Tsukuba Economics Working Papers
No. 2009-005

Small Business Set-asides in Procurement Auctions: An
Empirical Analysis
byJun Nakabayashi
November 2009

UNIVERSITY OF TSUKUBA
Department of Economics
1-1-1 Tennodai
Tsukuba, Ibaraki 305-8571
JAPAN

Small Business Set-asides in Procurement Auctions:
An Empirical Analysis
Jun NAKABAYASHI∗
First Draft: March 2009This Version: December 2010

Abstract
As part of public procurement, many governments adopt small business programs to provide
contract opportunities for businesses often with preferences for firms operated by members ofgroups designated as disadvantaged. The redistribution arising from such programs, however, canintroduce significant added costs to government procurement budgets. In this paper, the extent towhich small business set-asides increase government procurement costs is examined. The estimates
employ data on Japanese public construction projects, where approximately half of the procurement budget is set aside for small and medium enterprises (SMEs). Applying a positive relationshipbetween profitability and firm size obtained by the non-parametric estimation of asymmetric firstprice auctions with aﬃliated private values, a counterfactual analysis is undertaken to demonstratethat approximately 30 percent of SMEs would exit the procurement market if set-asides were to be
removed. Surprisingly, the resulting lack of competition would increase government procurement
costs more than it would oﬀset the production cost ineﬃciency.
Key words: procurement auctions, small business set-asides, nonparametric estimation
JEL classification: D44, H23, H57, L74

1

Introduction

As part of public procurement, many governments adopt a program for encouraging small businesses
to participate in procurement auctions.1 In the United States, the Small Business Administrationsuggests almost all agencies in the federal government spend an overall proportion of 23 percent of
their procurement budget with small firms.2 For some departments, such as the Department of Transportation, the expenditure for small firms in 2005 was approximately $670 million, which accounted
for 45 percent of the total annual expenditure. A similar program is seen in public procurementin Japan. For the central government, the spending target to small and medium-sized enterprises∗

Doctoral Program in Economics, Graduate School of Humanity and Social Sciences, University of Tsukuba Tenodai
1-1-1, Tsukuba, Ibaraki 305-8571, Japan. Tel.: +81(29)853-7432, E-mail: nakabayashi@dpipe.tsukuba.ac.jp. I am
grateful to Howard P. Marvel for his guidance. I also thank David Blau, Sukehiro Hosono, Michihiro Kandori, Mamoru
Kaneko, Lung-fei Lee, Matt Lewis, Hiroyuki Odagiri, Hiroshi Ohashi, Viplav Saini, and in particular, Lixin Ye for very
helpful suggestions and comments. All remaining errors are my own.
1
Bannock (1981) identifies the United States, Germany, Switzerland, and Japan as the countries in which governments
strongly support small businesses.
2
The Federal Acquisition Regulation (FAR), Subpart 19.5. states that if the contracts are no more than $100,000,
they are automatically reserved exclusively for small business concerns and shall be set aside for small businesses.

1

(SMEs)3 was 50.1 percent in 2007.4 As in the case of the United States federal government, the goalis achieved almost every year.
Reserving contracts to small businesses restricts competition, which can result in the market being
ineﬃcient. Nevertheless, some of the theoretical literature on auctions predicts that set-asides may
not hurt procurement budgets as much as had been anticipated. For instance, Ayres and Cramton(1996) investigate the aﬃrmative action program in FCC spectrum auctions and observe that setting
aside some contracts for disadvantaged bidders enhances competition among advantaged bidders,which can compensate the eﬃciency loss. Milgrom (2004) points out the analog of set-asides for pricediscrimination conducted by a multi-market monopoly seller.
Nonetheless, empirical literature in this field is somewhat lacking. In particular, to the best of
our knowledge, there is no existing work that estimates the extent that set-asides hurt government
budgets.
This paper is the first attempt to investigate the eﬀect of set-asides on government budgets byusing structural estimation techniques. In particular, the degree to which government procurement
costs are changed and the extent to which SMEs’ entry into procurement markets is promoted bysmall business set-asides are quantified.
The data set used in this research is from Japanese public procurement auctions for civil engineering works conducted by the Ministry of Land, Infrastructure and Transportation (MLIT). From
April 2005 to March 2009, the ministry spent nearly $20 billion5 for approximately 15,000 civil engineering contracts, having accepted nearly 130,000 bids. The ministry set aside approximately 60
percent of the procurement budget of civil engineering projects for SMEs. Another source of data is
the government database for certified contractors. It provides contractors’ information about theirannual sales, amounts of capital and debt, and number of engineers and employees. Based on theinformation, controls are established for firm size in order to measure the quantitative relationshipbetween firm size and profitability from competitive bidding processes.
To examine the eﬀect of a small business program on procurement costs, knowledge of what thecontract prices would be should the government eliminate the program from the procurement market
is necessary. However, such data are not available. Therefore, a counterfactual analysis is required to
conduct comparative statics analysis of small business set-asides.
Because of set-asides, the number of sample auctions in which large firms and SMEs competewith each other is considerably limited. Hence, the counterfactual analysis begins by creating thecompetition between large firms and SMEs.6 However, the size of SMEs participating diﬀers from one
to the other even in set-aside auctions. The approach taken in this study is to regress the recovered
production costs and profitabilities on firm sizes in each sample auction in order to measure the overall
quantitative relationship between profitability and firm size in procurement auctions.
Therefore, our empirical analysis consists of the following three-steps. First, a procedure is used of
nonparametric estimation for asymmetric first-price sealed-bid auctions with aﬃliated private values(APV) to identify the bidders’ costs from observed bids. Then, as a second step, a regression analysis isused to find the quantitative relationship between firm size and profitability in procurement auctions,in which profitability (expected payoﬀs) is defined by the profit margin (bid minus cost) times theprobability of winning. Finally, a static entry model is constructed in which the obtained relationshipbetween expected payoﬀs and firm size is employed. Regarding the estimated ex ante expected profits
as a payoﬀ from entry, the entry model predicts how many SMEs would drop out because of large firm
3

SMEs are defined as those that hire fewer than three hundred employees and are capitalized at equal to or less than
100 million Yen in Japan. These criteria are applied to the manufacturing, construction, and transportation industries.
Service businesses and some others have slightly diﬀerent criteria.
4
The law “Ensuring Opportunities for the Procurement of Receiving Orders from Government” encourages eachministry to employ set-asides to achieve the goal.
5This is calculated by $1 = � 105.
6
Although limited, there are auctions in which large firms and SMEs compete with each other since government
procurement laws do not allow contract oﬃcers to use set-asides in the case in which there are too few SMEs to provide
suﬃcient competition.

2

entry into a market that was previously reserved exclusively to SMEs under the set-aside program.
Furthermore, comparing the winning bid data and the number of participants in each auction, thedegree to which the resulting lack of competition aﬀects government procurement costs is estimated.
The model of auctions with entry is based on a two-stage game: potential bidders decide whether
to enter the first stage, and the second stage is a first-price auction. The first stage relies on theassumption that entry is sequential and the number of firms is treated as a continuous variable. As in
the case of McAfee and McMillan (1987b), an assumption is made that all actual bidders must incura fixed cost prior to bidding in order to know their own signal. In this setting, relevant estimates fromthe empirical analysis are used to predict a counterfactual situation in which the set-aside program
was to be ineﬀective.
Surprisingly, the estimation results suggest that the program indeed saves government procurement costs. Applying the quantitative relationship between firm size and productivity to the average
diﬀerence in firm size between large firms and SMEs, on average, the production cost of SMEs is 1.3
percent higher than that of large firms. Similarly, based on the quantitative relationship between firm
size and winning frequency, an SME would win 5.5 percent less frequently than a large firm if an SME
and a large firm competed one-on-one. These small diﬀerences in costs and winning probability leadto a non-trivial diﬀerence in profitability between the two groups of bidders. The expected payoﬀ ofan SME would be 48 percent lower than that of a large firm when both compete in the same auction.
The simulation result indicates that, due to the disadvantage in profitability, the participation of
SMEs would drop by 29 percent on average were set-asides to be removed. Consequently, the large
firms’ shifting their entry to originally set-aside projects would cause the following two competing
eﬀects on procurement costs. The prices of the originally set-aside projects would fall due to theentry by cost-eﬃcient large firms, whereas the prices of the related projects that would have been
reserved exclusively to SMEs under the set-aside program would rise because of an approximately 30
percent decline in the number of large firms. The simulation studies suggest that the latter eﬀect
dominates the former in our simulation so that the program should decrease the procurement costs
by 0.17 percent.
The empirical results conclude that the set-aside program has been successful. It improves equity
between advantaged and disadvantaged firms without substantial increase of procurement costs. The
results not only correspond to the prediction by the theoretical literature on asymmetric auctions
but also are in line with the seminal empirical work of Denes (1997) on set-aside programs, despite
the diﬀerence in approach and data. In addition, our structural estimation further illustrates thatthe subsidized SMEs drive non-subsidized bidders to give up more of the gain on the contracts they
award. The large firms’ expected net gain is 0.27 percent of the estimated project cost while itwould be 0.85 percent without the small business program. In other words, set-asides squeeze more
rents from large firms, which enables the procurement buyer to lower procurement costs more thanoﬀsetting the resulting production cost ineﬃciency.
The remainder of this paper is organized as follows. Section 2 addresses the related literature.
Section 3 provides a brief explanation on public construction procurement markets in Japan. Section
4 includes a description of the data. A theoretical model of asymmetric first-price sealed-bid auctions
is provided in Section 5. Section 6 includes a description of the theoretical and empirical models
about auctions with endogenous participation. Section 7 provides a illustrates the estimation andsimulation results. Section 8 is the discussion. The final section contains further discussion and theconclusion. The proofs are given in the Appendix.

2

Related literature

As a development of theoretical studies on auctions, the issues in procurement auctions have been
examined and given many insights in the literature (e.g. McAfee and McMillan (1986), (1989), Hansen(1988), Laﬀont and Tirole (1993), Jofre-Bonet and Pesendorfer (2003), Milgrom (2004), Asker and3Cantillon (2008)).
The development of these theoretical studies has inspired the recent development of empiricalstudies on procurement auctions based on structural estimation techniques. For instance, Jofre-Bonetand Pesendorfer (2003) established a theoretical model of dynamic auctions in which bidders choose
their bids to maximize their discounted payoﬀs from the sequence of infinitely repeated auctions.
Then, an estimation procedure is proposed for the bidder’s cost distribution inferred from the firstorder condition of the optimal bid. Bajari and Ye (2003) studied collusion in highway procurement
auctions. Assuming that bids by cartel members are correlated and that the members bid aggressively
against the outsiders but softly within the members, they proposed tests for detecting suspicious
bidding behavior of bid rigging. ? measured the eﬀect of unobserved heterogeneity in asymmetricfirst-price IPV auctions. Empirical studies of firm decisions to participate in an auction have also beendeveloped (e.g., Athey et al. (2008) and Li and Zheng (2009)). Empirical analyses for a preference
program in public procurement are provided by Marion (2007) and Krasnokutskaya and Seim (2009).
In particular, Marion (2007) first investigated the eﬀect of the bid preference program in highway
procurement auctions by the California Department of Transportation. Then, Marion argued thatby granting a bid credit to higher-cost bidders, the government loses surplus from lower-cost bidders
by awarding contracts to likely higher-cost competitors. At the same time, the preferential treatment
increases the competitive pressure exerted by favored bidders. In descriptive regressions, Marion foundthat the auctions with bidding credits increase procurement costs by 3.5 percent, possibly because
the likelihood of large firm participation is smaller for preference auctions than for non-preference
auctions.
Krasnokutskaya and Seim (2009) also conducted an empirical investigation on bid preference
programs in highway procurement auctions. A remarkable extension from Marion (2007) is that
their model includes the bidder’s endogenous participation. Then, they found that the program
substantially raises the small bidders’ probabilities of winning and participation but results in a small
increase in the government procurement cost.
A laboratory experiment on preference programs in procurement auctions is conducted by Corns
and Schotter (1999). They observed that, although preferences generally increased the disadvantaged
bidder’s winning probability, the procurement costs dropped only with a 5-percent price-preference
rule and not with any 10 percent or above price preferences. Corns and Schotter reported that theseresults are consistent with theoretical predictions introduced by McAfee and McMillan (1989) andconcluded that designing a cost-eﬀective preference program is possible if a procurement buyer canaccess the information about the bidder’s cost distribution.
The first economic study on small business set-asides is conducted by Ayres and Cramton (1996).
Their case studies focus on the aﬃrmative action program in United States FCC spectrum auctions,in which disadvantaged bidders, such as small businesses and female- or minority-owned firms, aregranted set-aside licenses.7 Their simulation suggests that this eﬀective set-aside program could
increase the government’s revenues by approximately $45 million or 12 percent of the government’s
total auction revenue.8
Denes (1997) provided the first thorough analysis for the impact of small business set-asides inpublic procurement. He investigates the federal dredging contracts during 1990 and 1991 and examines
the mean values of set-aside (or restricted) bids compared with the mean values of the unrestrictedbids on the data in eight categories and performs a series of paired t-tests. He found that in all
but one instance, there is no significant diﬀerence between the bids submitted for set-asides and thebids submitted on the related auctions with unrestricted solicitations. According to his study, 3.6
7

The preference program gives disadvantaged bidders a 40 percent bidding credit on ten of the thirty narrowband
licenses as well as a subsidy for their interest payments. Since the combination eﬀect is that favored bidders had to pay
the government only 50 percent of a winning bid, they consider that the credit is large enough to discourage entry byadvantaged firms. See Ayres and Cramton (1996) for more details.
8
They also note that set-aside auctions are able to raise the expected auctioneer’s welfare if 1) there is insuﬃcientcompetition among strong bidders; 2) the seller is able to identify who is strong or weak; 3) resale is prohibited.

