Job Search and Network Composition: Implications of the Strength-Of-Weak-Ties HypothesisAuthor(s): James D. MontgomerySource: American Sociological Review, Vol. 57, No. 5 (Oct., 1992), pp. 586-596Published by: American Sociological AssociationStable URL: http://www.jstor.org/stable/2095914Accessed: 21/08/2009 17:52

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JOB SEARCH AND NETWORK COMPOSITION: IMPLICATIONS OF THE STRENGTH-OF-WEAK-TIES HYPOTHESIS*

JAMEs D. MONTGOMERY Northwestern University

Workers find jobs through personal contacts (weak and strong ties) and formal sources. Alternative formulations of the strength-of-weak-ties hypothesis suggest (1) weak ties relay job offers more frequently than strong ties, or (2) weak-tie offers are drawn from a better distribution. A formal model shows that both formulations imply a correlation between net- work composition and a job seeker's minimum acceptable wage. However, the use of a weak tie is never associated with higher expected wages under the firstformulation, and is only sometimes associated with higher expected wages under the secondformulation. These re- sults suggest that researchers shouldfocus on job seekers' network structures.

Based on the finding that workers frequently locate jobs through acquaintances ("weak

ties") rather than close friends and relatives ("strong ties"), Granovetter (1973, 1974) argued that weak ties play an important role in determin- ing labor-market outcomes. Subsequent theoret- ical work in the social resources literature further emphasized the importance of weak ties (Lin 1982). However, Bridges and Villemez (1986) and Marsden and Hurlbert (1988) found no sig- nificant relationship between tie strength and wages after controlling for worker characteris- tics. Consequently, some researchers have argued against the strength-of-weak-ties hypothesis. Bridges and Villemez (1986), for example, con- cluded that "the strong-weak dimension of ties is not the only, or even the most important, attribute of personal relationships in the labor market.... Future research should concentrate on exploring other dimensions of social resources and their role in the job finding process" (pp. 579-80).

Reflection suggests that the Bridges and Ville- mez conclusion may be premature. While empir- ical analyses of the strength-of-weak-ties hypoth- esis have focused on the type of tie actually used to locate a job (although see Lai, Leung, and Lin 1990), the "networks as resources" argument (Campbell, Marsden, and Hurlbert 1986) sug- gests that network structure may be the crucial

independent variable. Moreover, alternative for- mulations of the strength-of-weak-ties hypothe- sis suggest that job seekers benefit from weak ties for two distinct reasons. Granovetter empha- sized that weak ties relay useful job information more frequently than strong ties, whereas Lin's formulation suggested that weak-tie job offers are drawn from a different (often superior) distri- bution. To examine the empirical implications of these two formulations of the strength-of-weak- ties hypothesis, I offer a formal model in which workers locate jobs through both personal con- tacts (weak and strong ties) and formal (imper- sonal) methods, building on previous work in the economics job-search literature (Mortensen 1986).'

THE MODEL: NETWORK STRUCTURE AND THE RESERVATION WAGE

Because job-seekers lack complete knowledge of vacancies and must rely on information obtained through various formal and informal channels (e.g., direct application to employers, newspaper ads, and personal referrals), economists often con- ceptualize job search as a sequence of wage of- fers drawn randomly from an offer distribution. (When the nonpecuniary aspects of employment differ across jobs, the "wage" might be interpret- ed as a broader index of job quality.) If job search were costless for both unemployed and employed * Direct all correspondence to James D. Montgom-

ery, Department of Economics, Northwestern Uni- versity, Evanston, IL 60208. Helpful comments were received from Peter Marsden. Financial support from National Science Foundation grant SES-9109056 is gratefully acknowledged.

I Boorman (1975) and Boxman, Flap, and Weesie (1991) present related models of job search through strong and weak ties. Halaby (1988) used a search- theoretic model to examine individuals' decisions to search for new jobs.

586 American Sociological Review, 1992, Vol. 57 (October:586-596)

JOB SEARCH AND NETWORK COMPOSITION 587

workers, job-seekers would accept any offer ex- ceeding their current wage (or value of leisure if unemployed) and continue searching for a better job while employed. But if job search becomes more costly once a worker is employed, the opti- mal search strategy is more complex: The job seeker sets a minimum acceptable (or "reserva- tion") wage, rejecting any offers below the reser- vation wage and accepting the first offer exceed- ing this wage (Lippman and McCall 1976; Mortensen 1986).

Consider the simplest case in which job search is costless for unemployed workers but is pro- hibitively expensive for employed workers. Even if an unemployed worker places no value on lei- sure (so that the current "wage" is zero), the work- er might reject a low-wage offer because em- ployment would preclude further search, which might lead to a better offer and higher lifetime earnings. However, the job-seeker would gener- ally not wait to receive the maximum possible offer because earnings foregone from rejecting a sufficiently "good" offer might exceed the net expected benefit from continued search. The fact that the job-seeker rejects relatively low-wage job offers but accepts relatively high-wage offers suggests the existence of a critical wage, i.e., the reservation wage, at which the job-seeker is in- different between accepting employment and continuing the job search.

