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Self-Enforcing Agreements and Relational Contracting:
Evidence from California Highway Procurement
Ricard Gil †
Justin Marion ‡
August 2011
Abstract
We empirically examine the impact of relationships between contractors and subcontractors
on firm pricing and entry decisions in the California highway procurement market using data
from auctions conducted by the California Department of Transportation. Relationships in
this market are valuable if they mitigate potential hold-up problems and incentives for ex post
renegotiation arising from contractual incompleteness. An important characteristic of informal
contracts is that they must be self-enforcing, so the value of relationships between firms and
suppliers depend on the extent of possibilities for future interaction. We construct measures of
the stock of contractors’ prior interactions with relevant subcontractors and, most importantly,
an exogenous instrument to measure the future value of ongoing relationships that is orthogonal
to contractor-subcontractor match specific productivity. We find that a larger stock of relation-
ships leads to a greater likelihood of entry and to lower bids. Importantly, this relationship does
not hold in periods of time and areas with little future contract volume, suggesting that the
value of the future is crucial in providing value for informal contracts.
∗We thank Francine Lafontaine and Ken Corts for their discussions and seminar participants at UC Santa Cruz,
International Industrial Organization Conference, Federal Trade Commission, George Washington University, De-
partment of Justice, Hitotsubashi University, Cornell University, Harvard/Massachusetts Institure of Technology
Organizations Seminar, International Society of New Institutinoal Economics Conference, Aarhus School of Business,
National Bureau Economic Research Organizational Economics, Simon Fraser University, American Economics Asso-
ciation meetings at Atlanta, UC Davis, UC San Diego, University of Michigan, UC Berkeley Haas School of Business,
University of Wisconsin and Sorbonne Business School for helpful comments. All remaining errors are ours.
†Johns Hopkins Carey Business School
‡University of California, Santa Cruz
2
1 Introduction
Relational contracting has long been considered an important component of the interaction between
firms and their suppliers. The close relationships that firms have with their suppliers allow them to
support implicit contracts, obtaining first-best outcomes not achievable otherwise through formal
contracts. In many circumstances it may be prohibitively expensive to completely specify in advance
all relevant contingencies and product attributes to the transaction at hand. It is in these cases
that relational contracting proves most useful since it helps a firm and its supplier respond to
unforeseen circumstances when needed or induces the supplier to provide the informally agreed
optimal product quality when the attributes of the supplied product are not verifiable to a third
party.
A growing empirical literature establishes the prevalence of informal contracts and their role in
vertical relations as well as the type of formal contracts chosen between parties in the presence of
long-standing relational contracts.1As noted by Bull (1987), Klein (1996) and others, an important
factor characterizing a relational contract is that it cannot be enforced by a third party and therefore
must be self-enforcing. The standard relational contract specifies an action that the supplier needs
to undertake at the risk of losing future business. When the value of deviating from the action
in the implicit contract exceeds the present value of continuing the relationship, the relationship
is no longer self-enforcing. Future business thus ceases to have value in solving the information
asymmetry problems that formal contracting, for whatever reason, could not address, including
potentially moral hazard or hold-up.
In this paper, we empirically examine the effect of past and future relationships between con-
tractors and subcontractors in the highway construction market on bidding, auction participation,
and subcontractor choices. In contrast to the extant literature, we empirically evaluate the role
of the continuation value of the contractor-subcontractor relationship. The highway construction
market is a particularly appealing setting to study this issue. In many other settings, the observed
continuation value is endogenous to the productivity of the firm-supplier match, as more success-
ful relationships lead to a higher volume of future business. This gives rise to a reverse causality
problem, as the measured volume of future business is related to lower prices in the current period
for reasons unrelated to the enforcement of informal contracts. In contrast, our empirical analysis
introduces an exogenous measure of the continuation value of ongoing relationships between con-
tractors and subcontractors that quantifies the arrival rate of public highway construction projects
3
in any given geographical area within a year of the auction. The arrival rate of projects in a geo-
graphical area is driven by transportation needs and is likely orthogonal to the productivity of the
contractor-subcontractor match. Hence, the introduction of this truly exogenous instrument for the
value of future relationships is a major contribution of this paper.
Most of the literature in this area measures relationships by the stock of prior interactions
between a firm and its supplier. While this does not directly measure continuation value, it may
proxy for the expected future value of the relationship if a regularly used supplier can expect to be
utilized by the firm in the future (Corts and Singh, 2004). However, prior relationships may also
have value through improving relationship specific productivity unrelated to contracting, such as
by mitigating coordination costs and enhancing learning by doing (Kellogg, 2008) or developing
reputations (Banerjee and Duflo, 2000). Therefore, it is useful to more directly measure both the
stock of prior interactions and the continuation value of the relationship.
We begin our analysis by describing the source of contracting difficulties between contrac-
tors and subcontractors. When subcontracting, bidders choose a subcontractor in part based on
subcontractor-specific coordination costs and the future value of their relationship. Whereas past
interactions with a subcontractor may diminish current coordination costs, the prospect of future
interactions is expected to deter subcontractors from engaging in moral hazard behavior. Thus it
lowers the cost of subcontracting and it enhances the value of present activities. We predict that
the higher the number of past interactions and the expected number of future interactions, the
lower the costs of subcontracting and therefore the lower the bids posted by the contractor and the
greater likelihood of auction participation.
We evaluate the empirical validity of these predictions using data from 5,120 highway procure-
ment auctions conducted by the California Department of Transportation (Caltrans) between May
1996 and October 2005. When submitting a bid in this market, firms must list the significant sub-
contractors they intend to use on the project up for bid. Overall, the data consist of 26,125 bids
from 1,735 contractors of which 805 win at least one contract. These bids specify roughly 2,900
unique subcontractors. We therefore are able to measure the stock of relationships a firm has with
its subcontractors over time and across markets.
We find that greater stocks of prior relationships are associated with lower bids by contractors,
as well as a greater likelihood of auction entry. This finding is robust to different measures of the
4
stock of prior relationships. Furthermore, firms are more likely to use subcontractors that they
have worked with in the past.
In the key result of the paper, we show that these estimated effects of relationships on bidding,
entry, and subcontractor utilization depend on the extent of future business. We interact prior rela-
tionships with the number and dollar value of upcoming Caltrans’s contracts within the geographic
market. If no contracts are up for bid within the following year, the value of the stock of prior rela-
tionships on bidding is statistically indistinguishable from zero. However, the greater is the extent
of future business, the more prior subcontractor relationships lower a firm’s bid. Importantly, only
upcoming projects occurring within one year matter, which is consistent both with firms having
better information regarding these projects and with discounting. Finally, we find that the impact
of relationships is particularly important for projects where subcontractors play a more important
role.
We also rule out several alternative explanations for our empirical findings. First, future
contracts could increase entry into the highway construction industry. Second, future contracts
could increase the value of contractor-specific investments, perhaps through learning-by-doing or
other spillovers across projects, which could drive bids down in the current period. Third, more
subcontractor-intensive firms may be able to participate in more auctions, and at the same time
be more efficient and submit lower bids. We show that the number of highway construction es-
tablishments does not respond to the amount of future business, which is not surprising in light of
the short-run barriers to entry into the market. Furthermore, we examine subcontractor-intensive
firms, and find that these firms do not bid lower, either in general or in times when there is signif-
icant future business. Lastly, we estimate two different models accounting for selection, and find
that if anything our results become stronger.
The paper is organized as follows. We describe first in Section 2 the relevant literature and
specify what is the contribution of this paper within it. Section 3 describes the institutional details
and section 4 presents a theoretical discussion of the contracting costs that contractors face when
using subcontractors. In section 5, we describe the data. In section 6 we discuss our empirical
methodology and present our results. Section 7 concludes.
5
2 Literature Review
As this paper focuses on the consequences of repeated interactions and long-standing relationships
on firm performance in California highway procurement contracts, we believe that this paper builds
on and contributes to two strands of the literature. These are the literature on implicit and relational
contracting and the literature on procurement and construction contracts specifically.
2.1 Literature on Implicit and Relational Contracting
The role and importance of informal agreements is sometimes dwarfed by the large existing lit-
erature on formal contracting. Despite this, the nature of informal agreements together with the
existence of implicit and relational contracting has been an important subject of study for some
time now. Klein and Leffler (1981) were among the earliest contributors on this topic followed by
others, such as Bull (1987), Klein and Murphy (1988), Baker, Gibbons and Murphy (1994), Klein
(1996) and more recently Board (2008) and Halac (2008). This literature studies the emergence
of informal contracting when formal contracting may yield suboptimal outcomes. These theories
revolve around two main points. First, they approach the question of whether informal agreements
and formal contracts are complements or substitutes as well as whether the latter will emerge when
the performance of the former proves to be dissatisfactory (see Poppo and Zenger (2002) and Laz-
zarini, Miller and Zenger (2004) respectively for motivating evidence). Second, their sustainability
hinges on the capacity of participating parties to enforce these agreements via gains derived from
future interactions.
The appeal of this latter idea has found applications in many different scenarios and as a
consequence a literature surrounding the idea of future interactions sustaining informal agreements
has developed. Some examples include studies of topics as diverse as subjective pay performance
(Baker, Gibbons and Murphy (1994)), quality provision (Klein and Leffler (1981)), the boundaries
of the firm (Baker, Gibbons and Murphy (2002)) and procurement contracting (Calzolari and
Spagnolo (2009)), and industries as varied as oil drilling (Corts and Singh (2004)), information
technology widely defined (Kalnins and Mayer (2004), Ryall and Sampson (2009), and Shi and
Susarla (2010)), dry cleaning (Gil and Hartmann (2011)), taxicabs (Jackson and Schneider (2011))
and movies (Gil (2011)).
A separate, related, literature focuses on prior interactions and their effect on contracting
outcomes. Papers such as Banerjee and Duflo (2000) or Crocker and Reynolds (1993) use the
6
number of prior interactions as reputational measure that allows for savings in ex-ante contracting
costs and defer any discussion regarding the role of continuation value of relationships. Banerjee
and Duflo (2000) in fact present a simple model of contracting that rules out explicitly any role of
continuation value and highlights reputational effects. On the other hand, McMillan and Woodruff
(1999) and Corts and Singh (2004) among others use the number of prior interactions as a measure
of future interactions, which mixes the current cost of contracting with the continuation value of
relationships. Our paper differs from these two strands of the literature in that we focus our analysis
on the role of continuation value with an exogenous measure with time and geographical variation
while allowing the impact to differ according to prior interactions. Ours, together with Macchiavello
and Morjaria (2011), is among the very few papers that account for variation in continuation value
and the stock of prior interactions and exploit plausible exogenous sources of variation that allows
for the study of the role and impact of relational contracting.
