of RAND
Journal Economics
Vol. 30, No. 2, Summer
1999
pp. 263-288
Ohio school milk markets: an analysis
of bidding
Robert H. Porter*
and
J. Douglas Zona**
We examine the institutional details of the school milk procurement process, bidding
data, statements of dairy executives, and supply characteristics in Ohio during the
1980s. We compare the bidding behavior of a group of firms in Cincinnati to a control
group. We find that the behavior of each of the firms differs from that of the control
group. We argue that the behavior of these firms is consistent with collusion. The
estimated average effect of collusion on market prices is about 6.5%, or roughly the
cost of shipping school milk about 50 miles.
1
Introduction
Sometime between May and August every year, school district officials throughout
*
the country independently solicit bids on annual supply contracts for milk and other
products. In response to these solicitations, dairies that are in a position to supply school
milk submit bids on these procurement contracts. Typically, the low bidder is selected
to supply milk in half-pints to the schools during the following school year. As we
describe below, the details of the procurement process, the nature of milk processing
and delivery, and the characteristics of demand for school milk are such that collusive
agreements among suppliers may be relatively easy to reach and maintain. Collusion
appears to be a pervasive phenomenon in school milk auctions.1 There have been recent
price-fixing investigations of procurement auctions for the provision of school milk in
more than twenty states. Guilty pleas have been entered in at least a dozen states, with
fines levied in excess of $90 million. About ninety people have been sent to jail, for
six-month sentences on average.
In State of Ohio v. Louis Trauth Dairies, Inc. et al., thirteen dairies were charged
with collusion in school milk auctions for the years 1980 through 1990 inclusive. As
* Northwestern
University and National Bureau of Economic Research; [e-mail].
Research; dzona @cornerstone.com.
This article is adapted from our reports and statements on behalf of the plaintiff in State qf Ohio v.
Louis Trauth Dairies, Inc. et al. The case was settled before it came to trial. We received helpful comments
from David Barth, Tim Bresnahan, David Genesove, Lou Guth, Wick Heath, Jim Hosek, Bernard Reddy,
and two anonymous referees as well as from the participants in a number of seminars.
i See, for example, Henriques and Baquet (1993).
** Cornerstone
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part of that case, bidding data were collected from school districts around Ohio. Statements from bidders, school district officials, and dairy officials were also gathered. In
this article we examine the information collected as part of the case. We discuss whether
the behavior of some of the firms operating in school milk markets around Cincinnati
is more consistent with competition or collusion.
Auctions are an important market institution. The economics literature extensively
characterizes competitive behavior in auction markets. In comparison, there has been
relatively little analysis of collusion or communication among bidders, in part because
the nature and effects of conspiracy depend on the specifics of the situation. Even
under a given set of market characteristics, it can be difficult to distinguish collusion
from competitive behavior. Our article describes one strategy for detecting collusion.
We employ a rich dataset and an extensive record to describe the workings of a bidrigging conspiracy. A number of characteristics of school milk procurement enable our
analysis. The rules of the auction are well understood, the product is relatively homogeneous, the set of potential market participants is fixed in the short run, and the
production process is straightforward. In addition, some conspirators have confessed.
In this article we describe the incentives to collude and the impact of collusion on
market outcomes.
Collusion is an arrangement among a group of firms that is designed to limit
competition between the participants. There are many alternative methods of colluding
in auction markets.2 For example, conspirators could refrain from bidding against each
other, say by allocating exclusive territories. Alternatively, they could submit several
bids at inflated levels, where the number of bids may be intended to create the appearance of competition. In either event, the members of the ring know that competition
has been limited in the affected-markets. Any of these firms knows that if it submits
a bid it does not have to worry about being undercut by another ring member. Observed
bids will differ from competitive bidding because the conspirators have coordinated
their actions. The expected winning bid will be higher because conspirators have coordinated their actions, whether or not a conspirator wins the auction.
We examine institutional details of the procurement process for Ohio school milk
auctions in the 1980s, bidding data, testimony of the executives of some dairies, and
supply characteristics. Our econometric analysis focuses on the decisions by a dairy
whether to submit a bid to supply milk to individual school districts, and on the level
of submitted bids. We examine the bidding data for a group of firms that were not
named as defendants in the collusion case, and the estimated econometric models are
generally consistent with competitive bidding. When we apply the same econometric
models to the bid data for each defendant, we observe systematic deviations between
predicted and realized bids. We investigate the nature of the deviations and find that
they are consistent with the conspiracies alleged by the state.
We provide evidence that the bidding behavior of the accused dairies was more
consistent with collusion than with competition. For example, several of the defendants
exhibit patterns of both local and distant bid submissions. That is, they submit bids
relatively near their plants and they also submit bids well beyond their local territories.
Further, our econometric analysis of bidding levels shows that the distant bids by the
defendants tend to be relatively low. In contrast, nondefendant bids are an increasing
function of the distance from the school district to the firm's nearest plant. These
features of bidding by the defendants are consistent with territorial allocation of districts
in the Cincinnati area that were close to the dairies' plants to restrict competition, and
2 Hendricks and Porter (1989) describe several collusive mechanisms, and why the detection of collusion
is necessarily case specific.
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PORTERAND ZONA /
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relatively competitive bidding at more distant locations, which were perhaps outside
the area of territorial allocation. If bidding for local districts had been competitive,
local bids should have been lower than distant bids, because shipping costs were lower
and because the Cincinnati area has many potential local suppliers. The relationship
between bidding behavior and distance is notable, because processed milk is relatively
expensive to ship (since value is low relative to weight), and therefore competition is
localized.
The article is organized as follows. We describe in Section 2 the demand and cost
characteristics of Ohio school milk markets. We argue in Section 3 that there were
strong economic incentives to collude during the alleged period of conspiracy. We
describe the milk procurement rules and argue that a number of characteristics of the
auction mechanism facilitated collusion. We discuss the nature of possible collusion in
these markets given the statements of market participants and the institutional details.
We then present in Section 4 a model of competitive behavior in these school milk
markets. We focus on the two interrelated decisions that a competitor would make:
where to bid and at what level. In Section 5 we focus on the behavior of the defendant
firms operating in the Cincinnati area. We find that the behavior of these defendant
firms differed from that of a hypothetical control group firm. We find that the pattern
of deviations from average control group behavior was consistent with the collusive
scheme described by market participants. The bidding behavior of the defendants is
suspicious, even without the comparison to the control group of nondefendants. Finally,
in Section 6 we estimate that collusion caused school districts to overpay for school
milk by about 6.5% in the affected area during the period analyzed, and much more
than that in some locations. Section 7 concludes.
Our analysis extends a recent empirical literature on the detection of bid rigging.
Porter and Zona (1993) describe bid rigging in New York state highway paving jobs
on Long Island in the early 1980s. A subset of firms is known to have participated in
preauction meetings in order to assign low bid privileges for specific contracts. The
conspirators often submitted complementary or phony bids above their low bid, perhaps
to create the appearance of competition. We compare the bids of firms that did not
participate in these meetings to those of the conspirators. We show that the ranking of
nonparticipant bids for individual contracts is correlated with cost measures such as
capacity and capacity utilization, whereas the rank distribution of conspirator bids is
not correlated with the same cost measures. In particular, bids higher than the conspirators' low bid are not correlated with the cost measures, consistent with a complementary bidding scheme. We focus on bid rankings within a contract, rather than bid levels,
because we do not have access to contract-specific information. In contrast, the Ohio
school milk dataset we employ here contains information about the school districts, as
well as information on individual contract terms.
Pesendorfer (1996) examines school milk bidding data from Florida and Texas.
His focus is on the differences between strong and weak cartels, where the distinction
refers to whether or not side payments were made. He argues that the bidding data are
consistent with the operation of a strong cartel in Florida and a weak cartel in Texas,
in accordance with trial evidence. In contrast, our goal here is to distinguish between
competitive and collusive bidding. Hewitt, McClave, and Sibley (1996) also analyze
the Texas data, and they conclude that there was collusion in the Dallas-Fort Worth
region.
The articles by Baldwin, Marshall, and Richard (1997) and Bajari (1997) compare
structural models of collusive and noncooperative bidding for Forest Service timber
contracts and Minnesota highway improvement jobs, respectively. In both cases, a
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specific model of collusion is considered. Our approach employs reduced-form methods
and infers collusion from suspicious departures from competitive bidding patterns. The
nature of the departures governs our inferences about the likely form of collusion.
2. The market
* Market outcomes are determined by three factors: the nature of demand, the nature
of the production process, and the nature of competitive interaction among suppliers.
