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a Dep. of Agric. Econ., The Univ. of Tennessee, 2621 Morgan Circle, Knoxville, TN 37996-4518
b Dep. of Plant and Soil Sci., West Tennessee Exp. Stn., The Univ. of Tennessee, 605 Airways Blvd., Jackson, TN 38301
* Corresponding author (rrobert3{at}utk.edu).
Received for publication August 19, 2003.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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Abbreviations: AN, ammonium nitrate • GS, Feekes' growth stage(s) • OLS, ordinary least squares • UAN, urea ammonium nitrate • WLS, weighted least squares
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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Previous research found that applying N at Feekes' Growth Stages (GS) 4 to 6 (Large, 1954) significantly increased yields (Alcoz et al., 1993). However, Boman et al. (1995) found that N can be delayed until later in the season without significantly affecting yield. Because disease stress can reduce N uptake (Dilz et al., 1982), N timing and fungicide applications should be based on the characteristics of each wheat crop and environment (Roth and Marshell, 1987). These studies evaluated the effects of N timing and disease severity on yield; however, they did not evaluate the risk effects of N timing in the presence of disease.
Glume blotch is a late-season grain-head infection (Ditsch and Grove, 1991) found in all wheat-growing areas of the world (Bowden, 2003). It is most prevalent in high-rainfall, humid areas (Stromberg, 2003) such as the southern United States (Howard et al., 2002b). Fungicide applications are often incomplete in controlling glume blotch (Bowden, 2003). Although N fertilization is an important determinant of wheat yield (Beuerlein et al., 1991), it can interact with glume blotch to limit yield (Boquet and Johnson, 1987). Lush vegetative growth that accompanies high N fertilization reduces air movement through the canopy, producing an environment more suited for glume blotch development (Ditsch and Grove, 1991; Wiese, 1987). Without fungicide application in the presence of glume blotch, higher N levels significantly reduced wheat yield (Kelley, 1993; Howard et al., 1994; Cox et al., 1989; Roth and Marshell, 1987; Ditsch and Grove, 1991). Although these studies found that N fertilization and timing affect glume blotch severity and yield, they did not evaluate the risk effects of N timing and glume blotch severity on the N timing decision.
The lack of resistant varieties and chemical control make the fungal root disease take-all root rot (take-all) the most important wheat root disease in the United States and in the world (Duffy and Weller, 2003; Monsanto, 2003). Take-all severity in wheat production was influenced by the N source, with more severe root damage in plots fertilized with nitrate 
compared with ammonium 
forms of N (Colbach et al., 1997; Wiese, 1987; MacNish, 1980; Brennan, 1992a, 1992b). Ammonium fertilizers may reduce take-all severity because of a decrease in rhizosphere pH that promotes more vigorous root growth, allowing roots to escape severe disease damage (Brennan, 1989). However, where take-all was at high levels, ammonium forms of N were ineffective in reducing take-all severity (MacNish, 1980). Take-all infections in autumn or early spring were most likely to affect wheat yield (Wiese, 1987) while later infections were less likely to affect yield. Nitrogen timing affected take-all severity, with greater severity accompanying delayed fertilization (Howard et al., 2002b). These studies showed that N source and N timing affect take-all severity and yield, but they did not evaluate the risk effects of N timing, N source, and take-all severity on the N timing decision.
The practice of surface broadcasting N sources in conservation tillage crop production may reduce the effectiveness of applied N in promoting yields. Broadcast fertilizers remain on the soil surface, reducing the effectiveness of certain N sources because of N immobilization and volatilization resulting from interaction with the surface residue (e.g., Bandel et al., 1984; Fox et al., 1986; Howard, 1986; Howard and Essington, 1998; Howard and Tyler, 1989). When comparing the effects of fertilization with urea-containing sources and AN on no-till corn (Zea mays L.) yields, Howard and Essington (1998) speculated that lower yields for the urea-containing N sources resulted from N volatilization losses. Howard (1986) reported that urea-containing N sources were less efficient than AN in promoting wheat yields. When comparing broadcast urea and UAN with broadcast AN, Howard et al. (2002a) found that wheat yield reductions of about 12% probably resulted from N volatilization losses for the urea-containing N sources. These studies found differences in broadcast N sources in promoting conservation tillage yields, but no literature was found evaluating N source interactions with disease and their effects on risk and the N timing decision.
