Discussion Paper No. 710

COLLUSION IN
REPEATED PROCUREMENT AUCTION:
A STUDY OF A PAVING MARKET
IN JAPAN
Rieko Ishii
The Tenth ISER-Moriguchi Prize (2008)
Awarded Paper

March 2008

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

Collusion in Repeated Procurement Auction:
A Study of a Paving Market in Japan∗
Rieko Ishii†
March 25, 2008

Abstract
We examine auction data to determine if bid rigging presents in procurement auctions for paving works in Ibaraki City, Osaka, Japan. We ﬁrst showthat sporadic bidding wars are caused by the participation of potential “outsiders.” Assuming that the ring is all-inclusive if the auction is not the bidding
war, we estimate the scheme by which the ring allocates a win to its members.
It is found that the ring tends to select a bidder whose winless period is long
and whose winning amount in the past is small relative to other bidders.
JEL Classiﬁcation D44, H57, L44
Keywords: Bid rigging, repeated auction.

∗

I am grateful to Masaki Aoyagi, Masahiro Ashiya, Daiji Kawaguchi, Yukihiro Kidokoro, Miki
Kohara, Akihiko Matsui, Shinichi Sakata, Tadashi Sekiguchi, and Noriyuki Yanagawa for helpful
suggestions and discussions. I also thank seminar participants at Kyoto University, Nagoya University, Nihon University, Osaka University, University of Tokyo, Toyama University, Japanese Fair
Trade Commission, National Graduate Institute for Policy Studies, Design Science Young Seminarin Osaka and Second Applied Econometric Conference in Miura for comments and discussions. Allerrors are mine. This paper is awarded the 10th ISER-Moriguchi Prize. Financial Support fromthe Zengin Foundation for Studies on Economics and Finance is gratefully acknowledged.
†
Institute of Social and Economic Research, Osaka University, 6-1, Mihogaoka, Ibaraki-shi,
Osaka, 567-0047, JAPAN; E-mail: rishii@iser.osaka-u.ac.jp

1

Introduction

Bid rigging is pervasive in public procurement auctions. As it becomes a major social
problem and attracts more public attention, the inner working of bidding rings is
gradually revealed by journalists, lawyers and industry experts some of whom wereformally involved in ring activities themselves.1 In a typical process of bid rigging,
the ring bidders gather in prior to each auction and discuss who win the auction.
According to Suzuki (2004) who documents all bid rigging cases between 1947 and
2000, typically the ring has its own “collusion scheme”, the rule under which thering chooses a winner.
Suzuki’s survey of a wide variety of collusion schemes reveals that a numberof rings use the history of auctions (such as the date, the identity of the winnerand other participants, and the winning price) as a basis for allocating contracts
to their members. For example, in a bid rigging case of water meter producers in1992 in Osaka Prefecture, they calculate each ring bidder’s win amount in the pastaccording to a particular calculation formula, and then, the bidder who has theleast win amount among the ring bidders is chosen as the winner. In another caseof pesticide suppliers in 1998 in Osaka Prefecture, the ring used the bid rotation
scheme, in which the ring members take turns being the winner in order.
We examine the public auction data of a paving market in Japan, in order todetermine whether the bid rigging occurred. Speciﬁcally, we illustrate the correlation
between the current auction result and the past results, which is more explained bycollusion than competition. If the ring exists and uses some collusion scheme which
is based on the history, there must be a link between each auction result and thehistory.
It has been pointed out that a correlation between the current result and thepast results is not necessarily due to collusion. Particularly, when bidders’ costfunctions exhibit decreasing returns to scale, bid rotation can also result from acompetitive bidding behavior. That is, ﬁrms with idle capacity have lower marginal
cost and hence, are more likely to win a contract than those with ongoing contracts(Zona (1986), Porter and Zona (1993), Porter (2005)). Our approach discriminates
between collusive and non-collusive bid rotation by separating the eﬀect of capacity
1

Hironaka (1994), Kato (2005). McMillan (1991) also documents the formation and the operation of Japanese bid rigging.

1

utilization from that of the collusion scheme. We construct variables for the usedcapacity and for the priority index that determines the turn in the collusion scheme,
separately, and analyze their eﬀect on the events of winning or losing. We candiscriminate competition and collusion by testing the independence of the eventsfrom the priority measure of the rotation scheme.
We look at auctions for road-paving works in Ibaraki City, Osaka, Japan in thefour-year period between 2002 and 2005. A remarkable characteristic of this market
is consistently high winning prices with the exception of sporadic bidding wars.2
Though there is no legal case of bid rigging ﬁled against the bidders participatingin these auctions, it suggests the coexistence of collusion and cartel breakdown.
We ﬁrst observe each incident of the bidding war and its participants, and ﬁndthat the bidding war during the data period mainly occurred when either of two
speciﬁc ﬁrms was present.3 It is supposed that the bidding wars were between thering and a small number of outsiders in the market, and that all the ring bidders
submitted low bids in order to prevent the outsiders from winning. We then examine
the data to see how the ring selects the winner among its members assuming thatthe high prices were maintained by an all-inclusive ring which allocates contracts to
its members by some prespeciﬁed rule. We ﬁnd that the ring tends to assign a win
to its member whose duration of no win is long and whose amount of win is small.
Theories of collusion in auctions highlight the role of pre-auction meeting ofbidders. The seminal paper by McAfee and McMillan (1992) show that the mosteﬃcient bidder collusion in a ﬁrst price auction is that the ring member with theminimum cost bids at the reserve price while the other members bid high. Incentives
are provided through monetary transfers from the winner to the losers. McAfee andMcMillan also characterize eﬃcient collusion when no side transfer is possible. It
is a static scheme in which the choice of the designed winner is independent of thehistory. The analysis is extended to a repeated framework by Aoyagi (2003) andSkrzypacz and Hopenhayn (2004), who analyze collusion without side transfer in
repeated auctions. In contrast to McAfee and McMillan’s static bid rotation, they
construct dynamic bid rotation schemes in which bid coordination is based on past2

In this paper, we use the term, a “bidding war” to indicate an auction whose winning price issigniﬁcantly lower than the other prices.
3
Yanagawa et.al. (2005) reports that bidding wars tend to occur in March, the end of the ﬁscal
year. We observe no such seasonal pattern of bidding wars in our data.

