A Note on Demand Estimation with Supply Information in Non-Linear Models

This paper compares demand estimation with and without full supply information in non-linear models. The main result is that, in a non-linear model, under general monotonicity conditions, there is a speci cation of the full supply model which is consistent with an arbitrarily speci ed auxiliary equation to account for endogeneity in demand estimation. In particular, there is a speci cation of the full supply model that is consistent with a typical linear auxiliary equation of the endogenous variable in a limited information approach of demand estimation. In general, in a non-linear model, a full supply model and the auxiliary equation speci cations do not represent the same model, but the auxiliary equation model covers a \larger" range of the space of potential models than a fully speci ed supply model. The paper presents an application to monopoly pricing with non-linear demand, and shows some simulation results of the relationship between the auxiliary equation and the full supply model in that application.