Now consider an unemployed worker search- ing for a job. Two simplifying assumptions are adopted in the present model. First, I assume that the worker searches only while unemployed.2 Sec- ond, I ignore the possibility of job dissolutions such as quits, layoffs, or retirement. Thus, after accepting an offer, the worker is assumed to re- main forever employed in that job.3 Assuming that the worker discounts next period's income by a factor B < 1, the present value of future earnings on a job paying wage w is thus equal to W + SW + 2W +B... = w/(I -_ ).4

Suppose that the worker receives some (po- tentially stochastic) number of offers each peri- od. The distribution of the highest offer received each period is represented by H(w), with proba- bility density h(w). Further, let WR represent the worker's reservation wage and let V represent the worker's "value of search," i.e., the present value of expected future earnings given that the worker remains unemployed at the end of a peri- od. Given this notation, consider the worker's expected future earnings viewed from the start of a period (before any offers are received). Be- cause the worker's expected future earnings are by definition equal to V if no offer exceeds WR

and are equal to wI(1 - B) if the highest offer exceeds WR, the worker's expected future earn- ings are

WR

f Vh(w)dw+ | 1-B h(w)dw. (1) 0 WR

Now consider the worker's expected future earn- ings viewed from the end of the preceding period (after all offers were rejected). Given that the worker discounts future earnings by the factor B, this "value of search" is defined implicitly by

WR

V= fjVh(w)dw+f |WB h(w) dw. (2)

Because the worker is indifferent between accept- ing a job at the reservation wage and continuing the job search, V = wR/(l - B). Substitution into equation 1 yields

(1-B)WR=B j(W-WR) h(w) dw (3) \ R

which implicitly defines the (unique) reservation wage.5

Equation 3 indicates that the worker's reserva- tion wage depends on the density, h(w), of the highest-offer distribution. Abstracting from the specific channels through which job information flows, economists commonly take this distribu- tion as given (for one exception, see Mortensen

2 The implications of on-the-job search are thus left for future work (Mortensen 1986, Sec. 3.1).

I The model could easily be extended to permit exogenously generated job loss so that the worker returns to unemployment with positive probability each period.

4The assumption of an "infinite horizon," made for the sake of mathematical tractability, implies that the worker's reservation wage is constant through time. Unless the worker is near retirement, the present val- ue of lifetime earnings (and consequently the reserva- tion wage) will be little influenced by changes in (or even the existence of) a retirement date.

I To derive equation 3 from equation 2, note that

WR ??

J Vh(w) dw = V- JVh(w) dw. 0 WR

588 AMERICAN SOCIOLOGICAL REVIEW

and Vishwanath 1990). But in order to explore the strength-of-weak-ties hypothesis, I derive the highest-offer distribution from more primitive assumptions on the sources of job information. Although the analysis could be generalized so that the worker receives offers from an arbitrary number of sources, I assume that the worker re- ceives job information through three channels: strong ties, weak ties, and formal (impersonal) search.

I assume that the worker possesses woN weak ties and (1 - o)N strong ties. The worker's net- work is thus described by two parameters: size (N) and composition (w). In each period, the work- er receives an offer through each weak tie with probability Pw and through each strong tie with probabilityps Each weak-tie wage offer is drawn from a distribution Fw(w) with probability densi- tyfw(w), while strong-tie offers are drawn from a distribution Fs(w) with densityfs(w). The worker also receives formal offers by applying directly to M firms during each period. Each firm makes an offer with probability PF; formal offers are drawn from a distribution FF(W) with density fF(w). Thus, the worker's highest offer is less than w only if each offer received is less than w. Assuming that wage offers are drawn indepen- dently, the distribution of the highest offer re- ceived each period can be written

H(w)= [1 PF[1 -FF(W)]jM

[I _pW [IFW (W)]] (N

[1 - Ps [1 - Fs (w)]](1-(O)N. (4)

While I have so far placed no restrictions on the relationship between the offer probabilities or offer distributions in equation 4, discussions of the strength-of-weak-ties hypothesis by Granovetter (1973, 1974, 1982) and Lin (1982, 1990) suggest two possibilities. Granovetter (1982, p. 105) asserted that "our acquaintances ('weak ties') are less likely to be socially in- volved with one another than are our close friends ('strong ties')."6 Accordingly, since weak ties are "more prone to move in circles different from one's own," there is a "structural tendency for those to whom one is only weakly tied to have better access to job information one does not already have" (Granovetter 1974, p. 52). In the present model, Granovetter's argument suggests

that Pw > ps because a given weak tie is more likely to produce new information than a given strong tie.7

