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 Bergemann and Morris [2013] 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 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.

Identification in discrete choice models with imperfect information

“…We do not impose restrictions on how the DM computes the expected payoff of the alternatives in her consideration set, because this depends on the DM's posterior about which the researcher remains ignorant. 5 This paper also relates to two important works, Magnolfi and Roncoroni (2017) and Syrgkanis, Tamer, and Ziani (2018), that use the notion of Bayesian Correlated Equilibrium to tractably characterise the sharp identified set while remaining agnostic about information structures and selection rules. In particular, Magnolfi and Roncoroni (2017) use the notion of Bayesian Correlated Equilibrium in an entry game framework, where each firm may or may not know the payoff of the competing firms.…”

“…Therefore, determining whether a given value of the preference parameters belongs to the sharp identified set amounts to finding whether the vector of empirical choice probabilities belongs to that convex set. By using insights from Beresteanu, Molchanov, and Molinari (2011), Magnolfi andRoncoroni (2017), andSyrgkanis, Tamer, andZiani (2018), we argue that this corresponds to solving quadratically constrained linear programming problems or linear programming problems (depending on which objects the econometrician wants to recover). Thus, constructing the sharp identified set becomes a computationally tractable exercise.…”

Inference in high-dimensional set-identified affine models

“…Linear models with interval outcome, that were originally studied in Manski and Tamer (2002) and Haile and Tamer (2003), is just one example of affine inequalities. Other examples include bounds on marginal effects in panel dynamic discrete choice models (Honoré and Tamer (2006), Torgovitsky (2016Torgovitsky ( , 2018), bounds on average treatment effects (Kasy (2016), Lafférs (2018), Russell (2017)), non-parametric instrumental variable models with shape restrictions (Manski and Pepp (2000), Freyberger and Horowitz (2015)), errors in variables (Molinari (2008)), intersection bounds (Honoré and Lleras-Muney (2006)), revealed preference restrictions (Kline and Tartari (2016), Shi et al (2018)), game-theoretic models (Pakes et al (2015), Syrgkanis et al (2017)).…”

Policy Transforms and Learning Optimal Policies

“…At a high level, the identification component of this paper is reminiscent of Ichimura and Taber (2000), who discuss a method for performing ex-ante policy experiments in the treatment effect literature without estimating the structural parameters, and without specifying the error distribution. More recent examples of counterfactual analysis without first estimating the (identified set for the) structural parameters can be found in Syrgkanis et al (2018), Tebaldi et al (2019) and Kalouptsidi et al (2019).…”