lecture 3: skills , entrepreneurs and wageserossi/macro/lecture_3_522.pdf · erh (princeton...

Lecture 3: Skills , Entrepreneurs and WagesEconomics 522

Esteban Rossi-Hansberg

Princeton University

Spring 2014

ERH (Princeton University ) Lecture 3: Skills , Entrepreneurs and Wages Spring 2014 1 / 109

Acemoglu (2002)

Theory of endogenous skill biased technological change

Increases in the supply of skills can lead to investments in technologies thatuse these skills intensively

The effect of technology and trade can be related to skill biased technologicalchange, not a competing explanation

This can explain the evolution of the skill premium in the US


Skill Premium and Skill Supply


A Simple Version of the MechanismAgents consume a final good which is produced using

Y =(Y ρl + Y

ρh

) 1ρ

where

Yl = NlL

Yh = NhH

and L denotes low skilled labor, H denotes high skilled labor, Nl and Nh canbe interpreted as the number of specialized machines used with skilled andunskilled workers, respectively.An increase in Nh relative to Nl will correspond to skill-biased technicalchange as long as σ = 1/(1− ρ) > 1Consumer maximization implies that

p =phpl=

(NhHNlL

)ρ−1

where ph is the price of Nh and pl the price of NlERH (Princeton University ) Lecture 3: Skills , Entrepreneurs and Wages Spring 2014 4 / 109

A Simple Version of the Mechanism

Suppose now that these specialized machines are created and sold byprofit-maximizing monopolists

Creating a new machine costs B units of the final good Y

The marginal cost of producing these machines, once created, is zero

The marginal willingness to pay for an additional machine in the two sectorsis given by the derivatives of phYh and plYl with respect to Nh and Nl , i.e.,phH and plL

SoI technologies producing more expensive goods will be improved fasterI larger clientele for a technology leads to more innovation


A Simple Version of the MechanismThe creation of new machines will stop when

phH = plL

p =LH

p adjusts until this equation is satisfied

Which implies that

NhNl= p

1ρ−1 LH=

(HL

) ρ1−ρ

So if ρ > 0 the market size effect dominates the price effect

The skill premium is given by

ω =phNhplNl

=

(HL

) ρ1−ρ−1

=

(HL

) 2ρ−11−ρ

If ρ > 1/2 or the elasticity of substitution is greater than 2 the skill premiumwill be an increasing function of the relative supply of skills


A Simple Version of the Mechanism


Sattinger (1993)

Review article on “Assignment Models of the Distribution of Earnings”

Focus here on models of continuous distributions of workers and jobsI The Differential Rents Model

In contrast to the Roy Model: Workers choose among a few job types oroccupations

I Roy has the advantage that there are many workers per jobI But see the many to one models in Rosen or Garicano and Rossi-Hansberg


The differential rents model

Arises when the output in the optimal assignment problem depends on asingle explicit characteristic of the worker and a single explicit characteristicof the job

Under certain conditions, a hierarchical assignment arises in which moreskilled workers perform jobs with greater resources

Important feature of market systems: Tendency to reinforce and exaggeratedifferences among workers

With heterogeneous jobs, more skilled workers (who would perhaps havegotten higher earnings anyway) have their earnings boosted by being assignedto jobs with more capital, responsibility, or subordinates


The model

Each job associated with one machine: one to one matching

Each machine has a ‘size’or productivity

Letaij = f (gi , kj )

I gi is a measure of worker i’s skillI kj is a measure of the size of machine j ,I f (g , k) is an increasing function of g and k and has continuous first andsecond order derivatives

Let G (x) be the proportion of workers with skill levels less than or equal to x ,and let K (x) be the proportion of machine sizes that are less than or equal tox

Let w (g) determine the relationship between wages and the skill level g

The owner of a machine of size k∗ will attempt to maximize the profitsobtained from that machine, which for skill g are given by

f (g , k∗)− w(g)


Machine Owner’s Problem

So machine owner k∗ solves

r (k∗) = maxgf (g , k∗)− w(g)

so

w ′ (g) =∂f (g , k∗)

∂g

The effect of an increase in the worker’s skill level, and the size of the wagedifferential, depend on which job the worker performs

To calculate the wage differential w ′(g), we would need to know the size ofthe machine k∗ of the employer who hires that labor


Assignment

Normally we need to solve for assignment and wages simultaneously

A number of simplifying assumptions make it possible to determine theassignment without first knowing the wage function

I The distribution of jobs or machines does not depend on w (g ) . That is, thenumber of jobs does not increase or decrease in response to a high or low profit

I Given that we use only one dimensional characteristic, in general, positive ornegative matching

So proceed as follows:I Assume assignmentI Solve for w (g )I Check second order condition

So with positive assortative matching

1− G (g) = 1−K (k)

which determines k (g)


Second Order ConditionOptimization implies that

∂2f (g , k∗)∂g2

− w ′′ (g) < 0 for k∗ = k (g)

Suffi cient to have complementarity or

∂2f (g , k)∂g∂k

> 0

To see this note that the FOC and optimal assignment k (g) imply

w ′′ (g) =∂2f (g , k (g))

∂g2+

∂2f (g , k (g))∂g∂k

[dkdg

]so

−∂2f (g , k (g))∂g∂k

[dkdg

]=

∂2f (g , k (g))∂g2

− w ′′ (g)

Hence if ∂2f (g ,k )∂g ∂k > 0, and dk/dg > 0 the SOC is satisfied with our guess


Wage Function

Integrate

w ′ (g) =∂f (g , k (g))

∂g

to obtain the wage function

Obtain constant of integrationI The labor market process in which employers choose workers determines onlyrelative wages and not their absolute level

I Reserve prices of labor and capital determine absolute levels of wages and rentsI Let pw and pr the minimum amount workers and machines should receive tobe willing to work

I Let gm be such that pw = w (gm)I Let km be such that pr = r (km)I Either gm is the minimum skill, km is the smallest machine, orpw + pr = f (gm , k (gm)) where km = k (gm)

Then we can solve for the constant


An Example

Let f (g , k) = gαkβ

Let skills and machines be lognormally distributed with variances of logsgiven by σ2g and σ2kThen the method above yields

w(g) = Ag (ασg+βσk )/σg + Cw

If α+ β = 1 and σk > σw (machine sizes are more unequally distributedthan skills) then w (g) is convex

If both workers and machines are unemployed, then Cw can be calculated as

Cw =pw βσk − ασg pr

ασg + βσk


Organization, Wages and Growth

The acquisition and organization of knowledge is an essential problem ofmodern production

I Knowledge is embedded in individuals with limited timeI Organizational problem is to use the time of knowledgable individualseffi ciently

F Time of experts should not be waisted on easy or routine tasks

The value of the knowledge of a particular individual depends on theknowledge of everyone else

I How do firms (and more broadly groups of individuals or society) manage theknowledge of their workforce?

F How many distinct groups of individuals? How much does each class know?How many of each of them?

