Flexible Bayesian analysis of first price auctions using a simulated likelihood

I propose a Bayesian method to analyze bid data from first-price auctions under private value paradigms. I use a series representation to specify the valuation density so that bidding monotonicity is always satisfied, and I impose density affiliation by the nonparametric technique of Beresteanu (2007). This flexible method is, therefore, fully compatible with the underlying economic theory. To handle such a rich specification, I use a simulated likelihood, yet obtain a correct posterior by regarding the draws used for simulation as a latent variable to be augmented in the Bayesian framework; see Flury and Shephard (2011). I provide a step-by-step guide of the method, report its performance from various perspectives, and compare the method with the existing one for a range of data generating processes and sample sizes. Finally, I analyze a bid sample for drilling rights in the outer continental shelf that has been widely studied and propose a reserve price that is decision theoretically optimal under parameter uncertainty.