CAPRI market model

1
CAPRI market model
CAPRICommon Agricultural Policy Regional Impact

• Torbjörn JanssonMarkus Kempen

Corresponding author 49-228-732323www.agp.uni-b
onn.de
Department for Economic and Agricultural
Policy Bonn University Nussallee 21 53115 Bonn,
Germany
CAPRI Training Session in Warzaw June 26-30, 2006
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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)

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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.ht
  m)
• WATSIM (http//www.agp.uni-bonn.de/agpo/rsrch/wats
  _e.htm)

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Elements of a Multi-Commodity Model

• Behavioural functionsdefining quantities as
  function of prices, e.g. demand and supply
  functions
• Price linkage functionsdefining e.g. import
  prices from border prices and tariffs
• Market balances

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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

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Flowchart of a Multi-Commodity Model
World Market Balance

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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

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Quantity relations in market model
Production,change in Intervention Stocks
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Price relations in market model
Producer Prices(PPri)
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Parameters and Variablesin the Market Module

• Scenario parameters

• Fixed 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

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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

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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

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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 subsidiesEnergy 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
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Final demand

• GLE with Armington

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Final demand GLE system
Indirect utility functionF and G functions,
homog. of deg. one in prices P,Y Income
Use Roys identity to derive demands Xi
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The Generalised Leontief Expenditure function
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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?
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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/taxe
  s directly to calculate overall welfare (change)
• Becomes part of the objective function(works as
  consumer surplus)

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Spatial models

• Bilateral trade streams included
• Two standard types
• Transport cost minimisation
• Armington assumptionQuality differences
  between origins,let consumers differentiate
• We want to allow simultaneous export and import
  of goods.

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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
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First order conditions for the Armington

• First order conditions(FOC) from CES-Utility
  aggregator( max U CES(M1,M2) P1M1P2M2 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)

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Flowchart
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Problems of the Armington Approach

• Few empirical estimations of the parametersgt
  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 ...)

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CES function Iso-utility lines
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Supply of primary and processed products

• Normalised quadratic profit function

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Reminder Micro Theory

• Production in implicit form
• Maximizing Profit
• Optimal Supply
• Input Demand
• Normalized Quadratic
• Profit Function

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Processing industry

• Normalised quadratic profit function plus
• Fixed processing yield for oilseed crushing
• Protein and fat balances for dairies

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Price Transmission

• Smoothing out corners with fudging functions

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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

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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 gt C can be
  approximatedusing logistic function, cumulative
  normal distribution function or GAMS internal
  sigmoid() to obtain S-shaped curve.

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Illustration TRQ
Tariff

• TRQ Tariff Rate Quota
• If import volume is below quota, tariff lt 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
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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(PcifTmfn -Pmin?((PcifTmfn -Pmin)2 ?2) -
  ?)

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Iterative solution
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Reminder General Model Layout
SupplyRegionaloptimisationmodelsPerennialsub
-module
Markets Multi-commodityspatial market model
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On convergence
p
s
s
d
q
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Conclusions

• If demand elasticity gt 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

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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

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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

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Approximating supply

• Assume the explosive situation

p
s
s
d
q
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Approximating supply

• 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

p
s
s
d
q
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Calibration issues
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Calibration of supply parameters

• Only one observation of Quantities and
  (normalized) prices
• ? additional information / constraints needed
• Micro Theory
• Symmetry
• Homogeniety
• Correct Curvature
• Literature
• Elasticities

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Parameter calibration
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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

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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
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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 Eurers law

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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)