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## CAPRI market model

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**Torbjörn Jansson*Markus Kempen**CAPRICommon Agricultural Policy Regional Impact CAPRI market model CAPRI Training Session in Warzaw June 26-30, 2006 *Corresponding author +49-228-732323www.agp.uni-bonn.de Department for Economic and Agricultural Policy Bonn University Nussallee 21 53115 Bonn, Germany**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)**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)**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**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”**Solver**World Market Prices Regional Prices Pr Regional Prices Pr Supply Sr=f(Pr) Demand Dr=f(Pr) Supply Sr=f(Pr) Demand Dr=f(Pr) Net Trade NTr=Sr-Dr Net Trade NTr=Sr-Dr Flowchart of a Multi-Commodity Model World Market Balance**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**Exports**Importaggregate(Armington 2) Domestic Sales Cakes,Oils, Dairy Demand aggregate(Armington 1) HumanConsumption Processing Feed Quantity relations in market model Production,change in Intervention Stocks**Processing margins**for dairy products(ProcMarg) Prices for milk fat and protein(PFatProt) Processing margins for oilseeds(ProcMarg) Processingyields Transport costs (tcost) ExportSubsidies (Expsub) Importtariffs (Tars,Tarv) TRQs, safeguards PSEs,margin Import Prices (Impp) Price for domesticallyproduced goods(PMrk) Average “import” Price from Armington 2 (Arm2P) Average priceof quantities consumed(Arm1P) ConsumerPrices(CPri) CSEs,margin Price relations in market model Producer Prices(PPri)**Parameters and Variablesin the Market Module**• Fixed parameters • Scenario parameters Endogenous Variables • Parameters in behavioural functions: • Supply • Processing • Human consumption • Feed Use • Technical parameters: • Crushing yields • Fat & protein contentof milk products • Prices: • Base year priceproducer • Marketing spanfor final products • Parameters in functions determining interventions and subsidized exports • Demand shifts: • Population growth • GDP development • Changes inconsumption pattern • Shifts in behavioural functions • Exchange ratesPolicy instruments: • Administrative prices • Maximal marketinterventions • Import Tariffs • Tariff Rate Quotas • Minimal import prices • Subsidised exportsCommitments • 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**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**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**GLE with Armington**Final demand**Final demand: GLE system**Indirect utility functionF and G functions, homog. of deg. one in prices P,Y = Income Use Roy’s identity to derive demands Xi**Expenditure remaining after commitments are covered**Value of minimum commitments Di = Consumption independent of prices and income The Generalised Leontief Expenditure function**Invert to expenditure functionusing U(X) = V(P,Y)**Final demand: GLE and welfare Indirect utility function Compute: “How much income would be required at the reference prices to let the consumer reach the Utility Level obtained in the simulation?”**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“)**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.**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 aggregatorfor goods consumedfrom different origins xi,r Aggregated utility of consuming this product Mi,r,s Import streams including domestic sales shift parameter share parameter parameter related to substitution elasticity i product,r importing regions, s exporting regions**First order conditions for the Armington**• First order conditions(FOC) from CES-Utility aggregator( max {U = CES(M1,M2): P1M1+P2M2 = 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)**Regional**Prices Pr Regional Prices Pr Supply Sr=f(Pr) Supply Sr=f(Pr) Domestic Sales DomesticSales Imports Imports GLE demand xi,r = f(PCES) GLE demand xi,r = f(PCES) Flowchart**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 pointsremains 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 ...)**Enforced in calibration by choice of **(M1,M2) (M1*,M2*) CES function: Iso-utility lines**Normalised quadratic profit function**Supply of primary and processed products**Reminder – Micro Theory**Production in implicit form: Maximizing Profit: Optimal Supply: Input Demand: Normalized Quadratic Profit Function:**Processing industry**• Normalised quadratic profit function plus • Fixed processing yield for oilseed crushing • Protein and fat balances for dairies**Smoothing out corners with fudging functions**Price Transmission**Motivation**Import price is foreign price minus subsidies plus transport costs and tariffs S = export subsidied of exporting countryC = transportation costTa = ad-valorem tariffTs = specific tariffD = 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**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 + (x2 + ) –)g* = ½(x + y–((x – y)2 + ) –) • h(x) = {l if x≤ C, u if x > C} can be approximatedusing logistic function, cumulative normal distribution function or GAMS internal sigmoid() to obtain S-shaped curve.**Illustration TRQ**Tariff • 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 = Tpref+ (Tmfn-Tpref)f(M–TRQ) Tmfn Tpref TRQ Import True function Sigmoid function**Pimp**D Pmin Tmfn Pcif True function Sigmoid function Illustration minimum border price • If Pcif 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 Dtrue = min (max (0,Pcif+Tmfn - Pmin) ,Tmfn) D = ½(F + Tmfn -((F- Tmfn)2 +2) - ) F = ½(Pcif+Tmfn -Pmin+((Pcif+Tmfn -Pmin)2 +2) - )**Reminder – General Model Layout**Quantities Prices Young animal tradeDirect payment model Iterations Comparative Static Equilibrium SupplyRegionaloptimisationmodelsPerennialsub-module MarketsMulti-commodityspatial market model**p**s p0 p0 d q On convergence p s s d q**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**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**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**Assume the “explosive situation”…**p0 Approximating supply p s s d q**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… s’ s’ p0 q0 Approximating supply p s s d q**Calibration of supply parameters**Only one observation of Quantities and (normalized) prices → additional information / constraints needed: • Micro Theory: • Symmetry • Homogeniety • Correct Curvature • Literature: • Elasticities**Objective:keep closeto original ones**Consistent parameters Consistent elasticities Original elasticities Constraints of minimisation problem Functionalform Homogeneity Symmetry CorrectCurvature Restrictions:Micro theory Parameter calibration**Calibration of parametersto given elasticities**• Search parameter vector which produces a regular demand system(here: symmetric pdb with non-negative off-diagonal elements) • Reproduces the observed combinationof prices and quantities • And leads to point elasticities „close“ to the given ones**Point elasticities of the Generalised Leontief Expenditure**function Marshallian Demands for any function G and Fand their derivatives versus prices Gi and Fi Income elasticities of demand Cross price elasticities of demand**Regularity conditions I**• Symmetry of second derivatives,here ensured if pdbp,p1 = pdbp1,p1 • Homogeniety of degree one in prices,guaranteed by functions F and G • Adding up fulfilled, use Eurer‘s law**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)