When the Highest Bidder Loses the Auction:
Theory and Evidence from Public Procurement
Francesco Decarolis
4th August 2010
Abstract
This paper analyzes two methods used in public procurement auctions to deal with
the risk of bidders’default: …rst price auctions with ex-post screening of bids’responsiveness (F P Ascr ) and average bid auctions (ABA) in which the bidder closest to the
average bid wins. It is shown that when both defaults and screening are costly an
auctioneer prefers using ABA. The e¤ect of the two auction formats on revenues and
e¢ ciency is empirically studied by estimating a structural model of …rms’ costs distributions using a new dataset of Italian public procurement auctions, run alternately
using F P Ascr or a form of ABA.
JEL: L22, L74, D44, D82, H57.
Department of Economics, University of Wisconsin at Madison. E-mail address: [email protected].
This paper is part of my Ph.D. thesis at the University of Chicago. I would like to thank Ali Hortacsu,
Roger Myerson, Philip Reny and Timothy Conley for their guidance. I also bene…ted from conversations
with Marianne Bertrand, Jeremy Fox, Ken Hendricks, J-F Houde, Greg Lewis, Gustavo Piga, Jesse Shapiro
and Giancarlo Spagnolo, as well as from comments of participants in seminars at the University of Chicago,
Bank of Italy, EIEF Rome, Penn, NYU Stern, LSE, Harvard KSG, Toronto, UW-Madison, PSU, Columbia,
Stanford and Minnesota, and at the conferences of the IIOC in Washington, ES in Pittsburgh, EEA in
Milan and EARIE in Toulouse, and the NBER Market Design and IO working groups where I presented
preliminary versions of this research. Financial support from the University of Chicago and the Bank of
Italy is gratefully acknowledged.
1
Introduction
Most of the vast literature on auctions assumes that bids represent binding commitments
for bidders. However, when the object of the auction is the procurement of a contract of
uncertain value, there is a line of thought that analyzes bidders’incentive to default. This
literature has described how the use of competitive bidding, for instance through a …rst price
sealed bid (FP) auction, may excessively favor those bidders who are more likely to default
(see Spulber, 1990).1 Moreover, it has also argued why the auctioneer’s preference for either
a …rst price or a second price auction depends on the cost that she2 faces in case of a winner’s
default (see Board, 2008). In this paper, I study two modi…cations of the FP auction used
by Italian Public Administrations (PA) to deal with the default risk in the procurement of
works and empirically analyze their e¤ects on the auctioneer’s revenues and on e¢ ciency.
The …rst modi…cation, frequently used in procurement, consists in augmenting a standard
FP auction with an ex post screening of bids. This screening process is an evaluation of the
reliability of the bids, aimed at excluding …rms o¤ering prices that are so low as to jeopardize
the correct execution of the job. The second modi…cation is more substantial and entails
using an awarding rule that punishes …rms o¤ering prices too low relative to those of the
other bidders. An example is in order. Suppose that the auctioneer announces her intention
to procure a work for which she is willing to pay at most the reserve price R, and that …rms
submit sealed bids expressed as discounts over R. In a standard FP auction, the highest
discount wins. Instead, a modi…ed awarding rule could state, for instance, that the bidder
closest to the average of the bids wins and receives his own price to perform the job. A realworld example of a similar rule comes from the Florida Department of Transportation (DoT),
which states: "If …ve or more responsive bids are received, the Department will average the
bids, excluding the highest and the lowest responsive bids. If three or four responsive bids are
received, the Department will average all bids. Award of the Contract will be to the winner
who submitted the responsive bid closest to the average of those bids." 3
1
Zheng (2001) and Rhodes-Kropf and Viswanathan (2005) derive similar results under di¤erent assumptions on bidders’values and information. See the literature review at the end of this Section.
2
Throughout the paper, I will refer to the auctioneer as "she" and to the bidder as "he." Sometimes I
will use Public Administration (PA) instead of auctioneer and …rms instead of bidders.
3
Source: Florida DoT Award and Execution of the Contract, Rev 2-7-97, 7-00, sub-article 3-2.1. This is
1
Both modi…cations imply that the highest discount may not win. Moreover, the latter
rule implies that the highest bid is automatically eliminated every time it is the lone highest
bid. Intuitively rules like that of the Florida DoT should not be of interest to an auctioneer
concerned with her revenues. However, the next Section documents that various forms of
similar auctions, which I will call average bid (AB) auctions, are in use in several countries.
In particular, the case of Italy is illustrated. Between 1998 and 2006 a form of the AB
auction was the only mechanism that Italian PA were allowed to use to procure contracts
for works worth less than e5 million. Two reforms required by the European Union then
changed this system. First, in 2006, all PA were given the freedom to choose alternately
between AB and FP auctions. FP auctions were mandated to be with ex post screening.
Then, in 2008, the FP auction became compulsory for contracts above e1 million, leaving
the possibility of using the AB only for contracts below this threshold (a market worth e6
billion yearly). For the periods around these policy changes, I have collected data on the
auctions, the contracts’completion and the bidders. I use them to describe the environment
in which PA operate and to document numerous facts, including the …xed-cost nature of
screening and the overwhelming preference of small PA for the AB rule despite the large
increases in the winning discount experienced by the few large PA that opt for the FP.
In light of these …ndings, I consider a model that reconciles the PA’ choices with the
behavior of a revenue-maximizing auctioneer. To match the Italian case, I assume that the
auctioneer is constrained to choose between an FP and an AB, each of which can be augmented by an ex post screening stage. When bidders can default and defaults are costly for the
auctioneer, it is shown that the observed behavior of the Italian PA might be the rational
sorting of PA with di¤erent screening costs between AB without screening and FP with
screening. In fact, although the AB with screening is dominated by the FP with screening,
the ranking of the other three mechanisms depends on the costs of defaults and of screening. In particular, an auctioneer may prefer the AB without screening in an environment
with high costs of both default and screening. In addition to providing this rationalization,
another contribution of the paper is to provide a characterization of equilibrium bidding in
the AB auction and to show that this format is equivalent to a random allocation.
one of the four rules the DoT can use to award its auctions, but it has not been used since 2001.
2
The results of the theoretical analysis are used, together with the data collected, to
conduct an empirical analysis of the e¤ects of the switch from AB to FP auctions on revenues
and e¢ ciency. Having access to data on both the winning price and the …nal price at the
contract’s end, I can observe all payments to the winner. The e¤ect of the two auction formats
on this relevant component of revenues is estimated using di¤erent reduced form methods,
taking into account the endogenous selection into the FP after the 2006 reform. The e¤ect
of a switch from AB to FP is estimated to signi…cantly increase the winning discount (i.e.,
the rebate bidders o¤er on the announced reserve price) by an amount ranging between
11% and 15% of the reserve price. However, switching to FP also signi…cantly increases the
extra payment renegotiated by the contractor by about 6% of the reserve price. Therefore,
on average, for the simple roadwork contracts studied, a PA switching to FP saves around
e125,000. Nevertheless, this estimate does not include either the transaction costs possibly
associated with the renegotiations or the cost of screening in the FP. Indeed, I present
evidence consistent with the fact that the FP are conducted with screening. Finally, I
introduce a "rule of thumb" approach to estimate the expected revenues in AB auctions.
As regards e¢ ciency, its evaluation requires the knowledge of …rms’ cost. Therefore,
a structural analysis is used to infer these unobserved costs from the observed bids. The
method employed extends to datasets containg only the winning bid and the reserve price the
procedure introduced by Krasnokutskaya (2009) to aemend for unobserved auction heterogeneity the nonparametric approach of Guerre et al. (2000). Two components of the …rm’s
cost are separately identi…ed: the one that each …rm privately observes, and the one all …rms
commonly observe. Since the AB auction is equivalent to a random allocation, the amount
of ine¢ ciency that it induces is proportional to the relevance of the private cost. Using a
homogeneous subsample of FP auctions conducted with screening, the results indicate that,
if the same type of …rms participate in both the AB and the FP auctions, the extra cost of a
winner of an AB auction relative to the winner of an FP auction is on average about 10% of
the reserve price. For a large PA that runs about 100 auctions per year, this amounts to e10
million. However, I also explain why this estimate may be either too small, because of the
entry in AB of ine¢ cient …rms that never attend FP, or too large, because …rms compensate
for this ine¢ ciency through an extensive use of subcontracts and even through collusion.
3
Overall, this paper suggests that the AB auction should be abandoned because it negatively a¤ects both revenues and e¢ ciency. Nevertheless, it should not be naively replaced
with a standard …rst price auction unless a reliable system ensuring the commitment of bidders to their bids is introduced along with it. In the Italian case, centralizing the screening
process appears to be a simple solution to allow even the small PA to reap the bene…ts of
…rms competition without incurring the high …xed cost of performing the screening.
Literature: This paper is related to various branches of the literature. First of all, it
contributes to literature on bidders’ default in auctions for contracts. To my knowledge,
the …rst paper on this subject was Spulber (1990). Other papers that, similarly to mine,
seek to link the nature of the awarding mechanism ex post bankruptcy are Waehrer (1995),
Rhodes-Kropf and Viswanathan (2000, 2005), Zheng (2001) and Board (2008). Chillemi and
Mezzetti (2009) show that when bidders can default and the auctioneer bears a high enough
cost of default, then the optimal mechanism takes the form of a random lottery. Finally,
a recent generalization of the adverse selection problem that lies behind the default risk
associated with competitive bidding is Che and Kim (2009). The second group of studies
to which this paper contributes is that concerned with …rms’ bidding in auctions where
the public procurement agency has introduced changes to the FP rule to limit defaults
and renegotiations. Papers in this literature are Bajari et al. (2007) on renegotiations in
the California DoT auctions, as well as the …rst papers that introduced the AB auction to
economics and presented examples of its (mis)functioning: Albano et al. (2006) and Engel
et al. (2006). Moreover, within the literature on the economics of public procurement, my
paper complements the study of Bandiera et al. (2009) regarding the procurement of goods
by Italian PA. Another branch of the literature to which this paper belongs is that originated
by the pioneering studies of Paarsch (1992) on the structural estimation of auctions. In
particular, I follow the adaptation by Krasnokutskaya (2009) of the methodology of Guerre,
Perrigne and Vuong (2000). Asker (2008) is an example of a paper using this method to
study collusion in stamp auctions. Finally, my quantitative assessment of the relative e¤ects
of AB and FP auctions is related to the similar analysis conducted by Athey et al. (2008)
to compare the revenues of …rst price sealed bid and open outcry auctions.
4
2
Average Bid Auctions: Institutional Facts
The awarding rule of the Florida DoT reported above and that of the Italian auctions that
will be presented next are remarkably di¤erent from those usually seen in the economics
literature. Both of them automatically eliminate the highest discount whenever at least two
bidders participate and the highest discount is unique. Given this intuitively unappealing
property of the Florida and Italian auctions, I …rst check to see if these are isolated cases, or
if similar auctions exist elsewhere. As shown in Table 1, a careful look at the rules of public
procurement in various countries reveals that these two cases are not an anomaly.
Table 1: Rules for Identi…cation and Elimination of Abnormal Bids
Automatic Elimination
Chile
China
Italy
Japan
Peru
Switzerland *
Taiwan
USA - Florida DoT
- NYS Proc.Ag.
Only Identification
Belgium
Brazil
Germany
Portugal
Romania
Spain
Turkey
UK
Rule Not Disclosed
USA - California DoT
* Based only on an indirect source of information: Engel et al. (2006)
Indeed, numerous countries, listed in the left column of Table 1, have rules that identify
and automatically eliminate "abnormally" high tenders.4 Generally, this means that discounts greater than some threshold de…ned as a function of the bids submitted (often their
average) are automatically eliminated from the auction, and the contract is awarded to the
highest non-eliminated bid. This often implies that the highest solo bidder is eliminated with
probability one. For the countries in the middle column, the identi…cation of an abnormal
tender does not mandate its automatic elimination. Generally, these countries run …rst price
auctions augmented by an ex post screening stage in which further checks on the reliability of
4
I classi…ed countries only on the basis of the rules contained in their codes of public procurement for
works, goods and services. In particular, a country is in the left column if, in any of its codes, there is a
rule allowing the use of an auction with automatic (i.e. using an algorithm based on the bids) elimination of
some tenders. It is in the middle column if there is any rule allowing for the use of automatic identi…cation
of abnormal bids but no rule requiring their automatic elimination. Finally, in the right column I report
cases of rules for dealing with abnormal bids that are not publicly disclosed.
