- 1. Job Search and Network Composition: Implications of the Strength-Of-Weak-Ties Hypothesis Author(s): James D. Montgomery Source: American Sociological Review, Vol. 57, No. 5 (Oct., 1992), pp. 586-596 Published by: American Sociological Association Stable URL: http://www.jstor.org/stable/2095914 Accessed: 21/08/2009 17:52 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=asa. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit organization founded in 1995 to build trusted digital archives for scholarship. We work with the scholarly community to preserve their work and the materials they rely upon, and to build a common research platform that promotes the discovery and use of these resources. For more information about JSTOR, please contact support@jstor.org. American Sociological Association is collaborating with JSTOR to digitize, preserve and extend access to American Sociological Review. http://www.jstor.org
- 2. JOB SEARCH AND NETWORK COMPOSITION: IMPLICATIONSOF THE STRENGTH-OF-WEAK-TIESHYPOTHESIS* JAMEsD. MONTGOMERY NorthwesternUniversity Workersfind jobs through personal contacts (weak and strong ties) and formal sources. Alternativeformulations of the strength-of-weak-tieshypothesis suggest (1) weak ties relay job offers more frequently than strong ties, or (2) weak-tie offers are drawnfrom a better distribution.Aformal model shows that bothformulations imply a correlation between net- work composition and a job seeker's minimumacceptable wage. However, the use of a weak tie is never associated with higher expected wages under thefirstformulation, and is only sometimes associated with higher expected wages under the secondformulation. These re- sults suggest that researchers shouldfocus on job seekers' networkstructures. Based on the findingthatworkersfrequently independent for- variable.Moreover,alternative locate jobs throughacquaintances ("weak mulationsof the strength-of-weak-ties hypothe- ties") rather than close friends and relatives sis suggest thatjob seekers benefit from weak ("strong ties"),Granovetter (1973, 1974) argued ties for two distinctreasons.Granovetterempha- thatweakties play an important in determin- role sized thatweak ties relay usefuljob information ing labor-market outcomes.Subsequent theoret- more frequentlythan strongties, whereasLin's ical workin the socialresourcesliterature further formulationsuggested that weak-tie job offers emphasized the importanceof weak ties (Lin aredrawnfroma different(oftensuperior) distri- 1982). However, Bridges and Villemez (1986) bution.To examinethe empiricalimplications of and Marsdenand Hurlbert (1988) found no sig- these two formulations the strength-of-weak- of nificant relationshipbetween tie strength and ties hypothesis,I offer a formalmodel in which wages after controllingfor workercharacteris- workerslocate jobs throughboth personalcon- tics.Consequently, someresearchers haveargued tacts (weak and strongties) and formal (imper- against the strength-of-weak-ties hypothesis. sonal)methods,buildingon previousworkin the Bridgesand Villemez (1986), for example,con- economics job-search literature (Mortensen cludedthat"thestrong-weak dimensionof ties is 1986).' nottheonly, oreven themostimportant, attribute of personalrelationships the labormarket.... in THE MODEL:NETWORKSTRUCTURE Future researchshouldconcentrate exploring on AND THE RESERVATIONWAGE and otherdimensions socialresources theirrole of in thejob findingprocess"(pp. 579-80). Becausejob-seekerslackcompleteknowledgeof Reflectionsuggeststhatthe BridgesandVille- vacanciesandmustrely on information obtained mez conclusionmay be premature. Whileempir- throughvarious formal and informalchannels ical analysesof the strength-of-weak-ties hypoth- to (e.g., directapplication employers,newspaper esis havefocusedon the type of tie actuallyused ads,andpersonal economists referrals), oftencon- to locate a job (althoughsee Lai, Leung,andLin ceptualizejob searchas a sequenceof wage of- 1990), the "networksas resources"argument fers drawnrandomlyfrom an offer distribution. (Campbell,Marsden,and Hurlbert1986) sug- (Whenthe nonpecuniary aspectsof employment gests that networkstructuremay be the crucial differacrossjobs, the "wage"mightbe interpret- ed as a broaderindexof job quality.)Ifjob search * werecostlessforbothunemployed employed and Directall correspondence JamesD. Montgom- to ery, Departmentof Economics, NorthwesternUni- I Boorman(1975) and Boxman,Flap, and Weesie versity,Evanston,IL 60208. Helpfulcommentswere (1991) presentrelatedmodels of job searchthrough receivedfromPeterMarsden.Financialsupport from strong and weak ties. Halaby (1988) used a search- National Science Foundationgrant SES-9109056 is theoreticmodel to examine individuals'decisions to gratefullyacknowledged. searchfor new jobs. 586 AmericanSociological Review, 1992, Vol. 57 (October:586-596)
