An economic viability study of crop revenue insurance for the South African maize market: a statistical copula approach

Abstract

The purpose of this dissertation is to conduct a viability study of a revenue-based crop insurance product, focussing on the white maize market in South Africa.

It has been established that multi-peril crop insurance (MPCI) schemes in South Africa have made losses in almost half of the 14 years between 2005 – 2018, hence the need for an alternative offering. Recent research has shown that when compared to MPCI, a revenue-based product is more viable and affordable to offer in the absence of government support, premised on an inverse relationship between the yield and prices of crops, that permits for a relatively stable expected revenue, referred to as a “natural hedge”.

A statistical copula approach was applied to establish the dependence relationship between white maize yields and prices in this research. Copulas have been established as a superior dependence modelling technique because their approach moves away from the normal model assumption as depicted by the Pearson correlation relied on by insurers. Copulas are flexible modelling instruments that permit the use of different statistical distributions in the marginals of the variables which is favourable because evidence exists suggesting that yield distributions are not normally distributed contrary to the insurers modelling approach.

Alternative statistical distribution models were therefore fit to the variables to get a better representation of their marginal distributions. The marginal distributions produce cumulative distribution (CDF) values used in the copula fitting procedures. From the established copula dependence structure, a Monte Carlo simulation produced CDF values that were converted back to price and yield variates for use in comparing yield- and revenue-based crop insurance policies. The two insurance products were compared on the premium rates achieved at identical insurance coverage levels while the former is ultimately determined by the expected loss outcomes. The premium rate achieved represents the affordability of the product while the expected loss outcome resembles the level of risk from insuring a product.

Findings were that an inverse relationship exists between the variables from the three selected maize producing districts namely, Bloemfontein, Vryburg and Delmas. The best-fitting copula models were achieved from a combination of alternative marginal distributions for both variables, as well as alternatives to the Gaussian copula. Revenue-based crop insurance policies achieved lower insurance premium rates than yield-based insurance policies for Bloemfontein and Vryburg, but not Delmas. The study recommends that insures consider production region modelling and insurance products.