Machine learning with screens for detecting bid-rigging cartels

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ContentslistsavailableatScienceDirect

International

Journal

of

Industrial

Organization

www.elsevier.com/locate/ijio

Machine

learning

with

screens

for

detecting

bid-rigging

cartels

R

Martin

Huber

a

,

David

Imhof

a,b,c,d,∗

a_Department_of_Economics,_University_of_Fribourg,_Switzerland

b_University_of_Bourgogne_{Franche-Comté,}_CRESE_EA_3190,_Besançon_F-25000,

France

c

Unidistance,Switzerland

d

SwissCompetitionCommissionCOMCO

a r t i c l e i n f o

Articlehistory:

Received29March2018 Revised25April2019 Accepted25April2019 Availableonline6May2019

JELclassiﬁcation: C21 C45 C52 K40 L40 L41 a bs t r a c t

We combine machine learning techniques with statistical screens computed from the distribution of bids in tenders within the Swiss construction sector to predict collusion throughbid-riggingcartels.Weassesstheoutofsample per-formanceofthisapproachandfindittocorrectlyclassifymore than84%ofthetotalofbiddingprocessesascollusiveor non-collusive. Wealso discusstradeoffsinreducing falsepositive vs.falsenegativepredictionsandfindthatfalsenegative pre-dictionsincreasemuchfasterinreducingfalsepositive predic-tions.Finally,wediscusspolicyimplicationsofourmethodfor competitionagenciesaimingatdetectingbid-riggingcartels.

Keywords:

Bidriggingdetection Screeningmethods Machinelearning Lasso

Ensemblemethods

R_Disclaimer:_All_views_contained_in_this_paper_are_solely_those_of_the_authors_and_cannot_be_attributed_to

theSwissCompetitionCommission,itsSecretariat,theUniversityofFribourg,theUniverstiyofBourgogne Franche-Comté,orUnidistance(Switzerland).

∗_Corresp_onding_author_at:_Comp_etition_Commission_COMCO,_{Hallwylstrasse}_4,₃₀₀₃_Bern,_Switzerland.

E-mailaddresses:[email protected](M. Huber),[email protected](D. Imhof). https://doi.org/10.1016/j.ijindorg.2019.04.002

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1. Introduction

Incompetitionpolicy,screensarespecificindicesderivedfromthebiddingdistribution in tenders for distinguishingbetween competition and collusion as well as for flagging marketsandfirms likelycharacterizedbycollusion.Theyarethusofinterestfor compe-titionagenciesinorderto detectcartels andtoenforcecompetitionlaws.Inthelight of thevastvariety ofscreensproposedintheliterature(seeHarrington,2008;Jimenezand Perdiguero,2012; OECD,2013; Froebet al., 2014),thequestion arises whichdetection methodsomecompetitionagencyshouldchooseinpractice.However,veryfewpapers,if any,systematicallyinvestigatetheperformanceofthescreensbasedonstatistical meth-ods.

Inthis paper, wecombine machinelearning techniqueswith several screening meth-odsforpredictingcollusion.Weevaluatetheoutofsamplepredictionaccuracyinadata set of 584 tenders that are representative for the construction sector in Switzerland. Thedata cover4diﬀerent bid-riggingcartelsand compriseboth collusiveand competi-tive(post-collusion)tenders,basedonwhichwedeﬁne abinarycollusionindicatorthat servesasdependentvariable.Moreconcisely,weconsiderthescreensproposedbyImhof (2017b) for detecting bid-rigging cartels and investigate the performance of machine learning techniques whenusing these screensas predictors.Firstly, we investigate lasso logitregression,(seeTibshirani,1996),topredictcollusionasafunctionofthescreensas wellastheirinteractionsandhigherorderterms.Secondly,weapplyanensemblemethod that consistsof a weightedaverageof predictionsbasedonbaggedregressiontrees (see Breiman,1996),randomforests(seeHo,1995;Breiman,2001),andneuralnetworks(see McCullochandPitts,1943;Ripley, 1996).

We usecross validation to determine theoptimal penalization in lasso regression as well as the optimal weighting in the ensemble method. We randomly split the data into trainingandtestsamples andestimatethemodel parameters inthetrainingdata, while out of sample performance is assessed in the test data. We repeat these steps 100 times to estimate the average mean squared errors and classiﬁcation errors. The latter is deﬁned by the mismatch of actual collusion and predicted collusion, which is 1 if the algorithm predicts the collusion probability to be 0.5 or higher and 0 otherwise.

In ouranalysis, we distinguishbetween false positive andfalse negative predictions. A false positive impliesthat the machinelearning algorithm flags a tender as collusive even though no collusion occurs. From the perspective of a competition agency, this mightappear to bethe worstkindof predictionerror,as itcouldinduce anunjustified investigation.Incontrast,afalsenegativeimpliesthatthemethoddoesnotflagatender ascollusive,althoughcollusionoccurs.Thisisundesirable,too,becauseanymethodthat produces too many falsenegatives appearsnot worthbeing implemented due to a lack of statistical power in detecting collusion.A method that is attractive for competition agencies therefore needs to have anacceptable overall out of sampleperformance that satisfactorilytradesoff falsepositive andfalsenegativepredictionrates.

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Ourresultssuggestthat thecombinationofmachinelearningandscreeningisa pow-erful tool for detecting bid rigging. Both the lasso and the ensemblemethod correctly predict 84% of alltenders out of sampleor put differently, theoverall misclassification rateofeithermethodis16%.Thelassoperformsslightlybetterincollusivethanin non-collusive periods with 14% false negative and 18% false positive predictions, while the opposite holds fortheensemblemethod with17% falsenegativeand 15%false positive predictions.Therefore,themethodsproposedinthispaperexhibitadecentperformance as the shares of false positives and negatives are low. Furthermore, we also consider reducingtheshareoffalsepositivesbytighteningtheruleforclassifyingtendersas col-lusive,i.e.bypredictingcollusiononlytobe1ifthecollusionprobabilitypredictedbythe algorithmexceedsaspecificthresholdhigherthanthedefaultvalueof0.5.Thisexercise appears interesting for competition agencies to find an optimal tradeoff between false positives and false negativesby gaugingthe choice of theprobability threshold. Inour data, wenot verysurprisingly findthat reducingfalse positives induces a considerable increasein falsenegativepredictions.

Aslassoisavariableselectionmethod(basedonconstrainingthesumoftheabsolute values of the estimated slope coefficients) for picking important predictors, it allows determining themostpowerfulscreens.Amonga setof65predictorsthatconsistofthe originalscreensaswellastheirinteractionsandsquaredterms,wefindthattwoscreens playamajorrolefordetectingbid-riggingcartels:theratioofthepricedifferencebetween thesecondand(winning)firstlowestbidstotheaveragepricedifferenceamong allbids and thecoefficientof variationofbidsin a tender.By far lessimportantpredictorsare thenumberandtheskewnessofbids.However,wealsofindthatdiscardingthetwomost powerful screens does not significantly affect the accuracy of the prediction, as other screens“stepin” assubstitutes.

As a policy recommendation, we propose a two-stepprocedure to detectbid-rigging cartels.Thefirststepreliesonourcombinationofmachinelearningandscreening. Com-petitionagencies maycalculatethescreensforeachtenderfromthedistributionof sub-mittedbids,aninformationtypicallyavailableinprocurementprocesses.Theymaythen apply the model based on screening suggested in our paper to predict collusive and competitive tenders.Concerningclassification into collusiveandcompetitive tenders,it seems (atleastinourdata)advisabletousea decisionrulethatisbasedonapredicted probability threshold between 0.5 to 0.7. The second step consists of scrutinizing ten-dersflaggedascollusivebymachinelearning. FollowingImhofetal.(2018),competition agencies should investigate if specific groups of firms or regions can be linked to the suspicious tenders. Inparticular, agencies can apply thebid rotation screen, see Imhof etal.(2018),whichinvestigatestheinteractionamongsuspectedfirms,tocheckwhether theirgroup-specific interactionsmatcha bid-riggingbehavior.