A comprehensive evaluation of the interactions among N timing, N source, glume blotch and take-all severity, and their effects on expected yield and risk has not been found (Walters, 2002). While limited research has evaluated the effects of risk on pest management decisions (e.g., Hurd, 1994; Larson et al., 2001; Pannell, 1995), we have found no research evaluating the effects of disease severity on risk in crop production decisions. Our objectives were (i) to evaluate the effects of N source, N timing, and disease severity on expected yield and risk in winter wheat production and (ii) to evaluate the risk–return trade-offs between N sources for farmers with different risk preferences.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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Analytical Framework
Farmers can use measures of expected net return and net-return variance to make agricultural production decisions such as the one addressed in this research (Barry, 1984). The Just–Pope model (Just and Pope, 1978, 1979) was used to evaluate the risk–return trade-offs of the N fertilization timing decision in wheat production. This method isolates the impacts of changes in a production variable on expected yield and yield variance. Results from the Just–Pope model can be used to determine the level of the production variable that maximizes certainty equivalent net return. Among others, the Just–Pope model has been used to evaluate the risk effects of (i) N as a nonpoint pollution problem with alternative policies and farmer response to those policies (Lambert, 1990); (ii) genetic improvement in wheat yields during the green revolution (Traxler et al., 1995); (iii) winter cover crop, tillage, and N fertilization systems in cotton (Gossypium hirsutum L.) production (Larson et al., 2001); (iv) genetic resources and diversity variables in wheat production (Smale et al., 1998); (v) variable-rate N application in corn production (Larson et al., 2002); (vi) integrated pest management in cotton production (Hurd, 1994); and (vii) input use in farm-raised salmon (Oncorhynchus spp.) production (Asche and Tveteras, 1999).
The Just-Pope model takes the form:
 | [1] |
are parameter vectors, 
is a random error term with a mean of zero, f is the mean yield production function that relates Xt to mean yield, and h1/2 is the yield standard deviation function that associates Zt with yield standard deviation and with yield variance through h. Representing the explanatory variables in the mean yield and yield variance functions as X and Z does not suggest that the variables must be different; only that they need not be the same (Smale et al., 1998). Our interest is in whether variables that affect mean yield (N timing, N source, and disease rating) also affect yield variance and whether their effects on yield variance affect optimal N timing and N source recommendations to wheat farmers. Data from the aforementioned experiment (Table 1) were used to evaluate the N fertilization timing decision in wheat production as affected by two N sources, two diseases, and risk under the maintained assumption that the farmer attempts to control glume blotch with the amounts of the fungicides applied in the experiment or ones of similar effectiveness. This maintained assumption was needed because the same amount of fungicide was applied each year to all plots, and a fungicide application variable would produce perfect collinearity in the econometric analysis of the Just–Pope model. In addition, farmers would not typically allow glume blotch infections to go untreated; consequently, their N timing decisions would be influenced by production risk, given appropriate fungicide treatment of glume blotch infections as they occur.
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 | [2] |
The quadratic functional form for T was chosen because early N fertilization is not timed for accelerated plant uptake and late fertilization does not provide sufficient time before maturation for optimal N uptake. Yield response to N timing was hypothesized to exhibit diminishing marginal productivity (ß1 > 0, ß2 < 0).
The glume blotch and take-all severity ratings in the experiment were visual ratings related to the condition of wheat plants in each plot (M. Newman, Extension Plant Pathologist, West Tennessee Experiment Station, personal communication, 2003). They were intended to be related to yield but not necessarily linearly related. A 0 rating indicated no detectable symptoms on any plant in the plot; a 1 indicated that minimal visible symptoms were discovered in the plot; a 2 indicated that 20% of plants in the plot were symptomatic; a 3 indicated that 30% of plants were symptomatic; and so on up to 10, indicting that 100% of plants in the plot were symptomatic. Some yield could be obtained from symptomatic plants that died after heading. Glume blotch severity (ß3 and ß4) and take-all severity (ß5 and ß6) were hypothesized to negatively influence yield.
