Endogenous Joint Venture Formation in
Procurement Auctions∗Kei Ikegami†

Ken Onishi‡

Naoki Wakamori§

June 18, 2023
Very Preliminary
Please find the updated version here.

Abstract
We examine the influence of joint ventures on procurement efficiency. On one hand,
the government anticipates the cost synergies derived from such collaborations. On
the other hand, this strength diminishes the incentive for new entrants, resulting ina decrease in the total number of bidders. We estimate a two-stage structural model
to simulate the balance between these two forces. Our model provides evidence ofthe existence of cost synergies and quantifies two obstacles to joint venture formation:
adjustment costs and search frictions. While these obstacles partially mitigate theanti-competitive path, our simulation demonstrates that excessive promotion of joint
venture formation by the government leads to a reduction in procurement efficiency.
JEL Classification Codes: L24; D22; D44; H57.
Keywords: Joint ventures; Cost synergies; Matching; Procurement auctions.

1

Introduction

In government procurement, many countries allow firms to participate in auctions as a joint
venture with the goal of creating cost synergies among the forming firms and promoting
the entry of construction firms who could not enter otherwise; This may increase the total∗

We thank Kei Kawai, Jun Nakabayashi, and seminar participants at JEMIOW and APIOC.
Department of Economics, New York University, 19 West 4th Street, 6th Floor, New York, NY 10012,
USA. Email: ki2047@nyu.edu.
‡
Hitotsubashi Institute for Advanced Studies, Hitotsubashi University, Naka 2-1, Kunitachi, Tokyo, 1868601, JAPAN. Email: ken.t.onishi@gmail.com.
§
Graduate School of Economics, Hitotsubashi University, Naka 2-1, Kunitachi, Tokyo, 186-8601, JAPAN.
Email: naoki.wakamori@r.hit-u.ac.jp.
†

1number of bidders and make their bids more competitive. However, joint bidding may reduce
the number of bidders. As a direct effect, the auction loses one bidder as two individual firms
submit one bid jointly. As an indirect effect, if joint ventures have cost synergies, individual
bidders may be discouraged from participating in the auctions as they would face stronger
competitors. Examining the trade-off between cost synergies and reduced competition istherefore key to understand the welfare implication of joint ventures.
The pro-competitiveness of joint ventures in several countries, including Japan andAustria, and EU has been empirically supported in the literature (Iimi, 2004; Estacheand Iimi, 2009; Branzoli and Decarolis, 2015; Gugler, Weichselbaumer and Zulehner, 2021).
While these studies have primarily focused on the cost synergies resulting from joint ventures
and their impact on procurement efficiency, little attention has been given to the effect of
joint ventures on market entry incentives within an integrated model. Thus, the primaryobjective of our study is to develop an integrated model that encompasses market entry,
joint venture formation, and procurement auction bidding, and to identify the sources ofpro-competitive and anti-competitive effects.
Our model consists of two stages: (i) the entry and joint venture formation stage and(ii) the bidding stage where the bidders engage in a scoring auction. The main focus of ourmodel is the first stage, where potential entrants decides whether they enter or not as well as
the mode of entry, i.e., enter as a single bidder or as a joint venture. The formation of joint
venture involves search friction, transaction costs, and externalities; (1) potential entrants
face search friction in finding a suitable partner to form a joint venture, (2) potential entrants
incur additional managerial costs to form a joint venture, and (3) the number of joint ventures
affects the incentive/strategy of bidders in the subsequent auction as well as the outcomeof the auction.1 We build a tractable model of group formation with externality, which isapplicable to broader research topics such as mergers and matching markets. The second
stage is modeled as an asymmetric scoring auction with two dimensional private information:
the construction cost and the auction score.
1

Modeling search friction and transaction costs are motivated by our observation that joint venturesappear in only 14% of ‘large’ scale auctions and a finding in (Gugler, Weichselbaumer and Zulehner, 2021)
that joint bids account for only 5% of total bids in Austria, though the value share is much bigger. Suchlimited practices of joint bidding in reality suggests some costs associated with joint venture formation andour model capture them through search friction and transaction costs.

2

In addition, our structural model enables us to identify obstacles that hinder the formationof joint ventures which causes the few number of successfully formed joint ventures. Despite
governments occasionally encourage joint ventures, joint bidding is not frequently observed,
as exemplified by the fact that joint bids account for only 5% of total bids in Austria(Gugler, Weichselbaumer and Zulehner, 2021). Given that the literature shows joint ventures
can generate synergies and provide potential bidders with the ability to enter markets, thelimited practice of joint bidding suggests the existence of countervailing power that hinders
joint venture formation. We quantify this obstacle using our model and decompose it into
two elements: additional entry cost arising from the management of the joint venture andsearch friction in finding suitable partners.
We estimate the model from the second stage. We first recover the individual cost factors
given the observed scores and then jointly plot the recovered cost factors and scores for single
bidders and joint ventures, separately. The distributions do not match each other, which
implies that the distributions of cost factors are different, the distributions of score aredifferent, or both of them are different for single bidders and joint ventures. When looking
at the score distributions depending on the mode of entry, the distributions are almost
identical, enabling us to conclude that the difference are mainly driven by the cost factor
distributions. Therefore, these results show the evidence that there exists a certain degreeof cost synergy generated by forming a joint venture.
The entry and joint venture formation stage involves two objects of interest: (1) entry
costs for single bidders and joint ventures, and (2) the friction in joint venture formation.
In our estimation, we find that the joint ventures incur higher entry costs than the single
bidders do. This is an evidence of the adjustment costs for managing joint ventures, as
known in the literature of the merger (Graebner et al., 2017). We also estimate the functionthat maps the number of potential entrants intending to form a joint venture to the numberof successfully formed joint ventures. Under the estimated model, we observe the evidence
for the search friction that not all entrants intending to form a joint venture can form ajoint venture and the number of realized joint ventures may not increase in proportion to
the number of bidders attempting to form them.
The counterfactual simulation evaluates procurement efficiency through varying joint
3

venture participation by either increasing or decreasing joint ventures’ entry cost. Our
analysis reveals that a mild reduction in the entry cost significantly enhances procurement
efficiency. The excessive reductions in entry cost lead to intensified competition among joint
ventures, reducing the likelihood of single bidders winning the auction. This subsequently
decreases the total number of bidders, outweighing the pro-competitive effect of the costsynergies generated by joint ventures.

1.1

Related Literature

Joint bidding is intensively studied in the context of common value auction where theauctioneer sells a natural resource like petroleum. The empirical and theoretical results
about the competitive effect of joint bidding are mixed. Mead (1967) and Levin (2004)
argue that the joint bidding plays like a bidding rings or a collusion and hence impedes thecompetitive bids among the bidders. Millsaps and Ott (1985), Moody and Kruvant (1988),
and Hendricks and Porter (1992) indicate the pro-competitive effects of joint bidding causedby pooling information, relaxing the budget constraint and risk sharing.
The theoretical literature on joint bidding is extended to include another form of auctions
like a patent auction (Asker, Baccara and Lee, 2021), the private value auctions (Cho,Jewell and Vohra, 2002; Cantillon, 2008; Chatterjee, Mitra and Mukherjee, 2017) and theauction with subcontracting (Bouckaert and Van Moer, 2021). These models are tailoredto the specific application. Empirical studies on the joint bidding are carried out almost
independently from the theoretical literature (Iimi, 2004; Estache and Iimi, 2009; Branzoli
and Decarolis, 2015). These papers show the reduced form evidence to support the procompetitive effect of joint bidding.
The literature on merger or joint venture in other context considers the similar problem
as the problem of joint venture in auction. Weese (2015); Akkus, Cookson and Horta¥ccsu(2016); Uetake and Watanabe (2020) consider the model of matching market in several
different areas. These papers estimate the effect of matching using moment inequality
approach developed by Fox (2018); Pakes (2010) due to the multiple equilibrium. In contrast
to these literature, we develop a model which has unique equilibrium in the entry stage, i.e.,
joint venture formation stage. Miller and Weinberg (2017) is one example of papers which
4treats the competition after forming a group. This paper focus on the joint venture in beerindustry which come to produce one item jointly after the formation. Their method is similar
to the conduct parameter approach which is not applicable to the current context.
The closest study to ours is Gugler, Weichselbaumer and Zulehner (2021), which carries
out a structural estimation of the auction with joint bidding. They focus on the types of thefirms to form a joint venture and analyze the difference between the case of restricting all
joint ventures and the case in which joint venture is allowed only to the small-sized firms toconclude that the joint venture by large-sized firms is the driving force of pro-competitiveeffect. In contrast to this study, we do not use the identity of the firm in our analysis.
Instead we focus only on the number of joint ventures and the single bidders in each auction.
Though this is a data limitation, our model can assure the unique equilibrium in the entry
stage which is not guaranteed in Gugler, Weichselbaumer and Zulehner (2021). Additionally,
we put a focus on the adjustment cost to form a joint venture while Gugler, Weichselbaumer
and Zulehner (2021)does not care about this point.
We consider the first-price sealed bid scoring auction. As the similar class of auctions,
Krasnokutskaya and Seim (2011) study the first-price auction with bid preference. They
point out that the bid preference in the bidding stage distorts the incentive to entry of theunfavored group and argue that the careful setting of the bid preference is necessary toachieve both the efficient procurement and improving the minority status. Other papers
also insist on this point (Corns and Schotter, 1999; Marion, 2007; Athey, Coey and Levin,2013; Nakabayashi, 2013; Rosa, 2019). All of these studies focus on the bid preference forthe small-sized firms: in the bidding stage, the firms categorized as “small-sized” according
to the number of employees or the size of the budget get favored by weighting their bid at
a fixed rate. While our paper also considers the relationship between the bid preference inthe bidding stage and the entry behavior in the entry stage, the situation is different fromthese existing ones: the first point is that the bid preference is based on the score which isdetermined by the characteristics of the entrant such as the size, whether or not the entrant
is a local one, and whether or not the entrant is joint venture, i.e., our bid preference is much
more complicated. The second point is that the potential bidders can decide to get favoredin the bidding stage by forming a joint venture. This endogeneous nature is not considered5