- 3. JOB SEARCHAND NETWORKCOMPOSITION 587 workers, job-seekerswould acceptany offer ex- Suppose that the workerreceives some (po- ceeding theircurrent wage (or value of leisureif tentiallystochastic)numberof offers each peri- unemployed)andcontinuesearchingfor a better od. The distribution the highestoffer received of job while employed.But if job searchbecomes each periodis represented H(w), with proba- by morecostly once a workeris employed,the opti- bility densityh(w). Further, WR representthe let mal search strategyis more complex: The job worker's reservationwage and let V represent seeker sets a minimumacceptable(or "reserva- the worker's"valueof search,"i.e., the present tion")wage, rejectinganyoffersbelow thereser- value of expectedfutureearningsgiven thatthe vationwage andacceptingthe firstoffer exceed- workerremainsunemployedat the end of a peri- ing this wage (Lippman and McCall 1976; od. Given this notation,consider the worker's Mortensen1986). expectedfutureearningsviewed fromthe startof Considerthe simplestcase in whichjob search a period (before any offers are received). Be- is costless for unemployedworkersbut is pro- cause the worker'sexpectedfutureearningsare hibitivelyexpensiveforemployedworkers. Even by definitionequal to V if no offer exceeds WR if an unemployedworkerplaces no value on lei- and are equal to wI(1 - B) if the highest offer sure(so thatthecurrent "wage" zero),thework- is exceeds WR, the worker'sexpected futureearn- er might reject a low-wage offer because em- ings are ploymentwould precludefurthersearch,which might lead to a betteroffer and higher lifetime WR earnings.However,thejob-seekerwould gener- f Vh(w)dw+ | 1-B h(w)dw. (1) ally not wait to receive the maximumpossible 0 WR offer becauseearningsforegonefromrejectinga sufficiently "good"offer might exceed the net Now considertheworker'sexpectedfutureearn- expectedbenefitfromcontinuedsearch.The fact ings viewed fromtheend of thepreceding period that the job-seeker rejects relatively low-wage (after all offers were rejected). Given that the job offersbutacceptsrelativelyhigh-wageoffers workerdiscountsfutureearningsby the factorB, suggeststhe existenceof a criticalwage, i.e., the is this "valueof search" definedimplicitlyby reservation wage, at which the job-seekeris in- different between accepting employment and WR continuingthejob search. V= fjVh(w)dw+f |WB h(w) dw. (2) Now consideran unemployedworkersearch- ing for a job. Two simplifyingassumptionsare adoptedin thepresentmodel.First,I assumethat Becausetheworker indifferent is betweenaccept- theworker searchesonlywhileunemployed.2 Sec- ing a job at the reservationwage and continuing ond, I ignore the possibility of job dissolutions the job search,V = wR/(l - B). Substitutioninto such as quits, layoffs, or retirement.Thus, after equation1 yields acceptingan offer, the workeris assumedto re- main forever employed in thatjob.3 Assuming thatthe workerdiscountsnext period's income (1-B)WR=B j(W-WR) h(w) dw (3) by a factor B < 1, the present value of future R earningson a job payingwage w is thusequalto W + SW + +B... 2W = w/(I -_ ).4 whichimplicitlydefinesthe (unique)reservation wage.5 2The implicationsof on-the-jobsearcharethusleft Equation indicatesthatthe worker'sreserva- 3 for futurework (Mortensen1986, Sec. 3.1). tion wage dependson the density, h(w), of the I The model could easily be extended to permit highest-offerdistribution. Abstractingfrom the exogenously generatedjob loss so that the worker specific channelsthrough whichjob information returnsto unemploymentwith positive probability flows, economistscommonlytake this distribu- each period. tion as given (for one exception,see Mortensen 4The assumption an"infinitehorizon," of madefor the sake of mathematical tractability, implies thatthe I To derive equation3 from equation2, note that worker'sreservationwage is constantthroughtime. Unless the workeris nearretirement, presentval- the ue of lifetimeearnings(andconsequentlythe reserva- WR ?? tion wage) will be little influencedby changes in (or J dw= V- JVh(w) dw. Vh(w) even the existence of) a retirement date. 0 WR
- 4. 588 AMERICANSOCIOLOGICAL REVIEW and Vishwanath1990). But in orderto explore thatPw > ps because a given weak tie is more the strength-of-weak-ties hypothesis,I derivethe likely to producenew information thana given highest-offerdistributionfrom more primitive strongtie.7 assumptionson the sources of job information. While Granovetter's assertionseems to im- Althoughthe analysis could be generalizedso pose a conditionon the offer probabilities, Lin's thatthe workerreceives offers from an arbitrary "strength-of-ties proposition"appears empha- to numberof sources,I assumethatthe workerre- size differences in the offer distributions. Lin ceives job informationthroughthree channels: (1982) arguedthat "strongties characterize the strongties, weak ties, and formal (impersonal) intimatesocial circle of individualswith similar search. characteristics weak ties characterize in- and the I assumethatthe workerpossesses woN weak frequent interactions peripheral and relationships ties and (1 - o)N strongties. The worker'snet- among dissimilarindividuals"(p. 134). In the work is thus describedby two parameters: size presentmodel, this suggests that the strong-tie (N)andcomposition Ineachperiod, work- (w). the and weak-tie offer distributions have the same er receives an offer througheach weak tie with mean but that the weak-tiedistribution more is probability and througheach strongtie with Pw dispersed.8 Given a lower bound on the wage probabilitypsEachweak-tiewage offeris drawn distribution, also suggeststhatweakties may Lin froma distribution Fw(w)withprobability densi- providea