Identifying price discrimination when product menus are endogenous

The standard approach to identifying second degree price discrimination is based on examining correlations between product menus and prices. When product menus are endogenous, however, tests for price discrimination may be biased by the fact that unobservables affecting costs or demand may jointly determine product menus and prices leading one to falsely infer price discrimination. Attempts to correct for this potential bias using observed product characteristics or fixed effects are shown to potentially confound inference on price discrimination leading one to reject it when firms are actually price discriminating. I propose a difference in differences type test that exploits the potential correlation between unobserved product attributes, product menus, and prices.