Abstract

This paper studies a selection bias problem in estimating demand for differentiated products. In this context, the selection equation—which represents firms' product entry decisions—fails to meet the typical monotonicity condition with respect to the unobservables. As a result, the propensity score alone is insufficient to correct for selection bias, leading traditional methods to produce inconsistent estimates of demand parameters. To address this, we propose an extended propensity score that incorporates latent variables capturing the correlation between firms' entry decisions and the non-monotonicity in the selection process. We then establish conditions under which this extended propensity score can be identified using the joint vector of all firms' and products' entry decisions. In a second step, we identify demand parameters while controlling for selection bias by integrating the extended propensity scores for each latent type. We apply this method to data from the airline industry, showing that conventional approaches to selection bias tend to underestimate demand price elasticities.