better(notmerelymoredispersed) dis- tyfw(w), while strong-tie offersaredrawnfroma tribution opportunities individuals of for withlow distribution Fs(w) withdensityfs(w).The worker initialpositions.9(Initialposition might referto also receives formaloffers by applyingdirectly the worker'sfather's relative wage or occupa- to M firmsduringeach period.Eachfirmmakes tional status.) Thus, beyond suggesting differ- an offer with probability formal offers are PF; ences in the dispersionof the offer distributions, drawn from a distributionFF(W) with density Lin's theoryalso implies thatthe offer distribu- fF(w). Thus, the worker's highest offer is less tions may (sometimes)be ranked.'0 thanw only if each offer receivedis less thanw. Returning the model,considerhow changes to Assuming that wage offers are drawnindepen- in the networkstructure and cl) influencethe (N of dently, the distribution the highest offer re- reservationwage (WR). (All results are proven ceived each periodcan be written in formally theAppendix.) Holdingnetwork com- position constant,the reservationwage rises as H(w)= [1 PF[1 -FF(W)]jM network size increases. Intuitively,the worker [I _pW [IFW (W)]] (N expectsmoreoffers (fromboth weak and strong ties) as N increasesandthusthe workerbecomes [1 - Ps [1 - Fs (w)]](1-(O)N. (4) more selective. AlthoughWR is unambiguously While I have so far placed no restrictions on 7To generatethis conditionendogenouslyfromthe the relationship between the offer probabilities presentmodel, one might assume thatjob offers are or offer distributions equation4, discussions in sometimes observedby dyads. Because triadbias is of the strength-of-weak-ties hypothesis by greateramongstrongties, the workeris morelikely to receive the same offer from two strong-tiefriends Granovetter (1973, 1974, 1982) and Lin (1982, thanfromtwo weak-tieacquaintances. 1990) suggest two possibilities. Granovetter 8 In the economics literature, increaseddispersion (1982, p. 105) assertedthat "ouracquaintances is typicallyformalizedas a "mean-preserving spread" ('weak ties') are less likely to be socially in- (Rothschild and Stiglitz 1970; see also Mortensen volvedwithone another thanareourclose friends 1986). Formally,the distribution H(w) is a mean-pre- ('strong ties')."6 Accordingly, since weak ties servingspreadof of(w) if are"moreproneto move in circlesdifferent from x x one's own," there is a "structural tendencyfor EHIWI = EH4w1 and dw IIH(w) > | Hf(w) dw those to whom one is only weaklytied to have 0 0 better access to job informationone does not for all x. alreadyhave" (Granovetter 1974, p. 52). In the 9Conversely,an upperboundon the offerdistribu- presentmodel, Granovetter's argument suggests tion implies thatstrongties are betterfor individuals with high initialpositions. 6 In the languageof biased networktheory,strong 10 sometimes I rankdistributions thebasisof "first- on ties areassumedto have a greater"triadbias"(Fararo orderstochasticdominance." Formally, H(w) stochas- and Skvoretz1987). tically dominatesof(w) if H(w) <!4(w)for all w.
- 5. JOB SEARCHAND NETWORKCOMPOSITION 589 betweenthe res- increasing N, the relationship in Thus, both the condition associated with ervationwage andnetworkcomposition depends Granovetter (equation6) and the conditionsas- sociatedwith Lin (equation8, sometimesequa- on the offer probabilities offer distributions. and As shown in the Appendix, the reservation tion 7) imply thatthe worker'sreservation wage wage is increasing the proportion weak ties in of increasesas networkcompositionshifts toward (o) if relativelymore weak ties. Because the value of search,which is equal to expected futureearn- Ps [1 - Fs (w)] -Pw [I -Fw (w)] <0. (5) ings, is directlyrelatedto the reservationwage, Thecondition expressed equation impliesthat each conditionimpliesthatweak ties arebenefi- in 5 WR is increasing o) if in cial for the job-seeker.Indeed,if networkcom- position were chosen to maximize futureearn- Pw >Ps given Fw (w) = Fs (w) for all w, (6) ings, the workerwould choose an all-weak-tie or if networkwheneverthese conditionshold. Fw (w) < Fs (w) for all w given Pw =Ps. (7) THE USE OF A WEAKTIE AND Thatis, the reservationwage is increasingin the EXPECTED WAGES proportion weak ties if weak ties relayjob of- of ferswithhigherprobability strong (equa- than ties The Granovetterand Lin formulationsof the tion 6) or the weak-tieoffer distribution supe- is strength-of-weak-ties hypothesiscould be tested rior to the strong-tiedistribution(equation7). empiricallyby examiningthe reservationwage Intuitively, increasein the proportion weak an of of job-seekers:Holding networksize constant, ties makesthe worker moreselectivebecausethe does the reservation wage rise as the proportion workerexpectseithermoreor betteroffers. of weakties increases? Echoingthe"networks as The reservation wage is also increasingin the resources" argument (Campbellet al. 1986), the proportion weak ties undera second condi- of modelthussuggestsa linkbetweenthe worker's 1 tion: network structureand labor-marketoutcome. 00 00 However,insteadof focusing on networkstruc- ture, empiricalstudies of the strength-of-weak- Pw = Ps, fwfw (w) dw = f wfs (w) dw, (8) 0 0 ties hypothesishave examinedthe relationship betweenwages and the type of tie actuallyused and there exists some fv'such that to find a job (BridgesandVillemez 1986;Mars- den andHurlbert 1988).The absenceof a signif- > Fs (w) if W< fw icantrelationship betweenwages andtie strength Fw(w) = Fs (w) if w .