in the previous literature.
The last contribution of this paper is the empirical evidence of the adjustment cost when
two or more firms form a consortium. This is a well-studied topic in management science,
surveyed in (Graebner et al., 2017). To generate synergy by forming a joint venture orafter merger, it is essential to adjust the culture and the customs among the related firms(Chatterjee et al., 1992; Stahl and Voigt, 2008; Reus and Lamont, 2009). And the knowledgetransfer, which is obviously necessary to make a synergy, requires a lot communication(Larsson and Finkelstein, 1999; Bresman, Birkinshaw and Nobel, 2010). We think theadjustment cost of this paper is an expression of this type of behavior. While almost all the
discussions in the existing literature is qualitative ones, we contribute a new quantitative
evidence to the existence and the size of this cost to from a consortium.
The first strand of the literature that this paper contributes to is the empirical literature
on joint venture formation and endogeneous merger formation. Forming a joint venture andmergers share some similarities where parties commit to make a collective decision with adifference that the joint venture can be a temporary commitment. The competitive effectof joint venture has been studied intensively as in the merger literature, e.g., Shapiro andWillig (1990), Estache and Iimi (2009) and Miller and Weinberg (2017). The incentives formergers and for joint venture formation are complex including externalities in the subsequent
competition, which makes it challenging to build a tractable and internally-consistent model.
The literature has developed in two strands: (i) building a long time horizon dynamic model
as in Gowrisankaran (1999) and Igami and Uetake (2020), and (ii) utilizing the matchingmodel, developed by Fox (2018), as in Akkus, Cookson and Horta¥ccsu (2016) and Uetakeand Watanabe (2020). This paper proposes a new tractable method to estimate a endogenous
joint venture/merger formation by extending the entry model developed by Seim (2006) andestimating the joint venture formation mechanism directly from the data. Our model andapproach are applicable to broader situation, including endogenous mergers, and allows us
to quantify the effect of joint ventures/mergers on entry incentive, incentive to form a joint
venture, incentive to merge, and competition in the subsequent periods.
Broadly speaking, joint venture formation, the focus of this paper, can be seen as aparticular type of joint bidding, which is studied by Cho, Jewell and Vohra (2002); Cantillon
6

(2008); Chatterjee, Mitra and Mukherjee (2017) and studied in some specific contexts ofprocurement auctions (Gugler, Weichselbaumer and Zulehner, 2021), subcontracting (Bouckaert
and Van Moer, 2021) or patent auctions (Asker, Baccara and Lee, 2021).2 The empiricalliterature on the joint bidding, including Iimi (2004); Estache and Iimi (2009); Branzoli and
Decarolis (2015), develops slightly independently from the theoretical literature, i.e., thefocuses of the literature is descriptively examining whether joint bidding indeed has procompetitive effects or anti-competitive effects and find the pro-competitive effect of joint
bidding. The notable exception is Gugler, Weichselbaumer and Zulehner (2021) that use astructural approach, endogenizing the entry and joint venture formation in a reduced-form
way with heterogeneous bidders, and find the pro-competitive effects of joint bidding. Our
paper complements Gugler, Weichselbaumer and Zulehner (2021) by explicitly modeling thejoint venture formation and imposing equilibrium restrictions, which allows us to conduct aricher set of counterfactual analyses.
The final contribution of our paper is to the empirical works on the procurement auction.
In particular, our modeling adds the joint venture formation process to the procurement
auction models with endogeneous entry such as Li and Zheng (2009); Krasnokutskaya andSeim (2011). Their works demonstrate that the decision regarding endogenous entry is
crucial for understanding the origins of efficiency in procurement auctions. Our paper
additionally finds that the choice of joint venture formation also plays a decisive role indetermining the efficiency of procurement auctions. Moreover, our empirical analysis focuses
specifically on the scoring auction, which is categorized as multi-attribute auctions (Perrigne
and Vuong, 2019). This type of auction incorporates non-monetary information to determine
the winning bidder in procurement auctions, evaluating the quality of projects submitted
by bidders to aim to long-term value maximization. Recent studies by Lewis and Bajari(2011); Kong, Perrigne and Vuong (2022) have empirically examined this auction format.3
2

There is another strand of literature that investigates the joint bidding in the context of common
value auctions where auctioneers sell natural resources such as petroleum. Although the theoretical papers,
including Mead (1967) and Levin (2004), argue that the joint bidding function as a bidding rings or a collusion
and hence impedes the competitive bids among the bidders, the empirical papers, including Millsaps andOtt (1985), Moody and Kruvant (1988), and Hendricks and Porter (1992), find the pro-competitive effects
of joint bidding caused by pooling information, relaxing the budget constraint and risk sharing.
3
There are other auction variants worth mentioning, such as the bid-preference or set aside policies, which
aim to promote equity in procurement. Notable references in this regard include Corns and Schotter (1999);

7

We contribute to this literature by modelling a second stage as a scoring auction within aclass of asymmetric auctions, which has not been considered in the literature yet.

2

Background and Motivating Facts

In this paper, we focus on the public procurement auctions held by five Regional Development
Bureaus of the Japanese Ministry of Land, Infrastructure, Transport and Tourism (MLIT),
which is the largest purchaser in Japan. We first provide the institutional backgroundin Subsection 2.1, emphasizing the procedure of auctions and describing how we collectand construct the data. We then demonstrate some descriptive statistics, highlighting thedifference between the bids of joint venture firms and the bids of non-joint venture firms(single bidders) in Subsection 2.2. One may concern collusive behavior of the Japaneseconstruction firms, as pointed out by Kawai and Nakabayashi (2022b), Chassang et al. (2022),
Kawai et al. (2022), Kawai and Nakabayashi (2022a) who establish some statistical evidence
for collusion. We therefore test whether or not this concern applies to our data by employing
a screening method proposed by Kawai and Nakabayashi (2022b) in Subsection 2.3.

2.1

Institutional Background and Data

This paper focuses on the public procurement auctions held by five Regional Development
Bureaus of the MLIT. The main reason why we focus on these regional offices is controllingfor auction rules; Though municipal and prefectural government offices also use procurement
auctions, their auction rules are not perfectly coincide with each other. The main tasks ofthese regional offices are developing and maintaining the public infrastructures, including
national routes, rivers, dams, ports and so on, under the direct control of the MLIT.
Depending on these tasks, procurement of construction work is categorized into 22 types:
Civil engineering, bridge building, pavement, landscaping and so on.4
A format of auctions used by each Regional Development Bureaus is a variant of firstMarion (2007); Krasnokutskaya and Seim (2011); Athey, Coey and Levin (2013); Nakabayashi (2013); Rosa
(2019).
4
See Table 1 for the list of the categories.

8

price sealed-bid auction with secret reserved prices.5 If a secret reserve price exceeds 100
million JPY in an auction, each procurer are strongly encouraged to use a scoring auction,
explained in Subsection 2.3. Moreover, if a secret reserve price roughly exceeds 500 million
JPY, each auction is now encouraged to invite joint ventures, aiming to generate somecomplementarities among the participating firms and taking advantages of scale economies.
Though there are few exceptions for some gigantic construction work with short deadlines,
the number of participating firms for each joint venture must be two or three firms, inprinciple. Furthermore, if a secret reserve price exceeds 680 million JPY, each procurement
is now subject to the Agreement of Government Procurement, a multilateral agreement
within the framework of World Trade Organization, implying that an equal treatment for
the foreign firms must be guaranteed.6
Depending on the purposes, there are four types of joint ventures: (i) project-specific(Tokutei) joint ventures, (ii) fixed-term (Keijo) joint ventures, (iii) maintaining-regionalinfrastructure-specific (Chiiki-iji) joint ventures, and (iv) restoration-projects-specific (FukkyuFukkou) joint ventures. In this paper, we focus on the first type, which appears the most in
the data.
We first collect the data from all 7 regional offices for all types of construction work
between 2006 to 2022.7

Procurement projects which involve joint ventures are mostly

observed in auctions with reserve prices above 680 million JPY, as in Panel (A) of Table
1. Moreover, if we look at these 1,712 auctions, joint ventures are mostly appeared in two
types of construction work—Civil Engineering and Bridge Building—and in five regions—
Kanto, Hokuriku, Kinki, Shikoku, and Kyushu—as in Panel (B) and Panel (C) in Table 1.
We therefore focus on the projects of civil engineering or bridge buidling with reserve prices
above 680 million JPY, procured in Kanto, Hokuriku, Kinki, Shikoku, and Kyushu, whichleaves 793 auctions out of 66,733.
5

Secret reserved prices are unknown ex ante and the bidders whose bid exceed this secret reserved prices
are disqualified.
6
These threshold values are varied across municipal and prefectural governments and that is why we focus
on the auctions held by each regional offices of the Japanese MLIT.
7
There are 8 Regional Development Bureaus of MLIT include, Tohoku, Kanto, Hokuriku, Chubu, Kinki,
Chugoku, Shikoku, and Kyushu. We exclude Tohoku area from our sample to remove the impact of the2011 off the Pacific coast of Tohoku Earthquake. Note that there are several missing years for some regional
development bureaus. See Appendix.

