Industrial Organization
Applied Econometrics

Industrial Organization
Applied Econometrics
Econometrics
Microeconomics
Labor Economics
Public Economics

October 1999 (Oral) Industrial Organization, Econometrics
May 1999 (Written) Microeconomic Theory, Macroeconomic Theory

Identification and Estimation of Auction Models under Unobserved Auction Heterogeneity

Professor Martin Pesendorfer
Professor Steven Berry
Professor Hanming Fang

May 2003

M.Phil. in Economics, Yale University, May 2000
M.S. in Economics, University of Wisconsin-Madison, May 1998
Diploma with Distinction in Mathematics and Applied
Mathematics, Moscow M.V. Lomonosov State University, June 1994

Yale University
   Cowles Foundation Fellowship, 1998-2002
   Yale University Graduate Fellowship, 1998 -2002
University of Wisconsin - Madison
   Graduate School Fellowship, 1997-1998
Moscow M.V. Lomonosov State University
   University Fellowship for Outstanding Academic Performance, 1989-1994

Teaching Assistant, Department of Economics, Yale University
   Intermediate Microeconomics, Fall 2000
   Game Theory, Fall 2001
   Data Analysis and Econometrics, Spring 2002
   Labor Economics, Fall 2002

Research Assistant, Professor Steven Berry and Professor Arial Pakes, Yale University, 2000-2001
Designed and implemented simulation study of the estimation technique for Dynamic Oligopoly Model.
Research Assistant to Professor Martin Pesendorfer and Professor Arial Pakes, Yale University, 1999-2000
Assessed the uncertainty in the acquisition plans of the Department of Defense and the effects of merger activities on such plans

"Auction Models with Unobserved Heterogeneity: Application to the Michigan Highway Procurement Auctions", September 2002 [job market paper]

"Identification of Bidders’ Cost Structure in the Electricity Pricing Auctions", September 2001, Working Paper

"Entry decisions and capacity constraints in the multi-unit auction environment: Application to the Food Procurement Auctions", Work in progress

My dissertation considers the problem of identifying and measuring private information in First-Price auctions when unobserved auction heterogeneity is present. Unobserved auction heterogeneity may arise due to any information that is known to all bidders at the time they submit their bids but is not observed by the econometrician. I derive conditions under which private information can be identified, develop a method for estimating private information and unobserved heterogeneity components, and apply this method to the data from Michigan highway procurement auctions. My results show that the bias induced by disregarding auction heterogeneity can be severe.

Several methods designed to infer bidders’ private information from the observed bid data have recently been proposed in the context of different auction environments. These methods attribute all the bid variation to bidders’ private information. They do not allow for the possibility that a part of the variation in bids may be generated by unobserved auction heterogeneity. If unobserved heterogeneity is present, these methods may lead to biased estimates, which can substantially exaggerate the importance of private information in explaining bids variation. The distribution of private information plays a crucial role in many policy applications including the assessment of auction efficiency, the measurement of informational rents to bidders (markups over the bidder’s cost), the choice of the optimal reserve price, and the detection of collusive behavior. My proposed approach allows an econometrician to correctly evaluate the magnitude of private information present in a particular market environment. My dissertation consists of four parts:

First, I study conditions under which unobserved heterogeneity can be identified. I assume that a firm’s cost for the project is equal to the product of a common and an individual component. The common component is auction-specific and includes all the information about the project that is shared by market participants at the time of bidding. The individual component is private bidder information. This cost structure translates into multiplicative separability of the equilibrium bid function with bids consisting of a common and an individual component. The econometrician does not observe the realization of the common component and, in general, will not be able to separate costs into their components. I show that under the assumption of independence of individual cost components both across bidders and from the common component, the auction model with unobserved heterogeneity and asymmetric bidders is identified from the joint distribution of two arbitrary bids. I also derive the identification result for a two-dimensional unobserved heterogeneity model. This more general model permits two common components, one affecting the mean and the other affecting the variance of the cost distribution. It is identified under similar conditions as long as at least four arbitrary bids are observed for each auction.

Second, I propose a two-step procedure that permits the estimation of the joint distribution function of private information and the unobserved heterogeneity factor. In the first step, a multiple indicators estimator, developed by Li and Vuong (2001), is used to estimate the distribution functions of the unobserved heterogeneity component and the individual bid component for every bidder type. In the second stage, the distributions of individual cost components are estimated from the distribution functions of the individual bid components following a similar procedure as proposed by Guerre, Perrigne and Vuong (2000) for the estimation of auction models with symmetric bidders in the case of independent private values. I provide conditions under which this estimation procedure produces uniformly consistent estimates for the distribution functions.

Third, I present results of a Monte-Carlo study. The results illustrate that models, which ignore unobserved heterogeneity, such as the independent private values model or the affiliated private values model, may lead to substantially biased estimates. In particular, both, the independent and the affiliated private values model, may lead to higher estimated mark-ups and overestimated mass in the left tail of the costs distribution function. These biases may result in erroneous policy conclusions. The over-estimated mark-ups exaggerate inefficiencies that arise in first-price auctions due to bidder asymmetry, while the described distortions in the shape of the cost distribution function tend to induce the auctioneer to set the reservation price at a lower than optimal level. The importance of both biases increases as the variation in the unobserved heterogeneity component increases.

Fourth, I apply my estimation method to highway procurement data obtained from the Michigan Department of Transportation for the sample period 1997 to 2002. I estimate the probability density functions of the individual and common components. I report the bid function, the density function of total costs, and compare these estimates to estimates obtained under the independent and the affiliated private values assumptions. The estimates suggest that the variation in the common component explains a larger part of the bid variation than the individual component. The estimated relative mark-up, normalized by the cost, equals 6.3% on average. The estimation results suggest that under the null of unobserved heterogeneity both, the independent and the affiliated private values model, tend to under-estimate the cost and over-estimate the mark-up. For example, at the sample average bid level of $570,000, the model with unobserved heterogeneity estimates the average bidder cost equal to $536,300, with a mark-up of $33,800 or 6.3%. For the same bid value, the model with independent private values estimates the bidder’s cost equal to $504,300 with a mark-up of $65,800 or 13%; the model with affiliated private values estimates the bidder’s cost equal to $479,000, with a mark-up of $91,100 or 19%.