Instrument-Free Demand Estimation

We consider the identification of empirical models of supply and demand with imperfect competition. As is well known, a supply-side instrument can resolve price endogeneity in demand estimation. We show that, under common assumptions, two other approaches also yield consistent estimates of the joint model: (i) a demand-side instrument, or (ii) a covariance restriction between unobserved demand and cost shocks. Covariance restrictions can obtain identification even the absence of instruments. Further, supply and demand assumptions alone may bound the structural parameters without additional restrictions. We illustrate the covariance restriction approach with applications to ready-to-eat cereal, cement, and airlines.