4

firms bid on set-asides, whereas only 3.1 firms bid in the remaining auctions. Although the marginal
eﬀect of a set-aside program on the procurement cost is ambiguous, he suggested that the increased
competition induces either no change or a lower-bid price on set-asides.
The thorough empirical analysis on auctions with endogenous participation by Li and Zheng(2009) is noteworthy. The theoretical analysis of auctions with endogenous participation consists of
two groups of literature. One group investigates either an asymmetric equilibrium (e.g., McAfee andMcMillan (1987b)) or a symmetric equilibrium (e.g., Levin and Smith (1994)), assuming that thepotential bidders decide whether to enter the auction before acquiring their signal. In contrast, theother group analyzes an entry equilibrium in which potential bidders first obtain a signal and thenmake their entry decision Samuelson (1985). Li and Zheng developed a fully structural framework
for entry and bidding admitting these theoretical models and applied the methods to quantify theeﬀect of the bidder’s entry decision on government procurement costs using data on procurement
auctions of Texas Department of Transportation. Model 2 in their analysis is closest to the entry
model employed in this paper.
The literature on structural estimation of auctions began with Paarsch (1992), and the nonparametnric estimation of the first-price auction model is first introduced by Guerre et al. (2000).
Most closely related to our research is that of Campo et al. (2003), which proposed an ingenious
way to estimate the model of asymmetric first-price auctions with aﬃliated private values (APV)
nonparametrically.

3

Public construction markets in Japan

3.1

Overview

Investment in the construction industry accounts for nearly 20 percent of the country’s GDP and employs more than 10 percent of the working population in Japan. The percentage of public investment
as a portion of all construction investment was 45.6 in 2001.
Public account law requires that all government and public entities practice competitive bidding
when they acquire construction works exceeding 2.5 million Yen. Three types of bidding systems
are used in the public sector: 1) open competitive bidding, 2) invited bidders, and 3) contract at
discretion. Although not a majority, scoring tenders are also used in the awarding mechanism, inwhich bidders submit not only the price but also another variable, such as the term of work or qualityof work.
An idiosyncratic feature of the Japanese public procurement system is in the screening process
for bidders. Contractors must take a preliminary qualification exam in order to bid for projects. The
exam measures a firm’s technological, financial, and geographical status and gives them scores as aresult of the evaluation. For each auction, the procurer selects, or makes an announcement to, a setof legislated contractors as qualified bidders, and the selection is based on the exam results.
In procurement auctions, governments face the risk of awarding the contract to less-qualified orinferior firms that might default. Some projects demand advanced technologies and skills as well asa suﬃcient amount of capital to complete.9 To mitigate such an asymmetric information problem,
screening processes for selecting qualified bidders are essential to the success of the auction.10 The
preliminary qualification exam works in the same manner as the bonding system in the United States
public construction market. A brief discussion of the preliminary qualification examination in Japanis presented in the next section.
Another major diﬀerence in the Japanese procurement system is in the contract principle. Unlikein the United States and many other countries, construction contracts are based on total price con9

The possibility of default or non-performance can have perverse eﬀects on the bidding in an auction; a bidder witha high likelihood of default tends to be chosen as a winning bidder. See Zheng (2001) for more details.
10
See also Bajari and Tadelis (2001) and Laﬀont and Tirole (1993) for further discussion on the importance of thescreening processes in procurement auctions.

5tracts, in which bidders submit only a total price without necessarily itemizing unit prices. Instead,engineering oﬃces regularly update market price lists and use them in the event that a change orderis called for during a certain performance. The yearly updates on these price lists are based on hearings, but the survey is conducted independently from procurement auctions. Unfortunately, there is
no formal theory that analyzes the eﬀect of contract formats on bidding behaviors. Therefore, theempirical analysis here ignores the contract format eﬀect.
Finally, the announcement policy of the reservation price and engineer’s estimated costs diﬀers
from that of many other countries, in which these are typically opened prior to bidding in auctions.
On the other hand, in most public procurement auctions in Japan, such information is secret until
the auction is over. However, the secrecy of the reservation price is mitigated with the auction design.
If no bid is below the reservation price, the next round auction begins immediately with the same
member. This process goes on at most three times. The project is reserved unless any contractor
bids below the reservation price at the third round. In this sense, reservation prices are not binding
in the first round.

3.2

Preliminary qualification examination

Preliminary qualification certifies a set of firms as bona fide bidders in procurement auctions to protect
the owner of a project against the risk of non-performance. Similar screening processes are widelyused at public procurement auctions in Europe and work in the same manner as the bonding systemin the United States public construction auctions in terms of reducing the risk of contractor’s default.
The preliminary qualification in Japan is based on the firm’s disclosure of information with respect
to their financial and technological performance. In particular, information includes the annual sales,
number of engineers in each area of expertise, experience, and business history. Based on the setof information as well as the evaluation of work performed, governments measure the firm’s overall
ability to perform. As a result of this evaluation, the qualified firms typically obtain two kinds ofscores for each area of their expertise.
The first score is called the “Business Evaluation” (BE) score, which is essentially a weighted
average of 1) the annual value of completed construction works by license classification, 2) the numberof technical staﬀ, 3) the business conditions (based on financial statement analysis), 4) the number ofengineers, and 5) the record of safety performance. For the qualified bidders of MLIT, the maximum
and minimum scores are 1,859 and 329, respectively, with an average of 851.1. The detailed summary
statistics on the BE score are available in Section 4. The BE score is given through the countrywide
criteria of measurement specified in construction industry law; thus, each firm has a unique scorevalue for each expertise.11
On the other hand, the second score, which is called the “Technology Evaluation” (TE) score is
the past performance evaluation measured by each procurement buyer.12 Unlike the BE score, themeasurement criteria vary across procurement buyers. Hence, it is possible, although not common,that BE and TE scores both are not high. If a government has multiple local divisions, each may
have a diﬀerent evaluation criterion for the TE score.
The assessment on whether a firm is favored in the set-aside program is based on the sum of the
BE and TE scores.13 However, the BE and the total scores are strongly correlated with each other.14
11

The number of expertise is 28, which is specified in the construction industry law. Firms must obtain a license foreach area of expertise to operate.
12
The criteria typically reflect the firm’s past works such as contribution to the quality of projects and schedule ofworks.
13
More precisely, governments assign grade for each firm based on the total score. For instance, MLIT gives either“A”, “B”, “C”, or “D” for each certified contractor with civil engineering expertise, where A is the top grade. Large
contractors are likely to have a grade of “B” or higher and are likely to have a grade of “A” if the firm operates
countrywide. Based on the grade, governments implement the set-aside program in such a way that firms with a gradeof A or B are excluded to bid for low-end projects.
14
The correlation between the total and BE scores is 0.91. The t-statistic of the regression of the total score on the6To avoid the heterogeneity of the TE score across locations, the analysis only uses the BE score as
the control variable for the corporation size.

3.3

Set-asides in the public construction market

The selection rule for bidders is primarily based on the “size-matching rule.” When a particular
project is auctioned, a set of bidders is chosen so that their sizes will match the project size. For
instance, only large firms are qualified to participate in the auctions for large and high-end projects
and are not allowed to bid on small and low-end projects, which are reserved for SMEs. Set-asides
are implemented as part of the size-matching rule. In the case of MLIT, it also grades every civilengineering work from A to D according to the size, where grade A is the highest end. The engineer’s
estimated costs are typically used as a proxy to determine the project size. Under the size-matching
rule, contractors are selected or allowed to participate in the auction so that their grades match
the project grade. The size-matching rule has priority in the selection of bidders unless the numberof designated bidders is too small to provide adequate competition. Table 1 demonstrates how thegovernment solicits firms for each project size.
Set-asides are the only explicit method to favor SMEs in Japanese public procurement auctions.
Every year, the Japanese central and local governments determine the objective set-aside budgets
by which the governments should assign contracts to SMEs.15 In 2005, central governments andpublic entities spent �8.8 trillion to purchase land and items, construction works, and services. �4.1
trillion was expended to SMEs, which accounted for 46.9 percent of the total budget (the target
amount was Y=4.3 trillion, accounting for 46.7 percent). For the Ministry of Land, Infrastructure andTransportation, 50.8 percent of the entire expenses were allocated to SMEs in the year. To achieve
the goal, approximately two thirds of civil engineering contracts were set aside for SMEs.

4

The data

4.1

Overview

The data used in the analysis contain the bid results of the procurement auctions for civil engineering
projects from April 2005 through March 2009. The number of contracts awarded was 15,020 during
this period.
MLIT posts the bid results on the website, Public works Procurement Information service (PPI).16
The information available in PPI includes the names of procurement buyers (local branch names),
project names, project types, date of auctions, reservation prices, auction formats (open competitive
bidding or invited bidders), and submitted bids with the bidder’s name.17 PPI also provides the listsof all qualified firms, which consist of the address of the firm’s headquarters, the name of the owner,
BE scores as well as grades for each area of expertise. All data in this empirical study are from thewebsite.
MLIT procures 21 types of construction works including civil engineering (or heavy and general
construction works), buildings, bridges, paving, dredging, and painting. The amount of civil engineering projects is approximately � 750 billion a year, which accounts for approximately 54 percentof the entire expenditure of the ministry as indicated in Figure 2 and 3 as well as for 7 percent of the
public construction investment in the country.
MLIT has 9 regional development divisions in 9 regional districts. The data includes the civilengineering projects in 8 districts indicated in Figure 1. Each of the regional development divisions
has a certified firms’ list from which it chooses the bidders for each procurement auction. The lists
BE score is 786.34 with 0.83 of the R-squared.
15
This policy is specified by the “Law on ensuring the receipt of orders from small and medium-size enterprises.”
16
The address is “http//www.ppi.go.jp.”
17
The information concerning work location is not generally available.

7

are updated every two years. The total number of firms on the lists was 43,522 in April 2007. Since
large firms typically operate across several regions, it is often the case that a particular firm is listed
on two or more of these lists. The number of firms without such duplication is 32,993, which accounts
for approximately 20 percent of all the licensed civil engineering construction firms in Japan.18
The data have some limitation in the identification of contractors. The bid results provide thebidder’s company name only. Therefore, in the case that two or more diﬀerent firms have an identicalcompany name, the bidder’s identity can be guessed but not ensured.19 The way to narrow down
the candidate list is on the basis that whether i) the location (prefecture) of the project matches
the location of headquarters, and ii) the bidder’s size matches the project size according to the sizematching rule. Through this process, almost all contractors on the bid results are identified.20 The
remaining unidentified firms in the auction are assumed to be the average-sized firm in the auction.