In the current analysis, demand and cost characteristics are relatively easily described.
The more difficult problem is determining the nature of competitive interaction given
the demand and cost characteristics; that is the focus of a subsequent section.
There are more than 600 school districts in Ohio. Most districts award annual
contracts for the supply of school milk. Generally, each district annually and independently solicits bids for certain types of milk between May and August for the following
school year. For example, a district will indicate that it expects to purchase 50,000
half-pints of whole white and 30,000 half-pints of whole chocolate milk. (This corresponds to a student population of about 450.) Firms that elect to bid submit a list of
prices for the various products. In addition to specifying categories of milk, the district
may require their supplier to provide coolers (for the refrigeration of milk), straws, or
napkins. Escalator clauses with price indexed to the price of raw milk are also provided
in some bid requests, to reduce the risk to the dairy associated with submitting a bid
on an annual contract, since the price of raw milk could fluctuate substantially over
that period.
Demand for school milk is relatively insensitive to the price charged. School lunch
programs are heavily subsidized, and milk demand may be inelastic in any event.3 If
school district purchasing is inelastic, a firm that controls the supply of milk for a
particular district could profit from a substantially higher price in that district.
Dairy processors receive raw milk from dairy farmers in the area. The price
charged for raw milk is typically regulated through an elaborate federal system based
on location and the type of milk. Although some milk producers are unregulated, the
market would tend to produce a single price for both regulated and unregulated raw
milk in the long run. The cost of the raw milk contained in a typical half-pint purchased
by a school district is about seven cents. (This figure varies seasonally and from year
to year.) Raw milk is processed by standardizing the butterfat content (e.g., 2% or skim
milk), pasteurized, packaged, and delivered. Typically, potential suppliers of school
milk pay about the same amount for raw milk, and they use much the same technology
to pasteurize, package, and deliver. Many firms use the same suppliers of packaging
materials and typically pay about two cents per half-pint for packaging. As described
below, we would expect incremental costs to be similar across different suppliers or
potential suppliers. Any differences in long-run incremental costs would likely arise
from differences in distance from the plant to the district.
When bids are solicited by school districts, firms in a position to supply will submit
a bid. Which firms are in a position to supply the district? A firm must have access to
a supply of school milk. The potential suppliers of school milk fall into one of two
categories: processors, which process and package raw milk in the half-pint containers
demanded by schools; and distributors, which often purchase milk wholesale from the
3Our 1997 working paper describes an OLS regression for a cross section of 609 school districts in
which demand for milk is inelastic. We regress the logarithm of total half-pints of milk purchased in May
1990 on the logarithm of 1993 student enrollment, and the logarithm of price, standardized to whole chocolate, in cents per half-pint.
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processors and resell it to a school district.4 For any firm interested in selling its own
milk in school milk markets, the costs of a processing plant may represent a substantial
entry barrier. For those processors for which we have data, the school milk business
represents a small fraction of their total revenues, typically less than 10%. Although a
processing plant is necessary to process school milk, school milk is only one of many
products. To our knowledge, no firm has ever built a processing plant solely to supply
school milk. Thus the decision to build a plant hinges on considerations in other product
markets such as supplying wholesale to supermarkets or to other institutions such as
restaurants. (It should also be noted that there was substantially more exit than entry
of processing plants during our sample period.) The costs of the processing plant that
are directly attributable to school milk are therefore quite small. We conclude that only
those firms with access to a milk processing plant, largely put into operation for other
reasons, would have the ability to enter the school milk business selling their own
product.5
If a firm has a plant relatively close to the school district in question, what costs
would be incurred should the firm submit a bid and win the contract? For example,
are there any important fixed costs associated with serving school districts? Because
data on the fixed costs of supplying school milk are not available, we analyze the size
distribution of firms in Ohio. For companies participating in school milk markets, the
scale of operations ranged from one firm supplying milk to about 1g%of Ohio public
school students annually to another that supplied milk to about 7% of the students.
Firms producing on vastly different scales coexist in these markets, even though marginal costs seem to be quite similar, indicating that the fixed costs associated with the
school milk business for a dairy serving other customers may be relatively small.
Given that a firm has a plant and is in the school milk business, there are incremental costs associated with starting service to a new school district, such as the costs
of providing a cooler and adding the district to existing delivery routes. The delivery
portion of total incremental cost may also be related to the number of deliveries per
week for the new district and how well that number fits with the firm's existing route
structure.6There are three main options for delivery: some dairies have dedicated school
milk routes; others add school deliveries to their regular retail commercial routes; and
other dairies use local delivery subcontractors for these services. Frequently a dairy
will use more than one option. Of course, delivery costs vary with distance. A typical
delivery cost is on the order of one cent per half-pint.
The cost of coolers is small relative to the other costs of school milk. For example,
a 16-case cooler can be purchased currently for $1,100. Using an eight-year depreciation schedule, which probably underestimates a cooler's useful life, this figure implies
a cost of about .2 cents per half-pint for a cooler that chills approximately 70,000 halfpints per year.
To summarize, the cost of ingredients for a half-pint of milk is on the order of
about seven cents per half-pint, packaging costs are about two cents per half-pint, and
delivery costs to serve a school district are about one cent per half-pint. Total delivered
4Distributor/processor
relationships can be classified into roughly three types: (1) distributors are granted exclusive territories and bid using the affiliated processor's name; (2) distributors purchase wholesale but
sell using their own name; as better terms are offered, distributors may switch processors; (3) less frequently,
distributors provide delivery to processor for a fee. As these three coexist in a market, any particular type
is unlikely to convey a competitive advantage.
I As noted earlier, firms can and do enter the market for the distribution of other firms' processed milk.
Thus, entry barriers into distribution would be lower.
6 Absent collusion,
bidders will not know exactly which school districts they will ultimately serve when
they bid on individual contracts. That is, they will not know the outcome of future contract lettings.
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incremental costs are on the order of ten cents per half-pint during the period analyzed.
We expect these incremental costs to be independent of the scale of operations and
similar across firms (after accounting for proximity). Fixed and other one-time costs
will affect a dairy's decision whether to enter or exit the school milk business, whereas
the incremental costs of supplying an additional half-pint of milk or servicing another
district are relevant for its pricing decisions.
3. The nature of possible collusion
* The market characteristics described so far suggest competition among firms producing a homogeneous product with similar and constant incremental costs. Firms are
likely to have good information about the costs of their competitors, since most cost
changes affect all firms similarly. There are unlikely to be substantial informational
advantages in the market. School districts would be willing to pay high prices for school
milk, if they had no other choice. Competition is likely to be localized, because of the
regulation of raw milk, which results in little variation in raw milk prices across dairies
in a given region, and because of relatively high transportation costs.
There are many features of Ohio's school milk markets that may affect the dairies'
competitive interaction. Specifically, a number of characteristics facilitate collusion.7
Firms compete only on price. Under the terms of the contract, the winning bidder
supplies the product with specified characteristics (e.g., butterfat content or flavoring).
A cartel need only coordinate submission and bid decisions, and not other characteristics of the product, which simplifies cartel operations. The policy of publicly announcing bids and the identity of the bidders allows cartel members to detect deviations
from cartel agreements. Undercutting and cheating on collusive arrangements would
not go unnoticed, and a collusive arrangement is more likely to be stable. Most school
districts hold their auctions annually but at different times during a year, and they act
on their own.8 The disorganized letting of contracts (as opposed to all contracts being
let on a particular day, for example) allows cartel members to adjust bidding behavior
during the bidding season to allocate market shares, and it provides an opportunity for
nearly immediate retaliation for bad cartel citizenship.
The predictability of the demand for school milk from year to year allows threats
of future retaliation in response to deviations to be credible. The fact that the markets
themselves are easily defined according to school district boundaries permits allocations
by assignment of territories. The set of firms potentially submitting bids in a particular
market is small and quite stable. These firms use similar production processes and
therefore face similar cost structures. The similarity of potential suppliers makes it more
likely that a group of firms could agree on joint behavior.
The same dairies encounter one another in more than one market, so competition
may not be fierce.9 Contact between competitors in multiple markets (school districts
as well as wholesale accounts) makes collusive schemes that allocate markets more
feasible. The practice of obtaining competitors' price lists through retail customers (e.g.,
grocery stores) is common, if not universal. Advance notification of list price increases
7These characteristics are also prevalent in other markets. See, for example, our 1993 article on the
detection of bid rigging.
8 Some school districts occasionally band together in cooperatives and solicit bids for the group. However, cooperative arrangements historically have not prevented districts from soliciting bids individually.
