On the Possibility of Private Crop Insurance Market: a Spatial Statistics Approach

Risk theory tells us if an insurer can effectively pool a large number of individuals to reduce the total risk, he then can provide the insurance by charging a premium close to the actuarially fair rate. There is, however, a common belief that the risk can be effectively pooled only when the random loss is independent, so that crop insurance markets cannot survive without government subsidy because crop yields are not independent among growers. In this paper, we take a a spatial statistics approach to examine the effectiveness of risk pooling for crop insurance under correlation. We develop a method for evaluating the effectiveness of risk pooling under correlation and apply the method to three major crops in the US: wheat, soybeans and corn. The empirical study shows that yields for the three crops present zero or negative correlation when two counties are far apart, which complies with a weaker condition than independence, finite-range positive dependency. The results show that effective risk pooling is possible and reveal a high possibility of a private crop insurance market in the US. Contact person: H. Holly Wang Dept. of Agricultural Economics Washington State University P. O. Box 646210 Pullman, WA99164 Ph: 509-335-8521 Fax:509-335-1173 [email protected] 1 The authors are assistant professors with the Department of Agricultural Economics and the Program in Statistics, Washington State University, respectively. ON THE POSSIBILITY OF PRIVATE CROP INSURANCE MARKET: A SPATIAL STATISTICS APPROACH Crop insurance has been an important instrument for protecting farmers’ income against low yield resulting from adverse weather and other natural disasters. Except for a few perils such as hail and fire, the multiple peril crop insurance (MPCI) has only been offered by the US government with a huge subsidy. MPCI was first introduced in 1938 on a trial basis, and extended in 1980 to most crops in the US. MPCI pays an indemnity to a farmer based on the difference between a pre-selected coverage yield level and the farmer’s realized yield level. For years, billions of dollars of financial deficits have been accumulated by the government to provide MPCI, and farmers’ participation rate is still low. These problems have been attributed to moral hazard, adverse selection, and high administrative costs (Knight and Coble,1997; Skees, Black and Barnett,1997; Goodwin and Smith,1995). To deal with these problems, a Group Risk Plan (GRP) was introduced in 1994, which pays a farmer an indemnity only when the realized average yield of his county falls below the pre-selected coverage level. Evaluation of county yields instead of individual farm yields for indemnification greatly reduces the insurer’s administrative costs. The disadvantage of GRP is that it does not protect farmers as effectively as MPCI when the farm yield and county yield are not highly correlated. In the late 1990s, revenue insurance programs were piloted that could protect farmers from both price and yield risks including those that were based on farm yields such as Income Protection, Crop Revenue Coverage and Revenue Assurance and those based on county average yields such as Group Revenue Insurance Programs. To cope with the actuarial problems with federal crop insurance programs, three lines of study in the area of agricultural risk protection are currently advanced by economists. The first line is to investigate the theory of area-based insurance and the risk protection effectiveness of GRP (Miranda, 1991; Wang et al, 1998). The second line is to study revenue insurance which takes the advantage of usually negatively correlated price and yield risks 1 and focuses on stabilizing the overall income (Hennessy, 1997; Skees et al, 1998). The third line is to study market instruments that are based on natural conditions, such as weather derivatives, which also deal with the moral hazard problem (Turvey,1999). The first two lines are focused on the current government programs, and the last line also fails to address the question of whether it is feasible for private insurers to provide agricultural insurance. Although positive correlation among farm yields is the basis for GRP and weather derivatives, it is perhaps the major factor that has discouraged the consideration of private crop insurance. It is a common belief that effective risk pooling is built upon the independence between risk exposure units, and that a private market for crop insurance is doomed to fail because of the systemic risk existing in crop yield (Miranda and Glauber, 1997). However, this belief has not been thoroughly studied. Therefore, it is important to investigate carefully whether private agricultural insurance and reinsurance markets can exist without or with a minimum government subsidy, what conditions are required, and whether these conditions are present in the current situation. The objectives of this research are (1) to explore necessary statistical conditions for effective risk pooling; (2) to investigate the pattern of US crop yields’ correlation; and (3) to develop a method to evaluate the effectiveness of risk pooling under correlation and apply it to the US crops. Each of the objectives is pursued in one of the following three sections, and the last section consists of a summary and discussion. Statistical Foundations of Insurance The primary function of insurance is risk pooling. Mehr, Cammack and Rose (1985) offer the following definition, “Insurance may be defined as a device for reducing risk by combining a sufficient number of exposure units to make their individual losses collectively predictable.” In the insurance literature, the occurrence of an aggregate loss that is so large as to deplete the insurance fund is captured by the concept of ruin. It has been suggested that a possible objective criterion for the management of an insurance pool is to minimize the probability of ruin in a given time period or perhaps maximize returns subject to maintaining a specified