While Granovetter's assertion seems to im- pose a condition on the offer probabilities, Lin's "strength-of-ties proposition" appears to empha- size differences in the offer distributions. Lin (1982) argued that "strong ties characterize the intimate social circle of individuals with similar characteristics and weak ties characterize the in- frequent interactions and peripheral relationships among dissimilar individuals" (p. 134). In the present model, this suggests that the strong-tie and weak-tie offer distributions have the same mean but that the weak-tie distribution is more dispersed.8 Given a lower bound on the wage distribution, Lin also suggests that weak ties may provide a better (not merely more dispersed) dis- tribution of opportunities for individuals with low initial positions.9 (Initial position might refer to the worker's father's relative wage or occupa- tional status.) Thus, beyond suggesting differ- ences in the dispersion of the offer distributions, Lin's theory also implies that the offer distribu- tions may (sometimes) be ranked.'0

Returning to the model, consider how changes in the network structure (N and cl) influence the reservation wage (WR). (All results are proven formally in the Appendix.) Holding network com- position constant, the reservation wage rises as network size increases. Intuitively, the worker expects more offers (from both weak and strong ties) as N increases and thus the worker becomes more selective. Although WR is unambiguously

6 In the language of biased network theory, strong ties are assumed to have a greater "triad bias" (Fararo and Skvoretz 1987).

7To generate this condition endogenously from the present model, one might assume that job offers are sometimes observed by dyads. Because triad bias is greater among strong ties, the worker is more likely to receive the same offer from two strong-tie friends than from two weak-tie acquaintances.

8 In the economics literature, increased dispersion is typically formalized as a "mean-preserving spread" (Rothschild and Stiglitz 1970; see also Mortensen 1986). Formally, the distribution H(w) is a mean-pre- serving spread of of(w) if

x x

EHIWI = EH4w1 and IIH(w) dw > | Hf(w) dw 0 0

for all x.

9 Conversely, an upper bound on the offer distribu- tion implies that strong ties are better for individuals with high initial positions.

10 I sometimes rank distributions on the basis of "first- order stochastic dominance." Formally, H(w) stochas- tically dominates of(w) if H(w) < !4(w) for all w.

JOB SEARCH AND NETWORK COMPOSITION 589

increasing in N, the relationship between the res- ervation wage and network composition depends on the offer probabilities and offer distributions.

As shown in the Appendix, the reservation wage is increasing in the proportion of weak ties (o) if

Ps [1 - Fs (w)] -Pw [I -Fw (w)] <0. (5)

The condition expressed in equation 5 implies that WR is increasing in o) if

Pw >Ps given Fw (w) = Fs (w) for all w, (6)

or if

Fw (w) < Fs (w) for all w given Pw =Ps. (7)

That is, the reservation wage is increasing in the proportion of weak ties if weak ties relay job of- fers with higher probability than strong ties (equa- tion 6) or the weak-tie offer distribution is supe- rior to the strong-tie distribution (equation 7). Intuitively, an increase in the proportion of weak ties makes the worker more selective because the worker expects either more or better offers.

The reservation wage is also increasing in the proportion of weak ties under a second condi- tion: 1

00 00

Pw = Ps, fwfw (w) dw = f wfs (w) dw, (8) 0 0

and there exists some fv' such that

> Fs (w) if W< fw

Fw(w) = Fs (w) if w .= i

< Fs (w) if W > fw .

That is, the reservation wage is increasing in the proportion of weak ties when both types of ties relay offers with the same probability, both offer distributions have the same mean, and the weak- tie distribution is "more dispersed" than the strong-tie distribution. As economists studying job search have long recognized, increased dis- persion of the offer distribution makes search more valuable since job seekers are concerned only with the upper tail of the distribution, i.e., those offers exceeding the reservation wage. Thus, if the weak-tie distribution is more dispersed, an increase in the proportion of weak ties improves the worker's chance of finding a high-wage job and thus raises the worker's reservation wage.

" Although this condition implies that Fw is a mean- preserving spread of Fs, mean-preserving spreads need not satisfy this "single-crossing" condition.

Thus, both the condition associated with Granovetter (equation 6) and the conditions as- sociated with Lin (equation 8, sometimes equa- tion 7) imply that the worker's reservation wage increases as network composition shifts toward relatively more weak ties. Because the value of search, which is equal to expected future earn- ings, is directly related to the reservation wage, each condition implies that weak ties are benefi- cial for the job-seeker. Indeed, if network com- position were chosen to maximize future earn- ings, the worker would choose an all-weak-tie network whenever these conditions hold.

THE USE OF A WEAK TIE AND EXPECTED WAGES

The Granovetter and Lin formulations of the strength-of-weak-ties hypothesis could be tested empirically by examining the reservation wage of job-seekers: Holding network size constant, does the reservation wage rise as the proportion of weak ties increases? Echoing the "networks as resources" argument (Campbell et al. 1986), the model thus suggests a link between the worker's network structure and labor-market outcome. However, instead of focusing on network struc- ture, empirical studies of the strength-of-weak- ties hypothesis have examined the relationship between wages and the type of tie actually used to find a job (Bridges and Villemez 1986; Mars- den and Hurlbert 1988). The absence of a signif- icant relationship between wages and tie strength after controlling for human capital variables has led these researchers to doubt the relevance of tie strength for labor-market outcomes.