=i aftercontrollingfor humancapitalvariableshas < Fs (w) if W> fw. led theseresearchers doubtthe relevanceof tie to strength labor-market for outcomes. Thatis, the reservationwage is increasingin the However, these "tests" of the strength-of- proportion weak ties when both types of ties of weak-tieshypothesismay be misguided.To ex- relayofferswith the sameprobability, bothoffer plorethe implications the preceding of modelfor distributionshave the samemean,andthe weak- expectedwages, some additional notationis nec- tie distribution is "more dispersed" than the essary.First,thehighest-offer distribution(equa- strong-tiedistribution. economists studying As tion 4) is re-writtenas job searchhave long recognized,increaseddis- persion of the offer distributionmakes search H (w) = L4DF(W)]M [DW(W)] (O [(Ds(W)]fI 'N, more valuable since job seekers are concerned i.e., where only with the uppertail of the distribution, thoseoffersexceedingthereservation wage.Thus, if the weak-tiedistribution moredispersed,an is (Di(wj 1 Pi [ I - F. (w)] -I increasein the proportion weak ties improves of }. for i E {IF,W,S (9) the worker'schanceof findinga high-wagejob andthusraisesthe worker'sreservation wage. The densityfunctioncan thenbe writtenas " AlthoughthisconditionimpliesthatFwis a mean- h(w) H'(w) = gF (W) + gw(W)+ gS (W), preserving spread Fs, mean-preserving of need spreads condition. not satisfy this "single-crossing" where
- 6. 590 AMERICANSOCIOLOGICAL REVIEW characteristics. Becausethe precedingmodelab- gF (W) MpFfF (w) VPF (W)]M_ [VW (W)] (ON stracts from human capital differences across [(DS (W)] ( 01, workers,this assumption equivalentto the be- is hypothesisim- lief thatthe strength-of-weak-ties plies E{ wlW} > E{ wIS}. But analysis of equation gw (w) o(Npwfw (w) VFF (W)]M 13 demonstrates none of the conditionsas- that ON [(DW(W)] [(DS (W)] (I-o)N, sociatedwith Granovetter Lin are sufficient and and to guarantee relationship. this Indeed,as shown in theAppendix, condition the expressedin equa- gs (W) (1 - o))Npsfs (w) VFF (W)]M tion6 unambiguously impliesthe opposite:If the [(DW(W)] ON[(DS (W)] (1-(O)N-1. (10) weak-tieandstrong-tie offerdistributions the are same, E{wIW} <E{wIS} if pw > ps. Thus, if Because the worker searchesuntil receiving Granovetter correctthat weak ties are more is wage,thework- anofferexceedingthereservation likely to providenew information arestrong than er becomesemployedin a givenperiodwithprob- ties,then,holdingeverything constant, else work- ability ers findingjobs throughweak ties will receive 00 lower averagewages. | h (w) dw. Although this result holds regardlessof net- WR worksize (N), networkcomposition(o)),andthe uponemployment,the worker'sex- Conditional probability obtaininga formaloffer (PF), it is of pectedwage can be writtenas instructive considerthe specialcase in which to 00 the workerholds one tie of each type, i.e., N = 2 J wh(w)dw and o)= 1/2, and never receives offers through E{w} = WR (11) formalchannels,i.e., PF = 0. Further assumethat 00 the worker almost always receives an offer | h (w) dw throughthe weak tie, i.e., Pw is close to 1, but WR almostneverreceivesan offerthrough strong the The workeraccepts a job throughchannel i, tie, i.e., Ps is close to zero.In the periodin which where i representseither F (formal), W (weak an offer is accepted,an individualacceptinga tie), or S (strongtie), with probability job througha strong tie is thus likely to have 00 received two offers. An individualacceptinga Jg, (w) dw. job througha weak tie, on the other hand, is WR likely to have received only one offer. Because Conditionalupon employment,the probability the expectedhighestoffer increasesas the num- thatthe workeraccepts a job throughchanneli berof offersrises,the use of a weak tie impliesa can be written lower expectedwage. 00 Intuitively,then,E{wIS} exceeds E{ w1W} un- Jgi (w) dw derthiscondition(equation becausethe use of 6) Pr(i) = WR for i E {F,S,W}. (12) a weak tie indicatesthatthe workerreceived(on 0o average)fewer offersduringthe periodin which Jh (w) dw an offer was accepted.But if periods are very WR short (implying that the offer probabilitiesare Conditional upon accepting an offer through close to zero), the workeris unlikelyto receive channel i, the worker's expected wage can be several offers simultaneouslyand the use of a written weak tie reveals almostnothingaboutthe num- 00 ber of offers received.'2In the limiting case in Jwgi (w) dw E{wli}= WR foriE {F,S,W}. '2Althoughsomewhatambiguous,periodlengthin oo the precedingmodelprobablybest corresponds the to |g, (w)dw (13) WR amountof time ajob-seekerhas to respondto a firm's offer. When periodsare long, the workeris likely to Researchershave assumedthat the strength- hold severaloffers simultaneously.As periodlength of-weak-tieshypothesisimpliesthatworkersob- approacheszero (implying that the job-seeker must tainingjobs throughweak ties should receive immediatelyaccept or reject each offer), the proba- higherwages aftercontrollingfor humancapital bility of multipleoffers becomes negligible.
