Estimating the Demand for Service Bundles under Three-Part Tariffs

The practice of selling multiple products or services under nonlinear pricing has a long history in the business community. Consumers may face demand uncertainty when choosing a service plan, and preferences for multiple products or services may be inter-dependent. To examine a demand system with these features, we construct a two-stage discrete/continuous choice model for service bundle demand under three-part tariffs, allowing for interactive utility and preference correlations. Implementing a piecewise maximization approach to the consumer utility maximization problem, which is non-differentiable under three-part tariffs, we estimate the model via simulated method of moments. We then apply our model to data from a major wireless service provider in China. Finally, our counterfactual analysis simulates outcomes under three-part tariffs with interchangeable units. Compared to existing tariffs, the proposed ones contain fewer instruments without a significant loss of revenue. We also illustrate the implications of incorporating ex-post usage shocks in model estimates, elasticities and counterfactual outcomes.