Corruption vs Collusion: Evidence from Russian

Procurement Auctions˚

Pasha Andreyanov: Alec Davidson; Vasily Korovkin §

April 15, 2016

Abstract

This paper uses a unique data set of Russian procurement auctions to test a new

method of detecting non-competitive behavior using timings of bids. We develop a

theory of how bid timings could matter in a first price sealed bid auction if non-

competitive behavior is present. We find patterns in the distribution of bid values

and bid timings that are consistent with several known illegal schemes. We distinguish

between collusion – horizontal agreement between the bidders and corruption – vertical

agreement between a bidder and an auctioneer. We estimate the proportion and type

of non-competitive auctions necessary to create the observed effects in our data. Our

results suggest that there is a significant proportion of auctions where non-competitive

behavior appears to be present. Finally we create a list of firms that our estimates

indicate are the most likely to be involved in some non-competitive arrangements.

˚We are grateful to John Asker, Leonardo Bursztyn, Christian Dippel, Kei Kawai and Romain Wacziarg

for helpful comments and suggestions.:pandreyanov@gmail.com;awdavids@ucla.edu§vaskorovkin@gmail.com

1

1 Introduction

The adoption of the Sherman Act in 1890 has deemed any behavior that is targeted on

reducing competition as unlawful in the US, and similar antitrust laws were later adopted in

most countries including Russia. Since then scholars and practitioners have been developing

tools to measure the extent of anti-competitive agreements and the associated damages. In

the context of procurement auctions these agreements can be sorted into two broad categories:

corruption and collusion. Collusion is a horizontal agreement between two or more bidders

and corruption is a vertical agreement between the auctioneer and one of the bidders. In

both scenarios the competition between the bidders is reduced and the cost of procurement

goes up.

The phenomenon of collusion is well-understood in economics and has been thoroughly

investigated by theorists as well as empiricists. The detection of collusion alone is the subject

of a large literature (see Porter (2005) for a review). Understanding and detecting corruption

is much harder, mainly because the foundation of most auction theory rests on a benevolent

auctioneer. At the same time, corruption may lead to losses comparable with that of collu-

sion. For example, in Menezes and Monteiro (2006) an auctioneer can approach the winner

and offer him a reduction of his bid to match that of the loser. The generated surplus then

can be split between the two. To our best knowledge no study has found empirical evidence

of such practices.

In this paper we try to detect and separate two scenarios: a classic collusive scheme

and the corruptive scheme described above. We examine a novel data-set of procurement

auctions in Russia spanning the years 2014-2015 which includes detailed records of the bids

of each player, as well as the time at which each bid was placed. The data spans a wide

range of industries, prices, locations and even auction structure. We narrow our focus to

only those auctions which are first price sealed bid (FPSB). The key insight is that while in

a competitive setting time is payoff-irrelevant, in collusive and corruptive scenarios it may

serve as a natural coordination device even in FPSB auctions. Therefore by observing the

timings of bids of multiple similar auctions one can statistically measure the frequency at

which corruptive and collusive schemes are exercised.

2

Our first step is to identify possible reasons why bids and times would exhibit statistical

correlation. As mentioned above, in fair auctions there is no strategic reason to consider the

timing of ones bid (although in the future we will relax this a little). As such we hypothesize

that any observed correlation must be a direct result of some non-competitive behavior. We

separate these correlations into two types. First if bidders bid extremely close together in

time we associate this with collusion. The argument here is that collusive bidders need a

way to enforce their agreement, one way to do this is to bid at the same time and observe

each others behavior.

On the other hand in a corruptive scheme where a bidder is cooperating with the auc-

tioneer there is no particular reason to bid close to the other bidders. We assume the scheme

works as follows: the auctioneer observes all bids placed in the auction and passes them

on to the corruptive bidder. Once the corrupt bidder is confident all other bids have been

placed he under bids the other bids by a small amount and splits the resulting surplus with

the other players. It is necessary for the corrupt bidder to bid after all other bids have been

placed. Furthermore the corrupt bidder cannot be sure of how many other players will bid,

as such he will want to place his bid as late as possible to ensure he wins the auction. Thus

to identify corrupt auctions we look for a pattern where the winning bid is placed after the

runner up’s bid, the winning bid is placed close to the auction deadline and the amount of

the winning bid is sufficiently close to that of the runner-up.

Our problem here is then two-fold: we want to propose a strategy for separately detecting

the presence of each scheme, we want to further estimate the prevalence of each type of

behavior, and finally we want to be able to separately identify each scheme in the cases

where they overlap. We develop statistical tests for detecting each scheme jointly, as well as

tests that separate the two. To do this we make several assumptions on the structure and

outcomes of each scheme, as mentioned above.

Ultimately our analysis suggests that there is a significant portion of auctions in our data

which were non-competitive. We find evidence of both of the schemes. This behavior is also

extremely widespread: it is consistent across almost all observable auction characteristics,

such as deadline times, location, value of reserve price, etc. We also identify the bidders

who most often appear in auctions our estimates identify as likely to be non-competitive

3

and propose some tests for detecting which firms are most likely to be part of some non-

competitive arrangement.

The main strand of literature that this paper contributes to is empirical literature on

collusion in auctions (see Porter (2005) and Asker et al. (2010) for a review). We draw a

distinction between the papers where the authors know, which firms are involved in violations

(Porter and Zona (1993, 1999); Pesendorfer (2000); Ingraham (2005); Asker (2010)) and the

papers that develop a method to detect firms without having a ”learning sample” of cartel

firms (Hendricks and Porter (1988); Baldwin et al. (1997); Bajari and Ye (2003); Ishii (2009);

Athey et al. (2011); Conley and Decarolis (Conley and Decarolis); Haile et al. (2012); Kawai

and Nakabayashi (2014)). Our paper belongs to the second group, since we do not need

information on the existing collusive behavior to use our method. The paper that is closest

to ours in its spirit is Kawai and Nakabayashi (2014). The authors use data on procurement

construction auctions in Japan to verify a new method of detection. They are using re-

auction data to show that in all the re-auction rounds the same firm tends to win. They

control for potential costs confounding by concentrating only on the subsample of firms with

close bids in the initial auction. They use a more formal model to justify this regression

discontinuity style analysis.

This paper also contributes to the theoretical literature that studies models of corruption

in auctions (Compte et al. (2005); Menezes and Monteiro (2006); Lengwiler and Wolfstetter

(2006); Burguet and Perry (2007); Arozamena and Weinschelbaum (2009); Lengwiler and

Wolfstetter (2010). Usually it is modeled by auctioneer communicating with the winner

in order to help him match the losing bid in exchange for a favor (Menezes and Monteiro

(2006)).

