Inference on Auctions with Weak Assumptions on Information

TL;DR

This paper develops a robust econometric framework for inference on auction fundamentals using bid data, relying on weak assumptions about information structures, and introduces computationally simple methods for set identification and confidence regions.

Contribution

It introduces a novel approach leveraging Bayesian equilibrium concepts to identify auction parameters without strong informational assumptions, applicable to private and common value auctions.

Findings

Constructed identified sets for valuation distributions and welfare measures.

Proposed finite sample methods for inference with confidence regions.

Validated methods through Monte Carlo simulations and real auction data.

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.