F What characteristics of the economy determine a firm’s organizational choices?F What are the margins of adjustment?

The answers to these questions will determine knowledge acquisition,productivity, and growth in the economy


Garicano and Rossi-Hansberg (2007)

How does information technology affect wages and organization?

Knowledge is becoming cheaper to store, access, and transmitI Data base access costI Communication costs

How do these improvements affect organization of production and theassociated reward structure?

Answering this question requires a model of internal organization embeddedin the labor market

I Large recent theoretical literature on hierarchies deals with internal, singlefirm, optimization (information processing, monitoring, etc.)

I Not embedded in an equilibrium frameworkF An exception is Rosen (1982), but equilibrium not characterized



In this paper we develop an equilibrium model of a ‘knowledge economy’I Organizations embedded in a labor market

PrimitivesI Production requires physical inputs and knowledge

F The aim of an organization is to structure the acquisition and communication ofknowledge

F It can be acquired or communicated by someone else

A continuum of heterogenous ability workers who may join inhierarchies/firms

I We use firms and hierarchies as synonymous. Boundary of the firm is not welldefined



Important to study interdependency between labor market and firm structure:

Changes in inequality are a function of the internal restructuring of firms

Changes in firm structure respond to changes in the wage schedule

Use this theory to relate changes in the

cost of acquiring knowledge and

cost of communicating knowledge

with changes in

organization of production (firms size, number of layers, spans and taskallocation) and

wage distribution (wage inequality, CEO/worker premium)


Preliminaries: Garicano (2000)

Communication allows knowledge to be acquired by some workers andcommunicated as needed

Organizational problem: decide who learns what, and to whom must eachperson ask

How easy is it to match knowledge with solutions?I If cheap, this organizational problem simple: horizontal specializationI In production, knowledge often tacit, embodied in individual. Hard to know ifanswer known. Assume matching cost is high


Preliminaries: Garicano (2000)

1 Specialized problem solvers and production workers2 Management by exception:

1 Production workers know solutions to common problems2 They ask successively to problem solvers who know increasingly exceptionalproblems

3 Pyramidal shape: smaller proportion of workers required further away fromproduction floor

4 Possibly several layers optimal. Trade-off:

1 Increase communication costs2 Decrease knowledge costs: less learn exceptions


The Model: Production and Knowledge

Production requires labor and knowledge

Agents spend time in production and must solve the problems they confrontin order to produce

Problems are ranked by the likelihood that they will be confronted, so thatproblem Z is associated with a continuous density f (Z ) and c.d.f. F (Z ),where f ′(Z ) < 0

Knowledge is cumulativeI An agent with knowledge z , can solve problems in [0, z ]I Let q = F (z). Then z = z(q), where z(·) = F−1(·), and so z ′ > 0, z ′′ > 0(by the properties of f (·))

I Thus, z(q) denotes the knowledge an agent needs to acquire in order to solvea proportion q of problems


The Model: Ability and Knowledge Acquisition

The distribution of ability in the population is described by a continuousdensity function, α ∼ φ(α), with support in [0, 1]

The cost of learning to solve an interval of problems of length 1 is given by

c(α; t) = t − α.

All agents are endowed with one unit of time


The Model: Communication and Organization

Workers draw a problem per unit of time

Consider an organization with n0 production workers with knowledgeq0 = F (z0) and nl problem solving managers in layers l = 1, ...L, withknowledge ql

I Workers draw one problem each, and solve a fraction q0. They pass on(1− q0)

I Managers in layer l are asked to solve n0 (1− ql−1) problems, which they canaddress in hn0 (1− ql−1) units of time. The number of managers in layer l is

hn0(1− ql−1) = nl

Expected total output produced by the organization is

y = qLn0


Agent’s Problem

Agents are income maximizers

Their problem is to choose their occupation to maximize income, given theavailable job opportunities

Available jobs are indexed by α′ and pay a wage plus learning costs given byw(α′) + c(α′; t)z(q (α′)) and require agents to know how to solve aproportion q (α′) of problems

The problem of an agent with ability α is to choose a job α′ that maximizesher income minus actual learning costs, c(α; t)z(q (α′)), so

U(α) = maxα′

[w(α′) + c(α′; t)z(q

(α′))]− c(α; t)z(q

(α′))

The FOC implies that α∗ = α when w ′ (α∗) = −c ′(α∗; t)z(q (α∗))


Firm’s Problem

The problem of a hierarchy of L layers that faces a wage schedule, w (α), is tochoose the ability, knowledge, and number of agents in each layer of the team

The expected profit of the hierarchy is then given by

Π(L) = maxql ,nl ,αl Ll=0

qLn0 −L∑l=0

nl [c(αl ; t)z(ql ) + w (αl )]

s.t. hn0(1− qL−1) = nL ≡ 1hn0(1− qL−2) = nL−1

...

hn0(1− q0) = n1

The first order conditions with respect to αl yield w ′ (α) = −c ′(α; t)z(q)So wages are such that agents choose the job designed for their own ability


Knowledge Transactions

Π(L) = maxqL ,qL−1

qL − qL−1 + p (qL−1;w)h(1− qL−1)

− [c(αL; t)z(qL) + w (αL)]

where

p(q0,w) ≡ q0 − (c(α0; t)z(q0) + w (α0)) and

p (ql ;w) ≡ maxql−1

[ql − ql−1 − h(1− ql−1) [c(αl ; t)z(ql ) + w (αl )] + p (ql−1;w)]

The wage structure of a firm can thus be interpreted as a transfer systemI Managers pay workers a fee to pass problem to them and managers keep theoutput

I These managers receive fees from the managers above them for passing theproblems that they cannot solve


Knowledge Transactions

Using p the problem is equivalent to

w (αl ) = maxql ,ql−1

[ql − ql−1 + p (ql−1; ·)− p (ql ; ·)

h (1− ql−1)− c(αl ; t)z(ql )

]w (α0) = max

q0[q0 − p (q0; ·)− c(α0; t)z(q0)]

given that in equilibrium top managers do not pass problems, so

p (q∗L;w) ≥ 0

Agents choose sequentially their knowledge and the knowledge of those belowthem so as to maximize their own earnings


Alternative Formulations: Referrals

Consider now a market in which there are two types of occupations:production workers and problem solvers

Production workers with skill α0 draw a problem per unit of time and usetheir knowledge q0 to try to solve it

If they can solve the problem, they do so and earn 1; if they cannot solve it,they sell it in the market at a price p(q0)

Problem solvers can deal with 1/h problemsThis formulation is just a reinterpretation of the problem above if we let

p (ql ) = −p(ql ; ·)1− ql−1


Alternative Formulations: Consultant services

Production workers draw a problem per unit of time, and keep ownership ofthe production associated with solving the problem

They pay a fee per problem to other agents for their advice

If production workers know the solution to the problem, they solve it; if not,they pay a fee p (q1) to the problem solvers in layer 1