9

Table 1. Summary Statistics
Log of Engineer’s Estimate# Bidders# of# of JV Rate ofProb.
Auctions Auctions JV auction JV winning Mean
Min
Med
Max
Mean Min
Panel (A): By Reserve Prices
Non WTO
66733
4
0.000
0.750
18.374 4.787 18.523 22.929 4.057
1
WTO
1712
245
0.143
0.408
21.025 16.097 20.885 24.350 10.411
1Panel (B): By Construction Types
Civil Engr.
806
120
0.149
0.475
21.284 18.081 21.161 24.350 11.428
1
PC
177
10
0.056
0.200
20.731 19.604 20.634 22.513 11.006
1Bridge
460
97
0.211
0.381
20.919 19.524 20.807 22.782 11.311
1machine
63
0
0.000
NaN
20.814 19.988 20.639 22.544 3.714
1building
99
11
0.111
0.182
21.083 19.399 20.914 23.126 6.606
1electricity
29
1
0.034
0.000
20.517 18.066 20.533 21.857 4.069
1
airconditioner
31
5
0.161
0.400
20.780 20.281 20.683 22.525 6.516
1
dredging
15
1
0.067
0.000
20.821 20.287 20.738 21.933 4.400
1
CC
7
0
0.000
NaN
20.209 19.837 20.041 20.610 9.143
4
management
18
0
0.000
NaN
17.518 16.097 17.118 20.609 2.833
1bridgerepair
1
0
0.000
NaN
20.796 20.796 20.796 20.796 4.000
4painting
1
0
0.000
NaN
17.824 17.824 17.824 17.824 2.000
2
slope
4
0
0.000
NaN
20.815 20.115 20.767 21.610 13.000
1
pavement
1
0
0.000
NaN
19.288 19.288 19.288 19.288 14.000 14
Panel (C): By Regions
Kanto
637
130
0.204
0.462
21.181 20.102 21.044 24.350 9.722
1
Chubu
195
6
0.031
0.167
20.896 20.107 20.783 22.935 12.354
1
Hokuriku
68
13
0.191
0.462
20.955 16.519 20.906 23.598 10.529
1
Kinki
402
16
0.040
0.188
20.909 17.028 20.790 23.334 10.846
1Chugoku
39
2
0.051
0.500
20.935 17.824 20.752 22.743 9.718
2
Shikoku
110
18
0.164
0.333
21.019 19.837 20.803 22.934 8.918
1
Kyushu
261
60
0.230
0.383
20.955 16.097 20.891 23.482 10.670
1Final Sample

793

194

0.245

0.459

21.24418.41621.11424.35010.810

1

Med

Max

3
10

52
35

10
12
12
4
5
3
6
5
11
2
4
2
10.5
14

35
19
24
9
28
12
14
8
14
8
4
2
30
14

9
12
11
10
10
8.5
10

33
35
32
32
19
22
32

10

33

Notes. Rate of JV auctions is the rate of the number of the auctions in which at least one joint venture participate to the total
number of auctions in each construction type. The second and the third panel is the detail about WTO type auctions.

2.2

Descriptive Statistics and Motivating Facts

In the auctions explained above, a bid submitted by each bidder–both single bidders andjoint ventures–is weighted by “score,” which is calculated by the combination of the bidder
attributes and the characteristics of the procurement project, based on the pre-determinedscoring rules.8 The auctioneers then compare the “effective bids,” defined as the ratio of thescore to the submitted bid, i.e., sbii × 108 where bi and si denote a bid and a score of bidder
i.9 A bidder with the highest effective bid wins the auction, implying that submitting thelower bid or obtaining higher score increase the likelihood of winning. The minimum scoreis 100, whereas the maximum score are varied by auctions, depending on difficulties andcomplexities of projects, which can be 200 at maximum. The effective bids are therefore
typically ranged from 0 to 200.
8

For joint ventures, we observe a score for a joint venture, not for individual firms.
In our data, the bids are typically in order of 108 JPY, implying that sbii become tiny values. Therefore,
in the data, effective bids are defined as Bi ≡ sbii × 108 .
910

In principle, score is not perfectly known to the bidders when submitting their bids,
because the scoring rule may contain some parts that involve uncertainty, as well as somedeterministic parts based on the bidders’ attributes. However, in our model, we assume
that bidders decide their bids, knowing their score. There are several justifications forour assumption. First, 15 years have passed since the Japanese government introduced thisscoring rules and it is reasonable to believe that the firms are now able to form an appropriate
expectation of their score in advance.10 Second, the data also support our assumption. Table
2 summarizes the results where we regress the logarithm of submitted bids on the score andsome other variables, as well as some fixed effects. We find the statistically significant positive
correlation between the submitted bids and the score, implying that their bids reflect theirscores and this results could not happen when bidders did not know their scores.
Figure 1 depicts the distributions of firm-level behavior in our sample: logarithm ofeffective bid (ln Bi ), logarithm of bid (ln bi ), and score (si ). The blue bins represent the joint
ventures, and orange bins represent the single bidders. The left column shows the histogramsof the three variables observed in all the auctions, while the right column is about the bids
observed in the auctions in which at least one joint venture exists. While we see the small
effective bids by joint ventures in Panel (a), Panel (b) shows this is due to selective entry.
From Panel (c), we know that joint ventures enter the relatively expensive projects evenwhen we focus on WTO type auctions. As to the score, the single bidders and the joint
ventures face the similar distributions and we do not find the systematic difference about
the auctions in which at least one joint venture exists.

2.3

Collusion in Our Data

Before proceeding to our main analysis, we check whether the bidding patterns observed inour data exhibit any symptoms of collusion. This is because it is well known that collusive
behaviors are suspected in the Japanese procurement auction (e.g. Kawai and Nakabayashi,
10
One evidence of this information structure is provided in Kawai and Nakabayashi (2022b). They argue
that the some firms in the scoring auction of Japanese procurement conduct bid rotations based on the levelof the score: after one firm with the high score wins an auction, another firm with the lower score takes
turn to win an auction. Such behaviors should not be observed when the firms did not know their scores inadvance.

11

(a)

(b)

(c)

(d)

(e)

(f)

Figure 1. Histograms of effective bids, log of bids, and entrants’ scores. Blue bins represent
joint ventures, and red bins represent single bidders. In the left column, we use all theauctions. In the right column, we use the auctions in which at least one joint venture
participates. The first row is about the log of effective bids, defined as the score’s ratio tothe bid. The second row is about the log of bids, and the third row is about the score.

12

Table 2. Regression Results

Score

(1)
ln(bid)0.003∗∗∗(0.000)(2)ln(bid)0.001∗∗(0.000)-0.021∗∗∗(0.001)

20.537∗∗∗(0.060)20.636∗∗∗(0.072)√√√(3)ln(bid)0.002∗∗∗(0.001)-0.004(0.008)-0.000∗∗(0.000)20.403∗∗∗(0.129)
√
√
√

8572
0.010

8572
0.172

8572
0.173

# bidders
Score × # bidders
Constant
Year FE
Region FE
Type FE
N
R2

Notes: Standard errors in parentheses. ∗ p < 0.1, ∗∗ p < 0.05, ∗∗∗ p < 0.01.

2022b; Chassang et al., 2022; Kawai et al., 2022; Kawai and Nakabayashi, 2022a) and, if
the firms indeed engage in collusion, our model/empirical strategy may not work in thesubsequent sections. We therefore examine our data with a screening method proposed by
Kawai and Nakabayashi (2022b) and show that our data do not indicate any suspicious
bidding behaviors.
Following Kawai and Nakabayashi (2022b), we first split our data by region and year andthen apply their screening method to each subset of our data to identify the sets of auction
which may suffer from collusion.11 The results are graphically demonstrated in Figure A1
and Figure A212 . We do not find any suspicious bidding patterns in our data, unlike Kawaiand Nakabayashi (2022b). This discrepancy between their results and our results is likely
to come from the difference between the type of the procurements; We focus on relatively
11

Their screening method is based on the fact that (we need briefly summarize Kawai and Nakabayashi below is just a copy and paste from IKegami-kun) It uses the mathematical fact that, when we focus on themarginally losing and winning bidders, the winner is determined at random if they do not form a collusion. If
the auction suffers from any collusive behavior, the submitted bid of the marginally loser unnaturally differsfrom the winning bid: for example, when the firm with the higher technology tries to loose the auction, thesubmitted bid must be unnaturally higher. By checking this gap, we can detect the collusive bids. As theexample of Nippo cooperation in Kawai and Nakabayashi (2022b), this method can be applied to each firm
and we find the set of suspicious firms.
12
If we detect a jump at the point of 0 in the figures, this implies that the high quality bidders, who arelikely to win, do carefully choose their bids to lose the auction. This is one evidence of the collusion.

13

large-scale auctions compared with the auctions studied in the existing literature and thebidders in our data would face much stricter compliance requirements. We therefore keep
all observations described in the previous subsection for our main analysis.

3

Model

We consider a two-stage model. In the first stage, entry and joint venture formation stage,
the potential entrants express their intentions regarding the entry type: to try to form ajoint venture, to enter as a single bidder, or to stay out from the market. Then, the set of
the intentions of the potential entrants leads to a distribution over the outcome, the numberof joint ventures and the number of single bidders. In the second stage, bidding stage, therealized entrants (realized in the first stage) compete in the scoring auction. Note that there
are two types of entrants: joint venture and single bidder. We treat them as a asymmetricentrants and we build the model as an asymmetric scoring auction. In the following, we
describe the details of the two stages in a reverse order.

3.1

Bidding stage model

In this section, we use the followings notations: given an auction, i denotes the index of theentrants in the auction, si denotes the score of the firm i, bi denotes the submitted bid of thefirm i, and the effective bid is defined as Bi ≡ sbii . The auction is a scoring auction, where
the bidder who submits the lowest effective bid wins the auction. The engineer’s estimateof the project cost is denoted by p.
When the entrant i wins the auction, the payoff is given bybi − c̃i p =si− c̃i p,Bi

where c̃i is the individual cost factor normalized by p, and the actual cost of the entrant i isequal to c̃i p. We assume that the score and the individual cost factor are private information.
We observe p, bi and si while the individual cost factor c̃ij is not observed.
The number of the joint ventures is denoted by M , and the number of single bidders is
14

denoted by N . In a slight abuse of notation, M and N also represent the sets of each typeof bidders. First, we describe the optimization problem for a single bidder i as
max P rB

BjJV

≤ B ∀j ∈ M ,

BjS ≤ B ∀j ∈ N \ {i}  si− c̃i p ,B

where we denote the effective bid of a single bidder, BjS , and a joint venture, BjJV , by capitalletters. By taking the logarithm of the effective bids, we have the following equivalent
problem:max P rBln BjJV ≤ ln B ∀j ∈ M ,ln BjS ≤ ln B ∀j ∈ N \ {i}  si− c̃i p .
B

We can define the problem for a joint venture in the similar manner just by replacing M by
M \ {i} and N \ {i} by N .
For each type of the entrant, we assume that the pair of the score and the individual cost
factor is drawn independently from an identical distribution.
Assumption 1. If the entrant i s a single bidder, the pair of the score and the individual
cost factor, (si , c̃i ), is drawn independently from GS . If i is a joint venture, (si , c̃i ), is drawn
independently from GJV . And we denote the distribution of sc̃ii of single bidders and the sameof joint ventures by G̃S and G̃JV .
Under this assumption and given M and N , and assuming that this auction has a uniqueequilibrium, the logarithm of the effective bids of single bidders and joint ventures follow two
distinct distributions independently in the equilibrium. We denote them by F S and F JV .
Then the payoff maximization problem of a single bidder i is written as follows:S

max F (ln B)
B

N −1

F

JV

(ln B)

M

s

i

B



− c̃i p .