4.2
4.2.1

Summary statistics of bids and scores
Normalization of the bidder’s size

In the observations, each auction has a unique set of bidders in general. Hence, a firm with a higherscore can be a smaller bidder if the opponents have a much higher score and vice versa. To model
the firm’s size in comparison to the size of its opponents, the BE score is normalized (hereafter,
normalized score) in the following procedure.
Let as assume that there are n bidders in an auction in which each bidder is indexed by i = 1, . . . , n.
Let Xi be the value of the BE score of�bidder i in the auction and X̄ be the mean score of the bidders
1in the auction, which satisfies X̄ = n ni=1 Xi . Then, bidder i’s normalized score xi is calculated asxi =Xi − X̄
.
X̄

(1)

In other words, the value xi represents the firm i’s relative size in the auction. xi is positive, forinstance, if bidder i’s firm size is greater than the average firm size.
None of the bidders is informed of who and how many the competitors are. In fact, however, thebidders may speculate about their competition based upon the project location, the project size, andthe auction date. Hence, as mentioned later on, the structural estimation model of auctions used inthis research assumes that a bidder knows his own score, the mean score of the bidders in the auction,and the distributions of the opponent bidders’ scores but not the exact values of the opponent bidders’scores. This assumption makes it easy for not only the structural estimation analysis to be realistic,
but also for more samples to be used to estimate the pseudo values of bidders’ production costs.
Table 4 provides the summary statistics on Xi and xi of the actual bidders in the data. Figure
2 depicts the histogram for the normalized score. The eﬀect of the set-aside program is glimpsedfrom the fact that the coeﬃcient of variation (CV) on Xi , which is defined by the standard deviation
divided by the mean of Xi , is approximately 13 percent. Therefore, if bidders are randomly pickedin each auction, the standard deviation of xi would be 13 percent. However, the actual standard
18

The total number of licensed civil engineering firms is 167,896 in 2005 (MLIT, 2005).
For example, there are seven “Showa Kensetsu Co., Ltd” on the contractor list of Kanto District Development
Bureau. The bid results do not indicate which “Showa Kensetsu” in fact bid.
20
Eity-seven percent of bidders are exactly identified from the firm list data by the uniqueness of the firm name on
the list, by the address or by the project size (Large firms never enter the auctions for small-size projects). Then, letter
grades are used for the further identification. Most of the auctions accept bids from the firms with a certain letter grade.
If the majority of the identified firm’s letter grade is ”C,” then the rest of the firms’ grades should be ”C.” In this way,
approximately 8 percent of bidders are additionally identified. The rest are guessed by the distance between the firm’s
headquarters and the construction site; if it is too far, the firm should not be a bidder for the auction. Then, 99.1
percent bidders are identified. Although the final process includes a slight amount of ambiguity, we carefully choose thefirm whose letter grade is the same as that of the remaining bidders in the auction, meaning that the BE score of theguessed firm is close to the score of the true firm.
198

deviation is 7.6 percent, which suggests that the participation restriction by government reduces theasymmetry of bidders.
4.2.2

Percentage bids

Figure 3 contains a description of the histogram on the project size. Since each construction projectis unique, there remains a great deal of heterogeneity in project size. The most typical contract is forapproximately �100 million measured in the engineer’s estimated costs. The largest is approximately
�12 billion, while the smallest is less than �1 million. Table 5 is a breakdown of the summary
statistics of project size.
To eliminate project heterogeneity, all bids in the empirical analysis are described by the percentage with respect to the engineer’s estimated cost. Let Est be the engineer’s estimated cost of
a project and Bidi be the value of the bidder i’s bid. If the procurement auction is held with theprice-only format, then the percentage bid of the bidder i’s bid is given by
Bidi
.
Est

(2)

In the data, 3,405 out of 15,020 procurement auctions are undertaken with price-only auctions,which account for approximately 23.0 percent. The rest are auctioned oﬀ with scoring auctions,in which bidders submit not only the price-bid but also some other factors, such as quality andcompletion time.
According to the MLIT scoring auction procedure, the bidder with the highest-score wins the
project in which the score is calculated by the factor-bid divided by the price-bid. The factor-bid
consists of multiple components, such as noise level, completion time, and experience.
The properties of scoring auctions have been investigated in the literature (e.g. Che (1993),
Asker and Cantillon (2008)). The assumption that existing studies rely on is that the scoring rule isquasi-linear, which, unfortunately, does not hold in our case. Hence, an alternative model of scoring
auctions is established in which the scoring rule is based on division, as will be discussed in Subsection
5.3.
To incorporate the data of scoring auctions into the model, let Scorei be the value of the price-bid
divided by the factor-bid submitted by bidder i.21 Furthermore, let Base be the base score that is theengineer’s estimated cost (the highest possible price-bid) divided by the factor-bid evaluating nothing(the lowest possible factor-bid). The base score is set in each scoring auction, and the winning scoring
bid must be below the base score.22 Then, the percentage scoring bid of bidder i is defined as
Scorei.
Base
Since the scoring bid and base score in the model are the inverse of the scoring bid and the base scorein the data, the winner of the scoring auction in our model is the lowest-score bidder conditional on
the scoring bid being below the base score.
4.2.3

Regression results for bids on corporate size

It is evident that, in each auction, larger firms bid lower prices than smaller ones. Table 6 contains a
description of the result of regression for the percentage bids on normalized scores. Auction-specificeﬀects are taken into account by fixed-eﬀect and random-eﬀect models. As in Corns and Schotter(1999), the auctions that contain “throw-away bids,” i.e., bids larger than 200 percent of the engineer’s
estimated cost, are dropped oﬀ in order to prevent those minor but extreme samples from dominating
21

As shown above, the actual scoring bid in the data is the factor bid divided by the price-bid.
In fact, the base score in our model is the inverse of the base score in the data. Hence, the winner’s scoring bid in
real-world scoring auctions must be equal to or above the actual base score.
22

9

the estimation.23 Then, the negative relationship between the normalized bids and size is significant(t-value : 6.15 in FE estimation). The number of observed bids after exclusion equals 110416 . Figure
4 shows that the bid density of larger firms (the score is 10 percent greater than the average) is shifted
downward when compared to that of smaller firms (the score is 10 percent smaller than the average).
Table 6 indicates that the bidder’s size yields a small but statistically significant diﬀerence in bids.
Finally, the production capacity utilization is explored in procurement auctions. Many small
businesses on the qualified-firm lists do not bid even with the set-aside program. Table 7 reportsthat approximately 80 percent of the large firms on the lists bid during the period whereas only
approximately 25 percent of the small businesses on the lists bid. The distribution of the scores ofactual bidders and that of qualified firms on the lists are shown in Figure 5 and Figure 6, respectively.
The density of the qualified-firms’ BE scores shifts toward the left. This tendency is trivial if the
distributions between the qualified LBs’ and actual bidder LBs’ scores are compared as in Figure 10
and Figure 9. However, a significant leftward shift is observed in the distribution of the actual SB
bidders’ scores in Figure 10 and Figure 9. This indicates that, despite set-asides, a suﬃcient volume
of production capacity remains available in small businesses.

5

Recovery of the bidders’ cost distribution

5.1

Overview

Our nonparametric estimation of first-price sealed-bid auctions is based on Campo et al. (2003), which
is an extension of Guerre et al. (2000) to cases with asymmetric bidders with the APV model. The
bidders’ costs could be correlated or even aﬃliated, since some bidders may use the same subcontractor
and employ materials and workers in the same market. Hence, it seems that the aﬃliated private
value is one of the most reasonable settings to analyze auctions for construction projects.24
The approach of Campo et al. (2003) relies on the assumption that the bidder’s asymmetry isrepresented by a finite number of segments. Hence, if the number of segments is equal to d, a (d + 1)dimensional kernel estimation is required. Therefore, if an empirical model assumes that the bidder’s
asymmetry is attributed to a continuous variable, then kernel estimation is not implementable.
More recently, Zhang and Guler (2005) proposed a simplified approach in which the only requirement is a two-dimensional kernel estimation regardless of the structure of bidder asymmetries. The
essence of their approach is to estimate the bidder’s signal separately for each bidder, expressing eachbidder’s payoﬀ function in terms of the equilibrium distribution of rival bids. They claim that the
detrimental eﬀect from the dimensionality of kernels can be avoided as long as the set of biddersin the sample is identical. Unfortunately, their approach results in another problem when the data
involves heterogeneity in the set of participants across auctions, as it does in this case.
Hence, a model of asymmetric auctions is reconstructed to utilize more samples in kernel estimation, assuming that bidders know their own firm size but have limited information about theircompetitors. In particular, we assume that bidder i knows Xi , his own score, FX , the cumulative
distribution function of the set of the bidders’ scores, and X̄, the mean of the score in the auction
but not the exact value of the set of opponent bidder’s scores X−i = (X1 , . . . , Xi−1 , Xi+1 , . . . , Xn ).
As shown in the next subsection, the bidders are still ex ante asymmetric on this assumption. Furthermore, this assumption is more realistic in actual procurement auctions, in which the participants
are endogenously determined and nobody knows who the actual opponents are upon bidding.
23

The number of such sample auctions in our data is 306, which accounts for 2.8 percent of 11,114, the total numberof sample auctions.
24
Another non-trivial source that correlates observed bids is auction-specific unobserved heterogeneity, which is observable for bidders but unobservable to an econometrician. A seminal paper by Krasnokutskaya (2009) introduced an
innovative methodology to identify a model of auctions with unobserved heterogeneity and quantified the impact on
the results of estimation as well as policy-relevant instruments. Furthermore, Krasnokutskaya’s approaches have been
applied to many empirical analyses on auctions, such as Athey et al. (2008).

10

5.2

An asymmetric APV model of first-price auctions

A single and indivisible project is auctioned to n risk-neutral bidders, indexed by i = 1, . . . , n. Let Xi
be the bidder i’s firm size, which is randomly and independently distributed following a cumulative
distribution function
FX . Let X̄ be the mean of the realized firm sizes in the auction, defined�nby X̄� ≡ (1/n)
X� i=1 i . Then, the bidder i’s normalized firm size in the auction is computed by
xi = Xi − X̄ /X̄.
Let H(·) be an n-dimensional cumulative distribution function. The vector of each bidder’snormalized score x ≡ (x1 , . . . , xn ) is a realization of a random vector with a joint distribution H(·).
Then, for each i ∈ {1, . . . , n} ≡ N , the conditional distribution of x−i ≡ (x1 , . . . , xi−1 , xi+1 , . . . , xn )and its density can be denoted by H−xi |xi (x−i |xi ) and h−xi |xi (x−i |xi ), respectively. Let us assume that,for all i, H−xi |xi (x−i |xi ) has support [x, x]n−1 and that the probability density function h−xi |xi (x−i |xi )is continuous in x−i .
Let us assume that FX and H(·) are common knowledge but Xi is known only to bidder i. Let
us further assume that the mean of the realized scores in the auction, X̄, is known to every bidder.
Hence, the conditional distribution of x−i , denoted by H−xi |xi (x−i |xi ), and its density, h−xi |xi (x−i |xi ),are common knowledge but x−i is not.
The asymmetric APV model with risk-neutral bidders is defined by an n-dimensional distribution
with a cumulative distribution function F (·|x). The vector of private information (c1 , ..., cn ) is arealization of a random vector with joint distribution F (·|x). The asymmetry of bidders is captured
by x such that xi aﬀects the marginal distribution of ci but not the distribution of cj for any j ∈ N \{i}.
In other words, the marginal distribution of ci is represented by Fci (ci |xi ) for all i ∈ N . The aﬃliation
is captured as follows: let us assume that the ith bidder’s signal is ci , then for some j, the marginal
distribution of cj and its density are given by Fcj |ci (cj |ci , xj ) and fcj |ci (cj |ci , xj ).
Using bi = β(ci |xi ) and β −1 (bi |xi ), let us denote the equilibrium bidding strategy and its inverse,
respectively. In equilibrium, the joint distribution of valuations F (·|x) and the distribution of bids
G(·|x) are related with G(b1 , ..., bn |x) = F (β −1 (b1 |x1 ), ..., β −1 (bn |xn )|x). Let us assume that themarginal distribution of costs Fcj |ci (cj |ci , xj ) has support [c, c] for any i, j, and x and that theprobability density function fcj |ci (cj |ci , xj ) is continuously diﬀerentiable (in cj ). Finally, let us assume
that for all i �= j, fcj |ci (·|ci , xj ) is bounded away from zero on [c, c]. Then, firm i’s conditional payoﬀ
can be written asu(bi |ci , xi ) = max(bi − ci ) Pr{bi ≤ Bi |ci , xi },bi(3)

where Bi is the bidder i’s minimum rival bid, namely Bi ≡ min {b1 , . . . , bi−1 , bi+1 , . . . , bn }.
Then, an increasing Bayesian-Nash equilibrium is considered in pure strategies. Let us assume that
there is an increasing equilibrium such that each firm i bids according to a strictly increasing function
β(ci |xi ). An equilibrium in pure strategies is an n-dimensional strategy profile (β(·|x1 ), . . . , β(·|xn ))such that β(·) maximizes u(bi |ci , xi ) in bi for all i and ci in its support.
Then, for any i ∈ N and j ∈ N \ {i}, Gbj |bi (b|bi , xi , xj ) ≡ Fcj |ci (β −1 (b|xj )|β −1 (bi |xi ), xj ) is definedas the probability that an opponent bidder j’s bid, bj , is equal to or greater than b given bi and x.
Note that Gbj |bi (·) satisfies the property of probability distribution since β(·) is strictly increasing.
For bidder i, the minimum rival bid Bi is a random variable conditional on bi and xi . Therefore,
GBi |bi (Bi |bi , xi , x−i ) is used to denote the conditional cumulative distribution of Bi .25 If x−i were
known to bidder i, then bidder i’s winning probability would be 1 − GBi |bi (·) conditional on otherbidders following β(·).
We have assumed, however, that bidder i knows the conditional distribution hx−i |xi (x−i |xi ) but
does not know the exact values of the opponents’ firm sizes, x−i . Therefore, the bidder i’s expected
25

By aﬃliation of c, bi influences GBi |bi , while, by heterogeneous distribution of c, xi aﬀects GBi |bi .

