Recruiting Talent Simon Board Moritz Meyer-ter-Vehn Tomasz Sadzik - PowerPoint PPT Presentation

Introduction Static Dynamic Welfare Extensions The End Recruiting Talent Simon Board Moritz Meyer-ter-Vehn Tomasz Sadzik UCLA July 13, 2016

Introduction Static Dynamic Welfare Extensions The End 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?

Introduction Static Dynamic Welfare Extensions The End 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.

Introduction Static Dynamic Welfare Extensions The End Literature Matching in labor markets ◮ 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).

Introduction Static Dynamic Welfare Extensions The End Static Model

Introduction Static Dynamic Welfare Extensions The End 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 .

Introduction Static Dynamic Welfare Extensions The End 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 � strictly increases in x ◮ Quality q ( x ) : positive for x > 0 , but q (0) = 0 . Wage posting equilibrium ◮ Equilibrium wage distribution { w ( r ) } r has no atoms or gaps.

Introduction Static Dynamic Welfare Extensions The End Firm-Applicant Matching Wage profile { w ( r ) } r induces firm-applicant matching Q ( r ) = q ( x ( w ( r )))

Introduction Static Dynamic Welfare Extensions The End 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 ) = ∂ ∂rλ ( q ; r ) ◮ IC: ∆( Q ( r )) rises in r . ◮ ∆( · ) is single-peaked, with maximum ˆ q ∈ (0 , 1) . ◮ λ ( q ; r ) is super-modular for q < ˆ q ; sub-modular for q > ˆ q .

Introduction Static Dynamic Welfare Extensions The End Scarce Talent — Positive Assortative Matching Theorem 1. If ¯ q ≤ ˆ q , 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 � r ◮ Profits π ( r ) = µ ∆( Q (˜ r )) d ˜ r. r ◮ Wages � r λ ′ ( Q (˜ r ) Q ′ (˜ w ( r ) = µ r ); ˜ r ) d ˜ r. r

Introduction Static Dynamic Welfare Extensions The End PAM: Example 0.45 0.7 0.4 0.6 0.35 0.5 0.3 Worker Quality 0.4 0.25 Payoffs Wages, w(x) Recruits, λ (x) 0.2 0.3 0.15 0.2 0.1 Profit, π (x) 0.1 Applicants, q(x) 0.05 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Firm rank, x Firm rank, x Assumptions: p H = 0 . 8 , p L = 0 . 2 , r ∼ U [0 , 1] , ¯ q = 0 . 25 , µ = 1 .

Introduction Static Dynamic Welfare Extensions The End Comparative Statics — Screening Skills 0.6 r=0.8 0.5 0.4 Wages 0.3 r~U[0,1] r=0.5 0.2 0.1 0 0 0.2 0.4 0.6 0.8 1 Firm rank, x Assumptions: p H = 0 . 8 , p L = 0 . 2 , ¯ q = 0 . 25 , µ = 1 .

Introduction Static Dynamic Welfare Extensions The End Comparative Statics — Technological Change 0.6 − µ H ,q L 0.5 Wages 0.4 Payoffs − 0.3 µ L ,q H 0.2 − µ L ,q H Profits 0.1 − µ H ,q L 0 0 0.2 0.4 0.6 0.8 1 Firm rank, x q H = . 25 , µ L = 1 ¯ ¯ q L = . 05 , µ H = 5 . →

Introduction Static Dynamic Welfare Extensions The End Abundant Talent Theorem 2. Assume ¯ q > ˆ q . There is a unique equilibrium. It has PAM on [ q ∗ , ˆ q ] and NAM on [ˆ q, ¯ q ] . Proof ◮ Key fact: ∆( Q ( r )) increases in r . ◮ Top firm ¯ r matches with ˆ q . ◮ Below, r matches with Q P ( r ) < ˆ q < Q N ( r ) s.t. ∆( Q P ( r )) = ∆( Q N ( r )) and Q P , Q N obey the usual differential equations.

Introduction Static Dynamic Welfare Extensions The End PAM-NAM: Example 0.7 0.7 λ P (x) 0.6 0.6 w N (x) 0.5 λ N (x) 0.5 Q N (x) Worker Quality 0.4 0.4 Payoffs 0.3 0.3 w P (x) 0.2 0.2 Q P (x) π (x) 0.1 0.1 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Firm rank, x Firm rank, x Assumptions: p H = 0 . 8 , p L = 0 . 2 , r ∼ U [0 , 1] , ¯ q = 0 . 5 .

Introduction Static Dynamic Welfare Extensions The End Dynamic Model

Introduction Static Dynamic Welfare Extensions The End 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 < ˆ q . 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 r t = α ( λ ( q t ; r t ) − r t ) . ˙ ◮ Firm value V t ( r ) .

Introduction Static Dynamic Welfare Extensions The End Firm’s Problem ◮ The firm solves � ∞ e − ρt ( µr t − αw t ( q t )) dt, V 0 ( r 0 ) = max { q t } 0 s.t. r t = α ( λ ( q t ; r t ) − r t ) . ˙ ◮ Bellman equation t ( r )[ λ ( q ; r ) − r ] + ˙ q { µr − αw t ( q ) + αV ′ ρV t ( r ) = max V t ( r ) } . ◮ First order condition λ ′ ( q ; r ) V ′ t ( r ) = w ′ t ( q ) .

Introduction Static Dynamic Welfare Extensions The End 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 .

Introduction Static Dynamic Welfare Extensions The End Constructing the Equilibrium Equilibrium Matching r t ( x ) , q t ( x ) ◮ Talent evolution r 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 w ′ t ( q ) = V ′ t ( r ) λ ′ ( q ; r ) where q = q t ( x ) , r = r t ( x ) and � ∞ t ( r t ) = ∂ V ′ e − ρ ( s − t ) [ µr ∗ s − αw s ( q ∗ s )] ds ∂r t t

Introduction Static Dynamic Welfare Extensions The End Constructing the Equilibrium Equilibrium Matching r t ( x ) , q t ( x ) ◮ Talent evolution r 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 w ′ t ( q ) = V ′ t ( r ) λ ′ ( q ; r ) where q = q t ( x ) , r = r t ( x ) and � ∞ e − ρ ( s − t ) ∂r ∗ V ′ s t ( r t ) = µ ds ∂r t t

Introduction Static Dynamic Welfare Extensions The End Constructing the Equilibrium Equilibrium Matching r t ( x ) , q t ( x ) ◮ Talent evolution r 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 w ′ t ( q ) = V ′ t ( r ) λ ′ ( q ; r ) where q = q t ( x ) , r = r t ( x ) and � ∞ � s V ′ e − t ( ρ + α (1 − ∆( q u ( x )))) du ds t ( r t ( x )) = µ t