Ourpaperisrelatedtoasmallliteratureonimplementingscreenstodetectbid-rigging cartels(seeFeinsteinetal.,1985;Imhofetal.,2018;Imhof,2017b).Thisliteraturediﬀers from themajority ofstudies ondetectingbid-riggingcartels that useeconometric tests typicallynotonlyrelyingonbiddinginformation,butalsoonproxiesforthecostsofthe

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ﬁrms (seePorter and Zona,1993;1999;Pesendorfer, 2000;Bajariand Ye,2003; Jakob-sson, 2007; Aryal and Gabrielli, 2013; Chotibhongs and Arditi, 2012a; 2012b; Imhof, 2017a). Finally, our paper is also related to studies on screens in markets not char-acterized by anauction process (see Abrantes-Metz et al., 2006; Esposito and Ferrero, 2006;HueschelrathandVeith,2011;JimenezandPerdiguero,2012;Abrantes-Metzetal., 2012).

The remainderof thepaper is organized as follows. Section 2 reviews ourdata that includesfourbid-riggingcartelsintheSwissconstructionsectoranddiscussesthescreens usedaspredictorsforcollusion.Section3presentsthemachinelearningtechniquesalong with the empirical results. Section 4 discusses several policy recommendations of our method.Section5 concludes.

2. Bid-rigging cartelsanddata 2.1. Sample description

Our data include 584 tenders with 3799 bids for a market volume of roughly 370 million Swiss francsand contain information aboutfour different bid-rigging cartels in Switzerland. The first cartel,denoted as cartel A, wasformed in the canton of Ticino (seeImhof,2017b),thesecondone,denoted ascartelB,inthecantonofSt.Gallen (see Imhof et al.,2018).TheSwiss CompetitionCommission(hereafter:COMCO) rendered a decisionforbid-riggingcartelBbut four firmsappealed thedecision.1 Thethirdand fourthcartelsaredenotedbyCandDandtheirdatahadnotbeenconsideredpriortothe present paper. For confidentiality reasons,we do notreport more detailed information oncartelsCandD.Alldataonthefourcasescomefromofficial recordsonthebidding processesatthecantonallevel.

Thefour bid-riggingcartelsconcerned roadconstructionand maintenanceaswell as related engineeringservices. Morespecialized engineering serviceslike bridge or tunnel constructionare, however, notincluded in thedata. Eventhough thefour cartels were formed in diﬀerent cantons of Switzerland, the structure of the construction sector is quitecomparableacross cantons.Therefore,thecontracts includedin thedataare rep-resentativeforthewhole ofSwitzerland.

For each of the cartels in our data, we observe collusive cartel periods as well as competitive post-cartel periods. Table 1 reports the number of tenders by cartel and period. Firmsriggedalltenders in cartelperiodsandallfirms submittingbidsincartel periods participatedin thebid-riggingcartel.Therefore, whenwesubsequentlyreferto tenders in cartel periods, it is implied that the bid-rigging cartels are complete (also called all-inclusive) in the sense that all firms participatingin thetender process were colluding.Furthermore,thefirmswere successfulinthesensethattheyadheredtotheir

1_See _{https://www.weko.admin.ch/weko/fr/home/actualites/communiques-}_de-_presse/nsb-_news.msg-

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Table1

Numberofcollusiveandcompetitivetenders.

Collusivetenders Perc.(%) Competitivetenders Perc.(%) Total

CartelA 148 82 33 18 181

CartelB 19 50 19 50 38

CartelC 93 35 174 65 267

CartelD 39 40 59 60 98

Total 299 51 285 49 584

agreements.Theoppositeholdsforalltendersinpost-cartelperiodsofourdata,inwhich ﬁrms competedto win contracts,sincethe selected tenders in post-cartel periods took place afterthecollapseofbid-riggingcartels oraftertheopeningofaninvestigation.

Our data thereforeoﬀera near-idealsetting as a laboratory of detectingbid-rigging cartels. On the one hand, the completeness of the cartels excludes the possibility of a collapsecausedbythepresenceofnon-cartelﬁrms.Ifitremainedunnoticed,sucha col-lapse could entailmisclassifying actuallycompetitivetenders as collusive.On theother hand,theuseofdataposterioritothecollapseofthebid-riggingcartelsortotheopening of aninvestigationshould ensure thattenders are actuallycompetitive. Tosum up,we have anuncontaminatedsampleinthesenseofhavingeither periodsofundisputed col-lusionorundisputedcompetitionforevaluatingtheperformanceofsimplescreensinour data.

Collusive agreementswere comparableacross thefourbid-riggingcartels and canbe described asa two-stepprocedure.Thefirststepconsistsofdeterminingthedesignated winner of the tender by the cartel. Various factors play a role for how contracts are distributed among firms in a cartel, namely the distance between firms and the con-tract location, capacity constraints, and specialization in terms of competencies (see Imhof, 2017b, and thecartelconventionofthe Ticino cartel,whichlistedthemain cri-teria forcontractallocation). Contractallocationhastobe beneficialtoallin thesense that all firms should win contracts, otherwise some firms would not have an incentive to participatein bid-rigging cartels.The second step consists of determining the price of the designated winner by the cartel. This is crucial because the cover bids should be higher than the bid of the designated winner to ensure contract allocation as in-tended by the cartel.In other words, allfirms knowthe price at whichthe designated winner of the cartel submits the bid. Even if cartel members communicate with each other onaregularbase, notallmembers necessarilysubmitbidsin eachtender. There-fore, we frequently observe different constellations of firms for distinct tenders in our data.

In all four cartels, the procurement procedure was based on a ﬁrst-price sealed bid auction.Theprocurementagencyannouncedadeadlineforsubmittingbidsfora partic-ular contract and provided all relevant documents for the tender process. Interested ﬁrms calculated and submitted their bids prior to the deadline. After the deadline passed, the call for bids was closed and the procurement agency opened the

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submit-ted bids to establish a bid summary, i.e. an oﬃcial record of the bid opening, which indicates thebids, the identities of the bidders,and thelocation and typeof the con-tract.

Prices indicated in the bids play a major role for allocating the contracts,although procurement agenciesinSwitzerland take alsofurthercriteriaintoconsideration.These include the organization of work, the quality of the solution offered by the firm, the referencesofthefirm,andenvironmentalaswellassocialaspects.Evenifsuchadditional criteria becomemore important as thecomplexity of the contracts increases,the price remains the mostdecisive feature in the procurement process, since the lowestbids in ourdataobtainedthecontractinmostcases.Therefore,pricecompetitionwasthemost importantdimension.2

EssentiallytwotypesofproceduresareusedbyprocurementagenciesinSwitzerland: the open procedure and the procedure by invitation. In an open procedure, all firms that meettheconditionsprovidedin thetenderdocumentationmay submita bid.It is legallystatedthatopenproceduresshould beusedforcontractsabove500’000CHF.In contrast, in theprocedure by invitation, the procurement agency determinespotential bidders by inviting a subset of firms (at least 3 firms, but generally more). Contracts above 500’000 CHF cannot be tenderedbased on invitation. Thus, competition might vary depending on the typeof procedure.Since information on the latter is only par-tiallyavailable from bidsummaries in ourdata, we include the number ofbidders and the mean value of submitted bids in a tender (to proxy contract value) as predictors in the empirical analysis in order to account for potential differences across types of procedure.

Inthepaper,weonlyuseinformationonbidscoming fromtheoﬃcial recordsofthe bidopening to calculatethescreens foreachtender.Since accessto thebidsummaries is eitherpubliclygranted or easilyestablishedthroughprocurement agencies, screening canbeorganizedinaratherdiscretemanner.Thatis,competitionagenciescanconduct thescreeningprocesswithoutattractingtheattentionofthebid-riggingcartel,whichis crucialforany detectionmethod.