9 Bernheim and Whinston (1990) examine how multimarket contact in a repeated market setting may
affect firms' incentives and behavior. They conclude that "multimarket contact relaxes the incentive constraints that limit the extent of collusion" (p. 22).
? RAND 1999.
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can lead to supracompetitive prices: The practice allows communication of intentions
to competitors (Holt and Scheffman, 1987).
Dairies are frequently customers of one another. This facilitates direct communication and allows a pretext for meetings between competitors. The practice allows
communication of pricing information (even for products that are not purchased)
through full price lists. Holt and Scheffman (1988) condemn this practice as potentially
facilitating collusion.
The many dairy trade associations in Ohio also allow a pretext for meetings of
competitors. Most meet on a regular basis to discuss issues of mutual interest. These
associations obviously understand the legal dangers, since the minutes of their meetings
often indicate that they begin with the reading of a statement warning members not to
discuss prices.
Price decks were often used. Districts were assigned to a small number of price
in the price decks. This practice can facilitate collusion, since it
categories-levels
makes complementary bidding easier. One level of the price deck can be for complementary bids that have no possibility of winning.
In 1993, representatives of two dairies operating in the southwestern part of Ohio
confessed to rigging bids during the period we analyze. These individuals testified that
they had rigged bids with other firms in the area (some of whom maintained their
innocence). Their testimony was offered as part of a settlement of the criminal and
civil cases against these firms (and perhaps individuals). Some of the testimony apparently contradicted earlier sworn testimony in which these individuals maintained
their innocence. The bid-rigging scheme described in their testimony was one of respecting incumbencies. If one of the cartel members had served a particular school
district in the previous year, then other firms were to submit high complementary bids
that were sure not to undercut the incumbent firm's bid, or else refrain from bidding.
The testimony described frequent communication among these competitors, as the specific details of the scheme were worked out through the bidding season. The individuals
testified that there was a breakdown in the cartel in two school years, 1983-1984 and
1989-1990.
Notwithstanding the testimony, a cartel among firms operating in the area is plausible and would be to the benefit of each of the participants. Since competition is
localized, prices will fall to competitive levels only in areas where there is a sufficient
number of local competitors. Distant competitors are disadvantaged by transportation
costs and can only limit price increases to a certain extent. The competitive significance
of each supplier depends on its relative distance from the school district. Any elevation
of price achieved through collusion could, in some circumstances, be defeated by the
entry of new firms from outside the market. In the case of school milk, entry will not
take the form of a new firm setting up a processing plant; instead, it will be in the
form of bids from firms whose plants are farther away. In this way, the transportation
cost for distant noncartel entrants will constrain the ability of a cartel to raise prices,
but if collusion is effective, then prices could be elevated by a significant amount. If
local firms could coordinate their bidding behavior, then some profits could be earned
without stimulating entry from distant suppliers. The reaction of any school district is
unlikely to limit the ability of a cartel to raise price. As noted above, demand for school
milk is inelastic and school districts would continue to purchase milk even at elevated
prices, to the detriment, of the school districts and to the benefit of cartel members.
A scheme of respecting incumbencies is one way for a cartel to coordinate bidding
behavior. Such a scheme would be attractive if cartel firms were near each other (as
some are in this case). The mechanism avoids the cartel problem of allocating school
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districts of varying profitability (because some are further away or otherwise require
more service) among the cartel members. Another way of coordinating bidding behavior would be the assignment of geographic territories to individual firms. Territorial
assignment would be a more practical collusive mechanism when firms are geographically separated, and some firm has a clear advantage in serving a particular district.
4. A model of competitive behavior
* In a competitive market, firms in the school milk business face two interrelated
decisions. First, should the firm submit a bid in a particular district? Second, if a bid
is submitted, what should the bid level be? We address these decisions in turn in the
subsections below. Here we describe a model of competitive bidding.
We estimate a reduced-form model of bidding behavior10 using a dataset provided
by the state of Ohio that contains information on school milk procurement for as many
as 509 of the approximately 600 school districts in the state from 1980 through 1990,
inclusive, with approximately 60 different bidders participating at some point in the
sample. We create a control group made up of nondefendant firms that bid on Ohio
school milk contracts. The dataset contains information on the identity of the districts,
their location and enrollment, and the timing of contract lettings; it also has information
on who submitted bids and on the nature of winning and losing bids, such as prices
and compliance with district specifications, that were submitted to each district. Table
1 provides some descriptive statistics for each year in our sample.
According to data obtained from the U.S. Department of Agriculture, a total of 68
milk processing plants had sales in Ohio at some point during the sample period and
potentially could have supplied school milk. Figure 1 displays the location and owners
of the 46 plants that supplied school milk in 1987. Superimposed on the plant location
map in Figure 1 is an index of dairy concentration." The darker the area, the more
concentrated is the ownership and control of local school milk processing facilities.
Figure 1 shows that the markets in the northeast section of Ohio are the least concentrated; if they were competitive, they should have the lowest prices, all else equal.
Columbus and the southernmost tip of Ohio have markets where the supply of school
milk is concentrated in the hands of relatively few producers. Over the period 19801990, the number of plants serving Ohio school districts fell from 54 to 43, and the
number of firms fell from 43 to 26.
Table 2 shows the distribution of bidder distances in the Ohio data. The table also
shows the distribution of potential supplier distances in the data. Approximately 85%
of the firms supplying school milk in a given year do so from plants located less than
75 miles from the school district. Firms considering entry in order to supply milk to
distant school districts appear to be disadvantaged by distance, even if they have a
plant in operation.
The distribution of processing plants in the state and the apparent disadvantage of
shipping long distances cause districts to receive a relatively small number of bids on
school milk. For the districts in our dataset, 45% received only one bid, 34% two bids,
and 18% three bids. Even though there are a large number of potential bidders for any
particular auction, very few bid. The mean number of bids is 1.8. The small number
of bids submitted indicates that there may not be significant firm-specific private information in the markets. If bidders knew their own costs as well as the costs of other
10In some circumstances a reduced-form model of bidding is behavioral, i.e., when each firm is "small"
relative to the market.
11We measure concentration using the Herfindahl index. For shares we use the fraction of plants within
75 miles of the region that are owned by each firm.
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PORTER AND ZONA
TABLE 1
Year
I
271
Characteristics of Ohio School Milk Dataset
Number of
Number of
Plants
Number of
School
Operated by
Dairies
Districts
Total Enrollment Submitting Submitting
or Cooperatives in School Districts
Dairies
Bids
Average Price
Per Half-Pint
($0.00)
Average FMO
Price for Raw
Milk
(a)
(b)
(c)
(d)
(e)
(f)
1980
366
1,257,925
54
43
.1282
.0718
1981
398
1,379,619
50
44
.1295
.0769
1982
415
1,371,164
46
40
.1295
.0760
1983
436
1,415,281
48
40
.1288
.0764
1984
448
1,430,644
53
38
.1313
.0741
1985
463
1,460,697
48
35
.1322
.0708
1986
481
1,457,437
47
36
.1304
.0700
1987
494
1,566,591
46
33
.1310
.0701
1988
509
1,520,635
44
30
.1338
.0666
1989
491
1,564,869
43
26
.1389
.0708
1990
412
1,296,587
43
26
.1575
.0797
Notes: Dollars per hundred weight, FMO #33 class 1 Fluid Milk, 186 half-pints per hundred weight. Prices
quoted for July of each year.
potential suppliers, then under a set of standard assumptions either one or two bids
would be observed. The low-cost supplier would submit a bid just below the cost of
the next-lowest-cost supplier, and the next-lowest-cost supplier would be indifferent
between bidding at its own cost or not bidding. About 43% of all bids are submitted
by the firms with the plant closest to the district, and 8% by the firm with the secondclosest plant. Among winning bids, 49% are submitted by the firms with the closest
plants, and 8% by those with the second-closest plant.
[E Bid submission. In a competitive market a firm will submit a bid in a particular
district whenever the probability of winning is relatively high, and when the expected
return covers both the costs of preparing the bid and the incremental costs of supplying
the district. A reduced-form model of bidding behavior should account for variables
that reflect the potential bidder's absolute and relative advantage in serving a district.