2.2 Literature on Procurement and Construction Contracts
Our paper also contributes to a more applied literature that documents the allocation of procure-
ment contracts and in particular procurement of construction contracts. Examples of the former
type are Guasch, Laffont and Straub (2008), who examine the contractual adjustments of procure-
ment contracts for utility concessions in a group of Latin American countries. Examples of the latter
are Bajari and Tadelis (2001) and (2006), Bajari, McMillan, and Tadelis (2008) and Bajari and
Lewis (2009), who examine theoretically and empirically procurement in the construction industry.
In general, these analyses ignore the fact that bidders in these auctions have ongoing relationships
with the public agency and reputations that leave room for some degree of ex post adjustment.
Similarly, subcontracting tends to be unobserved by the econometrician and is therefore omitted.
Our paper focuses on these two aspects specifically.
A number of papers have examined California highway procurement auctions. In particular,
Bajari, Houghton and Tadelis (2006) consider the role of incomplete contracts and ex post ad-
justments, and Krasnokutskaya (2003) estimates a structural auction model in the presence of
unobserved cost heterogeneity. Other papers examine the effect of preferential programs in these
auctions on both auction participation and bidding behavior. Examples include Krasnokutskaya
and Seim (2005), and Marion (2007, 2009). Our paper differs from these and others in that it
focuses on the subcontracting strategies for contractors bidding for highway construction projects
7
and estimates the consequences of repeated interactions with subcontractors in affecting contractor
performance in these auctions.
We also need to acknowledge, and differentiate from the current paper, two recent contributions
that study closely related topics to ours. Miller (2008) estimates the cost implications of contractual
incompleteness in subcontracting decisions for a set of bridge construction contracts procured by
the California Department of Transportation. Kellogg (2008) empirically examines the impact of
past interactions on the productivity of well drilling in Texas. Our paper differs from these in that
we focus on the role of future contracting possibilities as a way to mitigate moral hazard problems.
Our empirical findings demonstrate that in the setting of California procurement auctions even
though past repeated interactions are correlated with lower bids it is the future value of projects in
an area that drives down bids of contractors. These findings are consistent with the continuation
value of ongoing relationships being the main factor that drives down those bids.
Finally, this paper also relates to an economic literature on the construction industry proper. In
particular, we highlight the contributions of Eccles (1981), and Gonz´alez, Arru˜nada and Fern´andez
(1998 and 2000). The first documents the loose nature of the boundaries of the firm that appear
to sustain transactions in this industry, while the latter two focus on the fragmentation of this
sector and how specialization may lead firms to rely on subcontracting and outsourcing more
often than similar firms in other industries. Our paper adds to this literature in that we examine a
channel through which contractors may benefit from their subcontracting strategies, and we provide
evidence on how repeated subcontracting may enhance contractor performance.
3 Institutional Details: Bidding on California Highway Auctions
The California Department of Transportation (Caltrans) awards road construction and repair con-
tracts through sealed-bid first-price auctions. Potential bidders are solicited through a newsletter
that details the bid letting date and the specifics of the project. A contractor can bid on any
project in the category of work for which it has been prequalified. This prequalification is based
on the firm’s equipment, training, licensing, and past work history.2For each project, the engineer
provides a list of the items required to complete the project and the quantities of each item.3The
bidder then provides a unit price for each item, and its total bid is based on the sum across items
of the unit price by the quantity.
8
In its bid, the contractor must list each subcontractor whose work accounts for at least 0.5 per-
cent or $10,000, whichever is greater, of the contract value. Each subcontractor must be prequalified
to do the listed work. Following existing regulation, at most 40 percent of a project can be subcon-
tracted. The other important restriction regarding subcontracting that was in place through much
of the period of our study regards affirmative action. Until 1998 for contracts using state funds and
2006 for federally funded contracts, contractors were often required to award a certain percentage
of contract dollars to Disadvantaged Business Enterprises (DBEs), namely subcontractors owned
by minorities and women.
While Caltrans attempts ex ante to specify the relevant details of the work, unforeseen con-
tingencies often arise after contract award (see Bajari et al, 2006). These changes to project
specifications many times lead to costly renegotiation between the contractor and Caltrans. While
we do not have direct evidence regarding this, we expect that these change orders also alter the
scope or scale of the subcontractors’ tasks in ways difficult to specify ex ante.
4 Theory Discussion
In this section, we discuss the theoretical underpinnings of our empirical work. A more detailed
model is contained in Appendix 1. A road construction contractor potentially faces significant prob-
lems related to moral hazard and incomplete contracting when hiring a subcontractor to perform
a portion of the project. A prime contractor may wish to induce the subcontractor to undertake
actions that may be unobservable by a third party, yet known to both the contractor and the
subcontractor. Increasing the quality of the goods provided by the subcontractor, perhaps through
the timeliness of completing her portion of the project, is one such action that could lower the cost
of the prime contractor. Since switching subcontractors in the middle of a contract is potentially
costly, subcontractors have an incentive to provide suboptimal quality. To take advantage, the
subcontractor can either lower its cost by reducing quality, or demand extra payment from the
prime contractor through a renegotiation.
An additional complication with contracting in this industry is the need to cope with unforeseen
circumstances. Often, a construction project differs from the original design due to conditions that
are unobservable at the time of the design of the project. If these circumstances are significant, it
may require a renegotiation of the contract between Caltrans and the contractor, presumably as well
9
as the contracts between the prime contractor and its subcontractors. This renegotiation is costly,
and in the presence of switching costs may lead to hold-up opportunities for the subcontractor.
An informal contract, enforced using the continuation value of the relationship, can be used to
specify the correct action to be taken by the subcontractor. Since contractors recognize that sub-
contractors value future business opportunities, contractors use informal contracts that condition
future streams of revenue to good performance in current projects. These informal contracts will
then align incentives between a contractor and her subcontractors and solve or attenuate the moral
hazard and hold-up problem presented above.
Leveraging the value of future contracts lowers the cost of subcontracting, which in turn leads to
lower bids on auctions in which contractors participate. Similarly, since the choice of subcontractor
and auction participation is not random, prime contractors will prefer to subcontract tasks to
subcontractors with whom the continuation value of the relationship is highest. Finally, the cost
of subcontracting influences the cost of completing a project, and therefore the likelihood that the
firm’s expected profits exceeds the cost of entry into an auction. As a result, in situations where
the firm has a pool of available subcontractors with a high continuation value, the firm is more
likely to enter the bidding for the auction.
Contractors and their subcontractors utilize relationships to enforce contracts, but relationships
may also have value in other dimensions. The productivity of a given contractor-subcontractor
match is likely to depend in part on the degree of prior interactions. Coordinating the efforts of
members of the supply chain is important, as work-flow is important in the highway construction
industry. As firms work together more, coordination costs decline through learning-by-doing. Also,
the contractor and subcontractor may learn about each other’s productivity over the course of
working together.
One challenge in formulating testable implications is that the continuation value may alter
outcomes in the current period for reasons unrelated to enforcing informal contracts. Since the
continuation value of a relationship is correlated with expected future contracting opportunities,
it may be associated with firm entry, which potentially lowers the equilibrium price charged for
road construction services. Furthermore, firms may invest in relationships when future business is
anticipated to be significant.
For the reasons just described, both past interactions and future business opportunities may af-
fect bidding, auction participation, and subcontractor choice in the current period through channels
10
aside from informal contract enforcement. Rather than examine the effect of the stock of relation-
ships or future opportunities separately, our focus will be on the interaction of the two. We will
investigate whether existing relationships are more valuable in the presence of future contracting
opportunities. The interactive effect is sensible since, as we argued above, repeated interactions
between firms and their suppliers lead to greater productivity, perhaps due to lower coordination
cost. This suggests that in future projects, a firm is more likely to hire a subcontractor with which
it has a relationship, and this match is more likely to both win future auctions and earn higher
profits on those projects it wins. Thus, the continuation value is highest when there are both more
future contracts, and when a firm has more relationships established with its suppliers.
The two issues described above, those of future opportunities inviting entry and encouraging
relationship investment, are silent regarding the coefficient on the interaction term between past
relationships and future business. The first story regarding an increase in competition offers no
prediction about whether the effect should differ across contractors that hold different relationships
with their subcontractors. Similarly, the second story regarding stronger incentives to invest in their
current subcontracting relationships has no implications for the correlation between the interaction
of past interactions and continuation value and bids posted.
5DataDescription
The data used in this study includes the universe of 5,120 road construction and repair contracts put
up for bid by Caltrans between May 1996 and October 2005. For each project, a set of information
describing the project is given, including the road and county where the work will take place; a
short description of the nature of the work to be completed; the estimated number of working days
to complete the project; and an engineer’s estimate of the cost of completing the project. The
engineer’s estimate is formulated by Caltrans, and reflects project-specific factors and past bids on
similar projects. For every general contractor submitting a bid, the value of the bid and a list of
subcontractors is given.4Caltrans assigns a unique identifier to each firm, so it is possible to track
contractors across contracts. In addition, we assign unique identifiers to subcontractors based on
the names.5In all, we observe 26,125 bids from 1,735 different firms, of which 805 win at least one
contract. These bids listed roughly 2,900 subcontractors.
It is worth mentioning a few of the drawbacks of the data. First, we only observe contracts
administered by Caltrans and not those administered by local governments, which represent a
11
significant fraction of the market. According to the 2002 Census of Governments, local governments
in California expended $2.39 billion in capital outlay for highways compared to $2.99 billion for
the state government. As a result, our measures will tend to understate the stock of relationships
between contractors and subcontractors, the extent of future opportunities, and the degree of
project backlog. This is likely to reflect measurement error, which, if independent of the variables
of interest, will merely attenuate the estimated coefficients.
