If the producer sees customer characteristics we do not, then there will be a bias in our estimate.
Producers will set prices correlated with those characteristics.
We need alternative price data for this multinomial choice model.
These are not observed, and so we need to estimate them.
One option is to use list prices, or average prices, for all prices.
However, differences from this are likely correlated with individual characteristics, giving us bias.
By adding a dummy for each product we control for unobserved variables. This adds a parameter for each product, which can increase the variance of the estimates. Adding the dummies affects the other estimators. We can fix this using minimum distance estimator. The error no longer includes unobserved characteristics.
Dummies for groups. These create fewer new parameters.