Dubois, Pierre

Ivaldi, Marc

Magnac, Thierry

English

Research Papers in Economics

Introduction to the special issue on the Econometrics of
auctions
Pierre Dubois∗ , Marc Ivaldi†and Thierry Magnac‡
November 27, 2009
This special issue on the Econometrics of Auctions is a follow up to the conference on the same
topic organized in Toulouse in May 20061 as a tribute to Jean-Jacques Laﬀont who passed away
on May 1st 2004. Jean-Jacques Laﬀont’s contributions are important in many ﬁelds in economics,
yet he still managed to spare some of his time to help to trigger the scientiﬁc quality uplift in
the empirical analysis of auctions. Papers in this special issue continue this project and use
Jean-Jacques’ papers in the various dimensions of his work in theory, econometric identiﬁcation,
estimation and empirical results of auctions. This is why we wish to dedicate this special issue
to the memory of Jean-Jacques Laﬀont and to his so formidable capacity of doing and inspiring
excellent research in applied and theoretical economics.
In "Estimating Risk Aversion from Ascending and Sealed-bid Auctions", Jingfeng Lu and
Isabelle Perrigne rely on multiple source of data to identify the risk aversion of bidders. Previous
research using experimental or ﬁeld data had proven the importance of risk aversion albeit in
a parametric way. Risk aversion is diﬃcult to identify non parametrically in the private-value
paradigm if information consists only in observed bids (Athey and Haile, 2007). In particular,
the inﬂuence of risk-aversion on observed bids of diﬀerent organizational forms for the auction is
∗Toulouse School of Economics (GREMAQ, INRA, IDEI)
†Toulouse School of Economics (GREMAQ, IDEI)
‡Toulouse School of Economics (GREMAQ, IDEI)
1Conference web site is: http://idei.fr/activity.php?a=4611
1contrasted. In ascending auctions, it is a dominant strategy to announce each bidder’s private
value whatever risk aversion is. In ﬁrst-price sealed-bid auctions, risk-aversion has a rôle to play
considering the uncertainty attached to the bids of the other bidders. The comparison between
data obtained under these two designs should allow for the identiﬁcation of risk aversion. What
Jingfeng and Isabelle do is to provide a constructive proof of non parametric identiﬁcation of
bidders’ risk aversion and an estimation procedure that builds on it. Obviously, one needs to
assume that the distribution of private values remain the same across diﬀerent auction designs.
Jingfeng Lu and Isabelle Perrigne show that it seems a reasonable assumption in the data they
use that are drawn from timber auctions organized by the US Forest Service. They estimate risk
aversion non parametrically and show that although imperfect, a Constant Relative Risk Aversion
assumption leads to a better ﬁt than a CARA speciﬁcation.
In "Multi-Round Procurement Auctions with Secret Reserve Prices: Theory and Evidence",
Lu Ji and Tong Li tackle the estimation of a multi-round auction which is a complex game.
Some advances in the estimation of these games had been proposed by Elyakime, Laﬀont, Loisel
and Vuong (1997). What the authors focus on is that the auctioneer can auction again later the
objects that were not sold in the ﬁrst auction. This can happen because of the use of a reserve
price that, in the present case, is secret. Lu Ji and Tong Li ﬁrst construct a theoretical model
where bidders draw at each period but in a time-independent distribution, their private value for
the object. A secret reserve price is set by the auctioneer according to some evaluation of the
private value for the seller. The only thing that changes between rounds is thus the beliefs of the
bidders on the support of the reserve price. Lu Ji and Tong Li ﬁrst show that equilibrium bids
decline over rounds. Second, they estimate their model using data on auctions from the Indiana
Department of Transport. Because of the small number of bids, they use parametric speciﬁcations
and estimate the parameters using simulated maximum likelihood estimation methods. They are,
as a consequence, able to simulate counterfactuals that show the importance for the seller of using
a secret reserve price and setting it up at the right level.
In "Econometrics of Auctions by Least Squares", Leonardo Rezende proposes a simple way
to recover the estimates of the coeﬃcients of the determinants of the mean and variance of the
distribution of private values in an auction. What he proposes is a particular case of the method
2of moments developed by Laﬀont, Ossard and Vuong (1995). Leonardo restricts his attention
to symmetric independent private values where the distribution of private values is assumed to
belong to some speciﬁc families of distributions. Leonardo Rezende shows that in this case, simple
OLS leads to consistent estimates of the coeﬃcients of the determinants of the mean and variance