Implicit in the logarithmic functional forms for these disease ratings is the assumption that increases in ratings at the lower end of the scale (e.g., from 1 to 2) reduce yields by more than increases in ratings at the upper end of the scale (e.g., from 9 to 10). The logarithmic functional form required that 0 disease ratings be replaced by a number close to 0, in this case 0.01, because the natural logarithm of 0 is undefined. This small number was chosen because it fit the data better than other numbers close to it (e.g., 0.1 and 0.005).
An additional reason for assuming logarithmic functional forms for the disease ratings is the confounding of 0 disease ratings with the year effects that produced higher yields in disease-free years than in years when a particular disease was present. The data included positive glume blotch ratings for all plots in 1998 and 0 ratings for 1999 and 2000 when glume blotch was not present while take-all ratings were positive for all plots in 2000 and 0 for 1998 and 1999 when take-all was not present. Thus, the decrease in yield associated with an increase in the disease rating from 0 to 1 not only captured the decrease in yield in going from a disease-free situation to a situation of slight symptoms, but it also captured the decrease in yield associated with the other less favorable growing conditions that reduced yield and encouraged disease development in years when disease was present. Attempts were made to separate the years' effects from the effects of the 0 disease ratings by including (i) weather variables that might affect yield and (ii) year-effect dummy variables for 1998 and 2000. In both instances, severe multicollinearity (Belsley et al., 1980) seriously degraded the standard errors of the coefficients, further confusing interpretation of the results. Adding the year-effect dummy variables reduced adjusted R2's relative to those for the specification in Eq. [2], indicating that the year-effect variables added little to the explanatory power of the mean yield functions for AN or UAN. In addition, multicollinearity diagnostics revealed that the standard errors of the coefficients as specified in Eq. [2] were not seriously degraded for either N source, lending confidence to statistical tests associated with those standard errors.
Error sums of squares from ordinary least squares (OLS) regressions of the mean yield functions were used to develop an F test for identifying significant differences in yield variances between N sources. Significant differences in error sums of squares can help rank the yield variances of the N sources.
Efficiency gains in parameter estimates of the mean yield functions are possible with weighted least squares (WLS) when multiplicative heteroscedasticity is found. Multiplicative heteroscedasticity in the mean yield functions was tested using the Breusch–Pagan statistic (Breusch and Pagan, 1979) and the model F statistics from the yield variance functions described below (Judge et al., 1982). When evidence of heteroscedasticity was found for a particular N source, predicted values from the estimated yield variance function were used as weights in producing WLS estimates for the mean yield function for that N source.
An exponential yield variance function was estimated for each N source as (Hurd, 1994; Traxler et al., 1995):
 | [3] |
i (i = 0,1,..., 6) were parameters to be estimated; and other variables were defined in Eq. [2]. Although ut does not have a zero mean, this specification allowed asymptotically valid hypothesis testing of the marginal yield variance effects of the explanatory variables (Harvey, 1976; Hurd, 1994; Traxler et al., 1995).
Previous literature did not lend itself to developing firm hypotheses about the signs of the T parameters in Eq. [3] (1, 2, 4, and 6); nevertheless, one would expect earlier or later fertilization dates to produce more variation in yields than when N is applied on the optimal uptake date. In addition, early fertilization provides more time for the forces of nature to act upon the applied N through N losses to leaching and/or volatilization, suggesting more variation in yield with early fertilization. Therefore, T was hypothesized to reduce yield variance at first and then increase it (1 < 0, 2 > 0).
Larson et al. (2001) hypothesized that increased weed and insect pressure would increase yield variance in cotton production. As with weed and insect pressure, glume blotch and take-all severity may increase wheat yield variance because of their random effects on yields, but they may also decrease yield variance if they tend to equalize yields by disproportionately reducing yields in highly productive areas of a field and in high-rainfall years when growing conditions are more conducive to disease development. Thus, the effects of G (3 and 4) and A (5 and 6) on yield variance were uncertain.
