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.
First price sealed bid auctions affiliated private values revenue maximizing reserve price Bayesian analysis method of series simulated likelihood shape restriction