The literature on corruption in procurement is growing. Most of this literature is dedi-

cated to the countries with weaker institutions (Di Tella and Schargrodsky (2003); Ferraz and

Finan (2008); Bandiera et al. (2009); Lewis-Faupel et al. (2014); Mironov and Zhuravskaya

(2014)). Our contribution is to combine insights from this literature on corruption and auc-

tion literature that examines collusion and its welfare consequences (Porter (2005); Kawai

and Nakabayashi (2014)). As a result we can describe how the incentives of collusive firms

and the incentives of corrupt public bodies together shape the welfare loss on a scale of the

4

whole economy. Thus, we show how both lack of competition and weak institutions reinforce

each other.

The rest of the paper is organized as follows. Section 2 describes the background and the

details of the procurement procedures that we analyze. Section 3 discusses the data. Section

4 formulates the main assumptions for the reduced form analysis of collusion and corruption

in Section 5. Section 6 discusses the mechanisms behind the observed patterns in the data

and proposes the way to detect the violators.Section 7 concludes

2 Institutional Background

Starting January 2006, all public procurement in Russia is regulated by the 94-FZ law.

According to this law any firm or organization that is fully or partially owned by the state

has to determine its contractors on a competitive basis through one of the several allowed

auction types. The exceptions are military and strategic contracts that are not open for

public.

The two most popular auction types are open auctions which are descending English

auctions with a reserve price, and requests for quotations which are sealed bid first-price

auction with a reserve price. The first type are used for larger purchases, and these are more

transparent and well-regulated. The second type are used for small purchases, and require

less preparation but are also less transparent. There are other variations of these procedures,

such as a request for proposals1, but they cover an insignificant share of the contracts.

We focus on the requests for quotations, which are used for small contracts. The reserve

price of such a contract can be at most 500,000 rubles (˜$7,500), and at most 10% of annual

expenditures of a public body2 can be assigned this way, but not more than 100 million

rubles (˜$1.5 mln) per year. Typical examples of these contracts are: a purchase of office

supplies for a firm, books for a school, or medical supplies for a hospital. Small repairs, street

cleaning and all kind of services can be purchased through this procedure as well.

1When participants can not be ranked on the price basis, a double-envelope auction is used, where the

first envelope is a price quote, while the second one is some kind of a technical proposal.2School, hospital, whoever is posting a contract

5

The public body first posts a notification of the auction on a public website. The noti-

fication is standardized and it has sufficient information about the contract, including the

deadline to enter the auction and the requirements to qualify as a bidder. The notification

has to be posted no less than 7 business days before the deadline of the auction.3

During the time of the auction anyone can submit an application, which is a price quote

paired with a number of documents showing that this person is eligible for the contract.

Applications are accepted in sealed envelopes, by email or online through a special website.

Sealed envelopes usually have to be submitted on business days from 9AM to 1PM or from

2PM to 5PM, except for on state holidays.

After the auction has ended, the applications are opened and examined by a local commit-

tee. Some applications can be rejected if the bidders did not meet the posted requirements.

The winner is determined by the lowest quote. If the quotes are equal, the earliest applica-

tion submitted wins. The committee then writes a protocol with the results of the auction,

which is also stored on the public website.4

If all applications are rejected, or no applications are received at all, the auction enters

the prolongation phase of four business days, and the public body has to notify at least

three potential contractors about the auction. If after these four days there are still no valid

applications, the auction is cancelled and the notice is posted again. The auction can be

also cancelled if someone sends a complaint to the enforcing agency and they find that the

procedure was violated in some way. Finally, the auction can be cancelled by the public

body not less than two business days before the deadline in a unilateral way.5

We start by analyzing the incentives for the officials to prefer the request for quotation

over the open auction format. The first obvious reason is that the first format is quicker

and easier to run. However since these smaller auctions are relatively less regulated than

their larger counterparts they are also ripe for collusive behavior. In particular, while the

two auction types are roughly equivalent in terms of how easy it is for two bidders to collude

3For auctions with a reserve price of 250,000 rubles ($3,250) or less the notification can be posted up to

four business days before the deadline.4The bidders or their representatives have a right to participate in the opening procedure, can request to

disclose any information from the bidding envelopes and can make a recording of the procedure.5Sources for this Subsection: ”RusTenders” Website, Federal Law #44 and Balsevich et al. (in Russian)

6

within them, it is almost impossible for the auctioneer or other public official to have an

influence on the English auction without being detected. Conversely in the a FPSB auction

where the public official is able to view each player’s bid as they are submitted it is extremely

easy for him to rig the auction in some way.

We draw a line between two types of schemes: collusive and corruptive. The difference

comes from who forms an anti-competitive agreement. If it is a vertical agreement between

the official and the supplier than we call this corruption. If it is a horizontal agreement

between two or more suppliers than we call this collusion. We recognize that there can

be multiple collusive and multiple corruptive scenarios that happen simultaneously and we

might not be able to perfectly distinguish them from each other. Still, we believe that we

are able to detect the presence of at least one corruptive and at least one collusive scheme.

In this section we describe the most common anti-competitive scenarios, the economic

forces behind them, and how we expect them to reflect in the data.6

The incentives behind collusive schemes are fairly simple. Once two participants form an

agreement (a cartel/ring), they unambiguously improve their expected profit by not com-

peting against each other. This economic force is considered so strong that most countries

(including Russia) have adopted harsh anti-cartel laws.

Since the cartel agreement is illegal, enforcing its rules is a serious problem for the par-

ticipants. Since there are obviously no legal means to enforce such agreements the players

must adopt their own methods to ensure cooperation. There are two potential solutions to

this problem: the first solution is to use the expected future value of the cartel agreement

as a commitment device. This is a widely studied topic in auction theory. Another solution

is for the cartel members to simply monitor each others actions while writing and filing an

application. If doing this online, they will probably use the same computer sequentially in a

short period of time. As a result, the bids will be located next to each other in time, we call

this joint bidding. We believe that in the absence of sophisticated commitment devices this

kind of behavior is natural for the members of the cartel.

There is a straightforward reason for why the first commitment device may not work in

the setting we examine here. When examining how often bidders compete against each other

6Sources for this Subsection: Hramkin and Balsevich et al. (in Russian)

7

in different auctions we find that most bidders meet at most twice across separate auctions.

Since punishment devices amongst cartels depend on repeated interactions if bidders are

unlikely to meet again in a separate auction this will not be an effective deterrent to deviation.

As such a one shot method, such as joint bidding, should be adopted in scenarios where the

bidders do not expect to have repeated interactions.