2

history.
In contrast to the theoretical literature, the inner working of the ring has attracted little attention in the empirical literature although there is much empirical
work on bid rigging aiming at detecting collusion in procurement auctions.4 Mostof them illustrate how the bidding behavior of a set of collusive bidders is diﬀerent
from competitive behavior.
Porter and Zona (1993) study auctions for paving works on Long Island, New
York. They divide the bid data into collusive bids and competitive bids, knowing
which bidder is collusive. In each dataset, they examine if the impact of the cost
factors such as the capacity utilization on the realization probability of the bid ranks
is consistent with competitive equilibrium. They ﬁnd that in the collusive data theestimated impacts of the cost factors on the realization of the ﬁrst rank and on thehigher ranks are diﬀerent, while there is not such diﬀerence in the competitive data.
Porter and Zona (1999) analyze the ring members’ bidding behavior in school milk
procurement auctions in Ohio State. They focus on the relationship between the bids
and the distance between schools and bidders, and ﬁnd that the collusive bids andthe competitive bids reﬂect the distance diﬀerently, suggesting that the ring allocatescontracts by territory. Bajari and Ye (2003) observe the violation of two conditions,conditional independence and exchangeability, that a competitive bidding strategy
must satisfy, using the auction data for highway construction works in the Midwest.
These approaches make full use of observable cost asymmetry among bidders bymeasuring ﬁrms’ used capacity or the distance between the oﬃce and the work site.
The distinguishing feature of this paper is that we illustrate how the outcome ofauctions is consistent with a particular collusion scheme. In contrast to the previous works, we exclusively examine the identities of the winner and the participants,
ignoring the bid levels. Because the ring is very likely to be all-inclusive in mostauctions as described in Section 3.1, and if so, all the bids are phony and the bid
levels bring little information about the cost of the bidders or about how they collude. In that case, instead, the identity of the winner perfectly reﬂects the collusive
agreement.
The collusion schemes considered in this paper are most closely related to thoseanalyzed by Skrzypacz and Hopenhayn (2004) and Pesendorfer (2000). Skrzypacz
4Harrington (2005) provides a thorough survey of this ﬁeld.

3and Hopenhayn (2004) propose a collusion scheme named a “chips mechanism”, inwhich the winner gives one chip to each loser, and when a bidder runs out of chips
he is supposed to allow other bidders to win for a speciﬁc number of periods. An
important factor in the scheme is the number of winning and losing in the past. It
is known that such a mechanism was indeed used by some bidding rings in Japan,
and the aim of the paper includes detecting this type of scheme. We name it the“contribution point scheme”. Pesendorfer (2000) studies the diﬀerence between two
forms of cartel, in which one cartel in Florida uses side payments and the other in
Texas does not. He ﬁnds that the cartel without side payments maintains relatively
constant market shares, despite some eﬃciency losses from not allocating a contract
to the low cost ﬁrm, in order to maintain internal discipline. One of our targets ofdetection is the scheme which keeps the balance of the members’ total revenues in
the past, which is the very scheme used by the cartel in Texas.
The paper is organized as follows. In Section 2, we describe the market, theauction procedure, and the data we analyze. In Section 3, we document the bidding
war and analyze its cause. We also describe the collusion schemes that we expect
to be used by the ring. In Section 4, we show the empirical model to estimate thecollusion scheme, and the estimation results. We conclude in Section 5.

2

The market description

This study looks at auctions for paving contracts awarded by Ibaraki City, Osaka,
Japan, during four years between April 2002 and March 2006. In the data period,
Ibaraki City awards 139 contracts through auction. Typically, the contracted work
involves the resurfacing of local roads for hundreds of meters. The winning pricevaries from 1 to 40 million yen, with an average of about 7 million yen. Figure 1
shows the winning price of each auction. An annual total of 2-3 hundred million yen
is contracted out.
Thirteen ﬁrms participated in the auctions in the data period with one ﬁrm
exiting early. Most ﬁrms do paving work as their primary business, and othercivil engineering works as secondary. Nine ﬁrms are local in the sense that their
headquarters are located within Ibaraki City, and the rest that we call “out-of-town”
ﬁrms have only a branch in the city. Table 3 describes the ﬁrms.

4

2.1

Auction procedure

The auction is in the ﬁrst price sealed bid format with a maximum acceptable(reserve) price and a minimum acceptable price (henceforth a minimum price). The
minimum price is set for the purpose of prevent ﬁrms from doing low quality works.
A bidder with the lowest bid wins the contract if and only if his bid is between
the minimum price and the reserve price. Auction proceeds as follows: Prior toeach auction, the city oﬃcials estimate how much it will cost an average ﬁrm tocomplete the work, taking into account material prices and the budget of the city.
The estimated price plus some proﬁt margin is then used as the reserve price inthe auction. The minimum price is set at about 80% of the reserve price. The city
announces the reserve price and the minimum price one week before the auction.
Actual participants of the auction are chosen by the city. A limited number ofﬁrms are nominated from a list of candidates one week before each auction. Technicaldocuments, which are needed to estimate the cost, are distributed to eligible bidders
at the city oﬃce at the announced date and time prior to the auction. It gives thebidders a chance to see each other in advance and to know whether there is an
outsider. On the date of the auction, bidders gather and submit sealed bids. If
there are more than two bidders who submit the lowest bid, then the winner isdetermined by a public lottery. Bidders can refrain from bidding. In our data, 10
bidders refrained from bidding in four auctions (see Table 2).
When a bidder wins an auction, he would earn proﬁt equal to the winning priceminus the cost of doing the work. The cost of each contract is private informationof each bidder, and hence, each auction is a private value auction. However, a largepart of a bidder’s cost can be inferred by other bidders, since they operate in themarket for decades and the work is done according to a detailed speciﬁcation givenby the city oﬃcials.
The number of nominated bidders depends on the reserve price of the auction.
When the reserve price is high, the number of bidders tends to be large. Table 1
summarizes the number of bids per auction.

