The purpose of this paper is to consider whether and how panel data can be used to estimate individual demand, as opposed to market-level demand, while accounting for simultaneity resulting from prices being determined in markets. We consider linear demand models and random coefficient demand models, together with linear supply models. We find that the bias of individual demand estimates obtained using familiar panel data methods, like differencing, disappears as the number of consumers in each market grows, as long as the time-varying, i.e. idiosyncratic, component of preferences is orthogonal to the unobserved, time-varying component of supply. This approximate control is assumed in many panel discrete choice models and is plausible in other models where idiosyncratic preferences represent random variation in preferences over time. Macroeconomic effects can be allowed for by including regressors characterizing time effects, such as trends and time period dummies, or fixed time effects.
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