Correlation‐savvy sellers

A multi‐product monopolist sells sequentially to a buyer who privately learns his valuations. Using big data, the monopolist learns the intertemporal correlation of the buyer's valuations. Perfect price discrimination is generally unattainable—even when the seller learns the correlation perfectly, has full commitment, and in the limit where the consumption good about which the buyer has ex ante private information becomes insignificant. This impossibility is due to informational externalities that require information rents for the buyer's later consumption. These rents induce upward and downward distortions, violating the generalized no distortion at the top principle of dynamic mechanism design.