We construct a model of participation and bidding at multi-unit, sequential, clock auctions when bidders have multi-unit demand. We describe conditions sufficient to characterize a symmetric, perfect-Bayesian equilibrium and then demonstrate that this equilibrium induces an efficient allocation. We propose an algorithm, based on the generalized Vickrey auction, to calculate the expected winning bid for each unit sold. This algorithm allows us to construct a simulation-based estimator of the parameters for both the participation process and the distribution of latent valuations. We apply our method to data from 37 multi-lot, sequential, English auctions of export permits for timber held in Russia.