11winning probability, 1 − ḠBi |bi (·), is given by 26
�
1 − ḠBi |bi (b|bi , xi ) =[1 − GBi |bi (b|bi , xi , x−i )]hx−i |xi (x−i |xi )dx−i .
x−iHence, if other bidders follow β(·|xj ), then (3) is rewritten asu(bi |ci , xi ) = max(bi − ci )[1 − ḠBi |bi (bi |bi , xi )].
bi

The first-order condition givesc i = bi −1 − ḠBi |bi (bi |bi , xi ),ḡBi |bi (bi |bi , xi )(4)

where ḡBi |bi (·) is the density of ḠBi |bi (·).
The right-hand side of (4) gives a unique inverse bid function β −1 (bi |xi ), implying that i’s strategy
is also represented by β −1 (bi |xi ). Hence, it is a Bayesian-Nash equilibrium in asymmetric firstprice auctions with APV. The bidding function can be obtained by solving the system of diﬀerential
equation represented by β −1 (bi |xi ) for all i.

5.3

Application to scoring auctions

The model can be applied to scoring auctions. For simplicity, an independent private value (IPV) is
assumed to begin with, and the assumption is relaxed later on.
For all i ∈ {1, . . . , n}, bidder i obtains two-dimensional private information ci ∈ [c, c̄] and qi ∈ [q, q̄]
distributed independently following the publicly known cumulative distribution Fc and Fq , where q
is interpreted as the quality level the bidder will provide to complete the project.
The obtained cost-quality pair is considered as the one optimally selected from a set of feasible
cost-quality pairs, where the set can be considered as the firm’s cost function. The discussion on
how the bidder ends up choosing the cost-quality combination made in, for instance, Che (1993) andAsker and Cantillon (2008), is out of the scope of this research. However, we assume that, given qi ,bidder i estimates the production cost ci by incurring the information acquisition expense e.
In the scoring auction, bidder i submits a price-bid bi and a factor-bid qi . The scoring ruleS(b, q) ∈ R+ evaluates the paired bid and designates the lowest-scored bidder as the winner. Let Si
be the minimum rival scoring bid for bidder i. Then, bidder i’s maximization problem is given bymax (bi − ci ) Pr{S(bi , qi ) ≤ Si },biwhere the scoring rule S(·) is given by S(bi , qi ) = bi /qi . Then, as in Asker and Cantillon (2008), thei’s pseudo-type, θi , is defined as θi = ci /qi . Finally, si = bi /qi is defined for notational convention.
26

The right-hand side is more formally expressed as
�

...
x1

�

�

...

xi−1 xi+1

�

�

xn

�
1−GB |b (bi |bi , x1, . . . ,xi−1,xi+1, . . . ,xn ) h−x |x (x1, . . . ,xi−1,xi+1, . . . ,xn |xi )dx1 . . .dxi−1 dxi+1 . . .dxn .
i i
i i

12

Then, the maximization problem is rewritten as27
max (si − θi ) Pr{si ≤ Si }si

for some qi . It implies that the multi-dimensional scoring auction game can be reduced into thesingle-dimensional first-price sealed-bid auction in which bidder i receives a signal θi , submits the bid
si , and obtains the expected payoﬀ given above for all i = 1, . . . , n.
The way that this specification is taken to the asymmetric APV paradigm is given as follows.
Let us assume that the set of pseudo-types (θ1 , . . . , θn ) satisfies all the properties (c1 , . . . , cn ) in theprice-only auction. Then, let Fθ (·|x) be the cumulative distribution function and Fθj |θi (θj |θi , xj ) withthe support [θ, θ̄] be the marginal distribution of θj . The correlation between q and θi is admitted in
the model so that the cumulative distribution of q is given by Fq (qi |θi ) taking into account the casethat the bidder with higher θ is likely to have a higher-quality standard q. The above maximization
problem can then be rewritten as
max (si − θi ) Pr{si ≤ Si |θi , xi }.
si(5)Hence, the maximization problem of the asymmetric APV scoring auctions is equivalent to that ofprice-only auctions if si is replaced with bi and θi is replaced with ci in Equation (5).
Finally, we verify that the rest of the argument after Equation (3) in the previous subsection
holds in the case of scoring auctions. Suppose that there is an increasing function σ(θi |xi ) which
maximizes
Equation (5) for any�� θ ∈ [θ, θ̄]. We can then define Gs (·|x) as Gs (s1 , . . . , sn |x) =Fθ σ −1 (s1 |x1 ), . . . , σ −1 (sn |xn )|x . Therefore, the conditional cumulative distribution function of Si
is given by GSi |si (Si , xi , x−i ) and the i’s expected winning probability in the scoring auction is given
by 1 − ḠSi |si (·|bi , xi , x−i ). Thus, the first-order condition of the maximization problem in the scoring
auction, which is a counterpart of Equation (4), is given by
θi = s i −1 − ḠSi |si (si |si , xi ),ḡSi |si (si |si , xi )where ḡSi |si (·) is the density of ḠSi |si (si |si , xi ).
As is discussed in Subsection 9, the bid margin si − θi in the scoring auction is diﬀerent from thebidder’s conditional payoﬀ bi − ci . To identify the bidder’s expected payoﬀ as well as the ex ante
expected gain from participating in the auction, the diﬀerence has to be dealt with carefully. With
this exception, all the arguments in the following apply to scoring auctions by replacing bi with siand ci with θi .

5.4

Nonparametric estimation

Campo et al. (2003) show that the latent value ci can be estimated by using the inverse bid function
β −1 (·). They show that the estimator for costs can be obtained by computing the bid distribution
GBi |bi and its density gBi |bi without solving the system of diﬀerential equations.
As in Zhang and Guler (2005), the first step is to interpret (4). By definition, 1 − GBi |bi (b|bi , xi ) is
the probability that the minimum rival bid Bi is greater than b conditional on bi , and ḡBi |bi (b|bi , xi )27

Since qi is given and constant for bidder i and the scoring rule is specified in the above expression, the maximization
problem can be rearranged as
�
� �
�
bi
ci
bi
max qi−Pr≤ Si .
biqi
qiqi
bi /qi and ci /qi are replaced, respectively, with si and θi , and the remaining qi is suppressed due to the fact that it isredundant for the optimization problem. The rearranged optimization problem is then obtained. Note that the optimal
bid bi uniquely determines the optimal score si , since qi is given for bidder i.

13

is the derivative of ḠBi |bi (b|bi , xi ).
For the estimation, let us assume that there are k = 1, . . . , m auctions and that n bidders bid in
each. Unlike the standard estimation model, the assumption that the set of bidders in each sample
is the same is relaxed in the way that bidder i in auction k can be diﬀerent from bidder i in auctionk � in our model. Let Bi,k = minj�=i bj,k denote the i’s minimum rival bid for any sample auction k.
Then, the empirical correspondent of (4) is given byci,k = bi,k −1 − ḠBi,k |bi,k (bi,k |bi,k , xi,k )ḡBi,k |bi,k (bi,k |bi,k , xi,k ).

(6)

Although the number of combinations of xk ≡ (x1,k , . . . , xn,k ) in the observations is infinitely
large, ḠBi,k |bi,k and ḡBi,k |bi,k depend only on xi,k but are independent of
x−i,k ≡ (x1,k . . . , xi−1,k , xi+1,k , . . . , xnk ,k ).
Therefore, to know the latent value of bidder i in auction k, the values of bid i� in auction k � can beused if the counterpart bidder’s score xi� ,k� is the same or close enough to xi,k . The nonparametricestimation equations for the numerator and denominator in (6) are thus given by

�
�
m �
n
�

bi,k − bτ,l xi,k − xτ,l
 1 − Ḡ1
1(bi,k ≤ Bτ,l )KG,,
Bi,k |bi,k (bi,k |bi,k , xi,k ) = mhG hxhGhx
l=1 τ =1 �
(7)
�
m �
n
�

bi,k − Bτ,l bi,k − bτ,l xi,k − xτ,l

1

Kg
,
,
.

 ḡBi,k |bi,k (bi,k |bi,k , xi,k ) = m(hg )2 hx
hghghx
l=1 τ =1

These hold to the extent that the number of bidders is identical in the sample and there is noheterogeneity in the characteristics of the projects. In fact, the observations in the paper involve
significant heterogeneity in the number of bidders. The next subsection is an explanation of how tocontrol for heterogeneity.
5.4.1

Heterogeneity

Here, we essentially follow Guerre et al. (2000) to control the heterogeneity in the number of bidders and the characteristics of each auction. Guerre et al. (2000) report that these are tractable innonparametric identification by introducing additional dimensions on kernels. The data taken here
involve considerable heterogeneity in both the number of bidders28 and the auction format (scoring
auctions or price-only auctions). The procedure is described as follows.
Let zk denote the vector of associated characteristics in project k. Let us assume that the bidders’cost distribution for the auction, i.e., auction k, is given by the conditional distribution F (·|zk ) forsome zk . Then, the distribution of observed bids in auction k is given by G(·|nk , zk ). Hence, (4) isrewritten as
ci,k = bi,k −28

1 − ḠBi,k |bi,k (bi,k |bi,k , xi,k , nk , zk )ḡBi,k |bi,k (bi,k |bi,k , xi,k , nk , zk )The smallest number is two and the largest 53.

14

,

(8)

and (7) becomes
1 − ḠBi,k |bi,k (bi,k |bi,k , xi,k , nk , zk )



nl
m

�
�
�

1 �

bi,k −bτ,l xi,k −xτ,l nk −nl zk −zl
1

,
=
1(b
≤
B
)K
,
,
,

G
i,k
τ,l
mhG hx hn hz
hG
hx
hn
hz


nl

l=1

τ =1



ḡBi,k |bi,k (bi,k |bi,k , xi,k , nk , zk )



nl
m

�
�
�

1 �
bi,k −Bτ,l bi,k −bτ,l xi,k −xτ,l nk −nl zk −zl

1

=
K
,
,
,
,
,

g
2
hg
hg
hx
hn
hz

m(hg ) hx hn hz
nl
l=1

(9)

τ =1

where KG is a four-dimensional kernel and Kg is a five-dimensional kernel. The regularity assumption
for F and G is provided in Guerre et al. (2000).
�
−1/6 andAs usual,
is given by the so-called rule of thumb; hg = cg ( mk=1 nk )�mthe bandwidth−1/5
hG = cG ( k=1 nk ), where cG = cg = 2.978 × 1.06σ̂b and σ̂b is the sample variance of thenormalized bids. The following triweight kernel is used in the nonparametric identification:
K(u) =

35(1 − u2 )3 1(|u| < 1).
32

The calculation is executed using a program written in C++; it takes approximately an hour to obtain
100,000 latent variables.
The informational rents obtained by bidders decrease as the number of bidders increases. Figure
11 shows the bidding function in the case of a small number of participants (5 bidders), and Figure
12 describes the case of many participants (between 22 and 28 bidders). In both figures, the darkplots represent the bidding function and the light plots represent the 45-degree line. The bid margins
are larger in the case of a smaller number of competitors.
Table 6 shows the regression result for the estimated costs as a function of a firm’s size. Again, thefixed and random eﬀects control for the auction-specific heterogeneity, and all the throw-away bids
(greater than 200 percent of the reservation price) are dropped in the regression. Table 6 suggests thestatistical significance (t-value : 6.57 in the FE regression) that large firms have a cost advantage.
Literature on asymmetric first-price auctions predicts that disadvantaged bidders bid more aggressively than advantaged bidders in an auction. Table 9 shows the regression result of a log bid margin(a submitted bid minus the estimated cost) on bidders’ relative sizes. It is statistically significant(t-value : 6.22 in the fixed-eﬀect regression) that a smaller bidder in an auction is likely to bid witha thinner margin than a larger bidder.

6

A model for auctions with entry

6.1

Setting

Our stylized entry model considers that a government procures K H identical high-end projects, denoted by H, and K L identical low-end projects, denoted by L. There are two groups of risk-neutral
firms, large ones, denoted by LB, and small businesses, denoted by SB. Let us assume that every
firm is normalized to have a unit production capacity regardless of the group it belongs to. As in
real-world procurement auctions, a winning bidder who fails to start performing right after the auction will be severely punished i.e., getting a suﬃciently large amount of negative profit. Therefore,
also because of the unit production capacity, no firm will bid for two or more procurement auctions
simultaneously.29
29

In reality, a company may bid to multiple projects within a short time. Such a company is represented by multiple
firms in our model, each of which submits a bid to a single project.