of the private value distribution of the auction. This provides an interesting and easy ﬁrst step for
estimating these coeﬃcients. It can also give some information about the shape of the distribution
of private values. This procedure is illustrated using data on EBay auctions.
In "Approximation of Nash Equilibria in Bayesian Games", Olivier Armantier, Jean-Pierre
Florens and Jean-François Richard propose simple solutions to complex games. They propose to
look for Nash equilibria in games where the strategy space has been restricted. This is a method
which is akin to discretization or restrictions on policy functions in complex decision problems
(Judd, 1999). The authors show that some sequence of Nash equilibria of the restricted games
converges to a Nash equilibrium of the complete game. Furthermore, they develop measures of
the quality of approximation that restricting the set of strategies bring about. They show the
interest of their approach in the case of private-value auction examples. They are careful in
proceeding step-by-step. Their ﬁrst example is a simple private-value auction and allows for a
direct computation of the Nash equilibria and for the evaluation of the quality of the approximation
method they propose. In the second example, although more complex since the auction is now
asymmetric, there is another existing approximation method to which the Constrained Strategic
Equilibrium can be compared to. Finally, their last example is a demonstration of the simplicity
of their approach since no other method is known in that case.
In "Non parametric identiﬁcation and estimation of a class of common value auction models",
Philippe Février turns away from the private value paradigm and studies identiﬁcation in the pure
common value model. Identiﬁcation of structural parameters in this model is diﬃcult and cannot
be obtained without additional identifying restrictions (Laﬀont and Vuong, 1996). Such a set of
additional identifying restrictions was proposed by Li, Perrigne and Vuong (2000). Philippe Février
proposes another set of additional identifying restrictions. Philippe shows that it is suﬃcient that
the model be written as depending on three functions only: the density function of the true value
and two functions that deﬁne the conditional distribution of the signal, conditional on the true
3value. These two functions respectively deﬁne the conditional density function and the support
of the density function of the signal conditional on the true value. What Philippe Février shows
is that these three functions are identiﬁed from the distribution of observed bids. The interest
of this approach lies in the fact that it is possible to set up a direct estimation method from the
observed bids instead of relying on two-step methods. Philippe Février exhibits relatively mild
conditions under which the estimator that he proposes is uniformly consistent. Further research
would be needed to derive the asymptotic distribution of the estimates.
As a last word, we would like to acknowledge funding of the conference by Agence France
Trésor, Institut d’Economie Industrielle, INRA, Région Midi-Pyrénées, CEPR and the Journal of
Applied Econometrics and we would like to thank all the staﬀ of IDEI that were involved in the
organization and especially Christelle Fauchié and Florence Chauvet.
4References
Athey, S. and P., Haile, 2007, "Non Parametric Approaches to Auction", in J.J. Heckman
and E. Leamer eds, Handbook of Econometrics, Volume VI, Amsterdam North Holland.
Elyakime, B., J.J., Laﬀont, P., Loisel and Q., Vuong, 1997, "Auctioning and Bargaining:
An Econometric Study of Timber Auctions With Secret Reservation Prices", Annales d’Economie
et de Statistiques, 34:115-141.
Judd, K., 1999, Numerical Methods in Economics, Cambridge: MIT Press.
Laﬀont, J.J., H., Ossard and Q., Vuong, 1995, "Econometrics of ﬁrst-price auctions",
Econometrica, 63:953-980.
Laﬀont, J.J. and Q., Vuong, 1996, "Structural Analysis of Auction Data", American Eco-
nomic Review, Proceedings, 36:414-420.
Li, T., I. Perrigne and Q., Vuong, 2000, "Conditionally Independent Private Information
in OCS Wildcat Auctions", Journal of Econometrics, 98:129-161.
Paarsch H.J., and H. Hong, 2006, An introduction to the structural econometrics of auction
data, Cambridge: MIT Press.
5Table of Contents
1. Jingfeng Lu and Isabelle Perrigne, "Estimating Risk Aversion from Ascending and Sealed-bid
Auctions"
2. Lu Ji and Tong Li, "Multi-Round Procurement Auctions with Secret Reserve Prices: Theory
and Evidence"
3. Leonardo Rezende, "Econometrics of Auctions by Least Squares"
4. Olivier Armantier, Jean-Pierre Florens, Jean-François Richard, "Approximation of Nash
Equilibria in Bayesian Games"
5. Philippe Février, "Non parametric identiﬁcation and estimation of a class of common value
auction models"
6

Introduction to the Special Issue on the Econometrics of Auctions.

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