2.2. Screens

A screen is a statistical tool to verifywhether collusionlikely exists in a particular market flagging unlawful behavior through economic and statistical analysis. Using a broaderdefinition,screenscomprise allmethodsdesignedto detectmarkets,industries, orfirmsforfurtherinvestigationassociatedwithanincreasedlikelihoodofcollusion(see OECD, 2013). Theliterature typicallydistinguishes between behavioral andstructural

2

Intendersinwhichnotonlytheprice,butalsoqualitativecriteriaplayadecisiverole,anothervaluable informationfortheallocationofcontractscouldbethescoreassignedbytheprocurementagencytoeach ofthe bidsafteranalysing themindetail w.r.t.thevariouscriteria. Thiscouldbethe caseforcomplex construction projectsnotincluded inourdata, likebridges,tunnels, orotherspeciﬁcservices. However, scoresaretypicallynotpubliclyavailableinoﬃcialrecordsonbidopenings,asprocurementagenciesanalyse andrankthebidsonlyaftertheopening.

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screens (see Harrington, 2008; OECD, 2013). Behavioral screens aim to detect abnor-mal behaviorofﬁrms whereasstructuralscreensinvestigate thecharacteristicsofentire markets that may favor collusion, in order to indicate if an industry is likely prone to collusion.

Behavioral screensare dividedinto complexand simplemethods. Complexmethods generallyuseeconometrictoolsorstructuralestimationofauctionmodelstodetect suspi-ciousoutcomes(seePorterandZona,1993;1999;Baldwinetal.,1997;Pesendorfer,2000; Bajari and Ye, 2003; Banerjiand Meenakshi, 2004; Jakobsson, 2007; Chotibhongs and Arditi, 2012a, 2012b; Aryal and Gabrielli, 2013; Imhof, 2017a). Simple screensanalyze strategic variablesas prices andmarketshares to determinewhether ﬁrms departfrom competitive behavior. While there are many applications of simple screens to various regularmarkets(seeAbrantes-Metzetal.,2006;EspositoandFerrero,2006;Harrington, 2008;HueschelrathandVeith,2011;JimenezandPerdiguero,2012;Abrantes-Metzetal., 2012;Froebet al.,2014,forsomeexamples),applicationstobid-riggingcasesarerather rare(seeFeinstein etal.,1985;Imhofet al.,2018;Imhof,2017b,forexceptions).

In this paper, we propose the application of simplescreens combined with machine learning to detectbid-riggingcartels.FollowingImhof (2017b),we considerseveral sta-tistical screens constructed from the distribution of bids in each tenderto distinguish between competition and collusion. Because each screen captures a different aspect of thedistributionofbids,thecombineduseofdifferentscreenspotentiallyallows account-ingfordifferenttypesofbidmanipulation.Inthefollowing, wepresentthescreensused as predictorsintheempiricalanalysis.

First,bidriggingmay affectthedispersionofbidsintendersduetocoordination.We thus considerthestandard deviationof thebidsinsome tenderas screen.Secondly,we alsoinclude thecoefficientofvariationasrelatedscreen,whichisdefinedas theratioof thestandard deviationandtheaverageofbids:

CV t=

s t

μt

, (1)

where s t and μt arethestandard deviation andmean ofthebids, respectively, insome

tender t .

Wealsosuspectthatbidriggingaﬀectstheconvergenceofbidsthroughcoordination. Wethereforeconsiderthefollowingkurtosis statisticas screen:

Kurt (b t)= n (n +1) (n − 1)(n − 2)(n − 3) n i=1 b it − μt s t 4 − 3(n − 1) 2 (n − 2)(n − 3), (2) where n denotes the number of bidsin some tender t , b it the i th bid, s t the standard

deviation ofbids,and μt themeanofbidsintender t .3

3_As_the_kurtosis_can_only_be_calculated_for_tenders_with_more_than₃_bids,_our_data_contain_only_tenders

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Furthermore, it appears plausible that bid-rigging cartels manipulate the difference betweenthefirstandsecondlowestbidsforallocatingcontractstothedesignatedwinner bythecartel.Toanalyzeifdifferencesbetweenthesecondandfirstlowestbidsintenders matter,wecalculate thepercentagedifferenceusingthefollowingformula:

D if f.P er c. t=

b 2t − b1t

b 1t

, (3)

where b 1t is thelowest bidand b 2t thesecond lowest bidin tender t . As analternative

screen,wealsoconsider theabsolutediﬀerencebetweentheﬁrstandsecondlowestbids b 2t − b1tin the empirical analysis.

Moreover,bidmanipulation mayaﬀect thesymmetryofthedistributionofbidsin a tender.Wethereforeinclude thefollowingskewnessstatisticasscreen:

Skew( b t)= n (n − 1)(n − 2) n i=1 b it − μt s t 3 , (4)

where n denotesthenumber ofthebidsinsometender t , b it the i th bid, s t thestandard

deviationofthebids,and μt themeanofthebidsin tender t .4

Bidmanipulationin bid-riggingcartelsmightsimultaneouslyaffect thedifference be-tweenthesecondandfirstlowestbidsandthedifferencesamonglosingbids.Tocapture sucheffects,wefollowImhofetal.(2018) andconstructarelativedifferenceratioby di-vidingthedifferencebetweenthesecondandfirstlowestbidsbythestandarddeviation ofalllosingbids.

RD t=

b 2t − b1t

s t,losingbids

, (5)

where b 1t denotesthelowestbid, b 2t thesecond lowestbid,and s t,losingbidsthestandard

deviationcalculatedamongthelosing bidsinsome tender t .Arelativedifferencehigher than1indicatesthatthedifferencebetweenthesecondandfirstlowestbidsisgreaterthan one standard deviation among losing bids indicatinga (more) asymmetric distribution ofthebids.

Inaddition,wenormalizethedifferencebetweenthefirstandsecondlowestbidsina tenderdividingitbythemeanofthedifferencesbetweenall(intermsofvalue)adjacent bids.Wehenceforthcall thisscreenthenormalizeddistance:

N ORM D t=

b 2t − b 1t

(ni=1−1,j=i+1bjt−bit)

n−1

, (6)

where n is thenumber of bids, b 1t is the lowestbid, b 2t thesecond lowest bid,and b it,

b jt are adjacentbids in some tender t , with thevaluesof bidsbeing ordered increasing

4_The_skewness_can_only_be_computed_for_tenders_with_more_than₂_bids._Our_data_contains_only_tenders

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Table2

Descriptivestatistics.

Screens Mean Mean Std Min Max Obs

CartelPeriods Coefficientofvariation 3.42 2.97 1.73 0.69 13.74 299 Kurtosis 1.50 1.19 2.22 −4.03 8.14 299 Perc.difference 3.92 3.96 2.37 0.43 24.93 299 Skewness −0.58 −0.60 1.05 −2.76 2.21 299 Relativedistance 2.69 1.58 2.95 0.11 23.03 299 Normalizeddistance 2.23 1.96 1.31 0.19 6.95 299 Numberofbidders 6.74 6.00 2.35 4 13 299 Contractvalue 0.731 0.381 0.868 0.023 4.967 299 Standarddeviation 0.022 0.012 0.024 0.0007 0.136 299 Absolutedifference 0.028 0.011 0.035 0.0003 0.272 299

Competitiveperiods

Coefficientofvariation 8.05 7.16 4.48 1.49 34.14 285 Kurtosis 0.07 −0.15 1.86 −5.40 6.06 285 Perc.difference 4.89 3.52 4.87 0.03 38.93 285 Skewness 0.27 0.25 0.84 −1.83 2.36 285 Relativedistance 0.83 0.55 1.05 0.01 8.07 285 Normalizeddistance 1.01 0.85 0.74 0.01 3.77 285 Numberofbidders 6.26 6.00 2.02 4 13 285 ContractValue 0.627 0.392 0.767 0.044 7.385 285 Standarddeviation 0.050 0.028 0.101 0.002 1.499 285 Absolutedifference 0.026 0.012 0.041 0.0001 0.323 285 Note:“Std”,“Min”,“Max”,and“Obs” denotethestandarddeviation,minimum,maximum,andnumber ofobservations,respectively.

order. A valuelarger than1 indicates that the difference betweenthe second and first lowestbidsislarger thantheaveragedifferencebetweenalladjacentbidsina tender.