15Based on the fact observed at the end of Subsection 4.2.3, the number of large firms (LBs) is
assumed to be limited to a finite number NLB , whereas there is an infinitely large number of small
businesses (SBs). Furthermore, let us assume that the size of project H and L is identical.30 The
only diﬀerence between the two types of projects lies in the fact that H projects are so technologicallydemanding that SBs are not allowed to bid. The two types of projects are auctioned through K H +K L
independent first-price sealed-bid auctions that take place simultaneously.
The procurement proceeds in the following two-stage game: potential bidders decide their entry
in the first stage and auctions take place in the second stage. Once a potential bidder decides toparticipate in an auction, it will incur a participation cost e, obtain its own private information c,know the number of competitors, and submit a bid following a Nash bidding strategy in the secondstage auction game. The participation cost e is interpreted as an information acquisition cost and,hence, is reasonably assumed to be identical and common knowledge for all potential bidders andfor any type of projects. If the set-aside program is implemented, the low-end project is exclusively
oﬀered to SBs so that LBs cannot bid. Otherwise, an LB can be a recipient of an L project.
Despite the simplification, the entry game has many pure and mixed equilibria depending on theentry process.31 Therefore, it is further assumed that entry takes place sequentially, as in McAfee
and McMillan (1987a), and that the number of bidders is treated as a continuous variable.
Then, the number of players in our entry game can be reduced to the following two representative
agents, LB and SB. Each agent t ∈ {LB, SB} decides the number of participants Nts in the auctions
for type s ∈ {H, L} projects subject to the capacity constraint of LBs in the procurement market,
Hi.e., NLHB + NLLB ≤ NLB and the participation constraint, i.e. nSB= 0, and if the set-aside programL
is implemented, NLB = 0. It is also assumed that LB decides his entry first, and, successively, SB
makes his participation decision. Upon making their entry decision Nts , each representative player t
incurs participation costs e × Nts for the auctions of type s projects. This setting gives us a uniqueasymmetric Nash entry equilibrium. The timeline is described in Figure 13.
Let nst be the number of group t bidders in an auction for type s project. Since K s identical types projects are auctioned oﬀ simultaneously, nst satisfies
nst =

Nts
,
Ks

(10)

H
L
for all s and t. Given the equilibrium numbers of participants, (nLHB , nSB) and (nLLB , nSB), they submit
a bid following the optimal bidding strategies as will be discussed in the next subsection.

6.2

Analysis for the auction stage

In this subsection, we calculate the expected profit of a potential bidder who has decided to participate
in a procurement auction.
Consider a procurement auction in which there are two groups of risk-neutral bidders, LBs andSBs. For each t ∈ {SB, LB}, let nst denote the number of group t bidders in auction s ∈ {H, L}, i.e.,
the auction for project s. Bidder i in group t has cost cit , which is drawn from cumulative distributionfunction Fc (·|t) on [c, c̄].
Note that the bidders in the same group are ex ante symmetric, drawing their cost from an identical
distribution. However, we assume that Fc (·|SB) has conditional first-order stochastic dominance overFc (·|LB) as in Maskin and Riley (2000). Hence, the cost of an LB who participates in auction L ison average lower than that of an SB in the auction. The cost of an LB for project H is on average
the same as that for project L.
30

This assumption does not violate the definition of high- and low-end projects used in our empirical specification.
An L project here is assumed to consist of multiple low-end projects in data.
31
Levin and Smith (1994) show that the number of actual bidders will be stochastic if the entry is simultaneous.
Nakabayashi (2010) also analyzes that there are multiple equilibria in the simultaneous entry game if the potential
entrants are not ex ante identical.

16

For all i ∈ {1, . . . , nt }, let bit be the bid value of bidder i in group t. Then, the bidder’s problem
is to maximize his conditional interim expected payoﬀ ut given cit , nLB and nSB by choosing bit ;
��
i

�

s
ut (cit |nSB
, nLsB ) = max b − ctbi� �=i�si�Pr b ≤ bt

nt�
��
i=1

�
�
Pr b ≤ bit� , t� ∈ {SB, LB} and t� �= t.

Suppose that there is an increasing and group symmetric equilibrium in which for each t ∈ {SB, LB},
bidders in group t follow an identical bidding function βt (·). If all other bidders follow βt , then, bidder
i in group t’s problem (3) is rewritten as������ns −1 �
�
�� s
s
� nt�
ut (cit |nSB
, nLsB ) = max b − cit 1 − Fc βt−1 (b) |t t
1 − Fc βt−1.
� (b)|tb(11)

As usual, we take the derivative with respect to cit to apply the envelop theorem, impose the symmetry
condition such that b = βt (cit ), take integral on both sides from cit to c̄, and suppress the superscript
i. Then, we obtain
� c̄
�
�
�� s
s
s
s
� nt�
ut (ct |nSB , nLB ) =[1 − Fc (c|t)]nt −1 1 − Fc βt−1dc.
� (βt (c)) |t
ct

Taking the expectation yields U (·), the interim expected payoﬀ of a bidder in group t from the auctions bidders is given as
with nLsB and nSBss
Ut (nSB, nLsB ) ≡ E[ut (ct |nSB
, nLsB )]
� c̄
�
�
�� s
s
� nt�
=
Fc (c|t) [1 − Fc (c|t)]nt −1 1 − Fc βt−1dc.
� (βt (c)) |t

(12)

s
s
V (xt (nSB
, nLsB ), ns ) ≡ Ut (nSB
, nLsB ),(13)cThis equals each potential entrant’s conditional expected revenue from participating in the auctions .32 For any ns and ns , U could be
provided that the numbers of competitors are nLsB and nSBttt�
structurally estimated using Equation (12) and the cumulative distribution function of the recovered
pseudo-value c.
Unfortunately, this approach is not feasible here since, as will be discussed, the counterfactual
analysis requires a function Ut (·) on continuous variables, nst and nst� . To acquire Ut numerically (12),the number of necessary computations goes to infinity. Hence, a reduced form approach is adopted
to obtain the function Ut (·) as follows.
First, it is assumed that there exists a function V (·) such thats + ns . The identity indicates that the ex ante interim expected payoﬀ v(·) can bewhere ns = nSB
LB
decomposed into two components, i) the number of competitors represented by ns , and ii) the firm
size represented by the normalized score xt .
The function xt (·) is defined in the same manner as (1). Let X̄t be the average size of groupt firms in the procurement market. In addition, let X̄ s denote the bidders’ average size in auctions )/ns . Then, the normalized score of a group t firm ins, formulated by X̄ s = (X̄LB · nLsB + X̄SB · nSB
auction s is obtained bysxt (nSB, nLsB ) =X̄t − X̄ s
.
X̄ s

(14)

32
Other entry models, such as Li and Zheng (2009), assume that the number of bidders is unknown to bidders until
the auction is over. In this case, the ex ante expected gain integrates the interim expected profit over the possiblecombination of the numbers of participants. See Li and Zheng (2009) for more details.

17

The explicit form of xt (·, ·) is given in the Appendix.
By linear approximation, the logarithm of V (·) is given bylog V (xt (·), ns ) = log V(0, 0) + V1 · xt (·) + V2 · ns ,where V1 = ∂ log V (0, 0)/∂xt and V2 = ∂ log V (0, 0)/∂ns . Let log V(0, 0) = α0 , V1 = α1 , and V2 = α2 .
Then,
s
s
log Ut (nSB
, nLsB ) = α0 + α1 · xt (nSB
, nLsB ) + α2 · ns

(15)

is obtained. The coeﬃcient α1 is the firm-size elasticity of the ex ante interim expected payoﬀ fromthe auction, measuring the quantitative impact of the bidder’s relative size on the profitability fromthe auction. Note that the ex ante interim expected payoﬀ Ut (·) is the payoﬀ from participating in
an auction given the number of entrants ns . Based on these values, each potential entrant decides
whether to enter a procurement auction taking into account the expected gain of participation andthe participation costs as discussed in the next subsection.

6.3

Analysis for an entry equilibrium

Potential bidders continuously participate in an auction until their expected gain from entry exceeds
the costs of entry. A crucial assumption in the entry mode is that each firm has a unit production
capacity regardless of the group it belongs to.
First, the case in which set-asides are in use is analyzed. LBs may obtain positive profits fromparticipating in a procurement auction since their production capacity is limited, whereas the marginal
SB obtains zero expected payoﬀ because of participation by an unlimited number of SB. Therefore,a unique entry equilibrium consists of the numbers of actual bidders in auction s, which satisfy
�
L,r
NLB
USB (nSB, 0) = esubject to nLH,r
,
(16)
B ≤
ULB (0, nLH,r
)
≥
e,
KH
B
if set-asides are implemented. If LBs obtain positive rents, the constraint is binding such that nLH,rB =NLB /K H .
L,uAssuming that the constraint is binding, a counterfactual situation is considered. Let (nSB
, nLLB,u )and (0, nLH,uB ) be the number of large and small bidders in auction L and H, respectively, if set-asides
were removed (The second superscript u stands for unrestricted participation.). Without set-asides,
low-end projects receive bids from large firms as well. The rent of SBs is, however, still fully extracted
L,ubecause of the unlimited number of SBs. Hence, the SBs’ optimal entry decision nSB
satisfies
L,u
USB (nSB, nLLB,u ) = e

(17)

L,u
for some nLLB,u . Solving (17) for nSB
gives the SBs’ best response to the LB’s entry decision nLLB,u .
L,uL,uNow, let Γ(nLB ) be the SB’s best response function. Since USB is decreasing in both nSB
and nLLB,u ,Γ� (nLLB,u ) < 0 is obtained.
In addition, the number of large firms in the market is given and finite, and each bidder witha unit production capacity can bid only once. Therefore, the number of large bidders in high-end
L,uprojects nLH,u
B is a decreasing function of nLB .

18

Let Λ(nLLB,u ) be the decreasing function. It can be simply derived explicitly as 33
L,u
H,r
nLH,u
B = Λ(nLB ) ≡ nLB −K L L,un .
K H LB(18)

In equilibrium, the ex ante expected gain of each large bidder from participation must be the same
between the two projects. Hence, nLLB,u satisfies
ULB (Γ(nLLB,u ), nLLB,u ) = ULB (0, Λ(nLLB,u ))(19)subject to 0 ≤ nLLB,u and 0 ≤ Λ(nLLB,u ),where the left- and right-hand sides, respectively, represent the ex ante payoﬀ of an LB from low- andhigh-end projects. A unique solution of nLLB,u is thus obtained from the equation. Then, the unique
L,unSB
and nLH,u
B are obtained using Γ(·) and Λ(·).

6.4

An empirical model for auctions with entry

We first obtain Λ(·) empirically. Let ρ be the proportion of L projects in volume in the total budget for civil engineering contracts during the period. According to MLIT (2007), civil engineering
projects with their engineer’s estimated costs being less than �300 million are set aside for SMEs.34
Consequently, with this model, we consider that a project is H if the engineer’s estimated cost is
no less than �300 million and low-end if the estimated cost is less than �300 million. Then, ρ isapproximately 59 percent.
Since we normalize the project size as identical for both H and L projects, it is reasonable toconsider that the proportion of the number of (normalized) L projects is equal to ρ so that we have
K L / (K L + K H ) = ρ and K H / (K L + K H ) = 1 − ρ. Using these, Λ(·) is empirically obtained as
Λ(nLLB,u ) = nLH,rB −ρ
nL,u .
1 − ρ LB(20)

The bidders are then divided into either large firms or SMEs. In fact, the distinction between
SMEs and large firms in the data is somewhat ambiguous. The set-aside program allows large firms
to participate in relatively small projects unless a suﬃcient competition among SMEs is expected.
Consequently, quite a few large firms submit their bids in low-end projects. In addition, some SMEs
that met a quality standard were able to participate in some high-end projects. Hence, one dependable
way to distinguish these two groups of firms would be to assume that those that bid on high-end
projects are large firms and those that bid on low-end projects are SMEs. Since the average scoresin high- and low-end projects are 1419.3 and 990.3, respectively, X̄SB = 990.3 and X̄LB = 1419.3 wereset. Table 10 is a summary of the statistics of the bidders’ scores in both high- and low-end projects.
L,r
The equilibrium participation under the set-aside program, nSB= 7.46 and nLH,r
B = 8.49, is obtained
L,ufrom the data.35 Then, a counterfactual analysis is conducted to predict (nSB
, nLLB,u ) and (0, nLH,uB ).
First, the bidders’ ex ante expected payoﬀ Uks is estimated for all k auction samples.36 Let bs(1),k
33

L,u
H
H
L
L
From Equation (10), we have nLH,u
B = NLB /K , nLB = NLB /K . Since every firm can bid only once, we have
H
,u
nLH,u
+ nLLBK L = NLB .
B KHSolving for nLH,uwith nLH,rB and replacing NLB /K
B give the decreasing function.
34
More precisely, �300 million is the threshold value with which the government determines whether a project is
auctioned for contractors that are grade B or above or C or below. Although the contractors with grade C or below
may not satisfy the exact criteria of ”SMEs” in Japan, the empirical analysis used here considers them as SMEs for
simplicity.
35s�m They are estimated s by the sample means of the number of bidders in each type of the project as nt =k=1 1{sk = s} · nk,t /K for each s ∈ {H, L}, where nk,t is the number of group t bidders in sample auction k.
36
As has been discussed, Uk could be structurally estimated. However, solving nst numerically from the obtained V

19

be the lowest bid in auction k for a type s project, and, with a slight abuse of notation, let cs(1),kbe the cost of the lowest bidder.37 In addition, let Qs (xs(1),k , nsk |zs ) be the prior probability that abidder with the relative score xs(1),k becomes the lowest bidder in the auction given that the numberof bidders is equal to nsk . Then, the bidder’s ex ante expected profit Uks is characterized as��
Uks = bs(1),k − cs(1),k Qs (xs(1),k , nsk |zs ).
(21)