(1)

We write the maximized expected payoff by V S ( sc̃ii ; M, N, p) and the same one for joint
venture by V JV ( sc̃ii ; M, N, p).

15

3.1.1Equilibrium

Here, we discuss the existence and the uniqueness of the equilibrium in this auction according
to the argument of Lebrun (1999), which argues the existence and the uniqueness of theBayesian Nash equilibrium in the first price asymmetric auction. Though our model aredifferent from its setting in several aspects, we can still apply the similar argument to provethe existence and uniqueness of the equilibrium.
First, we take the first order condition of the problem (1) given the distributions of thelogarithm of the effective bids to characterize the bidding strategy. For a single bidder andfor a joint venture, the FOC’s are the following:


c̃i
1


1 − si pB = (N −1) f S (ln B) +M f JV (ln B) ,F S (ln B)

F JV (ln B)

(2)


c̃i
1


1 − si pB = N f S (ln B) +(M −1) f JV (ln B) .
F S (ln B)

F JV (ln B)

The optimal effective bid depends on the private information only through sc̃ii . Hence, given
the number of entrants of both types and the expected cost, we can solve the above twoconditions and get the optimal bidding strategies BS · ; F S , F JV and BJV · ; F S , F JV
that map sc̃ii to the effective bid. In other words, although our problem has two dimensional
private information, the optimization problem is reduced to a one-dimensional problem. We
define an equilibrium in this game as follows.
Definition 1. The pair of two invertible functions mapping sc̃ to an effective bid, BS⋆ (·) and⋆
BJV(·), is an equilibrium, if it satisfiesB ⋆ (·) = BS · ; F S , F JVSB ⋆ (·) = BJV · ; F S , F JV 
JV
where


  

F S (ln B) ≡ P r B ⋆ c̃i ≤ B
S si

 


c̃i
F JV (ln B) ≡ P r B ⋆
≤B .
JV
si
16

(3)

Now, assume that there is an equilibrium in this game and the bidding strategy isdecreasing in sc̃ii . This means that when the firm faces a higher cost or the score is lower, i.e.,
the firm is more competitive, the firm submits lower effective bids. If the bidding strategy
is increasing in sc̃ii , the reverse is true; then each entrant has an incentive to deviate tosubmitting more competitive bids. Hence it is not restrictive that we assume the bidding
strategy is decreasing in sc̃ii . Under an equilibrium, the problem (1) is transformed into thefollowing:
max
B




  M  si
N −1 ⋆,−1(B)
1 − G̃JV BJV
1 − G̃S BS⋆,−1 (B)− c̃i p .
B⋆
Here, we use the fact that BS⋆ (·) and BJV(·) are decreasing. We have an analogous problem

for a joint venture. By taking the first order conditions for both types and solving the systemof differential equations, we have the following two differential equations:


⋆,−1

(B) =
dB
dB

JV

⋆,−1
1−G̃JV (BJV(B)) 1
1
1
,
⋆,−1
⋆,−1
JV
N +M −1 g̃ (B(B)Bp−1(B)) B B
JV

JV

⋆,−1

1−G̃S (BS(B)) 1

d
1
1
 dB
.
BS⋆,−1 (B) = N +M
−1 g̃ S (B ⋆,−1 (B)) B B ⋆,−1 (B)Bp−1
SS

Note that the right hand side is continuous in B over [0, c̃siip ] for each i in both equations.
⋆,−1
We assume that the right hand side is Lipschitz continuous w.r.t. BJV(B) in the firstequation and BS⋆,−1 (B) in the second equation.
JV

S

(α)
1−G̃ (α)
11Assumption 2. 1−g̃G̃are Lipschitz continuous w.r.t. α.
JV (α) αBp−1 andg̃ S (α) αBp−1

Then there is a solution to the differential equation of each type and that is unique given
an initial condition. This implies that the equilibrium of this auction is unique up to theinitial condition if there is at least one equilibrium. Note that no firm bids the bid bigger
than the cost: for every entrant i, we have bi > c̃i p ⇔c̃ipBi − 1 < 0.
siThis implies thatddB ⋆,−1 (B) and dB
BS⋆,−1 (B) are negative, which does not contradict with our assumptiondB JV⋆
as BJV(·) and BS⋆ (·) are decreasing.

17

(a) Maximum of efficiency(b) Minimum of efficiency

Figure 2. Comparison between single bidder and joint venture with respect to the submitted
bids.
3.1.2

Ex-ante expected payoff

To analyze the incentive in the entry and joint venture formation stage, we define the exante expected payoffs that the potential entrant faces before his entry. As in Levin andSmith (1994), we assume that the potential entrants do not know his own cost score ratio
before the entry. This assumption on the information structure is reasonable and standard
in the literature because appropriate assessment on the project cost and score rating requires
certain effort and potential entrants need to decide whether to put such effort or not in thefirst place, which we view as the entry decision. Furthermore, for the score, the potential
entrants do not know the detail formula in advance. All they know is which characteristics
the government takes into account and the maximum points.
This model is justified by our data. Now we measure bid efficiency for each bidder ineach auction by comparing the engineer’s estimate to the submitted bid:
efficiency =Engineer’s estimate − Submitted bid
× 100.
Engineer’s estimate

Figure 2 compares the maximum and the minimum of the efficiencies within the single bidders
and the joint ventures. Panel (a) indicates that the joint venture is likely to bid the lower
price: there seem to exist cost synergy. However, as shown in Panel (b), this competitivenessof the joint venture does not always realize: the minimum efficiency of the joint ventures18

is relatively larger than those of the single bidders. In other words, the joint ventures canbe very weak in the scoring auction. We interpret Figure 2 as the evidence that the cost
information in the second stage is not known to the potential bidders in the first stage. This
assumption greatly simplifies our formulation of the first stage. Hereafter, in the model ofthe entry and joint venture formation, we assume that the distributions of the individual
cost and the score for the single bidder and the joint venture are all they know in the firststage.
We define the ex ante expected payoff conditional on the realized entry pattern for eachpair of (M, N, p) and the type of the entrant, and we denoted them by uJV (M, N ; p) anduS (M, N ; p) where the lower script represents the type of the entrant, joint venture andsingle bidder.
ihuJV (M, N ; p) = E c̃i V JV ( sc̃i ; M, N, p) ,
i
si
h
i

uS (M, N ; p) = E c̃i V S ( c̃i ; M, N, p) .
si
si

The expectations are taken with respect to the realization of the fraction sc̃ii . Note that
we consider the functions uJV and uS as the ex ante expected payoffs. Each value of thisfunction corresponds to the ex ante expected payoff conditional on the entry pattern (M, N )and the engineer’s estimate p.
When potential entrants make their entry decision, however, they do not know therealization of M and N yet. Given an engineer’s estimate p, to compute the unconditional
ex ante expected payoff, they need to take an expectation of these uJV and uS with someprobability distribution over the entry outcome. In the following section, we describe theintention choice problem in the entry and joint venture formation stage, and describe theprobability distribution as the outcome of potential entrants’ strategy.

3.2

Entry and joint venture formation stage

The goal of this section is to characterize the distribution over the entry patterns. Let us
emphasize that our model does not predict the realization and identity of entrant, joint
ventures and single bidders. Instead, our model predicts the distribution over the realization19

of the number of joint ventures and single bidders. In this sense, we assume homogeneous
potential entrants. In the particular context of procurement auctions, this observational
homogeneity is justifiable because the auctioneer (government) set the the entry criterion
that all the potential entrants must satisfy, which makes the potential entrants similar inobservables. For example, the project like a bridge building puts the minimum requirement
about the size and the technology of the potential entrants to guarantee that the project issuccessfully executed regardless of the auction result.
We parameterize the distribution over the outcomes by three types of parameters: theentry cost as a joint venture , cJV ∈ R, the entry cost as a single bidder, cS ∈ R, and a set ofoutcome mixing matrices R = RJV , RS , RN . Hereafter, first I describe the role of outcome
mixing matrices in our model and then characterize the equilibrium of our model.
3.2.1

Outcome mixing matrix

In our model, the observationally homogeneous potential entrants first express their intentions
about the mode of entry. There are three intentions: JV , S, and N . When the firm wants
to form a joint venture with the other firms, the firm chooses JV . Note that, even after
expressing this intention, the firm might not be able to form a joint venture because it
requires at least one another firm who wants to form a joint venture and the compatibility
with the other firms also matters to form a joint venture. In this sense, we call this choice as
an intention. We assume that when the firm chooses S, the firm enters as a single bidder in
the auction13 . When the firm chooses N , the firm stays out of the market. Note that S andN directly leads to the entry type in contrast to the case of JV . We denote the number offirms expressing each intention by L1 , L2 and L3 and call the triplet (L1 , L2 , L3 ) by intention
pattern. When we have the finite number of potential entrants, the total number of intention
patterns is finite, which is denoted by J.
For each firm, the possible entry realization is composed of the number of joint ventures
and the number of single bidders and the indicator of the entry type. We call the pair of
the number of joint ventures and the number of single bidders by entry pattern (M, N )13This is just an option. Our model can allow the possibility that the potential entrant does not enter orform a joint venture even after it chooses S as its intention.

