Probit Model Case Study

The main assumption underlying the regular probit model is that the errors are independent across individuals, but also across insurance types [10]. The multivariate probit model allows for correlations relating to the purchase decisions for the insurance types. Here the assumption is that the vector of errors, ,….., , follows a multivariate normal distribution with an unrestricted covariance matrix [5]. As these correlations result in dependencies relating to the purchase decision for the various services, the multivariate probit model results in probabilities with which a consumer purchases a certain portfolio of services.

In our empirical application both the multivariate probit model with an unrestricted covariance matrix and univariate

The bases for stratification are relationship duration, purchase level of insurances and claiming behavior. Using this sampling methodology, we obtain a representative sample on these important characteristics. The survey also includes questions on age, education, household size, income, and home ownership.
After deleting cases with missing values we obtained a final sample of 1612 consumers. In line with the profile of consumers of this corporation, our sample can be described as representing rather prosperous and well-educated people. A more detailed description of the sample characteristics is given in Appendix A.
Respondents were asked to indicate whether they had effected 12 types of insurance. To check the reliability of the answers, we compared the reported ownership with the available information from the consumer database. It turned out that there was not a single case where ownership was not reported, meaning there were no discrepancies with the consumer information file. This indicated that the answers on the ownership questions were

To reduce modeling efforts and to save some space, it was assumed that all consumers own these four types of insurance. The variation in latent value we wanted to explain therefore results from the remaining eight types of insurance. In order to capture nonlinear effects of the explanatory variables of age, income, and education, we used dummies for the separate classes in our models. The evaluation of the estimations was carried out on a sample that was not used for estimation. We split our sample into an estimation sample with 1000 households. The remaining 612 households were used to validate the models and to evaluate the estimation performance.

4.3 Estimation of Purchases
The estimation results for behavior at the lowest level of aggregation, the purchases of each insurance type, are presented in Table 2. All functions are significant (p<0.10). We do not report the parameter estimates for the models, but the general conclusion is that socio-demographic variables as well as purchase data from the CIF serve as estimators for ownership. Important socio-demographic estimators are age, income, marital status and the ownership of a