For example, variables that may be important in characterizing these advantages include
whether or not the firm (i) has significant transportation costs to the particular district,
as reflected by the distance from the district to the plant; (ii) is a distributor or a
processor of milk; (iii) is the closest potential supplier (and so the most likely low-cost
supplier for that district); (iv) is the second-closest, and hence likely the second-leastcostly, potential provider; (v) is bidding on a large or small school district, as larger
districts may require more time and energy to prepare a bid; and (vi) can efficiently
provide the specified milk under the terms of the contract (whether or not coolers are
required, or whether fixed price or indexed contracts are specified, for example).
From available bidding data, we estimate how these factors affect the bid-submission decision of the control group of nondefendants. A list of the variables employed
is
contained
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in
Table
3.
Table
4
presents
the
results
from
the
estimation
of
several
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/
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D
554
<
* /13
|
Cincinnatir
:::102
*
220,5 0, 64
0, 5
'
54
4.
10*
111 - Taylor
114 - Toft Dairy
116 - United Dairy
118 - Valley Bell
120 - Wayne Dairy
*124
*124
*10
Probability
2
TABLE
69 - McDonaldDairy
71
9/ - Meadowbrook
75 - Miller
86 - Oberlin Farms
102 - Schmitt Dairy
107 .- ,Smith )F1
b
/ 77
109 - Superior
110 - Tamarack
*118
t
Hefner Dairy
5
4 0 - H.lMeye
46 - H illside
11
of Bidding
and
Winning
124 - Winchester Farms
Conditional
Plant
from
on Distance
to School
District
Distance
Miles
in
Number
Districts
of
Probability
Bidding
of
Proportion
All
Bids
of
Probability
Winning
of
Proportion
Winning
(a)
(b)
(c)
(d)
(e)
0-10
2,115
19.5%
20.1%
13.6%
22.9%
10-20
3,197
14.0
21.7
8.9
22.5
20-30
3,840
7.6
14.2
4.9
15.0
30-40
4,526
5.5
12.1
3.4
12.1
40-50
5,637
2.3
6.3
.9
4.2
50-60
6,440
1.9
5.9
1.0
5.0
60-70
5,314
1.4
3.7
.5
2.0
70-80
6,732
1.4
4.7
.8
4.4
80-90
5,200
1.0
2.5
.6
2.5
90-100
4,885
1.2
2.8
.7
2.8
100-150
26,079
.5
6.1
.3
of
Bids
6.6
in which firms
of districts
the percentage
category,
Columns
(b) and (d) report, for each distance
Notes:
of
(c) and (e) total 100% and report the fraction
Columns
bid, respectively.
a bid or the winning
submitted
are based on a total of 2,053 submitted
Results
category.
in each distance
bids, respectively
all bids or winning
bids.
1,260 of these were winning
bid opportunities;
group firms out of 73,965
bids from control
? RAND
1999.
PORTER AND ZONA
/
273
probit models, where the dependent variable is one if a bid is submitted in a district
and the independent variables are described in Table 3. The sample is an unbalanced
panel of firms and district-years with available data. We present estimates based upon
three different specifications. The first is a pooled specification with common intercepts
and slopes across all districts and bidders. Column (a) displays the estimated coefficients and (b) the estimated t-statistics. The second specification allows for separate
bidder fixed effects. Column (c) displays the estimated coefficients from this specification and (d) the estimated t-statistics. The third specification allows for separate
bidder and district effects estimated using a subsample of the data where these effects
can be measured. District-specific dummies control for any effects that were specific
to a school district and invariant over time and over firms submitting a bid. The contract
term coefficients may be less reliable in the third specification, as they are often identified because information is missing for some years. Because of the large number of
coefficients to be estimated (over 400), we break the problem into two pieces.12 We
then average the two sets of coefficient estimates and t-statistics with weights proportional to relative sample size. Column (e) displays the estimated coefficients and (f)
the estimated t-statistics.13 The coefficients of interest are similar across all three specifications. 14
We interpret the result as follows. Processors are more likely to submit bids than
distributors, all else equal. This may reflect the fact that distributors tend to run a single
school milk route, while processors tend to run several routes with school delivery.
Firms are more likely to submit a bid in one particular direction as opposed to all
around their plant, particularly distributors. This may reflect the effects of existing route
structures. Firms are less likely to submit bids on school districts that are further away
from their plant. This probably reflects absolute cost differences. Districts that request
coolers or straws receive fewer bids than districts that do not. The other contract terms
do not affect bid submission behavior in a statistically significant way.
The likelihood of submitting a bid is a decreasing function of distance. Figure 2
displays the impact of distance on the probability of bidding for a hypothetical firm in
the control group. To construct this figure we assume that the firm is the closest supplier
to districts less than 10 miles from its plant and the second-closest potential supplier
at distances between 10 and 20 miles. The three curves correspond to the different
probit specifications in Table 4. There are two steps in the predicted probability of
bidding, where the firm loses its locational advantage and where it becomes neither
the closest nor the second-closest potential supplier.'5 The likelihood of bidding for this
hypothetical firm is above 50% at zero distance but decreases to nearly zero beyond
75 miles.
Bid level contingent on submission. In competitive markets, a firm submitting a
c
bid chooses its bid to maximize expected profit. A bid cannot be increased indefinitely;
the higher the bid, the lower the likelihood of winning. To the extent that bids are
12
We order the data by district number and split the data so that each subset has about the same number
of districts.
13 A likelihood
ratio test would reject the simpler models in favor of the more general model, suggesting
that no single intercept can represent all bidders or all districts. That is, there is no bidder in the data that
can be used to represent the bidding behavior of the others. The results should be interpreted in that light.
14 The third specification
is problematic in that a large number of fixed effects are estimated. If feasible,
it would be preferable to adapt the methods described by Kyriazidou (1997).
15 The steps occur because
our probit specifications
employ indicator variables for these categories.
However, we do not restrict the size or the direction of the measured average effect.
? RAND 1999.
274
THE RAND JOURNAL
/
TABLE 3
OF ECONOMICS
Variable Definitions
Continuous Variables
Direction
Proportion of the vendor's bids from 1980-1990 that were submitted in
the quadrant in which the district is located relative to the plant.
Distance
Approximate distance (in miles) between district and plant.
Size
Share of Ohio students represented in the dataset served by the vendor
in the given year.
District enrollment
Number of students enrolled in the district in the 1993-1994 school
year.
Inverse Mills Ratio
Inverse of the Mills Ratio, which is a function of the probability of submitting a bid.
Number deliveries
When available, number of deliveries per week (otherwise, Number Deliveries is zero and Delivery Missing is one).
Student spread
Variance of enrollment across districts belonging to a co-op or other
auction-conducting entity. This measure equals zero for districts that
do not belong to a co-op or other auction-conducting entity.
District spread
Mean distance (in miles) between each district and the auction-conducting entity. This measure equals zero for districts that do not belong to
a co-op or other auction-conducting entity.
Indicator Variables
Processor
One if the vendor is a processor, zero otherwise.
Closest
One if the plant is the closest to the district, zero otherwise.
Second closest
One if the plant is the second-closest to the district, zero otherwise.
No cooler
One if the information on coolers available and no cooler supplied, zero
otherwise.
Cooler provided
One if information on coolers available and cooler supplied, zero otherwise.
Fixed bid
One if information on escalator clauses available and bid is fixed, zero
otherwise.
Escalator
One if information on escalator clauses available and bid is not fixed,
zero otherwise.
Straws not included
One if information on straws available and no straws supplied, zero otherwise.
Straws included
One information if on straws available and straws supplied, zero otherwise.
Delivery missing
One if no information available on deliveries per week, zero otherwise.
Co-op
One if an entity is holding the auction on behalf of multiple school districts, zero otherwise.
1981-1990
One if bid was made in the indicated year, zero otherwise.
costly to submit, it would not be profit maximizing to submit bids that have no probability of winning. A firm maximizing expected profit trades off higher profits against
a lower probability of winning.16
Alternatively, bidders choose their markup over costs. The markup is affected by
the likelihood of winning the auction, which depends on the likelihood of other firms
16
See, for example, Wilson (1993), McAfee and McMillan (1987), or Milgrom and Weber (1982).
? RAND 1999.
