cognitive and commuication skills in a hierarchical labor market. · 2019-12-19 · a 2c (cognitive...

Cognitive and commuication skills in a hierarchical labormarket.

Robert J. McCann, Xianwen Shi, Aloysius Siow & Ronald Woltho¤

University of Toronto

January, 2013

Introduction

1 A common workplace is the 2 level hierarchy which consists of onemanager and several workers. 2 level hierarchies can be stand aloneestablishments, branches of a �rm, or a unit of a larger hierarchy suchas the in-house counsel of a �rm.

2 After controlling for industry and occupation, there are�rm/establishment �xed e¤ects in employees�log earnings. I.e. thereare high wage and low wage �rms.

3 The log earnings �xed e¤ect is positively correlated with its size. I.e.on average, large �rms/establishments pay better.

4 There is signi�cant residual variation in the earnings �xed e¤ectswhich are unexplained by observed �rm/establishment characteristics.I.e. many small �rms/establishments pay high wages.

5 The distribution of earnings in the economy is right skewed.

1C (cognitive skill) models

Economists (E.g. Rosen, Lucas, Garicano and collaborators, Gabaixand Landier) use one factor (cognitive skill) model of individualheterogeneity in hierarchical labor markets to explain 2, 3 & 5.

Consider a 2 level hierarchy. In a 1C model, the manager�s and herworkers�cognitive skills are complements in production. The span ofcontrol of the manager (how many workers she can manage) isincreasing in her cognitive skill.

Then a high skill manager matches with high skill workers (Lazear, et.al. 2012). Productive managers manage more workers. Rightskewness of earnings come from the scarcity of highly skilledemployees. Search frictions in the labor market can explain 4 (E.g.Mortensen, Shimer and Smith, etc.).

A 2C (cognitive and communication skills) model

Adam Smith discussed the gains to team production due tospecialization and the division of labor.

Subsequent authors have suggested that communication costs limitsthe gain to specialization and the size of the �rm (E.g. Becker andMurphy). Garicano and his coauthors modeled communication cost asa homogenous one sided time cost in frictionless hierarchical labormarkets.

This paper builds on Garicano and his coauthors by modellingcommunication skills as heterogeneity in the one sided time cost ofcommunication in frictionless hierarchical labor markets.

Why introduce communication skills? Team production is pervasive inhuman activities. Some people act alone whereas other act together.

Can it be separately identi�ed from cognitive skill?

Analyzing communication skills means considering team productionwhich includes matching considerations. Who matches with whomgenerates potential identi�cation restrictions not available to modelsof non-cognitive skills which only apply to single agent behavior.

Consider the log earnings regression of managers and workers across iteams in a �rm:

lnωim = βm0 + βm1E im + βm2S im + v

lnωiw = βw 0 + βw 1E im + βw 2S im + v

iw , w = 1, ..,S

The �rst equation is standard. The second equation is based on whomatches with whom. What should the coe¢ cients be?

A �rst pass model of the labor market with cognitive andcommunication skills.

iw , w = 1, ..,S

Results Overview

Given frictionless matching and e¢ cient team production, theproblem of matching within and across sectors is a linearprogramming problem. This is great for simulation and estimation.

(i) 2 level hierarchies emerges in the labor market, a commonlyobserved organizational form.

(ii) Individuals with high communication and cognitive skills becomemanagers and teachers.

Managers and workers match by cognitive skills.

Students with di¤erent communication skills and initial cognitiveabilities match with teachers of the same cognitive skill.

In the 2C model, controlling for the manager�s educationalattainment, the partial correlation between her workers�average logearnings and her span of control is negative. In the 1C model, thepartial correlation is zero.

Results Overview

Model Setup

Risk-neutral individuals live for two periods.

� Enter education market as students, and then work.� One unit of time endowment for each sector.� Free entry of �rms and schools.

Individuals are heterogenous in two dimensions:

� (�xed) gross communication skill η, with η 2hη, η

i� initial cognitive ability a, with a 2 [a, a]� education transforms a into adult cognitive skill k, with k 2

�k, k

�Individuals�net payo¤: wage (ω) � tuition (τ)

� Individual decision: who to match with in each sector.

Single Agent Production in each Sector

Output is produced by completion of two tasks, I and C :

� θIi , θCi : times i spent on task I and C respectively� time constraint in each sector: θIi + θCi � 1

Single agent production:

βki minn

θIi ,γθCi

o, β < 1;γ > 1 (Single)

� no need for coordination: gross communication skill ηi does not enterproduction.

Team versus Single Agent Production

Single Agent Production

βki minn

θIi ,γθCi

o, β < 1;γ > 1

Team Production

Consider a two-person team with (ηi , ki ) and (ηj , kj ) .

� θIi , θCj : times i and j spend on task I and task C respectively

Specialization needs coordination.

� Individual on task C bears (one-sided) coordination cost

Team output: pkikj min

nθIi ,γηj θ

o, ηj < 1 (Team)

Assume team production is always superior to working alone.

Specialization in the Labor Market

Let communication skill be n: n � γη. Team output:pkikj min

nθIi , nj θ

oω(nl , kl ) is total earnings of type l employee with skills (nl , kl ).