5

2.2

The data source

We have two data sources, bid data and corporate data. The bid data were provided
by Ibaraki City Oﬃce. The bid data contain the following information on every
project awarded: date of auctions, submitted bids, names of bidders, the reserve
price and the minimum price, the starting and ending dates of projects, and locationof projects.
The corporate data of each ﬁrm were provided by Construction Industry Information Center’s database. The corporate data contain the number of years of
running, number of technical workers, annual sales, and proﬁt per sales.
In the analyses, we used a variable which represents bidder’s used capacity. It
is not suﬃcient in capturing the ﬁrm’s used capacity as long as we see only thecontracts bought by Ibaraki City, since the ﬁrms do the works bought by private
ﬁrms and other local governments neighboring Ibaraki City. In calculating eachbidder’s used capacity, we used the data of contracts which were awarded by Osaka
Prefectural Government, as well as by Ibaraki City. Osaka Prefectural Governmentis one of the major clients of ﬁrms, and provides contract data through its website.
The deﬁnition of variables is shown in Table 4.

3

Possible collusion scheme

3.1

Agreement to fight against outsiders

We describe a series of bidding wars observed in the data and infer the cause. The
observation in this section shows that most bidders bid at the minimum price in thoseauctions that result in the bidding war, and that such a bidding war is triggered by
the presence of speciﬁc ﬁrms among the participants. It is natural to think that an
implicit agreement is behind such coordinated reversion to the minimum price. It
is likely that the ring bidders have an agreement to bid the minimum price when
they face an outsider in an auction. As mentioned previously, the bidders meet eachother prior to the auction. Once the existence of an outsider is conﬁrmed, all of thering bidders must be instructed to bid at the minimum price in the auction.55Bajari and Ye (2003) models a cartel behavior when it faces outsiders in auctions. In theirmodel, the member with the minimum cost in the cartel submits a serious bid, and the othermember submit phony high bids. In contrast to the model, all the ring members seem to besupposed to submit the lowest possible bid when they face an outsider in the market we analyze.

6Figure 2 shows the variance of “normalized bids” of each auction, and Figure 3
shows the “normalized winning bids” of each auction. “Normalized” means that thebids are divided by the reserve price. As Figure 3 shows, in 123 out of 139 auctions,winning prices are in the neighborhood of 93% of the reserve price.
On the other hand, remaining 16 contracts were won at the minimum price which
was set at 77-85% of the reserve price. We identify these 16 auctions as the bidding
wars. In no auction was the winning bid between 85% and 90% of the reserve price,and therefore, the distribution of winning bids has a gap as shown in Figure 3.
Furthermore, in 13 incidents of the bidding war, the variance of the normalized bids
is zero as shown in Figure 2, indicating that all the bids were at the minimum priceand that the winner was determined by a public lottery.
We further show that bidding wars are mainly caused by the participation ofeither of two speciﬁc ﬁrms. Figure 4 shows the participation of every ﬁrm in every
auction. The X axis shows auction ID, t = 1, 2, ..., 139, and the Y axis shows ﬁrm
ID, i = 1, 2, ..., 13. A white dot in the ﬁgure indicates that the auction was a bidding
war, and a black dot indicates that it was not. The square around a dot indicates
the winner: bidder y wins in auction x if there is a square at (x, y). For example,
the black dot with a frame at coordinate (15, 2) implies that ﬁrm 2 submitted a bid
and won in auction 15, and that the auction was not a bidding war.
In Figure 4, there exists a sequence of 4 white dots from coordinate (2, 13) tocoordinate (10, 13), which are indicated as A. The dots indicate the bidding wars
which may have been caused by the participation of ﬁrm 13. These auctions took
place during 3 months from May 2002 to July 2002. No bidding war was observed in
the absence of ﬁrm 13 in this period. It can be inferred that ﬁrm 13 is an outsider.
Firm 13 disappeared after auction 11 suggesting that it went out of the market,
perhaps because of the bidding war.
There exists another sequence of 8 white dots from coordinate (68, 8) to coordinate (81, 8) indicated as B. These incidents of the bidding war during 5 months
from May 2004 to October 2004, were probably caused by the participation of ﬁrm
8. The other 53 auctions in which ﬁrm 8 bid did not result in the bidding war.
This may suggest that ﬁrm 8 stayed out of the ring only during the 5 months, andreconciled with the ring after that.
We ﬁnd that the bidding war took place whenever ﬁrm 13 was present and in7

a series of auctions during 5 months where ﬁrm 8 was present. This suggests theexistence of a ring agreement to bid the minimum price when one of the two ﬁrms
participated. We further infer that the ring must have been all-inclusive after ﬁrm
13’s exit, except the ﬁve months in which ﬁrm 8 stayed out of the ring. 12 incidentsof the bidding wars out of 16 are explained: 4 of them were caused by ﬁrm 13, and8 were caused by ﬁrm 8. However, 4 incidents: auction 28, 78, 131 and 139 are left
unexplained. A possible interpretation is that the ring bidders failed in reaching anagreement and switched to a competitive bidding temporarily.
The exit of ﬁrm 13 suggests that the bidding war worked as predation. It is likelythat winning a contract at the minimum price is unproﬁtable for most of the ﬁrms,
since the proﬁt-to-sales ratio is 0.27% on average (Table 3). If so, we have a case of“deep pocket predation” which is aimed at driving the outsiders out while making aloss. When the number of the ring members is large relative to that of the outsiders,
the loss is not so severe for the ring members since they can take turns bearing theloss and recover by earning proﬁt of collusion in the absence of the outsiders. In
contrast, the bidding war brings about a ﬁnancial diﬃculty to the outsider since heeither win a contract with a very low price in auctions or loses. Sooner or later, theoutsiders have to give up and leave the market or join the ring, allowing the ring to
be all inclusive and recoup losses.
Predatory bidding war in auctions is not so rare in Japan. In a case of a bridge
construction cartel which allocated public contracts to 47 ﬁrms for years, the cartel
was nearly all-inclusive in the bridge construction market. It is reported that cartel
members submitted extremely low bids, which were sometimes as low as 60% of thereserve price when they faced an outsider in auctions, whereas they bid the reserve
price in the absence of the outsider. The low bids were aimed at preventing theoutsider from winning, even though they imply a negative proﬁt from winning. The
member who won in the bidding war was compensated with a proﬁtable contract
afterwards.(Asahi Shin bun May 19, 2005, Kahoku Shin pou, May 25, 2005.)
Meanwhile, the serial incidents of the bidding war in which ﬁrm 8 was targeted
can be interpreted as a punishment. The win of ﬁrm 8 in Auction No. 65, which
is just before the start of the incidents, may be the betrayal that triggered thepunishment.6
6

