Each experimental session consists of 26 periods. At the beginning of a session, participants are randomly matched into groups of five and are informed that their group’s composition will not change throughout the session. In each period, every participantiin group
k
simultaneously choosesaneffortleveleffort
i^0,10, 20,30, 40`
.Participanti’searningsinaperiodareequalto:ߨൌ ʹͲͲ െ ͷ ൈ ݂݂݁ݎݐ
ൈ ݂݂݁ݎݐ,
whereeffortkminis the minimum effort chosen in the group. To facilitate calculations, we provide participantswithanEarningsTable,reproducedasTable3.1.Attheendofeachperiod,participants areinformedoftheirearningsandthegroup’sminimumeffort.Participantscannotobserveothers’ effort choice, which makes it more difficult to escape coordination failure (Brandts and Cooper 2006b).
Eachsessionisdividedintotwoparts.Part1consistsofperiods1to8andPart2ofperiods9to26. ParticipantsknowthesessionhastwopartsbutarenotgiventhespecificinstructionsofPart2until theyreachthatpart.
In Part 1, participants play the weakͲlink game without a leader. Using the weakͲlink game in a laboratoryexperiment,VanHuycketal.(1990)showthatdecisionmakersaremorelikelytoplaythe game according to the “security principle”, rather than the “efficiency principle”. The efficiency principlesuggeststheselectionofthepayoffͲdominantequilibrium,thatis,everybodyinthegroup chooses40andearns240.Thesecurityprinciplesuggeststheselectionofthelargestpayoffinthe worstpossibleoutcome,whichistoselect200,assumingthat0willbetheminimumeffort.Brandts et al. (2015) explain in more detail why it is hard to achieve efficient coordination with the given
payoffstructure.Forexample,supposethatthedecisionmakerconsidersaneffortchoiceofeither0, whichyieldsacertainpayoffof200,or10,whichyieldsariskypayoffof210ifeveryoneelseinthe groupalsochooses10and150otherwise.Ariskneutraldecisionmakerwouldhavetoexpectthat the probability of a simultaneous effort choice of 10 is at least 5/6 to make the choice of 10 attractive. Since effort levels are chosen independently, the decision maker would have to expect thateveryoneelseinthegroupchooses10withaprobabilityofmorethan95%,whichmeansthat the decision maker would have to be almost sure that each and every other group member will choose the higher effort level as well. Thus, the parameters of the payoff equation are chosen to make it almost certain that by the end of the eighth period all groups are coordinating on an inefficient equilibrium, which makes the introduction of a leader more meaningful (Brandts and Cooper2006a;Brandtsetal.2015). Table3.1 Earningstable Minimumeffortchoseninthegroup 40 30 20 10 0 Your effort 40 240 180 120 60 0 30 230 170 110 50 20 220 160 100 10 210 150 0 200
Part2introduces leaders.Atthe beginningofperiod9,one participantineachgroupisrandomly assignedtobethegroup’sleader,whichleavestheothergroupmembersasfollowers.Theleader holdsthepositionuntiltheendofthesession.Everythreeperiods,whichwerefertoasmessage cycle, the leader has the option to send a written message visible to all followers. The message is sentbeforeeffortchoicesaremade.Leaderscanwriteanythingtheywish,includingnothing,except for content that can be used to identify them. Messages are nonͲbinding in that not following a message has no direct effect on earnings. Leaders make effort decisions and face the same incentivesasfollowers.
3.2.1Treatments
Thestudyusesa2x2betweenͲsubjectsfactorialdesign.Thetwofactorsarewhetherfollowerscan send messages and the gender of the leader. We randomly assigned groups to one of the four treatmentconditions.
ThefirsttreatmentvariationiswhetherthereisOneͲwayorTwoͲwaycommunication.InOneͲway, followerscannotsendanymessages,onlyleaderscandoso.InTwoͲway,eachfollowercansenda written message visible to the leader only. The message is sent before leaders can send their messages.Followerscanwriteanythingtheywish,includingnothing,exceptforcontentthatcould beusedtoidentifythem.
The second treatment variation is the gender of the leader. By randomly assigning the leadership position we randomly vary the leader’s gender across the groups. To reveal information about gender, participants had to choose a profile picture they identified with. This occurred after they consentedtotakepartinthestudybutbeforetheyreadtheinstructionstoavoidstrategicselection
ofprofilepictures.Wecreated12genericprofilesforeachgender,usingtheprofilecreatorwebsite pickaface.net(seeFigureB1inAppendix3B).Allpictureshavethesameclothing,facialexpression, faceform,andeyecolor.Wevariedhairlength,haircolor,skincolor,anddidsmallmodificationsto the lips, nose, eyes, and hairstyle to match generic racial features. We use profile pictures to preserveanonymitywhilstrevealinggender.Weoptedforpicturesthatalsocontainothercuessuch asraceandhairstylestodistractparticipantsfromdiscerningthepurposeofthestudy(Zizzo2010), which can potentially lead to intentional changes in behavior (Camerer 2011). We displayed the profilepicturesofleadersalongwiththeirmessagesvisibletotheirfollowers.
