Auctions with ex post uncertainty

• Date: 01 September 2018
• Author: Quang Vuong,Yao Luo,Isabelle Perrigne
• Published date: 01 September 2018
• DOI: http://doi.org/10.1111/1756-2171.12245

RAND Journal of Economics

Vol.49, No. 3, Fall 2018

pp. 574–593

Auctions with ex post uncertainty

Yao Lu o ∗

Isabelle Perrigne∗∗

and

Quang Vuong∗∗∗

Uncertainty about ex post realizedvalues is an inherent component in many auction environments.

In this article, we develop a structural framework to analyze auction data subject to ex post

uncertainty as a pure risk. We consider a low-price sealed-bid auction model with heterogeneous

bidders’ preferences and ex post uncertainty. The uncertainty can be common to all bidders

or idiosyncratic. We derive the model restrictions and study nonparametric and semiparametric

identification of the model primitives under exogenous and endogenous participation. We then

develop multistep nonparametric and semiparametric estimation procedures in both cases.

1. Introduction

Uncertainty ex post the auction is an inherent component in many auctions and procurement

auctions. Typicalexamples include oil tracts, timber, construction, and art to name a few. Ex post

uncertainty occurs because of an unknown ex post value. Forinstance, oil companies do not know

the exact amount of oil they can extract upon winning, despite some geological surveys. Mills

may collect their timber several years after the auction with an imperfect knowledge of future

demand in secondary markets at the time of the auction. Construction procurements may also

cover a number of years and the complexity of the projects introduces uncertainty of different

kinds, such as technical, logistical, or environmental risks.1In this article, we propose a model

inspired by Eso and White (2004) and an empirical methodology to assess the effect of ex post

uncertainty on bidding, considering this uncertainty as a pure risk, that is, a risk that cannot be

foreseen.

Considering the effects of ex post uncertainty on bidding was at the core of the early auction

theory literature. As early as the late 1960s with Wilson (1969), auction theorists developed the

∗University of Toronto; yao.luo@utoronto.ca.

∗∗Rice University; iperrigne@gmail.com.

∗∗∗New York University; qvuong@nyu.edu.

We are grateful to the Editor and two referees for their constructive comments. We thank seminar participants at

the University of Southern California and University of Chicago for their comments. Perrigne and Vuong gratefully

acknowledge financial support from the National Science Foundation through grant no. SES-1148149.

1See the civil engineering literature, such as Perry and Hayes (1985).

574 C2018, The RAND Corporation.

LUO, PERRIGNE AND VUONG / 575

concept of interdependent values in which bidders receive noisy signals about their unknown

ex post values. See Milgrom and Weber (1982) and Krishna (2009). At the end of the spectrum

of interdependent values is the pure common value model in which all bidders receive the same

(common) value ex post. This model has been largelyused by the early empirical auction literature

starting with Hendricks and Porter (1988) with the study of gas lease auctions. See also the survey

by Hendricks and Porter (2007). Alternative approaches to deal with ex post uncertainty have

been developed since then. Haile (2001) develops a private value model studying the effects of

resale opportunities on bidding with an application to timber auctions. In his model, bidders’

values are endogenous with the number of bidders becoming a signal of competition in the resale

market. More recently, Eso and White (2004) develop a model with interdependent values and a

random noise affecting the ex post bidders’ values. They interpret this random noise as a pure risk

on which bidders do not have ex ante information through some signals or in simple terms, some

randomness that cannot be foreseen by bidders. This pure risk affects bidding when bidders are

risk averse. The authors then uncover an interesting effect which they call precautionary bidding

that makes bidders better off with noisy values rather than with deterministic ones.2

As many aspects related to ex post uncertainty can be considered as unforeseen, we propose

a model with private values subject to an additive random shock that can be common to all

bidders or idiosyncratic to bidders.3In a private value setting with risk-neutral bidders, such

an uncertainty does not affect bidding. On the other hand, when bidders are risk averse, bidders

incorporate ex post uncertainty by adjusting their bids downward by at least the amount of the risk

premium.4Weconsider a reverse first-price sealed-bid auction with bidders having heterogeneous

preferences. The model can be easily extended to include further asymmetries. Ex post uncertainty

combined with asymmetric preferences lead to peculiar boundary conditions that prevent some

risk-averse bidders to participate in the auction because of their high-risk premium. In order to

develop a methodologyto estimate such an auction model, we first study the model restrictions and

identification of the model primitives. In addition to the utility functions and cost distribution(s),

the model also contains among its primitives the random shock distribution(s).

Bidders’ risk aversion has been recently studied in the empirical auction literature. Guerre,

Perrigne, and Vuong (2009) show that bidders’ utility function is identified under exogenous

participation, that is, when the latent private value distribution does not depend on the level of

competition. The idea is to exploit variations in the number of bidders that affect the bid dis-

tribution but not the private value distribution leading to so-called compatibility conditions. We

exploit here similar compatibility conditions, whereas distinguishing endogenous and exogenous

participation as they lead to different compatibility conditions. Under exogeneity of the number

of bidders, we obtain partial nonparametric identification. To identify the ex post shock distribu-

tion(s), we consider parameterization of the utility functions and the shock distribution(s) leading

to a semiparametric model, while leaving unspecified the underlying bidders’ cost distribution(s).

In addition, we derive the restrictions imposed by the model on observables. We then develop

a Minimum Distance estimator based on the model compatibility conditions. Our estimation

procedure also involves quantiles and sieves.

Our methodology has several advantages. First, our model offers a private value setting that

accounts for ex post uncertainty. Privatevalue models have become popular in the empirical auc-

tion literature because these models are in general identified and can be estimated using an indirect

2A recent empirical literature on ex post renegotiation focuses on the contract design resulting from construction

procurement auctions. Bajari, Houghton, and Tadelis (2014) view contracts as incomplete, whereas Bajari and Tadelis

(2001) recommend cost-plus over fixed-pricecontracts. Lewis and Bajari (2011, 2014) study the performance of scoring

rules with time incentives.

3Gupta and Lamba (2017) consider a common uncertainty in their empirical analysis of Indian treasury bills

auctions in a period of volatility in financial markets. They assume a known constant relativerisk aversion.

4When bidders face uncertainty on the harvested timber quantities, Athey and Levin (2001) study skewedbidding,

that is, bidders adjust their bids depending on whether the quantities are underestimated or overestimatedby the US Forest

Service. Their empirical results show risk diversification across timber species, suggesting bidders’ risk aversion.

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