Effects of risk on optimal nitrogen fertilization rates and dates in winter wheat production as affected by disease and nitrogen source

Efficient nitrogen (N) fertilization practices increase the economic benefit of N in wheat (Triticum aestivum L.) production and the timing of N in wheat production is an important management decision. Although N fertilization increases wheat yields, it can also affect production risk measured by yield variability (risk). Yield and risk can also be affected by interactions among N source, N rate, N timing and disease severity. Because of production risk, some farmers may apply more N than can be efficiently utilized by the crop and if N fertilization is not timed for accelerated N uptake by the plant, optimal yields are not obtained. By adjusting application of N fertilizer to efficient levels and adjusting the application date of N fertilizer to optimize N uptake, farmers can achieve greater economic returns.

The first objective of this research was to evaluate the effects of N source, N rate, N timing and disease severity on expected yield and risk in wheat production and to evaluate the risk-and-return trade-offs among alternative N sources for farmers with different risk preferences. The second objective was to determine utility-maximizing N rates, N fertilization dates, yields, and net returns.

A Just-Pope econometric analysis isolates the impacts of changes in input use on both expected yield and risk. The model takes the form:

(1)Y_t = ƒ(X_t,β)+h(Z_t,α)ε_t,

where Y was wheat yield (bu/acre); X and Z were matrices of explanatory variables; t was a subscript for year; β and α were parameter vectors; and )ε was a random error term with a mean of zero. The production function,ƒ(X_t,β), relates X_t to mean wheat yield. The variance function, h(Z_t,α)ε_t,, associates Z_t to risk.

The estimated mean yield response function and the variance function for each N source were used to predict certainty equivalent. The certainty equivalent maximizing N fertilizer levels and dates for each N source were found for risk neutrality (λ = 0) and two levels of risk aversion (λ = 0.01 and λ = 0.02).

The estimated coefficients for N and N² were positive and negative, respectively, but the N² coefficients for Urea and UAN were not significantly different from zero. The coefficients for time and time² were positive and negative, respectively.

The coefficient for the N-Take-All interaction (NTA) for Urea was significant at the 10-percent level and the N-Glume-Blotch interaction (NG) for UAN was significant at the 1-percent level. Notwithstanding the significance of these coefficients in the regressions, the F-tests indicated that N did not affect risk for any N source when all N variables (N, NG, NTA) were considered jointly. No time coefficients had an affect on risk.

Each N source was evaluated under the assumption of risk neutrality (λ = 0) and two level of risk aversion (λ = 0.01 and λ = 0.02) for mean disease ratings. In this evaluation neither N nor time had an affect on risk. At mean values of the disease variables, AN was the utility maximizing N source regardless of the farmer's risk preferences.

AN was the utility maximizing N source, with an optimal N rate around 90 lb/acre and an optimal fertilization date of March 8 regardless of the individual's risk aversion level.