Network Search: Climbing the Ladder Faster

Transcription

1 Network Search: Climbing the Ladder Faster Marcelo Arbex Dennis O Dea David Wiczer University of Windsor University of Washington Fed Reserve Bank of St. Louis. October 3, 2016 The views expressed herein do not reflect those of the Federal Reserve Bank of St. Louis or the Federal Reserve System Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

2 Motivation Motivation Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

3 Motivation Networks are important in labor market search Two well-established facts 1. Significant fraction of workers search using contacts NLSY: >85% use informal contacts when searching (Holzer, 1988) PSID: > 50% found their job through social network (Corcoran, Datcher and Duncan, 1980). 2. Firms use referrals when filling a vacancy. 37% - 53% use the social networks of their current employees to advertise jobs (Mardsen, 2001). EOPP: 36% of firms filled their last vacancy through a referral (Holzer, 1987). Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

4 Networks are irregular Motivation People differ in the number of links they have Implies heterogeneity in finding both on and off the job Implies heterogeneity in the quality of offers drawn Different people climb the ladder differently Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

5 Motivation This paper will systematize the implications Heterogeneity in network position has implications for differences in: The dynamics of matched wages (wage ladder) The duration and persistence of (un)employment (finding rate) Both of these are analytical results and empirical findings Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

6 Motivation What we do Describe a rich (though not arbitrary) network structure Apply the mean-field approach to make this tractable Put this irregular network into a model of on/off-the-job search Calibrate and compare vis-à-vis common empirical findings New evidence from SCE Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

7 Motivation Key results Jobs found through network search: Have higher wages on acquisition (Marmaros & Sacerdote, 2002) Occur after a shorter unemployment spell (Goel & Lang, 2009) Longer match duration (Dustmann et al 2014) More likely higher on the ladder (Us 2016) Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

8 Motivation Key results Jobs found through network search: Have higher wages on acquisition (Marmaros & Sacerdote, 2002) Occur after a shorter unemployment spell (Goel & Lang, 2009) Longer match duration (Dustmann et al 2014) More likely higher on the ladder (Us 2016) We reduce an 2 + -dimensional state to 3 Analytical results: Network search draws from a better (FOSD) distribution than direct search Better connected workers have higher wages Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

9 Motivation Basic environment On-the-job search (as in Burdett and Mortensen 1998) Workers are endowed with peers exogenously. Jobs offers passed from peers: new positions just like own (referral). Channels of job information: direct search and social networks. Easily extensible to other search environments Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

10 Motivation Before getting into the weeds The mechanism is thus: Workers with more connections sample jobs more quickly They climb the ladder faster Referrals are useful for 2 reasons: 1 Draw from the wage distribution rather than direct offer distribution 2 Draw from friends who are better connected (paradox of friendship) Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

11 Motivation Before getting into the weeds The mechanism is thus: Workers with more connections sample jobs more quickly They climb the ladder faster Referrals are useful for 2 reasons: 1 Draw from the wage distribution rather than direct offer distribution 2 Draw from friends who are better connected (paradox of friendship) Network search is done by better connected workers: Jobs through the network are higher paid Jobs through the network last longer Jobs through the network follow shorter unemployment Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

12 Motivation Literature Network theory: Vega-Redondo (2007), Calvo-Aremengol & Jackson (2007), Calvo-Aremengol & Jackson (2004) Empirical contributions: Cornelissen, Dustmann & Schoenberg (2015), Hellerstein, Kutzbach, Neumark (2014), Holzer (1988) Search and networks: Galenianos (2014), Fontaine (2008), Ioannides & Soetevent (2006), Mortensen & Vishwanath (1995) Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

13 Model Model of search and networks in labor markets Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

14 Model Technology, flows and types Technologies: Workers heterogeneous in number of peers, z Workers homogeneous in non-employment flow value, b Firms are homogeneous, with productivity p Labor is aggregated linearly Flows: Random search, matched via either direct or network search Jobs break up exogenously at rate δ Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

