What model for entry in first-price auctions? A nonparametric approach

Abstract

We develop a nonparametric approach that allows one to discriminate among alternative models of entry in …rst-price auctions. Three models of entry are considered: Levin and Smith (1994), Samuelson (1985), and a new model in which the information received at the entry stage is imperfectly correlated with valuations. We derive testable restrictions that these three models impose on the quantiles of active bidders' valuations, and develop nonparametric tests of these restrictions. We implement the tests on a dataset of highway procurement auctions in Oklahoma. Depending on the project size, we …nd no support for the Samuelson model, some support for the Levin and Smith model, and somewhat more support for the new model.

Identification and Estimation in First-Price Auctions with Risk-Averse Bidders and Selective Entry

“…Potential bidders have independent private values, observe signals of their values prior to entry, and choose whether to incur a fixed entry cost, with entrants learning their values and submitting bids. This framework flexibly nests a wide range of existing models as special cases, including the affiliated-signal (AS) models of Marmer, Shneyerov, and Xu (2013) and Gentry and Li (2014) (which build on the indicative bidding model of Ye (2007)), the mixed-strategy entry model of Levin and Smith (1994), the perfectly selective entry model of Samuelson (1985), and models with risk averse bidders but exogenous entry including Guerre, Perrigne, and Vuong (2009) and Campo, Guerre, Perrigne, and Vuong (2011). It thereby represents a natural focal point for researchers seeking to understand the structural interaction between risk aversion and entry.…”

“…For instance, Marmer, Shneyerov, and Xu (2013) develop nonparametric specification tests for the perfectly selective (Samuelson 10 The presence of entry implies that optimal bidding is characterized by a slightly different first order condition, but the systems are otherwise identical.…”

Identification and estimation in first-price auctions with risk-averse bidders and selective entry

“…13 While not universal in the literature, the assumption of unknown n is common in applied studies: see, for instance, Zheng (2009), Marmer, Shneyerov, andXu (2013), GL (2014) and Li, Lu, and Zhao (2014) among others. For closely related studies assuming both N and n are common knowledge, see for example Levin and Smith (1994) or Smith and Levin (1996) among others.…”

Identification and Inference in Ascending Auctions With Correlated Private Values

“…That is, valuations are stochastically increasing in N if a group of bidders sampled from a larger auction tend to have higher valuations than a group of bidders sampled from a smaller auction, where "higher" is measured as a first-order stochastic dominance ranking of the highest order statistic. In Appendix A.2, we discuss three standard models of endogenous participation in auctions -those of Levin and Smith (1996), Samuelson (1985), and Marmer, Shneyerov, and Xu (2010) -and show conditions under which equilibrium play in each model would lead to valuations stochastically increasing in N . Thus, our definition of stochastically increasing valuations accommodates many standard models of endogenous entry.…”

“…Theorem A3 If a symmetric equilibrium exists in cutoff strategies, then the entry game of Marmer, Shneyerov, and Xu (2010) generates valuations stochastically increasing in N .…”