In this specification, the probability Qs(1),k can be identified from a simple linear probability regression
model as follows.
Let Qi,k be the index of bidder i in auction k for a type s project where Qsi,k = 1 if the bidder
wins and Qsi,k = 0 otherwise. Then, the probability that i wins in the auction is estimated by
Qsi,k = δ1s

1s+ δ2s xsi,k + δ3s zsk + νi,k
,
nsk

(22)

where zsk controls for scoring auction and project size as zsk = (SCOREsk , ESTsk ).38 Table 11 shows
the regression results of Equation (22). Fixed eﬀects control the unobserved heterogeneity in project
locations. Due to the fact that the mean diﬀerence in scores for SMEs is 43 percent lower than thatfor large firms,39 it can be concluded that the mean diﬀerence in the frequency of winning for SMEs
is approximately 5.5 percent lower than that for large firms (t-value : 8.48 with FE).
Let δ̂1 , δ̂2 and δ̂3 denote the least square estimates of (22), and let xs(1),k denote the normalized
score of the lowest bidder in auction k for a type s project. Then, the estimator for the ex ante
winning probability, Q̂(·) is obtained asQ̂s (xs(1),k , nsk |zs ) = δ̂1s1
+ δ̂2s xs(1),k + δ̂3s zsk .
nsk

(23)

Since bs(1),k is observable and cs(1),k can be replaced with the estimates ĉs(1),k obtained in Section 5, Uks
is estimated for all k and s by using (21) as��Ûks = bs(1),k − ĉs(1),k Q̂s (xs(1),k , nsk |zs ).
Then, using the estimated Û and observed data, x, and n, the following linear regression is constructed:log Ûks = α0s + α1s xs(1),k + α2s nsk + α3 zsk + �sk ,where �sk is assumed to be an i.i.d., mean zero random variable. The regression results are shown in
Table 12.
Let α̂s ≡ (α̂0s , α̂1s , α̂2s , α̂3s ) be the least square estimates of αs ≡ (α0s , α1s , α2s , α3s ). Replacing α withs , ns ) on (15) yields its empirical counterpart asα̂ and xst with xt (nSB
LBsslog Uts (nSB
, nLsB |zs ) = α̂0s + α̂1s xt (nSB
, nLsB ) + α̂2s ns + α̂3s zs .

(24)

Specifically, αˆ1 measures the marginal eﬀect of the number of bidders on the profitability while αˆ2requires an infinitely large number of calculations because of the assumption that the number of bidders is continuous.
A reduced-form specification is thus employed to approximate a bidder’s probability of winning and the winner’s payoﬀ
in the counterfactual analysis.
37
Since our model assumes asymmetric first-price sealed-bid procurement auctions, it is possible that the lowest bidder
does not have the lowest signal.
38
Although percentage bids are used in order to control the project size heterogeneity, there still remains project size
heterogeneity in percentage bids. To further eliminate such heterogeneity, EST is included in z.
39 X̄BB −X̄SB= 0.39.
X̄
BB

20

captures the marginal eﬀect of bidder’s relative size on the profitability.
It is also used to identify the participation (information acquisition) cost e.40 As shown in (16),USB = e holds in equilibrium. The empirical counterpart of the zero-profit condition gives the estimator of the entry cost for a type s project, es as:
LL,rês = ÛSB
(nSB
, 0|zs ) ,assuming that the diﬀerence in the participation cost between H and L stems only from z.41 Finally,
the individual rationality condition for large firms in the case of set-asides:
H
H
ÛLHB (0, nLH,r
B |z ) ≥ log ê

is checked. The data show that the exponential of the left-hand side of 1.41 percent is greater thanthat of the right-hand side of 1.14 percent, which suggests that large firms obtain positive gains on
average in the procurement market. The individual rationality condition indeed holds.
The above argument can be applied to the scoring auction. The procedure is described in the
Appendix.

7

Counterfactual analysis

7.1

The procedure

With (24) and ê, a counterfactual analysis is simply implemented as follows. Replacing e with ê inEquation (17) and solving for nSB give the explicit form of the best response function
L,unSB= Γ(nLLB,u ).

The complete derivation is provided in the Appendix. Together with Λ(·) defined in (20), Equation(19) which characterizes the condition that LBs earn the same ex ante expected payoﬀ from H and L
projects becomesα̂0L + α̂1L · xLB (Γ(nLLB,u ), nLLB,u ) + α̂2L · [Γ(nLLB,u ) + nLLB,u ] + α̂3s zL =1−ρ H
[α̂2 · Λ(nLLB,u ) + α̂3H zH ] ,ρ(25)

where ρ � 0.59. The left-hand side describes the large businesses’ ex ante expected gain fromparticipating in low-end projects, whereas the right-hand side equals the ex ante expected gain fromhigh-end projects. Since low-end projects are greater in value terms than high-end projects, a weightvariable (1−ρ)/ρ � 0.69 is introduced so that (25) describes an equilibrium in which the gain of a large
firm from entering the low-end market is identical to that from entering the high-end market. For
simplicity in the calculation, Γ(·) and Λ(·) are linearized in Equation (25). The details are describedin the Appendix.
Finally, the comparative statics of the winning bid are described with respect to the participation
restriction. Let pk be the lowest bid in auction k. pk is considered to be a random variable conditionalon the numbers of bidders, the normalized score of each bidder, and exogenous variables, such as theauction-specific eﬀect.
Hence, assuming that �p follows an i.i.d. distribution, a linear model was established for the lowest
40

Since bids and costs as well as profits here are represented in the percentage of the engineer’s estimated cost of the
project, the participation cost e is also expressed as the percentage. The participation (information acquisition) cost in
dollar terms is a proportion of the engineer’s estimated cost of the project.
41
Since the firm’s profit is expressed as a percentage of the engineer’s estimated cost of a project, the participation
cost es for the project is also expressed as the percentage of the engineer’s estimated cost. Hence, the es is heterogeneousfor every project auction, depending on the size and the auction characteristics i.e., a scoring or price-only auction.

21

bids aspk = θ0 + θ1 · x(1),k + θ2 · nk + θ3 · yk + �pk .

(26)

yk = (SCOREk , ESTk , log ESTk , AUC FORMAT) controls for auction-specific eﬀects such as a scoring auction option, determination of project size by an engineer’s estimate, and choice of open competition or invited bidders, and x(1),k denotes the lowest bidder’s normalized score. Then, θ̂1 measuresthe diﬀerence of the winning bid between LBs and SBs.
Table 13 shows the result of the regression of the lowest bids on x. Fixed eﬀects control the
area-specific �eﬀects. �Let θ̂ ≡ θ̂1 , θ̂2 , θ̂3 be the least square estimates of θ ≡ (θ1 , θ2 , θ3 ). Using these estimates, themean winning bids are estimated in the low-end projects under the unrestricted participation situation
as follows.
It is assumed that the mean winning bids of LBs and SBs can be described by
L,u
L,u
L,u
pt (nSB, nLLB,u ) = θ̂0 + θ̂1 · xt (nSB
, nLLB,u ) + θ̂2 · (nSB
+ nLLB,u ) .

Let Qt be the winning probability of a group t bidder. By using (23), Qt is obtained empiricallyas
L,uQt (nSB, nLLB,u ) = δ̂1

L,u
SB

n

1
L,u
+ δ̂2 xt (nSB
, nLLB,u ),+ nLLB,uL,ufor each t ∈ {LB, SB}. Given the number of bidders (nSB
+ nLLB,u ) in a procurement auction for alow-end project, the probability that some LB wins the project is equal to QLB (·) · nLLB,u , and theL,uprobability that some SB wins is equal to QSB (·) · nSB. Then, the mean winning bids in the low-end
projects are given as
L,u
L,u
L,u
L,u
L,u
L,u
p(nSB
, nLLB,u ) = pSB (nSB
, nLLB,u ) · QSB (nSB
, nLLB,u ) · nSB+ pLB (nSB
, nLLB,u ) · QLB (nSB
, nLLB,u ) · nLLB,u ,and those of the high-end projects are given asH,up(0, nLH,uB ) = pLB (0, nLB ),The percentage change of the procurement cost for low-end projects is estimated by
L,u
L,r
p(nSB
, nLLB,u ) − p(nSB, 0),

and that for high-end projects is given by
H,rp(0, nLH,uB ) − p(nLB , 0).

7.2

Results

The empirical results suggest that the set-aside program likely decreases the procurement costs. The
counterfactual analysis predicts what the bidder’s entry decision and bidding behavior would be were
the program to be eliminated. The program yields the competing eﬀects in terms of government
procurement costs, the cost reduction in set-aside projects and the cost increase in the remaining
projects.
The analysis suggests that, were the program to be eliminated, 2.51 large firms on average would
switch their entry from high-end to low-end projects so that their ex ante payoﬀ from these two
projects must be identical in equilibrium. Since there is a diﬀerence in volume for each category of
projects, represented by ρ = 0.59, the mean number of large firms in low-end projects would be 1.72,
22

which is obtained by 2.51 times (1 − ρ)/ρ.
The serious problem by removing the participation restriction is that the number of participants
would decrease in both high- and low-end projects. In high-end projects, the number of large firms
would drop from 8.49 to 5.98, which would raise the procurement costs of those projects by 0.99
percent. At the same time, the large firms’ participation in low-end projects would depress SME
entry into low-end projects. The mean number of SME participants would decline from 7.46 to
5.29.42 The number of both large-firm and SME participants in low-end projects would drop from
7.46 to 7.01 on average since, according to the static entry model, the participation of one more large
firm in the low-end projects would eliminate 1.26 SME participants on average.43 The procurement
costs of low-end projects would fall by 0.40 percent, despite the presence of fewer participants, becauseof the entry of cost-eﬃcient large firms. The average score of bidders would be increased from 990.3
to 1095.7.
Surprisingly, the resulting lack of competition would drive up government procurement costs.
There are two competing eﬀects that set-asides have on government procurement costs, increasing
competition versus the participation of cost-ineﬃcient SMEs. Taking also into account the fact thatthe government spent approximately 60 percent of the procurement budget on low-end projects, theeﬀect of increasing competition would overcompensate for the eﬀect of production ineﬃciency cost.
The counterfactual analysis suggests that set-asides would decrease government procurement costs
by 0.17 percent.
It is interesting to observe how the ex ante expected profits of large firms are changed by setasides. Without set-asides, large firms obtain a positive expected gain (2.12 percent of the engineer’s
estimated cost for each auction), and the net positive gain from entry is almost 0.83 percent of the
project’s estimated cost. Set-asides completely squeeze the positive net gain from large firms so thatthe expected gain of large firms with set-asides is almost zero (-0.15 percent). Obviously, this rent
extraction from large firms contributes to lowering government procurement costs more than to oﬀset
the resulting production cost ineﬃciency.

8

Discussion

Most small business programs declare that the importance of providing more contract opportunities
for disadvantaged businesses lies in the encouragement of their long-run growth. The long-run benefit
on an economy has been assumed to outweigh the short-run cost of supporting small businesses. In
fact, even in the short run, the program can benefit the procurement buyer, as our analysis has
illustrated. Upon designing a public procurement policy, the non-trivial short-run gain should be
more carefully considered.
In addition, set-asides are robust against collusion in procurement auctions. Our simulation results
indicate that both high-end and low-end auctions receive more participants when set-asides are inuse. Obviously, more participants in auctions suggest fewer chances for bidders to be cooperative.
Procurement buyers may, therefore, have further short-run benefit from set-asides.
The assumption that the firm has unit production capacity can be relaxed so that multiple units ofproduction and, hence, participating in more than two auctions at the same time are possible withoutchanging the obtained results in this analysis. However, the model does rely on the production
capacity, especially, the capacity constraint of the cost-eﬃcient businesses. It is easy to imagine thatprocurement costs would always be lower by inviting only the cost-eﬃcient firms if their production
always exhibits constant returns to scale, although the situation is unrealistic for many procurement
buyers.
42
This outcome implicitly assumes that each group of bidders follows a Nash equilibrium bidding strategy. Should
the large firms intentionally make a low-ball bid to deter entry by SMEs, the decrease of SMEs would be much moresignificant.
43
The coeﬃcient is given by γ = 1.26.

