12 Xie Wu2005 Market Premium, Social Process

8/14/2019 12 Xie Wu2005 Market Premium, Social Process

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Reply: Market Premium, Social Process, and StatisticismAuthor(s): Yu Xie and Xiaogang WuSource: American Sociological Review, Vol. 70, No. 5 (Oct., 2005), pp. 865-870Published by: American Sociological AssociationStable URL: http://www.jstor.org/stable/4145364

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Reply oJannMarketPremium,SocialProcess,and StatisticismYu XieUniversity f Michigan

XiaogangWuHongKong University f Science & Technology

Statistics is a powerful,yet potentiallydan-gerous, ool. Morethan wodecadesago, thelate Otis Dudley Duncan (1984:226) warnedus concerning hedangerof"statisticism":"thenotion that computing is synonymous withdoingresearch, he naive faiththat statisticsisa complete or sufficient basis for scientificmethodology, the superstitionthat statisticalformulasexist forevaluatingsuchthingsas therelative merits of different substantive theo-ries." Duncan'swarninghas long been under-stood as applying to sociologists who doquantitative esearch.His concern,however, sequally applicableto readers,even some care-ful readers,of quantitative esearch.In our earlier work (Wu andXie 2003), weasked thequestion,"Does themarketpayoff?"Ouremphasiswas on thepotentialheterogene-ity of workers n themarketsector.Using workhistory data, we distinguished between twotypes of workers in the market sector: earlybirds and later entrants. We were concernedwith thepossibilitythatpooling earlybirds andlaterentrants,even if they each havethe sameeducationreturnsas stayers n the statesector,maymake thereturns o educationappearhigh-er in the marketsector thanin the state sector.Our main empiricalresults, which also wereconfirmedby Jann,showed that laterentrants,but not earlyentrants,have significantlyhigh-erreturns o education hanstayers.

The thrustof Jann's 2005) comment is thatthere s insufficient statisticalpower n the datafordifferentiatinghe educationreturnsof earlybirds from those of laterentrantsandthose ofstayers.'Thispointis technicallyvalid,althoughonly within the narrow statisticalparadigmof"null hypothesis significance testing,"whichhas been severely criticized in recent decades(e.g., Cohen 1994).A basicproblem s thatanydifference s boundto become"statistically ig-nificant" with sufficient data. The late JohnTukey 1991:100)hadthefollowingto sayaboutthis paradigm:"Statisticiansclassically askedthewrongquestion-and werewillingto answerwith a lie, one that was often a downright ie.They asked 'Are the effects of A andB differ-ent' and they were willing to answer 'no'....[Weknow]that heeffectsofA andB arealwaysdifferent-in some decimal place-for any AandB."In the final analysis,ourdisagreementwithJann s not about he technicalcorrectness f sta-tisticalmethods,but abouthow statisticalmeth-ods shouldbe used in sociologicalresearch.Weare strongbelievers in the viewpoint that sta-tistical methodology should not be separatedfrom substantiveconcernsin guidingresearch.Jann's"methodological" ritiqueof ourwork smisdirected precisely because it is narrowlymethodological, lacking an understandingofboth the substantiveresearchquestionandtheunderlyingsocial processes.As we show later,the substantiveresearchquestionrenders rrel-evanthis test for the difference between earlybirds and later entrants.

Directall correspondenceo YuXie, P.O.Box1248, 426 ThompsonStreet,PopulationStudiesCenter, niversityfMichigan,nnArbor,Michigan([email protected])rXiaogangWu,SocialScienceDivision,HongKong Universityof Science andTechnology,learWater ay,Kowloon,HongKong([email protected]).heauthorshankEmilyGreenman,JerryA. Jacobs, ndTonyPerez or comments ndsuggestions.

1Itwas he irstauthor hosuggestedo Jann hathis problemwith theWu andXie (2003) articleshouldberephraseds aproblemf insufficientta-tisticalpower.AMERICAN OCIOLOGICALEVIEW,oo5, VOL.70 (October.865-87o)


