Title: Inference on Auctions with Weak Assumptions on Information,
Abstract: Given a sample of bids from independent auctions, this paper examines the
question of inference on auction fundamentals (e.g. valuation distributions,
welfare measures) under weak assumptions on information structure. The question
is important as it allows us to learn about the valuation distribution in a
robust way, i.e., without assuming that a particular information structure
holds across observations. We leverage the recent contributions of
\cite{Bergemann2013} in the robust mechanism design literature that exploit the
link between Bayesian Correlated Equilibria and Bayesian Nash Equilibria in
incomplete information games to construct an econometrics framework for
learning about auction fundamentals using observed data on bids. We showcase
our construction of identified sets in private value and common value auctions.
Our approach for constructing these sets inherits the computational simplicity
of solving for correlated equilibria: checking whether a particular valuation
distribution belongs to the identified set is as simple as determining whether
a {\it linear} program is feasible. A similar linear program can be used to
construct the identified set on various welfare measures and counterfactual
objects. For inference and to summarize statistical uncertainty, we propose
novel finite sample methods using tail inequalities that are used to construct
confidence regions on sets. We also highlight methods based on Bayesian
bootstrap and subsampling. A set of Monte Carlo experiments show adequate
finite sample properties of our inference procedures. We illustrate our methods
using data from OCS auctions.