Asmentionedanddiscussedintheprevioussection,alsothenumberofbiddersandthe meanof thebidssubmittedin atenderareincludedinadditionto thescreens,yielding allin all10predictors.

2.3. Descriptive statistics for the screens

Table2providesdescriptivestatisticsforallscreens,separatelyforcollusiveand com-petitiveperiods. Weseethat mostofthescreensgenerallydifferin termsofmeansand standard deviationsacross bothgroups ofperiods.Themeanofthecoefficientof varia-tion amounts to3.42 in cartelperiods whichmore thandoubles in competitiveperiods (8.05). Moreover,thespreadofthecoefficientofvariationislowerincartelperiodswith a standard deviation of 1.73, compared to 4.48for competitive periods. Bids are thus more similarin collusivethanincompetitiveperiods.Thesameappliesto thestandard deviation of thebids. Moreover, themean of the kurtosis is 1.50 in cartelperiods and 0.07 in competitive periods. This points to a more compressed distribution of bids in

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Table3

Statisticaltestsforthescreens.

Screens z-statistic p-valueMW KSa p-valueKS Coefficientofvariation 16.30 <.0001 8.05 <.0001 Kurtosisstatistic −7.91 <.0001 3.42 <.0001 Percentagedifference 0.10 0.9211 2.14 0.0002 Skewnessstatistic 9.69 < .0001 4.67 < .0001 Relativedistance -12.10 < .0001 5.24 < .0001 Normalizeddistance −12.78 < .0001 5.63 < .0001 Numberofbidders −2.20 0.0279 1.20 0.1146 Contractvalue −0.55 0.5854 0.85 0.4596 Standarddeviation 8.28 <.0001 3.75 <.0001 Absolutedifference −1.30 0.1951 1.33 0.0596 Note:“Screens”,“z-statistic”,“p-valueMW” denotethescreenstested,thez-statisticoftheMann-Whitney testandthep-valueoftheMann-Whitneytest,respectively.“KSa” and“p-valueKS” denotetheasymptotic Kolmogorov–Smirnovstatisticandthep-valueoftheKolmogorov–Smirnovtest,respectively.

collusive periods than in competitive periods, meaning that bids converge when cartel membersrig contracts.

Turning to skewness, we find a mean of −0.58 in cartel periods, i.e. a tendency to left skewed distributions, contrastingwith a mean of 0.25in competitiveperiods. This indicates that bidriggingtransformsthedistributionof thebidsin amore asymmetric distributionthaninthecompetitiveperiods.Furthermore,themeansoftherelativeand normalizeddistancesamountto2.69and2.23,respectively,incartelperiods,butto0.83 and 1.01, respectively, in competitive periods. Under collusion, the difference between thefirstandsecondlowestbidstendstoincreaserelativetodifferencesamongthetotal of (losing) bids. For the percentage difference between the first and the second lowest bids, the relative changes across periods are smaller: The mean and median amount to 3.92 and 3.96,respectively, forcartel periods and to 4.89 and 3.52,respectively, for competitive periods. However, the standard deviation of the percentage difference in cartel periods (2.37) is only half of that in competitive periods (4.87), pointing to a potential manipulations of the difference betweenthe first and the second lowest bids. Concerningtheabsolutedifference,we findnosuspiciouschangesin themeanorin the spread acrossperiods.Finally,thecontractvalueexhibitsa meanof0.73and amedian of 0.38 million CHF in cartel periods, which is not too different from the respective values of 0.63 and 0.39 million CHF in competitive periods. In both types of periods, the number of bidders lies between 6 and 7 on average, but may vary between 4 to 13.

Table3reportsMann-WhitneyandtheKolmogorov-Smirnovtestsforthepredictors. Accordingtoeither test,thedifferencesobservedbetweencollusiveandcompetitive pe-riods arestatisticallysignificant at 1%levelforthecoefficient ofvariation,thekurtosis statistic, the skewness statistic, the relative distance, thenormalized distance and the standarddeviation.Thenumberofbiddersissignificantlydifferentat5%levelaccording to theMann-Whitney test but not to the Kolmogorov-Smirnov test. The difference in thepercentagedifferenceissignificantat1%levelaccordingtotheKolmogorov-Smirnov

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test. Finally, the contract value (approximated by the mean of the bids) and the ab-solute difference betweenthe firstand second lowestbidsare notsignificantly different at the5%level. Allin all,thenumerousstatistically significantresultspointto the po-tential usefulnessof screens for predicting collusion. Note that for thelasso procedure discussed in thenext section, wein additionalto the 10 originalpredictors include in-teraction and second order terms for the predictors so that all in all 65 variables are used.

3. Empiricalanalysisusingmachinelearning

Weapplymachinelearningmethodstotrainandtestmodelsforpredictingbid-rigging cartels basedonthe screenspresented in theprevious section.Speciﬁcally, we consider two approaches:Lasso regression(seeTibshirani,1996)forlogitmodels anda so called ensemble method that consists ofa weighted average ofseveral algorithms, in ourcase bagged regression trees (see Breiman, 1996), random forests (see Ho, 1995; Breiman, 2001),andneuralnetworks(seeMcCullochandPitts,1943;Ripley, 1996).

3.1. Lasso regression

Wesubsequentlydiscusspredictionbasedonlassologitregressionaswellasthe eval-uation of its out of sample performance. First, we randomly split the data into two subsamples. Theso-calledtrainingsamplecontains75% ofthetotalofobservationsand is tobeused forestimatingthemodelparameters.Theso-calledtest sampleconsistsof 25% oftheobservationsandisto beusedforoutofsamplepredictionandperformance evaluation.Aftersplitting,thepresenceofacartelisestimatedinthetrainingsampleas a functionofa range ofpredictors, namelythe originalscreens as well as theirsquares and interactiontermsto allowfora ﬂexiblefunctionalrelation.

Lasso estimationcorrespondsto a penalizedlogitregression, wherethepenaltyterm restrictsthesumofabsolutecoefficientsontheregressors.Dependingonthevalueofthe penaltyterm,theestimatorshrinksthecoefficientsoflesspredictivevariablestowardsor evenexactly tozeroandthereforeallowsselectingthemostrelevantpredictorsamonga possibly largeset ofcandidatevariables. Theestimationofthelasso logitcoefficientsis basedonthefollowingoptimizationproblem:

max β0,β ⎧ ⎨ ⎩ n i=1 ⎡ ⎣y i ⎛ ⎝β0+ p j=1 βjx ij ⎞ ⎠_{− log}1+e β0+pj=1βjxij ⎤ ⎦_{− λ}p j=1 |βj| ⎫ ⎬ ⎭. (7) β0, β denotetheinterceptandslopecoeﬃcientsonthepredictors,respectively, x isthe

vector ofpredictors, i indexesanobservation in ourdataset (with n beingthenumber of observations), j indexesa predictor(with p being thenumberofpredictors),and λ is a penaltytermlargerthanzero.Weusethepredictorsdescribedintheprevioussection

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and also include interaction and squared terms such that altogether 65 regressors are usedin thelassologit regression.

Weusethelassologitprocedureinthe“hdm” packageforthestatisticalsoftware“R” byChernozhukovetal.(2016) andselectthepenaltyterm λ such that itminimizesthe meansquarederror,whichweestimateby15-foldcross-validation.Thisisperformedby randomlysplittingthetrainingsampleinto15subsamples,alsocalled folds.14folds are used to estimate the lasso coefficientsunder different candidate values for the penalty term. 1 fold is used as so-called validation data set for predictingcartels basedon the differentsetsofcoefficientsrelatedtothevarious penaltiesandforcomputingthemean squared error(MSE). The latter corresponds to the average of squared differences be-tweenthepredictionandtheactualpresenceofa cartelin thevalidation data.Therole offoldsisthenswappedinthesensethateachofthemisusedonceasvalidationdataset and14timesforcoefficientestimation,yielding15MSEsperpenaltyterm.Theoptimal penalty term is chosen as the value that minimizes the average over the 15 respective MSEestimates.