23

Regarding the entry model, Li and Zheng (2009) show a series of models of auctions with endogenous participation. Among these, Model 2 is closest to the entry model employed in this paper.
However, their method does not apply to our case because it requires the assumption that potential
bidders are identical to estimate the distribution of the potential bidder’s participation cost.44 In
fact, the empirical specification of the distribution is extremely complicated or even impossible when
the asymmetry of bidders varies across the auctions as exhibited in our data.
Due to the limitation, the reduced-form approach is chosen, where the expected gain from participation is assumed to be a decreasing function of the expected numbers of large and small participantsin the auction. Although the obtained value of the expected gain using such mean numbers diﬀers
from the expected gain from participation computed by integrating all possible profits over the possible numbers of bidders, these two are strongly correlated. Hence, the former satisfies the suﬃcientcondition to become a proxy for the latter. The reduced-form approach is thus chosen with the consideration that it is the most eﬃcient way to predict the potential bidder’s participation decisions
without small business set-asides.
The entry model assumes a positive participation cost incurred by every bidder. The interpretationof such sunk cost comes from the fact that information acquisition for articipating in a procurement
auction is quite a costly process especially for construction projects. Bidders must carefully readdrawings and specifications and thoroughly examine them, including all the notes and references.
When subcontracts are needed, bidders must solicit bids from subcontractors. The estimation of
subcontract costs is not available until all subcontract bids are opened and pre-award subcontract
agreements are made with the chosen subcontractors. These processes are extremely time-consuming.
Furthermore, the accuracy of estimation is very important since an error could lead to losing thecontract or getting a winner’s curse. Hence, those sunk costs crucially aﬀect the bidder’s participation
decision into a procurement auction.

9

Conclusion

Set-asides are widely used in real-world public procurement. The encouragement of SMEs has evokeda controversy on the extent of the extra cost society is paying. However, there is no previous systematic
analysis to measure the impact on procurement costs.
In this paper, we provide the first systematic analysis of the eﬀect of small business set-asides on
government procurement costs, bidding behaviors, and bidder participation in competitive bidding
processes. The simulation study suggests that the program dramatically increases SME participation
but is almost neutral with respect to the procurement costs. The production ineﬃciency causedby set-asides is overcompensated by the increased entry and resulting enhancement of competition
by large firms. The set-aside program was observed to increase SME participation in procurement
auctions by approximately 30 percent.
The empirical results show that the set-aside program has been successful. It improves equity
between advantaged and disadvantaged firms and reduces government procurement costs. The results
also suggest that the government cost of set-aside auctions is exaggerated if only the excess amounton contracts allocated to SMEs is considered. The theoretical literature suggests that, despite theeﬃciency loss, the encouragement of less advantaged bidders in the auction can reduce procurement
costs. For instance, Bulow and Roberts (1989) and McAfee and McMillan (1989) insist that bidding
credits (or bid discounts in procurement auctions) for disadvantaged bidders increase the auctioneer’s
welfare, yielding more competitive pressure on advantaged bidders. Similarly, subsidized SMEs drive
non-subsidized bidders to give up more of the gain on the contracts they award.
The conclusion also provides an economic rationale on why several countries, such as the UnitedStates and Japan, opt out of SMEs from the Government Procurement Agreement (GPA) of the
44
Furthermore, if potential bidders are not symmetric, random participation results in multiple equilibria as shownin Nakabayashi (2010). Empirical specification is, then, impossible or extremely diﬃcult.

24World Trade Organization (WTO). Although Article 4 in the GPA prohibits the member countries
from giving unfavorable treatment to any company, the set-aside programs are exempted in the GPAAppendix. EU countries have also been renegotiating with the WTO to obtain the exclusion of
their SMEs. An important question, however, is whether those practices are robust for corruption or
favoritism. Further theoretical and empirical consideration is needed.
A limitation of this study is that it does not consider the long-term eﬀect of set-asides. In thelong run, there are positive and negative eﬀects of set-asides on procurement costs. If SMEs could
win more auctions, they would have more chances to develop their production skills through learningby doing. On the other hand, subsidization of SMEs may discourage them to develop their businesses
to a stage in which they could not be favored in the preference program. Given the sheer volume
of public sector procurement, it is clear that more serious research and evaluation are needed toinvestigate the long-run eﬀect of the set-aside program.

AppendixLinearization of Γ(·)
L,u
The linear approximation for nSB= Γ(nLLB,u ) at nLLB,u = 0 is given by,
L,unSB= Γ(0) − Γ� (0)nLLB,u .

L,rL,rSince USB (nSB
, 0) = e by (17), Γ(0) = nSB. Therefore,
L,u
L,r
nSB
= nSB
− Γ� (0)nLLB,u .

(A-1)

L
To obtain the explicit form of Γ� (0), take total derivative of (17) with respect to nSB
and nLLB , andthe following is obtained

0 = α̂2L ·L
L∂ x̄SB (nSB
, nLLB )∂ x̄SB (nSB
, nLLB )
L
L
L
∆n
+
α̂
·
∆nLLB + α̂3L · (∆nSB+ ∆nLLB ).
SB
2
L
∂nSB
∂nLLB

(A-2)

L
L
By the chain rule, ∂ x̄SB (nSB
, nLLB )/∂ n̄Lt = ∂ x̄SB (nSB
, nLLB )/∂ X̄L · ∂ X̄L /∂ n̄t,L holds for each t ∈L
L
L{SB, LB}. Since ∂ x̄SB (nSB
, nLLB )/∂ X̄L = −X̄SB /(X̄L )2 , ∂ X̄L /∂nSB= 0 and ∂ X̄L /∂nLLB = (X̄LB − X̄SB )nSB/(nL )2
Lwith X̄L = X̄SB and nL = nSB ,L∂ x̄SB (nSB
, nLLB )X̄LB − X̄SB
=−
and
L
L
∂nLB
X̄SB · nSB
L∂ x̄SB (nSB
, nLLB )=0
L∂nSB

are obtained. Plug them into Equation (A-2), and the following is obtained
L−∆nSB= Γ� (0)∆nLLB .

Hence,
Γ� (0) =α̂2L X̄LB − X̄SB
+ 1 = 1.26
L
α̂3L X̄SB · nSB

is obtained.

25

Application to scoring auctions:
In particular, it is shown that there is one-to-one mapping between the percentage markup, bi − ĉiand the informational rent in the scoring auction, si − θi :Proof. Let S̄ be the base score which is defined as Est/q. Let πi be the i’s conditional informational
rent in the scoring auction that satisfies πi = si − θi .
First, we show that the informational rent measured with the dollar term bid and cost is identicalto that measured with the percentage bid and cost. Let $bi and $ci be the bid and cost in dollar
terms. Let $si and $θi be the scoring bid and the pseudo-type measured with the dollar term bid andcost, which satisfy
$si ≡

S̄
S̄
, $θi ≡.
qi /$biqi /$ci

Note that $si and $θi are identical to si and θi .45 Given qi , there is one-to-one mapping between thescoring bid and the price-bid and between the pseudo-type and the cost:��
bi q c i q(si , θi ) =
,
qi qi
q
= (bi , ci )qiHence, the percentage conditional payoﬀ, π̂i , in the scoring auction is estimated byπ̂i ≡ bi − ĉi =qi(si − θ̂i ).
q

Using the transformation, the percentage conditional payoﬀ of the winning bidder in the scoring
auction is obtained.

References
Asker, John and Estelle Cantillon, “Properties of scoring auctions,” RAND Journal of Economics, 2008, 39 (1), 69–85.
Athey, Susan, Jonathan Levin, and Enrique Seira, “Comparing Open and Sealed Bid Auctions:
Evidence from Timber Auctions,” NBER Working Papers, National Bureau of Economic Research,
Inc December 2008.
Ayres, Ian and Peter Cramton, “Deficit Reduction Through Diversity: How Aﬃrmative Action
at the FCC Increased Auction Competition,” Technical Report 1996.
45

�
S̄
S̄
,
qi /$bi qi /$ci
�
�
q/Est
q/Est
=
,
qi /(bi Est) qi /(ci Est)
�
�
q
q
=
,
qi /bi qi /ci≡ (si , θi ) .

($si , $θi ) ≡�Hence, the scoring bid and pseudo-type are, respectively, the same regardless of whether they are measured with thepercentage bid, bi , and cost, ci or with the dollar bid $bi and the dollar cost $ci .

26

Bajari, Patrick and Lixin Ye, “Deciding Between Competition and Collusion,” The Review of
Economics and Statistics, November 2003, 85 (4), 971–989.
and Steven Tadelis, “Incentives versus Transaction Costs: A Theory of Procurement Contracts,”
RAND Journal of Economics, Autumn 2001, 32 (3), 387–407.
Bannock, Graham, The Economics of Small Firms: Return from the Wilderness, Oxford: BasilBlackwell, 1981.
Bulow, Jeremy and John Roberts, “The Simple Economics of Optimal Auctions,” Journal of
Political Economy, October 1989, 97 (5), 1060–90.
Campo, Sandra, Isabelle Perrigne, and Quang Vuong, “Asymmetry in first-price auctions
with aﬃliated private values,” Journal of Applied Econometrics, 2003, 18 (2), 179–207.
Che, Yeon-Koo, “Design Competition through Multidimensional Auctions,” RAND Journal of
Economics, Winter 1993, 24 (4), 668–680.
Corns, Allan and Andrew Schotter, “Can Aﬃrmative Action Be Cost Eﬀective? An Experimental Examination of Price-Preference Auctions,” American Economic Review, March 1999, 89 (1),291–305.
Denes, Thomas A., “Do Small Business Set-Asides Increase the Cost of Government Contracting?,”
Public Administration Review, 1997, 57 (5), 441–444.
Guerre, Emmanuel, Isabelle Perrigne, and Quang Vuong, “Optimal Nonparametric Estimation of First-Price Auctions,” Econometrica, 2000, 68 (3), 525–574.
Hansen, Robert G., “Auctions with Endogenous Quantity,” RAND Journal of Economics, Spring
1988, 19 (1), 44–58.
Jofre-Bonet, Mireia and Martin Pesendorfer, “Estimation of a Dynamic Auction Game,”
Econometrica, 09 2003, 71 (5), 1443–1489.
Krasnokutskaya, Elena, “Identification and Estimation in Highway Procurement Auctions under
Unobserved Auction Heterogeneity,” Review of Economic Studies, 2009. forthcoming.
and Katja Seim, “Bid Preference Programs and Participation in Highway Procurement Auctions,” working paper, 2009.
Laﬀont, Jean-Jacques and Jean Tirole, A theory of incentives in procurement and regulation,
Cambridge, MA: The MIT Press, 1993.
Levin, Dan and James L Smith, “Equilibrium in Auctions with Entry,” American Economic
Review, June 1994, 84 (3), 585–99.
Li, Tong and Xiaoyong Zheng, “Entry and competition eﬀects in first-price auctions: theory andevidence from procurement auctions,” Review of Economic Studies, 2009, (76), 1397–1429.
Marion, Justin, “Are bid preferences benign? The eﬀect of small business subsidies in highway
procurement auctions,” Journal of Public Economics, August 2007, 91 (7-8), 1591–1624.
Maskin, Eric and John Riley, “Asymmetric Auctions,” Review of Economic Studies, July 2000,
67 (3), 413–38.
McAfee, R. Preston and John McMillan, “Bidding for Contracts: A Principal-Agent Analysis,”
RAND Journal of Economics, Autumn 1986, 17 (3), 326–338.
27

and

, “Auctions and Bidding,” Journal of Economic Literature, June 1987, 25 (2), 699–738.

and, “Auctions with entry,” Economics Letters, 1987, 23 (4), 343–347.

and , “Government procurement and international trade,” Journal of International Economics,
May 1989, 26 (3-4), 291–308.
Milgrom, Paul, Putting Auction Theory to Work, Campridge University Press, 2004.
MLIT, Ministry of Land, Infrastructure, Transportation and Tourism, Construction
Contracts: Annual Report: Tyokkatsu Koji Keiyaku Kankei Shiryou 2007.
available at
http://www.mlit.go.jp/chotatsu/contractsystem/keiyaku/.
Nakabayashi, Jun, “Equilibria in Asymmetric Auctions with Entry,” January 2010.
Paarsch, Harry J., “Deciding between the common and private value paradigms in empirical models
of auctions,” Journal of Econometrics, 1992, 51 (1-2), 191–215.
Samuelson, William F., “Competitive bidding with entry costs,” Economics Letters, 1985, 17 (1-2),
53–57.
Zhang, Bin and Kemal Guler, “Nonparametric estimation of asymmetric first price auctions: A
simplified approach,” Economics Letters, September 2005, 88 (3), 318–322.
Zheng, Charles Z., “High Bids and Broke Winners,” Journal of Economic Theory, September 2001,
100 (1), 129–171.