There is another scenario which may lead to the same outcome in this setting. Sometimes

a participant wants to create an illusion of competition to divert potential entrants, or maybe

he does not want to look like a monopolist to the authorities. For this purpose he can create

a dummy firm that will participate in the auction but never actually compete, we call this

a phony bidder scheme. He faces no commitment problems, but since he is managing both

firms the timings of two bids are likely to correlate.

To distinguish the shares of the phony bidding and the joint bidding schemes we will use

balance sheets data. ”Fake firms” will not have profits or any other tax relevant activity.7

There is a wide range of incentives behind corruptive schemes. We will enumerate the

most popular ones according to anecdotal evidence.

• Kickbacks. This is the simplest and probably the most popular scenario behind the

vertical agreement. The official helps his favored supplier to win the auction, and gets

a share of the generated surplus.

• Relations. Often contracting with a new supplier incurs additional costs for the official.

These could be direct costs from monitoring and instructing the new firm, or indirect

costs from abandoning a successive relation with the old firm.

• Money burning. Sometimes when the accounting year ends, there are unspent funds

left from the federal budget. In this case the next year budget will be likely reduced

by that amount. Anticipating this, the official has incentives to maximize expenditure.

As one can see, the incentives behind corruption are not always ”corrupt” in a bad sense,

sometimes it is an outcome of the official trying to do his job well. Nevertheless, irrespective

of the intentions of the official , we mark this kind of behavior as corruptive.

7In progress.

8

We have anecdotal evidence of multiple methods by which the auctioneer can affect the

outcome of the auction. Despite the fact that these schemes are almost common knowledge

there is almost no way to detect them directly. We will present a few common schemes that

were documented by participants and various organizations studying these auctions. The

rest of this paper involves developing statistical methods for detecting said schemes.

• Entry deterrance. If the official writes the name of the contract with mistakes, potential

suppliers might not find it in the search engine. Moreover the contract documentation

may be overly complicated, or the requirements can be so tight that only one firm fits

them.

• Force reject. The official may choose to reject the bid on a valid or invalid basis. If the

rejected participant is not fluent with the law, he may decide not to complain to the

monitoring agencies. But even if he does, the chances of winning the case are low and

might not be worth the effort.

• Force cancel. The official can cancel the auction two days before the deadline if he

sees that something is going wrong. If, for example, he puts a small mistake into the

notification then he can even cancel it ex post.

• Quote matching. Despite the fact that the envelopes are sealed and the online appli-

cations are digitally protected, most participants agree that the official can learn the

quotes if he wants to. Therefore, he can communicate this information to his favored

supplier so that he undercuts the winning bid by a small margin.

In this paper we focus on the quote matching scheme. The important implication of this

scenario is that the favored supplier puts his bid after all others. Moreover, since the number

of participants is uncertain, he will try to do it as late as possible.

The Russian anti-monopoly agency FAS typically does not pay attention to requests for

quotation, because the sum of contracts is too small. In fact an investigation can only be

launched if there was a complaint from one of the participants. But even if the participant

is educated enough to find a breach in the procedure and report it to the authorities the

auction will be simply cancelled and re-run. At the same time proving that quote matching

9

took place is almost impossible. As there is little risk to the auctioneer of running such a

scheme.

Most of FAS efforts are channeled to preventing collusion between large producers inher-

ited from the Soviet Union, or suppliers competing for big government contracts. Compared

to them, a small local school trying to spend more than needed is probably not worth the

effort.

3 Data

We use a digital archive8 of all procurement auctions that took place starting in January 2014.

The archive consists of notifications and protocols, in a standardized .xml format. Auction

characteristics like reserve price, contracting terms, deadlines for submitting applications are

stored in the notifications. Protocols have a quote for each application, timing of bids and

also information about the bid being accepted or rejected.

After matching notifications to the protocols, and extracting the sufficient information

we obtain a dataset of roughly 450,000 requests for quotations. We drop the auctions with

at least one rejected bid, because it can interfere with agent’s strategic behavior in too many

ways.

The first variable of interest is the number of bidders. From Table 1 (left column - no

rejected bids, right column - rejected bids allowed) one can see that these auctions typically

have very few, if any participants. The most popular outcomes are 1 and 2, and they

have similar shares. The probability of n ą 3 participants coming to the auction decays

geometrically in n with a factor of 2.

The second variable of interest is the reserve price (in rubles). From Figure 1 one can

see that the distribution of reserves prices has a full support from 0 to 500,000 rubles, is

monotonically decreasing (except for an economically insignificant neighborhood of 0), but

there is also a huge spike around the maximum level of 500,000 rubles, a smaller but still

significant spike at 250,000 rubles and also still noticeable small spikes at round numbers like

300,000, 250,000 e.t.c. The winning quotes have a somewhat similar distribution.

8Available in FTP or HTML formats from the official website zakupki.gov.ru.

10

Table 1: Number of Bidders

Bidders Number (w/o rej.) Per cent (w/o rej.) Number (all) Per cent (all)

0 36,731 9 36,732 8

1 147,874 36 151,077 33

2 146,018 36 159,061 35

3 42,635 10 54,848 12

4 17,120 4 23,980 5

5 7,952 2 11,786 3

6 4,058 1 6,414 1

ą6 5,303 1 9,000 2

Total 407,691 100 452,898 100

Figure 1. Reserve Price and Winning Bid

050

001.

0e+0

41.

5e+0

4Fr

eque

ncy

0 100000 200000 300000 400000 500000

Winning Bid Reserve Price

11

The third variable of interest is the time of the bid (in minutes to the deadline). From

Figure 2 one can see that the time of the bid has a certain pattern. In every day (except for

the day of the deadline) the distribution is hump-shaped with one small gap in the middle.

The share of bids is monotonically increasing in time til deadline. A large share of bids occur

the day before the deadline and a large share of those bids occur in the last hour before the

deadline. One can also observe small spikes at round numbers like 10, 15 or 20 minutes,

which we attribute to software protocols.

Figure 2. Winner time

0.1

.2.3

Density

0 50 100 150flt

The other variables are: quote and time of the winning bid, quote and time of the

second-best bid. We only need to focus on the two strongest bids, because they reflect most

of the competition in this setting. We introduce two additional variables as measures of the

auction competitiveness: percentage distance from the reserve price to the winning quote and

percentage distance between the winning and the second best quote. We are also interested

in the distance between the timings (measured in minutes to the deadline) of the winning

12

and second best bids.

Table 2 shows summary statistics.

