The bidder exclusion effect

• Author: Kane Sweeney,Dominic Coey,Bradley Larsen
• Date: 01 March 2019
• Published date: 01 March 2019
• DOI: http://doi.org/10.1111/1756-2171.12263

RAND Journal of Economics

Vol.50, No. 1, Spring 2019

pp. 93–120

The bidder exclusion effect

Dominic Coey∗

Bradley Larsen∗∗

and

Kane Sweeney∗∗∗

We introduce a new, simple-to-compute test of independence of valuations and the number of

bidders for ascending button auctions with symmetric, conditionally independent private values.

The test involves estimating the expected revenue drop from excluding a bidder at random, which

can be computed as a scaled sample average of a difference of order statistics. This object

also provides a bound on counterfactual revenuechanges from optimal reserve pricing or bidder

mergers. We illustrate the approachusing data from timber auctions, where we find some evidence

that bidder valuations and the number of participants are not independent.

1. Introduction

A number of recent innovationsin empirical methodologies for auctions rely on the assump-

tion that bidders’ valuations are independent of the number of bidders participating in the auction.

In these articles, it is assumed that when one additional bidder arrives at an auction that originally

had nbidders, this additional bidder’s valuation represents a random draw from the same data

generating process that led to the original nbidders’ valuations. In this article, we demonstrate

that this assumption is easily testable in no-reserve ascending (button) auctions with symmetric,

conditionally independent, private values where bidders play the weakly dominant strategy of

truthful bidding.1The data requirements are that the researcher observe two order statistics of

∗Facebook; coey@fb.com.

∗∗Stanford University and NBER; bjlarsen@stanford.edu.

∗∗∗Uber; kane@uber.com.

Wethank Gaurab Aryal, Matt Backus, Tom Blake, Jeremy Bulow,Alex Frankel, Amit Gandhi, Phil Haile, Bob Hammond,

Jason Hartline, Jakub Kastl, Tatiana Komarova, Elena Krasnokutskaya, Nicola Lacetera, Jon Levin, Vadim Marmer,

Dimitriy Masterov,Rob Porter, Dan Quint, Jimmy Roberts, Art Shneyerov, Paulo Somaini, Steve Tadelis,Caio Waisman,

Glen Weyl, and seminar and conference participants at the 2013 Stanford-Berkeley IO Fest, Vanderbilt (2014), USC

(2014), the FederalTrade Commission (2014), the 2014 International Industrial Organization Conference, the 2014 North

American Econometric Society Meetings, the 2015 European Econometric Society Winter Meetings, the 2015 AEA

Meetings, the 2015 Stanford Institute for Theoretical Economics, the 2015 Becker Friedman Advances in Price Theory

Conference, the 2016 NBER IO Winter Meetings, and EC 2016 for helpful comments. This work was done while Coey

and Sweeney were researchers at eBayResearch Labs.

1Throughout the article, we will adopt the phrase conditionally independent private values, as used in Li, Perrigne,

and Vuong (2003), refering to a setting wherebidders have private valuations that are correlated and where there exists a

C2019, The RAND Corporation. 93

94 / THE RAND JOURNAL OF ECONOMICS

bids and the number of participants. We also demonstrate a number of extensions to this test,

including bounding counterfactual revenue under optimal reserve pricing or bidder mergers. We

demonstrate that our environmental assumptions can be relaxed in a number of ways.

Throughout the article, we refer to the decrease in expected auction revenue when a random

bidder is excluded from the auction as the bidder exclusion effect. In an ascending button auction

with private values, this effect can easily be computed without the need to estimate a complex

model, unlike many objects of interest in auction settings. In such an auction, with nbidders

participating, if a bidder is excluded at random from the auction, with probability n−2

nhe will be

one of the n−2 lowest bidders, and so his exclusion will not affect revenue. With probability 2

n,

he will be one of the two highest bidders, and revenue will drop from the second-highest to the

third-highest value of the nbidders. The bidder exclusion effect is therefore 2

ntimes the expected

difference between the second- and third-highest values.

The bidder exclusion effect can yield several diagnostics for ascending auction settings. The

first and foremost is that of testing the independence of bidder valuations and the number of

bidders. By comparing the bidder exclusion effect in an nbidder auction to the actual decrease

in revenue between nbidder and n−1 bidder auctions observed in the data, the researcher can

test whether bidder valuations are indeed independent of the number of bidders. We demonstrate

how this test can be performed in practice. The order statistic relationship we exploit here has

been used elsewhere by maintaining the assumption that bidder valuations are independent of the

number of bidders and instead testing for private versus common values(Athey and Haile, 2002).

Second, the bidder exclusion effect serves as a bound on the revenue gain to a seller from

choosing the optimal reserve price, thus aiding the practitioner in deciding whether or not to adopt

a reserve price at all. To do so, we rely on the result of Bulow and Klemperer (1996), that adding

an additional random bidder does more to improve seller revenue than does an optimal reserve

price. Third, the bidder exclusion effect can be used to bound the revenue losses to a seller from

counterfactual mergers between bidders.

We evaluate the bidder exclusion effect in US timber auction data. In this setting, we first

ask the following question: should the seller—in this case, the government—bother to compute

an optimal reserve price? Computing an optimal reserve price can be computationally costly

in practice, and mistakenly implementing too high a reserve price can be very detrimental to

revenue. The bidder exclusion effect can provide the seller a simple tool for evaluating the size

of the potential gains from optimal reserve pricing. We find that an upper bound on this gain is

13% of revenue on average in our data.

We then ask the question, if the seller does wish to compute an optimal reserve price, can

she safely rely on exogenousvariation in the number of bidders in doing so? Existing methods for

computing bounds on the optimal reserve price itself rely on the assumption that bidder valuations

are independent of the number of bidders in order to obtain tight, meaningful bounds (e.g., Haile

and Tamer,2003; Aradillas-L ´

opez, Gandhi, and Quint, 2013; and Coey et al., 2017). Weapply our

test to our data and find evidence against the assumption that bidder valuations are independent

of the number of bidders. However, after controlling for bidder asymmetries, this evidence is less

strong.

We highlight a number of extensions of the auction environments in which the bidder ex-

clusion effect can be used. For example, we demonstrate that it can be computed in ascending

button auctions with symmetric common values (i.e., when bidders have symmetric values and

symmetric bidding strategies) or in ascending nonbutton auctions when bidders have private

values but may potentially drop out below their values (such as in the setting of Haile and

Tamer, 2003). We also discuss extensions of these diagnostics to data from ascending auctions

random variable U, unknown to bidders and to the econometrician, such that, conditional on U, bidders’ valuations are

independent. In the setting we focus on in the main body of the article—that of ascending button auctions—all of results

also apply if this random variable Uis known to the bidders, but still unobserved to the econometrician; such a setting is

referred to in the literature as a setting of independent private values with unobserved heterogeneity. The distinction is

inconsequential for our main results, but it is important for first-price auctions, which we discuss in Appendix B.

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