28

0

.02

.04

Fraction
.06

.08

.1

Figure 1: Data area

−.4

−.2

0
.2
Normalized BE Score

.4

.6

®

Figure 2: Normalized score of actual bidders

29

2000
1500
Frequency
1000
500
0
6

7

8
Log10(EST)

9

10

fi

0

.5

1

density
1.5

2

2.5

Figure 3: Project size (log10 of the engineer’s estimate).5

1bid (%)
kdensity larger

1.5
kdensity smallerfi

Figure 4: Densities (Percentage bids)

30

.1
.08
Fraction
.06
.04
.02
0
0

500

1000
BE Score

1500

2000

fi

0

.02

Fraction
.04

.06

.08

Figure 5: BE score of actual bidders

0

500

1000
BE Score

1500

2000

fi

0

0

.002

.002

Density.004

Density
.004

.006

.006

.008

Figure 6: BE score of all firms on the certified contractor lists

1000

1200

1400
Bidders (LBs)

1600

1800

1000

1200

1400
1600
Qualified firms (LBs)

1800

®

®

Figure 7: BE score of LB bidders

Figure 8: BE score of all LBs on the lists
31

.004

.005

.003

.004

Density.002

Density
.003

.001

.002

0

.001
0

400

600

800
1000
Bidders (SBs)

1200

1400

400

600

800
1000
Qualified firms (SBs)

1200

1400

®

®

Figure 9: BE score of SB bidders

Figure 10: BE score of all SBs on the lists

Figure 11: Few bidders: n = 5

Figure 12: Many bidders: 22 ≤ n ≤ 28

Time Line
Large firms
SMEs

nQ,L, nQ,H

entry
cost

nq,L

First Stageesignalci,jbid

Second Stage

Figure 13: The model of auctions with entry

32

Project A,
Est. ≤ 730
obs.
percentage

Project B,
300 < Est. ≤ 730
obs.
percentage

Project C,
60 < Est. ≤ 300
obs. percentage

Project D,
Est. ≤ 60
obs.
percentage

Firm’s letter-grade
A
B
C
D

3,269
430
62
0

86.92 %
11.43 %
1.65 %
0.00 %

781
4,218
387
0

14.5 %
78.31 %
7.19 %
0.00 %

128
2,588
103,0932,716

0.12 %
2.38 %
94.99 %
2.5 %

0
16
4,365
9,472

0.00 %
0.12 %
31.51 %
68.38 %

Total

3,761

100.00 %5,386

100.00 %108,525100.00 %13,853100.00 %Observations count the total number of participants by the letter grade.

Table 1:Category
General & Heavy
PavingBridgeLandscaping
Architecture
Painting
MaintenanceDredging
Machinery & equipment
Info & telecom facility
OthersTotal

Amount963,309140,078
95,166
10,48563,8807,089
172,592
5,885
32,10841,644
154,412
1,686,658

FY2008(%)
Count(57.1)
4,219
(8.3)
846
(5.6)
184
(0.6)
276
(3.8)
607
(0.4)
219
(10.2)
2,396
(0.3)
24
(1.9)
473
(2.5)
733
(9.2)
987
(100.0)10,964(%)(38.5)
(7.7)
(1.7)
(2.5)
(5.5)
(2.0)
(21.9)
(0.2)
(4.3)
(6.7)
(9.0)
(100.0)

Amount806,667
113,252
118,931
10,85860,817
6,552
151,119
5,929
27,35543,824
139,645
1,484,949

FY2007(%)
Count(54.3)
4,092
(7.6)
789
(8.0)
218
(0.7)
313
(4.0)
674
(0.4)
223
(10.2)
2,535
(0.4)
25
(1.8)
434
(3.0)
731
(9.4)
1,209
(100.0)
11,243(%)(36.4)
(7.0)
(1.9)
(2.8)
(6.1)
(2.0)
(22.5)
(0.2)
(3.9)
(6.5)
(10.7)(100.0)Category
General & Heavy
PavingBridgeLandscaping
Architecture
Painting
MaintenanceDredging
Machinery & equipment
Info & telecom facility
OthersTotal

Amount606,795
132,088
96,592
10,301
51,4046,800
141,751
4,792
37,102
37,102
140,766
1,265,492

FY2006(%)
Count(47.9)
4,068(10.4)
862
(7.6)
208
(0.8)
311
(4.1)
692
(0.5)
231
(11.2)
2,718
(0.4)
19
(2.9)
560
(2.9)
848
(11.1)
1,216(100.0)11,733(%)(34.7)
(7.3)
(1.8)
(2.7)
(5.9)
(2.0)
(23.2)
(0.2)
(4.8)
(7.2)
(10.4)(100.0)

Amount626,493
123,043
30,407
13,52442,6706,009
138,855
4,050
37,221
43,657
108,786
1,174,715

FY2005(%)
Count(53.3)
3,752(10.5)
799
(2.6)
148
(1.2)
356
(3.6)
717
(0.5)
241
(11.8)
2,919
(0.3)
21
(3.2)
594
(3.7)
998
(9.3)
1,118
(100.0)11,663(%)(32.2)
(6.9)
(1.3)
(3.1)
(6.1)
(2.1)
(25.0)
(0.2)
(5.1)
(8.6)
(9.6)
(100.0)

Table 2: Projects yearly (�million)

33

Category
General & Heavy
PavingBridgeLandscaping
Architecture
Painting
MaintenanceDredging
Machinery & equipment
Info & telecom facility
OthersTotal

Amount
3,003,265
508,461
341,096
45,168
218,771
26,460604,318
20,656
133,786
166,226
543,610
5,611,817

FY2005-2008
(%)
Count
(53.5)
16,131
(9.1)
3,296
(6.1)
758
(0.8)
1,256
(3.9)
2,690
(0.5)
914
(10.8) 10,568
(0.4)
89
(2.4)
2,061
(3.0)
3,310
(9.7)
4,530
(100.0)45,603(%)(35.4)
(7.2)
(1.7)
(2.8)
(5.9)
(2.0)
(23.2)
(0.2)
(4.5)
(7.3)
(9.9)
(100.0)

Table 3: Projects from FY2005 through FY2008 (�million)

BE Score
Normalized Score: Xi,k: xi,kNo. Obs.
130,050130,050

Mean
1,020.04-0.001

Std.Dev.
155.270.0778

Coeﬀ. of Var.
0.132
-

Max
1,859
0.57

Table 4: Summary statistics : The BE score of actual bidders

Project
Size
730 or more
300 - 730
60 - 300
less than 60
Total

No.
Observation
333
654
12,203
1,830
15,020=Y Million∗
Engineer’s Estimated Costs
Mean
Std.Dev.
MaxMin
2,127.56 1,718.66 17,600
737
474.24117.19725
300
144.78
63.99
299
60.01
38.191
16.95
59.99
.0075
190.10400.6017,600 .0075∗ The amount of money is based on the engineer’s estimate.

Table 5: Summary statistics on project size

34

Min
475
-0.42

Bids

Costs

OLS

FE

RE

OLS

FE

RE

xi,k

-0.027(4.55)**-0.023(6.15)**-0.023(6.31)**-0.033(5.04)**-0.029(6.57)**-0.029(6.73)**

Auction date

-0.000(121.38)**---0.000(118.99)**--

Scoring auction dummy-0.067(32.32)**---0.077(33.74)**--

Auction form dummy 2

0.019(6.16)**

-

-

0.021
(6.07)**--

Auction form dummy 3

0.044(22.08)**

-

-

0.042
(19.01)**--

Auction form dummy 4

0.020(7.95)**

-

-

0.020
(7.95)**--

Constant

129.8770.856
0.841(122.22)** (3004.12)** (613.72)**

Observations
R-squared
Number of auctions

1104160.36-1103240.00
14857

11032414857

141.618
0.813
0.783(119.72)** (2436.29)** (496.88)**1104160.35-1103240.00
14857

11032414857

Absolute value of t statistics in parentheses; * significant at 5%; ** significant at 1%
xi,k : % diﬀerence from average bidders in auction k

Table 6: Regression results of normalized bids and estimated costs

Letter grade
Large firms
Small firms

BE scores
Std. Dev. Min
173.25997

Actual

Obs
155

Mean
1333.4

Max
1859

Registered197

1327.4160.85997

1859

ActualRegistered

7,986
31,535

915.0
823.1

112.03125.53

475
329

1460
1460

Actual large (small) firms are the bidders in high-(low-)end projects. Registered large (small) firms are the firms with letter grades A and B (C andD).

Table 7: BE scores of actual and registered bidders

Letter grade

BE scores
Std. Dev. Min
138.491239
132.71
1239

A

ActualRegistered

Obs
34
37

Mean
1,580.97
1,580.51

Max
1859
1859

B

ActualRegistered

118
160

1,264.09
1,268.88

104.99
97.74

997
997

1526
1526

C

ActualRegistered

3,829
5,148

987.52997.55

93.30
97.48

668
668

1460
1460

D

ActualRegistered

3,766
26,387846.62789.09

79.12
99.42

475
329

1086
1118

Table 8: BE scores of actual and registered bidders (by letter grade)
35

OLS

Robust OLS

FE

xij

0.342
(5.23)**

0.342(4.90)**

0.292(4.81)**

No. Bidders-0.096(83.91)**-0.096(45.70)**-0.091(77.90)**Auction date

0.256
(25.57)**0.256(24.82)**

ESTk

0.006
(8.89)**

0.006(4.11)**

logESTk-0.01(1.14)-0.01(0.76)

Scoring auction dummy

0.098(2.76)**

0.098(2.03)*

Auction format dummy 1

0.245(6.41)**

0.245(4.97)**

Constant-2.264(13.86)**-2.264(9.27)**-1.406(8.56)**

Observations
R-squared

10709
0.48

10709
0.48

10709

No. auctions

204

Absolute value of t statistics in parentheses* significant at 5%; ** significant at 1%
FE controls auction-specific eﬀects. Invited bidders are excluded.

Table 9: Regression result for bid margins

Project Category

Mean

No. obs

Std. dev.

Max.

Min.

Low-end990.3

121,046100.981,750

475High-end

1419.3

8,977

199.65

1,859

799

Total

1,019.78

131,552

151.63

1,859

475

<=
Y 300 mn≥=
Y 300 mn

Table 10: Project category

36

OLS

Robust OLS

FE

xij

(δ1 )

0.128
(8.48)**

0.128(8.48)**

0.128(8.48)**(No. Bidders)−1

(δ2 )

1.019
(104.46)**1.019(111.68)**1.014(94.60)**Auction date

0.002
(0.89)

0.002(0.91)

0.004(1.63)

ESTk-0(0.14)-0(0.15)

0(0.25)

logESTk-0(0.26)-0(0.27)-0.001(0.57)

Scoring auction dummy

0.005(0.63)

0.005(0.68)

0.006(0.74)

Auction format dummy 1-0.006(0.71)-0.006(0.75)-0.011(1.26)

Constant

0.026(0.57)

Observations
R-squared

79327
0.25

79327
0.25

79327
0.11

Absolute value of t statistics in parentheses* significant at 5%; ** significant at 1%
Except invited bidders

Table 11: Regression result for the linear probability model

low-end : s = L
OLS
Robust OLS

high-end : s = H
OLS
Robust OLS

xij (α1s )1.083(12.20)**1.083(12.14)**2.835(9.22)**

2.835(9.59)**

No. Bidders (α2s )-0.238(152.00)**-0.238(65.88)**-0.155(31.92)**-0.155(19.83)**s
Scoring auction dummy (α3,1)

0.716(22.73)**0.716(17.51)**0.601(5.26)**

0.601(5.29)**

s
Estimated cost (α3,2)-0.029(3.00)**-0.029(2.86)**

0.006(2.80)**

0.006(2.88)**

Constant (α0s )-3.103(81.93)**-3.103(56.97)**-3.577(30.32)**-3.577(27.55)**Observations
R-squared

9782
0.72

9782
0.72

927
0.54

927
0.54

Absolute value of t statistics in parentheses, * significant at 5%; ** significant at 1%
Invited bidders are excluded

Table 12: Regression result for expected payoﬀs

37

OLS

Robust OLS

xij (θ1 )-0.07(5.28)**-0.063(5.53)**

No. bidders (θ2 )-0.003(14.74)**-0.004(18.67)**

Auction date

-0.138(68.07)**-0.143(68.07)**

ESTk

0.001
(5.74)**

0.001(5.74)**

logESTk-0.066(39.29)**-0.062(39.29)**

Scoring auction dummy-0.065(8.91)**-0.051(8.91)**

Auction format dummy 1

0.002(0.25)

0.01(0.25)

Constant

2.227(70.21)**

2.155(70.21)**

Observations
R-squared

11453
0.46

11453
0.53

Absolute value of t statistics in parentheses* significant at 5%; ** significant at 1%
Except invited bidders

Table 13: Regression result for lowest bids

Set-asides
Low
High∗

Unrestricted
Low
High∗

Mean no. small bidders

7.46

0

5.29

0

Mean no. large bidders

0

8.49

1.72

5.98

Mean no. total bidders

7.46

8.49

7.01

5.98

Mean Scores

990.3

1419.31095.71419.3

Procurement cost change---0.40%

0.99%

Overall eﬀect--

Project volume (Y= bn.)

1854.97

1273.03

1854.97

1273.03

Sum of engineer’s estimates(Share %)(59.0)(41.0)(59.0)(41.0)

Entry costs

1.29%

1.14%

1.29%

1.14%

Profits (large firms)

-

1.41%

1.96%

2.12%

Project category(% of engineer’s estimates)

0.17%(% of engineer’s estimates)∗ High-end projects are those in which the engineer-estimated cost is no less than �300 million.

Table 14: Estimation for the eﬀect of set-asides
38