However, these "tests" of the strength-of- weak-ties hypothesis may be misguided. To ex- plore the implications of the preceding model for expected wages, some additional notation is nec- essary. First, the highest-offer distribution (equa- tion 4) is re-written as

H (w) = L4DF(W)]M [DW(W)] (O [(Ds(W)]fI 'N,

where

(Di (wj 1 -I Pi [ I - F. (w)]

for i E {IF,W,S }. (9)

The density function can then be written as

h (w) H'(w) = gF (W) + gw (W) + gS (W),

where

590 AMERICAN SOCIOLOGICAL REVIEW

gF (W) MpFfF (w) VPF (W)]M_ [VW (W)] (ON

[(DS (W)] ( 01,

gw (w) o(Npwfw (w) VFF (W)]M

[(DW (W)] ON

[(DS (W)] (I-o)N,

and

gs (W) (1 - o))Npsfs (w) VFF (W)]M

[(DW (W)] ON[(DS (W)] (1-(O)N-1. (10)

Because the worker searches until receiving an offer exceeding the reservation wage, the work- er becomes employed in a given period with prob- ability

00

| h (w) dw. WR

Conditional upon employment, the worker's ex- pected wage can be written as

00

J wh(w) dw E{w} = WR (11)

00

| h (w) dw WR

The worker accepts a job through channel i, where i represents either F (formal), W (weak tie), or S (strong tie), with probability

00

J g, (w) dw. WR

Conditional upon employment, the probability that the worker accepts a job through channel i can be written

00

J gi (w) dw Pr(i) = WR for i E { F,S,W} . (12)

0o

J h (w) dw WR

Conditional upon accepting an offer through channel i, the worker's expected wage can be written

00

J wgi (w) dw E{wli}= WR foriE {F,S,W}.

oo

|g, (w)dw (13) WR

Researchers have assumed that the strength- of-weak-ties hypothesis implies that workers ob- taining jobs through weak ties should receive higher wages after controlling for human capital

characteristics. Because the preceding model ab- stracts from human capital differences across workers, this assumption is equivalent to the be- lief that the strength-of-weak-ties hypothesis im- plies E{ wlW} > E{ wIS }. But analysis of equation 13 demonstrates that none of the conditions as- sociated with Granovetter and Lin are sufficient to guarantee this relationship. Indeed, as shown in the Appendix, the condition expressed in equa- tion 6 unambiguously implies the opposite: If the weak-tie and strong-tie offer distributions are the same, E{wIW} <E{wIS} if pw > ps. Thus, if Granovetter is correct that weak ties are more likely to provide new information than are strong ties, then, holding everything else constant, work- ers finding jobs through weak ties will receive lower average wages.

Although this result holds regardless of net- work size (N), network composition (o)), and the probability of obtaining a formal offer (PF), it is instructive to consider the special case in which the worker holds one tie of each type, i.e., N = 2 and o) = 1/2, and never receives offers through formal channels, i.e., PF = 0. Further assume that the worker almost always receives an offer through the weak tie, i.e., Pw is close to 1, but almost never receives an offer through the strong tie, i.e., Ps is close to zero. In the period in which an offer is accepted, an individual accepting a job through a strong tie is thus likely to have received two offers. An individual accepting a job through a weak tie, on the other hand, is likely to have received only one offer. Because the expected highest offer increases as the num- ber of offers rises, the use of a weak tie implies a lower expected wage.

Intuitively, then, E{ wIS } exceeds E{ w1W} un- der this condition (equation 6) because the use of a weak tie indicates that the worker received (on average) fewer offers during the period in which an offer was accepted. But if periods are very short (implying that the offer probabilities are close to zero), the worker is unlikely to receive several offers simultaneously and the use of a weak tie reveals almost nothing about the num- ber of offers received.'2 In the limiting case in

'2Although somewhat ambiguous, period length in the preceding model probably best corresponds to the amount of time a job-seeker has to respond to a firm's offer. When periods are long, the worker is likely to hold several offers simultaneously. As period length approaches zero (implying that the job-seeker must immediately accept or reject each offer), the proba- bility of multiple offers becomes negligible.

JOB SEARCH AND NETWORK COMPOSITION 591

which period length is infinitesimal, the worker will receive at most one offer (through all chan- nels) in each period. In this case, holding every- thing else constant, E{ wIW} = E{ wIS .

While equation 6 always implies E{ wIS > E{ wIW , the conditions associated with Lin (equa- tions 7 and 8) do not permit an unambiguous ranking of the mean wages. Two examples dem- onstrate that these conditions are consistent with E{wIS} > E{wIW}. To make these examples as transparent as possible, I assume that the wage offers are discrete random variables. However, examples in which offers are drawn from contin- uous distributions could be constructed to prove the same point.