If they cannot solve it they pay a fee to problem solvers in layer 2, and so on

Again, this is just a reinterpretation of the setup in the previous section if welet

p (ql ) =ql − p (ql ;w)− [ql−1 − p (ql−1;w)]

1− ql−1


Labor Market Equilibrium Condition

n (α) : total number of agents hired as direct subordinates of agents withability α in equilibrium

a (α) : ability of the manager assigned to an employee of ability α inequilibrium

AS : set of agents with subordinates and AM : set of agents that are not atthe top of a hierarchy

Labor markets clear if for every α ∈ AM∫[0,α]∩AM

φ(α′)dα′ =∫[a(0),a(α)]∩AS

n(α′)n(a(α′))

φ(α′)dα′

The LHS is the supply of employees in the interval [0, α]

The RHS is the demand for employees by agents in [a(0), a(α)]: Managersand entrepreneurs of ability α hire n (α) employees and there are n(a(α)) ofthem


EquilibriumA competitive equilibrium is

the set of numbers of layers of hierarchies operating, L, where L ∈ L is thenumber of layers of the highest hierarchy,

a collection of sets Al = AlM ∪ AlE Ll=0a wage function, w(α) : [0, 1]→ R+,

an assignment function, a(α) : [0, 1]→ AS ,

a knowledge function q (α) : [0, 1]→ [0, 1] and

a total number of direct subordinates of agents with ability α,n (α) : AS → R+,

such that:

Agents choose occupations to maximize utility

Firms choose the skill of their employees, their knowledge, and spans ofcontrol so as to maximize profits

Firms make zero profits and so p (q (α) ; ·) ≥ 0, for α ∈ AlE , l = 0, ..., LLabor markets clear


Assignment

Proposition: Any equilibrium of this economy involves positive sortingI Complementarity in production between the knowledge of team members

∂a(α)∂α

=

1−q(α)

1−q(a−1(α))φ(α)

φ(a(α)) for α ∈ AM \A0Mh (1− q(α)) φ(α)

φ(a(α)) for α ∈ A0M

Slope given by the number of managers per subordinate over the ratio ofavailable agents

0 Ability*01

*00 αα = *

11α *22

*12 αα = 1*

23 =α

( )0a ( )*00αa

( )*00αa


Wages

Continuous, not differentiable everywhere, and increasing

w ′ (α) = −c ′(α; t)z(q (α)) = z(q (α)) > 0

More inequality when technology leads agents to learn more tasks

The wage function is also convex since

w ′′ (α) = z ′(q (α))q′ (α)

Proposition: Any equilibrium wage function, w(α) : [0, 1]→ R+, isincreasing and convex. Furthermore, the knowledge function q (α) isincreasing

Proposition: Relative to an economy without organization, organizationincreases the knowledge of entrepreneurs and decreases the knowledge ofproduction workers


Occupational Stratification

In equilibrium occupations are stratified by abilityI Lowest skilled agents are workers, then managers of all layers, thenentrepreneurs of layer L− 1 and L

Proposition: Any equilibrium allocation with a maximum number of L ≥ 0layers is characterized by a set of thresholds,

α∗ll , α

∗ll+1

Ll=0

, such that

αii ≤ αij ≤ αjj , for i < j ,I α∗LL+1 = 1I[α∗L−1L−1, 1

]are entrepreneurs of layers L− 1 and L,

I[α∗00, α

∗L−1L−1

]are managers of layers 1 to L− 1, and

I [0, α∗00 ] are workersI α∗ll = α∗ll+1 for all l = 0, ..., L− 2, and α∗L−1L = α∗LL


Equilibrium Construction

Workersl = 0

Entrep.1 = 1

Managersl = 1

Entrep.l = 2

0

Earn

ings

Ability*01

*00 αα = *

11α *22

*12 αα = 1*

23 =α

)(αw)0(w

)()( *010

*010 αα DS =

)()( *121

*121 αα DS =

)(lim)(lim*01

*01

αααααα

ww↓↑

=

)(lim)(lim*12

*12

αααααα

ww↓↑

=

)( *01αw

)(lim)(lim*11

*11

αααααα

ww↓↑

=


Existence and Optimality

Proposition: There exists a unique equilibrium allocationI The proof of existence is constructive and so it develops a computationalalgorithm

Proposition: The equilibrium allocation is Pareto optimalI Total time endowment used, and the problems that are not solved are toodiffi cult (and therefore p (·) ≥ 0)

I Even though the technology exhibits complementarity, all interactions betweenagents are priced


Effect of IT on Wages and Organization

Assume problem density is exponential: f (z) = e−λz

Assume skill density uniform: α ∼ U [0, 1]Two experiments:

I Decrease t: lower cost of acquiring or accessing knowledgeI Decrease h: lower cost of communicating information


Effect of CT on Wages and Organization

Wage and Knowledge function (t=1.1, h=0.98)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 0.2 0.4 0.6 0.8 1

Ability α

Earn

ings

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Kno

wle

dge

Knowledge

Earnings

Workers




0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.0 0.2 0.4 0.6 0.8 1.0

Ability α

Earn

ings

0

0.2

0.4

0.6

0.8

1

1.2

Kno

wle

dge

Earnings

Knowledge

Workers

Selfemployed

Entrepreneurs




0.1

0.3

0.5

0.7

0.9

1.1

1.3

1.5

1.7

0.0 0.2 0.4 0.6 0.8 1.0

Ability α

Earn

ings

0

0.2

0.4

0.6

0.8

1

1.2

Kno

wle

dge

Earnings

Knowledge

Workers ManagersEntrepreneurs l = 1Entrepreneurs l = 2




0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.0 0.2 0.4 0.6 0.8 1.0

Ability α

Earn

ings

0

0.1

0.2

0.3

0.4

0.5

0.6

Kno

wle

dge

Earnings

Knowledge

Workers Selfemployed Entrepreneurs




0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 0.2 0.4 0.6 0.8 1

Ability α

Earn

ings

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Kno

wle

dge

Knowledge

Earnings

Workers




0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.0 0.2 0.4 0.6 0.8 1.0

Ability α

Earn

ings

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Kno

wle

dge

Earnings

Knowledge

Workers Entrepreneurs




0.1

0.3

0.5

0.7

0.9

1.1

1.3

1.5

1.7

0.0 0.2 0.4 0.6 0.8 1.0

Ability α

Earn

ings

0

0.2

0.4

0.6

0.8

1

1.2

Kno

wle

dge

Earnings

Knowledge

Workers ManagersEntrepreneurs l = 1Entrepreneurs l = 2


Earnings

Earnings function

0

0.2

0.4

0.6

0.8

1

1.2

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

Ability α

Earn

ings

h=0.7, t=1.9

h=0.98, t=1.9

h=0.8, t=1.9

h=0.98, t=1.1

h=0.8, t=1.1h=0.7, t=1.1

E(1) = 1.6


Earnings

Total wage inequality,SD

h\t 1.9 1.10.98 0.068 0.2020.80 0.057 0.2060.70 0.063 0.300

Span of Control (α = 1)

h\t 1.9 1.10.98 1.02 00.80 1.25 6.160.70 1.43 109.89

Worker/Self-employedwage inequality, SD

h\t 1.9 1.10.98 0.038 0.2020.80 0 0.1190.70 0 0.091

Wage for α = 0

h\t 1.9 1.10.98 0.01 0.120.80 0.07 0.190.70 0.11 0.26


Earnings

Entrepreneur/Managerwage inequality, SD

h\t 1.9 1.10.98 0.018 N/A0.80 0.055 0.1320.70 0.060 0.243Q of highest ability worker

h\t 1.9 1.10.98 0 0.950.80 0 0.800.70 0 0.78


Some Evidence

5.4

5.6

5.8

6

6.2

6.4

6.6

6.8

1975 1980 1985 1990 1995 2000

Mean Log Firm Size (FS)

