CAPRI Common Agricultural Policy Regional Impact CAPRI market

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

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

What is a Multi-Commodity Model ? CAPRI • 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: – – – CAPRI SWOPSIM (http: //usda. mannlib. cornell. edu/data-sets/trade/92012/) AGLink OECD FAPRI (http: //www. fapri. missouri. edu/) Ag. Memod (http: //tnet. teagasc. ie/agmemod/public. htm) WATSIM (http: //www. agp. uni-bonn. de/agpo/rsrch/wats_e. htm) 3 CAPRI Training Session in Warzaw, June 26 -30, 2006

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

CAPRI Result as an economic equilibrium CAPRI • 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” 5 CAPRI Training Session in Warzaw, June 26 -30, 2006

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

CAPRI Components of Mult. Reg CAPRI • 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 7 CAPRI Training Session in Warzaw, June 26 -30, 2006

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

Price relations in market model CAPRI Processing margins for oilseeds CAPRI Processing margins Prices for milk for dairy products fat and protein (Proc. Marg) (PFat. Prot) Processing yields Producer Prices Transport costs Export Subsidies Import tariffs (PPri) (tcost) (Expsub) (Tars, Tarv) TRQs, safeguards PSEs, margin Import Prices (Impp) Price for domestically produced goods Average “import” Price from Armington 2 (Arm 2 P) (PMrk) Average price of quantities consumed CSEs, margin (Arm 1 P) Consumer Prices (CPri) 9 CAPRI Training Session in Warzaw, June 26 -30, 2006

CAPRI Parameters and Variables in the Market Module Fixed parameters Scenario parameters • 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 CAPRI Endogenous Variables • 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 10 CAPRI Training Session in Warzaw, June 26 -30, 2006

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

CAPRI Processing in the CAPRI Market Model CAPRI • 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 CAPRI Training Session in Warzaw, June 26 -30, 2006 12

CAPRI Functional forms CAPRI Quantity variable (vriable name) Functional form (equation name/names) Driving variables (variable names) Supply (Production) Normalized nonsymmetric quadratic (Prod. NQ_) Producer prices (PPri) Supply of cakes and oils (Production) Leontief (Proc. O_) Processing of oilseeds (Proc), processing yield Supply of dairy products (Production) Normalized nonsymmetric quadratic (Dairy. NQ_, Proc. Marg. M_) Processing margin (Proc. Marg) as market price (PPri) minus value of milk fat and protein Feed (Feed. Use) Normalized nonsymmetric quadratic (Feed. NQ_, Feed. Shift_) Average price domestic/imports (Arm 1 P) minus feed subsidies Energy shifter (Feed. Shift, depends on animal production) Processing (Proc) Normalized nonsymmetric quadratic (Proc. NQ_) Producer prices (Ppri) exemption: processing margin (Proc. Marg) for oilseed processing Human consumption (Hcon) Generalised Leontief Expenditure System Consumer prices (Cpri), income, population 13 CAPRI Training Session in Warzaw, June 26 -30, 2006

CAPRI Final demand • GLE with Armington

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

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

CAPRI Final demand: GLE and welfare CAPRI 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? ” 17 CAPRI Training Session in Warzaw, June 26 -30, 2006

CAPRI 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“) CAPRI 18 CAPRI Training Session in Warzaw, June 26 -30, 2006

CAPRI • • Spatial models CAPRI 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. 19 CAPRI Training Session in Warzaw, June 26 -30, 2006

CAPRI 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 CAPRI xi, r Aggregated utility of consuming this product Mi, r, s Import streams including domestic sales shift parameter share parameter related to substitution elasticity i r s product, importing regions, exporting regions 20 CAPRI Training Session in Warzaw, June 26 -30, 2006

CAPRI First order conditions for the Armington CAPRI • 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) 21 CAPRI Training Session in Warzaw, June 26 -30, 2006

Flowchart CAPRI Regional Prices Pr Supply Sr=f(Pr) Domestic Sales Imports GLE demand xi, r = f(PCES) 22 CAPRI Training Session in Warzaw, June 26 -30, 2006

CAPRI Problems of the Armington Approach CAPRI • Few empirical estimations of the parameters => substitution elasticities are set by a “rule-ofthumb” • 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. . . ) 23 CAPRI Training Session in Warzaw, June 26 -30, 2006

CAPRI CES function: Iso-utility lines CAPRI Enforced in calibration by choice of (M 1, M 2) (M 1*, M 2*) 24 CAPRI Training Session in Warzaw, June 26 -30, 2006

CAPRI Supply of primary and processed products • Normalised quadratic profit function

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

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

CAPRI Price Transmission • Smoothing out corners with fudging functions

Motivation CAPRI Import price is foreign price minus subsidies plus transport costs and tariffs S C Ta Ts D = export subsidied of exporting country = transportation cost = ad-valorem tariff = specific tariff = 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 29 CAPRI Training Session in Warzaw, June 26 -30, 2006

CAPRI Handling functions with corners CAPRI • 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. 30 CAPRI Training Session in Warzaw, June 26 -30, 2006

CAPRI 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() CAPRI Tariff Tmfn Tpref T = Tpref + (Tmfn-Tpref)f(M – TRQ) TRQ Import True function Sigmoid function 31 CAPRI Training Session in Warzaw, June 26 -30, 2006

CAPRI 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) CAPRI Pimp D Pmin Tmfn D = ½(F + Tmfn - ((F- Tmfn)2 + 2) - ) F = ½(Pcif+Tmfn -Pmin+ ((Pcif+Tmfn -Pmin)2 + 2) - ) Pcif True function Sigmoid function 32 CAPRI Training Session in Warzaw, June 26 -30, 2006

CAPRI Iterative solution

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

CAPRI p p 0 On convergence CAPRI p s s p 0 d d q q 35 CAPRI Training Session in Warzaw, June 26 -30, 2006

CAPRI Conclusions CAPRI • 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 36 CAPRI Training Session in Warzaw, June 26 -30, 2006

CAPRI Different ways of promoting convergence CAPRI • 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 37 CAPRI Training Session in Warzaw, June 26 -30, 2006

CAPRI Approximation of supply functions CAPRI • 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 38 CAPRI Training Session in Warzaw, June 26 -30, 2006

CAPRI Approximating supply CAPRI • Assume the “explosive situation”… p s p 0 d q 39 CAPRI Training Session in Warzaw, June 26 -30, 2006

CAPRI • • • Approximating supply Supply function is unknown (supply is a black box) Assume any supply function Starting with some price, compute p supply Calibrate the assumed supply function to that point Solve supply + demand simultaneously for new price Iterate… p 0 CAPRI s’ s’ s d q 0 q 40 CAPRI Training Session in Warzaw, June 26 -30, 2006

CAPRI Calibration issues

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

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

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

CAPRI Point elasticities of the Generalised Leontief Expenditure function CAPRI 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 45 CAPRI Training Session in Warzaw, June 26 -30, 2006

CAPRI • • • Regularity conditions I CAPRI Symmetry of second derivatives, here ensured if pdbp, p 1 = pdbp 1, p 1 Homogeniety of degree one in prices, guaranteed by functions F and G Adding up fulfilled, use Eurer‘s law 46 CAPRI Training Session in Warzaw, June 26 -30, 2006

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