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866 AMERICANOCIOLOGICALEVIEWTo be fair,Jannshouldnotbe singledoutforfalling into the trapof "statisticism"becausesuchpracticeis so widespread n currentsoci-

ology that it oftenmakesquantitative esearchunappealing.Jann's omment llustratesa com-mon temptation among quantitativesociolo-gists: relianceon cannedstatistical ests ratherthansubstantiveknowledge.Thus,we takethisopportunity o draw a generallesson for all ofus: only when combined with a substantiveunderstanding f the social processes involvedcan statistical methods result in fruitfulresearch.At a fundamentalevel, Wuand Xie's (2003)studywasdescriptive.Weemphasizedhispointthroughouthe articleby alertingreaders o thedangerof aggregationwhenworkers n a singlegroupare in fact heterogeneous.Althoughwequestionedthe prevailingwisdom that marke-tizationperse "caused"he education eturnsobe higher, we never intended our statisticalanalysisto be morethan a descriptiveexercise.In such an exercise, formalstatistical ests canbe informativewhenthere is sufficientstatisti-cal power. In the absence of strongstatisticalinformation, ubstantive nowledgeshouldpre-vail.In his comment,Jann reats hethreegroupsunderdiscussion-stayers, earlybirds,and laterentrants-as thoughtheyweresymmetric, ikethoseof anexperimental esign.Indoingso, heborrowsthe language of multiple-groupcom-parisons commonly used in analysis of vari-ance (ANOVA)associated with experimentaldesigns. However, because we were dealingwith observational ata,ourconcernswere withthe between-groupand within-grouphetero-geneitygenerated ysocialprocesses.Theearn-ings regimesfor the threegroupsresultedfroma cumulativehistoricalprocess that clearly isasymmetrical (Figure 1) and thus should betreated as such in an analysis.Comparing hethreegroupsas if theywerethreeexperimentalconditions s both nappropriatendmisleading.Figure 1 presentsa schematicflow chartoftherespondent ypes in the 1996 surveyof LifeHistoriesandSocial Changein ContemporaryChina, he datausedbyWuandXie (2003).They-axis represents he employmentsector(statevs. market),andthe x-axis representshistoricaltime. We make the convenientassumption hatthe market sector is an absorbingstate so thatthere is no reverse transitionfromthe market

sector to the statesector.2 n 1978,atthebegin-ning of the Chinese economic reform, 1,197respondentsworked nthe statesector.By 1987,11percenthadmadethe transitionntothe mar-ket sector (d = 1) andarecalled "earlybirds."Amongtheremaining1,068workersn the statesector andthe 522 new entrantswho started nthe sectorbetween 1978 and 1987, 16percentmade the transition nto the marketsector(d =2) and arecalled"laterentrants."3heremain-ing 1,337 respondentsare called "stayers."The Wu and Xie (2003) article was partlyresponsible for causing Jann's confusion,becausehis reanalysis s modeledafterWu andXie's (2003) regressionsof logged earningsoneducation, sector, and their interactions.Extensive discussionin Wu andXie (2003) onthe differentialreturnsto educationby sectormakes it appearas if education s the causal ac-tor, with sector as a covariate.However,ourreal researchquestionconcernedearningsdif-ferences by sector, with education as a con-founder.Let us revisita passage (WuandXie2003:430) cited andemphasizedby Jann.

The crucialdifference etweenhetwohypothe-ses is thetreatmentf earlybirds. nHypothesis1, earlybirdsaregroupedwithin aterentrantsbecause heysharehe commoneature f beingin the market ector.... In Hypothesis , earlybirdsaregroupedwithstayersbecause hetwotypesof workers ereapproachingconvergence,againstwhich laterentrantswere selectivelyrecruitednto hemarket ector.Jannassumes hat hephrase"aregroupedwith"here means "share he same educationcoeffi-cientwith."Thisis incorrect, s shown nFigure1 of WuandXie (2003:431). It is possible,forexample,thatearlybirdsand laterentrantsdif-fer in earningsandeducationdistributionsbuthave the sameeducationreturnsas stayers,yetpooling earlybirdsand later entrants ogetherstill could yield higher returnsto education

2Thats, weexcluded smallnumberf"marketlosers" romFigure1becauseof the group'smallsize (WuandXie2003).Webased heclassificationonWuandXie'scomprehensiveeasurefthemar-ketsector.

3Here275workers,ncluding 2"later ntrants"inWuandXie's 2003)original rticlewhoenteredthe labor orce after1987weredroppedrom heanalysis.


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COMMENTND REPLY 867NewEntrantso theStateSector522)

o Experienced Stayers Stayers Stayersa Workers1,197) (1,068) (1,590) (1,337)

d = P= 0.11 d=2 P2= 0.16

Later ntrantsS(253)

EarlyBirds EarlyBirds(129) (129)

1978 1987 1996Year

Figure1. FlowChartof LaborMarketTransitionsn China,1978-1996.