If so, the punishment seems to be so called “stick-and-carrot” type, which gives a severe damage8

It is noteworthy that the normalized winning bids are not so high in auctions
that are not the bidding war: They are below 95% with one exception. We think thisis due to the warning made by the city oﬃcials. We ﬁnd a notice near the auction
room at the city oﬃce, which says “in case that the normalized winning bid is higher
than a certain level, signing the contract is postponed and bidders are required toshow their cost estimates”. Knowing that collusion will be under investigation incase of a high price, the ring must lower the price elaborately.
Note that the bidding wars cannot be an evidence of collusion by itself. There
still remains a possibility that there is no agreement among bidders.7 However, theobservation described above gives a strong support for the assumption we use in themain analysis that all the bidders belong to the ring if the auction is not the bidding
war.

3.2

Operation of a collusion scheme as a comparison of bidders’ priority

We next hypothesize the rules under which the winner is selected when the ring is allinclusive in the auction. These schemes are based on comparing its members’ priority
to win the contract. We focus on the following four classes of history dependent
schemes that are common in the past bid rigging cases.
1) Simple rotation
In a simple rotation scheme, the ring members rotate the winning right. In
the presence of the nomination process by the local government, simple rotation
chooses the winner based on the duration of winless period sustained by eachbidder. That is , a bidder is chosen as the winner if his winless period up to thedate is longer than that of any other bidder in the ring.
2) Revenue equalization
A revenue equalization scheme maintains equity of the revenue of its members
for ﬁnite periods.
7
Consider a situation where the minimum price is higher than the cost of every bidder, thatis, bidders earn a positive proﬁt even when they win at the minimum price. If ﬁrm 8 and ﬁrm
13 are known to be so low cost ﬁrms that every other bidder always expects them to bid at theminimum price, then a series of bidding wars we observe can be an equilibrium outcome without
any agreement.

9

by assigning a contract to the bidder whose total revenue as measured by thewinning amount in the past is the smallest among the members.
3) Contribution point
A contribution-point scheme chooses as the winner the bidder who has the highest
contribution point. A ring bidder earns a contribution point when he submitsa phony bid which allows another ring bidder to win. A bidder’s contribution
point is decreased once he wins.
In some cases in Japan, the ring uses a sophisticated way in calculating the contribution point. For example, in a case in Tokushima City, a bidder’s contribution
point equals the sum of pt /nt for all past auctions t in which he lost, minus thesum of ps for all past auctions s in which he won, where pt is the price and nt is
the number of bidders in auction t.8
In this paper, we consider the most simple way to calculate the contribution
point in which it equals (the total number of losing) − c ×(the total number ofwinning), where c is some constant.
4) Combination
The combination scheme combines some or all elements of the above schemes.
For example, a bidding ring in Okayama prefecture used a combination of thesimple rotation scheme and the revenue equalization scheme, that is, the ringbasically uses revenue equalization scheme, and in case of a tie, they compared
the number of days elapsed from one’s last win.
Each of the above schemes is “public” in the sense that its operation depends
only on the public history such as the date of auctions, the participants, the winner’s
identity, and their bids, and not on the private information such as cost of doing
the work. A merit of these schemes is their simplicity: They do not require any
communication among bidders even when there is private information. They sustain
collusion without side transfer by giving each member the expectation that they will
win in the near future.
When any of above schemes is in operation, it is possible for us to detect it,
since the scheme creates a link between the outcome of each auction and history.
8

A speech at Tokushima City Council by Councilor Satoru Kako, June, 2004.

10

Competitive bidding, on the other hand, creates no such link. Therefore, we test if
the history impacts the auction result in a supposed way in Section 4.

4

Estimation of the model of the ring’s decision

In what follows, we analyze if the data can be explained by any of the collusion
schemes described above. Speciﬁcally, we examine if there is a factor that has
nothing to do with the cost, but has an impact on the auction result. The existenceof bid rigging is supported by the existence of such a factor. In the analysis, we
use the data from 123 auctions that did not result in the bidding war in the sense
described in Section 3.1.
An important assumption here is that the ring was all-inclusive in these auctions.
When the ring is all-inclusive in an auction, the designated winner wins the contract
for sure. Therefore, the winner’s characteristic in all-inclusive ring must reﬂect
characteristics of the collusion scheme.

4.1

Empirical model

Porter and Zona (1993) model the probability of a bidder’s win under competitive
bidding. They specify a bidder’s bidding function to be linear in observable cost
factors imposing an assumption that their coeﬃcients are the same among ﬁrms,
and then analyze the probability of each bidder’s win given the cost factors as aconditional logit model.
We extend their model by allowing the ring to designate the winner according
to the collusion schemes described in Section 3.2. Their model is adapted to thering’s choice as follows. We suppose that the ring chooses bidder i as the winner if
his measure of priority wit∗ is the highest among the set of bidders Mt in auction t,
wherewit∗ = β  xit + γ  zit + uit, i ∈ Mt .

(1)

xit denotes the vector of factors that determine bidder i’s priority in the collusion
schemes. zit is a vector of observable variables aﬀecting bidder i’s cost on project t.
uit is the disturbance that arises in bidder’s priority.