The partial derivatives of the exponential of Eq. [3] with respect to T, G, and A were evaluated at the means of the variables for each N source to estimate marginal yield variance effects. Joint F statistics were used to test the null hypothesis that the coefficients for T, T2, T x G, and T x A were jointly equal to zero for each N source. Rejection of the null hypothesis for a particular N source would suggest that N fertilization timing significantly affected yield variance when N was applied using that N source. In addition, pair-wise F tests were performed to examine the null hypothesis that the coefficients for these variables were the same between N sources. Differences in these coefficients between N sources would suggest that N fertilization timing affected yield variance differently between N sources. Similar F tests were performed for the glume blotch severity coefficients (G and T x G) and the take-all severity coefficients (A and T x A).
The estimated mean yield response and yield variance functions for each N source were used to predict certainty-equivalent–optimizing N fertilization dates, yields, and net returns above N costs. Expected net returns and variance of net returns were calculated using an average wheat price of $0.126 kg–1 and a wheat price variance of $0.022 kg–1 for 1991 to 2000 (Tennessee Dep. of Agric., 2001). Wheat prices were inflated to 2002 dollars by the Gross Domestic Product Implicit Price Deflator (Bureau of Economic Analysis, 2002) before averaging. Tennessee average retail prices paid by farmers in 2002 for N were $0.57 kg–1 for AN and $0.51 kg–1 for UAN (J. Duke, Tennessee Farmers Cooperative, personal communication, 2002). These N prices included the cost of application equipment but not the cost of the tractor to pull the equipment. Tractor costs were assumed equal across N sources because the dry and liquid N sources evaluated have about the same tractor-size and speed requirements for broadcast application. Other wheat production costs were also assumed constant between N sources.
Certainty equivalent net return for a decision between risky and risk-free alternatives is the net return from the risk-free alternative that makes the decision maker indifferent between the expected net return from the risky alternative and the certain net return from the risk-free alternative (Larson et al., 2002). Certainty equivalent net return per hectare (CE) was approximated as (Robison and Barry, 1987):
 | [4] |
was the Pratt–Arrow absolute risk aversion coefficient, and Var(NR) was the variance of net returns. Freund (1956) showed that the linear mean variance objective function is consistent with normally distributed profits and the negative exponential (or exponential) utility function that exhibits constant absolute risk aversion. E(NR) was calculated as:
 | [5] |
was mean wheat yield predicted from the mean yield function estimated in Eq. [2] (kg ha–1), 
was average wheat price for 1991 to 2000 in 2002 dollars ($ kg–1), 101 was the N rate in the experiment (kg ha–1), and 
was the 2002 price of N for AN or UAN ($ kg–1). Var(NR) was calculated as (Bohrnstedt and Goldberger, 1969):
 | [6] |
2WP was the wheat price variance for 1991 to 2000 in 2002 dollars ($ kg–1), 2Y was the wheat yield variance obtained by taking the exponential of the yield variance function estimated in Eq. [3] (kg ha–1), and other variables were defined in Eq. [5].
The CE-maximizing N fertilization date for each N source was found by solving:
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= 0) and risk aversion represented by = 0.008. The latter level of was consistent with the upper end of the range of absolute risk aversion evaluated by Lambert (1990) and Larson et al. (2001). For consistency, was scaled to represent net returns per hectare by multiplying their = 0.02 by 0.405 ha acre–1. |
RESULTS AND DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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Joint F statistics for the N timing and disease coefficients for the yield variance functions and the marginal yield variance effects for T, G, and A are presented in Table 5. The fertilization date (T, T2, T x G, T x A) coefficients were statistically different from zero for AN, and the marginal yield variance effect was positive, suggesting that delayed N fertilization increased yield variance. The coefficients for glume blotch severity (G and T x G) and take-all severity (A and T x A) were statistically significant for AN as well, and their positive marginal effects suggest that glume blotch severity and take-all severity increased yield variance when evaluated at the means of the variables. None of the explanatory variables significantly affected yield variance when UAN was the N source. Only the effect of take-all severity on yield variance was statistically different between N sources (Table 5).