20

and denote the indicator by δ ∈ {JV, S, N }. From the potential entrant’s point of view,
an outcome is a triplet of (M, N, δ). We assume M and N has a upper bound, M̄ and N̄ ,respectively. Therefore, the total number of outcomes is finite; The total number of entry
patterns is denoted by K = (M̄ + 1)(N̄ + 1) where +1 is necessary to express the case of noentry and the total number of outcomes is 3K. With slight loss of generality, let us assume
N̄ to be equal to the number of potential entrants. Then, we will have J =N̄ +2 C2 .
Next, we describe the correspondence between the intention and realization of outcome.
There are two different approaches: (1) specifying the coalition formation process andapplying a “reasonable” solution concept, or (2) leaving it unspecified and directly inferring
the correspondence directly from the data. Since there is no “standard” model in coalition
formation with externality and researchers cannot observe the actual process, we take thesecond approach. Namely, Given an intention pattern (L1 , L2 , L3 ) and one intention I ∈{JV, S, N }, we assume an outcome (M, N, δ) realizes with probability r(M, N, δ | L1 , L2 , L3 ; I),e.g., r(M, N, JV | L1 , L2 , L3 ; JV ) is the probability that M joint ventures enter and N single
bidders enter and the firm can form a joint venture when the total numbers of firms choosing
JV /S/N are L1 /L2 /L3 and he chooses JV . We naturally assume that the intention of S
and N determines the entry type directly, i.e., r(M, N, JV | L1 , L2 , L3 ; S) = r(M, N, N |L1 , L2 , L3 ; S) = r(M, N, JV | L1 , L2 , L3 ; N ) = r(M, N, S | L1 , L2 , L3 ; N ) = 0 for all the pairsPof (M, N ), and (M,N ) r(M, N, S | L1 , L2 , L3 ; S) = 1 for all (L1 , L2 , L3 ) with L2 ≥ 1.
By collecting these probabilities, we make a probability vector for (L1 , L2 , L3 ). And by
stacking these columns row-wisely, we make up RI . In other words, RI is a 3K × J column
stochastic matrix jth column is the probability vector over the outcomes for jth intention
pattern. We can make up RI for each intention {JV, S, N }. Each of these are called an
outcome mixing matrix.
Let us provide an example of a outcome mixing matrix. Suppose there is a deterministic
link between L1 and M , such as all potential entrants expressing the intent to form a
JV get matched with someone else randomly and ⌊ L21 ⌋ JVs are formed (if L1 is a evennumber, L21 pairs are formed and if L1 is a odd number, ⌊ L21 ⌋ − 1 pairs are formed and one
trio is formed). Under this coalition formation process, r(⌊ L21 ⌋, L2 , JV ; L1 , L2 , L3 ; JV ) =r(⌊ L21 ⌋, L2 , S; L1 , L2 , L3 ; S) = 1.
21

Figure 3. The illustration of feasible Φ. The orange line is one example of feasible Φ. The
blue line is the upper bound for any feasible Φ. This upper bound is obtained by ⌊ L21 ⌋.
Even though we do not specify the coalition formation process, assuming a deterministic
relationship between L1 and M drastically reduce the number of parameters in our modeland improve the quality and reliability of estimation. Hence, we assume there is that there
is a mapping Φ : N → N from the number of potential entrants choosing JV as his intention
to the number of successfully formed joint ventures.
The nice property of this type of outcome mixing matrix is that the number of feasible
Φ is finite. We say Φ is feasible when Φ has no jump of size two or more and is below ⌊ L21 ⌋,which is the upper bound for the number of the formed joint ventures because it requires atleast two firms to form a joint venture. Suppose there are 8 potential entrants. The orange
line in Figure 3 is one example of feasible Φ. Under this Φ, even when 5 firms choose JV
as their intentions, only one joint venture is successfully formed. Note that, in this exampleof R, we do not restrict the number of firms to form a joint venture, i.e., we allow three ormore firms form a joint venture. Also, we do not impose Φ(N ) = ⌊ N2 ⌋ because there may befriction in JV formation, i.e., not all potential entrants interested in JV cannot form a JV,
and/or more than two potential entrants may form a JV. The total number of such functions
is finite for any number of potential entrants and so we can collect all the functions. Even22

under with a deterministic mapping Φ(N ), the realization of (M, N ) is still random given(L1 , L2 , L3 ). This is because we do not specify how potential entrants behave when theyfailed to form a JV; they may enter as a single bidder or stay out.
3.2.2

Equilibrium

Here we define the Bayesian Nash equilibrium in the entry and joint venture formation
stage given one set of outcome mixing matrices R = RJV , RS , RN . First, we introduce
a probability vector P with length of 3K which is the prediction over the outcomes foreach intention. The elements from 1 to K The elements from the first to Kth of P are theprobabilities over the entry patterns given the firm can form a joint venture. The next K
elements are the probabilities over the entry patterns given the firm enters as a single bidder.
And the last K elements of P are the the probabilities over the entry patterns given the firm
does not enter.
Using this prediction P and entry costs, the potential entrant computes the expected
payoff attached to each intention:





JV
JV
JV


vJV (P JV ) = P1:K
· uJV − cJV + PK+1:2K· uS − cS + P2K+1:3K
·0




S
S
·
u
−
c
v
(P
)
=
P
S
S
S
K+1:2KN vN (P N ) = P2K+1:3K·0where the upper script of P represents the chosen intention. Hereafter we use P = (P JV , P S , P N ).
uJV and uS is the vector containing the ex ante expected payoffs of each entry type. By
this formulation, we interpret cJV as the entry cost as joint venture, which includes the
management cost necessary to decide the bid in the auction as a joint venture or any frictional
cost associated with forming a joint venture. By comparing with the entry cost as a single
bidder, cS , the additional execution cost incurred by forming and managing a joint venture
is computed by cJV − cS . Note that we normalize the benefit of staying out to 0.
The potential entrants face a discrete choice problem among the three intentions {JV, S, N }.
We include the additive disturbance term ϵi = (ϵi (JV ), ϵi (S), ϵi (N )) as the unobserved costin their decision problem. We assume that ϵi follows a Type I extreme value distribution.
23

The choice probabilities are written as follows:v(P JV )
m(JV ; P ) = vJV (P JV )e JVvS (P S ) vN (P N )

e
+e
+e


S)
v
(P
m(S; P ) = vJV (P JV ) e SvS (P S ) vN (P N )

e
+e
+e



vN (P N )em(N ; P ) =vJV (P JV )vS (P S )vN (P N )
e

+e

.

+e

We write m (P ) as the triplet of the choice probabilities given one prediction triplet P .
Then we have the distribution over the intention patterns which is denoted by Q(m(P )),which is the multinomial distribution of the probability vector is m(P ) and the total numberof trials is N̄ − 114 . Now we can express the distribution over the outcomes by the mixtureof the distributions in each intention pattern using outcome mixing matrices: for the firm
who chooses JV , the distributions over the outcomes can be expressed by
RJV Q(m(P )).
Also for the firms who choose S or N , we have the similar expressions: RS Q(m(P )) andRN Q(m(P )).
As in the definition of the Bayesian Nash equilibrium in Seim (2006), we characterize theequilibrium of this game by the prediction P ⋆ which is equal to the realized distributions over
the outcomes. In other words, P ⋆ solves the following fixed point problem is the equilibrium
prediction of our model:P ⋆,JV = RJV Q(m(P ⋆ ))P ⋆,S = RS Q(m(P ⋆ ))





P ⋆,N = RN Q(m(P ⋆ )).
This is equivalent toP ⋆ = RQ(m(P ⋆ ))14

(4)

Because we fix the intention of one firm, we have to consider the distribution of the intentions of theother potential entrants.

24

where R is the stack of RJV , RS , RN .
By Proposition 1, we know that RQ(m(P )) is a contraction mapping. This implies thatthe equilibrium level of prediction P ⋆ is unique in our model.
Proposition 1. RQ(m(P )) is a contraction mapping w.r.t. P .
Proof. See Appendix.
Finally, we can compute the distribution over the entry patterns based on P ⋆ . First
we compute the marginal distributions over the entry patterns for each intention and thencompute the weighted average of the marginal distributions. We denote this equilibrium
distributions over the entry patterns by g(M, N ).
Remark 1. The studies about coalition formation, see Ray and Vohra (2015) for a survey,
have proposed a lot of models to describe how groups are formed. In their framework,
we can analyze even the group formation under externality. However, the outcome of themodel heavily depends on the assumption about the farsightedness of the players, like in theexample 5.5. in Ray and Vohra (2015), and on the protocol which specifies the process of thegroup formation such as the order of the group formation proposer. For an empirical work
about the group formation in the procurement auction, we need a model which avoids these
specifications, because we do not know the exact process of the joint venture formation. This
is why we do not adopt the models in the coalition formation.

4

Estimation

In this section, we describe the estimation strategies for the two stages separately. In thebidding stage, the estimation target is the distributions of the pair (c̃i , si ) of a joint venture
and a single bidder. This is achieved by retrieving the individual cost factor c̃i from the firstorder condition. Given the estimated distributions, we then estimate the ex-ante expected
payoffs, uJV , uS , for the different levels of the expected cost. In the entry stage, we use theexpected ex-ante payoffs to estimate the entry cost of a joint venture and a single bidder
and the outcome mixing matrices.

