Private crop insurers and the reinsurance fund allocation decision.

A unique aspect of the federal crop insurance program since passage of the Federal Crop Insurance Act of 1980 has been the role of private insurance companies in program delivery and risk sharing (Glauber and Collins 2002). Unlike other federal insurance programs (e.g., flood insurance), private insurance companies not only sell and service crop insurance policies but also annually share with the federal government underwriting risks on over $45 billion of liability.

Because of the wide disparity in underwriting gains across regions and crops (Vedenov et al. 2004), a problem facing the federal crop insurance program has been how to encourage companies to deliver insurance policies in areas where expected gains are low or exposure is high. To encourage the provision of federal crop insurance to all eligible producers, the government shares risks with companies through the Standard Reinsurance Agreement (SRA) (USDA-RMA 1998, 2005). Under the SRA, if a company elects to write crop insurance policies in a state it must offer coverage to any farmer in that state. In addition, it must accept the rates and underwriting provisions set by the Federal Crop Insurance Corporation (FCIC). In exchange, the company is allowed to place some crop insurance policies in an Assigned Risk Fund where its exposure is minimal and to place other policies in funds where potential underwriting gains and losses are greater.

While much has been written on the federal crop insurance program (see reviews by Goodwin and Smith 1995, Knight and Coble 1997, and Glauber 2004), little research has appeared on the SRA. Notable exceptions include simulations of the SRA by Miranda and Glauber (1997), Mason, Hayes, and Lence (2003), and Vedenov et al. (2004). These works have developed large-scale stochastic simulations to investigate potential changes in the structure of the SRA given an assumed fund allocation of the firm. In addition, Vedenov et al. (2006) used a simulation model based on representative insurance contracts to examine possible reinsurance allocations under alternative SRA specifications. Ker and McGowan (2000) modeled the potential for companies to use El Nino/La Nina information to earn economic rents from the SRA reinsuring an area yield design. More recently, Ker and Ergun (forthcoming) made an important step toward understanding actual insurance firm allocations and through out-of-sample testing found evidence that firms have significant private information. However, their analysis used data aggregated to the county level and did not allow for examination of individual policies attributes or individual company behavior.

In contrast, we examine policy-level allocation decisions made by individual crop insurance companies, analyzing firm-level reinsurance fund allocations made over 1998-2003. Using a logit model, we examine the characteristics of over 2 million individual crop insurance policies to identify the factors influencing the allocation of policies to the Assigned Risk Fund and how these factors differ across companies. We then examine the allocation decisions of crop insurance firms and compare their actual post-SRA gains to those of a simple county-level allocation system and to those based on an econometric model. The results show that firms are not equally effective in allocating policies to the Assigned Risk Fund. Although, in aggregate, firms are more effective in their actual allocations of policies than they would be if the simple county-level decision rule were used, allocations based on an out-of-sample econometric model forecasts generally result in greater underwriting gains than actual allocations.

Conceptual Framework

The terms under which private companies sell, service, and underwrite federal crop insurance are specified in the SRA, which is negotiated from time to time by the companies and the federal government. Our analysis is based on the 1998 SRA (USDA-RMA 1998), the SRA that was in effect with minor modifications from 1998 through 2004, the time period for which data on individual policy allocations were available. Based on Vedenov et al. (2006) the relatively minor changes in the more recent SRA would not change the implications of the analysis.

Under the SRA, companies retain risks, or alternatively cede risks to FCIC, by designating individual crop insurance policies to reinsurance funds. Different parameters of each of the funds allow a company to retain or cede different proportions of premium and associated liability (proportional reinsurance) and to share with FCIC different amounts of the eventual underwriting gains or losses on retained premium and liability (nonproportional reinsurance). The levels of retention and of potential gains and losses to a company are highest on policies placed in commercial funds (three funds, each for a different type of insurance coverage) and lowest on policies placed in the Assigned Risk Fund. Intermediate levels of retention and gain and loss sharing are available in developmental funds. In the Assigned Risk Fund, 80% of the premium and associated liability is ceded to FCIC; the company retains 20%. Under the developmental fund, companies must retain at least 35% (and may retain up to 100%) of the premium and associated liability; under the commercial fund, companies must retain a minimum of 50% (and may retain up to 100%) of the premium and associated liability. Of the liability retained by the company, FCIC pays increasing shares of the indemnities, depending on the company's state-level loss ratio (indemnities divided by total premium) in the fund, with FCIC paying the entire loss as the loss ratio exceeds 5.0.