amongworkers nthe market ector hanamongstayers n the statesector.To advancethis inquiry, et us reconceptual-ize the substantiveproblemwith explicitcoun-terfactuals n the languageof causal inference(Heckman2005; Holland1986;Manski 1995;Winshipand Morgan 1999). Suppose we areinterestedn the causal mpactof theentry o themarketsectoron (potential)futureearnings n1996.Conceptually, hereare two causalques-tions in this setup: (1) what is the effect of anearlytransition? i.e., d = 1)and(2) whatis theeffectof a late transition?i.e., d= 2). Of course,thesetwoquestionsareinherentlyasymmetric.The second is sensible only for those workerswho did not experience an early transition,whereas the first involves the counterfactualcomparisonbetween thosewho experiencedanearlytransitionand those who didnot, regard-less whathappened o themlater.Toborrow henotation or causalinferencewithtime-varyingtreatmentsBrandand Xie 2005), let Yi denotethe ithperson'spotentialoutcomeif thepersonhasmadea transition ttime d (d= 1,2, oo),withd = oo denotingthatthe personhas not made a

transitionby the end of the study (i.e., a stay-er).Note that orapersonwho has madeanearlytransition(d = 1), the counterfactualoutcomeshould follow theprincipleof "forward-lookingsequentialexpectation" BrandandXie 2005),a combination of a late transition(d = 2) andstaying (d = oo).We thus define the averagecausal effect for the first questionasE(ydl) - E(yd>l) = E(Yd=) -[E(Yd=2)P2 E(yd=m)(1 P2)].

Note that thetransitionprobabilitiesare condi-tional so thatP2 = P(d = 2 Id > 1).Forthe second question,the comparisonissimpler, nvolvingtwo regime-specificmeans:E(Yd=2) E(Yd>2)= E(Yd=2) E(Yd=o) (2)

It is neverpossible ocomputequantities efinedby equations1 and2 because we observeonlyone of the three potential outcomes for eachworker. To infer causality, it is necessary tointroduce the ignorabilityassumption,whichmustbe takenasprovisional ecause t is unlike-ly to hold inreality.Theignorability ssumption


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868 AMERICANOCIOLOGICALEVIEWstatesthat all systematicdifferencesassociatedwith the transitions can be summarizedby aset of observedcovariates X)(RosenbaumandRubin 1984).Given this assumption,the expected earn-ings can be estimated on the basis of theobserved covariates,including education.Asshownin equations1 and2, we need four con-ditional expectations for the causalanalyses:E(YdlIX) andE(YP'lIX)for the firstquestion,andE(yd=2X) andE(yd>2X) forthesecond question.The ignorability assumptionmeansthatE(YdI X) can be estimatedamongearlybirds,E(yd=2X) among aterentrants, ndE(yd>2X) among stayers.However,E(Y>2IX),as a weightedsum of two conditionalexpecta-tions, should be estimated from both laterentrantsandstayers.GiventhatP2 is small (at.16), a crudeapproximationof E(Y"> IX) canbe estimated from stayers (i.e., giving a fullweight to stayers).This approximationis aninterpretation f Wu and Xie's (2003) analysisstrategy.Because laterentrants onstitutedonlya small proportionof the appropriategroupagainstwhichearlybirds areto be compared,tmakes little sense to compare,as Jann recom-mends, later entrantsdirectlywith earlybirds.To illustrate he utility of this reconceptual-ization,we performpropensityscoreanalyses.Becauseof spacelimitation,we presentonlythemost importantindingsin thisdiscussion.Thefull resultsfrom this exercisearereportedelse-where (Xie and Wu 2005). To borrow thejar-gon from the causal inference literature,weconsider wo "treatments"nourstudy:anearlyentryto themarket ector anda lateentryto themarketsector.Forthe firsttreatment,he "con-trol" group consists of workers who did notmake an early entry,and thus includes stayersas well as later entrants.Forthe second treat-ment, the "control"group consists of stayersonly.Thepropensityscore method allows us tosummarizeall thedifferencesbetween hetreat-ment and controlgroupswith a single dimen-sion: the probabilityof receiving a particulartreatment.We then computethe averagetreat-ment effect on earningswithin each propensi-ty score stratum.There are two main findings from thispropensityscoreanalysis.First,thepropensitymodel for a late transitiondiffers from thatforanearlytransitionbecause the mechanismsformaking transitionschanged.Whereas human

capitalandpolitical capitalmeasuressuch aseducation, party membership, seniority, andcadreconnectionnegativelypredicted heprob-abilityof an earlytransition o the market ec-tor,this patternwas muchless pronounced ora latetransition.