Table 2: Summary statistics

Variable Mean Std. Dev.

number of bidders n 2.663 1.325

reserve price r 180261.977 150232.798

winners bid bf 154035.112 347997.884

winners time tf 86.09 17295.817

winning bid to reserve price d1 “r´bfr

94.41 952.532

winning to second best quote distance d2 “bs´bfbs

7.31 11.37

winning to second best time distance δfs “ ts ´ tf 2.99 718.257

There are a few of anti-competitive scenarios that may lead to irregular patterns in the

distributions of variables that we observe.

Shares of 1 and 2 bidders are too large. The fact that the shares of auctions

with 1 and 2 bidders do not fit the general pattern of the distribution may be indicative of

two facts. First, there is a substantial entry deterrance that leads to a unique participant

appearing too often. Second, there is a substantial phony bidding which makes auctions with

one participant appear as auctions with two participants.

Spikes of price distribution. The spikes in the distribution reflects the love for round

numbers. Since the starting price does not matter a lot, the official picks a round number

more often. However, the spikes at 250,000 and 500,000 also reflect the discontinuity of the

mechanism. Auctions with the starting price above the first threshold are held in 7 rather

than 4 days. Auctions with the starting price above the second threshold have to be open

auctions rather than requests for quotations. These spikes may be indicative of the official

trimming the starting price so to fit the threshold, or inflating the starting price right up to

the threshold.

Shape and spikes of time distribution. The repeating two-humped pattern on the

histogram reflects the daily frequency of bidding. It starts at 6am in the morning, then there

is a lunch break at 1pm and it ends at 5pm, the cycle repeats every day and only the day

13

of the deadline looks different. A slightly bigger share at the day before the deadline may

reflect the fact that the auction can be cancelled without any basis up to 2 days before the

deadline, therefore experienced bidders don’t bid before that. Finally the explosion right

before the deadline might indicate the quote matching or attempts to defend from it.

4 Identifying Assumptions

For the rest of this section we consider a family of auctions with observable characteristics X

and unobservable characteristics Z. We index theses auctions by i for i “ 1, ..., n.9 Within

auctions we index bidders by k for k “ 1, .., Ki where Ki denotes the number of bidders in

auction i. Thus we denote the bid of player k in auction i by bki and likewise for the timing

tki .

The baseline model is a classic independent private value setting. In the IPV case the

bids are monotonic transformations of costs, so we treat them as random draws from some

distribution. The assumptions that are vital for our analysis is the assumptions on the

correlation between timings and bids. In this section we condition all the assumptions on

the observed characteristics of an auction x and we suppress conditioning throughout the

section.

Our starting point for this model will be the payoff irrelevance of bid timing in a first

price sealed bid auction with independent values. All known auction theory on competitive

auctions ignore timings in such auctions as under the assumption of fair play (i.e. bidders

cannot observe each others bids) the timing of ones bid does not affect the probability of

winning the auction. As such under the null hypothesis of perfectly competitive auctions each

players bid and timing should be independent. Furthermore there should be no correlation of

players bids or times within auctions: such a correlation would suggest that players observe

each others bids which would again suggest the auction was not competitive. We combine

these two requirements to get our first assumption, which we call time-bid independence

(TBI).

9We drop the i index for the most of the section, unless it is important.

14

Assumption 1. TBI

bk K tk, @ k (1)

pbk, tkq K pbj, tjq, @ k, j. (2)

These assumptions have slightly different implications: first note that even under collusive

behavior we would expect that each players bid and time are independent. While it is

expected that a colluders bid would be correlated with another bid in the auction this would

not lead to correlation between his own bid and time. The second assumption is the one

which would be violated in the presence of non-competitive behavior. We include the first

assumption because most of our future tests will be unable to differentiate between correlation

between each players bid and time and correlation between separate players bid and timing

pairs.

If we rank all the bid-timing pairs by the strength of bids a typical pair inside an auction

would be pbpkq, tpkqq, where bk is k-th order statistic of bids, and tpkq is the corresponding

timing (i.e. bp1q is the bid placed by the winner and tp1q is the timing of the winner). Then

TBI implies a following assumption that we call ranked independence of timings (RIT).

Assumption 2. RIT

tpkq K tpjq

Proof

We wish to show that P ptpkq ă T |tpjq ă Sq “ P ptpkq ă T q @ S. Note:

P ptpkq ă T |tpjq ă Sq “ P pmaxtti, tju ă T |mintti, tju ă Sq

“ P pti ă T |tj ă S, bi ă bjq ˚ P pbi ă bjq ` P ptj ă T |ti ă S, bj ă biq ˚ P pbj ă biq

“ P pti ă T q ˚ P pbi ă bjq ` P ptj ă T q ˚ P pbj ă biq “ P ptpkq ă T q

Where the third equality follows from TBI.

We can decompose the timing into day to the deadline and hour inside the day. The hour

variable can take non-integer values in the interval r0, 24q. Thus, t “ pd, hq.

15

In addition to RIT we use two pairs of assumptions for our reduced form analysis of

collusion and corruption in section 5. The first one is used for detecting collusion and we

denote it as CL. It states that the bidding patterns inside the day should be the same for

all the bidders and for all of the days except for the last day before the deadline. This

assumption follows from RIT.

Assumption 3. CL

fphpkq, hpjq|dpkq “ dpjqq “ fphpkq, hpjq|dpkq ‰ dpjqq @ k, j.

One particular corollary of this assumption is that bidding at the same hour of a day

should be the same for the same-day bids and for different-day bids. We abuse notation and

write hp1q “ hp2q when we actually require |hp1q´hp2q| ă w, where w is some arbitrarily small

constant. With this abuse of notations we narrow the CL assumption to get.

Assumption 4. PCL

P rhpkq “ hpjq|dpkq “ dpjqs “ P rhpkq “ hpjq|dpkq ‰ dpjqs @ k, j

Assumption 4 yields a natural estimator for the abnormal joint bidding of the winner and

the runner-up. If PCL is violated we can define,

β :“ P rhp1q “ hp2q|dp1q “ dp2qs ´ P rhp1q “ hp2q|dp1q ‰ dp2qs

If PCL is satisfied and there is no joint bidding β “ 0, one natural estimator for β is an

OLS estimator in a regression of Ithpi1q “ hp

i2qu on Itdpi1q “ dp

i2qu. The estimator will have

a following form:

β̂OLS “

ř

i Ithp1qi “ h

p2qi u ¨ pItd

p1qi “ d

p2qi u ´

1n

ř

i Itdp1qi “ d

p2qi uq

ř

i Itdp1qi “ d

p2qi u ¨ pItd

p1qi “ d

p2qi u ´

1n

ř

i Itdp1qi “ d

p2qi uq

Proposition 1

plimpβ̂OLSq “ β

Proof

plimpβ̂OLSq “P th

p1qi “ h

p2qi , d

p1qi “ d

p2qi u ´ P th

p1qi “ h

p2qi uP td

p1qi “ d

p2qi u

P tdp1qi “ d

p2qi up1´ P td

p1qi “ d

p2qi uq

“

16

“P th

p1qi “ h

p2qi |d

p1qi “ d

p2qi u

P tdp1qi ‰ d

p2qi u

´P td

p1qi “ d

p2qi u ¨ P th

p1qi “ h

p2qi |d

p1qi “ d

p2qi u

P tdp1qi ‰ d

p2qi u

´

´P td

p1qi ‰ d

p2qi u ¨ P th

p1qi “ h

p2qi |d

p1qi ‰ d

p2qi us

P tdp1qi ‰ d

p2qi u

“

“ P th1i “ h2i |d1i “ d2i u ´ P th

1i “ h2i |d

1i ‰ d2i u “ β.

