Yield risk is defined here as the risk that the yield of a crop may differ from that which was expected at planting time. Crops are subject to many types of damage. Weather affects yields in many ways. Inadequate supply of water at critical points in the growth of the plant reduces yield and extreme drought can kill the plant. Excessive heat or frost can damage or kill plants. Severe storms can damage or kill plants by hail, wind, or flooding. Fire, whether started by lightning or other cause, poses a risk to crops. Biological factors also affect yields. Disease, fungus, insects, weeds, birds and other animals all can reduce crop yields in terms of quality and quantity.

Yield risk can be quantified in several ways. By recording yields in different fields each season, a frequency distribution can be assembled for each type of crop. Historical fre­quency distributions can be adjusted for trends in average yields to estimate probability distributions for the coming crop season. Crop insurance underwriters may estimate prob­ability distributions for crops to determine what level of yield to insure and what premium to charge for insurance. Note that yield is conditional on many factors. Distinct yield prob­ability distributions may be estimated for the same crop grown under different conditions. Locational factors, such as soil type and climate, affect historical yield frequency distribu­tions as well as estimated probability distributions. Managerial factors, such as seed variety or genetic type, particularly in relation to planting date and days required for crop maturity, can affect the estimated probability distribution. Similarly, irrigated crops can have very different yield probability distributions than dryland crops of the same type.

Figure 15.2 illustrates three yield probability distributions. The horizontal axis indicates yield and the probability of occurrence is indicated on the vertical axis. Each of the curved

lines represents a different yield probability distribution. The middle curve represents a symmetric distribution with similar probabilities of yields above and below the mean or average (point B). The curve with higher probabilities of lower yields and a long tail of declining probability to the right has mean labeled ‘A’ and represents a crop that seldom achieves its potential and often suffers reduced yields. This probability distribution can represent a crop being grown in adverse conditions. Conversely, the curve with a long tail of declining probability to the left and higher probabilities of high yields with mean ‘C’ represents a crop that frequently achieves near maximum yields. This probability distribution may represent a crop that is being grown in favorable conditions and could represent an irrigated crop. A general observation from this example is that crop yield probability distributions may differ both with respect to their mean or expected yield as well as the probability of various degrees of yield loss below the mean.

The economic effects of yield risk are many. Farmers incur routine costs to prevent or reduce risk of yield loss. Herbicides, pesticides, and fungicides are examples of inputs that are not used directly by the plant for growth but that reduce the frequency of losses due to pests. Irrigation and fertilizers provide inputs used by the plant and affect both average yield and the probability of yield loss. Farmers also incur costs of excess input use when yield is reduced or crops fail. For example, fertilizer may be applied at a rate sufficient for the expected yield or for a higher yield that is quite possible. When a lower yield is realized, the value of excess fertilizer is wasted. In other words, had they known the yield would be so low, the farmer could have applied less fertilizer and saved some input cost. Conversely, if a farmer applies only enough fertilizer for the average or expected yield and conditions occur that would have supported a higher yield, the farmer loses the value of foregone yield net of the additional fertilizer cost. The purchase of crop insurance is a common method of mitigating the financial effects of yield risk.