Second,we find the treatment ffectof mar-ket entryto be very differentfor a late transi-tion than for an early transition.For an earlytransition,we find no effects on earningsinany of the propensity score strata. For a latetransition, heestimated reatment ffect is rel-atively large and significantly different fromzero for the four lowest propensityscore stra-ta. Wepresent heresults n Figure2. Ifwe poolthe differentstrata ogetherfor an overall reat-ment effect under the homogeneous effectassumption, the estimate is 236 RMB yuan(Chinese currency),with a standarderror of54, resultingin a highly significant t value of4.36. However,the assumptionof a homoge-neous treatment ffect is clearlyviolatedbythedownward rendobservedin Figure2. Using ahierarchical inearmodel, we find thatthe sizeof the treatmenteffect stronglyandnegativelydepends on the propensityscore, with a unitchangein stratum ank(i.e., crossingapropen-sity scorestratum)associatedwith a reductionof 94 RMB yuanin the treatment ffect (a sig-nificant relationship,with t = -3.6). That is,the benefit of a late transition nto the marketsector is greatestamongthose who were leastlikely to make the transitionand diminisheswith thepropensityformakingthe transition.To the question"does the marketpay off?"thesenew resultsyield no simpleanswer.We donot find a generic market effect on earnings.Rather, he effectsvaryacrosstwo dimensions.First, confirmingWu and Xie's (2003) earlierresults,we againfind no evidenceof a premi-umforanearlymarket ransition,whereasa latetransitioninto the marketsector is associatedwith higher earnings. Furthermore,we showthat even among laterentrants, he benefit ofworkingin the market sectorsharplydecreas-es with thepropensityof havingmadethetran-sition. Hence, the summary finding of ourreanalysis s that the marketpremium s limit-ed to onlylaterentrantswho otherwisehada lowlikelihoodof makinga transition o themarketsector.Who arethey?In all likelihood,these low-propensity aterentrants reworkersdoing especiallywell in the


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COMMENT ND REPLY 869900 -

* 6.07 * Stratum-specific -Linear fit (HLM)700-

500 -Y = 645.2 - 94.3 X STRATUM_RANK

'o500 -o 300 t 3.33, 0.31S100-.9

-100-* -0.65

1 2 3 4 5 6 7 8PropensityScore Stratum

Figure2. MarketTreatment ffectonEarningsbyPropensityStratum: aterEntrants ersusStayers.Notes: Numbersn thescatterplot re tvaluesforanearnings omparison etween aterentrantstreatmentgroup)andstayers controlgroup); < 1.96 indicates hat here s no significantdifferencenearningsbetweenthe treatment ndcontrolgroupswithina propensitycore stratum. he linear it is based on thehierarchicallinearmodel estimates level2 modelwithslopesfrom he level 1 model as outcomesregressedon propensitystratumank); ffectof propensitytratumank s statistically ignificant t = -3.6).

statesector.A cost-benefitanalysis uggests hatfor a personto make a transition rom the statesectorto the marketsector,the benefit of vol-untarily ntering hemarketmust exceed thatofstaying nthe statesector.Workerswho do wellin the state sector andareunlikelyto lose theirjobs have a good incentive o stayput.For hem,the attractionof themarketsectormustbe suf-ficiently largeto more thancompensatefortheadvantages hey alreadyenjoyin the state sec-tor.Therefore,only those with the best marketopportunitiesactuallymake the transition.Wehighlighted hese individualsgraphicallynWuand Xie (2003:435), referringto them as vol-untary ater entrants.These results illustrateaclassic violation of theignorabilityassumption,the problemof endogeneity.Individualsselecttheir "treatment" n the basis of the anticipat-ed outcome,which is nothomogeneousacrossworkers.This kind of insight nto socialprocess-es can never be producedby analyses such asJann's.His critique ocuses on aninappropriatecomparison between early birds and laterentrants,a resultof his relianceon uninforma-

tive statistical ests at theexpenseof substantiveknowledge.As such, Jann'sstatisticalexercisecontributes little to the understandingof thesocial processes underlyingthe empirical pat-ternsreportedby Wuand Xie (2003).YuXie is OtisDudleyDuncan rofessor fSociologyand Statistics at the University of Michigan; aResearchProfessorat thePopulationStudiesCenterand theSurveyResearchCenter f theInstituteorSocialResearch;and a FacultyAssociateat theCenter or Chinese Studies.His main interests aresocial stratification,demography,tatisticalmethods,Chinesetudies,andsociologyofscience.Hispub-lished works include Statistical Methods forCategoricalDataAnalysis Academic ress2000)with Daniel Powers,Women n Science:CareerProcesses ndOutcomesHarvard niversityress2003)withKimberleehauman,ndA DemographicPortraitfAsianAmericansRussell ageFoundationand Population ReferenceBureau2004) withKimberlyGoyette.XiaogangWus Assistantrofessor fSocialScienceat theHongKongUniversityfScience&Technology(HKUST). isresearchnterestsnclude ocialstrat-ification ndmobility,abormarkets ndeconomic


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12 Xie Wu2005 Market Premium, Social Process