# **1. Introduction**

There is a vast body of actuarial literature on design and ratemaking for crop insurance; for example Josephson et al. (2000) and Skees et al. (1997) document the methodologies implemented for the US Multiple Peril Crop Insurance (MPCI) program and Group Risk Plan (GRP) respectively, and Stohs and LaFrance (2004) propose a more sophisticated methodology for the MPCI program. However, despite the recent growth of crop insurance programs in low and middle-income countries, there is little literature on how to apply actuarial techniques outside high-income countries.

Any methodology for design and ratemaking should be robust and statistically efficient. Moreover in low-income environments where actuarial expertise is often lacking, it should be transparent enough for senior management to scrutinize and flexible enough to allow the inclusion of expert judgment.

Currently, many of the design and ratemaking procedures being used in developing countries are product-based approaches, where calculations are conducted separately for each product (Syroka 2007), rather than portfolio-based approaches, where calculations are conducted jointly for all products. By utilizing only the time dimension of historical data, these approaches are statistically inefficient (Efron and Morris 1975). There are a number of ways of incorporating the spatial dimension of data into statistical procedures, such as Hierarchical Bayes methods or seemingly unrelated regressions (SUR). However, these approaches may be challenging to implement and scrutinize when there is limited actuarial capacity. Empirical Bayes Credibility Theory is suggested as one way to increase the statistical efficiency of design and ratemaking while retaining transparency in intermediate calculations and the flexibility to apply expert judgment (Bühlmann 1967).

In this paper we document the design and rating methodology implemented by the Agriculture Insurance Company of India for the modified National Agricultural Insurance Scheme (mNAIS), which was piloted during the spring (Rabi) season 2010-11. The approach uses long term data series, available in India, to calculate premium rates that are stable yet reflective of regional differences and responsive to changes in risk over time. This enhanced risk classification increases the equity of the mNAIS as compared to its predecessor, the NAIS, and helps to protect the crop insurance portfolio from adverse selection.

In the Indian context the development of this design and ratemaking methodology had much wider implications than just improving the current crop insurance scheme; it has allowed the Government of India to transition to a market-based crop insurance program with involvement from private sector insurers and reinsurers, improved fiscal management for government by enabling ex-ante budgeting for government subsidies towards premium, and increased equity and faster claim settlement for farmers. While the current paper is targeted at a technical actuarial audience, we refer readers interested in the wider policy agenda to Mahul et al. (2011).

While the product details are specific to India, the principles can be applied much more generally to indexed insurance products in low and middle income countries. However, while we hope that others will find this paper useful, it does not substitute for the expert advice of an appointed actuary.

# _The Modified NAIS_

At the time of writing the modified NAIS (mNAIS) is in a pilot phase and may be amended in the future. In this paper the following structure for mNAIS is assumed:

- The primary benefit to farmers from mNAIS is calculated on an area-yield-based approach: if the observed seasonal area-yield per hectare of the insured crop for the defined geographical area (the _insurance unit_ ) falls below a specific threshold yield, all insured

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