A Multinomial Logit Framework to Estimate Bid Shading in Procurement Auctions: Application to Cattle Sales in the Texas Panhandle

Abstract

We develop an empirical methodology based upon multinomial probability models to estimate the magnitude of bid shading in cattle procurement in the Texas Panhandle region. The methodology works well in settings where data allow a good estimation of a bidder’s probability of winning, but the approach does not rely upon the bidding process following any particular structural framework or on the existence of a control group. Estimated markdowns of price from the competitive level are in the range of 5–10% and are somewhat larger than estimates of oligopsony markdowns from previous studies of cattle procurement in the U.S. Copyright Springer 2005

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A Multinomial Logit Framework to Estimating Bid Shading
in Procurement Auctions, With Application to Cattle Sales
in the Texas Panhandle


John M. Crespi
Kansas State University

Richard J. Sexton
University of California, Davis


Abstract: Many auctions have complicated and idiosyncratic features that, individually or in
combination, make structural analysis difficult or impossible. In these more complicated auction
settings, theory may only provide heuristic guidance as to the factors that determine equilibrium
bids and the selling or acquisition price of the item(s) being auctioned. In this paper, we develop
an empirical model to estimate the magnitude of bid shading present in an auction based upon
multinomial probability models. The methodology works well in settings where data allow a
good estimation of a bidder’s probability of winning, but the approach doesn’t rely upon the
bidding process following any particular structural framework or on the existence of a control
group. We apply the model to bidding for live cattle by beef-packing plants in the Panhandle
region of Texas, where idiosyncratic features of the bidding environment make structural
analysis difficult or impossible.



Funding for this study was provided by the USDA Economic Research Service (ERS), and some
of the data were provided by the USDA Grain Inspection, Packers and Stockyards
Administration (GIPSA). The views and opinions expressed in the paper do not necessarily
reflect the views of ERS, GIPSA, or USDA. The authors are grateful to Ted Schroeder and
Rodney Jones for helpful discussions.

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A Multinomial Logit Framework to Estimating Bid Shading in Procurement Auctions,
With Application to Cattle Sales in the Texas Panhandle

I. Introduction

Considerable progress has been made in empirical analysis of auctions that have been designed
around a particular structural format (e.g., government telecommunications auctions (The
Economist [1997])), or can be assumed to fit a familiar structural format (e.g., Laffont, Ossard,
and Vuong [1995], Baldwin, Marshall, and Richard [1997]). However, many auctions in the real
world have complicated and idiosyncratic features that, individually or in combination, make
structural analysis difficult or impossible. Prominent examples include sequential auctions
where multiple units of a product are sold over time, auctions with multiple, competing sellers,
or auctions that feature irrational bidders (Goeree, Holt, and Palfrey [2002]), asymmetric bidders
(Campo, Perrigne, and Vuong [2003]), risk-averse bidders (Campo, Perrigne, and Vuong
[2002]), and bidders who may collude (Graham and Marshall [1987]). In these more
complicated auction settings, theory may only provide heuristic guidance as to the factors that
determine equilibrium bids and the selling or acquisition price of the item(s) being auctioned.
An important policy question for many instances is the “competitiveness” of the auction
in the sense of its ability to generate maximum revenues for a seller or minimum costs for a
buyer in the case of a procurement auction.1 To date, the competitiveness of bidding has been
evaluated in two ways: (a) by comparing the behavior of known or suspected colluding bidders
with a control group of competitive bidders (Porter and Zona [1993, 1999] and Pesendorfer
[2000]), or, if the auction fits or can be assumed to fit a standard structure, by recovering
bidders’ valuations from observed bidding behavior (Monier-Dilhan and Ossard [1998]). These
approaches, while valuable, are limited in application because many auctions lack an adequate

1 For example, Blair and Kaserman [1993, pp. 4-7] motivate their treatise on monopsony with several examples
from procurement auctions (see the references they cite for specific examples).

