Bayesian premium calculations of Multiperil Crop Insurance (MPCI) based on Bayesian Beta mixed regression model

Abstract

Crop insurance policy in Indonesia is based on Multi-Peril Crop Insurance (MPCI). Farmers are allowed to purpose claim when at least 75% of their insured paddy fields suffer loss. The indemnity given by the insurer is expected to cover the next planting costs (IDR 6 million per hectare). Previous simulation studies found that the premium of MPCI is irrelevant and too low. Nevertheless, there were some considerations on how the design of the previous simulations were developed. Henceforward, in this study we would like to improve the previous simulation results by incorporating farmer harvest loss rate data and significant independent variable affecting the loss rates. The estimates of these variables were driven by the Bayesian Beta Mixed Regression Model. Results show that Bayesian Beta Mixed Models have better fits and predictions compared to Mixed Beta Regression Models. The occurrence of Drought, Tornadoes, Flood, Plant Disease, and other risks were proven significant and had positive estimate values indicating that higher values cause higher possibility of higher average harvest failure rate. As a reflection, the current policy covers most of this risk, except other risks and tornadoes that need to considered in the future crop insurance policy. Next, MPCI premium calculations were simulated based Bayesian Markov Chain Monte Carlo (MCMC) algorithm which was developed based on different scenarios. Simulation results indicate that for a threshold of 65% and assuming that the loss rates have a beta distribution the current premium is still sufficient when samples are large. Nevertheless, estimations are very sensitive towards the determination of thresholds and in which area it is examined. Accordingly, the diversity of harvest failure rate between municipalities and determining on which threshold to be used needs to be handled with cautions.