Example 1: Stochastic Dominance

Assume that the worker has one tie of each type and never receives offers through formal chan- nels, i.e., N = 2, X = 1/2, and PF = 0. Further as- sume that wage offers from strong ties are equal- ly likely to be either 1 or 5:

fs (1)=fs (5)= 1/2. (14)

Thus, the cumulative distribution of strong-tie offers can be written

0 forw< 1 Fs(w)= 1/2 for I< w<5

1 for w > 5. (15)

Assume that offers from weak ties are drawn from a three-point distribution in which

fw (1) = fw (4) = 1/4., fw (5) = 1/2. (16)

This implies the following cumulative distribu- tion of weak-tie offers:

0 forw< 1 F. -) 1/4 forl< w<4

1/2 for4< w<5 1 forw?5. (17)

Comparing the cumulative distributions, it is ap- parent that Fw(w) "stochastically dominates" Fs(w): Fw(w) < Fs(w) for all w. Assuming Pw = Ps = p, the condition expressed in equation 7 is thus satisfied.

Given assumptions on B and p, the reservation wage and mean wages can be calculated. For ex- ample, suppose B = .8 andp = .5. Using Appendix equation Al (or the discrete analog of equation 3), the reservation wage is WR = 3.280. In this case, the worker will accept an offer of either 4 or

5 but reject an offer of 1. Now consider the work- er's expected wage conditioned on the type of tie used. Because strong-tie offers will only be ac- cepted if w = 5, E I wIS I = 5. But the worker will accept a weak-tie offer of either 4 or 5. Assuming that the worker randomly chooses between offers if both the strong tie and weak tie offers are equal to 5, E{wIW} = 4.7 <5= E(wIS}.

Example 2: Mean-Preserving Spread

To show that the condition expressed by equa- tion 8 is also consistent with the relationship E I wIS > E I wIW}, I again assume N= 2, X = 1/2, and PF = 0. Further assume that strong-tie offers are drawn from a three-point distribution in which

fs (1)= 1/4, fs (3)= 1/2, fs (5)= 1/4, (18)

and thus,

0 forw< 1

Fs(w)= 1/4 for l< w < 3 3~/4 for3? w<5 1 forw?5. (19)

Assume that weak-tie offers are distributed such that

fw(1) =fw(2) =fw(4) =fw(5) = 1/4, (20)

and thus,

0 forw< 1 1/4 forl<w<2

Fw(w) 1/2 for2< w<4 3/4 for4< w<5 I forw?5. (21)

Comparing the distribution functions, Fw(w) > Fs(w) for w < 3 and Fw(w) < Fs(w) for w ? 3. Because E{ w I = 3 for both distributions, the con- dition expressed by equation 8 holds: Fw(w) is a "mean-preserving spread" of Fs(w).

Assuming B =.9 andp= .5,WR= 3.538. In this case, as in example 1, the worker accepts only offers of 4 or 5. Because only strong-tie offers of 5 are acceptable, E{ wIS) = 5. Again assuming that the worker chooses randomly when receiv- ing offers of 5 through both weak and strong ties, E{wIW) = 4.517 < 5 =E{wIS}.

Although these examples establish that the con- ditions expressed by equations 7 and 8 are not theoretically inconsistent with the negative find- ings reported by Bridges and Villemez (1986), alternative distributional assumptions imply

592 AMERICAN SOCIOLOGICAL REVIEW

E( wIWI > Ef wIS 1. In the next example, I assume that wage offers are distributed lognormally.

Example 3: Lognormal Offer Distributions

Assume that the offer distributions are lognor- mal with means ,UF = .75, gw = Us = 1, and stan- dard deviations aF = 6W= 1, (s = .75. The weak- tie distribution thus stochastically dominates the formal distribution and is a mean-preserving spread of the strong-tie distribution. Assuming PF=PW=PS = 1,N=6, 0)=.5,M= 8, andB3=.8, it can be shown that WR = 1.884 and

Et wIW = 4.185 > Et wIF I = 3.821

> E(wIS I = 3.159.

Under either equation 7 or 8, i.e., Fw stochasti- cally dominates or is a mean-preserving spread of Fs, it seems likely thatE(wIWI > E(wISI for a large class of distributions.)3 Although I have made little progress defining this class analyti- cally, a rather strong condition on the offer distri- butions that guarantees this inequality is present- ed in the Appendix.

EMPIRICAL IMPLICATIONS

The preceding analysis suggests that the conclu- sion reached by Bridges and Villemez (1986) that tie strength is a relatively unimportant factor in labor market success - may be premature. Suppose that weak ties are beneficial because they are more likely to relay job information as Granovetter suggests. In this case, I have estab- lished that the worker's reservation wage (and thus expected future earnings) rises as the pro- portion of weak ties in the worker's network in- creases. But although network composition is an important determinant of labor market success, the use of a weak tie does not imply higher ex- pected wages.

