Introduction Static Dynamic Welfare Extensions The End. Recruiting Talent. Simon Board Moritz Meyer-ter-Vehn Tomasz Sadzik UCLA.

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1 Recruiting Talent Simon Board Moritz Meyer-ter-Vehn Tomasz Sadzik UCLA July 13, 2016

2 Motivation Talent is source of competitive advantage Universities: Faculty are key asset. Netflix: We endeavor to have only outstanding employees. Empirics: Managers (Bertrand-Schoar), workers (Lazear). Talent perpetuates via hiring Uni: Faculty responsible for recruiting juniors and successors. N: Building a great team is manager s most important task. Empirics: Stars help recruit future talent (Waldinger) Key questions Can talent dispersion persist/avoid regression to mediocrity? Why don t bad firms just compete advantage away?

3 Overview Three ingredients for persistence High wages attract talented applicants Skilled management screens wheat from chaff. Today s recruits become tomorrow s managers. Static Model When talent is scarce, matching is positive assortative. Efficient matching is negative assortative. Dynamic model Persistent dispersion of talent, productivity and wages. Regression to mediocrity offset by PAM. Gradual adjustment to steady state.

4 Matching in labor markets Literature Becker (1973), Lucas (1978), Garicano (2000), Levin & Tadelis (2005), Anderson & Smith (2010). Adverse selection Greenwald (1986), Lockwood (1991), Chakraborty et al (2010), Lauermann & Wolitzky (2015), Kurlat (2016). Wage & productivity dispersion Albrecht & Vroman (1992), Burdett & Mortensen (1998). Firm dynamics Prescott & Lucas (1971), Jovanovic (1982), Hopenhayn (1992), Hopenhayn & Rogerson (1993), Board & MtV (2014).

5 Static Model

6 Baseline Model Gameform Unit mass of firms r F [r, r] post wages w(r). Unit mass of workers apply from top to bottom wage. Proportion q talented, 1 q untalented. Firms sequentially screen applicants, hire one each. Proportion r skilled recruiters θ = H; 1 r unskilled θ = L. Screening Talented workers pass test. Untalented screened out with iid prob. p θ ; 0 < p L < p H < 1. Quality when recruiter θ hires from applicant pool q λ(q; θ) = q/(1 (1 q)p θ ) Quality at firm r: λ(q; r) = rλ(q; H) + (1 r)λ(q; L) Profits π := µλ(q(w); r) w k.

7 Preliminary Analysis Applicant Pool Quality Top wage: Proportion q(1) = q talented workers. Wage rank x: Applicant pool quality q(x) obeys q (x) = λ(q(x); r(x)) q(x) x Quality q(x): { strictly increases in x positive for x > 0, but q(0) = 0. Wage posting equilibrium Equilibrium wage distribution {w(r)} r has no atoms or gaps.

8 Firm-Applicant Matching Wage profile {w(r)} r induces firm-applicant matching Q(r) = q(x(w(r)))

9 Equilibrium Matching - Necessary Condition Incentive Compatibility in Equilibrium {w(r)} r Firms r, r do not mimic each other: µλ(q(r); r) w(r) µλ(q( r); r) w( r) µλ(q( r); r) w( r) µλ(q(r); r) w(r) Hence, λ(q( r); r) supermodular in ( r, r). Return to Recruiter Quality (q) := λ(q; H) λ(q; L) = λ(q; r) r IC: (Q(r)) rises in r. ( ) is single-peaked, with maximum ˆq (0, 1). λ(q; r) is super-modular for q < ˆq; sub-modular for q > ˆq.

10 Scarce Talent Positive Assortative Matching Theorem 1. If q ˆq, there is a unique equilibrium. It exhibits PAM. Proof (q) increases for q q, and (Q(r)) must increase. Hence, Q(r) must increase. Equilibrium described by Profits Wages π(r) = µ r r (Q( r))d r. r w(r) = µ λ (Q( r); r)q ( r)d r. r

11 PAM: Example Worker Quality Recruits, λ(x) Payoffs Wages, w(x) Applicants, q(x) 0.05 Profit, π(x) Firm rank, x Firm rank, x Assumptions: p H = 0.8, p L = 0.2, r U[0, 1], q = 0.25, µ = 1.

12 Comparative Statics Screening Skills r= Wages 0.3 r=0.5 r~u[0,1] Firm rank, x Assumptions: p H = 0.8, p L = 0.2, q = 0.25, µ = 1.

13 Comparative Statics Technological Change µ H,q L Wages 0.4 Payoffs 0.3 µ L,q H 0.2 µ L,q H 0.1 µ H,q L Profits Firm rank, x q H =.25, µ L = 1 q L =.05, µ H = 5.

14 Abundant Talent Theorem 2. Assume q > ˆq. There is a unique equilibrium. It has PAM on [q, ˆq] and NAM on [ˆq, q]. Proof Key fact: (Q(r)) increases in r. Top firm r matches with ˆq. Below, r matches with Q P (r) < ˆq < Q N (r) s.t. (Q P (r)) = (Q N (r)) and Q P, Q N obey the usual differential equations.