Ina nextstep,we run lassologit regressionin the(entire)trainingsample basedon the(sample-sizeadjusted)optimalpenaltytermtoestimatethecoefficients.Finally,we use these coefficients to predict the collusion probability in the test sample. To assess theperformanceofoutofsampleprediction,weconsidertwomeasures:first,theMSEof thepredictedcollusionprobabilitiesin thetest sampleand second,the shareof correct classifications. To compute the latter measure, we create a variable which takes the value one for predicted collusion probabilities greater than or equal to 0.5 and zero otherwise, and compare it to the actual incidence of collusion in the test sample. We repeatrandomsamplesplittinginto75%trainingand25%testdataandallsubsequent steps previously mentioned 100 times and take averages of our performance measures overthe100repetitions.

3.2. Ensemble method

Prediction andperformanceevaluation fortheensemblemethod hasin principlethe same structure as forthe lasso approach.The differenceis that rather than lassologit regression,anyestimationstepnowconsistsofaweightedaverageofbaggedclassification trees, random forests, and neural networks. The first two algorithms depend on tree methods, i.e.recursivelysplittingthedatainto subsamplesin awaythat minimizesthe sumofsquareddifferencesofactualincidencesofcollusionfromthecollusionprobabilities within thesubsamples. Both methods estimate thetrees in a largenumber of samples repeatedlydrawnfromtheoriginaldataandobtainpredictionsofcollusionbyaveraging over the tree (or splitting) structure across samples. However, one difference is that bagging considers all explanatory variables as candidates for further data splitting at each step, while random forests only use a random subset of the total of variables to prevent correlation of trees across samples. Finally, neural networks aim at fitting a systemoffunctionsthatflexibly andaccuratelymodels theinfluence oftheexplanatory

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Table4

Performanceofthelassoandensemblemethods.

MSE MSE.cart MSE.comp corr corr.cart corr.comp

Lasso 0.122 0.116 0.128 0.838 0.857 0.819

Ensemble 0.119 0.121 0.116 0.840 0.828 0.854 Note: “MSE”, “MSE.cart”, “MSE.comp” denote the mean squared errors in the total sample, in cartel periods,andinperiodswithcompetition,respectively.“corr”,“corr.cart”,and“corr.comp” denoteratesof correctclassiﬁcationinthetotalsample,incartelperiods,andinperiodswithcompetition,respectively.

variables oncollusion.Wenotethat forthese threemachinelearning algorithms,which are explained in more detailin the appendix,no higher order or interaction terms are includedinadditiontotheoriginalpredictors,astree-basedmethodsare(incontrastto lassologit)inherentlynonparametric.

Cross-validation in the training sample determines the optimal weight each of the three machinelearning algorithm obtains in the ensemblemethod, justanalogously to thedetermination oftheoptimalpenaltytermin lassoregression.Tothisend weapply the“SuperLearner” packagefor“R” byvanderLaanetal.(2007)withdefaultvaluesfor baggedregressiontree,randomforest,andneuralnetworkalgorithmsinthe“ipredbagg”, “cforest”, and “nnet” packages, respectively. Theoptimal combination of algorithms is then used to predictthe collusion probabilitiesin thetest sample and to computethe performancemeasures.

3.3. Empirical results

Table4reportstheoutofsampleperformanceoflassoregressionandensemble meth-ods in the total of the test data, as well as separately for periods with and without collusion.Both algorithmsperformsimilarly wellin termsoftheMSE andtheshare of correctly classified cartels in outof sample data containingboth cartel andpost-cartel periods.LassoexhibitsaMSEof0.12andacorrectclassificationrateof84%,quasi iden-ticaltothoseoftheensemblemethod.Theoverallshareofincorrectpredictionstherefore amounts to16%foreither method.Whenseparatelyconsideringcartelandcompetitive periods, lasso performs slightly better for correctly classifying collusive tenders (86%) thantheensemblemethod(83%).Thelatter,however, ismoderatelysuperiorfor classi-fying competitivetenders(85%)thanlassoregression(82%).Put differently,theresults indicate that lassoproduces18%offalsepositiveand 14%offalsenegativepredictions, whereas theensemblemethod produces15% of falsepositive and17% of falsenegative predictions.

From a policy perspective, incorrectly classifying cases of non-collusion as collusion (falsepositives)andthus,unnecessarilyﬁling aninvestigation,mightberelativelymore harmful than incorrectly classifyingcasesof collusionas non-collusion(falsenegatives) and thus not detecting a subset of bid-rigging cartels. A way to reduce the incidence of incorrectclassiﬁcationsofactualnon-collusionisraisingtheprobabilitythresholdfor classifying a prediction as collusionfrom 0.5 to some higher value between 0.5 and 1.

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Fig.1. Falsepositiveandfalsenegativeresultsbytighteningthedecisionrule.

This,however, generallycomesatthecostofreducingthelikelihoodofdetectingactual cartels andincreasesthereforethefalsenegativeresults.Competitionagencies therefore needto appropriatelytradeoﬀ the likelihoodof falsepositiveand falsenegativeresults toderive anoptimalruleconcerningtheprobabilitythreshold.

Tosee thetradeoffs inclassification accuracy,Fig.1 reportsthecorrectclassification rates of either methods in the total test data as well as separately for periods with and without collusionacross different probability thresholds. As expected, the correct classification rate in competitive periods increases in the probability threshold for the decisionrule(falsepositiveresultsdecrease).Incontrast,thecorrectclassificationratein cartelperiodsdeterioratesmuchfasterinthethreshold(falsenegativeresultsincrease). Ifacompetitionagencydesirestominimizetheriskoffalsepositives,itcouldraisethe probabilitythresholdvalueto0.7.Insuchacase,thelassoandensemblemethodsclassify roughly70%ofcollusivetendersandmorethan90%ofthecompetitivetenderscorrectly, implyingapproximatively10%offalsepositiveand30%offalsenegativeresults.Thegain ofreducingtheriskoffalsepositivesthereforeinducesadisproportionateincreaseinfalse negatives. Moreover, any further tightening of the decisionrule would leadto aneven more severeincreaseof falsenegatives:Ata probability thresholdof0.8, bothmethods produce40–45% offalsenegatives.It thereforeseems that forourdata,thebest-suited probability threshold lies between values of 0.5 and 0.7. One advantage of combining screening methods and machine learning consists in quantifying the trade-off of false positives andfalse negativesso that competitionagencies arecapable todetermine the decisionrulethatoptimallymatchestheirneeds.

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Table5

Averageabsolutevaluesofimportantlassocoeﬃcients.

Variable NORMD CVBID SKEW NBRBID

Value 1.02 0.34 0.11 0.06

Note:“NORMD”,“CVBID”,“SKEW”,and“NBRBID” denotethethenormalizeddiﬀerence,thecoeﬃcient ofvariation,theskewness,andthenumberofbids,respectively.

Table6

Logitcoeﬃcientsforselectedscreens.

(1) (2) (3) (4) Constant 1.46∗∗∗ 1.56∗∗∗ 1.74∗∗∗ −1.92∗∗∗ (0.48) (0.41) (0.39) (0.20) NORMD 1.02∗∗∗ 1.04∗∗∗ 0.89∗∗∗ 1.32∗∗∗ (0.21) (0.20) (0.15) (0.13) CVBID −0.62∗∗∗ _−0.61∗∗∗ _−.61∗∗∗ (0.06) (0.06) (0.06) SKEW 0.20 0.23 (0.20) (0.18) NBRBID 0.02 (0.06) Obs 584 584 584 584 Pseudo-R2 _0.45 _0.45 _0.44 _0.23

Note:“NORMD”,“CVBID”,“SKEW”,and“NBRBID” denotethethenormalizeddifference,thecoefficient ofvariation,theskewness,andthenumberofbids, respectively.∗∗∗,∗∗,∗denotesignificanceatthe1%, 5%,and10%level,respectively.“Obs” and“Pseudo-R2_{” denote}_the_number_of_observations_and_the_pseudo

Rsquared.

