Cornhusker Economics July 10, 2019The Economic Evaluation of Input Use Prescription Maps: Are You Paying to Make Less Profit?
Technological advances in data collection and analysis engines have made variable rate input use application much more common. Producers typically purchase software that produces site-specific prescription maps or purchase maps from consultants. The process of generating prescriptions maps is typically black-box, i.e. the process is unknown. Does using these purchased maps lead to more profits for producers?
This article discusses a method of verifying the economic profitability of site-specific prescription maps using an on-farm field experiment and statistical and economic analysis. A 76-acre field in Crawford County, Ohio is used for the study.
The maps below are almost identical in their management zone delineations. The consultant created four management zones, each of which is assigned a unique seed-nitrogen rate combination. The four combinations are presented in Table 1. It suggests that high target seed rates are combined with low nitrogen rates.
An on-farm randomized experiment on seed and nitrogen rates was developed to test whether these recommendations are profitable.
| Zone | Nitrogen (lb/acre) |
Seeds |
|---|---|---|
| 1 | 144 | 32 |
| 2 | 134 | 34 |
| 3 | 124 | 36 |
| 4 | 114 | 38 |
There are four steps to testing the economic soundness of the consultant’s recommendations. Only Zones 2 and 3 will be tested because there is too small a number of observations in Zones 1 and 4 for reliable statistical analysis. First, estimates are made of the quantitative relationship between yield, seed, and nitrogen rates for each of the consultant-defined management zones. Second, the profit-maximizing rate of seed and nitrogen per zone is estimated. Next, profits are estimated for each management zone for the economically optimal rates and the consultant’s recommended rates. Finally, the consultant’s recommendation is evaluated by contrasting its profitability against the possible maximum profit.
Table 2 shows the estimated quantitative relationships between yield, seed, and nitrogen for each management zone.
| Dependent Variable 34-134 (Zone 2) |
Yield (bu/acre) 36-124 (Zone 3) |
|
|---|---|---|
| Seed | 23.688*** (6.425) |
7.814* (3.240) |
| Seed squared | -0.335*** (0.096) |
-0.093* (0.046) |
| Nitrogen | -1.012 (0.799) |
-0.635 (0.420) |
| Nitrogen squared | 0.004 (0.003) |
0.003 (0.002) |
| Constant | -146.531 (120.399) |
89.197 (63.853) |
| Observations Adjusted R2 |
564 0.044 |
1,427 0.054 |
Note: *p<0.05; **p<0.01; ***p<0.001
The regression results show that while seed rate generally has positive impacts on yield, nitrogen has no statistically significant impacts on yield on this field.
Table 3 compares the optimal nitrogen and seed rates with the consultant’s recommended rates.
| Zone | Optimal N | Consultant’s N | Optimal S | Consultant’s S |
|---|---|---|---|---|
| 2 | 90 | 134 | 33,950 | 34,000 |
| 3 | 90 | 124 | 37,000 | 36,000 |
For the economic analysis, the price of corn was set at $3.50, the price of seed was set at $3.20 per 1,000 kernels, and the price of fertilizer was set at $.40 per pound.
The consultant recommended 34,000 and 36,000 seeds per acre for management Zones 2 and 3, respectively. The consultant’s recommendations would have under-applied seed in Zone 3 but the recommendations for Zone 2 was close to optimal. However, even though the consultant would have under-applied seed for management in Zone 3, the economic cost of the error would have been very small. This is because the loss in revenue ($3.4 per acre) due to the lower yield caused by the smaller seed rate was almost completely offset by the saving in seed costs ($3.2 per acre).
Over application of nitrogen is the main cause of the loss of profits. The regression analysis suggested that nitrogen has no impact on yield for the ranges analyzed. Since the yield outcome of a nitrogen application of less than 90 pounds per acre could not be extrapolated because they are out of the range of the statistical analysis, that rate was used as the optimal nitrogen rate within the range tested in the experiment. The consultant recommended much higher application rates for all zones. By following the consultant’s recommendations, the producer lost $11.15 and $7.87 per acre for zones two and three, respectively.
The results suggest producers should carefully examine the prescriptions made by consultants. An on-farm randomized experiment can help. They allow producers to discover the optimal average amount of nitrogen. In the sample field, the largest loss in profit was due to the over-application nitrogen almost everywhere across the field.
There is an important caveat to this study. It is based on only one year of data. Yield response to nitrogen and seed can vary dramatically based on weather, especially for rain-fed production. Therefore, it is possible that consultant’s recommendations happened to be quite off for nitrogen. Another experiment conducted in a different year could have yielded much different results. Nonetheless, this method of verifying the profitability of prescription maps can be valuable to producers and consultants.
Taro Mieno
Assistant Professor
Department of Agricultural Economics
University of Nebraska-Lincoln
402-472-4134
tmieno2@unl.edu
Grant Gardner
Master's Student
Department of Agricultural Economics
University of Nebraska-Lincoln