Identification and Estimation of Demand Models with Endogenous Product Entry and Exit

Firms are more likely to introduce products in markets where they anticipate stronger demand. They also possess information that is unobserved to researchers. This creates endogenous selection bias in the estimation of demand parameters. With differentiated products, the entry decision violates the monotonicity conditions required for standard selection-correction methods to yield consistent demand estimates. Existing studies address this issue either by imposing strong assumptions about firms' information on demand at the time of entry or by jointly estimating a full equilibrium model of demand, pricing, and entry. Both strategies make the estimation of demand heavily reliant on supply-side assumptions. We propose a new semiparametric estimation method that addresses these limitations. Our approach exploits the correlation across products in their market-entry decisions to identify entry probabilities conditional not only on observable characteristics but also on latent variables that capture unobserved interdependencies among firms' entry choices. We refer to these probabilities as latent propensity scores. We show that the selection bias term in the demand equation is a convolution of these latent propensity scores and is therefore identifiable. Building on this result, we develop a two-step semiparametric estimator in the spirit of standard sample-selection correction methods. Applying our method to data from the airline industry, we find that conventional approaches to correcting for selection bias substantially underestimate price elasticities of demand.