5
bids higher than some thresholds are undertaken before the contract can be awarded to such
a bidder.5 Finally, in the right column the case of the California DoT is reported. Although
in this case there are no explicitly disclosed rules for detecting abnormal bids, …rms believe
that in fact the DoT uses an algorithm based on the average of the bids.6
The exact rules for automatic elimination of bids di¤er between the countries listed in
the left column of Table 1. A straightforward algorithm that awards the contract to the
bidder closest to the average (regardless of whether from above or from below) exists in the
codes of Taiwan and the Florida DoT. More complicated functions of the average of the bids
are used in other countries.7 In Switzerland, Engel et al. (2006) report the use of an auction
in which the highest bidder is eliminated and the second-highest wins at his own price. In
the rest of this paper I will loosely refer to all these types of auctions with automatic elimination as average bid (AB) auctions and, although I will analyze in depth only the Italian
AB auction, I will stress which conclusions are likely valid for other forms of AB auctions.
The case of Italy: The AB rule and the transition toward FP auctions
The essential features of the Italian system of public procurement of contracts for works are
as follows. First, the public administration (PA) releases a call for tenders that illustrates
the contract characteristics, including the maximum price that it is willing to pay for the
contract (the reserve price) and the awarding rule used. Then every …rm quali…ed to bid
for public contracts can submit its sealed bid consisting of a discount over this reserve price.
Finally, bids are all opened at the same time and, if the awarding rule is the AB rule, then
the winner is selected in the following way. First, discounts are ordered from the lowest to
the highest. Then, a trim mean (A1) is calculated excluding the 10 percent of the highest
and lowest bids. Then a new threshold (A2) is calculated as the sum of A1 and the average
di¤erence between A1 and discounts greater than A1, but lower than the lowest discount in
the top 10% of bids. Discounts equal or above A2 are eliminated, and the highest discount
5
For instance, BESCHA (the German Federal Procurement Agency) requires additional explanations
from the highest bidder whenever his bid deviates by more than 20% from the second-highest bid. Several
other cases are discussed in Engel et al. (2006).
6
This is one of the relevant features of the bidding model of Bajari, Houghton and Tadelis (2007).
7
Ioannou and Leu (1993), Albano et al. (2006) and Zheng (2006) document the use of these rules in
Taiwan, Florida, New York State (solely for liquid bituminous materials), Peru and China (Guangdong
region). In Japan, several prefectures, including Nagano, recently introduced the AB to procure roadwork
contracts. See Epstein et al. (2004) for its use in Chile for school meals auctions.
6
strictly below A2 wins, Dwin .8 Figure 1 shows an example with 17 bids.
Figure 1: An Illustration of the Italian AB Rule
The rule described above was introduced in 1998, and until June 2006, it has been the
compulsory auction format for all contracts with a reserve price below (approximately) e5
million.9 Above this value the European regulation mandated the use of FP auctions. During
this period in Italy, approximately 75% of all contracts were procured through AB auctions,
while only 9% were procured through FP.10 However, to comply with changes in European
norms, this system was modi…ed in 2006, and then again in 2008. The …rst reform made all
PA free to choose whether to use FP or AB in each auction, starting from July 2006. The
PA had to announce in the auction notice whether an AB or an FP were used. Moreover,
even at FP auctions, it became mandatory to use the AB algorithm to mark abnormal
bids. The awarding to an abnormal bid was conditional on it passing a formal screening
process (consisting of three phases, two written and one oral) in which the …rm’engineers
have to convince the PA engineers that the …rm can perform the job at the promised price.
Therefore, this FP auction with ex post screening is similar to those used in the countries
listed in the central column of Table 1. The second policy change occurred in October 2008,
when the FP became compulsory for every contract worth more than e1 million. Below this
threshold a PA could still choose freely between AB and FP.
Given the evolution of the regulation, it is not surprising that, before the 2006 reform,
contracts awarded with AB auctions were worth as much as e10 billion per year, roughly
.7% of Italy’s GDP in 2004. Nevertheless, what might be surprising is that, even after
the 2008 reform, these auctions remained in use for contracts worth about e6 billion per
year. The reason for this is twofold: i) the vast majority of contracts are small, well below
8
See Art. 21 Law 109/94, later modi…ed by Art. 86 and 122 Law 163/06. The rule described applies
only if 5 (10 after 2006) or more bidders participate. Otherwise the winner is, like in the FP, the highest
responsive bidder. In my samples, less than 5% of the AB auctions have less than 5 bidders (less than 7%
have less than 10 bidders after 2006). These auctions are excluded from my analysis.
9
The next section brie‡y describes what preceded the introduction of this rule.
10
In terms of value, FP were worth 45% of the total value and AB 42%. The remaining contracts were
procured using negotiated procedures or scoring rule auctions. However, the law strictly limited their usage.
7
the e1 million threshold, and ii) almost all PA chose to remain with the AB when they
could choose. For instance, Figure 2 illustrates the pattern of adoption of the FP by local
administrations (counties and municipalities) in …ve regions in the North for simple roadwork
contracts (mostly paving and roundabout constructions) worth less than e2.5 million.11
Figure 2: Geographical Distribution of the Adoption of AB and FP
Voluntary Adoption of FP
Forced and Voluntary Adoption of FP
(Jul. 2006 - Sep. 2008)
(Oct. 2008 - Dec. 2009 )
Figure 2 divides the territory by municipalities, thus showing the high decantralization
of procurement. The left panel of the …gure shows that few PA, 30 out of 481, voluntarily
moved from AB to FP. They are 9 counties and 21 municipalities and they are, on average,
signi…cantly larger in terms of population than the ones that remained with the AB auction. This limited number of switches seems at odds with the substantial increases in the
winning discount associated with a transition to the FP: from 15 to 31% of the reserve price
(see Section 5). Understanding what could have generated the seemingly puzzling behavior
reported in Figure 2 is both interesting in itself, and essential to be able to use the variation
produced by the Italian change from AB to FP to empirically study the e¤ects on revenues
and e¢ ciency. In Section 4, I will introduce a model that achieves this result by looking at
the interaction between the auction format, the screening cost and the bidders’default. The
next section explains why this model …ts the environment studied well.
11
This subset of auctions is of great relevance because: i) roadwork contracts are among the most frequently
auctioned works; ii) counties and municipalities are the PA that run most of the auctions; iii) the …ve regions
used are among the most important in terms of GDP. See the data description in Section 5.
8
3
Modeling Choices
In the studies that advocated the use of AB instead of FP auctions in the construction
industry,12 a major motivating factor is the risk of bidders’default. Although these studies
use arguments based on models with non-strategic bidders, the next section will show that
it is possible to have a model with strategic bidders in which a cost-minimizing auctioneer
may prefer an AB auction over an FP one. Such rationalization necessarily requires the
relaxation of some of the assumptions of Myerson (1981)’s optimal auction. In particular,
the key ingredients of the model will be that: i) bidders are ex ante uncertain about their
costs and can default ex post, ii) defaults are costly for the PA, iii) the PA can choose only
between an AB or a FP format but can augment both auctions with an ex post screening
of bids and iv) the screening is costly. In this environment, the pattern shown in Figure 2
is explained as the rational sorting of PA with di¤erent screening costs between AB without
screening and FP with screening. However, before turning to the model, it is useful to discuss
why its key ingredients are indeed useful to understand the evidence shown in Figure 2. First
of all, I will argue why the four elements listed above are salient features of the environment.
1) Cost uncertainty and strategic defaults: Spulber (1990) argues that cost uncertainty
is what primarily distinguishes an auction for a contract from an auction for a good (like a
painting). Since transactions do not take place immediately, cost overrun can occur during
the life of the contract. For the auctions that I analyze, the deadline for submitting bids is
on average 4 months before starting date of the work, and then the work lasts for about 6
months.13 During this period some shocks can a¤ect the cost of the contract. For instance, a
shock could be that associated with bad weather. At the time of the auction, …rms can only
use time series data to forecast the likelihood of rain during the time they will be paving the
road. However, only ex post does the winner …nd out the true cost.
12
In the civil engineering literature, propronents of di¤erent types of AB methods are Ioannou and Leu
(1993) and Liu and Lai (2000). Among policy studies, the European Commission: EC (2002) report suggests
awarding construction contracts with a type of AB consisting of a modi…ed FP auction in which the 20% of
the highest discounts are automatically eliminated.
13
For the auctions in the IE sample, the average contract length (called “duration” in the summary
statistics in Section 5) is 177 days, and the corresponding value for the other sample, the Authority sample,
is 239 days. Moreover, the works start several months after the date of the auction: on average 121 days
after.
9
When a shock increases the cost of completing a contract, a …rm might decide to default.
However, a more subtle result is that this possibility of default may be used by some …rms
to obtain an advantage during the bidding stage of FP auctions. Zheng (2001) shows this
phenomenon in a context where bidders have asymmetric budgets and the budget is the
penalty in case of default. In this case, low-budget …rms o¤er high discounts but default
whenever the ex post cost is high. In the Italian auctions studied, the presence of signi…cant
asymmetries in the cost of default seems highly likely. First of all, the subscribed capital
(a possible measure of the budget) of the …rms exhibits substantial variations, ranging from
e10,000 to more than e10 million across bidders.14 Not only is this capitalization asymmetric, but it is often small relative to the possible cost overrun.15 Secondly, the standard
penalty for a …rm defaulting on a contract with a PA entails the exclusion for one year from
the auctions of that speci…c PA. Hence, the observed large variation in the distance between
the bidders and the PA suggests that contractors located far away from the PA have a lower
cost of default (i.e. the cost of being excluded) relative to …rms close to the PA.16
2) Defaults are costly for the PA: There is rich evidence about the costs induced by
defaults in construction contracts (see Ganuza, 2007). These costs include, at least, the
expenses associated with awarding the contract again. Moreover, the likely presence of some
relationship-speci…c investment on the part of the auctioneer could cause her to be stuck
in a classical "hold up" problem, so that she would su¤er some loss if the winner were to
interrupt the execution of the work. Finally, the next point explains why often the monetary
reimbursement that the auctioneer can receive after the contractor’s default is quite small.17
3) Choosing the auction format to deal with the default risk: A crucial assumption of the
model in Section 4 is that the PA decides only whether to use an AB or FP auction and
The mean is e538,000 (standard deviation e4 million) while the …rst, second and third quartiles are,
respectively, e20,000, e52,000 and e105,000. The variation is similarly strong within auctions.
15
If we take the reserve price as a measure of the highest possible cost, then a measure of the possible cost
overrun is the di¤erence between the reserve price and the winning price.
16
The distance between the bidder and the place of the work (measured at the zip code and interpreted
here as a a proxy for the distance between the …rm and the PA) ranges from zero to more than 1,100
miles, with an average of 78 miles (standard deviation 134 miles). Therefore, since the average area of a
municipality is just 23 squared miles, the presence of asymmetric default costs seems likely.
17
Another approach, not pursued in this paper, looks at the welfare loss. An example is Bajari and Lewis
(2008) where the auctioneer is concerned with the welfare loss generated by delays in the execution of works.
14
10
whether to augment the auction with an ex post screening of bids. Indeed, in the environment
that I study, the PA has neither the freedom to design its (optimal) procurement method
nor to augment the auction with di¤erent institutions (such as contract insurance). There
are several other solutions, possibly superior, that the Italian legislatur could have adopted.
Among them, it is worth mentioning the method applied in the United States under the Miller
Act: the performance bond. The act requires that the winner of a federal contract above
$100,000 posts a 100% performance bond that guarantees the execution of the contract by a
third party (the surer) in case the contractor defaults (see Calveras et al., 2004). This system
eliminates the default risk and might explain why FP auctions are generally used in the U.S.
construction industry. On the contrary, in Italy there is only a system of letters of credit
through which a minimum guarantee is enforced. This guarantee is always partial, around
20% of the reserve price in my data. Furthermore, from interviews with PA representatives,
it emerged that, because of the slow legal system, it is hard to obtain the payment of this
credit or to recover the damages by suing the contractor.18 Therefore, the model ignores the
system of letters of credit19 as well as the presence of pre-quali…cation requirements,20 and
leaves to the PA only the choice of the auction format to reduce the default risk.