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descriptive structural model due to their complexity and no competitive control group of bidders
can be identified.2 Recently, Bajari and Ye [2003] have developed tests to detect collusive
behavior that do not rely upon identifying a control group of noncolluding firms.
This paper presents an alternative framework for evaluating the competitiveness of an
auction. We develop an empirical model to estimate the magnitude of bid shading present in an
auction based upon simple probability estimations. The methodology works well in settings
where data allow a good estimation of a bidder’s probability of winning, but the approach
doesn’t rely upon the bidding process following any particular structural framework or on the
existence of a control group. We apply the model to bidding for live cattle by beef-packing
plants in the Panhandle region of Texas, where idiosyncratic features of the bidding environment
make structural analysis difficult or impossible. Another rather unique feature of our application
is that we lack data on losing bids and, in fact, don’t even know how many bids were received on
the lots of cattle in our data set. We argue that, outside the realm of the sealed-bid government
procurement auctions that have been the subject of most prior empirical investigations of
behavior in auctions, this data limitation will be relatively common, making methods that can
proceed without such data of considerable interest.
The competitiveness of livestock procurement in the U.S. has been a subject of frequent
economic analysis and fierce policy debate. Surveys by Azzam and Anderson [1996] and Ward
[2002] summarize much of the economic analysis. On balance, this research suggests a
disconnect between the angst expressed by many producers and policy makers as to the
consequences of the dramatic structural evolution of the industry, and the industry’s actual

2 On this point, both the Porter and Zona [1993, 1999] and Pesendorfer [2000] studies relied on antitrust
prosecutions to distinguish competitive bidders from those suspected of collusion.

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performance.3 Azzam and Anderson opine “that the body of empirical evidence . . . is not
persuasive enough to conclude that the industry is not competitive” (p. 124). Ward’s read of the
empirical evidence suggests to him that price distortions from imperfect competition in
meatpacking are on the order of three percent or less. Azzam [1997] and Morrison-Paul [2001]
concluded that the positive efficiency aspects of packer consolidation dominated small, negative
impacts due to packer market power.
Producer groups and policy makers, however, have continued to express concerns about
the competitiveness of cattle procurement in the U.S. (McEowen, Carstensen and Harl [2002],
Rogers [2002]). The U.S. Senate Judiciary Committee held hearings in August 2002 on the
impacts of increasing consolidation in meatpacking on producers and consumers, and Senator
Tom Daschle and others have called for greater antitrust enforcement in the industry (Pore
[2002]). Pending legislation in the U.S. Congress would ban most packer ownership of cattle,
and, as well, a number of private lawsuits have been filed and are pending under Federal or state
antitrust statutes.
Most prior empirical work on competition issues in the cattle/beef industry has relied
upon aggregate time-series data and utilized either the reduced-form approach of the structure-
conduct-performance paradigm or various structural frameworks associated with the new
empirical industrial organization (NEIO). Either approach has faced the daunting task of

3 Development of the “boxed-beef” packing technology in the late 1970s induced important efficiency gains and
significant economies of scale in the processing sector. At the same time, the U.S. experienced declining demand
for red meats, with per capita consumption falling from 95 lbs. in 1976 to the mid 60 lb. range during the 1990s
(Purcell [2000]). These factors led to rapid consolidation in the packing sector. A relatively unconcentrated
industry, with four-firm concentration (CR4) in the range of 25% in 1976 quickly became a rather tight structural
oligopoly/oligopsony with CR4 = 80% in 1998 (USDA [1998], Ward [2002]).

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isolating the influences of dramatic changes in demand, processing technology, concentration,
and marketing arrangements on key performance variables.4
Researchers have seldom taken the bidding processes in cattle procurement into account.
Those who have attempted to address the uncertainty inherent in markets that include bidding,
have not investigated the structure of the auction or the probabilities of buyers obtaining
particular lots of cattle, but rather have sought to measure the effects of industry structure
variables, such as concentration ratios, number of bidders, or usage of vertical contracting, on
prices bid (e.g., Ward [1981, 1982, 1992], Schroeder et al. [1993]). Although various papers in
the NEIO framework have utilized bid data, none have taken the probabilistic nature of the
bidding environment into account when analyzing competition in the market. Rather, firms have
been modeled as being able to purchase supplies as needed, according to a known producer
supply curve. As such, unlike the present study, these models do not incorporate the reality that
a firm’s bid affects only its probability of obtaining supplies in livestock markets.
II. Economic Analysis of Auctions
Because they often represent stylized markets with well-defined rules, some auctions have
proven to be quite amenable to analysis using the tools of noncooperative game theory.
Common features among the auctions analyzed in theory are a monopoly seller or a monopsony
buyer (e.g., a government soliciting bids on a project) and asymmetry of information among
participants (Klemperer [1999]). Unlike standard models where quantities are presumed certain
for given prices, a model of a procurement auction must reflect that a player’s probability of
winning is a function of the amount bid. Further, the buyer’s profit margin is inversely related to
the amount bid. Thus, the optimal noncooperative bidding strategy must balance this tradeoff

4 See Azzam and Anderson [1996], Sexton [2000], and Ward [2002] for more extended critiques of the extant
empirical work.