This paper studies whether we can learn how individual consumers change their buying when prices change, using panel data (that is, repeated observations of the same consumers over time) even though prices are set by market supply and demand. The authors show that standard panel methods, such as taking time differences or using fixed effects, give nearly correct estimates of individual price sensitivity when each market contains many consumers and a key independence condition holds. In plain terms: when any one person’s choices have almost no effect on the market price, that person faces an effectively exogenous price.

To reach this conclusion the authors analyze simple, transparent models. They study linear demand models and random coefficient (individual-specific price response) demand models together with linear supply. They work with panel data where we observe each consumer’s quantity and the common market price over several time periods. By differencing over time they remove time-constant individual taste differences. They then show mathematically that the bias created by the simultaneity of price and demand falls as the number of consumers in the market grows. The paper gives the rate at which this bias shrinks: roughly proportional to 1 divided by the number of consumers.

A central assumption makes the result possible. The time-varying, idiosyncratic part of each consumer’s preference (the small shocks that change a person’s taste from one period to the next) must be uncorrelated with the time-varying unobserved shock to supply. The authors also assume those idiosyncratic preference shocks are uncorrelated across different consumers. Under these conditions, the contribution of one person’s shock to the market price vanishes as the market gets large, so the endogeneity problem is negligible from an individual’s point of view. The paper also discusses how to allow for common macro time effects by adding trends or time-period dummies, and it treats the case with both individual and time fixed effects.