modeling can be used to develop crop insurance contracts. Ratemaking procedures for existing insurance schemes and new schemes are detailed in Section 5. Section 6 examines how to extend coverage to address price risk through crop revenue insurance. Finally, the key issues are summarized in the conclusions.

# **2.  Practical Considerations in Devising Crop Insurance**

The theory underlying the construction of insurance contracts is generally straightforward. However, there are a number of issues that are relevant to any practical application of these principles. Indeed, it is attention to such issues that makes up much of actuarial sciences. In this section, we discuss these issues and various approaches used in the practical development of crop insurance tools.

# **_2.1.  Data Availability_**

The feasibility of any particular crop insurance plan is often influenced by the availability of yield data. Detailed time series of individual farm data of the sort needed in measuring yield risks are usually rare, even in cases where farm records are maintained. In the case of the U.S. crop insurance program, only 4-10 years of yield data are used in determining the yield guarantees. Seldom, if ever, do substantially rich yield records exist at the individual farm level that would permit the detailed rating of crop insurance contracts at the individual level. This suggests that the development of rates and levels of protection for individual farmers may be difficult and that developers will likely need to give consideration to the use of aggregate data. The use of such aggregate data in devising crop insurance contracts may follow two distinct avenues: individual insurance coverage, and index-based insurance coverage.<sup>3</sup>

# _Individual insurance coverage_

One may wish to use aggregate data to make inferences about the risks facing individual farmers. This is very common in the development of individual plans. For example, under the U.S. crop insurance program, twenty years of the loss cost experience at the county level is used to obtain a measure of the typical level of risk for farmers in the county.<sup>4</sup> Rates at the individual level are adjusted in accordance with how the individual farm’s average yield compares to the county average.

Other approaches have been used to combine individual farm yield data with aggregate data. The developers of the U.S. Income Protection (IP) program, a revenue insurance scheme, combine county yield data with individual farm yields to make use of the longer county series and thus improve the amount of yield information used in developing the IP contracts. In the case of the IP program, an attempt is made to distinguish yield variability specific to the farm from yield variability experienced by the entire county. Under provisions of the U.S. federal crop insurance program, farmers lacking a yield history are assigned a yield that is based upon the county average yield (in

> 3 A conceptual discussion on the role of information in insurance contract design is provided in the Appendix.

> 4 Loss cost is given by the ratio of indemnities to total liability and represents a measure of the expected loss rate which, in turn, is a measure of the actuarially fair premium rate. The ratemaking procedures are discussed in Section 6.

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