Department of Economics
303 Kern Building
University Park, PA, 16802
Job Market Paper
Nonparametric Inference in Asymmetric First-price Auctions with k-rationalizable Beliefs
In this paper I study bidding behavior in first-price sealed bid auctions with risk- neutral bidders. Instead of assuming that bids and beliefs correspond to a Bayesian Nash equilibrium (BNE), I only assume that they are consistent with k steps of iterated elimination of dominated strategies (k-rationalizability). The focus of my paper is to provide econometric tests for whether k is finite and to identify the largest value of k that is consistent with the data. This is important because rejecting any finite k would immediately rule out BNE and (full) rationalizability and it allows to quantify deviations from (fully) rationalizable behavior and improve counterfactual predictions. My framework includes “cognitive hierarchy” or “level-k” models as special cases but, unlike those models, I make no assumptions about how beliefs are selected. My approach relies only on inequalities between functionals of conditional distributions that are implied by k-rationalizability. As an empirical illustration I apply my tests to USFS timber auction data. The results show that values of k as low as 2 can be rejected in some auctions. Counterfactual exercises allow me to quantify the loss in expected payoff derived from the presence of incorrect beliefs.
Research in progress
Inference in First-price Auction with Endogenous Entry under k-rationalizable beliefs
Most models of bidders’ participation in auctions assume that bidders' decisions are based at least partially on their predicted expected profit (continuation payoffs). All of the existing models assume that bidders expect a Nash equilibrium outcome in the auction stage. In this paper I relax this assumption and analyze auction participation decisions when bidders have heterogeneous (and possibly incorrect) expectations about the outcome of the auction game. Focusing on first-price auctions, I only assume that these expectations can be rationalized by iterated elimination of dominated strategies. In the context of a semiparametric model, this produces conditional moment inequalities for probabilities of participation which are used to construct confidence sets for the parameters. The analysis can be done assuming that a Nash equilibrium outcome in the first-stage (the "entry" game) and can be extended to the case where the outcome of the first-stage game is only rationalizable itself.