Private crop insurers and the reinsurance fund allocation decision.

The next variable, yield span, has a positive relationship with the observed loss ratio. In general, RMA premium rates decline as the unit's APH increases relative to the base county yield. This result would suggest that perhaps the rate reduction is greater than justified by actual loss experience. Coverage level also has a positive relationship, suggesting that policies with a higher coverage level would be expected to have a higher loss ratio. This may be the result of decreasing deductibles and greater moral hazard at higher coverage levels. Net acres are shown to have a positive relationship with the observed loss ratio. In other words, larger farms, all else equal, tend to have slightly higher loss ratios. The number of years of continuous participation since 1994 has a positive effect, indicating that policies with more years of continuous participation have a higher loss ratio.

The next set of variables characterizes insurance design. CAT insurance is associated with a lower expected loss ratio. In other words, premiums for these policies tend to exceed indemnities over the period examined. CRC and RA policies have a higher expected loss ratio than the default yield insurance plan, while IP is less likely to have a high loss ratio. Among the crops, the expected loss ratios for wheat and soybeans tend to be higher than that of the default corn category.

Having estimated a naive, county-level model and a more sophisticated, policy-level model to allocate policies to the Assigned Risk Fund and to estimate expected loss ratios, the implications of firm allocation decisions can be examined. This is done by applying provisions of the SRA on the outcomes of the alternative fund designation rules. We applied a simplified version of the 1998 SRA, the SRA that was in effect during the time period from which our data were drawn. We simplified the SRA by allowing policies to be placed in either the Assigned Risk Fund or in one of the three commercial funds. We also assumed, for simplification, that companies would retain 100% of the premium and associated liability on the commercial fund policies (and retain 20% of the premium and associated liability for policies in the Assigned Risk Fund, as required under the SRA).

Comparison of Alternative Policy Assignment Strategies

Table 5 reports the aggregate underwriting gains and losses under the alternative decision rules and under the actual allocation of the crop insurance firms when applied to the out-of-sample data for 1998-2003. Under the actual allocation, companies placed $436.1 million out of a total $2,318 million (18.8%) in the Assigned Risk Fund. Over the out-of-sample observations, gross underwriting gains of policies placed in the commercial fund were $387.4 million while policies in the Assigned Risk Fund had a gross underwriting loss of $91.7 million. Total gross underwriting gains were thus $295.7 million. The gain and loss sharing under the provisions of the 1998 SRA resulted in net (post-SRA) underwriting gains of $297.8 million.

Under the county-based model, companies would have placed a much smaller proportion of total premium in the Assigned Risk Fund, $135.1 million or 5.8%, than under the actual allocation. However, net underwriting gains under the county-based model were only $289.7 million, about $8.2 million or 2.7% less than under the actual allocation. This suggests that the current allocation used by companies is more discriminating than a model that allocates policies based on county-level performance.

Under the policy-level model, companies would have placed 21.3% of total premium in the Assigned Risk Fund ($493.4 million). Aggregate net underwriting gains for all firms would have been $333.6 million, about 12% higher under the policy-level model than under the actual allocation and 15% higher than under the county allocation model. Moreover, the more premium in the Assigned Risk Fund and less retained by the companies, increases the rate of return on retained premium. Under the policy-level model the net underwriting gains would have over 17% of retained premium, compared with about fifteen for the actual allocation and thirteen for the county-level allocation. To assess the statistical significance of the differences found here, we performed a randomized sampling within the out-of-sample data and are able confirm the differences found here are statistically significant at the 1% level. Further, we investigated whether the superior performance of the policy-level model was due to disaggregation to the policy level or due to the robustness of the explanatory variables used. An auxiliary model was estimated using the policy-level model variables aggregated to the county level. Aggregate company gains were only 1.1% less than obtained with the policy-level data. This suggests that the use of policy characteristics provides most of the additional gains rather than disaggregation.

Although the policy model improves underwriting of the companies in aggregate, its performance at the individual firm level varies. Table 6 presents proportion of premium in Assigned Risk and rates of return for the twenty-two private companies selling crop insurance during portions of the 1998-2003 period. While companies in aggregate placed somewhat less premium in Assigned Risk Fund under the actual than under the policy-level allocation, twelve of the twenty-two placed a larger proportion of premium in Assigned Risk Fund under the actual allocation. Net underwriting gains, as a percentage of retained premium, were highest under the policy-level allocation for nineteen of the twenty-two companies. Generally, the policy-level allocation tended to produce the highest net underwriting gain of the three methods when the gross (pre-SRA) loss ratio was high. For example, for those companies where the gross loss ratio was greater than 1.0, the policy-level allocation tended to produce the highest return. When the gross loss ratio was less than 1.0, the results were more mixed. This suggests that for firms operating primarily in states where the actuarial performance has been generally profitable (e.g., Iowa, Minnesota, and Illinois) it may be less important to discriminate between policies. In these states, the "cost" of placing business in Assigned Risk--the loss of potential underwriting gains--offsets the benefits of protecting against the risk of underwriting loss. In states where the actuarial performance is poor, however, companies may be able to improve underwriting gains by carefully discriminating between policies.

Conclusions

With the rapid growth of the crop insurance program over the past ten years, retained premiums by companies has grown dramatically from $466 million in 1992 to almost $2.6 billion in 2003 (Glauber 2004). As companies have retained more risk, their exposure has increased proportionately. In 2003, for example, the maximum possible underwriting loss to companies was almost $2.4 billion. With increased liability and risk exposure, companies must discriminate between crop policies between those that are profitable and those that are not.

Our analysis suggests that companies incorporate available information on policyholders in allocating crop policies to the Assigned Risk Fund. Variables such as a policy's previous actuarial experience relative to peers in the county were found to be significant suggesting that companies take into account information regarding the potential profitability of a policy in making the fund allocation decision.

In general, the current allocation strategy employed by companies outperforms more simplistic strategies that allocate policies based on aggregate measures such as county loss ratios. However, our analysis also suggests that some additional underwriting profits could be gained by a more careful estimation of a policy's expected loss ratio, particularly in those states where underwriting performance is generally poor. Here, net underwriting profits can be improved or net underwriting losses can be reduced by more carefully discriminating between policies.

[Received May 2005; accepted August 2006.]

References

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