Modeling selectivity in households' purchase quantity outcomes: A count data approach

We present an econometric technique for modeling endogenous selectivity in households' quantity outcomes as observed in scanner panel data. Simultaneous models of incidence, brand choice and quantity, that treat quantity outcomes as count data, ignore such self-selectivity considerations in quantity outcomes. Previously proposed approaches to modeling selectivity in continuous quantity outcomes do not apply to count data. Therefore, we adopt a recently proposed econometric technique to deal with selectivity in count data, and then appropriately extend it to handle correlations of quantity outcomes not only with incidence outcomes but also with brand choice outcomes. Our proposed methodology will be useful to researchers who want to estimate simultaneous models of whether, what and how much to buy decisions of households, treating quantity data as counts.