We use this result in estimation in the next section with β being a measure of excessive

joint bidding.

An alternative way to build a measure of collusion is to assume that there are auctions,

where collusion never happens and the auctions, where collusion always happens, and the

share of the latter is γ. If the auction is not collusive or it is collusive, but bidding happens in

different days, same hour bidding is characterized by a constant probability θ. If an auctions

is collusive and bidders bid at the same day, then they bid at the same hour. This alternative

set of assumptions leads to following conditions:

P th1i “ h2i |d1i “ d2i , non´ collusiveu “ P th1i “ h2i |d

1i ‰ d2i , non´ collusiveu “

P th1i “ h2i |d1i ‰ d2i , collusiveu “ θ.

P th1i “ h2i |d1i “ d2i , collusiveu “ 1.

One can show that the estimate for the share of collusive auctions x̂ can be derived from

an OLS regression as before.

γ̂ “ β̂OLS{p1´ θ̂OLSq,

where θ̂OLS is the constant.

Our baseline assumptions 1 and 2 imply some sort of symmetry for the timings of bids.

We exploit this to study information leakage and corruption. The first assumption that we

use (CR1) states that the probability of bidding the last should not differ across rankings

of bids. This follows from the fact that time orderings and bid orderings are not correlated.

The strongest version of this assumption will imply that for bidder with rank j in auction

i her chance of bidding later than all other bidders should be just 1{Ki, where Ki is the

number of bidders.

17

We build on this assumption to study last minute bidding. Last minute bidding by any

of the bidders should not be correlated with the rankings of the bidders that bids later if

there is no bid leakage. We state this formally in the assumption CR2. In reality last hour

bidding is highly correlated by winner bidding the last.

Finally the distance in bids between any of the bidders should not be correlated with the

timing patterns discussed in CR2. This is our assumption CR3.

Assumption 5. CR (symmetry)

1. P!

hji “ minth´ji u

)

“ 1{Ki, @j P 1, ..Ki

2. P!

hji “ minth´ji u|I´ KiŤ

k“1

thpkq ă 1u¯

“ 1)

“ P!

hji “ minth´ji u|I´ KiŤ

k“1

thpkq ă 1u¯

“ 0)

3. bji ´ bik K ph

1, ..., hKiq.

If there is some asymmetry in the data it can be indicative of corruption. Similarly to β

we define a measure of deviation from the CR2 assumption.

α :“ P!

hji “ minth´ji u|I´

Kiď

k“1

thpkq ă 1u¯

“ 1)

´ P!

hji “ minth´ji u|I´

Kiď

k“1

thpkq ă 1u¯

“ 0)

.

An OLS estimate of α in a regression of Ithji “ minth´ji uu on I´ KiŤ

k“1

thpkq ă 1u¯

is a

consistent estimate for the asymmetry – α.

5 Reduced Form Analysis

5.1 Collusive Patterns

We start by studying one particular collusive scheme - joint bidding. It implies that the

bidders are putting their bids extremely close in time. This can be either a fake firm that

has the same owner and that bids at the same time to avoid entry of other firms or two firms

in a cartel monitoring each other’s actions.

Under the assumption of ranked independence of bids (RIT) that we discussed in the

previous sections the distribution of the winner’s time is the same as anyone else’s. In this

case a scatterplot of timings – hours to the deadline when the bid is placed should look like

a direct product of two identical distributions. It cannot exhibit any correlation between

18

the timings of bids. Figure 3 shows the scatterplot of the hours to the deadline with first

bidder’s timing depicted on the x-axis and second bidder’s timing depicted on the y-axis.

The figure reveals a pattern that indicates of the joint bidding – an excess density on the

diagonal, when bids are placed at the same day, but no excess density, when bids are placed

on different days.

Figure 3. Hours to the deadline for the two strongest

2040

6080

100

flt

20 40 60 80 100slt

N=19894

Note: bidding Monday-Thursday with a deadline on Friday 10am;

The figure is similar for other deadlines.

Now we directly use our assumption 4 (PCL) from the previous section. We start by

illustrating of how we construct an estimator that is conceptually simpler then the OLS, but

it can be shown that it is asymptotically equivalent. Assuming that the distribution of hi

does not depend on di, we can come up with a simple estimator of β based on comparing

two neighboring clouds on this scatterplot. The ”treatment group” will be the Thursday-

Thursday cloud, and the ”control group” will be the Thursday-Wednesday cloud, see Figure

4.

19

Figure 4. Two days: intuition

1520

25flt

15 20 25slt

2084 6004 1618

2022

2426

flt

40 45 50slt

122 1545

here we assume that observed characteristics Xi is just the information about the deadline: Friday

10am.

The idea is that the treatment group is an overlay of two scatterplots, one coming from

competitive bidding and one coming from joint bidding. Under the PCL assumption the

distribution of competitive bidding is the same in both treatment and control groups. It is

possible to remove the competitive layer and measure the remainder. For this we need to

isolate the part of the distribution that is mixed with colluders from the uncontaminated one.

If we guess the size of the bandwidth around the diagonal such that all colluders are within

it, we will get a consistent estimator of the fraction of corrupt auctions in the treatment

group by just comparing shares of bids:10

2084´ 122 ¨ 6004´20841545´122

6004“ 29%.

To reinforce the results of graphical analysis we rewrite it in terms of a regression. We

regress an indicator of bidding within a 20-minute window on an indicator of bidding within

the same day. If the choice of day and hour are indeed independent, then the coefficient

would be zero.

Formally,

It|hp1qi ´ hp2qi | ď wu “ β0 ` β1 ¨ Itdp1qi “ d

p2qi u ` µi ` εi.

and

Erεi|Itdp1qi “ dp2qi u, µis “ 0.