11

The probability that bidder i is chosen as the winner in auction t conditional on
Mt and xt is written as:∗
Pr(wt = i | Mt , xt, zt) = Pr(wit∗ ≥ wjt∀j ∈ Mt , j = i | Mt , xt, zt),

where wt indicates the identity of the winner in auction t, and xt and zt are vectorsthat consist of xit and zit for all i ∈ Mt , respectively. McFadden (1973) showed thatwhen the uit’s are independent and identically distributed with the Type I extreme
distribution, the above probability can be written as:
exp(β xit + γ  zit).
j∈M t exp(β xjt + γ zjt )Pr(wt = i| Mt , xt, zt ) = (2)

We obtain the estimator of parameters by maximizing the following log likelihood
function:ln L(β, γ|wt, Mt , xt, zt ) =

eit ln Pr(wt = i| Mt , xt , zt),t∈S i∈M t

where eit is an index variable which is 1 if i won in auction t and 0 otherwise and S
is the set of auctions that were not the bidding wars.
Recall that the determinant of bidder i’s priority in auction t is 1) the number ofdays elapsed from i’s last win (simple rotation), 2) i’s total revenue up to t (revenue
equalization), 3) the number of wins and the number of losses up to t (contribution
point). Therefore, xit = (NUMDAYSit , WINVALUEit , WINNUMit , LOSENUMit ).
We construct two variables which capture the revenue in the past, WINVALUE1it
and WINVALUE2it , since the ring may refer to the total revenue in a long timeor in a relatively short time in case that the revenue equalization scheme is used.
WINVALUE1it is the total value of contracts that Firm i has won since the start ofthe data period until the date of auction t, and WINVALUE2it is that within halfa year of auction t. Since the total revenue and the number of wins in the past arehighly correlated, we estimate some speciﬁcations dropping either of them.
The variables which represent observable cost factors in our model are zit =(CAPit , CAPSQit , YEARSi, WORKERi, PROFRATEi, DISTit , OUTOFTOWNi ).9
We also estimate a model with bidder speciﬁc intercept αi in wit∗ .
9

In Porter and Zona (1993), the cost factors zit include the capacity utilization rate (CAPit ),squared utilization rate (CAPSQit), a ﬁrm’s maximum capacity, squared maximum capacity, andonly CAPit and CAPSQit are statistically signiﬁcant.

12Since we are interested in whether xit has an impact on the winning probability,
we test the null hypothesis H0 : β = 0 against H1 : β = 0.
We also try the following extension in which the impact of xit on the priority isallowed to be diﬀerent across bidders:wit∗ = eδi β  xit + γ  zit + uit.

(3)This extension allows us to estimate the schemes which treat the ring members
diﬀerently. Bidders may be treated diﬀerently because, for example, some are moreestablished members of the ring than the others. We set δ1 = 0 for bidder 1. The
greater the value of δi the better treatment does bidder i receive.

4.2

ResultTable 5 shows the estimation results of the conditional logit model. We have estimated both models with and without bidder ﬁxed eﬀects. Columns (1)-(6) shows
the results of equation (1). Columns (1) and (2) contain the results using WINVALUE1 as the proxy for the total revenue in the past, and columns (3) and (4) use
WINVALUE2. Columns (5) and (6) show the results using the number of wins in thepast, instead of the total revenue. Column (7) corresponds to the extended model
which allows the heterogeneity of bargaining power given in equation (3). Columns(8) and (9) show the estimation results of equation (1) under the assumption β = 0.
In all speciﬁcations except for (8) and (9), the coeﬃcient of NUMDAYS, thelength of time since the last win, is positive and statistically signiﬁcant at 1% level.
It can be said that the impact of the duration of no win period has a robust positive
impact on the winning probability. The total revenue in the past is negative inall columns and statistically signiﬁcant at 1% or 5 % in columns (2), (3) and (4).
These results suggest that either simple rotation scheme or the combination of simple
rotation and revenue equalization is most likely used. That is, the ring selects thewinner based on the duration of the winless period and the winning value up to theauction.
The coeﬃcient of the OUTOFTOWN dummy is negative and statistically signiﬁcant at least 5% level in all columns, suggesting that having a headquarter inthe city increases the ﬁrm’s bargaining power in collusive negotiations. Table 3 also

13

shows that the number of win tends to be small if a ﬁrm is out-of-town. Firms 1,2,6
and 11 are out-of-town ﬁrms, and they won half as many times as the local ﬁrms.
These ﬁndings can be the evidence of collusion if competitive bidding is neveraﬀected by the duration of the winless period. However, there remains a possibility
that the duration of no win creates ﬁnancial diﬃculty which leads to more aggressive
bidding in competitive paradigm. When bidders are in ﬁnancial diﬃculty, theirobjective is not to maximize the proﬁt but to earn for the operational expenses
immediately. If this is the case, it is natural that the winner tends to have a longer
winless period or a less amount of win in the past.
In order to see if these properties lead to aggressive bidding, we examine theirimpact on the bid levels of losing bids. Table 6 and Table 7 show the results of OLS
estimations and Tobit estimations, respectively.
In Table 6, estimations in the ﬁrst four columns use all bids in non-bidding
war auctions, whereas only losing bids are used in the remaining columns. The
dependent variable of columns (1), (2), (5) and (6) is the normalized bid, and thatof the remaining columns is log of the normalized bid. It can be seen that the
impact of NUMDAYS is signiﬁcant and has expected sign in the results using allbids (columns (1)-(4)), whereas it turns out to be insigniﬁcant when winning bids
are removed from the dataset (columns (5)-(8)). The impact of WINVALUE2 isinsigniﬁcant throughout datasets and speciﬁcations.
In Table 7, the dependent variable of the Tobit models is the diﬀerence between
the bid level and the minimum price, divided by the diﬀerence between the reserve
price and the minimum price. In contrast to the OLS estimations, we include bid
data of bidding wars where the dependent variable is left truncated at the minimum
price. All bids are used in the ﬁrst two columns, and only losing bids are used in
the latter two columns. In all columns, WINVALUE2 is signiﬁcant but NUMDAYS
is not.
In summary, there is little support for the alternative explanation for the resultsof the conditional logit model that the positive impact of the duration of the winlessperiod and the negative impact of the winning value up to the auction, on thewinning probability is due to ﬁnancial diﬃculty. We therefore conclude that those
impacts are due to collusion.
The reuslts in columns (8) and (9) in Table 5 show that when we omit variables
14

such as NUMDAYS in the conditional logit model, CAP turns out to be signiﬁcant.
It means that when our data are analyzed using a model with only cost relevantterms, the estimation result looks competitive because of the negative correlation
between CAP and NUMDAYS. We conﬁrm that it is diﬃcult for the standard model
to discriminate whether the data are competitive or collusive when the ring uses bid
rotation.
We should note that there may exist other factors omitted in our model. Figure 5
shows the relationship between the size of the contract and the identity of the winner.
A small, medium, big dot indicates a small (less than 5 million yen), medium (5-10
million yen) and big (greater than 10 million yen) contract, respectively. It can beseen from the ﬁgure that ﬁrm 3 tends to win big contracts with long intervals, whileﬁrms 9 and 10 tend to win small or medium contracts with short intervals. Thissuggests the presence of ﬁrm speciﬁc patterns not captured in our analysis.

