Premium Rating in the Federal Crop Insurance Program (FCIP)

Overview

Premium rating in the FCIP is guided by a complex principle known as the loss‐cost ratio rate‐making (Coble et al. 2010; Coble et al. 2020) to develop insurance pool level (the lowest sub‐county aggregation for rating in the FCIP) rates for a common coverage level, and subsequent adjustments via mechanisms analogous to how other property and casualty insurance rate factors are developed from a combination of experience and differential exposure information (Sherrick, Schnitkey and Woodward 2014). Here, the aim is to simplify this process.

Individual-level insurance

Individual-level insurance are based on actual on‐farm experiences. These include actual production history [APH], yield protection [YP], revenue protection [RP], and RP with harvest price exclusion [RP-HPE] plans.

Individual-level yield insurance plans (YP and APH) consist of eight main components: rate yield ($\bar{y}$), approved yield ($\ddot{y}$), coverage level ($\theta$), indemnity ($I$), premium rate ($\tau$), premium ($P$), and subsidy ($S$). The rate and approved yields are calculated from the average actual production history (APH) reported by farmers. The key distinction is that the approved yield is typically adjusted upwards through various elements of the RMA’s actuarial process, such as yield exclusion, yield substitution, and trend adjustments.

For each contract, producers may insure their approved yield at a chosen coverage level ($\theta$), establishing a yield guarantee (liability) of $\theta\ddot{y}$. The indemnity per acre, given a specific yield outcome $y$, is calculated as $$I(y) = \max\{0, \theta\ddot{y} - y\}.$$

Premium rates are designed to be actuarially fair, implying that over time, the total premiums collected equal the total indemnities paid. The premium rate per dollar of liability is thus defined as:

$$\tau(\theta)=\frac{E[I(y)]}{\theta\ddot{y}}=\frac{1}{\theta\ddot{y}}\int_{0}^{\theta\ddot{y}} (\theta\ddot{y}-y)f(y)dy \quad \text{(1)}$$

Here, $f(y)$ represents the probability density function of $y$, which assumes that indemnities are stochastic and not predetermined when the policy is issued. Crop insurance policies are generally developed under the assumption that $f(y)$ is conditional upon an adjustment mechanism. This mechanism adjusts for the underlying risk profile of the insured producer, which, although not directly observable, is estimated by comparing the producer's productivity to that of their peers. The extent of this adjustment is derived using RMA’s “continuous rating formula” (Milliman & Robertson 2000; Risk Management Agency [RMA] 2000; Risk Management Agency [RMA] 2009).

For simplicity, the continuous rating formula for yield‐based plans (YP and APH) is specified according to the following equation:

$$\tau_{ijt} = \Bigl[\alpha_{jt} \Bigl({\bar{y}_{ijt}}\backslash{\bar{y}_{cjt}}\Bigr)^{\beta_{jt}} + \delta_{jt}\Bigr] F_{ijt}^{\theta} F_{ijt}^{u} \quad \text{(2)}$$

Here, the subscript $ijt$ represents an insured $(i)$ seeking protection defined by an insurance pool $(j)$ for crop year $t$. The parameters $\alpha_{jt}$ and $\delta_{jt}$ respectively represent the reference rate and catastrophic fixed loading factor for a common coverage level (conventionally at the 65% level) for the insurance pool. The term $\bar{y}_{ijt}$ (the rate yield) represents a producer’s simple average yield of their actual production history, and $\bar{y}_{cjt}$ represents the average yield of producers in the county. Thus, the term $${\bar{y}_{ijt}}\backslash{\bar{y}_{cjt}}$$ represents a producer’s typical yield relative to that of other producers in their chosen pool. This ratio is then adjusted by a negative continuous rating exponent, $\beta_{jt}$, which has the effect of scaling the rate down for more productive producers. This is done under the assumption that risk covaries with yield such that more productive farms are less risky which is based on an early body of research (Botts and Boles 1958; Skees 1986). The entire term, $${\bar{y}_{ijt}}\backslash{\bar{y}_{cjt}}^{\beta_{jt}},$$ is referred to as the rate multiplier curve. The terms $F_{ijt}^{\theta}$ and $F_{ijt}^{u}$ represent scaling factors that adjust the rate based on the producer's choice of coverage level $\theta_{ijt}$ and insurance unit election $u_{ijt}$.

For a producer seeking revenue protection (RP and RP-HPE), premium rates are calculated using a simulation that combines yield and price distributions with their correlation. This process yields a "revenue load" by subtracting a simulated yield rate from a simulated revenue rate. The revenue load, representing the extra risk of covering revenue over yield, is added to the base rate of yield insurance plans (YP and APH). This approach ensures the premium rate charged for revenue coverage accurately reflects the additional risk, providing a fair and tailored insurance solution for producers. The total price of the insurance contract, $P$, is set equal to the product of the premium rate, $\tau(\cdot)$, and the yield guarantee, $\theta\ddot{y}$, such that $$P=\tau(\cdot)\theta\ddot{y}.$$ The final price paid by the insured is subsidized at a rate $S(\theta,u)$ that is tied to coverage level and insurance unit—and not to location or the crop.

This formula integrates both the relative yield performance of a producer and additional scaling factors that account for the selected coverage options, thereby providing a nuanced continuous rating for yield-based insurance plans.

Group/index based insurance

Reference

• Adhikari, S., T.O. Knight, and E.J. Belasco. 2013. “Yield Guarantees and the Producer Welfare Benefits of Crop Insurance.” Journal of Agricultural and Resource Economics 38(1):78–92.
• Botts, R.R., and J.N. Boles. 1958. “Use of Normal-Curve Theory in Crop Insurance Ratemaking.” Journal of Farm Economics 40(3):733–740.
• Coble, K., et. al. 2020. Review of the Pasture, Rangeland, Forage Rainfall Index Crop Insurance Program Indexing and Rating Methodology Final Report. Report to RMA by Sigma Agricultural Risk and Actuarial Services, LLC.
• Coble, K.H., et. al. 2010. A Comprehensive Review of the RMA APH and COMBO Rating Methodology Final Report.
• Milliman & Robertson. 2000. “Actuarial Documentation of Multiple Peril Crop Insurance Ratemaking Procedures.” RMA Actuarial Methodology Publications.
• Risk Management Agency [RMA]. 2000. “Premium Rate Calculations for the Continuous Rating Model.”
• Risk Management Agency [RMA]. 2009. Rate Methodology Handbook Actual Production History (APH).
• Sherrick, B.J., G.D. Schnitkey, and J.D. Woodward. 2014. “Crop insurance loss experience, ratings changes, and impacts on participants.” Agricultural Finance Review 74(4):443–463.
• Skees, J.R. 1986. “Rate Making for Farm‐Level Crop Insurance: Implications for Adverse Selection.” American Journal of Agricultural Economics 68(3):653–659.

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