We exploit a unique feature of data from Canadian treasury bill auctions, in which some bidders have information about rivals’ bids, to develop a test if values are private. Information about a rival’s bid causes a bidder to bid differently when she has a private value than when her value depends on rivals’ information. In a divisible good setting, such as treasury bill auctions, bidders with private values who obtain information about rivals’ bids use this information only to update their prior about the distribution of residual supply. In the model with interdependent (or common) values, they also update their prior about the value of the good being auctioned. We use these differential updating effects to construct our test. We cannot reject the null hypothesis of private values in our data for 3-months treasury bills, but we reject private values for 12-months treasury bills. Furthermore, we use the estimated model to quantify the value of customer order flow to a dealer. We find that the extra information contained in customers’ bids leads on average to an increase in payoff equal to about 0.5 of a basis point, or 32% of the expected surplus of dealers from participating in these auctions.