Estimating parameters of a constrained NLP model using several observations

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Estimating parameters of a constrained NLP model
using several observations

• Torbjörn Jansson
• Marcel Adenäuer

Institute for Food and Resource Economics Bonn
University Nussallee 21 53115 Bonn, Germany
Corresponding author 49-228-732323www.agp.uni-b
onn.de
Presented at the Ecomod Conference on Regional
and Urban Modelling, June 2, 2006 in Brussels
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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
New CAPRI regional supply model
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New supply model

• Maximise
• gross margin per hectare x hectares
• quadratic cost term PMP
• subject to
• yield f(hectares,plant protection)
• other input use f(plant protection)
• land constraint
• set-aside constraint

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Estimation problem
With ltj acreage of crop j in simulation t, and
c, B coefficients of the quadratic cost term
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Explorative implementation

• Create fake Farm Models (Cobb-D.)
• Simulate with different prices (n50)
• Estimate CAPRI with sim. outcomes
• Evaluate fitted model behaviour
• compare elasticities
• compute R2
• ?

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Results elasticities
CERE OILS POTA FODD
CERE 0.724 -0.142 -0.160 -0.097
OILS -1.692 1.705 -0.340 -0.169
POTA -0.317 -0.057 1.919 -0.068
FODD -1.908 -0.280 -0.675 1.504
OSET 0.379 0.122 -0.186 -0.107
VSET -3.764 -1.160 -0.214 0.414
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 -0.100
POTA -1.500 -0.500 2.000 -0.100
FODD -2.000 -1.000 -0.500 2.000
OSET 0.100 0.100 -0.900 -0.500
VSET -2.000 -0.500 -0.400 -0.100
FALL -1.750 -1.125 -0.275 0.025
Assumed Farm Model
Fitted CAPRI model
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Results R2
Activity R2
CERE 0.967
OILS 0.867
POTA 0.597
FODD 0.702
OSET 0.072
VSET 0.521
FALL 0.648
Best fit, due to lack of weights
Really bad fit, due to contradictory data
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Open questions

• How evaluate fit?
• How handle dual values?
• How handle fitted zeros?