Binary choice models for rare events data: a crop insurance fraud application

Abstract

This study implements a recently proposed score test that could help guide insurance fraud researchers in deciding whether to use a logit or a probit model in predicting insurance fraud probabilities, especially when the occurrence of ones in the dependent variable is much less than zeros. The test is easily implemented in a crop insurance fraud context and seems to be a promising method that could be applicable to analysing and detecting potentially fraudulent claims in various lines of insurance.

Acknowledgements

The authors would like to thank Mike Cross for extracting the data set from the data warehouse of the Center for Agribusiness Excellence at Tarleton State University. Note that this work was undertaken when Yufei Jin was a Post-Doctoral Research Associate at Texas Tech University.

Notes

 Although there are other binary choice models that can be used to estimate fraud probabilities (e.g. semi-parametric models and models with different distributional assumptions), these methods are still not commonly used in the insurance fraud literature and the insurance industry. This is because most of these methods are computationally more intensive than the logit and probit models, which precludes its applicability for insurance data sets that have an enormous number of observations. As such, these methods are not explicitly considered in this study.

 RMA is the government agency under the US Department of Agriculture that oversees the crop insurance programme in the USA.

 For a detailed description of the algorithm used to flag anomalous prevented planting claims, the reader is referred to Rejesus et al. (2003).

 Essentially, P ₁ and P ₂ represent the predicted probabilities from the maximum likelihood estimation of the logit and probit models.