10 x Standard Deviation of Log Hourly Wages (All Men, March, WI)

Source: Mean Log Firm Size :Compustat, SD of Log Hourly Wages: March CPS using the methodology in Card and DiNardo (2002).

Correlation (FS,WI) = 0.9502


Some Evidence

0

100

200

300

400

500

600

1975 1980 1985 1990 1995 2000

Ratio of Average CEO Total Pay (Including Options Valued at GrantDate) toAverage Annual Earnings of Production Workers

Source: CEO sample is based on all CEOs included in the S&P 500, using data from Forbes and ExecuComp. CEO total pay includes cash pay,restricted stock, payouts from longterm pay programs, and the value of stock options granted using ExecuComp's modified BlackScholes approach.(Total pay prior to 1978 excludes option grants, while total pay between 1978 and 1991 is computed using the amounts realized from exercising stockoptions during the year, rather than grantdate values.) Worker pay represents 52 times the average weekly hours of production workers multiplied bythe average hourly earnings, based on data from the Current Employment Statistics, Bureau of Labor Statistics. We thank Kevin Murphy for this data.


Some Evidence

0

10

20

30

40

50

60

70

80

1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 20001.00E07

1.00E06

1.00E05

1.00E04

1.00E03Number of Internet Hosts (Millions, LHS Scale)

Online Access (Percent of Population, LHS Scale)

Cell Phones (Percent of Population, LHS Scale)

Average Transistor Price (US$, RHS Scale)

Source: Number of Internet Hosts: Internet Software Consortium, Online Access: The Harris Poll® #8, Cell Phones: United Nations Statistics Division,Average Transistor Price: Dataquest/Intel.


Other Applications, Extensions, and Related Evidence

We want to discuss how organizational choices affect growth, productivity,and the characteristics of firms and the agents they hire

I First think about the organization of aggregate technologies and howorganization affects technological innovation and growth

F Organizing Growth (with Garicano, JET 2012)

I Then incorporate organization in a Melitz-like model of heterogenous firms tothink about individual firm choices and productivity

F The Impact of Trade on Organization and Productivity (with Caliendo, QJE2012)

I Then link findings to firm level data of France to check if firms manageorganization actively and how

F The Anatomy of French Production Hierarchies (with Caliendo and Monte)


Organizing Growth

Economic development is linked to the development of organizationsI Organizations as groups of individuals that exchange knowledgeI Encompasses firms, referral markets, consultant markets, etc.

When a new innovation is developed, entrepreneurs work on their ownI Ineffi cient since many problems are not solvedI Incentives for some agents to specialize in harder problems: a new layer

As more layers of problem solvers are addedI More knowledge is optimally accumulated which increases output per worker

F At a decreasing rate

Progressive investments in new technologies imply sporadic radicalinnovations

I Technological CyclesI This is a theory of endogenous labor productivity (H) that can be embeddedin a neoclassical growth model: AF (K ,HL)


The Model

The economy is populated by a mass of size 2 of ex-ante identical agentsthat live for two periods

I Work when young only (so mass of workers is 1)I Will save by investing in new technologies (abstract from savings and capitalaccumulation, but easy to introduce)

I Every period a mass 1 of identical agents is born

Agents have linear preferences in the consumption of the unique goodproduced in the economy

At the start of the period agents choose an occupation and a level ofknowledge to perform their job

Agents can either work in organizations that use the current prevalenttechnology, or they can decide to switch to a new technology


The Model

A technology is a method to produce goods using labor and knowledge

One unit of labor generates a project or problem

To produce, agents need to have the knowledge to solve the problemI If they do, they solve the problem and output is producedI If they do not, they have the possibility to transfer or sell the problem toanother agent

F Agent only knows that they could not solve it: hierarchical organization

Communication of a problem to another agent is costlyI Buyer spends h units of time


Organization within a given Technology

Suppose a new technology, A ≥ 1, is put in place at time t = 0Obtaining A units of output from this technology requires a unit of time anda random level of knowledge

An agent specialized in production uses his unit of time to generate oneproblem, which is a draw from the probability distribution f (z)

I We assume that f (z) is continuous and decreasing, f ′(z) < 0, withcumulative distribution function F (z)

Knowledge can be acquired at a constant cost c > 0, so that acquiringknowledge about problems in [0, z ] costs cz

Denote the wage of an agent working in layer ` ∈ 0, 1, .... of anorganization with highest layer L by w `L


Problem Prices and the Price of Knowledge

An agents in layer ` sells problems to agents in layer `+ 1 at price r `LI Use referral market interpretationI Include all the relevant market information about organization

Same information as:I Wages: If organizations are constituted in firmsI The price of expertise or knowledge: If organizations are constituted inconsultant markets

Markets are assumed to develop sequentiallyI Coordination frictions or adjustment costsI Organization dynamics are driven by the time to ‘build’a market



At t = 0w00 = maxz

AF (z)− cz

At time t = 1 agents have a choice between becoming production workers orspecialized problem solvers. If they become production workers they earn

w01 = maxzAF (z) + (1− F (z))r01 − cz

where r01 is the equilibrium price at which workers in layer 0 sell their problems

The wage of the layer-one-problem-solver is then given by

w11 = maxz1h

(AF (z01 + z)− F (z01 )

1− F (z01 )− r01

)− cz



In general

w0L = maxzAF (z) + (1− F (z))r0L − cz

w `L = maxz

1h

A(F (Z `−1L + z)− F (Z `−1L )

)(1− F (Z `−1L )

)+

(1− F (Z `−1L + z)

)r `L(

1− F (Z `−1L )) − r `−1L

− czwLL = max

z

1h

(AF (ZL−1L + z)− F (ZL−1L )

1− F (ZL−1L )− rL−1L

)− cz

where Z `L = ∑i<` z iL



In equilibrium markets for problems clear

w `L = w`+1L ≡ w(A, L) for all ` = 0, ..., L− 1

Equilibrium in the markets for problems given L then implies that there are anumber

n`L = h(1− F (Z `−1L )

