzaw, June 26-30, 2006 38 Approximation of supply functions The implicit supply function is unknown –Difficult to derive for CAPRI –Has non-differential points (corners)  difficult to solve together with market model Assume “any” simple supply function that approximates the supply model Calibrate the parameters in each step so that the supply response of last step is reproduced

39. CAPRI CAPRI Training Session in Warzaw, June 26-30, 2006 39 Approximating supply p0p0 q p s d s Assume the “explosive situation”…

40. CAPRI CAPRI Training Session in Warzaw, June 26-30, 2006 40 Approximating supply p0p0 q p s d s s’ q0q0 Supply function is unknown (supply is a black box) Assume any supply function Starting with some price, compute supply Calibrate the assumed supply function to that point Solve supply + demand simultaneously for new price Iterate…

41. CAPRI Calibration issues

42. CAPRI CAPRI Training Session in Warzaw, June 26-30, 2006 42 Calibration of supply parameters Only one observation of Quantities and (normalized) prices → additional information / constraints needed: Micro Theory: –Symmetry –Homogeniety –Correct Curvature Literature: –Elasticities

43. CAPRI CAPRI Training Session in Warzaw, June 26-30, 2006 43 Parameter calibration Original elasticities Restrictions: Micro theory Constraints of minimisation problem SymmetryHomogeneity Correct Curvature Objective: keep close to original ones Consistent elasticities Consistent parameters Functional form

44. CAPRI CAPRI Training Session in Warzaw, June 26-30, 2006 44 Calibration of parameters to given elasticities Search parameter vector which produces a regular demand system (here: symmetric pdb with non-negative off- diagonal elements) Reproduces the observed combination of prices and quantities And leads to point elasticities „close“ to the given ones

45. CAPRI CAPRI Training Session in Warzaw, June 26-30, 2006 45 Point elasticities of the Generalised Leontief Expenditure function Marshallian Demands for any function G and F and their derivatives versus prices Gi and Fi Income elasticities of demand Cross price elasticities of demand

46. CAPRI CAPRI Training Session in Warzaw, June 26-30, 2006 46 Regularity conditions I Symmetry of second derivatives, here ensured if pdb p,p1 = pdb p1,p1 Homogeniety of degree one in prices, guaranteed by functions F and G Adding up fulfilled, use Eurer‘s law

47. CAPRI CAPRI Training Session in Warzaw, June 26-30, 2006 47 Regularity conditions II And the correct „curvature“, i.e. marginal utility decreasing in quantities is fulfilled if all off- diagonal elements of pdb are non-negative... However, then the form does not allow for Hicksian complemetarity (not fully flexible)