A Model of Brand Choice and Purchase Quantity Price Sensitivities

Many consumer decisions involve a discrete choice and a continuous outcome. Examples of such decisions are whether to own a home or rent one and how much to spend, which brand of orange juice to buy and how many ounces to buy. In cases like these, the choice decision is typically modeled separately, say, using a logit model and the continuous outcomes modeled separately using regression analysis. However, the continuous outcomes may not be independent of the discrete choice and vice versa, and modeling the two decisions independently can lead to inefficient choice parameter estimates and biased and inconsistent regression parameter estimates. In this paper, we present a methodology from the limited-dependent variable literature to model the dependence between the choice and quantity decisions. Our substantive interest is in the role of price in the choice and quantity decisions. When choosing among alternatives, we argue that consumers consider prices of all the competitive brands. In the quantity decision on the other hand, only the price of the chosen alternative is expected to impact how much of the alternative is purchased. The analysis of three brands, using disaggregate level panel data, strongly supports our hypothesis about the role of competitive prices in the choice and quantity decisions.