To judge therelative importanceof predictorsfor determiningcollusion, Table5 re-portstheaverageabsolutevaluesoflassocoefficientsacrossregressionsinthe100 train-ings samples (obtained by repeatedly splitting the total sample into training and test samples)thatarelargerthanorequalto0.05.Itneedstobepointedoutthatingeneral, theestimatesdonotallowinferringcausalassociations,aslassomayimportantlyshrink thecoefficientofarelevantpredictorifitishighlycorrelatedwithanotherrelevant pre-dictor.5 _{Nevertheless,} _Table ₅ _allows _spotting_the _most_prominently_selected _predictors amongthetotalofregressorsprovidedinthelassoregressions.Weobservethatthe nor-malized difference(NORMD) andthe coefficientof variation(CVBID) have by farthe highestpredictivepower.

Table 6 reports the coefficients of standard logit regressions using various sets of screens according to their importance in lasso regression as indicated in Table 5. The coefficient of variation(CVBID) is negatively related withthe probability of collusion. That is, bidriggingdecreases thecoefficientof variation,even conditionalon theother predictorsusedinthefourdifferentspecifications.Incontrast,thenormalizeddifference

5

Wealsonotethatinourframework,causalitygoesfromthedependentvariabletothepredictorsrather than theother wayround as it wouldbethe case in contexts ofcausal inference.In causal terms,the incidence ofcollusionasexplanatoryvariableaﬀectsthedistributionofbidsandthusthescreens,which can beregarded as outcomevariables. Our prediction problemthereforeconsists of analyzinga reverse causality:Byinvestigatingthescreens,oneinferstheexistenceoftheircause,namelycollusion.

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Table7

Marginaleﬀectsforselectedscreens.

(1) (2) (3) (4) NORMD 0.25∗∗∗ 0.26∗∗∗ 0.22∗∗∗ 0.33∗∗∗ (0.05) (0.05) (0.04) (0.03) CVBID −0.15∗∗∗ _−0.15∗∗∗ _−0.15∗∗∗ (0.01) (0.01) (0.01) SKEW 0.05 0.06 (0.05) (0.05) NBRBID 0.01 (0.01)

Note:“NORMD”,“CVBID”,“SKEW”,and“NBRBID” denotethenormalizeddifference,thecoefficientof variation,theskewness,andthenumberofbids,respectively.∗∗∗,∗∗,∗denotesignificanceatthe1%,5%, and10%level,respectively.

(NORMD)hasa(conditionally) positiveassociation. Suchresultsindicatethat bid rig-ging affects the distribution of the bids in two manners in our data. First, it reduces the variance in the distribution of the bids indicating that bids are closer each other than in competitive tenders. Second, it produces asymmetry in the distribution of the bidssincethedifferencesbetweenthesecondandfirstlowestbidsaresignificantlyhigher thanthedifferencesbetweenthelosing bidsin cartelperiods.Finally,thecoefficientsof thenumberofbidders(NBRBIDS)arepositiveandthereforegoagainsttheexpectation that ahighernumber ofbiddersshould increasecompetition,butareneverstatistically significantatthe5%level.Skewness(SKEW)doesnotshowanystatisticallysignificant associationeither,atleastconditionalontheother,more predictivescreens.

Table 7 reports the “marginal” effects (albeit not to be interpreted causally in our predictiveframework)fortheaverageobservationinthesample(i.e.atthesamplemeans ofthepredictors)andvarioussetsofscreens.InaccordancewiththeestimatesinTable6, thecoefficientofvariationandthenormalizeddistance,whicharesignificantinallmodels, have in absolutetermsbyfarthe largestmarginal effects forexplainingtheprobability ofcollusion.Augmentingthecoefficientofvariationbyoneunitdecreasestheprobability ofcollusionbyroughly15percentagepoints,whileanincreaseofoneunitinnormalized distance raise theprobability ofcollusion by22 to 33 percentagepoints, depending on themodel.Themarginaleffects oftheotherpredictorsare muchcloserto zeroandnot statisticallysignificant atthe5%level.

3.4. Robustness analysis

To investigate the robustness of our methods to the omission of predictors, we dis-cardthetwomostimportantvariables,namelythenormalizeddifference(NORMD)and the coefficientof variation (CVBID) and we apply thelasso and the ensemblemethod procedurestotheremainingvariables.Table8reportstheMSEandtheshareofcorrectly classified cartels in outofsample data.Both thelassoand ensemblemethodsexhibit a correctpredictionrateof83%,implyingthattheremainingpredictorsappeartobegood

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Table8

Performancewhendropping2mostimportantpredictors.

Lasso 0.129 0.128 0.130 0.830 0.827 0.835

Table9

Performanceusingonlyscale-invariantvariables.

Lasso 0.122 0.115 0.129 0.840 0.862 0.818

substitutes forthe omittedones in ourcontext. Theresultsshow that whenimportant predictorsaredropped,otheronesbecomemoreimportantand“stepin”,suchthatthe correctpredictionratesarehardlyaﬀected.Thisindicatesthat machinelearningcanbe quiterobusttotheuseofamore limitedsetofpredictors.

Toinvestigatetherobustnessofourmethodswithrespecttothechoiceofthescreens, we apply the lasso and the ensemble procedures using only scale-invariant variables.6 Table 9 reports theMSE andthe share of correctly classiﬁed tenders in outof sample datacontainingbothcartelandpost-cartelperiods.Boththelassoandtheensemble pro-cedures exhibitcorrectpredictionratesofnearly84%,implyingthatthescale-invariant variables predict the presence or absence of bid rigging rather decently. The normal-ized distance (NORMD) and the coeﬃcient of variation (CVBID) again are the most importantpredictors.

In the next robustness check, we change how data are split into training and test samples. Instead of randomly splitting across cartels,we trainthe algorithms on three cartels anduseobservationsfromthefourthcartelastestsample.Inthespirit ofk-fold cross-validation,eachcartelservesonceastestdatasetandthreetimesastrainingdata. Table 10 reports the average values for the MSE and the share of correctly classified cartels in theoutofsampledata.Wefind acorrectpredictionrateof81% forthelasso and of85%fortheensemblemethod.Lassoregressionexhibitsa correctpredictionrate of 80%forcollusiveandof87% forcompetitiveperiods.Thiscontrastswiththecorrect predictionratesfortheensemblemethod,whichamountsto97%forcollusiveandto75% for competitiveperiods.Suchdifferences (alsow.r.t.ourmain analysisabove) aremost likely explainedbytheunbalancedsamplesofcollusiveandcompetitiveperiodsforeach cartel,asshowninTable1.Nevertheless,thisrobustnesscheckbyandlargeconfirmsthe

6_{Scale-invariant}_variables_are_the_coeﬃcient_of_variation,_the_kurtosis_statistic,_the_percentage_diﬀerence,

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Table10

Performancewhenusing3cartelsfortrainingand1fortesting.

Lasso 0.143 0.156 0.098 0.805 0.795 0.870

Ensemble 0.112 0.034 0.179 0.853 0.970 0.748 Note: “MSE”, “MSE.cart”, “MSE.comp” denote themean squared errors in the total sample, in cartel periods,andinperiodswithcompetition,respectively.“corr”,“corr.cart”,and“corr.comp” denoteratesof correctclassiﬁcationinthetotalsample,incartelperiods,andinperiodswithcompetition,respectively.

Table11

Performanceundermisclassiﬁcationof15%ofobservations.

Lasso 0.195 0.185 0.205 0.725 0.769 0.680

Ensemble 0.189 0.182 0.197 0.735 0.744 0.726 Note: “MSE”, “MSE.cart”, “MSE.comp” denote themean squared errors in the total sample, in cartel periods,andinperiodswithcompetition,respectively.“corr”,“corr.cart”,and“corr.comp” denoteratesof correctclassiﬁcationinthetotalsample,incartelperiods,andinperiodswithcompetition,respectively.

attractivenessofmachinelearning,as inparticulartheensemblemethodattainsalmost thesamecorrectpredictionrateasin ourmain analysis.

