Economists have developed a range of empirically tractable demand systems for fixed price markets. But auction mechanisms also play an important part in allocating goods, and yet existing empirical auction techniques treat each auction in isolation, obscuring market interactions. Here we provide a framework for estimating a demand system in a large auction platform market with a dynamic population of buyers, heterogeneous objects and unit demand. We construct a model of repeated second-price auctions in which bidders have multidimensional private valuations, developing an equilibrium concept under which strategies reflect option values. We prove existence of this equilibrium and characterize the ergodic distribution of types. Having developed a demand system, we show that it is non-parametrically identified from panel data. Relatively simple nonparametric and semiparametric estimation procedures are proposed and tested by Monte Carlo simulation. Our analysis highlights the importance of both dynamic bidding strategies and panel data sample selection issues when analyzing these markets.