Estimation of Discrete Choice Models with Many Alternatives Using Random Subsets of the Full Choice Set: With an Application to Demand for Frozen Pizza

A common problem in estimation of discrete choice models is that the complete choice set is very large.  A good example is supermarket consumer goods, like breakfast cereal where there are often a hundred or more varieties (SKUs or UPCs) to choose from.  In that case, estimation of complex discrete choice models where choice probabilities have no closed form can be very computationally burdensome.  We show how use of random subsets of the full choice set can be a useful device to reduce computational burden.  We apply this approach to estimating demand for frozen pizza, where there are nearly 100 varieties to choose from.  We provide some interesting new results on how price changes for a particular variety of a brand lead to variety switching within the brand vs. brand switching.  In particular, when a variety raises its price, most switching is to other brands, rather than to other varieties of the same brand.