15 Model Networks The network is fixed and exogenous Connected in a large, random network: degree distribution Ω(z), z [1, ). * Ω(z) is the fraction of agents who have z peers. We assume a power-law distribution Ω(z) = (α 1)z α Power-law distributions: "fat tails"; small-worlds properties of empirical social networks (Calvó-Armengol and Jackson, 2004; Vega-Redondo, 2008). Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

16 Model Vanilla direct search Firms post wages w, distributed as F (w), firm offer distribution A worker learns of job vacancy at rate γ i γ 0 > γ 1 : search is more effective when unemployed. If a job arrives, worker exits unemployment if w R( ) An employed worker will accept the job if it is above her current wage Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

17 Model Networks search Worker sample jobs via their network connections Connections pass jobs with the same wage as theirs (from their firm) Searchers accept if offer is above current wage w/reservation wage R( ). Workers may consider only one job each period Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

18 Model What is a worker type? Define χ recursively: Each worker has z peers χ is z 3. Element c is a triple i(c), the labor status w(c), the wage χ(c), the position in the network χ(c) is also a s 3 dimensional object, s.t. s is the number of peers of peer c To forecast the value of a peer: His wage that might be passed His potential wage next period Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

19 Model The mean-field approach Goal: Remove local information from the state Rather than the neighboring atom affecting another, how does the average atom affect it Will take the position in network from χ to z Requires: 1 Incomplete information about peers 2 A locally tree-like structure Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

20 Model We didn t make this up Vega-Redondo (2007) uses this approach so that The average state of the network is replicated locally: No neighborhood effects (Vega-Redondo 2007). Good representation of the long-run dynamics of networks (Vega-Redondo 2007, Jackson 2008). This or similar idea used in search papers: Calvo-Armengol & Zenou (2005) or Bramoulle & Saint Paul (2010) Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

21 Model Assumption 1: Incomplete information Assumption: Agents do not know the state (i(c), w(c), χ(c)) of peer c Agents know c exists and can use degree distribution, Ω and peer distribution is Ψ( (i, w, z)) The effect: I update beliefs (î(c), ŵ(c), ˆχ(c)) c Information for beliefs is my own state Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

22 Model Assumption 2: Tree structure Assumption: The network is described by the degree distribution Ω As nodes n, probability of a cluster 0 The effect: For any χ and χ if z = z then χ = χ in expectation (i, w, z) has no information for (î(c), ŵ(c), ŝ(c)) Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

23 Model Summary of assumptions We construct the large, complex network Hold fixed the degree distribution Ω In each period draw links by the Chang-Lu procedure The number of agents Result: z is a sufficient statistic for network position Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

24 Model Networks we rule out A clustered subgraph where z = 4 The clustered network has local structure The regular network is uninteresting A regular subgraph where z = 4 Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

25 Model Our network structure: A tree No local neighborhood, but number of connections differs Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

26 Model Paradox of friendship Ψ(s): probability a worker s peer has s peers herself Ψ(s) = sω(s) z Ψ(s) < Ω(s) is the paradox of friendship Mean-field integrate over Ψ to infer about connections Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

27 Model Netowrk offer distribution/earnings distribution The earnings distribution among agents of type z G(w, z) Earnings distribution in the population: G(w) = G(w, z)ω(z)dz Earnings distribution of peers: G(w) = z s G(w, s)ψ(s)ds Offers through the network are drawn from G(w) Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

28 Model Network search arrival rate The probability a worker of type z, in state i, receives an offer via a peer is ( [ ] z ) ρ i (z) = 1 1 Ψ(s)n(s)γ 1 νi s s ds ( = 1 [1 γ1 ν i n ] z ) s n(s)γ 1 is the probability this peer is employed and hears of an vacancy at her firm ν i /s is the probability this information is passed along n : employment rate in the economy Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

29 Model Workers value functions Model of search and networks in labor markets: Workers value functions Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