- 7. JOB SEARCHAND NETWORKCOMPOSITION 591 which periodlength is infinitesimal,the worker 5 butrejectanofferof 1. Now considerthe work- will receive at most one offer (throughall chan- er's expectedwage conditioned thetype of tie on nels) in each period.In this case, holdingevery- used. Because strong-tieoffers will only be ac- thingelse constant,E{wIW}= E{wIS . ceptedif w = 5, E IwISI = 5. But the workerwill While equation 6 always implies E{ wIS > accepta weak-tieofferof either4 or 5. Assuming E{wIW, theconditions associated withLin(equa- thatthe worker randomly choosesbetweenoffers tions 7 and 8) do not permit an unambiguous if boththe strongtie andweaktie offersareequal ranking the meanwages. Two examplesdem- of to 5, E{wIW}= 4.7 <5= E(wIS}. onstrate these conditionsareconsistentwith that E{wIS} > E{wIW}.To make these examples as Spread Example2: Mean-Preserving transparent possible, I assume that the wage as offers are discreterandomvariables.However, To show that the conditionexpressedby equa- examplesin whichoffersaredrawnfromcontin- tion 8 is also consistent with the relationship uous distributions could be constructed prove to E IwIS > E IwIW},I againassumeN= 2, X = 1/2, the same point. andPF = 0. Further assumethatstrong-tieoffers aredrawn froma three-pointdistribution which in Example1: StochasticDominance fs (1)= 1/4, fs (3)= 1/2, fs (5)= 1/4, (18) Assume thatthe workerhas one tie of each type and never receives offers throughformalchan- andthus, nels, i.e., N = 2, X = 1/2, andPF = 0. Furtheras- 0 forw< 1 sumethatwage offersfromstrongties areequal- ly likely to be either 1 or 5: Fs(w)= 1/4 for l< w < 3 3~/4 for3? w<5 1 forw?5. (19) fs (1)=fs (5)= 1/2. (14) Assume thatweak-tieoffers aredistributedsuch Thus, the cumulativedistributionof strong-tie that offerscan be written fw(1) =fw(2) =fw(4) =fw(5) = 1/4, (20) 0 forw< 1 Fs(w)= 1/2 for I< w<5 andthus, 1 for w > 5. (15) 0 forw< 1 Assumethatoffersfromweakties aredrawn from a three-point in distribution which 1/4 forl<w<2 Fw(w) 1/2 for2< w<4 fw (1) = fw (4) = 1/4., fw (5) = 1/2. (16) 3/4 for4< w<5 I forw?5. (21) This implies the following cumulativedistribu- Comparingthe distribution functions,Fw(w) > tion of weak-tieoffers: Fs(w) for w < 3 and Fw(w) < Fs(w) for w ? 3. BecauseE{w I = 3 forbothdistributions, con- the 0 forw< 1 ditionexpressedby equation8 holds:Fw(w)is a F. -) 1/4 forl< w<4 "mean-preserving of spread" Fs(w). 1/2 for4< w<5 Assuming B=.9 andp= .5,WR= 3.538. In this 1 forw?5. (17) case, as in example 1, the workeraccepts only Comparing cumulativedistributions, is ap- offersof 4 or 5. Becauseonly strong-tie the it offersof parent that Fw(w) "stochastically dominates" 5 are acceptable,E{ wIS) = 5. Again assuming Fs(w):Fw(w) < Fs(w) for all w. AssumingPw = thatthe workerchooses randomlywhen receiv- Ps = p, the conditionexpressedin equation7 is ing offersof 5 through bothweakandstrongties, thussatisfied. E{wIW)= 4.517 < 5 =E{wIS}. Given assumptions Bandp, the reservation on wage andmeanwages can be calculated. ex-For Although theseexamplesestablish thecon- that ample,supposeB= .8 andp = .5. Using Appendix ditions expressedby equations7 and 8 are not equationAl (or the discreteanalog of equation theoretically with the negativefind- inconsistent 3), the reservationwage is WR= 3.280. In this ings reportedby Bridges and Villemez (1986), case, the workerwill acceptanofferof either4 or alternative distributional assumptions imply
- 8. 592 AMERICANSOCIOLOGICAL REVIEW E( wIWI> Ef wIS Inthenextexample,I assume empirical evidence. Although little is known 1. thatwage offers are distributed lognormally. aboutthe shapeof actualoffer distributions, ex- amplesusing the lognormal(andother)distribu- Example3: LognormalOfferDistributions tions suggest that the use of a weak tie should imply higherexpectedwages when the weak-tie Assume that the offer distributions lognor- distribution eithermoredispersedor stochasti- are is mal with means ,UF .75, gw = Us = 1, and stan- cally dominant. = darddeviationsaF = 6W= 1, (s = .75. The weak- Lin's hypothesismightbe reconciledwith the tie distribution thus stochastically dominatesthe empiricalevidence by assumingthatbothof the formal distributionand is a mean-preserving conditionsassociatedwith Granovetter Lin and spreadof the strong-tiedistribution. Assuming hold: Pw > Ps and Fw(w) is superiorto Fs(w). PF=PW=PS = 1,N=6, 0)=.5,M= 8, andB3=.8, Because I have proventhatthe use of a weak tie it can be shown thatWR = 1.884 and implies lower wages given Pw > Ps and suggest- ed that a superiorweak-tie distribution implies Et wIW = 4.185 > Et wIF I = 3.821 higherwages,thesetwo effectsmightoffseteach other. However, as the next example suggests, > E(wIS I = 3.159. the magnitudeof the negativeeffect is likely to be quitesmall (andmay be statistically insignifi- Undereitherequation7 or 8, i.e., Fw stochasti- cant in empiricalwork). Thus, the effect of dif- cally dominatesor is a mean-preserving spread ferences in the offer distributionsis likely to of Fs, it seems likely thatE(wIWI> E(wISIfor a swampany effect due to differencesin the offer large class of distributions.)3 Although I have probabilities. made little progressdefining this class analyti- Althoughresearchers havebeen unableto find cally, a rather strongconditionon the offerdistri- a significantrelationship betweenwages andthe butionsthatguarantees inequality present- use