An actuarial, experience based approach to design and ratemaking would use long term data and incorporate spatial dimensions of yields across India to increase the quality of risk classification. By comparison, the existing approach to design and ratemaking for the NAIS uses the three year moving average yield as the average yield estimate for some crops, despite over ten years of yield data being available. An actuarial approach would also allow for noticeable trends in historical yield data caused by changes over time to farming practices, technologies, or inputs.

The statistical subtleties of risk classification are important. For example, consider the case of the NAIS cotton product in Gujarat leading up to 2009. The rapid uptake of Bt cotton across Gujarat, reaching 66% of the cultivatable area under cotton in 2009, led to a substantial increase in the average cotton yield over the 2000s.<sup>7</sup> However, the NAIS farmer premium rate was calculated using a Normal Theory Method without detrending, and so this trend in yields was mistaken for uncertainty. The NAIS farmer premium rate for cotton in Gujarat rose from 11.9% in 2003 to 17.2% in 2008 without a commensurate increase in the threshold yield. This product was increasing considered to be poor value by farmers and over the period 2000 to 2008 insured acreage for cotton in Gujarat state fell by 96%, from 567,000 ha to 20,000 ha. Incorporating a detrending methodology led to a decrease in farmer premiums by up to 80% (see Table 3).

Table 3: Statistical investigation of aggregate linear trends for six NAIS cotton products

|State|Crop|Premium,<br>no<br>detrending|Best estimate<br>trend<br>(kg/ha/year)|P-<br>value|Indicative<br>premium,<br>with<br>detrending|Percentage<br>premium<br>reduction due<br>to detrending|
|---|---|---|---|---|---|---|
|Gujarat|Cotton|17.4%|111|4.8%|6.2%|64%|
|Maharashtra|Cotton|17.3%|62|0.4%|3.1%|82%|
|Karnataka|Cotton<br>(irrigated)|8.5%|28|2.4%|3.1%|64%|
|Andhra<br>Pradesh|Cotton<br>(irrigated)|10.5%|80|0.2%|1.6%|85%|
|Gujarat|Groundnut|26.6%|83|32.7%|n/a|n/a|
|Gujarat|Pearl Millet|17.4%|40|17.1%|n/a|n/a|

Note: Premiums are commercial premiums rates, based on the existing NAIS normal theory method without detrending, and using an indemnity level of 60% and within-state weighting by 2007 area sown.

Source: World Bank (2011a), based on data from AICI.

For risk classification to be possible, there must be flexibility to determine either premium rates or threshold yields on an actuarial basis, that is using statistical analysis of past experience, incorporating expert opinion and allowing for noticeable trends in past experience. Under the NAIS, neither the premium rate nor the threshold yield is flexible, but rather determined using simple formulae, and in practice there is significant inequity within states.

For political economy and administrative reasons, varying the threshold yields across the state may be preferred over varying the premium rates across the state. One attractive option would be for threshold yields to be determined on an actuarial basis with government mandating the premium rate to be paid by farmers and the premium subsidy rates to be paid by central and state governments. The underlying actuarial premium rates would therefore be uniform across each state: for the same premium rate high average yield, low-risk areas would be offered a higher

> 7 Estimate of the degree of Bt cotton planting across Gujarat from Business Standard, 25 March 2009.

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