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Risk–Return Trade-Offs
Table 6 presents risk–return trade-offs for scenarios when: (i) the disease ratings are at their 3-yr means; (ii) the glume blotch and take-all ratings are at their 1998 and 3-yr means, respectively; and (iii) the glume blotch and take-all ratings are at their 3-yr and 2000 means, respectively.
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= 0.008) produced only imperceptible changes in optimal fertilization dates, yields, and net returns for both N sources (Table 6). Optimal fertilization dates were 8 March for AN and 11 March for UAN regardless of risk preferences. Optimal wheat yields were 4415 and 4039 kg ha–1, and optimal net returns were $498.63 and $457.89 ha–1 for AN and UAN, respectively. A combination of the higher net return for AN and the small effect of fertilization date on risk resulted in maximum CE for AN being higher than for UAN for risk-averse farmers ( = 0.008); thus, at average disease levels, AN is the utility-maximizing N source regardless of risk preferences, and net-return–maximizing wheat farmers ( = 0) who broadcast AN as the N source have a $40.74 ha–1 net return advantage over those who broadcast UAN.
When the glume blotch rating is at its higher 1998 average level, net-return–maximizing yields fall to 3256 and 2987 kg ha–1, and net returns decline to $352.59 and $325.31 ha–1 for AN and UAN, respectively. The economic advantage for the net-return–maximizing farmer who broadcasts AN instead of UAN is reduced from $40.74 ha–1 to $27.28 ha–1 for this more severe glume blotch infection. Furthermore, net-return–maximizing N fertilization dates ( = 0) increase by 7 d for AN and 4 d for UAN, both to 15 March, encouraging delayed fertilization when serious glume blotch infections are anticipated. Under this more severe glume blotch infection, maximum CE is higher for AN than for UAN, and risk aversion has almost no effect on the optimal N fertilization date, yield, and net return for AN, and the effects are imperceptible for UAN; thus, at high anticipated levels of glume blotch infection, AN is still the utility-maximizing N source regardless of risk preferences.
For the higher level of take-all infection in 2000, net-return–maximizing yields are reduced to 2521 and 2258 kg ha–1, and net returns fall to $259.88 and $233.47 ha–1 for AN and UAN, respectively. The more severe take-all infection reduces the fertilization date by 1 d to 7 March for the risk-neutral farmer, but for the risk-averse farmer, the optimal fertilization date increases by 3 d to 11 March. Ammonium nitrate is still the utility-maximizing N source regardless of risk preferences. A net-return–maximizing farmer who broadcasts AN has an economic advantage of $26.41 ha–1 over one who broadcasts UAN.
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CONCLUSIONS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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Results indicated that N timing and disease severity significantly affected mean winter wheat yields when AN and UAN were broadcast at 101 kg ha–1. In addition, results suggest that N timing had little to no effect on risk. For farmers who expected average disease severity, AN fertilization on 8 March was the utility-maximizing N source and date regardless of risk preferences. Although risk was not a factor in determining the optimal fertilization date and N source in winter wheat production, this finding is important because it suggests that the yield-maximizing fertilization date also maximizes profit and utility. Furthermore, the finding that AN is the utility-maximizing N source is not trivial because this information is worth as much as $40.74 ha–1 to wheat farmers who adjust their N source from UAN to AN. These findings are important to winter wheat farmers with similar expected disease levels and growing conditions in Tennessee and surrounding states because AN is the optimal N source for a wide range of risk preferences and disease severity levels; thus, wheat farmers can broadcast AN instead of UAN with a great deal of confidence.
The experimental data used in this analysis were for a single N rate of 101 kg ha–1. Further research is needed to determine the profit-maximizing N rate and whether interactions among N rate, N timing, N source, and disease severity affect risk and the utility-maximizing N rate and fertilization date.
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ACKNOWLEDGMENTS |
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REFERENCES |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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