While I have shown that the use of a weak tie is consistent with lower expected wages even when weak-tie offers are drawn from a superior distribution, Lin's (1982) "strength-of-ties prop- osition" is more difficult to reconcile with the

13 In the limiting case in which the worker receives at most one offer (through all channels) in each peri- od, it is straightforward to prove Es wlW) > Es wiS ) if weak-tie offers are distributed uniformly in [a,b] while strong-tie offers are uniform in [c,d] where a + b > c + d and b> d.

empirical evidence. Although little is known about the shape of actual offer distributions, ex- amples using the lognormal (and other) distribu- tions suggest that the use of a weak tie should imply higher expected wages when the weak-tie distribution is either more dispersed or stochasti- cally dominant.

Lin's hypothesis might be reconciled with the empirical evidence by assuming that both of the conditions associated with Granovetter and Lin hold: Pw > Ps and Fw(w) is superior to Fs(w). Because I have proven that the use of a weak tie implies lower wages given Pw > Ps and suggest- ed that a superior weak-tie distribution implies higher wages, these two effects might offset each other. However, as the next example suggests, the magnitude of the negative effect is likely to be quite small (and may be statistically insignifi- cant in empirical work). Thus, the effect of dif- ferences in the offer distributions is likely to swamp any effect due to differences in the offer probabilities.

Although researchers have been unable to find a significant relationship between wages and the use of a weak tie after controlling for human capital variables, both Bridges and Villemez (1986) and Marsden and Hurlbert (1988) report a positive zero-order correlation. If, as Bridges and Villemez suggest, human capital variables are proxies for social capital formation, the zero- order correlation might be explained by differ- ences in network structure across workers. To see this, consider a final example in which the condition associated with Granovetter holds, i.e., Pw > Ps , while the condition associated with Lin does not, i.e., Fw(w) = Fs(w) for all w. Assume wage offers are drawn from lognormal distribu- tions with means R = gw = gS = 1 and variances a, = a'w = a's = 1. Further assume M = 6, B =.8, and pw = .2 > Ps = .1 > PF = .05. The worker's reservation and expected wages given several al- ternative assumptions on the size and composi- tion of the worker's network are presented in Table 1.

This example illustrates results already estab- lished: Individuals with large networks and/or a large proportion of weak ties in their networks will set relatively high reservation wages. In this example, such individuals also receive relatively high expected wages. This relationship is consis- tent with the findings of Campbell et al. (1986): Individuals of high socioeconomic status are like- ly to have larger but less tightly knit networks than individuals of low socioeconomic status. But while Et w I is increasing in N and co, Et wIW} is

JOB SEARCH AND NETWORK COMPOSITION 593

Table 1. Reservation Wages, Expected Wages, and Prob- ability of Using Search Method by Network Structure

Network Structure

Wagesand N=3 N=3 N=6 N=6 Probabilities cl)= 1/3 clo= 2/3 co= 1/3 cl)= 2/3

Reservation WR 1.679 1.804 2.125 2.310 wage

Expected E{wI 3.847 4.031 4.513 4.785 wage

Expected wage conditional upon using a Formal E{wIFI 3.858 4.046 4.525 4.800

method

Weak tie E{wIW} 3.830 4.019 4.502 4.779

Strong tie E{wIS} 3.849 4.037 4.517 4.793

Probability offinding job through a Formal Pr(F) .425 .371 .271 .229

method

Weak tie Pr(W) .290 .505 .367 .618

Strong tie Pr(S) .285 .124 .363 .153

approximately equal to Et wIS I for each network structure.14

Assume that the labor force comprises two types of workers: half have small, mostly strong- tie networks (N = 3, co = 1/3) while the other half have large, mostly weak-tie networks (N = 6, co = 2/3). The former group is represented by column 1 in Table 1 and the latter group is represented by column 4. The mean wages for the population can be written

E (wIW} = SPr(W)EIwIWI X Pr(W)

(.290)(3.830) + (.618)(4.779)

.290 + .618

= 4.476;

E I wISI = EPr(S) Et wISI I Pr(S)

- (.285)(3.849) + (.153)(4.793) .285 + .153

= 4.179,

where the summations are taken over worker types. In the absence of controls for network struc-

ture, heterogeneity in the population thus induces EtwIW} > EtwIS}. This result is driven by the differences in the proportions Pr(W) and Pr(S) across worker types: Workers with a large pro- portion of weak ties (and thus high expected wag- es) are much more likely to use weak ties (and less likely to use strong ties).

In this analysis, I have contrasted alternative informal job-finding methods - weak versus strong ties - rather than informal and formal methods. However, given the symmetry of the model with respect to each of the job-finding methods, the analysis is easily generalized. Par- alleling Bridges and Villemez (1986), Corcoran, Datcher, and Duncan (1980) found that the use of a personal contact is not associated with high- er wages and concluded that such contacts are unimportant in labor market success. But if in- formal and formal offers are drawn from the same distribution, no differences should be expected in the average wage across job-finding methods used. Network structure, however, should be cor- related with wages if personal contacts increase the offer arrival rate.

