Chapter Preview. Many datasets feature dependent variables that have a large proportion of zeros. This chapter introduces a standard econometric tool, known as a tobit model, for handling such data. The tobit model is based on observing a left-censored dependent variable, such as sales of a product or claim on a health-care policy, where it is known that the dependent variable cannot be less than zero. Although this standard tool can be useful, many actuarial datasets that feature a large proportion of zeros are better modeled in “two parts,” one part for frequency and one part for severity. This chapter introduces two-part models and provides extensions to an aggregate loss model, where a unit under study, such as an insurance policy, can result in more than one claim.

Introduction

Many actuarial datasets come in “two parts:”

1. One part for the frequency, indicating whether a claim has occurred or, more generally, the number of claims

2. One part for the severity, indicating the amount of a claim

In predicting or estimating claims distributions, we often associate the cost of claims with two components: the event of the claim and its amount, if the claim occurs. Actuaries term these the claims frequency and severity components, respectively. This is the traditional way of decomposing two-part data, where one can consider a zero as arising from a policy without a claim (Bowers et al., 1997, Chapter 2).