PORTER AND ZONA
TABLE 4
I
275
Estimated Coefficients: Control Group Submission Model
Base Probit
Submission Model
Variable Name
Coefficient
(a)
Constant
Direction
Direction*distance
Processor*direction
Processor*direction*
distance
-2.5599
t-statistic
Bidder Fixed-Effect
Submission Model
District and Bidder
Fixed-Effect
Submission Model
t-statistic
(b)
(c)
(d)
-23.3
NA
Coefficient
t-statistic
(e)
Coefficient
(f)
NA
1.1461
16.1
1.2726
15.5
1.3600
8.4
.0056
3.6
.0130
7.0
.0286
7.6
-.9047
.0319
-6.1
11.1
-1.0068
.0315
-4.6
5.9
-1.1091
.0486
-2.6
4.7
Processor*distance
-.0353
-15.4
-.0475
-13.2
-.0549
-7.8
Distance
-.0155
-10.1
-.0230
-12.4
-.0432
-11.4
Processor
Size
Size*distance
1.7782
18.6
1.6897
10.4
1.5505
5.0
27.8765
17.0
12.2028
4.6
18.9323
4.0
.1664
3.2
.1223
2.1
.0655
.6
-.1
.0022
.2
Closest
.3707
9.9
.3300
7.3
.2028
2.3
Second closest
.0892
1.6
.1890
3.0
District enrollment
.0000
(Size*distance)A2
-.0335
-4.5
-4.2
-.0008
.0000
-3.4
-.0136
-.1
.0003
2.0
No cooler
.1419
2.3
.1601
2.4
.2971
1.0
Cooler provided
.0920
2.9
.0823
2.3
.1123
1.0
.0156
.3
.0089
.0
.0089
.4
Fixed bid
-.0533
-1.2
Escalator
-.0910
-1.6
-.0332
-.5
Straws not included
-.0952
-.9
-.1345
-1.2
Straws included
-.0814
-2.0
-.1008
-2.2
.1716
.6
-.2148
-1.5
Delivery missing
.2890
3.4
.2736
2.9
-.0869
-.2
Number deliveries
.0668
3.2
.0652
2.8
-.0216
-.2
Cooperative
-.0318
-.3
-.0095
- .1
Geographic spread
.0006
.6
.0001
.1
Variance of population
.0000
1.9
.0000
1.8
Bidder-specific effects
No
Yes
Yes
District-specific effects
No
No
Yes
Log-likelihood
-5,964
-5,052
-3,727
Average Log-likelihood
-.0806
-.0683
-.07699
Observations
73,965
73,965
48,406
25
89
536
Number of parameters
? RAND 1999.
276
THE RAND JOURNAL
/
OF ECONOMICS
FIGURE 2
PREDICTED PROBABILITYOF SUBMITTINGA BID BY DISTANCE
1.0
v
Base model
fixed effect
and districtfixed effect
--Bidder
.8
A........Bidder
.0
.4\
.0
a
.2 -
0
20
40
60
80
Distance (miles)
submitting bids. The markup is chosen to maximize expected profit given the level of
cost. There are two categories of variables that would tend to explain bidding behavior.
First, there are variables that may contribute to cost: distance from the plant to the
district; whether or not the bidder is a processor; whether or not coolers or other items
are required or supplied; the number of required deliveries; and whether or not there
is an escalator clause. Second, there are variables that reflect competitive characteristics
of the market: the bidder's relative cost advantage, and the number and costs of other
suppliers. For example, if a bidder is the closest vendor, then that bidder can bid more
than it would otherwise without decreasing the probability of winning. A second example is a variable that affects the probability that a firm submits a bid. Firms that are
likely to submit bids on particular districts are those that have a high probability of
winning, and those expecting to earn relatively high profits if they win the auction.
To analyze bid prices we construct a summary measure of each firm's vector of
bids, accounting for differences in butterfat content and flavoring. We predict the price
of 2% chocolate milk, in dollars per half-pint, based upon each of the other prices
submitted, in a pairwise manner. For example, in those instances where both a 2%
chocolate and a white whole milk bid were entered, we regress the chocolate milk price
on the white milk price and a constant. The estimated equation is used to forecast a
2% chocolate price based on the white whole milk price that was submitted. The
average of the forecasts based on all observed components of bids is used as the
summary measure of price. The base is 2% chocolate. This procedure may introduce
a form of heteroskedasticity into the model, and the statistical results should be interpreted accordingly. One alternative to our approach would be to estimate separate
equations for each type of milk using a GLS procedure.
We measure the effects of the factors described above on the bid-level decision
for the control group of nondefendants. Table 5 presents the results of the estimation
procedures. Again, we present three sets of results. The first is based upon the simple
pooled probit specification for bid submission and a corresponding OLS regression for
bid levels, with correlation in the errors accounted for via a Heckit procedure.17 The
second allows bidder-specific constant terms in the probit estimates and in the bid-level
17
The statistical issues are described in Heckman (1976).
? RAND 1999.
PORTER AND ZONA
TABLE 5
I
277
Estimated Coefficients: Control Group Bid Level
Bidder Fixed-Effect
Bid Model
Bid Model
Variable Name
Coefficient
(a)
t-statistic
(b)
Coefficient
(c)
t-statistic
(d)
District and Bidder
Fixed-Effect
Bid Model
Coefficient
t-statistic
(e)
(f)
Constant
.1235
59.5
.1285
33.9
.1229
.0
Processor*distance
.0000
.6
.0001
2.9
.0001
2.5
Distance
.0000
2.3
.0000
.3
.0000
Processor
Closest
Closest*distance
-.0022
.0035
-.0001
-3.1
4.1
-.0013
.0005
-.7
.6
-.0040
-1.4
-1.9
.0010
.8
-2.3
.0000
-.1
.0000
.1
-3.2
.0000
-1.3
.0000
.0
District enrollment
.0000
Inverse Mills Ratio
.0017
2.9
No cooler
.0023
2.4
Cooler provided
.0008
1.5
.0013
3.2
Fixed bid
.0023
3.1
.0012
2.0
Escalator
-.0030
-3.5
Straws not included
-.0004
-.2
Straws included
-.0016
-2.4
.0016
-.0004
-.0009
.0004
2.6
-.5
-1.3
.3
-.0011
-2.1
Delivery missing
.0017
1.1
-.0010
-.9
Number deliveries
.0005
1.3
-.0005
-1.6
Cooperative
.0013
.7
Geographic spread
.0000
-.5
.0000
-.9
Variance of population
.0000
-.5
.0000
-3.2
1981 Indicator
.0016
1.6
.0032
1982 Indicator
.0001
.1
.0003
1983 Indicator
.0000
.0
1984 Indicator
.0025
1985 Indicator
.0030
1986 Indicator
1987 Indicator
.0003
.0021
3.5
-.1
-.0002
.0006
-.0012
1.0
-1.3
.0009
.8
.0032
1.6
-.0006
.0006
-.7
.3
-.0001
-.1
-.0035
-1.9
.2
.0000
.0
4.4
.0030
4.4
.4
.0002
.3
.0007
.9
.0006
.9
2.6
.0021
2.5
.0020
2.5
2.9
.0027
3.1
.0027
3.4
.0009
.9
.0014
1.6
.0014
1.7
.0011
1.1
.0016
1.9
.0018
2.2
1988 Indicator
.0040
4.0
.0045
5.3
.0049
6.0
1989 Indicator
.0102
10.3
.0015
13.2
.0116
13.8
1990 Indicator
.0317
31.0
.0325
36.1
.0336
37.5
Bidder-specific effects
No
Yes
Yes
District-specific effects
No
No
Yes
R2
.4891
.7337
.8347
Observations
2,053
2,053
2,053
Degrees of freedom
2,024
1,959
1,580
Notes: Inverse Mills Ratios were computed using the appropriate probit coefficients-i.e.,
sion model uses the base probit coefficients.
the base regres-
278
/
THE RAND JOURNAL
OF ECONOMICS
equation. The third allows for both bidder- and district-specific fixed effects. Districtspecific effects control for any variables that were specific to a school district and
invariant over time and over firms submitting a bid.18
We interpret the results as follows. Bids increase with distance. A bid 100 miles
away would be over one cent higher than in a district adjacent to the plant, all else
equal. Firms in the control group are unlikely to submit bids to districts at these distances from the plant, however. Distributors submit bids that are almost half a cent
higher than those of processors. Firms closest to the district have some competitive
advantage, but that advantage seems to diminish with distance. Firms that are likely to
submit bids are more likely to bid low, as reflected in the Inverse Mills Ratio coefficient. Some of the contract specifications are statistically significant. For example, when
a firm submits an escalating bid as opposed to a fixed bid, the bid level is about .2
cents lower, all else equal, according to the bidder fixed-effect model.
Figure 3 summarizes how control group bids vary with distance. We plot predicted
bids for a hypothetical control group firm holding variables other than distance constant.
The figure incorporates the effect of distance on the probability of submitting a bid
and the resulting impact on the bid. We present the results for the three different
specifications of the control group bidding model. In the district fixed-effect model we
adjust the constant so that the predicted line is comparable to the other models, which
constrain the effects to be the same across all districts.19The effect of distance on bids
submitted ranges between 1 and 2 cents over a hundred miles, with a larger effect in
the third specification.