of a weak tie after controllingfor human this is ed in the Appendix. capital variables, both Bridges and Villemez (1986) and Marsdenand Hurlbert (1988) report EMPIRICAL IMPLICATIONS a positive zero-order correlation.If, as Bridges and Villemez suggest, humancapital variables The precedinganalysissuggeststhatthe conclu- areproxiesfor social capitalformation, zero- the sion reachedby BridgesandVillemez (1986) ordercorrelationmight be explainedby differ- thattie strength a relativelyunimportant is factor ences in network structureacross workers.To in labor marketsuccess - may be premature. see this, considera final example in which the Supposethatweakties arebeneficial becausethey conditionassociatedwithGranovetter holds,i.e., are more likely to relay job information as Pw> Ps , while the conditionassociatedwith Lin Granovetter suggests. In this case, I have estab- does not, i.e., Fw(w) = Fs(w) for all w. Assume lished that the worker'sreservationwage (and wage offers are drawnfrom lognormaldistribu- thus expected futureearnings)rises as the pro- tions with meansR = gw = gS = 1 andvariances portionof weak ties in the worker'snetworkin- a, = a'w = a's = 1. Furtherassume M = 6, B =.8, creases.But althoughnetworkcompositionis an andpw = .2 > Ps = .1 > PF = .05. The worker's important determinant labormarketsuccess, reservation expectedwages given severalal- of and the use of a weak tie does not imply higherex- ternativeassumptionson the size and composi- pectedwages. tion of the worker's network are presentedin While I have shown thatthe use of a weak tie Table 1. is consistent with lower expected wages even This example illustratesresultsalreadyestab- when weak-tieoffers are drawnfrom a superior lished:Individualswith large networksand/ora distribution, Lin's (1982) "strength-of-ties prop- large proportion weak ties in their networks of osition" is more difficult to reconcile with the will set relativelyhigh reservation wages. In this example,suchindividuals also receiverelatively 13 In the limitingcase in which the workerreceives highexpectedwages. Thisrelationship consis- is at most one offer (throughall channels)in each peri- tent with the findingsof Campbellet al. (1986): od, it is straightforward proveEs wlW) > Es wiS) if Individuals highsocioeconomic to of statusarelike- weak-tieoffersaredistributed uniformly [a,b]while ly to have largerbut less tightly knit networks in strong-tieoffers areuniformin [c,d] wherea + b > c + thanindividuals low socioeconomic of status.But d and b> d. while Et w I is increasingin N and co,Et wIW}is
- 9. JOB SEARCHAND NETWORKCOMPOSITION 593 Table 1. ReservationWages, Expected Wages, and Prob- ture,heterogeneity thepopulation in thusinduces ability of Using Search Method by Network EtwIW} > EtwIS}. This result is driven by the Structure differences in the proportionsPr(W)and Pr(S) Network Structure across workertypes: Workerswith a large pro- portion weakties (andthushighexpectedwag- of Wagesand N=3 N=3 N=6 N=6 Probabilities cl)= 1/3 clo=2/3 co= 1/3 cl)= 2/3 es) are much more likely to use weak ties (and less likely to use strongties). Reservation WR 1.679 1.804 2.125 2.310 In this analysis, I have contrastedalternative wage informaljob-finding methods - weak versus Expected E{wI 3.847 4.031 4.513 4.785 strong ties - ratherthan informaland formal wage methods. However, given the symmetryof the Expectedwage conditionalupon using a model with respect to each of the job-finding Formal E{wIFI 3.858 4.046 4.525 4.800 methods,the analysisis easily generalized.Par- method allelingBridgesandVillemez (1986), Corcoran, Weak tie E{wIW} 3.830 4.019 4.502 4.779 Datcher,and Duncan (1980) found that the use Strongtie E{wIS} 3.849 4.037 4.517 4.793 of a personalcontactis not associatedwith high- Probabilityoffinding job througha er wages and concluded that such contacts are Formal Pr(F) .425 .371 .271 .229 unimportant labor marketsuccess. But if in- in method formalandformaloffersaredrawn fromthe same Weak tie Pr(W) .290 .505 .367 .618 distribution, differencesshould be expected no Strongtie Pr(S) .285 .124 .363 .153 in the averagewage acrossjob-findingmethods used.Networkstructure, however,shouldbe cor- relatedwith wages if personalcontactsincrease the offer arrivalrate. equalto Et wISI for each network approximately structure.14 CONCLUSION Assume that the labor force comprises two typesof workers: have small,mostly strong- half Bridges and Villemez (1986) argued that tie tie networks(N = 3, co= 1/3) while the otherhalf strengthis not an important dimensionof social havelarge,mostlyweak-tienetworks(N = 6, co= capitalbecausetheyfailedto find a positiverela- 2/3). The formergroupis represented column by tionshipbetweenthe use of a weaktie andwages 1 in Table 1 andthe lattergroupis representedby after controllingfor workercharacteristics. My column 4. The mean wages for the population analysis, based on an economic model of job can be written search,suggeststhatthis conclusionmay be pre- mature. Alternative of formulations the strength- E (wIW} = SPr(W)EIwIWI of-weak-ties hypothesis suggest that weak ties X Pr(W) may be beneficial for two distinct reasons. Granovetter emphasized weakties relayuse- that (.290)(3.830) + (.618)(4.779) ful job information more frequentlythan strong .290 + .618 ties, whereas Lin's formulation suggests that = 4.476; weak-tiejob offers are drawnfrom a different (oftensuperior) AlthoughLin's for- distribution. mulationseems difficult (althoughnot theoreti- E IwISI = EPr(S) Et wISI cally impossible)to reconcilewith the empirical I Pr(S) evidence on wages, Granovetter'sformulation -(.285)(3.849) + (.153)(4.793) implies that the use of a weak tie will be nega- .285 + .153 tively (although perhapsweakly)relatedto aver- = 4.179, age wages. My analysis suggests that researchers should where the summationsare taken over worker devotemoreattention therelationship to between for types.Intheabsenceof controls network struc- networkstructureand labor-market outcomes. The relationship betweenwages andthe use of a 14 This resultwould still hold if the common offer particular job-findingmethodmay be counterin- distribution improvesas N or corises as suggestedby tuitive:The use of a weaktie couldbe associated Lin's (1982) "strength-of-positions proposition." with lower wages even though weak ties relay
- 10. 594 REVIEW AMERICANSOCIOLOGICAL offersmorefrequently thanstrongties andweak- Appendix tie offersare(on average)superior offersfrom to othersources.However,the presentmodel pre- NetworkStructureand the ReservationWage dicts an unambiguous relationshipbetween res- Integrating parts,equation3 may be rewrittenas by ervation wages and network structure:Both ,00 Granovetter's and Lin's formulations of the (1-B)wRH ={ f l-H(w)dwj ' (Al) strength-of-weak-ties hypothesisimply that the tWR) reservation wage rises as the proportion weak of wherewWH the reservation is wage corresponding theH(w) to ties in a job-seeker'snetworkincreases. distribution. Consideran alternativeoffer distribution,M(w),where Economicmodels of job searchseem to offer 00 00 a useful framework examinationof the rela- for f I - H(w) dw > | I - M(w) dw for all x, (A2) tionshipbetweensocialnetworksandlabor-mar- x x ket outcomes.By relaxingseveralof the simpli- or stateddifferently, fying assumptionsadoptedin the presentanaly- 00 sis, researchers could addressa varietyof other J H(w) - H(w) dw <0 for all x. (A3) x issues raisedin the strength-of-weak-ties litera- wage for the M(w)distribu- Let wHrepresent the reservation ture. Extendingthe model to permiton-the-job tion so that searchwould allow examination the relation- of ship betweenthe type of tie used, priorwage (or (1-awe=~ fJ1- (w) dwj. (A4) prestige), thecurrent and wage (Wegener1991).'5 tR) Further,by specifying the costs of searching I establishwiH> wf If Hby contradiction. wWH WH, inequal- < through alternativechannels(as in Holzer 1988), ity A2 implies that researchers could examineGranovetter's (1974, 00 00 00 p. 54) claim that unemployedjob-seekers are morelikely thanemployedjob seekersto turnto f 1 -Hw) dw < f 1 H(w) dw < f I-H(w) dw (AS) WR WR WR their strong ties.'6 Alternatively,contact status could be incorporated the model to evaluate in Thus, the right-hand side of equationAl exceeds the right- Lin's (Linet al. 1981;Lai et al. 1990) pathanal- hand side of equationA4. However, underthe assumption that w H < WH, the left-handside of equationA4 must (at yses. Finally,following Marsdenand Campbell least weakly)exceed the left-handside of equationAl. This (1990), future researchcould incorporateboth contradictionestablishes that w H cannot be less than or sides of the labormarket employersas well as - equal to (i.e., must exceed) wRf. workers- into the analysis. Once recruitment SupposethatH(w) represents offer distribution the given methods and wage determinationare endog- networksize NH and f(w) representsthe distribution given enized,researchers couldexaminetheinteraction networksize NL whereNH > NL.Fromequation9, betweensocial networkstructure the income and H(w) - Hf(w)= H(w) [['14W(W)I)(NH -NL) distribution (Mortensenand Vishwanath' 1990; Montgomery1990, 1991a, 1991b). [(T>S(W)](l-())(NHNL) _- I] (A6) JAMESD. MONTGOMERY AssistantProfessorof Eco- is Because the bracketedexpression is negative for all w, nomicsand a FacultyFellow at the Centerfor Urban inequality A3 holds. Holding network composition con- Affairsand Policy Researchat Northwestern Univer- stant, the reservationwage is thus increasing in network sity. In his research he explores the relationshipbe- size. tween social networksand labor-marketoutcomes, Now let M(w) representthe highest-offer distribution attemptingto integrate economic and sociological when the workerhas 0N weak ties and (1 - o)N strongties; conceptionsof labor markets.Building upon ethno- H(w) representsthis distributionwhen the workerhas one graphicaccountsof urbanpoverty,he is also working additionalweak tie (and thus one less strongtie). Equation 9 implies to develop rational-choice models of "underclass" behavior. H(w) - M(w) = [(Dw(w) - (Ds(w)] H(w) (A7) (Ds(w) 15 Note that a job-seeker's currentposition may Because H(w)/'Ds(w) is always positive, H(w) - M(w)is also influence networkstructure, offer distributions, negative (and thus WR is increasingin w) if the bracketed and offer probabilities. expression - which is rewrittenas ps[l - Fs(w)] - Pw[l- 16 The increaseduse of strongties may be relatedto Fw(w)] in equation5 - is negative. Holding networksize liquidityconstraintsfaced by unemployedjob seek- constant,the conditionexpressedby equation5 implies that ers, which imply that the reservationwage is falling the reservationwage increases as the proportionof weak over time (Mortensen1986, pp. 859-61). ties increases.
