Modeling DVD Preorder and Sales: An Optimal Stopping Approach

Abstract

When a DVD title is announced prior to actual distribution, consumers can often preorder the title and receive it as soon as it is released. Alternatively, once a title becomes available (i.e., formally released), consumers can obtain it upon purchase with minimal delay. We propose an individual-level behavioral model that captures the aggregate preorder/postrelease sales of motion picture DVDs. Our model is based on an optimal stopping framework. Starting with the utility function of a forward-looking consumer, and allowing for consumer heterogeneity, we derive the aggregate preorder/postrelease sales distribution. Even under a parsimonious specification for the heterogeneity distribution, our model recovers the typically observed temporal pattern of DVD preorder and sales, a pattern which exhibits an exponentially increasing number of preorder units before the release, peaks at release, and drops exponentially afterward. Using data provided by a major Internet DVD retailer, we demonstrate a number of important managerial implications stemming from our model. We investigate the role of preorder timing through a policy experiment, estimate residual sales, and forecast post-release sales based only on preorder information. We show that our model has substantially better predictive validity than benchmark models.

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