Bids by the control group increase with distance on average. The bidding data are
consistent with competitive bidding under standard models of spatial competition,
where each firm may exercise local monopoly power. As described above, competition
is localized, because regulation results in little local variation in raw milk prices and
because of relatively high transportation costs.
5. Behavior of defendants
*
Comparison to control group behavior. We now examine the bidding practices
of the three dairies located in Cincinnati and compare them with the control group. We
consider both the bid-submission decision and the level of the bid contingent on submission. Our 1997 working paper discusses the behavior of the other three defendant
firms with operations in southwestern Ohio.
We test for differences between the slope coefficients estimated for control group
bid-submission behavior and those estimated for each of the Cincinnati defendants. For
each of the firms we use the following procedure: (1) append the submission data for
a given defendant to the control group data; (2) estimate a model under the null hypothesis that the slope coefficients are the same for the firm and the control group
firms (the intercept is allowed to differ); (3) estimate a model under the alternative
hypothesis of separate slope coefficients for the defendant; and (4) construct a likelihood ratio test statistic. The test statistics lead us to reject the hypotheses that the
defendants submitted bids according to the control group model at any conventional
significance level. The test statistics were also computed for the specifications with
18 These effects could include the number of schools in a district or any characteristics that remained
constant over time, such as the condition of the roads within the school district, or the traffic density in the
area to the extent it was constant over time, among many other possible factors.
19 We select a district effect so that the predicted bid at zero distance is near the predicted bids at zero
distance for the other specifications. One should not attribute any significance to the absolute difference
between the lines plotted.
(C RAND 1999.
PORTER AND ZONA
I
279
FIGURE 3
PREDICTED LEVELOF SUBMITTED BIDS BY DISTANCE: CONTROL GROUP
.15
Bidderfixed effect
.:
.Bidder
.14-
'0
model
--Base
and districtfixed effect
.13 -
.12
II
0
20
40
60
80
Distance (miles)
bidder fixed effects and with district and bidder fixed effects, and the tests lead to the
same conclusion.
Next, we test for differences in the statistical process generating the level of bids,
using a LaGrange Multiplier test of equal slope coefficients in the bid-level equations.20
For each of the Cincinnati defendants we use the following procedure: (1) compute the
predicted bid for the firm based on the control group bid equation estimates; (2) construct a residual (the difference between actual and predicted bids) for each school
district and year when possible; (3) regress these residuals on the independent variables
in the control group bid equation; and (4) compute an F-statistic to test whether all the
slope coefficients equal zero. The null hypothesis is that the slope coefficients for the
control group data and the defendants are identical. The intercepts could differ, allowing
a firm to have higher or lower bids, on average, under the null. Each of the test statistics
leads to a rejection of the null hypothesis at any conventional significance level. The
test statistic was computed for the other specifications considered, bidder fixed effects
and district and bidder fixed effects, and we reach the same conclusions.
We conducted similar tests of the determinants of the level of bids for each of the
15 control group firms for which sufficiently many observations are available. In all
but three cases, we cannot reject the null hypothesis of identical slope coefficients at
5% significance levels.
To summarize, the bidding behavior of each of the Cincinnati defendants differs
from that of the control group. Behavioral differences are not necessarily the result of
anticompetitive behavior. We are interested in the nature of the differences in behavior
of the defendants from the control group.
Comparison to a collusive strategy. We are faced with a standard problem in
antitrust economics: distinguishing between competitive and collusive behavior.2' In
our previous work in highway construction auctions, we identify collusion by (1) focusing on bid levels rather than submission decisions, because conspirators apparently
submitted complementary bids; (2) identifying differences in the determinants of the
rank order of cartel bids relative to that of other firms; and (3) observing that the rank
E
20 The LM test was used for convenience. Of course, other test procedures (such as likelihood ratio)
could have been used.
21 Baker and Bresnahan (1992) discuss related methods of detecting the exercise of market power.
? RAND 1999.
280
/
THE RAND JOURNAL
OF ECONOMICS
order of cartel bids seemed not to be cost based, in contrast to the rank order of bids
submitted by other firms. Because these differences exist, we conclude that conspiracy
is more likely than not. In a study of a 19th century railway cartel, Porter (1983)
proposes statistical tests to identify whether competition or collusion is more consistent
with observed data based on pricing patterns over time. Some observed price fluctuations do not appear to be the result of demand shifts or changes in observable cost
factors. Instead, the observed pattern of occasional price wars, following periods of
unusually turbulent market shares, is unlikely to be observed under competition. Under
a specific theory of conspiracy, such a pattern is possible. The existence of this pattern
informs an inference of collusion.
Our strategy for the problem at hand is similar. The nondefendant firms behave,
on average, in a manner consistent with competition. The Cincinnati defendants behave
in a statistically significantly different manner relative to the nondefendant firms. Is it
likely that these differences are attributable to idiosyncratic effects of cost or competition? If not, are the differences attributable to independent factors, or are there suspicious patterns of correlation? We now address these two questions.
Since distance is an important factor in the control group model, we focus on that
dimension. Moderate increases in shipping distance are associated with large declines
in the probability of submitting a bid (Figure 2). Similar increases in distance are
associated with increases in bid levels in the control group (about 10% at 70 miles in
Figure 3). We examine the deviations of defendant firms' bidding behavior from the
control group predictions in this context.
Table 6 tabulates the differences between predicted and actual bid submission
behavior for each of the three Cincinnati dairies. The table displays the differences for
several distance bands as a percent of the total number of school districts in each
distance band. For example, column (a) in Table 6 indicates that Coors Brothers submitted 24.2% more bids in districts zero to ten miles from its plant than the control
group data predict (after allowing for a firm-specific effect). If 100 district/years fall
in this band in the data, then about 24 more bids were observed than were predicted.
In this case, the difference is statistically significant.22
There are some notable patterns in the table. First, all three dairies bid more
frequently than the control group model predicts at distances of about 30 miles or less.
Second, Meyer and Trauth bid more frequently at some of the greater distance intervals.
Meyer is unusually likely to bid in districts 100 to 110 miles away, and Trauth in
districts 60 to 80 miles away.
A similar tabulation for residuals based on the difference between the actual submitted bid23 and the control group prediction is displayed in Porter and Zona (1997).
The average percent deviation for a particular distance category can be calculated by
regressing the residuals for each firm on a set of indicator variables for distance categories. A shift in the bid function is not telling from a competitive point of view,24 but
the bids of Meyer and Trauth decrease significantly with distance relative to the control
group prediction. In particular, their bids are significantly lower in the distance ranges
where the residuals of Table 6 indicate that they were unusually likely to bid-Meyer
at 100 to 110 miles, and Trauth at 60 to 80 miles. As further evidence, Table 7 presents
22 We
compute the standard error of the fraction based on an approximation to a Bernoulli random
variable. For the purposes of this calculation we ignore the fact that the predicted probability is a random
variable with associated uncertainty.
23 By actual bid, we are referring to the standardized bids rather than any element of the vector of bids
that the firm may have submitted.
24 It is hard to explain why bids that are substantially above average can persist in a competitive market,
however.
(C)RAND
1999.
PORTER AND ZONA
TABLE 6
/
281
Percent Deviations in Predicted and Actual Bid Submissions by
Distance: Cincinnati Dairies
Distance in Miles
Coors Brothers
Meyer
Louis Trauth
(a)
(b)
(c)
24.2% >
5.6% >
10-20
42.9%
8.2%
15.2% >
20-30
22.9% >
18.5% >
20.6% >
30-40
-17.1% <
18.6% >
.1%
40-50
-9.5% <
-2.2%
50-60
-6.0%
-5.5%
60-70
-6.0%
-18.6% <
47.1% >
70-80
-4.9% <
-25.0% <
10.0% >
80-90
-2.4% <
-17.5% <
-2.5% <
-11.8% <
0-10
>
7.0% >
-4.3%
6.9%
90-100
-1.7%
-7.7% <
100-110
-1.3%
30.7%
110-120
-.6%
.5%
120-130
-.5%
-.9%
-3.6% <
130-140
-.2%
-.3%
-2.0%
140-150
-.2%
-.1%
-1.2%
>
8.7% >
-4.2% <
Notes: A "<" indicates that actual bidding was statistically significantly below the predicted level. A ">" indicates that actual bidding was statistically significantly above the
predicted level. Standard error of each prediction was computed using p*(l - p) approximation to variance of a Bermoulli random variable. Probit model incorporating no fixed
effects were used for these calculations. The other models present similar patterns.
bid-level regressions, comparable to the control group regressions in Table 5, for the
three Cincinnati dairies. For both Meyer and Trauth, which submitted distant bids, bid
levels are a significantly decreasing function of distance. In contrast, the distance coefficient is significantly positive for the control group as a whole. Further, among the
15 most active nondefendants, only one's bid levels decrease significantly with distance
in the region where its plant is not closest.
