Job Contact Networks JET Antoni Calvó-Armengol

Transcription

1 Job Contact Networks JET 2004 Antoni Calvó-Armengol

2 About half of jobs are filled through contacts networks of personal contacts and word-of-mouth communication play a central role in many labor markets

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5 Aim of this paper relate social embeddedness to information gathering, job-finding and aggregate labor market outcomes What does he do? model job contact networks as graphs model communication on the network

6 What does he get? word-of-mouth information gathering exhibits decreasing marginal returns to network size (endogenous) unemployment is inefficient: unemployment premium due to over-socializing robustness to communication protocols

7 Related literature Granovetter (1974) Getting a Job Boorman (1975) Bell Journal Diamond (1981) JPE Jackson and Wolinsky (1996) JET

8 Search with wage posting Montgomery (1991) AER Mortensen and Vishwanath (1994) LE Kugler (1997) Working Paper UPF Calvo-Armengol Jackson AER 2004 (Dynamics)

9 Plan of the lecture network of personal contacts and word-of-mouth communication... a starting point for (a) job matching (b) employment dynamics (c) social structure labor outcomes endogenous networks aggregate unemployment

10 The job contact network N = {1,...,n}: finite set of players g: two-sided graph on N ij g: a link N i (g): playeri s direct neighborhood n i (g): itssize

11 j i g

12 The communication protocol b: breakup probability a: arrival probability an unemployed worker hearing directly of a vacancy fills this job immediately an employed hearing directly of a vacancy transmits it to any of his unemployed friends (generalization: employed-to-employed relays)

13 Word-of-mouth communication and job-finding Given a network g, any player i gets a job through social contacts with probability P i (g) =1 Y j N i (g) 1 a (1 b) 1 (1 b)n j(g) bn j (g) I direct contacts exacerbate information gathering while indirect contacts constrain it I P i (g) decreases with b and increases with a

14 Explain this probability P i (g) Fix an unemployed worker i and consider some other worker j in direct contact with i. Worker j is employed and aware of a redundant job offer with probability a(1 b).

15 Worker i is the selected recipient for this information with probability: n j (g) 1 X k=0 ³ n j (g) 1 k = 1 (1 b)n j(g) bn j (g) 1 k +1 (1 b)n j(g) k 1 b k Indeed, a random draw of n j (g) social contacts by worker j contains 0 k n j (g) 1 additional unemployed workers, besides i, with probability ³ nj (g) 1 (1 k b) n j (g) k 1 b k The job information vacancy held by j is then assigned to any of these k +1unemployed with uniform probability, and worker i receives such information with conditional probability 1/ (k +1).

16 This implies that a(1 b) 1 (1 b)n j(g) bn j (g) is the probability that a worker j is informed about a job (probability v), does not need it (probability (1 u)) and transmits this information to worker i. Thus proba that i does not get a job from j is 1 a(1 b) 1 (1 b)n j(g) bn j (g)

17 Remark: P i (g) increases with N i (g) and decreases with n j (g), j N i (g). Direct contacts are beneficial whereas two-links-away contacts are detrimental.

18 The network microstructure matters g g 2 P 1 (g) >P 1 ³ g 0 P 3 (g) <P 3 ³ g 0 P 4 (g) >P 4 ³ g 0

19 Aggregate unemployment U(g) =b (1 a) 1 1 n where n is the number of workers. X i N P i (g)

20 Symmetric networks of size s P (s) = 1 = 1 [q(s)] s "1 a (1 b) 1 (1 b)s sb # s q(s) =1 a (1 b) 1 (1 b)s sb : proba that i does not find a job from j 1 q(s): proba that i find a job thanks to j positive impact: at least one neighbor is informed with probability 1 (1 a) s 1

21 negative impact: I am the recipient of this information with probability 1 (1 b) s bs 0

22 P(s) P max P min s 1 (congestion threshold value) s

23 When the network size s increases, on average, the unemployed workers hear about more vacancies through their social network but, at the same time, it is more likely that multiple vacancies reach the same unemployed worker. Critical network size s above which the second effect dominates the first one. In sparse networks, more connections alleviate coordination failures by allowing a better partial replacement or job matches. In dense networks, though, more connections harm the matching process and slow down information exchange.

24 Positive (access) and negative (sharing) effect of acquaintance size in symmetric networks I networking (passive search) exhibits decreasing marginal returns to network size I information transmission slowed down in dense network: congestion constraints overwhelm opportunities in dense networks " [1 (1 a) s 1 (1 b) s # ] 0 {z } bs opportunities {z } constraints

25 Aggregate unemployment I the aggregate unemployment rate in a symmetric network of size s is U (s) =b (1 a)[1 P (s)]

26 u(s) u max u min 1 (congestion threshold value) s

27 I job-finding through word-of-mouth communication increases when restrictions eliminated I neighbor value results from a trade-off between information sharing (constraint) and information gathering (opportunity) I congestion persists in dense networks I... but local network topology now matters!

