In many environments, including credit and online markets, records about participants are collected, published, and erased after some time. We study the effects of erasing past records in a dynamic market where the quality of sellers follows a Markov process, and buyers leave feedback about sellers to an information intermediary. When the average quality of sellers is low, unlimited records lead to a market breakdown in the long run. We consider the information design problem and characterize information policies that can sustain trade and that maximize social welfare. These policies hide some information from the market in order to foster socially desirable experimentation. We show that these outcomes can be implemented by appropriately deleting past records. Crucially, positive and negative records play opposite roles with different intensities and must have different lengths: negative records must be deleted sufficiently late, and positive ones sufficiently early.