CONCLUSION

Bridges and Villemez (1986) argued that tie strength is not an important dimension of social capital because they failed to find a positive rela- tionship between the use of a weak tie and wages after controlling for worker characteristics. My analysis, based on an economic model of job search, suggests that this conclusion may be pre- mature. Alternative formulations of the strength- of-weak-ties hypothesis suggest that weak ties may be beneficial for two distinct reasons. Granovetter emphasized that weak ties relay use- ful job information more frequently than strong ties, whereas Lin's formulation suggests that weak-tie job offers are drawn from a different (often superior) distribution. Although Lin's for- mulation seems difficult (although not theoreti- cally impossible) to reconcile with the empirical evidence on wages, Granovetter's formulation implies that the use of a weak tie will be nega- tively (although perhaps weakly) related to aver- age wages.

My analysis suggests that researchers should devote more attention to the relationship between network structure and labor-market outcomes. The relationship between wages and the use of a particular job-finding method may be counterin- tuitive: The use of a weak tie could be associated with lower wages even though weak ties relay

14 This result would still hold if the common offer distribution improves as N or co rises as suggested by Lin's (1982) "strength-of-positions proposition."

594 AMERICAN SOCIOLOGICAL REVIEW

offers more frequently than strong ties and weak- tie offers are (on average) superior to offers from other sources. However, the present model pre- dicts an unambiguous relationship between res- ervation wages and network structure: Both Granovetter's and Lin's formulations of the strength-of-weak-ties hypothesis imply that the reservation wage rises as the proportion of weak ties in a job-seeker's network increases.

Economic models of job search seem to offer a useful framework for examination of the rela- tionship between social networks and labor-mar- ket outcomes. By relaxing several of the simpli- fying assumptions adopted in the present analy- sis, researchers could address a variety of other issues raised in the strength-of-weak-ties litera- ture. Extending the model to permit on-the-job search would allow examination of the relation- ship between the type of tie used, prior wage (or prestige), and the current wage (Wegener 199 1).'5 Further, by specifying the costs of searching through alternative channels (as in Holzer 1988), researchers could examine Granovetter's (1974, p. 54) claim that unemployed job-seekers are more likely than employed job seekers to turn to their strong ties.'6 Alternatively, contact status could be incorporated in the model to evaluate Lin's (Lin et al. 1981; Lai et al. 1990) path anal- yses. Finally, following Marsden and Campbell (1990), future research could incorporate both sides of the labor market - employers as well as workers - into the analysis. Once recruitment methods and wage determination are endog- enized, researchers could examine the interaction between social network structure and the income distribution (Mortensen and Vishwanath' 1990; Montgomery 1990, 1991a, 1991b).

JAMES D. MONTGOMERY is Assistant Professor of Eco- nomics and a Faculty Fellow at the Centerfor Urban Affairs and Policy Research at Northwestern Univer- sity. In his research he explores the relationship be- tween social networks and labor-market outcomes, attempting to integrate economic and sociological conceptions of labor markets. Building upon ethno- graphic accounts of urban poverty, he is also working to develop rational-choice models of "underclass" behavior.

Appendix

Network Structure and the Reservation Wage

Integrating by parts, equation 3 may be rewritten as ,00

(1-B)wRH ={ f l-H(w)dwj ' (Al) tWR)

where wWH is the reservation wage corresponding to the H(w) distribution.

Consider an alternative offer distribution, M(w), where 00 00

f I - H(w) dw > | I - M(w) dw for all x, (A2) x x

or stated differently, 00 J H(w) - H(w) dw <0 for all x. (A3) x

Let w Hrepresent the reservation wage for the M(w) distribu- tion so that

(1-awe=~ fJ1 - (w) dwj. (A4)

tR)

I establish wiH > wf Hby contradiction. If wWH < WH, inequal- ity A2 implies that

00 00 00

f 1 -Hw) dw < f 1 H(w) dw < f I-H(w) dw (AS) WR WR WR

Thus, the right-hand side of equation Al exceeds the right- hand side of equation A4. However, under the assumption that w H < WH, the left-hand side of equation A4 must (at least weakly) exceed the left-hand side of equation Al. This contradiction establishes that w H cannot be less than or equal to (i.e., must exceed) wRf.

Suppose that H(w) represents the offer distribution given network size NH and f(w) represents the distribution given network size NL where NH > NL. From equation 9,

H(w) - Hf(w) = H(w) [['14W (W)I)(NH -NL)

[(T>S (W)](l-())(NHNL) _- I] (A6)

Because the bracketed expression is negative for all w, inequality A3 holds. Holding network composition con- stant, the reservation wage is thus increasing in network size.