It is worth considering when the measurement error will not be independent. First, the flow of
local projects could be positively correlated with the flow of state projects due to complementarities
between local and state highway improvements. On the other hand the correlation could be negative
if local jurisdictions account for the adverse effect state projects have on the capacity of local
contractors. The correlation between state and local future opportunities could either be positive
or negative. Second, at the contractor level, a firm that wins a state contract may be capacity
constrained, making it less likely to win local contracts. Furthermore, some contractors might
specialize in state contracts rather than local, also leading to a negative correlation between state
and local contracts won. Therefore, our estimates of the effect of the stock of a firm’s relationships
is likely to be be biased toward zero due to a negative correlation with the error term.
A second issue is that our data is truncated in May 1996. Thus we are unable to form measures
of prior relationships and project backlog that include projects prior to this date. The initial stock
of relationships using contractor fixed effects will account for much of the variation across firms in
the initial stock of relationships. While we do not have the degrees of freedom to consider the full set
of contractor*subcontractor fixed effects in the bid regression, one robustness check we considered
was to include contractor*district effects, which account for the initial stock of relationships firms
have in a particular district. Our results turn out to be robust to the inclusion of these effects.
Finally, even among the contracts in our data, we do not observe subcontractors to which only
a small portion of the contract was awarded, nor do we know if subcontractor switching occurred
after the awarding of the project. The former is a problem depending on the form of the production
function of relationships. If relationships are related to the intensity of utilization, then this is less
of a problem than if relationships depend only on whether or not two firms have interacted.
In Table 1 we present summary statistics for our main variables. In Panel A, we describe
auction characteristics. The average auction has 5.15 participants. The maximum number of
bidders observed in the data is 30, though most auctions have fewer than eight bidders. The
12
average engineer’s estimate is $3.13 million, and there are significant differences in scale across
projects. The engineer’s estimate for the median project is only $620,000, and ranges from a low
of $12,930 to a high of $800 million. This considerable variation in project scale is also reflected in
the workdays the engineer anticipates will be required. The average working days are 163.4, while
the median is only 70. The average project requires 34.8 work items.
In Panel B, we describe the observed bids. The average observed bid is $3.12 million, closely
matching the average engineer’s estimate. On average, the bids are nine percent above the engineer’s
estimate. While high bids are sometimes rejected for exceeding the engineer’s estimate by more
than ten percent, we still see some firms bidding substantially above the engineer’s estimate, with
the highest being 37 times greater. The average bidder lists 4.35 first tier subcontractors, with the
most intensive user of subcontractors listing 38. Finally, we describe the experience of the typical
contractor and the average stock of relationships with subcontractors. The average bidder enters
an auction having won 18 prior auctions, with the median bidder having won 4. The average bidder
has used the subcontractors listed in the bid a total of 7.6 times on previous auctions won. This
figure is particularly skewed, as the median bid involves only one prior subcontractor relationship
while the max involves 404.
Panel C of Table 1 describes the winning bids. While the average bidder submitted a bid nine
percent above the engineer’s estimate, the average winning bid was four percent under the engineer’s
estimate. Winning bids are not more or less apt to subcontract, as they include virtually the same
number of subcontractors as the broader population of bids. Winning contractors do tend to have
significantly more experience, however, as the average winning bidder has won 26 prior auctions.
They also have a higher stock of past interactions with the listed subcontractors, having used them
11.9 times on prior winning bids. This appears to be in large part due to the contractor’ greater
number of past wins.
In the empirical analysis below, we consider the entry and subcontractor utilization decisions
of the largest firms in the industry. We limit that part of our analysis to the largest firms because
of problems with degrees of freedom when we include all participating bidders. Also, the actions
of this subsample of firms provide enough variation to examine the issues of interest. We will also
define the stock of relationships the firm has developed with subcontractors in a relevant geographic
market. To better understand these aspects of our work, we next describe the concentration of the
market across contractors and geographical areas.
13
In Table 2 we show the top twenty contractors in terms of contracts won.6The industry is
remarkably unconcentrated, with the largest 20 accounting for only 28 percent of contracts won.
Granite Construction, to our knowledge, is the only publicly traded company in the data. It wins
the most auctions, capturing nearly eight percent of contracts, and 7.5 percent of total awarded
contract dollars. The next largest firm, Peterson Chase, won only 1.9 percent of contracts.
This lack of concentration in the Caltrans highway construction market may mask a potentially
significant degree of geographic concentration. Costs have been found to rise significantly with
distance in this industry (see for instance Bajari and Ye, 2003). One might expect that in a large
state like California, relevant markets are more local. In our analysis below, we consider a definition
of the relevant market using Caltrans districts, of which there are 12. Figure 1 displays a map of
the districts of California laid over counties. Geographically, these districts are quite large. The
most significant exception to this is Orange County which comprises a district of its own.
In Table 3, we present evidence regarding the degree to which contractors operate within one
district. In this table, we show the average number of wins of contractors who win at least one
contract and the fraction of those wins that came in the contractor’s primary district.7We see t h at
the average contractor wins 6.4 auctions, 82 percent of which are in its primary district. Since this
may be skewed due to the significant fraction that win only one contract, we also restrict attention
to those that win more than one contract. Of these, 69 percent of auction wins are from within the
contractor’s primary district.
The subcontractor market surprisingly exhibits a similar degree of geographic concentration.
Among subcontractors who appeared on at least one winning bid, the average subcontractor was
utilized 9.5 times. Of this utilization, 84 percent occurred within the subcontractor’s primary
district, almost identical to that observed for contractors. Similarly, if we restrict attention to
subcontractors that participate more than once, 67 percent of utilizations occur within the primary
district. Subcontractor operations therefore seem to be quite geographically concentrated, but
interestingly no more so than those of contractors.
6 Empirical Methodology and Results
6.1 Empirical Methodology
In this section, we describe how we investigate the role of relationships between contractors and
their subcontractors. We will use two definitions of relationships. First, we consider the number of
14
interactions a bidder has had on prior completed contracts with each subcontractor listed in its bid.
In our second measure, we define the relevant set of subcontractors as those headquartered in the
same Caltrans district as the current project. The advantage of the first measure is that it focuses
on the relationships with subcontractors most relevant for the current project. The second measure
could also be justified. If a firm has a valuable relationship with a subcontractor in the district, yet
a different subcontractor was chosen for the project, it reveals that the chosen subcontractor had
some cost advantage on that particular contract. It is still the case, however, that the relationship
has value, and that a firm with strong relationships within the district will on average have lower
costs.
We then utilize these measures of the stock of past interactions with subcontractors, sik ,for
contractor ion project k, in a regression of the form
yik =β0+β1log(1 + sik)+BXik +φi+ik (1)
where yik is the relevant outcome variable, either the log of the submitted bid or an entry indicator,
Xik is a vector of covariates, and φiis a contractor fixed effect. We add one prior to taking the log
of the stock variable as a significant portion of the observations is zero. When investigating entry,
we focus attention on the 20 largest firms in terms of auction participation, forming an auction
participation indicator for each of these firms on each auction conducted in the sample.
The vector Xik contains covariates describing project characteristics such as year and month
effects, an engineer’s estimate of project cost, the number of items required for the project, and the
number of working days the project is likely to require. It also includes firm specific covariates that
potentially vary across auctions, such as prior experience on projects in the area and an estimate of
the firm’s backlog of uncompleted projects.8Controlling for these variables is important. Since the
subcontractor stock variable is based on subcontractor utilization on past winning projects, it will
be directly correlated with the number of wins the firm has and with recently won contracts that
are not yet completed. While the effect of experience on bids is mixed, firms have been found to bid
systematically higher when facing short run capacity constraints (see Jofre-Bonet and Pesendorfer,
2003).
Finally, as previously mentioned, the firm fixed effect potentially plays an important role. Our
data is truncated at May of 1996, so it is not possible to measure firm interactions prior to this
date. The initial stock of subcontractor interactions is captured in this fixed effect.
15
As already discussed, the coefficient β1should depend on the continuation value of relationships,
since relational contracts must be self-enforcing. One approach to measuring the continuation value
of a relationship at a given point in time would be to sum the value of actual future interactions
between the contractor and subcontractor. While in many settings this may be the only available
approach, it is problematic in that the degree to which a pair of firms works together depends on
the quality of the match and would therefore be endogenous – a successful match would lead to
both lower bids now and more interactions in the future.
Instead we use the total number of future contracts, fik , auctioned off by Caltrans within a
district as our measure of future interactions. This measure will be correlated with the number of
future contracts on which a contractor-subcontractor pair may work together but is still uncorre-
lated with their specific productivity match since it is determined by district-level transportation
needs and budgeting process. We introduce this measure into the empirical specification by itself
and also by interacting it with the firm’s stock of prior interactions:
yik =β0+β1log(1 + sik)+β2log(1 + fik )∗log(1 + sik)+β3log(1 + fik)+BXik +φi+ik.(2)
To account for forward looking bidders who rationally anticipate future capacity constraints brought
on by winning the current auction, we only consider those future projects occurring after the
anticipated completion of the current project. Our primary coefficient of interest will be β2,which
describes how the value of relationships depends on future contracting opportunities.
Controlling directly for future contract volume accounts for several possible confounding factors.
First, anticipated future contract opportunities may invite the market entry of potential subcon-
tractors in the current period. The thicker market for subcontracting could lower costs for bidders
if it leads to lower prices for items typically subcontracted. Second, if learning by doing is im-
portant, then the effect of learning on future costs will be in part priced into the current bid. A
period of high anticipated contract volume creates an incentive for a firm to win contracts now to
lower costs for future contracts. Nevertheless, the current shadow price of capital may increase and
therefore current bids may increase. Overall, the sign of the direct effect of future contract volume
is ambiguous.
We are also cautious in interpreting the estimated coefficient β1. As discussed in Section 4,
prior relationships could have value outside of contract enforcement. This would be true if the
coordination costs between a firm and its suppliers goes down with repeated interaction, or if
learning-by-doing allows them to work together more efficiently.
