Calibration of shadow values in constrained optimisation models of agricultural supply

This paper proposes a new information-based method to calibrate the shadow values of constraints in Positive Mathematical Programming models of agricultural supply. Shadow values are chosen so as to minimise model deviation from observed activity- and input-specific expenditures, enhancing the informational basis of the calibrated model. We provide an application to nitrogen policy in California using an agronomically and economically calibrated regionalised model. Regional shadow values of water are generally much higher than those suggested by the traditional method of Howitt, R. E. (1995b. American Journal of Agricultural Economics 77(2): 329-342). The implied statewide elasticity of demand for nitrogen is minimally affected by the choice of shadow values, however predicted environmental outcomes differ as this choice affects the distribution of nitrogen across regions and crops.