This example illustrated the application of models of yield risk to a simple problem of rating an all-peril yield insurance contract. Essential to constructing accurate insurance contract parameters is an adequate measure of the risks underlying random yields. Conceptually, these risks are represented by yield density estimates. As discussed previously, a number of different parametric and nonparametric techniques are available to estimate yield densities. Alternative approaches each have relative merits and shortcomings. Our application to groundnut yield data demonstrates that insurance parameters such as premium rates are likely to be quite sensitive to the assumptions made in modeling yield distributions.

# **5.  Crop Insurance Ratemaking Procedures**

Two ratemaking procedures can be considered, depending on the previous existence of the insurance product. If the insurance scheme has been offered for several years (at least 15-20 years), as it is the case many crops covered by the U.S. Multi-peril crop insurance (MPCI) program, then historical indemnity and liability data can be used to assess the premium rate through the loss cost ratio. The main advantage of this procedure is that changes in farming practice once the farmer is insured (for each level of coverage), i.e., moral hazard, is captured in the expected value of future costs. When a new insurance product is launched, such historical data are not available and thus the ratemaking procedure relies on the yield data available and on simulated losses.

# **_5.1.  Rating an Existing Insurance Scheme_**

It is first noteworthy that there is no single ratemaking approach that will apply to all insurance contracts. Insurance companies have derived their own ratemaking procedures. The case of U.S. MPCI scheme is detailed here to illustrate how public-private multiperil crop insurance contracts are rated. The involvement of the Federal government in the MPCI program creates a social insurance program which operates on different principles than a privately underwritten insurance market. For example, insurers are required to accept all applicants. The U.S. Department of Agriculture (USDA) is mandated by law to set a base premium rate with an expected loss ratio of 107.5 percent. Subsidies are applied to this rate. All base rates are either produced or approved by the Risk Management Agency (RMA) and companies are not allowed to load or modified the RMA-produced rate. As a branch of the federal government, the USDA fully subsidizes the administrative delivery costs associated with this program. Companies are thus compensated for delivery expense. Currently, Congress has authorized an expense reimbursement of 24.5% of the premium. However, the actual expenses of the crop insurance industry may exceed the amount of the expense reimbursement (Deloitte & Touche LLP 204). These costs are excluded from the rate paid by the producers.

Crop insurance ratemaking is a particular case of property and casualty (P&C) insurance ratemaking. Unlike standard P&C contract, MPCI coverage is not triggered by an event. Instead, the indemnity payment is determined after the crop is harvested. As for many other insurance coverages, the ratemaking process for MPCI has evolved over time. Josephson et al. (2000) and Schnapp et al. (2000) provide a detailed analysis of the current MPCI ratemaking procedures. The ratemaking process relies on two important 20