5Conclusion

We analyze procurement auction data to determine if bid rigging is present. We ﬁrst
observe the incidents of the bidding war and ﬁnd that most bidding wars occurred
when either of speciﬁc two ﬁrms submitted bids. It is inferred that the two ﬁrms are
possible outsiders and that all the ring bidders submit bids at the minimum priceonly when the outsiders were in the auction.
We next analyze if the auction results is explained by some collusion scheme
in which the ring chooses the winner based on the history of auctions, assumingthat the auction is all-inclusive if it is not a bidding war. Speciﬁcally, we model
four collusion schemes typically used in Japan, as the ring’s multinomial choice of
the winner. In the schemes, the ring compares each member’s priority to win, andselects the member whose priority is the greatest among the bidders. The members’
priority is measured based on the history. It is found that a bidder tends to win
when his duration of no win is long, and his amount of win in the past is low relative
to other bidders.
The duration of no win or the win value in the past may be related to the ﬁnancialpressure which makes a competitive bidder aggressive, and therefore, their impacts
can be due to competition. We further conﬁrm that there is little support for such15

an explanation by analyzing the bid level of losing bids. We then conclude that the
impacts of those variables on the winning probability are due to collusion.
Our ﬁnding ﬁgures out the behavior of the ring. The ring allocates contracts
to the ring bidders, balancing the frequency of winning and the revenue among its
members, and when an outsider is in an auction, all the ring bidders bid at theminimum price.
We should note the limitation of our approach. First, the measure of bidders’backlog is inaccurate since it is based only on the public contracts and their private
contracts are not taken into account. Second, the correlation between the current
result and the past results in competitive auctions may come from some unknown
causality other than capacity constraint or ﬁnancial pressure, but we do not handle
it. Finally, our analysis is eﬀective only when the ring is nearly all inclusive in themarket and multimarket contact of bidders is infrequent. Otherwise it is diﬃcult
for us to analyze if the auction results are consistent with some collusion scheme.

References[1] Aoyagi, M. (2003), “Bid Rotation and Collusion in Repeated Auctions,” Journalof Economic Theory, 112, pages 79-105.
[2] Bajari, P. and Ye, L. (2003), “Deciding Between Competition and Collusion,”
Review of Economics and Statistics, 85.4, pages 971-989.
[3] Harrington, J. E. (2005), “Detecting Cartels”, Economics Working Paper
Archive, Johns Hopkins University.
[4] Hironaka, K. (1994), “Dango survives after all (Soredemo dango ha nakunaranai),” Tokei Publishing (in Japanese).
[5] Kato, M. (2005), “We did Dango (Dango shimashita)”, Saizusha (in Japanese).
[6] McAfee, R. P. and McMillan, J. (1992), “Bidding Rings,” American Economic
Review, 82.3, pages 579-599.
[7] McFadden, D. (1973) “Conditional Logit Analysis of Qualitative Choice Behavior,” in Frontier in Econometrics, edited by Paul Zarembka. Academic Press.

16[8] McMillan, J. (1991) “Dango: Japans Price Fixing Conspiracies”, Economics
and Politics, 3, pages 201-218.
[9] Motta, M. (2004), “Competition Policy,” Cambridge University Press.
[10] Pesendorfer, M. (2000), “A Study of Collusion in First-Price Auctions,” Review
of Economic Studies, 67, pages 381-411.
[11] Porter, R. H. (2005), “Detecting Collusion,” Review of Industrial Organization,
26, pages 147-167.
[12] Porter, R. H. and Zona, J. D. (1993), “Detecting of Bid Rigging in Procurement
Auctions,” Journal of Political Economy, 101.3, pages 518-538.
[13] Porter, R. H. and Zona, J. D. (1999), “Ohio school milk markets: an analysisof bidding,” RAND Journal of Economics, 30.2, pages 263-288.
[14] Skrzypacz, A. and Hopenhayn, H. (2004), “Tacit collusion in repeated auctions,” Journal of Economic Theory.
[15] Suzuki, M. (2004), “A study of bid rigging (Nyusatsu dango no kenkyu),” Shinzansha (in Japanese).
[16] Yanagawa, N., Kimura, Y., and Suzuki, T. (2005), “An Empirical Analysis
about Japanese Dango (Nyusatsu dango no keizai bunseki),” CPRC Report
Series, CR 02-05, Competition Policy Reserch Center Fair Trade Commissionof Japan. (in Japanese)[17] Zona, J. D. (1986), “Bid-rigging and the Competitive Bidding Process: Theory and Evidence.” Ph.D. dissertation, State University of New York at Stony
Brook.

17

18
Local/Out- Num.
of-town
workers

6
52

7 8
28 5

Num.
oﬃces

Bidding war
No
No
No
Yes

9 Total
2 139

Bidder8
4,5,9,11
6,7,9
5,7

Years ofoperating

Sales

5.79%
-0.33%
1.21%
1.27%
1.14%
-0.86%
2.58%
0.41%
0.60%
1.04%
-9.50%-0.17%-

Proﬁt-sales
ratio

Table 3: Information of ﬁrms

Auction ID
39
137
138
139

1
O
158
12
55 13,059,582
2
O
22
2
15
344,8323
L
16
1
15575,2854L121
31242,3615
L
19
1
36
628,7766
O
9
2
34
286,7487
L
3
1
30
115,7448L9
1
24
318,9859L
6
1
22144,42310L4
1
6
249,260
11
O
16
2
26
380,57312L
7
1
21
67,056
13
L
Note: Sales and Total win amount are in 1000 yen.