16
6.2 Results
6.2.1 Firm bidding
We begin by presenting the results documenting the correlation between the stock of subcontractor
relationships and bidding behavior. In Table 4, we present estimates of equation (1) using as a
measure of relationships the prior interactions with subcontractors listed in the current bid. In
column 1 we find a significant negative relationship between the stock of interactions and the bid
a firm submits. This beneficial effect on the firm’s bid holds up after controlling for bidder fixed
effects in column 2. This result is consistent both with the existence of learning by doing and with
our prediction that a higher number of past interactions between contractor and subcontractor
will lower bids. Similarly, note that experience, as measured by the total number of projects
that a contractor has won in the past within the same county, is negatively correlated with the bid
posted. This result is also consistent with general (non-specific) learning by doing on the contractor
side. The effects of other covariates are largely consistent with the prior literature on the highway
construction market. Backlog is associated with higher bids, consistent with the presence of short-
run capacity constraints. Also, competition lowers prices, as each opposing bidder reduces the
firm’s bid by around one percent. We also find that while past wins are positively associated with
bids, past wins within the project county are negatively associated with bids. It is not surprising
that experience would improve productivity and lower costs, but it is interesting that the coefficient
on prior wins is in fact positively associated with a firm’s bid. One explanation is that, since we
have conditioned on firm wins inside the county, more firm wins overall indicates a firm that has a
focus in other regions of the state.9
In column 3 of Table 4, we examine whether the age of the relationship matters by separating
past interactions occurring within the past year into three month intervals, and also separately
considering those contractor-subcontractor interactions occurring more than one year prior to the
auction date. We find that our initial results are driven by interactions occurring at least nine
months prior, suggesting that more established relationships are more important than recent inter-
actions with subcontractors. To interpret this result we must take into consideration the fact that
the average project is estimated to last 163 days and therefore it is not surprising to observe that it
takes more than 6 months to learn about the productivity of the listed (and used) subcontractors.
In columns 4 and 5 of Table 4, we consider the interaction of the stock of relationships with the
degree of future contracting opportunities in the project district. We consider separately the number
17
of future contracts and the dollar value of these contracts. We find that both more future contracts
and more future contract dollars increase the value of the stock of relationships. Interestingly, when
this interaction is included in the specification, the main effect of the relationship stock variable
is cut in magnitude by at least one-half and becomes statistically indistinguishable from zero.
This suggests that relationships have little value when the continuation value of the relationship
is zero. This result is consistent, in general, with the implications from the relational contracting
literature. The coefficients of all the other covariates remain unchanged in magnitude and statistical
significance when we include the number and value of future interactions.
To assess the magnitude of the gains of past relationships, and how they depend on the degree
of future business, consider a one standard deviation increase (a value of 1.228) in the stock of
relationships variable. Using the coefficients presented in column 5, this increase results in a
reduction of 0.89 percent when the future contract volume is one standard deviation below its
median and 1.9 percent when future contract volume is one standard deviation above its median.
Evaluated at the value of the average winning bid of $3.17 million, these percentage improvements
in the winning bid represent $28.0 thousand when the continuation value is relatively low and $60.7
thousand when the continuation value is relatively high. A useful way to gauge the magnitude of
the marginal effect is to consider how it affects the likelihood of winning the auction. The average
firm has a 16.15 percent chance of submitting the low bid. A firm that reduced its bid by 1.9
percent would increase its likelihood of being the low bidder by 5.7 percentage points, or around
one-third.
In Table 5, we present similar estimates using an alternative measure of the stock of relation-
ships, past interactions with the subcontractors whose headquarters are within the project district.
We obtain results that are very similar to those using the first measure of the stock of relation-
ships. We again find that firms with more relationships bid lower, and that the beneficial effect of
relationships is greater as there is a greater degree of future potential business. Again, without the
self-enforcement mechanism of future business, past relationships seem to have little effect on their
own. All other controls used in the specifications presented in Table 5 have the same qualitative
effect on the dependent variable as they did in Table 4.
Relationships should be most valuable in projects where subcontracting is more important.
When a project requires less subcontracting, less advantage is conferred on those firms who are
able to subcontract at a lower cost. To investigate this, we allow the coefficient β2to vary across
18
projects depending on the number of specialty items required. Specialty items are designated by
Caltrans and require capabilities that the typical prime contractor does not possess. These must
normally be subcontracted out. In Table 6, we establish the relationship between the number of
specialty items and the utilization of subcontractors. In these specifications, we regress the number
of listed subcontractors on the number of specialty items listed in the contract by Caltrans. We see a
positive and statistically significant relationship, where each additional specialty item is associated
with an additional 0.15 subcontractors. Furthermore, 42 percent of the variation in the number of
subcontractors across bidders is explained by the number of specialty items alone.10 The estimated
coefficient is little changed with the inclusion of firm fixed effects, so the correlation is not likely due
to the sorting of more subcontractor-intensive firms into projects with many specialty items. In the
final column, we include a full set of controls. This reduces the estimated coefficient to 0.07, likely
due to the inclusion of the number of contract items, which is correlated both with subcontractor
demand and the number of specialty items.
Having established that specialty items strongly influence the demand for subcontractors, we
next examine whether the effect of continuation value depends on the importance of subcontracting.
The median project requires seven specialty items. We therefore break our data into three parts
and run our main specification above for projects that list no specialty items, projects that list
between one and seven specialty items, and projects that list more than seven specialty items.
We present our findings in Table 7. The results suggest that the interaction between the stock of
relationships in the project district and future contracts in a district has a statistically significant
effect on posted bids only when the number of specialty items is above the median.11 This is a useful
result, as it establishes a more direct link between subcontracting and our measure of continuation
value. Consequently, these results point away from alternative explanations that rely on a spurious
correlation between future contracts and current bids, for instance due to unobserved variables that
happen to be correlated with our interaction term. These unobserved variables would need to be
relevant only for projects with high numbers of specialty items.
Timing of future contracts
One may worry that our measures of future business volume may capture unobserved differences
between high- and low-volume areas that are correlated with more aggressive bidding but have
nothing to do with the self-enforcing informal agreement between contractor and subcontractor.
One way to address this concern is to consider the timing of the arrival of future contracts. The
19
timing of the arrival of projects is relevant for self-enforcing agreements since there is less advance
knowledge of projects in the distant future. Also, discounting makes these projects less important
in the continuation value of the relationship, and there is also an element of uncertainty regarding
how the contractor-subcontractor relationship will evolve in the intervening time.
In Table 8, we present the results of estimating specifications where we distinguish future
contracts taking place within one year of the current period from those taking place between one
and two years from the current period. Our results show that only the number and volume of future
contracts within a year of the current period matter and these lower the current bid of contractors.
The fact that future contracts that are further away in time do not matter is not surprising since
contractors and subcontractors are less likely to be aware of their existence so far in advance and
shows that there is no underlying correlation across periods and districts driving our results in
Tables 4 and 5.
Relationship depth
Thus far, our results do not shed light on the role of the depth of relationships between con-
tractors and subcontractors. The two measures of subcontractor relationships do not distinguish
between contractors who have developed a deeper relationship with a particular subcontractor and
contractors whose relationships are spread more evenly across subcontractors. To investigate the
role of relationship depth, we consider how unequally distributed a firm’s interactions are across its
subcontractors. For this purpose, we examine the share of a contractor’s subcontractor interactions
in a district that are held with its most used subcontractor.12 Conditional on the total stock of re-
lationships, this measure will indicate whether it is more valuable to concentrate these relationships
among a few suppliers or spread them among many suppliers. We then form a triple interaction
between this variable, the firm’s total stock of relationships, and future business opportunities.
From this, we can tell whether the self-enforcement value of future business is more important for
deeper relationships.
Results in Table 9 suggest that the stock of prior relationships is more valuable when con-
centrated with one subcontractor. However, concentrating to one supplier does not increase the
importance of future business opportunities. This is true whether future business opportunities
are measured using the number of contracts or their dollar value. This may suggest that concen-
trating interactions with a few suppliers may lower bids through lower coordination costs, while
relationship depth is not important for self-enforcement.
20
Other Alternative Explanations
Earlier in the paper, we discussed two other alternative explanations. First, an increase in
the number of future contracts in a district could increase contractor entry in that district and
consequently drive bids down mainly due to a competitive effect. Second, an increase in the
number of future contracts could push firms to invest in their current relationships as there will be
future opportunities to recover that investment. This investment comes in the form of lower bids
as contractors and subcontractors may want to acquire experience together in the current period
to perform at lower costs in the future.13
As explained in the theoretical discussion and methodology sections, both these alternative
explanations would yield a negative coefficient on the variables measuring continuation value. Im-
portantly, however, they do not make any predictions regarding the coefficient on the interaction
term. The first story regarding an increase in competition offers no prediction about whether the
effect should differ across contractors that hold different relationships with their subcontractors.
The second story regarding stronger incentives to invest in their current subcontracting relation-
ships also has no implications for the interaction of past interactions and continuation value and
bids posted. As a matter fact, this second story would predict that as firms invest in their rela-
tionships firms get better at working with each other and therefore the impact of past interactions
would not disappear when there are no future contracts at stake.
Moreover, we have obtained information on the number of firms in California in the highway
and street construction sector from the County Business Patterns. As we show in Table A1 in
Appendix 2, future contracts do not seem to be correlated with entry of firms in this sector. In this
table, we also consider whether the number of contemporary Caltrans contracts is correlated with
entry, finding no evidence to that effect once again after controlling for district fixed effects. This
holds once we account for district fixed effects, which is necessary since larger districts both have
more construction contracts as well as more firms. In columns 7-10 of this table, we also consider
whether changes in contract volume is associated with changes in establishments. As shown in
columns (1) and (7), there is a correlation between current and future contract growth and the
current number of establishments, however this does not hold once we control for year effects.
Together, these results suggest that there are periods of time where road construction funding is
growing statewide that may induce entry, however this is not true across regions in the same year.
Given that our empirical strategy in this paper conditions on year effects and therefore utilizes
21
variation in future contract volume across areas, we can conclude that entry is not a driving factor
in our results.
A potential third alternative explanation has to do with the selection of contractors into auctions
for larger projects that require more subcontracting. Certain types of contractors might be better
at dealing with a larger number of subcontractors and also dealing with more than one project
at a time. This kind of selection would also yield the negative correlation that we find in our
results between bids and the number of prior interactions between the contractor and their listed
subcontractors. Further, it is conceivable that the magnitude of this productivity difference varies
across projects and time in ways that are conveniently timed with the increase in future contracts
at the district level. To explore the empirical impact of this type of selection, we measure a firm’s
propensity to subcontract as its average subcontractor utilization across the projects in which it
participates. We then introduce this new variable in our regressions, along with its interaction with
the log of future contracts. Results in Table 10 show that average subcontractor utilization has no
statistical impact on bids and, if anything, subcontractor intensity is positively correlated with the
log bid. The results in columns (2) and (3) show that the effect of the interaction of subcontractor
intensity with future contracts is not statistically significant. Furthermore, we show in column (4)
that the inclusion of this interaction has no impact on our coefficient of interest. This evidence
shows that our main results are not driven by contractor selection characterized by a lower cost of
subcontracting and simultaneously dealing with a large number of subcontractors and projects.