)n0L

of agents working in layer `

Since the economy is populated by a unit mass of agents, the number ofworkers is given by

n0L =1

1+ h∑L`=1(1− F (Z `−1L )

)


Exponential case

Let F (z) = 1− e−λz

Then closed-form solutions for z’s and w’s

We use this case in what followsI Propositions 2 to 4 characterize the solution

Look at limiting case as L→ ∞I Then r `∞ = r∞ for all ` and z `∞ = z∞ for all ` > 0


Output per Capita

0 1 2 3 4 5 6 7 8 9 100.23

0.235

0.24

0.245

0.25

0.255

0.26

0.265

0.27

Hierarchy 's Number of Layers

Out

put p

er A

gent

(w)


Size of Hierarchies

0 1 2 3 4 50

10

20

30

40

50

60

70

80

Time

Num

ber o

f Age

nts

Each color represents one layer


Problem Prices

0 1 2 3 4 5 60

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Problem's Layer

Prob

lem

's Pr

ice

5 layer' hierarchy

7 layer' hierarchy


Agent’s Knowledge

0 1 2 3 4 5 60.42

0.43

0.44

0.45

0.46

0.47

0.48

0.49

0.5

0.51

0.52

Agent's Layer

Agen

t's K

nowl

edge

5 layer' hierarchy

7 layer' hierarchy


Agent’s Knowledge

0 1 2 3 4 5 6 7 8 90

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Time

Cum

mul

ative

Kno

wled

ge

Eac h c olor represents one lay er


Long-run Growth

Development of a given technology can go on forever, but growth rateconverges to zero: Output bounded in levels

Assume agents can invest in ‘innovation knowledge’I Will improve the frontier technology, but frontier technology may not be in useI A new technology requires new organizationsI Adjustment costs for accumulation of ‘innovation knowledge’

Need to scale learning costs to the productivity of the new technology:c = cA

I More complex technologies are harder to learnF Essential for balanced growth since then w (A, L) is linear in A


Long-run Growth

Because of linear utility, same as studying the problem of one infinitely livedagent at time zero

I Rest is just transfers between agents

Hence

V(A,A′, L

)=

[max

[maxζ w (A, L)− Aψζ2 + βV (A,A′′, L+ 1) ,

V (A′,A′, 0)

]]where

A′′ = A′ (1+ ζ) ,

w (A, L) = Aw (L) ≡ A(1− c

λ

(1− ln c

λ(1− r0L

)))


Homogeneity and Sequential Problem

Problem homogenous so

V (G , L) = max[maxζ w (L)− ψζ2 + βV (G ′, L+ 1) ,

GV (1, 0)

]where

G ′ = G (1+ ζ)

Can be shown to be equivalent (given the properties of w (·)) to

V ∗ = maxL,ζ(`)L`=0>0

∑L`=0 β`(w (`)− ψζ (`)2

)1− βL+1 ∏L

`=0 (1+ ζ (`))


Innovation Knowledge

First order conditions imply

ζ∗ (l) (1+ ζ∗ (l)) = β−l[V ∗βL

∗+1

ψ2

L∗

∏`=0

(1+ ζ∗ (`))

]

So ζ∗ (l) increases with lI ζ∗ (l) (1+ ζ∗ (l)) increases at a constant rate β


Technology Prices and Appropiability

The problem can be decentralized with two period lived agents using prices P

max[maxζ w (L) + βP (G ′, L+ 1)− P (G , L)− ψζ2,

maxζ G ′ (w (0) + βP (G ′, 1))− P (G , L)− ψζ2

]where

G ′ = G (1+ ζ)

In equilibrium P is identical to V except for it’s levelI Level depends on the ability to extract resources from future generations

Note that β is the discount factor, but also measures the extent to whichfuture technology can be appropiated

I Key to determine the effect of ICT on growth


Growth: An Example

0 5 10 15 20 251.5

2

2.5

3

Max Layer

V

0 50 100 150 200 250 3002

1

0

1

2

3

Time

Log

(wt)

0 5 10 15 200

0.01

0.02

0.03

0.04

Layer

ζ

0 10 20 30 40 502

1.5

1

0.5

Time

Log

(wt)

β = 0.87, h = .5, c = .9


Growth: Communication Technology

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.02

0.04

0.06

0.08

0.1

h

Gro

wth

Rat

e

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

15

20

25

h

Max

Lay

er

β = 0.87β = 0.88β = 0.89β = 0.90

β = 0.87β = 0.88β = 0.89β = 0.90


Growth: Cost of Knowledge

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 10

0.01

0.02

0.03

0.04

0.05

0.06

c

Gro

wth

Rat

e

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 10

5

10

15

20

25

30

c

Max

Lay

er

β = .87β = .88β = .89β = .90

β = .87β = .88β = .89β = .90


Lessons for Growth

Appropiability (β ↑):I Increases growthI Smaller organizations with shorter cyclesI Low β leads to stagnation

Communication technology (h ↓):I Increases growth if β high and/or h lowI Decreases growth if β low and h highI Larger organizations with longer cycles

Information technology (c ↓)I Increases growthI Smaller organizations with shorter cycles

Welfare increases with reductions in h and c


The Impact of Trade on Organization and Productivity

How does organization affect firms and their productivity?I Mom-and-pop shop is organized very differently than IBM, Microsoft, or GEI Large firms build complicated management hierarchies

Most general equilibrium models (e.g. trade models) assume firms are justtechnologies

I Emphasis on selectionI No within-firm effects

Here we aim to understand the impact of trade on within-firm outcomes aswell as across firms

I Not only focus on who does what, as with selection, but also how do they do it


The Model: Preferences

N identical agents with CES preferences with ES σ > 1

U (x (·)) =(∫

Ωα1σ x (α)

σ−1σ Mµ (α) dα

) σσ−1

I x (α) denotes the consumption of variety α

F Agents like varieties with higher α better

I M is the mass of products available and µ (·) the probability distribution overvarieties in Ω

Agents are endowed with one unit of time that they supply inelasticallyI Agents obtain an equilibrium wage w for their unit of timeI If an agent learns an interval of knowledge of length z she has to pay wcz,which she receives back as part of her compensation


Technology

An entrepreneur pays a fixed entry cost f E in units of labor to design herproduct

I It obtains a demand draw α from G (·) (later G (α) = 1− α−γ)I α determines the level of demand of the firm

If entrepreneur decides to produce she pays a fixed cost f in units of labourI Needs to build an organization


Cost Minimization

Consider a firm that produces a quantity q. The variable cost function isgiven by

C (q;w) = minL≥0CL (q;w)

where CL (q;w) is the minimum cost of producing q with an organizationwith L+ 1 layers, namely,

CL (q;w) = minnlL ,z lLLl=0≥0

∑Ll=0 n

lLw(cz lL + 1

)subject to

q ≤ F (ZLL )An0L,

nlL = hn0L(1− F (Z l−1L )) for L ≥ l > 0,nLL = 1

Propositions 1 to 6 characterize the cost function


Marginal and Average Costs

q

AC

(q;w

) an

d M

C(q

;w)