4) Asymmetric cost of screening: A key fact related to the adoption of the FP auction
illustrated in Figure 2 is that large PA are more likely to choose FP than small PA. Indeed,
Table 2 shows how the PA that adopted the two formats di¤er in terms of two measures of
size: the population that they administer (in thousands) and their "experience" (i.e., the
number of auctions for roadwork that they held per year). These di¤erences in PA size are
relevant because they are likely associated with di¤erences in the cost of screening bids. This
is because the screening cost is mostly a …xed cost, as clari…ed by the two arguments below.
18
This …nding is consistent with the results of the 2009 "Doing Business" report of the World Bank, which
ranks Italy 156’(the US is 6’) in terms of the e¢ ciency of the judiciary system for the recovery of a credit.
19
Interestingly, in the 1994 formulation of the Italian law, the idea of using an endogenous algorithm to
identify risky bids was associated with the requirement for these bidders to give an higher letter of credit:
bidders giving a discount 20% higher than the average discount were required to give higher guarantees in
order to be awarded the contract. However, by 1998 the algorithm had evolved into the form with automatic
elimination described at the beginning of Section 3, and the linkage with the guarantees was abandoned.
20
Pre-quali…cation criteria exist in Italy. Nevertheless, they have a limited role: they are based on very
mild quantitative requirements assessed every three years. Once a …rm is quali…ed, the PA is forced to admit
it to its auctions. In fact, the fear of a distorted use of discretion by corrupted PA induced the legislatur to
eliminate the possibility of single PA denying access to auctions regardless of a …rm’s reputation.
11
First, to perform the highly formalized screening process required by the law, the PA
needs to have its own team of specialized engineers (this activity cannot be contracted out).
Secondly, interviews with PA’s representative revealed that the legal o¢ ce also plays a key
role: lawyers are needed because eliminated …rms often appeal the PA’s decision in court. A
large PA can amortize these costs over many auctions and have a lower cost per auction than
a small PA running few auctions. In line with this interpretation of screening as a mostly
…xed cost, 28 out of the 30 PA that switched to FP never went back to AB.
5) Alternative Explanations: I conclude this section with a discussion of some factors that
could a¤ect the choice of the PA in favor of AB auctions, but are excluded from my analysis.
First of all, the proponents of the AB auction often argue that another reason to prefer the
AB over the FP is the risk of awarding the contract to the …rm that mostly underestimated
the expected cost (see European Commission, 2002). Defaults due to this sort of "winner’s
curse" problem are possible in some environments, and could rationalize a preference for
the AB. However, this does not seem appropriate for the environment that I study. First of
all, the market for small roadworks has been characterized as one of predominantly private
and not common value (Hong and Shum, 2004). Moreover, this market is well established,
and experienced …rms repeatedly bid in similar auctions taking place with high frequency,
making unlikely the presence of systematic errors in forecasting costs.21
A more relevant concern regards the role of quality. A model, isomorphic to the one built
in the next section to address the risk of default, can be constructed for the risk of poorquality work. In construction contracts quality matters, especially when the project design is
incomplete. However, more contract incompleteness is likely associated with more complex
works (Bajari and Tadelis, 2001). Hence, focusing the analysis only on basic roadwork
contracts (like pavings and roundabouts) reduces the relevance of quality concerns. For
these contracts, it is possible to assume that an experienced auctioneer can fully specify the
21
On the other hand, the winner’s curse might have been an issue in the case of new inexpereinced …mrs
joining the market, or with …rms having to bid on very complex contracts. See Kagel and Levin (1986).
12
project design and, hence, …x the quality required. Thus, I focus my analysis exclusively on
these contracts under the assumption that the choice between AB and FP is not being driven
by quality issues.22 The case motivating this approach is the experience of Padua. Arguing
that minimum quality standards are too di¢ cult to specify for complex contracts, this large
city in the North ruled to move to FP auctions exclusively for roadwork contracts and to
continue using AB auctions for more complex contracts, like the construction of buildings.
Finally, Table 3 summarizes with a probit analysis the role of some other factors that
may a¤ect the probability that a PA chooses FP over AB. A corrupted PA may prefer FP
to favor a connected …rm.23 However, the estimated coe¢ cient for this variable is never
statistically signi…cant.24 Nevertheless, to reduce further the risk that corruption a¤ects the
PA choices, I focus all my analysis on only …ve Northern regions where corruption is not
highly relevant. As regards the other regressors, apart from the size of the PA (population
and experience), neither the proximity between the PA and Turin, the …rst adopter of the
FP, nor the average winning discount in 2005 are signi…cant.25 Therefore, this evidence does
not contradict the idea that a model based on the default risk matches the environment well.
22
Moreover, the 2006 reform allowed PA to freely use scoring rule auctions. Indeed, PA started to use
them for complex contracts, where quality likely mattered, but never for the simple contracts that I study.
23
In an FP, a corrupted auctioneer may let his favored …rm win at a very high discount and then renegotiate
the price ex post. In an augmented FP, a corrupted auctioneer may, instead, use the screening stage to
selectively eliminate bids. On the other hand, in an AB the winning price is endogenous. Hence, to help the
favored …rm, she should open all the sealed bids before the auction and let the favored …rm revise its bid.
24
In Table 3 the Golden-Picci corruption index is used. See the Web Appendix for further analysis.
25
The coe¢ cient on the variable MilesTO (distance in miles/100 from the PA to Turin) indicates that
there is no evidence of social learning starting from Turin. This city was the very …rst adopter of the FP
(it was introduced there in 2003 in derogation of the national law), and in 2006 the …rst administrations
to move to FP were those close to Turin. However, this e¤ect has vanished rapidly. The meaning of the
estimate of WBid05 , the "focal" winning bid in 2005 before the …rst reform, will become clear in Section 6.
13
4
Theoretical Analysis
The model proposed here is mostly based on Zheng (2001). He considers an environment
where, both ex ante and ex post, …rms all value a good of ex ante uncertain value the same.
Firms can default on their bids under a limited liability regulation, and in this case they
lose their budget. Budgets are bidders’private information and asymmetric across bidders.
In my model, I add a privately observed value to the formulation of bidders’ valuations.
However, I assume bidders’penalties in case of default (i.e., the budget) are observable to all
bidders. Finally, while Zheng analyzed only the case of an FP rule, I consider four: an AB
auction and an FP auction, both of which can be with or without the ex post screening of
bids. The model is formulated using the language of auctions instead of that of procurement.
At the heart of the model there is the problem of a risk-neutral, revenue-maximizing
auctioneer who has to choose between four auction formats to sell an indivisible object to
one of N buyers. Figure 4 illustrates it: the auctioneer observes how much the screening
would cost, and then decides which auction to use based on the associated expected revenues.
Figure 4: The Auctioneer’s Decision Problem
If ex post the winner defaults on his bid, the auctioneer is left with a salvage value K.
However, I assume that by paying the screening cost, I
0, this risk can be eliminated:
Assumption (i): (Screening Technology) If the screening cost, I ; is paid, then all bidders
that have a positive probability of defaulting are identi…ed and disquali…ed.26
The main result is Proposition 4, which shows that the AB with screening is never optimal
but that the ranking of the other formats depends on the value of the screening cost, I; and
the salvage value, K. Characterizing bidders’behavior in the four formats is the …rst step.
26
Therefore, this assumptions says two di¤erent things. First, the screening is "perfect", in the sense that
all risky bidders are identi…ed. Second, all risky bidders are disquali…ed. A high cost of default is what may
induce the auctioneer to disqualify some bidders, despite the associated decrease in bidders’competition.
14
4.1
Firms’bidding behavior under the four auction formats
Bidders compete to win the object, knowing what auction format was chosen by the auctioneer. The winner has the option to default on his bid but, in that case, his payo¤ is
equal to a penalty,
p
0; that he pays. The reason why defaulting might be valuable is
that, at the bidding stage, the object’s value is uncertain. For any bidder i with probability
); the value of the good is vi = y + xi ; while with probability ; 0 <
(1
is vi
< 1; the value
"; 0 < " < y: One part of the valuation, xi , is only privately observed by bidder i,
while the other part, y; is commonly observed by all bidders. Likewise, " and
are constants
known to all bidders. There are N risk-neutral bidders, and this is common knowledge.
Figure 5: Game Timeline
The game timeline is reported in Figure 5. Its analysis employs the assumptions below:
Assumption (ii): (Asymmetric Bidders) There are two types of bidders, L and H, who
face di¤erent penalties for defaulting. There are nH > 2 bidders of type H, who pay a large
penalty ( pH ), and nL = N
nL bidders of type L, who pay a low penalty ( pL ), pH > pL
0:
Types are observable to all bidders and also to the auctioneer if she pays the screening cost.
Assumption (iii): (Values’ Independence) For any bidder i of type j = fL; Hg the
private, xij , and the commonly observed, y, components of the valuation are realizations of
random variables Xj and Y independently distributed according to joint density:
F (y; x1L ; :::; xnL L ; x1H ; :::; xnH H ) = FY (y)
nL
i=1 FXL (xiL )
nH
j=1 FXH (xjH );
where FY ; FXL ; FXH are the marginal distributions of Y; XL and XL . FY and FXj are absolutely continuous, have support respectively on [y ; y]; [xj ; xj ]; where y
and 0
0; y < y; xj < xj
xj < 1: The density function of Xj is C 1 and strictly positive on [xj ; xj ]:
Assumption (iv): (Reservation Price) There is a reservation price, R = 0, which is not
binding but ensures non-negative bids.
15
Assumption (ii) serves to simplify the analysis, while the other two assumptions will be
needed for the econometric analysis. Provided with the setup described above, it is possible
to characterize bidders’behavior. First of all, situations in which the winner declares himself
insolvent even if the value of the object is high can be disregarded.27 Therefore, the expected
payo¤ for a bidder of type j = fL; Hg; who has a value v = y + x and chooses a bidding
strategy bj ; can be written as
[(1
)(y + x
bj ) + maxf pj ; y + x
"
bj g] Pr(winjbj ):
An assumption regarding the size of the penalties greatly simpli…es the analysis without
making it trivial. First a lemma and then the assumption:
Lemma 1. Assuming " > ( 1 1 )xL , then there exist pH and pL such that whenever
pH
"; bidders of type H neither play bH > y + xH
pH = y + xH
and whenever pL < pL = (1
)"
" nor ever default;
xL and the format is FP, bidders of type L ful…ll their
bids only if the object’s value is high.
Assumption (v): " > ( 1 1 )xL ; and the two types of bidders have p H >p H and p L <p L :
This implies that H types always ful…ll their bid, while L types do so exclusively when
the object’s value is high.28 Hence, the payo¤s in case of victory simplify to:
Type H: (1
)(y + xH
bH ) + (y + xH
Type L: (1
)(y + xL
bL ) + ( pL ) = (1
where A
(y
") and B
(y
1
"
bH ) = A + x H
)[B + xL
bL ]
bH
(1:a)
(1:b);
pL ):
Provided with these bidders’payo¤s, the type-symmetric Bayes-Nash equilibria (BNE)
for the four auction formats can be characterized. Throughout the paper I will focus on
this type of equilibrium, which consists for every bidder i of type j = fL; Hg in a function
bj : [y + xj ; y + xj ] ! R+ and a decision of whether to default if the value of the good is low;
these two elements together maximize i’s payo¤ conditional on the other bidders bidding bj :
27
They would entail playing a dominated strategy. Under the stated assumptions, if a bidder optimally
chooses to pay the penalty and not get the object when its value is high, then he must do so also when the
value is low. Therefore, the payo¤ of this strategy in case of victory is p
0. However, this strategy is
strictly dominated by bidding v "; which guarantees a payo¤ in case of victory of (1
)" > 0.
28
Therefore, in this environment the screening cost is a cost paid by the auctioneer to learn the bidder’s
type and its bene…t is to perfectly eliminate those bidders that may default.
16
1) First price auction with screening (F P1 ): Under Assumption (i), the bids of all
bidders with a positive probability of default are disquali…ed. Hence, the presence of L types
is irrelevant for H types,29 and there is a multiplicity of type-symmetric BNE, all having
type H bidders always ful…lling their bids and bidding as in a standard FP with nH bidders
according to the bidding function30 bFHP1 such that:31
bFHP1
Rx
H
xH
= A + [xH
FXH (u)nH
FXH (xH )nH
1 du
1
]
(2).