30 Model Workers value functions Unemployed Worker s Value Function The value function of an unemployed worker of type z is rv 0 (z) = { w [ ] } b + γ 0 V 1 (z, x) V 0 (z) df (x) R(z) }{{} The value of direct search w [( )] + (1 γ 0 )ρ 0 (z) V 1 (z, x) V 0 (z) d G(x) } R(z) {{ } The value of network search The value of an unemployed worker with z peers is the unemployment benefit, the expected value of hearing about a job directly, plus the expected value of hearing about a job from a peer. Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

31 Model Workers value functions Employed Worker s Value Function The value of an employed worker with z connections and wage w is rv 1 (z, w) = [ ] { w [ ] } w + δ V 0 (z) V 1 (z, w) + γ 1 V 1 (z, x) V 1 (z, w) df (x) w }{{} The value of direct search w [( )] + (1 γ 1 )ρ 1 (z) V 1 (z, x) V 1 (z, w) d G(x) } R(z) {{ } The value of network search Expected lifetime income of a worker currently employed, with z peers in his network, is his wage w plus the expected value of becoming unemployed plus the expected value of hearing of a better job either directly from firms or through his social network. Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

32 Model Workers value functions Reservation Wage At the reservation wage R(z), we have that V 1 (z, R(z)) = V 0 (z). R(z) b = (γ 0 γ 1) { w [ ] } V 1 (z, w) V 0 (z) df (w) R(z) [ (1 γ + 0 )ρ 0 ] { (z) w [ ( )] } (1 γ 1 )ρ 1 θ(w) V 1 (z, w) V 0 (z) dw (z) R(z) = (γ 0 γ 1) { w + R(z) [ (1 γ 0 )ρ 0 (z) (1 γ 1 )ρ 1 (z) } V 1 (z, w) [1 F (w)] dw ] { w } V 1 (z, w)(1 G(w))dw R(z) (1) Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

33 Model Workers value functions Wage Distribution and Workers per Firm l(w, z): Labor force of type z per firm at a firm paying wage w L(w): Total labor input per firm paying wage w: L(w) = 1 l(w, z)ω(z)dz (2) Each employer offers a wage that maximizes its steady state profit: π(w) = (p w)l(w) (3) For different L(w) and w Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

34 The steady state equilibrium The steady state equilibrium Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

35 The steady state equilibrium The steady state equilibrium Definition A Sufficient Recursive Equilibrium: V 0, V 1, R, π and F (w), G(w, z), n(w), such that, given F: V 0, V 1, R solve household problem G, n consistent with worker flows F implies π(w) = π w Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

36 The steady state equilibrium Steady State Flow of Workers Flows in and out of unemployment must balance, give the steady state employment rate: n (z) = Recruiting from direct search Recruiting from network search {}}{{}}{ γ 0 [1 F (R(z))] + (1 γ 0 )ρ 0 (z) [ 1 G (R(z)) ] δ + γ 0 [1 F (R(z))] + (1 γ 0 )ρ 0 (z) [ 1 G ], (4) (R(z)) The economy s employment rate is given by n = 1 n (z)ω(z)dz (5) Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

37 The steady state equilibrium Steady State Flow of Workers In the steady state, the flow of workers of type z leaving this firm must equal the flow of workers of type z entering this firm: where β(w, z) = δ + γ 1 (1 F (w)) }{{} Loss to poaching via direct search l(w, z)β(w, z) = h(w, z) (6) + (1 γ 1 )ρ 1 (z) [ 1 G(w) ] }{{} Loss to poaching via network search Hired via direct search h(w, z) = Ω(z) {{}} }{ [1 n(z)] γ 0 I M R(z) w + n(z)γ 1 G(w, z) + { } l(w, t)tψ(z) [1 n(z)] ν 0 I R(z) w + n(z)ν 1 G(w, z) dt t=1 }{{} Hired via network search Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

38 The steady state equilibrium Equilibrium measure of workers A firm offering wage w will attract workers of many different types. The firm s total labor force is given by L(w) = z=1 h(w, z) β(w, z) dz Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

39 Results from the calibrated economy Results from the calibrated economy Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