Average Costs: The Lower Envelope

q

AC

(q;w

)


Marginal Costs

q

AC

(q;w

) an

d M

C(q

;w)


Productivity

Productivity is given by

a (q) =q

C (q; 1)=

1AC (q; 1)

where the average cost is net of any fixed costs of production and ismeasured at constant factor prices w = 1

When c/λ→ 0 and L ≥ 1 the model generates another fixed cost that weneed to subtract from costs. Hence,

a (q) =q

limc/λ→0 C (q; 1)− 1= A

As c/λ→ 0 economy converges to Melitz (2003). In this case productivity isfixed and given by A. This is not the case when c/λ > 0


Profit Maximization

Given CES preferences demand is given by p (α) = q (α)−1σ (αR)

1σ where R

is total revenue and P = 1

The problem of an entrepreneur with draw α is

π (α) ≡ maxq(α)≥0

p (α) q (α)− C (q (α) ;w)− wf

Hence,p (α) =

σ

σ− 1MC (q(α);w)

and

q (α) = αR(

σ

σ− 1MC (q(α);w))−σ

MC (q(α);w) increasing in q (α) and jumps down with new layerI Proposition 8: q (α) and p (α) increase in α given L and jump (up for q (α)and down for p (α)) across L’s


Equilibrium in the Closed Economy

We consider a “stationary” equilibriumI So [1− G (α)]ME = δM where ME is the mass of entrants, M is the mass offirms operating, and δ is the fraction of firm that exit in a period

Entry threshold α is given by π (α) = 0

Free entry implies ∫ ∞

α

π (α)

δg (α) dα = wf E

Labor market clearing requires

N =M

1− G (α)

(δf E +

∫ ∞

α(C (α; 1) + f ) g (α) dα

)Good market clearing requires R = wN


Productivity

0.174

0.176

0.178

0.18

0.182

0.184

0.186

0.188

Pro

duct

ivity

0.34

0.36

0.38

0.4

0.42

0.44

Rev

enue

pro

duct

ivity

0.2

0.205

0.21

0.215

0.22

0.225

0.23

0.235

Labo

r pr

oduc

tivity

0.38

0.42

0.46

0.5

0.54

0.58

Rev

enue

labo

r pr

oduc

tivity

Autarky

Open Economy

DF

DD

DF

DD

DF

DD

DF

_

DD

__ _ _ _

_ _ _ __ _


Changing the Cost of Knowledge

0.2 0.3 0.4 0.5 0.6 0.70.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

c

% r

elat

ive

to a

utar

ky

Average productivity

0.2 0.3 0.4 0.5 0.6 0.70.2

0.25

0.3

0.35

0.4

c

wi

Wages

Open EconomyAutarky

0.2 0.3 0.4 0.5 0.6 0.78

8.2

8.4

8.6

c

% r

elat

ive

to a

utar

ky

Welfare gains

Calibratedeconomy

Calibratedeconomy

Calibratedeconomy


Changing Communication Costs

0.2 0.4 0.6 0.8

0.16

0.18

0.2

0.22

0.24

0.26

0.28

0.3

0.32

0.34

h

% r

elat

ive

to a

utar

ky

Average productivity

0.2 0.4 0.6 0.80.2

0.25

0.3

0.35

0.4

h

wi

Wages

Open EconomyAutarky

0.2 0.4 0.6 0.87.9

8

8.1

8.2

8.3

h

% r

elat

ive

to a

utar

ky

Welfare gains

Calibratedeconomy

Calibratedeconomy

Calibratedeconomy


The Anatomy of French Production Hierarchies

Aim is to understand empirically how firms are organized and if they activelymanage their organization

Study the following empirical implicationsI Firms are hierarchical, n0L ≥ ...n`L... ≥ nLL for all LI Layers L, sales pq, and total labor demand ∑ n`L, increase with αI Given L, w `L and n

`L increase with α at all `

I Given α, w `L decreases and n`L increases with an increase in L at all `


Sketch of Theory in CRH (2012)

0 2 4 6 8 10

Hierarchy at

0 2 4 6 8 10

Number of employees

Hierarchy at ''0 2 4 6 8 10

Hierarchy at '

Average cost function AC(q)

C(q

)/q

w02('') < w0

1()

w12('') < w1

1()

w01(') > w0

1()

w11(') > w1

1()

w11()

w01()

w11(')

w01(')

w22('')

w12('')

w02('')

q() q('')q(')


Data description

Dataset collected by the French National Statistical Institute (INSEE)I We use the period from 2002 to 2007

F Before 2002 different occupational categories

We match two sources from mandatory reports:I BRN: private firms balance sheet data

F 553,125 firm-year observations in manufacturing

I DADS: occupation, hours and earning reports of salaried employees

We lose 11% of the observations from cleaning, and 5.9% from matching

The sample covers on average 90.7% of total value added in manufacturingI Small firms can choose not to report in BRN, but insignificant in terms ofvalue added


Layers: occupational categoriesPCS-ESE classification codes that belong to manufacturing:

2 Firm owners receiving a wageF CEO or firm directors

3 Senior staff or top management positionsF chief financial offi cers, head of HR, logistics, purchasing managers

4 Employees at the supervisor levelF quality control technicians, technical, accounting, and sales supervisors

5 Qualified and non-qualified clerical employees (administrative tasks)F secretaries, HR or accounting, telephone operators, sales employees

6 Blue collar qualified and non-qualified workers (manual tasks)F welders, assemblers, machine operators and maintenance

Classification code 1 (farmers) does not belong to manufacturingWe group 5 and 6 since the distribution of wages coincide


Firms with different number of layers are different0

.1.2

.3.4

.5D

ensi

ty

1 10 100 1000 10000 100000Value added (log scale)

0 lyrs 1 lyr 2 lyrs 3 lyrs

Kernel density estimate

Raw data − thousands of 2005 eurosValue added distribution by number of layers

0.1

.2.3

.4.5

Den

sity

10 100 1000 10000 100000 1000000Hours (log scale)



Raw dataHours distribution by number of layers

Average

Year Firms # of layers

2002 79,260 1.59

2003 77,768 1.58

2004 76,448 1.58

2005 75,426 1.55

2006 74,818 1.53

2007 72,918 1.50

0.5

11.