10One can show that this approach is asymptotically equivalent to OLS estimation that we described in

the previous section and that we do below.

20

Once we take into account all of the information about the deadline, using the day and

hour fixed effects – µi the fact, whether the bids are placed in the same day or one or

more days apart should not play a role for the exact spacing of bids inside the days and in

particular of closeness of the winning and the second best bids. We explore the results for

several specifications of this regression in Table 3 below.

Table 3: Indicator regressions by number of bidders

(1) (2) (3) (4) (5) (6) (7)Friday 10AM

2 squares Two Bidders Three BiddersFour & More 44LAW 94LAW

Thick diag. 0.185*** 0.215*** 0.255*** 0.113*** 0.0907*** 0.226*** 0.213***(0.0110) (0.00105) (0.00130) (0.00233) (0.00305) (0.00239) (0.00117)

Constant 0.0725*** 0.0871*** 0.0851*** 0.0909*** 0.0920*** 0.0753*** 0.0899***(0.0100) (0.000789) (0.001000) (0.00164) (0.00214) (0.00181) (0.000877)

N 9,787 560,624 398,153 91,047 50,542 108,022 452,602R-squared 0.028 0.072 0.090 0.027 0.021 0.077 0.070

Standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1

Whole Week, Day*Hour Deadline Dummies

Note: deadline day-hour fixed effects are included in all the columns (2)-(7).

First column of Table 3 shows the results for the comparison between Thursday-Thursday

”treatment group” and Thursday-Wednesday ”control group”, with a deadline on Friday

10AM. The coefficient represents the difference between the probabilities of bidding close in

hours conditional on bidding at the same and at different days. So it is exactly the OLS

estimator from Section 4 and it can be used as a measure of collusion.

Column (2) shows the results for a pool of auctions with deadlines on weekdays, from

8AM to 6PM. We omit the auctions that have one of the winning bids placed on the last

day, because the distribution of ti is clearly different there. In order to control for deadline

specific patterns in bidding we include a fixed effect for each hour of each deadline day of

the week.

The results suggest that joint bidding is most popular when there are only two bidders

in the auction. Indeed, colluding is easiest when there are only two potential participants.

When the number of participants increases, colluding becomes harder. Another important

21

dimension of heterogeneity is the difference in laws. Joint bidding became more popular

since the new laws were introduced in 2014.

If we use an alternative approach and estimate γ – share of the collusive auctions from

the previous sections our estimates become slightly larger then β̂. Namely, for two bidders

the result is that 27.8% of the auctions are collusive.

The observed differences in bid densities translate into the final prices. Our variable of

interest is the winning bid normalized by the reserve price. The regression that we run is

alike a difference in difference regression:

ratioi “ θ0 ` θ1 ¨ It|hp1qi ´ hp2qi | ď wu ` θ2 ¨ Itdp1qi “ d

p2qi u`

`θ3 ¨ It|hp1qi ´ hp2qi | ď wu ¨ Itdp1qi “ d

p2qi u ` µi ` ηi.

and

Erηi|Itdp1qi “ dp2qi u, It|h

p1qi ´ h

p2qi | ď wu, It|hp1qi ´ h

p2qi | ď wu ¨ Itdp1qi “ d

p2qi u, µis “ 0.

Table 4: Prices and distances in time

(1) (2) (3) (4) (5) (6) (7)Friday 10AM

2 squares Whole Week Two Bidders Three Bidders Four & Five 44LAW 94LAW

Thin Diag.# 12.34*** 5.721*** 3.306*** 2.916*** 0.178 8.716*** 5.215***Thick Diag. (1.658) (0.132) (0.119) (0.331) (0.481) (0.357) (0.140)Thin Diag. -5.266*** -0.781*** -0.713*** -0.0929 1.127*** -2.136*** -0.645***

(1.600) (0.116) (0.107) (0.269) (0.383) (0.320) (0.123)Thick Diag. 2.970*** 1.772*** 1.376*** 0.388*** 0.269 3.606*** 1.342***

(0.484) (0.0489) (0.0437) (0.120) (0.171) (0.124) (0.0527)Constant 80.93*** 85.45*** 91.03*** 80.37*** 70.22*** 80.95*** 86.52***

(0.431) (0.0344) (0.0311) (0.0817) (0.117) (0.0879) (0.0369)

N 9,787 560,624 398,153 91,047 50,542 108,022 452,602R-sq 0.040 0.031 0.021 0.013 0.008 0.044 0.024

Day*Hour Dummies

Standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1

In Table 4 we see that the drop of the price is much smaller in the auctions where two

strongest bidders were bidding in a 20 minutes window and at the same day. The coefficient

22

does not change a lot when we pool the auctions with different deadlines together. Columns

(3-5) show that the effect is decaying as the number of bidders grow.

Economic intuition suggests that collusion leads to higher prices, however it is not nec-

essarily the case in one of the two potential mechanisms that we discussed. If joint bidding

is a commitment device then it can be that it is the auctions with smaller potential for col-

lusion is on the thin diagonal. Thus, the joint bidding will translate into price drops, rather

than price increases. However, our analysis shows that the suspicious simultaneous behavior

indeed is correlated with a price increase.

Table 4 supports the idea that collusion leads to higher prices. If we take auctions out of

”thin diagonal” and out of ”thick diagonal” – their average normalized price is represented

by a constant. The estimate of the collusion effect on the normalized price varies from 15.2%

in the first column (”narrow specification”) to 3.6% in the case of two bidders.11

5.2 Corruptive Patterns

We study a particular corruptive scheme - quote matching. The idea is thus: an auctioneer

agrees to cooperate with one of the bidders in an auction. Since the auctioneer is able to

observe other bidder’s bids before the conclusion of the auction he informs his partner of

each bid as it is received. Then once the bidder is confident all other bids have been placed

he places a bid so as to win the auction by as little as possible, thus maximizing the surplus.

Thus if with one hour until the auction deadline the lowest bid was 100 we would expect

the corrupt bidder to place a bid of 99.9 to undercut the current winner (alternately if the

current winning bid is below the marginal cost of the corrupt bidder he will simply decline

to bid or place a suitably high bid).

There are two testable implications of this: first any winner in such a corruptive scheme

will by necessity be the last to bid (if he is successful). Thus we are looking for auctions

where the winner bids after all other bids have been placed. Second, while the bidder has

access to all information submitted to the auctioneer he has no way of knowing the total

number of firms planning to bid. Thus the only way for him to ensure that he observes all

11Estimates θ̂3 divided by an estimate of the constant θ̂0.

23

other bids before he places his own is to place his bid as late in the process as possible.