Table 7 also indicates that the bids of the three Cincinnati dairies were lower in
1983 and 1989 than in the preceding years, in contrast to the control group. This pattern
is consistent with the testimony, cited above, that there was a breakdown in the cartel
in those two years.
To see whether firms behave in a parallel fashion, we test for statistical independence in the probability of bidding for the defendant firms using a standard pairwise
procedure.25 Under the null hypothesis of independent action based on public information and the maintained specifications of our probit submission model, knowledge
of whether one particular firm bids should not help predict whether another firm has
also bid. Under an alternative hypothesis of either complementary bidding or territorial
allocation, the submission decisions are interrelated, and knowing how one cartel member behaves helps predict what the other does. In the case of complementary bidding,
25
See Greene (1997) or Kiefer (1982).
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TABLE 7
OF ECONOMICS
Estimated Coefficients: Cincinnati Dairies Bid Level
Coors Brothers
Variable Name
Meyer
Coefficient
t-statistic
Coefficient
Trauth
t-statistic
Coefficient
t-statistic
(a)
(b)
(c)
(d)
(e)
(f)
Constant
.1194
5.6
.1327
30.0
.1219
23.8
Distance
.0012
2.2
-.0001
-1.6
Closest
.0315
1.8
-.0042
-1.7
Closest*distance
District enrollment
-.0007
.0000
-1.4
.0001
-.5
.0000
Inverse Mills Ratio
-.0093
-1.5
No cooler
-.0013
-.2
Cooler provided
.0088
Fixed bid
-.0067
Escalator
-.0004
Straws not included
-.0021
Straws included
- .0072
Delivery missing
Number deliveries
2.6
-2.6
.0
.0001
-.0057
2.1
-2.4
.1
-2.6
.0015
1.1
.0012
.9
-.0007
-.3
-.0001
-2.4
.0026
.9
.0000
.5
.0000
-2.7
.0016
1.1
.0041
1.5
.0004
.2
-.0023
.0035
-1.7
1.2
-.9
.0022
1.3
-2.2
.0010
.7
.0013
.8
-.0056
-.6
.0070
2.1
.0038
1.0
-.0029
-1.1
2.6
.0010
.9
-.4
.0011
.3
.0000
- .8
.0000
.2
.0178
5.1
1.4
.0028
Cooperative
.0166
Geographic spread
.0000
-.4
.0000
Variance of population
.0000
-.2
.0000
-.4
.0090
-.5
-3.3
1981 Indicator
1982 Indicator
-.0058
-1.4
-.0014
-.0008
.8
1.7
1983 Indicator
-1.6
-7.2
-.0089
-3.3
.0056
1.9
-.0069
-2.3
1984 Indicator
.0039
1985 Indicator
.0028
.6
-.0049
-1.8
.0076
2.5
1986 Indicator
.0071
1.7
-.0032
-1.2
.0097
3.3
1987 Indicator
.0137
3.2
-.0024
-.9
.0117
4.0
1988 Indicator
.0214
5.0
.0142
4.8
1989 Indicator
-.0010
1990 Indicator
.0322
R2
.9
-.0044
-.0193
.0073
-.2
7.1
.0035
-.0043
.0204
1.3
-1.6
7.1
.0111
3.5
.0426
13.9
.6747
.5439
.6546
Observations
128
411
371
Degrees of freedom
102
384
344
Notes: Inverse Mills Ratios were computed using the appropriate probit coefficients-i.e.,
sion model uses the base probit coefficients.
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283
if one cartel member bids, then other ring members also bid. In this case the unexplained portion of the competitive bidding equation is positively correlated across cartel
firms. In the case of territorial allocation, if a particular cartel member bids, then other
cartel members will tend not to bid. Then the unexplained portion of the competitive
bidding equation is negatively correlated across cartel members. We consider the Spearman correlation coefficients computed using pairs of weighted residuals based on the
control group probit models. The test for independence, or zero correlation, that we
use has power against both alternatives.26The results show that the unexplained portion
of the Coors submission decision was positively correlated with the unexplained portion
of the Meyer decision, with a Spearman correlation coefficient of .58. The Spearman
statistic is .43 for Coors and Trauth, and .54 for Meyer and Trauth. All three Spearman
correlation coefficients are significant at any standard level.
We perform a similar analysis for residuals based on the level of the submitted
bids. We calculate the Spearman correlation coefficient and the results of a test for
pairwise independence of bidding behavior.27Under the null hypothesis of independent
action based on public information and the maintained specification of the bid-level
equations, knowledge of what one particular firm bid does not help predict what another
firm will bid. Under an alternative hypothesis of complementary bidding, knowing that
one cartel member bid above the predicted level helps predict whether other cartel
firms will bid above that level. If one cartel member bids high, then other ring members
are also likely to bid high.28 The pairwise Spearman correlation coefficients are .66 for
Coors and Meyer, .54 for Coors and Trauth, and .67 for Meyer and Trauth. All are
significantly different from zero. The sample sizes are 126, 114, and 267, respectively.
Our results support the testimony by representatives of Meyer and Coors. The
behavior of Coors, Meyer, and Trauth are consistent with a complementary bidding
scheme in the area close to their plants, since more bids than expected are submitted
at distances of less than 30 miles. Further, these bids tend to be relatively high. The
Spearman correlation results for these three firms are also consistent with a complementary bidding scheme. There are statistically significant correlations in bid submissions by these firms, suggesting that if one of these firms bids then the others also tend
to bid (to a greater extent than their proximity, size, and the like would predict). In
addition, when these firms bid on the same districts in the same years, their bids tend
to move together (to a greater extent than their proximity, size, and the like would
predict). It is difficult to craft a competitive story where bid levels decrease with
distance, as they do for these firms. The behavior of the Cincinnati dairies is suspicious,
even without a comparison to the behavior of nondefendant firms. On the basis of our
results, we believe that the collective behavior of these three firms is best characterized
as collusive.
6. Effect of collusion on prices paid
* Assuming that a conspiracy involving the southwestern Ohio defendants was in
force throughout the 1980s, what are the likely damages? Our methodology for estimating damages to the plaintiff school districts involves determining the percent markup in price attributable to collusion in various auctions.
26
The test statistic may also reject the null hypothesis of independent action if an important variable
was omitted from the control group probit model that affects these firms similarly.
27
The test statistic is the Spearman correlation coefficient computed for the residuals based on the
control group bidding model for each pair of defendants.
28
This test has little power to reject the null under an effective territorial allocation conspiracy, if there
are no complementary
bids, because we might not observe bids from ring members in the same district in
the same year.
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We estimate using OLS the effect of variables that determine costs for the most
efficient provider and other variables on the standardized price of the winning bid for
district-year combinations in our sample. Table 8 describes the variables used in the
analysis. The sample covers about 400 districts, including those outside the southwestern region. Annual dummy variables control for changes in the raw milk price,
changes in uncertainties in the raw milk price over time, and changes in the costs of
packaging year to year. We also control for district enrollment, the number of deliveries,
and other characteristics of the school district. We include two relative location variables. One accounts for the effects of the distance from the closest plant to the school
TABLE 8
Variable Definitions
Dependent Variable
Log of standard bid
The natural logarithm of the standardized bid of the winner of the district.
Independent Variables
Equivalent firms
The equivalent number of equal-sized firms assuming competition, based
on the Herfindhal index described in the text.
Equivalent firmsA2
The square of Equivalent firms.
Delta
The difference between the equivalent number of equal-sized firms assuming competition and the equivalent number of equal-sized firms
assuming collusion.
DeltaA2
The square of Delta.
Closest
Approximate distance (in miles) between the district and the closest
plant.
Second closest
Approximate distance (in miles) between the district and the secondclosest plant.
Log of district
enrollment
The natural logarithm of the number of students enrolled in the district
in the 1993-1994 school year.
Number deliveries
When available, number of deliveries per week (otherwise Number deliveries is zero and Delivery missing is one).
Indicator Variables
No cooler
One if information on coolers available and no cooler supplied, zero otherwise.