5D

ensi

ty

10 25 50 100Wage (log scale)



Raw data − 2005 eurosFirm hourly wage distribution by number of layers

# of layers Firm‐years

0 81,909

1 126,069

2 161,449

3 87,211


Hours and wages are hierarchicalPercentage of firms that satisfy a hierarchyN`L = hours at layer ` of a firm with L layers

Unweighted# of layers N`L≥ N

`+1L all ` N0L ≥N1L N1L ≥N2L N2L ≥N3L

1 85.3 85.3 - -2 62.0 85.2 74.0 -3 54.3 85.8 76.4 86.6

Unweighted# of layers w `+1L ≥w `L all ` w1L ≥w0L w2L ≥w1L w3L ≥w2L

1 92.1 92.1 - -2 86.2 93.6 92.5 -3 79.7 96.5 94.4 87.8


Representative hierarchies: normalized hours

0 20 40 60 80

29.44

Average hours normalized by the top layer

Ave

rage

hou

rly w

age

Hierarchy of a 0 layer firm

0 20 40 60 8017.78

30.18


Ave

rage

hou

rly w

age


0 20 40 60 8016.09

23.63

41.61


Ave

rage

hou

rly w

age


0 20 40 60 8016.08

23.08

38.63

72.04


Ave

rage

hou

rly w

age



Layer transitionsDistribution of # of layers at time t+1 given the # of layers at time t

# of layers at t + 1Exit 0 1 2 3 Total

0 15.4 67.1 15.3 2.0 0.2 100# of layers 1 9.9 10.8 62.0 16.2 1.1 100at t 2 7.6 1.2 13.2 67.5 10.5 100

3 6.1 0.2 2.0 20.5 71.2 100


Transitions across layers depend on value added0

.1.2

.3.4

.5

Fra

ctio

n of

firm

s


to 1 lyr to 2 lyrs to 3 lyrs

Transitions of firms out of 0 layers

0.1

.2.3

.4.5

Fra

ctio

n of

firm

s


to 0 lyrs to 2 lyrs to 3 lyrs

Transitions of firms out of 1 layer

0.1

.2.3

.4.5

Fra

ctio

n of

firm

s


to 0 lyrs to 1 lyr to 3 lyrs


0.1

.2.3

.4.5

Fra

ctio

n of

firm

s


to 0 lyrs to 1 lyr to 2 lyrs



Change in firm level outcomes during transitionAverage behavior of firms by change in the number of layers

All Increase L No change in L Decrease Ldlnhours -0.014*** 0.056*** -0.011*** -0.093***- detrended - 0.070*** 0.003*** -0.079***

dln ∑L`=0 n

`L -0.011*** 1.366*** 0.012*** -1.408***

- detrended - 1.377*** 0.023*** -1.400***dlnVA -0.008*** 0.032*** -0.007*** -0.049***- detrended - 0.039*** 0.001 -0.040***dln avg wage 0.018*** 0.001 0.018*** 0.038***- detrended - -0.020*** -0.000 0.020***- common layers 0.020*** -0.117*** 0.018*** 0.156***- - detrended - -0.137*** -0.002*** 0.136***

% firms 100 12.75 73.48 13.78% VA change 100 39.21 65.65 -4.87*** significant at 1%.

Sources of changes during transition


Normalized hours change according to the theoryAverage log change in normalized hours for firms that transition

# of layers Layer Change s.e. p‐value obs

Before After

0 1 0 1.520 0.017 0.00 10432

0 2 0 1.745 0.053 0.00 1350

0 3 0 2.312 0.193 0.00 111

1 0 0 ‐1.585 0.017 0.00 11356

1 2 0 0.710 0.012 0.00 17052

1 2 1 0.533 0.012 0.00 17052

1 3 0 1.218 0.048 0.00 1168

1 3 1 1.018 0.047 0.00 1168

2 0 0 ‐1.801 0.046 0.00 1698

2 1 0 ‐0.696 0.012 0.00 17927

2 1 1 ‐0.537 0.012 0.00 17927

2 3 0 1.338 0.014 0.00 14228

2 3 1 1.277 0.016 0.00 14228

2 3 2 1.167 0.016 0.00 14228

3 0 0 ‐2.203 0.157 0.00 142

3 1 0 ‐1.112 0.041 0.00 1493

3 1 1 ‐0.948 0.039 0.00 1493

3 2 0 ‐1.427 0.014 0.00 15303

3 2 1 ‐1.359 0.015 0.00 15303

3 2 2 ‐1.274 0.015 0.00 15303


Normalized hours change according to the theoryElasticity of n`L with VA for firms that do not change LReporting β`L from d ln n`Lit = α`L + β`Ld lnVAit + εit

# oflayers in Layer β`L s.e. p-value obs

the firm (L) `1 0 0.044 0.012 0.00 65,1142 0 0.046 0.009 0.00 91,8332 1 0.019 0.010 0.07 91,8333 0 0.109 0.014 0.00 53,0533 1 0.048 0.013 0.00 53,0533 2 0.037 0.013 0.01 53,053


Wages change according to the theoryAverage log change in wages for firms that transition


Before After

0 1 0 ‐0.131 0.005 0.00 10432

0 2 0 ‐0.432 0.024 0.00 1350

0 3 0 ‐0.943 0.131 0.00 111

1 0 0 0.201 0.005 0.00 11356

1 2 0 ‐0.041 0.003 0.00 17052

1 2 1 ‐0.245 0.004 0.00 17052

1 3 0 ‐0.165 0.018 0.00 1168

1 3 1 ‐0.416 0.020 0.00 1168

2 0 0 0.489 0.022 0.00 1698

2 1 0 0.085 0.003 0.00 17927

2 1 1 0.275 0.004 0.00 17927

2 3 0 ‐0.008 0.002 0.00 14228

2 3 1 ‐0.054 0.003 0.00 14228

2 3 2 ‐0.185 0.004 0.00 14228

3 0 0 1.102 0.120 0.00 142

3 1 0 0.188 0.014 0.00 1493

3 1 1 0.417 0.017 0.00 1493

3 2 0 0.029 0.002 0.00 15303

3 2 1 0.060 0.003 0.00 15303

3 2 2 0.153 0.004 0.00 15303


Wages change according to the theoryElasticity of w `L with VA for firms that do not change LReporting γ`L from d lnw `Lit = δ`L + γ`Ld lnVAit + εit

# oflayers in Layer γ`L s.e. p-value obs

the firm (L) `0 0 0.077 0.007 0.00 45,6061 0 0.098 0.006 0.00 65,1141 1 0.116 0.006 0.00 65,1142 0 0.145 0.006 0.00 91,8332 1 0.156 0.006 0.00 91,8332 2 0.172 0.006 0.00 91,8333 0 0.173 0.009 0.00 53,0533 1 0.187 0.009 0.00 53,0533 2 0.189 0.010 0.00 53,0533 3 0.218 0.011 0.00 53,053