In a ﬁnal check, we introduce measurement error in the outcome variable based on randomlyreclassifying15% ofobservations bysettingcollusiontocompetitionandvice versa (using the same approach for splitting the data into training and test sets as in the main analysis). Intuitively, this introduction of measurement erroris similar to an increaseoftheerrortermin aclassical econometricmodel,implyingthat thesignals of thepredictorsforclassifyingcollusiongetrelativelyweaker.Theresultsarepresentedin Table11.Thecorrectpredictionratesforthelassoandensemblemethodsamountto73% and 74%, respectively. This appears still satisfactory in the light of the non-negligible amount ofmeasurementerror.

4. Policyimplications

Ourresultsdemonstratetheusefulnessofsimplescreenscombinedwithmachine learn-ing, amounting to an out of sample rate of correct classifications of 84% in our main analysis for both the lasso and the ensemble method. Furthermore, we discussed that themachinelearningapproachallowstradingoff thelikelihoodoffalsepositiveandfalse negative predictions bychanging the probability threshold in a way that is considered optimal by a competition agency. This appears to be an important innovation in the literature on detecting collusion, as to the best of our knowledge no other study has directlyassessedtheperformanceoftheirmethodwithrespecttofalsepositiveandfalse negative results. We subsequentlydiscuss some further implications of our method for policy makers,namelyitsadvantages in termsofdata requirementsand use,its appar-ent generalizability to different empirical contexts of collusion,and its integration in a processofex-ante detectionof collusion.

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4.1. Data requirements and data use

The method proposed in this paper has several advantages relative to other studies in the field. First, data requirements are comparably low. Implementing the machine learning approach and calculating the screens is straightforward and solely relies on informationcoming fromofficialrecordsofthebidopeningandthebidssubmitted.Not even the identification of bidders is essential, which allows collecting information and implementing the method discretionarily, without attracting the attention of a cartel. Thisappearscrucial,becauseifsomecartelbecomeawareoftheprocess,itmightdestroy evidence such that opening an investigation would be unsuccessful. In contrast, other detection methods, such as the econometric tests proposed by Bajari and Ye (2003), require data on cost variables, which are difficult to obtain without having access to firmleveldata. Thismaycompromise thesecrecyinwhichcompetitionagenciesshould implement anymethod aimedatdetectingcollusion.

Wenotethatiftheoﬃcialrecordsofthebidopeningsarenumerousandrepresentative for a large share of the market, it may be possible to compute cost variables for an econometricestimationofthebiddingfunctionevenwithoutdirectlyaccessingﬁrmlevel data, (seeImhof,2017a).Eveninthiscase,theconstructionofthecostvariablesmight be time-consuming(relativetothesimplescreens)andthereforepotentiallywastefulfor competitionagencies,whichshouldideallyconcentratetheirresourcesontheprosecution ofcartels.Theresourceargumentisparticularlyrelevantinthelightofthehighnumber of falsenegativesproducedbythemethodof Bajariand Ye(2003) whenapplied tothe Ticino case,seeImhof(2017a),implyingthatsuchcostvariable-basedapproachesmight have lowpower.

Finally,thecombinationofscreeningandmachinelearningallowsassessingand gaug-ing the accuracy of classifying collusion out of sample, which is relevant for data yet to be analyzed. It therefore tells us something about how well past data can be used to predict collusion in future data. To the best of our knowledge, none of the other detectingmethodshassofarproperlyassessedoutofsampleperformancebasedon dis-tinguishing between training and test data. Furthermore, by applying cross-validation to tune the algorithms, we aim at deﬁning the best predictive model for the screens at hand, while other approaches neglect this optimization step w.r.t. model selection. Wrapping up, our paper appears to be the only one in the literature on detecting collusion that acknowledges the merits of machine learning for optimizing the pre-dictive performance of estimators and for appropriately assessing their out of sample behavior.

4.2. Generalization of results

An importantquestion forthe attractiveness ofour method is whether it yields de-cent results also in other contexts thanthat investigatedin this paper. Weexpect our approach to performwell even in other industries or countrieswheneverone can

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ratio-nallyassumethatbidriggingaffectsthedistributionofthebids.Thisisevenmoretrueif theprocurementprocedureissimilartothatconsideredinthispaper,i.e.corresponding to a first-sealed bid auction. Furthermore, the transferability of our approach is facili-tatedbytheuseofseveral, distinctscreensthat aresensitivetodifferentfeaturesofthe distributionofbidsand thuspotentially coverdifferentbid-riggingmechanisms.

Becausethedetectionmethodbasedonsimplescreensisinductive,it,however,needs to be verified in the empiricalcontext at hand.As competitionagencies typically have accessto datafromformercases,theycouldeasilyapplythesuggestedscreenstocheck their appropriateness even in different industries or countries. Moreover, ifthe data is largeenough,anagencymightdirectlyestimateitsownpredictivemodelbasedon screen-ingand machinelearningto identify suspicioustenders.Thisis fundamentallydifferent to establishingrigorous models fortestingcollusionin adeductive approach,seeBajari andYe(2003). Whiledeductionallows forsystematicgeneralizationifthemodel is cor-rectlyspecified, thereis thethreatthata specificempiricalcontext doesnotmatch the model parametrization and hypotheses it is based upon. At least for the Ticino case, Imhof(2017a)hasshownthatsimplescreensoutperformtheeconometrictestsproposed Bajari and Ye (2003). Combining screening with machinelearning makes this flexible, data-drivenapproachattractive asagenerallyapplicabletoolfordetectingcollusion.

4.3. Ex ante detection of collusion

Thetrainedpredictivemodels obtainedbymachinelearningcan beappliedto newly collecteddatainordertoscreentendersforbidrigginginanexanteprocedure.Following Imhofet al.(2018),weoutlinepossiblestepsofsuchaprocedure.

Initially, a competition agency has to collect data from official records of the bid openingandcomputethescreensforeachtenderasoutlinedin Section2.Applyingthe trainedmodels,e.g. thelassocoefficientsfrom thetrainingdata,to thesescreensallows computingthepredictedcollusionprobabilitiesinthenewlycollecteddataset.Next,the competitionagency needsto selecta probability thresholdto flag tenders assuspicious or competitive. Based on our results, we recommend to use a threshold between 0.5 and 0.7, but this could be reconsideredin other empirical contexts.We stress that the determination of suspicious tenders of such an approach is not (exclusively) based on humanjudgement,butdata-drivenanditsaccuracygenerallyimproveswiththeamount ofobservations usedtotrainthemodels.

If a competition agency has too few or even no data on episodes of documented cartelstotraintheirownmodelsforpredictingbidrigging,itmayinsteadusethemodel parameters estimated in this paper for detecting suspicious cases. If tenders in other jurisdictionsorindustriessharesimilarstructuralandinstitutionalfeaturesasourSwiss roadconstructiondata,thenourtrainedmodelshavethepotentialtoworksatisfactorily for detectingcollusionin othercountries andeconomic sectors, too. Whetherthis is in fact thecasewillbe investigatedin futureresearch.

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Once suspicioustenders have been identified, thereappear two possible options con-cerningnextsteps.Thefirstconsistsofimmediatelyopeninganinvestigation,thesecond oneofsubstantiatingtheinitialsuspicion.Thedecisiontolaunchaninvestigationshould be drivenby the predictedresultsbased on machinelearning. If the detectionmethod classifies a largeshare of tenders in a specific periodas collusive, competition agencies mightwanttoinitiatea deeperinvestigationimmediately.Forinstance,ashareofmore than 50% may appear sufficientto inquire theopeningof aninvestigation. Incontrast, shares between20% and 50% mightseemtoo small tolaunch a (potentiallycostly) in-vestigation.Inthiscase,themarketmightbeanalyzedfurthertosubstantiatetheinitial suspicion.

