What Model for Entry in First-Price Auctions? A Nonparametric Approach

Abstract

We develop a selective entry model for first-price auctions that nests several models earlier proposed in the literature, and features a pro-competitive selection effect. The selection effect is shown to be nonparametrically identifiable, and a nonparametric test for its presence is proposed. In the empirical application to highway procurement, we find that the selection effect overwhelms the anticompetitive entry effect identified in earlier research, and restricting competition is not optimal.

Selective entry and auction design

“…They also estimate that entry is moderately selective (mean value of α is 0.5) and they use the approach of Gentzkow and Shapiro (2014) to illustrate which moments of the data parametrically identify the parameters. The results are broadly consistent with the intuition from Marmer et al (2013) and Gentry and Li (2014) in that changes in the number of realized entrants as the number of potential entrants varies play an important role in determining the degree of selection. All of these papers take a full information approach to estimation in the sense that it is necessary to be able to solve the selective entry and bidding games as part of the estimation process.…”

“…Symmetry implies that variation in the amount of entry then comes from variation in auction-level variables, such as the number of potential entrants, the reserve price or the level of entry costs. Marmer et al (2013) show that one can nonparametrically distinguish the NS, FS, and partially selective entry models using exogenous variation in the number of potential bidders and estimates of the quantiles of the value distributions of entrants conditional on the number of potential entrants (which can be calculated from inverting bid functions, which will be specific to the number of potential entrants, using the methodology proposed by Guerre et al, 2000). 54 The basic intuition is that under NS these quantiles should be invariant to the number of potential entrants, whereas with selection the quantiles should tend to increase with the number of potential entrants as the equilibrium signal threshold for entry should rise.…”

“…Hubbard and Paarsch (2009) use a computational approach to consider the effects of bid preferences to some subset of symmetric players in first-price auctions under the FS assumption. 6 Ye (2007), Bhattacharya et al (2014), Roberts and Sweeting (2013), Marmer et al (2013) and Gentry and Li (2014) consider models where players face a common entry cost but have noisy signals about their values before they enter, as we assume in this article. 7 Moreno andWooders (2011), Cremer et al (2009) and Lu and Ye (2013) consider a variant of the NS model where players have heterogeneous entry costs.…”

Estimating first-price auctions with an unknown number of bidders: A misclassification approach

“…In Samuelson's (1985) model, N * potential entrants observe their valuations, and must decide whether or not to pay an entry cost k > 0 to bid in the auction. In this model (see Li andZheng (2009) andMarmer et al (2009)), the distribution of the valuations of the bidders who enter the auction, F N * (v), varies depending on N * . As Marmer et al (2009) show, the inverse bidding strategy for this model, analogous to Eq.…”

Entry and Bidding in Common and Private Value Auctions with an Unknown Number of Rivals

“…Menezes and Monteiro (2000) assume that the bidders learn their values before they incur the bid preparation cost. Marmer et al (2007) consider a model within the IPV setting in which bidders receive information at the entry stage that is imperfectly correlated with their valuations; they pay a bid preparation cost to learn the actual private cost of the contract and bid without knowing the number of competitors. Li and Zheng (2008) is most closely related to our work, as they have the same informational assumptions as we do; however, they restrict attention to the IPV model.…”