Firm ID

5
52

Table 2: Abstention from bidding

Number of bidders
Number of auctions

Table 1: Bid concentration

29
40
93
95
97
37
95
61
72
83
39
81
4

Num.
bids

4
5
14
17
13
3
14
13
20
13
6
17
0

Num.
winning

54,12852,605
178,941
129,749
100,044
17,71480,126
68,103
110,670
59,34633,096
104,4700Total winamountTable 4: Deﬁnition of variables
Variable name
CAPit

CAPSQitYEARSi
WORKERi
PROFRATEi
DISTitOUTOFTOWNiNUMDAYSit
WINVALUE1it

WINVALUE2it
WINNUMit
LOSENUMit

Description
The measure of capacity utilization.
Deﬁned as the value of backlog contracts divided by the ﬁrm’s annual
sales in 2004. (If the ﬁrm has morethan two oﬃces, sales are divided by
the number of the oﬃces.) Firm i’sbacklog contract at auction t is thecontract won by Firm i in public auctions in Ibaraki City or Osaka Prefecture, overlapping the contract ofauction t.
Square of CAP.
Years since Firm i’s establishment,
as of 2004.
Number of technical employees ofFirm i, as of 2004, divided by the
number of oﬃces.
Proﬁt-sales ratio as of 2004.
Direct distance in kilometer between
the work site and Firm i’s oﬃce.
A dummy variable that takes 0 if
Firm i has a headquarter in Ibaraki
City, and 1 otherwise.
The number of days between Firm
i’s last winning and the date of auction t.
The total value of contracts that
Firm i has won since the start of thedata period until the date of auctiont (in million yen).
The total value of contracts that
Firm i has won within half a yearof auction t (in million yen).
The number of times that Firm i won
in auctions from the start of the data
period until the date of auction t.
The number of times that Firm i lostin auctions from the start of the data
period until the date of auction t.

19

Num.Obs. Mean Std. Dev. Min Max
725
0.04
0.07
0 0.59

725
725

0.01
24.74

0.02
10.58

0
6

0.35
55

725

9.57

5.24

3

19

725
725

0.53
3.64

2.64
2.29

725

0.18

0.39

0

1

725

106.31 112.50

0

695

725

47.04

39.13

0 176.27

725

10.56

9.53

0

47.04

725

6.67

4.77

0

20

725

31.90

21.40

0

82

-9.50 5.79
0.21 14.92

Table 5: Estimation results for conditional logit model
WINVALUE1
WINVALUE2
WINNUMLOSENUM
NUMDAYS
CAP
CAPSQ
YEARS
WORKERPROFRATEDISTOUTOFTOWN
δ2
δ3
δ4
δ5
δ6
δ7
δ8
δ9
δ10
δ11
δ12

(1)
(2)
-0.010 -0.027**(0.006) (0.009)

(3)

(4)

(5)

(6)

(7)
-0.007(0.010)(8)(9)-0.033* -0.038*(0.016) (0.018)-0.065 -0.139(0.060) (0.077)
0.006 0.031 -0.005 -0.006 -0.004 0.008 0.021(0.015) (0.023) (0.014) (0.021) (0.014) (0.021) (0.020)
0.006** 0.006** 0.006** 0.006** 0.006** 0.006** 0.012**(0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.004)-3.810 -5.978 -2.126 -3.401 -3.793 -5.100 -3.587 -8.586* -9.804*(3.985) (4.116) (4.186) (4.291) (4.022) (4.106) (4.809) (3.834) (3.941)
5.024 7.278 2.500 3.310 4.587 5.119 3.603 12.012 12.391(10.120)(10.690)(11.235)(11.785)(10.032)(10.560)(12.354)(9.478) (9.863)-0.004 -0.042 -0.002 -0.047 0.002 -0.042 -0.018 -0.005 -0.018(0.012) (0.027) (0.012) (0.027) (0.012) (0.027) (0.027) (0.011) (0.024)-0.013 0.011 -0.021 -0.069 -0.034 -0.079 0.089 -0.032 -0.044(0.026) (0.057) (0.024) (0.046) (0.022) (0.045) (0.053) (0.020) (0.039)-0.052 0.032 -0.053 0.033 -0.065 0.029 -0.367* -0.037 0.018(0.056) (0.071) (0.055) (0.070) (0.056) (0.071) (0.149) (0.052) (0.061)-0.146** -0.114 -0.152* -0.125 -0.139* -0.116 -0.107 -0.129* -0.121(0.062) (0.064) (0.062) (0.064) (0.062) (0.064) (0.065) (0.061) (0.062)-2.287** -1.722* -2.300** -1.728* -2.561** -1.750* -3.349* -0.822* -0.212(0.560) (0.732) (0.552) (0.734) (0.659) (0.790) (1.477) (0.391) (0.521)
0.108(0.263)-1.179(0.797)-0.005(0.384)-1.191(1.017)-0.092(0.244)0.620(0.384)-0.240(0.502)0.201(0.456)-0.034(0.552)-1.791(1.256)0.273(0.461)
No
Yes
No
Yes
No
Yes
No
No
Yes
-194.23 -187.70 -193.39 -189.65 -195.15 -190.52 -181.30 -208.71 -206.13
0.105 0.135 0.108 0.126 0.100 0.122 0.164 0.037 0.049
Yes
No
No
No
Yes
No
No
No
Yes

Bidder ﬁxed eﬀect
Log likelihood
Pseudo R2
IIA violation
Notes:(i) **: 1% signiﬁcance level, *: 5% signiﬁcance level.
(ii) The number of observations of each model is 725.
(iii) ‘Yes’ in ‘IIA violation’ implies that the Hausman test suggests that the model violates
Independence of Irrelevant Alternatives (IIA) assumption.