3.2.2Procedures
The experiment was conducted at the Columbia Experimental Laboratory in the Social Sciences (CELSS)atColumbiaUniversityinMarch2015.ParticipantswererecruitedthroughORSEE(Greiner 2015) and the experiment was programmed with zͲTree (Fischbacher 2007). We ran 10 sessions, each in the afternoon. One session lasted around 60 minutes. Every participant signed a written consentform.Earningswereexpressedinpointsandwereconvertedtodollarsatarateof$1per 345points.31Averageearningsequaled$15.75. Participantswereseatedrandomly.Beforeperiod1,andbeforereadingtheinstructions,everybody answeredashortgeneralquestionnaireaboutgender,race,age,yearsofstudy,andmajorfieldof studies.Next,participantshadtochooseaprofilepicture(seeFigureB1inAppendix3B). WehadseparateinstructionsforPart1andPart2,andparticipantsreadtheinstructionsonlyprior to each part. To facilitate calculations for the participants, we handed out printed versions of the instructionsforPart1,whichcontainedtheEarningsTableshowinghowearningsweredetermined in each period. The same table applied in Part 2. Instructions were displayed on the computer screens and were read aloud by the experimenter. After reading the instructions for Part 1, participants completed a payoff quiz to check whether everybody understood the game’s payoff structure.InstructionsandscreenshotscanbefoundinAppendix2B.
The game was described using a workplace context to be in line with earlier papers, ease comprehensionofthetask,andenrichthewordingandanalysisofthefreeformmessages(Cooper 2007;Brandtsetal.2015).AsinBrandtsetal.(2015),individualgroupmemberswerereferredtoas “employees”, and they were told that they were working for a “firm”. The leader was called the “manager”.FollowingBrandtsetal.(2015),wedidnotusetheterm“effort”becauseofitsstrong connotation.Insteadweaskedparticipantstothinkofeachperiodasa“workweek”lasting40hours andchoosehowmanyhourstodevotetothefirm’s“bonusproject”.
Participantscouldentertheirmessagesintoachatbox,andtheycouldeitherclickonabuttonto sendthemessageorclickonabuttonlabeledas“Sendnosuggestion”.Theleader’smessage,along with the leader’s profile picture, was displayed on all screens throughout the three periods of a messagecycle.InTwoͲway,followerscouldseetheleader’sprofilepicturealreadyontheirmessage enteringscreensandfollowermessagesweredisplayedwithoutfollowers’profilepicturesandonly 31 Ineachsession,weallowedonlyamultipleoffivepeopletoparticipateinthestudy.Peoplewhoshowedup butdidnotparticipatewerepaidashowͲupfeeof$5.00.ParticipantsplayedwithoutashowͲupfee,inorder toincentivizethemmore.
on the leader’s message screen. Participants knew from the instructions of Part 2 that the profile pictureoftheleaderwillbedisplayed.
InPart2,afterparticipantsmadetheireffortchoice,weelicitedtheirbeliefconcerningthenumber of other group members who will follow the leader’s message by asking “Out of the four other participantsinyourfirm,howmanywillfollowtheManager’ssuggestion?”Participantscouldenter guessesfrom0to4,ortheycouldindicate“Notapplicable”forcaseswheretheleaderdidnotmake anysuggestion.Beliefquestionswereonlyaskedinthefirstperiodofeachmessagecycle.Table3.2 summarizesthesequenceofeventsintheexperiment. Table3.2 Timelineoftheexperiment OneͲwaycommunication TwoͲwaycommunication Beforeperiod1 Demographicsandchoiceofprofilepicture InstructionsforPart1andpayoffquiz Periods1Ͳ8 Effortchoice Feedbackscreen Beforeperiod9 InstructionsforPart2 Randomassignmentoftheleaderrole Periods9Ͳ26 Followerssendmessagetotheleader (everythirdperiod) Leadersendsmessagetothefollowers(everythirdperiod) Effortchoice Beliefquestion(everythirdperiod) Feedbackscreen Afterperiod26 Finalquestionnaire
At the end of each period, participants saw their effort choice, the group minimum effort, their earnings in that period, and their accumulated earnings. Participants could not observe individual effortchoices.