6.2.2 Participation decision
Next we consider the role of subcontractor relationships on the entry decisions of firms. Reduc-
ing contracting costs via the continuation value of a firm’s relationship with its subcontractors
raises expected profits conditional on entry, and therefore increases the likelihood that expected
profits clear the fixed cost of entry. Therefore, more valuable relationships should raise the likeli-
hood of auction entry, and to test this we will first estimate a linear probability model of auction
participation similar to the bid regression specified by equation (2).
As we will show in this section, auction entry responds to relationship continuation value.
This highlights a potentially important issue for our bid results. Auction entry is endogenous
even though we have treated the pool of auction participants as exogenous in the bid regressions.
The typical selection story would suggest that our uncorrected OLS estimates are attenuated. If
22
relationships lower bids, they lower the bids of a firm that would have otherwise participated, but
more valuable relationships also draw into the bidding a marginal firm that would have otherwise
not participated. The group of bidders with strong relationships may therefore be weaker in other
respects. Presumably other more complicated selection stories could work in the opposite direction.
In this section, we address this issue, taking two approaches to correct for endogenous entry.
First, under some assumptions, theory suggests that the highest bidding firm is the marginal
entrant. A general finding in the literature is that bidding functions are monotonic, and expected
profits decline as costs rise. With a fixed cost of entry, this implies a cutoff cost above which firms
choose not to enter.14 We therefore expect that the bids we do not observe due to firms’ decision
not to participate are all higher than the bids we do observe. Therefore, the latent distribution of
desired bids of all potential entrants can be thought of as censored at the maximum observed bid,
which suggests a tobit specification. The tobit specification will account formally for the possible
attenuation mentioned above.
A second approach to addressing endogenous entry in a more general fashion is to estimate
a two-step Heckman selection model. Doing so requires an instrument for participation, or else
identification comes only through distributional assumptions. The auction participation setting
is particularly challenging. Firms enter when expected profits clear the fixed cost of entry, yet
expected profits are driven by firm costs. Therefore, a valid instrument must shift only the entry
cost, as any other factor that shifts entry will necessarily operate through costs and therefore bids.
The instrument we use is the length of time between the date a project is advertised and when the
bid letting occurs. We hypothesize that the longer a firm has to assess the project and prepare its
bid, the lower its entry cost will be.15
To study entry, we must characterize the relevant set of potential entrants. It is not practical
or desirable to consider all firms for each auction. First, with 5,120 auctions, and 1,735 firms that
are observed submitting a bid, we would be estimating an entry specification on the basis of nearly
nine million observations. In addition to the problem of dimension, irrelevant firms will not be
induced to enter by marginal improvements in the covariates, thereby leading us to understate the
effects of our variables of interest. We treat a firm as a potential entrant if it submits a bid in the
same year and district as the current project appears.
In Table 11 we present the results. Columns (1) and (2) display the results of estimating a linear
probability model of auction participation, where the dependent variable is a dummy variable taking
23
on a value of one if the firm chooses to enter. We find that the stock of relationships a firm has
with subcontractors in a district raises the likelihood of entry, and this effect is enhanced in the
presence of future contracts.
In column (3), we show the results of estimating the Tobit specification. We estimate a coef-
ficient on the interaction between the stock of relationships and future contract volume of -0.007,
which is substantially larger than the OLS estimate shown in Table 5 of -0.002. This is consistent
with the notion that the OLS estimates may understate the effect of continuation value for the
average firm due to the increased participation of marginal bidders.
Finally, in columns (4) and (5) we present the estimates for the bid and entry equations from the
Heckman two step procedure. We again see that increasing the stock of relationships is associated
with a lower bid, and that this effect is enhanced by a high volume of future contracts. As with
the Tobit, the estimated coefficients here are substantially larger than in the linear OLS, which
again suggests that selection seems to be a factor attenuating estimated coefficients. As with the
linear probability specification, entry is more likely when the stock of relationships a firm has with
area subcontractors is greater, and this effect grows when future contract volume is higher. The
estimates are substantially larger than in the linear probability model. The instrument that we
employ, the lead time between project advertisement and bid letting, is positive and significant, with
a t-statistic of nearly 3. Each additional ten days of lead time raises the likelihood of participation
by 0.1 percent.
6.2.3 Subcontractor utilization decision
Last, we examine the subcontractor utilization decision. As with the participation specifications,
we must reduce the dimensionality. In this section, we limit our sample to the twenty largest
contractors. We consider all subcontractors that any of these large contractors has ever listed during
our sample period. We then form a dummy variable indicating whether firm iused subcontractor j
in its bid on project k. We then regress this utilization dummy on the stock of prior relationships
between the two firms. As before, we also consider an interaction between this measure and future
contract opportunities within the project district.16
One concern with this specification is the fact that subcontractors are chosen on the basis of
lower joint construction and coordination costs. Since we do not observe construction costs, if these
are correlated with coordination costs and thus also with relationship stocks, we may obtain biased
24
estimates of the effect of past interactions on subcontractor utilization. To address this, we add
two variables that reflect subcontractor cost. One is an indicator of whether other bidders also use
the same subcontractor, which captures the unobserved subcontractor cost advantages. The other
is an indicator of whether the project takes place in the subcontractor’s primary district. Since
distance is an important determinant of a firm’s cost in this industry, subcontractors located near
the project will have a cost advantage.
Our results are presented in Table 12. Subcontractors with whom the contractor has an existing
relationship are more likely to be chosen. Furthermore, this becomes even more true as future
business opportunities, as measured by the number of contracts, increases. In contrast to our prior
results, this does not hold true when future opportunities are measured by contract dollars. As
expected, the bidder is more likely to use a particular subcontractor if other firms in the same
auction are using that same subcontractor. Also, firms are more likely to choose subcontractors
located in the same district as the project.
7 Conclusions
In this paper we have examined how relationships between contractors and subcontractors influence
bidding behavior and participation decisions of contractors in California highway procurement
auctions. To do so, we construct a measure of past interactions between contractors and listed
subcontractors as well as an exogenous measure of the future value of ongoing relationships using
the arrival rate of projects in a predetermined geographical area and within a year of an auction.
We highlight that the latter is a valid instrument for future value of ongoing relationships because
this is determined by repair needs and it is orthogonal to the contractor-subcontractor productivity
match that drives succesful relationships in this industry.
Our paper is, to our knowledge, the first to test the importance of relationship continuation
value. We find that a higher number of past interactions is correlated with lower posted bids, and
importantly that past relationships are valuable only in periods of time where there exist future
contracting opportunities. Prior empirical literature in relational contracting has tended to use past
interactions as a proxy for future interactions, and our result demonstrates that such a strategy
could lead to potentially wrong conclusions. We also examine the effect of past and future interac-
tions on auction participation and subcontractor choice and find qualitatively similar results. These
findings imply that firms are only able to use gains from repeated past interactions when future
25
business opportunities are present. To bolster our interpretation of the empirical results, we find
that the stock of relationships is only important for projects that are more subcontractor-intensive.
And we rule out several alternative explanations, including the possibility that endogenous auction
participation is driving our bid results.
As we empirically examined in this paper the impact of past and future interactions on bidding
behavior, auction participation and subcontractor choice, future research could extend the present
study to consider the efficiency implications of these effects. Specifically, gains from past and future
interactions may drive contractors to choose subcontractors that do not have the lowest production
costs. This may increase overall construction costs if more efficient subcontractors are passed over
due to a lack stock of past relationships.
26
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Appendix 1: Model
In this model, the government procures a project in any given period with a probability p. Once the
announcement is done in period t, a contractor i, of all possible Icontractors, considers submitting
a bid for a project kin period t. The government allocates projects to contractors using first-price
sealed-bid auctions.
Assume that every project is comprised of two tasks. Task 1 is required to be conducted by
the contractor herself, while task 2 is outsourced to a subcontractor j(out of the Javailable
subcontractors). Let the cost of task 1 be c1kit, while the cost of a subcontractor jto produce task
2isc2kjt.
There exists a coordination cost γij kt (e, n) of hiring a subcontractor jthat depends on effort e
exerted ex post by subcontractor j. This effort is non-contractible because it cannot be observed
ex-post by a third party. The coordination cost also depends on nwhich is the number of past
interactions between contractor iand subcontractor j. Not surprisingly, coordination cost is lower
the higher levels of effort and the higher the number of past interactions. These coordination costs
vary across contractor-subcontractor match quality as well as the number of times that they have
actually worked together in the past. To switch ex post from the initially chosen subcontractor j
to another subcontractor −j, the contractor incurs a switching cost φi−jtk.
The game we describe evolves over four periods. The firm, who knows its construction cost and
that of each of the potential subcontractors, selects the subcontractor that will lead to the lowest
cost. In period 2, the contractor and its chosen subcontractor bargain over the compensation for
the completion of task 2. In period 3, the firm makes its decision to enter the bidding for the
auction, and submits a bid that maximizes expected profits. Finally, in period 4, the project is
awarded to the firm submitting the lowest bid, and the subcontractor decides whether to hold-up
the contractor. Our approach is to characterize the solution to the model by backward induction,
which we now describe period-by-period.
8.1 Solution by backward induction
8.1.1 Period 4: The Moral Hazard Problem of the Subcontractor
We now solve the model through backward induction. Once contractor iwins the auction for project
k, it must deliver the project at the quality and time agreed with the buyer. To do this, it relies
on the performance of the subcontractor jthrough the coordination cost γijkt(e, n). Assume that
30
subcontractor effort ecan take two possible values, e={e∗,0}. This effort cannot be contracted
upon ex ante because it is not observable to third parties, but the contractor can observe it. The
coordination costs will be higher if e=0suchthat
γijtk (0,n)>γ
ijtk (e∗,n).(1)
Due to the switching cost φi−jkt, the subcontractor can hold-up the contractor by demanding
additional payment to provide ex-post the desired effort level e∗. In this case, the contractor iwill
hold-up subcontractor jas long as
φi−jkt ≥γijtk (0,n)−γijtk (e∗,n)(2)
or, in other words, the maximum amount that the subcontractor can hold up the contractor is the
amount of the switching cost.
