1. 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 +49-228-732323 www.agp.uni-bonn.de Presented at the Ecomod Conference on Regional and Urban Modelling, June 2, 2006 in Brussels

2. Brussels, June 2, 20062 Objectives Formulate a new CAPRI supply model with endogenous yield Estimate parameters using multiple outcomes of other models (focus)

3. Brussels, June 2, 20063 Model fitting problem Farm model Data set simulation experiments New CAPRI regional supply model estimation These do not yet exist –- invented! Prototypes developed in this paper

4. Brussels, June 2, 20064 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 We want to estimate the parameters of this term Technical coefficients assumed known

5. Brussels, June 2, 20065 Estimation problem is negative semi-definite ( -B = u’u ) subject to (no complementary slackness conditions) With l tj = acreage of crop j in simulation t, and c, B coefficients of the quadratic cost term: CAPRI base year is fitted exactly acreage input use yield

6. Brussels, June 2, 20066 Explorative implementation 1.Create fake Farm Models (Cobb-D.) 2.Simulate with different prices (n=50) 3.Estimate CAPRI with sim. outcomes 4.Evaluate fitted model behaviour compare elasticities compute R 2 ?

7. Brussels, June 2, 20067 Results: elasticities CEREOILSPOTAFODD CERE0.724-0.142-0.160-0.097 OILS-1.6921.705-0.340-0.169 POTA-0.317-0.0571.919-0.068 FODD-1.908-0.280-0.6751.504 OSET0.3790.122-0.186-0.107 VSET-3.764-1.160-0.2140.414 FALL-3.455-1.652-0.1840.323 Assumed Farm ModelFitted CAPRI model CEREOILSPOTAFODD CERE0.800-0.100 -0.050 OILS-1.5002.000-0.100 POTA-1.500-0.5002.000-0.100 FODD-2.000-0.5002.000 OSET0.100 -0.900-0.500 VSET-2.000-0.500-0.400-0.100 FALL-1.750-1.125-0.2750.025

8. Brussels, June 2, 20068 Results: R 2 ActivityR2R2 CERE0.967 OILS0.867 POTA0.597 FODD0.702 OSET0.072 VSET0.521 FALL0.648 Really bad fit, due to contradictory data Best fit, due to lack of weights

9. Brussels, June 2, 20069 Open questions How evaluate fit? How handle dual values? How handle fitted zeros?