Agronomic research on crop response to nitrogen fertilizer suggests that a plateau function may be appropriate, but the plateau varies across fields and years. Available models that treat the plateau as a stochastic variable are not readily extendable to handle field or year random effects as seems to be appropriate based on the agronomic data. This article develops a method of estimating a response function with a stochastic plateau that can capture random effects. The method is then used to determine economically optimal levels of nitrogen fertilizer for wheat (Triticum aestivum).

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