To address this problem, the contractor can leverage the continuation value of the relationship,
V, which is the present discounted value of surplus accruing to the subcontractor through future
interactions with with the prime contractor. The manner in which surplus arises for the subcon-
tractor is described in the next section. The contractor will then offer an informal contract to the
subcontractor that specifies the subcontractor high level effort e∗.
Following the standard literature of relational contracting, the self-enforcing mechanism is the
threat of the contractor to end the relationship. The continuation value of the relationship is
given by V, which is the present discounted value of surplus accruing to the subcontractor through
future interactions with with the prime contractor. The manner in which surplus arises for the
subcontractor is described in the next section. There is no increase in disutility for effort e∗since
the initial contract was already compensating this amount of effort and therefore the problem at
hand is all based on the moral hazard on the subcontractor side.
The subcontractor will find optimal to exert e∗if
V≥γijtk (0,n)−γijtk(e∗,n), (3)
or in other words, if the gain from shirking is outweighed by the continuation value of the relation-
ship. Therefore, ebecomes a function of Vand φi−jkt such that e=e(V,φi−jkt).
The cost to contractor iof subcontracting task 2 to subcontractor jis therefore
c2kjt(e)=γijt(e(V,φi−jkt),n)+c2kjt +zkjt,(4)
where zkjt is the mark-up above cost on the task performed by subcontractor jand eis determined
by evaluating the incentive compatibility constraint above.
31
8.1.2 Period 3: Bid strategy
Each contractor iin auction kchooses its bid to maximize expected profits:
πikt =(bijkt −c1kit −c2kjt(e)) ∗Pr(bijkt <b
−ikt).(5)
The bid here is subscripted by jsince the optimal bid will depend on which subcontractor is chosen
in period 1. The first-order condition of the bidder’s problem is
b∗
ijkt =c1kit +c2kjt(e)+Pr(b∗
ijkt <b
−ikt)
∂Pr(b∗
ijkt <b−ikt )
∂bijkt
.(6)
The first-order conditions for each of the participants in the auction represents a system of
differential equations, and each are satisfied in the Bayes-Nash equilibrium. While we do not ex-
plicitly solve for the equilibrium of the auction game, the characteristics of the resulting equilibrium
bid strategy is well known in the literature. Bids are monotonically increasing in costs, and firm
profits are decreasing in costs. For this reason, the subcontractor choices the firm makes in periods
1 and 2 are not affected by strategic bidding considerations – it will maximize profits to choose a
subcontracting strategy that minimizes cost.
8.1.3 Period 2: Bargaining Between Contractor and Subcontractor
In this stage, the contractor is simultaneously bargaining at no extra cost with all available sub-
contractors over the cost of providing task 2, and therefore it seems right to assume that all the
bargaining power is on the contractor side. For this reason we take the total cost for contractor ito
deal with subcontractor jthe sum of the amount of the coordination and task costs plus the cost
difference with the second cheapest subcontractor available to contractor isuch that
c2kjt(e)=γijkt (e, n)+c2kjt +zkjt.(7)
8.1.4 Period 1: Contractor’s Choice of Subcontractor
Finally, in period 1 the contractor decides what subcontractor to outsource task 2 to in order to
maximize total expected profit. To do so, the contractor takes as given the mark-up in the bid
originated in period 3 and the resulting level of c2kjt in period 2 to make a choice in this period
that maximizes its expected total profit.
32
In this case, contractor iwill maximize its profit by solving the following problem
max
j∈Jπijkt =(bijkt(c1kit,c2kjt(e)) −c1kit −c2kjt(e)) ∗Pr(bijkt(c1kit,c2kjt(e)) <b
−ikt)(8)
where
c2kjt(e(V,φi−jkt)) = γijtk(e(V, φi−jkt),n)+c2kjt +zkjt.(9)
The contractor ithen chooses subcontractor jof the Javailable to maximize its expected profit
such that
j∗=argmaxπijkt(bik ,c
1kit,c2kjt(e(V,φi−jkt),n),b
−ikt). (10)
Appendix 2: Market entry
33
Table A1: Firm entry and contract volume
Dependent variable:
Establishments ΔEstablishments ΔLn(Establishments)
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14)
Contracts t + 1 1.00 0.09 0.13
(0.32)*** (0.07) (0.13)
Contracts t 1.40 0.18 -0.02
(0.36)*** (0.11) (0.17)
ΔContracts t+1 0.31 0.13
(0.09)*** (0.12)
Δ Contracts t 0.29 0.07
(0.09)** (0.09)
ΔLn(Contractst+1) -0.04 -0.26
(0.12) (0.22)
ΔLn(Contractst) 0.07 0.05
(0.07) (0.08)
District FE No Yes Yes No Yes Yes No No No No No No No No
Year FE No No Yes No No Yes No Yes No Yes No Yes No Yes
Observations 79 79 79 79 79 79 67 67 67 67 67 67 67 67
R-squared 0.27 0.96 0.98 0.43 0.97 0.98 0.23 0.44 0.17 0.42 0.02 0.27 0.02 0.11
Data includes information between 1996 and 2002. NAICS changed industry classification in 2003 and therefore we left out 2003 and 2004.
Robust standard errors in parentheses and clustered at the district level. * significant at 10%; ** significant at 5%; *** significant at 1%
34
Notes
1Early examples of this empirical work include Macaulay (1963) or Asanuma (1989).
2Calzolari and Spagnolo (2009) show that when relational contracting between government and main contractor
is valuable to solve moral hazard problems, the government may find it optimal to screen contractors ex-ante and
reduce the number of potential bidders so that the continuation value of relationships increases.
3The item prices are used when relatively small differences arise between the quantity of an item the engineer
predicts will be required and how much is actually required. When large differences between project specifications
and actual required work occur, a potentially costly renegotiation of contract terms is undertaken. (Bajari et al,
2006)
4More specifically, the list includes all first tier subcontractor, which are those that perform at least $10,000 or
half of a percent of the contract, whichever is greater.
5Due to many small permutations of spellings for the same firm, these were assigned by hand.
6We define market share based on the number of contracts won rather than on the dollar value of those contracts.
We observe several joint ventures between firms that occur only once or very few times. We do not attempt to allocate
market share between the firms in a joint venture, but we treat the joint venture as a separate firm. There are also a
handful of very large large projects that significantly skew the data. In one instance, a firm won only one auction in
the entire data for $1.4 billion, making them the largest firm in market share above Granite Construction, who won
407 auctions.
7We define primary district here as the one in which the contractor won the highest number of auctions.
8We measure backlog by the fraction of the dollar value of outstanding projects that are not yet completed. To
obtain this measure, we assume that projects are completed linearly by day, that the firm begins work on the project
award date, and that the firm takes the estimated working days to complete a project it has won.
9Another explanation is that large firms are able to select projects where they are able to choose a higher mark-up
of bid above costs.
10Estimating the number of subcontractor specification with only project fixed effects indicates that 81 percent of
the variation in the number of subcontractors across all bids can be explained by project characteristics.
11It is important to note that here we examine the stock of relationships in the district, rather than the alternative
measure of relationships, the prior interaction with listed subcontractors. The latter is potentially problematic here,
35
as contracts requiring specialty items have more listed subcontractors.
12While our primary measure of a firm’s relationship to this point has been the contractor’s interaction with the
subcontractors listed in its bid, in this case it is more sensible to use the overall relationships with subcontractors
in the district. If we were to instead use listed subcontractors, the measure would have less meaning since there are
generally only a handful of listed subcontractors.
13A similar “investment” that firms may make involves their relationship with Caltrans. The contractor may behave
better in completing a current project in order to improve its relationship with Caltrans. Uncooperative behavior
now, in the form of unnecessary cost overruns or taking a tough stance in negotiating change orders, may result in
worse treatment from Caltrans in future contracts. Therefore, upcoming contracts in a district may affect current
behavior. We were able to obtain final contract payments for around one-quarter of the projects in our data. We
find no statistical relationship between project overrun and future contracts, prior relationships with subcontractors,
or the interaction between the two.
14Two exceptions to this are notable. First, an alternative model of entry holds that firms are identical ex ante and
only learn their cost draw after paying the entry cost. If this is the case, however, then entry is not endogenous to ex
pos t cost, and therefore selection will not bias our empirical results. A second scenario is if firms are not identical,
then the cutoff cost will not be exactly the same. Consider an auction with two “high cost” firms and two “low cost
firms.” A firm drawing from the higher cost distribution will face a tougher set of opponents – two low cost firms and
only one high cost firm – than those drawing from the low cost distribution who only face one other low cost firm
in the auction. This is very unlikely to lead to a substantial difference in the cutoff cost, however, since the markup
over cost tends to be quite low at higher points in the cost distribution.
15Some bid lettings occur with very little notice, often just a matter of days. These appear to be unique situations,
and so projects with lead times of shorter than two weeks are excluded. Lead time is unsuccessful at predicting entry
for these extremely short lead times, but it is successful for somewhat longer lead times. We also see some extremely
long lead times, which are likely due to delays or postponements in bid letting. We therefore also exclude lead times
of longer than 100 days. Together, this drops approximately 8 percent of bid observations. The median auction has
an advertising lead time of 30 days.
16Subcontractor utilization decisions are not independent since there can be only one subcontractor for a given
task. Subcontractor choice is also unlikely to be independent across bidders within the same project since some
36
subcontractors will have unobserved cost advantages. For these reasons, we cluster standard errors at the contract
level.
37
Figure 1: Caltrans districts
38
Table 1: Summary statistics
Mean Median SD Min Max
PanelA:Contractcharacteristics
Bidders 5.15 5 2.81 1 30
Engineer’s estimate $3.13 mill. 0.62 mill. 19.0 mill 12930 800 mill
Workdays 163.4 70 233.9 5 2310
Num. of items 34.77 23 38.1 1 349
Panel B: All bidders
Bid $3.12 mill 0.64 mill 18.4 mill 16410 1.4 bill.
