Instrument-free Identification and Estimation of Differentiated Products Models using Cost Data

We propose a new methodology for identifying and estimating demand in differentiated products models when demand and cost data are available. The method deals with the endogeneity of prices to demand shocks and the endogeneity of outputs to cost shocks by using cost data rather than instruments. Further, we allow for unobserved market size. Using Monte Carlo experiments, we show that our method works well in contexts where commonly used instruments are invalid. We also apply our method to the estimation of deposit demand in the US banking industry.