capri capri market model torbjörn jansson* markus kempen *corresponding author +49-228-732323 ...

CAPRI CAPRI

CAPRI market model

Torbjörn Jansson*Markus Kempen

*Corresponding author+49-228-732323www.agp.uni-bonn.de

Department for Economic and Agricultural PolicyBonn UniversityNussallee 2153115 Bonn, Germany

CAPRI Training Session in WarzawJune 26-30, 2006

CAPRICommon Agricultural Policy Regional Impact

CAPRI 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)

CAPRI CAPRI


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)

CAPRI CAPRI


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

CAPRI CAPRI


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”

CAPRI CAPRI


6

Solver

World MarketPrices

Flowchart of a Multi-Commodity Model

World MarketBalance

RegionalPrices Pr

SupplySr=f(Pr)

DemandDr=f(Pr)

Net TradeNTr=Sr-Dr

RegionalPrices Pr

SupplySr=f(Pr)

DemandDr=f(Pr)

Net TradeNTr=Sr-Dr

CAPRI CAPRI


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

CAPRI CAPRI


8

Quantity relations in market model

Production,change in

Intervention StocksExports

Domestic Sales

Demand aggregate(Armington 1)

Cakes,Oils,Dairy

Processing Feed HumanConsumption

Importaggregate

(Armington 2)

CAPRI CAPRI


9

Price relations in market model

ProducerPrices

(PPri)

Average priceof quantities consumed

(Arm1P)

Import Prices(Impp)

Average “import” Pricefrom Armington 2

(Arm2P)

Pricefor domesticallyproduced goods

(PMrk)

PSEs,margin

ConsumerPrices

(CPri)

CSEs,margin

Processing marginsfor oilseeds

(ProcMarg)

Processingyields

Processing marginsfor dairy products

(ProcMarg)

Prices for milkfat and protein

(PFatProt)

Importtariffs

(Tars,Tarv)

ExportSubsidies

(Expsub)

TRQs, safeguards

Transportcosts (tcost)

CAPRI CAPRI


10

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 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

CAPRI CAPRI


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

CAPRI CAPRI


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

CAPRI CAPRI


13

Functional formsQuantity 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

CAPRI CAPRI

Final demand

GLE with Armington

CAPRI CAPRI


15

Final demand: GLE system

Y

YPv

P

YPvX

ii

),(),(

)(

)(),(

PFY

PGYPv

Indirect utility functionF and G functions, homog. of deg. one in prices P,Y = Income

)()()(

)(PFPFY

PG

PGi

i

Use Roy’s identity to derive demands Xi

CAPRI CAPRI


16

The Generalised Leontief Expenditure function

PopFYG

GDx i

ii

ii

i PDF

i j

jiji PPBG ,

jijjii

i

PPBGP

G,

Expenditure remaining after commitments are covered

iii

DFP

F

Value of minimum commitments

Di = Consumption independent of prices and income

CAPRI CAPRI


17

Final demand: GLE and welfare

)(,

),( simsimsim

refref

simsim

refrefrefsim FY

G

GF

YPv

GFPUe

)(

)(),(

PFY

PGYPv

Indirect utility function

),(

)()(),(

YPv

PGPFPUeY 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?”

CAPRI CAPRI


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“)

CAPRI CAPRI


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.

CAPRI CAPRI


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 aggregatorfor goods consumedfrom different origins

1

,,,,,,

ssrisririri Mx

xi,r Aggregated utility of consuming this productMi,r,s Import streams including domestic sales

shift parameter share parameter parameter related to substitution elasticity

i product,r importing regions, s exporting regions

CAPRI CAPRI


21

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)

11

1,,

2,,

2,,

1,,

2,,

1,,

rri

rri

rri

rri

rri

rri

P

P

M

M

CAPRI CAPRI


22

Flowchart

RegionalPrices Pr

SupplySr=f(Pr)

DomesticSales

Imports

RegionalPrices Pr

SupplySr=f(Pr)

Domestic Sales

Imports

GLE demandxi,r = f(PCES)

1

11,,1,,,,

rrrirririri Mx

1

11,,1,,,,

rrrirririri Mx

GLE demandxi,r = f(PCES)

CAPRI CAPRI


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 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 ...)

