Estimating models of supply and demand : instruments and covariance restrictions

We consider the identification of empirical models of supply and demand. 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. The covariance restriction approach can obtain identification even the absence of instruments. Further, supply and demand assumptions alone may bound the structural parameters. We develop an estimator for the covariance restriction approach that is constructed from the output of ordinary least squares regression and performs well in small samples. We illustrate the methodology with applications to ready-to-eat cereal, cement, and airlines