Thus, if there are a significant portion of auctions affected by this scheme we would expect

to observe a large portion of auctions where the winner bids both after all other bidders and

very close to the deadline. Specifically we expect a much higher proportion of auctions where

the winner bids last than where players in other ranks bid last.

We start by looking on simple averages that reflect this phenomenon. Table 5 shows

what are the share of each of the order statistics in terms of bids by auctions with different

number of bidders.

Table 5: Shares of each rank bidding the last

1 2 3 4 5 6 Uniform ∆p1q

2 41.0% 59.0% - - - - 50.0% -9.0%

3 36.7% 34.0% 29.2% - - - 33.3% 3.4%

4 30.1% 26.5% 22.6% 20.8% - - 25.0% 5.1%

5 25.4% 21.2% 19.2% 17.6% 16.6% 20.0% 5.4%

6 21.7% 17.7% 16.3% 15.7% 14.4% 14.1% 16.7% 5.0%

For most of the auctions we observe the pattern that exactly matches our prior intuition

– winners bid more often later than the other participants. The only exception, where the

pattern is reverted is auctions with two bidders. This case does not directly interfere with

our analysis in this section, but we need to study it in more details. Table 5 is indicative of

the violation of the CR1 assumption.

Now we look on how predictive last hour bidding is for the winner bidding later (and for

other bidders bidding earlier). Table 6 looks at the difference of shares from Table 5 between

last hour and non-last hour bidding.

24

Table 6: Last hour bidding and winner bidding later

∆ “ spkqrlasthours´ 1 2 3 4 5 6 Total

´spkqrnot lasthours #of Auctions

2 +5.0% -5.0% - - - - 1,476,878

3 +6.6% -3.3% -3.3% - - - 441,797

4 +5.3% -1.9% -1.4% -2.0% - - 195,157

5 +4.7% -0.2% -1.5% -1.7% -1.4% 96,223

6 +4.1% -0.4% -0.9% -0.7% -1.0% -1.1% 50,202

Table 6 is indicative that assumption CR2 is likely to not hold. One way to measure

the size of this violation is to run a regression of Itthji “ minth´ji uu – winner being the last

to bid on I! KiŤ

k“1

thpkq ă 1u)

– the fact that one of the bids is placed at the very last hour.

If CR2 holds then the OLS estimate should not be significantly different from 0. We use a

following regression to derive the estimator of the asymmetry – α1:

Itthji “ minth´ji uu “ α0 ` α1 ¨ I!

Kiď

k“1

thpkq ă 1u)

` µi ` ξi

and

E”

ξi|I!

Kiď

k“1

thpkq ă 1u)

, µi

ı

“ 0.

Table 7 reports the results of this regression with deadline fixed effects for four specifica-

tions: pooled and by the number of bidders from two to four.

25

Table 7: Corruption and Quote matching

(1) (2) (3) (4)

Two Bidders Three Bidders Four Bidders

Someone bids 0.0471*** 0.0804*** 0.0706*** 0.0569***at the last hour (0.000632) (0.000840) (0.00146) (0.00216)Constant 0.317*** 0.327*** 0.324*** 0.261***

(0.000411) (0.000481) (0.00104) (0.00170)

N 2,329,017 1,476,878 441,797 195,157R-sq 0.003 0.008 0.006 0.004

Standard errors in parentheses: *** p<0.01, ** p<0.05, * p<0.1

Day*Hour Dummies Whole WeekWinner is the Latest

From Table 7 it is clear that when the winner bids after other bidders is predicted by

last hour bidding of any of the bidders. So symmetry is violated and the size of α̂1OLS is

estimate for the size of this violation.

The auctioneer who is planning to use the quote matching scheme with one of the par-

ticipants will leak the information and bids and this will push the bids closer to each other.

So now we use a normalized difference in bids as an outcome in the regression.

Table 8: Corruption, Quote matching and Bids’ Differences

(1) (2) (3) (4)

Two BiddersThree BiddersFour Bidders

Someone bids at the last hour# -1.594*** -1.054*** -1.665*** -1.476***Winner bids the latest (0.0252) (0.0293) (0.0644) (0.105)Someone bids at the last hour 1.535*** 0.966*** 0.665*** 0.0225

(0.0149) (0.0182) (0.0387) (0.0563)Winner bids the latest 1.646*** 1.849*** 1.952*** 0.938***

(0.0168) (0.0175) (0.0471) (0.0849)Constant 4.144*** 3.304*** 5.971*** 6.778***

(0.00950) (0.00999) (0.0269) (0.0437)

N 2,328,895 1,476,849 441,770 195,126R-sq 0.011 0.013 0.008 0.007

Standard errors in parentheses: *** p<0.01, ** p<0.05, * p<0.1

Day*Hour Dummies Whole Week

26

From Table 8 one can see that the difference in bids is smaller by 22-39% depending to

the specification as compared to the group with potentially less information leakage.

6 Mechanisms

6.1 Collusion: Detection of Cartels and Fake Firms

Once we established that excessive joint bidding is present and it is correlated with higher

prices in auctions we want to study the mechanism behind these phenomena. Is it coming

from fake firms that are only created for bidding purposes or from collusion between the two

real firms that monitor each other?

We start by several informal observations. If two firms participate in a large number of

auctions together and one firm never wins it might mean that this firm is less productive and

it just should not win any of the contracts. However, there are two cases, when it happens

and when it does not look like one of the firms is less productive. In these cases it seems

that one of the firms is just a fake firm that is created only for bidding purposes.

One case is when the gap in bids between the firms is always very small as a percentage

of the reserve price. Under certain mild assumptions in the spirit of Kawai and Nakabayashi

(2014) we can use it as an indicator of the similarity in costs distribution between firms. In

this case, they have to reverse the order of bids if they participate in many auctions together.

If this does not happen we mark these firms as suspicious. Suspicious firms are the ones that

participate in ten or more auctions together, one of the firms wins in 90% of cases and the

average difference of bids is less than 1% of the reserve price.

The second case is when, while two firms bid a lot together, they do not participate

in many auctions otherwise. We look at the pairs where firms participate in at least ten

auctions together, one of the firms wins at least 90% of the time and for the loser the share

of auctions of the pair is at least 90%.

Finally, our definition of cartel is when firms bid close to each other in time fairly often,

bid often together, and split the number of auctions they win.

In this section we decompose the joint bidding and the change in prices caused by it, into

27

a component created by fake firms (the first or the second type) and of cartels. We define a

binary variable – fake – if one of the firms in the auctions satisfy our criteria for fake firms.

We define a binary variable – cartel, if both of the firms in an auction satisfy our definition

of cartel. Finally, if firms participated in more than ten auctions together, but they do not

belong neither to a cartel, nor to a fake firm we code them ”often bidders”.