Now let M(w) represent the highest-offer distribution when the worker has 0N weak ties and (1 - o)N strong ties; H(w) represents this distribution when the worker has one additional weak tie (and thus one less strong tie). Equation 9 implies

H(w) - M(w) = [(Dw (w) - (Ds (w)] H(w) (A7) (Ds (w)

Because H(w)/'Ds(w) is always positive, H(w) - M(w) is negative (and thus WR is increasing in w) if the bracketed expression - which is rewritten as ps[l - Fs(w)] - Pw[l- Fw(w)] in equation 5 - is negative. Holding network size constant, the condition expressed by equation 5 implies that the reservation wage increases as the proportion of weak ties increases.

15 Note that a job-seeker's current position may also influence network structure, offer distributions, and offer probabilities.

16 The increased use of strong ties may be related to liquidity constraints faced by unemployed job seek- ers, which imply that the reservation wage is falling over time (Mortensen 1986, pp. 859-61).

JOB SEARCH AND NETWORK COMPOSITION 595

Now assume the condition expressed by equation 8 holds and let Pw = ps = p. From inequality A3 and equation A7, WR is increasing in 0) if

00 J p [Fw (w) - Fs (w)] ['tF (W)]M [I (W)]WN x

[(DS (W)](' - co)N-I dW < 0 for all x. (A8)

Because the last three terms in the integrand are positive and increasing in w, and because the condition expressed in equation 8 implies [Fw (w) - Fs (w)] < 0 if and only if x > w, the left-hand side of inequality A8 is less than

P [DF (0)] [DW (0)]()N [(DS (0)](I - o))N- I

00 J [Fw (w) - Fs (w)] dw. (A9) x

Because the condition expressed by equation 8 implies that 00

f [Fw (w) - Fs (w)] dw = 0, 0

0o

J [Fw (w) - Fs (w)] dw < O for all x 2 w, x

and x

J [Fw (W) - Fs (w)] dw > O for all x < w, 0

the integral in expression A9 is negative for all x. Since all other terms in expression A9 are positive, inequality A8 is satisfied: the condition expressed by equation 8 implies that WR is increasing in (0.

OfferProbabilities, OfferDistributions, and Expected Wages Suppose that the expected wage functions could be written as

Etw1WI = w x(w) ,(w) dw/ 7x(w) t(w) dw, (AIO) WR WR

and 00 00

EIw1SI = ,fw ,(w) dw/ Jf(w) dw, (All) WR WR

where t(w) ? 0 for all w and x(w) is continuous and mono- tonic. Note that E{wlWI = E{wISI if x(w) is simply a con- stant. To show that E I wIWI is greater (less) than E I wIS I if x(w) is increasing (decreasing) in w, define wv such that

00 00

x(wv) ,f (w) dw = ,fx(w) 4(w) dw. (A12) WR WR

Given the conditions on x(w) and 4(w), a unique w E (WR ,??)

always exists. Multiply both the numerator and denomina- tor of equation A 1 by x(w). Subtracting this from equation AlO yields the condition

ElwiWI >Ejw1SI if and only if 00

f w [x(w) _ x(wA)] 4(w) dw > 0. (A13)

WR

Further, given the conditions on x(w) and 4(w),

00

fw [x(w) - x(w)] ,(w) dw WR

0o

> w|[x(w) - x(w)] ,(w) dw = O if dx(w) / dw > O WR

0o

<w J[x(w) - x(w2)] ,(w) dw = 0 if dx(w) / dw < 0. WR (A14)

Assume that the condition expressed by equation 6 holds and let Fw(w) = Fs(w) = F(w) with density f(w) for all w. The expected wages are thus given by equations AlO and Al l where

x(w) = (Ds (w)A1Dw (w)

= [1 - ps[l - F(w)]]/[l - pw[l - F(w)]], and

t(x) = flw) ['Dr (W)]M [(w (w)]

[(Ds (w)10 -1))N-I dw. (A15)

Because dx(w)/dw =f(w)(ps - pw)/Vtw(w)]2 < 0, equation 6 implies E(wISI > E(wIWI.

Now consider the conditions expressed by equations 7 and 8 which imply Pw = Ps = p but Fw(w) ? FS(w). The expected wages are again given by equations A10 and A 1I where

fw (w) (Ds (w) aln(Dw (w))Iaw x(w) ==

X()-(w (w) fs (w) Dln((Ds (w)O/w

and

t(W) =JS(W) PDF (W)] PDW (W)] [(DS (W)]l @)N-I dw.

(A16)

Thus, dx(w)/dw > 0 is a (sufficient) condition guaranteeing EIwIWI > EI wISI. A related condition - log concavity of the offer distribution - arises frequently in the job-search literature (Burdett 1981; see also the discussion of log con- cavity in Heckman and Honor6 1990). However, numerical examples (not reported here) using the normal and lognor- mal distributions with gw 2 gs and aw 2 as generate E I w1WI > El wIS I even though x(w) is sometimes not monotonically increasing. This suggests that a weaker (sufficient) condi- tion on the offer distributions may be found.

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