25

4.1

Estimation of bidding sage

Hereafter, we denote the index of auction by the subscript j. From equation (2), we havethe following inversions for the cost of both types:
c̃ij =



sij 
1

1−
S
f (ln Bij )f JV (ln Bij )pj Bij(Nj − 1) S
+ Mj JVF (ln Bij )F(5)(ln Bij )for a single bidder, andc̃ij =



1
sij 

1−
S
f (ln Bij )f JV (ln Bij )pj BijNj S+ (Mj − 1) JV
F (ln Bij )F(6)(ln Bij )for a joint venture. Once we estimate the two distributions of the effective bids for a single
bidder and a joint venture, we can retrieve the individual cost factor for each firm using theabove equation using these equations.
Now we describe the estimation procedure for the distributions of the effective bids. Notethat the optimization problem implies that the optimal level of effective bid is dependent on
the combination of (p, M, N ) and whether or not the firm is a single bidder or a JV. First
we assume that the logarithm of the effective bids follow a Normal distribution.
Assumption 3.
ln BijJV ∼ N θjJV , σj2,JV , ln BijS ∼ N θjS , σj2,SWe estimate these distributions by sieve methods, i.e., we estimate the mean and thevariance using the following regerssion:ln Bij = poly(dJVij , pj , Mj , Nj ; β) + ϵij .
where dJV
ij is the dummy variable for the joint venture and poly(X, β) represents the polynomial
function of the variables X with some degree when the coefficients are β. Using all the data,
run the above regression and denote the estimated coefficients by β̂. Given this result, the26

estimated distributions in auction j are as follows:


2,JV
, and
ln BjJV ∼ N poly(dJV
=
1,
p
,
M
,
N
;
β̂),
σ̂
j
j
j
ij


2,S
ln BjS ∼ N poly(dJV
=
0,
p
,
M
,
N
;
β̂),
σ̂
.
j
j
j
ij
where the estimated variances areσ̂ 2,JV =σ̂ 2,S =

1
#JV

X 

2
ln Bij − poly(dJV
=
1,
p
,
M
,
N
;
β̂)
, and
j
j
j
ij

ij:dJVij =1

1#SingleX 

2
ln Bij − poly(dJV
=
0,
p
,
M
,
N
;
β̂)
.
j
j
j
ij

ij:dJVij =0

Based on the estimated distributions, we retrieve the individual cost factors by theequation (5) and (6).
4.1.1

Computation of ex-ante expected payoffs

We compute the ex-ante expected payoffs based on the estimated joint distribution of (c̃i , si ).
In particular, we compute the followings: uJV (M, N, p) and uS (M, N, p). Because p is acontinuous variable, we cannot expect many auctions have the same expected cost. Thisrequires us to approximate the set of auctions having the same expected cost in some way.
Here, we split the space of p into 2 sub-groups and compute two sets of ex-ante expected
payoffs. In other words, we consider the auctions within the same group as homogeneous
ones and make use of the variations within the group to infer the ex-ante expected payoffs15 .
We use the following notations to describe the specific process of the inference. p̄ and p
denote the maximum and the minimum of the engineer’s estimate in our data. pcut is thecutoff to divide the total number of auctions into equal-sized two sets. We compute two
representative engineer’s estimates for each group, p̃1 , p˜2 , they are the mean of the observed
expected costs in each group. Let the upper bounds of M, N be M̄ , N̄ . Hence, for each typeof entry, S and JV , we infer 2 × M̄ × N̄ expected payoffs.
15

Another possible way is to conduct local estimation using some type of kernel function over the expected
cost.

27

We compute the ex-ante expected payoffs by simulation. When we focus on the single
bidder and on one entry pattern (M, N ) and one size of auction k ∈ {1, 2}, our inference
procedure is as follows:
1. Draw 2000 observed single bidders from the auctions in k.

Note that, from theestimation of the bidding stage, we know the individual costs of them as well as thescores.
2. For each single bidder i, compute the maximized expected payoff under the entry
pattern (M, N ) given his pair of (c̃i , si ) and the representative engineer’s estimate p̃k .
3. Take the average of the maximized expected payoffs among the drawn single bidders.
This corresponds to uS (M, N, p̃k ).
The similar process is applied to all the pair of possible entry patterns, to all the size, andto the entrant as a joint venture.

4.2

Estimation of entry and joint venture formation stage

Remember that we have two entry costs and one matrix as our parameters: (cJV , cS , R).
We take an estimation strategy using MPEC (Su and Judd (2012)) where the equilibrium
constraint is (4) and the objective function is
LL(cJV , cS , R) =X

T (M, N ) × ln g(M, N ; cJV , cS , R).

(M,N )

Here g(M, N ; cJV , cS , R) is the equilibrium distribution over the entry patterns and we clarify
its dependence on the parameters.
Without any further specification, R is high dimensional object. To stabilize our estimationand to identify the parameters, we assume a specific type of R as described in Section 3.2.1.
Here, we further parametrize R by two objects: (Φ, z) where Φ : N → N maps the numberof firms choosing JV as his intention to the number of successfully formed joint venturesand z ∈ [0, 1], the probability of entry as a single bidder when the firm fails to form a joint
venture. As we explained in Section 3.2.1, the number of feasible Φ is finite. This allows us
28

to solve MPEC for each fixed Φ to estimate the other parameters. After estimations under
all the possible Φ’s, we choose the pair that maximize (minimize) the value of the objectivefunctions.
Furthermore, to reduce the number of possible Φ’s, we use the following function toexpress Φ16 :
L1
Φ(L1 ; α) = max 0, ⌊α × ln ⌋ .
2Here α determines the shape of Φ. So in the estimation, we first identify the set of α’s which
gives the feasible Φ’s and then solve MPEC for each possible α’s to determine the best setof estimates.
This estimation procedure is one way to estimate the static entry game under incomplete
information, such as Seim (2006), via MPEC. The standard entry game corresponds to thecase where the outcome mixing matrix R is the identity matrix and the number of intention
patterns and the number of the entry patterns are the same. In our case, because we do notknow the detail mechanism to govern the joint venture formation, we have to include non
identity and unknown R in our estimation.
We implement this constrained maximization problem in JuMP using Ipopt as a solver.
When we set the number of potential entrants to 11 and focus on the Φ which finally reaches
4 at L1 = 11, the number of feasible Φ is 7. So we solve 7 MPEC problems to get theestimation result.

4.3

Identification and Monte Carlo simulation

We argue informally the identification of the parameters in the entry and joint venture
formation stage: Φ, p and cJV , cS . Our objective here is to state that the true prediction
vector P , which is computed as the equilibrium under the true set of parameters, cannot be
generated under any other set of parameters.
The prediction vector P is a mixture of the columns of the outcome mixing matrix R
where the weights are the distribution over the intention patterns Q. Because we assume the16This restriction is due to the computational resource constraint.

29

potential entrants choose their intentions independently, this Q represents a probabilities
generated by a multinomial distribution. In other words, the weights in the mixture areconstrained by the model. Under this restriction, two different outcome mixing matrices
cannot generate the same prediction vector even by arbitrarily choosing other parameters.
This is easily seen when we focus on two extreme entry patterns: no additional single
bidders entering after failing to form a joint venture and all the potential entrants who failto form a joint venture enter as single bidders. Pick one number of joint ventures and put afocus on the entry patterns corresponding to it. Note that each column of R is just a binomialP
distribution. The prediction probability of the first entry pattern is i (1 − p)ni × wi where
i denotes the relevant column index and ni is the number of potential entrants who fails toform a joint venture and wi is the weight on the column i. The same probability for thePsecond case is j pnj wj . Because both of them are monotone in p, we can find appropriate
p’s for the two extreme cases for any weight and for any set of relevant columns. But theweights are not arbitrary, we cannot always find just one p consistent with the two cases.
In practice, to cover the support of the function Φ, we need the auctions which have manypotential entrants try to form a joint venture and the auctions which reduces the incentive toform a joint venture to identify Φ. To do so, we do not separate R for each class of auctions,instead we have just one R governing the number of joint venture in all auctions.
We conduct a Monte Carlo simulation to show our estimation strategy and validate theimplementation result. We set the number of potential entrants to 5 and set the maximum
number of joint ventures to 2. Under this setting, we solve the equilibrium of our model
under a set of ex-ante expected payoffs, which is computed from our data. Based on thisequilibrium distribution, we draw a set of realized entries, which is the simulated data in our
experiment.
Our parameter setting is as follows: cJV = 105, cS = 55 and α = 2.12. In the current
setting, we have another possible α which gives a feasible Φ which is α = 2.57. In thisexperiment, we fixed cS to the true value and compute the value of the log-likelihood for theseveral values of cJV and the two α’s. Figure 4 summarizes the two log-likelihood functions,where the left axis represents the value of the log-likelihood for the true α and the rightaxis represents the same one for the higher α. Panel (a) of Figure 4 shows the log-likelihood
30

(a) Maximizer for the true α(b) Maximizer for the wrong α

Figure 4. The log likelihood function of the two different α’s. The blue line is obtained when
we use the true α and the red line is the obtained when we use one wrong α. Panel (a) is
the snapshot around true entry cost. Panel (b) is the snapshot around the maximizer of thelog likelihood of the wrong α.
functions around the true value of cJV which is 105. We find that, when we adopt the true
α, which is 2.12, the log-likelihood takes its maximum around the true value. On the other
hand, Panel (b) of Figure 4 shows the region around the maximizer of the log-likelihood
function for the wrong α, which is α = 2.57. As you find, the maximized lo-likelihood forthe true α is around −4726 while the same one for the wrong α is around −18547. THhis
difference allows us to identify the true shape of Φ.

5

Estimation Results

This section presents a series of estimation results for the structural model discussed in
the previous sections. Section 5.1 shows the estimation results for the bidding stage: The
retrieved individual costs and the ex-ante expected payoffs. Section 5.2 shows the estimation
results for the entry and joint venture formation stage. In particular, our main interest here
lies in estimating (i) the outcome mixing matrix, in particular, Φ, which determines thenumber of successfully formed joint ventures and (ii) the additional entry cost as a joint
venture.

31

(a) A Homoskedasticity Case(b) A Heteroskedastic Case

Figure 5. Density estimations of sc̃ii . Panel (a) demonstrates the result when we assume
homoskedastic variances. Panel (b) is the result when we use type-dependent varianceestimations. In each panel, the blue line represents the density for joint venture and redline represents the density for single bidder.

5.1

Bidding stage

First, we show the estimation results for the bidding stage, assuming, the degree of polynomial
to 1 when estimating the distributions of the logarithm of effective bids.17 Figure 5 depicts
the estimated densities of sc̃ii for single bidders and joint ventures, assuming homoskedastic
variance in Panel (a) and heteroskedastic variance in Panel (b). This is because the variancesof the effective bids of single bidders and joint ventures could be different. We retrieve c̃iand take the fraction sc̃ii for every i in the data and then plot the estimated densities basedon these empirical data points. In each panel, the blue line demonstrates the density forjoint ventures, whereas the red line demonstrates the density for single bidders.
There are two important observations in this figure: (i) the estimated distribution forjoint ventures has first order stochastic dominance over the estimated distribution for single
bidders in both panels and (ii) the density of the cost-score ratio of joint ventures has twomodals. As the fraction sc̃ii is smaller when the entrant i is more competitive in the current
scoring auction, this result indicates that joint ventures are more likely to win the auctions.
17

We check the robustness of our results by changing the choice of this degree of polynomial. Figure A3
in Appendix demonstrates the results when we set the degree of polynomial is equal to 2.