2) First price auction without screening (F P0 ): This is essentially an FP with
asymmetric bidders. Therefore, provided with one more assumption, the equilibria can be
characterized in Proposition 1 building on results from Maskin and Riley (2000):32
Assumption (vi): for every r<q with r and q belonging to [B; B + xL ];
FXL (r)
FXL (q)
<
FXH (r)
:
FXH (q)
Proposition 1. A type-symmetric equilibrium exists. In equilibrium, two cases are
possible: (a) if [(B
A) > (xH
xL )], then type L bidders always bid above the greatest
bid of type H bidders; (b) if 0 < (B
A) < (xH
xL ), then the bids distribution of type
L bidders dominates that of type H bidders, despite the fact that type L bidders shade their
value more than type H, bFHP0 (x) > bFL P0 (x).
Part (a) of the proposition means that if the low penalty gives the L bidders a large
advantage, they will always outbid the H bidders in equilibrium. In this case, the auctioneer’s
revenues depend only on the type L bidders. Part (b) of the proposition, instead, says that
if the advantage of type L over type H is not too big, then L bidders do not necessarily
win. However, H bidders are less likely to win because, despite the fact that they bid more
aggressively than type L do (bFHP0 (x) > bFL P0 (x)); their bid distribution is dominated.
29
The L types have a zero probability of winning: if they bid strictly less than y
"; they are not
eliminated but they cannot win; if they bid above that value, they are eliminated through the screening.
P1
30
The derivation of bF
is standard; see, for instance, Krishna (2002).
H
31
To complete the description of the BNE we need to specify the behavior of the type L bidders. One
P1
equilibria is the one in which the type L always bid the constant bid bF
= y
"; and default only
L
F P1
F P1
if the object’s value is low. Clearly, bH and bL are mutually best responses, but they are not the
unique equilibria. Other type-symmetric equilibria have di¤erent strategies for the L types (where they bid
P1
P1
bF
2 [0; A]). However, bF
is unique, and this is all that matters to determine revenues.
L
H
32
Notice also that Assumption (vi) is always veri…ed if marginals distributions and supports of the private
cost components are the same for the two types. In this case it is easy to verify that the distribution of
bidders’L valuation is just a rightward shift of the distribution of the H bidders.
17
3) Average bid auctions with screening (I_AB1 and S_AB1 ): The previous results
for the F P0 and F P1 auctions come from the literature, while the characterization of the
BNE of the AB auction is a contribution of this study. Results are presented for both the
Italian rule (I_AB), described in Section 2, and for a "simple" AB (S_AB), where the
bidder closest to the average (regardless of whether from above or from below) wins and
pays his own price.33 In all cases, ties are broken with a fair lottery. I begin the exposition
introducing two lemmas that characterize the equilibria in two simple environments in which
all bidders belong to the same type (so the subscripts L and H are dropped):
Lemma 2: Assume N > 2 ; p =1 (no defaults), " = y = 0 (no uncertainty and no
common element) and the reserve price is R = x. Then, for any N, the strategy pro…le
in which all players bid according to the constant bidding function b(x) = x for every
possible x is a symmetric BNE of the S_AB. Moreover, four properties characterize any
other symmetric BNE that might exist. The bidding function (1) is weakly increasing, (2)
is ‡at at the top, (3) has all types greater than the lowest one bidding strictly less than
their own value and (4) for any (absolutely continuous FX ) and 8 " > 0; 9 N";F such
that 8N
N
N(N
1
_
N";F the following is true: jv ";F
_
2
)[FV (v ";F )(1
1
_
_
xj < "; where v ";F is implicitly de…ned by
FV (v ";F )) 1 ] = 0:
Lemma 3: Assume N>2, p H =p L =1 and "=x=R=0 (no uncertainty, no privately obseved value and reserve price equal to zero). Then, for any N, the only symmetric equilibria
of the S_AB are those in which all the players bid the same constant, c, in the interval [0; y]:
The …rst part of Lemma 2 says that the strategy pro…le in which all bidders bid the
minimum acceptable bid is a BNE. The second part adds that any other symmetric BNE
that might exist lies close to this one, in the sense that the di¤erence between the highest
equilibrium bid and x can be made arbitrarily small by picking a large enough N.34 Lemma
3 says that when all bidders share the same value, a multiplicity of equilibria exist, but they
are all ‡at bidding functions. The equilibria of I_AB1 and S_AB1 follow from the lemmas:
33
This game has some of the features of the so-called p-mean games studied by Nagel (1995).
As N grows, the function describing the probability that N draws from FX are all greater than x,
(1 FX (x))N ; rapidly becomes more and more convex. This gives an incentive to reduce the bids toward x:
34
Moreover, bidding x is the unique equilibrium with N=2. The exact arguments are in the Appendix.
18
Proposition 2: Every strategy pro…le in which all bidders, regardless of their type and
their value, bid the same constant value c, where c 2 [0; minfA+xH ; B +xL ; y "+pL +xL g];
and always ful…ll their bid is a type-symmetric BNE of the S_AB 1 .
Proposition 3: In the I_AB 1 with nH > 4 ; there is a unique type-symmetric BNE. In
this equilibrium, all bidders submit the minimum bid, b =R = 0, and never default.
4) Average bid auctions without screening (I_AB0 and S_AB0 ): For the I_AB 0 ;
the equilibrium is the same of the I_AB 1 . For S_AB 0 , instead, the set of type-symmetric
BNE on which I focus is such that all bidders, regardless of their type and value, bid the
same constant value c, where c 2 [0; minfA + xH ; B + xL g]: Moreover, type H never defaults,
while type L does so only if x < (y + pL
"
c) and the object’s value is low.
Discussion of the AB auctions equilibria: First of all, the results indicate that
AB auctions are ine¢ cient: they induce a pooling of bids, transforming the auction into
a lottery. The equilibrium allocation of the I_AB is equivalent to a random allocation at
the minimum price. The S_AB is, instead, equivalent to random allocation at a random
price. As regards revenues, AB auctions lower the winning price relative to FP auctions.
Moreover, the auctioneer’s worst scenario, all bids equal to the reserve price, is an equilibrium
of both I_AB0 and S_AB0 . However, this is not the same as revenue minimization, because
the cost of defaults also needs to be considered. AB formats reduce defaults both because
they randomize across all bidders, so that type L have no advantages, and because, by
eliminating competition, they reward the winner with a higher payo¤, making him less likely
to default. Nevertheless, they seem a suboptimal mechanism and one wonders the reason for
their widespread use. One possible explanation is that, as shown by Chillemi and Mezzetti
(2010), when the auctioneer faces a high cost of default and cannot eliminate those bidders
that might optimally decide to default, then a random lottery is the optimal mechanism.
The AB rule, indeed, induces a lottery in equilibrium. The other possible reason for the use
of AB auctions is that the equlibrium prediction of identical and low bids is too vulnerable
to collusion to hold in practice. Indeed, Conley and Decarolis (2010) study collusion in
AB auctions and describe various cases where competition among multiple cartels generated
better revenues for the auctioneer than those predicted by the competitive benchmark.
19
4.2
Revenue ranking of the auction formats
It is now possible to analyze the auctioneer’s expected revenues under the di¤erent auction
formats. The following proposition is the main theoretical result:
Proposition 4: The expected revenues under the AB auctions with monitoring are
strictly dominated by those of the FP with monitoring, E[RF P1 ] > E[RS_AB1 ]
E[RI_AB1 ]:
Without knowledge of I and K , the pairwise ranking of the expected revenues of the FP with
monitoring, E[RF P1 ]; of the FP without monitoring, E[RF P0 ], of the I_AB without monitoring, E[RI_AB0 ], and of the S_AB without monitoring, E[RS_AB0 ], are not determined.
The rationale for the …rst part of the proposition is straightforward. Once the screening
cost is paid, no default can occur, so it is strictly better to use F P1 ; which fosters competition
among bidders. Moreover, the simple AB is weakly better than the Italian AB, because in
the I_AB1 all bidders always bid the minimum bid, while in the S_AB1 there are equilibria
in which bidders bid strictly more than the minimum. The idea of the second part of
the proposition is that there is always a value of K such that defaults are so costly for
the auctioneer that the …rst price without screening cannot be the preferred mechanism.
Analogously, there is always a value of I such that screening is so costly that the …rst price
with screening cannot be the preferred mechanism. Therefore, there are combinations of high
screening cost and high default cost for which the AB0 formats are better than F P0 and F P1 .
Finally, without knowledge of K; it is not even possible to rank I_AB0 and S_AB0 ; since
with S_AB0 the probability of default, albeit small, is greater than with I_AB0 . Overall,
Proposition 4 gives a clear guideline on which formats the Italian PA may use and why.
5
Data
For this research I collected a new set of data on public procurement auctions, which are
alternately run under the Italian version of the AB rule or under the FP rule. Variations in
auction format are rare and, hence, these data are rather unique. Moreover, to my knowledge
there are no other empirical studies of the AB auctions. I grouped data into two samples.
20
1) The IE sample: The …rst sample contains all the AB and voluntary FP auctions for
road construction works (mostly pavings and roundabouts) worth less than e2.5 million held
between November 2005 and December 2009 by counties and municipalities in …ve regions
in the North of Italy (Piedmont, Lombardy, Veneto, Emilia and Liguria). It contains all
the bids and bidders’ identities and it is part of a broader dataset containing information
on all Italian public procurement auctions for works that I bought from an "information
entrepreneur," or IE.35 Table 4 reports the summary statistics.36 They indicate that FP
auctions attract less bidders: on average 9 compared to 57 in the AB. On the other hand,
in the FP sample the winning discount, the reserve price and the measures of the size of
the PA are greater than their counterparts in the AB sample. Moreover, in the AB auctions
both the average winning discount and its standard deviation are not zero as required by the
equilibrium behavior described before. These issues will be addressed in the next section.
2) The Authority sample: The second sample is obtained by applying the PA/contract
…lters of the IE sample to the database of the Observatory of the Italian Authority for Public
Contracts, which contains information on the life of all public contracts above e150,000. The
earliest auctions in this sample are from the year 2000, while the latest are from January 2008.
Compared to the IE sample, the Authority sample does not contain the bid and identity of all
the bidders, but it contains ex post information on the auctioned contracts (like the amount
of renegotiation and whether a default occurred). Several summary statistics are reported
in Table 5. Unfortunately, since the …rst national reform dates from July 2006, the complete
ex post information is available only for few post-reform auctions. However, the interesting
feature of this sample is that two of the biggest PA of the Piedmont region, the county and
municipality of Turin, had already switched to the FP in 2003.37 This implies that many of
the jobs they procured were completed by the end date of the sample. The auctions held by
Turin are, thus, the core of my analysis of bidders’ex post behavior in FP auctions.
35
An IE is a private …rm that sells to bidders information about both forthcoming and awarded auctions.
The IE sample does not contain the FP auctions of the PA that were "forced" to use the FP rule by the
2008 reform (i.e., auctions for contracts above e1 million held after October 2008 by those PA that always
choose the AB when it is allowed). In the next section I will explain how I used these extra auctions.
37
The o¢ cial reasons put forward by Turin to explain its choice were that under the AB rule participation
was rising, but all bids were always converging to the same discount and that collusion was widespread (see
Conley and Decarolis, 2010). Moreover, it may also be the case that the increased number of works needed
for the winter Olympics of 2006 implied a lower per-auction cost of the screening technology.
36
21
Various other data have been collected for this analysis. In particular, detailed …rms’
…nancial and ownership data were obtained from the Bank of Italy. Moreover, data on
characteristics of the PA were obtained from the ISTAT (Italy’s national statistical institute).
The Web Appendix gives further details about all the data used.
Finally, since the reserve price will play an important role in my analysis, it is worth
discussing here. In the auctions that I analyze, the PA are not in full control of the reserve
price. The PA’s engineers evaluate the types and quantities of inputs needed to complete a
project. However, prices for inputs are set every year by the regions, and the counties and
municipalities must adhere to them. Indeed, the similarity of these prices in the northern
regions has been one of the reasons why I have focused my analysis on them.38 Furthermore,
38
The analysis of the data from all Italy (not reported) shows that often in the South the winning discounts
are much higher than in the North. The reason appears to lie in input prices posted by the regions.