Let a �rm hires i and j to produce δpkikj units of output where δ is

small.

Need to allocate δ units of e¤ective time to tasks I and C .

Let θIi and (δ� θIi ) be times i and j allocate to task I respectively.Then θCj = θIi n

�1j and θCi = (δ� θIi )n

�1i are times j and i allocate to

task C respectively.

Firm pays for time used. Leftover time sold elsewhere.The expenditure of the �rm�s allocations is:

ω(ni , ki )(θIi +(δ� θIi )

ni) +ω(nj , kj )(δ� θIi +

θIinj)

The �rm chooses θIi to minimize above.

Proposition. Full task specialization is optimal, i.e., an individual isassigned to task I or C .

Corollary.(Ricardo): Specialization is by comparative advantage. Let ido I if

ω(ni , ki )ω(nj , kj )

�1� n�1j1� n�1i

Many-to-one matching in teams: one member (manager) on task Cand several members (workers) on task I .

Manager communication skill: span of control or leadership.

Workers�communication skills have no value for team production. Soω(ni , ki ) = w(ki ).

Proposition.There is a cuto¤ bn (k) such that a type-(n, k) individualdoes task C if and only if n � bn (k).

Managers are individuals with better communication skills.Occupation choice is based on cognitive and communication skills.

PAM in the Labor Market

Consider a type-(nm , km) manager who chooses nm workers of type(ni , ki ) at wage ω(ki ) to maximize

max(k1,...,knm )

∑i=1

hpkmki �ω(ki )

i� In optimum, workers have the same kw .So problem of manager can be written as:

hpkmkw nm �ω(kw )nm

i� De�ne equilibrium matching µ (km) 2 argmaxkw

�pkmkw �ω(kw )

�Proposition.(Becker) Equilibrium exhibits positive assortativematching (PAM) along cognitive skills: µ0 (k) > 0

Equilibrium Wages in the Labor Market

Letφ (k) = max

hpkk 0 �ω(k 0)

iDue to free entry of �rms, a type-(n, k) manager earns

nφ (k)

Education Market

Task assignment is exogenous:

� teachers do task C� students do task I

A student of initial cognitive ability ai matched with a teacher ofcognitive skill kt will attain

paikt adult cognitive skill.

A teacher of communcation skill nt can teach nt students in oneperiod.

Tuition and teacher�s wages

� tuition τ (kt ) depends on school quality � teacher�s cognitive skill kt� teacher�s wages: ntτ (kt )

Equilibrium Education Choice

Education choices maximize future net payo¤

nnsφ(

paskt ),ω(

paskt ), nsτ(

paskt )

o� τ (kt )

� Future managers choose higher kt if a and n are larger: endogenouspositive correlation between communication and cognitive skills.

� Consider two managers with the same kt . The manager who has largerspan of control will have lower initial ability a. She will also acquire lessk. I.e. conditional on kt , nm and km are negatively correlated.

� Future workers choose more kt if a is larger. kw and kt are positivelycorrelated.

Proposition. Within a team, kw = µ(km), µ0 > 0.[1] In 1C and 2C models, controlling for the workers�educationalattainment, the partial correlation between her workers�log earnings andher span of control is zero.[2] In the 2C model, controlling for the manager�s educational attainment,the partial correlation between her workers�log earnings and her span ofcontrol is negative. In the 1C model, the partial correlation is zero.

General Equilibrium

All markets clear

� labor market clears: equilibrium wages for workers, managers, andteachers equal demand with supply for each type of adult.

� education market clears: school tuitions are set such that availableslots in schools equal the total supply for each type of student.

Equilibrium equivalent to a utilitarian communication planner solvinga linear programming problem.

Linear Programming

communication planner chooses number (measure) of(nm , km , nw , kw ) �rms and number of (nt , kt , ns , as ) schools tomaximize:

∑�rm types

# �rm type (nm , km , nw , kw )��nmpkmkw

�subject to, for each adult type (n, k),

demand by �rms + schools � supply of adults

and for each student type (n, a),

school slots for students � supply of students

wages and student payo¤s: multipliers attached to the constraints.

in�nite dimensional, dual program.

Related Literature (Partial List)

Importance of non-cognitive (including communication) skills:

� Almlund, Duckworth, Heckman and Kautz (2011), Heckman (2011) ...

Tradeo¤ between specialization and communication cost:

Becker and Murphy (1992), Dessein and Santos (2006).

Task assignments and hierarchies:

� Roy (1951), Sattinger (1975) ...� Lucas (1978), Rosen (1978, 1982), Eeckhout and Kircher (2011)

Communication costs, organization design, time use, occupationalchoice, human capital investment, one factor labor market matching:

� Garicano (2000), Garicano and Rossi Hansberg (2004,2006)

Linear programming models of frictionless matching labor market:Prescott and Townsend (2005)

Numerical Simulation: Occupation Choice

Numerical Simulation: Education Choice

Numerical Simulation: Equilibrium Wage

Numerical Simulation: Wage Distribution

cognitive and commuication skills in a hierarchical labor market. · 2019-12-19 · a 2c (cognitive...

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