40 Parameter values Results from the calibrated economy Parameter Value Moment γ Matching rate out of unemployment, 40% γ Matching rate from employment, 2.2% ν Fraction of hires through the network, 36% δ 0.03 Unemployment rate, 6% b 0 Normalization p 1 Normalization α 3.0 Must be Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

41 Results from the calibrated economy Average offer distribution by type Cumulative distribution Direct Contact Average for low z Average for high z Network Wage quantile Figure: Average distribution of wage offers by contact method conditional on number of peers. Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

42 Results from the calibrated economy Finding rates by type Off the job On the job -4 Log arrival rate z Figure: Offer arrival rate through the network Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

43 Results from the calibrated economy Average matched and steady-state wages Wage quantile Average Wage Average Wage Out of Unemployment z Figure: Average wage on initial offer and in steady state employment Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

44 Results from the calibrated economy The half-life by connections Offer = 68 pctile Offer = 52 pctile Offer = 6 pctile Half-life (months) to maximum wage z Figure: Half-life of wage growth paths to maximum wage: different starting wages and different network connections z. Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

45 Results from the calibrated economy The effect is not just heterogeneous search We let arrival rates differ by z, but not the offer distribution Half-life (months) to maximum wage Offer = 68 pctile, with network Offer = 6 pctile, with network Offer = 68 pctile, heterogenous rates Offer = 6 pctile, heterogenous rates z Figure: Half-life of wage growth comparing heterogeneous search rates and network search model Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

46 Results from the calibrated economy Relationship to empirical findings Results from the calibrated economy: Relationship to empirical findings Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

47 Results from the calibrated economy Relationship to empirical findings Different types find jobs through a network On average, a worker who finds job through a network has more connections z (1 n(z)) ρ 0 (z) ( 1 G(R(z)) ) dω(z) (1 n(z)) ρ0 (z) ( 1 G(R(z)) ) dω(z) > z (1 n(z)) γ 0 (1 F (R(z))) dω(z) (1 n(z)) γ0 (1 F (R(z))) dω(z) This will drive many empirical findings about the value of network search Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

48 Results from the calibrated economy Relationship to empirical findings The different distributions of workers Log density of number of peers Direct contact Network search z Figure: Distribution of number of peers: Direct search and network search. Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

49 Results from the calibrated economy Relationship to empirical findings Summarizing the effects Network Direct Pctile Initial Wage 48.48% 24.50% Duration of Job Match 7.91 years 3.72 years Relative z from Unemp Relative Search Time Table: Expected differences between workers finding jobs through network or directed search. Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

50 Results from the calibrated economy Relationship to empirical findings SCE: Higher wage workers use networks more Model prediction: higher-wage workers find jobs through networks Probability Wage quantile Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

51 Results from the calibrated economy Relationship to empirical findings SCE: Higher wage workers use networks more Model prediction: higher-wage workers find jobs through networks Residual Probability Percentile Weekly Salary in Prior Job Except for the SCE, little data on job search by the employed Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

52 Results from the calibrated economy Relationship to empirical findings SCE: setup and inference Employed workers describe how they found prior job: (1) (2) (3) (4) Log weekly salary <500 employees Voluntary Job-to-Job Part-time Firm Size Dummies X X X Industry Dummies X X X X Observations Probability of network-find by current wage Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

53 Results from the calibrated economy Relationship to empirical findings SCE: setup and inference Employed workers describe how they found prior job: (1) (2) (3) Log prior employer weekly salary <500 employees Voluntary Job-to-Job Part-time Firm Size Dummies X X Industry Dummies X X X Observations p < 0.10, p < 0.05, p < 0.01 Probability of network-find by last wage Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

54 Conclusion Conclusion Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51

55 Conclusion Conclusions We presented a model of network search The mean-field approach allows for tractable, irregular networks Highly extensible to other search frameworks Empirical findings on search consistent with type heterogeneity Arbex, O Dea, Wiczer (FRB StL) Network Search: Climbing the Ladder Faster October 3, / 51