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CAPRI
Outline
• Introduction: Armington approach
• Implementation in CAPRI model
• Design of country aggregate with Armington approach
• Data for country aggregate
3rd CAP-STRAT Workshop, 24./25.03.2003, Bologna
CAPRI
CAPRI
Armington Assumptions
CAPRI
• Consumer preferences differ by product origin
“EU cheese (e.g. Parmesan) is different from U.S. cheese
(e.g. Cheddar)”
• Assumption of heterogenous goods
within the same product (U.S. cheese, ...,EU cheese)
• That implies ...
• Modeling of trade streams between regions necessary
• Detailed representation of trade policy possible
• Modeling of price differences between domestically
produced and imported products possible
3rd CAP-STRAT Workshop, 24./25.03.2003, Bologna
CAPRI
Comparison Net trade / Armington
Net trade
CAPRI
Armington
• Homogenous goods
(all the cheese is identical)
• Heterogeneous goods
(cheese is different by origin)
• Only one price for wheat
(world price for cheese)
• Price differs by origin
(no world price for cheese)
• Demand function
• Demand function
defines tons for each product
defines utility for each product
(<= same utility per ton)
(<= different utility per ton)
from price/ton
from price/utility
3rd CAP-STRAT Workshop, 24./25.03.2003, Bologna
CAPRI
Armington Approach
CAPRI
• Problem:
Modeling of demand for products with utility differences
by origin
• Solution:
Two stage demand system:
• (on top) demand system, working on utility quantities
ui = f(prices) -> expenditures per product i ei=ui*pi
• (below) CES-utility aggregator function per product i
to distribute expenditure to different origins
<=> aggregator function ui = f(xi,r,r1 ,.., xi,r,rn)
<=> defines price/utility pi = (xir,r1 pir,r1 +...+ xi,r,rn pir,rn) /ui
3rd CAP-STRAT Workshop, 24./25.03.2003, Bologna
Aggregator function for utility
CAPRI
max u i, r
M i , r , r1
Aggregated utility

 i ,r 
 i, r  i, r , r1x i, r , r1

 r1

s.t.  x i, r , r1Pi, r , r1  ei, r
r1
Price depending
on origin
CAPRI
1 i ,r
Parameter derived
from substitution
elasticity
Trade flow
(incl. domestic sales)
Expenditure set by demand system
e.g. for wheat consumed in the EU
i product, r importing regions, r1 origins,  shift parameter,  share parameter
• Fix substitution elasticity for each product between different
origins
3rd CAP-STRAT Workshop, 24./25.03.2003, Bologna
CAPRI
FOC of the Aggregator Function
• FOC from CES utility aggregation
yield the following relation between trade flows
x i, r , r1
x i, r , r 2
1 1 i ,r 
 i, r , r1 Pi, r , r 2 


 i, r , r 2 Pi, r , r1 
• Relation between trade flows depends on:
• so called “share parameters” 
• multiplied with the inverse import price relation
• substitution elasticity 1/(1+)
• Imperfect substitution (“sticky” import shares)
3rd CAP-STRAT Workshop, 24./25.03.2003, Bologna
CAPRI
CAPRI
Flowchart Armington with two regions
Regional
Prices Pr
Regional
Prices Pr
Supply
Sr=f(Pr)
Supply
Sr=f(Pr)
Domestic Sales
Imports

 
ui ,r   i ,r   i ,r ,r1M i ,r ,r1 
 r1

CAPRI
1 
Domestic
Sales
Imports

 
ui ,r   i ,r   i ,r ,r1M i ,r ,r1 
 r1

Demand
ui,r=f(pr)
Demand
ui,r=f(pr)
Substitution between
domestic and imports
3rd CAP-STRAT Workshop, 24./25.03.2003, Bologna
1 
CAPRI
Problems of the Armington Approach
CAPRI
• 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 flows in tons (domestic sales + imports)
is not equal to the utility aggregate in simulations !!!
(demand “quantities” are an utility measurement ...)
• Recalculation of physical quantities after simulation necessary
3rd CAP-STRAT Workshop, 24./25.03.2003, Bologna
CAPRI
CAPRI: Two Stage Armington
CAPRI
Demand (Arm1) =
Human consumption
+ Feed Use + Processing

Arm i ,r  sp1i ,r dpi ,r ,rwImports i ,r
Domestic Sales
(DSales)

 dpi ,r ,r DSales i ,r

  1 
Imports (Arm2)
Imports i ,r

 
 sp 2i ,r  dpi ,r ,r1Streamsi ,r ,r1 
 r1

1 
Imports from
different origins
Streams(R,R1,XX)
....
Streams(R,Rn,XX)
3rd CAP-STRAT Workshop, 24./25.03.2003, Bologna
CAPRI
Overview on a country aggregate
Regional
Prices
Supply
Intervention sales
Domestic Sales
Armington
Stage 2
Aggregate
Armington
Stage 1
aggregate
Processing
Human
consumption
Feed Use
3rd CAP-STRAT Workshop, 24./25.03.2003, Bologna
Export
subsidies ?
Export streams
Import Streams
and prices
CAPRI
Data for country aggregates
CAPRI
CEE
IND
CHN
Base year data (1998)
Exogenous assumptions
Quantities
FAO
Quantity
developments
@2030, FAPRI
Trade streams
FAO
GDP growth
FAO, FAPRI
Prices
FAPRI, WBank
Population growth
FAO
Exchange rates
As in base year
Inflation
1,9 % p.a.
ANZ
CAD
USA
ACP
MED
HIT
CAN
ROW
For EU + MS:
CAPRI data base,
Parameters
behav. functions
(Elasticities)
@2030,WATSIM
Substitution
elasticities
(Armington)
Rule of thumb,
Italian team ?
EU “Prospects for ...”,
3rd CAP-STRAT Workshop, 24./25.03.2003, Bologna
EUROSTAT
CAPRI
Policy data
... next
presentation
CAPRI
Trimming ...
CAPRI
• Base year quantity and price framework from different
sources for all aggregates must fit ... balancing necessary
• Trimming of elasticity sets for each country aggregate,
(supply, human consumption, feed, processing of oilseeds,
processing of dairy products)
to ensure compliance with micro-theory
• Shift of all exogenously driven quantities and prices to
simulation year
... balancing ensures mutually compatible assumptions
3rd CAP-STRAT Workshop, 24./25.03.2003, Bologna
CAPRI
Challenges ...
CAPRI
• Market model consists of around 10.000 equations
• Simulation results obtained for
12 country aggregates
x 20 products
x ( 4 elements of product balances
+ 12 trade flows
+ prices ...)
• Unresolved issue how to access and analyse information
for non-EU country aggregates + trade flows
3rd CAP-STRAT Workshop, 24./25.03.2003, Bologna