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Structural Econometrics of Auctions: a Review Full text available at: http://dx.doi.org/10.1561/0800000031 Structural Econometrics of Auctions: A Review Matthew L. Gentry London School of Economics and Political Science [email protected] Timothy P. Hubbard Colby College [email protected] Denis Nekipelov University of Virginia [email protected] Harry J. Paarsch University of Central Florida [email protected] Boston — Delft Full text available at: http://dx.doi.org/10.1561/0800000031 Foundations and Trends R in Econometrics Published, sold and distributed by: now Publishers Inc. PO Box 1024 Hanover, MA 02339 United States Tel. +1-781-985-4510 www.nowpublishers.com [email protected] Outside North America: now Publishers Inc. PO Box 179 2600 AD Delft The Netherlands Tel. +31-6-51115274 The preferred citation for this publication is M. L. Gentry, T. P. Hubbard, D. Nekipelov, and H. J. Paarsch. Structural Econometrics of Auctions: A Review. Foundations and Trends R in Econometrics, vol. 9, nos. 2-4, pp. 79–302, 2018. R This Foundations and Trends issue was typeset in LATEX using a class file designed by Neal Parikh. Printed on acid-free paper. ISBN: 978-1-68083-446-8 c 2018 M. L. Gentry, T. P. Hubbard, D. Nekipelov, and H. J. Paarsch All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, mechanical, photocopying, recording or otherwise, without prior written permission of the publishers. Photocopying. In the USA: This journal is registered at the Copyright Clearance Cen- ter, Inc., 222 Rosewood Drive, Danvers, MA 01923. Authorization to photocopy items for internal or personal use, or the internal or personal use of specific clients, is granted by now Publishers Inc for users registered with the Copyright Clearance Center (CCC). The ‘services’ for users can be found on the internet at: www.copyright.com For those organizations that have been granted a photocopy license, a separate system of payment has been arranged. Authorization does not extend to other kinds of copy- ing, such as that for general distribution, for advertising or promotional purposes, for creating new collective works, or for resale. In the rest of the world: Permission to pho- tocopy must be obtained from the copyright owner. Please apply to now Publishers Inc., PO Box 1024, Hanover, MA 02339, USA; Tel. +1 781 871 0245; www.nowpublishers.com; [email protected] now Publishers Inc. has an exclusive license to publish this material worldwide. Permission to use this content must be obtained from the copyright license holder. Please apply to now Publishers, PO Box 179, 2600 AD Delft, The Netherlands, www.nowpublishers.com; e-mail: [email protected] Full text available at: http://dx.doi.org/10.1561/0800000031 Foundations and Trends R in Econometrics Volume 9, Issue 2-4, 2018 Editorial Board Editor-in-Chief William H. Greene New York University United States Editors Manuel Arellano Jan Kiviet CEMFI, Spain University of Amsterdam Wiji Arulampalam Gary Koop University of Warwick University of Strathclyde Orley Ashenfelter Michael Lechner Princeton University University of St. Gallen Jushan Bai Lung-Fei Lee Columbia University Ohio State University Badi Baltagi Larry Marsh Syracuse University University of Notre Dame Anil Bera James MacKinnon University of Illinois Queen’s University Tim Bollerslev Bruce McCullough Duke University Drexel University David Brownstone Jeff Simonoff UC Irvine New York University Xiaohong Chen Joseph Terza Yale University Purdue University Steven Durlauf Ken Train University of Wisconsin UC Berkeley Amos Golan Pravin Trivedi American University Indiana University Bill Griffiths Adonis Yatchew University of Melbourne University of Toronto James Heckman University of Chicago Full text available at: http://dx.doi.org/10.1561/0800000031 Editorial Scope Topics Foundations and Trends R in Econometrics publishes survey and tuto- rial articles in the following topics: Econometric models Latent variable models • • Simultaneous equation models Qualitative response models • • Estimation frameworks Hypothesis testing • • Biased estimation Econometric theory • • Computational problems Financial econometrics • • Microeconometrics Measurement error in survey • • data Treatment modeling • Productivity measurement and Discrete choice modeling • • analysis Models for count data • Semiparametric and • Duration models nonparametric estimation • Limited dependent variables Bootstrap methods • • Panel data Nonstationary time series • • Time series analysis Robust estimation • • Information for Librarians Foundations and Trends R in Econometrics, 2018, Volume 9, 4 issues. ISSN paper version 1551-3076. ISSN online version 1551-3084. Also available as a combined paper and online subscription. Full text available at: http://dx.doi.org/10.1561/0800000031 Foundations and Trends R in Econometrics Vol. 9, Nos. 2-4 (2018) 79–302 c 2018 M. L. Gentry, T. P. Hubbard, D. Nekipelov, and H. J. Paarsch DOI: 10.1561/0800000031 Structural Econometrics of Auctions: A Review Matthew L. Gentry London School of Economics and Political Science [email protected] Timothy P. Hubbard Denis Nekipelov Colby College University of Virginia [email protected] [email protected] Harry J. Paarsch University of Central Florida [email protected] Full text available at: http://dx.doi.org/10.1561/0800000031 Contents 1 Introduction and Motivation 2 1.1 Recommended, Additional Reading concerning Auctions . 