32

And, as we see in Panel (f) of Figure 1f where we find that the distributions of score forsingle bidders and joint ventures are almost identical, joint ventures are more competitive
due to cost reduction which, we believe, is from cost synergies.
Also, the cost distribution being bi-model suggests that there are two types of joint
ventures: joint ventures who materialize the cost synergies and who does not materialize
the cost synergies. As the latter type of the joint venture has similar cost distribution as
single bidders, the social benefit of joint ventures comes from the former type of the joint
venture. “What makes the joint venture more cost effective? And how can we facilitate thecost efficiency?” is a very important topic for future studies and is beyond the scope of ourstudies because this paper does not put any structure on how the cost synergies materialize.
Based on the estimated distribution of (c̃i , si ), we then estimate the ex-ante expected
payoffs in each auction. Figure A4 shows the estimated ex-ante expected payoffs for a single
bidder and a joint venture, dividing the auctions into two classes by its engineers estimates;
If an engineers’ estimates of an auction i is below median, it is categorized into small-sizedauction, otherwise large-sized auction, as discussed in Section 4.1.1. For each pair of thenumber of a joint venture, M , and the number of single bidders, N , we plot the estimatedex-ante expected payoff. In general, we find that the payoffs are larger when the number ofentrants is smaller, which is consistent with the theoretical prediction18 .
To check the fit of our model, we compare the observed bids with the optimal bids
obtained as the solutions to the expected profit maximization problem, defined in Equation(1). Figure A5 compares the observed effective bids with the simulated optimal effective bids
for each category. The orange line depicts the estimated density of the observed effective bids,
whereas the blue line depicts the estimated density of the simulated bids. The comparison
confirms that the model fits the data reasonably well; the simulated bid distribution and theobserved bid distribution have their peak at similar points. However, there are discrepancy
as well; the simulated distributions have thinner tails than the observed bids. As we fit
the model with a limited number of parameters and smooth distributional assumptions, wecannot avoid the simulated distribution to have thicker tails. We would be able to fit the18

The value for the case when there is a single entrant is set to the corresponding expected cost in Figure

A4.

33

model better if we would increase the number of parameters. Doing so comes with a costthat the computation may become infeasible and the reliability of the estimates may become
vulnerable to outlier observations. Given this trade-off, we decide to adopt the current
specification, splitting the auctions to two class.

5.2

Entry and joint venture formation stage

In this section, we show the estimation results for the first stage. Figure 6 depicts theestimated Φ with the orange line and the upper bound of the number of joint ventures withthe blue line. The x-axis shows the number of potential bidders with the intent to form a joint
venture, L1 , and the y-axis shows the number of realized joint ventures, M . The estimatedΦ indicates that no joint ventures are formed until 3 potential entrants try to form a joint
venture. If four firms attempt to form a joint venture, then one joint venture will be formed.
The number of joint ventures formed increases, as the number of firms attempt to form ajoint venture.
The difference between the two lines represents the friction in joint venture formation.
Forming a joint venture requires the potential entrants to find another partner, and no joint
venture is formed even if there are two potential bidders with the intent to form a joint
venture. The non-linearity in Φ suggests that the friction is the smallest when the number ofpotential bidder with the intent is medium. It could be that (1) finding a partner is difficult
when the potential bidder with the intent is small and (2) a congestion effect exists when
the number of potential bidder gets large.
Table 3 shows the estimation results of the cost parameters for each α. The α withthe highest log-likelihood, −1, 955, and the estimated costs for joint ventures and single
bidders are α = 2.413, cJV = 19.368, and cS = 11.002, respectively. The standard errors
indicate that the difference between cJV and cS is statistically significant. Entry as a
joint venture requires the firms to spend additional 8.366 million yen. This highlights theexistence of the adjustment costs to manage the joint venture, which is well recognized in
the merger literature. This additional entry costs are equivalent to 0.21% of the average
engineers’ estimates (expected costs) in the larger-sized auctions and 0.85% in the smallersized auctions. While these numbers are very small, when we compare this additional costs
34

Figure 6. Estimated pattern of the formation of joint ventures. The horizontal axis is thetotal number of potential entrants who choose JV . The vertical line is the number of formed
joint ventures. Blue line is the upper bound for the number of joint ventures, i.e., ⌊ L21 ⌋.
Table 3. Estimation Results in Entry Stage
α

LL

cJV

cS

2.373
2.413

-1963
-1955

2.453
2.563
2.683
2.794
2.904

-2065
-2062
-2054
-2039
-2722

18.65119.368(0.511)
14.26614.10414.05316.4082.570

11.01311.002(0.032)
10.662
10.66510.667
10.6080.474

Notes: The unit of the cost is 1, 000, 000 yen. Standard errors are computed only for α that gives the highest
log-likelihood, which are contained in the brackets below the estimated values.

to the inferred ex-ante expected payoffs, it becomes a significant factor in the entry decision,
especially when the probability of winning the auction is taken into account. For example,
in the smaller-sized auctions, when there are one joint venture and one single bidder in theauction, the additional entry costs account 23.72% of the expected payoff for joint venture.
We conclude that this additional entry cost can be a driving force of the small number of35

observed joint ventures in spite of their competitiveness in the auction stage.

6

Counterfactual Simulations

Given the estimated model, we conduct a counterfactual analysis where we change the entry
costs of joint ventures to investigate whether the government should further pursuit joint
venture formations in procurement auctions.19 On the one hand, joint venture formation
should be encouraged from the viewpoint of cost synergies, according to our estimation
results. On the other hand, as we mentioned in the introduction, increasing number of joint
ventures may decreases the incentive to participate in the auction due to the competitivenessof the joint ventures. We therefore must quantify the gross benefits of this policy, taking
into account these two countervailing effects.
Measure of Outcome Efficiency To measure the efficiency of auction outcomes, wedefine procurement efficiency for a set of auctions as follows:
total amount of engineer’s estimate − total amount of winning bid
× 100.
total amount of engineer’s estimatePj (Engineer’s Estimates)j −PPj (Winning bid)jj (Engineer’s Estimates)j× 100.

In the small-sized auctions, the observed level of procurement efficiency is 11.31 and thesame one for the large-sized auctions is 12.25. In the following counterfactual analysis, we
compute this value for each class of auctions when the government changes the additional
entry cost to enumerate the gross effect on the efficiency of the procurement auctions.
For this counterfactual analysis, we need simulated sets of auctions and the entrants.
Below we describe how to generate them based on our estimation results. First, set the total
19

In principle, there are two possible policy interventions to encouraging joint venture formation: (i)lowering entry costs as a joint venture, and (ii) changing scoring rules to give preferential treatment for joint
ventures. Our data do not contain the detailed information on the score for each bidder, which prevents us
from conducting the second type of counterfactual simulations. Therefore, in this counterfactual simulations,
we focus on the former type.

36

number of auctions, T , for a fixed class of auction, p,
1. From the empirical distribution of the expected costs, we draw T expected costs.
2. Based on the estimated values of (α, cS , z) and an arbitrarily set cJV , compute theequilibrium prediction pf p and the distribution over the entry patterns.
3. Draw the entry pattern for each auction based on the above equilibrium distribution.
4. Draw the individual cost factor and the score for each firm from the estimated distributionof individual cost and score for single bidders and joint ventures.
5. Compute the optimal bid by solving the optimization problem for each bidder.
6. Determine the winner in each auction and decide the winning bid by comparing theeffective bids.
We have two technical remarks on this counterfactual simulation. First, we set the rangeof cJV as cJV ∈ [7, 30] to compute the procurement efficiencies. In the range, we check themodel can be solved, i.e., we obtain the equilibrium level of predictions and the corresponding
distribution over the entry patterns. Out of this range, our fixed point problem might not
behave well, which makes it hard to compute the counterfactual distribution. Having said
that, we still believe that [7, 30] is enough to consider the realistic situations. Second, as we
do not specify or estimate the distribution of the expected costs for each class, we use thesame distribution for both classes.

6.1

Simulation Results

Figure 7 demonstrates procurement efficiencies for each class of auctions, when we change
the cost of entry as a joint venture. The blue solid line represents the computed procurement
efficiency for the small-sized auctions, whereas the orange solid line represents the same one
for the large-sized auctions. The green dotted vertical line corresponds to the estimatedvalue of the entry costs as joint venture, c̃JV , and the purple dotted vertical line represents
the estimated value of the entry costs as single bidders, c̃S

37

Figure 7. Counterfactual procurement efficiency vs the entry cost as a joint venture
Notes: The blue solid line represents the computed procurement efficiency in the smaller-sizedauctions, whereas the orange solid line represents the same one for the larger-sized auctions. The
green dotted line corresponds to the estimated value of the entry costs as joint venture, c̃JV , andthe purple dotted line represents the estimated value of the entry costs as single bidders, c̃S .

From the figure, we can immediately see that the impacts of changing entry costs for joint
ventures has heterogeneous effects with respect to the size of auctions. When we focus on
small-sized auctions, changing entry costs for joint ventures would not change procurement
efficiency. This is due to the increasing number of entrants by decreasing the joint venture:i.e., the firms who would enter as a joint venture entry as single bidders separately. This leads
to more competitive bids. On the other hand, for the larger auction class, we find a decreasein procurement efficiency. This is because we cannot expect the cost reduction associatedwith the synergy of the joint venture. For larger-sized auctions, the effect of decreasing thecost efficiency overwhelms the effect of increasing the number of entrants.
Next, we analyze the effect of encouraging joint venture formation by decreasing theadditional entry cost. In the area between two dotted vertical lines in Figure 7 corresponds tothis type of policy. Although the gross effects are again heterogeneous in the size of auctions,in particular in the larger-sized auctions, we find the mild reduction in the additional costis the key to increase the procurement efficiency. Too much reduction induces more entry of38

joint ventures, which threatens the other potential entrants. Then the pro-competitive effectof cost synergy is overwhelmed by the anti-competitive effect of the decreasing number ofbidders. On the other hand, by decreasing the additional cost a little bit, the auctioneer canbenefit from the cost synergy of joint ventures. This is shown in the sharp decrease in justleft of the green dotted line.
Overall, changing the additional costs as a joint venture influences the larger-sized auctions
more than the smaller-sized auctions. The blue line is almost constant, regardless of cJV .
This heterogeneity also helps the policy maker to focus on the most sensitive type of auctions.
Moreover, the policymakers should note that this type of cost changing policy is delicate.
In the larger-sized auctions, the procurement efficiency changes a lot by a small change
in cJV . This is due to the low expected payoffs in the auction stage. Hence, the levelof encouragement should be determined gradually as the government observes the realized
impact.