22
in the case of simple roadwork jobs, it seems plausible to assume that there is not too much
discretion in the type and quantity of inputs to use. The technology of the work determines
them. Therefore, since the geographical area that I study is rather homogeneous, similar
roadwork jobs likely require the same types and quantities of inputs in all the PA in my
sample. In light of this reasoning, I assume that the reserve price is not in the hands of
the single auctioneer and that the reserve prices of di¤erent PA are drawn from the same
distributions. Finally, regarding the assumption that the reserve price is not binding, I found
overwhelming support for this assumption from market participants (both PA and …rms),
who explain this fact with the in‡ated prices that regions post. Moreover, as the summary
statistics clearly illustrate, there is very broad participation at AB auctions. This may be
seen as an indication that even ine¢ cient …rms have a positive expected payo¤ conditional
on winning the auction at the reserve price. On the other hand, the low participation in
FP auctions is associated with winning discounts frequently around 40% or above. The last
point that is worth noting is that PA cannot set the reserve price in a di¤erent way on the
basis of the auction format chosen. This should be clear from the description given above
of how the reserve price is set. However, this is also con…rmed by a regression analysis
(not reported) of the reserve price on a list of regressors including the FP dummy. For this
dummy, no statistically signi…cant e¤ect is detected.
6
Reduced Form Analysis
One of the main objectives of this paper is to study the e¤ect of AB and FP on revenues.
Since the payments made by the PA to the contractor are observable, the policy changes
of 2006 and 2008 represent a unique source of variation to study how a switch from AB
to FP a¤ects this component of the PA’s revenues. Although the analysis will draw on
both reforms, the 2008 one is rather recent, and the number of available auctions is limited.
For the 2006 reform, instead, although data are available, the self-selection into the format
complicates the identi…cation of a causal e¤ect. I will …rst explain how this latter di¢ culty
has been addressed, then I will show the main results, and, …nally, I will discuss them.
23
Empirical Strategy: The idea developed in the previous sections that the choice of
the auction format is linked to the amount of the monitoring cost is used to address the
endogeneity issue. The PA size is taken as a proxy for its monitoring cost and used as the
selection rule. Data from both the Authority and the IE samples are used. As regards the
Authority sample, the analysis is based on a di¤erence-in-di¤erences (DinD) model:
Yist = As + Bt + cXist + F Pst + "ist
The objective is to estimate ; the e¤ect of a dummy equal to one for FP auctions on
the dependent variable Y, conditional on dummy variables for auctioneers (A) and time
(B) and on other covariates (X). As explained in Section 5, the FP auctions in this sample
are those held by Turin after 2003. In light of the role the PA size plays in the 2006 reform, I constructed the control group for the DinD model by selecting only administrations
similar to Turin in terms of size. Results with three di¤erent control groups are reported.39
Figure 6: Winning Bid Densities
Treated Group (County & Municipality Turin)
Untreated Group (Other Large Piedmont PA)
Figure 6 illustrates, for the case of the winning discount, Bw ; the type of variation that
the DinD model captures: the di¤erence in the average Bw in Turin before and after the
switch to FP is compared to the di¤erence in the average Bw before and after 2003 for a
comparable group of PA that always used AB. The basic idea is that, were these PA to
switch to FP, they would experience the average change in Bw of Turin. However, I o¤er a
quali…cation of this interpretation after all the results are presented. In particular, I focus on
three sets of results: i) a robustness check of the e¤ect on Bw based on both the IE dataset
and the 2008 reform; ii) the analysis …rms’bidding in AB; and iii) the analysis of screening.
39
Three control groups are employed: i) the PA that have a population greater than 500,000 people; ii)
the PA that in the sample have more than 200 auctions; and iii) the PA in the same region of Turin that
have a population greater than 50,000. The latter group is employed in the right panel of Figure 6.
24
Results: The E¤ect of the Two Auction Formats on Revenues
The approach illustrated above is employed to estimate of the e¤ect of the transition from
AB to FP auctions on both the winning discount, Bw ; and the ex post renegotiation. Renegotiation is measured as the di¤erence between the winning price and the …nal price and it
is expressed as a percentage of the original reserve price.40 Table 6 presents the results for
the Authority sample of the DinD estimates. The results are similar across the three control
groups used. Although the winning discount increases, the same is true for the renegotiation,
so that the net e¤ect is a saving between 3% and 5% of the reserve price.41 This does not
seem to be a large saving, especially given that the FP may entail a screening cost and that
renegotiation may generate some transaction costs. Indeed, the presence of screening is likely
as both the lack of defaults and the other evidence provided below shows.42
Table 6: DinD Estimates of Winning Bids and Renegotiations
It is possible to check the robustness of the estimates of the e¤ect of FP on Bw using the
IE sample. Table 7 reports the results of two standard methods: a propensity score matching
(PSM) and a Heckman selection model (HSM). In both cases, I use a probit based on the PA
size to control for sample selection. The left panel of Table 7 presents the probit regression
used to form the score.43 Only auctions with a score in [.025, .975] are then used to generate
the nonparametric PSM estimates. Instead, for the HSM, I use the whole IE sample. In
this case, the probit regression is the …rst step of a two-step parametric procedure. Hence,
40
In my database, the …nal price is measured with error. In the Web Appendix, I brie‡y describe results
using other measurements as proxy for the true …nal cost of procurement.
41
Moreover, results not reported here indicate that there is no statistically signi…cant association between
the change in the auction format and the ex post changes in the number of days taken to complete the work.
42
In particular, in the entire Authority sample there is no single bankruptcy case associated with FP and
only 12 defaults out of the 17,000 contracts auctioned with AB. Looking at the whole Observatory dataset,
defaults appear to be a characteristic only of the very expensive contracts not included in my samples.
43
Although the Probit dependent variable is the same as in in Table 3, here only the IE dataset is used.
For Table 3, instead, data for the whole country is used to assess, for instance, the relevance of corruption.
25
it is useful to compare the results of these two estimators that achieve identi…cation under
di¤erent assumptions. The right panel of Table 7 shows the results, including those of the
OLS for comparison. The estimates indicate for the FP dummy a positive and signi…cant
e¤ect larger than that of the DinD, and ranging between 11% and 15% of the reserve price.
TABLE 7: OLS, PSE and HSM Estimates of the Winning Discount
The last result uses the 2008 reform to address the endogeneity concern in a di¤erent
way. Under the assumption that the auctioneer is not in control of the reserve price, a sharp
regression discontinuity design (RDD) could be used. Unfortunately, my sample of auctions
worth more than e1 million and held after this reform has only 30 observations. Hence, the
RDD is used only as a robustness check for the other results. Despite the limited relevance
due to the small sample size, it is encouraging to see that the estimated e¤ect of FP is an
increase of Bw of 9.7 points, which closely resembles those obtained with the other methods:
Bwi =
+ Di + R i + "i
=9.7 (3.7) ; R2 = :24; Obs.=129 (30 with D=1),
where Ri is the reserve price and Di = 1 if Ri > e1 million and Di = 0 otherwise. This result
is una¤ected by the use of higher order polynomials, which are not statistically signi…cant.
Other Results: Firms’Bidding and Auctioneers’Screening Behavior
The next two sets of results clarify the mechanism through which the auction formats generated the observed e¤ects on the revenues and set the basis for the analysis of e¢ ciency.
26
1) Bidding Behavior in AB and FP - For the AB auctions, the summary statistics of
Section 5 already showed that the prediction of all bids equal to zero is violated. Figure
7 illustrates this point by showing that for the AB auctions (dashed lines): i) the highest
bid is systematically larger than the winning bid and ii) the winning bid, although almost
identical to the next highest bid (i.e. the 2’ranked bid), is almost always greater than zero.
As regards the FP auctions, the highest bid and the winning one are not always identical,
because for a small fraction of auctions the highest bid is eliminated. A possible evidence
of screening. Moreover, a large di¤erence between the winning bid and the 2’ranked bid is
observed. This is generally taken as an indication of the presence of private information.
Figure 7: Distribution of the Highest, Winning and 2nd-Ranked Bids in AB and FP
To understand what may determine the substantial within-auction variation in the bids,
Table 8 reports the results of OLS regressions for a standard reduced form speci…cation of the
bidding function (see Bajari et al., 2007). The IE sample is divided into two samples: one of
FP and one of AB auctions. The dependent variable is the discount o¤ered by every bidder
in every auction. The results in the …rst three columns for the FP sample resemble those in
the literature. For instance, a greater distance between the …rm and the site of the work,
generally considered a proxy for the private cost, lowers the discount o¤ered.44 However, the
results in the last three columns for the AB auctions show that, without …xed e¤ects, the
proxy for the private cost has the "wrong" sign. With …xed e¤ects, the coe¢ cient becomes
statistically insigni…cant. In general, the estimates for the two samples are very di¤erent and,
in the AB case, none of the covariates matter once the …xed e¤ects are included. Therefore,
for the AB auctions neither bids conform to the theoretical model, nor do they respond to
44
The result is una¤ected by the inclusions of …rm-speci…c (a limited liability dummy and the level of capitalization) or contract-speci…c (the reserve price, the duration and the number of tasks) controls. However,
the coe¢ cient loses its signi…cance in the speci…cation with the auction …xed e¤ects, possibly indicating that
the common cost component prevails over the idiosyncratic one (more on this in Section 7).
27
cost factors like the bids in FP auctions do. Thus, how do …rms in AB auctions bid?
The surprising answer consistently given by the market participants is that bidding is
a randomization around a "focal value" speci…c to each PA and work type. That is, both
…rms and PA know that each PA gets "stuck" at a certain value on which most of the bids
converge. An example will clarify this point. All of Sicily is "stuck" at a winning discount
of 7.3xx. That is, a …rm that wants to win a public contract has only to decide the few
decimals it wants to add to the 7.3 discount. The …rm already knows that all other bidders
are doing the same and, hence, converging to 7.3 is the only way to be close to the average.
That this "rule of thumb" works …ne is supported by the following OLS regression estimated
w
using the AB auctions in the Authority sample: Biad
=
w
w
Xiad + Biad
+ "iad : Biad
is the
w
winning discount in auction i held by the auctioneer a at time d: Instead, Biad
; is a proxy
for the focal value: it is the average of all winning discounts in auctions held by a in the 365
days before auction i for contracts of the same type of i (and similar reserve price). Although
the rule of thumb suggests
= 1; the estimates obtained are rather close, albeit not identical:
where Z contains the reserve price, the number of bids and dummies for type of PA and of
w
w
contract. Moreover, Biad
explains a large fraction of the variation of Biad
. Therefore, this
rule of thumb o¤ers a simple way to estimate the expected revenues of an auctioneer whenever
28
she has a history of AB auctions. As regards the within-auction variation in bids, instead, I
defer the discussion to Section 7, where I discuss results on …rms collusion in AB auctions.
2) The Auctioneer’s Decision to Screen Bids - There are several indications that screening
in FP auctions occurs. First, it has been mentioned in Section 2 that the policy changes had
explicitely required to conduct FP with screening. Indeed, in the IE sample, in about 10%
of the FP auctions the highest bid is excluded (see also Figure 7), while this never occurs
in AB. A similar result is also true for the auctions held by Turin after its 2003 reform.
Moreover, using the DinD approach, it is possible to identify an increase of about 14 days in
the time that it takes to award the contract (after the bids are opened) associated with the
FP. This extra time may be justi…ed as the time needed for an attentive ex post screening.
Finally, two more results suggests that FP bids are screened.
2.1) Winners’ optimal default decision: No defaults are observed in FP auctions. However, to the extent that renegotiations re‡ect the auctioneer’s concessions when the threat of
bankruptcy is credible, then a renegotiation should occur in equilibrium only when the …rm
is a low-penalty type. Therefore, if the FP auctions in my sample were without screening,
the data should reveal a positive probability of a renegotiation conditional on a victory by
a low-penalty bidder and no renegotiation at all conditional on a victory by a high-penalty
bidder. To test this key prediction, I collected data on …rms’budgets from Infocamere (the
database of the Italian Registry of Firms in the version managed by the Bank of Italy).