At the end of the experiment participants filled in a final questionnaire. We asked which role assignment(“Manager”or“Employee”)participantswouldpreferiftheycouldchoose(“Ifyouwere to play Part 2 again and you could choose your role, which role would you choose?”). After reminding theindividualaverageearningsoftheparticipantinPart2,weaskedforthesubjective evaluationabouttheperformanceoftheleaderonafiveͲpointscalefrom“completelydisagree”to “completely agree” (“How much do you agree/disagree with the following statement: My firm’s performanceinPart2ismostlyduetothejudgmentoftheManager.”).Finally,weaskedageneral riskattitudequestion(“Howdoyouseeyourself:areyougenerallyapersonwhoisfullypreparedto takerisksordoyoutrytoavoidtakingrisks?”),whereparticipantscouldindicatetheirwillingnessto takerisksonascalefrom0for“notatallwillingtotakerisks”to10for“verywillingtotakerisks” (Dohmenetal.2011). Attheendoftheexperiment,participantswereshowntheirearningsseparatelyforeachpartandin total.Participantswerethankedandpaidindividuallyfortheirparticipation.
3.3Predictions
The main interest in this study is to show whether men and women differ in leader effectiveness across communication conditions and which channels explain leader effectiveness: a difference in leader behavior or a difference in follower behavior. Naturally, all predictions refer to behavior in Part2.
Kriss and Eil (2012) already showed that incoming follower messages increase leader credibility in TwoͲway, compared to OneͲway. Holding leader message content constant, an increase in leader credibilityislikelytoincreaseleadereffectiveness.Thereforethefirstpredictionis:
Prediction1:MinimumeffortinTwoͲwayishigherthaninOneͲway.
Sincemenhavehistoricallyheldmostoftheleadershiprolesinsociety,followersmightholdbiased stereotype beliefs that consider men to be better, more competent and more credible leaders (Ridgeway2001;Day2014;Goldin2002;AkerlofandKranton2005).Reubenetal.(2014)showthat, inanexperimentalmarket,stereotypesmakebothmaleandfemaleparticipantstwicemorelikelyto hire a man than a woman when no other information is available than a candidate’s appearance (which makes gender clear), despite the fact that on average both genders perform equally well. Grossman et al. (2016) show, using the turnaround game, that followers are more likely to follow men than women, holding leader messages constant. Even if followers do not hold biased beliefs themselves,itmightberationaltoadapttothesupposedbiasiftheyexpectotherstofollowmento agreaterextentthanwomen.Further,inTwoͲway,followersmightsendforthesamereasonlower effort level suggestions to female rather than male leaders. The low follower suggestions might affectleadersnegatively(KrissandEil2012),butevenifleadersignorethefollowermessages,the followers,whosentthelowsuggestions,mightdoubttheleaders’credibilitymoreifleadersrequest a high rather than low effort level. Thus, in TwoͲway, the leader credibility of men, rather than women,mightbeboostedmore.
Prediction 2: In both OneͲway and TwoͲway, male leaders are followed to a greater extent than
femaleleaders.InTwoͲway,thegendergapislarger.
Leaderswilltendtosendmessagesinlinewiththeirowneffortchoicesatleastinthefirstperiodof the threeͲperiod message cycles. Otherwise leaders would not get feedback on their credibility, becausetheycouldnotruleoutthattheyaretheonlyoneswhodonotfollowtheirownmessage.In thissense,leadersfaceanexplorationcost.32Further,leaderswhodonotfollowtheirownmessage wouldlosecredibilityalreadyinthefirstperiod.Sinceapossiblelossinearningsinthefirstperiodis lessseverethanthelossofcredibilityforallthecomingperiods,leadersfaceacostofscrewingup others.33Giventhatrequestingandchoosingahigheffortlevelisriskyandrequireshighcredibility, 32
Leaders can minimize the exploration cost if they communicate a conditional strategy, for example, that theywillfollowtheirownmessageinthefirstperiodofthemessagecycle,buttheywillstopdoingsoifothers donotfollowaswell.
33
In a recent related paper, Cooper et al. (2016) study the “social credibility” of leaders in an experiment whereleaderstrytoinducefollowerstoinvestinajointventure.Theauthorsfindthat“leadersmanagesocial credibility by forgoing potentially profitable requests for investment in order to make it more likely that subsequentrecommendationstoinvestarefollowed”.Leadersinourstudymightalsorecognizetheneedto build up credibility, which is more than having other regarding preferences. For example, less confident
more risk averse or less confident leaders might request and choose a low effort level, whereas leaders who are more willing to take risks, or who are overconfident about the number of their followers,orboth,arealsotheoneswhowillrequestandchoosehigheffortlevels.Menhavebeen showntobemorewillingtotakerisksandtobemoreoverconfident(Reubenetal.2012;Reubenet al.(inpress);Dohmenetal.2011).Therefore: Prediction3:InbothOneͲwayandTwoͲway,maleleadersrequestmoreoftenthehighesteffortlevel thanfemaleleaders. IfPredictions2and3hold: Prediction 4:InbothOneͲwayandTwoͲway,menaremoreeffectiveleadersthanwomen.InTwoͲ way,thegendergapislarger.
