Determining Optimal Levels of Nitrogen Fertilizer Using Random Parameter Models

The parameters of yield response functions can vary by year. Past studies usually assume yield functions are nonstochastic or “limited” stochastic. In this study, we estimate rye–ryegrass yield functions in which all parameters are random. The three functional forms considered are the linear response plateau, the quadratic, and the Spillman-Mitscherlich. Nonstochastic yield models are rejected in favor of stochastic parameter models. Quadratic functional forms fit the data poorly. Optimal nitrogen application recommendations are calculated for the linear response plateau and Spillman-Mitscherlich. The stochastic models lead to smaller recommended levels of nitrogen, but the economic benefits of using fully stochastic crop yield functions are small because expected profit functions are relatively flat for the stochastic yield functions. Stochastic crop yield functions provide a way of incorporating production, uncertainty into input decisions.