However, the result indicates that the same amount of renegotiation takes place regardless
of the size of the penalty of the winner. The picture below shows this result for the case in
which the …rm’s underwritten capital is taken as a measure of the penalty.
Figure 8: Contract Renegotiations
29
I consider a winner as "low budget" if his underwritten capital is less than the di¤erence
between the auction’s reserve price and his bid.45 A "high-budget" winner is one that is
not "low-budget." Although the average renegotiation of low-budget winners exceeds that
of high-budget winners the di¤erence is not statistically signi…cant. Moreover, I tried operationalizing the idea of high/low penalty bidders with numerous other possible measures of
the …rm’s own in‡icted damages in case of default. However, also with these other measures,
I was not able to identify any signi…cant di¤erence in the behavior of the two groups.46
2.2) Drop in the number of bidders: The switch toward FP is associated with a striking
drop in bidders’participation. Table 9 presents estimates of a negative binomial model for
the e¤ect of the switch from AB to FP on participation.47 The result is a reduction of about
40 bidders per auction. Although this is clearly compatible with an e¤ective screening of
bids, the interpretation is rather complex, since regards not only the screening but also the
end of forms of collusion speci…c to AB and the exit of ine¢ cient …rms due to competition
in FP. Conley and Decarolis (2010) study these issues in greater detail.
Discussion of the results: Overall, these latter …ndings allow us to qualify the interpretation of the DinD estimates. The coe¢ cient
45
in the Bw regression captures ( BwT urin
In the model of Section 4, this means that if the shock hits the cost of completing the job is R.
I also tested these behavioral implications using di¤erent concepts of penalty, but the result was always
the same. For instance, I explained in Section 2 why the distance from the auctioneer could be used to divide
bidders into high/low penalty categories. However, as with the capitalization, I could not detect signi…cant
di¤erences in the renegotiation behavior conditional on the distance between the winner and the PA.
47
The variable measuring the number of bidders in both my samples is highly not normal (the skewness
and kurtosis are respectively much greater than zero and three). Hence, a negative binomial regression
model with robust standard errors is used. The negative binomial model is preferred to a Poisson regression
because the variance of the number of bidders variable is quite a bit larger than its mean, and the estimated
coe¢ cient on dispersion in the negative binomial model is statistically di¤erent from zero.
46
30
BwControl ). However, the focal bid argument suggests that
BwControl should equal zero if
the control group contains auctions of the same PA. Moreover,
BwT urin should equal the
di¤erence between the average Bw in FP and the focal bid of Turin, which is about 18%.
Therefore, the magnitude of
depends crucially on the focal bid of the treated PA. Since
the average focal bid in the two samples is between 12% and 15%, it seems plausible that
the switch to FP may generate a larger
BwT reated relative to that occurred in Turin. In-
deed, the larger PSM and HSM estimates are in part capturing this e¤ect. Nevertheless,
not all the increase in Bw (net of renegotiations) translates into savings. Since FP occurr
with screening, my estimates can be interpreted as a measure of the saving possible if this
screening cost were negligible for the single PA. Section 7 and 8 develop further this issue.
7
Structural Analysis
The usefulness of a structural analysis is that it allows us to infer …rms’unobservable costs
from their observed bids. Estimating these costs is essential to evaluate the e¤ect of the
auction formats on e¢ ciency and hence to complete the comparison of their performance.
However, the caveat of the analysis I present is that only FP auctions are used to estimate
…rms’costs. The problem with the bids of AB auctions is that they cannot be related in a
clear way to the corresponding costs since, when …rms compete, all bids should be the same
regardless of the cost (Proposition 3 of the model). Moreover, results in Section 6 suggest the
presence of rather complex forms behavior associated with bids’randomization and bidders’
collusion. On the contrary, the reduced form analysis suggests that the FP auctions in the
sample are likely to be FP plus screening, and for these auctions there is a clear thoretical
prediction regarding how costs are related to bids. Therefore, only the subsample of FP
auctions is used to recover the costs, and two assumptions are maintained: i) that the FP
auctions are with screening;48 and ii) that bidders compete in these auctions.49
48
Moreover, since type L bidders are irrelevant in F P1 auctions, I will assume that all valid bids submitted
are by type H bidders. Evidence consistent with this assumption is reported in the Web Appendix, where it
is shown that FP bidders are bigger than AB bidders in terms of capital, workforce, pro…ts and revenues.
49
The combined results of the reduced form bidding function, the drop in participation and the aggressive
discounts o¤ered seem compatible with the assumption of competitive behavior in these auctions.
31
The method that I use to estimate the underlying bidders’ costs in the sample of FP
auctions is based on the extension by Krasnokutskaya (2009) of the fundamental result of
Guerre, Perrigne and Vuong (2000; GPV from now on) that the …rst order condition of a
bidder’s problem can be expressed in terms of observables. In essence, Krasnokutskaya’s
approach allows one to recover the underlying distributions of both the private and the
commonly observed components of …rms’ costs from observed bids. These distributions
can then be used to measure the ine¢ ciency produced by AB auctions using the FP as the
e¢ cient benchmark. In this Section, I will …rst discuss identi…cation and estimation and then
present the results. However, since the details of the methodology are throughly explained
by Krasnokutskaya (2009) and by Asker (2010),50 my presentation of both identi…cation and
estimation is kept short and non technical, stressing the few departures from their method.51
7.1
Outline of the Method: Identi…cation and Estimation
Identi…cation: First, it will be convenient to adopt the standard notation of procurement.
Therefore, relabelling as cost what was de…ned in Section 4 as value, the …rm cost is C = x+A
and the payo¤ in case of victory is (b x A): The identi…cation problem consists in whether
it is possible to separately back out the distributions of both the privately, x; and the
commonly, A; observed components of costs from bids, b(C). Essentially, this is a matter of
unobserved auction heterogeneity, where bidders observe A but the econometrician observes
only realizations of b(C).52 My solution to this problem follows that based on deconvolution
methods proposed by Krasnokutskaya (2009).53 Using U.S. data, her study showed that
unobserved heterogeneity is a crucial feature of auctions for roadwork contracts.
As a preliminary step, since the …ndings of Section 5 revealed the presence of systematic
renegotiations, the expected payo¤ is modi…ed to account for that. I abstain from modeling the bargaining process behind the renegotiation and assume that all bidders expect to
50
Asker (2009) analyses collusion in stamp auctions applying the method of Krasnokutskaya (2009).
The techincal details of the method are fully illustrated in the Web Appendix accompanying this paper.
52
A di¤erent approach, based on control function methods, is used by Roberts (2009) to deal with unobserved heterogeneity in auctions for which only data on the winning bid and the reserve price are available.
53
The …rst paper to propose the use of deconvolution was Li and Vuong (1998) in the context of a classical
measurement error problem. The …rst application to auctions is by Li, Perrigne and Vuong (2000).
51
32
renegotiate a constant fraction
bFHP1
= (A
2 (0; 1) of the reserve price, R.54 Equation (2) becomes:
R) + [xH +
R x_
H
xH [1
FXH (u)]nH
[1 FXH (xH )nH
1 du
1]
]
(2’)
Assuming that …rms bid according to (2’) and that the econometrician observes , R and
_
the winning bid, B w , for a sample of auctions, then results in Krasnokutskaya (2009) can be
applied with minor changes to show identi…cation of the distributions of x and A. First of all,
the knowledge of
and R permits to purge the bids of the expected renegotiation, R: Then,
_
the invariance of the equilibrium to a shift factor is used to establish that B w = A + Bw ;
where Bw is the equilibrium bid with A = 0. If A or Bw were known, the strict monotonicity
of the equilibrium bids in the private costs would allow us to apply the standard GPV method
to recover the distributiion of x. However, neither Bw nor A are observed separately.
Krasnokutskaya’solution to this problem takes advantage of the variation of bids both
across auctions and within the same auction. However, because of limitations in my data, I
take the alternative approach of relying on the within-auction variation between the winning
bid and the reserve price. In particular, I assume that the reserve price has a separable
structure, R = A + Xr ; where Xr , A and x are all independent of each other.55 Under
separability and independence,56 it becomes possible to apply a result due to Kotlarsky
(1966), which leads to the identi…cation of the characteristic functions of A; Bw and Xr from
_
the joint characteristic function of B w and R.57 This joint characteristic function is in turn
_
identi…ed nonparametrically from the observed data (B w ; R). Once the distribution of Bw
is recovered it can be used to simulate a sample of pseudo-winning-bids, and the variation
across these bids is what identi…es the distribution of x as in the standard GPV framework.
The Web Appendix gives further details and presents a comparison of my method using
R to the standard one for a small sample of 2-bidder auctions for which I have all the bids.
54
This assumption seems compatible with the results on renegotiation reported at point 2.1 in Section 6.
The rationale behind this assumption is that the auctioneer observes what all the bidders commonly observe, A. To form R she adds to A a (very in‡ated) measure of the private cost which is drawn independently
from x, possibly because of the completely di¤erent price list used, as seen in Section 5. The usefulness
of
_
this assumption is that it allows addressing unobserved hetherogeneity even with very sparse data: (B w ; R).
Its limitation is that, in many settings, it might be more restrictive than that of Krasnokutskaya (2009).
56
A recent study by Hu, McAdams and Shum (2009) illustrates that neither independence of all the
components nor separability are essential for the identi…cation argument when more information is available.
57
This is possible under a normalization that …xes the location of one of the distributions; I use E(Bw ) = 0.
55
33
l0
m
0
Estimation:The data consist of m auctions, for which (ni ; bw
i ; bi ; ; Ri; zi )i=1 are recorl
ded: ni is the number of bidders, bw
i is the winning bid, bi is the last classi…ed bid (i.e., the
highest price o¤ered),
is the average fraction of the reserve price that is renegotiated, Ri
is the reserve price and zi is a vector of auction characteristics. The estimation procedure
described below is for the case of a subsample with ni = n0 and zi = z0 : The estimation
method closely follows the identi…cation procedure and consists of the following steps:58
1) Accounting for expected renegotiation: For every auction i; the value Ri is added to
l0
w
l
0
both bw
i and bi : The resulting bids are indicated respectively with bi and bi :
2) Estimation of the distributions of the common and idiosyncratic components of bids:
First of all, the joint characteristic function of a winning bid and the relative auction’s reserve
^
P
w
price is estimated nonparametrically using:
(t1 ; t2 ) = m1 m
j=1 exp(it1 bj + it2 rj );
where i denotes the imaginary number. Then, the result of Kotlarski (1966) is exploited to-
gether with the normalization and independence assumptions to estimate the characteristic
functions of the common and idiosyncratic components of bids. Finally, the estimated densities of A, Bw and Xr are obtained through an inverse Fourier transformation.59
3) Estimating the distribution of the idiosyncratic component of …rms’cost: This step involves constructing a sample of size M of pseudo-winning-bids, Bws ; from the estimated density of Bw . Then a nonparametric estimation of the cdf and the pdf of these bids is obtained
using, respectively, the empirical analog of the cdf and the triweight kernel desnsity estimator suggested by GPV. With these estimates available, a sample of pseudo costs of the winner, Xws , can be generated as Xws = [Bws
(1
^
F B s (Bws ))=((N
^
1)f B s (Bws ))]:
Finally, with this sample of pseudo winners’costs, the distribution of Xw can be nonparametrically estimated. Moreover, since the winners’cost is the lowest order statistic of the
costs, then by properties of the order statistics the distribution of x can also be estimated.
The following results on e¢ ciency are based on the estimated distributions of A and x.
58
The whole procedure could be preceded by an homogenization (see Haile et al., 2006) of the bids to
remove observed heterogeneity. This assumes that the hetherogeneity a¤ects the bids in a separable way.
Instead, I found it preferable to select a sample that, albeit small, contains only observably similar auctions.
59
One problem of the above procedure is that the estimated densities are imprecise at the endpoint of the
support. As explained in the Web Appendix, the solution adopted follows that of Krasnokutskaya (2009)
and requires the observability of the last classi…ed bid, which, instead, was not required for the identi…cation.
