I advance and test a theory that in sequential auctions price rises with the number of bidders. I allow for stochastically arriving and departing bidders, so the number of bidders changes with every auction round both endogenously through the winner of the previous round dropping from future rounds and exogenously through the bidders’ stochastic arrival and departure. I test the theory on the Mecum auctions for collectible cars using the instrumental variables method. The timing of the car going to auction affects price only through the number of bidders present at the time and the number of cars still left to auction. This allows me to instrument time for the number of bidders. The empirical test shows support for the theory and provides a missing explanation for the declining price anomaly prevalent in sequential auctions.