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The Yield Response to Nitrogen: Subjective Belief Bias in Nitrogen Management

Sandip Agarwal, Keri Jacobs, John Sawyer, and Quinn Weninger

Agricultural scientists and economists have long been interested in quantifying the optimal amount of nitrogen needed on an acre of corn. Notions of optimality are sometimes based on principles of cost and revenue, sometimes on yield targets, and other times on environmental concerns. Ask any producer, fertilizer retailer, or agronomist how much nitrogen a corn producer needs to apply and you will probably not be surprised to hear, repeatedly, “It depends.” Even if the optimal amount of nitrogen can be computed for a single field, being right ex post hinges critically on weather and other factors. The nitrogen management decision is complicated because the yield response to nitrogen depends on a host of variables, most of which are uncertain when nitrogen is applied and beyond the control of the producer: rainfall amounts and timing, in-field nutrient availability, and growing conditions top the list.

Further complicating the nitrogen decision is a producer’s beliefs about the underlying relationship between nitrogen and yields, and the roles played by external factors (e.g., weather). In 2014, we surveyed producers in Central Iowa to gain an understanding of the real-world decision processes used by farmers when making nitrogen decisions on their fields. The survey was designed to elicit individual producers’ beliefs about how much nitrogen is needed on a specific field, the field’s expected yields, and the expected impact on yields when lesser and greater amounts of nitrogen are applied.

An important contribution of this work is to compare farmers’ underlying beliefs about the relationship between nitrogen and corn yields, these are subjective beliefs, with what agronomists have quantified as the actual relationship— this is the objective yield distribution and its response to varying amounts of nitrogen. Iowa State University researchers in the Department of Agronomy have maintained long-term trials of nitrogen and yield on several research farms located across the state (Sawyer et al. 2006). These trials occur on land of varying quality that experience variation in weather similar to the type of variation that would be experienced by producers in our survey. At the research sites, variables such as soil fertility, planting date, hybrid, etc. are held constant in order to compare yields under different nitrogen rates and rotation. In order to properly condition our analysis, we asked producers to report on field specific measures including corn suitability rating (CSR), rotation, soil fertility, their nitrogen application plans and, importantly, their expected yield outcomes.

Figure 1. Corn yield outcomes at varying nitrogen application levels
Figure 1

Figure 1 shows a histogram of actual yield outcomes for three different levels of nitrogen application (i.e., 0 lbs/acre, 120 lbs/acre and 240 lbs/acre) based on long-term nitrogen trials conducted by ISU agronomists.1 Note that as more nitrogen is used, the probability of a high yield outcome increases. However, consistent with other studies, these data also show why nitrogen is considered a risk increasing input: the more nitrogen that is applied, the greater the variability in yield outcomes.

In helping producers make decisions about how much nitrogen to use, agronomists and other advisers often suggest using a metric such as the return to nitrogen: the expected increase in bushels produced when nitrogen application is increased. One example of this is the Corn N Rate Calculator (Sawyer et al. 2006), which calculates the maximum return to nitrogen (MRTN). The MRTN shows the nitrogen rate at which the return to nitrogen is maximized given user-supplied fertilizer costs and corn prices.

Figure 2. Comparison of the objective and subjective relationship between nitrogen and corn yields
Figure 2

The expected marginal product of nitrogen can be constructed from both the subjective and objective data. Figure 2 shows the expected marginal product of nitrogen derived from both the actual or objective yield data (the downward sloping curve) and the surveyed farmers’ subjective beliefs (the plotted points). Based on the objective trial data, the expected marginal product of nitrogen (the solid fitted curve) is positive and decreasing over most of the application range: as more nitrogen is added, the expected benefit in terms of yield increase is positive but declining. The broken lines above and below the fitted line frame a 95 percent confidence interval in this estimation. In contrast, the analysis from our survey finds that producers report an underlying belief that the yield response to nitrogen is substantially greater than indicated in N rate response research. Put another way, most producers, whether they considered their best performing field, an average field, or an underperforming field, mirror a belief that, in their fields, nitrogen application has a larger positive impact on corn yield than shown by the long-term nitrogen studies.2

Our research finds differences in the actual yield response to changes in nitrogen application and the response perceived by producers. What are the underlying causes of this difference? One explanation is that decision makers may not assign the correct (true) probabilities to uncertain outcomes. Another explanation is that differences in the actual and perceived nitrogen response stems from being overly optimistic. For example, producers may attach too great of a probability to ‘good’ growing conditions, where nitrogen’s role in plant growth is perhaps greatest. A third possibility is that producers perceive nitrogen to be a relatively inexpensive risk-limiting input: this is the nitrogen-as-insurance argument. For example, “If I apply more nitrogen, nitrogen won’t be the limiting factor,” or “I have a greater probability of a larger yield, somewhat regardless of the weather outcome.”

The source of the bias in producers’ perceptions about nitrogen’s role in crop growth is the subject of our ongoing research. What we have learned so far is that the bias can be large. That it exists at all has implications for designing policies for water quality and nutrient use and gives important insight into how educational programs of nitrogen management might be more effective.


Babcock, B.A. Effects of Uncertainty on Optimal Nitrogen Applications. Rev. Agr. Econ. 14 (1992): 271–80.

Sawyer, J., E. Nafziger, G. Randall, L. Bundy, G. Rehm, B. Joern. 2006. Concepts and Rationale for Regional Nitrogen Rate Guidelines for Corn, Iowa State University Extension Publication, available at


1. The trial data depicted here are from four research farms in Iowa from 1999–2013. Nitrogen application rates range from 0 to 240 lbs/acre in multiples of 40 or 60 lbs/acre of nitrogen; for brevity we show only three nitrogen rates here. In both the survey data and ISU ??ield experiments, we do not control for the amount of nitrogen that exists in the soil pre-planting.
2. The timing of this type of survey matters because producers’ perceptions of the growing conditions and impact of nitrogen will change as weather uncertainty over the growing season is resolved. Our survey was conducted during mid-to-late June 2014. It is possible that the conditions observed at that time by producers did suggest the expected return to nitrogen would be different than the typical year.

Suggested citation

Agarwal, S., K. Jacobs, J. Sawyer, and Q. Weninger. 2016. "The Yield Response to Nitrogen: Subjective Belief Bias in Nitrogen Management." Agricultural Policy Review, Spring 2016. Center for Agricultural and Rural Development, Iowa State University. Available at