- 11. JOB SEARCHAND NETWORKCOMPOSITION 595 Now assumethe conditionexpressedby equation8 holds 00 and let Pw = ps = p. From inequalityA3 and equationA7, fw [x(w) - x(w)] ,(w)dw WR is increasingin 0) if WR 0o 00 x J p [Fw (w) - Fs (w)] ['tF (W)]M [I (W)]WN > w|[x(w) - x(w)] ,(w)dw = O WR if dx(w) / dw > O [(DS(W)](' - co)N-IdW < 0 for all x. (A8) 0o <w J[x(w) - x(w2)] ,(w)dw = 0 if dx(w) / dw < 0. Because the last three terms in the integrandare positive WR (A14) andincreasingin w, andbecause the conditionexpressedin equation8 implies [Fw (w) - Fs (w)] < 0 if andonly if x > w, Assume thatthe conditionexpressedby equation6 holds the left-handside of inequalityA8 is less than and let Fw(w) = Fs(w) = F(w) with densityf(w) for all w. The expected wages are thus given by equationsAlO and P [DF (0)] [DW (0)]()N [(DS (0)](I - o))N- I Al l where J 00 x(w) = (Ds(w)A1Dw (w) [Fw (w) - Fs (w)] dw. (A9) x = [1 - ps[l - F(w)]]/[l - pw[l - F(w)]], and Because the conditionexpressedby equation8 implies that 00 t(x) = flw) ['Dr (W)]M [(w (w)] f [Fw (w) - Fs (w)] dw = 0, [(Ds (w)10 -1))N-I dw. (A15) 0 0o Because dx(w)/dw=f(w)(ps - pw)/Vtw(w)]2 < 0, equation6 J x [Fw (w) - Fs (w)] dw <O for all x 2 w, implies E(wISI > E(wIWI. Now consider the conditions expressed by equations7 and 8 which imply Pw = Ps = p but Fw(w) ? FS(w). The and x expected wages are again given by equationsA10 and A 1I J0 [Fw (W)- Fs (w)] dw >O for all x < w, where fw (w) (Ds(w) aln(Dw (w))Iaw x(w) == the integralin expressionA9 is negative for all x. Since all X()-(w (w) fs (w) Dln((Ds (w)O/w otherterms in expressionA9 are positive, inequalityA8 is and satisfied:the conditionexpressedby equation8 implies that WR is increasingin (0. t(W) =JS(W) PDF (W)] PDW (W)] [(DS (W)]l @)N-I dw. (A16) OfferDistributions, ExpectedWages OfferProbabilities, and Suppose thatthe expected wage functionscould be written Thus, dx(w)/dw> 0 is a (sufficient)conditionguaranteeing as EIwIWI> EI wISI. A relatedcondition- log concavity of the offer distribution- arises frequentlyin the job-search Etw1WI = w x(w) ,(w) dw/ 7x(w) t(w) dw, (AIO) literature(Burdett1981; see also the discussion of log con- WR WR cavity in Heckmanand Honor61990). However,numerical and examples (not reportedhere) using the normaland lognor- 00 00 mal distributions gw 2 gs andaw 2 as generate Iw1WI with E EIw1SI= ,fw ,(w)dw/ Jf(w) dw, (All) > El wISI even thoughx(w) is sometimesnot monotonically WR WR increasing.This suggests that a weaker (sufficient) condi- may be found. tion on the offer distributions wheret(w) ? 0 for all w andx(w) is continuousand mono- tonic. Note thatE{wlWI = E{wISI if x(w) is simply a con- stant.To show thatE IwIWIis greater(less) thanE IwIS if I such that x(w) is increasing(decreasing)in w, define wv REFERENCES 00 00 x(wv) (w) dw ,f = ,fx(w) 4(w) dw. (A12) Boorman,Scott A. 1975. "A Combinatorial Optimi- WR WR zation Model for Transmission Job Information of throughContactNetworks."Bell Journal of Eco- Given the conditionson x(w) and4(w), a uniquew E (WR ,??) nomics 6:216-49. always exists. Multiplyboth the numerator denomina- and Boxman, Ed, Henk Flap, and Jeroen Weesie. 1991. torof equationA 1 by x(w). Subtracting fromequation this "Social Capitaland InformalJob Search."Depart- AlO yields the condition mentof Social Sciences,Universityof Utrecht,The ElwiWI >Ejw1SI if and only if Netherlands. Unpublishedmanuscript. 00 Bridges, William P. and Wayne J. Villemez. 1986. f w [x(w) _x(wA)] dw > 0. 4(w) (A13) "InformalHiring and Income in the Labor Mar- WR ket."AmericanSociological Review51:574-82. given the conditionson x(w) and 4(w), Further, Burdett,Kenneth.1981. "A Useful Restrictionon the
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