Endogeneity and measurement errors when estimating demand functions with average prices: an example from the movie market

Due to a lack of information about the prices faced by consumers, demand functions are sometimes estimated using average prices, namely total revenue divided by the number of consumers. Examples of this type of estimation can be found for cinema, sporting events and the performing arts since box office revenue is frequently available, though it is also common in other industrial markets. We construct a straightforward theoretical model showing that this practice introduces a specific type of measurement error that generates a major source of endogeneity into empirical research. Our theoretical framework also allows us, however, to find proper instruments for the endogenous price variables. An empirical application is provided using Spanish data on cinema attendance to illustrate the validity of the strategy proposed here to address this sort of endogeneity in an instrumental variable framework.