34
7.2
Results
The data used for this analysis are a subset of auctions chosen to be particularly homogeneous. Their reserve price is between e500,000 and e1 million, and they were held by Turin
at least one year after its switch to FP. This choice avoids using bids submitted by …rms
inexperienced with the FP, for which the assumption of equilibrium bidding would be less
credible. Table 10 reports the summary statistics by the number of bidders (values are in
e/100,000). The limit of this strategy is twofold. First of all, the small sample size leads to
noisy estimates. To address this issue, I present results obtained performing Step 2 of the
estimation routine with di¤erent deconvolution estimatiors: the Li and Vuong (1998) estimator (L-V) used by Krasnokutskaya and the Bonhomme and Robin (2009) estimator (B-R).
The conditions for identi…cation are slightly di¤erent and, for some families of distributions,
the latter estimator performs well in small samples. Figure 9 reports the model …t for both
estimators using auctions with 6 bidders. The second limit regards the relevance of results
based on a single PA. However, not only is Turin one of the largest and most economically
relevant PA but, more importantly, because of the similar regulation and the mature technology, the structure of …rms’costs that is revealed is likely similar to that prevalent among
the other …rms bidding in FP auctions througout the …ve northern regions analyzed.
Table 10: Summary Statistics - Structural Analysis Sample
Figure 9: Fit of the Model - Bootstrap con…dence interval 5% and 95%
35
1) E¢ ciency of the two formats: The FP rule under which the distributions of x and
A are estimated is an e¢ cient mechanism. The AB, instead, is equivalent to a random
allocation, and hence it can be e¢ cient only in the trivial case in which the whole variation
in costs is due only to A. However, my estimates60 indicate that about 35% of the variation
in the total cost is due to x.61 Another way to measure the e¢ ciency loss is to simulate T
auctions and compare the total …rms’costs under the two formats. Assuming that there are
N bidders, then when the format is FP, the total cost is the sum of the lowest of the N costs
realized in each of the T auctions. Instead, for the same T auctions, when the format is AB,
the total cost is calculated by picking randomly a cost out of the N simulated for each auction
and summing them up. Table 11 reports the results obtained averaging over 100 simulations
with N=6 and T=5, 100. The di¤erence between the …rst and third columns (or between the
second and fourth) is a measure of the waste produced by the AB. For a PA like Turin that
runs about 100 auctions per year both estimates indicate that the extra cost of using the AB
relative to the FP auction is about e8.5 million. This corresponds to approximately 12% of
the reserve price. Since at country level about 10,000 AB auctions for a cumulative reseve
price of e6 million are held every year, the potential waste is huge. However, this result has
two caveats. On the one hand, since many ine¢ cient bidders participate only in AB auctions,
the e¢ cency loss may be underestimated. On the other hand, Conley and Decarolis (2010)
document that …rms partly correct this ine¢ ciency through the use of subcontracts and even
through collusion. The fraction of the contract that the winner subcontracts is signi…cantly
higher in AB than in FP auctions. However, in the contracts analyzed here the legal limit to
subcontracts is about 51% of the total value. As regards collusion, the evidence from known
cartels indicates that they often tilt the probability of winning AB auctions in favor of those
local …rms that are the ones most likely to have a low private cost.
60
Reported results use data on auctions with N=6 bidders. Other values of N generate comparable results.
The decomposition V (C) = V (x)+V (A) uses x ? A. Krasnokutskaya’s analogous calculation, conducted
under the assumption C = xA; indicates that x accounts for 14% of the total cost variation in her data.
61
36
2) Auctioneer’s Revenues: The same simulation method illustrated above can be used
to calculate the total cost of procurement as the sum of the winning prices of T auctions.
For the FP auctions, once the winners’ costs are determined, they can be converted into
the corresponding equilibrium bids. For AB, using the same T draws from the distribution
of A; T reserve prices are simulated, and then the total cost is computed by applying to
them a "focal discount" (net of renegotiation), B . The right side of Table 11 presents
the results with B =6.1.62 A PA that runs only 5 auctions per year faces a greater cost of
procurement under the AB of about e800,000. This estimate is larger than the corresponding
one of e650,000 implied by the data in the Authority sample. However, the main reason for
this di¤erence is that the average winning bid in the structural estimation sample is higher,
40.2% instead of 32.6%. Although both estimates seem high, they do not seem unreasonably
larger than what it might cost a small PA maintaining even a small team of engineers and,
possibly, lawyers. Finally, it is not possible to fully rule out that the estimated large waste
re‡ects other factors like the ine¢ ciency or corruption of the PA. In a related study on the
public procurement of goods by Italian PA, Bandiera, Prat and Valletti (2009) show that the
purchasing behavior of PAs is consistent with high levels of "passive waste" (ine¢ ciency)
as opposed to "active waste" (corruption). Their estimates have a similar magnitude to
those presented in this paper. Interestingly, associating the use of an FP rule with a greater
centralization of the winner’s selection process may be a valid solution, regardless of whether
the source of the problem is the cost of screening or active or passive waste.
3) Bidders’Markup: The last result concerns the bidders’revenues. Despite the highest
price paid by the auctioneer in AB, the winner’s markup (i.e., the di¤erence between the
winner’s price and his cost) is on average 8.4% of the total cost with both mechanisms
when N=6.63 The reason lies in the random selction of the AB winner. However, the
aforementioned caveats about how e¢ ciency is a¤ected by participation, subcontracts and
collusion also apply here. Less e¢ cient …rms participate in AB auctions, thus depressing
the markups even more. However, the possibility of subcontracts and the existence of …rms’
collusion both imply that markups may be higher than the estimates presented here.
62
63
This value is the di¤erence between the mean values of Bw and renegotiation (11.9 and 5.8) in Table 4.
The estimates range from 6% with N=9 to 10% with N=5:
37
8
Conclusions
In this paper, I have analyzed the use of auctions in which the highest bidder may not win.
In the context of the Italian public procurement of works, the rationale for using either
an AB auction or an FP auction with screening was found in the risk that a standard FP
auction may excessively favor those bidders less likely to ful…ll their bid. However, it was
shown that the AB rule achieves this result at the price of transforming the auction into a
lottery that pays the winner the reserve price. Using information both on the auctions and
on the contracts’ex post completion, the analysis of the data produced by a change from
AB to FP has revealed that winners of the AB auctions receive higher payments. Finally, a
structural analysis of …rms’costs has shown that AB auctions create large ine¢ ciencies.
This paper leaves open several questions for future research. First of all, it may be
interesting to further test whether …rms respond to the subtle incentives created by the AB
rule. A study along this line is Conley and Decarolis (2010), in which it is shown that bidding
rings are formed to take advantage of the possibility of manipulating the awarding rule.
Another relevant question regards how to deal with the default risk in auctions for contracts. The main policy implication of this paper is that the AB rule should be abandoned,
but that it should not be naively replaced by a standard FP auction. The proper functioning
of the FP rule requires the presence of institutions limiting the adverse selection problem
behind the default risk. One example of them is the bids’screening regulation. Indeed, a
policy suggestion for the Italian case would be to centralize the screening process so that
the high …xed cost of screening would not prevent the adoption of the FP by small PA that
run infrequent auctions. Another solution could involve the use of rigorous pre-quali…cation
mechanisms that focus on how likely the bidder is to default. Finally, it might be possible to
rely on market-based mechanisms like surety bonds or letters of credit. Identifying the best
solution is an interesting research problem. Solving it would help to avoid the same inappropriate solutions eventually reappearing over time as is happening with the AB auction in
Italy, where, at the time of writing this paper, its return is invoked by many PA and …rms
disappointed by the problems that a naive introduction of the FP auction generated.
38
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40
Appendix: Proofs
Proof of Lemma 1: That a bidder i of type H always ful…lls his bid when pH pH follows
from the observation that this would be a dominated strategy. Suppose he defaults in the
bad state, i.e. pH bH (y + xi "); then his payo¤ in case of victory is:
(1
)(y + xi
bH )
pH
(1
)(y + xi bH )
(y + xH
")
(1
)(y + xi pH (y + xi "))
(y + xH
")
= " (y + xH ) < 0
Therefore, given that this bidder never defaults, his expected value in case of victory is
y + xi
" y + xH
" so that bidding anything above y + xH
" generates a negative
payo¤ in case of victory and is thus strictly dominated by bidding b y + xi
". As regards
the second part of the lemma, notice that if the format is FP with screening, no bid is less
than y
" (it follows from a simple Bertrand argument). Therefore, if pL < pL a type L
bidder will always default in the bad state because pL < (1
)" xL bL (y + xL "):
Proof of Proposition 1: Existence of a pure strategy monotone equilibrium is proved by
showing that my model satis…es all the assumptions of the existence theorem in Reny and
Zamir (2004), RZ from now on. RZ-Assumption 1 (utility function): de…ne rL
B + xL
and rH
A + xH and let l 2 [0; min(A + xH ; B + xL )]. Then the bid space conforms to that
of RZ: Bi 2 flg [ [ri ; 1): Moreover, notice that in my formulation ui = ct + xi bi , where ct
is equal to A or B depending on whether the bidder is type H or L. This payo¤ function is:
(i) measurable, it is bounded in [xt ; xt ] for each bi and continuous in bi for each x; (ii) de…ne
b
max(A + xH ; B + xL ), then ui (bi ; x) < 0 for all bi > b and for any x 2 [xt ; xt ]; (iii)
for every bid bi
ct + xt I have that ui (bi ; x) is constant in x
i
and strictly increasing in xi ;
_
(iv) ui (bi ; x)
ui (bi ; x) is constant in x. As regards RZ-Assumption 2 (signals): assume that
the private value x is a monotonic function x : [0; 1]N ! [x; x]N ; then my assumption that
signals are independently distributed means that signal’s a¢ liation weakly holds and that
for any xi the support of i’s conditional distribution does not change. Hence Assumption 1
and 2 or FR are satis…ed and existence follows. Having assured existence, then the claims
(a) and (b) in the proposition follow from the analysis of Maskin and Riley (2000).
Proof of Lemma 3: All bidders have the same valuation, y: Hence, the strategy pro…le
in which all bidders bid the same constant c 2 [x; y] is both feasible and does not allow
any unilateral pro…table deviation. In fact, when c 2 [x; y] deviating always leads to a zero
expected payo¤ while bidding c leads to (1=N )(y c) 0 with strict inequality if y > c. With
perfectly correlated values bidders are symmetric not only ex ante (before the realization of
their signal) but also ex post (after the realization of the signal), hence the kind of strategy
just described represents the unique (pure strategy) symmetric equilibria.
Proof of Proposition 2: It follows directly from the combined results of Lemma 2 and
Lemma 3.
1
Proof of Lemma 2: It is clear that the strategy pro…le in which all bidders o¤er the
minimum bid is an equilibrium: a unilateral deviation leads to a zero probability of winning
instead of having probability 1/N of winning a non negative amount. When N=2 this is the
unique symmetric BNE. Although I cannot rule out the presence of other symmetric BNE,
I can characterize four properties that they must have. The last one implies that for a large
enough N the auctioneer’s expected revenues is approximately equal to the reserve price.
PROPERTY 1: NON DECREASING FUNCTION
The proof is by contradiction. Assume that the BNE bidding function, b, has a decreasing
trait. Then I can take two types, x1 and x0 ; with x1 > x0 such that b(x1 ) < b(x0 ): Then by
b being BNE it follows that:
[x1
b(x1 )] Pr(winjb(x1 ))
[x1
b(x0 )] Pr(winjb(x0 )) and
[x0
b(x0 )] Pr(winjb(x0 ))
[x0
b(x1 )] Pr(winjb(x1 )):
Therefore from the …rst and from the second inequalities I have respectively that:
Pr(winjb(x1 ))
Pr(winjb(x0 ))
f[x1
f[x0
b(x0 )]=[x1
b(x1 )]g Pr(winjb(x0 ))
b(x1 )]=[x0
b(x0 )]g Pr(winjb(x1 ))
De…ne P0 Pr(winjb(x0 )) and P1 Pr(winjb(x1 )): Then for the these inequalities to hold
there must exist a solution to the following system of two equations in two unknowns (P0 ; P1 ) :
P0 f[x1 b(x1 )]=[x1 b(x0 )]gP1
P0 f[x0 b(x1 )]=[x0 b(x0 )]gP1
Therefore for a solution to exist it must be that
f[x1
b(x1 )]=[x1
b(x0 )]g
f[x0
b(x1 )]=[x0
b(x0 )]g
However, the above requires: [x0 x1 ][b(x0 ) b(x1 )]
was assumed that: x1 > x0 and b(x1 ) < b(x0 ):
0
0 but this is impossible because it
PROPERTY 2: NON STRICTLY INCREASING FUNCTION AT THE TOP
This property signi…cantly distinguishes the AB from the FP: under
the stated assumptions
_
no BNE can have the highest type bidding the highest value. If x is the highest
type and, by
_
_
_
contradiction, it is assumed that the equilibrium bid is such that b(x) = b > b(x) 5x 6= x
then it is easy to show that a unilateral pro…table deviation exists.
