Transcript Estimating parameters of a constrained optimisation model

Estimating parameters of a
constrained NLP model using
several observations
Torbjörn Jansson*
Marcel Adenäuer
Presented at the Ecomod Conference on Regional and
Urban Modelling, June 2, 2006 in Brussels
*Corresponding author
+49-228-732323
www.agp.uni-bonn.de
Institute for Food and Resource Economics
Bonn University
Nussallee 21
53115 Bonn, Germany
Objectives
• Formulate a new CAPRI supply model
with endogenous yield
• Estimate parameters using multiple
outcomes of other models (focus)
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Model fitting problem
Farm
model
simulation
experiments
These do not
yet exist
–- invented!
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Data
set
estimation
New CAPRI
regional
supply model
Prototypes
developed
in this paper
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New supply model
• Maximise …
+ “gross margin per hectare” x “hectares”
- quadratic cost term “PMP”
We want to estimate
• subject to …
Technical
coefficients
assumed
known
yield = f(“hectares”,”plant protection”)
other input use = f(“plant protection”)
land constraint
set-aside constraint
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the parameters
of this term
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Estimation problem
With ltj = acreage of crop j in simulation t,
and c, B coefficients of the quadratic cost term:
min
c, B
 l
OBS
tj
 ltj

2
t
L
L

0
,
0
subject to
ltj
xtj
2L
is negative semi-definite (-B = u’u)
ltj ltk
acreage
CAPRI base year is fitted exactly input use
yield
(no complementary slackness conditions)
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Explorative implementation
1.
2.
3.
4.
Create fake Farm Models (Cobb-D.)
Simulate with different prices (n=50)
Estimate CAPRI with sim. outcomes
Evaluate fitted model behaviour
•
•
•
compare elasticities
compute R2
?
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Results: elasticities
Assumed Farm Model
Fitted CAPRI model
CERE
OILS
POTA
FODD
CERE
0.724
-0.142
-0.160
-0.097
-0.100
OILS
-1.692
1.705
-0.340
-0.169
2.000
-0.100
POTA
-0.317
-0.057
1.919
-0.068
-1.000
-0.500
2.000
FODD
-1.908
-0.280
-0.675
1.504
0.100
0.100
-0.900
-0.500
OSET
0.379
0.122
-0.186
-0.107
VSET
-2.000
-0.500
-0.400
-0.100
VSET
-3.764
-1.160
-0.214
0.414
FALL
-1.750
-1.125
-0.275
0.025
FALL
-3.455
-1.652
-0.184
0.323
CERE
OILS
POTA
FODD
CERE
0.800
-0.100
-0.100
-0.050
OILS
-1.500
2.000
-0.100
POTA
-1.500
-0.500
FODD
-2.000
OSET
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Results: R2
Best fit,
due to lack of weights
Really bad fit,
due to contradictory data
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Activity
CERE
OILS
POTA
FODD
OSET
VSET
FALL
R2
0.967
0.867
0.597
0.702
0.072
0.521
0.648
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Open questions
• How evaluate fit?
• How handle dual values?
• How handle fitted zeros?
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