19 2 Theoretical Models 20 2.1 IPV Model . 20 2.2 CV Model . 28 2.3 AV Model . 34 2.4 Complications . 41 3 Mapping Theory to Observables 67 3.1 Deriving the pdfs of Bids, and Winning Bids . 68 3.2 Empirical Specifications . 76 3.3 Complications . 79 4 Identification 80 4.1 Notation and Definitions . 81 4.2 Vickrey Auctions . 83 4.3 English Auctions . 84 4.4 Sealed, Pay-Your-Bid Auctions . 90 4.5 Dutch Auctions . 98 4.6 Complications . 99 ii Full text available at: http://dx.doi.org/10.1561/0800000031 iii 5 Two Approaches 114 5.1 Reduced-Form Approach . 116 5.2 Structural Approach . 122 5.3 Summary . 127 6 Estimation Strategies 128 6.1 Nonparametric Methods . 128 6.2 Semi-Nonparametric Methods . 133 6.3 Parametric Methods . 139 7 Asymmetries 149 7.1 Asymmetric IPV Model . 152 8 Dependence 166 8.1 Copulas . 170 8.2 Using Copulas . 172 9 Multi-Unit and Multi-Object Auctions 175 9.1 Multi-Unit Auctions . 176 9.2 Multi-Object Auctions . 190 9.3 Long-Lived, Dynamic Auctions . 191 10 Summary, Conclusions, and Suggestions 194 Acknowledgements 199 Appendices 200 A.1 Permanent and Order Statistics with Different Urns . 200 A.2 Extreme-Value Distributions . 203 A.3 Approximation Methods . 204 A.4 B-Splines . 206 References 208 Full text available at: http://dx.doi.org/10.1561/0800000031 Abstract We review the literature concerned with the structural econometrics of observational data from auctions, discussing the problems that have been solved and highlighting those that remain unsolved as well as sug- gesting areas for future research. Where appropriate, we discuss differ- ent modeling choices as well as the fragility or robustness of different methods. Keywords: auctions; structural econometrics. JEL Classifications: C57, Econometrics of Games and Auctions; D44, Auctions. M. L. Gentry, T. P. Hubbard, D. Nekipelov, and H. J. Paarsch. Structural Econometrics of Auctions: A Review. Foundations and Trends R in Econometrics, vol. 9, nos. 2-4, pp. 79–302, 2018. DOI: 10.1561/0800000031. Full text available at: http://dx.doi.org/10.1561/0800000031 1 Introduction and Motivation One of the great success stories in economics during the latter half of the twentieth century was the systematic theoretical investigation of incomplete information in various economic environments—for exam- ple, moral hazard in insurance markets and adverse selection in such market institutions as auctions, to name just two. Developed in tandem with the incredible advances in game theory since the Second World War, an important by-product of this research program was the for- mulation of many incomplete information problems as the design of optimal mechanisms.1 From an econometrician’s perspective, theoretical models of in- complete information are particularly compelling because they provide richer explanations of the observed heterogeneity in data than ones re- lying on measurement error or productivity shocks. For example, when individual agents use private information strategically to make deci- sions, the equilibrium interactions of those decisions with the decisions of others can generate new explanations of observed phenomena, par- ticularly in the field of industrial organization. 1The book by Tilman Börgers [2015], with chapter by Daniel Krähmer and Roland Strausz, provides a useful introduction to the topic. 2 Full text available at: http://dx.doi.org/10.1561/0800000031 3 As is common in economics, however, econometric and empirical de- velopments involving models of incomplete information lagged behind those in theory. For even though using theoretical models to put struc- ture on economic data was advocated by the late Nobel laureates Tryge Haavelmo [1944] and Tjalling C. Koopmans [1947, 1949, 1953] as well as associates of Koopmans at the Cowles Foundation, Yale University, in the 1950s (for example, the late Nobel laureate Leonid Hurwicz [1950]), the approach did not become generally accepted, let alone widespread, until the last quarter of the twentieth century, particularly in response to the devastating evaluation of reduced-form methods by the Nobel laureate Robert E. Lucas, Jr. [1976], which is now commonly referred to as the Lucas critique. In this review, we summarize a subset of this literature—that de- voted to the structural econometric analysis of observational data from auctions, as opposed to data from either laboratory or field experi- ments, although we mention some studies involving the latter two in passing. A classic, canonical problem in economic theory involves a seller of an object who faces several potential buyers. Although the seller probably knows the object’s value to himself, he typically has little or no information concerning what value any one of the potential buyers places on the object.
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