Implications of simultaneity in a physical damage function

A modeler must often rely on highly simplified representations of complex physical systems when analyzing associated economic issues. Herein, we consider a management problem in which a bioeconomic system exhibits simultaneity in processes governing productivity and damage. In this case, it may benefit the producer to sacrifice productivity to reduce the costs associated with increased damage. We specify empirically a structural damage relationship that explains the biological process by which an invasive species damages a host and estimate the structural model and its reduced form with an exceptional dataset on infestation of olives by the olive fruit fly. We contrast the results of these models with the approach typically taken in the economic literature, which expresses damage as a function of pest density. The population-based approach introduces significantly greater bias into the individual grower's choice of damage-control inputs than estimates based on the structural model.