Several approachesmay be used to substantiate theinitial suspicion forbid rigging. First, thefirms participating in the suspicioustenders couldbe more closely examined to identify a specific group logic. Inorder tohave a well-functioningbid-riggingcartel, firms mustcooperateregularlyovera certainperiod.Regularinteractionsbetweenfirms mightmakeitpossibleto findaparticulargrouplogicinsuspicioustenders.Second, ge-ographicalanalysismayhelpidentifyingbid-riggingcartelssituatedinparticularregions (see also Abrantes-Metz et al., 2006, for such a geographical screening activity). One therefore needs to determine where the suspicioustenders are localized. If theyare all clusteredin thesamearea,thismightpointtoalocalbid-riggingcartel.(Notealsothat if one identifiesa local bid-riggingcartel,one should generallyalso identify a colluding group offirms basedintheregion.)Third,Imhof etal.(2018) assumesthatbid-rigging cartelsproducearotationalpattern,whichcanbecapturedwiththebidrotationscreen. If oneisabletodeterminea specificgroup offirmsregularlyparticipatingin suspicious tenders(e.g.insomeregion)andfindthatcontractplacementinthepotentialbid-rigging carteloperatesinarotationalscheme,thisprovidesfurtherindicesforsubstantiatingthe initial suspicion.

ThestepsproposedbyImhofetal.(2018)arenotexhaustiveandcompetitionagencies mightwanttoperformfurthertestsandchecks(e.g.accordingtorecommendationsofthe OECD)tosubstantiatetheirinitialsuspicion.Attheendoftheprocess,thecompetition agencies should ideallybe capable tocredibly demonstratethat thesuspicious bidsare notcoincidental,butfollow anidentiﬁablelogicofcollusion.

5. Conclusion

Inthispaper,wecombinedtwomachinelearningalgorithms,namelylassoregression andanensemblemethod(includingbagging,randomforests,andneuralnetworks),with screensforpredictingcollusionintenderprocedureswithintheSwissconstructionsector that are based on patterns in the distribution of bids. We assessed the out of sample performance of ourapproach by splitting thedata into training samplesfor model pa-rameter estimation andtest samples formodel evaluation. Morethan 84% of thetotal of biddingprocesseswere correctly classiﬁed byboth lassoregression andtheensemble methods ascollusiveornon-collusive.

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Wealsoinvestigatedtradeoﬀsinreducingfalsepositive vs.falsenegativepredictions. That is, rather than classifying a tender process as collusive whenever the collusion probabilitypredictedbymachinelearningisgreaterthanorequalto0.5,onecouldusea higherprobability thresholdforclassiﬁcation. Thisreduces incorrectpredictionsamong truly non-collusive processes, i.e. false positives, at thecost of substantially increasing errorsamong trulycollusive processes,i.e. falsenegatives.We arguedthat in ourdata, probability thresholdsbetween0.5and0.7appear appropriate.

Wefoundthat thetwo mostpowerfulscreensarethecoefficientofvariationand the normalized distance. Conditional on other screens, the coefficient of variation is nega-tively andthenormalized relativedistance positively associatedwith theprobabilityof collusion. This impliesthat bidrigging reduces the varianceof thebids and entails an asymmetry in the distribution of bids, as the difference between the first and second lowest bids increases whereas the difference between losing bids decreases in collusive tenders of our data. However, we found that dropping these two important predictors barelyaffectedpredictionaccuracy.Thisimpliesthat otherscreensaregood substitutes and”stepin” toreplacethem.Thisconfirmstheflexibilityof ourapproach,whichdoes not rely on making strong assumptions about the exact relationship of one particular screenandcollusion.Aslongasone canassumethatbidriggingaffectsthedistribution ofthebids,ourapproach ofcombiningmachinelearningandscreenswilllikelypickthis upthroughchanges inpatternsofscreens.

Finally, we discussed several policy implications for competitionagencies aiming at detecting bid-rigging cartels, namely advantages of our method in terms of data re-quirements/use, its generalizability to diﬀerent empirical contexts of collusion, and its integrationin aprocessofex-ante detectionofcollusion.

Acknowledgement

The authors would like to thank Christian At, Philippe Bontems, Yavuz Karagök, EvelynImhof,ThierryMadiès,MounirMensi,Pierre-HenriMorand,ArminSchmutzler, HannesWallimannandtwoanonymousrefereesforsupportandhelpful comments. AppendixA

Wesubsequentlydiscussinmoredetailthethreemachinelearningapproachesincluded in theensemblemethod. Baggedtreesand randomforests areso-called tree-based pre-diction methods. Theideaof a treeapproach is to recursively split thepredictor space in the training data, i.e. the set of possible values of the screens, into a number of nonoverlapping subregions. The incidence of collusioncan then be predicted based on theshare ofcollusiveor competitiveoutcomes ofobservations thatare (intermsof the values of the screens)situated in the same subregion as theobservation for which the prediction should be made. The name of such methods comes from the fact that the set of splitting rules for segmenting the predictor space can be summarized in a

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deci-siontreewithso-callednodes,i.e.predictorvaluesat whichthetrainingsampleissplit, and leaves,whicharetheterminalnodesbeyondwhichnofurthersplitting occurs.The splitting rulescould, however, also be represented in regression equations by means of dummy variables for (not) surpassing specific predictor values as well as appropriate interactions betweenthedummies.Ateachnode,splittingofthepredictorspaceisp er-formed such that after thesplit, a specificgoodness of fit criterionis minimized across the newlycreatedsubregions. Popularexamples forsuchcriteriaarethe Giniindex (as it is used forbinary outcomeslike collusion) andthe sumof squared residuals,i.e. the squared differencesof the actualand average outcomesin specific subregions (used for continuous outcomes). The splitting process is repeated until a specific stopping rule is reached (e.g. maximum number of nodes or minimum number of observations in a subregion).

As with any econometric method, there exists a bias-variance trade-off in terms of model generality. Just like adding more variables or interaction terms in a regression model, moresplits make thespecification more flexible,which reducesbias, but entails a larger variance in the test data due to smaller subregions. A single tree with many leaves therefore likely suffers from a high variance. This issue can, however, be miti-gated by bootstrap aggregation or ‘bagging’. The idea is to repeatedly draw so-called bootstrapsamplesfromtheoriginaltrainingdatawithreplacement(suchthatan obser-vation mightbe drawnseveral timesornotat allina newlycreated bootstrapsample) andestimatethetreesinallsamples.Then,theoutcomeispredictedbasedon aggregat-ing thepredictionsin theindividual trees,e.g. bytaking themostfrequentlypredicted value acrosstrees (e.g.collusionor no collusion)in case ofbinary outcomes,or the av-erage ofpredictionsin caseof continuousoutcomes.Randomforests aresimilar inthat theyrelyoncreatingbootstrapsamplesforestimating manytreesandaggregating pre-dictions. They are, however, different in that at each split, only a random subset of screens(ratherthanall)ischosenaspotentialvariablesforsplitting.Randomlypicking predictors prevents correlated trees across bootstrap samples, which generally further reduces thevariance.

Neuralnetworksaredifferentinspirit.Ratherthansplittingthepredictorspace,they aim at fittinga systemof nonlinear functions that flexibly models the influence of the predictors on collusion. Specifically, the predictors are assumed to affect specific non-linear (conventionally sigmoid) intermediate functions, so called hidden nodes, which themselves affect the outcome ofinterest. The hidden nodes bearsome similarity with the baseline functions in spline or series estimation, with the difference that they are learnedfromthedataratherthanpredetermined,andwithprincipalcomponents,which are dimension-reducing linear(rather than nonlinear) functions of the predictors. Fur-thermore,whenreplacingthenonlinearfunctionsbylinearones,neuralnetworkscollapse to a linearmodel,whichiswhytheycan be thoughtof asa nonlineargeneralizationof the latter. Depending on the model complexity, hidden nodes may affect the outcome either directly or throughotherhidden nodes, suchthat several layers ofhidden nodes allow modelling interactions between the functions. The number of hidden nodes and

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layers gauges the ﬂexibility of the model,with more parameters reducing thebias but increasingthevariance.

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