Representative hierarchies for one layer transitions

0 1 2 3 4 5

28.5


Ave

rage

hou

rly w

age

Firms with 0 layers

0 1 2 3 4 5

25

36.9


Ave

rage

hou

rly w

age

After transition

0 10 20 30

23


Ave

rage

hou

rly w

age

After transition

0 10 20 30

18.8

31.4


Ave

rage

hou

rly w

age

Firms with 1 layer

0 2 4 6 8 10

17.6

31.7


Ave

rage

hou

rly w

age

Firms with 1 layer

0 2 4 6 8 10

16.9

24.8

38.8


Ave

rage

hou

rly w

age

After transition

0 10 20 30 40 50

16.2

24.1

40.9


Ave

rage

hou

rly w

age

Firms with 2 layers

0 10 20 30 40 50

17.6

31.7


Ave

rage

hou

rly w

age

After transition

0 10 20 30

16.5

25

46.9


Ave

rage

hou

rly w

age

Firms with 2 layers

0 10 20 30

16.4

23.6

39

60.4


Ave

rage

hou

rly w

age

After transition

0 50 100 150 200

16

22.9

38.3

68.4


Ave

rage

hou

rly w

age

Firms with 3 layers

0 50 100 150 200

16.5

24.3

44.6


Ave

rage

hou

rly w

age

After transition


Distribution of wages after minus before transition

0 10 20 30 40 50 60 70 80 90 1000

0.05

0.1

0.15

Percentiles

Log

wag

e di

ffere

nces

Transition from 1 to 0

0 10 20 30 40 50 60 70 80 90 100-0.025

0

0.025

0.05

PercentilesLo

g w

age

diffe

renc

es


0 10 20 30 40 50 60 70 80 90 100-0.05

-0.025

0

0.02

Percentiles

Log

wag

e di

ffere

nces


0 10 20 30 40 50 60 70 80 90 100-0.07

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0

Percentiles

Log

wag

e di

ffere

nce


0 10 20 30 40 50 60 70 80 90 100-0.02

-0.01

0

0.01

0.02

Percentiles

Log

wag

e di

ffere

nces


0 10 20 30 40 50 60 70 80 90 100

-0.01

0

0.01

0.02

Percentiles

Log

wag

e di

ffere

nces



Distribution of wages after minus before transitionCommon layers

0 10 20 30 40 50 60 70 80 90 1000

0.25

0.5

Percentiles

Log

wag

e di

ffere

nces


0 10 20 30 40 50 60 70 80 90 1000

0.05

0.1

0.15

0.2

0.25

0.3

PercentilesLo

g w

age

diffe

renc

es


0 10 20 30 40 50 60 70 80 90 1000

0.05

0.1

Percentiles

Log

wag

e di

ffere

nces


0 10 20 30 40 50 60 70 80 90 100-0.25

-0.2

-0.15

-0.1

-0.05

0

Percentiles

Log

wag

e di

ffere

nces


0 10 20 30 40 50 60 70 80 90 100

-0.25

-0.2

-0.15

-0.1

-0.05

0

Percentiles

Log

wag

e di

ffere

nces


0 10 20 30 40 50 60 70 80 90 100-0.2

-0.15

-0.1

-0.05

0

Percentiles

Log

wag

e di

ffere

nces



Distribution of wages after minus beforeConditioning on increase in VA > 0 and no transition

0 10 20 30 40 50 60 70 80 900

0.02

0.04

0.06

0.08

0.1

0.12

Percentiles

Log

wag

e di

ffere

nces

Firms with 0 layers

0 10 20 30 40 50 60 70 80 900

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Percentiles

Log

wag

e di

ffere

nces

Firms with 1 layer

0 10 20 30 40 50 60 70 80 900

0.01

0.02

0.03

0.04

0.05

0.06

Percentiles

Log

wag

e di

ffere

nces

Firms with 2 layers

0 10 20 30 40 50 60 70 80 90 1000

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

Percentiles

Log

wag

e di

ffere

nces

Firms with 3 layers


How do firms change the average wage in a layer?

Log diff. in hourly wage (after minus before the transition) for hours staying in the layer


Before After

0 1 0 0.001 0.00 0.79 8779

0 2 0 ‐0.072 0.02 0.00 953

0 3 0 ‐0.338 0.13 0.01 68

1 0 0 0.114 0.00 0.00 9645

1 2 0 0.022 0.00 0.00 15118

1 2 1 0.022 0.00 0.00 9358

1 3 0 ‐0.034 0.01 0.02 981

1 3 1 ‐0.034 0.02 0.10 536

2 0 0 0.243 0.02 0.00 1264

2 1 0 0.059 0.00 0.00 16048

2 1 1 0.086 0.00 0.00 10055

2 3 0 0.020 0.00 0.00 13455

2 3 1 0.028 0.00 0.00 11975

2 3 2 0.037 0.00 0.00 8912

3 0 0 0.557 0.13 0.00 80

3 1 0 0.111 0.01 0.00 1276

3 1 1 0.165 0.02 0.00 723

3 2 0 0.039 0.00 0.00 14508

3 2 1 0.046 0.00 0.00 12948

3 2 2 0.049 0.00 0.00 10348

Log diff. in hourly wage of hours entering the layer (after transition) versus hours leaving the layer (before

transition)


Before After

0 1 0 ‐0.268 0.01 0.00 7564

0 2 0 ‐0.571 0.03 0.00 1133

0 3 0 ‐0.954 0.13 0.00 94

1 0 0 0.233 0.01 0.00 7848

1 2 0 ‐0.130 0.00 0.00 13375

1 2 1 ‐0.391 0.01 0.00 11406

1 3 0 ‐0.246 0.02 0.00 982

1 3 1 ‐0.515 0.02 0.00 929

2 0 0 0.527 0.02 0.00 1321

2 1 0 0.072 0.00 0.00 13707

2 1 1 0.378 0.01 0.00 11530

2 3 0 ‐0.087 0.00 0.00 12604

2 3 1 ‐0.154 0.00 0.00 10045

2 3 2 ‐0.339 0.01 0.00 10329

3 0 0 1.059 0.12 0.00 123

3 1 0 0.199 0.02 0.00 1226

3 1 1 0.497 0.02 0.00 1137

3 2 0 ‐0.033 0.00 0.00 13584

3 2 1 0.021 0.00 0.00 10771

3 2 2 0.188 0.01 0.00 10450


Sources of changes in average wage during a transition

w `≤LL′ it+1/wLit wL′L′ it+1/wLit

from/to 1 2 3 from/to 1 2 30 0.975∗∗

(10,422)0.838∗∗(1,348)

0.679(111)

∗∗ 0 1.531∗∗(10,421)

1.435∗∗(1,349)

1.461∗∗(110)

1 0.940∗∗(17,036)

0.886∗∗(1,167)

1 2.067(17,035)

∗∗ 2.034∗∗(1,167)

2 0.974(14,214)

2 4.357∗∗(14,213)

s d ln wLitfrom/to 1 2 3 from/to 1 2 30 0.741

(10,422)∗∗ 0.621∗∗

(1,350)0.572(111)

∗∗ 0 −0.008∗(10,421)

−0.195(1,350)

∗∗ −0.589∗∗(111)

1 0.853(17,036)

∗∗ 0.775(1,167)

∗∗ 1 0.014(17,035)

∗∗ −0.050(1,167)

∗∗

2 0.947(14,214)

∗∗ 2 0.013(14,212)

∗∗

All results from trimmed sample at 0.05%. *significant at 10% ** significant at 1%. Number of observations in parenthesis.

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