Merchant (2012) provides an overview on gender differences in communication styles and points out that men and women have different purposes when using communication. Women value the processofcommunicationitself,whereasmenviewcommunicationasatooltoreachacertaingoal. Womenusecommunicationtoenhancesocialconnections,whilemenexertdominanceandremain goalͲoriented. In interactions, women tend to be more social, while men value independence and remainunemotionalandlessattachedtoconversations.Therefore,thelanguagethatwomenuseis more expressive and polite, while men use a more assertive and dominating language, signaling statusandoverconfidence.Merchant(2012)showsthatgenderdifferencesincommunicationstyles areoftenpersistentinleadershipstylesaswell.
Eagly etal.(2003)classifythreeleadershipstyles:transformational,transactional,andlaissezͲfaire leadership style, described in more detail in the introduction. In our context, transformational leaderswouldrequestahigheffortlevelandemphasizethemutualbenefitargumentandbeingpart ofthegroup.Wecallsuch“transformational”messages“relevantmessages”,sinceEaglyetal.find that leader effectiveness relates positively to the transformational leadership style, and Cooper (2007) also finds the same message strategy leading to effectiveness. Transactional leaders, who engage in contingent reward behavior, would request a high effort level in an ordering style, give moreoftenpositivefeedback,andencouragetheirfollowerswithpositiveemotionalcontent,rather thanlongexplanations.Bothtransformationalandtransactionalleadersrecognizetheirpivotalrole and are likely to communicate assertively. Eagly et al. (2003) show small gender differences in leadership styles. The authors find that female leaders engage more often than male leaders in transformational leadership and in contingent reward behavior as part of the transactional leadershipstyle.
Prediction5:Maleleaderssendassertive,goalͲorientedmessagesandclearordersmoreoftenthan
their female counterparts. Female leaders send more often relevant messages containing mutual benefitarguments,alongwithencouraging,positiveemotionalcontentandexpressionsemphasizing thattheleaderisanequalmemberofthegroup(usingthepersonalpronoun“we”moreoften).We expect that these gender differences in communication and leadership styles are stable across communicationconditions.
leaders,whointendtochoosealoweffortlevel,canstaycredibleiftheypreventtheirfollowersfromlossesby requestingaloweffortlevel.
3.4Results
184subjects showeduptothestudy. Weallowed onlyamultipleoffive peopletoparticipate,so that165subjectsparticipatedintotal,withanoverallgenderdistributionof67menand98women, which is a gender ratio of 4:6 and corresponds to the gender ratio in the subject pool and the university as a whole. In OneͲway, we had 80 participants in 16 groups with 8 male and 8 female leaders,andinTwoͲwaywehad85participantsin17groupswith8maleand9femaleleaders.
3.4.1TreatmentEffects
Westartouranalysisbylookingatthetreatmenteffectsonleadereffectivenessinthefourdifferent treatment conditions. Figure 3.1 depicts the group minimum effort by treatment conditions in all periods.Inperiods1to8,withoutaleader,31ofthe33groupsconvergedtothemostinefficient effort level, so the first part of the turnaround game reliably induced failure to coordinate on the efficientequilibrium(BrandtsandCooper2006a).Thesecondpartoftheturnaroundgamestarted in period 9, when all leaders successfully managed the turnaround on average at least above the minimum effort level of 20. Graphically, male leaders who receive follower messages are more effectivethantheirfemalecounterparts,orleadersinOneͲway.
Figure3.1 Treatmenteffectsbytreatmentconditions
Table 3.3 summarizes the results from regressions containing aggregate treatment effects and comparingtreatmentconditions.FortheestimationsweusegroupͲlevelrandomeffectsgeneralized least squares (GLS) regressions. Both models contain 594 observations over 18 periods and 33 groups.Wecorrectstandarderrorsforclusteringatthegrouplevel.Thedependentvariableisgroup minimum effort in both models. Model 1 contains two indicator variables, one for the communicationtreatmentandoneforthegenderoftheleader,asexplanatoryvariables.Minimum effort is by 2.95 units higher in TwoͲway rather than OneͲway, thus leaders are slightly more
0 10 20 30 40 Mi ni mum Ef fo rt 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 Period
One-way, male leader One-way, female leader Two-way, male leader Two-way, female leader
effective if they receive input from followers, but this difference is not statistically significant. The difference between male and female leaders has a similar magnitude. Male leaders achieve