Estimating Primary Demand for Substitutable Products from Sales Transaction Data
We propose a method for estimating substitute and lost demand when only sales and product availability data are observable, not all products are displayed in all periods (e.g., due to stock-outs or availability controls), and the seller knows its aggregate market share. The model combines a multinomial logit (MNL) choice model with a non-homogeneous Poisson model of arrivals over multiple periods. Our key idea is to view the problem in terms of primary (or first-choice) demand; that is, the demand that would have been observed if all products had been available in all periods.