Bid/estimate 1.09 1.05 0.37 0.21 37.3
Num. of subs. 4.35 4.0 3.58 0 38
Past wins 18.05 4.0 49.80 0 405
Past utilization of listed subs 7.57 1.0 22.16 0 404
Panel C: Winning bidders
Bid $3.17 mill 0.59 mill 27.0 mill 16410 1.4 bill.
Bid/estimate 0.96 0.94 0.22 0.21 3.00
Num. of subs. 4.36 4.0 3.57 0 34
Past wins 26.15 7.0 63.03 0 405
Past utilization of listed subs 11.91 2.0 30.85 0 404
Panel A describes the summary statistics of 5120 contracts awarded by Caltrans from May
1996 through October 2005, nearly all contracts awarded during this time. The number of
items reflects how many distinct items are listed on the contract. The workdays variable
measures the engineer’s evaluation of the time to completion in days. Panel B provides
information on the 25631 bids observed on these auctions. Panel C provides information on
the bids that won the 5120 auctions.
39
Table 2: Market concentration
Contracts won Value ($mill)
Granite Construction 407 7.95% 1230.0 7.59%
Peterson Chase 99 1.93% 139.1 0.86%
All American Asphalt 71 1.39% 116.2 0.72%
Teichert Construction 68 1.33% 172.9 1.07%
American Civil Constructors 61 1.19% 228.5 1.41%
Clayborn Contracting Group 59 1.15% 19.8 0.12%
Parnum Paving 57 1.11% 82.3 0.51%
Western States Surfacing Inc. 56 1.09% 47.1 0.29%
J.F. Shea Co. Inc. 55 1.07% 147.9 0.91%
W. Jaxon Baker Inc. 55 1.07% 142.4 0.88%
TDS Engineering 52 1.02% 16.0 0.10%
M. Bumgarner Inc. 50 0.98% 31.8 0.20%
J. McLoughlin Engineering Co. 47 0.92% 66.9 0.41%
E.L. Yeager Construction 45 0.88% 814.9 5.03%
Watkin and Bortolussi 41 0.80% 25.1 0.15%
Mercer Fraser Co. 41 0.80% 48.2 0.30%
Sim J. Harris Co. 41 0.80% 29.6 0.18%
Baldwin Contracting Co. 40 0.78% 92.2 0.57%
Modern Alloys Inc. 39 0.76% 31.6 0.20%
Beador Construction Co. 37 0.72% 16.9 0.10%
1421 27.7% 3499.5 21.5%
These are the twenty largest firms in terms of number of contracts won. Listed are the
number of contracts won by firm and the share this represents of all contracts awarded
between May 1996 and October 2005. Also listed are the dollar value of contracts won
and the firm’s share of the total value of awarded contracts.
40
Table 3: Geographic concentration
Mean Median SD Min Max
Prime contractors
All prime contractors
Total wins 6.36 2 17.31 1 407
In primary district 0.82 1 0.25 0.2 1
N 805
Greater than one win
Total wins 10.12 4 21.82 2 407
In primary district 0.69 0.67 0.26 0.2 1
N 473
Subcontractors
Al l s ubcontractors
Part. in winning bid 9.54 2 37.03 1 932
In primary district 0.84 1 0.25 0.13 1
N 2076
Greater than one participation
Part. in winning bid 17.98 5 50.84 2 932
In primary district 0.68 0.67 0.26 0.13 1
N 1044
The set of prime contractors includes all those firms that were ob-
served winning at least one Caltrans contract between May 1996
and October 2005. Total wins describes the number of times in the
sample a firm won an auction. The variable “In primary district”
describes the fraction of these wins in that occurred in the district
where the firm won the most auctions. The sample is further nar-
rowed down to include only those firms that won more than won
auction. For subcontractors, we count the number of times the firm
appeared as a subcontractor on a winning bid, and the fraction of
those appearances that occurred in the district where the firm had
the most appearances.
41
Table 4: Subcontractor relationships with listed subcontractors and firms’ bids
Dependent variable: Log of bid
(1) (2) (3) (4) (5)
Log Stock with listed subs. -0.016 -0.011 -0.005 -0.002
(0.003)*** (0.003)*** (0.004) (0.004)
Log Stock past 90 days -0.001
(0.003)
Log Stock past 90-180 days 0.007
(0.004)*
Log Stock past 180-270 days -0.002
(0.004)
Log Stock past 270-360 days -0.012
(0.004)***
Log Stock >360 days prior -0.010
(0.003)***
Log stock*Log future dist. contracts -0.002
(0.001)**
Log future contracts in district -0.011
(0.004)***
Log stock*Log future dist. $ -0.063
(0.023)***
Log future dist. $ -0.135
(0.078)*
Log past wins 0.002 0.035 0.033 0.036 0.036
(0.002) (0.005)*** (0.005)*** (0.005)*** (0.005)***
Log past wins in project county -0.014 -0.010 -0.010 -0.010 -0.010
(0.003)*** (0.003)*** (0.003)*** (0.003)*** (0.003)***
Log backlog 0.000 0.001 0.001 0.001 0.001
(0.000) (0.000)** (0.000)* (0.000)** (0.000)**
Bidders -0.009 -0.010 -0.010 -0.010 -0.010
(0.001)*** (0.001)*** (0.001)*** (0.001)*** (0.001)***
Log(items) 0.017 0.025 0.025 0.022 0.023
(0.004)*** (0.005)*** (0.005)*** (0.005)*** (0.005)***
Number of workdays 0.000 0.000 0.000 0.000 0.000
(0.000)*** (0.000)*** (0.000)*** (0.000)*** (0.000)***
Log engineer’s estimate 0.958 0.948 0.948 0.946 0.948
(0.003)*** (0.003)*** (0.003)*** (0.003)*** (0.003)***
Firm effects X X X X
Month, year, and district effects X X X X X
Observations 25714 25714 25714 25714 25714
R-squared 0.97 0.97 0.97 0.97 0.97
The dependent variable is the log of the firm’s bid. The stock of subcontractors is the sum of the firm’s prior
interactions on winning bids with subcontractors listed in the firm’s bid. Future contract dollars in district is
the sum of the engineer’s estimate for all projects occurring in the next 360 days in the pro ject’s district. One
has been added to each variable for which logs were taken, except for the number of items and the engineer’s
estimate, to deal with missing values.
Standard errors corrected for clustering by contract are in parenthesis.
*,**,*** denote significance at the 90%, 95%, and 99% level, respectively.
42
Table 5: Alternative Measure: Subcontractor relationships within district and the firms’ bids
Dependent variable: Log of bid
(1) (2) (3) (4) (5)
Log stock of subs. in district -0.009 -0.009 -0.003 -0.002
(0.002)*** (0.003)*** (0.004) (0.004)
Log stock in Dist. past 90 days -0.001
(0.003)
Log stock in Dist. 90-180 days prior 0.003
(0.003)
Log stock in Dist. 180-270 days prior 0.003
(0.003)
Log stock in Dist. 270-360 days prior -0.009
(0.003)***
Log stock in Dist. >360 days prior -0.008
(0.002)***
Log stock*Log future contracts in dist. -0.002
(0.001)*
Log future contracts in district -0.011
(0.004)***
Log stock*Log future dist. $ (X100) -0.045
(0.021)**
Log future dist. $ (X100) -0.146
(0.081)*
Log # past wins -0.002 0.030 0.029 0.031 0.031
(0.002) (0.005)*** (0.005)*** (0.005)*** (0.005)***
Log # wins in project county -0.012 -0.008 -0.007 -0.007 -0.008
(0.003)*** (0.003)** (0.003)** (0.003)** (0.003)**
Log backlog 0.000 0.001 0.001 0.001 0.001
(0.000) (0.000)*** (0.000)** (0.000)*** (0.000)***
Bidders -0.008 -0.010 -0.010 -0.010 -0.010
(0.001)*** (0.001)*** (0.001)*** (0.001)*** (0.001)***
Log(items) 0.014 0.024 0.024 0.022 0.022
(0.004)*** (0.005)*** (0.005)*** (0.005)*** (0.005)***
Number of workdays 0.000 0.000 0.000 0.000 0.000
(0.000)*** (0.000)*** (0.000)*** (0.000)** (0.000)**
Log engineer’s estimate 0.956 0.946 0.946 0.944 0.945
(0.003)*** (0.003)*** (0.003)*** (0.003)*** (0.003)***
Firm effects X X X X
Month, year, and district effects X X X X X
Observations 24763 24763 24763 24763 24763
R-squared 0.97 0.98 0.98 0.98 0.98
The dependent variable is the log of the firm’s bid. The stock of subcontractors is the sum of the firm’s prior
interactions on winning bids with subcontractors headquartered in the pro ject district. Future contract dollars
in district is the sum of the engineer’s estimate for all pro jects occurring in the next 360 days in the project’s
district. One has been added to each variable for which logs were taken, except for the number of items and the
engineer’s estimate, to deal with missing values.
Standard errors corrected for clustering by contract are in parenthesis.
*,**,*** denote significance at the 90%, 95%, and 99% level, respectively.
43
Table 6: Specialty items and subcontractor utilization
Dependent variable: Number of subcontractors
(1) (2) (3)
No. Specialty Items 0.148 0.139 0.073
(0.004)*** (0.004)*** (0.005)***
Firm effects No Yes Yes
Controls No No Yes
Observations 25876 25876 25713
R-squared 0.42 0.67 0.74
Controls included in the specification shown in column 3 include
backlog, number of bidders, year and month dummies, district
effects, number of contract items, workdays, and log engineer’s
estimate.
Standard errors corrected for clustering by contract are in paren-
thesis.
*,**,*** denote significance at the 90%, 95%, and 99% level,
respectively.