CAPRI CAPRI


24

CES function: Iso-utility lines

0

2

4

6

8

10

12

0 2 4 6 8 10 12

Consumption of domestic beef

Con

sum

ptio

n of

impo

rted

bee

f

(M1,M2)

(M1*,M2

*)

),(),( *2

*121 MMxMMx

Enforced in calibration by choice of

21 MM *2

*1 MM

CAPRI CAPRI

Supply of primary and processed products

Normalised quadratic profit function

CAPRI CAPRI


26

Reminder – Micro Theory

Production in implicit form:

Maximizing Profit:

Optimal Supply:

Input Demand:

Normalized Quadratic

Profit Function:

)21( max 2

1110 XXqpXX

012

11

**

5.0)(

),(

ananan

qVpXqp

21110 2

1 XXV

p

qX

Xp

qa

p

qa

1 11

111 11 1

1*

0

2

11

2

1111

21

0*

2

11

2

1

2

1a

q

pa

q

pV

CAPRI CAPRI


27

Processing industry

• Normalised quadratic profit function plus

– Fixed processing yield for oilseed crushing

– Protein and fat balances for dairies

CAPRI CAPRI

Price Transmission

Smoothing out corners with fudging functions

CAPRI CAPRI


29

Motivation

srssr

asrrss

mrks

impsr DTTCSPP ,,,,, 1

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

CAPRI CAPRI


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 + (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.

CAPRI CAPRI


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 = Tpref + (Tmfn-Tpref)f(M – TRQ) TRQ Import

Tpref

Tmfn

Tariff

True functionSigmoid function

CAPRI CAPRI


32

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) - )

Tmfn

Pcif

Pimp

True functionSigmoid function

DPmin

CAPRI CAPRI

Iterative solution

CAPRI CAPRI


34

SupplyRegionaloptimisation

models

Perennialsub-module

Markets Multi-commodityspatial market model

Prices

Reminder – General Model Layout

Quantities

Iterations Comparative Static Equilibrium

Young animal tradeDirect payment model

CAPRI CAPRI


35

On convergence

d

s

q

p

p0 p0

q

ps

d

CAPRI CAPRI


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

CAPRI CAPRI


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

CAPRI CAPRI


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

CAPRI CAPRI


39

Approximating supply

p0

q

ps

d

• Assume the “explosive situation”…

CAPRI CAPRI


40

Approximating supply

p0

q

ps

d

s’s’

q0

• 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…

CAPRI CAPRI

Calibration issues

CAPRI CAPRI


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

ii ikk npbspcsX *

CAPRI CAPRI


43

Parameter calibration

Original elasticities

Restrictions:Micro theory

Constraints of minimisation problem

SymmetryHomogeneityCorrect

Curvature

Objective:keep close

to original ones

Consistent elasticities

Consistent parameters

Functionalform

CAPRI CAPRI


44

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

CAPRI CAPRI


45

Point elasticities of the Generalised Leontief Expenditure function

PopFYG

GiPCDDemand i

pp

PopDemand

Y

G

GiPop

Demand

Y

Y

Demand

r

ipYp

,

jiPricePricePbdPbdPrice

GiGij

where

jiPopFYG

GiGi

G

Gij

Price

Demand

ppppppp

ppp

pppp

p

ppp

11,1,21

11,

2

11,

11,

:

Marshallian Demands for any function G and Fand their derivatives versus prices Gi and Fi

Income elasticities of demand

Cross price elasticities of demand

CAPRI CAPRI


46

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

i

i i

xx

xaxa

)()(

YFFYG

G

PricePCDFYG

PriceGi

PriceDemandp

ppp

pp

ppp

)(

CAPRI CAPRI


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)

capri capri market model torbjörn jansson* markus kempen *corresponding author +49-228-732323 ...

Documents

capri capri training

germany capri training

function of prices

border prices

functions market balances

market model production

srdr slide

fpr demand dr