Shares of gains and losses that fall to the private insurance companies differ markedly by fund (table 1). For example, the maximum possible underwriting loss on Assigned Risk policies is 11% of company-retained premium. The company's potential for underwriting gains on policies placed in the Assigned Risk Fund, however, is also small: maximum of 7.6% of retained premium. In contrast, companies can gain as much as 48.9% of retained premium for policies in the commercial fund. However, the downside risks are larger as well. The maximum possible underwriting loss on policies placed in the commercial fund is 107.6% of retained premium.

Companies designate policies to the reinsurance funds within thirty days of the crop insurance sales closing dates. In general this puts the allocation deadline slightly before planting. Insurance companies may use information available at that time to decide how much risk on which policies to retain or to cede. While limited information is available regarding prospective growing conditions, companies have access to a great deal of information regarding the insurance policy, including past experience.

The fund designation decision can be characterized by the information sets used by FCIC and the company to determine the actuarial soundness of an insurance policy, that is, the relationship between total premium (producer-paid premium plus premium subsidy), [PI], and the expected indemnity E(I). The FCIC uses an insurance premium rating system that is largely based on historical loss experience in a county for a particular crop and adjusted to policy specific characteristics. The FCIC, the government, G, assumes the expected indemnity is equal to premium resulting from these rate factors. Premiums are conditioned on crop price, [P.sub.g], coverage level, [C.sub.i], actual production history or APH yield, [[??].sub.i], number of acres insured, [A.sub.i]. and premium rate, R. The premium rate, in turn, depends on the insurance type (one of several revenue and yield insurance plans), [T.sub.i], the crop insured, [K.sub.i], coverage level, [C.sub.i], the APH yield, the base county yield, [[??].sub.i], the number of actual yields in the APH, [N.sub.i], unit selection (whether a policy's acreage is subdivided into optional units), [U.sub.i], and the specific crop type and practice, [P.sub.i]. The expected indemnity for the Government is summarized as follows:

(1)

E(I | G) = [PI]([P.sub.g], [C.sub.i], [[??].sub.i], [A.sub.i], R([T.sub.i], [K.sub.i], [C.sub.i], [[bar.Y.sub.i],[[??.sub.i], [N.sub.i], [U.sub.i],[P.sub.i])).

The insurance firm is concerned with the net return of the policy, [NR.sub.i] = ([PI] - E(I)), which is driven by the perceived accuracy of the rating factors and other information about the policy. In particular, the insurance firm can utilize information from past participation, underwriting experience, and early season growing conditions to adjust expectations of the net returns. Thus, we write the insurance firm's expectation of net return E(NR | F) as a function of the policy characteristics from equation (1) and add the firm's information set, F, which includes the firm's knowledge of historical loss ratios for the policy relative to peers, [FI.sub.i], the policy's continuous participation in the insurance program, [FC.sub.i], and year-specific early season growing conditions, [FY.sub.i].

(2)

E(NR | F) = NR([P.sub.g], [C.sub.i], [[bar.Y].sub.i], [A.sub.i], R([T.sub.i], [K.sub.i], [C.sub.i], [[bar.Y].sub.i], [[??].sub.i] [N.sub.i], [U.sub.i], [P.sub.i]), [FI.sub.i], [FC.sub.i], [FY.sub.i]).

Having defined the firm's expectation of the net return to the insurance policy, the policy allocation decision may be written as follows:

(3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]