For instance, for a small
_
_
_
" > 0 player 1 could deviate bidding:_ b(x) for any x 6= x and b " for x =_x. His expected
revenues are unchanged for any x 6= x and they are strictly higher for x = x since in case of
victory his payo¤ is strictly greater and the probability of winning goes from being zero to
being positive.
PROPERTY 3: IN EQUILIBRIUM BIDDERS SHADE THEIR VALUE
This property is standard in auction models with imperfect information. Clearly any strategy
pro…le requiring a bidder to bid above its valuation is strictly dominated and cannot be an
equilibrium. Moreover, for any strategy pro…le requiring some type, x0, above the lowest one
to bid b(x0) = x0 it is easy to construct a unilateral pro…table deviation by picking small
" > 0 and modifying his strategy exclusively for b(x0) = x0 ": His expected revenues are
unchanged for any x 6= x0 and they are strictly higher for x = x0 since in case of victory his
payo¤ goes from being zero to being strictly positive while the probability remains positive.
2
PROPERTY 4: RESTRICTION ON THE HIGHEST EQUILIBRIUM BID
The following argument develops a bound for the highest bid compatible with a symmetric
_
_
_
BNE. I look at the highest type, v,_ such that for all x 2 [v; x] bidding some constant b (the
_
‡at top of Property 2) with x < b < v gives no unilateral incentive to deviate to a lower
_
bid: Hence, assume b is a symmetric BNE that is weakly
increasing
and
such
that
b
=
b _if
_
_
_ _
_
x v: Then, if agent N draws v it must be that: u(v; b; b N ) u(v; b; b N ) for any b < b.
_ _
_
_
_
This can be states
as
Pr(winj
b)[
v
b]
Pr(winjb)[
v
b]
for
any
b
<
b;where by the event
_
_
that the bid b wins, I mean that b is the bid closest to the average bid conditional on all
other players playing b : The probabilities of certain events are then de…ned:
p
_
v) \ (X2
Pr[(X1
_
Pr[(X1 < v) \ (X2
q1
...
qN
_
v) \ ::: \ (XN
_
_
v)];
1
_
v) \ (X3
v) \ ::: \ (XN
_
Pr[(X1 < v) \ (X2 < v) \ ::: \ (XN
2
_
M
_
1
N
Pr[j b
N
X
r=1
1
N
br j < jb(xj )
N
X
r=1
_
v)];
1
_
2
< v) \ (XN
_
v)];
1
_
br j for any xj < v and j = 1; :::; M jqM = 1]; where
_
_
M=1,...,N-2. Therefore I can now rewrite Pr(winj b) as: Pr(winj b) = p( N1 ) + [q1 ( N 1 1 ) + q2
( N 1 2 ) + ::: + qN 0 N 0 ( N 1N 0 )]; where N 0 is ( N2 1); or the closest lower integer if N is odd.
2
_
Whenever there is at least one bidder
drawing a valuation strictly less_than v then the
_
_
0
average bid will be strictly less than b: Therefore I can always take
a
b
<
b
but
"-close
to
b;
_
0
such that conditional on having _at least one player drawing x < v; b leads to a probability
of winning strictly greater than b: Moreover the _payment in case of victory with the bid b0
is strictly less than that in case of winning with b: De…ne M as follows:
M
Pr[jb
1
N
0
N
X
r=1
br j < jb(xj )
1
N
N
X
r=1
_
br j for any xj < v and j = 1; 2; :::; M jqM = 1];
where M=1,2,...,N-2. Therefore I can now rewrite Pr(winjb0 ) as Pr(winjb0 ) = [q1 + q2 2
+::: + qN 2 N 2 ]: Now, given the way b0 was chosen,
it must be that [q1 + q2 2 +::: +
_
_
_
0
qN 2 N 2 ][
v b ] > [q1 + q2 2 +::: + qN 0 N 0 ][v b]: The left hand side of this inequality is
_
exactly u(v; b0 ; b N ): A necessary condition for b to be equilibrium is fp( N1 )+[q1 ( N 1 1 )+q2 2
_
_
_
_
( N 1 2 ) + ::: + qN 0 N 0 ( N 1N 0 )]g[v b] > [q1 + q2 2 +::: + qN 0 N 0 ][v b]: Hence, it must be that
2
p > N q1 ( N
); which can be rewritten using the de…nitions of p and q1 as:
N 1
(1
_
F (v))N
1
N(N
N
_
2
)[F (v)(1
1
_
F (v))N
2
] > 0: ( )
_
_
Therefore, considering the
left hand side
of the above inequality as a function of v; say g(v),
_
_
then only the values of v such that g(v) > 0 respect the necessary condition. The function
_
_
_
g(v) starts at 1 for v equal to x and converges toward zero v equal to x. Moreover with
N
> 2 the function has a unique critical point, a minimum that is attained at the value of
_
v = z, where z is the (unique) value such that the following equation is satis…ed:
F (z) =
2N 2 4N +1
:
N 3 N 2 +1
3
Since the denominator is larger
than the nominator with F absolutely continuous, z must
_
always exist. Therefore g(v) starts at one, decreases until it _
reaches a minimum value and
then
converges to zero from below, reaching exactly zero at v _= 1: Hence it must be that
_
g(v) crosses zero from above just once so that the only values of v for
which ( ) is respected
_
are those that lie in [x; v ) where v is de…ned to be the value of v such that the inequality
of ( ) would be an equality. Moreover since v < x the following results:
For any (absolutely
continuous) FX and 8
_
is true: jv ;F xj < ":
> 0; 9 N
;F
such that 8N
N
;F
the following
_
To see why this is the case just consider
that by de…nition
of v the values of v such that
_
_
( ) holds are the ones for which g(v) > g(v ) ! v < v because g is strictly decreasing
until z > v . However the expression de…ning z is such that, in the limit
for N that goes to
_
in…nity, z = x: Therefore it must be the case that also v and hence v go to x as N goes
to in…nity. Therefore there is always an
N ;F that for any F and for any > 0 it is large
_
enough so that the di¤erence between v and x is less than : Finally one can see that using
( ) as threshold for checking that any symmetric BNE must have an highest bid strictly
lower than v is very conservative. In particular, while for N=3 this is almost as a good
characterization as one can get, for a greater N the actual maximum bid
might be much
_
lower than this bound. However, given the very high concavity of (1 F (v))N 1 this is not
likely to reduce the usefulness of this bound because as N rises the bound reduces the size
of the interval [x; v ) very rapidly by bringing v closer to x: Therefore even for small N, v
will be close to x: This is the reason why even for small N ( ) gives a bound that is useful.
Proof of Proposition 3: As with the S_AB, the strategy pro…le in which all bidders
bid the minimum bid and never default is a BNE. As regards its uniqueness, recall that the
I_AB di¤ers from the S_AB because of: (1) the trimming of the tails of the bid distribution,
(2) the use of a threshold, called A2, given by a trimmed average plus a positive standard
deviation and (3) the requirement that the winning discount is the closest from below to the
threshold. Moreover, there are two di¤erent rules that PA can use to deal with the event
that, because of ties, the top 10% of the bids contains more than 10% of the bidders. The
…rst rule, R1, says that all these bids are trimmed ,while the second rule, R2, says that only
(:1xN ) of them are randomly trimmed. It should be noticed that Step 1, 2 and 3 in the
proof of Lemma 2 hold unchanged in the I_AB case. Therefore, like_ for Lemma 2 (and using
the same notation),_I focus on the problem of the marginal type, v; the type such that the
_
equilibrium is b = b if x v: In the I_AB, it is easy to see that _regardless of whether R1
or R2 is used, unless the ‡at top equals the
minimum bid, then v always has a unilateral
_
_
pro…table
deviation
by
bidding
less
than
b.
In
the
event
that
all
bidders
draw
x
v; the
_
type v has a unilateral
pro…t
deviation:
by
lowering
his
bid
he
wins
with
probability
1 and
_
pays less than b. Under R1 this is clear since the trimming eliminates all the other bidders
and he is left as the only valid bidder. Under R2 the anomaly threshold, A2, coincides with
the ‡at top. Hence, the deviating strategy leads him to be the only valid bidder. Moreover,
_
_
in any other event (i.e., when at least one bidder
draws
x
<
v)
deviating
to
some
b0
<
b
_
cannot worsen the payo¤ since, in this case, b has a zero probability of winning.
4
Proof of Proposition 4: As regards the …rst part of the proposition, the fact that
E[RS_AB1 ]
E[RI_AB1 ] is because in both cases I is paid but all the possible equilibrium winning bids of the S_AB1 are greater or equal than the unique equilibrium of the
S_AB1 : As regards E[RF P1 ] > E[RS_AB1 ]; in both formats the auctioneer pays I and avoids
defaults. However, the density of the winning bid in the F P1 is positive in the interval
(A + xH ; A + xH ) while this density in the S_AB1 is positive only on [0; A + xH ]:
As regards the second part of the proposition, I will …rst show why E[RF P1 ] and E[RF P0 ]
cannot be ranked without knowing K and I. For F P1 the standard result (see Krishna, 2002)
(nH )
about the auctioneer’s expected revenues applies: E[RF P1 ] = A + E(XH;2nd
) I: Revenues
equal the sum of the common component A = y " and the expectation of the second highest
(nH )
value of XH among the nH bidders (I denote this value E(XH;2nd
)) minus the screening cost
I. Instead, for F P0 there are two possible cases depending on how large the di¤erence
between A and B is (see Maskin and Riley, 2000). Denote by K; K < A + max(xH ; xL );
the salvage value that the auctioneer gets in case the winner of the auction defaults on his
(nH )
bid.64 Furthermore, denote by E(XL;2nd
) the expectation of the second highest value of XL
among the nL bidders. Then the expected revenues are:
(
(nL )
(1
)(B + E(XL;2nd
)) + K
if (B A) > (xH xL )
F P0
E[R ] =
(1
)E[RAsym:F P0 ] + Pr(L wins)K
otherwise
where E[RAsym:F P0 ] is the expected revenue in an auction where bids are binding (no default
is possible) and there are nL and nH asymmetric bidders having expected payo¤s described
by (1). Notice that these revenues must be greater than those that a second price auction
would raise in this same environment. In turn, the revenues of a second price auction with
(nL + nH ) bidders are greater than those of a second price auction with just nH bidders,
which are identical to E[RF P1 ] + I by revenue equivalence. Therefore, it cannot be concluded
that E[RAsym:F P0 ] > E[RF P1 ]: However, it is clear that, without knowledge of I and K; the
ranking of E[RF P0 ] and E[RF P1 ] is not possible.
The above results regarding the FP formats come from the literature. Instead, the results
for the AB formats are novel. As regards AB0 , the expected revenues are:
E[RS_AB0 ] = c + (K
L
)
c)( nLn+n
H
;
where c 2 [0; minfA + xH ; B + xL g] and
= FXL (c + "
pL
y) is the probability that a
low penalty bidders who wins by bidding c decides to default when the good turns out to
have low value. Fixing c = 0 the above formula equals E[RI_AB0 ]. First of all notice that
since c enters into ; E[RI_AB0 ] and E[RS_AB0 ] cannot be ranked without knowledge of K:
Moreover, there is always an I low enough so that E[RF P1 ] > E[RS_AB0 ]: However, for a
high I and a low K, E[RF P1 ] < E[RS_AB0 ]: Therefore, without knowledge of I and K no
pairwise ranking of E[RF P0 ]; E[RF P1 ]; E[RI_AB0 ] and E[RS_AB0 ] can be established.
64
The salvage value K is likely a¤ected by many factors. A minimum assumption is that K
(y
") +
max(xH ; xL ); by which I require that K is smaller than the highest value the good can take in the bad state
of the world. A winner’s default, in fact, reveals that the good value is low. K is not restricted to be positive.
5