Estimating parameters of a constrained NLP model using several observations Torbjörn Jansson* Marcel Adenäuer Institute for Food and Resource Economics Bonn University Nussallee Bonn, Germany *Corresponding author Presented at the Ecomod Conference on Regional and Urban Modelling, June 2, 2006 in Brussels

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

Brussels, June 2, 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

Brussels, June 2, 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

Brussels, June 2, 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

Brussels, June 2, 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 ?

Brussels, June 2, Results: elasticities CEREOILSPOTAFODD CERE OILS POTA FODD OSET VSET FALL Assumed Farm ModelFitted CAPRI model CEREOILSPOTAFODD CERE OILS POTA FODD OSET VSET FALL

Brussels, June 2, 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

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