28 These results: a building-block I for micro-founded matching function B Job Matching, Social Network and Word-of-Mouth Communication, Calvo and Zenou (JUE 2004) I for employment dynamics: duration dependence, acquaintance dependence, persistence, social clustering, de-socialization B Labor Networks and Duration Dependence, Calvo and Jackson (AER 2004)

29 I for impact (endogenous) social structure on job-finding and labor market outcomes B now!

30 The individual payoffs c: cost of a direct link ij to both i and j w: exogenous wage w =1 expected net payoff for player i u i (g) = (1 b) {z } i keeps job = 1 β cn i (g) cn i (g) Y j N i (g) + b {z} a +(1 a) P i (g) {z } market {z contact } i fired and reemployed 1 a (1 b) 1 (1 b)n j(g) bn j (g)

31 0 P i (g) 1 Negative externalities Symmetric networks of size s u(s) = (1 b) {z } i keeps job + b {z} a +(1 a) {1 [q(s)] s {z } market {z contact } i fired and reemployed u(s) =1 β [q(s)] s β = b(1 a) means that i has lost his job and did not find another through the market q(s) proba for i do not to find a job from j

32 Endogenous network formation: the equilibrium concept pairwise Nash equilibrium: Pairwise stability (Jackson and Wolinsky, 1996) + Nash equilibrium (Myerson 1991). Definition 1 A network g is a pairwise-nash equilibrium if and only if there exists a Nash equilibrium strategy profile s that supports g, thatisg = g(s ), and, for all i N and all ij / g,if u i (g) <u i (g + ij) then u j (g) >u j (g + ij). In words, g is a pairwise-nash equilibrium network if no player gains by altering the current configuration of links, neither by adding a new link nor by eliminating any subset of the existing links.

33 Remark: This model is 1 convex in own current links on g. Thus (Calvo and Ilkilic 2006) PS(u) =PNE(u) Thus only check one-link deviation (in deleting)

34 Denote α = a (1 b) and β = b (1 a). Proposition 1: If c>αβ, the empty graph is the only PNE network. α = a (1 b) means that j the direct contact of i is employed and is aware of a job opportunity β = b(1 a) means that i has lost his job and did not find another through the market Equilibrium networks are non-empty if the net value of a first link αβ c is non-negative.

35 Proposition 2: If c αβ, anetworkg G, g 6=, is a PNE network iff both: min {P i(g) P i (g ij)} c/β (1) ij g and ij / g hold. P i (g + ij) P i (g) >c/β (2) P j (g + ij) P i (g) <c/β Proof. u i (g) u i (g ij) =β [P i (g) P i (g ij)] Condition (1): individual rationality constraint. Any existing link is necessarily worth its cost for the two involved players. Condition (2): reflects lack of mutual consent between any two players not directly linked at equilibrium.

36 Symmetric network of size s c max (s) =βq(s) s 1 [1 q(s)] is the current individual per-link reward and c min (s) =βq(s) s [1 q(s +1)] is the individual marginal benefit from an extra link.

37 Proposition 3: For all n 2 s 1, the graph g(s) is a PNE network iff c min c c max (s) Furthermore, g (n 1) = g N is a PNE iff c c max (n 1)

38 Asymmetric networks Definition 2 We say that ij g is a loose-end if either n i (g) =1or n j (g) =1. Notation m (a, b) =argmax{m N 1 q(m) >q(m)[1 q(2)]} 1 q(m): Given that everybody has m links, this is the proba that i finds a job from j q(m): Given that everybody has m links,thisistheproba that i does not to find a job from j 1 q(2): Given that everybody has 2 links, this is the proba that i finds a job from j

39 Proposition 4: Let j arg max {n k (g) k N}. If ij g is a loose-end and n j (g) >n k (g) for some k N j (g), k 6= i, thenm (a, b) n j (g). Show that if j is willing to invest in at least m +1 connections then any loose-end appended to j and any of j 0 s direct connections mutually consent to link each other. Prop 4 implies that stars encompassing m m +1 players are ruled out in equilibrium.

40 Example Suppose a = b =1/2 thus α = β =1/4. Then 1 (1 b)m q(m) = 1 α bm = m 2m m (a, b) =argmax{m N 1 q(m) >q(m)[1 q(2)]} =argmax ( " m N m 2m > # m 2m ) 3 16 =argmax n m N m m m+1 < 19 6 =3.167o

41 Thus m ( 1 2, 1 2 )=2 Indeed, for m = = < 19 6 =3.167 while for m = = < 19 6 =3.167 Not true

42 Asymmetric networks u i (g) = 1 β = Y j N i (g) Y j N i (g) 1 α 1 (1 b)n j(g) bn j (g) n j (g) n j (g)

43 g I g II g III g IV g V g VI

44 By Proposition 4: networks g II and g VI are not PNE Let us show that g IV is not an equilibrium If g IV PNE, then player 1 does not gain by cutting link 13. u 1 (12, 13, 14) = µ µ µ = u 1 (12, 14) = = 1 1 µ µ

45 Thus when player 1 does not gain by cutting 13 iff c < u 1 (12, 13, 14) u 1 (12, 14) µ c< If g IV PNE then player 2 does not gain from creating link 24. Trueiff c > u 2 (21, 23, 24) u 2 (21, 23) c> µ µ µ c> These two conditions are not compatible since = 1 4 µ > 1 4 µ =0.024

46 Same thing to show that g V is not an equilibrium Observe that if i is linked to someone who has no links at all, then: P i (g) = 1 [1 a (1 b)] = a (1 b) =α =1/4 u i (g) = (1 b)+b [a +(1 a) P i (g)] = while someone who is alone has u i (0) = (1 b)+ba = 3 4 Only equilibrium networks: g I and g III

47 Suppose a =1/2 and b =1/4. Only equilibrium networks: g I, g II and g III

48 General communication with employed-to-employed relays Restriction: Informationgoestoanemployedcontactonlywhenno direct contacts are unemployed. I with just one relay: Information is lost during relays with probability 0 1 δ 1.

49 P (1) i =1 Y j N i " 1 a (1) ij (1 b) 1 (1 b)n j bn j # where a (1) ij = a+δ (1 a) 1 Y k N j d ik =2 Ã 1 a (1 b)n k n k! d ik : geodesic distance I with more relays: recursively