Research Approach

The choice of bundled AIP is similar to selecting features from a menu available for customization. Consumers may decide simultaneously which coverage should be included in their insurance package. An AIP alternative (i.e. possible outcomes of the decision process) thus consists of a combination of different coverage. However, the total number of AIP alternatives in our choice problem may be relatively large, especially when the number of available insurance coverage increases. For model development, inclusion of all alternatives

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in an individual model would increase the difficulty of model calibration and interpretation of parameter estimates. To simplify the complex choice problem, a model system involving separate models would become more feasible. The development of a simplified model can serve as a preliminary step towards a more general and behaviorally realistic model.

The proposed model system for the choice of bundled AIP in this study consists of two components. The first component is the decision to select physical damage coverage. The insured can select from among three types of physical damage coverage and/or without any coverage. The second component in the model system is the choice of non-physical damage coverage involving third party liability as a basic protection with addition of passenger liability or other endorsement, such as the coverage for bodily injury due to intoxicated driver and/or injury to any persons in the vehicle, including the driver. This research focuses on the first component of the model system, and the decision for choosing non-physical damage coverage involving third party liability is included in the bundle of physical damage coverage.

Car owners who have disposed of their vehicles more than five years old may do so in part because of the yearly inspection requirement by the motor vehicles department or the rapidly increasing repair cost for such old vehicles. Thus, the data set for model development and estimations consists of the insured repeatedly purchasing bundled AIP from the selected company over three, four and five years.

To gain insights into the insured’s repeated choice behaviors in the first few years after purchasing a new car, this research develops a discrete choice modeling framework for analysis of repeated choices associated with physical damage coverage types, and the number of consecutive years the insured has purchased the same type of physical damage coverage.

Our proposed model extends the work by Wen, et al. (2005) which examined a selection of

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bundled AIP using a one year cross-sectional database from a non-life insurance company. To capture the dynamic aspects of AIP choice behavior, this research uses panel data offered by a non-life insurance company that include the sequence of AIP choices made by the insured.

The discrete choice model is derived from random utility theory. An insured faces a choice among a set of mutually exclusive and exhaustive alternatives in terms of combinations of physical damage coverage types and the number of consecutive years the insured has purchased the same coverage. Under the principle of utility maximization, the insured chooses the alternative with the highest utility. The utility function of an alternative consists of the deterministic and random error components. Depending on assumptions which impose on distributions of error terms, various discrete choice models can be derived.

The multinomial logit model is the most commonly used discrete choice model due to its simple mathematical structure and ease of estimation and interpretation of coefficient estimates. The multinomial logit model is derived from the assumptions that the error terms are independent and identically Gumbel distributed. Due to the restrictive assumptions, the multinomial logit model exhibits the property of Independence from Irrelevant Alternatives (IIA), which is unrealistic in many choice problems.

The most widely used model to relax the undesirable IIA property is the nested logit (McFadden, 1978; Williams, 1977), which accounts for interdependence between pairs of alternatives by grouping alternatives in the nest. In the nested logit model, each alternative only appears in one nest, and each nest consists of one or multiple alternatives. In our case, a two-level nested model with physical damage coverage choice (Types A, B, and C) at the upper level and number of consecutive years purchasing the same type of physical damage coverage at the lower level is developed. An alternative nested structure which includes the

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number of consecutive years at the upper level and coverage type choice at the lower level is also tested.

Although the nested logit model accounts for interdependence between pairs of alternatives in the same grouping, the restriction on the identical correlations of the alternative pairs in the same nest may be unrealistic in some cases. The paired combinatorial logit Model enables better representation of substitution patterns among the bundled AIP alternatives. The paired combinatorial logit model has a more flexible error correlation structure than the multinomial logit and nested logit models and allows differential correlation between pairs of alternatives.

The formulation of the proposed choice models such as the multinomial logit, nested logit and paired combinatorial logit is explicitly described.

The data used for empirical analysis were drawn from a non-life insurance company that has the largest market share among the 16 non-life insurance companies in Taiwan. The data set consists of the new car owners who repeatedly purchased bundled AIP from 2000. We selected the data in which the insured purchased new cars in 2000 and also repeatedly purchased physical damage coverage from the same company.

The estimation results of the multinomial logit, nested logit and paired combinatorial logit models were performed using the NLOGIT and GAUSS software. The parameter estimates in the models were tested, and the model performance was evaluated using goodness-of-fit indices and likelihood ratio tests. The applicability of the proposed choice models is explicitly demonstrated.

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