Table 7: Bid regressions by number of specialty items
Dependent variable: Log of bid
(1) (2) (3)
Sample: #s items=0 #s items 1-7 #s items 7
Log(1+stock in district) -0.013 -0.012 0.001
(0.023) (0.008) (0.005)
Log(1+stock in district)*log(1+future contracts) 0.005 0.000 -0.003
(0.006) (0.002) (0.001)***
Log(1+future contracts) -0.046 -0.014 -0.005
(0.025)* (0.008)* (0.005)
Constant 1.355 0.851 0.822
(0.254)*** (0.099)*** (0.071)***
Observations 2349 9907 13922
R-squared 0.96 0.95 0.98
The dependent variable is the log of the firm’s bid. The number of s items is the number of specialty
items listed in the contract, which typically must provided by a subcontractor, and the median
number of s items is seven. The stock of subcontractors is the sum of the firm’s prior interactions
on winning bids with subcontractors headquartered in the project district. Future contracts is the
sum of the number of projects occurring in the next 360 days in the project’s district. One has been
added to each variable for which logs were taken, except for the number of items and the engineer’s
estimate, to deal with missing values. Other covariates included in the specifications match those
describedinTable4.
Standard errors corrected for clustering by contract are in parenthesis.
*,**,*** denote significance at the 90%, 95%, and 99% level, respectively.
44
Table 8: Contract opportunities in the more distant future
Dependent variable: Log of bid
Measure of stock of relationships
Stock with listed subs Stock in district
(1) (2) (3) (4)
Log stock*Log # future contracts <1yr -0.003 -0.002
(0.001)** (0.001)*
Log # future contracts <1yr -0.011 -0.011
(0.004)** (0.004)**
Log stock*Log # future contracts 1-2 yrs 0.001 0.000
(0.001) (0.001)
Log # future contracts <1-2 years 0.015 0.015
(0.007)** (0.007)**
Log stock*Log future contract $ <1yr (X100) -0.063 -0.044
(0.024)*** (0.022)**
Log future contract $ <1yr -0.134 -0.148
(0.081)* (0.084)*
Log stock*Log future contract $ 1-2 yrs 0.002 -0.006
(0.031) (0.029)
Log future contract $ <1-2 years 0.243 0.263
(0.182) (0.183)
Log stock -0.007 -0.002 -0.004 -0.001
(0.005) (0.006) (0.005) (0.006)
Constant 0.828 0.795 0.626 0.608
(0.055)*** (0.055)*** (0.216)*** (0.214)***
N 25714 25714 24763 24763
R-squared 0.97 0.97 0.98 0.98
The dependent variable is the log of the firm’s bid. The stock of subcontractors measure used in specifications
(1) and (2) is the sum of the firm’s prior interactions on winning bids in the same district as the current
project. The stock of subcontractors measure used in specifications (3) and (4) is the sum of the firm’s prior
interactions on winning bids with subcontractors listed by the firm on the current project. Future contract
dollars in district is the sum of the engineer’s estimate for all projects occurring either within one year or
between one and two years in the project’s district. One has been added to each variable for which logs
were taken, except for the number of items and the engineer’s estimate, to deal with missing values. Other
covariates included in the specifications match those described in Table 4.
Standard errors corrected for clustering by contract are in parenthesis.
*,**,*** denote significance at the 90%, 95%, and 99% level, respectively.
45
Table 9: Value of relationship depth
Dependent variable: Log of bid
(1) (2) (3)
Top sub. share*Log stock in district -0.011 -0.021 -0.017
(0.006)* (0.013)* (0.015)
Log stock in district -0.007 0.001 0.001
(0.003)** (0.005) (0.005)
Top sub. share*Log stock in district*Log # future contracts 0.004
(0.004)
Log stock in district*Log future contracts in district -0.003
(0.001)**
Log # future contracts in district -0.012
(0.004)***
Top sub. share*Log stock in district*Log future dist $ (X100) 0.043
(0.088)
Log stock in district*Log future dist $ (X100) -0.053
(0.028)*
Log future dist $ (X100) -0.152
(0.084)*
Constant 0.564 0.571 0.561
(0.213)*** (0.209)*** (0.212)***
N 24763 24763 24763
R-squared 0.98 0.98 0.98
The dependent variable is the log of the firm’s bid. The stock of subcontractors is the sum of the firm’s prior
interactions on winning bids in the same district as the current project. The top subcontractor share is the
fraction of the firm’s relationship stock concentrated in its most frequently used subcontractor. Future contract
dollars in district is the sum of the engineer’s estimate for all projects occurring in the next 360 days in the
project’s district. One has been added to each variable for which logs were taken, except for the number of
items and the engineer’s estimate, to deal with missing values. Other covariates included in the specifications
match those described in Table 4.
Standard errors corrected for clustering by contract are in parenthesis.
*,**,*** denote significance at the 90%, 95%, and 99% level, respectively.
46
Table 10: Bidding and firm propensity to subcontract
Dependent variable: Log of bid
(1) (2) (3) (4)
Log stock in district -0.011 -0.011 -0.009 -0.003
(0.003)*** (0.003)*** (0.003)*** (0.004)
Firm Avg Sub. Util. 0.003 0.002
(0.001)** (0.002)
Avg Sub. Util. * Log future contracts in dist. 0.000 0.000 0.001
(0.001) (0.001) (0.001)
Log # future contracts in dist. -0.015 -0.017 -0.014
(0.005)*** (0.005)*** (0.005)***
Log stock*Log future contracts in dist. -0.002
(0.001)**
Firm effects No No Yes Yes
Observations 24763 24763 24763 24763
R-squared 0.97 0.97 0.98 0.98
The dependent variable is the log of the firm’s bid. Average subcontractor utilization varies at the firm level,
measuring the number of subcontractors the firm uses on an average contract. The stock of subcontractors
is the sum of the firm’s prior interactions on winning bids with subcontractors headquartered in the project
district. Future contracts is the sum of the number of projects occurring in the next 360 days in the project’s
district. One has been added to each variable for which logs were taken, except for the number of items
and the engineer’s estimate, to deal with missing values. Other covariates included in the specifications
match those described in Table 4.
Since coefficients on the interaction Avg Sub Util*Log(1 + future contracts in district) are hard to read,
we report the p-values: 0.56, 0.64, and 0.41 for columns 2,3, and 4, respectively.
Standard errors corrected for clustering by contract are in parenthesis.
*,**,*** denote significance at the 90%, 95%, and 99% level, respectively.
47
Table 11: Firm participation
Dep Variable, Methodology Heckman
Participation, OLS log(Bid), Tobit Bid equation Part. equation
(1) (2) (3) (4) (5)
Log(1+stock in district) 0.022 0.013 -0.081 -0.1366 0.1852
(0.001)*** (0.001)*** (0.003)*** (0.040)*** (0.005)***
Log(1+stock in dist.)*log(1+future contracts) 0.001 0.002 -0.007 -0.0125 0.0159
(0.000)*** (0.000)*** (0.001)*** (0.004)*** (0.002)***
Log(1+future contracts) -0.001 -0.001 0.015 0.0103 -0.0335
(0.000)*** (0.000)*** (0.002)*** (0.009) (0.005)***
Auction advertise lead time (days) 0.0010
(0.0003)**
Other Controls Yes Yes Yes Yes
Firm effects No Yes No No
Observations 514597 514597 514596 476331
R-squared 0.04 0.06
In each specification, the pool of potential entrants we consider to include all firms who bid in the same year in
the project district. The dependent variable in the specification shown in columns (1) and (2) is an indicator for
auction participation. In column (3), we show the results from estimating a specification of the log bid using a
Tobit, where the distribution of observed bids in an auction is assumed to be truncated at the maximum bid.
The final two columns show the results of a Heckman two step selection estimation, where the excluded variable
from the bid equation is the number of days in advance the project was advertised.
The stock of subcontractors is the sum of the firm’s prior interactions on winning bids with subcontractors
headquartered in the project district. Future contract is the number of projects occurring in the same district
within the following 360 days. One has been added to each variable for which logs were taken, except for the
number of items and the engineer’s estimate, to deal with missing values.
Other controls include the log of the engineer’s estimate, the log of prior wins by the firm, log backlog, the
number of opponents, the log number of items specified on the project, the number of working days, plus year,
month and district dummy variables.
Standard errors corrected for clustering by contract are in parenthesis.
*,**,*** denote significance at the 90%, 95%, and 99% level, respectively.
48
Table 12: The subcontractor utilization decision of the twenty largest firms
Dependent variable: Indicator for bidder iusing subcontractor jon contract k
(1) (2) (3) (4) (5)
Log stock prior interactions 2.431 2.762 2.061 1.690 2.246
(0.041)*** (0.044)*** (0.035)*** (0.106)*** (0.130)***
Log stock*Log # future contracts 0.084
(0.023)***
Log # future contracts -0.009
(0.028)
Log stock*Log future contract $ (X100) -0.010
(0.007)
Log future contract $ (X100) 0.008
(0.005)
# of other bidders using sub. 0.321 0.321 0.322
(0.005)*** (0.005)*** (0.005)***
Project in sub.’s primary district 0.016 0.016 0.016
(0.000)*** (0.000)*** (0.000)***
Log past wins (X100) -0.064 -0.073 -0.064
(0.036)* (0.036)** (0.036)*
Log past wins in project county (X100) -0.036 -0.036 -0.036
(0.011)*** (0.011)*** (0.011)***
Number of bidders -0.042 -0.042 -0.042
(0.004)*** (0.004)*** (0.004)***
Log engineer’s estimate 0.039 0.038 0.038
(0.011)*** (0.011)*** (0.011)***
Number of workdays 0.000 0.000 0.000
(0.000)*** (0.000)*** (0.000)***
Log number of items (X100) 0.363 0.363 0.363
(0.020)*** (0.020)*** (0.020)***
Log backlog (X100) 0.004 0.004 0.004
(0.003) (0.003) (0.003)
Firm effects X X X X
Month, year, and district effects X X X
N 1790046 1788088 1774881 1774881 1774881
R-squared 0.01 0.02 0.16 0.16 0.16
The dependent variable is an indicator for whether a particular subcontractor was used by the contractor on that
particular auction. The sample includes the 20 largest firms in terms of auction participation. The stock of prior
interactions represents the number of times the contractor has worked with that particular subcontractor on prior
winning contracts. Future contract dollars in district is the sum of the engineer’s estimate for all projects occurring
in the next 360 days in the pro ject’s district. One has been added to each variable for which logs were taken,
except for the number of items and the engineer’s estimate, to deal with missing values.
All specifications include controls for year and firm effects, and columns 2-4 contain controls for month dummies.
Standard errors corrected for clustering by contract are in parenthesis.
*,**,*** denote significance at the 90%, 95%, and 99% level, respectively.
49