15 PAM-NAM: Example λ P (x) w N (x) 0.5 Q N (x) λ N (x) 0.5 Worker Quality Payoffs w P (x) 0.2 Q P (x) 0.2 π(x) Firm rank, x Firm rank, x Assumptions: p H = 0.8, p L = 0.2, r U[0, 1], q = 0.5.

16 Dynamic Model

17 Model Basics Continuous time t, discount rate ρ. Workers enter and retire at flow rate α. Talented workers become skilled recruiters. Assume talent is scarce, q < ˆq. Firm s problem Firm s product µr t ; initially, r 0 exogenous. Attract applicants q t with wage w t (q t ) to manage talent r t ṙ t = α(λ(q t ; r t ) r t ). Firm value V t (r).

18 Firm s Problem The firm solves V 0 (r 0 ) = max {q t} Bellman equation 0 e ρt (µr t αw t (q t ))dt, s.t. ṙ t = α(λ(q t ; r t ) r t ). ρv t (r) = max{µr αw t (q) + αv q t (r)[λ(q; r) r] + V t (r)}. First order condition λ (q; r)v t (r) = w t(q).

19 Positive Assortative Matching Theorem 3. Equilibrium exists and is unique. Firms with more talent post higher wages. The distribution of talent has no atoms at t > 0. Idea The value function V t (r) is convex. FOC implies matching is PAM. FOC also implies atoms immediately dissolve. Thus Time-invariant firm-rank x, s.t. r t (x), q t (x) increase in x.

20 Constructing the Equilibrium Equilibrium Matching r t (x), q t (x) Talent evolution ṙ t (x) = α(λ(q t (x); r t (x)) r t (x)) Sequential Screening q t(x) = (λ(q t (x); r t (x)) q t (x))/x Equilibrium Wages where q = q t (x), r = r t (x) and V t (r t ) = r t w t(q) = V t (r)λ (q; r) t e ρ(s t) [µr s αw s (q s)]ds

21 Constructing the Equilibrium Equilibrium Matching r t (x), q t (x) Talent evolution ṙ t (x) = α(λ(q t (x); r t (x)) r t (x)) Sequential Screening q t(x) = (λ(q t (x); r t (x)) q t (x))/x Equilibrium Wages where q = q t (x), r = r t (x) and w t(q) = V t (r)λ (q; r) V t (r t ) = µ t e ρ(s t) r s r t ds

22 Constructing the Equilibrium Equilibrium Matching r t (x), q t (x) Talent evolution ṙ t (x) = α(λ(q t (x); r t (x)) r t (x)) Sequential Screening q t(x) = (λ(q t (x); r t (x)) q t (x))/x Equilibrium Wages where q = q t (x), r = r t (x) and V t (r t (x)) = µ w t(q) = V t (r)λ (q; r) t e s t (ρ+α(1 (qu(x))))du ds

23 Equilibrium Firm Dynamics Talent Talent Over Time Firm x= Applicants Over Time Firm x= Talent, r Firm x=0.5 Applicants, q Firm x= Firm x= Time, t Firm x= Time, t Assumptions: p H = 0.8, p L = 0.2, µ = 1, ρ = 0.1, α = 0.2, and q = 0.25.

24 Equilibrium Firm Dynamics Payoffs 0.45 Wages Over Time 0.45 Values Over Time 0.05 Profits Over Time 0.4 Firm x=1 0.4 Firm x= Firm x= Wages, w Firm x=0.5 Value net of Legacy Wages Firm x=0.5 Profits, π Firm x=0.5 Firm x= Firm x= Time, t 0.05 Firm x= Time, t Time, t Assumptions: p H = 0.8, p L = 0.2, µ = 1, ρ = 0.1, α = 0.2, and q = 0.25.

25 The Equilibrium Steady State Steady-state matching r (x), q (x) Constant quality, λ(q; r) = r, links q and r. Seq. screen., q (x) = (λ(q; r) q)/x, determines r(x), q(x). Steady state wages w (q) Marginal value of talent Marginal wages V (r) = w (q) = µ ρ + α(1 (q)). µ ρ + α(1 (q)) λ (q; r).

26 Convergence to Steady State Theorem 4. a) Steady State {r (x), q (x), w (q)} is unique; no gaps or atoms. b) For any initial talent distribution, equilibrium converges to SS. Persistence of competitive advantage Random hiring: regression to mean at rate α. Screening applicants q: regression to mean at α(1 (q)). But under PAM, high-quality firms pay more. Hence, talent is source of sustainable competitive advantage.

27 Comparative Statics Talent dispersion rises in talent-skill correlation β Suppose recruiting skill is (1 β) q + βr. PAM if β > 0, but NAM if β < 0. Talent dispersion r (1) r (0) rises in β. Wages rise in turnover α Does not affect steady-state talent. Raises steady-state flow wages (ρ + α)w t. (ρ + α)w (q(x)) = µλ ρ + α (q(x); r(x)) ρ + α(1 (q(x))) Intuition: Effect of talent outlasts employment.