20

21
0.956
717
0.054
No

(0.002)

717
0.99
Yes

-

0.394∗∗(0.003)0.011∗∗(0.002)∗∗0.001∗(0.000)0.001∗(0.000)(0.000)(0.000)(0.000)-0.016∗∗0.001∗∗

0.000

0.052∗∗

0.000(0.000)(0.000)0.000∗(0.000)0.000∗(0.000)

0.033

717
0.054
No

(0.002)-0.046∗∗(0.002)0.012∗∗(0.000)0.001∗(0.000)0.001∗∗(0.000)0.000∗(0.047)0.021(0.046)(0.019)-0.0120.032(0.019)(0.007)-0.028∗∗(0.007)(0.045)-0.009(0.006)(0.006)(0.018)-0.026∗∗-0.026∗∗-0.012(0.007)(0.007)

0.005

717
0.905
Yes

-

(0.003)-0.008∗∗(0.000)0.001∗(0.000)0.002∗∗(0.000)-0.002∗∗(0.000)0.000(0.048)0.022(0.020)-0.009(0.007)-0.028∗∗(0.008)0.006(0.091)

0.963

594
0.042
No

(0.002)∗∗(0.002)0.007∗∗(0.000)0.000(0.000)0.001∗∗(0.000)0.000(0.000)0.000∗∗(0.041)

0.032(0.017)-0.014(0.006)-0.007(0.007)

0.003

594
0.999
Yes

-

(0.003)0.395∗∗(0.000)0.000(0.000)-0.016∗∗(0.000)0.052∗∗(0.000)0.000∗∗(0.042)0.022(0.018)-0.018(0.006)-0.007(0.007)0.006(0.082)

594
0.042
No

(0.002)-0.038∗∗(0.002)0.007∗∗(0.000)0.000(0.000)0.001∗∗(0.000)0.000(0.000)0.000∗∗(0.043)0.033(0.018)-0.015(0.006)-0.008(0.007)0.003(0.084)

594
0.914
Yes

-

(0.003)-0.008∗∗(0.000)0.000(0.000)0.002∗∗(0.000)-0.002∗∗(0.000)0.000∗(0.044)0.023(0.019)-0.018(0.007)-0.007(0.008)0.006(0.085)(0.081)

0.006

0.005

(0.090)(0.086)(0.087)

Losing bids
Normalized bidlog(Norm. bid)
(5)
(6)
(7)
(8)
-0.081-0.072-0.083-0.074All bids
Normalized bidlog(Norm. bid)
(1)
(2)
(3)
(4)
-0.0040.004-0.0030.005

Notes:(i) **: 1% signiﬁcance level, *: 5% signiﬁcance level.
(ii) The data sets do not include bids submitted in bidding wars.
(iv) The units of Reserve price and NUMDAYS are in 109 yen and 1000 days, respectively.

Num. of Obs.
R2
Bidder Fixed Eﬀect

Intercept

OUTOFTOWNDISTPROFRATE

WORKER

YEARS

CAPSQ

CAP

NUMDAYSWINVALUE2

Reserve price

Data set
Dependent Variable

Table 6: OLS estimations for bid levels

Reserve price

Table 7: Estimation results of Tobit models
(1)
(2)
(3)
∗∗
∗∗
-6.165-6.425-6.393∗∗(1.485)

CAP
CAPSQ
YEARS
WORKERPROFRATEDISTOUTOFTOWNWINVALUE2
NUMDAYS
Intercept(1.494)∗(1.601)(1.606)

0.595

0.779

0.496

0.799∗(0.320)(0.335)(0.353)(0.371)-1.244-1.547-0.721-1.173(0.805)(0.820)(0.869)(0.885)-0.0010.001-0.001

0.003(0.001)(0.002)(0.001)(0.002)∗∗-0.0020.034-0.0040.030∗∗(0.002)(0.004)(0.002)(0.004)∗∗0.002-0.0140.001-0.015∗∗(0.004)(0.005)(0.005)(0.005)-0.006-0.008-0.005-0.007(0.004)(0.004)(0.005)(0.005)0.111∗∗

0.343∗∗

0.108∗∗

0.336∗∗(0.036)(0.048)(0.039)(0.052)0.324∗∗

0.335∗∗

0.389∗∗

0.392∗∗(0.123)(0.130)(0.135)(0.143)-0.043-0.042

0.035

0.020

(0.111)(0.114)(0.127)(0.130)0.714∗∗-(0.040)

Num. of Obs.
Log-likelihood
Bidder Fixed Eﬀect(4)-7.020∗∗812-220.398
No0.728∗∗-(0.044)812-216.398
Yes

673-186.183
No

673-179.038
Yes

Notes:(i) **: 1% signiﬁcance level, *: 5% signiﬁcance level.
(ii) The deﬁnition of the dependent variables:(bid level−minimum price)/(reserve price−minimum price)(iv) The units of Reserve price and NUMDAYS are in 109 yen and 1000 days, respectively.

22

23

Winning price (in million yen)

0

5

10

15

20

25

30

35

40

45

0

5

10

15

20

25

30

35

40

45

50

55

60

70

75

Auction ID

65

Figure 1: Winning price

80

85

90

95 100 105 110 115 120 125 130 135 14024

00.00010.00020.00030.00040.00050.00060.00070.00080.0009

0.001

0

5

Auction No.

10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140

Figure 2: Variance of normalized bids

Note: The ﬁgure does not include three exceptionally large values 0.0023, 0.0011, and 0.0076 for Auction No. 2, 74, and 139,
respectively.

Variance of normalized bids

25

0.75

0.80

0.85

0.90

0.95

1.00

0

5

Auction No.

10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140

Figure 3: Normalized winning bids

Notes: For each auction, the normalized winning bid and the minimum price are indexed by • and ×, respectively.

Normalized winning bid

26

Firm ID

0

1

2

3

4

5

6

7

8

9

10

11

12

13

0

5

10

15

A

20

25

30

35

40

45

50

55

60

70

75

Auction ID

65

80

85

B

Figure 4: Participation and bidding wars

90

No bidding war
Bidding war
Winner95 100 105 110 115 120 125 130 135 140

27

Firm ID

0

1

2

3

4

5

6

7

8

9

10

11

12

13

0

5

Small (-5mln Yen)

Medium (5-10mln Yen)

Auction ID
Large (10-mln Yen)

Price war

10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140

Figure 5: Winner of auctions