Existing hedonic methods cannot be easily adapted to estimate willingness to pay for product characteristics when willingness to pay depends on a very large basket of goods. We show how to marry these methods with revealed preference arguments to estimate bounds on willingness to pay using data on purchases of seemingly impossibly high dimensional baskets of goods. This allows us to use observed purchase prices and quantities on a large basket of products to learn about individual houshold's willingness to pay for characteristics, while maintaining a high degree of flexibility and also avoiding the biases that arise from inappropriate aggregation.

We illustrate the approach using scanner data on food purchases to estimate bounds on willingness to pay for the organic characteristic.