Recently, economists have developed methods for structural estimation of auction models. Many researchers object to these methods because they find the strict rationality assumptions to be implausible. Using bid data from first-price auction experiments, we estimate four alternative structural models: (1) risk-neutral Bayes-Nash, (2) risk-averse Bayes-Nash, (3) a model of learning, and (4) a quantal response model of bidding. For each model, we compare the estimated valuations and the valuations assigned to bidders in the experiments. We find that the risk aversion model is able to generate reasonable estimates of bidder valuations.