Table 9: Fake bidders, cartels and timings

(1) (2) (3) (4) (5) (6)

Law 94 Law 94 Law 94

Thick Diag. 0.207*** 0.202*** 0.203*** 0.198*** 0.189*** 0.182***(0.00115) (0.00130) (0.00115) (0.00130) (0.00127) (0.00145)

Fake 0.0102*** 0.00992*** 0.0102*** 0.00993*** 0.0125*** 0.0124***(0.00219) (0.00233) (0.00218) (0.00232) (0.00221) (0.00236)

Cartel -0.0176 -0.0157 -0.0155 -0.0133(0.0270) (0.0290) (0.0269) (0.0290)

Often 0.0132*** 0.0138***(0.00232) (0.00249)

Thick Diag.#Fake 0.0441*** 0.0494*** 0.0452*** 0.0509*** 0.0597*** 0.0663***(0.00284) (0.00303) (0.00283) (0.00303) (0.00288) (0.00309)

Thick Diag.#Cartel 0.424*** 0.424*** 0.436*** 0.437***(0.0280) (0.0301) (0.0279) (0.0300)

Thick Diag.#Often 0.0658*** 0.0625***(0.00299) (0.00322)

Constant 0.0857*** 0.0884*** 0.0857*** 0.0885*** 0.0836*** 0.0860***(0.000855) (0.000960) (0.000853) (0.000957) (0.000930) (0.00106)

N 563,079 454,232 563,079 454,232 563,079 454,232R-sq 0.073 0.072 0.078 0.078 0.081 0.081

Standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1

Fake Fake and Cartel Fake and Cartel and Often

Table 9 decomposes abnormal within-day bidding from Section 5.1 into fake firms, cartels

and often bidders. The results for cartels are large by construction. However, fake firms also

explain a lot of variation in same hour timing. ”Often bidders” have an effect similar to the

one of fake firms.

Armed with this knowledge we decompose the effect on prices and difference in bids in

Table 10.

28

The effects on prices are large for both cartels and fake firms, however it is smaller for

”often bidders”. The results for the distance in bids are similar.

Overall the results of this section indicate that both fake bidders and cartels are at least

partly responsible for the joint bidding patterns that we documented in Section 5.1.

Table 10: Fake bidders, cartels and prices

(1) (2) (3) (4)

Cartel 5.075*** 5.604*** -1.414*** -1.574***(0.299) (0.296) (0.137) (0.136)

Often 0.368*** 1.795*** -0.224*** -0.655***(0.0605) (0.0609) (0.0277) (0.0281)

Fake 7.047*** -2.125***(0.0593) (0.0273)

Constant 87.21*** 85.80*** 4.290*** 4.715***(0.0024) (0.0264) (0.0110) (0.0122)

Comparedto Control 5,8% 6,5% -33,0% -33,4%N 563,079 563,079 561,828 561,828R-sq 0.011 0.035 0.005 0.016

Win Bid to Reserve Price

Difference in Bids

Standard errors in parentheses: *** p<0.01, ** p<0.05, * p<0.1

7 Conclusion

In this paper we point out two different anti-competitive schemes in Russian procurement

auctions, one of a collusive and one of a corruptive type. We show that both schemes are

consistent with the patterns of the distributions of time variables in our data. We also

observe a significant increase in costs of procurement associated with these patterns.

Our findings suggest several policies that might improve efficiency of procurement. Firstly,

29

timing of bids should be stored and analyzed as well as the quotes. Secondly, based on our

techniques it is possible to attach a certain score to each bidder and auctioneer that represents

the probability of him being present in collusive or corruptive schemes. Based on these score

more detailed investigations may be launched by respective agencies. Thirdly, one can think

of developing mechanisms that will make the auctions more robust to known schemes.

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Appendix A: Robustness of the results for collusion to

the choice of the window

Table 11: A1. Indicator regression by the size of the window

(1) (2) (3) (4) (5)

5 mins 15 mins 30 mins 45 mins 60 mins

Thick Diag. 0.103*** 0.181*** 0.202*** 0.201*** 0.205***(0.00818) (0.0107) (0.0119) (0.0125) (0.0129)

Constant 0.0202*** 0.0589*** 0.119*** 0.175*** 0.227***(0.0074) (0.0098) (0.0109) (0.0114) (0.0118)

N 9,787 9,787 9,787 9,787 9,787R-sq 0.016 0.028 0.029 0.025 0.025

(6) (7) (8) (9) (10)

5 mins 15 mins 30 mins 45 mins 60 mins

Thick Diag. 0.121*** 0.209*** 0.244*** 0.251*** 0.247***(0.000825) (0.00102) (0.00113) (0.00120) (0.00125)

Constant 0.0426*** 0.0755*** 0.127*** 0.171*** 0.231***(0.0006) (0.0008) (0.0009) (0.0009) (0.0009)

N 565,854 565,854 565,854 565,854 565,854R-sq 0.038 0.072 0.078 0.074 0.066

Standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1

Friday 10AM two squares

Weekdays 8AM-6PM

We test our results by picking different time windows. Table A1 shows that bigger windows

can detect more collusive bids. However, there is a saturation point around 30 minutes

window, after which the size of the coefficient almost does not change.

We also try different time windows, see Table A2. Clearly, the closer the bids, the more

collusive the auction looks like. In Table A2 we study the robustness of the results from the

Table 4 by varying the bandwidth for the thin diagonal similar to Table 4. All the results

for proximity of timings remain the same, although the result for significant estimate of θ1

is somewhat less stable and small in magnitude.

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Table 12: A2. Prices and robustness

(1) (2) (3) (4) (5)

5 mins 15 mins 30 mins 45 mins 60 mins

Thin Diag.# 3.324*** 5.509*** 5.691*** 5.669*** 4.879***Thick Diag. (0.179) (0.139) (0.115) (0.104) (0.0966)Thin Diag. 1.052*** -0.469*** -0.722*** -0.993*** -0.307***

(0.161) (0.123) (0.0979) (0.0865) (0.0773)Thick Diag. 2.658*** 1.855*** 1.395*** 1.180*** 1.067***

(0.0461) (0.0482) (0.0505) (0.0523) (0.0547)Constant 85.35*** 85.43*** 85.48*** 85.56*** 85.46***

(0.0335) (0.0340) (0.0349) (0.0359) (0.0373)

N 565,854 565,854 565,854 565,854 565,854R-sq 0.026 0.031 0.033 0.032 0.032

Whole Week Day*Hour dummies

Standard errors in parentheses: *** p<0.01, ** p<0.05, * p<0.1

34