7

Conclusion

We study the joint bidding in procurement auction using the Japanese procurement data,
developing a two-stage model where the bidders make their decisions on entry and joint
venture formation in the first stage and they subsequently bid in the second stage. The resultsfrom the second stage highlight the presence of cost synergies that benefit the joint ventures.
This is evident by comparing the estimated joint distribution of individual project cost andthe score for the single bidders with the same one for the joint ventures. Furthermore, though
joint ventures bid stronger than single bidders do on average, joint ventures occasionally bid
weaker than single bidders do, suggesting that the cost synergies involves uncertainty at thetime of joint venture formation, which is unknown even for the forming parties.
Our empirical results in the first stage indicate the existence of search frictions andadjustment costs associated with joint venture formation, which act as obstacles to form ajoint venture. The presence of joint ventures may discourage the entry incentives of singlebidders, as joint ventures become relatively stronger when formed successfully. Thus, fromthe viewpoint of procurers, when optimizing government procurement efficiency, it is crucial
39

to consider both a pro-competitive effect driven by cost synergies and an anti-competitiveeffect resulting from the lower number of bidders. Our counterfactual simulations show
that, depending on the size of auctions, the excessive promotion of joint venture formation
through lowering entry costs as joint venture could be worsen procurement efficiency, due toa reduction in the number of participating firms.
Lastly, we describe the limitations of our study and the possible future research directions.
Our model assumes homogeneity among potential entrants and focuses solely on the realized
number of joint ventures and single bidders, without considering their individual identities.
This simplification is motivated by the empirical context of our study, where all potential
bidders qualified for the World Trade Organization (WTO) type auction must be preregistered as qualified companies. Consequently, we contend that heterogeneity among
companies is not a deterministic factor in assessing the effectiveness of joint ventures. Nevertheless,incorporating identity information into the analysis could enable a more detailed examinationof the mechanisms underlying cost synergies, search frictions, and adjustment costs. In
essence, policymakers would benefit from understanding which specific pairs of companies
are more effective in achieving desired outcomes.
Our estimation method accommodates such heterogeneity by expanding the range ofpossible entry patterns and intention patterns. Although in this paper, we define the entry
pattern as the combination of the number of joint ventures and the number of single bidders,
it is possible to consider the power set of entry decisions made by each potential entrant,
thereby accounting for their identities. However, it is important to note that such an
approach substantially increases the size of the outcome mixing matrix, which can impede
efficient and stable estimation. Consequently, employing this method would necessitatea relatively small number of potential entrants to maintain computational feasibility andreliability in the estimation process.
Another important consideration is the dynamic aspects of joint venture formation.
For example, the costs associated with the joint venture formation may decrease as firms
accumulate the experience by forming joint ventures or even just attempting to form joint
ventures. Taking into account such a learning-by-doing effect may be an interesting research
direction.
40

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44

Appendix A

Additional figures

Appendix A.1

Collusive behavior

We demonstrate the results for collusion screening tests by Kawai and Nakabayashi (2022b)
for each subset of region in Figure A1 and for each year in Figure A2.
Region: Shikoku
.1

−.1

−.05

−.05

% Diff. in Price
0.05% Diff. in Price
0
.05

.1

Region: Hokuriku

−.1

−.08

−.06
−.04
% Diff. in Eff. Bid

−.02

−.1

0

−.08

−.06
−.04
% Diff. in Eff. Bid

−.02

0

−.02

0

kernel = epanechnikov, degree = 0, bandwidth = .03, pwidth = .04

kernel = epanechnikov, degree = 0, bandwidth = .03, pwidth = .04

Region: Kyushu

−.1

−.2

−.05

−.1

% Diff. in Price
0.05% Diff. in Price
0
.1

.1

.2

.15

Region: Kanto

−.1

−.08

−.06
−.04
% Diff. in Eff. Bid

−.02

0

−.1

kernel = epanechnikov, degree = 0, bandwidth = .02, pwidth = .03

−.08

−.06
−.04
% Diff. in Eff. Bid

kernel = epanechnikov, degree = 0, bandwidth = .02, pwidth = .03

Figure A1. Region-by-Region Collusion Screening Tests by Kawai and Nakabayashi (2022a)

45

.1
−.1

% Diff. in Price0.1% Diff. in Price
0

−.2

−.2

−.1

0

−.1

% Diff. in Price
.1

.2

.2

Year: 2008

.2

Year: 2007.3

Year: 2006

−.1

−.08

−.06
−.04
% Diff. in Eff. Bid

−.02

0

−.1

kernel = epanechnikov, degree = 0, bandwidth = .02, pwidth = .03

−.08

−.06
−.04
% Diff. in Eff. Bid

−.02

0

−.1

kernel = epanechnikov, degree = 0, bandwidth = .03, pwidth = .04

Year: 2010

−.02

0

−.02

0

−.02

0

−.02

0

−.02

0

Year: 2011

.1
−.1

−.08

−.06
−.04
% Diff. in Eff. Bid

−.02

0

% Diff. in Price
0
.05
−.1

−.1

−.05

−.05

−.05

% Diff. in Price
0.05% Diff. in Price
0
.05

.1

.1

−.06
−.04
% Diff. in Eff. Bid.15

Year: 2009−.08

kernel = epanechnikov, degree = 0, bandwidth = .03, pwidth = .04−.1

kernel = epanechnikov, degree = 0, bandwidth = .03, pwidth = .05

−.08

−.06
−.04
% Diff. in Eff. Bid

−.02

0

.15
.1

.06

−.05

% Diff. in Price
0
.05

.04
−.02
−.02

0

−.1

−.04
−.06
−.04
% Diff. in Eff. Bid−.1kernel = epanechnikov, degree = 0, bandwidth = .03, pwidth = .05

−.08

−.06
−.04
% Diff. in Eff. Bid

−.02

0

−.1

kernel = epanechnikov, degree = 0, bandwidth = .03, pwidth = .04

−.08

−.06
−.04
% Diff. in Eff. Bid

kernel = epanechnikov, degree = 0, bandwidth = .03, pwidth = .05

Year: 2016

−.1

−.08

−.06
−.04
% Diff. in Eff. Bid

−.02

0

% Diff. in Price
0
.05
−.05

−.05

−.05

0

% Diff. in Price.05% Diff. in Price
0
.05

.1

.1

Year: 2017.1

Year: 2015
.15

−.06
−.04
% Diff. in Eff. Bid

Year: 2014

% Diff. in Price
0
.02

.1
% Diff. in Price
.05
0
−.05

−.08

−.08

kernel = epanechnikov, degree = 0, bandwidth = .02, pwidth = .03

Year: 2013.15

Year: 2012

−.1

−.1

kernel = epanechnikov, degree = 0, bandwidth = .02, pwidth = .03−.1kernel = epanechnikov, degree = 0, bandwidth = .06, pwidth = .1

−.08

−.06
−.04
% Diff. in Eff. Bid

−.02

0

−.1

kernel = epanechnikov, degree = 0, bandwidth = .02, pwidth = .04

Year: 2019

Year: 2020

% Diff. in Price
0
.05

.1
% Diff. in Price
0
.05

.1
−.1

−.08

−.06
−.04
% Diff. in Eff. Bid−.02kernel = epanechnikov, degree = 0, bandwidth = .02, pwidth = .03

0

−.1

−.05

−.05

−.05

% Diff. in Price
0
.05

−.06
−.04
% Diff. in Eff. Bid.1

Year: 2018−.08

kernel = epanechnikov, degree = 0, bandwidth = .02, pwidth = .03

−.1

−.08

−.06
−.04
% Diff. in Eff. Bid−.02kernel = epanechnikov, degree = 0, bandwidth = .03, pwidth = .05

0

−.1

−.08

−.06
−.04
% Diff. in Eff. Bid

kernel = epanechnikov, degree = 0, bandwidth = .03, pwidth = .04

Year: 2022

−.02

−.05

0

% Diff. in Price.02.04% Diff. in Price
0
.05

.06

.08

.1

Year: 2021

−.1

−.08

−.06
−.04
% Diff. in Eff. Bid

kernel = epanechnikov, degree = 0, bandwidth = .01, pwidth = .02

−.02

0

−.1

46

kernel = epanechnikov, degree = 0, bandwidth = .02, pwidth = .02

−.08

−.06
−.04
% Diff. in Eff. Bid

−.02

0

Figure A2. Year-by-Year Collusion Screening Tests by Kawai and Nakabayashi (2022a)

Appendix A.2

Estimates of the density of sc̃ii

Figure A3 shows the estimation results when we use the polynomials with degree 2. Basically,
we see the same pattern as in the case of degree 1.

(a) Homoskedasticity case(b) Type dependent variance case

Figure A3. Density estimations of sc̃ii . We focus on the entrants in the auctions in which
at least one joint venture participate. Blue line represents the density for joint venture andred line represents the density for single bidder. Panel (a) is the result when we assume
homoskedastic variances. Panel (b) is the result when we use type-dependent varianceestimations.

47

Appendix A.3

Ex-ante expected payoff

Figure A4 shows the ex-ante expected payoffs for each class of auctions. The results here
are obtained when assuming the polynomial of degree 1.

(a) Smaller size(b) Larger size

Figure A4. Estimates of the ex-ante expected payoffs. For each category of auctions, we
compute the expected payoffs by entering the auction for a single bidder and a joint venture
given the number of entering single bidders and joint ventures.

Appendix A.4

Model fit

Here we compare the simulated optimal effective bids with the observed effective bids. Figure
A5 shows the comparison results for all the classes of auctions.

(a) Smaller size(b) Larger size

Figure A5. Comparison of the observed bids with the computed optimal bids. For eachcategory of auctions, the blue line represents the estimated density function of computed
optimal effective bids solving the profit maximization problem and the orange line is theestimated density of the observed effective bids.

48