28 Dynamic Model with Heterogenous Technology

29 Heterogeneous Technology Two types of heterogeneity Exogenous technology µ {µ L, µ H }; mass ν low. Evolving talent r t. Firms stratified, if r t and µ correlate perfectly. Wages increase in µ and r Recall FOC w t(q) = V t (r; µ)λ (q; r) Higher r raises V t (r; µ) and λ (q; r). Higher µ raises V t (r; µ).

30 Convergence to Steady State Theorem 5. a) There is a unique steady-state equilibrium. b) The steady state is stratified. c) Any equilibrium converges to this steady-state. d) Distribution r (x), q (x) independent of {µ L, µ H }. Idea Talent distribution becomes continuous. High-tech firms outbid low-tech firms when talent is close.

31 Adjustment Dynamics of Single Firm Steady state with firms r r high tech; wages w (r). Low-tech firm with r < r becomes high-tech. Theorem 6. a) Wages satisfy w t (w (r t ), w (r )] b) Talent r t converges to r as t. Idea w t > w (r t ) since firm has higher tech. w t w (r ) since firm has less talent. Since w t > w (r t ), talent r t rises over time.

32 Saddle-point Stable Adjustment Path 0.45 Worker Quality 0.4 Adjustment Dynamics Hired, R(µ) 0.35 dr/dt= dr/dt= Market, q(µ) Report, r Productivity, µ Firm Quality, R r 0 chosen to hit r. Near steady state, [ rt r ] [ r t r = (r 0 r ) 1 ] e t.

33 Welfare

34 Welfare Introducing Welfare Entry cost k > 0. Marginal firm: µλ(q(ř); ř) = k. Welfare 1 ˇx (µλ(q(x); r(x)) k)dx. Maximize Aggregate Sorting Planner chooses entry and rank x for every firm r. Equilibrium entry threshold ˇx is efficient (given PAM). But, does PAM for x [ˇx, 1] maximize employed talent?

35 Efficient Matching Theorem 7. For any entry threshold ˇx, NAM maximizes employed talent. Two economics forces Becker: PAM maximizes comparative advantage (if q < ˆq). Akerlof: PAM also maximizes adverse selection. And...

36 Efficient Matching Theorem 7. For any entry threshold ˇx, NAM maximizes employed talent. Two economics forces Becker: PAM maximizes comparative advantage (if q < ˆq). Akerlof: PAM also maximizes adverse selection. And... Akerlof wins!

37 Proof Sketch Marginal Employed Talent Employed talent ω(ˇx), where ω(x) = q xq(x) Effect of better screening skills at rank x ζ(x) := ω(ˆx) r(x) = ω(ˆx) ω(x) ω(x) r(x) ( x λ ) (q(x); r(x)) = exp dx (q(x)) x ˆx Shifting Screening Skills Up ζ (x) (q(x))q (x) λ (q(x); r(x)) (x)/x < 0. }{{}}{{} Becker Akerlof

38 Dynamic Efficiency Upfront entry cost k/ρ > 0. Present surplus 0 e ρt (µr t k)dt, with R t = 1 ˇx r t(x)dx. Choose entry and wage ranks to maximize surplus. Theorem 8. For any ˇx, NAM surplus exceeds PAM surplus at all times. Idea For fixed recruiting skills R t, NAM maximizes talent input. Additional talent under NAM helps recruit even more talent.

39 Extensions

40 Model of Hierarchies Hierarchy N + 1 layers: Level n = 0 directors; level n = N workers. Mass 1 of firms; each has α n positions at level n. Mass α n of job seekers at each level; proportion q skilled. Firms Director quality r 0 exogenous. Level n agents hire level n + 1 agents, r n+1 = λ(q n+1, r n ). Only workers produce, v N = µα N r N.

41 Hierarchies: Equilibrium Wages Equilibrium with q < ˆq Assume r 0 F 0 steady state; then r n+1 = r n. Level-(n 1) value v n 1 (r) := v n (λ(q n ; r)) α n w n ; then v n(r) = µα N (q) N n Marginal level-n wages w n(q) = λ (q; r)µ(α (q)) N n. Assume α (q) > 1; then wages increase in rank. Wage dispersion across firms q > q and levels n < ñ Inter-firm dispersion greater at high levels: wn(q) w n( q) w ñ(q) wñ( q). Intra-firm dispersion greater at high firms: wn(q) wñ(q) wn( q) wñ( q).

42 Conclusion We ve proposed a model in which Firms compete to identify and recruit talent. Today s recruits become tomorrow s recruiters. Main results Positive assortative matching. Persistent productivity dispersion. Equilibrium inefficiency due to adverse selection. Next steps Characterize dynamic matching with q > ˆq. Characterize dynamic and steady state dispersion. Study dynamics when µ t are stochastic.