Cooler provided
One if information on coolers available and cooler supplied, zero otherwise.
Fixed bid
One if information on escalator clauses available and bid is fixed, zero
otherwise.
Escalator
One if information on escalator clauses available and bid is not fixed,
zero otherwise.
Straws not included
One if information on straws available and no straws supplied, zero otherwise.
Straws included
One if information on straws available and straws supplied, zero otherwise.
Delivery missing
One if no information available on deliveries per week, zero otherwise.
Region
One if the district is in the western part of Ohio, zero otherwise.
1981-1990
One if bid was made in the indicated year, zero otherwise.
?) RAND 1999.
PORTER AND ZONA
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285
district, as we expect price to be increasing with distance to the closest plant as shipping
costs increase. The second is the distance between the district and the second-closest
plant. When the latter distance is large, all else equal, we expect the price paid by the
school district to be higher, as the closest firm can charge a higher price.
We also control for the level of competition in each of the markets. We measure
competition in these markets using the number of equivalent firms defined by the
inverse of the Herfindahl index.29 We expect higher prices in more concentrated markets
where fewer firms compete with one another. There is no reason to expect a linear
relationship between price and the competition index, and we also include a quadratic
term. We expect changes in the competition index to have a diminishing effect on price
in competitive markets.
If there is collusion in these markets, prices are on average above the competitive
level. Therefore, we include Delta, an index of collusion based on the number of alleged
conspirators who are within 75 miles of the school district in question.30 There is also
no reason to expect a linear relationship between the measure of the degree of collusion
in these markets and price, and we include a quadratic term. We also include an interaction between the collusion index and the number of equivalent firms, since the effect
of a restriction of competition will depend on the initial level of competition. We
interact these indices of collusion with the annual dummy variables so as to measure,
to the extent they exist, differences in the degree of collusion from year to year.
In Table 9 we display some of the estimated coefficients for the regression. The
dependent variable is the logarithm of the winning standardized bid for 2% chocolate
milk. In general, the coefficients are of the anticipated signs and statistically significant.
The number of firms in the market, as measured by the two variables described above,
indicate a significant effect of concentration on the price paid by the school districts.
In Table 10 we display the estimated regression coefficients for the variables related
to collusion. We estimate separate coefficients for Delta and its interactions for each
year. If the conspiracy was more effective in some years than in others, then the annual
differences can be reflected. The predicted increase in price caused by collusion in
these auctions is measured as the difference between the predicted value when indices
of collusion are included and the predicted value that is obtained when all indices of
collusion are set to zero. The difference is the predicted percentage change in standardized price resulting from collusion. Column (d) in Table 10 reports the estimated
effect of collusion on the average district in southwestern Ohio by year. Column (e) in
Table 10 reports the estimated effect of collusion on the average district in southwestern
Ohio conditional on incumbency by a defendant, by year. A district has an incumbent
defendant in a given year if a defendant won the supply contract in the previous year.
Note that the estimated effect of collusion is small in 1983-1984 and after 1989,
according to both columns (d) and (e), consistent with the statements of market participants, and consistent with the results in Table 7.
The average effect of collusion on price is an increase of about 6.5%. This is
consistent with our estimate of the average effect of distance on school milk bids. If,
for example, two nearby firms conspired to serve a district adjacent to their plants and
faced competition only from firms located at least 50 miles from that school district,
29
The Herfindahl indices are based on each producer's fraction of school milk processing plants within
75 miles of the district. Given ten different processors, each with a plant in the area, the Herfindahl is 1/10
and our competition measure is 10. Given ten dissimilar firms, some of which control more than one plant,
the Herfindahl exceeds 1/10, and the number of equivalent firms will be less than 10.
30 The index of collusion
is the difference between the number of equivalent firms assuming competition
and the number of equivalent firms assuming collusion.
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TABLE 9
Estimated Market Price Equation
Variable
Coefficient
t-statistic
(a)
(b)
-1.7794
114.3
Equivalent firms
-.0150
6.9
Equivalent firmsA2
-.0003
1.1
Closest
-.0004
3.2
Constant
Second closest
Log of district enrollment
.0003
-.0134
3.4
13.7
No cooler
.0041
.9
Cooler provided
.0076
3.3
Fixed bid
-.0024
.3
Escalator
-.0096
3.0
Straws not included
-.0020
.9
Straws included
.0033
1.1
Number deliveries
.0007
.8
Delivery missing
-.0009
.4
1981 Indicator
-.0303
1.1
1982 Indicator
-.0572
1.4
1983 Indicator
-.0744
4.1
1984 Indicator
-.0814
5.7
1985 Indicator
-.0593
3.3
1986 Indicator
-.0987
7.3
1987 Indicator
-.1118
8.3
1988 Indicator
-.0927
6.3
1989 Indicator
-.0367
1990 Indicator
.0992
Observations
3,431
Degrees of freedom
.2
3,407
14.2
.6239
Note: Model is estimated using data from all districts. The model controls
for the effects of collusion by including the variable Delta and related
variables. The estimated effect of collusion is presented on the next table.
then prices could be about half a cent (or about 5%) higher than they otherwise would
be. Districts further from potential competitors face higher markups, and districts closer
to the plants of competitive firms would pay lower markups.
7. Summary
* The empirical work in this article exploits specific features of school milk markets,
and we would not necessarily advocate using similar methods to study other auction
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TABLE 10
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287
Estimated Effect of Collusion on the Price Paid by School Districts
School
Year
Estimated
Delta
Coefficient
(a)
(b)
(c)
(d)
(e)
1980-1981
-.00140
-.00150
.00163
3.0%
3.2%
Estimated DeltaA2
Coefficient
Estimated
Interaction
Coefficient
Estimated
Average
Effect
Estimated Effect
Conditional on
Incumbency
1981-1982
.01304
.01167
.00103
11.3%
40.2%
1982-1983
.02731
.00225
.00098
8.6%
23.2%
1983-1984
.02995
.00156
4.5%
1.1%
1984-1985
.02147
1985-1986
.02684
1986-1987
.02425
1987-1988
.00368
-.00970
.00106
.00199
6.7%
19.7%
.00122
5.4%
11.5%
.00173
.00130
6.5%
20.5%
.02901
.00060
3.3%
49.0%
2.9%
29.4%
-.00230
1988-1989
-.02270
.03636
.00229
1989-1990
-.04940
.01340
.00410
-1.6%
1990-1991
-.02010
.00634
-.3%
-.01260
3.4%
-8.3%
Note: The table reports the estimated coefficients on the collusion indices described in the text. We have
estimated the effect of collusion based on the mean values of the variables used in the regression. The results
reported in column (d) are the expected markups for all districts over competitive prices, in percent.
markets. For example, an unusual feature of Ohio school milk auctions is that few bids
are submitted, even relative to school milk auctions in other states. An important component of strategic decisions in this market is whether to submit a bid.
We also focus on the role of distance in bidding decisions. Processed milk is
relatively expensive to ship, and competition is localized. We emphasize the fact that
two of the three Cincinnati dairies tend to submit relatively low bids for distant school
district contracts, and yet submit higher bids close to their plant. We document these
patterns with a reduced-form bidding model that ignores characteristics of potential
rivals, except to the extent that we control for district-specific fixed effects, in large
part because we cannot be sure whether other firms were indeed rivals. In the case of
the Cincinnati dairies, this omission should bias the results in their favor. Had they
competed aggressively, bids for nearby districts should have been relatively low, as
there were three local potential suppliers. Yet the local Cincinnati prices were relatively
high, especially in comparison with the distant bids of the Cincinnati dairies. An inverted price umbrella is consistent with local monopoly power, but local monopoly
power in Cincinnati is consistent only with collusion.
The detection of collusion in auction or other markets is necessarily case specific,
as the details of an optimal collusive scheme depend on a number of factors. The study
of auction markets can nevertheless inform the study of collusion in other markets.
Data are often available on the bids of all participants in an auction, and the auction
rules define the set of strategic considerations. Under these circumstances, a detailed
study of strategic behavior is feasible, and it may be possible to isolate behavior that
is inconsistent with competition. A contribution of this article is to describe some
features of a conspiracy among a group of neighboring suppliers, when the conspirators
are protected locally from competition by the transportation costs borne by distant
suppliers, and when the conspirators compete on a relatively equal footing with other
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THE RAND JOURNAL OF ECONOMICS
firms outside their local market. Our methods highlight the inverted price umbrella
associated with lower prices at more distant locations that is consistent with a local
conspiracy and inconsistent with competitive behavior.
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